%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP179-3 : 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 10:37:22 EDT 2022
% Result : Unsatisfiable 24.84s 25.04s
% Output : CNFRefutation 25.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 100
% Number of leaves : 576
% Syntax : Number of clauses : 2541 (1287 unt; 0 nHn;1231 RR)
% Number of literals : 4347 (4346 equ;1809 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 5022 ( 54 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(associativity_of_glb,axiom,
greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) ).
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(idempotence_of_gld,axiom,
greatest_lower_bound(X,X) = 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_glb1,axiom,
multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_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(monotony_glb2,axiom,
multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) ).
cnf(p18_1,hypothesis,
inverse(identity) = identity ).
cnf(p18_2,hypothesis,
inverse(inverse(X)) = X ).
cnf(p18_3,hypothesis,
inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) ).
cnf(prove_p18,negated_conjecture,
least_upper_bound(inverse(a),identity) != inverse(greatest_lower_bound(a,identity)) ).
cnf(refute_0_0,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_1,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_2,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( least_upper_bound(X,Y) != least_upper_bound(Y,X)
| least_upper_bound(Y,X) = least_upper_bound(X,Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X,Y))),bind(Y0,$fot(least_upper_bound(Y,X)))]]) ).
cnf(refute_0_4,plain,
least_upper_bound(Y,X) = least_upper_bound(X,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(X,Y),least_upper_bound(Y,X)) )],[symmetry_of_lub,refute_0_3]) ).
cnf(refute_0_5,plain,
least_upper_bound(inverse(a),identity) = least_upper_bound(identity,inverse(a)),
inference(subst,[],[refute_0_4:[bind(X,$fot(identity)),bind(Y,$fot(inverse(a)))]]) ).
cnf(refute_0_6,plain,
( least_upper_bound(identity,inverse(a)) != inverse(greatest_lower_bound(a,identity))
| least_upper_bound(inverse(a),identity) != least_upper_bound(identity,inverse(a))
| least_upper_bound(inverse(a),identity) = inverse(greatest_lower_bound(a,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(a),identity),least_upper_bound(identity,inverse(a))) ),[1],$fot(inverse(greatest_lower_bound(a,identity)))]]) ).
cnf(refute_0_7,plain,
( least_upper_bound(identity,inverse(a)) != inverse(greatest_lower_bound(a,identity))
| least_upper_bound(inverse(a),identity) = inverse(greatest_lower_bound(a,identity)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(a),identity),least_upper_bound(identity,inverse(a))) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
least_upper_bound(identity,inverse(a)) != inverse(greatest_lower_bound(a,identity)),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(a),identity),inverse(greatest_lower_bound(a,identity))) )],[refute_0_7,prove_p18]) ).
cnf(refute_0_9,plain,
multiply(multiply(inverse(X_93),X_93),X_94) = multiply(inverse(X_93),multiply(X_93,X_94)),
inference(subst,[],[associativity:[bind(X,$fot(inverse(X_93))),bind(Y,$fot(X_93)),bind(Z,$fot(X_94))]]) ).
cnf(refute_0_10,plain,
multiply(inverse(X_93),X_93) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_93))]]) ).
cnf(refute_0_11,plain,
( multiply(multiply(inverse(X_93),X_93),X_94) != multiply(inverse(X_93),multiply(X_93,X_94))
| multiply(inverse(X_93),X_93) != identity
| multiply(identity,X_94) = multiply(inverse(X_93),multiply(X_93,X_94)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_93),X_93),X_94),multiply(inverse(X_93),multiply(X_93,X_94))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_12,plain,
( multiply(multiply(inverse(X_93),X_93),X_94) != multiply(inverse(X_93),multiply(X_93,X_94))
| multiply(identity,X_94) = multiply(inverse(X_93),multiply(X_93,X_94)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_93),X_93),identity) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
multiply(identity,X_94) = multiply(inverse(X_93),multiply(X_93,X_94)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_93),X_93),X_94),multiply(inverse(X_93),multiply(X_93,X_94))) )],[refute_0_9,refute_0_12]) ).
cnf(refute_0_14,plain,
multiply(identity,X_94) = X_94,
inference(subst,[],[left_identity:[bind(X,$fot(X_94))]]) ).
cnf(refute_0_15,plain,
( multiply(identity,X_94) != X_94
| multiply(identity,X_94) != multiply(inverse(X_93),multiply(X_93,X_94))
| X_94 = multiply(inverse(X_93),multiply(X_93,X_94)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_94),multiply(inverse(X_93),multiply(X_93,X_94))) ),[0],$fot(X_94)]]) ).
cnf(refute_0_16,plain,
( multiply(identity,X_94) != multiply(inverse(X_93),multiply(X_93,X_94))
| X_94 = multiply(inverse(X_93),multiply(X_93,X_94)) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_94),X_94) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
X_94 = multiply(inverse(X_93),multiply(X_93,X_94)),
inference(resolve,[$cnf( $equal(multiply(identity,X_94),multiply(inverse(X_93),multiply(X_93,X_94))) )],[refute_0_13,refute_0_16]) ).
cnf(refute_0_18,plain,
X_96 = multiply(inverse(least_upper_bound(X_66,inverse(X_96))),multiply(least_upper_bound(X_66,inverse(X_96)),X_96)),
inference(subst,[],[refute_0_17:[bind(X_93,$fot(least_upper_bound(X_66,inverse(X_96)))),bind(X_94,$fot(X_96))]]) ).
cnf(refute_0_19,plain,
multiply(least_upper_bound(X_66,inverse(X_65)),X_65) = least_upper_bound(multiply(X_66,X_65),multiply(inverse(X_65),X_65)),
inference(subst,[],[monotony_lub2:[bind(X,$fot(X_65)),bind(Y,$fot(X_66)),bind(Z,$fot(inverse(X_65)))]]) ).
cnf(refute_0_20,plain,
multiply(inverse(X_65),X_65) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_65))]]) ).
cnf(refute_0_21,plain,
( multiply(inverse(X_65),X_65) != identity
| multiply(least_upper_bound(X_66,inverse(X_65)),X_65) != least_upper_bound(multiply(X_66,X_65),multiply(inverse(X_65),X_65))
| multiply(least_upper_bound(X_66,inverse(X_65)),X_65) = least_upper_bound(multiply(X_66,X_65),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_66,inverse(X_65)),X_65),least_upper_bound(multiply(X_66,X_65),multiply(inverse(X_65),X_65))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_22,plain,
( multiply(least_upper_bound(X_66,inverse(X_65)),X_65) != least_upper_bound(multiply(X_66,X_65),multiply(inverse(X_65),X_65))
| multiply(least_upper_bound(X_66,inverse(X_65)),X_65) = least_upper_bound(multiply(X_66,X_65),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_65),X_65),identity) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
multiply(least_upper_bound(X_66,inverse(X_65)),X_65) = least_upper_bound(multiply(X_66,X_65),identity),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_66,inverse(X_65)),X_65),least_upper_bound(multiply(X_66,X_65),multiply(inverse(X_65),X_65))) )],[refute_0_19,refute_0_22]) ).
cnf(refute_0_24,plain,
least_upper_bound(multiply(X_66,X_65),identity) = least_upper_bound(identity,multiply(X_66,X_65)),
inference(subst,[],[refute_0_4:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_66,X_65)))]]) ).
cnf(refute_0_25,plain,
( multiply(least_upper_bound(X_66,inverse(X_65)),X_65) != least_upper_bound(multiply(X_66,X_65),identity)
| least_upper_bound(multiply(X_66,X_65),identity) != least_upper_bound(identity,multiply(X_66,X_65))
| multiply(least_upper_bound(X_66,inverse(X_65)),X_65) = least_upper_bound(identity,multiply(X_66,X_65)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_66,inverse(X_65)),X_65),least_upper_bound(identity,multiply(X_66,X_65))) ),[0],$fot(least_upper_bound(multiply(X_66,X_65),identity))]]) ).
cnf(refute_0_26,plain,
( multiply(least_upper_bound(X_66,inverse(X_65)),X_65) != least_upper_bound(multiply(X_66,X_65),identity)
| multiply(least_upper_bound(X_66,inverse(X_65)),X_65) = least_upper_bound(identity,multiply(X_66,X_65)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_66,X_65),identity),least_upper_bound(identity,multiply(X_66,X_65))) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
multiply(least_upper_bound(X_66,inverse(X_65)),X_65) = least_upper_bound(identity,multiply(X_66,X_65)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_66,inverse(X_65)),X_65),least_upper_bound(multiply(X_66,X_65),identity)) )],[refute_0_23,refute_0_26]) ).
cnf(refute_0_28,plain,
multiply(least_upper_bound(X_66,inverse(X_96)),X_96) = least_upper_bound(identity,multiply(X_66,X_96)),
inference(subst,[],[refute_0_27:[bind(X_65,$fot(X_96))]]) ).
cnf(refute_0_29,plain,
( X_96 != multiply(inverse(least_upper_bound(X_66,inverse(X_96))),multiply(least_upper_bound(X_66,inverse(X_96)),X_96))
| multiply(least_upper_bound(X_66,inverse(X_96)),X_96) != least_upper_bound(identity,multiply(X_66,X_96))
| X_96 = multiply(inverse(least_upper_bound(X_66,inverse(X_96))),least_upper_bound(identity,multiply(X_66,X_96))) ),
introduced(tautology,[equality,[$cnf( $equal(X_96,multiply(inverse(least_upper_bound(X_66,inverse(X_96))),multiply(least_upper_bound(X_66,inverse(X_96)),X_96))) ),[1,1],$fot(least_upper_bound(identity,multiply(X_66,X_96)))]]) ).
cnf(refute_0_30,plain,
( X_96 != multiply(inverse(least_upper_bound(X_66,inverse(X_96))),multiply(least_upper_bound(X_66,inverse(X_96)),X_96))
| X_96 = multiply(inverse(least_upper_bound(X_66,inverse(X_96))),least_upper_bound(identity,multiply(X_66,X_96))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_66,inverse(X_96)),X_96),least_upper_bound(identity,multiply(X_66,X_96))) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
X_96 = multiply(inverse(least_upper_bound(X_66,inverse(X_96))),least_upper_bound(identity,multiply(X_66,X_96))),
inference(resolve,[$cnf( $equal(X_96,multiply(inverse(least_upper_bound(X_66,inverse(X_96))),multiply(least_upper_bound(X_66,inverse(X_96)),X_96))) )],[refute_0_18,refute_0_30]) ).
cnf(refute_0_32,plain,
inverse(X_220) = multiply(inverse(least_upper_bound(least_upper_bound(X_220,X_221),inverse(inverse(X_220)))),least_upper_bound(identity,multiply(least_upper_bound(X_220,X_221),inverse(X_220)))),
inference(subst,[],[refute_0_31:[bind(X_66,$fot(least_upper_bound(X_220,X_221))),bind(X_96,$fot(inverse(X_220)))]]) ).
cnf(refute_0_33,plain,
multiply(least_upper_bound(X_66,X_67),inverse(X_66)) = least_upper_bound(multiply(X_66,inverse(X_66)),multiply(X_67,inverse(X_66))),
inference(subst,[],[monotony_lub2:[bind(X,$fot(inverse(X_66))),bind(Y,$fot(X_66)),bind(Z,$fot(X_67))]]) ).
cnf(refute_0_34,plain,
multiply(inverse(inverse(X_1)),inverse(X_1)) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(inverse(X_1)))]]) ).
cnf(refute_0_35,plain,
inverse(inverse(X_1)) = X_1,
inference(subst,[],[p18_2:[bind(X,$fot(X_1))]]) ).
cnf(refute_0_36,plain,
( multiply(inverse(inverse(X_1)),inverse(X_1)) != identity
| inverse(inverse(X_1)) != X_1
| multiply(X_1,inverse(X_1)) = identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X_1)),inverse(X_1)),identity) ),[0,0],$fot(X_1)]]) ).
cnf(refute_0_37,plain,
( multiply(inverse(inverse(X_1)),inverse(X_1)) != identity
| multiply(X_1,inverse(X_1)) = identity ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_1)),X_1) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
multiply(X_1,inverse(X_1)) = identity,
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_1)),inverse(X_1)),identity) )],[refute_0_34,refute_0_37]) ).
cnf(refute_0_39,plain,
multiply(X_66,inverse(X_66)) = identity,
inference(subst,[],[refute_0_38:[bind(X_1,$fot(X_66))]]) ).
cnf(refute_0_40,plain,
( multiply(X_66,inverse(X_66)) != identity
| multiply(least_upper_bound(X_66,X_67),inverse(X_66)) != least_upper_bound(multiply(X_66,inverse(X_66)),multiply(X_67,inverse(X_66)))
| multiply(least_upper_bound(X_66,X_67),inverse(X_66)) = least_upper_bound(identity,multiply(X_67,inverse(X_66))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_66,X_67),inverse(X_66)),least_upper_bound(multiply(X_66,inverse(X_66)),multiply(X_67,inverse(X_66)))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_41,plain,
( multiply(least_upper_bound(X_66,X_67),inverse(X_66)) != least_upper_bound(multiply(X_66,inverse(X_66)),multiply(X_67,inverse(X_66)))
| multiply(least_upper_bound(X_66,X_67),inverse(X_66)) = least_upper_bound(identity,multiply(X_67,inverse(X_66))) ),
inference(resolve,[$cnf( $equal(multiply(X_66,inverse(X_66)),identity) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
multiply(least_upper_bound(X_66,X_67),inverse(X_66)) = least_upper_bound(identity,multiply(X_67,inverse(X_66))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_66,X_67),inverse(X_66)),least_upper_bound(multiply(X_66,inverse(X_66)),multiply(X_67,inverse(X_66)))) )],[refute_0_33,refute_0_41]) ).
cnf(refute_0_43,plain,
multiply(least_upper_bound(X_220,X_221),inverse(X_220)) = least_upper_bound(identity,multiply(X_221,inverse(X_220))),
inference(subst,[],[refute_0_42:[bind(X_66,$fot(X_220)),bind(X_67,$fot(X_221))]]) ).
cnf(refute_0_44,plain,
( multiply(least_upper_bound(X_220,X_221),inverse(X_220)) != least_upper_bound(identity,multiply(X_221,inverse(X_220)))
| inverse(X_220) != multiply(inverse(least_upper_bound(least_upper_bound(X_220,X_221),inverse(inverse(X_220)))),least_upper_bound(identity,multiply(least_upper_bound(X_220,X_221),inverse(X_220))))
| inverse(X_220) = multiply(inverse(least_upper_bound(least_upper_bound(X_220,X_221),inverse(inverse(X_220)))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_221,inverse(X_220))))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(X_220),multiply(inverse(least_upper_bound(least_upper_bound(X_220,X_221),inverse(inverse(X_220)))),least_upper_bound(identity,multiply(least_upper_bound(X_220,X_221),inverse(X_220))))) ),[1,1,1],$fot(least_upper_bound(identity,multiply(X_221,inverse(X_220))))]]) ).
cnf(refute_0_45,plain,
( inverse(X_220) != multiply(inverse(least_upper_bound(least_upper_bound(X_220,X_221),inverse(inverse(X_220)))),least_upper_bound(identity,multiply(least_upper_bound(X_220,X_221),inverse(X_220))))
| inverse(X_220) = multiply(inverse(least_upper_bound(least_upper_bound(X_220,X_221),inverse(inverse(X_220)))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_221,inverse(X_220))))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_220,X_221),inverse(X_220)),least_upper_bound(identity,multiply(X_221,inverse(X_220)))) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
inverse(X_220) = multiply(inverse(least_upper_bound(least_upper_bound(X_220,X_221),inverse(inverse(X_220)))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_221,inverse(X_220))))),
inference(resolve,[$cnf( $equal(inverse(X_220),multiply(inverse(least_upper_bound(least_upper_bound(X_220,X_221),inverse(inverse(X_220)))),least_upper_bound(identity,multiply(least_upper_bound(X_220,X_221),inverse(X_220))))) )],[refute_0_32,refute_0_45]) ).
cnf(refute_0_47,plain,
least_upper_bound(X_12,greatest_lower_bound(X_12,X_13)) = X_12,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_12)),bind(Y,$fot(X_13))]]) ).
cnf(refute_0_48,plain,
greatest_lower_bound(X_13,X_12) = greatest_lower_bound(X_12,X_13),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_13)),bind(Y,$fot(X_12))]]) ).
cnf(refute_0_49,plain,
( greatest_lower_bound(X_13,X_12) != greatest_lower_bound(X_12,X_13)
| greatest_lower_bound(X_12,X_13) = greatest_lower_bound(X_13,X_12) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X_13,X_12))),bind(Y0,$fot(greatest_lower_bound(X_12,X_13)))]]) ).
cnf(refute_0_50,plain,
greatest_lower_bound(X_12,X_13) = greatest_lower_bound(X_13,X_12),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_13,X_12),greatest_lower_bound(X_12,X_13)) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
( greatest_lower_bound(X_12,X_13) != greatest_lower_bound(X_13,X_12)
| least_upper_bound(X_12,greatest_lower_bound(X_12,X_13)) != X_12
| least_upper_bound(X_12,greatest_lower_bound(X_13,X_12)) = X_12 ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_12,greatest_lower_bound(X_12,X_13)),X_12) ),[0,1],$fot(greatest_lower_bound(X_13,X_12))]]) ).
cnf(refute_0_52,plain,
( least_upper_bound(X_12,greatest_lower_bound(X_12,X_13)) != X_12
| least_upper_bound(X_12,greatest_lower_bound(X_13,X_12)) = X_12 ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_12,X_13),greatest_lower_bound(X_13,X_12)) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
least_upper_bound(X_12,greatest_lower_bound(X_13,X_12)) = X_12,
inference(resolve,[$cnf( $equal(least_upper_bound(X_12,greatest_lower_bound(X_12,X_13)),X_12) )],[refute_0_47,refute_0_52]) ).
cnf(refute_0_54,plain,
least_upper_bound(least_upper_bound(X_21,Y),greatest_lower_bound(X_21,least_upper_bound(X_21,Y))) = least_upper_bound(X_21,Y),
inference(subst,[],[refute_0_53:[bind(X_12,$fot(least_upper_bound(X_21,Y))),bind(X_13,$fot(X_21))]]) ).
cnf(refute_0_55,plain,
greatest_lower_bound(X_21,least_upper_bound(X_21,Y)) = X_21,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_21))]]) ).
cnf(refute_0_56,plain,
( greatest_lower_bound(X_21,least_upper_bound(X_21,Y)) != X_21
| least_upper_bound(least_upper_bound(X_21,Y),greatest_lower_bound(X_21,least_upper_bound(X_21,Y))) != least_upper_bound(X_21,Y)
| least_upper_bound(least_upper_bound(X_21,Y),X_21) = least_upper_bound(X_21,Y) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_21,Y),greatest_lower_bound(X_21,least_upper_bound(X_21,Y))),least_upper_bound(X_21,Y)) ),[0,1],$fot(X_21)]]) ).
cnf(refute_0_57,plain,
( least_upper_bound(least_upper_bound(X_21,Y),greatest_lower_bound(X_21,least_upper_bound(X_21,Y))) != least_upper_bound(X_21,Y)
| least_upper_bound(least_upper_bound(X_21,Y),X_21) = least_upper_bound(X_21,Y) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_21,least_upper_bound(X_21,Y)),X_21) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
least_upper_bound(least_upper_bound(X_21,Y),X_21) = least_upper_bound(X_21,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_21,Y),greatest_lower_bound(X_21,least_upper_bound(X_21,Y))),least_upper_bound(X_21,Y)) )],[refute_0_54,refute_0_57]) ).
cnf(refute_0_59,plain,
( least_upper_bound(X,least_upper_bound(Y,Z)) != least_upper_bound(least_upper_bound(X,Y),Z)
| least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(Y,Z)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X,Y),Z)))]]) ).
cnf(refute_0_60,plain,
least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,Z)),least_upper_bound(least_upper_bound(X,Y),Z)) )],[associativity_of_lub,refute_0_59]) ).
cnf(refute_0_61,plain,
least_upper_bound(least_upper_bound(X_21,Y),X_21) = least_upper_bound(X_21,least_upper_bound(Y,X_21)),
inference(subst,[],[refute_0_60:[bind(X,$fot(X_21)),bind(Z,$fot(X_21))]]) ).
cnf(refute_0_62,plain,
( least_upper_bound(least_upper_bound(X_21,Y),X_21) != least_upper_bound(X_21,Y)
| least_upper_bound(least_upper_bound(X_21,Y),X_21) != least_upper_bound(X_21,least_upper_bound(Y,X_21))
| least_upper_bound(X_21,least_upper_bound(Y,X_21)) = least_upper_bound(X_21,Y) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_21,Y),X_21),least_upper_bound(X_21,Y)) ),[0],$fot(least_upper_bound(X_21,least_upper_bound(Y,X_21)))]]) ).
cnf(refute_0_63,plain,
( least_upper_bound(least_upper_bound(X_21,Y),X_21) != least_upper_bound(X_21,Y)
| least_upper_bound(X_21,least_upper_bound(Y,X_21)) = least_upper_bound(X_21,Y) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_21,Y),X_21),least_upper_bound(X_21,least_upper_bound(Y,X_21))) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
least_upper_bound(X_21,least_upper_bound(Y,X_21)) = least_upper_bound(X_21,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_21,Y),X_21),least_upper_bound(X_21,Y)) )],[refute_0_58,refute_0_63]) ).
cnf(refute_0_65,plain,
least_upper_bound(X_23,least_upper_bound(X_22,X_23)) = least_upper_bound(X_23,X_22),
inference(subst,[],[refute_0_64:[bind(Y,$fot(X_22)),bind(X_21,$fot(X_23))]]) ).
cnf(refute_0_66,plain,
least_upper_bound(X_23,X_22) = least_upper_bound(X_22,X_23),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_23)),bind(Y,$fot(X_22))]]) ).
cnf(refute_0_67,plain,
( least_upper_bound(X_23,X_22) != least_upper_bound(X_22,X_23)
| least_upper_bound(X_22,X_23) = least_upper_bound(X_23,X_22) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X_23,X_22))),bind(Y0,$fot(least_upper_bound(X_22,X_23)))]]) ).
cnf(refute_0_68,plain,
least_upper_bound(X_22,X_23) = least_upper_bound(X_23,X_22),
inference(resolve,[$cnf( $equal(least_upper_bound(X_23,X_22),least_upper_bound(X_22,X_23)) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
( least_upper_bound(X_22,X_23) != least_upper_bound(X_23,X_22)
| least_upper_bound(X_23,least_upper_bound(X_22,X_23)) != least_upper_bound(X_23,X_22)
| least_upper_bound(X_23,least_upper_bound(X_23,X_22)) = least_upper_bound(X_23,X_22) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_23,least_upper_bound(X_22,X_23)),least_upper_bound(X_23,X_22)) ),[0,1],$fot(least_upper_bound(X_23,X_22))]]) ).
cnf(refute_0_70,plain,
( least_upper_bound(X_23,least_upper_bound(X_22,X_23)) != least_upper_bound(X_23,X_22)
| least_upper_bound(X_23,least_upper_bound(X_23,X_22)) = least_upper_bound(X_23,X_22) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_22,X_23),least_upper_bound(X_23,X_22)) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
least_upper_bound(X_23,least_upper_bound(X_23,X_22)) = least_upper_bound(X_23,X_22),
inference(resolve,[$cnf( $equal(least_upper_bound(X_23,least_upper_bound(X_22,X_23)),least_upper_bound(X_23,X_22)) )],[refute_0_65,refute_0_70]) ).
cnf(refute_0_72,plain,
least_upper_bound(identity,least_upper_bound(identity,multiply(X_221,inverse(X_220)))) = least_upper_bound(identity,multiply(X_221,inverse(X_220))),
inference(subst,[],[refute_0_71:[bind(X_22,$fot(multiply(X_221,inverse(X_220)))),bind(X_23,$fot(identity))]]) ).
cnf(refute_0_73,plain,
multiply(inverse(least_upper_bound(X_220,X_221)),least_upper_bound(identity,least_upper_bound(identity,multiply(X_221,inverse(X_220))))) = multiply(inverse(least_upper_bound(X_220,X_221)),least_upper_bound(identity,least_upper_bound(identity,multiply(X_221,inverse(X_220))))),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(X_220,X_221)),least_upper_bound(identity,least_upper_bound(identity,multiply(X_221,inverse(X_220))))))]]) ).
cnf(refute_0_74,plain,
( multiply(inverse(least_upper_bound(X_220,X_221)),least_upper_bound(identity,least_upper_bound(identity,multiply(X_221,inverse(X_220))))) != multiply(inverse(least_upper_bound(X_220,X_221)),least_upper_bound(identity,least_upper_bound(identity,multiply(X_221,inverse(X_220)))))
| least_upper_bound(identity,least_upper_bound(identity,multiply(X_221,inverse(X_220)))) != least_upper_bound(identity,multiply(X_221,inverse(X_220)))
| multiply(inverse(least_upper_bound(X_220,X_221)),least_upper_bound(identity,least_upper_bound(identity,multiply(X_221,inverse(X_220))))) = multiply(inverse(least_upper_bound(X_220,X_221)),least_upper_bound(identity,multiply(X_221,inverse(X_220)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(X_220,X_221)),least_upper_bound(identity,least_upper_bound(identity,multiply(X_221,inverse(X_220))))),multiply(inverse(least_upper_bound(X_220,X_221)),least_upper_bound(identity,least_upper_bound(identity,multiply(X_221,inverse(X_220)))))) ),[1,1],$fot(least_upper_bound(identity,multiply(X_221,inverse(X_220))))]]) ).
cnf(refute_0_75,plain,
( least_upper_bound(identity,least_upper_bound(identity,multiply(X_221,inverse(X_220)))) != least_upper_bound(identity,multiply(X_221,inverse(X_220)))
| multiply(inverse(least_upper_bound(X_220,X_221)),least_upper_bound(identity,least_upper_bound(identity,multiply(X_221,inverse(X_220))))) = multiply(inverse(least_upper_bound(X_220,X_221)),least_upper_bound(identity,multiply(X_221,inverse(X_220)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_220,X_221)),least_upper_bound(identity,least_upper_bound(identity,multiply(X_221,inverse(X_220))))),multiply(inverse(least_upper_bound(X_220,X_221)),least_upper_bound(identity,least_upper_bound(identity,multiply(X_221,inverse(X_220)))))) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
multiply(inverse(least_upper_bound(X_220,X_221)),least_upper_bound(identity,least_upper_bound(identity,multiply(X_221,inverse(X_220))))) = multiply(inverse(least_upper_bound(X_220,X_221)),least_upper_bound(identity,multiply(X_221,inverse(X_220)))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(identity,multiply(X_221,inverse(X_220)))),least_upper_bound(identity,multiply(X_221,inverse(X_220)))) )],[refute_0_72,refute_0_75]) ).
cnf(refute_0_77,plain,
least_upper_bound(X_220,least_upper_bound(X_221,X_220)) = least_upper_bound(X_220,X_221),
inference(subst,[],[refute_0_64:[bind(Y,$fot(X_221)),bind(X_21,$fot(X_220))]]) ).
cnf(refute_0_78,plain,
inverse(inverse(X_220)) = X_220,
inference(subst,[],[p18_2:[bind(X,$fot(X_220))]]) ).
cnf(refute_0_79,plain,
least_upper_bound(X_221,inverse(inverse(X_220))) = least_upper_bound(X_221,inverse(inverse(X_220))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_221,inverse(inverse(X_220))))]]) ).
cnf(refute_0_80,plain,
( inverse(inverse(X_220)) != X_220
| least_upper_bound(X_221,inverse(inverse(X_220))) != least_upper_bound(X_221,inverse(inverse(X_220)))
| least_upper_bound(X_221,inverse(inverse(X_220))) = least_upper_bound(X_221,X_220) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_221,inverse(inverse(X_220))),least_upper_bound(X_221,inverse(inverse(X_220)))) ),[1,1],$fot(X_220)]]) ).
cnf(refute_0_81,plain,
( inverse(inverse(X_220)) != X_220
| least_upper_bound(X_221,inverse(inverse(X_220))) = least_upper_bound(X_221,X_220) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_221,inverse(inverse(X_220))),least_upper_bound(X_221,inverse(inverse(X_220)))) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
least_upper_bound(X_221,inverse(inverse(X_220))) = least_upper_bound(X_221,X_220),
inference(resolve,[$cnf( $equal(inverse(inverse(X_220)),X_220) )],[refute_0_78,refute_0_81]) ).
cnf(refute_0_83,plain,
least_upper_bound(X_220,least_upper_bound(X_221,inverse(inverse(X_220)))) = least_upper_bound(X_220,least_upper_bound(X_221,inverse(inverse(X_220)))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_220,least_upper_bound(X_221,inverse(inverse(X_220)))))]]) ).
cnf(refute_0_84,plain,
( least_upper_bound(X_220,least_upper_bound(X_221,inverse(inverse(X_220)))) != least_upper_bound(X_220,least_upper_bound(X_221,inverse(inverse(X_220))))
| least_upper_bound(X_221,inverse(inverse(X_220))) != least_upper_bound(X_221,X_220)
| least_upper_bound(X_220,least_upper_bound(X_221,inverse(inverse(X_220)))) = least_upper_bound(X_220,least_upper_bound(X_221,X_220)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_220,least_upper_bound(X_221,inverse(inverse(X_220)))),least_upper_bound(X_220,least_upper_bound(X_221,inverse(inverse(X_220))))) ),[1,1],$fot(least_upper_bound(X_221,X_220))]]) ).
cnf(refute_0_85,plain,
( least_upper_bound(X_221,inverse(inverse(X_220))) != least_upper_bound(X_221,X_220)
| least_upper_bound(X_220,least_upper_bound(X_221,inverse(inverse(X_220)))) = least_upper_bound(X_220,least_upper_bound(X_221,X_220)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_220,least_upper_bound(X_221,inverse(inverse(X_220)))),least_upper_bound(X_220,least_upper_bound(X_221,inverse(inverse(X_220))))) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
least_upper_bound(X_220,least_upper_bound(X_221,inverse(inverse(X_220)))) = least_upper_bound(X_220,least_upper_bound(X_221,X_220)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_221,inverse(inverse(X_220))),least_upper_bound(X_221,X_220)) )],[refute_0_82,refute_0_85]) ).
cnf(refute_0_87,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_88,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_2,refute_0_87]) ).
cnf(refute_0_89,plain,
( least_upper_bound(X_220,least_upper_bound(X_221,X_220)) != least_upper_bound(X_220,X_221)
| least_upper_bound(X_220,least_upper_bound(X_221,inverse(inverse(X_220)))) != least_upper_bound(X_220,least_upper_bound(X_221,X_220))
| least_upper_bound(X_220,least_upper_bound(X_221,inverse(inverse(X_220)))) = least_upper_bound(X_220,X_221) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(least_upper_bound(X_220,least_upper_bound(X_221,inverse(inverse(X_220)))))),bind(Y0,$fot(least_upper_bound(X_220,least_upper_bound(X_221,X_220)))),bind(Z0,$fot(least_upper_bound(X_220,X_221)))]]) ).
cnf(refute_0_90,plain,
( least_upper_bound(X_220,least_upper_bound(X_221,X_220)) != least_upper_bound(X_220,X_221)
| least_upper_bound(X_220,least_upper_bound(X_221,inverse(inverse(X_220)))) = least_upper_bound(X_220,X_221) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_220,least_upper_bound(X_221,inverse(inverse(X_220)))),least_upper_bound(X_220,least_upper_bound(X_221,X_220))) )],[refute_0_86,refute_0_89]) ).
cnf(refute_0_91,plain,
least_upper_bound(X_220,least_upper_bound(X_221,inverse(inverse(X_220)))) = least_upper_bound(X_220,X_221),
inference(resolve,[$cnf( $equal(least_upper_bound(X_220,least_upper_bound(X_221,X_220)),least_upper_bound(X_220,X_221)) )],[refute_0_77,refute_0_90]) ).
cnf(refute_0_92,plain,
least_upper_bound(least_upper_bound(X_220,X_221),inverse(inverse(X_220))) = least_upper_bound(X_220,least_upper_bound(X_221,inverse(inverse(X_220)))),
inference(subst,[],[refute_0_60:[bind(X,$fot(X_220)),bind(Y,$fot(X_221)),bind(Z,$fot(inverse(inverse(X_220))))]]) ).
cnf(refute_0_93,plain,
( least_upper_bound(X_220,least_upper_bound(X_221,inverse(inverse(X_220)))) != least_upper_bound(X_220,X_221)
| least_upper_bound(least_upper_bound(X_220,X_221),inverse(inverse(X_220))) != least_upper_bound(X_220,least_upper_bound(X_221,inverse(inverse(X_220))))
| least_upper_bound(least_upper_bound(X_220,X_221),inverse(inverse(X_220))) = least_upper_bound(X_220,X_221) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_220,X_221),inverse(inverse(X_220))))),bind(Y0,$fot(least_upper_bound(X_220,least_upper_bound(X_221,inverse(inverse(X_220)))))),bind(Z0,$fot(least_upper_bound(X_220,X_221)))]]) ).
cnf(refute_0_94,plain,
( least_upper_bound(X_220,least_upper_bound(X_221,inverse(inverse(X_220)))) != least_upper_bound(X_220,X_221)
| least_upper_bound(least_upper_bound(X_220,X_221),inverse(inverse(X_220))) = least_upper_bound(X_220,X_221) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_220,X_221),inverse(inverse(X_220))),least_upper_bound(X_220,least_upper_bound(X_221,inverse(inverse(X_220))))) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
least_upper_bound(least_upper_bound(X_220,X_221),inverse(inverse(X_220))) = least_upper_bound(X_220,X_221),
inference(resolve,[$cnf( $equal(least_upper_bound(X_220,least_upper_bound(X_221,inverse(inverse(X_220)))),least_upper_bound(X_220,X_221)) )],[refute_0_91,refute_0_94]) ).
cnf(refute_0_96,plain,
inverse(least_upper_bound(least_upper_bound(X_220,X_221),inverse(inverse(X_220)))) = inverse(least_upper_bound(least_upper_bound(X_220,X_221),inverse(inverse(X_220)))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(least_upper_bound(X_220,X_221),inverse(inverse(X_220)))))]]) ).
cnf(refute_0_97,plain,
( inverse(least_upper_bound(least_upper_bound(X_220,X_221),inverse(inverse(X_220)))) != inverse(least_upper_bound(least_upper_bound(X_220,X_221),inverse(inverse(X_220))))
| least_upper_bound(least_upper_bound(X_220,X_221),inverse(inverse(X_220))) != least_upper_bound(X_220,X_221)
| inverse(least_upper_bound(least_upper_bound(X_220,X_221),inverse(inverse(X_220)))) = inverse(least_upper_bound(X_220,X_221)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(X_220,X_221),inverse(inverse(X_220)))),inverse(least_upper_bound(least_upper_bound(X_220,X_221),inverse(inverse(X_220))))) ),[1,0],$fot(least_upper_bound(X_220,X_221))]]) ).
cnf(refute_0_98,plain,
( least_upper_bound(least_upper_bound(X_220,X_221),inverse(inverse(X_220))) != least_upper_bound(X_220,X_221)
| inverse(least_upper_bound(least_upper_bound(X_220,X_221),inverse(inverse(X_220)))) = inverse(least_upper_bound(X_220,X_221)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(X_220,X_221),inverse(inverse(X_220)))),inverse(least_upper_bound(least_upper_bound(X_220,X_221),inverse(inverse(X_220))))) )],[refute_0_96,refute_0_97]) ).
cnf(refute_0_99,plain,
inverse(least_upper_bound(least_upper_bound(X_220,X_221),inverse(inverse(X_220)))) = inverse(least_upper_bound(X_220,X_221)),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_220,X_221),inverse(inverse(X_220))),least_upper_bound(X_220,X_221)) )],[refute_0_95,refute_0_98]) ).
cnf(refute_0_100,plain,
multiply(inverse(least_upper_bound(least_upper_bound(X_220,X_221),inverse(inverse(X_220)))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_221,inverse(X_220))))) = multiply(inverse(least_upper_bound(least_upper_bound(X_220,X_221),inverse(inverse(X_220)))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_221,inverse(X_220))))),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(least_upper_bound(X_220,X_221),inverse(inverse(X_220)))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_221,inverse(X_220))))))]]) ).
cnf(refute_0_101,plain,
( multiply(inverse(least_upper_bound(least_upper_bound(X_220,X_221),inverse(inverse(X_220)))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_221,inverse(X_220))))) != multiply(inverse(least_upper_bound(least_upper_bound(X_220,X_221),inverse(inverse(X_220)))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_221,inverse(X_220)))))
| inverse(least_upper_bound(least_upper_bound(X_220,X_221),inverse(inverse(X_220)))) != inverse(least_upper_bound(X_220,X_221))
| multiply(inverse(least_upper_bound(least_upper_bound(X_220,X_221),inverse(inverse(X_220)))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_221,inverse(X_220))))) = multiply(inverse(least_upper_bound(X_220,X_221)),least_upper_bound(identity,least_upper_bound(identity,multiply(X_221,inverse(X_220))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(least_upper_bound(X_220,X_221),inverse(inverse(X_220)))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_221,inverse(X_220))))),multiply(inverse(least_upper_bound(least_upper_bound(X_220,X_221),inverse(inverse(X_220)))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_221,inverse(X_220)))))) ),[1,0],$fot(inverse(least_upper_bound(X_220,X_221)))]]) ).
cnf(refute_0_102,plain,
( inverse(least_upper_bound(least_upper_bound(X_220,X_221),inverse(inverse(X_220)))) != inverse(least_upper_bound(X_220,X_221))
| multiply(inverse(least_upper_bound(least_upper_bound(X_220,X_221),inverse(inverse(X_220)))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_221,inverse(X_220))))) = multiply(inverse(least_upper_bound(X_220,X_221)),least_upper_bound(identity,least_upper_bound(identity,multiply(X_221,inverse(X_220))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(least_upper_bound(X_220,X_221),inverse(inverse(X_220)))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_221,inverse(X_220))))),multiply(inverse(least_upper_bound(least_upper_bound(X_220,X_221),inverse(inverse(X_220)))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_221,inverse(X_220)))))) )],[refute_0_100,refute_0_101]) ).
cnf(refute_0_103,plain,
multiply(inverse(least_upper_bound(least_upper_bound(X_220,X_221),inverse(inverse(X_220)))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_221,inverse(X_220))))) = multiply(inverse(least_upper_bound(X_220,X_221)),least_upper_bound(identity,least_upper_bound(identity,multiply(X_221,inverse(X_220))))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(X_220,X_221),inverse(inverse(X_220)))),inverse(least_upper_bound(X_220,X_221))) )],[refute_0_99,refute_0_102]) ).
cnf(refute_0_104,plain,
( multiply(inverse(least_upper_bound(X_220,X_221)),least_upper_bound(identity,least_upper_bound(identity,multiply(X_221,inverse(X_220))))) != multiply(inverse(least_upper_bound(X_220,X_221)),least_upper_bound(identity,multiply(X_221,inverse(X_220))))
| multiply(inverse(least_upper_bound(least_upper_bound(X_220,X_221),inverse(inverse(X_220)))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_221,inverse(X_220))))) != multiply(inverse(least_upper_bound(X_220,X_221)),least_upper_bound(identity,least_upper_bound(identity,multiply(X_221,inverse(X_220)))))
| multiply(inverse(least_upper_bound(least_upper_bound(X_220,X_221),inverse(inverse(X_220)))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_221,inverse(X_220))))) = multiply(inverse(least_upper_bound(X_220,X_221)),least_upper_bound(identity,multiply(X_221,inverse(X_220)))) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(multiply(inverse(least_upper_bound(least_upper_bound(X_220,X_221),inverse(inverse(X_220)))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_221,inverse(X_220))))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(X_220,X_221)),least_upper_bound(identity,least_upper_bound(identity,multiply(X_221,inverse(X_220))))))),bind(Z0,$fot(multiply(inverse(least_upper_bound(X_220,X_221)),least_upper_bound(identity,multiply(X_221,inverse(X_220))))))]]) ).
cnf(refute_0_105,plain,
( multiply(inverse(least_upper_bound(X_220,X_221)),least_upper_bound(identity,least_upper_bound(identity,multiply(X_221,inverse(X_220))))) != multiply(inverse(least_upper_bound(X_220,X_221)),least_upper_bound(identity,multiply(X_221,inverse(X_220))))
| multiply(inverse(least_upper_bound(least_upper_bound(X_220,X_221),inverse(inverse(X_220)))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_221,inverse(X_220))))) = multiply(inverse(least_upper_bound(X_220,X_221)),least_upper_bound(identity,multiply(X_221,inverse(X_220)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(least_upper_bound(X_220,X_221),inverse(inverse(X_220)))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_221,inverse(X_220))))),multiply(inverse(least_upper_bound(X_220,X_221)),least_upper_bound(identity,least_upper_bound(identity,multiply(X_221,inverse(X_220)))))) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
multiply(inverse(least_upper_bound(least_upper_bound(X_220,X_221),inverse(inverse(X_220)))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_221,inverse(X_220))))) = multiply(inverse(least_upper_bound(X_220,X_221)),least_upper_bound(identity,multiply(X_221,inverse(X_220)))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_220,X_221)),least_upper_bound(identity,least_upper_bound(identity,multiply(X_221,inverse(X_220))))),multiply(inverse(least_upper_bound(X_220,X_221)),least_upper_bound(identity,multiply(X_221,inverse(X_220))))) )],[refute_0_76,refute_0_105]) ).
cnf(refute_0_107,plain,
( multiply(inverse(least_upper_bound(least_upper_bound(X_220,X_221),inverse(inverse(X_220)))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_221,inverse(X_220))))) != multiply(inverse(least_upper_bound(X_220,X_221)),least_upper_bound(identity,multiply(X_221,inverse(X_220))))
| inverse(X_220) != multiply(inverse(least_upper_bound(least_upper_bound(X_220,X_221),inverse(inverse(X_220)))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_221,inverse(X_220)))))
| inverse(X_220) = multiply(inverse(least_upper_bound(X_220,X_221)),least_upper_bound(identity,multiply(X_221,inverse(X_220)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(X_220),multiply(inverse(least_upper_bound(least_upper_bound(X_220,X_221),inverse(inverse(X_220)))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_221,inverse(X_220)))))) ),[1],$fot(multiply(inverse(least_upper_bound(X_220,X_221)),least_upper_bound(identity,multiply(X_221,inverse(X_220)))))]]) ).
cnf(refute_0_108,plain,
( inverse(X_220) != multiply(inverse(least_upper_bound(least_upper_bound(X_220,X_221),inverse(inverse(X_220)))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_221,inverse(X_220)))))
| inverse(X_220) = multiply(inverse(least_upper_bound(X_220,X_221)),least_upper_bound(identity,multiply(X_221,inverse(X_220)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(least_upper_bound(X_220,X_221),inverse(inverse(X_220)))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_221,inverse(X_220))))),multiply(inverse(least_upper_bound(X_220,X_221)),least_upper_bound(identity,multiply(X_221,inverse(X_220))))) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
inverse(X_220) = multiply(inverse(least_upper_bound(X_220,X_221)),least_upper_bound(identity,multiply(X_221,inverse(X_220)))),
inference(resolve,[$cnf( $equal(inverse(X_220),multiply(inverse(least_upper_bound(least_upper_bound(X_220,X_221),inverse(inverse(X_220)))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_221,inverse(X_220)))))) )],[refute_0_46,refute_0_108]) ).
cnf(refute_0_110,plain,
inverse(greatest_lower_bound(X_394,X_152)) = multiply(inverse(least_upper_bound(greatest_lower_bound(X_394,X_152),X_394)),least_upper_bound(identity,multiply(X_394,inverse(greatest_lower_bound(X_394,X_152))))),
inference(subst,[],[refute_0_109:[bind(X_220,$fot(greatest_lower_bound(X_394,X_152))),bind(X_221,$fot(X_394))]]) ).
cnf(refute_0_111,plain,
inverse(multiply(X_32,inverse(X))) = multiply(inverse(inverse(X)),inverse(X_32)),
inference(subst,[],[p18_3:[bind(X,$fot(X_32)),bind(Y,$fot(inverse(X)))]]) ).
cnf(refute_0_112,plain,
( inverse(multiply(X_32,inverse(X))) != multiply(inverse(inverse(X)),inverse(X_32))
| inverse(inverse(X)) != X
| inverse(multiply(X_32,inverse(X))) = multiply(X,inverse(X_32)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_32,inverse(X))),multiply(inverse(inverse(X)),inverse(X_32))) ),[1,0],$fot(X)]]) ).
cnf(refute_0_113,plain,
( inverse(multiply(X_32,inverse(X))) != multiply(inverse(inverse(X)),inverse(X_32))
| inverse(multiply(X_32,inverse(X))) = multiply(X,inverse(X_32)) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p18_2,refute_0_112]) ).
cnf(refute_0_114,plain,
inverse(multiply(X_32,inverse(X))) = multiply(X,inverse(X_32)),
inference(resolve,[$cnf( $equal(inverse(multiply(X_32,inverse(X))),multiply(inverse(inverse(X)),inverse(X_32))) )],[refute_0_111,refute_0_113]) ).
cnf(refute_0_115,plain,
inverse(multiply(greatest_lower_bound(X_46,inverse(inverse(X_99))),inverse(X_99))) = multiply(X_99,inverse(greatest_lower_bound(X_46,inverse(inverse(X_99))))),
inference(subst,[],[refute_0_114:[bind(X,$fot(X_99)),bind(X_32,$fot(greatest_lower_bound(X_46,inverse(inverse(X_99)))))]]) ).
cnf(refute_0_116,plain,
multiply(greatest_lower_bound(X_46,inverse(X_45)),X_45) = greatest_lower_bound(multiply(X_46,X_45),multiply(inverse(X_45),X_45)),
inference(subst,[],[monotony_glb2:[bind(X,$fot(X_45)),bind(Y,$fot(X_46)),bind(Z,$fot(inverse(X_45)))]]) ).
cnf(refute_0_117,plain,
multiply(inverse(X_45),X_45) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_45))]]) ).
cnf(refute_0_118,plain,
( multiply(greatest_lower_bound(X_46,inverse(X_45)),X_45) != greatest_lower_bound(multiply(X_46,X_45),multiply(inverse(X_45),X_45))
| multiply(inverse(X_45),X_45) != identity
| multiply(greatest_lower_bound(X_46,inverse(X_45)),X_45) = greatest_lower_bound(multiply(X_46,X_45),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_46,inverse(X_45)),X_45),greatest_lower_bound(multiply(X_46,X_45),multiply(inverse(X_45),X_45))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_119,plain,
( multiply(greatest_lower_bound(X_46,inverse(X_45)),X_45) != greatest_lower_bound(multiply(X_46,X_45),multiply(inverse(X_45),X_45))
| multiply(greatest_lower_bound(X_46,inverse(X_45)),X_45) = greatest_lower_bound(multiply(X_46,X_45),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_45),X_45),identity) )],[refute_0_117,refute_0_118]) ).
cnf(refute_0_120,plain,
multiply(greatest_lower_bound(X_46,inverse(X_45)),X_45) = greatest_lower_bound(multiply(X_46,X_45),identity),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_46,inverse(X_45)),X_45),greatest_lower_bound(multiply(X_46,X_45),multiply(inverse(X_45),X_45))) )],[refute_0_116,refute_0_119]) ).
cnf(refute_0_121,plain,
( greatest_lower_bound(X,Y) != greatest_lower_bound(Y,X)
| greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X,Y))),bind(Y0,$fot(greatest_lower_bound(Y,X)))]]) ).
cnf(refute_0_122,plain,
greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X)) )],[symmetry_of_glb,refute_0_121]) ).
cnf(refute_0_123,plain,
greatest_lower_bound(multiply(X_46,X_45),identity) = greatest_lower_bound(identity,multiply(X_46,X_45)),
inference(subst,[],[refute_0_122:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_46,X_45)))]]) ).
cnf(refute_0_124,plain,
( multiply(greatest_lower_bound(X_46,inverse(X_45)),X_45) != greatest_lower_bound(multiply(X_46,X_45),identity)
| greatest_lower_bound(multiply(X_46,X_45),identity) != greatest_lower_bound(identity,multiply(X_46,X_45))
| multiply(greatest_lower_bound(X_46,inverse(X_45)),X_45) = greatest_lower_bound(identity,multiply(X_46,X_45)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_46,inverse(X_45)),X_45),greatest_lower_bound(identity,multiply(X_46,X_45))) ),[0],$fot(greatest_lower_bound(multiply(X_46,X_45),identity))]]) ).
cnf(refute_0_125,plain,
( multiply(greatest_lower_bound(X_46,inverse(X_45)),X_45) != greatest_lower_bound(multiply(X_46,X_45),identity)
| multiply(greatest_lower_bound(X_46,inverse(X_45)),X_45) = greatest_lower_bound(identity,multiply(X_46,X_45)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_46,X_45),identity),greatest_lower_bound(identity,multiply(X_46,X_45))) )],[refute_0_123,refute_0_124]) ).
cnf(refute_0_126,plain,
multiply(greatest_lower_bound(X_46,inverse(X_45)),X_45) = greatest_lower_bound(identity,multiply(X_46,X_45)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_46,inverse(X_45)),X_45),greatest_lower_bound(multiply(X_46,X_45),identity)) )],[refute_0_120,refute_0_125]) ).
cnf(refute_0_127,plain,
multiply(greatest_lower_bound(X_46,inverse(inverse(X_99))),inverse(X_99)) = greatest_lower_bound(identity,multiply(X_46,inverse(X_99))),
inference(subst,[],[refute_0_126:[bind(X_45,$fot(inverse(X_99)))]]) ).
cnf(refute_0_128,plain,
( multiply(greatest_lower_bound(X_46,inverse(inverse(X_99))),inverse(X_99)) != greatest_lower_bound(identity,multiply(X_46,inverse(X_99)))
| inverse(multiply(greatest_lower_bound(X_46,inverse(inverse(X_99))),inverse(X_99))) != multiply(X_99,inverse(greatest_lower_bound(X_46,inverse(inverse(X_99)))))
| inverse(greatest_lower_bound(identity,multiply(X_46,inverse(X_99)))) = multiply(X_99,inverse(greatest_lower_bound(X_46,inverse(inverse(X_99))))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(greatest_lower_bound(X_46,inverse(inverse(X_99))),inverse(X_99))),multiply(X_99,inverse(greatest_lower_bound(X_46,inverse(inverse(X_99)))))) ),[0,0],$fot(greatest_lower_bound(identity,multiply(X_46,inverse(X_99))))]]) ).
cnf(refute_0_129,plain,
( inverse(multiply(greatest_lower_bound(X_46,inverse(inverse(X_99))),inverse(X_99))) != multiply(X_99,inverse(greatest_lower_bound(X_46,inverse(inverse(X_99)))))
| inverse(greatest_lower_bound(identity,multiply(X_46,inverse(X_99)))) = multiply(X_99,inverse(greatest_lower_bound(X_46,inverse(inverse(X_99))))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_46,inverse(inverse(X_99))),inverse(X_99)),greatest_lower_bound(identity,multiply(X_46,inverse(X_99)))) )],[refute_0_127,refute_0_128]) ).
cnf(refute_0_130,plain,
inverse(greatest_lower_bound(identity,multiply(X_46,inverse(X_99)))) = multiply(X_99,inverse(greatest_lower_bound(X_46,inverse(inverse(X_99))))),
inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(X_46,inverse(inverse(X_99))),inverse(X_99))),multiply(X_99,inverse(greatest_lower_bound(X_46,inverse(inverse(X_99)))))) )],[refute_0_115,refute_0_129]) ).
cnf(refute_0_131,plain,
inverse(inverse(X_99)) = X_99,
inference(subst,[],[p18_2:[bind(X,$fot(X_99))]]) ).
cnf(refute_0_132,plain,
greatest_lower_bound(X_46,inverse(inverse(X_99))) = greatest_lower_bound(X_46,inverse(inverse(X_99))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X_46,inverse(inverse(X_99))))]]) ).
cnf(refute_0_133,plain,
( greatest_lower_bound(X_46,inverse(inverse(X_99))) != greatest_lower_bound(X_46,inverse(inverse(X_99)))
| inverse(inverse(X_99)) != X_99
| greatest_lower_bound(X_46,inverse(inverse(X_99))) = greatest_lower_bound(X_46,X_99) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_46,inverse(inverse(X_99))),greatest_lower_bound(X_46,inverse(inverse(X_99)))) ),[1,1],$fot(X_99)]]) ).
cnf(refute_0_134,plain,
( inverse(inverse(X_99)) != X_99
| greatest_lower_bound(X_46,inverse(inverse(X_99))) = greatest_lower_bound(X_46,X_99) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_46,inverse(inverse(X_99))),greatest_lower_bound(X_46,inverse(inverse(X_99)))) )],[refute_0_132,refute_0_133]) ).
cnf(refute_0_135,plain,
greatest_lower_bound(X_46,inverse(inverse(X_99))) = greatest_lower_bound(X_46,X_99),
inference(resolve,[$cnf( $equal(inverse(inverse(X_99)),X_99) )],[refute_0_131,refute_0_134]) ).
cnf(refute_0_136,plain,
inverse(greatest_lower_bound(X_46,inverse(inverse(X_99)))) = inverse(greatest_lower_bound(X_46,inverse(inverse(X_99)))),
introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(X_46,inverse(inverse(X_99)))))]]) ).
cnf(refute_0_137,plain,
( greatest_lower_bound(X_46,inverse(inverse(X_99))) != greatest_lower_bound(X_46,X_99)
| inverse(greatest_lower_bound(X_46,inverse(inverse(X_99)))) != inverse(greatest_lower_bound(X_46,inverse(inverse(X_99))))
| inverse(greatest_lower_bound(X_46,inverse(inverse(X_99)))) = inverse(greatest_lower_bound(X_46,X_99)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X_46,inverse(inverse(X_99)))),inverse(greatest_lower_bound(X_46,inverse(inverse(X_99))))) ),[1,0],$fot(greatest_lower_bound(X_46,X_99))]]) ).
cnf(refute_0_138,plain,
( greatest_lower_bound(X_46,inverse(inverse(X_99))) != greatest_lower_bound(X_46,X_99)
| inverse(greatest_lower_bound(X_46,inverse(inverse(X_99)))) = inverse(greatest_lower_bound(X_46,X_99)) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_46,inverse(inverse(X_99)))),inverse(greatest_lower_bound(X_46,inverse(inverse(X_99))))) )],[refute_0_136,refute_0_137]) ).
cnf(refute_0_139,plain,
inverse(greatest_lower_bound(X_46,inverse(inverse(X_99)))) = inverse(greatest_lower_bound(X_46,X_99)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_46,inverse(inverse(X_99))),greatest_lower_bound(X_46,X_99)) )],[refute_0_135,refute_0_138]) ).
cnf(refute_0_140,plain,
multiply(X_99,inverse(greatest_lower_bound(X_46,inverse(inverse(X_99))))) = multiply(X_99,inverse(greatest_lower_bound(X_46,inverse(inverse(X_99))))),
introduced(tautology,[refl,[$fot(multiply(X_99,inverse(greatest_lower_bound(X_46,inverse(inverse(X_99))))))]]) ).
cnf(refute_0_141,plain,
( multiply(X_99,inverse(greatest_lower_bound(X_46,inverse(inverse(X_99))))) != multiply(X_99,inverse(greatest_lower_bound(X_46,inverse(inverse(X_99)))))
| inverse(greatest_lower_bound(X_46,inverse(inverse(X_99)))) != inverse(greatest_lower_bound(X_46,X_99))
| multiply(X_99,inverse(greatest_lower_bound(X_46,inverse(inverse(X_99))))) = multiply(X_99,inverse(greatest_lower_bound(X_46,X_99))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_99,inverse(greatest_lower_bound(X_46,inverse(inverse(X_99))))),multiply(X_99,inverse(greatest_lower_bound(X_46,inverse(inverse(X_99)))))) ),[1,1],$fot(inverse(greatest_lower_bound(X_46,X_99)))]]) ).
cnf(refute_0_142,plain,
( inverse(greatest_lower_bound(X_46,inverse(inverse(X_99)))) != inverse(greatest_lower_bound(X_46,X_99))
| multiply(X_99,inverse(greatest_lower_bound(X_46,inverse(inverse(X_99))))) = multiply(X_99,inverse(greatest_lower_bound(X_46,X_99))) ),
inference(resolve,[$cnf( $equal(multiply(X_99,inverse(greatest_lower_bound(X_46,inverse(inverse(X_99))))),multiply(X_99,inverse(greatest_lower_bound(X_46,inverse(inverse(X_99)))))) )],[refute_0_140,refute_0_141]) ).
cnf(refute_0_143,plain,
multiply(X_99,inverse(greatest_lower_bound(X_46,inverse(inverse(X_99))))) = multiply(X_99,inverse(greatest_lower_bound(X_46,X_99))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_46,inverse(inverse(X_99)))),inverse(greatest_lower_bound(X_46,X_99))) )],[refute_0_139,refute_0_142]) ).
cnf(refute_0_144,plain,
( multiply(X_99,inverse(greatest_lower_bound(X_46,inverse(inverse(X_99))))) != multiply(X_99,inverse(greatest_lower_bound(X_46,X_99)))
| inverse(greatest_lower_bound(identity,multiply(X_46,inverse(X_99)))) != multiply(X_99,inverse(greatest_lower_bound(X_46,inverse(inverse(X_99)))))
| inverse(greatest_lower_bound(identity,multiply(X_46,inverse(X_99)))) = multiply(X_99,inverse(greatest_lower_bound(X_46,X_99))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(X_46,inverse(X_99)))),multiply(X_99,inverse(greatest_lower_bound(X_46,inverse(inverse(X_99)))))) ),[1],$fot(multiply(X_99,inverse(greatest_lower_bound(X_46,X_99))))]]) ).
cnf(refute_0_145,plain,
( inverse(greatest_lower_bound(identity,multiply(X_46,inverse(X_99)))) != multiply(X_99,inverse(greatest_lower_bound(X_46,inverse(inverse(X_99)))))
| inverse(greatest_lower_bound(identity,multiply(X_46,inverse(X_99)))) = multiply(X_99,inverse(greatest_lower_bound(X_46,X_99))) ),
inference(resolve,[$cnf( $equal(multiply(X_99,inverse(greatest_lower_bound(X_46,inverse(inverse(X_99))))),multiply(X_99,inverse(greatest_lower_bound(X_46,X_99)))) )],[refute_0_143,refute_0_144]) ).
cnf(refute_0_146,plain,
inverse(greatest_lower_bound(identity,multiply(X_46,inverse(X_99)))) = multiply(X_99,inverse(greatest_lower_bound(X_46,X_99))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(X_46,inverse(X_99)))),multiply(X_99,inverse(greatest_lower_bound(X_46,inverse(inverse(X_99)))))) )],[refute_0_130,refute_0_145]) ).
cnf(refute_0_147,plain,
inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(X_151,inverse(X_152)))))) = multiply(multiply(X_151,inverse(X_152)),inverse(greatest_lower_bound(identity,multiply(X_151,inverse(X_152))))),
inference(subst,[],[refute_0_146:[bind(X_46,$fot(identity)),bind(X_99,$fot(multiply(X_151,inverse(X_152))))]]) ).
cnf(refute_0_148,plain,
multiply(greatest_lower_bound(X_46,X_47),inverse(X_47)) = greatest_lower_bound(multiply(X_46,inverse(X_47)),multiply(X_47,inverse(X_47))),
inference(subst,[],[monotony_glb2:[bind(X,$fot(inverse(X_47))),bind(Y,$fot(X_46)),bind(Z,$fot(X_47))]]) ).
cnf(refute_0_149,plain,
multiply(X_47,inverse(X_47)) = identity,
inference(subst,[],[refute_0_38:[bind(X_1,$fot(X_47))]]) ).
cnf(refute_0_150,plain,
( multiply(X_47,inverse(X_47)) != identity
| multiply(greatest_lower_bound(X_46,X_47),inverse(X_47)) != greatest_lower_bound(multiply(X_46,inverse(X_47)),multiply(X_47,inverse(X_47)))
| multiply(greatest_lower_bound(X_46,X_47),inverse(X_47)) = greatest_lower_bound(multiply(X_46,inverse(X_47)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_46,X_47),inverse(X_47)),greatest_lower_bound(multiply(X_46,inverse(X_47)),multiply(X_47,inverse(X_47)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_151,plain,
( multiply(greatest_lower_bound(X_46,X_47),inverse(X_47)) != greatest_lower_bound(multiply(X_46,inverse(X_47)),multiply(X_47,inverse(X_47)))
| multiply(greatest_lower_bound(X_46,X_47),inverse(X_47)) = greatest_lower_bound(multiply(X_46,inverse(X_47)),identity) ),
inference(resolve,[$cnf( $equal(multiply(X_47,inverse(X_47)),identity) )],[refute_0_149,refute_0_150]) ).
cnf(refute_0_152,plain,
multiply(greatest_lower_bound(X_46,X_47),inverse(X_47)) = greatest_lower_bound(multiply(X_46,inverse(X_47)),identity),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_46,X_47),inverse(X_47)),greatest_lower_bound(multiply(X_46,inverse(X_47)),multiply(X_47,inverse(X_47)))) )],[refute_0_148,refute_0_151]) ).
cnf(refute_0_153,plain,
greatest_lower_bound(multiply(X_46,inverse(X_47)),identity) = greatest_lower_bound(identity,multiply(X_46,inverse(X_47))),
inference(subst,[],[refute_0_122:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_46,inverse(X_47))))]]) ).
cnf(refute_0_154,plain,
( multiply(greatest_lower_bound(X_46,X_47),inverse(X_47)) != greatest_lower_bound(multiply(X_46,inverse(X_47)),identity)
| greatest_lower_bound(multiply(X_46,inverse(X_47)),identity) != greatest_lower_bound(identity,multiply(X_46,inverse(X_47)))
| multiply(greatest_lower_bound(X_46,X_47),inverse(X_47)) = greatest_lower_bound(identity,multiply(X_46,inverse(X_47))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_46,X_47),inverse(X_47)),greatest_lower_bound(identity,multiply(X_46,inverse(X_47)))) ),[0],$fot(greatest_lower_bound(multiply(X_46,inverse(X_47)),identity))]]) ).
cnf(refute_0_155,plain,
( multiply(greatest_lower_bound(X_46,X_47),inverse(X_47)) != greatest_lower_bound(multiply(X_46,inverse(X_47)),identity)
| multiply(greatest_lower_bound(X_46,X_47),inverse(X_47)) = greatest_lower_bound(identity,multiply(X_46,inverse(X_47))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_46,inverse(X_47)),identity),greatest_lower_bound(identity,multiply(X_46,inverse(X_47)))) )],[refute_0_153,refute_0_154]) ).
cnf(refute_0_156,plain,
multiply(greatest_lower_bound(X_46,X_47),inverse(X_47)) = greatest_lower_bound(identity,multiply(X_46,inverse(X_47))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_46,X_47),inverse(X_47)),greatest_lower_bound(multiply(X_46,inverse(X_47)),identity)) )],[refute_0_152,refute_0_155]) ).
cnf(refute_0_157,plain,
multiply(greatest_lower_bound(X_151,X_152),inverse(X_152)) = greatest_lower_bound(identity,multiply(X_151,inverse(X_152))),
inference(subst,[],[refute_0_156:[bind(X_46,$fot(X_151)),bind(X_47,$fot(X_152))]]) ).
cnf(refute_0_158,plain,
( multiply(greatest_lower_bound(X_151,X_152),inverse(X_152)) != greatest_lower_bound(identity,multiply(X_151,inverse(X_152)))
| greatest_lower_bound(identity,multiply(X_151,inverse(X_152))) = multiply(greatest_lower_bound(X_151,X_152),inverse(X_152)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(greatest_lower_bound(X_151,X_152),inverse(X_152)))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(X_151,inverse(X_152)))))]]) ).
cnf(refute_0_159,plain,
greatest_lower_bound(identity,multiply(X_151,inverse(X_152))) = multiply(greatest_lower_bound(X_151,X_152),inverse(X_152)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_151,X_152),inverse(X_152)),greatest_lower_bound(identity,multiply(X_151,inverse(X_152)))) )],[refute_0_157,refute_0_158]) ).
cnf(refute_0_160,plain,
( greatest_lower_bound(identity,multiply(X_151,inverse(X_152))) != multiply(greatest_lower_bound(X_151,X_152),inverse(X_152))
| inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(X_151,inverse(X_152)))))) != multiply(multiply(X_151,inverse(X_152)),inverse(greatest_lower_bound(identity,multiply(X_151,inverse(X_152)))))
| inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(X_151,inverse(X_152)))))) = multiply(multiply(X_151,inverse(X_152)),inverse(multiply(greatest_lower_bound(X_151,X_152),inverse(X_152)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(X_151,inverse(X_152)))))),multiply(multiply(X_151,inverse(X_152)),inverse(greatest_lower_bound(identity,multiply(X_151,inverse(X_152)))))) ),[1,1,0],$fot(multiply(greatest_lower_bound(X_151,X_152),inverse(X_152)))]]) ).
cnf(refute_0_161,plain,
( inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(X_151,inverse(X_152)))))) != multiply(multiply(X_151,inverse(X_152)),inverse(greatest_lower_bound(identity,multiply(X_151,inverse(X_152)))))
| inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(X_151,inverse(X_152)))))) = multiply(multiply(X_151,inverse(X_152)),inverse(multiply(greatest_lower_bound(X_151,X_152),inverse(X_152)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_151,inverse(X_152))),multiply(greatest_lower_bound(X_151,X_152),inverse(X_152))) )],[refute_0_159,refute_0_160]) ).
cnf(refute_0_162,plain,
inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(X_151,inverse(X_152)))))) = multiply(multiply(X_151,inverse(X_152)),inverse(multiply(greatest_lower_bound(X_151,X_152),inverse(X_152)))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(X_151,inverse(X_152)))))),multiply(multiply(X_151,inverse(X_152)),inverse(greatest_lower_bound(identity,multiply(X_151,inverse(X_152)))))) )],[refute_0_147,refute_0_161]) ).
cnf(refute_0_163,plain,
inverse(multiply(X_151,inverse(X_152))) = multiply(X_152,inverse(X_151)),
inference(subst,[],[refute_0_114:[bind(X,$fot(X_152)),bind(X_32,$fot(X_151))]]) ).
cnf(refute_0_164,plain,
greatest_lower_bound(identity,inverse(multiply(X_151,inverse(X_152)))) = greatest_lower_bound(identity,inverse(multiply(X_151,inverse(X_152)))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,inverse(multiply(X_151,inverse(X_152)))))]]) ).
cnf(refute_0_165,plain,
( greatest_lower_bound(identity,inverse(multiply(X_151,inverse(X_152)))) != greatest_lower_bound(identity,inverse(multiply(X_151,inverse(X_152))))
| inverse(multiply(X_151,inverse(X_152))) != multiply(X_152,inverse(X_151))
| greatest_lower_bound(identity,inverse(multiply(X_151,inverse(X_152)))) = greatest_lower_bound(identity,multiply(X_152,inverse(X_151))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,inverse(multiply(X_151,inverse(X_152)))),greatest_lower_bound(identity,inverse(multiply(X_151,inverse(X_152))))) ),[1,1],$fot(multiply(X_152,inverse(X_151)))]]) ).
cnf(refute_0_166,plain,
( inverse(multiply(X_151,inverse(X_152))) != multiply(X_152,inverse(X_151))
| greatest_lower_bound(identity,inverse(multiply(X_151,inverse(X_152)))) = greatest_lower_bound(identity,multiply(X_152,inverse(X_151))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(multiply(X_151,inverse(X_152)))),greatest_lower_bound(identity,inverse(multiply(X_151,inverse(X_152))))) )],[refute_0_164,refute_0_165]) ).
cnf(refute_0_167,plain,
greatest_lower_bound(identity,inverse(multiply(X_151,inverse(X_152)))) = greatest_lower_bound(identity,multiply(X_152,inverse(X_151))),
inference(resolve,[$cnf( $equal(inverse(multiply(X_151,inverse(X_152))),multiply(X_152,inverse(X_151))) )],[refute_0_163,refute_0_166]) ).
cnf(refute_0_168,plain,
multiply(identity,greatest_lower_bound(identity,inverse(multiply(X_151,inverse(X_152))))) = greatest_lower_bound(identity,inverse(multiply(X_151,inverse(X_152)))),
inference(subst,[],[left_identity:[bind(X,$fot(greatest_lower_bound(identity,inverse(multiply(X_151,inverse(X_152))))))]]) ).
cnf(refute_0_169,plain,
( greatest_lower_bound(X,least_upper_bound(X,Y)) != X
| least_upper_bound(X,Y) != least_upper_bound(Y,X)
| greatest_lower_bound(X,least_upper_bound(Y,X)) = X ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X,least_upper_bound(X,Y)),X) ),[0,1],$fot(least_upper_bound(Y,X))]]) ).
cnf(refute_0_170,plain,
( greatest_lower_bound(X,least_upper_bound(X,Y)) != X
| greatest_lower_bound(X,least_upper_bound(Y,X)) = X ),
inference(resolve,[$cnf( $equal(least_upper_bound(X,Y),least_upper_bound(Y,X)) )],[symmetry_of_lub,refute_0_169]) ).
cnf(refute_0_171,plain,
greatest_lower_bound(X,least_upper_bound(Y,X)) = X,
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,least_upper_bound(X,Y)),X) )],[glb_absorbtion,refute_0_170]) ).
cnf(refute_0_172,plain,
greatest_lower_bound(greatest_lower_bound(X_15,Y),least_upper_bound(X_15,greatest_lower_bound(X_15,Y))) = greatest_lower_bound(X_15,Y),
inference(subst,[],[refute_0_171:[bind(X,$fot(greatest_lower_bound(X_15,Y))),bind(Y,$fot(X_15))]]) ).
cnf(refute_0_173,plain,
least_upper_bound(X_15,greatest_lower_bound(X_15,Y)) = X_15,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_15))]]) ).
cnf(refute_0_174,plain,
( greatest_lower_bound(greatest_lower_bound(X_15,Y),least_upper_bound(X_15,greatest_lower_bound(X_15,Y))) != greatest_lower_bound(X_15,Y)
| least_upper_bound(X_15,greatest_lower_bound(X_15,Y)) != X_15
| greatest_lower_bound(greatest_lower_bound(X_15,Y),X_15) = greatest_lower_bound(X_15,Y) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_15,Y),least_upper_bound(X_15,greatest_lower_bound(X_15,Y))),greatest_lower_bound(X_15,Y)) ),[0,1],$fot(X_15)]]) ).
cnf(refute_0_175,plain,
( greatest_lower_bound(greatest_lower_bound(X_15,Y),least_upper_bound(X_15,greatest_lower_bound(X_15,Y))) != greatest_lower_bound(X_15,Y)
| greatest_lower_bound(greatest_lower_bound(X_15,Y),X_15) = greatest_lower_bound(X_15,Y) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_15,greatest_lower_bound(X_15,Y)),X_15) )],[refute_0_173,refute_0_174]) ).
cnf(refute_0_176,plain,
greatest_lower_bound(greatest_lower_bound(X_15,Y),X_15) = greatest_lower_bound(X_15,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_15,Y),least_upper_bound(X_15,greatest_lower_bound(X_15,Y))),greatest_lower_bound(X_15,Y)) )],[refute_0_172,refute_0_175]) ).
cnf(refute_0_177,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,Z)) != greatest_lower_bound(greatest_lower_bound(X,Y),Z)
| greatest_lower_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(Y,Z)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X,Y),Z)))]]) ).
cnf(refute_0_178,plain,
greatest_lower_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(greatest_lower_bound(X,Y),Z)) )],[associativity_of_glb,refute_0_177]) ).
cnf(refute_0_179,plain,
greatest_lower_bound(greatest_lower_bound(X_15,Y),X_15) = greatest_lower_bound(X_15,greatest_lower_bound(Y,X_15)),
inference(subst,[],[refute_0_178:[bind(X,$fot(X_15)),bind(Z,$fot(X_15))]]) ).
cnf(refute_0_180,plain,
( greatest_lower_bound(greatest_lower_bound(X_15,Y),X_15) != greatest_lower_bound(X_15,Y)
| greatest_lower_bound(greatest_lower_bound(X_15,Y),X_15) != greatest_lower_bound(X_15,greatest_lower_bound(Y,X_15))
| greatest_lower_bound(X_15,greatest_lower_bound(Y,X_15)) = greatest_lower_bound(X_15,Y) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_15,Y),X_15),greatest_lower_bound(X_15,Y)) ),[0],$fot(greatest_lower_bound(X_15,greatest_lower_bound(Y,X_15)))]]) ).
cnf(refute_0_181,plain,
( greatest_lower_bound(greatest_lower_bound(X_15,Y),X_15) != greatest_lower_bound(X_15,Y)
| greatest_lower_bound(X_15,greatest_lower_bound(Y,X_15)) = greatest_lower_bound(X_15,Y) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_15,Y),X_15),greatest_lower_bound(X_15,greatest_lower_bound(Y,X_15))) )],[refute_0_179,refute_0_180]) ).
cnf(refute_0_182,plain,
greatest_lower_bound(X_15,greatest_lower_bound(Y,X_15)) = greatest_lower_bound(X_15,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_15,Y),X_15),greatest_lower_bound(X_15,Y)) )],[refute_0_176,refute_0_181]) ).
cnf(refute_0_183,plain,
greatest_lower_bound(X_17,greatest_lower_bound(X_16,X_17)) = greatest_lower_bound(X_17,X_16),
inference(subst,[],[refute_0_182:[bind(Y,$fot(X_16)),bind(X_15,$fot(X_17))]]) ).
cnf(refute_0_184,plain,
greatest_lower_bound(X_17,X_16) = greatest_lower_bound(X_16,X_17),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_17)),bind(Y,$fot(X_16))]]) ).
cnf(refute_0_185,plain,
( greatest_lower_bound(X_17,X_16) != greatest_lower_bound(X_16,X_17)
| greatest_lower_bound(X_16,X_17) = greatest_lower_bound(X_17,X_16) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X_17,X_16))),bind(Y0,$fot(greatest_lower_bound(X_16,X_17)))]]) ).
cnf(refute_0_186,plain,
greatest_lower_bound(X_16,X_17) = greatest_lower_bound(X_17,X_16),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,X_16),greatest_lower_bound(X_16,X_17)) )],[refute_0_184,refute_0_185]) ).
cnf(refute_0_187,plain,
( greatest_lower_bound(X_16,X_17) != greatest_lower_bound(X_17,X_16)
| greatest_lower_bound(X_17,greatest_lower_bound(X_16,X_17)) != greatest_lower_bound(X_17,X_16)
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_16)) = greatest_lower_bound(X_17,X_16) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_17,greatest_lower_bound(X_16,X_17)),greatest_lower_bound(X_17,X_16)) ),[0,1],$fot(greatest_lower_bound(X_17,X_16))]]) ).
cnf(refute_0_188,plain,
( greatest_lower_bound(X_17,greatest_lower_bound(X_16,X_17)) != greatest_lower_bound(X_17,X_16)
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_16)) = greatest_lower_bound(X_17,X_16) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_16,X_17),greatest_lower_bound(X_17,X_16)) )],[refute_0_186,refute_0_187]) ).
cnf(refute_0_189,plain,
greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_16)) = greatest_lower_bound(X_17,X_16),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,greatest_lower_bound(X_16,X_17)),greatest_lower_bound(X_17,X_16)) )],[refute_0_183,refute_0_188]) ).
cnf(refute_0_190,plain,
greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_17,X_91))) = greatest_lower_bound(X_17,multiply(X_17,X_91)),
inference(subst,[],[refute_0_189:[bind(X_16,$fot(multiply(X_17,X_91)))]]) ).
cnf(refute_0_191,plain,
multiply(X_36,greatest_lower_bound(X_37,identity)) = greatest_lower_bound(multiply(X_36,X_37),multiply(X_36,identity)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(X_36)),bind(Y,$fot(X_37)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_192,plain,
inverse(multiply(identity,X_33)) = multiply(inverse(X_33),inverse(identity)),
inference(subst,[],[p18_3:[bind(X,$fot(identity)),bind(Y,$fot(X_33))]]) ).
cnf(refute_0_193,plain,
( inverse(multiply(identity,X_33)) != multiply(inverse(X_33),inverse(identity))
| inverse(identity) != identity
| inverse(multiply(identity,X_33)) = multiply(inverse(X_33),identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(identity,X_33)),multiply(inverse(X_33),inverse(identity))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_194,plain,
( inverse(multiply(identity,X_33)) != multiply(inverse(X_33),inverse(identity))
| inverse(multiply(identity,X_33)) = multiply(inverse(X_33),identity) ),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[p18_1,refute_0_193]) ).
cnf(refute_0_195,plain,
inverse(multiply(identity,X_33)) = multiply(inverse(X_33),identity),
inference(resolve,[$cnf( $equal(inverse(multiply(identity,X_33)),multiply(inverse(X_33),inverse(identity))) )],[refute_0_192,refute_0_194]) ).
cnf(refute_0_196,plain,
multiply(identity,X_33) = X_33,
inference(subst,[],[left_identity:[bind(X,$fot(X_33))]]) ).
cnf(refute_0_197,plain,
inverse(multiply(identity,X_33)) = inverse(multiply(identity,X_33)),
introduced(tautology,[refl,[$fot(inverse(multiply(identity,X_33)))]]) ).
cnf(refute_0_198,plain,
( multiply(identity,X_33) != X_33
| inverse(multiply(identity,X_33)) != inverse(multiply(identity,X_33))
| inverse(multiply(identity,X_33)) = inverse(X_33) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(identity,X_33)),inverse(multiply(identity,X_33))) ),[1,0],$fot(X_33)]]) ).
cnf(refute_0_199,plain,
( multiply(identity,X_33) != X_33
| inverse(multiply(identity,X_33)) = inverse(X_33) ),
inference(resolve,[$cnf( $equal(inverse(multiply(identity,X_33)),inverse(multiply(identity,X_33))) )],[refute_0_197,refute_0_198]) ).
cnf(refute_0_200,plain,
inverse(multiply(identity,X_33)) = inverse(X_33),
inference(resolve,[$cnf( $equal(multiply(identity,X_33),X_33) )],[refute_0_196,refute_0_199]) ).
cnf(refute_0_201,plain,
( inverse(multiply(identity,X_33)) != multiply(inverse(X_33),identity)
| inverse(multiply(identity,X_33)) != inverse(X_33)
| inverse(X_33) = multiply(inverse(X_33),identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(identity,X_33)),multiply(inverse(X_33),identity)) ),[0],$fot(inverse(X_33))]]) ).
cnf(refute_0_202,plain,
( inverse(multiply(identity,X_33)) != multiply(inverse(X_33),identity)
| inverse(X_33) = multiply(inverse(X_33),identity) ),
inference(resolve,[$cnf( $equal(inverse(multiply(identity,X_33)),inverse(X_33)) )],[refute_0_200,refute_0_201]) ).
cnf(refute_0_203,plain,
inverse(X_33) = multiply(inverse(X_33),identity),
inference(resolve,[$cnf( $equal(inverse(multiply(identity,X_33)),multiply(inverse(X_33),identity)) )],[refute_0_195,refute_0_202]) ).
cnf(refute_0_204,plain,
inverse(inverse(X)) = multiply(inverse(inverse(X)),identity),
inference(subst,[],[refute_0_203:[bind(X_33,$fot(inverse(X)))]]) ).
cnf(refute_0_205,plain,
( inverse(inverse(X)) != X
| inverse(inverse(X)) != multiply(inverse(inverse(X)),identity)
| inverse(inverse(X)) = multiply(X,identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X)),multiply(inverse(inverse(X)),identity)) ),[1,0],$fot(X)]]) ).
cnf(refute_0_206,plain,
( inverse(inverse(X)) != multiply(inverse(inverse(X)),identity)
| inverse(inverse(X)) = multiply(X,identity) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p18_2,refute_0_205]) ).
cnf(refute_0_207,plain,
inverse(inverse(X)) = multiply(X,identity),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),multiply(inverse(inverse(X)),identity)) )],[refute_0_204,refute_0_206]) ).
cnf(refute_0_208,plain,
( inverse(inverse(X)) != X
| inverse(inverse(X)) != multiply(X,identity)
| X = multiply(X,identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X)),multiply(X,identity)) ),[0],$fot(X)]]) ).
cnf(refute_0_209,plain,
( inverse(inverse(X)) != multiply(X,identity)
| X = multiply(X,identity) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p18_2,refute_0_208]) ).
cnf(refute_0_210,plain,
X = multiply(X,identity),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),multiply(X,identity)) )],[refute_0_207,refute_0_209]) ).
cnf(refute_0_211,plain,
X_36 = multiply(X_36,identity),
inference(subst,[],[refute_0_210:[bind(X,$fot(X_36))]]) ).
cnf(refute_0_212,plain,
( X_36 != multiply(X_36,identity)
| multiply(X_36,identity) = X_36 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_36)),bind(Y0,$fot(multiply(X_36,identity)))]]) ).
cnf(refute_0_213,plain,
multiply(X_36,identity) = X_36,
inference(resolve,[$cnf( $equal(X_36,multiply(X_36,identity)) )],[refute_0_211,refute_0_212]) ).
cnf(refute_0_214,plain,
( multiply(X_36,greatest_lower_bound(X_37,identity)) != greatest_lower_bound(multiply(X_36,X_37),multiply(X_36,identity))
| multiply(X_36,identity) != X_36
| multiply(X_36,greatest_lower_bound(X_37,identity)) = greatest_lower_bound(multiply(X_36,X_37),X_36) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_36,greatest_lower_bound(X_37,identity)),greatest_lower_bound(multiply(X_36,X_37),multiply(X_36,identity))) ),[1,1],$fot(X_36)]]) ).
cnf(refute_0_215,plain,
( multiply(X_36,greatest_lower_bound(X_37,identity)) != greatest_lower_bound(multiply(X_36,X_37),multiply(X_36,identity))
| multiply(X_36,greatest_lower_bound(X_37,identity)) = greatest_lower_bound(multiply(X_36,X_37),X_36) ),
inference(resolve,[$cnf( $equal(multiply(X_36,identity),X_36) )],[refute_0_213,refute_0_214]) ).
cnf(refute_0_216,plain,
multiply(X_36,greatest_lower_bound(X_37,identity)) = greatest_lower_bound(multiply(X_36,X_37),X_36),
inference(resolve,[$cnf( $equal(multiply(X_36,greatest_lower_bound(X_37,identity)),greatest_lower_bound(multiply(X_36,X_37),multiply(X_36,identity))) )],[refute_0_191,refute_0_215]) ).
cnf(refute_0_217,plain,
greatest_lower_bound(multiply(X_36,X_37),X_36) = greatest_lower_bound(X_36,multiply(X_36,X_37)),
inference(subst,[],[refute_0_122:[bind(X,$fot(X_36)),bind(Y,$fot(multiply(X_36,X_37)))]]) ).
cnf(refute_0_218,plain,
( multiply(X_36,greatest_lower_bound(X_37,identity)) != greatest_lower_bound(multiply(X_36,X_37),X_36)
| greatest_lower_bound(multiply(X_36,X_37),X_36) != greatest_lower_bound(X_36,multiply(X_36,X_37))
| multiply(X_36,greatest_lower_bound(X_37,identity)) = greatest_lower_bound(X_36,multiply(X_36,X_37)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_36,greatest_lower_bound(X_37,identity)),greatest_lower_bound(X_36,multiply(X_36,X_37))) ),[0],$fot(greatest_lower_bound(multiply(X_36,X_37),X_36))]]) ).
cnf(refute_0_219,plain,
( multiply(X_36,greatest_lower_bound(X_37,identity)) != greatest_lower_bound(multiply(X_36,X_37),X_36)
| multiply(X_36,greatest_lower_bound(X_37,identity)) = greatest_lower_bound(X_36,multiply(X_36,X_37)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_36,X_37),X_36),greatest_lower_bound(X_36,multiply(X_36,X_37))) )],[refute_0_217,refute_0_218]) ).
cnf(refute_0_220,plain,
multiply(X_36,greatest_lower_bound(X_37,identity)) = greatest_lower_bound(X_36,multiply(X_36,X_37)),
inference(resolve,[$cnf( $equal(multiply(X_36,greatest_lower_bound(X_37,identity)),greatest_lower_bound(multiply(X_36,X_37),X_36)) )],[refute_0_216,refute_0_219]) ).
cnf(refute_0_221,plain,
multiply(X_17,greatest_lower_bound(X_91,identity)) = greatest_lower_bound(X_17,multiply(X_17,X_91)),
inference(subst,[],[refute_0_220:[bind(X_36,$fot(X_17)),bind(X_37,$fot(X_91))]]) ).
cnf(refute_0_222,plain,
( multiply(X_17,greatest_lower_bound(X_91,identity)) != greatest_lower_bound(X_17,multiply(X_17,X_91))
| greatest_lower_bound(X_17,multiply(X_17,X_91)) = multiply(X_17,greatest_lower_bound(X_91,identity)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X_17,greatest_lower_bound(X_91,identity)))),bind(Y0,$fot(greatest_lower_bound(X_17,multiply(X_17,X_91))))]]) ).
cnf(refute_0_223,plain,
greatest_lower_bound(X_17,multiply(X_17,X_91)) = multiply(X_17,greatest_lower_bound(X_91,identity)),
inference(resolve,[$cnf( $equal(multiply(X_17,greatest_lower_bound(X_91,identity)),greatest_lower_bound(X_17,multiply(X_17,X_91))) )],[refute_0_221,refute_0_222]) ).
cnf(refute_0_224,plain,
( greatest_lower_bound(X_17,multiply(X_17,X_91)) != multiply(X_17,greatest_lower_bound(X_91,identity))
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_17,X_91))) != greatest_lower_bound(X_17,multiply(X_17,X_91))
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_17,X_91))) = multiply(X_17,greatest_lower_bound(X_91,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_17,X_91))),greatest_lower_bound(X_17,multiply(X_17,X_91))) ),[1],$fot(multiply(X_17,greatest_lower_bound(X_91,identity)))]]) ).
cnf(refute_0_225,plain,
( greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_17,X_91))) != greatest_lower_bound(X_17,multiply(X_17,X_91))
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_17,X_91))) = multiply(X_17,greatest_lower_bound(X_91,identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,multiply(X_17,X_91)),multiply(X_17,greatest_lower_bound(X_91,identity))) )],[refute_0_223,refute_0_224]) ).
cnf(refute_0_226,plain,
greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_17,X_91))) = multiply(X_17,greatest_lower_bound(X_91,identity)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_17,X_91))),greatest_lower_bound(X_17,multiply(X_17,X_91))) )],[refute_0_190,refute_0_225]) ).
cnf(refute_0_227,plain,
greatest_lower_bound(identity,greatest_lower_bound(X_91,identity)) = greatest_lower_bound(identity,X_91),
inference(subst,[],[refute_0_182:[bind(Y,$fot(X_91)),bind(X_15,$fot(identity))]]) ).
cnf(refute_0_228,plain,
multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_91,identity))) = multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_91,identity))),
introduced(tautology,[refl,[$fot(multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_91,identity))))]]) ).
cnf(refute_0_229,plain,
( multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_91,identity))) != multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_91,identity)))
| greatest_lower_bound(identity,greatest_lower_bound(X_91,identity)) != greatest_lower_bound(identity,X_91)
| multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_91,identity))) = multiply(X_17,greatest_lower_bound(identity,X_91)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_91,identity))),multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_91,identity)))) ),[1,1],$fot(greatest_lower_bound(identity,X_91))]]) ).
cnf(refute_0_230,plain,
( greatest_lower_bound(identity,greatest_lower_bound(X_91,identity)) != greatest_lower_bound(identity,X_91)
| multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_91,identity))) = multiply(X_17,greatest_lower_bound(identity,X_91)) ),
inference(resolve,[$cnf( $equal(multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_91,identity))),multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_91,identity)))) )],[refute_0_228,refute_0_229]) ).
cnf(refute_0_231,plain,
multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_91,identity))) = multiply(X_17,greatest_lower_bound(identity,X_91)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_91,identity)),greatest_lower_bound(identity,X_91)) )],[refute_0_227,refute_0_230]) ).
cnf(refute_0_232,plain,
least_upper_bound(greatest_lower_bound(Y,X_21),greatest_lower_bound(X_21,greatest_lower_bound(Y,X_21))) = greatest_lower_bound(Y,X_21),
inference(subst,[],[refute_0_53:[bind(X_12,$fot(greatest_lower_bound(Y,X_21))),bind(X_13,$fot(X_21))]]) ).
cnf(refute_0_233,plain,
greatest_lower_bound(X_21,greatest_lower_bound(Y,X_21)) = greatest_lower_bound(X_21,Y),
inference(subst,[],[refute_0_182:[bind(X_15,$fot(X_21))]]) ).
cnf(refute_0_234,plain,
( greatest_lower_bound(X_21,greatest_lower_bound(Y,X_21)) != greatest_lower_bound(X_21,Y)
| least_upper_bound(greatest_lower_bound(Y,X_21),greatest_lower_bound(X_21,greatest_lower_bound(Y,X_21))) != greatest_lower_bound(Y,X_21)
| least_upper_bound(greatest_lower_bound(Y,X_21),greatest_lower_bound(X_21,Y)) = greatest_lower_bound(Y,X_21) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(Y,X_21),greatest_lower_bound(X_21,greatest_lower_bound(Y,X_21))),greatest_lower_bound(Y,X_21)) ),[0,1],$fot(greatest_lower_bound(X_21,Y))]]) ).
cnf(refute_0_235,plain,
( least_upper_bound(greatest_lower_bound(Y,X_21),greatest_lower_bound(X_21,greatest_lower_bound(Y,X_21))) != greatest_lower_bound(Y,X_21)
| least_upper_bound(greatest_lower_bound(Y,X_21),greatest_lower_bound(X_21,Y)) = greatest_lower_bound(Y,X_21) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_21,greatest_lower_bound(Y,X_21)),greatest_lower_bound(X_21,Y)) )],[refute_0_233,refute_0_234]) ).
cnf(refute_0_236,plain,
least_upper_bound(greatest_lower_bound(Y,X_21),greatest_lower_bound(X_21,Y)) = greatest_lower_bound(Y,X_21),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(Y,X_21),greatest_lower_bound(X_21,greatest_lower_bound(Y,X_21))),greatest_lower_bound(Y,X_21)) )],[refute_0_232,refute_0_235]) ).
cnf(refute_0_237,plain,
least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) = greatest_lower_bound(multiply(X,Z),multiply(X,Y)),
inference(subst,[],[refute_0_236:[bind(Y,$fot(multiply(X,Z))),bind(X_21,$fot(multiply(X,Y)))]]) ).
cnf(refute_0_238,plain,
( multiply(X,greatest_lower_bound(Y,Z)) != greatest_lower_bound(multiply(X,Y),multiply(X,Z))
| greatest_lower_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,greatest_lower_bound(Y,Z)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X,greatest_lower_bound(Y,Z)))),bind(Y0,$fot(greatest_lower_bound(multiply(X,Y),multiply(X,Z))))]]) ).
cnf(refute_0_239,plain,
greatest_lower_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) )],[monotony_glb1,refute_0_238]) ).
cnf(refute_0_240,plain,
( greatest_lower_bound(multiply(X,Y),multiply(X,Z)) != multiply(X,greatest_lower_bound(Y,Z))
| least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) != greatest_lower_bound(multiply(X,Z),multiply(X,Y))
| least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) = greatest_lower_bound(multiply(X,Z),multiply(X,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),greatest_lower_bound(multiply(X,Y),multiply(X,Z))),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) ),[0,1],$fot(multiply(X,greatest_lower_bound(Y,Z)))]]) ).
cnf(refute_0_241,plain,
( least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) != greatest_lower_bound(multiply(X,Z),multiply(X,Y))
| least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) = greatest_lower_bound(multiply(X,Z),multiply(X,Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,Y),multiply(X,Z)),multiply(X,greatest_lower_bound(Y,Z))) )],[refute_0_239,refute_0_240]) ).
cnf(refute_0_242,plain,
least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) = greatest_lower_bound(multiply(X,Z),multiply(X,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),greatest_lower_bound(multiply(X,Y),multiply(X,Z))),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) )],[refute_0_237,refute_0_241]) ).
cnf(refute_0_243,plain,
least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)) = greatest_lower_bound(Y,Z),
inference(subst,[],[refute_0_236:[bind(X_21,$fot(Z))]]) ).
cnf(refute_0_244,plain,
multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))) = multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))),
introduced(tautology,[refl,[$fot(multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))))]]) ).
cnf(refute_0_245,plain,
( multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))) != multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)))
| least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)) != greatest_lower_bound(Y,Z)
| multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))) = multiply(X,greatest_lower_bound(Y,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))),multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)))) ),[1,1],$fot(greatest_lower_bound(Y,Z))]]) ).
cnf(refute_0_246,plain,
( least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)) != greatest_lower_bound(Y,Z)
| multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))) = multiply(X,greatest_lower_bound(Y,Z)) ),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))),multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)))) )],[refute_0_244,refute_0_245]) ).
cnf(refute_0_247,plain,
multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))) = multiply(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),greatest_lower_bound(Y,Z)) )],[refute_0_243,refute_0_246]) ).
cnf(refute_0_248,plain,
( multiply(X,least_upper_bound(Y,Z)) != least_upper_bound(multiply(X,Y),multiply(X,Z))
| least_upper_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X,least_upper_bound(Y,Z)))),bind(Y0,$fot(least_upper_bound(multiply(X,Y),multiply(X,Z))))]]) ).
cnf(refute_0_249,plain,
least_upper_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Y),multiply(X,Z))) )],[monotony_lub1,refute_0_248]) ).
cnf(refute_0_250,plain,
least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))) = multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))),
inference(subst,[],[refute_0_249:[bind(Y,$fot(greatest_lower_bound(Y,Z))),bind(Z,$fot(greatest_lower_bound(Z,Y)))]]) ).
cnf(refute_0_251,plain,
( multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))) != multiply(X,greatest_lower_bound(Y,Z))
| least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))) != multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)))
| least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))) = multiply(X,greatest_lower_bound(Y,Z)) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))))),bind(Y0,$fot(multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))))),bind(Z0,$fot(multiply(X,greatest_lower_bound(Y,Z))))]]) ).
cnf(refute_0_252,plain,
( multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))) != multiply(X,greatest_lower_bound(Y,Z))
| least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))) = multiply(X,greatest_lower_bound(Y,Z)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))),multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)))) )],[refute_0_250,refute_0_251]) ).
cnf(refute_0_253,plain,
least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))) = multiply(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))),multiply(X,greatest_lower_bound(Y,Z))) )],[refute_0_247,refute_0_252]) ).
cnf(refute_0_254,plain,
greatest_lower_bound(multiply(X,Z),multiply(X,Y)) = multiply(X,greatest_lower_bound(Z,Y)),
inference(subst,[],[refute_0_239:[bind(Y,$fot(Z)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_255,plain,
least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) = least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))),
introduced(tautology,[refl,[$fot(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))))]]) ).
cnf(refute_0_256,plain,
( greatest_lower_bound(multiply(X,Z),multiply(X,Y)) != multiply(X,greatest_lower_bound(Z,Y))
| least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) != least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y)))
| least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) = least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))),least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y)))) ),[1,1],$fot(multiply(X,greatest_lower_bound(Z,Y)))]]) ).
cnf(refute_0_257,plain,
( greatest_lower_bound(multiply(X,Z),multiply(X,Y)) != multiply(X,greatest_lower_bound(Z,Y))
| least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) = least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))),least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y)))) )],[refute_0_255,refute_0_256]) ).
cnf(refute_0_258,plain,
least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) = least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Z,Y))) )],[refute_0_254,refute_0_257]) ).
cnf(refute_0_259,plain,
( least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))) != multiply(X,greatest_lower_bound(Y,Z))
| least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) != least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y)))
| least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) = multiply(X,greatest_lower_bound(Y,Z)) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))))),bind(Y0,$fot(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))))),bind(Z0,$fot(multiply(X,greatest_lower_bound(Y,Z))))]]) ).
cnf(refute_0_260,plain,
( least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))) != multiply(X,greatest_lower_bound(Y,Z))
| least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) = multiply(X,greatest_lower_bound(Y,Z)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))),least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y)))) )],[refute_0_258,refute_0_259]) ).
cnf(refute_0_261,plain,
least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) = multiply(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))),multiply(X,greatest_lower_bound(Y,Z))) )],[refute_0_253,refute_0_260]) ).
cnf(refute_0_262,plain,
least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) = least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))),
inference(subst,[],[refute_0_4:[bind(X,$fot(multiply(X,greatest_lower_bound(Y,Z)))),bind(Y,$fot(greatest_lower_bound(multiply(X,Z),multiply(X,Y))))]]) ).
cnf(refute_0_263,plain,
( least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) != multiply(X,greatest_lower_bound(Y,Z))
| least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) != least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y)))
| least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) = multiply(X,greatest_lower_bound(Y,Z)) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))))),bind(Y0,$fot(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))))),bind(Z0,$fot(multiply(X,greatest_lower_bound(Y,Z))))]]) ).
cnf(refute_0_264,plain,
( least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) != multiply(X,greatest_lower_bound(Y,Z))
| least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) = multiply(X,greatest_lower_bound(Y,Z)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))),least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y)))) )],[refute_0_262,refute_0_263]) ).
cnf(refute_0_265,plain,
least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) = multiply(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))),multiply(X,greatest_lower_bound(Y,Z))) )],[refute_0_261,refute_0_264]) ).
cnf(refute_0_266,plain,
( least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) != multiply(X,greatest_lower_bound(Y,Z))
| least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) != greatest_lower_bound(multiply(X,Z),multiply(X,Y))
| multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Z),multiply(X,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) ),[0],$fot(multiply(X,greatest_lower_bound(Y,Z)))]]) ).
cnf(refute_0_267,plain,
( least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) != greatest_lower_bound(multiply(X,Z),multiply(X,Y))
| multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Z),multiply(X,Y)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))),multiply(X,greatest_lower_bound(Y,Z))) )],[refute_0_265,refute_0_266]) ).
cnf(refute_0_268,plain,
( multiply(X,greatest_lower_bound(Y,Z)) != greatest_lower_bound(multiply(X,Z),multiply(X,Y))
| greatest_lower_bound(multiply(X,Z),multiply(X,Y)) != multiply(X,greatest_lower_bound(Z,Y))
| multiply(X,greatest_lower_bound(Y,Z)) = multiply(X,greatest_lower_bound(Z,Y)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))) ),[0],$fot(greatest_lower_bound(multiply(X,Z),multiply(X,Y)))]]) ).
cnf(refute_0_269,plain,
( multiply(X,greatest_lower_bound(Y,Z)) != greatest_lower_bound(multiply(X,Z),multiply(X,Y))
| multiply(X,greatest_lower_bound(Y,Z)) = multiply(X,greatest_lower_bound(Z,Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Z,Y))) )],[refute_0_254,refute_0_268]) ).
cnf(refute_0_270,plain,
( least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) != greatest_lower_bound(multiply(X,Z),multiply(X,Y))
| multiply(X,greatest_lower_bound(Y,Z)) = multiply(X,greatest_lower_bound(Z,Y)) ),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) )],[refute_0_267,refute_0_269]) ).
cnf(refute_0_271,plain,
multiply(X,greatest_lower_bound(Y,Z)) = multiply(X,greatest_lower_bound(Z,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) )],[refute_0_242,refute_0_270]) ).
cnf(refute_0_272,plain,
( multiply(X,greatest_lower_bound(Y,Z)) != multiply(X,greatest_lower_bound(Z,Y))
| multiply(X,greatest_lower_bound(Z,Y)) = multiply(X,greatest_lower_bound(Y,Z)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X,greatest_lower_bound(Y,Z)))),bind(Y0,$fot(multiply(X,greatest_lower_bound(Z,Y))))]]) ).
cnf(refute_0_273,plain,
multiply(X,greatest_lower_bound(Z,Y)) = multiply(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))) )],[refute_0_271,refute_0_272]) ).
cnf(refute_0_274,plain,
multiply(X_17,greatest_lower_bound(greatest_lower_bound(X_91,identity),identity)) = multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_91,identity))),
inference(subst,[],[refute_0_273:[bind(X,$fot(X_17)),bind(Y,$fot(identity)),bind(Z,$fot(greatest_lower_bound(X_91,identity)))]]) ).
cnf(refute_0_275,plain,
( multiply(X_36,greatest_lower_bound(X_37,identity)) != greatest_lower_bound(X_36,multiply(X_36,X_37))
| greatest_lower_bound(X_36,multiply(X_36,X_37)) = multiply(X_36,greatest_lower_bound(X_37,identity)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X_36,greatest_lower_bound(X_37,identity)))),bind(Y0,$fot(greatest_lower_bound(X_36,multiply(X_36,X_37))))]]) ).
cnf(refute_0_276,plain,
greatest_lower_bound(X_36,multiply(X_36,X_37)) = multiply(X_36,greatest_lower_bound(X_37,identity)),
inference(resolve,[$cnf( $equal(multiply(X_36,greatest_lower_bound(X_37,identity)),greatest_lower_bound(X_36,multiply(X_36,X_37))) )],[refute_0_220,refute_0_275]) ).
cnf(refute_0_277,plain,
greatest_lower_bound(X_17,multiply(X_17,greatest_lower_bound(X_91,identity))) = multiply(X_17,greatest_lower_bound(greatest_lower_bound(X_91,identity),identity)),
inference(subst,[],[refute_0_276:[bind(X_36,$fot(X_17)),bind(X_37,$fot(greatest_lower_bound(X_91,identity)))]]) ).
cnf(refute_0_278,plain,
( multiply(X_17,greatest_lower_bound(greatest_lower_bound(X_91,identity),identity)) != multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_91,identity)))
| greatest_lower_bound(X_17,multiply(X_17,greatest_lower_bound(X_91,identity))) != multiply(X_17,greatest_lower_bound(greatest_lower_bound(X_91,identity),identity))
| greatest_lower_bound(X_17,multiply(X_17,greatest_lower_bound(X_91,identity))) = multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_91,identity))) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(greatest_lower_bound(X_17,multiply(X_17,greatest_lower_bound(X_91,identity))))),bind(Y0,$fot(multiply(X_17,greatest_lower_bound(greatest_lower_bound(X_91,identity),identity)))),bind(Z0,$fot(multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_91,identity)))))]]) ).
cnf(refute_0_279,plain,
( multiply(X_17,greatest_lower_bound(greatest_lower_bound(X_91,identity),identity)) != multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_91,identity)))
| greatest_lower_bound(X_17,multiply(X_17,greatest_lower_bound(X_91,identity))) = multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_91,identity))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,multiply(X_17,greatest_lower_bound(X_91,identity))),multiply(X_17,greatest_lower_bound(greatest_lower_bound(X_91,identity),identity))) )],[refute_0_277,refute_0_278]) ).
cnf(refute_0_280,plain,
greatest_lower_bound(X_17,multiply(X_17,greatest_lower_bound(X_91,identity))) = multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_91,identity))),
inference(resolve,[$cnf( $equal(multiply(X_17,greatest_lower_bound(greatest_lower_bound(X_91,identity),identity)),multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_91,identity)))) )],[refute_0_274,refute_0_279]) ).
cnf(refute_0_281,plain,
greatest_lower_bound(X,greatest_lower_bound(X_26,X_27)) = greatest_lower_bound(greatest_lower_bound(X_26,X_27),X),
inference(subst,[],[symmetry_of_glb:[bind(Y,$fot(greatest_lower_bound(X_26,X_27)))]]) ).
cnf(refute_0_282,plain,
greatest_lower_bound(X_26,greatest_lower_bound(X_27,X)) = greatest_lower_bound(greatest_lower_bound(X_26,X_27),X),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_26)),bind(Y,$fot(X_27)),bind(Z,$fot(X))]]) ).
cnf(refute_0_283,plain,
( greatest_lower_bound(X_26,greatest_lower_bound(X_27,X)) != greatest_lower_bound(greatest_lower_bound(X_26,X_27),X)
| greatest_lower_bound(greatest_lower_bound(X_26,X_27),X) = greatest_lower_bound(X_26,greatest_lower_bound(X_27,X)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X_26,greatest_lower_bound(X_27,X)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X_26,X_27),X)))]]) ).
cnf(refute_0_284,plain,
greatest_lower_bound(greatest_lower_bound(X_26,X_27),X) = greatest_lower_bound(X_26,greatest_lower_bound(X_27,X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_26,greatest_lower_bound(X_27,X)),greatest_lower_bound(greatest_lower_bound(X_26,X_27),X)) )],[refute_0_282,refute_0_283]) ).
cnf(refute_0_285,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_26,X_27)) != greatest_lower_bound(greatest_lower_bound(X_26,X_27),X)
| greatest_lower_bound(greatest_lower_bound(X_26,X_27),X) != greatest_lower_bound(X_26,greatest_lower_bound(X_27,X))
| greatest_lower_bound(X,greatest_lower_bound(X_26,X_27)) = greatest_lower_bound(X_26,greatest_lower_bound(X_27,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X,greatest_lower_bound(X_26,X_27)),greatest_lower_bound(X_26,greatest_lower_bound(X_27,X))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_26,X_27),X))]]) ).
cnf(refute_0_286,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_26,X_27)) != greatest_lower_bound(greatest_lower_bound(X_26,X_27),X)
| greatest_lower_bound(X,greatest_lower_bound(X_26,X_27)) = greatest_lower_bound(X_26,greatest_lower_bound(X_27,X)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_26,X_27),X),greatest_lower_bound(X_26,greatest_lower_bound(X_27,X))) )],[refute_0_284,refute_0_285]) ).
cnf(refute_0_287,plain,
greatest_lower_bound(X,greatest_lower_bound(X_26,X_27)) = greatest_lower_bound(X_26,greatest_lower_bound(X_27,X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_26,X_27)),greatest_lower_bound(greatest_lower_bound(X_26,X_27),X)) )],[refute_0_281,refute_0_286]) ).
cnf(refute_0_288,plain,
greatest_lower_bound(multiply(X_27,X_91),greatest_lower_bound(X_26,X_27)) = greatest_lower_bound(X_26,greatest_lower_bound(X_27,multiply(X_27,X_91))),
inference(subst,[],[refute_0_287:[bind(X,$fot(multiply(X_27,X_91)))]]) ).
cnf(refute_0_289,plain,
multiply(X_27,greatest_lower_bound(X_91,identity)) = greatest_lower_bound(X_27,multiply(X_27,X_91)),
inference(subst,[],[refute_0_220:[bind(X_36,$fot(X_27)),bind(X_37,$fot(X_91))]]) ).
cnf(refute_0_290,plain,
( multiply(X_27,greatest_lower_bound(X_91,identity)) != greatest_lower_bound(X_27,multiply(X_27,X_91))
| greatest_lower_bound(X_27,multiply(X_27,X_91)) = multiply(X_27,greatest_lower_bound(X_91,identity)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X_27,greatest_lower_bound(X_91,identity)))),bind(Y0,$fot(greatest_lower_bound(X_27,multiply(X_27,X_91))))]]) ).
cnf(refute_0_291,plain,
greatest_lower_bound(X_27,multiply(X_27,X_91)) = multiply(X_27,greatest_lower_bound(X_91,identity)),
inference(resolve,[$cnf( $equal(multiply(X_27,greatest_lower_bound(X_91,identity)),greatest_lower_bound(X_27,multiply(X_27,X_91))) )],[refute_0_289,refute_0_290]) ).
cnf(refute_0_292,plain,
( greatest_lower_bound(X_27,multiply(X_27,X_91)) != multiply(X_27,greatest_lower_bound(X_91,identity))
| greatest_lower_bound(multiply(X_27,X_91),greatest_lower_bound(X_26,X_27)) != greatest_lower_bound(X_26,greatest_lower_bound(X_27,multiply(X_27,X_91)))
| greatest_lower_bound(multiply(X_27,X_91),greatest_lower_bound(X_26,X_27)) = greatest_lower_bound(X_26,multiply(X_27,greatest_lower_bound(X_91,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_27,X_91),greatest_lower_bound(X_26,X_27)),greatest_lower_bound(X_26,greatest_lower_bound(X_27,multiply(X_27,X_91)))) ),[1,1],$fot(multiply(X_27,greatest_lower_bound(X_91,identity)))]]) ).
cnf(refute_0_293,plain,
( greatest_lower_bound(multiply(X_27,X_91),greatest_lower_bound(X_26,X_27)) != greatest_lower_bound(X_26,greatest_lower_bound(X_27,multiply(X_27,X_91)))
| greatest_lower_bound(multiply(X_27,X_91),greatest_lower_bound(X_26,X_27)) = greatest_lower_bound(X_26,multiply(X_27,greatest_lower_bound(X_91,identity))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_27,multiply(X_27,X_91)),multiply(X_27,greatest_lower_bound(X_91,identity))) )],[refute_0_291,refute_0_292]) ).
cnf(refute_0_294,plain,
greatest_lower_bound(multiply(X_27,X_91),greatest_lower_bound(X_26,X_27)) = greatest_lower_bound(X_26,multiply(X_27,greatest_lower_bound(X_91,identity))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_27,X_91),greatest_lower_bound(X_26,X_27)),greatest_lower_bound(X_26,greatest_lower_bound(X_27,multiply(X_27,X_91)))) )],[refute_0_288,refute_0_293]) ).
cnf(refute_0_295,plain,
greatest_lower_bound(X_81,greatest_lower_bound(X_82,greatest_lower_bound(Y,X_82))) = greatest_lower_bound(X_82,greatest_lower_bound(greatest_lower_bound(Y,X_82),X_81)),
inference(subst,[],[refute_0_287:[bind(X,$fot(X_81)),bind(X_26,$fot(X_82)),bind(X_27,$fot(greatest_lower_bound(Y,X_82)))]]) ).
cnf(refute_0_296,plain,
greatest_lower_bound(X_82,greatest_lower_bound(Y,X_82)) = greatest_lower_bound(X_82,Y),
inference(subst,[],[refute_0_182:[bind(X_15,$fot(X_82))]]) ).
cnf(refute_0_297,plain,
( greatest_lower_bound(X_81,greatest_lower_bound(X_82,greatest_lower_bound(Y,X_82))) != greatest_lower_bound(X_82,greatest_lower_bound(greatest_lower_bound(Y,X_82),X_81))
| greatest_lower_bound(X_82,greatest_lower_bound(Y,X_82)) != greatest_lower_bound(X_82,Y)
| greatest_lower_bound(X_81,greatest_lower_bound(X_82,Y)) = greatest_lower_bound(X_82,greatest_lower_bound(greatest_lower_bound(Y,X_82),X_81)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_81,greatest_lower_bound(X_82,greatest_lower_bound(Y,X_82))),greatest_lower_bound(X_82,greatest_lower_bound(greatest_lower_bound(Y,X_82),X_81))) ),[0,1],$fot(greatest_lower_bound(X_82,Y))]]) ).
cnf(refute_0_298,plain,
( greatest_lower_bound(X_81,greatest_lower_bound(X_82,greatest_lower_bound(Y,X_82))) != greatest_lower_bound(X_82,greatest_lower_bound(greatest_lower_bound(Y,X_82),X_81))
| greatest_lower_bound(X_81,greatest_lower_bound(X_82,Y)) = greatest_lower_bound(X_82,greatest_lower_bound(greatest_lower_bound(Y,X_82),X_81)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_82,greatest_lower_bound(Y,X_82)),greatest_lower_bound(X_82,Y)) )],[refute_0_296,refute_0_297]) ).
cnf(refute_0_299,plain,
greatest_lower_bound(X_81,greatest_lower_bound(X_82,Y)) = greatest_lower_bound(X_82,greatest_lower_bound(greatest_lower_bound(Y,X_82),X_81)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_81,greatest_lower_bound(X_82,greatest_lower_bound(Y,X_82))),greatest_lower_bound(X_82,greatest_lower_bound(greatest_lower_bound(Y,X_82),X_81))) )],[refute_0_295,refute_0_298]) ).
cnf(refute_0_300,plain,
greatest_lower_bound(X_26,greatest_lower_bound(X_27,greatest_lower_bound(Y,X_27))) = greatest_lower_bound(greatest_lower_bound(X_26,X_27),greatest_lower_bound(Y,X_27)),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_26)),bind(Y,$fot(X_27)),bind(Z,$fot(greatest_lower_bound(Y,X_27)))]]) ).
cnf(refute_0_301,plain,
greatest_lower_bound(X_27,greatest_lower_bound(Y,X_27)) = greatest_lower_bound(X_27,Y),
inference(subst,[],[refute_0_182:[bind(X_15,$fot(X_27))]]) ).
cnf(refute_0_302,plain,
( greatest_lower_bound(X_26,greatest_lower_bound(X_27,greatest_lower_bound(Y,X_27))) != greatest_lower_bound(greatest_lower_bound(X_26,X_27),greatest_lower_bound(Y,X_27))
| greatest_lower_bound(X_27,greatest_lower_bound(Y,X_27)) != greatest_lower_bound(X_27,Y)
| greatest_lower_bound(X_26,greatest_lower_bound(X_27,Y)) = greatest_lower_bound(greatest_lower_bound(X_26,X_27),greatest_lower_bound(Y,X_27)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_26,greatest_lower_bound(X_27,greatest_lower_bound(Y,X_27))),greatest_lower_bound(greatest_lower_bound(X_26,X_27),greatest_lower_bound(Y,X_27))) ),[0,1],$fot(greatest_lower_bound(X_27,Y))]]) ).
cnf(refute_0_303,plain,
( greatest_lower_bound(X_26,greatest_lower_bound(X_27,greatest_lower_bound(Y,X_27))) != greatest_lower_bound(greatest_lower_bound(X_26,X_27),greatest_lower_bound(Y,X_27))
| greatest_lower_bound(X_26,greatest_lower_bound(X_27,Y)) = greatest_lower_bound(greatest_lower_bound(X_26,X_27),greatest_lower_bound(Y,X_27)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_27,greatest_lower_bound(Y,X_27)),greatest_lower_bound(X_27,Y)) )],[refute_0_301,refute_0_302]) ).
cnf(refute_0_304,plain,
greatest_lower_bound(X_26,greatest_lower_bound(X_27,Y)) = greatest_lower_bound(greatest_lower_bound(X_26,X_27),greatest_lower_bound(Y,X_27)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_26,greatest_lower_bound(X_27,greatest_lower_bound(Y,X_27))),greatest_lower_bound(greatest_lower_bound(X_26,X_27),greatest_lower_bound(Y,X_27))) )],[refute_0_300,refute_0_303]) ).
cnf(refute_0_305,plain,
greatest_lower_bound(greatest_lower_bound(X_26,X_27),Y) = greatest_lower_bound(X_26,greatest_lower_bound(X_27,Y)),
inference(subst,[],[refute_0_178:[bind(X,$fot(X_26)),bind(Y,$fot(X_27)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_306,plain,
greatest_lower_bound(X_27,greatest_lower_bound(greatest_lower_bound(X_26,X_27),Y)) = greatest_lower_bound(X_27,greatest_lower_bound(greatest_lower_bound(X_26,X_27),Y)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X_27,greatest_lower_bound(greatest_lower_bound(X_26,X_27),Y)))]]) ).
cnf(refute_0_307,plain,
( greatest_lower_bound(X_27,greatest_lower_bound(greatest_lower_bound(X_26,X_27),Y)) != greatest_lower_bound(X_27,greatest_lower_bound(greatest_lower_bound(X_26,X_27),Y))
| greatest_lower_bound(greatest_lower_bound(X_26,X_27),Y) != greatest_lower_bound(X_26,greatest_lower_bound(X_27,Y))
| greatest_lower_bound(X_27,greatest_lower_bound(greatest_lower_bound(X_26,X_27),Y)) = greatest_lower_bound(X_27,greatest_lower_bound(X_26,greatest_lower_bound(X_27,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_27,greatest_lower_bound(greatest_lower_bound(X_26,X_27),Y)),greatest_lower_bound(X_27,greatest_lower_bound(greatest_lower_bound(X_26,X_27),Y))) ),[1,1],$fot(greatest_lower_bound(X_26,greatest_lower_bound(X_27,Y)))]]) ).
cnf(refute_0_308,plain,
( greatest_lower_bound(greatest_lower_bound(X_26,X_27),Y) != greatest_lower_bound(X_26,greatest_lower_bound(X_27,Y))
| greatest_lower_bound(X_27,greatest_lower_bound(greatest_lower_bound(X_26,X_27),Y)) = greatest_lower_bound(X_27,greatest_lower_bound(X_26,greatest_lower_bound(X_27,Y))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_27,greatest_lower_bound(greatest_lower_bound(X_26,X_27),Y)),greatest_lower_bound(X_27,greatest_lower_bound(greatest_lower_bound(X_26,X_27),Y))) )],[refute_0_306,refute_0_307]) ).
cnf(refute_0_309,plain,
greatest_lower_bound(X_27,greatest_lower_bound(greatest_lower_bound(X_26,X_27),Y)) = greatest_lower_bound(X_27,greatest_lower_bound(X_26,greatest_lower_bound(X_27,Y))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_26,X_27),Y),greatest_lower_bound(X_26,greatest_lower_bound(X_27,Y))) )],[refute_0_305,refute_0_308]) ).
cnf(refute_0_310,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_26,X_27)) != greatest_lower_bound(X_26,greatest_lower_bound(X_27,X))
| greatest_lower_bound(X_26,greatest_lower_bound(X_27,X)) = greatest_lower_bound(X,greatest_lower_bound(X_26,X_27)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(X_26,X_27)))),bind(Y0,$fot(greatest_lower_bound(X_26,greatest_lower_bound(X_27,X))))]]) ).
cnf(refute_0_311,plain,
greatest_lower_bound(X_26,greatest_lower_bound(X_27,X)) = greatest_lower_bound(X,greatest_lower_bound(X_26,X_27)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_26,X_27)),greatest_lower_bound(X_26,greatest_lower_bound(X_27,X))) )],[refute_0_287,refute_0_310]) ).
cnf(refute_0_312,plain,
greatest_lower_bound(greatest_lower_bound(X_26,X_27),greatest_lower_bound(Y,X_27)) = greatest_lower_bound(X_27,greatest_lower_bound(greatest_lower_bound(X_26,X_27),Y)),
inference(subst,[],[refute_0_311:[bind(X,$fot(X_27)),bind(X_26,$fot(greatest_lower_bound(X_26,X_27))),bind(X_27,$fot(Y))]]) ).
cnf(refute_0_313,plain,
( greatest_lower_bound(X_27,greatest_lower_bound(greatest_lower_bound(X_26,X_27),Y)) != greatest_lower_bound(X_27,greatest_lower_bound(X_26,greatest_lower_bound(X_27,Y)))
| greatest_lower_bound(greatest_lower_bound(X_26,X_27),greatest_lower_bound(Y,X_27)) != greatest_lower_bound(X_27,greatest_lower_bound(greatest_lower_bound(X_26,X_27),Y))
| greatest_lower_bound(greatest_lower_bound(X_26,X_27),greatest_lower_bound(Y,X_27)) = greatest_lower_bound(X_27,greatest_lower_bound(X_26,greatest_lower_bound(X_27,Y))) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(X_26,X_27),greatest_lower_bound(Y,X_27)))),bind(Y0,$fot(greatest_lower_bound(X_27,greatest_lower_bound(greatest_lower_bound(X_26,X_27),Y)))),bind(Z0,$fot(greatest_lower_bound(X_27,greatest_lower_bound(X_26,greatest_lower_bound(X_27,Y)))))]]) ).
cnf(refute_0_314,plain,
( greatest_lower_bound(X_27,greatest_lower_bound(greatest_lower_bound(X_26,X_27),Y)) != greatest_lower_bound(X_27,greatest_lower_bound(X_26,greatest_lower_bound(X_27,Y)))
| greatest_lower_bound(greatest_lower_bound(X_26,X_27),greatest_lower_bound(Y,X_27)) = greatest_lower_bound(X_27,greatest_lower_bound(X_26,greatest_lower_bound(X_27,Y))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_26,X_27),greatest_lower_bound(Y,X_27)),greatest_lower_bound(X_27,greatest_lower_bound(greatest_lower_bound(X_26,X_27),Y))) )],[refute_0_312,refute_0_313]) ).
cnf(refute_0_315,plain,
greatest_lower_bound(greatest_lower_bound(X_26,X_27),greatest_lower_bound(Y,X_27)) = greatest_lower_bound(X_27,greatest_lower_bound(X_26,greatest_lower_bound(X_27,Y))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_27,greatest_lower_bound(greatest_lower_bound(X_26,X_27),Y)),greatest_lower_bound(X_27,greatest_lower_bound(X_26,greatest_lower_bound(X_27,Y)))) )],[refute_0_309,refute_0_314]) ).
cnf(refute_0_316,plain,
( greatest_lower_bound(X_26,greatest_lower_bound(X_27,Y)) != greatest_lower_bound(greatest_lower_bound(X_26,X_27),greatest_lower_bound(Y,X_27))
| greatest_lower_bound(greatest_lower_bound(X_26,X_27),greatest_lower_bound(Y,X_27)) != greatest_lower_bound(X_27,greatest_lower_bound(X_26,greatest_lower_bound(X_27,Y)))
| greatest_lower_bound(X_26,greatest_lower_bound(X_27,Y)) = greatest_lower_bound(X_27,greatest_lower_bound(X_26,greatest_lower_bound(X_27,Y))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_26,greatest_lower_bound(X_27,Y)),greatest_lower_bound(X_27,greatest_lower_bound(X_26,greatest_lower_bound(X_27,Y)))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_26,X_27),greatest_lower_bound(Y,X_27)))]]) ).
cnf(refute_0_317,plain,
( greatest_lower_bound(X_26,greatest_lower_bound(X_27,Y)) != greatest_lower_bound(greatest_lower_bound(X_26,X_27),greatest_lower_bound(Y,X_27))
| greatest_lower_bound(X_26,greatest_lower_bound(X_27,Y)) = greatest_lower_bound(X_27,greatest_lower_bound(X_26,greatest_lower_bound(X_27,Y))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_26,X_27),greatest_lower_bound(Y,X_27)),greatest_lower_bound(X_27,greatest_lower_bound(X_26,greatest_lower_bound(X_27,Y)))) )],[refute_0_315,refute_0_316]) ).
cnf(refute_0_318,plain,
greatest_lower_bound(X_26,greatest_lower_bound(X_27,Y)) = greatest_lower_bound(X_27,greatest_lower_bound(X_26,greatest_lower_bound(X_27,Y))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_26,greatest_lower_bound(X_27,Y)),greatest_lower_bound(greatest_lower_bound(X_26,X_27),greatest_lower_bound(Y,X_27))) )],[refute_0_304,refute_0_317]) ).
cnf(refute_0_319,plain,
( greatest_lower_bound(X_26,greatest_lower_bound(X_27,Y)) != greatest_lower_bound(X_27,greatest_lower_bound(X_26,greatest_lower_bound(X_27,Y)))
| greatest_lower_bound(X_27,greatest_lower_bound(X_26,greatest_lower_bound(X_27,Y))) = greatest_lower_bound(X_26,greatest_lower_bound(X_27,Y)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X_26,greatest_lower_bound(X_27,Y)))),bind(Y0,$fot(greatest_lower_bound(X_27,greatest_lower_bound(X_26,greatest_lower_bound(X_27,Y)))))]]) ).
cnf(refute_0_320,plain,
greatest_lower_bound(X_27,greatest_lower_bound(X_26,greatest_lower_bound(X_27,Y))) = greatest_lower_bound(X_26,greatest_lower_bound(X_27,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_26,greatest_lower_bound(X_27,Y)),greatest_lower_bound(X_27,greatest_lower_bound(X_26,greatest_lower_bound(X_27,Y)))) )],[refute_0_318,refute_0_319]) ).
cnf(refute_0_321,plain,
greatest_lower_bound(X_82,greatest_lower_bound(Y,greatest_lower_bound(X_82,X_81))) = greatest_lower_bound(Y,greatest_lower_bound(X_82,X_81)),
inference(subst,[],[refute_0_320:[bind(Y,$fot(X_81)),bind(X_26,$fot(Y)),bind(X_27,$fot(X_82))]]) ).
cnf(refute_0_322,plain,
greatest_lower_bound(greatest_lower_bound(Y,X_82),X_81) = greatest_lower_bound(Y,greatest_lower_bound(X_82,X_81)),
inference(subst,[],[refute_0_178:[bind(X,$fot(Y)),bind(Y,$fot(X_82)),bind(Z,$fot(X_81))]]) ).
cnf(refute_0_323,plain,
greatest_lower_bound(X_82,greatest_lower_bound(greatest_lower_bound(Y,X_82),X_81)) = greatest_lower_bound(X_82,greatest_lower_bound(greatest_lower_bound(Y,X_82),X_81)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X_82,greatest_lower_bound(greatest_lower_bound(Y,X_82),X_81)))]]) ).
cnf(refute_0_324,plain,
( greatest_lower_bound(X_82,greatest_lower_bound(greatest_lower_bound(Y,X_82),X_81)) != greatest_lower_bound(X_82,greatest_lower_bound(greatest_lower_bound(Y,X_82),X_81))
| greatest_lower_bound(greatest_lower_bound(Y,X_82),X_81) != greatest_lower_bound(Y,greatest_lower_bound(X_82,X_81))
| greatest_lower_bound(X_82,greatest_lower_bound(greatest_lower_bound(Y,X_82),X_81)) = greatest_lower_bound(X_82,greatest_lower_bound(Y,greatest_lower_bound(X_82,X_81))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_82,greatest_lower_bound(greatest_lower_bound(Y,X_82),X_81)),greatest_lower_bound(X_82,greatest_lower_bound(greatest_lower_bound(Y,X_82),X_81))) ),[1,1],$fot(greatest_lower_bound(Y,greatest_lower_bound(X_82,X_81)))]]) ).
cnf(refute_0_325,plain,
( greatest_lower_bound(greatest_lower_bound(Y,X_82),X_81) != greatest_lower_bound(Y,greatest_lower_bound(X_82,X_81))
| greatest_lower_bound(X_82,greatest_lower_bound(greatest_lower_bound(Y,X_82),X_81)) = greatest_lower_bound(X_82,greatest_lower_bound(Y,greatest_lower_bound(X_82,X_81))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_82,greatest_lower_bound(greatest_lower_bound(Y,X_82),X_81)),greatest_lower_bound(X_82,greatest_lower_bound(greatest_lower_bound(Y,X_82),X_81))) )],[refute_0_323,refute_0_324]) ).
cnf(refute_0_326,plain,
greatest_lower_bound(X_82,greatest_lower_bound(greatest_lower_bound(Y,X_82),X_81)) = greatest_lower_bound(X_82,greatest_lower_bound(Y,greatest_lower_bound(X_82,X_81))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(Y,X_82),X_81),greatest_lower_bound(Y,greatest_lower_bound(X_82,X_81))) )],[refute_0_322,refute_0_325]) ).
cnf(refute_0_327,plain,
( greatest_lower_bound(X_82,greatest_lower_bound(Y,greatest_lower_bound(X_82,X_81))) != greatest_lower_bound(Y,greatest_lower_bound(X_82,X_81))
| greatest_lower_bound(X_82,greatest_lower_bound(greatest_lower_bound(Y,X_82),X_81)) != greatest_lower_bound(X_82,greatest_lower_bound(Y,greatest_lower_bound(X_82,X_81)))
| greatest_lower_bound(X_82,greatest_lower_bound(greatest_lower_bound(Y,X_82),X_81)) = greatest_lower_bound(Y,greatest_lower_bound(X_82,X_81)) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(greatest_lower_bound(X_82,greatest_lower_bound(greatest_lower_bound(Y,X_82),X_81)))),bind(Y0,$fot(greatest_lower_bound(X_82,greatest_lower_bound(Y,greatest_lower_bound(X_82,X_81))))),bind(Z0,$fot(greatest_lower_bound(Y,greatest_lower_bound(X_82,X_81))))]]) ).
cnf(refute_0_328,plain,
( greatest_lower_bound(X_82,greatest_lower_bound(Y,greatest_lower_bound(X_82,X_81))) != greatest_lower_bound(Y,greatest_lower_bound(X_82,X_81))
| greatest_lower_bound(X_82,greatest_lower_bound(greatest_lower_bound(Y,X_82),X_81)) = greatest_lower_bound(Y,greatest_lower_bound(X_82,X_81)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_82,greatest_lower_bound(greatest_lower_bound(Y,X_82),X_81)),greatest_lower_bound(X_82,greatest_lower_bound(Y,greatest_lower_bound(X_82,X_81)))) )],[refute_0_326,refute_0_327]) ).
cnf(refute_0_329,plain,
greatest_lower_bound(X_82,greatest_lower_bound(greatest_lower_bound(Y,X_82),X_81)) = greatest_lower_bound(Y,greatest_lower_bound(X_82,X_81)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_82,greatest_lower_bound(Y,greatest_lower_bound(X_82,X_81))),greatest_lower_bound(Y,greatest_lower_bound(X_82,X_81))) )],[refute_0_321,refute_0_328]) ).
cnf(refute_0_330,plain,
( greatest_lower_bound(X_81,greatest_lower_bound(X_82,Y)) != greatest_lower_bound(X_82,greatest_lower_bound(greatest_lower_bound(Y,X_82),X_81))
| greatest_lower_bound(X_82,greatest_lower_bound(greatest_lower_bound(Y,X_82),X_81)) != greatest_lower_bound(Y,greatest_lower_bound(X_82,X_81))
| greatest_lower_bound(X_81,greatest_lower_bound(X_82,Y)) = greatest_lower_bound(Y,greatest_lower_bound(X_82,X_81)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_81,greatest_lower_bound(X_82,Y)),greatest_lower_bound(Y,greatest_lower_bound(X_82,X_81))) ),[0],$fot(greatest_lower_bound(X_82,greatest_lower_bound(greatest_lower_bound(Y,X_82),X_81)))]]) ).
cnf(refute_0_331,plain,
( greatest_lower_bound(X_81,greatest_lower_bound(X_82,Y)) != greatest_lower_bound(X_82,greatest_lower_bound(greatest_lower_bound(Y,X_82),X_81))
| greatest_lower_bound(X_81,greatest_lower_bound(X_82,Y)) = greatest_lower_bound(Y,greatest_lower_bound(X_82,X_81)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_82,greatest_lower_bound(greatest_lower_bound(Y,X_82),X_81)),greatest_lower_bound(Y,greatest_lower_bound(X_82,X_81))) )],[refute_0_329,refute_0_330]) ).
cnf(refute_0_332,plain,
greatest_lower_bound(X_81,greatest_lower_bound(X_82,Y)) = greatest_lower_bound(Y,greatest_lower_bound(X_82,X_81)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_81,greatest_lower_bound(X_82,Y)),greatest_lower_bound(X_82,greatest_lower_bound(greatest_lower_bound(Y,X_82),X_81))) )],[refute_0_299,refute_0_331]) ).
cnf(refute_0_333,plain,
( greatest_lower_bound(X_81,greatest_lower_bound(X_82,Y)) != greatest_lower_bound(Y,greatest_lower_bound(X_82,X_81))
| greatest_lower_bound(Y,greatest_lower_bound(X_82,X_81)) = greatest_lower_bound(X_81,greatest_lower_bound(X_82,Y)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X_81,greatest_lower_bound(X_82,Y)))),bind(Y0,$fot(greatest_lower_bound(Y,greatest_lower_bound(X_82,X_81))))]]) ).
cnf(refute_0_334,plain,
greatest_lower_bound(Y,greatest_lower_bound(X_82,X_81)) = greatest_lower_bound(X_81,greatest_lower_bound(X_82,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_81,greatest_lower_bound(X_82,Y)),greatest_lower_bound(Y,greatest_lower_bound(X_82,X_81))) )],[refute_0_332,refute_0_333]) ).
cnf(refute_0_335,plain,
greatest_lower_bound(multiply(X_27,X_91),greatest_lower_bound(X_26,X_27)) = greatest_lower_bound(X_27,greatest_lower_bound(X_26,multiply(X_27,X_91))),
inference(subst,[],[refute_0_334:[bind(Y,$fot(multiply(X_27,X_91))),bind(X_81,$fot(X_27)),bind(X_82,$fot(X_26))]]) ).
cnf(refute_0_336,plain,
( greatest_lower_bound(multiply(X_27,X_91),greatest_lower_bound(X_26,X_27)) != greatest_lower_bound(X_26,multiply(X_27,greatest_lower_bound(X_91,identity)))
| greatest_lower_bound(multiply(X_27,X_91),greatest_lower_bound(X_26,X_27)) != greatest_lower_bound(X_27,greatest_lower_bound(X_26,multiply(X_27,X_91)))
| greatest_lower_bound(X_27,greatest_lower_bound(X_26,multiply(X_27,X_91))) = greatest_lower_bound(X_26,multiply(X_27,greatest_lower_bound(X_91,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_27,X_91),greatest_lower_bound(X_26,X_27)),greatest_lower_bound(X_26,multiply(X_27,greatest_lower_bound(X_91,identity)))) ),[0],$fot(greatest_lower_bound(X_27,greatest_lower_bound(X_26,multiply(X_27,X_91))))]]) ).
cnf(refute_0_337,plain,
( greatest_lower_bound(multiply(X_27,X_91),greatest_lower_bound(X_26,X_27)) != greatest_lower_bound(X_26,multiply(X_27,greatest_lower_bound(X_91,identity)))
| greatest_lower_bound(X_27,greatest_lower_bound(X_26,multiply(X_27,X_91))) = greatest_lower_bound(X_26,multiply(X_27,greatest_lower_bound(X_91,identity))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_27,X_91),greatest_lower_bound(X_26,X_27)),greatest_lower_bound(X_27,greatest_lower_bound(X_26,multiply(X_27,X_91)))) )],[refute_0_335,refute_0_336]) ).
cnf(refute_0_338,plain,
greatest_lower_bound(X_27,greatest_lower_bound(X_26,multiply(X_27,X_91))) = greatest_lower_bound(X_26,multiply(X_27,greatest_lower_bound(X_91,identity))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_27,X_91),greatest_lower_bound(X_26,X_27)),greatest_lower_bound(X_26,multiply(X_27,greatest_lower_bound(X_91,identity)))) )],[refute_0_294,refute_0_337]) ).
cnf(refute_0_339,plain,
greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_17,X_91))) = greatest_lower_bound(X_17,multiply(X_17,greatest_lower_bound(X_91,identity))),
inference(subst,[],[refute_0_338:[bind(X_26,$fot(X_17)),bind(X_27,$fot(X_17))]]) ).
cnf(refute_0_340,plain,
( greatest_lower_bound(X_17,multiply(X_17,greatest_lower_bound(X_91,identity))) != multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_91,identity)))
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_17,X_91))) != greatest_lower_bound(X_17,multiply(X_17,greatest_lower_bound(X_91,identity)))
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_17,X_91))) = multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_91,identity))) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_17,X_91))))),bind(Y0,$fot(greatest_lower_bound(X_17,multiply(X_17,greatest_lower_bound(X_91,identity))))),bind(Z0,$fot(multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_91,identity)))))]]) ).
cnf(refute_0_341,plain,
( greatest_lower_bound(X_17,multiply(X_17,greatest_lower_bound(X_91,identity))) != multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_91,identity)))
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_17,X_91))) = multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_91,identity))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_17,X_91))),greatest_lower_bound(X_17,multiply(X_17,greatest_lower_bound(X_91,identity)))) )],[refute_0_339,refute_0_340]) ).
cnf(refute_0_342,plain,
greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_17,X_91))) = multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_91,identity))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,multiply(X_17,greatest_lower_bound(X_91,identity))),multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_91,identity)))) )],[refute_0_280,refute_0_341]) ).
cnf(refute_0_343,plain,
( multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_91,identity))) != multiply(X_17,greatest_lower_bound(identity,X_91))
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_17,X_91))) != multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_91,identity)))
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_17,X_91))) = multiply(X_17,greatest_lower_bound(identity,X_91)) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_17,X_91))))),bind(Y0,$fot(multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_91,identity))))),bind(Z0,$fot(multiply(X_17,greatest_lower_bound(identity,X_91))))]]) ).
cnf(refute_0_344,plain,
( multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_91,identity))) != multiply(X_17,greatest_lower_bound(identity,X_91))
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_17,X_91))) = multiply(X_17,greatest_lower_bound(identity,X_91)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_17,X_91))),multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_91,identity)))) )],[refute_0_342,refute_0_343]) ).
cnf(refute_0_345,plain,
greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_17,X_91))) = multiply(X_17,greatest_lower_bound(identity,X_91)),
inference(resolve,[$cnf( $equal(multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_91,identity))),multiply(X_17,greatest_lower_bound(identity,X_91))) )],[refute_0_231,refute_0_344]) ).
cnf(refute_0_346,plain,
( greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_17,X_91))) != multiply(X_17,greatest_lower_bound(X_91,identity))
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_17,X_91))) != multiply(X_17,greatest_lower_bound(identity,X_91))
| multiply(X_17,greatest_lower_bound(identity,X_91)) = multiply(X_17,greatest_lower_bound(X_91,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_17,X_91))),multiply(X_17,greatest_lower_bound(X_91,identity))) ),[0],$fot(multiply(X_17,greatest_lower_bound(identity,X_91)))]]) ).
cnf(refute_0_347,plain,
( greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_17,X_91))) != multiply(X_17,greatest_lower_bound(X_91,identity))
| multiply(X_17,greatest_lower_bound(identity,X_91)) = multiply(X_17,greatest_lower_bound(X_91,identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_17,X_91))),multiply(X_17,greatest_lower_bound(identity,X_91))) )],[refute_0_345,refute_0_346]) ).
cnf(refute_0_348,plain,
multiply(X_17,greatest_lower_bound(identity,X_91)) = multiply(X_17,greatest_lower_bound(X_91,identity)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_17,X_91))),multiply(X_17,greatest_lower_bound(X_91,identity))) )],[refute_0_226,refute_0_347]) ).
cnf(refute_0_349,plain,
( multiply(X_17,greatest_lower_bound(identity,X_91)) != multiply(X_17,greatest_lower_bound(X_91,identity))
| multiply(X_17,greatest_lower_bound(X_91,identity)) = multiply(X_17,greatest_lower_bound(identity,X_91)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X_17,greatest_lower_bound(identity,X_91)))),bind(Y0,$fot(multiply(X_17,greatest_lower_bound(X_91,identity))))]]) ).
cnf(refute_0_350,plain,
multiply(X_17,greatest_lower_bound(X_91,identity)) = multiply(X_17,greatest_lower_bound(identity,X_91)),
inference(resolve,[$cnf( $equal(multiply(X_17,greatest_lower_bound(identity,X_91)),multiply(X_17,greatest_lower_bound(X_91,identity))) )],[refute_0_348,refute_0_349]) ).
cnf(refute_0_351,plain,
multiply(identity,greatest_lower_bound(inverse(multiply(X_151,inverse(X_152))),identity)) = multiply(identity,greatest_lower_bound(identity,inverse(multiply(X_151,inverse(X_152))))),
inference(subst,[],[refute_0_350:[bind(X_17,$fot(identity)),bind(X_91,$fot(inverse(multiply(X_151,inverse(X_152)))))]]) ).
cnf(refute_0_352,plain,
( multiply(identity,greatest_lower_bound(identity,inverse(multiply(X_151,inverse(X_152))))) != greatest_lower_bound(identity,inverse(multiply(X_151,inverse(X_152))))
| multiply(identity,greatest_lower_bound(inverse(multiply(X_151,inverse(X_152))),identity)) != multiply(identity,greatest_lower_bound(identity,inverse(multiply(X_151,inverse(X_152)))))
| multiply(identity,greatest_lower_bound(inverse(multiply(X_151,inverse(X_152))),identity)) = greatest_lower_bound(identity,inverse(multiply(X_151,inverse(X_152)))) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(multiply(identity,greatest_lower_bound(inverse(multiply(X_151,inverse(X_152))),identity)))),bind(Y0,$fot(multiply(identity,greatest_lower_bound(identity,inverse(multiply(X_151,inverse(X_152))))))),bind(Z0,$fot(greatest_lower_bound(identity,inverse(multiply(X_151,inverse(X_152))))))]]) ).
cnf(refute_0_353,plain,
( multiply(identity,greatest_lower_bound(identity,inverse(multiply(X_151,inverse(X_152))))) != greatest_lower_bound(identity,inverse(multiply(X_151,inverse(X_152))))
| multiply(identity,greatest_lower_bound(inverse(multiply(X_151,inverse(X_152))),identity)) = greatest_lower_bound(identity,inverse(multiply(X_151,inverse(X_152)))) ),
inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(inverse(multiply(X_151,inverse(X_152))),identity)),multiply(identity,greatest_lower_bound(identity,inverse(multiply(X_151,inverse(X_152)))))) )],[refute_0_351,refute_0_352]) ).
cnf(refute_0_354,plain,
multiply(identity,greatest_lower_bound(inverse(multiply(X_151,inverse(X_152))),identity)) = greatest_lower_bound(identity,inverse(multiply(X_151,inverse(X_152)))),
inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(identity,inverse(multiply(X_151,inverse(X_152))))),greatest_lower_bound(identity,inverse(multiply(X_151,inverse(X_152))))) )],[refute_0_168,refute_0_353]) ).
cnf(refute_0_355,plain,
greatest_lower_bound(identity,multiply(identity,inverse(multiply(X_151,inverse(X_152))))) = multiply(identity,greatest_lower_bound(inverse(multiply(X_151,inverse(X_152))),identity)),
inference(subst,[],[refute_0_276:[bind(X_36,$fot(identity)),bind(X_37,$fot(inverse(multiply(X_151,inverse(X_152)))))]]) ).
cnf(refute_0_356,plain,
( multiply(identity,greatest_lower_bound(inverse(multiply(X_151,inverse(X_152))),identity)) != greatest_lower_bound(identity,inverse(multiply(X_151,inverse(X_152))))
| greatest_lower_bound(identity,multiply(identity,inverse(multiply(X_151,inverse(X_152))))) != multiply(identity,greatest_lower_bound(inverse(multiply(X_151,inverse(X_152))),identity))
| greatest_lower_bound(identity,multiply(identity,inverse(multiply(X_151,inverse(X_152))))) = greatest_lower_bound(identity,inverse(multiply(X_151,inverse(X_152)))) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(greatest_lower_bound(identity,multiply(identity,inverse(multiply(X_151,inverse(X_152))))))),bind(Y0,$fot(multiply(identity,greatest_lower_bound(inverse(multiply(X_151,inverse(X_152))),identity)))),bind(Z0,$fot(greatest_lower_bound(identity,inverse(multiply(X_151,inverse(X_152))))))]]) ).
cnf(refute_0_357,plain,
( multiply(identity,greatest_lower_bound(inverse(multiply(X_151,inverse(X_152))),identity)) != greatest_lower_bound(identity,inverse(multiply(X_151,inverse(X_152))))
| greatest_lower_bound(identity,multiply(identity,inverse(multiply(X_151,inverse(X_152))))) = greatest_lower_bound(identity,inverse(multiply(X_151,inverse(X_152)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(identity,inverse(multiply(X_151,inverse(X_152))))),multiply(identity,greatest_lower_bound(inverse(multiply(X_151,inverse(X_152))),identity))) )],[refute_0_355,refute_0_356]) ).
cnf(refute_0_358,plain,
greatest_lower_bound(identity,multiply(identity,inverse(multiply(X_151,inverse(X_152))))) = greatest_lower_bound(identity,inverse(multiply(X_151,inverse(X_152)))),
inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(inverse(multiply(X_151,inverse(X_152))),identity)),greatest_lower_bound(identity,inverse(multiply(X_151,inverse(X_152))))) )],[refute_0_354,refute_0_357]) ).
cnf(refute_0_359,plain,
( greatest_lower_bound(identity,multiply(identity,inverse(multiply(X_151,inverse(X_152))))) != greatest_lower_bound(identity,inverse(multiply(X_151,inverse(X_152))))
| greatest_lower_bound(identity,inverse(multiply(X_151,inverse(X_152)))) != greatest_lower_bound(identity,multiply(X_152,inverse(X_151)))
| greatest_lower_bound(identity,multiply(identity,inverse(multiply(X_151,inverse(X_152))))) = greatest_lower_bound(identity,multiply(X_152,inverse(X_151))) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(greatest_lower_bound(identity,multiply(identity,inverse(multiply(X_151,inverse(X_152))))))),bind(Y0,$fot(greatest_lower_bound(identity,inverse(multiply(X_151,inverse(X_152)))))),bind(Z0,$fot(greatest_lower_bound(identity,multiply(X_152,inverse(X_151)))))]]) ).
cnf(refute_0_360,plain,
( greatest_lower_bound(identity,inverse(multiply(X_151,inverse(X_152)))) != greatest_lower_bound(identity,multiply(X_152,inverse(X_151)))
| greatest_lower_bound(identity,multiply(identity,inverse(multiply(X_151,inverse(X_152))))) = greatest_lower_bound(identity,multiply(X_152,inverse(X_151))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(identity,inverse(multiply(X_151,inverse(X_152))))),greatest_lower_bound(identity,inverse(multiply(X_151,inverse(X_152))))) )],[refute_0_358,refute_0_359]) ).
cnf(refute_0_361,plain,
greatest_lower_bound(identity,multiply(identity,inverse(multiply(X_151,inverse(X_152))))) = greatest_lower_bound(identity,multiply(X_152,inverse(X_151))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(multiply(X_151,inverse(X_152)))),greatest_lower_bound(identity,multiply(X_152,inverse(X_151)))) )],[refute_0_167,refute_0_360]) ).
cnf(refute_0_362,plain,
inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(X_151,inverse(X_152)))))) = inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(X_151,inverse(X_152)))))),
introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(X_151,inverse(X_152)))))))]]) ).
cnf(refute_0_363,plain,
( greatest_lower_bound(identity,multiply(identity,inverse(multiply(X_151,inverse(X_152))))) != greatest_lower_bound(identity,multiply(X_152,inverse(X_151)))
| inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(X_151,inverse(X_152)))))) != inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(X_151,inverse(X_152))))))
| inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(X_151,inverse(X_152)))))) = inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_151)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(X_151,inverse(X_152)))))),inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(X_151,inverse(X_152))))))) ),[1,0],$fot(greatest_lower_bound(identity,multiply(X_152,inverse(X_151))))]]) ).
cnf(refute_0_364,plain,
( greatest_lower_bound(identity,multiply(identity,inverse(multiply(X_151,inverse(X_152))))) != greatest_lower_bound(identity,multiply(X_152,inverse(X_151)))
| inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(X_151,inverse(X_152)))))) = inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_151)))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(X_151,inverse(X_152)))))),inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(X_151,inverse(X_152))))))) )],[refute_0_362,refute_0_363]) ).
cnf(refute_0_365,plain,
inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(X_151,inverse(X_152)))))) = inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_151)))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(identity,inverse(multiply(X_151,inverse(X_152))))),greatest_lower_bound(identity,multiply(X_152,inverse(X_151)))) )],[refute_0_361,refute_0_364]) ).
cnf(refute_0_366,plain,
( inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(X_151,inverse(X_152)))))) != multiply(multiply(X_151,inverse(X_152)),inverse(multiply(greatest_lower_bound(X_151,X_152),inverse(X_152))))
| inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(X_151,inverse(X_152)))))) != inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_151))))
| inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_151)))) = multiply(multiply(X_151,inverse(X_152)),inverse(multiply(greatest_lower_bound(X_151,X_152),inverse(X_152)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(X_151,inverse(X_152)))))),multiply(multiply(X_151,inverse(X_152)),inverse(multiply(greatest_lower_bound(X_151,X_152),inverse(X_152))))) ),[0],$fot(inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_151)))))]]) ).
cnf(refute_0_367,plain,
( inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(X_151,inverse(X_152)))))) != multiply(multiply(X_151,inverse(X_152)),inverse(multiply(greatest_lower_bound(X_151,X_152),inverse(X_152))))
| inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_151)))) = multiply(multiply(X_151,inverse(X_152)),inverse(multiply(greatest_lower_bound(X_151,X_152),inverse(X_152)))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(X_151,inverse(X_152)))))),inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_151))))) )],[refute_0_365,refute_0_366]) ).
cnf(refute_0_368,plain,
inverse(X) = multiply(inverse(inverse(Y)),multiply(inverse(Y),inverse(X))),
inference(subst,[],[refute_0_17:[bind(X_93,$fot(inverse(Y))),bind(X_94,$fot(inverse(X)))]]) ).
cnf(refute_0_369,plain,
( inverse(multiply(X,Y)) != multiply(inverse(Y),inverse(X))
| multiply(inverse(Y),inverse(X)) = inverse(multiply(X,Y)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(multiply(X,Y)))),bind(Y0,$fot(multiply(inverse(Y),inverse(X))))]]) ).
cnf(refute_0_370,plain,
multiply(inverse(Y),inverse(X)) = inverse(multiply(X,Y)),
inference(resolve,[$cnf( $equal(inverse(multiply(X,Y)),multiply(inverse(Y),inverse(X))) )],[p18_3,refute_0_369]) ).
cnf(refute_0_371,plain,
( multiply(inverse(Y),inverse(X)) != inverse(multiply(X,Y))
| inverse(X) != multiply(inverse(inverse(Y)),multiply(inverse(Y),inverse(X)))
| inverse(X) = multiply(inverse(inverse(Y)),inverse(multiply(X,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(X),multiply(inverse(inverse(Y)),multiply(inverse(Y),inverse(X)))) ),[1,1],$fot(inverse(multiply(X,Y)))]]) ).
cnf(refute_0_372,plain,
( inverse(X) != multiply(inverse(inverse(Y)),multiply(inverse(Y),inverse(X)))
| inverse(X) = multiply(inverse(inverse(Y)),inverse(multiply(X,Y))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(Y),inverse(X)),inverse(multiply(X,Y))) )],[refute_0_370,refute_0_371]) ).
cnf(refute_0_373,plain,
inverse(X) = multiply(inverse(inverse(Y)),inverse(multiply(X,Y))),
inference(resolve,[$cnf( $equal(inverse(X),multiply(inverse(inverse(Y)),multiply(inverse(Y),inverse(X)))) )],[refute_0_368,refute_0_372]) ).
cnf(refute_0_374,plain,
inverse(multiply(multiply(X,Y),inverse(Y))) = multiply(Y,inverse(multiply(X,Y))),
inference(subst,[],[refute_0_114:[bind(X,$fot(Y)),bind(X_32,$fot(multiply(X,Y)))]]) ).
cnf(refute_0_375,plain,
multiply(inverse(inverse(Y)),inverse(multiply(X,Y))) = inverse(multiply(multiply(X,Y),inverse(Y))),
inference(subst,[],[refute_0_370:[bind(X,$fot(multiply(X,Y))),bind(Y,$fot(inverse(Y)))]]) ).
cnf(refute_0_376,plain,
( multiply(inverse(inverse(Y)),inverse(multiply(X,Y))) != inverse(multiply(multiply(X,Y),inverse(Y)))
| inverse(multiply(multiply(X,Y),inverse(Y))) != multiply(Y,inverse(multiply(X,Y)))
| multiply(inverse(inverse(Y)),inverse(multiply(X,Y))) = multiply(Y,inverse(multiply(X,Y))) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(multiply(inverse(inverse(Y)),inverse(multiply(X,Y))))),bind(Y0,$fot(inverse(multiply(multiply(X,Y),inverse(Y))))),bind(Z0,$fot(multiply(Y,inverse(multiply(X,Y)))))]]) ).
cnf(refute_0_377,plain,
( inverse(multiply(multiply(X,Y),inverse(Y))) != multiply(Y,inverse(multiply(X,Y)))
| multiply(inverse(inverse(Y)),inverse(multiply(X,Y))) = multiply(Y,inverse(multiply(X,Y))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(Y)),inverse(multiply(X,Y))),inverse(multiply(multiply(X,Y),inverse(Y)))) )],[refute_0_375,refute_0_376]) ).
cnf(refute_0_378,plain,
multiply(inverse(inverse(Y)),inverse(multiply(X,Y))) = multiply(Y,inverse(multiply(X,Y))),
inference(resolve,[$cnf( $equal(inverse(multiply(multiply(X,Y),inverse(Y))),multiply(Y,inverse(multiply(X,Y)))) )],[refute_0_374,refute_0_377]) ).
cnf(refute_0_379,plain,
( multiply(inverse(inverse(Y)),inverse(multiply(X,Y))) != multiply(Y,inverse(multiply(X,Y)))
| inverse(X) != multiply(inverse(inverse(Y)),inverse(multiply(X,Y)))
| inverse(X) = multiply(Y,inverse(multiply(X,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(X),multiply(inverse(inverse(Y)),inverse(multiply(X,Y)))) ),[1],$fot(multiply(Y,inverse(multiply(X,Y))))]]) ).
cnf(refute_0_380,plain,
( inverse(X) != multiply(inverse(inverse(Y)),inverse(multiply(X,Y)))
| inverse(X) = multiply(Y,inverse(multiply(X,Y))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(Y)),inverse(multiply(X,Y))),multiply(Y,inverse(multiply(X,Y)))) )],[refute_0_378,refute_0_379]) ).
cnf(refute_0_381,plain,
inverse(X) = multiply(Y,inverse(multiply(X,Y))),
inference(resolve,[$cnf( $equal(inverse(X),multiply(inverse(inverse(Y)),inverse(multiply(X,Y)))) )],[refute_0_373,refute_0_380]) ).
cnf(refute_0_382,plain,
( inverse(X) != multiply(Y,inverse(multiply(X,Y)))
| multiply(Y,inverse(multiply(X,Y))) = inverse(X) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(X))),bind(Y0,$fot(multiply(Y,inverse(multiply(X,Y)))))]]) ).
cnf(refute_0_383,plain,
multiply(Y,inverse(multiply(X,Y))) = inverse(X),
inference(resolve,[$cnf( $equal(inverse(X),multiply(Y,inverse(multiply(X,Y)))) )],[refute_0_381,refute_0_382]) ).
cnf(refute_0_384,plain,
multiply(inverse(X_152),inverse(multiply(greatest_lower_bound(X_151,X_152),inverse(X_152)))) = inverse(greatest_lower_bound(X_151,X_152)),
inference(subst,[],[refute_0_383:[bind(X,$fot(greatest_lower_bound(X_151,X_152))),bind(Y,$fot(inverse(X_152)))]]) ).
cnf(refute_0_385,plain,
multiply(X_151,multiply(inverse(X_152),inverse(multiply(greatest_lower_bound(X_151,X_152),inverse(X_152))))) = multiply(X_151,multiply(inverse(X_152),inverse(multiply(greatest_lower_bound(X_151,X_152),inverse(X_152))))),
introduced(tautology,[refl,[$fot(multiply(X_151,multiply(inverse(X_152),inverse(multiply(greatest_lower_bound(X_151,X_152),inverse(X_152))))))]]) ).
cnf(refute_0_386,plain,
( multiply(X_151,multiply(inverse(X_152),inverse(multiply(greatest_lower_bound(X_151,X_152),inverse(X_152))))) != multiply(X_151,multiply(inverse(X_152),inverse(multiply(greatest_lower_bound(X_151,X_152),inverse(X_152)))))
| multiply(inverse(X_152),inverse(multiply(greatest_lower_bound(X_151,X_152),inverse(X_152)))) != inverse(greatest_lower_bound(X_151,X_152))
| multiply(X_151,multiply(inverse(X_152),inverse(multiply(greatest_lower_bound(X_151,X_152),inverse(X_152))))) = multiply(X_151,inverse(greatest_lower_bound(X_151,X_152))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_151,multiply(inverse(X_152),inverse(multiply(greatest_lower_bound(X_151,X_152),inverse(X_152))))),multiply(X_151,multiply(inverse(X_152),inverse(multiply(greatest_lower_bound(X_151,X_152),inverse(X_152)))))) ),[1,1],$fot(inverse(greatest_lower_bound(X_151,X_152)))]]) ).
cnf(refute_0_387,plain,
( multiply(inverse(X_152),inverse(multiply(greatest_lower_bound(X_151,X_152),inverse(X_152)))) != inverse(greatest_lower_bound(X_151,X_152))
| multiply(X_151,multiply(inverse(X_152),inverse(multiply(greatest_lower_bound(X_151,X_152),inverse(X_152))))) = multiply(X_151,inverse(greatest_lower_bound(X_151,X_152))) ),
inference(resolve,[$cnf( $equal(multiply(X_151,multiply(inverse(X_152),inverse(multiply(greatest_lower_bound(X_151,X_152),inverse(X_152))))),multiply(X_151,multiply(inverse(X_152),inverse(multiply(greatest_lower_bound(X_151,X_152),inverse(X_152)))))) )],[refute_0_385,refute_0_386]) ).
cnf(refute_0_388,plain,
multiply(X_151,multiply(inverse(X_152),inverse(multiply(greatest_lower_bound(X_151,X_152),inverse(X_152))))) = multiply(X_151,inverse(greatest_lower_bound(X_151,X_152))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_152),inverse(multiply(greatest_lower_bound(X_151,X_152),inverse(X_152)))),inverse(greatest_lower_bound(X_151,X_152))) )],[refute_0_384,refute_0_387]) ).
cnf(refute_0_389,plain,
multiply(multiply(X_151,inverse(X_152)),inverse(multiply(greatest_lower_bound(X_151,X_152),inverse(X_152)))) = multiply(X_151,multiply(inverse(X_152),inverse(multiply(greatest_lower_bound(X_151,X_152),inverse(X_152))))),
inference(subst,[],[associativity:[bind(X,$fot(X_151)),bind(Y,$fot(inverse(X_152))),bind(Z,$fot(inverse(multiply(greatest_lower_bound(X_151,X_152),inverse(X_152)))))]]) ).
cnf(refute_0_390,plain,
( multiply(X_151,multiply(inverse(X_152),inverse(multiply(greatest_lower_bound(X_151,X_152),inverse(X_152))))) != multiply(X_151,inverse(greatest_lower_bound(X_151,X_152)))
| multiply(multiply(X_151,inverse(X_152)),inverse(multiply(greatest_lower_bound(X_151,X_152),inverse(X_152)))) != multiply(X_151,multiply(inverse(X_152),inverse(multiply(greatest_lower_bound(X_151,X_152),inverse(X_152)))))
| multiply(multiply(X_151,inverse(X_152)),inverse(multiply(greatest_lower_bound(X_151,X_152),inverse(X_152)))) = multiply(X_151,inverse(greatest_lower_bound(X_151,X_152))) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(multiply(multiply(X_151,inverse(X_152)),inverse(multiply(greatest_lower_bound(X_151,X_152),inverse(X_152)))))),bind(Y0,$fot(multiply(X_151,multiply(inverse(X_152),inverse(multiply(greatest_lower_bound(X_151,X_152),inverse(X_152))))))),bind(Z0,$fot(multiply(X_151,inverse(greatest_lower_bound(X_151,X_152)))))]]) ).
cnf(refute_0_391,plain,
( multiply(X_151,multiply(inverse(X_152),inverse(multiply(greatest_lower_bound(X_151,X_152),inverse(X_152))))) != multiply(X_151,inverse(greatest_lower_bound(X_151,X_152)))
| multiply(multiply(X_151,inverse(X_152)),inverse(multiply(greatest_lower_bound(X_151,X_152),inverse(X_152)))) = multiply(X_151,inverse(greatest_lower_bound(X_151,X_152))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_151,inverse(X_152)),inverse(multiply(greatest_lower_bound(X_151,X_152),inverse(X_152)))),multiply(X_151,multiply(inverse(X_152),inverse(multiply(greatest_lower_bound(X_151,X_152),inverse(X_152)))))) )],[refute_0_389,refute_0_390]) ).
cnf(refute_0_392,plain,
multiply(multiply(X_151,inverse(X_152)),inverse(multiply(greatest_lower_bound(X_151,X_152),inverse(X_152)))) = multiply(X_151,inverse(greatest_lower_bound(X_151,X_152))),
inference(resolve,[$cnf( $equal(multiply(X_151,multiply(inverse(X_152),inverse(multiply(greatest_lower_bound(X_151,X_152),inverse(X_152))))),multiply(X_151,inverse(greatest_lower_bound(X_151,X_152)))) )],[refute_0_388,refute_0_391]) ).
cnf(refute_0_393,plain,
( multiply(multiply(X_151,inverse(X_152)),inverse(multiply(greatest_lower_bound(X_151,X_152),inverse(X_152)))) != multiply(X_151,inverse(greatest_lower_bound(X_151,X_152)))
| inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_151)))) != multiply(multiply(X_151,inverse(X_152)),inverse(multiply(greatest_lower_bound(X_151,X_152),inverse(X_152))))
| inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_151)))) = multiply(X_151,inverse(greatest_lower_bound(X_151,X_152))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_151)))),multiply(multiply(X_151,inverse(X_152)),inverse(multiply(greatest_lower_bound(X_151,X_152),inverse(X_152))))) ),[1],$fot(multiply(X_151,inverse(greatest_lower_bound(X_151,X_152))))]]) ).
cnf(refute_0_394,plain,
( inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_151)))) != multiply(multiply(X_151,inverse(X_152)),inverse(multiply(greatest_lower_bound(X_151,X_152),inverse(X_152))))
| inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_151)))) = multiply(X_151,inverse(greatest_lower_bound(X_151,X_152))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_151,inverse(X_152)),inverse(multiply(greatest_lower_bound(X_151,X_152),inverse(X_152)))),multiply(X_151,inverse(greatest_lower_bound(X_151,X_152)))) )],[refute_0_392,refute_0_393]) ).
cnf(refute_0_395,plain,
( inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(X_151,inverse(X_152)))))) != multiply(multiply(X_151,inverse(X_152)),inverse(multiply(greatest_lower_bound(X_151,X_152),inverse(X_152))))
| inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_151)))) = multiply(X_151,inverse(greatest_lower_bound(X_151,X_152))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_151)))),multiply(multiply(X_151,inverse(X_152)),inverse(multiply(greatest_lower_bound(X_151,X_152),inverse(X_152))))) )],[refute_0_367,refute_0_394]) ).
cnf(refute_0_396,plain,
inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_151)))) = multiply(X_151,inverse(greatest_lower_bound(X_151,X_152))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(X_151,inverse(X_152)))))),multiply(multiply(X_151,inverse(X_152)),inverse(multiply(greatest_lower_bound(X_151,X_152),inverse(X_152))))) )],[refute_0_162,refute_0_395]) ).
cnf(refute_0_397,plain,
inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394)))) = multiply(X_394,inverse(greatest_lower_bound(X_394,X_152))),
inference(subst,[],[refute_0_396:[bind(X_151,$fot(X_394))]]) ).
cnf(refute_0_398,plain,
( inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394)))) != multiply(X_394,inverse(greatest_lower_bound(X_394,X_152)))
| multiply(X_394,inverse(greatest_lower_bound(X_394,X_152))) = inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394)))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394)))))),bind(Y0,$fot(multiply(X_394,inverse(greatest_lower_bound(X_394,X_152)))))]]) ).
cnf(refute_0_399,plain,
multiply(X_394,inverse(greatest_lower_bound(X_394,X_152))) = inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394)))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394)))),multiply(X_394,inverse(greatest_lower_bound(X_394,X_152)))) )],[refute_0_397,refute_0_398]) ).
cnf(refute_0_400,plain,
( multiply(X_394,inverse(greatest_lower_bound(X_394,X_152))) != inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394))))
| inverse(greatest_lower_bound(X_394,X_152)) != multiply(inverse(least_upper_bound(greatest_lower_bound(X_394,X_152),X_394)),least_upper_bound(identity,multiply(X_394,inverse(greatest_lower_bound(X_394,X_152)))))
| inverse(greatest_lower_bound(X_394,X_152)) = multiply(inverse(least_upper_bound(greatest_lower_bound(X_394,X_152),X_394)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394)))))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X_394,X_152)),multiply(inverse(least_upper_bound(greatest_lower_bound(X_394,X_152),X_394)),least_upper_bound(identity,multiply(X_394,inverse(greatest_lower_bound(X_394,X_152)))))) ),[1,1,1],$fot(inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394)))))]]) ).
cnf(refute_0_401,plain,
( inverse(greatest_lower_bound(X_394,X_152)) != multiply(inverse(least_upper_bound(greatest_lower_bound(X_394,X_152),X_394)),least_upper_bound(identity,multiply(X_394,inverse(greatest_lower_bound(X_394,X_152)))))
| inverse(greatest_lower_bound(X_394,X_152)) = multiply(inverse(least_upper_bound(greatest_lower_bound(X_394,X_152),X_394)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394)))))) ),
inference(resolve,[$cnf( $equal(multiply(X_394,inverse(greatest_lower_bound(X_394,X_152))),inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394))))) )],[refute_0_399,refute_0_400]) ).
cnf(refute_0_402,plain,
inverse(greatest_lower_bound(X_394,X_152)) = multiply(inverse(least_upper_bound(greatest_lower_bound(X_394,X_152),X_394)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394)))))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_394,X_152)),multiply(inverse(least_upper_bound(greatest_lower_bound(X_394,X_152),X_394)),least_upper_bound(identity,multiply(X_394,inverse(greatest_lower_bound(X_394,X_152)))))) )],[refute_0_110,refute_0_401]) ).
cnf(refute_0_403,plain,
inverse(inverse(X_394)) = X_394,
inference(subst,[],[p18_2:[bind(X,$fot(X_394))]]) ).
cnf(refute_0_404,plain,
greatest_lower_bound(X_152,inverse(inverse(X_394))) = greatest_lower_bound(X_152,inverse(inverse(X_394))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X_152,inverse(inverse(X_394))))]]) ).
cnf(refute_0_405,plain,
( greatest_lower_bound(X_152,inverse(inverse(X_394))) != greatest_lower_bound(X_152,inverse(inverse(X_394)))
| inverse(inverse(X_394)) != X_394
| greatest_lower_bound(X_152,inverse(inverse(X_394))) = greatest_lower_bound(X_152,X_394) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_152,inverse(inverse(X_394))),greatest_lower_bound(X_152,inverse(inverse(X_394)))) ),[1,1],$fot(X_394)]]) ).
cnf(refute_0_406,plain,
( inverse(inverse(X_394)) != X_394
| greatest_lower_bound(X_152,inverse(inverse(X_394))) = greatest_lower_bound(X_152,X_394) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_152,inverse(inverse(X_394))),greatest_lower_bound(X_152,inverse(inverse(X_394)))) )],[refute_0_404,refute_0_405]) ).
cnf(refute_0_407,plain,
greatest_lower_bound(X_152,inverse(inverse(X_394))) = greatest_lower_bound(X_152,X_394),
inference(resolve,[$cnf( $equal(inverse(inverse(X_394)),X_394) )],[refute_0_403,refute_0_406]) ).
cnf(refute_0_408,plain,
inverse(greatest_lower_bound(X_152,inverse(inverse(X_394)))) = inverse(greatest_lower_bound(X_152,inverse(inverse(X_394)))),
introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(X_152,inverse(inverse(X_394)))))]]) ).
cnf(refute_0_409,plain,
( greatest_lower_bound(X_152,inverse(inverse(X_394))) != greatest_lower_bound(X_152,X_394)
| inverse(greatest_lower_bound(X_152,inverse(inverse(X_394)))) != inverse(greatest_lower_bound(X_152,inverse(inverse(X_394))))
| inverse(greatest_lower_bound(X_152,inverse(inverse(X_394)))) = inverse(greatest_lower_bound(X_152,X_394)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X_152,inverse(inverse(X_394)))),inverse(greatest_lower_bound(X_152,inverse(inverse(X_394))))) ),[1,0],$fot(greatest_lower_bound(X_152,X_394))]]) ).
cnf(refute_0_410,plain,
( greatest_lower_bound(X_152,inverse(inverse(X_394))) != greatest_lower_bound(X_152,X_394)
| inverse(greatest_lower_bound(X_152,inverse(inverse(X_394)))) = inverse(greatest_lower_bound(X_152,X_394)) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_152,inverse(inverse(X_394)))),inverse(greatest_lower_bound(X_152,inverse(inverse(X_394))))) )],[refute_0_408,refute_0_409]) ).
cnf(refute_0_411,plain,
inverse(greatest_lower_bound(X_152,inverse(inverse(X_394)))) = inverse(greatest_lower_bound(X_152,X_394)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_152,inverse(inverse(X_394))),greatest_lower_bound(X_152,X_394)) )],[refute_0_407,refute_0_410]) ).
cnf(refute_0_412,plain,
multiply(multiply(X_92,inverse(X_92)),X_94) = multiply(X_92,multiply(inverse(X_92),X_94)),
inference(subst,[],[associativity:[bind(X,$fot(X_92)),bind(Y,$fot(inverse(X_92))),bind(Z,$fot(X_94))]]) ).
cnf(refute_0_413,plain,
multiply(X_92,inverse(X_92)) = identity,
inference(subst,[],[refute_0_38:[bind(X_1,$fot(X_92))]]) ).
cnf(refute_0_414,plain,
( multiply(X_92,inverse(X_92)) != identity
| multiply(multiply(X_92,inverse(X_92)),X_94) != multiply(X_92,multiply(inverse(X_92),X_94))
| multiply(identity,X_94) = multiply(X_92,multiply(inverse(X_92),X_94)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_92,inverse(X_92)),X_94),multiply(X_92,multiply(inverse(X_92),X_94))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_415,plain,
( multiply(multiply(X_92,inverse(X_92)),X_94) != multiply(X_92,multiply(inverse(X_92),X_94))
| multiply(identity,X_94) = multiply(X_92,multiply(inverse(X_92),X_94)) ),
inference(resolve,[$cnf( $equal(multiply(X_92,inverse(X_92)),identity) )],[refute_0_413,refute_0_414]) ).
cnf(refute_0_416,plain,
multiply(identity,X_94) = multiply(X_92,multiply(inverse(X_92),X_94)),
inference(resolve,[$cnf( $equal(multiply(multiply(X_92,inverse(X_92)),X_94),multiply(X_92,multiply(inverse(X_92),X_94))) )],[refute_0_412,refute_0_415]) ).
cnf(refute_0_417,plain,
( multiply(identity,X_94) != X_94
| multiply(identity,X_94) != multiply(X_92,multiply(inverse(X_92),X_94))
| X_94 = multiply(X_92,multiply(inverse(X_92),X_94)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_94),multiply(X_92,multiply(inverse(X_92),X_94))) ),[0],$fot(X_94)]]) ).
cnf(refute_0_418,plain,
( multiply(identity,X_94) != multiply(X_92,multiply(inverse(X_92),X_94))
| X_94 = multiply(X_92,multiply(inverse(X_92),X_94)) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_94),X_94) )],[refute_0_14,refute_0_417]) ).
cnf(refute_0_419,plain,
X_94 = multiply(X_92,multiply(inverse(X_92),X_94)),
inference(resolve,[$cnf( $equal(multiply(identity,X_94),multiply(X_92,multiply(inverse(X_92),X_94))) )],[refute_0_416,refute_0_418]) ).
cnf(refute_0_420,plain,
inverse(greatest_lower_bound(X_46,inverse(X_140))) = multiply(X_140,multiply(inverse(X_140),inverse(greatest_lower_bound(X_46,inverse(X_140))))),
inference(subst,[],[refute_0_419:[bind(X_92,$fot(X_140)),bind(X_94,$fot(inverse(greatest_lower_bound(X_46,inverse(X_140)))))]]) ).
cnf(refute_0_421,plain,
inverse(greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140))))) = multiply(inverse(X_140),inverse(greatest_lower_bound(X_46,inverse(X_140)))),
inference(subst,[],[refute_0_146:[bind(X_99,$fot(inverse(X_140)))]]) ).
cnf(refute_0_422,plain,
( inverse(greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140))))) != multiply(inverse(X_140),inverse(greatest_lower_bound(X_46,inverse(X_140))))
| multiply(inverse(X_140),inverse(greatest_lower_bound(X_46,inverse(X_140)))) = inverse(greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140))))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140))))))),bind(Y0,$fot(multiply(inverse(X_140),inverse(greatest_lower_bound(X_46,inverse(X_140))))))]]) ).
cnf(refute_0_423,plain,
multiply(inverse(X_140),inverse(greatest_lower_bound(X_46,inverse(X_140)))) = inverse(greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140))))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140))))),multiply(inverse(X_140),inverse(greatest_lower_bound(X_46,inverse(X_140))))) )],[refute_0_421,refute_0_422]) ).
cnf(refute_0_424,plain,
( multiply(inverse(X_140),inverse(greatest_lower_bound(X_46,inverse(X_140)))) != inverse(greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140)))))
| inverse(greatest_lower_bound(X_46,inverse(X_140))) != multiply(X_140,multiply(inverse(X_140),inverse(greatest_lower_bound(X_46,inverse(X_140)))))
| inverse(greatest_lower_bound(X_46,inverse(X_140))) = multiply(X_140,inverse(greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140)))))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X_46,inverse(X_140))),multiply(X_140,multiply(inverse(X_140),inverse(greatest_lower_bound(X_46,inverse(X_140)))))) ),[1,1],$fot(inverse(greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140))))))]]) ).
cnf(refute_0_425,plain,
( inverse(greatest_lower_bound(X_46,inverse(X_140))) != multiply(X_140,multiply(inverse(X_140),inverse(greatest_lower_bound(X_46,inverse(X_140)))))
| inverse(greatest_lower_bound(X_46,inverse(X_140))) = multiply(X_140,inverse(greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140)))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_140),inverse(greatest_lower_bound(X_46,inverse(X_140)))),inverse(greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140)))))) )],[refute_0_423,refute_0_424]) ).
cnf(refute_0_426,plain,
inverse(greatest_lower_bound(X_46,inverse(X_140))) = multiply(X_140,inverse(greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140)))))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_46,inverse(X_140))),multiply(X_140,multiply(inverse(X_140),inverse(greatest_lower_bound(X_46,inverse(X_140)))))) )],[refute_0_420,refute_0_425]) ).
cnf(refute_0_427,plain,
inverse(inverse(X_140)) = X_140,
inference(subst,[],[p18_2:[bind(X,$fot(X_140))]]) ).
cnf(refute_0_428,plain,
multiply(X_46,inverse(inverse(X_140))) = multiply(X_46,inverse(inverse(X_140))),
introduced(tautology,[refl,[$fot(multiply(X_46,inverse(inverse(X_140))))]]) ).
cnf(refute_0_429,plain,
( multiply(X_46,inverse(inverse(X_140))) != multiply(X_46,inverse(inverse(X_140)))
| inverse(inverse(X_140)) != X_140
| multiply(X_46,inverse(inverse(X_140))) = multiply(X_46,X_140) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_46,inverse(inverse(X_140))),multiply(X_46,inverse(inverse(X_140)))) ),[1,1],$fot(X_140)]]) ).
cnf(refute_0_430,plain,
( inverse(inverse(X_140)) != X_140
| multiply(X_46,inverse(inverse(X_140))) = multiply(X_46,X_140) ),
inference(resolve,[$cnf( $equal(multiply(X_46,inverse(inverse(X_140))),multiply(X_46,inverse(inverse(X_140)))) )],[refute_0_428,refute_0_429]) ).
cnf(refute_0_431,plain,
multiply(X_46,inverse(inverse(X_140))) = multiply(X_46,X_140),
inference(resolve,[$cnf( $equal(inverse(inverse(X_140)),X_140) )],[refute_0_427,refute_0_430]) ).
cnf(refute_0_432,plain,
greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140)))) = greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140)))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140)))))]]) ).
cnf(refute_0_433,plain,
( multiply(X_46,inverse(inverse(X_140))) != multiply(X_46,X_140)
| greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140)))) != greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140))))
| greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140)))) = greatest_lower_bound(identity,multiply(X_46,X_140)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140)))),greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140))))) ),[1,1],$fot(multiply(X_46,X_140))]]) ).
cnf(refute_0_434,plain,
( multiply(X_46,inverse(inverse(X_140))) != multiply(X_46,X_140)
| greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140)))) = greatest_lower_bound(identity,multiply(X_46,X_140)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140)))),greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140))))) )],[refute_0_432,refute_0_433]) ).
cnf(refute_0_435,plain,
greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140)))) = greatest_lower_bound(identity,multiply(X_46,X_140)),
inference(resolve,[$cnf( $equal(multiply(X_46,inverse(inverse(X_140))),multiply(X_46,X_140)) )],[refute_0_431,refute_0_434]) ).
cnf(refute_0_436,plain,
inverse(greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140))))) = inverse(greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140))))),
introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140))))))]]) ).
cnf(refute_0_437,plain,
( greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140)))) != greatest_lower_bound(identity,multiply(X_46,X_140))
| inverse(greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140))))) != inverse(greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140)))))
| inverse(greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140))))) = inverse(greatest_lower_bound(identity,multiply(X_46,X_140))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140))))),inverse(greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140)))))) ),[1,0],$fot(greatest_lower_bound(identity,multiply(X_46,X_140)))]]) ).
cnf(refute_0_438,plain,
( greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140)))) != greatest_lower_bound(identity,multiply(X_46,X_140))
| inverse(greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140))))) = inverse(greatest_lower_bound(identity,multiply(X_46,X_140))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140))))),inverse(greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140)))))) )],[refute_0_436,refute_0_437]) ).
cnf(refute_0_439,plain,
inverse(greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140))))) = inverse(greatest_lower_bound(identity,multiply(X_46,X_140))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140)))),greatest_lower_bound(identity,multiply(X_46,X_140))) )],[refute_0_435,refute_0_438]) ).
cnf(refute_0_440,plain,
multiply(X_140,inverse(greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140)))))) = multiply(X_140,inverse(greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140)))))),
introduced(tautology,[refl,[$fot(multiply(X_140,inverse(greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140)))))))]]) ).
cnf(refute_0_441,plain,
( multiply(X_140,inverse(greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140)))))) != multiply(X_140,inverse(greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140))))))
| inverse(greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140))))) != inverse(greatest_lower_bound(identity,multiply(X_46,X_140)))
| multiply(X_140,inverse(greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140)))))) = multiply(X_140,inverse(greatest_lower_bound(identity,multiply(X_46,X_140)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_140,inverse(greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140)))))),multiply(X_140,inverse(greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140))))))) ),[1,1],$fot(inverse(greatest_lower_bound(identity,multiply(X_46,X_140))))]]) ).
cnf(refute_0_442,plain,
( inverse(greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140))))) != inverse(greatest_lower_bound(identity,multiply(X_46,X_140)))
| multiply(X_140,inverse(greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140)))))) = multiply(X_140,inverse(greatest_lower_bound(identity,multiply(X_46,X_140)))) ),
inference(resolve,[$cnf( $equal(multiply(X_140,inverse(greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140)))))),multiply(X_140,inverse(greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140))))))) )],[refute_0_440,refute_0_441]) ).
cnf(refute_0_443,plain,
multiply(X_140,inverse(greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140)))))) = multiply(X_140,inverse(greatest_lower_bound(identity,multiply(X_46,X_140)))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140))))),inverse(greatest_lower_bound(identity,multiply(X_46,X_140)))) )],[refute_0_439,refute_0_442]) ).
cnf(refute_0_444,plain,
( multiply(X_140,inverse(greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140)))))) != multiply(X_140,inverse(greatest_lower_bound(identity,multiply(X_46,X_140))))
| inverse(greatest_lower_bound(X_46,inverse(X_140))) != multiply(X_140,inverse(greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140))))))
| inverse(greatest_lower_bound(X_46,inverse(X_140))) = multiply(X_140,inverse(greatest_lower_bound(identity,multiply(X_46,X_140)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X_46,inverse(X_140))),multiply(X_140,inverse(greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140))))))) ),[1],$fot(multiply(X_140,inverse(greatest_lower_bound(identity,multiply(X_46,X_140)))))]]) ).
cnf(refute_0_445,plain,
( inverse(greatest_lower_bound(X_46,inverse(X_140))) != multiply(X_140,inverse(greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140))))))
| inverse(greatest_lower_bound(X_46,inverse(X_140))) = multiply(X_140,inverse(greatest_lower_bound(identity,multiply(X_46,X_140)))) ),
inference(resolve,[$cnf( $equal(multiply(X_140,inverse(greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140)))))),multiply(X_140,inverse(greatest_lower_bound(identity,multiply(X_46,X_140))))) )],[refute_0_443,refute_0_444]) ).
cnf(refute_0_446,plain,
inverse(greatest_lower_bound(X_46,inverse(X_140))) = multiply(X_140,inverse(greatest_lower_bound(identity,multiply(X_46,X_140)))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_46,inverse(X_140))),multiply(X_140,inverse(greatest_lower_bound(identity,multiply(X_46,inverse(inverse(X_140))))))) )],[refute_0_426,refute_0_445]) ).
cnf(refute_0_447,plain,
( inverse(greatest_lower_bound(X_46,inverse(X_140))) != multiply(X_140,inverse(greatest_lower_bound(identity,multiply(X_46,X_140))))
| multiply(X_140,inverse(greatest_lower_bound(identity,multiply(X_46,X_140)))) = inverse(greatest_lower_bound(X_46,inverse(X_140))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(greatest_lower_bound(X_46,inverse(X_140))))),bind(Y0,$fot(multiply(X_140,inverse(greatest_lower_bound(identity,multiply(X_46,X_140))))))]]) ).
cnf(refute_0_448,plain,
multiply(X_140,inverse(greatest_lower_bound(identity,multiply(X_46,X_140)))) = inverse(greatest_lower_bound(X_46,inverse(X_140))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_46,inverse(X_140))),multiply(X_140,inverse(greatest_lower_bound(identity,multiply(X_46,X_140))))) )],[refute_0_446,refute_0_447]) ).
cnf(refute_0_449,plain,
multiply(inverse(X_394),inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394))))) = inverse(greatest_lower_bound(X_152,inverse(inverse(X_394)))),
inference(subst,[],[refute_0_448:[bind(X_140,$fot(inverse(X_394))),bind(X_46,$fot(X_152))]]) ).
cnf(refute_0_450,plain,
( multiply(inverse(X_394),inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394))))) != inverse(greatest_lower_bound(X_152,inverse(inverse(X_394))))
| inverse(greatest_lower_bound(X_152,inverse(inverse(X_394)))) != inverse(greatest_lower_bound(X_152,X_394))
| multiply(inverse(X_394),inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394))))) = inverse(greatest_lower_bound(X_152,X_394)) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(multiply(inverse(X_394),inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394))))))),bind(Y0,$fot(inverse(greatest_lower_bound(X_152,inverse(inverse(X_394)))))),bind(Z0,$fot(inverse(greatest_lower_bound(X_152,X_394))))]]) ).
cnf(refute_0_451,plain,
( inverse(greatest_lower_bound(X_152,inverse(inverse(X_394)))) != inverse(greatest_lower_bound(X_152,X_394))
| multiply(inverse(X_394),inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394))))) = inverse(greatest_lower_bound(X_152,X_394)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_394),inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394))))),inverse(greatest_lower_bound(X_152,inverse(inverse(X_394))))) )],[refute_0_449,refute_0_450]) ).
cnf(refute_0_452,plain,
multiply(inverse(X_394),inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394))))) = inverse(greatest_lower_bound(X_152,X_394)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_152,inverse(inverse(X_394)))),inverse(greatest_lower_bound(X_152,X_394))) )],[refute_0_411,refute_0_451]) ).
cnf(refute_0_453,plain,
least_upper_bound(inverse(greatest_lower_bound(identity,X_73)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_73)))) = inverse(greatest_lower_bound(identity,X_73)),
inference(subst,[],[refute_0_53:[bind(X_12,$fot(inverse(greatest_lower_bound(identity,X_73)))),bind(X_13,$fot(identity))]]) ).
cnf(refute_0_454,plain,
multiply(inverse(X_38),greatest_lower_bound(X_37,X_38)) = greatest_lower_bound(multiply(inverse(X_38),X_37),multiply(inverse(X_38),X_38)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(inverse(X_38))),bind(Y,$fot(X_37)),bind(Z,$fot(X_38))]]) ).
cnf(refute_0_455,plain,
multiply(inverse(X_38),X_38) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_38))]]) ).
cnf(refute_0_456,plain,
( multiply(inverse(X_38),X_38) != identity
| multiply(inverse(X_38),greatest_lower_bound(X_37,X_38)) != greatest_lower_bound(multiply(inverse(X_38),X_37),multiply(inverse(X_38),X_38))
| multiply(inverse(X_38),greatest_lower_bound(X_37,X_38)) = greatest_lower_bound(multiply(inverse(X_38),X_37),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_38),greatest_lower_bound(X_37,X_38)),greatest_lower_bound(multiply(inverse(X_38),X_37),multiply(inverse(X_38),X_38))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_457,plain,
( multiply(inverse(X_38),greatest_lower_bound(X_37,X_38)) != greatest_lower_bound(multiply(inverse(X_38),X_37),multiply(inverse(X_38),X_38))
| multiply(inverse(X_38),greatest_lower_bound(X_37,X_38)) = greatest_lower_bound(multiply(inverse(X_38),X_37),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_38),X_38),identity) )],[refute_0_455,refute_0_456]) ).
cnf(refute_0_458,plain,
multiply(inverse(X_38),greatest_lower_bound(X_37,X_38)) = greatest_lower_bound(multiply(inverse(X_38),X_37),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_38),greatest_lower_bound(X_37,X_38)),greatest_lower_bound(multiply(inverse(X_38),X_37),multiply(inverse(X_38),X_38))) )],[refute_0_454,refute_0_457]) ).
cnf(refute_0_459,plain,
greatest_lower_bound(multiply(inverse(X_38),X_37),identity) = greatest_lower_bound(identity,multiply(inverse(X_38),X_37)),
inference(subst,[],[refute_0_122:[bind(X,$fot(identity)),bind(Y,$fot(multiply(inverse(X_38),X_37)))]]) ).
cnf(refute_0_460,plain,
( multiply(inverse(X_38),greatest_lower_bound(X_37,X_38)) != greatest_lower_bound(multiply(inverse(X_38),X_37),identity)
| greatest_lower_bound(multiply(inverse(X_38),X_37),identity) != greatest_lower_bound(identity,multiply(inverse(X_38),X_37))
| multiply(inverse(X_38),greatest_lower_bound(X_37,X_38)) = greatest_lower_bound(identity,multiply(inverse(X_38),X_37)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_38),greatest_lower_bound(X_37,X_38)),greatest_lower_bound(identity,multiply(inverse(X_38),X_37))) ),[0],$fot(greatest_lower_bound(multiply(inverse(X_38),X_37),identity))]]) ).
cnf(refute_0_461,plain,
( multiply(inverse(X_38),greatest_lower_bound(X_37,X_38)) != greatest_lower_bound(multiply(inverse(X_38),X_37),identity)
| multiply(inverse(X_38),greatest_lower_bound(X_37,X_38)) = greatest_lower_bound(identity,multiply(inverse(X_38),X_37)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(inverse(X_38),X_37),identity),greatest_lower_bound(identity,multiply(inverse(X_38),X_37))) )],[refute_0_459,refute_0_460]) ).
cnf(refute_0_462,plain,
multiply(inverse(X_38),greatest_lower_bound(X_37,X_38)) = greatest_lower_bound(identity,multiply(inverse(X_38),X_37)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_38),greatest_lower_bound(X_37,X_38)),greatest_lower_bound(multiply(inverse(X_38),X_37),identity)) )],[refute_0_458,refute_0_461]) ).
cnf(refute_0_463,plain,
multiply(inverse(X_51),greatest_lower_bound(identity,X_51)) = greatest_lower_bound(identity,multiply(inverse(X_51),identity)),
inference(subst,[],[refute_0_462:[bind(X_37,$fot(identity)),bind(X_38,$fot(X_51))]]) ).
cnf(refute_0_464,plain,
inverse(X_51) = multiply(inverse(X_51),identity),
inference(subst,[],[refute_0_210:[bind(X,$fot(inverse(X_51)))]]) ).
cnf(refute_0_465,plain,
( inverse(X_51) != multiply(inverse(X_51),identity)
| multiply(inverse(X_51),identity) = inverse(X_51) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(X_51))),bind(Y0,$fot(multiply(inverse(X_51),identity)))]]) ).
cnf(refute_0_466,plain,
multiply(inverse(X_51),identity) = inverse(X_51),
inference(resolve,[$cnf( $equal(inverse(X_51),multiply(inverse(X_51),identity)) )],[refute_0_464,refute_0_465]) ).
cnf(refute_0_467,plain,
( multiply(inverse(X_51),greatest_lower_bound(identity,X_51)) != greatest_lower_bound(identity,multiply(inverse(X_51),identity))
| multiply(inverse(X_51),identity) != inverse(X_51)
| multiply(inverse(X_51),greatest_lower_bound(identity,X_51)) = greatest_lower_bound(identity,inverse(X_51)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_51),greatest_lower_bound(identity,X_51)),greatest_lower_bound(identity,multiply(inverse(X_51),identity))) ),[1,1],$fot(inverse(X_51))]]) ).
cnf(refute_0_468,plain,
( multiply(inverse(X_51),greatest_lower_bound(identity,X_51)) != greatest_lower_bound(identity,multiply(inverse(X_51),identity))
| multiply(inverse(X_51),greatest_lower_bound(identity,X_51)) = greatest_lower_bound(identity,inverse(X_51)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_51),identity),inverse(X_51)) )],[refute_0_466,refute_0_467]) ).
cnf(refute_0_469,plain,
multiply(inverse(X_51),greatest_lower_bound(identity,X_51)) = greatest_lower_bound(identity,inverse(X_51)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_51),greatest_lower_bound(identity,X_51)),greatest_lower_bound(identity,multiply(inverse(X_51),identity))) )],[refute_0_463,refute_0_468]) ).
cnf(refute_0_470,plain,
multiply(inverse(greatest_lower_bound(identity,X_16)),greatest_lower_bound(identity,greatest_lower_bound(identity,X_16))) = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_16))),
inference(subst,[],[refute_0_469:[bind(X_51,$fot(greatest_lower_bound(identity,X_16)))]]) ).
cnf(refute_0_471,plain,
greatest_lower_bound(identity,greatest_lower_bound(identity,X_16)) = greatest_lower_bound(identity,X_16),
inference(subst,[],[refute_0_189:[bind(X_17,$fot(identity))]]) ).
cnf(refute_0_472,plain,
( multiply(inverse(greatest_lower_bound(identity,X_16)),greatest_lower_bound(identity,greatest_lower_bound(identity,X_16))) != greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_16)))
| greatest_lower_bound(identity,greatest_lower_bound(identity,X_16)) != greatest_lower_bound(identity,X_16)
| multiply(inverse(greatest_lower_bound(identity,X_16)),greatest_lower_bound(identity,X_16)) = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_16))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_16)),greatest_lower_bound(identity,greatest_lower_bound(identity,X_16))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_16)))) ),[0,1],$fot(greatest_lower_bound(identity,X_16))]]) ).
cnf(refute_0_473,plain,
( multiply(inverse(greatest_lower_bound(identity,X_16)),greatest_lower_bound(identity,greatest_lower_bound(identity,X_16))) != greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_16)))
| multiply(inverse(greatest_lower_bound(identity,X_16)),greatest_lower_bound(identity,X_16)) = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_16))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(identity,X_16)),greatest_lower_bound(identity,X_16)) )],[refute_0_471,refute_0_472]) ).
cnf(refute_0_474,plain,
multiply(inverse(greatest_lower_bound(identity,X_16)),greatest_lower_bound(identity,X_16)) = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_16))),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_16)),greatest_lower_bound(identity,greatest_lower_bound(identity,X_16))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_16)))) )],[refute_0_470,refute_0_473]) ).
cnf(refute_0_475,plain,
multiply(inverse(greatest_lower_bound(identity,X_16)),greatest_lower_bound(identity,X_16)) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(greatest_lower_bound(identity,X_16)))]]) ).
cnf(refute_0_476,plain,
( multiply(inverse(greatest_lower_bound(identity,X_16)),greatest_lower_bound(identity,X_16)) != greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_16)))
| multiply(inverse(greatest_lower_bound(identity,X_16)),greatest_lower_bound(identity,X_16)) != identity
| identity = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_16))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_16)),greatest_lower_bound(identity,X_16)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_16)))) ),[0],$fot(identity)]]) ).
cnf(refute_0_477,plain,
( multiply(inverse(greatest_lower_bound(identity,X_16)),greatest_lower_bound(identity,X_16)) != greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_16)))
| identity = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_16))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_16)),greatest_lower_bound(identity,X_16)),identity) )],[refute_0_475,refute_0_476]) ).
cnf(refute_0_478,plain,
identity = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_16))),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_16)),greatest_lower_bound(identity,X_16)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_16)))) )],[refute_0_474,refute_0_477]) ).
cnf(refute_0_479,plain,
identity = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_73))),
inference(subst,[],[refute_0_478:[bind(X_16,$fot(X_73))]]) ).
cnf(refute_0_480,plain,
( identity != greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_73)))
| greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_73))) = identity ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(identity)),bind(Y0,$fot(greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_73)))))]]) ).
cnf(refute_0_481,plain,
greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_73))) = identity,
inference(resolve,[$cnf( $equal(identity,greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_73)))) )],[refute_0_479,refute_0_480]) ).
cnf(refute_0_482,plain,
( greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_73))) != identity
| least_upper_bound(inverse(greatest_lower_bound(identity,X_73)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_73)))) != inverse(greatest_lower_bound(identity,X_73))
| least_upper_bound(inverse(greatest_lower_bound(identity,X_73)),identity) = inverse(greatest_lower_bound(identity,X_73)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(identity,X_73)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_73)))),inverse(greatest_lower_bound(identity,X_73))) ),[0,1],$fot(identity)]]) ).
cnf(refute_0_483,plain,
( least_upper_bound(inverse(greatest_lower_bound(identity,X_73)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_73)))) != inverse(greatest_lower_bound(identity,X_73))
| least_upper_bound(inverse(greatest_lower_bound(identity,X_73)),identity) = inverse(greatest_lower_bound(identity,X_73)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_73))),identity) )],[refute_0_481,refute_0_482]) ).
cnf(refute_0_484,plain,
least_upper_bound(inverse(greatest_lower_bound(identity,X_73)),identity) = inverse(greatest_lower_bound(identity,X_73)),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(identity,X_73)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_73)))),inverse(greatest_lower_bound(identity,X_73))) )],[refute_0_453,refute_0_483]) ).
cnf(refute_0_485,plain,
least_upper_bound(inverse(greatest_lower_bound(identity,X_73)),identity) = least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_73))),
inference(subst,[],[refute_0_4:[bind(X,$fot(identity)),bind(Y,$fot(inverse(greatest_lower_bound(identity,X_73))))]]) ).
cnf(refute_0_486,plain,
( least_upper_bound(inverse(greatest_lower_bound(identity,X_73)),identity) != inverse(greatest_lower_bound(identity,X_73))
| least_upper_bound(inverse(greatest_lower_bound(identity,X_73)),identity) != least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_73)))
| least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_73))) = inverse(greatest_lower_bound(identity,X_73)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(identity,X_73)),identity),inverse(greatest_lower_bound(identity,X_73))) ),[0],$fot(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_73))))]]) ).
cnf(refute_0_487,plain,
( least_upper_bound(inverse(greatest_lower_bound(identity,X_73)),identity) != inverse(greatest_lower_bound(identity,X_73))
| least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_73))) = inverse(greatest_lower_bound(identity,X_73)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(identity,X_73)),identity),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_73)))) )],[refute_0_485,refute_0_486]) ).
cnf(refute_0_488,plain,
least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_73))) = inverse(greatest_lower_bound(identity,X_73)),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(identity,X_73)),identity),inverse(greatest_lower_bound(identity,X_73))) )],[refute_0_484,refute_0_487]) ).
cnf(refute_0_489,plain,
least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394))))) = inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394)))),
inference(subst,[],[refute_0_488:[bind(X_73,$fot(multiply(X_152,inverse(X_394))))]]) ).
cnf(refute_0_490,plain,
multiply(inverse(X_394),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394)))))) = multiply(inverse(X_394),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394)))))),
introduced(tautology,[refl,[$fot(multiply(inverse(X_394),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394)))))))]]) ).
cnf(refute_0_491,plain,
( multiply(inverse(X_394),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394)))))) != multiply(inverse(X_394),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394))))))
| least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394))))) != inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394))))
| multiply(inverse(X_394),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394)))))) = multiply(inverse(X_394),inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_394),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394)))))),multiply(inverse(X_394),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394))))))) ),[1,1],$fot(inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394)))))]]) ).
cnf(refute_0_492,plain,
( least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394))))) != inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394))))
| multiply(inverse(X_394),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394)))))) = multiply(inverse(X_394),inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_394),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394)))))),multiply(inverse(X_394),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394))))))) )],[refute_0_490,refute_0_491]) ).
cnf(refute_0_493,plain,
multiply(inverse(X_394),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394)))))) = multiply(inverse(X_394),inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394))))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394))))),inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394))))) )],[refute_0_489,refute_0_492]) ).
cnf(refute_0_494,plain,
least_upper_bound(X_394,greatest_lower_bound(X_394,X_152)) = X_394,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_394)),bind(Y,$fot(X_152))]]) ).
cnf(refute_0_495,plain,
inverse(least_upper_bound(X_394,greatest_lower_bound(X_394,X_152))) = inverse(least_upper_bound(X_394,greatest_lower_bound(X_394,X_152))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(X_394,greatest_lower_bound(X_394,X_152))))]]) ).
cnf(refute_0_496,plain,
( inverse(least_upper_bound(X_394,greatest_lower_bound(X_394,X_152))) != inverse(least_upper_bound(X_394,greatest_lower_bound(X_394,X_152)))
| least_upper_bound(X_394,greatest_lower_bound(X_394,X_152)) != X_394
| inverse(least_upper_bound(X_394,greatest_lower_bound(X_394,X_152))) = inverse(X_394) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_394,greatest_lower_bound(X_394,X_152))),inverse(least_upper_bound(X_394,greatest_lower_bound(X_394,X_152)))) ),[1,0],$fot(X_394)]]) ).
cnf(refute_0_497,plain,
( least_upper_bound(X_394,greatest_lower_bound(X_394,X_152)) != X_394
| inverse(least_upper_bound(X_394,greatest_lower_bound(X_394,X_152))) = inverse(X_394) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_394,greatest_lower_bound(X_394,X_152))),inverse(least_upper_bound(X_394,greatest_lower_bound(X_394,X_152)))) )],[refute_0_495,refute_0_496]) ).
cnf(refute_0_498,plain,
inverse(least_upper_bound(X_394,greatest_lower_bound(X_394,X_152))) = inverse(X_394),
inference(resolve,[$cnf( $equal(least_upper_bound(X_394,greatest_lower_bound(X_394,X_152)),X_394) )],[refute_0_494,refute_0_497]) ).
cnf(refute_0_499,plain,
X_96 = multiply(inverse(greatest_lower_bound(X_46,inverse(X_96))),multiply(greatest_lower_bound(X_46,inverse(X_96)),X_96)),
inference(subst,[],[refute_0_17:[bind(X_93,$fot(greatest_lower_bound(X_46,inverse(X_96)))),bind(X_94,$fot(X_96))]]) ).
cnf(refute_0_500,plain,
multiply(greatest_lower_bound(X_46,inverse(X_96)),X_96) = greatest_lower_bound(identity,multiply(X_46,X_96)),
inference(subst,[],[refute_0_126:[bind(X_45,$fot(X_96))]]) ).
cnf(refute_0_501,plain,
( X_96 != multiply(inverse(greatest_lower_bound(X_46,inverse(X_96))),multiply(greatest_lower_bound(X_46,inverse(X_96)),X_96))
| multiply(greatest_lower_bound(X_46,inverse(X_96)),X_96) != greatest_lower_bound(identity,multiply(X_46,X_96))
| X_96 = multiply(inverse(greatest_lower_bound(X_46,inverse(X_96))),greatest_lower_bound(identity,multiply(X_46,X_96))) ),
introduced(tautology,[equality,[$cnf( $equal(X_96,multiply(inverse(greatest_lower_bound(X_46,inverse(X_96))),multiply(greatest_lower_bound(X_46,inverse(X_96)),X_96))) ),[1,1],$fot(greatest_lower_bound(identity,multiply(X_46,X_96)))]]) ).
cnf(refute_0_502,plain,
( X_96 != multiply(inverse(greatest_lower_bound(X_46,inverse(X_96))),multiply(greatest_lower_bound(X_46,inverse(X_96)),X_96))
| X_96 = multiply(inverse(greatest_lower_bound(X_46,inverse(X_96))),greatest_lower_bound(identity,multiply(X_46,X_96))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_46,inverse(X_96)),X_96),greatest_lower_bound(identity,multiply(X_46,X_96))) )],[refute_0_500,refute_0_501]) ).
cnf(refute_0_503,plain,
X_96 = multiply(inverse(greatest_lower_bound(X_46,inverse(X_96))),greatest_lower_bound(identity,multiply(X_46,X_96))),
inference(resolve,[$cnf( $equal(X_96,multiply(inverse(greatest_lower_bound(X_46,inverse(X_96))),multiply(greatest_lower_bound(X_46,inverse(X_96)),X_96))) )],[refute_0_499,refute_0_502]) ).
cnf(refute_0_504,plain,
inverse(least_upper_bound(X_46,X_326)) = multiply(inverse(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326))))),greatest_lower_bound(identity,multiply(X_46,inverse(least_upper_bound(X_46,X_326))))),
inference(subst,[],[refute_0_503:[bind(X_96,$fot(inverse(least_upper_bound(X_46,X_326))))]]) ).
cnf(refute_0_505,plain,
inverse(multiply(least_upper_bound(inverse(inverse(X)),X_173),inverse(X))) = multiply(X,inverse(least_upper_bound(inverse(inverse(X)),X_173))),
inference(subst,[],[refute_0_114:[bind(X_32,$fot(least_upper_bound(inverse(inverse(X)),X_173)))]]) ).
cnf(refute_0_506,plain,
multiply(least_upper_bound(inverse(X_65),X_67),X_65) = least_upper_bound(multiply(inverse(X_65),X_65),multiply(X_67,X_65)),
inference(subst,[],[monotony_lub2:[bind(X,$fot(X_65)),bind(Y,$fot(inverse(X_65))),bind(Z,$fot(X_67))]]) ).
cnf(refute_0_507,plain,
( multiply(inverse(X_65),X_65) != identity
| multiply(least_upper_bound(inverse(X_65),X_67),X_65) != least_upper_bound(multiply(inverse(X_65),X_65),multiply(X_67,X_65))
| multiply(least_upper_bound(inverse(X_65),X_67),X_65) = least_upper_bound(identity,multiply(X_67,X_65)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(X_65),X_67),X_65),least_upper_bound(multiply(inverse(X_65),X_65),multiply(X_67,X_65))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_508,plain,
( multiply(least_upper_bound(inverse(X_65),X_67),X_65) != least_upper_bound(multiply(inverse(X_65),X_65),multiply(X_67,X_65))
| multiply(least_upper_bound(inverse(X_65),X_67),X_65) = least_upper_bound(identity,multiply(X_67,X_65)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_65),X_65),identity) )],[refute_0_20,refute_0_507]) ).
cnf(refute_0_509,plain,
multiply(least_upper_bound(inverse(X_65),X_67),X_65) = least_upper_bound(identity,multiply(X_67,X_65)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_65),X_67),X_65),least_upper_bound(multiply(inverse(X_65),X_65),multiply(X_67,X_65))) )],[refute_0_506,refute_0_508]) ).
cnf(refute_0_510,plain,
multiply(least_upper_bound(inverse(inverse(X)),X_173),inverse(X)) = least_upper_bound(identity,multiply(X_173,inverse(X))),
inference(subst,[],[refute_0_509:[bind(X_65,$fot(inverse(X))),bind(X_67,$fot(X_173))]]) ).
cnf(refute_0_511,plain,
( multiply(least_upper_bound(inverse(inverse(X)),X_173),inverse(X)) != least_upper_bound(identity,multiply(X_173,inverse(X)))
| inverse(multiply(least_upper_bound(inverse(inverse(X)),X_173),inverse(X))) != multiply(X,inverse(least_upper_bound(inverse(inverse(X)),X_173)))
| inverse(least_upper_bound(identity,multiply(X_173,inverse(X)))) = multiply(X,inverse(least_upper_bound(inverse(inverse(X)),X_173))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(least_upper_bound(inverse(inverse(X)),X_173),inverse(X))),multiply(X,inverse(least_upper_bound(inverse(inverse(X)),X_173)))) ),[0,0],$fot(least_upper_bound(identity,multiply(X_173,inverse(X))))]]) ).
cnf(refute_0_512,plain,
( inverse(multiply(least_upper_bound(inverse(inverse(X)),X_173),inverse(X))) != multiply(X,inverse(least_upper_bound(inverse(inverse(X)),X_173)))
| inverse(least_upper_bound(identity,multiply(X_173,inverse(X)))) = multiply(X,inverse(least_upper_bound(inverse(inverse(X)),X_173))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(inverse(X)),X_173),inverse(X)),least_upper_bound(identity,multiply(X_173,inverse(X)))) )],[refute_0_510,refute_0_511]) ).
cnf(refute_0_513,plain,
inverse(least_upper_bound(identity,multiply(X_173,inverse(X)))) = multiply(X,inverse(least_upper_bound(inverse(inverse(X)),X_173))),
inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(inverse(inverse(X)),X_173),inverse(X))),multiply(X,inverse(least_upper_bound(inverse(inverse(X)),X_173)))) )],[refute_0_505,refute_0_512]) ).
cnf(refute_0_514,plain,
least_upper_bound(inverse(inverse(X)),X_173) = least_upper_bound(inverse(inverse(X)),X_173),
introduced(tautology,[refl,[$fot(least_upper_bound(inverse(inverse(X)),X_173))]]) ).
cnf(refute_0_515,plain,
( inverse(inverse(X)) != X
| least_upper_bound(inverse(inverse(X)),X_173) != least_upper_bound(inverse(inverse(X)),X_173)
| least_upper_bound(inverse(inverse(X)),X_173) = least_upper_bound(X,X_173) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(inverse(X)),X_173),least_upper_bound(inverse(inverse(X)),X_173)) ),[1,0],$fot(X)]]) ).
cnf(refute_0_516,plain,
( inverse(inverse(X)) != X
| least_upper_bound(inverse(inverse(X)),X_173) = least_upper_bound(X,X_173) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(inverse(X)),X_173),least_upper_bound(inverse(inverse(X)),X_173)) )],[refute_0_514,refute_0_515]) ).
cnf(refute_0_517,plain,
least_upper_bound(inverse(inverse(X)),X_173) = least_upper_bound(X,X_173),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p18_2,refute_0_516]) ).
cnf(refute_0_518,plain,
inverse(least_upper_bound(inverse(inverse(X)),X_173)) = inverse(least_upper_bound(inverse(inverse(X)),X_173)),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(inverse(inverse(X)),X_173)))]]) ).
cnf(refute_0_519,plain,
( inverse(least_upper_bound(inverse(inverse(X)),X_173)) != inverse(least_upper_bound(inverse(inverse(X)),X_173))
| least_upper_bound(inverse(inverse(X)),X_173) != least_upper_bound(X,X_173)
| inverse(least_upper_bound(inverse(inverse(X)),X_173)) = inverse(least_upper_bound(X,X_173)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(inverse(inverse(X)),X_173)),inverse(least_upper_bound(inverse(inverse(X)),X_173))) ),[1,0],$fot(least_upper_bound(X,X_173))]]) ).
cnf(refute_0_520,plain,
( least_upper_bound(inverse(inverse(X)),X_173) != least_upper_bound(X,X_173)
| inverse(least_upper_bound(inverse(inverse(X)),X_173)) = inverse(least_upper_bound(X,X_173)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(inverse(X)),X_173)),inverse(least_upper_bound(inverse(inverse(X)),X_173))) )],[refute_0_518,refute_0_519]) ).
cnf(refute_0_521,plain,
inverse(least_upper_bound(inverse(inverse(X)),X_173)) = inverse(least_upper_bound(X,X_173)),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(inverse(X)),X_173),least_upper_bound(X,X_173)) )],[refute_0_517,refute_0_520]) ).
cnf(refute_0_522,plain,
multiply(X,inverse(least_upper_bound(inverse(inverse(X)),X_173))) = multiply(X,inverse(least_upper_bound(inverse(inverse(X)),X_173))),
introduced(tautology,[refl,[$fot(multiply(X,inverse(least_upper_bound(inverse(inverse(X)),X_173))))]]) ).
cnf(refute_0_523,plain,
( multiply(X,inverse(least_upper_bound(inverse(inverse(X)),X_173))) != multiply(X,inverse(least_upper_bound(inverse(inverse(X)),X_173)))
| inverse(least_upper_bound(inverse(inverse(X)),X_173)) != inverse(least_upper_bound(X,X_173))
| multiply(X,inverse(least_upper_bound(inverse(inverse(X)),X_173))) = multiply(X,inverse(least_upper_bound(X,X_173))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X,inverse(least_upper_bound(inverse(inverse(X)),X_173))),multiply(X,inverse(least_upper_bound(inverse(inverse(X)),X_173)))) ),[1,1],$fot(inverse(least_upper_bound(X,X_173)))]]) ).
cnf(refute_0_524,plain,
( inverse(least_upper_bound(inverse(inverse(X)),X_173)) != inverse(least_upper_bound(X,X_173))
| multiply(X,inverse(least_upper_bound(inverse(inverse(X)),X_173))) = multiply(X,inverse(least_upper_bound(X,X_173))) ),
inference(resolve,[$cnf( $equal(multiply(X,inverse(least_upper_bound(inverse(inverse(X)),X_173))),multiply(X,inverse(least_upper_bound(inverse(inverse(X)),X_173)))) )],[refute_0_522,refute_0_523]) ).
cnf(refute_0_525,plain,
multiply(X,inverse(least_upper_bound(inverse(inverse(X)),X_173))) = multiply(X,inverse(least_upper_bound(X,X_173))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(inverse(X)),X_173)),inverse(least_upper_bound(X,X_173))) )],[refute_0_521,refute_0_524]) ).
cnf(refute_0_526,plain,
( multiply(X,inverse(least_upper_bound(inverse(inverse(X)),X_173))) != multiply(X,inverse(least_upper_bound(X,X_173)))
| inverse(least_upper_bound(identity,multiply(X_173,inverse(X)))) != multiply(X,inverse(least_upper_bound(inverse(inverse(X)),X_173)))
| inverse(least_upper_bound(identity,multiply(X_173,inverse(X)))) = multiply(X,inverse(least_upper_bound(X,X_173))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(X_173,inverse(X)))),multiply(X,inverse(least_upper_bound(inverse(inverse(X)),X_173)))) ),[1],$fot(multiply(X,inverse(least_upper_bound(X,X_173))))]]) ).
cnf(refute_0_527,plain,
( inverse(least_upper_bound(identity,multiply(X_173,inverse(X)))) != multiply(X,inverse(least_upper_bound(inverse(inverse(X)),X_173)))
| inverse(least_upper_bound(identity,multiply(X_173,inverse(X)))) = multiply(X,inverse(least_upper_bound(X,X_173))) ),
inference(resolve,[$cnf( $equal(multiply(X,inverse(least_upper_bound(inverse(inverse(X)),X_173))),multiply(X,inverse(least_upper_bound(X,X_173)))) )],[refute_0_525,refute_0_526]) ).
cnf(refute_0_528,plain,
inverse(least_upper_bound(identity,multiply(X_173,inverse(X)))) = multiply(X,inverse(least_upper_bound(X,X_173))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(X_173,inverse(X)))),multiply(X,inverse(least_upper_bound(inverse(inverse(X)),X_173)))) )],[refute_0_513,refute_0_527]) ).
cnf(refute_0_529,plain,
inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46)))) = multiply(X_46,inverse(least_upper_bound(X_46,X_326))),
inference(subst,[],[refute_0_528:[bind(X,$fot(X_46)),bind(X_173,$fot(X_326))]]) ).
cnf(refute_0_530,plain,
( inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46)))) != multiply(X_46,inverse(least_upper_bound(X_46,X_326)))
| multiply(X_46,inverse(least_upper_bound(X_46,X_326))) = inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46)))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46)))))),bind(Y0,$fot(multiply(X_46,inverse(least_upper_bound(X_46,X_326)))))]]) ).
cnf(refute_0_531,plain,
multiply(X_46,inverse(least_upper_bound(X_46,X_326))) = inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46)))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46)))),multiply(X_46,inverse(least_upper_bound(X_46,X_326)))) )],[refute_0_529,refute_0_530]) ).
cnf(refute_0_532,plain,
( multiply(X_46,inverse(least_upper_bound(X_46,X_326))) != inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46))))
| inverse(least_upper_bound(X_46,X_326)) != multiply(inverse(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326))))),greatest_lower_bound(identity,multiply(X_46,inverse(least_upper_bound(X_46,X_326)))))
| inverse(least_upper_bound(X_46,X_326)) = multiply(inverse(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326))))),greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46)))))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_46,X_326)),multiply(inverse(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326))))),greatest_lower_bound(identity,multiply(X_46,inverse(least_upper_bound(X_46,X_326)))))) ),[1,1,1],$fot(inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46)))))]]) ).
cnf(refute_0_533,plain,
( inverse(least_upper_bound(X_46,X_326)) != multiply(inverse(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326))))),greatest_lower_bound(identity,multiply(X_46,inverse(least_upper_bound(X_46,X_326)))))
| inverse(least_upper_bound(X_46,X_326)) = multiply(inverse(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326))))),greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46)))))) ),
inference(resolve,[$cnf( $equal(multiply(X_46,inverse(least_upper_bound(X_46,X_326))),inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46))))) )],[refute_0_531,refute_0_532]) ).
cnf(refute_0_534,plain,
inverse(least_upper_bound(X_46,X_326)) = multiply(inverse(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326))))),greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46)))))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_46,X_326)),multiply(inverse(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326))))),greatest_lower_bound(identity,multiply(X_46,inverse(least_upper_bound(X_46,X_326)))))) )],[refute_0_504,refute_0_533]) ).
cnf(refute_0_535,plain,
inverse(inverse(X_46)) = X_46,
inference(subst,[],[p18_2:[bind(X,$fot(X_46))]]) ).
cnf(refute_0_536,plain,
least_upper_bound(X_326,inverse(inverse(X_46))) = least_upper_bound(X_326,inverse(inverse(X_46))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_326,inverse(inverse(X_46))))]]) ).
cnf(refute_0_537,plain,
( inverse(inverse(X_46)) != X_46
| least_upper_bound(X_326,inverse(inverse(X_46))) != least_upper_bound(X_326,inverse(inverse(X_46)))
| least_upper_bound(X_326,inverse(inverse(X_46))) = least_upper_bound(X_326,X_46) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_326,inverse(inverse(X_46))),least_upper_bound(X_326,inverse(inverse(X_46)))) ),[1,1],$fot(X_46)]]) ).
cnf(refute_0_538,plain,
( inverse(inverse(X_46)) != X_46
| least_upper_bound(X_326,inverse(inverse(X_46))) = least_upper_bound(X_326,X_46) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_326,inverse(inverse(X_46))),least_upper_bound(X_326,inverse(inverse(X_46)))) )],[refute_0_536,refute_0_537]) ).
cnf(refute_0_539,plain,
least_upper_bound(X_326,inverse(inverse(X_46))) = least_upper_bound(X_326,X_46),
inference(resolve,[$cnf( $equal(inverse(inverse(X_46)),X_46) )],[refute_0_535,refute_0_538]) ).
cnf(refute_0_540,plain,
inverse(least_upper_bound(X_326,inverse(inverse(X_46)))) = inverse(least_upper_bound(X_326,inverse(inverse(X_46)))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(X_326,inverse(inverse(X_46)))))]]) ).
cnf(refute_0_541,plain,
( inverse(least_upper_bound(X_326,inverse(inverse(X_46)))) != inverse(least_upper_bound(X_326,inverse(inverse(X_46))))
| least_upper_bound(X_326,inverse(inverse(X_46))) != least_upper_bound(X_326,X_46)
| inverse(least_upper_bound(X_326,inverse(inverse(X_46)))) = inverse(least_upper_bound(X_326,X_46)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_326,inverse(inverse(X_46)))),inverse(least_upper_bound(X_326,inverse(inverse(X_46))))) ),[1,0],$fot(least_upper_bound(X_326,X_46))]]) ).
cnf(refute_0_542,plain,
( least_upper_bound(X_326,inverse(inverse(X_46))) != least_upper_bound(X_326,X_46)
| inverse(least_upper_bound(X_326,inverse(inverse(X_46)))) = inverse(least_upper_bound(X_326,X_46)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_326,inverse(inverse(X_46)))),inverse(least_upper_bound(X_326,inverse(inverse(X_46))))) )],[refute_0_540,refute_0_541]) ).
cnf(refute_0_543,plain,
inverse(least_upper_bound(X_326,inverse(inverse(X_46)))) = inverse(least_upper_bound(X_326,X_46)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_326,inverse(inverse(X_46))),least_upper_bound(X_326,X_46)) )],[refute_0_539,refute_0_542]) ).
cnf(refute_0_544,plain,
inverse(least_upper_bound(X_280,inverse(X_92))) = multiply(X_92,multiply(inverse(X_92),inverse(least_upper_bound(X_280,inverse(X_92))))),
inference(subst,[],[refute_0_419:[bind(X_94,$fot(inverse(least_upper_bound(X_280,inverse(X_92)))))]]) ).
cnf(refute_0_545,plain,
inverse(multiply(least_upper_bound(X_66,inverse(inverse(X_99))),inverse(X_99))) = multiply(X_99,inverse(least_upper_bound(X_66,inverse(inverse(X_99))))),
inference(subst,[],[refute_0_114:[bind(X,$fot(X_99)),bind(X_32,$fot(least_upper_bound(X_66,inverse(inverse(X_99)))))]]) ).
cnf(refute_0_546,plain,
multiply(least_upper_bound(X_66,inverse(inverse(X_99))),inverse(X_99)) = least_upper_bound(identity,multiply(X_66,inverse(X_99))),
inference(subst,[],[refute_0_27:[bind(X_65,$fot(inverse(X_99)))]]) ).
cnf(refute_0_547,plain,
( multiply(least_upper_bound(X_66,inverse(inverse(X_99))),inverse(X_99)) != least_upper_bound(identity,multiply(X_66,inverse(X_99)))
| inverse(multiply(least_upper_bound(X_66,inverse(inverse(X_99))),inverse(X_99))) != multiply(X_99,inverse(least_upper_bound(X_66,inverse(inverse(X_99)))))
| inverse(least_upper_bound(identity,multiply(X_66,inverse(X_99)))) = multiply(X_99,inverse(least_upper_bound(X_66,inverse(inverse(X_99))))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(least_upper_bound(X_66,inverse(inverse(X_99))),inverse(X_99))),multiply(X_99,inverse(least_upper_bound(X_66,inverse(inverse(X_99)))))) ),[0,0],$fot(least_upper_bound(identity,multiply(X_66,inverse(X_99))))]]) ).
cnf(refute_0_548,plain,
( inverse(multiply(least_upper_bound(X_66,inverse(inverse(X_99))),inverse(X_99))) != multiply(X_99,inverse(least_upper_bound(X_66,inverse(inverse(X_99)))))
| inverse(least_upper_bound(identity,multiply(X_66,inverse(X_99)))) = multiply(X_99,inverse(least_upper_bound(X_66,inverse(inverse(X_99))))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_66,inverse(inverse(X_99))),inverse(X_99)),least_upper_bound(identity,multiply(X_66,inverse(X_99)))) )],[refute_0_546,refute_0_547]) ).
cnf(refute_0_549,plain,
inverse(least_upper_bound(identity,multiply(X_66,inverse(X_99)))) = multiply(X_99,inverse(least_upper_bound(X_66,inverse(inverse(X_99))))),
inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(X_66,inverse(inverse(X_99))),inverse(X_99))),multiply(X_99,inverse(least_upper_bound(X_66,inverse(inverse(X_99)))))) )],[refute_0_545,refute_0_548]) ).
cnf(refute_0_550,plain,
least_upper_bound(X_66,inverse(inverse(X_99))) = least_upper_bound(X_66,inverse(inverse(X_99))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_66,inverse(inverse(X_99))))]]) ).
cnf(refute_0_551,plain,
( inverse(inverse(X_99)) != X_99
| least_upper_bound(X_66,inverse(inverse(X_99))) != least_upper_bound(X_66,inverse(inverse(X_99)))
| least_upper_bound(X_66,inverse(inverse(X_99))) = least_upper_bound(X_66,X_99) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_66,inverse(inverse(X_99))),least_upper_bound(X_66,inverse(inverse(X_99)))) ),[1,1],$fot(X_99)]]) ).
cnf(refute_0_552,plain,
( inverse(inverse(X_99)) != X_99
| least_upper_bound(X_66,inverse(inverse(X_99))) = least_upper_bound(X_66,X_99) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_66,inverse(inverse(X_99))),least_upper_bound(X_66,inverse(inverse(X_99)))) )],[refute_0_550,refute_0_551]) ).
cnf(refute_0_553,plain,
least_upper_bound(X_66,inverse(inverse(X_99))) = least_upper_bound(X_66,X_99),
inference(resolve,[$cnf( $equal(inverse(inverse(X_99)),X_99) )],[refute_0_131,refute_0_552]) ).
cnf(refute_0_554,plain,
inverse(least_upper_bound(X_66,inverse(inverse(X_99)))) = inverse(least_upper_bound(X_66,inverse(inverse(X_99)))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(X_66,inverse(inverse(X_99)))))]]) ).
cnf(refute_0_555,plain,
( inverse(least_upper_bound(X_66,inverse(inverse(X_99)))) != inverse(least_upper_bound(X_66,inverse(inverse(X_99))))
| least_upper_bound(X_66,inverse(inverse(X_99))) != least_upper_bound(X_66,X_99)
| inverse(least_upper_bound(X_66,inverse(inverse(X_99)))) = inverse(least_upper_bound(X_66,X_99)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_66,inverse(inverse(X_99)))),inverse(least_upper_bound(X_66,inverse(inverse(X_99))))) ),[1,0],$fot(least_upper_bound(X_66,X_99))]]) ).
cnf(refute_0_556,plain,
( least_upper_bound(X_66,inverse(inverse(X_99))) != least_upper_bound(X_66,X_99)
| inverse(least_upper_bound(X_66,inverse(inverse(X_99)))) = inverse(least_upper_bound(X_66,X_99)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_66,inverse(inverse(X_99)))),inverse(least_upper_bound(X_66,inverse(inverse(X_99))))) )],[refute_0_554,refute_0_555]) ).
cnf(refute_0_557,plain,
inverse(least_upper_bound(X_66,inverse(inverse(X_99)))) = inverse(least_upper_bound(X_66,X_99)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_66,inverse(inverse(X_99))),least_upper_bound(X_66,X_99)) )],[refute_0_553,refute_0_556]) ).
cnf(refute_0_558,plain,
multiply(X_99,inverse(least_upper_bound(X_66,inverse(inverse(X_99))))) = multiply(X_99,inverse(least_upper_bound(X_66,inverse(inverse(X_99))))),
introduced(tautology,[refl,[$fot(multiply(X_99,inverse(least_upper_bound(X_66,inverse(inverse(X_99))))))]]) ).
cnf(refute_0_559,plain,
( multiply(X_99,inverse(least_upper_bound(X_66,inverse(inverse(X_99))))) != multiply(X_99,inverse(least_upper_bound(X_66,inverse(inverse(X_99)))))
| inverse(least_upper_bound(X_66,inverse(inverse(X_99)))) != inverse(least_upper_bound(X_66,X_99))
| multiply(X_99,inverse(least_upper_bound(X_66,inverse(inverse(X_99))))) = multiply(X_99,inverse(least_upper_bound(X_66,X_99))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_99,inverse(least_upper_bound(X_66,inverse(inverse(X_99))))),multiply(X_99,inverse(least_upper_bound(X_66,inverse(inverse(X_99)))))) ),[1,1],$fot(inverse(least_upper_bound(X_66,X_99)))]]) ).
cnf(refute_0_560,plain,
( inverse(least_upper_bound(X_66,inverse(inverse(X_99)))) != inverse(least_upper_bound(X_66,X_99))
| multiply(X_99,inverse(least_upper_bound(X_66,inverse(inverse(X_99))))) = multiply(X_99,inverse(least_upper_bound(X_66,X_99))) ),
inference(resolve,[$cnf( $equal(multiply(X_99,inverse(least_upper_bound(X_66,inverse(inverse(X_99))))),multiply(X_99,inverse(least_upper_bound(X_66,inverse(inverse(X_99)))))) )],[refute_0_558,refute_0_559]) ).
cnf(refute_0_561,plain,
multiply(X_99,inverse(least_upper_bound(X_66,inverse(inverse(X_99))))) = multiply(X_99,inverse(least_upper_bound(X_66,X_99))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_66,inverse(inverse(X_99)))),inverse(least_upper_bound(X_66,X_99))) )],[refute_0_557,refute_0_560]) ).
cnf(refute_0_562,plain,
( multiply(X_99,inverse(least_upper_bound(X_66,inverse(inverse(X_99))))) != multiply(X_99,inverse(least_upper_bound(X_66,X_99)))
| inverse(least_upper_bound(identity,multiply(X_66,inverse(X_99)))) != multiply(X_99,inverse(least_upper_bound(X_66,inverse(inverse(X_99)))))
| inverse(least_upper_bound(identity,multiply(X_66,inverse(X_99)))) = multiply(X_99,inverse(least_upper_bound(X_66,X_99))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(X_66,inverse(X_99)))),multiply(X_99,inverse(least_upper_bound(X_66,inverse(inverse(X_99)))))) ),[1],$fot(multiply(X_99,inverse(least_upper_bound(X_66,X_99))))]]) ).
cnf(refute_0_563,plain,
( inverse(least_upper_bound(identity,multiply(X_66,inverse(X_99)))) != multiply(X_99,inverse(least_upper_bound(X_66,inverse(inverse(X_99)))))
| inverse(least_upper_bound(identity,multiply(X_66,inverse(X_99)))) = multiply(X_99,inverse(least_upper_bound(X_66,X_99))) ),
inference(resolve,[$cnf( $equal(multiply(X_99,inverse(least_upper_bound(X_66,inverse(inverse(X_99))))),multiply(X_99,inverse(least_upper_bound(X_66,X_99)))) )],[refute_0_561,refute_0_562]) ).
cnf(refute_0_564,plain,
inverse(least_upper_bound(identity,multiply(X_66,inverse(X_99)))) = multiply(X_99,inverse(least_upper_bound(X_66,X_99))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(X_66,inverse(X_99)))),multiply(X_99,inverse(least_upper_bound(X_66,inverse(inverse(X_99)))))) )],[refute_0_549,refute_0_563]) ).
cnf(refute_0_565,plain,
inverse(least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92))))) = multiply(inverse(X_92),inverse(least_upper_bound(X_280,inverse(X_92)))),
inference(subst,[],[refute_0_564:[bind(X_66,$fot(X_280)),bind(X_99,$fot(inverse(X_92)))]]) ).
cnf(refute_0_566,plain,
( inverse(least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92))))) != multiply(inverse(X_92),inverse(least_upper_bound(X_280,inverse(X_92))))
| multiply(inverse(X_92),inverse(least_upper_bound(X_280,inverse(X_92)))) = inverse(least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92))))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92))))))),bind(Y0,$fot(multiply(inverse(X_92),inverse(least_upper_bound(X_280,inverse(X_92))))))]]) ).
cnf(refute_0_567,plain,
multiply(inverse(X_92),inverse(least_upper_bound(X_280,inverse(X_92)))) = inverse(least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92))))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92))))),multiply(inverse(X_92),inverse(least_upper_bound(X_280,inverse(X_92))))) )],[refute_0_565,refute_0_566]) ).
cnf(refute_0_568,plain,
( multiply(inverse(X_92),inverse(least_upper_bound(X_280,inverse(X_92)))) != inverse(least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92)))))
| inverse(least_upper_bound(X_280,inverse(X_92))) != multiply(X_92,multiply(inverse(X_92),inverse(least_upper_bound(X_280,inverse(X_92)))))
| inverse(least_upper_bound(X_280,inverse(X_92))) = multiply(X_92,inverse(least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92)))))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_280,inverse(X_92))),multiply(X_92,multiply(inverse(X_92),inverse(least_upper_bound(X_280,inverse(X_92)))))) ),[1,1],$fot(inverse(least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92))))))]]) ).
cnf(refute_0_569,plain,
( inverse(least_upper_bound(X_280,inverse(X_92))) != multiply(X_92,multiply(inverse(X_92),inverse(least_upper_bound(X_280,inverse(X_92)))))
| inverse(least_upper_bound(X_280,inverse(X_92))) = multiply(X_92,inverse(least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92)))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_92),inverse(least_upper_bound(X_280,inverse(X_92)))),inverse(least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92)))))) )],[refute_0_567,refute_0_568]) ).
cnf(refute_0_570,plain,
inverse(least_upper_bound(X_280,inverse(X_92))) = multiply(X_92,inverse(least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92)))))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_280,inverse(X_92))),multiply(X_92,multiply(inverse(X_92),inverse(least_upper_bound(X_280,inverse(X_92)))))) )],[refute_0_544,refute_0_569]) ).
cnf(refute_0_571,plain,
inverse(inverse(X_92)) = X_92,
inference(subst,[],[p18_2:[bind(X,$fot(X_92))]]) ).
cnf(refute_0_572,plain,
multiply(X_280,inverse(inverse(X_92))) = multiply(X_280,inverse(inverse(X_92))),
introduced(tautology,[refl,[$fot(multiply(X_280,inverse(inverse(X_92))))]]) ).
cnf(refute_0_573,plain,
( multiply(X_280,inverse(inverse(X_92))) != multiply(X_280,inverse(inverse(X_92)))
| inverse(inverse(X_92)) != X_92
| multiply(X_280,inverse(inverse(X_92))) = multiply(X_280,X_92) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_280,inverse(inverse(X_92))),multiply(X_280,inverse(inverse(X_92)))) ),[1,1],$fot(X_92)]]) ).
cnf(refute_0_574,plain,
( inverse(inverse(X_92)) != X_92
| multiply(X_280,inverse(inverse(X_92))) = multiply(X_280,X_92) ),
inference(resolve,[$cnf( $equal(multiply(X_280,inverse(inverse(X_92))),multiply(X_280,inverse(inverse(X_92)))) )],[refute_0_572,refute_0_573]) ).
cnf(refute_0_575,plain,
multiply(X_280,inverse(inverse(X_92))) = multiply(X_280,X_92),
inference(resolve,[$cnf( $equal(inverse(inverse(X_92)),X_92) )],[refute_0_571,refute_0_574]) ).
cnf(refute_0_576,plain,
least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92)))) = least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92)))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92)))))]]) ).
cnf(refute_0_577,plain,
( multiply(X_280,inverse(inverse(X_92))) != multiply(X_280,X_92)
| least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92)))) != least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92))))
| least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92)))) = least_upper_bound(identity,multiply(X_280,X_92)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92)))),least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92))))) ),[1,1],$fot(multiply(X_280,X_92))]]) ).
cnf(refute_0_578,plain,
( multiply(X_280,inverse(inverse(X_92))) != multiply(X_280,X_92)
| least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92)))) = least_upper_bound(identity,multiply(X_280,X_92)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92)))),least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92))))) )],[refute_0_576,refute_0_577]) ).
cnf(refute_0_579,plain,
least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92)))) = least_upper_bound(identity,multiply(X_280,X_92)),
inference(resolve,[$cnf( $equal(multiply(X_280,inverse(inverse(X_92))),multiply(X_280,X_92)) )],[refute_0_575,refute_0_578]) ).
cnf(refute_0_580,plain,
inverse(least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92))))) = inverse(least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92))))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92))))))]]) ).
cnf(refute_0_581,plain,
( inverse(least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92))))) != inverse(least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92)))))
| least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92)))) != least_upper_bound(identity,multiply(X_280,X_92))
| inverse(least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92))))) = inverse(least_upper_bound(identity,multiply(X_280,X_92))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92))))),inverse(least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92)))))) ),[1,0],$fot(least_upper_bound(identity,multiply(X_280,X_92)))]]) ).
cnf(refute_0_582,plain,
( least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92)))) != least_upper_bound(identity,multiply(X_280,X_92))
| inverse(least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92))))) = inverse(least_upper_bound(identity,multiply(X_280,X_92))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92))))),inverse(least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92)))))) )],[refute_0_580,refute_0_581]) ).
cnf(refute_0_583,plain,
inverse(least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92))))) = inverse(least_upper_bound(identity,multiply(X_280,X_92))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92)))),least_upper_bound(identity,multiply(X_280,X_92))) )],[refute_0_579,refute_0_582]) ).
cnf(refute_0_584,plain,
multiply(X_92,inverse(least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92)))))) = multiply(X_92,inverse(least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92)))))),
introduced(tautology,[refl,[$fot(multiply(X_92,inverse(least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92)))))))]]) ).
cnf(refute_0_585,plain,
( multiply(X_92,inverse(least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92)))))) != multiply(X_92,inverse(least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92))))))
| inverse(least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92))))) != inverse(least_upper_bound(identity,multiply(X_280,X_92)))
| multiply(X_92,inverse(least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92)))))) = multiply(X_92,inverse(least_upper_bound(identity,multiply(X_280,X_92)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_92,inverse(least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92)))))),multiply(X_92,inverse(least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92))))))) ),[1,1],$fot(inverse(least_upper_bound(identity,multiply(X_280,X_92))))]]) ).
cnf(refute_0_586,plain,
( inverse(least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92))))) != inverse(least_upper_bound(identity,multiply(X_280,X_92)))
| multiply(X_92,inverse(least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92)))))) = multiply(X_92,inverse(least_upper_bound(identity,multiply(X_280,X_92)))) ),
inference(resolve,[$cnf( $equal(multiply(X_92,inverse(least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92)))))),multiply(X_92,inverse(least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92))))))) )],[refute_0_584,refute_0_585]) ).
cnf(refute_0_587,plain,
multiply(X_92,inverse(least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92)))))) = multiply(X_92,inverse(least_upper_bound(identity,multiply(X_280,X_92)))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92))))),inverse(least_upper_bound(identity,multiply(X_280,X_92)))) )],[refute_0_583,refute_0_586]) ).
cnf(refute_0_588,plain,
( multiply(X_92,inverse(least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92)))))) != multiply(X_92,inverse(least_upper_bound(identity,multiply(X_280,X_92))))
| inverse(least_upper_bound(X_280,inverse(X_92))) != multiply(X_92,inverse(least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92))))))
| inverse(least_upper_bound(X_280,inverse(X_92))) = multiply(X_92,inverse(least_upper_bound(identity,multiply(X_280,X_92)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_280,inverse(X_92))),multiply(X_92,inverse(least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92))))))) ),[1],$fot(multiply(X_92,inverse(least_upper_bound(identity,multiply(X_280,X_92)))))]]) ).
cnf(refute_0_589,plain,
( inverse(least_upper_bound(X_280,inverse(X_92))) != multiply(X_92,inverse(least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92))))))
| inverse(least_upper_bound(X_280,inverse(X_92))) = multiply(X_92,inverse(least_upper_bound(identity,multiply(X_280,X_92)))) ),
inference(resolve,[$cnf( $equal(multiply(X_92,inverse(least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92)))))),multiply(X_92,inverse(least_upper_bound(identity,multiply(X_280,X_92))))) )],[refute_0_587,refute_0_588]) ).
cnf(refute_0_590,plain,
inverse(least_upper_bound(X_280,inverse(X_92))) = multiply(X_92,inverse(least_upper_bound(identity,multiply(X_280,X_92)))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_280,inverse(X_92))),multiply(X_92,inverse(least_upper_bound(identity,multiply(X_280,inverse(inverse(X_92))))))) )],[refute_0_570,refute_0_589]) ).
cnf(refute_0_591,plain,
( inverse(least_upper_bound(X_280,inverse(X_92))) != multiply(X_92,inverse(least_upper_bound(identity,multiply(X_280,X_92))))
| multiply(X_92,inverse(least_upper_bound(identity,multiply(X_280,X_92)))) = inverse(least_upper_bound(X_280,inverse(X_92))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(least_upper_bound(X_280,inverse(X_92))))),bind(Y0,$fot(multiply(X_92,inverse(least_upper_bound(identity,multiply(X_280,X_92))))))]]) ).
cnf(refute_0_592,plain,
multiply(X_92,inverse(least_upper_bound(identity,multiply(X_280,X_92)))) = inverse(least_upper_bound(X_280,inverse(X_92))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_280,inverse(X_92))),multiply(X_92,inverse(least_upper_bound(identity,multiply(X_280,X_92))))) )],[refute_0_590,refute_0_591]) ).
cnf(refute_0_593,plain,
multiply(inverse(X_46),inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46))))) = inverse(least_upper_bound(X_326,inverse(inverse(X_46)))),
inference(subst,[],[refute_0_592:[bind(X_280,$fot(X_326)),bind(X_92,$fot(inverse(X_46)))]]) ).
cnf(refute_0_594,plain,
( multiply(inverse(X_46),inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46))))) != inverse(least_upper_bound(X_326,inverse(inverse(X_46))))
| inverse(least_upper_bound(X_326,inverse(inverse(X_46)))) != inverse(least_upper_bound(X_326,X_46))
| multiply(inverse(X_46),inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46))))) = inverse(least_upper_bound(X_326,X_46)) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(multiply(inverse(X_46),inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46))))))),bind(Y0,$fot(inverse(least_upper_bound(X_326,inverse(inverse(X_46)))))),bind(Z0,$fot(inverse(least_upper_bound(X_326,X_46))))]]) ).
cnf(refute_0_595,plain,
( inverse(least_upper_bound(X_326,inverse(inverse(X_46)))) != inverse(least_upper_bound(X_326,X_46))
| multiply(inverse(X_46),inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46))))) = inverse(least_upper_bound(X_326,X_46)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_46),inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46))))),inverse(least_upper_bound(X_326,inverse(inverse(X_46))))) )],[refute_0_593,refute_0_594]) ).
cnf(refute_0_596,plain,
multiply(inverse(X_46),inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46))))) = inverse(least_upper_bound(X_326,X_46)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_326,inverse(inverse(X_46)))),inverse(least_upper_bound(X_326,X_46))) )],[refute_0_543,refute_0_595]) ).
cnf(refute_0_597,plain,
multiply(inverse(least_upper_bound(identity,Y)),greatest_lower_bound(identity,least_upper_bound(identity,Y))) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y))),
inference(subst,[],[refute_0_469:[bind(X_51,$fot(least_upper_bound(identity,Y)))]]) ).
cnf(refute_0_598,plain,
greatest_lower_bound(identity,least_upper_bound(identity,Y)) = identity,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(identity))]]) ).
cnf(refute_0_599,plain,
( multiply(inverse(least_upper_bound(identity,Y)),greatest_lower_bound(identity,least_upper_bound(identity,Y))) != greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y)))
| greatest_lower_bound(identity,least_upper_bound(identity,Y)) != identity
| multiply(inverse(least_upper_bound(identity,Y)),identity) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,Y)),greatest_lower_bound(identity,least_upper_bound(identity,Y))),greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y)))) ),[0,1],$fot(identity)]]) ).
cnf(refute_0_600,plain,
( multiply(inverse(least_upper_bound(identity,Y)),greatest_lower_bound(identity,least_upper_bound(identity,Y))) != greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y)))
| multiply(inverse(least_upper_bound(identity,Y)),identity) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(identity,Y)),identity) )],[refute_0_598,refute_0_599]) ).
cnf(refute_0_601,plain,
multiply(inverse(least_upper_bound(identity,Y)),identity) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,Y)),greatest_lower_bound(identity,least_upper_bound(identity,Y))),greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y)))) )],[refute_0_597,refute_0_600]) ).
cnf(refute_0_602,plain,
( X != multiply(X,identity)
| multiply(X,identity) = X ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X)),bind(Y0,$fot(multiply(X,identity)))]]) ).
cnf(refute_0_603,plain,
multiply(X,identity) = X,
inference(resolve,[$cnf( $equal(X,multiply(X,identity)) )],[refute_0_210,refute_0_602]) ).
cnf(refute_0_604,plain,
multiply(inverse(least_upper_bound(identity,Y)),identity) = inverse(least_upper_bound(identity,Y)),
inference(subst,[],[refute_0_603:[bind(X,$fot(inverse(least_upper_bound(identity,Y))))]]) ).
cnf(refute_0_605,plain,
( multiply(inverse(least_upper_bound(identity,Y)),identity) != greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y)))
| multiply(inverse(least_upper_bound(identity,Y)),identity) != inverse(least_upper_bound(identity,Y))
| inverse(least_upper_bound(identity,Y)) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,Y)),identity),greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y)))) ),[0],$fot(inverse(least_upper_bound(identity,Y)))]]) ).
cnf(refute_0_606,plain,
( multiply(inverse(least_upper_bound(identity,Y)),identity) != greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y)))
| inverse(least_upper_bound(identity,Y)) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,Y)),identity),inverse(least_upper_bound(identity,Y))) )],[refute_0_604,refute_0_605]) ).
cnf(refute_0_607,plain,
inverse(least_upper_bound(identity,Y)) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,Y)),identity),greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y)))) )],[refute_0_601,refute_0_606]) ).
cnf(refute_0_608,plain,
( inverse(least_upper_bound(identity,Y)) != greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y)))
| greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y))) = inverse(least_upper_bound(identity,Y)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(least_upper_bound(identity,Y)))),bind(Y0,$fot(greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y)))))]]) ).
cnf(refute_0_609,plain,
greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y))) = inverse(least_upper_bound(identity,Y)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,Y)),greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y)))) )],[refute_0_607,refute_0_608]) ).
cnf(refute_0_610,plain,
greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46))))) = inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46)))),
inference(subst,[],[refute_0_609:[bind(Y,$fot(multiply(X_326,inverse(X_46))))]]) ).
cnf(refute_0_611,plain,
multiply(inverse(X_46),greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46)))))) = multiply(inverse(X_46),greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46)))))),
introduced(tautology,[refl,[$fot(multiply(inverse(X_46),greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46)))))))]]) ).
cnf(refute_0_612,plain,
( multiply(inverse(X_46),greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46)))))) != multiply(inverse(X_46),greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46))))))
| greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46))))) != inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46))))
| multiply(inverse(X_46),greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46)))))) = multiply(inverse(X_46),inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_46),greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46)))))),multiply(inverse(X_46),greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46))))))) ),[1,1],$fot(inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46)))))]]) ).
cnf(refute_0_613,plain,
( greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46))))) != inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46))))
| multiply(inverse(X_46),greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46)))))) = multiply(inverse(X_46),inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_46),greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46)))))),multiply(inverse(X_46),greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46))))))) )],[refute_0_611,refute_0_612]) ).
cnf(refute_0_614,plain,
multiply(inverse(X_46),greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46)))))) = multiply(inverse(X_46),inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46))))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46))))),inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46))))) )],[refute_0_610,refute_0_613]) ).
cnf(refute_0_615,plain,
greatest_lower_bound(X_46,least_upper_bound(X_46,X_326)) = X_46,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_46)),bind(Y,$fot(X_326))]]) ).
cnf(refute_0_616,plain,
inverse(inverse(least_upper_bound(X_46,X_326))) = least_upper_bound(X_46,X_326),
inference(subst,[],[p18_2:[bind(X,$fot(least_upper_bound(X_46,X_326)))]]) ).
cnf(refute_0_617,plain,
greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326)))) = greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326)))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326)))))]]) ).
cnf(refute_0_618,plain,
( greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326)))) != greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326))))
| inverse(inverse(least_upper_bound(X_46,X_326))) != least_upper_bound(X_46,X_326)
| greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326)))) = greatest_lower_bound(X_46,least_upper_bound(X_46,X_326)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326)))),greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326))))) ),[1,1],$fot(least_upper_bound(X_46,X_326))]]) ).
cnf(refute_0_619,plain,
( inverse(inverse(least_upper_bound(X_46,X_326))) != least_upper_bound(X_46,X_326)
| greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326)))) = greatest_lower_bound(X_46,least_upper_bound(X_46,X_326)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326)))),greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326))))) )],[refute_0_617,refute_0_618]) ).
cnf(refute_0_620,plain,
greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326)))) = greatest_lower_bound(X_46,least_upper_bound(X_46,X_326)),
inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(X_46,X_326))),least_upper_bound(X_46,X_326)) )],[refute_0_616,refute_0_619]) ).
cnf(refute_0_621,plain,
( greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326)))) != greatest_lower_bound(X_46,least_upper_bound(X_46,X_326))
| greatest_lower_bound(X_46,least_upper_bound(X_46,X_326)) != X_46
| greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326)))) = X_46 ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326)))))),bind(Y0,$fot(greatest_lower_bound(X_46,least_upper_bound(X_46,X_326)))),bind(Z0,$fot(X_46))]]) ).
cnf(refute_0_622,plain,
( greatest_lower_bound(X_46,least_upper_bound(X_46,X_326)) != X_46
| greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326)))) = X_46 ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326)))),greatest_lower_bound(X_46,least_upper_bound(X_46,X_326))) )],[refute_0_620,refute_0_621]) ).
cnf(refute_0_623,plain,
greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326)))) = X_46,
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_46,least_upper_bound(X_46,X_326)),X_46) )],[refute_0_615,refute_0_622]) ).
cnf(refute_0_624,plain,
inverse(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326))))) = inverse(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326))))),
introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326))))))]]) ).
cnf(refute_0_625,plain,
( greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326)))) != X_46
| inverse(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326))))) != inverse(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326)))))
| inverse(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326))))) = inverse(X_46) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326))))),inverse(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326)))))) ),[1,0],$fot(X_46)]]) ).
cnf(refute_0_626,plain,
( greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326)))) != X_46
| inverse(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326))))) = inverse(X_46) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326))))),inverse(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326)))))) )],[refute_0_624,refute_0_625]) ).
cnf(refute_0_627,plain,
inverse(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326))))) = inverse(X_46),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326)))),X_46) )],[refute_0_623,refute_0_626]) ).
cnf(refute_0_628,plain,
multiply(inverse(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326))))),greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46)))))) = multiply(inverse(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326))))),greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46)))))),
introduced(tautology,[refl,[$fot(multiply(inverse(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326))))),greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46)))))))]]) ).
cnf(refute_0_629,plain,
( multiply(inverse(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326))))),greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46)))))) != multiply(inverse(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326))))),greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46))))))
| inverse(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326))))) != inverse(X_46)
| multiply(inverse(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326))))),greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46)))))) = multiply(inverse(X_46),greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46)))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326))))),greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46)))))),multiply(inverse(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326))))),greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46))))))) ),[1,0],$fot(inverse(X_46))]]) ).
cnf(refute_0_630,plain,
( inverse(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326))))) != inverse(X_46)
| multiply(inverse(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326))))),greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46)))))) = multiply(inverse(X_46),greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46)))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326))))),greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46)))))),multiply(inverse(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326))))),greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46))))))) )],[refute_0_628,refute_0_629]) ).
cnf(refute_0_631,plain,
multiply(inverse(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326))))),greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46)))))) = multiply(inverse(X_46),greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46)))))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326))))),inverse(X_46)) )],[refute_0_627,refute_0_630]) ).
cnf(refute_0_632,plain,
( multiply(inverse(X_46),greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46)))))) != multiply(inverse(X_46),inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46)))))
| multiply(inverse(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326))))),greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46)))))) != multiply(inverse(X_46),greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46))))))
| multiply(inverse(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326))))),greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46)))))) = multiply(inverse(X_46),inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46))))) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326))))),greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46)))))))),bind(Y0,$fot(multiply(inverse(X_46),greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46)))))))),bind(Z0,$fot(multiply(inverse(X_46),inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46)))))))]]) ).
cnf(refute_0_633,plain,
( multiply(inverse(X_46),greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46)))))) != multiply(inverse(X_46),inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46)))))
| multiply(inverse(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326))))),greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46)))))) = multiply(inverse(X_46),inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326))))),greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46)))))),multiply(inverse(X_46),greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46))))))) )],[refute_0_631,refute_0_632]) ).
cnf(refute_0_634,plain,
multiply(inverse(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326))))),greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46)))))) = multiply(inverse(X_46),inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46))))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_46),greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46)))))),multiply(inverse(X_46),inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46)))))) )],[refute_0_614,refute_0_633]) ).
cnf(refute_0_635,plain,
( multiply(inverse(X_46),inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46))))) != inverse(least_upper_bound(X_326,X_46))
| multiply(inverse(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326))))),greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46)))))) != multiply(inverse(X_46),inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46)))))
| multiply(inverse(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326))))),greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46)))))) = inverse(least_upper_bound(X_326,X_46)) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326))))),greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46)))))))),bind(Y0,$fot(multiply(inverse(X_46),inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46))))))),bind(Z0,$fot(inverse(least_upper_bound(X_326,X_46))))]]) ).
cnf(refute_0_636,plain,
( multiply(inverse(X_46),inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46))))) != inverse(least_upper_bound(X_326,X_46))
| multiply(inverse(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326))))),greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46)))))) = inverse(least_upper_bound(X_326,X_46)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326))))),greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46)))))),multiply(inverse(X_46),inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46)))))) )],[refute_0_634,refute_0_635]) ).
cnf(refute_0_637,plain,
multiply(inverse(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326))))),greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46)))))) = inverse(least_upper_bound(X_326,X_46)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_46),inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46))))),inverse(least_upper_bound(X_326,X_46))) )],[refute_0_596,refute_0_636]) ).
cnf(refute_0_638,plain,
( multiply(inverse(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326))))),greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46)))))) != inverse(least_upper_bound(X_326,X_46))
| inverse(least_upper_bound(X_46,X_326)) != multiply(inverse(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326))))),greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46))))))
| inverse(least_upper_bound(X_46,X_326)) = inverse(least_upper_bound(X_326,X_46)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_46,X_326)),multiply(inverse(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326))))),greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46))))))) ),[1],$fot(inverse(least_upper_bound(X_326,X_46)))]]) ).
cnf(refute_0_639,plain,
( inverse(least_upper_bound(X_46,X_326)) != multiply(inverse(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326))))),greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46))))))
| inverse(least_upper_bound(X_46,X_326)) = inverse(least_upper_bound(X_326,X_46)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326))))),greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46)))))),inverse(least_upper_bound(X_326,X_46))) )],[refute_0_637,refute_0_638]) ).
cnf(refute_0_640,plain,
inverse(least_upper_bound(X_46,X_326)) = inverse(least_upper_bound(X_326,X_46)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_46,X_326)),multiply(inverse(greatest_lower_bound(X_46,inverse(inverse(least_upper_bound(X_46,X_326))))),greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(X_326,inverse(X_46))))))) )],[refute_0_534,refute_0_639]) ).
cnf(refute_0_641,plain,
( inverse(least_upper_bound(X_46,X_326)) != inverse(least_upper_bound(X_326,X_46))
| inverse(least_upper_bound(X_326,X_46)) = inverse(least_upper_bound(X_46,X_326)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(least_upper_bound(X_46,X_326)))),bind(Y0,$fot(inverse(least_upper_bound(X_326,X_46))))]]) ).
cnf(refute_0_642,plain,
inverse(least_upper_bound(X_326,X_46)) = inverse(least_upper_bound(X_46,X_326)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_46,X_326)),inverse(least_upper_bound(X_326,X_46))) )],[refute_0_640,refute_0_641]) ).
cnf(refute_0_643,plain,
inverse(least_upper_bound(greatest_lower_bound(X_394,X_152),X_394)) = inverse(least_upper_bound(X_394,greatest_lower_bound(X_394,X_152))),
inference(subst,[],[refute_0_642:[bind(X_326,$fot(greatest_lower_bound(X_394,X_152))),bind(X_46,$fot(X_394))]]) ).
cnf(refute_0_644,plain,
( inverse(least_upper_bound(X_394,greatest_lower_bound(X_394,X_152))) != inverse(X_394)
| inverse(least_upper_bound(greatest_lower_bound(X_394,X_152),X_394)) != inverse(least_upper_bound(X_394,greatest_lower_bound(X_394,X_152)))
| inverse(least_upper_bound(greatest_lower_bound(X_394,X_152),X_394)) = inverse(X_394) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(inverse(least_upper_bound(greatest_lower_bound(X_394,X_152),X_394)))),bind(Y0,$fot(inverse(least_upper_bound(X_394,greatest_lower_bound(X_394,X_152))))),bind(Z0,$fot(inverse(X_394)))]]) ).
cnf(refute_0_645,plain,
( inverse(least_upper_bound(X_394,greatest_lower_bound(X_394,X_152))) != inverse(X_394)
| inverse(least_upper_bound(greatest_lower_bound(X_394,X_152),X_394)) = inverse(X_394) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(greatest_lower_bound(X_394,X_152),X_394)),inverse(least_upper_bound(X_394,greatest_lower_bound(X_394,X_152)))) )],[refute_0_643,refute_0_644]) ).
cnf(refute_0_646,plain,
inverse(least_upper_bound(greatest_lower_bound(X_394,X_152),X_394)) = inverse(X_394),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_394,greatest_lower_bound(X_394,X_152))),inverse(X_394)) )],[refute_0_498,refute_0_645]) ).
cnf(refute_0_647,plain,
multiply(inverse(least_upper_bound(greatest_lower_bound(X_394,X_152),X_394)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394)))))) = multiply(inverse(least_upper_bound(greatest_lower_bound(X_394,X_152),X_394)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394)))))),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(greatest_lower_bound(X_394,X_152),X_394)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394)))))))]]) ).
cnf(refute_0_648,plain,
( multiply(inverse(least_upper_bound(greatest_lower_bound(X_394,X_152),X_394)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394)))))) != multiply(inverse(least_upper_bound(greatest_lower_bound(X_394,X_152),X_394)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394))))))
| inverse(least_upper_bound(greatest_lower_bound(X_394,X_152),X_394)) != inverse(X_394)
| multiply(inverse(least_upper_bound(greatest_lower_bound(X_394,X_152),X_394)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394)))))) = multiply(inverse(X_394),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394)))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(greatest_lower_bound(X_394,X_152),X_394)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394)))))),multiply(inverse(least_upper_bound(greatest_lower_bound(X_394,X_152),X_394)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394))))))) ),[1,0],$fot(inverse(X_394))]]) ).
cnf(refute_0_649,plain,
( inverse(least_upper_bound(greatest_lower_bound(X_394,X_152),X_394)) != inverse(X_394)
| multiply(inverse(least_upper_bound(greatest_lower_bound(X_394,X_152),X_394)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394)))))) = multiply(inverse(X_394),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394)))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(greatest_lower_bound(X_394,X_152),X_394)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394)))))),multiply(inverse(least_upper_bound(greatest_lower_bound(X_394,X_152),X_394)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394))))))) )],[refute_0_647,refute_0_648]) ).
cnf(refute_0_650,plain,
multiply(inverse(least_upper_bound(greatest_lower_bound(X_394,X_152),X_394)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394)))))) = multiply(inverse(X_394),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394)))))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(greatest_lower_bound(X_394,X_152),X_394)),inverse(X_394)) )],[refute_0_646,refute_0_649]) ).
cnf(refute_0_651,plain,
( multiply(inverse(X_394),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394)))))) != multiply(inverse(X_394),inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394)))))
| multiply(inverse(least_upper_bound(greatest_lower_bound(X_394,X_152),X_394)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394)))))) != multiply(inverse(X_394),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394))))))
| multiply(inverse(least_upper_bound(greatest_lower_bound(X_394,X_152),X_394)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394)))))) = multiply(inverse(X_394),inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394))))) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(multiply(inverse(least_upper_bound(greatest_lower_bound(X_394,X_152),X_394)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394)))))))),bind(Y0,$fot(multiply(inverse(X_394),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394)))))))),bind(Z0,$fot(multiply(inverse(X_394),inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394)))))))]]) ).
cnf(refute_0_652,plain,
( multiply(inverse(X_394),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394)))))) != multiply(inverse(X_394),inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394)))))
| multiply(inverse(least_upper_bound(greatest_lower_bound(X_394,X_152),X_394)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394)))))) = multiply(inverse(X_394),inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(greatest_lower_bound(X_394,X_152),X_394)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394)))))),multiply(inverse(X_394),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394))))))) )],[refute_0_650,refute_0_651]) ).
cnf(refute_0_653,plain,
multiply(inverse(least_upper_bound(greatest_lower_bound(X_394,X_152),X_394)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394)))))) = multiply(inverse(X_394),inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394))))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_394),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394)))))),multiply(inverse(X_394),inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394)))))) )],[refute_0_493,refute_0_652]) ).
cnf(refute_0_654,plain,
( multiply(inverse(X_394),inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394))))) != inverse(greatest_lower_bound(X_152,X_394))
| multiply(inverse(least_upper_bound(greatest_lower_bound(X_394,X_152),X_394)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394)))))) != multiply(inverse(X_394),inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394)))))
| multiply(inverse(least_upper_bound(greatest_lower_bound(X_394,X_152),X_394)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394)))))) = inverse(greatest_lower_bound(X_152,X_394)) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(multiply(inverse(least_upper_bound(greatest_lower_bound(X_394,X_152),X_394)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394)))))))),bind(Y0,$fot(multiply(inverse(X_394),inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394))))))),bind(Z0,$fot(inverse(greatest_lower_bound(X_152,X_394))))]]) ).
cnf(refute_0_655,plain,
( multiply(inverse(X_394),inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394))))) != inverse(greatest_lower_bound(X_152,X_394))
| multiply(inverse(least_upper_bound(greatest_lower_bound(X_394,X_152),X_394)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394)))))) = inverse(greatest_lower_bound(X_152,X_394)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(greatest_lower_bound(X_394,X_152),X_394)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394)))))),multiply(inverse(X_394),inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394)))))) )],[refute_0_653,refute_0_654]) ).
cnf(refute_0_656,plain,
multiply(inverse(least_upper_bound(greatest_lower_bound(X_394,X_152),X_394)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394)))))) = inverse(greatest_lower_bound(X_152,X_394)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_394),inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394))))),inverse(greatest_lower_bound(X_152,X_394))) )],[refute_0_452,refute_0_655]) ).
cnf(refute_0_657,plain,
( multiply(inverse(least_upper_bound(greatest_lower_bound(X_394,X_152),X_394)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394)))))) != inverse(greatest_lower_bound(X_152,X_394))
| inverse(greatest_lower_bound(X_394,X_152)) != multiply(inverse(least_upper_bound(greatest_lower_bound(X_394,X_152),X_394)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394))))))
| inverse(greatest_lower_bound(X_394,X_152)) = inverse(greatest_lower_bound(X_152,X_394)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X_394,X_152)),multiply(inverse(least_upper_bound(greatest_lower_bound(X_394,X_152),X_394)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394))))))) ),[1],$fot(inverse(greatest_lower_bound(X_152,X_394)))]]) ).
cnf(refute_0_658,plain,
( inverse(greatest_lower_bound(X_394,X_152)) != multiply(inverse(least_upper_bound(greatest_lower_bound(X_394,X_152),X_394)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394))))))
| inverse(greatest_lower_bound(X_394,X_152)) = inverse(greatest_lower_bound(X_152,X_394)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(greatest_lower_bound(X_394,X_152),X_394)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394)))))),inverse(greatest_lower_bound(X_152,X_394))) )],[refute_0_656,refute_0_657]) ).
cnf(refute_0_659,plain,
inverse(greatest_lower_bound(X_394,X_152)) = inverse(greatest_lower_bound(X_152,X_394)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_394,X_152)),multiply(inverse(least_upper_bound(greatest_lower_bound(X_394,X_152),X_394)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_152,inverse(X_394))))))) )],[refute_0_402,refute_0_658]) ).
cnf(refute_0_660,plain,
( inverse(greatest_lower_bound(X_394,X_152)) != inverse(greatest_lower_bound(X_152,X_394))
| inverse(greatest_lower_bound(X_152,X_394)) = inverse(greatest_lower_bound(X_394,X_152)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(greatest_lower_bound(X_394,X_152)))),bind(Y0,$fot(inverse(greatest_lower_bound(X_152,X_394))))]]) ).
cnf(refute_0_661,plain,
inverse(greatest_lower_bound(X_152,X_394)) = inverse(greatest_lower_bound(X_394,X_152)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_394,X_152)),inverse(greatest_lower_bound(X_152,X_394))) )],[refute_0_659,refute_0_660]) ).
cnf(refute_0_662,plain,
inverse(greatest_lower_bound(identity,a)) = inverse(greatest_lower_bound(a,identity)),
inference(subst,[],[refute_0_661:[bind(X_152,$fot(identity)),bind(X_394,$fot(a))]]) ).
cnf(refute_0_663,plain,
inverse(greatest_lower_bound(identity,X_51)) = multiply(inverse(least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(identity,inverse(X_51)))),least_upper_bound(identity,multiply(greatest_lower_bound(identity,inverse(X_51)),inverse(greatest_lower_bound(identity,X_51))))),
inference(subst,[],[refute_0_109:[bind(X_220,$fot(greatest_lower_bound(identity,X_51))),bind(X_221,$fot(greatest_lower_bound(identity,inverse(X_51))))]]) ).
cnf(refute_0_664,plain,
multiply(least_upper_bound(X_66,identity),X_65) = least_upper_bound(multiply(X_66,X_65),multiply(identity,X_65)),
inference(subst,[],[monotony_lub2:[bind(X,$fot(X_65)),bind(Y,$fot(X_66)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_665,plain,
multiply(identity,X_65) = X_65,
inference(subst,[],[left_identity:[bind(X,$fot(X_65))]]) ).
cnf(refute_0_666,plain,
( multiply(identity,X_65) != X_65
| multiply(least_upper_bound(X_66,identity),X_65) != least_upper_bound(multiply(X_66,X_65),multiply(identity,X_65))
| multiply(least_upper_bound(X_66,identity),X_65) = least_upper_bound(multiply(X_66,X_65),X_65) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_66,identity),X_65),least_upper_bound(multiply(X_66,X_65),multiply(identity,X_65))) ),[1,1],$fot(X_65)]]) ).
cnf(refute_0_667,plain,
( multiply(least_upper_bound(X_66,identity),X_65) != least_upper_bound(multiply(X_66,X_65),multiply(identity,X_65))
| multiply(least_upper_bound(X_66,identity),X_65) = least_upper_bound(multiply(X_66,X_65),X_65) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_65),X_65) )],[refute_0_665,refute_0_666]) ).
cnf(refute_0_668,plain,
multiply(least_upper_bound(X_66,identity),X_65) = least_upper_bound(multiply(X_66,X_65),X_65),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_66,identity),X_65),least_upper_bound(multiply(X_66,X_65),multiply(identity,X_65))) )],[refute_0_664,refute_0_667]) ).
cnf(refute_0_669,plain,
least_upper_bound(multiply(X_66,X_65),X_65) = least_upper_bound(X_65,multiply(X_66,X_65)),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_65)),bind(Y,$fot(multiply(X_66,X_65)))]]) ).
cnf(refute_0_670,plain,
( multiply(least_upper_bound(X_66,identity),X_65) != least_upper_bound(multiply(X_66,X_65),X_65)
| least_upper_bound(multiply(X_66,X_65),X_65) != least_upper_bound(X_65,multiply(X_66,X_65))
| multiply(least_upper_bound(X_66,identity),X_65) = least_upper_bound(X_65,multiply(X_66,X_65)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_66,identity),X_65),least_upper_bound(X_65,multiply(X_66,X_65))) ),[0],$fot(least_upper_bound(multiply(X_66,X_65),X_65))]]) ).
cnf(refute_0_671,plain,
( multiply(least_upper_bound(X_66,identity),X_65) != least_upper_bound(multiply(X_66,X_65),X_65)
| multiply(least_upper_bound(X_66,identity),X_65) = least_upper_bound(X_65,multiply(X_66,X_65)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_66,X_65),X_65),least_upper_bound(X_65,multiply(X_66,X_65))) )],[refute_0_669,refute_0_670]) ).
cnf(refute_0_672,plain,
multiply(least_upper_bound(X_66,identity),X_65) = least_upper_bound(X_65,multiply(X_66,X_65)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_66,identity),X_65),least_upper_bound(multiply(X_66,X_65),X_65)) )],[refute_0_668,refute_0_671]) ).
cnf(refute_0_673,plain,
multiply(least_upper_bound(inverse(X_51),identity),greatest_lower_bound(identity,X_51)) = least_upper_bound(greatest_lower_bound(identity,X_51),multiply(inverse(X_51),greatest_lower_bound(identity,X_51))),
inference(subst,[],[refute_0_672:[bind(X_65,$fot(greatest_lower_bound(identity,X_51))),bind(X_66,$fot(inverse(X_51)))]]) ).
cnf(refute_0_674,plain,
( multiply(inverse(X_51),greatest_lower_bound(identity,X_51)) != greatest_lower_bound(identity,inverse(X_51))
| multiply(least_upper_bound(inverse(X_51),identity),greatest_lower_bound(identity,X_51)) != least_upper_bound(greatest_lower_bound(identity,X_51),multiply(inverse(X_51),greatest_lower_bound(identity,X_51)))
| multiply(least_upper_bound(inverse(X_51),identity),greatest_lower_bound(identity,X_51)) = least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(identity,inverse(X_51))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(X_51),identity),greatest_lower_bound(identity,X_51)),least_upper_bound(greatest_lower_bound(identity,X_51),multiply(inverse(X_51),greatest_lower_bound(identity,X_51)))) ),[1,1],$fot(greatest_lower_bound(identity,inverse(X_51)))]]) ).
cnf(refute_0_675,plain,
( multiply(least_upper_bound(inverse(X_51),identity),greatest_lower_bound(identity,X_51)) != least_upper_bound(greatest_lower_bound(identity,X_51),multiply(inverse(X_51),greatest_lower_bound(identity,X_51)))
| multiply(least_upper_bound(inverse(X_51),identity),greatest_lower_bound(identity,X_51)) = least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(identity,inverse(X_51))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_51),greatest_lower_bound(identity,X_51)),greatest_lower_bound(identity,inverse(X_51))) )],[refute_0_469,refute_0_674]) ).
cnf(refute_0_676,plain,
multiply(least_upper_bound(inverse(X_51),identity),greatest_lower_bound(identity,X_51)) = least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(identity,inverse(X_51))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_51),identity),greatest_lower_bound(identity,X_51)),least_upper_bound(greatest_lower_bound(identity,X_51),multiply(inverse(X_51),greatest_lower_bound(identity,X_51)))) )],[refute_0_673,refute_0_675]) ).
cnf(refute_0_677,plain,
least_upper_bound(X_23,least_upper_bound(X_23,multiply(X_69,X_23))) = least_upper_bound(X_23,multiply(X_69,X_23)),
inference(subst,[],[refute_0_71:[bind(X_22,$fot(multiply(X_69,X_23)))]]) ).
cnf(refute_0_678,plain,
multiply(least_upper_bound(X_69,identity),X_23) = least_upper_bound(X_23,multiply(X_69,X_23)),
inference(subst,[],[refute_0_672:[bind(X_65,$fot(X_23)),bind(X_66,$fot(X_69))]]) ).
cnf(refute_0_679,plain,
( multiply(least_upper_bound(X_69,identity),X_23) != least_upper_bound(X_23,multiply(X_69,X_23))
| least_upper_bound(X_23,multiply(X_69,X_23)) = multiply(least_upper_bound(X_69,identity),X_23) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(X_69,identity),X_23))),bind(Y0,$fot(least_upper_bound(X_23,multiply(X_69,X_23))))]]) ).
cnf(refute_0_680,plain,
least_upper_bound(X_23,multiply(X_69,X_23)) = multiply(least_upper_bound(X_69,identity),X_23),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_69,identity),X_23),least_upper_bound(X_23,multiply(X_69,X_23))) )],[refute_0_678,refute_0_679]) ).
cnf(refute_0_681,plain,
( least_upper_bound(X_23,multiply(X_69,X_23)) != multiply(least_upper_bound(X_69,identity),X_23)
| least_upper_bound(X_23,least_upper_bound(X_23,multiply(X_69,X_23))) != least_upper_bound(X_23,multiply(X_69,X_23))
| least_upper_bound(X_23,multiply(least_upper_bound(X_69,identity),X_23)) = least_upper_bound(X_23,multiply(X_69,X_23)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_23,least_upper_bound(X_23,multiply(X_69,X_23))),least_upper_bound(X_23,multiply(X_69,X_23))) ),[0,1],$fot(multiply(least_upper_bound(X_69,identity),X_23))]]) ).
cnf(refute_0_682,plain,
( least_upper_bound(X_23,least_upper_bound(X_23,multiply(X_69,X_23))) != least_upper_bound(X_23,multiply(X_69,X_23))
| least_upper_bound(X_23,multiply(least_upper_bound(X_69,identity),X_23)) = least_upper_bound(X_23,multiply(X_69,X_23)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_23,multiply(X_69,X_23)),multiply(least_upper_bound(X_69,identity),X_23)) )],[refute_0_680,refute_0_681]) ).
cnf(refute_0_683,plain,
least_upper_bound(X_23,multiply(least_upper_bound(X_69,identity),X_23)) = least_upper_bound(X_23,multiply(X_69,X_23)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_23,least_upper_bound(X_23,multiply(X_69,X_23))),least_upper_bound(X_23,multiply(X_69,X_23))) )],[refute_0_677,refute_0_682]) ).
cnf(refute_0_684,plain,
least_upper_bound(identity,least_upper_bound(X_69,identity)) = least_upper_bound(identity,X_69),
inference(subst,[],[refute_0_64:[bind(Y,$fot(X_69)),bind(X_21,$fot(identity))]]) ).
cnf(refute_0_685,plain,
multiply(least_upper_bound(identity,least_upper_bound(X_69,identity)),X_23) = multiply(least_upper_bound(identity,least_upper_bound(X_69,identity)),X_23),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(identity,least_upper_bound(X_69,identity)),X_23))]]) ).
cnf(refute_0_686,plain,
( multiply(least_upper_bound(identity,least_upper_bound(X_69,identity)),X_23) != multiply(least_upper_bound(identity,least_upper_bound(X_69,identity)),X_23)
| least_upper_bound(identity,least_upper_bound(X_69,identity)) != least_upper_bound(identity,X_69)
| multiply(least_upper_bound(identity,least_upper_bound(X_69,identity)),X_23) = multiply(least_upper_bound(identity,X_69),X_23) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(X_69,identity)),X_23),multiply(least_upper_bound(identity,least_upper_bound(X_69,identity)),X_23)) ),[1,0],$fot(least_upper_bound(identity,X_69))]]) ).
cnf(refute_0_687,plain,
( least_upper_bound(identity,least_upper_bound(X_69,identity)) != least_upper_bound(identity,X_69)
| multiply(least_upper_bound(identity,least_upper_bound(X_69,identity)),X_23) = multiply(least_upper_bound(identity,X_69),X_23) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(X_69,identity)),X_23),multiply(least_upper_bound(identity,least_upper_bound(X_69,identity)),X_23)) )],[refute_0_685,refute_0_686]) ).
cnf(refute_0_688,plain,
multiply(least_upper_bound(identity,least_upper_bound(X_69,identity)),X_23) = multiply(least_upper_bound(identity,X_69),X_23),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_69,identity)),least_upper_bound(identity,X_69)) )],[refute_0_684,refute_0_687]) ).
cnf(refute_0_689,plain,
least_upper_bound(multiply(X_67,X_65),multiply(X_66,X_65)) = least_upper_bound(multiply(X_66,X_65),multiply(X_67,X_65)),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(multiply(X_67,X_65))),bind(Y,$fot(multiply(X_66,X_65)))]]) ).
cnf(refute_0_690,plain,
multiply(least_upper_bound(X_66,X_67),X_65) = least_upper_bound(multiply(X_66,X_65),multiply(X_67,X_65)),
inference(subst,[],[monotony_lub2:[bind(X,$fot(X_65)),bind(Y,$fot(X_66)),bind(Z,$fot(X_67))]]) ).
cnf(refute_0_691,plain,
( multiply(least_upper_bound(X_66,X_67),X_65) != least_upper_bound(multiply(X_66,X_65),multiply(X_67,X_65))
| least_upper_bound(multiply(X_66,X_65),multiply(X_67,X_65)) = multiply(least_upper_bound(X_66,X_67),X_65) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(X_66,X_67),X_65))),bind(Y0,$fot(least_upper_bound(multiply(X_66,X_65),multiply(X_67,X_65))))]]) ).
cnf(refute_0_692,plain,
least_upper_bound(multiply(X_66,X_65),multiply(X_67,X_65)) = multiply(least_upper_bound(X_66,X_67),X_65),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_66,X_67),X_65),least_upper_bound(multiply(X_66,X_65),multiply(X_67,X_65))) )],[refute_0_690,refute_0_691]) ).
cnf(refute_0_693,plain,
( least_upper_bound(multiply(X_66,X_65),multiply(X_67,X_65)) != multiply(least_upper_bound(X_66,X_67),X_65)
| least_upper_bound(multiply(X_67,X_65),multiply(X_66,X_65)) != least_upper_bound(multiply(X_66,X_65),multiply(X_67,X_65))
| least_upper_bound(multiply(X_67,X_65),multiply(X_66,X_65)) = multiply(least_upper_bound(X_66,X_67),X_65) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_67,X_65),multiply(X_66,X_65)),least_upper_bound(multiply(X_66,X_65),multiply(X_67,X_65))) ),[1],$fot(multiply(least_upper_bound(X_66,X_67),X_65))]]) ).
cnf(refute_0_694,plain,
( least_upper_bound(multiply(X_67,X_65),multiply(X_66,X_65)) != least_upper_bound(multiply(X_66,X_65),multiply(X_67,X_65))
| least_upper_bound(multiply(X_67,X_65),multiply(X_66,X_65)) = multiply(least_upper_bound(X_66,X_67),X_65) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_66,X_65),multiply(X_67,X_65)),multiply(least_upper_bound(X_66,X_67),X_65)) )],[refute_0_692,refute_0_693]) ).
cnf(refute_0_695,plain,
least_upper_bound(multiply(X_67,X_65),multiply(X_66,X_65)) = multiply(least_upper_bound(X_66,X_67),X_65),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_67,X_65),multiply(X_66,X_65)),least_upper_bound(multiply(X_66,X_65),multiply(X_67,X_65))) )],[refute_0_689,refute_0_694]) ).
cnf(refute_0_696,plain,
( multiply(least_upper_bound(Y,Z),X) != least_upper_bound(multiply(Y,X),multiply(Z,X))
| least_upper_bound(multiply(Y,X),multiply(Z,X)) = multiply(least_upper_bound(Y,Z),X) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(Y,Z),X))),bind(Y0,$fot(least_upper_bound(multiply(Y,X),multiply(Z,X))))]]) ).
cnf(refute_0_697,plain,
least_upper_bound(multiply(Y,X),multiply(Z,X)) = multiply(least_upper_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Y,X),multiply(Z,X))) )],[monotony_lub2,refute_0_696]) ).
cnf(refute_0_698,plain,
least_upper_bound(multiply(X_67,X_65),multiply(X_66,X_65)) = multiply(least_upper_bound(X_67,X_66),X_65),
inference(subst,[],[refute_0_697:[bind(X,$fot(X_65)),bind(Y,$fot(X_67)),bind(Z,$fot(X_66))]]) ).
cnf(refute_0_699,plain,
( least_upper_bound(multiply(X_67,X_65),multiply(X_66,X_65)) != multiply(least_upper_bound(X_66,X_67),X_65)
| least_upper_bound(multiply(X_67,X_65),multiply(X_66,X_65)) != multiply(least_upper_bound(X_67,X_66),X_65)
| multiply(least_upper_bound(X_67,X_66),X_65) = multiply(least_upper_bound(X_66,X_67),X_65) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_67,X_65),multiply(X_66,X_65)),multiply(least_upper_bound(X_66,X_67),X_65)) ),[0],$fot(multiply(least_upper_bound(X_67,X_66),X_65))]]) ).
cnf(refute_0_700,plain,
( least_upper_bound(multiply(X_67,X_65),multiply(X_66,X_65)) != multiply(least_upper_bound(X_66,X_67),X_65)
| multiply(least_upper_bound(X_67,X_66),X_65) = multiply(least_upper_bound(X_66,X_67),X_65) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_67,X_65),multiply(X_66,X_65)),multiply(least_upper_bound(X_67,X_66),X_65)) )],[refute_0_698,refute_0_699]) ).
cnf(refute_0_701,plain,
multiply(least_upper_bound(X_67,X_66),X_65) = multiply(least_upper_bound(X_66,X_67),X_65),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_67,X_65),multiply(X_66,X_65)),multiply(least_upper_bound(X_66,X_67),X_65)) )],[refute_0_695,refute_0_700]) ).
cnf(refute_0_702,plain,
( multiply(least_upper_bound(X_67,X_66),X_65) != multiply(least_upper_bound(X_66,X_67),X_65)
| multiply(least_upper_bound(X_66,X_67),X_65) = multiply(least_upper_bound(X_67,X_66),X_65) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(X_67,X_66),X_65))),bind(Y0,$fot(multiply(least_upper_bound(X_66,X_67),X_65)))]]) ).
cnf(refute_0_703,plain,
multiply(least_upper_bound(X_66,X_67),X_65) = multiply(least_upper_bound(X_67,X_66),X_65),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_67,X_66),X_65),multiply(least_upper_bound(X_66,X_67),X_65)) )],[refute_0_701,refute_0_702]) ).
cnf(refute_0_704,plain,
multiply(least_upper_bound(least_upper_bound(X_69,identity),identity),X_23) = multiply(least_upper_bound(identity,least_upper_bound(X_69,identity)),X_23),
inference(subst,[],[refute_0_703:[bind(X_65,$fot(X_23)),bind(X_66,$fot(least_upper_bound(X_69,identity))),bind(X_67,$fot(identity))]]) ).
cnf(refute_0_705,plain,
( multiply(least_upper_bound(X_66,identity),X_65) != least_upper_bound(X_65,multiply(X_66,X_65))
| least_upper_bound(X_65,multiply(X_66,X_65)) = multiply(least_upper_bound(X_66,identity),X_65) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(X_66,identity),X_65))),bind(Y0,$fot(least_upper_bound(X_65,multiply(X_66,X_65))))]]) ).
cnf(refute_0_706,plain,
least_upper_bound(X_65,multiply(X_66,X_65)) = multiply(least_upper_bound(X_66,identity),X_65),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_66,identity),X_65),least_upper_bound(X_65,multiply(X_66,X_65))) )],[refute_0_672,refute_0_705]) ).
cnf(refute_0_707,plain,
least_upper_bound(X_23,multiply(least_upper_bound(X_69,identity),X_23)) = multiply(least_upper_bound(least_upper_bound(X_69,identity),identity),X_23),
inference(subst,[],[refute_0_706:[bind(X_65,$fot(X_23)),bind(X_66,$fot(least_upper_bound(X_69,identity)))]]) ).
cnf(refute_0_708,plain,
( multiply(least_upper_bound(least_upper_bound(X_69,identity),identity),X_23) != multiply(least_upper_bound(identity,least_upper_bound(X_69,identity)),X_23)
| least_upper_bound(X_23,multiply(least_upper_bound(X_69,identity),X_23)) != multiply(least_upper_bound(least_upper_bound(X_69,identity),identity),X_23)
| least_upper_bound(X_23,multiply(least_upper_bound(X_69,identity),X_23)) = multiply(least_upper_bound(identity,least_upper_bound(X_69,identity)),X_23) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(least_upper_bound(X_23,multiply(least_upper_bound(X_69,identity),X_23)))),bind(Y0,$fot(multiply(least_upper_bound(least_upper_bound(X_69,identity),identity),X_23))),bind(Z0,$fot(multiply(least_upper_bound(identity,least_upper_bound(X_69,identity)),X_23)))]]) ).
cnf(refute_0_709,plain,
( multiply(least_upper_bound(least_upper_bound(X_69,identity),identity),X_23) != multiply(least_upper_bound(identity,least_upper_bound(X_69,identity)),X_23)
| least_upper_bound(X_23,multiply(least_upper_bound(X_69,identity),X_23)) = multiply(least_upper_bound(identity,least_upper_bound(X_69,identity)),X_23) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_23,multiply(least_upper_bound(X_69,identity),X_23)),multiply(least_upper_bound(least_upper_bound(X_69,identity),identity),X_23)) )],[refute_0_707,refute_0_708]) ).
cnf(refute_0_710,plain,
least_upper_bound(X_23,multiply(least_upper_bound(X_69,identity),X_23)) = multiply(least_upper_bound(identity,least_upper_bound(X_69,identity)),X_23),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_69,identity),identity),X_23),multiply(least_upper_bound(identity,least_upper_bound(X_69,identity)),X_23)) )],[refute_0_704,refute_0_709]) ).
cnf(refute_0_711,plain,
( multiply(least_upper_bound(identity,least_upper_bound(X_69,identity)),X_23) != multiply(least_upper_bound(identity,X_69),X_23)
| least_upper_bound(X_23,multiply(least_upper_bound(X_69,identity),X_23)) != multiply(least_upper_bound(identity,least_upper_bound(X_69,identity)),X_23)
| least_upper_bound(X_23,multiply(least_upper_bound(X_69,identity),X_23)) = multiply(least_upper_bound(identity,X_69),X_23) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(least_upper_bound(X_23,multiply(least_upper_bound(X_69,identity),X_23)))),bind(Y0,$fot(multiply(least_upper_bound(identity,least_upper_bound(X_69,identity)),X_23))),bind(Z0,$fot(multiply(least_upper_bound(identity,X_69),X_23)))]]) ).
cnf(refute_0_712,plain,
( multiply(least_upper_bound(identity,least_upper_bound(X_69,identity)),X_23) != multiply(least_upper_bound(identity,X_69),X_23)
| least_upper_bound(X_23,multiply(least_upper_bound(X_69,identity),X_23)) = multiply(least_upper_bound(identity,X_69),X_23) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_23,multiply(least_upper_bound(X_69,identity),X_23)),multiply(least_upper_bound(identity,least_upper_bound(X_69,identity)),X_23)) )],[refute_0_710,refute_0_711]) ).
cnf(refute_0_713,plain,
least_upper_bound(X_23,multiply(least_upper_bound(X_69,identity),X_23)) = multiply(least_upper_bound(identity,X_69),X_23),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(X_69,identity)),X_23),multiply(least_upper_bound(identity,X_69),X_23)) )],[refute_0_688,refute_0_712]) ).
cnf(refute_0_714,plain,
( least_upper_bound(X_23,multiply(least_upper_bound(X_69,identity),X_23)) != multiply(least_upper_bound(identity,X_69),X_23)
| least_upper_bound(X_23,multiply(least_upper_bound(X_69,identity),X_23)) != least_upper_bound(X_23,multiply(X_69,X_23))
| multiply(least_upper_bound(identity,X_69),X_23) = least_upper_bound(X_23,multiply(X_69,X_23)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_23,multiply(least_upper_bound(X_69,identity),X_23)),least_upper_bound(X_23,multiply(X_69,X_23))) ),[0],$fot(multiply(least_upper_bound(identity,X_69),X_23))]]) ).
cnf(refute_0_715,plain,
( least_upper_bound(X_23,multiply(least_upper_bound(X_69,identity),X_23)) != least_upper_bound(X_23,multiply(X_69,X_23))
| multiply(least_upper_bound(identity,X_69),X_23) = least_upper_bound(X_23,multiply(X_69,X_23)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_23,multiply(least_upper_bound(X_69,identity),X_23)),multiply(least_upper_bound(identity,X_69),X_23)) )],[refute_0_713,refute_0_714]) ).
cnf(refute_0_716,plain,
( multiply(least_upper_bound(identity,X_69),X_23) != least_upper_bound(X_23,multiply(X_69,X_23))
| least_upper_bound(X_23,multiply(X_69,X_23)) != multiply(least_upper_bound(X_69,identity),X_23)
| multiply(least_upper_bound(identity,X_69),X_23) = multiply(least_upper_bound(X_69,identity),X_23) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(identity,X_69),X_23),multiply(least_upper_bound(X_69,identity),X_23)) ),[0],$fot(least_upper_bound(X_23,multiply(X_69,X_23)))]]) ).
cnf(refute_0_717,plain,
( multiply(least_upper_bound(identity,X_69),X_23) != least_upper_bound(X_23,multiply(X_69,X_23))
| multiply(least_upper_bound(identity,X_69),X_23) = multiply(least_upper_bound(X_69,identity),X_23) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_23,multiply(X_69,X_23)),multiply(least_upper_bound(X_69,identity),X_23)) )],[refute_0_680,refute_0_716]) ).
cnf(refute_0_718,plain,
( least_upper_bound(X_23,multiply(least_upper_bound(X_69,identity),X_23)) != least_upper_bound(X_23,multiply(X_69,X_23))
| multiply(least_upper_bound(identity,X_69),X_23) = multiply(least_upper_bound(X_69,identity),X_23) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_69),X_23),least_upper_bound(X_23,multiply(X_69,X_23))) )],[refute_0_715,refute_0_717]) ).
cnf(refute_0_719,plain,
multiply(least_upper_bound(identity,X_69),X_23) = multiply(least_upper_bound(X_69,identity),X_23),
inference(resolve,[$cnf( $equal(least_upper_bound(X_23,multiply(least_upper_bound(X_69,identity),X_23)),least_upper_bound(X_23,multiply(X_69,X_23))) )],[refute_0_683,refute_0_718]) ).
cnf(refute_0_720,plain,
( multiply(least_upper_bound(identity,X_69),X_23) != multiply(least_upper_bound(X_69,identity),X_23)
| multiply(least_upper_bound(X_69,identity),X_23) = multiply(least_upper_bound(identity,X_69),X_23) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(identity,X_69),X_23))),bind(Y0,$fot(multiply(least_upper_bound(X_69,identity),X_23)))]]) ).
cnf(refute_0_721,plain,
multiply(least_upper_bound(X_69,identity),X_23) = multiply(least_upper_bound(identity,X_69),X_23),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_69),X_23),multiply(least_upper_bound(X_69,identity),X_23)) )],[refute_0_719,refute_0_720]) ).
cnf(refute_0_722,plain,
multiply(least_upper_bound(inverse(X_51),identity),greatest_lower_bound(identity,X_51)) = multiply(least_upper_bound(identity,inverse(X_51)),greatest_lower_bound(identity,X_51)),
inference(subst,[],[refute_0_721:[bind(X_23,$fot(greatest_lower_bound(identity,X_51))),bind(X_69,$fot(inverse(X_51)))]]) ).
cnf(refute_0_723,plain,
( multiply(least_upper_bound(inverse(X_51),identity),greatest_lower_bound(identity,X_51)) != multiply(least_upper_bound(identity,inverse(X_51)),greatest_lower_bound(identity,X_51))
| multiply(least_upper_bound(inverse(X_51),identity),greatest_lower_bound(identity,X_51)) != least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(identity,inverse(X_51)))
| multiply(least_upper_bound(identity,inverse(X_51)),greatest_lower_bound(identity,X_51)) = least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(identity,inverse(X_51))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(X_51),identity),greatest_lower_bound(identity,X_51)),least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(identity,inverse(X_51)))) ),[0],$fot(multiply(least_upper_bound(identity,inverse(X_51)),greatest_lower_bound(identity,X_51)))]]) ).
cnf(refute_0_724,plain,
( multiply(least_upper_bound(inverse(X_51),identity),greatest_lower_bound(identity,X_51)) != least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(identity,inverse(X_51)))
| multiply(least_upper_bound(identity,inverse(X_51)),greatest_lower_bound(identity,X_51)) = least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(identity,inverse(X_51))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_51),identity),greatest_lower_bound(identity,X_51)),multiply(least_upper_bound(identity,inverse(X_51)),greatest_lower_bound(identity,X_51))) )],[refute_0_722,refute_0_723]) ).
cnf(refute_0_725,plain,
multiply(least_upper_bound(identity,inverse(X_51)),greatest_lower_bound(identity,X_51)) = least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(identity,inverse(X_51))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_51),identity),greatest_lower_bound(identity,X_51)),least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(identity,inverse(X_51)))) )],[refute_0_676,refute_0_724]) ).
cnf(refute_0_726,plain,
multiply(X_53,least_upper_bound(X_54,identity)) = least_upper_bound(multiply(X_53,X_54),multiply(X_53,identity)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(X_53)),bind(Y,$fot(X_54)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_727,plain,
X_53 = multiply(X_53,identity),
inference(subst,[],[refute_0_210:[bind(X,$fot(X_53))]]) ).
cnf(refute_0_728,plain,
( X_53 != multiply(X_53,identity)
| multiply(X_53,identity) = X_53 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_53)),bind(Y0,$fot(multiply(X_53,identity)))]]) ).
cnf(refute_0_729,plain,
multiply(X_53,identity) = X_53,
inference(resolve,[$cnf( $equal(X_53,multiply(X_53,identity)) )],[refute_0_727,refute_0_728]) ).
cnf(refute_0_730,plain,
( multiply(X_53,identity) != X_53
| multiply(X_53,least_upper_bound(X_54,identity)) != least_upper_bound(multiply(X_53,X_54),multiply(X_53,identity))
| multiply(X_53,least_upper_bound(X_54,identity)) = least_upper_bound(multiply(X_53,X_54),X_53) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_53,least_upper_bound(X_54,identity)),least_upper_bound(multiply(X_53,X_54),multiply(X_53,identity))) ),[1,1],$fot(X_53)]]) ).
cnf(refute_0_731,plain,
( multiply(X_53,least_upper_bound(X_54,identity)) != least_upper_bound(multiply(X_53,X_54),multiply(X_53,identity))
| multiply(X_53,least_upper_bound(X_54,identity)) = least_upper_bound(multiply(X_53,X_54),X_53) ),
inference(resolve,[$cnf( $equal(multiply(X_53,identity),X_53) )],[refute_0_729,refute_0_730]) ).
cnf(refute_0_732,plain,
multiply(X_53,least_upper_bound(X_54,identity)) = least_upper_bound(multiply(X_53,X_54),X_53),
inference(resolve,[$cnf( $equal(multiply(X_53,least_upper_bound(X_54,identity)),least_upper_bound(multiply(X_53,X_54),multiply(X_53,identity))) )],[refute_0_726,refute_0_731]) ).
cnf(refute_0_733,plain,
least_upper_bound(multiply(X_53,X_54),X_53) = least_upper_bound(X_53,multiply(X_53,X_54)),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_53)),bind(Y,$fot(multiply(X_53,X_54)))]]) ).
cnf(refute_0_734,plain,
( multiply(X_53,least_upper_bound(X_54,identity)) != least_upper_bound(multiply(X_53,X_54),X_53)
| least_upper_bound(multiply(X_53,X_54),X_53) != least_upper_bound(X_53,multiply(X_53,X_54))
| multiply(X_53,least_upper_bound(X_54,identity)) = least_upper_bound(X_53,multiply(X_53,X_54)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_53,least_upper_bound(X_54,identity)),least_upper_bound(X_53,multiply(X_53,X_54))) ),[0],$fot(least_upper_bound(multiply(X_53,X_54),X_53))]]) ).
cnf(refute_0_735,plain,
( multiply(X_53,least_upper_bound(X_54,identity)) != least_upper_bound(multiply(X_53,X_54),X_53)
| multiply(X_53,least_upper_bound(X_54,identity)) = least_upper_bound(X_53,multiply(X_53,X_54)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_53,X_54),X_53),least_upper_bound(X_53,multiply(X_53,X_54))) )],[refute_0_733,refute_0_734]) ).
cnf(refute_0_736,plain,
multiply(X_53,least_upper_bound(X_54,identity)) = least_upper_bound(X_53,multiply(X_53,X_54)),
inference(resolve,[$cnf( $equal(multiply(X_53,least_upper_bound(X_54,identity)),least_upper_bound(multiply(X_53,X_54),X_53)) )],[refute_0_732,refute_0_735]) ).
cnf(refute_0_737,plain,
multiply(greatest_lower_bound(identity,X_115),least_upper_bound(inverse(X_115),identity)) = least_upper_bound(greatest_lower_bound(identity,X_115),multiply(greatest_lower_bound(identity,X_115),inverse(X_115))),
inference(subst,[],[refute_0_736:[bind(X_53,$fot(greatest_lower_bound(identity,X_115))),bind(X_54,$fot(inverse(X_115)))]]) ).
cnf(refute_0_738,plain,
multiply(greatest_lower_bound(X_46,identity),X_45) = greatest_lower_bound(multiply(X_46,X_45),multiply(identity,X_45)),
inference(subst,[],[monotony_glb2:[bind(X,$fot(X_45)),bind(Y,$fot(X_46)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_739,plain,
multiply(identity,X_45) = X_45,
inference(subst,[],[left_identity:[bind(X,$fot(X_45))]]) ).
cnf(refute_0_740,plain,
( multiply(greatest_lower_bound(X_46,identity),X_45) != greatest_lower_bound(multiply(X_46,X_45),multiply(identity,X_45))
| multiply(identity,X_45) != X_45
| multiply(greatest_lower_bound(X_46,identity),X_45) = greatest_lower_bound(multiply(X_46,X_45),X_45) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_46,identity),X_45),greatest_lower_bound(multiply(X_46,X_45),multiply(identity,X_45))) ),[1,1],$fot(X_45)]]) ).
cnf(refute_0_741,plain,
( multiply(greatest_lower_bound(X_46,identity),X_45) != greatest_lower_bound(multiply(X_46,X_45),multiply(identity,X_45))
| multiply(greatest_lower_bound(X_46,identity),X_45) = greatest_lower_bound(multiply(X_46,X_45),X_45) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_45),X_45) )],[refute_0_739,refute_0_740]) ).
cnf(refute_0_742,plain,
multiply(greatest_lower_bound(X_46,identity),X_45) = greatest_lower_bound(multiply(X_46,X_45),X_45),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_46,identity),X_45),greatest_lower_bound(multiply(X_46,X_45),multiply(identity,X_45))) )],[refute_0_738,refute_0_741]) ).
cnf(refute_0_743,plain,
greatest_lower_bound(multiply(X_46,X_45),X_45) = greatest_lower_bound(X_45,multiply(X_46,X_45)),
inference(subst,[],[refute_0_122:[bind(X,$fot(X_45)),bind(Y,$fot(multiply(X_46,X_45)))]]) ).
cnf(refute_0_744,plain,
( multiply(greatest_lower_bound(X_46,identity),X_45) != greatest_lower_bound(multiply(X_46,X_45),X_45)
| greatest_lower_bound(multiply(X_46,X_45),X_45) != greatest_lower_bound(X_45,multiply(X_46,X_45))
| multiply(greatest_lower_bound(X_46,identity),X_45) = greatest_lower_bound(X_45,multiply(X_46,X_45)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_46,identity),X_45),greatest_lower_bound(X_45,multiply(X_46,X_45))) ),[0],$fot(greatest_lower_bound(multiply(X_46,X_45),X_45))]]) ).
cnf(refute_0_745,plain,
( multiply(greatest_lower_bound(X_46,identity),X_45) != greatest_lower_bound(multiply(X_46,X_45),X_45)
| multiply(greatest_lower_bound(X_46,identity),X_45) = greatest_lower_bound(X_45,multiply(X_46,X_45)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_46,X_45),X_45),greatest_lower_bound(X_45,multiply(X_46,X_45))) )],[refute_0_743,refute_0_744]) ).
cnf(refute_0_746,plain,
multiply(greatest_lower_bound(X_46,identity),X_45) = greatest_lower_bound(X_45,multiply(X_46,X_45)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_46,identity),X_45),greatest_lower_bound(multiply(X_46,X_45),X_45)) )],[refute_0_742,refute_0_745]) ).
cnf(refute_0_747,plain,
multiply(greatest_lower_bound(greatest_lower_bound(X_106,identity),identity),inverse(X_106)) = greatest_lower_bound(inverse(X_106),multiply(greatest_lower_bound(X_106,identity),inverse(X_106))),
inference(subst,[],[refute_0_746:[bind(X_45,$fot(inverse(X_106))),bind(X_46,$fot(greatest_lower_bound(X_106,identity)))]]) ).
cnf(refute_0_748,plain,
multiply(greatest_lower_bound(X_105,identity),inverse(X_105)) = greatest_lower_bound(inverse(X_105),multiply(X_105,inverse(X_105))),
inference(subst,[],[refute_0_746:[bind(X_45,$fot(inverse(X_105))),bind(X_46,$fot(X_105))]]) ).
cnf(refute_0_749,plain,
multiply(X_105,inverse(X_105)) = identity,
inference(subst,[],[refute_0_38:[bind(X_1,$fot(X_105))]]) ).
cnf(refute_0_750,plain,
( multiply(X_105,inverse(X_105)) != identity
| multiply(greatest_lower_bound(X_105,identity),inverse(X_105)) != greatest_lower_bound(inverse(X_105),multiply(X_105,inverse(X_105)))
| multiply(greatest_lower_bound(X_105,identity),inverse(X_105)) = greatest_lower_bound(inverse(X_105),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_105,identity),inverse(X_105)),greatest_lower_bound(inverse(X_105),multiply(X_105,inverse(X_105)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_751,plain,
( multiply(greatest_lower_bound(X_105,identity),inverse(X_105)) != greatest_lower_bound(inverse(X_105),multiply(X_105,inverse(X_105)))
| multiply(greatest_lower_bound(X_105,identity),inverse(X_105)) = greatest_lower_bound(inverse(X_105),identity) ),
inference(resolve,[$cnf( $equal(multiply(X_105,inverse(X_105)),identity) )],[refute_0_749,refute_0_750]) ).
cnf(refute_0_752,plain,
multiply(greatest_lower_bound(X_105,identity),inverse(X_105)) = greatest_lower_bound(inverse(X_105),identity),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_105,identity),inverse(X_105)),greatest_lower_bound(inverse(X_105),multiply(X_105,inverse(X_105)))) )],[refute_0_748,refute_0_751]) ).
cnf(refute_0_753,plain,
multiply(X_36,greatest_lower_bound(inverse(X_36),X_38)) = greatest_lower_bound(multiply(X_36,inverse(X_36)),multiply(X_36,X_38)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(X_36)),bind(Y,$fot(inverse(X_36))),bind(Z,$fot(X_38))]]) ).
cnf(refute_0_754,plain,
multiply(X_36,inverse(X_36)) = identity,
inference(subst,[],[refute_0_38:[bind(X_1,$fot(X_36))]]) ).
cnf(refute_0_755,plain,
( multiply(X_36,greatest_lower_bound(inverse(X_36),X_38)) != greatest_lower_bound(multiply(X_36,inverse(X_36)),multiply(X_36,X_38))
| multiply(X_36,inverse(X_36)) != identity
| multiply(X_36,greatest_lower_bound(inverse(X_36),X_38)) = greatest_lower_bound(identity,multiply(X_36,X_38)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_36,greatest_lower_bound(inverse(X_36),X_38)),greatest_lower_bound(multiply(X_36,inverse(X_36)),multiply(X_36,X_38))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_756,plain,
( multiply(X_36,greatest_lower_bound(inverse(X_36),X_38)) != greatest_lower_bound(multiply(X_36,inverse(X_36)),multiply(X_36,X_38))
| multiply(X_36,greatest_lower_bound(inverse(X_36),X_38)) = greatest_lower_bound(identity,multiply(X_36,X_38)) ),
inference(resolve,[$cnf( $equal(multiply(X_36,inverse(X_36)),identity) )],[refute_0_754,refute_0_755]) ).
cnf(refute_0_757,plain,
multiply(X_36,greatest_lower_bound(inverse(X_36),X_38)) = greatest_lower_bound(identity,multiply(X_36,X_38)),
inference(resolve,[$cnf( $equal(multiply(X_36,greatest_lower_bound(inverse(X_36),X_38)),greatest_lower_bound(multiply(X_36,inverse(X_36)),multiply(X_36,X_38))) )],[refute_0_753,refute_0_756]) ).
cnf(refute_0_758,plain,
multiply(X_36,greatest_lower_bound(inverse(X_36),multiply(inverse(X_36),X_91))) = greatest_lower_bound(identity,multiply(X_36,multiply(inverse(X_36),X_91))),
inference(subst,[],[refute_0_757:[bind(X_38,$fot(multiply(inverse(X_36),X_91)))]]) ).
cnf(refute_0_759,plain,
multiply(inverse(X_36),greatest_lower_bound(X_91,identity)) = greatest_lower_bound(inverse(X_36),multiply(inverse(X_36),X_91)),
inference(subst,[],[refute_0_220:[bind(X_36,$fot(inverse(X_36))),bind(X_37,$fot(X_91))]]) ).
cnf(refute_0_760,plain,
( multiply(inverse(X_36),greatest_lower_bound(X_91,identity)) != greatest_lower_bound(inverse(X_36),multiply(inverse(X_36),X_91))
| greatest_lower_bound(inverse(X_36),multiply(inverse(X_36),X_91)) = multiply(inverse(X_36),greatest_lower_bound(X_91,identity)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(inverse(X_36),greatest_lower_bound(X_91,identity)))),bind(Y0,$fot(greatest_lower_bound(inverse(X_36),multiply(inverse(X_36),X_91))))]]) ).
cnf(refute_0_761,plain,
greatest_lower_bound(inverse(X_36),multiply(inverse(X_36),X_91)) = multiply(inverse(X_36),greatest_lower_bound(X_91,identity)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_36),greatest_lower_bound(X_91,identity)),greatest_lower_bound(inverse(X_36),multiply(inverse(X_36),X_91))) )],[refute_0_759,refute_0_760]) ).
cnf(refute_0_762,plain,
( multiply(X_36,greatest_lower_bound(inverse(X_36),multiply(inverse(X_36),X_91))) != greatest_lower_bound(identity,multiply(X_36,multiply(inverse(X_36),X_91)))
| greatest_lower_bound(inverse(X_36),multiply(inverse(X_36),X_91)) != multiply(inverse(X_36),greatest_lower_bound(X_91,identity))
| multiply(X_36,multiply(inverse(X_36),greatest_lower_bound(X_91,identity))) = greatest_lower_bound(identity,multiply(X_36,multiply(inverse(X_36),X_91))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_36,greatest_lower_bound(inverse(X_36),multiply(inverse(X_36),X_91))),greatest_lower_bound(identity,multiply(X_36,multiply(inverse(X_36),X_91)))) ),[0,1],$fot(multiply(inverse(X_36),greatest_lower_bound(X_91,identity)))]]) ).
cnf(refute_0_763,plain,
( multiply(X_36,greatest_lower_bound(inverse(X_36),multiply(inverse(X_36),X_91))) != greatest_lower_bound(identity,multiply(X_36,multiply(inverse(X_36),X_91)))
| multiply(X_36,multiply(inverse(X_36),greatest_lower_bound(X_91,identity))) = greatest_lower_bound(identity,multiply(X_36,multiply(inverse(X_36),X_91))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_36),multiply(inverse(X_36),X_91)),multiply(inverse(X_36),greatest_lower_bound(X_91,identity))) )],[refute_0_761,refute_0_762]) ).
cnf(refute_0_764,plain,
multiply(X_36,multiply(inverse(X_36),greatest_lower_bound(X_91,identity))) = greatest_lower_bound(identity,multiply(X_36,multiply(inverse(X_36),X_91))),
inference(resolve,[$cnf( $equal(multiply(X_36,greatest_lower_bound(inverse(X_36),multiply(inverse(X_36),X_91))),greatest_lower_bound(identity,multiply(X_36,multiply(inverse(X_36),X_91)))) )],[refute_0_758,refute_0_763]) ).
cnf(refute_0_765,plain,
( X_94 != multiply(X_92,multiply(inverse(X_92),X_94))
| multiply(X_92,multiply(inverse(X_92),X_94)) = X_94 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_94)),bind(Y0,$fot(multiply(X_92,multiply(inverse(X_92),X_94))))]]) ).
cnf(refute_0_766,plain,
multiply(X_92,multiply(inverse(X_92),X_94)) = X_94,
inference(resolve,[$cnf( $equal(X_94,multiply(X_92,multiply(inverse(X_92),X_94))) )],[refute_0_419,refute_0_765]) ).
cnf(refute_0_767,plain,
multiply(X_36,multiply(inverse(X_36),greatest_lower_bound(X_91,identity))) = greatest_lower_bound(X_91,identity),
inference(subst,[],[refute_0_766:[bind(X_92,$fot(X_36)),bind(X_94,$fot(greatest_lower_bound(X_91,identity)))]]) ).
cnf(refute_0_768,plain,
( multiply(X_36,multiply(inverse(X_36),greatest_lower_bound(X_91,identity))) != greatest_lower_bound(X_91,identity)
| multiply(X_36,multiply(inverse(X_36),greatest_lower_bound(X_91,identity))) != greatest_lower_bound(identity,multiply(X_36,multiply(inverse(X_36),X_91)))
| greatest_lower_bound(X_91,identity) = greatest_lower_bound(identity,multiply(X_36,multiply(inverse(X_36),X_91))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_36,multiply(inverse(X_36),greatest_lower_bound(X_91,identity))),greatest_lower_bound(identity,multiply(X_36,multiply(inverse(X_36),X_91)))) ),[0],$fot(greatest_lower_bound(X_91,identity))]]) ).
cnf(refute_0_769,plain,
( multiply(X_36,multiply(inverse(X_36),greatest_lower_bound(X_91,identity))) != greatest_lower_bound(identity,multiply(X_36,multiply(inverse(X_36),X_91)))
| greatest_lower_bound(X_91,identity) = greatest_lower_bound(identity,multiply(X_36,multiply(inverse(X_36),X_91))) ),
inference(resolve,[$cnf( $equal(multiply(X_36,multiply(inverse(X_36),greatest_lower_bound(X_91,identity))),greatest_lower_bound(X_91,identity)) )],[refute_0_767,refute_0_768]) ).
cnf(refute_0_770,plain,
multiply(X_36,multiply(inverse(X_36),X_91)) = X_91,
inference(subst,[],[refute_0_766:[bind(X_92,$fot(X_36)),bind(X_94,$fot(X_91))]]) ).
cnf(refute_0_771,plain,
greatest_lower_bound(identity,multiply(X_36,multiply(inverse(X_36),X_91))) = greatest_lower_bound(identity,multiply(X_36,multiply(inverse(X_36),X_91))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,multiply(X_36,multiply(inverse(X_36),X_91))))]]) ).
cnf(refute_0_772,plain,
( multiply(X_36,multiply(inverse(X_36),X_91)) != X_91
| greatest_lower_bound(identity,multiply(X_36,multiply(inverse(X_36),X_91))) != greatest_lower_bound(identity,multiply(X_36,multiply(inverse(X_36),X_91)))
| greatest_lower_bound(identity,multiply(X_36,multiply(inverse(X_36),X_91))) = greatest_lower_bound(identity,X_91) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_36,multiply(inverse(X_36),X_91))),greatest_lower_bound(identity,multiply(X_36,multiply(inverse(X_36),X_91)))) ),[1,1],$fot(X_91)]]) ).
cnf(refute_0_773,plain,
( multiply(X_36,multiply(inverse(X_36),X_91)) != X_91
| greatest_lower_bound(identity,multiply(X_36,multiply(inverse(X_36),X_91))) = greatest_lower_bound(identity,X_91) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_36,multiply(inverse(X_36),X_91))),greatest_lower_bound(identity,multiply(X_36,multiply(inverse(X_36),X_91)))) )],[refute_0_771,refute_0_772]) ).
cnf(refute_0_774,plain,
greatest_lower_bound(identity,multiply(X_36,multiply(inverse(X_36),X_91))) = greatest_lower_bound(identity,X_91),
inference(resolve,[$cnf( $equal(multiply(X_36,multiply(inverse(X_36),X_91)),X_91) )],[refute_0_770,refute_0_773]) ).
cnf(refute_0_775,plain,
( greatest_lower_bound(X_91,identity) != greatest_lower_bound(identity,multiply(X_36,multiply(inverse(X_36),X_91)))
| greatest_lower_bound(identity,multiply(X_36,multiply(inverse(X_36),X_91))) != greatest_lower_bound(identity,X_91)
| greatest_lower_bound(X_91,identity) = greatest_lower_bound(identity,X_91) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_91,identity),greatest_lower_bound(identity,X_91)) ),[0],$fot(greatest_lower_bound(identity,multiply(X_36,multiply(inverse(X_36),X_91))))]]) ).
cnf(refute_0_776,plain,
( greatest_lower_bound(X_91,identity) != greatest_lower_bound(identity,multiply(X_36,multiply(inverse(X_36),X_91)))
| greatest_lower_bound(X_91,identity) = greatest_lower_bound(identity,X_91) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_36,multiply(inverse(X_36),X_91))),greatest_lower_bound(identity,X_91)) )],[refute_0_774,refute_0_775]) ).
cnf(refute_0_777,plain,
( multiply(X_36,multiply(inverse(X_36),greatest_lower_bound(X_91,identity))) != greatest_lower_bound(identity,multiply(X_36,multiply(inverse(X_36),X_91)))
| greatest_lower_bound(X_91,identity) = greatest_lower_bound(identity,X_91) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_91,identity),greatest_lower_bound(identity,multiply(X_36,multiply(inverse(X_36),X_91)))) )],[refute_0_769,refute_0_776]) ).
cnf(refute_0_778,plain,
greatest_lower_bound(X_91,identity) = greatest_lower_bound(identity,X_91),
inference(resolve,[$cnf( $equal(multiply(X_36,multiply(inverse(X_36),greatest_lower_bound(X_91,identity))),greatest_lower_bound(identity,multiply(X_36,multiply(inverse(X_36),X_91)))) )],[refute_0_764,refute_0_777]) ).
cnf(refute_0_779,plain,
greatest_lower_bound(inverse(X_105),identity) = greatest_lower_bound(identity,inverse(X_105)),
inference(subst,[],[refute_0_778:[bind(X_91,$fot(inverse(X_105)))]]) ).
cnf(refute_0_780,plain,
( multiply(greatest_lower_bound(X_105,identity),inverse(X_105)) != greatest_lower_bound(inverse(X_105),identity)
| greatest_lower_bound(inverse(X_105),identity) != greatest_lower_bound(identity,inverse(X_105))
| multiply(greatest_lower_bound(X_105,identity),inverse(X_105)) = greatest_lower_bound(identity,inverse(X_105)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_105,identity),inverse(X_105)),greatest_lower_bound(identity,inverse(X_105))) ),[0],$fot(greatest_lower_bound(inverse(X_105),identity))]]) ).
cnf(refute_0_781,plain,
( multiply(greatest_lower_bound(X_105,identity),inverse(X_105)) != greatest_lower_bound(inverse(X_105),identity)
| multiply(greatest_lower_bound(X_105,identity),inverse(X_105)) = greatest_lower_bound(identity,inverse(X_105)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_105),identity),greatest_lower_bound(identity,inverse(X_105))) )],[refute_0_779,refute_0_780]) ).
cnf(refute_0_782,plain,
multiply(greatest_lower_bound(X_105,identity),inverse(X_105)) = greatest_lower_bound(identity,inverse(X_105)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_105,identity),inverse(X_105)),greatest_lower_bound(inverse(X_105),identity)) )],[refute_0_752,refute_0_781]) ).
cnf(refute_0_783,plain,
multiply(greatest_lower_bound(X_106,identity),inverse(X_106)) = greatest_lower_bound(identity,inverse(X_106)),
inference(subst,[],[refute_0_782:[bind(X_105,$fot(X_106))]]) ).
cnf(refute_0_784,plain,
( multiply(greatest_lower_bound(X_106,identity),inverse(X_106)) != greatest_lower_bound(identity,inverse(X_106))
| multiply(greatest_lower_bound(greatest_lower_bound(X_106,identity),identity),inverse(X_106)) != greatest_lower_bound(inverse(X_106),multiply(greatest_lower_bound(X_106,identity),inverse(X_106)))
| multiply(greatest_lower_bound(greatest_lower_bound(X_106,identity),identity),inverse(X_106)) = greatest_lower_bound(inverse(X_106),greatest_lower_bound(identity,inverse(X_106))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(greatest_lower_bound(X_106,identity),identity),inverse(X_106)),greatest_lower_bound(inverse(X_106),multiply(greatest_lower_bound(X_106,identity),inverse(X_106)))) ),[1,1],$fot(greatest_lower_bound(identity,inverse(X_106)))]]) ).
cnf(refute_0_785,plain,
( multiply(greatest_lower_bound(greatest_lower_bound(X_106,identity),identity),inverse(X_106)) != greatest_lower_bound(inverse(X_106),multiply(greatest_lower_bound(X_106,identity),inverse(X_106)))
| multiply(greatest_lower_bound(greatest_lower_bound(X_106,identity),identity),inverse(X_106)) = greatest_lower_bound(inverse(X_106),greatest_lower_bound(identity,inverse(X_106))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_106,identity),inverse(X_106)),greatest_lower_bound(identity,inverse(X_106))) )],[refute_0_783,refute_0_784]) ).
cnf(refute_0_786,plain,
multiply(greatest_lower_bound(greatest_lower_bound(X_106,identity),identity),inverse(X_106)) = greatest_lower_bound(inverse(X_106),greatest_lower_bound(identity,inverse(X_106))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(greatest_lower_bound(X_106,identity),identity),inverse(X_106)),greatest_lower_bound(inverse(X_106),multiply(greatest_lower_bound(X_106,identity),inverse(X_106)))) )],[refute_0_747,refute_0_785]) ).
cnf(refute_0_787,plain,
greatest_lower_bound(identity,greatest_lower_bound(X_106,identity)) = greatest_lower_bound(identity,X_106),
inference(subst,[],[refute_0_182:[bind(Y,$fot(X_106)),bind(X_15,$fot(identity))]]) ).
cnf(refute_0_788,plain,
multiply(greatest_lower_bound(identity,greatest_lower_bound(X_106,identity)),inverse(X_106)) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_106,identity)),inverse(X_106)),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_106,identity)),inverse(X_106)))]]) ).
cnf(refute_0_789,plain,
( multiply(greatest_lower_bound(identity,greatest_lower_bound(X_106,identity)),inverse(X_106)) != multiply(greatest_lower_bound(identity,greatest_lower_bound(X_106,identity)),inverse(X_106))
| greatest_lower_bound(identity,greatest_lower_bound(X_106,identity)) != greatest_lower_bound(identity,X_106)
| multiply(greatest_lower_bound(identity,greatest_lower_bound(X_106,identity)),inverse(X_106)) = multiply(greatest_lower_bound(identity,X_106),inverse(X_106)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_106,identity)),inverse(X_106)),multiply(greatest_lower_bound(identity,greatest_lower_bound(X_106,identity)),inverse(X_106))) ),[1,0],$fot(greatest_lower_bound(identity,X_106))]]) ).
cnf(refute_0_790,plain,
( greatest_lower_bound(identity,greatest_lower_bound(X_106,identity)) != greatest_lower_bound(identity,X_106)
| multiply(greatest_lower_bound(identity,greatest_lower_bound(X_106,identity)),inverse(X_106)) = multiply(greatest_lower_bound(identity,X_106),inverse(X_106)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_106,identity)),inverse(X_106)),multiply(greatest_lower_bound(identity,greatest_lower_bound(X_106,identity)),inverse(X_106))) )],[refute_0_788,refute_0_789]) ).
cnf(refute_0_791,plain,
multiply(greatest_lower_bound(identity,greatest_lower_bound(X_106,identity)),inverse(X_106)) = multiply(greatest_lower_bound(identity,X_106),inverse(X_106)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_106,identity)),greatest_lower_bound(identity,X_106)) )],[refute_0_787,refute_0_790]) ).
cnf(refute_0_792,plain,
greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_105,X_17))) = greatest_lower_bound(X_17,multiply(X_105,X_17)),
inference(subst,[],[refute_0_189:[bind(X_16,$fot(multiply(X_105,X_17)))]]) ).
cnf(refute_0_793,plain,
multiply(greatest_lower_bound(X_105,identity),X_17) = greatest_lower_bound(X_17,multiply(X_105,X_17)),
inference(subst,[],[refute_0_746:[bind(X_45,$fot(X_17)),bind(X_46,$fot(X_105))]]) ).
cnf(refute_0_794,plain,
( multiply(greatest_lower_bound(X_105,identity),X_17) != greatest_lower_bound(X_17,multiply(X_105,X_17))
| greatest_lower_bound(X_17,multiply(X_105,X_17)) = multiply(greatest_lower_bound(X_105,identity),X_17) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(greatest_lower_bound(X_105,identity),X_17))),bind(Y0,$fot(greatest_lower_bound(X_17,multiply(X_105,X_17))))]]) ).
cnf(refute_0_795,plain,
greatest_lower_bound(X_17,multiply(X_105,X_17)) = multiply(greatest_lower_bound(X_105,identity),X_17),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_105,identity),X_17),greatest_lower_bound(X_17,multiply(X_105,X_17))) )],[refute_0_793,refute_0_794]) ).
cnf(refute_0_796,plain,
( greatest_lower_bound(X_17,multiply(X_105,X_17)) != multiply(greatest_lower_bound(X_105,identity),X_17)
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_105,X_17))) != greatest_lower_bound(X_17,multiply(X_105,X_17))
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_105,X_17))) = multiply(greatest_lower_bound(X_105,identity),X_17) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_105,X_17))),greatest_lower_bound(X_17,multiply(X_105,X_17))) ),[1],$fot(multiply(greatest_lower_bound(X_105,identity),X_17))]]) ).
cnf(refute_0_797,plain,
( greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_105,X_17))) != greatest_lower_bound(X_17,multiply(X_105,X_17))
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_105,X_17))) = multiply(greatest_lower_bound(X_105,identity),X_17) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,multiply(X_105,X_17)),multiply(greatest_lower_bound(X_105,identity),X_17)) )],[refute_0_795,refute_0_796]) ).
cnf(refute_0_798,plain,
greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_105,X_17))) = multiply(greatest_lower_bound(X_105,identity),X_17),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_105,X_17))),greatest_lower_bound(X_17,multiply(X_105,X_17))) )],[refute_0_792,refute_0_797]) ).
cnf(refute_0_799,plain,
greatest_lower_bound(identity,greatest_lower_bound(X_105,identity)) = greatest_lower_bound(identity,X_105),
inference(subst,[],[refute_0_182:[bind(Y,$fot(X_105)),bind(X_15,$fot(identity))]]) ).
cnf(refute_0_800,plain,
multiply(greatest_lower_bound(identity,greatest_lower_bound(X_105,identity)),X_17) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_105,identity)),X_17),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_105,identity)),X_17))]]) ).
cnf(refute_0_801,plain,
( multiply(greatest_lower_bound(identity,greatest_lower_bound(X_105,identity)),X_17) != multiply(greatest_lower_bound(identity,greatest_lower_bound(X_105,identity)),X_17)
| greatest_lower_bound(identity,greatest_lower_bound(X_105,identity)) != greatest_lower_bound(identity,X_105)
| multiply(greatest_lower_bound(identity,greatest_lower_bound(X_105,identity)),X_17) = multiply(greatest_lower_bound(identity,X_105),X_17) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_105,identity)),X_17),multiply(greatest_lower_bound(identity,greatest_lower_bound(X_105,identity)),X_17)) ),[1,0],$fot(greatest_lower_bound(identity,X_105))]]) ).
cnf(refute_0_802,plain,
( greatest_lower_bound(identity,greatest_lower_bound(X_105,identity)) != greatest_lower_bound(identity,X_105)
| multiply(greatest_lower_bound(identity,greatest_lower_bound(X_105,identity)),X_17) = multiply(greatest_lower_bound(identity,X_105),X_17) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_105,identity)),X_17),multiply(greatest_lower_bound(identity,greatest_lower_bound(X_105,identity)),X_17)) )],[refute_0_800,refute_0_801]) ).
cnf(refute_0_803,plain,
multiply(greatest_lower_bound(identity,greatest_lower_bound(X_105,identity)),X_17) = multiply(greatest_lower_bound(identity,X_105),X_17),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_105,identity)),greatest_lower_bound(identity,X_105)) )],[refute_0_799,refute_0_802]) ).
cnf(refute_0_804,plain,
least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),greatest_lower_bound(multiply(Y,X),multiply(Z,X))) = greatest_lower_bound(multiply(Z,X),multiply(Y,X)),
inference(subst,[],[refute_0_236:[bind(Y,$fot(multiply(Z,X))),bind(X_21,$fot(multiply(Y,X)))]]) ).
cnf(refute_0_805,plain,
( multiply(greatest_lower_bound(Y,Z),X) != greatest_lower_bound(multiply(Y,X),multiply(Z,X))
| greatest_lower_bound(multiply(Y,X),multiply(Z,X)) = multiply(greatest_lower_bound(Y,Z),X) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(greatest_lower_bound(Y,Z),X))),bind(Y0,$fot(greatest_lower_bound(multiply(Y,X),multiply(Z,X))))]]) ).
cnf(refute_0_806,plain,
greatest_lower_bound(multiply(Y,X),multiply(Z,X)) = multiply(greatest_lower_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Y,X),multiply(Z,X))) )],[monotony_glb2,refute_0_805]) ).
cnf(refute_0_807,plain,
( greatest_lower_bound(multiply(Y,X),multiply(Z,X)) != multiply(greatest_lower_bound(Y,Z),X)
| least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),greatest_lower_bound(multiply(Y,X),multiply(Z,X))) != greatest_lower_bound(multiply(Z,X),multiply(Y,X))
| least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),multiply(greatest_lower_bound(Y,Z),X)) = greatest_lower_bound(multiply(Z,X),multiply(Y,X)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),greatest_lower_bound(multiply(Y,X),multiply(Z,X))),greatest_lower_bound(multiply(Z,X),multiply(Y,X))) ),[0,1],$fot(multiply(greatest_lower_bound(Y,Z),X))]]) ).
cnf(refute_0_808,plain,
( least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),greatest_lower_bound(multiply(Y,X),multiply(Z,X))) != greatest_lower_bound(multiply(Z,X),multiply(Y,X))
| least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),multiply(greatest_lower_bound(Y,Z),X)) = greatest_lower_bound(multiply(Z,X),multiply(Y,X)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(Y,X),multiply(Z,X)),multiply(greatest_lower_bound(Y,Z),X)) )],[refute_0_806,refute_0_807]) ).
cnf(refute_0_809,plain,
least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),multiply(greatest_lower_bound(Y,Z),X)) = greatest_lower_bound(multiply(Z,X),multiply(Y,X)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),greatest_lower_bound(multiply(Y,X),multiply(Z,X))),greatest_lower_bound(multiply(Z,X),multiply(Y,X))) )],[refute_0_804,refute_0_808]) ).
cnf(refute_0_810,plain,
multiply(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),X) = multiply(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),X),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),X))]]) ).
cnf(refute_0_811,plain,
( multiply(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),X) != multiply(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),X)
| least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)) != greatest_lower_bound(Y,Z)
| multiply(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),X) = multiply(greatest_lower_bound(Y,Z),X) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),X),multiply(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),X)) ),[1,0],$fot(greatest_lower_bound(Y,Z))]]) ).
cnf(refute_0_812,plain,
( least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)) != greatest_lower_bound(Y,Z)
| multiply(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),X) = multiply(greatest_lower_bound(Y,Z),X) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),X),multiply(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),X)) )],[refute_0_810,refute_0_811]) ).
cnf(refute_0_813,plain,
multiply(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),X) = multiply(greatest_lower_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),greatest_lower_bound(Y,Z)) )],[refute_0_243,refute_0_812]) ).
cnf(refute_0_814,plain,
least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),multiply(greatest_lower_bound(Z,Y),X)) = multiply(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),X),
inference(subst,[],[refute_0_697:[bind(Y,$fot(greatest_lower_bound(Y,Z))),bind(Z,$fot(greatest_lower_bound(Z,Y)))]]) ).
cnf(refute_0_815,plain,
( multiply(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),X) != multiply(greatest_lower_bound(Y,Z),X)
| least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),multiply(greatest_lower_bound(Z,Y),X)) != multiply(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),X)
| least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),multiply(greatest_lower_bound(Z,Y),X)) = multiply(greatest_lower_bound(Y,Z),X) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),multiply(greatest_lower_bound(Z,Y),X)))),bind(Y0,$fot(multiply(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),X))),bind(Z0,$fot(multiply(greatest_lower_bound(Y,Z),X)))]]) ).
cnf(refute_0_816,plain,
( multiply(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),X) != multiply(greatest_lower_bound(Y,Z),X)
| least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),multiply(greatest_lower_bound(Z,Y),X)) = multiply(greatest_lower_bound(Y,Z),X) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),multiply(greatest_lower_bound(Z,Y),X)),multiply(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),X)) )],[refute_0_814,refute_0_815]) ).
cnf(refute_0_817,plain,
least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),multiply(greatest_lower_bound(Z,Y),X)) = multiply(greatest_lower_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),X),multiply(greatest_lower_bound(Y,Z),X)) )],[refute_0_813,refute_0_816]) ).
cnf(refute_0_818,plain,
greatest_lower_bound(multiply(Z,X),multiply(Y,X)) = multiply(greatest_lower_bound(Z,Y),X),
inference(subst,[],[refute_0_806:[bind(Y,$fot(Z)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_819,plain,
least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))) = least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))),
introduced(tautology,[refl,[$fot(least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))))]]) ).
cnf(refute_0_820,plain,
( greatest_lower_bound(multiply(Z,X),multiply(Y,X)) != multiply(greatest_lower_bound(Z,Y),X)
| least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))) != least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X)))
| least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))) = least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),multiply(greatest_lower_bound(Z,Y),X)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))),least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X)))) ),[1,1],$fot(multiply(greatest_lower_bound(Z,Y),X))]]) ).
cnf(refute_0_821,plain,
( greatest_lower_bound(multiply(Z,X),multiply(Y,X)) != multiply(greatest_lower_bound(Z,Y),X)
| least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))) = least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),multiply(greatest_lower_bound(Z,Y),X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))),least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X)))) )],[refute_0_819,refute_0_820]) ).
cnf(refute_0_822,plain,
least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))) = least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),multiply(greatest_lower_bound(Z,Y),X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),multiply(greatest_lower_bound(Z,Y),X)) )],[refute_0_818,refute_0_821]) ).
cnf(refute_0_823,plain,
( least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),multiply(greatest_lower_bound(Z,Y),X)) != multiply(greatest_lower_bound(Y,Z),X)
| least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))) != least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),multiply(greatest_lower_bound(Z,Y),X))
| least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))) = multiply(greatest_lower_bound(Y,Z),X) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))))),bind(Y0,$fot(least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),multiply(greatest_lower_bound(Z,Y),X)))),bind(Z0,$fot(multiply(greatest_lower_bound(Y,Z),X)))]]) ).
cnf(refute_0_824,plain,
( least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),multiply(greatest_lower_bound(Z,Y),X)) != multiply(greatest_lower_bound(Y,Z),X)
| least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))) = multiply(greatest_lower_bound(Y,Z),X) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))),least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),multiply(greatest_lower_bound(Z,Y),X))) )],[refute_0_822,refute_0_823]) ).
cnf(refute_0_825,plain,
least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))) = multiply(greatest_lower_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),multiply(greatest_lower_bound(Z,Y),X)),multiply(greatest_lower_bound(Y,Z),X)) )],[refute_0_817,refute_0_824]) ).
cnf(refute_0_826,plain,
least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),multiply(greatest_lower_bound(Y,Z),X)) = least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))),
inference(subst,[],[refute_0_4:[bind(X,$fot(multiply(greatest_lower_bound(Y,Z),X))),bind(Y,$fot(greatest_lower_bound(multiply(Z,X),multiply(Y,X))))]]) ).
cnf(refute_0_827,plain,
( least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))) != multiply(greatest_lower_bound(Y,Z),X)
| least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),multiply(greatest_lower_bound(Y,Z),X)) != least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X)))
| least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),multiply(greatest_lower_bound(Y,Z),X)) = multiply(greatest_lower_bound(Y,Z),X) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),multiply(greatest_lower_bound(Y,Z),X)))),bind(Y0,$fot(least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))))),bind(Z0,$fot(multiply(greatest_lower_bound(Y,Z),X)))]]) ).
cnf(refute_0_828,plain,
( least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))) != multiply(greatest_lower_bound(Y,Z),X)
| least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),multiply(greatest_lower_bound(Y,Z),X)) = multiply(greatest_lower_bound(Y,Z),X) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),multiply(greatest_lower_bound(Y,Z),X)),least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X)))) )],[refute_0_826,refute_0_827]) ).
cnf(refute_0_829,plain,
least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),multiply(greatest_lower_bound(Y,Z),X)) = multiply(greatest_lower_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))),multiply(greatest_lower_bound(Y,Z),X)) )],[refute_0_825,refute_0_828]) ).
cnf(refute_0_830,plain,
( least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),multiply(greatest_lower_bound(Y,Z),X)) != multiply(greatest_lower_bound(Y,Z),X)
| least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),multiply(greatest_lower_bound(Y,Z),X)) != greatest_lower_bound(multiply(Z,X),multiply(Y,X))
| multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Z,X),multiply(Y,X)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),multiply(greatest_lower_bound(Y,Z),X)),greatest_lower_bound(multiply(Z,X),multiply(Y,X))) ),[0],$fot(multiply(greatest_lower_bound(Y,Z),X))]]) ).
cnf(refute_0_831,plain,
( least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),multiply(greatest_lower_bound(Y,Z),X)) != greatest_lower_bound(multiply(Z,X),multiply(Y,X))
| multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Z,X),multiply(Y,X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),multiply(greatest_lower_bound(Y,Z),X)),multiply(greatest_lower_bound(Y,Z),X)) )],[refute_0_829,refute_0_830]) ).
cnf(refute_0_832,plain,
( multiply(greatest_lower_bound(Y,Z),X) != greatest_lower_bound(multiply(Z,X),multiply(Y,X))
| greatest_lower_bound(multiply(Z,X),multiply(Y,X)) != multiply(greatest_lower_bound(Z,Y),X)
| multiply(greatest_lower_bound(Y,Z),X) = multiply(greatest_lower_bound(Z,Y),X) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(Y,Z),X),multiply(greatest_lower_bound(Z,Y),X)) ),[0],$fot(greatest_lower_bound(multiply(Z,X),multiply(Y,X)))]]) ).
cnf(refute_0_833,plain,
( multiply(greatest_lower_bound(Y,Z),X) != greatest_lower_bound(multiply(Z,X),multiply(Y,X))
| multiply(greatest_lower_bound(Y,Z),X) = multiply(greatest_lower_bound(Z,Y),X) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),multiply(greatest_lower_bound(Z,Y),X)) )],[refute_0_818,refute_0_832]) ).
cnf(refute_0_834,plain,
( least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),multiply(greatest_lower_bound(Y,Z),X)) != greatest_lower_bound(multiply(Z,X),multiply(Y,X))
| multiply(greatest_lower_bound(Y,Z),X) = multiply(greatest_lower_bound(Z,Y),X) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))) )],[refute_0_831,refute_0_833]) ).
cnf(refute_0_835,plain,
multiply(greatest_lower_bound(Y,Z),X) = multiply(greatest_lower_bound(Z,Y),X),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),multiply(greatest_lower_bound(Y,Z),X)),greatest_lower_bound(multiply(Z,X),multiply(Y,X))) )],[refute_0_809,refute_0_834]) ).
cnf(refute_0_836,plain,
( multiply(greatest_lower_bound(Y,Z),X) != multiply(greatest_lower_bound(Z,Y),X)
| multiply(greatest_lower_bound(Z,Y),X) = multiply(greatest_lower_bound(Y,Z),X) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(greatest_lower_bound(Y,Z),X))),bind(Y0,$fot(multiply(greatest_lower_bound(Z,Y),X)))]]) ).
cnf(refute_0_837,plain,
multiply(greatest_lower_bound(Z,Y),X) = multiply(greatest_lower_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(Y,Z),X),multiply(greatest_lower_bound(Z,Y),X)) )],[refute_0_835,refute_0_836]) ).
cnf(refute_0_838,plain,
multiply(greatest_lower_bound(greatest_lower_bound(X_105,identity),identity),X_17) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_105,identity)),X_17),
inference(subst,[],[refute_0_837:[bind(X,$fot(X_17)),bind(Y,$fot(identity)),bind(Z,$fot(greatest_lower_bound(X_105,identity)))]]) ).
cnf(refute_0_839,plain,
( multiply(greatest_lower_bound(X_46,identity),X_45) != greatest_lower_bound(X_45,multiply(X_46,X_45))
| greatest_lower_bound(X_45,multiply(X_46,X_45)) = multiply(greatest_lower_bound(X_46,identity),X_45) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(greatest_lower_bound(X_46,identity),X_45))),bind(Y0,$fot(greatest_lower_bound(X_45,multiply(X_46,X_45))))]]) ).
cnf(refute_0_840,plain,
greatest_lower_bound(X_45,multiply(X_46,X_45)) = multiply(greatest_lower_bound(X_46,identity),X_45),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_46,identity),X_45),greatest_lower_bound(X_45,multiply(X_46,X_45))) )],[refute_0_746,refute_0_839]) ).
cnf(refute_0_841,plain,
greatest_lower_bound(X_17,multiply(greatest_lower_bound(X_105,identity),X_17)) = multiply(greatest_lower_bound(greatest_lower_bound(X_105,identity),identity),X_17),
inference(subst,[],[refute_0_840:[bind(X_45,$fot(X_17)),bind(X_46,$fot(greatest_lower_bound(X_105,identity)))]]) ).
cnf(refute_0_842,plain,
( multiply(greatest_lower_bound(greatest_lower_bound(X_105,identity),identity),X_17) != multiply(greatest_lower_bound(identity,greatest_lower_bound(X_105,identity)),X_17)
| greatest_lower_bound(X_17,multiply(greatest_lower_bound(X_105,identity),X_17)) != multiply(greatest_lower_bound(greatest_lower_bound(X_105,identity),identity),X_17)
| greatest_lower_bound(X_17,multiply(greatest_lower_bound(X_105,identity),X_17)) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_105,identity)),X_17) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(greatest_lower_bound(X_17,multiply(greatest_lower_bound(X_105,identity),X_17)))),bind(Y0,$fot(multiply(greatest_lower_bound(greatest_lower_bound(X_105,identity),identity),X_17))),bind(Z0,$fot(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_105,identity)),X_17)))]]) ).
cnf(refute_0_843,plain,
( multiply(greatest_lower_bound(greatest_lower_bound(X_105,identity),identity),X_17) != multiply(greatest_lower_bound(identity,greatest_lower_bound(X_105,identity)),X_17)
| greatest_lower_bound(X_17,multiply(greatest_lower_bound(X_105,identity),X_17)) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_105,identity)),X_17) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,multiply(greatest_lower_bound(X_105,identity),X_17)),multiply(greatest_lower_bound(greatest_lower_bound(X_105,identity),identity),X_17)) )],[refute_0_841,refute_0_842]) ).
cnf(refute_0_844,plain,
greatest_lower_bound(X_17,multiply(greatest_lower_bound(X_105,identity),X_17)) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_105,identity)),X_17),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(greatest_lower_bound(X_105,identity),identity),X_17),multiply(greatest_lower_bound(identity,greatest_lower_bound(X_105,identity)),X_17)) )],[refute_0_838,refute_0_843]) ).
cnf(refute_0_845,plain,
greatest_lower_bound(multiply(X_105,X_27),greatest_lower_bound(X_26,X_27)) = greatest_lower_bound(X_26,greatest_lower_bound(X_27,multiply(X_105,X_27))),
inference(subst,[],[refute_0_287:[bind(X,$fot(multiply(X_105,X_27)))]]) ).
cnf(refute_0_846,plain,
multiply(greatest_lower_bound(X_105,identity),X_27) = greatest_lower_bound(X_27,multiply(X_105,X_27)),
inference(subst,[],[refute_0_746:[bind(X_45,$fot(X_27)),bind(X_46,$fot(X_105))]]) ).
cnf(refute_0_847,plain,
( multiply(greatest_lower_bound(X_105,identity),X_27) != greatest_lower_bound(X_27,multiply(X_105,X_27))
| greatest_lower_bound(X_27,multiply(X_105,X_27)) = multiply(greatest_lower_bound(X_105,identity),X_27) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(greatest_lower_bound(X_105,identity),X_27))),bind(Y0,$fot(greatest_lower_bound(X_27,multiply(X_105,X_27))))]]) ).
cnf(refute_0_848,plain,
greatest_lower_bound(X_27,multiply(X_105,X_27)) = multiply(greatest_lower_bound(X_105,identity),X_27),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_105,identity),X_27),greatest_lower_bound(X_27,multiply(X_105,X_27))) )],[refute_0_846,refute_0_847]) ).
cnf(refute_0_849,plain,
( greatest_lower_bound(X_27,multiply(X_105,X_27)) != multiply(greatest_lower_bound(X_105,identity),X_27)
| greatest_lower_bound(multiply(X_105,X_27),greatest_lower_bound(X_26,X_27)) != greatest_lower_bound(X_26,greatest_lower_bound(X_27,multiply(X_105,X_27)))
| greatest_lower_bound(multiply(X_105,X_27),greatest_lower_bound(X_26,X_27)) = greatest_lower_bound(X_26,multiply(greatest_lower_bound(X_105,identity),X_27)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_105,X_27),greatest_lower_bound(X_26,X_27)),greatest_lower_bound(X_26,greatest_lower_bound(X_27,multiply(X_105,X_27)))) ),[1,1],$fot(multiply(greatest_lower_bound(X_105,identity),X_27))]]) ).
cnf(refute_0_850,plain,
( greatest_lower_bound(multiply(X_105,X_27),greatest_lower_bound(X_26,X_27)) != greatest_lower_bound(X_26,greatest_lower_bound(X_27,multiply(X_105,X_27)))
| greatest_lower_bound(multiply(X_105,X_27),greatest_lower_bound(X_26,X_27)) = greatest_lower_bound(X_26,multiply(greatest_lower_bound(X_105,identity),X_27)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_27,multiply(X_105,X_27)),multiply(greatest_lower_bound(X_105,identity),X_27)) )],[refute_0_848,refute_0_849]) ).
cnf(refute_0_851,plain,
greatest_lower_bound(multiply(X_105,X_27),greatest_lower_bound(X_26,X_27)) = greatest_lower_bound(X_26,multiply(greatest_lower_bound(X_105,identity),X_27)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_105,X_27),greatest_lower_bound(X_26,X_27)),greatest_lower_bound(X_26,greatest_lower_bound(X_27,multiply(X_105,X_27)))) )],[refute_0_845,refute_0_850]) ).
cnf(refute_0_852,plain,
greatest_lower_bound(multiply(X_105,X_27),greatest_lower_bound(X_26,X_27)) = greatest_lower_bound(X_27,greatest_lower_bound(X_26,multiply(X_105,X_27))),
inference(subst,[],[refute_0_334:[bind(Y,$fot(multiply(X_105,X_27))),bind(X_81,$fot(X_27)),bind(X_82,$fot(X_26))]]) ).
cnf(refute_0_853,plain,
( greatest_lower_bound(multiply(X_105,X_27),greatest_lower_bound(X_26,X_27)) != greatest_lower_bound(X_26,multiply(greatest_lower_bound(X_105,identity),X_27))
| greatest_lower_bound(multiply(X_105,X_27),greatest_lower_bound(X_26,X_27)) != greatest_lower_bound(X_27,greatest_lower_bound(X_26,multiply(X_105,X_27)))
| greatest_lower_bound(X_27,greatest_lower_bound(X_26,multiply(X_105,X_27))) = greatest_lower_bound(X_26,multiply(greatest_lower_bound(X_105,identity),X_27)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_105,X_27),greatest_lower_bound(X_26,X_27)),greatest_lower_bound(X_26,multiply(greatest_lower_bound(X_105,identity),X_27))) ),[0],$fot(greatest_lower_bound(X_27,greatest_lower_bound(X_26,multiply(X_105,X_27))))]]) ).
cnf(refute_0_854,plain,
( greatest_lower_bound(multiply(X_105,X_27),greatest_lower_bound(X_26,X_27)) != greatest_lower_bound(X_26,multiply(greatest_lower_bound(X_105,identity),X_27))
| greatest_lower_bound(X_27,greatest_lower_bound(X_26,multiply(X_105,X_27))) = greatest_lower_bound(X_26,multiply(greatest_lower_bound(X_105,identity),X_27)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_105,X_27),greatest_lower_bound(X_26,X_27)),greatest_lower_bound(X_27,greatest_lower_bound(X_26,multiply(X_105,X_27)))) )],[refute_0_852,refute_0_853]) ).
cnf(refute_0_855,plain,
greatest_lower_bound(X_27,greatest_lower_bound(X_26,multiply(X_105,X_27))) = greatest_lower_bound(X_26,multiply(greatest_lower_bound(X_105,identity),X_27)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_105,X_27),greatest_lower_bound(X_26,X_27)),greatest_lower_bound(X_26,multiply(greatest_lower_bound(X_105,identity),X_27))) )],[refute_0_851,refute_0_854]) ).
cnf(refute_0_856,plain,
greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_105,X_17))) = greatest_lower_bound(X_17,multiply(greatest_lower_bound(X_105,identity),X_17)),
inference(subst,[],[refute_0_855:[bind(X_26,$fot(X_17)),bind(X_27,$fot(X_17))]]) ).
cnf(refute_0_857,plain,
( greatest_lower_bound(X_17,multiply(greatest_lower_bound(X_105,identity),X_17)) != multiply(greatest_lower_bound(identity,greatest_lower_bound(X_105,identity)),X_17)
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_105,X_17))) != greatest_lower_bound(X_17,multiply(greatest_lower_bound(X_105,identity),X_17))
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_105,X_17))) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_105,identity)),X_17) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_105,X_17))))),bind(Y0,$fot(greatest_lower_bound(X_17,multiply(greatest_lower_bound(X_105,identity),X_17)))),bind(Z0,$fot(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_105,identity)),X_17)))]]) ).
cnf(refute_0_858,plain,
( greatest_lower_bound(X_17,multiply(greatest_lower_bound(X_105,identity),X_17)) != multiply(greatest_lower_bound(identity,greatest_lower_bound(X_105,identity)),X_17)
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_105,X_17))) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_105,identity)),X_17) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_105,X_17))),greatest_lower_bound(X_17,multiply(greatest_lower_bound(X_105,identity),X_17))) )],[refute_0_856,refute_0_857]) ).
cnf(refute_0_859,plain,
greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_105,X_17))) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_105,identity)),X_17),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,multiply(greatest_lower_bound(X_105,identity),X_17)),multiply(greatest_lower_bound(identity,greatest_lower_bound(X_105,identity)),X_17)) )],[refute_0_844,refute_0_858]) ).
cnf(refute_0_860,plain,
( multiply(greatest_lower_bound(identity,greatest_lower_bound(X_105,identity)),X_17) != multiply(greatest_lower_bound(identity,X_105),X_17)
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_105,X_17))) != multiply(greatest_lower_bound(identity,greatest_lower_bound(X_105,identity)),X_17)
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_105,X_17))) = multiply(greatest_lower_bound(identity,X_105),X_17) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_105,X_17))))),bind(Y0,$fot(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_105,identity)),X_17))),bind(Z0,$fot(multiply(greatest_lower_bound(identity,X_105),X_17)))]]) ).
cnf(refute_0_861,plain,
( multiply(greatest_lower_bound(identity,greatest_lower_bound(X_105,identity)),X_17) != multiply(greatest_lower_bound(identity,X_105),X_17)
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_105,X_17))) = multiply(greatest_lower_bound(identity,X_105),X_17) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_105,X_17))),multiply(greatest_lower_bound(identity,greatest_lower_bound(X_105,identity)),X_17)) )],[refute_0_859,refute_0_860]) ).
cnf(refute_0_862,plain,
greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_105,X_17))) = multiply(greatest_lower_bound(identity,X_105),X_17),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_105,identity)),X_17),multiply(greatest_lower_bound(identity,X_105),X_17)) )],[refute_0_803,refute_0_861]) ).
cnf(refute_0_863,plain,
( greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_105,X_17))) != multiply(greatest_lower_bound(X_105,identity),X_17)
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_105,X_17))) != multiply(greatest_lower_bound(identity,X_105),X_17)
| multiply(greatest_lower_bound(identity,X_105),X_17) = multiply(greatest_lower_bound(X_105,identity),X_17) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_105,X_17))),multiply(greatest_lower_bound(X_105,identity),X_17)) ),[0],$fot(multiply(greatest_lower_bound(identity,X_105),X_17))]]) ).
cnf(refute_0_864,plain,
( greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_105,X_17))) != multiply(greatest_lower_bound(X_105,identity),X_17)
| multiply(greatest_lower_bound(identity,X_105),X_17) = multiply(greatest_lower_bound(X_105,identity),X_17) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_105,X_17))),multiply(greatest_lower_bound(identity,X_105),X_17)) )],[refute_0_862,refute_0_863]) ).
cnf(refute_0_865,plain,
multiply(greatest_lower_bound(identity,X_105),X_17) = multiply(greatest_lower_bound(X_105,identity),X_17),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_105,X_17))),multiply(greatest_lower_bound(X_105,identity),X_17)) )],[refute_0_798,refute_0_864]) ).
cnf(refute_0_866,plain,
( multiply(greatest_lower_bound(identity,X_105),X_17) != multiply(greatest_lower_bound(X_105,identity),X_17)
| multiply(greatest_lower_bound(X_105,identity),X_17) = multiply(greatest_lower_bound(identity,X_105),X_17) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(greatest_lower_bound(identity,X_105),X_17))),bind(Y0,$fot(multiply(greatest_lower_bound(X_105,identity),X_17)))]]) ).
cnf(refute_0_867,plain,
multiply(greatest_lower_bound(X_105,identity),X_17) = multiply(greatest_lower_bound(identity,X_105),X_17),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_105),X_17),multiply(greatest_lower_bound(X_105,identity),X_17)) )],[refute_0_865,refute_0_866]) ).
cnf(refute_0_868,plain,
multiply(greatest_lower_bound(greatest_lower_bound(X_106,identity),identity),inverse(X_106)) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_106,identity)),inverse(X_106)),
inference(subst,[],[refute_0_867:[bind(X_105,$fot(greatest_lower_bound(X_106,identity))),bind(X_17,$fot(inverse(X_106)))]]) ).
cnf(refute_0_869,plain,
( multiply(greatest_lower_bound(greatest_lower_bound(X_106,identity),identity),inverse(X_106)) != multiply(greatest_lower_bound(identity,greatest_lower_bound(X_106,identity)),inverse(X_106))
| multiply(greatest_lower_bound(identity,greatest_lower_bound(X_106,identity)),inverse(X_106)) != multiply(greatest_lower_bound(identity,X_106),inverse(X_106))
| multiply(greatest_lower_bound(greatest_lower_bound(X_106,identity),identity),inverse(X_106)) = multiply(greatest_lower_bound(identity,X_106),inverse(X_106)) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(multiply(greatest_lower_bound(greatest_lower_bound(X_106,identity),identity),inverse(X_106)))),bind(Y0,$fot(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_106,identity)),inverse(X_106)))),bind(Z0,$fot(multiply(greatest_lower_bound(identity,X_106),inverse(X_106))))]]) ).
cnf(refute_0_870,plain,
( multiply(greatest_lower_bound(identity,greatest_lower_bound(X_106,identity)),inverse(X_106)) != multiply(greatest_lower_bound(identity,X_106),inverse(X_106))
| multiply(greatest_lower_bound(greatest_lower_bound(X_106,identity),identity),inverse(X_106)) = multiply(greatest_lower_bound(identity,X_106),inverse(X_106)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(greatest_lower_bound(X_106,identity),identity),inverse(X_106)),multiply(greatest_lower_bound(identity,greatest_lower_bound(X_106,identity)),inverse(X_106))) )],[refute_0_868,refute_0_869]) ).
cnf(refute_0_871,plain,
multiply(greatest_lower_bound(greatest_lower_bound(X_106,identity),identity),inverse(X_106)) = multiply(greatest_lower_bound(identity,X_106),inverse(X_106)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_106,identity)),inverse(X_106)),multiply(greatest_lower_bound(identity,X_106),inverse(X_106))) )],[refute_0_791,refute_0_870]) ).
cnf(refute_0_872,plain,
( multiply(greatest_lower_bound(greatest_lower_bound(X_106,identity),identity),inverse(X_106)) != multiply(greatest_lower_bound(identity,X_106),inverse(X_106))
| multiply(greatest_lower_bound(greatest_lower_bound(X_106,identity),identity),inverse(X_106)) != greatest_lower_bound(inverse(X_106),greatest_lower_bound(identity,inverse(X_106)))
| multiply(greatest_lower_bound(identity,X_106),inverse(X_106)) = greatest_lower_bound(inverse(X_106),greatest_lower_bound(identity,inverse(X_106))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(greatest_lower_bound(X_106,identity),identity),inverse(X_106)),greatest_lower_bound(inverse(X_106),greatest_lower_bound(identity,inverse(X_106)))) ),[0],$fot(multiply(greatest_lower_bound(identity,X_106),inverse(X_106)))]]) ).
cnf(refute_0_873,plain,
( multiply(greatest_lower_bound(greatest_lower_bound(X_106,identity),identity),inverse(X_106)) != greatest_lower_bound(inverse(X_106),greatest_lower_bound(identity,inverse(X_106)))
| multiply(greatest_lower_bound(identity,X_106),inverse(X_106)) = greatest_lower_bound(inverse(X_106),greatest_lower_bound(identity,inverse(X_106))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(greatest_lower_bound(X_106,identity),identity),inverse(X_106)),multiply(greatest_lower_bound(identity,X_106),inverse(X_106))) )],[refute_0_871,refute_0_872]) ).
cnf(refute_0_874,plain,
greatest_lower_bound(inverse(X_106),inverse(X_106)) = inverse(X_106),
inference(subst,[],[idempotence_of_gld:[bind(X,$fot(inverse(X_106)))]]) ).
cnf(refute_0_875,plain,
greatest_lower_bound(identity,greatest_lower_bound(inverse(X_106),inverse(X_106))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X_106),inverse(X_106))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_106),inverse(X_106))))]]) ).
cnf(refute_0_876,plain,
( greatest_lower_bound(identity,greatest_lower_bound(inverse(X_106),inverse(X_106))) != greatest_lower_bound(identity,greatest_lower_bound(inverse(X_106),inverse(X_106)))
| greatest_lower_bound(inverse(X_106),inverse(X_106)) != inverse(X_106)
| greatest_lower_bound(identity,greatest_lower_bound(inverse(X_106),inverse(X_106))) = greatest_lower_bound(identity,inverse(X_106)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_106),inverse(X_106))),greatest_lower_bound(identity,greatest_lower_bound(inverse(X_106),inverse(X_106)))) ),[1,1],$fot(inverse(X_106))]]) ).
cnf(refute_0_877,plain,
( greatest_lower_bound(inverse(X_106),inverse(X_106)) != inverse(X_106)
| greatest_lower_bound(identity,greatest_lower_bound(inverse(X_106),inverse(X_106))) = greatest_lower_bound(identity,inverse(X_106)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_106),inverse(X_106))),greatest_lower_bound(identity,greatest_lower_bound(inverse(X_106),inverse(X_106)))) )],[refute_0_875,refute_0_876]) ).
cnf(refute_0_878,plain,
greatest_lower_bound(identity,greatest_lower_bound(inverse(X_106),inverse(X_106))) = greatest_lower_bound(identity,inverse(X_106)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_106),inverse(X_106)),inverse(X_106)) )],[refute_0_874,refute_0_877]) ).
cnf(refute_0_879,plain,
greatest_lower_bound(greatest_lower_bound(Y,X_83),greatest_lower_bound(X_82,X_83)) = greatest_lower_bound(X_82,greatest_lower_bound(X_83,greatest_lower_bound(Y,X_83))),
inference(subst,[],[refute_0_287:[bind(X,$fot(greatest_lower_bound(Y,X_83))),bind(X_26,$fot(X_82)),bind(X_27,$fot(X_83))]]) ).
cnf(refute_0_880,plain,
greatest_lower_bound(X_83,greatest_lower_bound(Y,X_83)) = greatest_lower_bound(X_83,Y),
inference(subst,[],[refute_0_182:[bind(X_15,$fot(X_83))]]) ).
cnf(refute_0_881,plain,
( greatest_lower_bound(X_83,greatest_lower_bound(Y,X_83)) != greatest_lower_bound(X_83,Y)
| greatest_lower_bound(greatest_lower_bound(Y,X_83),greatest_lower_bound(X_82,X_83)) != greatest_lower_bound(X_82,greatest_lower_bound(X_83,greatest_lower_bound(Y,X_83)))
| greatest_lower_bound(greatest_lower_bound(Y,X_83),greatest_lower_bound(X_82,X_83)) = greatest_lower_bound(X_82,greatest_lower_bound(X_83,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(Y,X_83),greatest_lower_bound(X_82,X_83)),greatest_lower_bound(X_82,greatest_lower_bound(X_83,greatest_lower_bound(Y,X_83)))) ),[1,1],$fot(greatest_lower_bound(X_83,Y))]]) ).
cnf(refute_0_882,plain,
( greatest_lower_bound(greatest_lower_bound(Y,X_83),greatest_lower_bound(X_82,X_83)) != greatest_lower_bound(X_82,greatest_lower_bound(X_83,greatest_lower_bound(Y,X_83)))
| greatest_lower_bound(greatest_lower_bound(Y,X_83),greatest_lower_bound(X_82,X_83)) = greatest_lower_bound(X_82,greatest_lower_bound(X_83,Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_83,greatest_lower_bound(Y,X_83)),greatest_lower_bound(X_83,Y)) )],[refute_0_880,refute_0_881]) ).
cnf(refute_0_883,plain,
greatest_lower_bound(greatest_lower_bound(Y,X_83),greatest_lower_bound(X_82,X_83)) = greatest_lower_bound(X_82,greatest_lower_bound(X_83,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(Y,X_83),greatest_lower_bound(X_82,X_83)),greatest_lower_bound(X_82,greatest_lower_bound(X_83,greatest_lower_bound(Y,X_83)))) )],[refute_0_879,refute_0_882]) ).
cnf(refute_0_884,plain,
greatest_lower_bound(X_15,greatest_lower_bound(greatest_lower_bound(X_26,X_27),X_15)) = greatest_lower_bound(X_15,greatest_lower_bound(X_26,X_27)),
inference(subst,[],[refute_0_182:[bind(Y,$fot(greatest_lower_bound(X_26,X_27)))]]) ).
cnf(refute_0_885,plain,
greatest_lower_bound(X_26,greatest_lower_bound(X_27,X_15)) = greatest_lower_bound(greatest_lower_bound(X_26,X_27),X_15),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_26)),bind(Y,$fot(X_27)),bind(Z,$fot(X_15))]]) ).
cnf(refute_0_886,plain,
( greatest_lower_bound(X_26,greatest_lower_bound(X_27,X_15)) != greatest_lower_bound(greatest_lower_bound(X_26,X_27),X_15)
| greatest_lower_bound(greatest_lower_bound(X_26,X_27),X_15) = greatest_lower_bound(X_26,greatest_lower_bound(X_27,X_15)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X_26,greatest_lower_bound(X_27,X_15)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X_26,X_27),X_15)))]]) ).
cnf(refute_0_887,plain,
greatest_lower_bound(greatest_lower_bound(X_26,X_27),X_15) = greatest_lower_bound(X_26,greatest_lower_bound(X_27,X_15)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_26,greatest_lower_bound(X_27,X_15)),greatest_lower_bound(greatest_lower_bound(X_26,X_27),X_15)) )],[refute_0_885,refute_0_886]) ).
cnf(refute_0_888,plain,
( greatest_lower_bound(X_15,greatest_lower_bound(greatest_lower_bound(X_26,X_27),X_15)) != greatest_lower_bound(X_15,greatest_lower_bound(X_26,X_27))
| greatest_lower_bound(greatest_lower_bound(X_26,X_27),X_15) != greatest_lower_bound(X_26,greatest_lower_bound(X_27,X_15))
| greatest_lower_bound(X_15,greatest_lower_bound(X_26,greatest_lower_bound(X_27,X_15))) = greatest_lower_bound(X_15,greatest_lower_bound(X_26,X_27)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_15,greatest_lower_bound(greatest_lower_bound(X_26,X_27),X_15)),greatest_lower_bound(X_15,greatest_lower_bound(X_26,X_27))) ),[0,1],$fot(greatest_lower_bound(X_26,greatest_lower_bound(X_27,X_15)))]]) ).
cnf(refute_0_889,plain,
( greatest_lower_bound(X_15,greatest_lower_bound(greatest_lower_bound(X_26,X_27),X_15)) != greatest_lower_bound(X_15,greatest_lower_bound(X_26,X_27))
| greatest_lower_bound(X_15,greatest_lower_bound(X_26,greatest_lower_bound(X_27,X_15))) = greatest_lower_bound(X_15,greatest_lower_bound(X_26,X_27)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_26,X_27),X_15),greatest_lower_bound(X_26,greatest_lower_bound(X_27,X_15))) )],[refute_0_887,refute_0_888]) ).
cnf(refute_0_890,plain,
greatest_lower_bound(X_15,greatest_lower_bound(X_26,greatest_lower_bound(X_27,X_15))) = greatest_lower_bound(X_15,greatest_lower_bound(X_26,X_27)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_15,greatest_lower_bound(greatest_lower_bound(X_26,X_27),X_15)),greatest_lower_bound(X_15,greatest_lower_bound(X_26,X_27))) )],[refute_0_884,refute_0_889]) ).
cnf(refute_0_891,plain,
greatest_lower_bound(X_83,greatest_lower_bound(X_82,greatest_lower_bound(Y,X_83))) = greatest_lower_bound(X_83,greatest_lower_bound(X_82,Y)),
inference(subst,[],[refute_0_890:[bind(X_15,$fot(X_83)),bind(X_26,$fot(X_82)),bind(X_27,$fot(Y))]]) ).
cnf(refute_0_892,plain,
greatest_lower_bound(greatest_lower_bound(Y,X_83),greatest_lower_bound(X_82,X_83)) = greatest_lower_bound(X_83,greatest_lower_bound(X_82,greatest_lower_bound(Y,X_83))),
inference(subst,[],[refute_0_334:[bind(Y,$fot(greatest_lower_bound(Y,X_83))),bind(X_81,$fot(X_83))]]) ).
cnf(refute_0_893,plain,
( greatest_lower_bound(X_83,greatest_lower_bound(X_82,greatest_lower_bound(Y,X_83))) != greatest_lower_bound(X_83,greatest_lower_bound(X_82,Y))
| greatest_lower_bound(greatest_lower_bound(Y,X_83),greatest_lower_bound(X_82,X_83)) != greatest_lower_bound(X_83,greatest_lower_bound(X_82,greatest_lower_bound(Y,X_83)))
| greatest_lower_bound(greatest_lower_bound(Y,X_83),greatest_lower_bound(X_82,X_83)) = greatest_lower_bound(X_83,greatest_lower_bound(X_82,Y)) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(Y,X_83),greatest_lower_bound(X_82,X_83)))),bind(Y0,$fot(greatest_lower_bound(X_83,greatest_lower_bound(X_82,greatest_lower_bound(Y,X_83))))),bind(Z0,$fot(greatest_lower_bound(X_83,greatest_lower_bound(X_82,Y))))]]) ).
cnf(refute_0_894,plain,
( greatest_lower_bound(X_83,greatest_lower_bound(X_82,greatest_lower_bound(Y,X_83))) != greatest_lower_bound(X_83,greatest_lower_bound(X_82,Y))
| greatest_lower_bound(greatest_lower_bound(Y,X_83),greatest_lower_bound(X_82,X_83)) = greatest_lower_bound(X_83,greatest_lower_bound(X_82,Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(Y,X_83),greatest_lower_bound(X_82,X_83)),greatest_lower_bound(X_83,greatest_lower_bound(X_82,greatest_lower_bound(Y,X_83)))) )],[refute_0_892,refute_0_893]) ).
cnf(refute_0_895,plain,
greatest_lower_bound(greatest_lower_bound(Y,X_83),greatest_lower_bound(X_82,X_83)) = greatest_lower_bound(X_83,greatest_lower_bound(X_82,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_83,greatest_lower_bound(X_82,greatest_lower_bound(Y,X_83))),greatest_lower_bound(X_83,greatest_lower_bound(X_82,Y))) )],[refute_0_891,refute_0_894]) ).
cnf(refute_0_896,plain,
( greatest_lower_bound(greatest_lower_bound(Y,X_83),greatest_lower_bound(X_82,X_83)) != greatest_lower_bound(X_82,greatest_lower_bound(X_83,Y))
| greatest_lower_bound(greatest_lower_bound(Y,X_83),greatest_lower_bound(X_82,X_83)) != greatest_lower_bound(X_83,greatest_lower_bound(X_82,Y))
| greatest_lower_bound(X_83,greatest_lower_bound(X_82,Y)) = greatest_lower_bound(X_82,greatest_lower_bound(X_83,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(Y,X_83),greatest_lower_bound(X_82,X_83)),greatest_lower_bound(X_82,greatest_lower_bound(X_83,Y))) ),[0],$fot(greatest_lower_bound(X_83,greatest_lower_bound(X_82,Y)))]]) ).
cnf(refute_0_897,plain,
( greatest_lower_bound(greatest_lower_bound(Y,X_83),greatest_lower_bound(X_82,X_83)) != greatest_lower_bound(X_82,greatest_lower_bound(X_83,Y))
| greatest_lower_bound(X_83,greatest_lower_bound(X_82,Y)) = greatest_lower_bound(X_82,greatest_lower_bound(X_83,Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(Y,X_83),greatest_lower_bound(X_82,X_83)),greatest_lower_bound(X_83,greatest_lower_bound(X_82,Y))) )],[refute_0_895,refute_0_896]) ).
cnf(refute_0_898,plain,
greatest_lower_bound(X_83,greatest_lower_bound(X_82,Y)) = greatest_lower_bound(X_82,greatest_lower_bound(X_83,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(Y,X_83),greatest_lower_bound(X_82,X_83)),greatest_lower_bound(X_82,greatest_lower_bound(X_83,Y))) )],[refute_0_883,refute_0_897]) ).
cnf(refute_0_899,plain,
( greatest_lower_bound(X_83,greatest_lower_bound(X_82,Y)) != greatest_lower_bound(X_82,greatest_lower_bound(X_83,Y))
| greatest_lower_bound(X_82,greatest_lower_bound(X_83,Y)) = greatest_lower_bound(X_83,greatest_lower_bound(X_82,Y)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X_83,greatest_lower_bound(X_82,Y)))),bind(Y0,$fot(greatest_lower_bound(X_82,greatest_lower_bound(X_83,Y))))]]) ).
cnf(refute_0_900,plain,
greatest_lower_bound(X_82,greatest_lower_bound(X_83,Y)) = greatest_lower_bound(X_83,greatest_lower_bound(X_82,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_83,greatest_lower_bound(X_82,Y)),greatest_lower_bound(X_82,greatest_lower_bound(X_83,Y))) )],[refute_0_898,refute_0_899]) ).
cnf(refute_0_901,plain,
greatest_lower_bound(inverse(X_106),greatest_lower_bound(identity,inverse(X_106))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X_106),inverse(X_106))),
inference(subst,[],[refute_0_900:[bind(Y,$fot(inverse(X_106))),bind(X_82,$fot(inverse(X_106))),bind(X_83,$fot(identity))]]) ).
cnf(refute_0_902,plain,
( greatest_lower_bound(identity,greatest_lower_bound(inverse(X_106),inverse(X_106))) != greatest_lower_bound(identity,inverse(X_106))
| greatest_lower_bound(inverse(X_106),greatest_lower_bound(identity,inverse(X_106))) != greatest_lower_bound(identity,greatest_lower_bound(inverse(X_106),inverse(X_106)))
| greatest_lower_bound(inverse(X_106),greatest_lower_bound(identity,inverse(X_106))) = greatest_lower_bound(identity,inverse(X_106)) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(greatest_lower_bound(inverse(X_106),greatest_lower_bound(identity,inverse(X_106))))),bind(Y0,$fot(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_106),inverse(X_106))))),bind(Z0,$fot(greatest_lower_bound(identity,inverse(X_106))))]]) ).
cnf(refute_0_903,plain,
( greatest_lower_bound(identity,greatest_lower_bound(inverse(X_106),inverse(X_106))) != greatest_lower_bound(identity,inverse(X_106))
| greatest_lower_bound(inverse(X_106),greatest_lower_bound(identity,inverse(X_106))) = greatest_lower_bound(identity,inverse(X_106)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_106),greatest_lower_bound(identity,inverse(X_106))),greatest_lower_bound(identity,greatest_lower_bound(inverse(X_106),inverse(X_106)))) )],[refute_0_901,refute_0_902]) ).
cnf(refute_0_904,plain,
greatest_lower_bound(inverse(X_106),greatest_lower_bound(identity,inverse(X_106))) = greatest_lower_bound(identity,inverse(X_106)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_106),inverse(X_106))),greatest_lower_bound(identity,inverse(X_106))) )],[refute_0_878,refute_0_903]) ).
cnf(refute_0_905,plain,
( multiply(greatest_lower_bound(identity,X_106),inverse(X_106)) != greatest_lower_bound(inverse(X_106),greatest_lower_bound(identity,inverse(X_106)))
| greatest_lower_bound(inverse(X_106),greatest_lower_bound(identity,inverse(X_106))) != greatest_lower_bound(identity,inverse(X_106))
| multiply(greatest_lower_bound(identity,X_106),inverse(X_106)) = greatest_lower_bound(identity,inverse(X_106)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(identity,X_106),inverse(X_106)),greatest_lower_bound(identity,inverse(X_106))) ),[0],$fot(greatest_lower_bound(inverse(X_106),greatest_lower_bound(identity,inverse(X_106))))]]) ).
cnf(refute_0_906,plain,
( multiply(greatest_lower_bound(identity,X_106),inverse(X_106)) != greatest_lower_bound(inverse(X_106),greatest_lower_bound(identity,inverse(X_106)))
| multiply(greatest_lower_bound(identity,X_106),inverse(X_106)) = greatest_lower_bound(identity,inverse(X_106)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_106),greatest_lower_bound(identity,inverse(X_106))),greatest_lower_bound(identity,inverse(X_106))) )],[refute_0_904,refute_0_905]) ).
cnf(refute_0_907,plain,
( multiply(greatest_lower_bound(greatest_lower_bound(X_106,identity),identity),inverse(X_106)) != greatest_lower_bound(inverse(X_106),greatest_lower_bound(identity,inverse(X_106)))
| multiply(greatest_lower_bound(identity,X_106),inverse(X_106)) = greatest_lower_bound(identity,inverse(X_106)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_106),inverse(X_106)),greatest_lower_bound(inverse(X_106),greatest_lower_bound(identity,inverse(X_106)))) )],[refute_0_873,refute_0_906]) ).
cnf(refute_0_908,plain,
multiply(greatest_lower_bound(identity,X_106),inverse(X_106)) = greatest_lower_bound(identity,inverse(X_106)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(greatest_lower_bound(X_106,identity),identity),inverse(X_106)),greatest_lower_bound(inverse(X_106),greatest_lower_bound(identity,inverse(X_106)))) )],[refute_0_786,refute_0_907]) ).
cnf(refute_0_909,plain,
multiply(greatest_lower_bound(identity,X_115),inverse(X_115)) = greatest_lower_bound(identity,inverse(X_115)),
inference(subst,[],[refute_0_908:[bind(X_106,$fot(X_115))]]) ).
cnf(refute_0_910,plain,
( multiply(greatest_lower_bound(identity,X_115),inverse(X_115)) != greatest_lower_bound(identity,inverse(X_115))
| multiply(greatest_lower_bound(identity,X_115),least_upper_bound(inverse(X_115),identity)) != least_upper_bound(greatest_lower_bound(identity,X_115),multiply(greatest_lower_bound(identity,X_115),inverse(X_115)))
| multiply(greatest_lower_bound(identity,X_115),least_upper_bound(inverse(X_115),identity)) = least_upper_bound(greatest_lower_bound(identity,X_115),greatest_lower_bound(identity,inverse(X_115))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_115),least_upper_bound(inverse(X_115),identity)),least_upper_bound(greatest_lower_bound(identity,X_115),multiply(greatest_lower_bound(identity,X_115),inverse(X_115)))) ),[1,1],$fot(greatest_lower_bound(identity,inverse(X_115)))]]) ).
cnf(refute_0_911,plain,
( multiply(greatest_lower_bound(identity,X_115),least_upper_bound(inverse(X_115),identity)) != least_upper_bound(greatest_lower_bound(identity,X_115),multiply(greatest_lower_bound(identity,X_115),inverse(X_115)))
| multiply(greatest_lower_bound(identity,X_115),least_upper_bound(inverse(X_115),identity)) = least_upper_bound(greatest_lower_bound(identity,X_115),greatest_lower_bound(identity,inverse(X_115))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_115),inverse(X_115)),greatest_lower_bound(identity,inverse(X_115))) )],[refute_0_909,refute_0_910]) ).
cnf(refute_0_912,plain,
multiply(greatest_lower_bound(identity,X_115),least_upper_bound(inverse(X_115),identity)) = least_upper_bound(greatest_lower_bound(identity,X_115),greatest_lower_bound(identity,inverse(X_115))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_115),least_upper_bound(inverse(X_115),identity)),least_upper_bound(greatest_lower_bound(identity,X_115),multiply(greatest_lower_bound(identity,X_115),inverse(X_115)))) )],[refute_0_737,refute_0_911]) ).
cnf(refute_0_913,plain,
greatest_lower_bound(least_upper_bound(X_22,Y),least_upper_bound(Y,least_upper_bound(X_22,Y))) = least_upper_bound(X_22,Y),
inference(subst,[],[refute_0_171:[bind(X,$fot(least_upper_bound(X_22,Y)))]]) ).
cnf(refute_0_914,plain,
least_upper_bound(Y,least_upper_bound(X_22,Y)) = least_upper_bound(Y,X_22),
inference(subst,[],[refute_0_64:[bind(Y,$fot(X_22)),bind(X_21,$fot(Y))]]) ).
cnf(refute_0_915,plain,
( greatest_lower_bound(least_upper_bound(X_22,Y),least_upper_bound(Y,least_upper_bound(X_22,Y))) != least_upper_bound(X_22,Y)
| least_upper_bound(Y,least_upper_bound(X_22,Y)) != least_upper_bound(Y,X_22)
| greatest_lower_bound(least_upper_bound(X_22,Y),least_upper_bound(Y,X_22)) = least_upper_bound(X_22,Y) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_22,Y),least_upper_bound(Y,least_upper_bound(X_22,Y))),least_upper_bound(X_22,Y)) ),[0,1],$fot(least_upper_bound(Y,X_22))]]) ).
cnf(refute_0_916,plain,
( greatest_lower_bound(least_upper_bound(X_22,Y),least_upper_bound(Y,least_upper_bound(X_22,Y))) != least_upper_bound(X_22,Y)
| greatest_lower_bound(least_upper_bound(X_22,Y),least_upper_bound(Y,X_22)) = least_upper_bound(X_22,Y) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_22,Y)),least_upper_bound(Y,X_22)) )],[refute_0_914,refute_0_915]) ).
cnf(refute_0_917,plain,
greatest_lower_bound(least_upper_bound(X_22,Y),least_upper_bound(Y,X_22)) = least_upper_bound(X_22,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_22,Y),least_upper_bound(Y,least_upper_bound(X_22,Y))),least_upper_bound(X_22,Y)) )],[refute_0_913,refute_0_916]) ).
cnf(refute_0_918,plain,
greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),least_upper_bound(multiply(X,Y),multiply(X,Z))) = least_upper_bound(multiply(X,Z),multiply(X,Y)),
inference(subst,[],[refute_0_917:[bind(Y,$fot(multiply(X,Y))),bind(X_22,$fot(multiply(X,Z)))]]) ).
cnf(refute_0_919,plain,
( greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),least_upper_bound(multiply(X,Y),multiply(X,Z))) != least_upper_bound(multiply(X,Z),multiply(X,Y))
| least_upper_bound(multiply(X,Y),multiply(X,Z)) != multiply(X,least_upper_bound(Y,Z))
| greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = least_upper_bound(multiply(X,Z),multiply(X,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),least_upper_bound(multiply(X,Y),multiply(X,Z))),least_upper_bound(multiply(X,Z),multiply(X,Y))) ),[0,1],$fot(multiply(X,least_upper_bound(Y,Z)))]]) ).
cnf(refute_0_920,plain,
( greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),least_upper_bound(multiply(X,Y),multiply(X,Z))) != least_upper_bound(multiply(X,Z),multiply(X,Y))
| greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = least_upper_bound(multiply(X,Z),multiply(X,Y)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,Y),multiply(X,Z)),multiply(X,least_upper_bound(Y,Z))) )],[refute_0_249,refute_0_919]) ).
cnf(refute_0_921,plain,
greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = least_upper_bound(multiply(X,Z),multiply(X,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),least_upper_bound(multiply(X,Y),multiply(X,Z))),least_upper_bound(multiply(X,Z),multiply(X,Y))) )],[refute_0_918,refute_0_920]) ).
cnf(refute_0_922,plain,
greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)) = least_upper_bound(Y,Z),
inference(subst,[],[refute_0_917:[bind(Y,$fot(Z)),bind(X_22,$fot(Y))]]) ).
cnf(refute_0_923,plain,
multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) = multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))),
introduced(tautology,[refl,[$fot(multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))))]]) ).
cnf(refute_0_924,plain,
( multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) != multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)))
| greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)) != least_upper_bound(Y,Z)
| multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) = multiply(X,least_upper_bound(Y,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))),multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)))) ),[1,1],$fot(least_upper_bound(Y,Z))]]) ).
cnf(refute_0_925,plain,
( greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)) != least_upper_bound(Y,Z)
| multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) = multiply(X,least_upper_bound(Y,Z)) ),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))),multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)))) )],[refute_0_923,refute_0_924]) ).
cnf(refute_0_926,plain,
multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) = multiply(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),least_upper_bound(Y,Z)) )],[refute_0_922,refute_0_925]) ).
cnf(refute_0_927,plain,
greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) = multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))),
inference(subst,[],[refute_0_239:[bind(Y,$fot(least_upper_bound(Y,Z))),bind(Z,$fot(least_upper_bound(Z,Y)))]]) ).
cnf(refute_0_928,plain,
( multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) != multiply(X,least_upper_bound(Y,Z))
| greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) != multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)))
| greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) = multiply(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))))),bind(Y0,$fot(multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))))),bind(Z0,$fot(multiply(X,least_upper_bound(Y,Z))))]]) ).
cnf(refute_0_929,plain,
( multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) != multiply(X,least_upper_bound(Y,Z))
| greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) = multiply(X,least_upper_bound(Y,Z)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))),multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)))) )],[refute_0_927,refute_0_928]) ).
cnf(refute_0_930,plain,
greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) = multiply(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))),multiply(X,least_upper_bound(Y,Z))) )],[refute_0_926,refute_0_929]) ).
cnf(refute_0_931,plain,
least_upper_bound(multiply(X,Z),multiply(X,Y)) = multiply(X,least_upper_bound(Z,Y)),
inference(subst,[],[refute_0_249:[bind(Y,$fot(Z)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_932,plain,
greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))))]]) ).
cnf(refute_0_933,plain,
( greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) != greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y)))
| least_upper_bound(multiply(X,Z),multiply(X,Y)) != multiply(X,least_upper_bound(Z,Y))
| greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))),greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y)))) ),[1,1],$fot(multiply(X,least_upper_bound(Z,Y)))]]) ).
cnf(refute_0_934,plain,
( least_upper_bound(multiply(X,Z),multiply(X,Y)) != multiply(X,least_upper_bound(Z,Y))
| greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))),greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y)))) )],[refute_0_932,refute_0_933]) ).
cnf(refute_0_935,plain,
greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Z,Y))) )],[refute_0_931,refute_0_934]) ).
cnf(refute_0_936,plain,
( greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) != multiply(X,least_upper_bound(Y,Z))
| greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) != greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y)))
| greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = multiply(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))))),bind(Y0,$fot(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))))),bind(Z0,$fot(multiply(X,least_upper_bound(Y,Z))))]]) ).
cnf(refute_0_937,plain,
( greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) != multiply(X,least_upper_bound(Y,Z))
| greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = multiply(X,least_upper_bound(Y,Z)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))),greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y)))) )],[refute_0_935,refute_0_936]) ).
cnf(refute_0_938,plain,
greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = multiply(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))),multiply(X,least_upper_bound(Y,Z))) )],[refute_0_930,refute_0_937]) ).
cnf(refute_0_939,plain,
greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))),
inference(subst,[],[refute_0_122:[bind(X,$fot(multiply(X,least_upper_bound(Y,Z)))),bind(Y,$fot(least_upper_bound(multiply(X,Z),multiply(X,Y))))]]) ).
cnf(refute_0_940,plain,
( greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) != multiply(X,least_upper_bound(Y,Z))
| greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) != greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y)))
| greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = multiply(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))))),bind(Y0,$fot(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))))),bind(Z0,$fot(multiply(X,least_upper_bound(Y,Z))))]]) ).
cnf(refute_0_941,plain,
( greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) != multiply(X,least_upper_bound(Y,Z))
| greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = multiply(X,least_upper_bound(Y,Z)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))),greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y)))) )],[refute_0_939,refute_0_940]) ).
cnf(refute_0_942,plain,
greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = multiply(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))),multiply(X,least_upper_bound(Y,Z))) )],[refute_0_938,refute_0_941]) ).
cnf(refute_0_943,plain,
( greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) != multiply(X,least_upper_bound(Y,Z))
| greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) != least_upper_bound(multiply(X,Z),multiply(X,Y))
| multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Z),multiply(X,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))),least_upper_bound(multiply(X,Z),multiply(X,Y))) ),[0],$fot(multiply(X,least_upper_bound(Y,Z)))]]) ).
cnf(refute_0_944,plain,
( greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) != least_upper_bound(multiply(X,Z),multiply(X,Y))
| multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Z),multiply(X,Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))),multiply(X,least_upper_bound(Y,Z))) )],[refute_0_942,refute_0_943]) ).
cnf(refute_0_945,plain,
( multiply(X,least_upper_bound(Y,Z)) != least_upper_bound(multiply(X,Z),multiply(X,Y))
| least_upper_bound(multiply(X,Z),multiply(X,Y)) != multiply(X,least_upper_bound(Z,Y))
| multiply(X,least_upper_bound(Y,Z)) = multiply(X,least_upper_bound(Z,Y)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) ),[0],$fot(least_upper_bound(multiply(X,Z),multiply(X,Y)))]]) ).
cnf(refute_0_946,plain,
( multiply(X,least_upper_bound(Y,Z)) != least_upper_bound(multiply(X,Z),multiply(X,Y))
| multiply(X,least_upper_bound(Y,Z)) = multiply(X,least_upper_bound(Z,Y)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Z,Y))) )],[refute_0_931,refute_0_945]) ).
cnf(refute_0_947,plain,
( greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) != least_upper_bound(multiply(X,Z),multiply(X,Y))
| multiply(X,least_upper_bound(Y,Z)) = multiply(X,least_upper_bound(Z,Y)) ),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) )],[refute_0_944,refute_0_946]) ).
cnf(refute_0_948,plain,
multiply(X,least_upper_bound(Y,Z)) = multiply(X,least_upper_bound(Z,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))),least_upper_bound(multiply(X,Z),multiply(X,Y))) )],[refute_0_921,refute_0_947]) ).
cnf(refute_0_949,plain,
( multiply(X,least_upper_bound(Y,Z)) != multiply(X,least_upper_bound(Z,Y))
| multiply(X,least_upper_bound(Z,Y)) = multiply(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X,least_upper_bound(Y,Z)))),bind(Y0,$fot(multiply(X,least_upper_bound(Z,Y))))]]) ).
cnf(refute_0_950,plain,
multiply(X,least_upper_bound(Z,Y)) = multiply(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) )],[refute_0_948,refute_0_949]) ).
cnf(refute_0_951,plain,
multiply(greatest_lower_bound(identity,X_115),least_upper_bound(inverse(X_115),identity)) = multiply(greatest_lower_bound(identity,X_115),least_upper_bound(identity,inverse(X_115))),
inference(subst,[],[refute_0_950:[bind(X,$fot(greatest_lower_bound(identity,X_115))),bind(Y,$fot(identity)),bind(Z,$fot(inverse(X_115)))]]) ).
cnf(refute_0_952,plain,
( multiply(greatest_lower_bound(identity,X_115),least_upper_bound(inverse(X_115),identity)) != multiply(greatest_lower_bound(identity,X_115),least_upper_bound(identity,inverse(X_115)))
| multiply(greatest_lower_bound(identity,X_115),least_upper_bound(inverse(X_115),identity)) != least_upper_bound(greatest_lower_bound(identity,X_115),greatest_lower_bound(identity,inverse(X_115)))
| multiply(greatest_lower_bound(identity,X_115),least_upper_bound(identity,inverse(X_115))) = least_upper_bound(greatest_lower_bound(identity,X_115),greatest_lower_bound(identity,inverse(X_115))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_115),least_upper_bound(inverse(X_115),identity)),least_upper_bound(greatest_lower_bound(identity,X_115),greatest_lower_bound(identity,inverse(X_115)))) ),[0],$fot(multiply(greatest_lower_bound(identity,X_115),least_upper_bound(identity,inverse(X_115))))]]) ).
cnf(refute_0_953,plain,
( multiply(greatest_lower_bound(identity,X_115),least_upper_bound(inverse(X_115),identity)) != least_upper_bound(greatest_lower_bound(identity,X_115),greatest_lower_bound(identity,inverse(X_115)))
| multiply(greatest_lower_bound(identity,X_115),least_upper_bound(identity,inverse(X_115))) = least_upper_bound(greatest_lower_bound(identity,X_115),greatest_lower_bound(identity,inverse(X_115))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_115),least_upper_bound(inverse(X_115),identity)),multiply(greatest_lower_bound(identity,X_115),least_upper_bound(identity,inverse(X_115)))) )],[refute_0_951,refute_0_952]) ).
cnf(refute_0_954,plain,
( multiply(least_upper_bound(identity,inverse(X_51)),greatest_lower_bound(identity,X_51)) != least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(identity,inverse(X_51)))
| least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(identity,inverse(X_51))) = multiply(least_upper_bound(identity,inverse(X_51)),greatest_lower_bound(identity,X_51)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(identity,inverse(X_51)),greatest_lower_bound(identity,X_51)))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(identity,inverse(X_51)))))]]) ).
cnf(refute_0_955,plain,
least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(identity,inverse(X_51))) = multiply(least_upper_bound(identity,inverse(X_51)),greatest_lower_bound(identity,X_51)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_51)),greatest_lower_bound(identity,X_51)),least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(identity,inverse(X_51)))) )],[refute_0_725,refute_0_954]) ).
cnf(refute_0_956,plain,
least_upper_bound(greatest_lower_bound(identity,X_115),greatest_lower_bound(identity,inverse(X_115))) = multiply(least_upper_bound(identity,inverse(X_115)),greatest_lower_bound(identity,X_115)),
inference(subst,[],[refute_0_955:[bind(X_51,$fot(X_115))]]) ).
cnf(refute_0_957,plain,
( multiply(greatest_lower_bound(identity,X_115),least_upper_bound(identity,inverse(X_115))) != least_upper_bound(greatest_lower_bound(identity,X_115),greatest_lower_bound(identity,inverse(X_115)))
| least_upper_bound(greatest_lower_bound(identity,X_115),greatest_lower_bound(identity,inverse(X_115))) != multiply(least_upper_bound(identity,inverse(X_115)),greatest_lower_bound(identity,X_115))
| multiply(greatest_lower_bound(identity,X_115),least_upper_bound(identity,inverse(X_115))) = multiply(least_upper_bound(identity,inverse(X_115)),greatest_lower_bound(identity,X_115)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(identity,X_115),least_upper_bound(identity,inverse(X_115))),multiply(least_upper_bound(identity,inverse(X_115)),greatest_lower_bound(identity,X_115))) ),[0],$fot(least_upper_bound(greatest_lower_bound(identity,X_115),greatest_lower_bound(identity,inverse(X_115))))]]) ).
cnf(refute_0_958,plain,
( multiply(greatest_lower_bound(identity,X_115),least_upper_bound(identity,inverse(X_115))) != least_upper_bound(greatest_lower_bound(identity,X_115),greatest_lower_bound(identity,inverse(X_115)))
| multiply(greatest_lower_bound(identity,X_115),least_upper_bound(identity,inverse(X_115))) = multiply(least_upper_bound(identity,inverse(X_115)),greatest_lower_bound(identity,X_115)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,X_115),greatest_lower_bound(identity,inverse(X_115))),multiply(least_upper_bound(identity,inverse(X_115)),greatest_lower_bound(identity,X_115))) )],[refute_0_956,refute_0_957]) ).
cnf(refute_0_959,plain,
( multiply(greatest_lower_bound(identity,X_115),least_upper_bound(inverse(X_115),identity)) != least_upper_bound(greatest_lower_bound(identity,X_115),greatest_lower_bound(identity,inverse(X_115)))
| multiply(greatest_lower_bound(identity,X_115),least_upper_bound(identity,inverse(X_115))) = multiply(least_upper_bound(identity,inverse(X_115)),greatest_lower_bound(identity,X_115)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_115),least_upper_bound(identity,inverse(X_115))),least_upper_bound(greatest_lower_bound(identity,X_115),greatest_lower_bound(identity,inverse(X_115)))) )],[refute_0_953,refute_0_958]) ).
cnf(refute_0_960,plain,
multiply(greatest_lower_bound(identity,X_115),least_upper_bound(identity,inverse(X_115))) = multiply(least_upper_bound(identity,inverse(X_115)),greatest_lower_bound(identity,X_115)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_115),least_upper_bound(inverse(X_115),identity)),least_upper_bound(greatest_lower_bound(identity,X_115),greatest_lower_bound(identity,inverse(X_115)))) )],[refute_0_912,refute_0_959]) ).
cnf(refute_0_961,plain,
( multiply(greatest_lower_bound(identity,X_115),least_upper_bound(identity,inverse(X_115))) != multiply(least_upper_bound(identity,inverse(X_115)),greatest_lower_bound(identity,X_115))
| multiply(least_upper_bound(identity,inverse(X_115)),greatest_lower_bound(identity,X_115)) = multiply(greatest_lower_bound(identity,X_115),least_upper_bound(identity,inverse(X_115))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(greatest_lower_bound(identity,X_115),least_upper_bound(identity,inverse(X_115))))),bind(Y0,$fot(multiply(least_upper_bound(identity,inverse(X_115)),greatest_lower_bound(identity,X_115))))]]) ).
cnf(refute_0_962,plain,
multiply(least_upper_bound(identity,inverse(X_115)),greatest_lower_bound(identity,X_115)) = multiply(greatest_lower_bound(identity,X_115),least_upper_bound(identity,inverse(X_115))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_115),least_upper_bound(identity,inverse(X_115))),multiply(least_upper_bound(identity,inverse(X_115)),greatest_lower_bound(identity,X_115))) )],[refute_0_960,refute_0_961]) ).
cnf(refute_0_963,plain,
multiply(least_upper_bound(identity,inverse(X_51)),greatest_lower_bound(identity,X_51)) = multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51))),
inference(subst,[],[refute_0_962:[bind(X_115,$fot(X_51))]]) ).
cnf(refute_0_964,plain,
( multiply(least_upper_bound(identity,inverse(X_51)),greatest_lower_bound(identity,X_51)) != multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))
| multiply(least_upper_bound(identity,inverse(X_51)),greatest_lower_bound(identity,X_51)) != least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(identity,inverse(X_51)))
| multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51))) = least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(identity,inverse(X_51))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_51)),greatest_lower_bound(identity,X_51)),least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(identity,inverse(X_51)))) ),[0],$fot(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51))))]]) ).
cnf(refute_0_965,plain,
( multiply(least_upper_bound(identity,inverse(X_51)),greatest_lower_bound(identity,X_51)) != least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(identity,inverse(X_51)))
| multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51))) = least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(identity,inverse(X_51))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_51)),greatest_lower_bound(identity,X_51)),multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))) )],[refute_0_963,refute_0_964]) ).
cnf(refute_0_966,plain,
multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51))) = least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(identity,inverse(X_51))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_51)),greatest_lower_bound(identity,X_51)),least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(identity,inverse(X_51)))) )],[refute_0_725,refute_0_965]) ).
cnf(refute_0_967,plain,
( multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51))) != least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(identity,inverse(X_51)))
| least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(identity,inverse(X_51))) = multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51))))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(identity,inverse(X_51)))))]]) ).
cnf(refute_0_968,plain,
least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(identity,inverse(X_51))) = multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51))),least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(identity,inverse(X_51)))) )],[refute_0_966,refute_0_967]) ).
cnf(refute_0_969,plain,
( inverse(greatest_lower_bound(identity,X_51)) != multiply(inverse(least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(identity,inverse(X_51)))),least_upper_bound(identity,multiply(greatest_lower_bound(identity,inverse(X_51)),inverse(greatest_lower_bound(identity,X_51)))))
| least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(identity,inverse(X_51))) != multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))
| inverse(greatest_lower_bound(identity,X_51)) = multiply(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),least_upper_bound(identity,multiply(greatest_lower_bound(identity,inverse(X_51)),inverse(greatest_lower_bound(identity,X_51))))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,X_51)),multiply(inverse(least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(identity,inverse(X_51)))),least_upper_bound(identity,multiply(greatest_lower_bound(identity,inverse(X_51)),inverse(greatest_lower_bound(identity,X_51)))))) ),[1,0,0],$fot(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51))))]]) ).
cnf(refute_0_970,plain,
( inverse(greatest_lower_bound(identity,X_51)) != multiply(inverse(least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(identity,inverse(X_51)))),least_upper_bound(identity,multiply(greatest_lower_bound(identity,inverse(X_51)),inverse(greatest_lower_bound(identity,X_51)))))
| inverse(greatest_lower_bound(identity,X_51)) = multiply(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),least_upper_bound(identity,multiply(greatest_lower_bound(identity,inverse(X_51)),inverse(greatest_lower_bound(identity,X_51))))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(identity,inverse(X_51))),multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))) )],[refute_0_968,refute_0_969]) ).
cnf(refute_0_971,plain,
inverse(greatest_lower_bound(identity,X_51)) = multiply(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),least_upper_bound(identity,multiply(greatest_lower_bound(identity,inverse(X_51)),inverse(greatest_lower_bound(identity,X_51))))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,X_51)),multiply(inverse(least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(identity,inverse(X_51)))),least_upper_bound(identity,multiply(greatest_lower_bound(identity,inverse(X_51)),inverse(greatest_lower_bound(identity,X_51)))))) )],[refute_0_663,refute_0_970]) ).
cnf(refute_0_972,plain,
inverse(multiply(greatest_lower_bound(identity,X_269),inverse(greatest_lower_bound(identity,inverse(X_269))))) = multiply(inverse(inverse(greatest_lower_bound(identity,inverse(X_269)))),inverse(greatest_lower_bound(identity,X_269))),
inference(subst,[],[p18_3:[bind(X,$fot(greatest_lower_bound(identity,X_269))),bind(Y,$fot(inverse(greatest_lower_bound(identity,inverse(X_269)))))]]) ).
cnf(refute_0_973,plain,
X_94 = multiply(inverse(inverse(greatest_lower_bound(identity,X_94))),multiply(inverse(greatest_lower_bound(identity,X_94)),X_94)),
inference(subst,[],[refute_0_17:[bind(X_93,$fot(inverse(greatest_lower_bound(identity,X_94))))]]) ).
cnf(refute_0_974,plain,
inverse(multiply(inverse(X_52),greatest_lower_bound(identity,X_52))) = multiply(inverse(greatest_lower_bound(identity,X_52)),inverse(inverse(X_52))),
inference(subst,[],[p18_3:[bind(X,$fot(inverse(X_52))),bind(Y,$fot(greatest_lower_bound(identity,X_52)))]]) ).
cnf(refute_0_975,plain,
multiply(inverse(X_52),greatest_lower_bound(identity,X_52)) = greatest_lower_bound(identity,inverse(X_52)),
inference(subst,[],[refute_0_469:[bind(X_51,$fot(X_52))]]) ).
cnf(refute_0_976,plain,
( multiply(inverse(X_52),greatest_lower_bound(identity,X_52)) != greatest_lower_bound(identity,inverse(X_52))
| inverse(multiply(inverse(X_52),greatest_lower_bound(identity,X_52))) != multiply(inverse(greatest_lower_bound(identity,X_52)),inverse(inverse(X_52)))
| inverse(greatest_lower_bound(identity,inverse(X_52))) = multiply(inverse(greatest_lower_bound(identity,X_52)),inverse(inverse(X_52))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X_52),greatest_lower_bound(identity,X_52))),multiply(inverse(greatest_lower_bound(identity,X_52)),inverse(inverse(X_52)))) ),[0,0],$fot(greatest_lower_bound(identity,inverse(X_52)))]]) ).
cnf(refute_0_977,plain,
( inverse(multiply(inverse(X_52),greatest_lower_bound(identity,X_52))) != multiply(inverse(greatest_lower_bound(identity,X_52)),inverse(inverse(X_52)))
| inverse(greatest_lower_bound(identity,inverse(X_52))) = multiply(inverse(greatest_lower_bound(identity,X_52)),inverse(inverse(X_52))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_52),greatest_lower_bound(identity,X_52)),greatest_lower_bound(identity,inverse(X_52))) )],[refute_0_975,refute_0_976]) ).
cnf(refute_0_978,plain,
inverse(greatest_lower_bound(identity,inverse(X_52))) = multiply(inverse(greatest_lower_bound(identity,X_52)),inverse(inverse(X_52))),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_52),greatest_lower_bound(identity,X_52))),multiply(inverse(greatest_lower_bound(identity,X_52)),inverse(inverse(X_52)))) )],[refute_0_974,refute_0_977]) ).
cnf(refute_0_979,plain,
inverse(multiply(inverse(X),X_33)) = multiply(inverse(X_33),inverse(inverse(X))),
inference(subst,[],[p18_3:[bind(X,$fot(inverse(X))),bind(Y,$fot(X_33))]]) ).
cnf(refute_0_980,plain,
( inverse(multiply(inverse(X),X_33)) != multiply(inverse(X_33),inverse(inverse(X)))
| inverse(inverse(X)) != X
| inverse(multiply(inverse(X),X_33)) = multiply(inverse(X_33),X) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X),X_33)),multiply(inverse(X_33),inverse(inverse(X)))) ),[1,1],$fot(X)]]) ).
cnf(refute_0_981,plain,
( inverse(multiply(inverse(X),X_33)) != multiply(inverse(X_33),inverse(inverse(X)))
| inverse(multiply(inverse(X),X_33)) = multiply(inverse(X_33),X) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p18_2,refute_0_980]) ).
cnf(refute_0_982,plain,
inverse(multiply(inverse(X),X_33)) = multiply(inverse(X_33),X),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X),X_33)),multiply(inverse(X_33),inverse(inverse(X)))) )],[refute_0_979,refute_0_981]) ).
cnf(refute_0_983,plain,
inverse(multiply(inverse(X_52),greatest_lower_bound(identity,X_52))) = multiply(inverse(greatest_lower_bound(identity,X_52)),X_52),
inference(subst,[],[refute_0_982:[bind(X,$fot(X_52)),bind(X_33,$fot(greatest_lower_bound(identity,X_52)))]]) ).
cnf(refute_0_984,plain,
multiply(inverse(greatest_lower_bound(identity,X_52)),inverse(inverse(X_52))) = inverse(multiply(inverse(X_52),greatest_lower_bound(identity,X_52))),
inference(subst,[],[refute_0_370:[bind(X,$fot(inverse(X_52))),bind(Y,$fot(greatest_lower_bound(identity,X_52)))]]) ).
cnf(refute_0_985,plain,
( multiply(inverse(greatest_lower_bound(identity,X_52)),inverse(inverse(X_52))) != inverse(multiply(inverse(X_52),greatest_lower_bound(identity,X_52)))
| inverse(multiply(inverse(X_52),greatest_lower_bound(identity,X_52))) != multiply(inverse(greatest_lower_bound(identity,X_52)),X_52)
| multiply(inverse(greatest_lower_bound(identity,X_52)),inverse(inverse(X_52))) = multiply(inverse(greatest_lower_bound(identity,X_52)),X_52) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(identity,X_52)),inverse(inverse(X_52))))),bind(Y0,$fot(inverse(multiply(inverse(X_52),greatest_lower_bound(identity,X_52))))),bind(Z0,$fot(multiply(inverse(greatest_lower_bound(identity,X_52)),X_52)))]]) ).
cnf(refute_0_986,plain,
( inverse(multiply(inverse(X_52),greatest_lower_bound(identity,X_52))) != multiply(inverse(greatest_lower_bound(identity,X_52)),X_52)
| multiply(inverse(greatest_lower_bound(identity,X_52)),inverse(inverse(X_52))) = multiply(inverse(greatest_lower_bound(identity,X_52)),X_52) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_52)),inverse(inverse(X_52))),inverse(multiply(inverse(X_52),greatest_lower_bound(identity,X_52)))) )],[refute_0_984,refute_0_985]) ).
cnf(refute_0_987,plain,
multiply(inverse(greatest_lower_bound(identity,X_52)),inverse(inverse(X_52))) = multiply(inverse(greatest_lower_bound(identity,X_52)),X_52),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_52),greatest_lower_bound(identity,X_52))),multiply(inverse(greatest_lower_bound(identity,X_52)),X_52)) )],[refute_0_983,refute_0_986]) ).
cnf(refute_0_988,plain,
( multiply(inverse(greatest_lower_bound(identity,X_52)),inverse(inverse(X_52))) != multiply(inverse(greatest_lower_bound(identity,X_52)),X_52)
| inverse(greatest_lower_bound(identity,inverse(X_52))) != multiply(inverse(greatest_lower_bound(identity,X_52)),inverse(inverse(X_52)))
| inverse(greatest_lower_bound(identity,inverse(X_52))) = multiply(inverse(greatest_lower_bound(identity,X_52)),X_52) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_52))),multiply(inverse(greatest_lower_bound(identity,X_52)),inverse(inverse(X_52)))) ),[1],$fot(multiply(inverse(greatest_lower_bound(identity,X_52)),X_52))]]) ).
cnf(refute_0_989,plain,
( inverse(greatest_lower_bound(identity,inverse(X_52))) != multiply(inverse(greatest_lower_bound(identity,X_52)),inverse(inverse(X_52)))
| inverse(greatest_lower_bound(identity,inverse(X_52))) = multiply(inverse(greatest_lower_bound(identity,X_52)),X_52) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_52)),inverse(inverse(X_52))),multiply(inverse(greatest_lower_bound(identity,X_52)),X_52)) )],[refute_0_987,refute_0_988]) ).
cnf(refute_0_990,plain,
inverse(greatest_lower_bound(identity,inverse(X_52))) = multiply(inverse(greatest_lower_bound(identity,X_52)),X_52),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_52))),multiply(inverse(greatest_lower_bound(identity,X_52)),inverse(inverse(X_52)))) )],[refute_0_978,refute_0_989]) ).
cnf(refute_0_991,plain,
inverse(greatest_lower_bound(identity,inverse(X_94))) = multiply(inverse(greatest_lower_bound(identity,X_94)),X_94),
inference(subst,[],[refute_0_990:[bind(X_52,$fot(X_94))]]) ).
cnf(refute_0_992,plain,
( inverse(greatest_lower_bound(identity,inverse(X_94))) != multiply(inverse(greatest_lower_bound(identity,X_94)),X_94)
| multiply(inverse(greatest_lower_bound(identity,X_94)),X_94) = inverse(greatest_lower_bound(identity,inverse(X_94))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(greatest_lower_bound(identity,inverse(X_94))))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(identity,X_94)),X_94)))]]) ).
cnf(refute_0_993,plain,
multiply(inverse(greatest_lower_bound(identity,X_94)),X_94) = inverse(greatest_lower_bound(identity,inverse(X_94))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_94))),multiply(inverse(greatest_lower_bound(identity,X_94)),X_94)) )],[refute_0_991,refute_0_992]) ).
cnf(refute_0_994,plain,
( X_94 != multiply(inverse(inverse(greatest_lower_bound(identity,X_94))),multiply(inverse(greatest_lower_bound(identity,X_94)),X_94))
| multiply(inverse(greatest_lower_bound(identity,X_94)),X_94) != inverse(greatest_lower_bound(identity,inverse(X_94)))
| X_94 = multiply(inverse(inverse(greatest_lower_bound(identity,X_94))),inverse(greatest_lower_bound(identity,inverse(X_94)))) ),
introduced(tautology,[equality,[$cnf( $equal(X_94,multiply(inverse(inverse(greatest_lower_bound(identity,X_94))),multiply(inverse(greatest_lower_bound(identity,X_94)),X_94))) ),[1,1],$fot(inverse(greatest_lower_bound(identity,inverse(X_94))))]]) ).
cnf(refute_0_995,plain,
( X_94 != multiply(inverse(inverse(greatest_lower_bound(identity,X_94))),multiply(inverse(greatest_lower_bound(identity,X_94)),X_94))
| X_94 = multiply(inverse(inverse(greatest_lower_bound(identity,X_94))),inverse(greatest_lower_bound(identity,inverse(X_94)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_94)),X_94),inverse(greatest_lower_bound(identity,inverse(X_94)))) )],[refute_0_993,refute_0_994]) ).
cnf(refute_0_996,plain,
X_94 = multiply(inverse(inverse(greatest_lower_bound(identity,X_94))),inverse(greatest_lower_bound(identity,inverse(X_94)))),
inference(resolve,[$cnf( $equal(X_94,multiply(inverse(inverse(greatest_lower_bound(identity,X_94))),multiply(inverse(greatest_lower_bound(identity,X_94)),X_94))) )],[refute_0_973,refute_0_995]) ).
cnf(refute_0_997,plain,
inverse(multiply(greatest_lower_bound(identity,inverse(X_94)),inverse(greatest_lower_bound(identity,X_94)))) = multiply(greatest_lower_bound(identity,X_94),inverse(greatest_lower_bound(identity,inverse(X_94)))),
inference(subst,[],[refute_0_114:[bind(X,$fot(greatest_lower_bound(identity,X_94))),bind(X_32,$fot(greatest_lower_bound(identity,inverse(X_94))))]]) ).
cnf(refute_0_998,plain,
multiply(inverse(inverse(greatest_lower_bound(identity,X_94))),inverse(greatest_lower_bound(identity,inverse(X_94)))) = inverse(multiply(greatest_lower_bound(identity,inverse(X_94)),inverse(greatest_lower_bound(identity,X_94)))),
inference(subst,[],[refute_0_370:[bind(X,$fot(greatest_lower_bound(identity,inverse(X_94)))),bind(Y,$fot(inverse(greatest_lower_bound(identity,X_94))))]]) ).
cnf(refute_0_999,plain,
( multiply(inverse(inverse(greatest_lower_bound(identity,X_94))),inverse(greatest_lower_bound(identity,inverse(X_94)))) != inverse(multiply(greatest_lower_bound(identity,inverse(X_94)),inverse(greatest_lower_bound(identity,X_94))))
| inverse(multiply(greatest_lower_bound(identity,inverse(X_94)),inverse(greatest_lower_bound(identity,X_94)))) != multiply(greatest_lower_bound(identity,X_94),inverse(greatest_lower_bound(identity,inverse(X_94))))
| multiply(inverse(inverse(greatest_lower_bound(identity,X_94))),inverse(greatest_lower_bound(identity,inverse(X_94)))) = multiply(greatest_lower_bound(identity,X_94),inverse(greatest_lower_bound(identity,inverse(X_94)))) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(multiply(inverse(inverse(greatest_lower_bound(identity,X_94))),inverse(greatest_lower_bound(identity,inverse(X_94)))))),bind(Y0,$fot(inverse(multiply(greatest_lower_bound(identity,inverse(X_94)),inverse(greatest_lower_bound(identity,X_94)))))),bind(Z0,$fot(multiply(greatest_lower_bound(identity,X_94),inverse(greatest_lower_bound(identity,inverse(X_94))))))]]) ).
cnf(refute_0_1000,plain,
( inverse(multiply(greatest_lower_bound(identity,inverse(X_94)),inverse(greatest_lower_bound(identity,X_94)))) != multiply(greatest_lower_bound(identity,X_94),inverse(greatest_lower_bound(identity,inverse(X_94))))
| multiply(inverse(inverse(greatest_lower_bound(identity,X_94))),inverse(greatest_lower_bound(identity,inverse(X_94)))) = multiply(greatest_lower_bound(identity,X_94),inverse(greatest_lower_bound(identity,inverse(X_94)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(greatest_lower_bound(identity,X_94))),inverse(greatest_lower_bound(identity,inverse(X_94)))),inverse(multiply(greatest_lower_bound(identity,inverse(X_94)),inverse(greatest_lower_bound(identity,X_94))))) )],[refute_0_998,refute_0_999]) ).
cnf(refute_0_1001,plain,
multiply(inverse(inverse(greatest_lower_bound(identity,X_94))),inverse(greatest_lower_bound(identity,inverse(X_94)))) = multiply(greatest_lower_bound(identity,X_94),inverse(greatest_lower_bound(identity,inverse(X_94)))),
inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(identity,inverse(X_94)),inverse(greatest_lower_bound(identity,X_94)))),multiply(greatest_lower_bound(identity,X_94),inverse(greatest_lower_bound(identity,inverse(X_94))))) )],[refute_0_997,refute_0_1000]) ).
cnf(refute_0_1002,plain,
( X_94 != multiply(inverse(inverse(greatest_lower_bound(identity,X_94))),inverse(greatest_lower_bound(identity,inverse(X_94))))
| multiply(inverse(inverse(greatest_lower_bound(identity,X_94))),inverse(greatest_lower_bound(identity,inverse(X_94)))) != multiply(greatest_lower_bound(identity,X_94),inverse(greatest_lower_bound(identity,inverse(X_94))))
| X_94 = multiply(greatest_lower_bound(identity,X_94),inverse(greatest_lower_bound(identity,inverse(X_94)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_94,multiply(greatest_lower_bound(identity,X_94),inverse(greatest_lower_bound(identity,inverse(X_94))))) ),[0],$fot(multiply(inverse(inverse(greatest_lower_bound(identity,X_94))),inverse(greatest_lower_bound(identity,inverse(X_94)))))]]) ).
cnf(refute_0_1003,plain,
( X_94 != multiply(inverse(inverse(greatest_lower_bound(identity,X_94))),inverse(greatest_lower_bound(identity,inverse(X_94))))
| X_94 = multiply(greatest_lower_bound(identity,X_94),inverse(greatest_lower_bound(identity,inverse(X_94)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(greatest_lower_bound(identity,X_94))),inverse(greatest_lower_bound(identity,inverse(X_94)))),multiply(greatest_lower_bound(identity,X_94),inverse(greatest_lower_bound(identity,inverse(X_94))))) )],[refute_0_1001,refute_0_1002]) ).
cnf(refute_0_1004,plain,
X_94 = multiply(greatest_lower_bound(identity,X_94),inverse(greatest_lower_bound(identity,inverse(X_94)))),
inference(resolve,[$cnf( $equal(X_94,multiply(inverse(inverse(greatest_lower_bound(identity,X_94))),inverse(greatest_lower_bound(identity,inverse(X_94))))) )],[refute_0_996,refute_0_1003]) ).
cnf(refute_0_1005,plain,
X_269 = multiply(greatest_lower_bound(identity,X_269),inverse(greatest_lower_bound(identity,inverse(X_269)))),
inference(subst,[],[refute_0_1004:[bind(X_94,$fot(X_269))]]) ).
cnf(refute_0_1006,plain,
( X_269 != multiply(greatest_lower_bound(identity,X_269),inverse(greatest_lower_bound(identity,inverse(X_269))))
| multiply(greatest_lower_bound(identity,X_269),inverse(greatest_lower_bound(identity,inverse(X_269)))) = X_269 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_269)),bind(Y0,$fot(multiply(greatest_lower_bound(identity,X_269),inverse(greatest_lower_bound(identity,inverse(X_269))))))]]) ).
cnf(refute_0_1007,plain,
multiply(greatest_lower_bound(identity,X_269),inverse(greatest_lower_bound(identity,inverse(X_269)))) = X_269,
inference(resolve,[$cnf( $equal(X_269,multiply(greatest_lower_bound(identity,X_269),inverse(greatest_lower_bound(identity,inverse(X_269))))) )],[refute_0_1005,refute_0_1006]) ).
cnf(refute_0_1008,plain,
( multiply(greatest_lower_bound(identity,X_269),inverse(greatest_lower_bound(identity,inverse(X_269)))) != X_269
| inverse(multiply(greatest_lower_bound(identity,X_269),inverse(greatest_lower_bound(identity,inverse(X_269))))) != multiply(inverse(inverse(greatest_lower_bound(identity,inverse(X_269)))),inverse(greatest_lower_bound(identity,X_269)))
| inverse(X_269) = multiply(inverse(inverse(greatest_lower_bound(identity,inverse(X_269)))),inverse(greatest_lower_bound(identity,X_269))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(greatest_lower_bound(identity,X_269),inverse(greatest_lower_bound(identity,inverse(X_269))))),multiply(inverse(inverse(greatest_lower_bound(identity,inverse(X_269)))),inverse(greatest_lower_bound(identity,X_269)))) ),[0,0],$fot(X_269)]]) ).
cnf(refute_0_1009,plain,
( inverse(multiply(greatest_lower_bound(identity,X_269),inverse(greatest_lower_bound(identity,inverse(X_269))))) != multiply(inverse(inverse(greatest_lower_bound(identity,inverse(X_269)))),inverse(greatest_lower_bound(identity,X_269)))
| inverse(X_269) = multiply(inverse(inverse(greatest_lower_bound(identity,inverse(X_269)))),inverse(greatest_lower_bound(identity,X_269))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_269),inverse(greatest_lower_bound(identity,inverse(X_269)))),X_269) )],[refute_0_1007,refute_0_1008]) ).
cnf(refute_0_1010,plain,
inverse(X_269) = multiply(inverse(inverse(greatest_lower_bound(identity,inverse(X_269)))),inverse(greatest_lower_bound(identity,X_269))),
inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(identity,X_269),inverse(greatest_lower_bound(identity,inverse(X_269))))),multiply(inverse(inverse(greatest_lower_bound(identity,inverse(X_269)))),inverse(greatest_lower_bound(identity,X_269)))) )],[refute_0_972,refute_0_1009]) ).
cnf(refute_0_1011,plain,
inverse(multiply(greatest_lower_bound(identity,X_269),inverse(greatest_lower_bound(identity,inverse(X_269))))) = multiply(greatest_lower_bound(identity,inverse(X_269)),inverse(greatest_lower_bound(identity,X_269))),
inference(subst,[],[refute_0_114:[bind(X,$fot(greatest_lower_bound(identity,inverse(X_269)))),bind(X_32,$fot(greatest_lower_bound(identity,X_269)))]]) ).
cnf(refute_0_1012,plain,
multiply(inverse(inverse(greatest_lower_bound(identity,inverse(X_269)))),inverse(greatest_lower_bound(identity,X_269))) = inverse(multiply(greatest_lower_bound(identity,X_269),inverse(greatest_lower_bound(identity,inverse(X_269))))),
inference(subst,[],[refute_0_370:[bind(X,$fot(greatest_lower_bound(identity,X_269))),bind(Y,$fot(inverse(greatest_lower_bound(identity,inverse(X_269)))))]]) ).
cnf(refute_0_1013,plain,
( multiply(inverse(inverse(greatest_lower_bound(identity,inverse(X_269)))),inverse(greatest_lower_bound(identity,X_269))) != inverse(multiply(greatest_lower_bound(identity,X_269),inverse(greatest_lower_bound(identity,inverse(X_269)))))
| inverse(multiply(greatest_lower_bound(identity,X_269),inverse(greatest_lower_bound(identity,inverse(X_269))))) != multiply(greatest_lower_bound(identity,inverse(X_269)),inverse(greatest_lower_bound(identity,X_269)))
| multiply(inverse(inverse(greatest_lower_bound(identity,inverse(X_269)))),inverse(greatest_lower_bound(identity,X_269))) = multiply(greatest_lower_bound(identity,inverse(X_269)),inverse(greatest_lower_bound(identity,X_269))) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(multiply(inverse(inverse(greatest_lower_bound(identity,inverse(X_269)))),inverse(greatest_lower_bound(identity,X_269))))),bind(Y0,$fot(inverse(multiply(greatest_lower_bound(identity,X_269),inverse(greatest_lower_bound(identity,inverse(X_269))))))),bind(Z0,$fot(multiply(greatest_lower_bound(identity,inverse(X_269)),inverse(greatest_lower_bound(identity,X_269)))))]]) ).
cnf(refute_0_1014,plain,
( inverse(multiply(greatest_lower_bound(identity,X_269),inverse(greatest_lower_bound(identity,inverse(X_269))))) != multiply(greatest_lower_bound(identity,inverse(X_269)),inverse(greatest_lower_bound(identity,X_269)))
| multiply(inverse(inverse(greatest_lower_bound(identity,inverse(X_269)))),inverse(greatest_lower_bound(identity,X_269))) = multiply(greatest_lower_bound(identity,inverse(X_269)),inverse(greatest_lower_bound(identity,X_269))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(greatest_lower_bound(identity,inverse(X_269)))),inverse(greatest_lower_bound(identity,X_269))),inverse(multiply(greatest_lower_bound(identity,X_269),inverse(greatest_lower_bound(identity,inverse(X_269)))))) )],[refute_0_1012,refute_0_1013]) ).
cnf(refute_0_1015,plain,
multiply(inverse(inverse(greatest_lower_bound(identity,inverse(X_269)))),inverse(greatest_lower_bound(identity,X_269))) = multiply(greatest_lower_bound(identity,inverse(X_269)),inverse(greatest_lower_bound(identity,X_269))),
inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(identity,X_269),inverse(greatest_lower_bound(identity,inverse(X_269))))),multiply(greatest_lower_bound(identity,inverse(X_269)),inverse(greatest_lower_bound(identity,X_269)))) )],[refute_0_1011,refute_0_1014]) ).
cnf(refute_0_1016,plain,
( multiply(inverse(inverse(greatest_lower_bound(identity,inverse(X_269)))),inverse(greatest_lower_bound(identity,X_269))) != multiply(greatest_lower_bound(identity,inverse(X_269)),inverse(greatest_lower_bound(identity,X_269)))
| inverse(X_269) != multiply(inverse(inverse(greatest_lower_bound(identity,inverse(X_269)))),inverse(greatest_lower_bound(identity,X_269)))
| inverse(X_269) = multiply(greatest_lower_bound(identity,inverse(X_269)),inverse(greatest_lower_bound(identity,X_269))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(X_269),multiply(inverse(inverse(greatest_lower_bound(identity,inverse(X_269)))),inverse(greatest_lower_bound(identity,X_269)))) ),[1],$fot(multiply(greatest_lower_bound(identity,inverse(X_269)),inverse(greatest_lower_bound(identity,X_269))))]]) ).
cnf(refute_0_1017,plain,
( inverse(X_269) != multiply(inverse(inverse(greatest_lower_bound(identity,inverse(X_269)))),inverse(greatest_lower_bound(identity,X_269)))
| inverse(X_269) = multiply(greatest_lower_bound(identity,inverse(X_269)),inverse(greatest_lower_bound(identity,X_269))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(greatest_lower_bound(identity,inverse(X_269)))),inverse(greatest_lower_bound(identity,X_269))),multiply(greatest_lower_bound(identity,inverse(X_269)),inverse(greatest_lower_bound(identity,X_269)))) )],[refute_0_1015,refute_0_1016]) ).
cnf(refute_0_1018,plain,
inverse(X_269) = multiply(greatest_lower_bound(identity,inverse(X_269)),inverse(greatest_lower_bound(identity,X_269))),
inference(resolve,[$cnf( $equal(inverse(X_269),multiply(inverse(inverse(greatest_lower_bound(identity,inverse(X_269)))),inverse(greatest_lower_bound(identity,X_269)))) )],[refute_0_1010,refute_0_1017]) ).
cnf(refute_0_1019,plain,
( inverse(X_269) != multiply(greatest_lower_bound(identity,inverse(X_269)),inverse(greatest_lower_bound(identity,X_269)))
| multiply(greatest_lower_bound(identity,inverse(X_269)),inverse(greatest_lower_bound(identity,X_269))) = inverse(X_269) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(X_269))),bind(Y0,$fot(multiply(greatest_lower_bound(identity,inverse(X_269)),inverse(greatest_lower_bound(identity,X_269)))))]]) ).
cnf(refute_0_1020,plain,
multiply(greatest_lower_bound(identity,inverse(X_269)),inverse(greatest_lower_bound(identity,X_269))) = inverse(X_269),
inference(resolve,[$cnf( $equal(inverse(X_269),multiply(greatest_lower_bound(identity,inverse(X_269)),inverse(greatest_lower_bound(identity,X_269)))) )],[refute_0_1018,refute_0_1019]) ).
cnf(refute_0_1021,plain,
multiply(greatest_lower_bound(identity,inverse(X_51)),inverse(greatest_lower_bound(identity,X_51))) = inverse(X_51),
inference(subst,[],[refute_0_1020:[bind(X_269,$fot(X_51))]]) ).
cnf(refute_0_1022,plain,
least_upper_bound(identity,multiply(greatest_lower_bound(identity,inverse(X_51)),inverse(greatest_lower_bound(identity,X_51)))) = least_upper_bound(identity,multiply(greatest_lower_bound(identity,inverse(X_51)),inverse(greatest_lower_bound(identity,X_51)))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,multiply(greatest_lower_bound(identity,inverse(X_51)),inverse(greatest_lower_bound(identity,X_51)))))]]) ).
cnf(refute_0_1023,plain,
( multiply(greatest_lower_bound(identity,inverse(X_51)),inverse(greatest_lower_bound(identity,X_51))) != inverse(X_51)
| least_upper_bound(identity,multiply(greatest_lower_bound(identity,inverse(X_51)),inverse(greatest_lower_bound(identity,X_51)))) != least_upper_bound(identity,multiply(greatest_lower_bound(identity,inverse(X_51)),inverse(greatest_lower_bound(identity,X_51))))
| least_upper_bound(identity,multiply(greatest_lower_bound(identity,inverse(X_51)),inverse(greatest_lower_bound(identity,X_51)))) = least_upper_bound(identity,inverse(X_51)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(greatest_lower_bound(identity,inverse(X_51)),inverse(greatest_lower_bound(identity,X_51)))),least_upper_bound(identity,multiply(greatest_lower_bound(identity,inverse(X_51)),inverse(greatest_lower_bound(identity,X_51))))) ),[1,1],$fot(inverse(X_51))]]) ).
cnf(refute_0_1024,plain,
( multiply(greatest_lower_bound(identity,inverse(X_51)),inverse(greatest_lower_bound(identity,X_51))) != inverse(X_51)
| least_upper_bound(identity,multiply(greatest_lower_bound(identity,inverse(X_51)),inverse(greatest_lower_bound(identity,X_51)))) = least_upper_bound(identity,inverse(X_51)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(greatest_lower_bound(identity,inverse(X_51)),inverse(greatest_lower_bound(identity,X_51)))),least_upper_bound(identity,multiply(greatest_lower_bound(identity,inverse(X_51)),inverse(greatest_lower_bound(identity,X_51))))) )],[refute_0_1022,refute_0_1023]) ).
cnf(refute_0_1025,plain,
least_upper_bound(identity,multiply(greatest_lower_bound(identity,inverse(X_51)),inverse(greatest_lower_bound(identity,X_51)))) = least_upper_bound(identity,inverse(X_51)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(X_51)),inverse(greatest_lower_bound(identity,X_51))),inverse(X_51)) )],[refute_0_1021,refute_0_1024]) ).
cnf(refute_0_1026,plain,
multiply(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),least_upper_bound(identity,multiply(greatest_lower_bound(identity,inverse(X_51)),inverse(greatest_lower_bound(identity,X_51))))) = multiply(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),least_upper_bound(identity,multiply(greatest_lower_bound(identity,inverse(X_51)),inverse(greatest_lower_bound(identity,X_51))))),
introduced(tautology,[refl,[$fot(multiply(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),least_upper_bound(identity,multiply(greatest_lower_bound(identity,inverse(X_51)),inverse(greatest_lower_bound(identity,X_51))))))]]) ).
cnf(refute_0_1027,plain,
( multiply(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),least_upper_bound(identity,multiply(greatest_lower_bound(identity,inverse(X_51)),inverse(greatest_lower_bound(identity,X_51))))) != multiply(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),least_upper_bound(identity,multiply(greatest_lower_bound(identity,inverse(X_51)),inverse(greatest_lower_bound(identity,X_51)))))
| least_upper_bound(identity,multiply(greatest_lower_bound(identity,inverse(X_51)),inverse(greatest_lower_bound(identity,X_51)))) != least_upper_bound(identity,inverse(X_51))
| multiply(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),least_upper_bound(identity,multiply(greatest_lower_bound(identity,inverse(X_51)),inverse(greatest_lower_bound(identity,X_51))))) = multiply(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),least_upper_bound(identity,inverse(X_51))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),least_upper_bound(identity,multiply(greatest_lower_bound(identity,inverse(X_51)),inverse(greatest_lower_bound(identity,X_51))))),multiply(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),least_upper_bound(identity,multiply(greatest_lower_bound(identity,inverse(X_51)),inverse(greatest_lower_bound(identity,X_51)))))) ),[1,1],$fot(least_upper_bound(identity,inverse(X_51)))]]) ).
cnf(refute_0_1028,plain,
( least_upper_bound(identity,multiply(greatest_lower_bound(identity,inverse(X_51)),inverse(greatest_lower_bound(identity,X_51)))) != least_upper_bound(identity,inverse(X_51))
| multiply(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),least_upper_bound(identity,multiply(greatest_lower_bound(identity,inverse(X_51)),inverse(greatest_lower_bound(identity,X_51))))) = multiply(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),least_upper_bound(identity,inverse(X_51))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),least_upper_bound(identity,multiply(greatest_lower_bound(identity,inverse(X_51)),inverse(greatest_lower_bound(identity,X_51))))),multiply(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),least_upper_bound(identity,multiply(greatest_lower_bound(identity,inverse(X_51)),inverse(greatest_lower_bound(identity,X_51)))))) )],[refute_0_1026,refute_0_1027]) ).
cnf(refute_0_1029,plain,
multiply(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),least_upper_bound(identity,multiply(greatest_lower_bound(identity,inverse(X_51)),inverse(greatest_lower_bound(identity,X_51))))) = multiply(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),least_upper_bound(identity,inverse(X_51))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(greatest_lower_bound(identity,inverse(X_51)),inverse(greatest_lower_bound(identity,X_51)))),least_upper_bound(identity,inverse(X_51))) )],[refute_0_1025,refute_0_1028]) ).
cnf(refute_0_1030,plain,
( multiply(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),least_upper_bound(identity,multiply(greatest_lower_bound(identity,inverse(X_51)),inverse(greatest_lower_bound(identity,X_51))))) != multiply(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),least_upper_bound(identity,inverse(X_51)))
| inverse(greatest_lower_bound(identity,X_51)) != multiply(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),least_upper_bound(identity,multiply(greatest_lower_bound(identity,inverse(X_51)),inverse(greatest_lower_bound(identity,X_51)))))
| inverse(greatest_lower_bound(identity,X_51)) = multiply(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),least_upper_bound(identity,inverse(X_51))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,X_51)),multiply(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),least_upper_bound(identity,multiply(greatest_lower_bound(identity,inverse(X_51)),inverse(greatest_lower_bound(identity,X_51)))))) ),[1],$fot(multiply(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),least_upper_bound(identity,inverse(X_51))))]]) ).
cnf(refute_0_1031,plain,
( inverse(greatest_lower_bound(identity,X_51)) != multiply(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),least_upper_bound(identity,multiply(greatest_lower_bound(identity,inverse(X_51)),inverse(greatest_lower_bound(identity,X_51)))))
| inverse(greatest_lower_bound(identity,X_51)) = multiply(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),least_upper_bound(identity,inverse(X_51))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),least_upper_bound(identity,multiply(greatest_lower_bound(identity,inverse(X_51)),inverse(greatest_lower_bound(identity,X_51))))),multiply(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),least_upper_bound(identity,inverse(X_51)))) )],[refute_0_1029,refute_0_1030]) ).
cnf(refute_0_1032,plain,
inverse(greatest_lower_bound(identity,X_51)) = multiply(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),least_upper_bound(identity,inverse(X_51))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,X_51)),multiply(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),least_upper_bound(identity,multiply(greatest_lower_bound(identity,inverse(X_51)),inverse(greatest_lower_bound(identity,X_51)))))) )],[refute_0_971,refute_0_1031]) ).
cnf(refute_0_1033,plain,
multiply(identity,least_upper_bound(identity,inverse(X_51))) = least_upper_bound(identity,inverse(X_51)),
inference(subst,[],[left_identity:[bind(X,$fot(least_upper_bound(identity,inverse(X_51))))]]) ).
cnf(refute_0_1034,plain,
multiply(least_upper_bound(X_66,inverse(X_51)),greatest_lower_bound(identity,X_51)) = least_upper_bound(multiply(X_66,greatest_lower_bound(identity,X_51)),multiply(inverse(X_51),greatest_lower_bound(identity,X_51))),
inference(subst,[],[monotony_lub2:[bind(X,$fot(greatest_lower_bound(identity,X_51))),bind(Y,$fot(X_66)),bind(Z,$fot(inverse(X_51)))]]) ).
cnf(refute_0_1035,plain,
( multiply(inverse(X_51),greatest_lower_bound(identity,X_51)) != greatest_lower_bound(identity,inverse(X_51))
| multiply(least_upper_bound(X_66,inverse(X_51)),greatest_lower_bound(identity,X_51)) != least_upper_bound(multiply(X_66,greatest_lower_bound(identity,X_51)),multiply(inverse(X_51),greatest_lower_bound(identity,X_51)))
| multiply(least_upper_bound(X_66,inverse(X_51)),greatest_lower_bound(identity,X_51)) = least_upper_bound(multiply(X_66,greatest_lower_bound(identity,X_51)),greatest_lower_bound(identity,inverse(X_51))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_66,inverse(X_51)),greatest_lower_bound(identity,X_51)),least_upper_bound(multiply(X_66,greatest_lower_bound(identity,X_51)),multiply(inverse(X_51),greatest_lower_bound(identity,X_51)))) ),[1,1],$fot(greatest_lower_bound(identity,inverse(X_51)))]]) ).
cnf(refute_0_1036,plain,
( multiply(least_upper_bound(X_66,inverse(X_51)),greatest_lower_bound(identity,X_51)) != least_upper_bound(multiply(X_66,greatest_lower_bound(identity,X_51)),multiply(inverse(X_51),greatest_lower_bound(identity,X_51)))
| multiply(least_upper_bound(X_66,inverse(X_51)),greatest_lower_bound(identity,X_51)) = least_upper_bound(multiply(X_66,greatest_lower_bound(identity,X_51)),greatest_lower_bound(identity,inverse(X_51))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_51),greatest_lower_bound(identity,X_51)),greatest_lower_bound(identity,inverse(X_51))) )],[refute_0_469,refute_0_1035]) ).
cnf(refute_0_1037,plain,
multiply(least_upper_bound(X_66,inverse(X_51)),greatest_lower_bound(identity,X_51)) = least_upper_bound(multiply(X_66,greatest_lower_bound(identity,X_51)),greatest_lower_bound(identity,inverse(X_51))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_66,inverse(X_51)),greatest_lower_bound(identity,X_51)),least_upper_bound(multiply(X_66,greatest_lower_bound(identity,X_51)),multiply(inverse(X_51),greatest_lower_bound(identity,X_51)))) )],[refute_0_1034,refute_0_1036]) ).
cnf(refute_0_1038,plain,
least_upper_bound(multiply(X_66,greatest_lower_bound(identity,X_51)),greatest_lower_bound(identity,inverse(X_51))) = least_upper_bound(greatest_lower_bound(identity,inverse(X_51)),multiply(X_66,greatest_lower_bound(identity,X_51))),
inference(subst,[],[refute_0_4:[bind(X,$fot(greatest_lower_bound(identity,inverse(X_51)))),bind(Y,$fot(multiply(X_66,greatest_lower_bound(identity,X_51))))]]) ).
cnf(refute_0_1039,plain,
( multiply(least_upper_bound(X_66,inverse(X_51)),greatest_lower_bound(identity,X_51)) != least_upper_bound(multiply(X_66,greatest_lower_bound(identity,X_51)),greatest_lower_bound(identity,inverse(X_51)))
| least_upper_bound(multiply(X_66,greatest_lower_bound(identity,X_51)),greatest_lower_bound(identity,inverse(X_51))) != least_upper_bound(greatest_lower_bound(identity,inverse(X_51)),multiply(X_66,greatest_lower_bound(identity,X_51)))
| multiply(least_upper_bound(X_66,inverse(X_51)),greatest_lower_bound(identity,X_51)) = least_upper_bound(greatest_lower_bound(identity,inverse(X_51)),multiply(X_66,greatest_lower_bound(identity,X_51))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_66,inverse(X_51)),greatest_lower_bound(identity,X_51)),least_upper_bound(greatest_lower_bound(identity,inverse(X_51)),multiply(X_66,greatest_lower_bound(identity,X_51)))) ),[0],$fot(least_upper_bound(multiply(X_66,greatest_lower_bound(identity,X_51)),greatest_lower_bound(identity,inverse(X_51))))]]) ).
cnf(refute_0_1040,plain,
( multiply(least_upper_bound(X_66,inverse(X_51)),greatest_lower_bound(identity,X_51)) != least_upper_bound(multiply(X_66,greatest_lower_bound(identity,X_51)),greatest_lower_bound(identity,inverse(X_51)))
| multiply(least_upper_bound(X_66,inverse(X_51)),greatest_lower_bound(identity,X_51)) = least_upper_bound(greatest_lower_bound(identity,inverse(X_51)),multiply(X_66,greatest_lower_bound(identity,X_51))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_66,greatest_lower_bound(identity,X_51)),greatest_lower_bound(identity,inverse(X_51))),least_upper_bound(greatest_lower_bound(identity,inverse(X_51)),multiply(X_66,greatest_lower_bound(identity,X_51)))) )],[refute_0_1038,refute_0_1039]) ).
cnf(refute_0_1041,plain,
multiply(least_upper_bound(X_66,inverse(X_51)),greatest_lower_bound(identity,X_51)) = least_upper_bound(greatest_lower_bound(identity,inverse(X_51)),multiply(X_66,greatest_lower_bound(identity,X_51))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_66,inverse(X_51)),greatest_lower_bound(identity,X_51)),least_upper_bound(multiply(X_66,greatest_lower_bound(identity,X_51)),greatest_lower_bound(identity,inverse(X_51)))) )],[refute_0_1037,refute_0_1040]) ).
cnf(refute_0_1042,plain,
multiply(least_upper_bound(inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity)),inverse(X_197)),greatest_lower_bound(identity,X_197)) = least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),multiply(inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity)),greatest_lower_bound(identity,X_197))),
inference(subst,[],[refute_0_1041:[bind(X_51,$fot(X_197)),bind(X_66,$fot(inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity))))]]) ).
cnf(refute_0_1043,plain,
inverse(multiply(inverse(X_58),least_upper_bound(X_58,identity))) = multiply(inverse(least_upper_bound(X_58,identity)),inverse(inverse(X_58))),
inference(subst,[],[p18_3:[bind(X,$fot(inverse(X_58))),bind(Y,$fot(least_upper_bound(X_58,identity)))]]) ).
cnf(refute_0_1044,plain,
multiply(inverse(X_57),least_upper_bound(X_57,identity)) = least_upper_bound(inverse(X_57),multiply(inverse(X_57),X_57)),
inference(subst,[],[refute_0_736:[bind(X_53,$fot(inverse(X_57))),bind(X_54,$fot(X_57))]]) ).
cnf(refute_0_1045,plain,
multiply(inverse(X_57),X_57) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_57))]]) ).
cnf(refute_0_1046,plain,
( multiply(inverse(X_57),X_57) != identity
| multiply(inverse(X_57),least_upper_bound(X_57,identity)) != least_upper_bound(inverse(X_57),multiply(inverse(X_57),X_57))
| multiply(inverse(X_57),least_upper_bound(X_57,identity)) = least_upper_bound(inverse(X_57),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_57),least_upper_bound(X_57,identity)),least_upper_bound(inverse(X_57),multiply(inverse(X_57),X_57))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_1047,plain,
( multiply(inverse(X_57),least_upper_bound(X_57,identity)) != least_upper_bound(inverse(X_57),multiply(inverse(X_57),X_57))
| multiply(inverse(X_57),least_upper_bound(X_57,identity)) = least_upper_bound(inverse(X_57),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_57),X_57),identity) )],[refute_0_1045,refute_0_1046]) ).
cnf(refute_0_1048,plain,
multiply(inverse(X_57),least_upper_bound(X_57,identity)) = least_upper_bound(inverse(X_57),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_57),least_upper_bound(X_57,identity)),least_upper_bound(inverse(X_57),multiply(inverse(X_57),X_57))) )],[refute_0_1044,refute_0_1047]) ).
cnf(refute_0_1049,plain,
least_upper_bound(inverse(X_57),identity) = least_upper_bound(identity,inverse(X_57)),
inference(subst,[],[refute_0_4:[bind(X,$fot(identity)),bind(Y,$fot(inverse(X_57)))]]) ).
cnf(refute_0_1050,plain,
( multiply(inverse(X_57),least_upper_bound(X_57,identity)) != least_upper_bound(inverse(X_57),identity)
| least_upper_bound(inverse(X_57),identity) != least_upper_bound(identity,inverse(X_57))
| multiply(inverse(X_57),least_upper_bound(X_57,identity)) = least_upper_bound(identity,inverse(X_57)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_57),least_upper_bound(X_57,identity)),least_upper_bound(identity,inverse(X_57))) ),[0],$fot(least_upper_bound(inverse(X_57),identity))]]) ).
cnf(refute_0_1051,plain,
( multiply(inverse(X_57),least_upper_bound(X_57,identity)) != least_upper_bound(inverse(X_57),identity)
| multiply(inverse(X_57),least_upper_bound(X_57,identity)) = least_upper_bound(identity,inverse(X_57)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_57),identity),least_upper_bound(identity,inverse(X_57))) )],[refute_0_1049,refute_0_1050]) ).
cnf(refute_0_1052,plain,
multiply(inverse(X_57),least_upper_bound(X_57,identity)) = least_upper_bound(identity,inverse(X_57)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_57),least_upper_bound(X_57,identity)),least_upper_bound(inverse(X_57),identity)) )],[refute_0_1048,refute_0_1051]) ).
cnf(refute_0_1053,plain,
multiply(inverse(X_58),least_upper_bound(X_58,identity)) = least_upper_bound(identity,inverse(X_58)),
inference(subst,[],[refute_0_1052:[bind(X_57,$fot(X_58))]]) ).
cnf(refute_0_1054,plain,
( multiply(inverse(X_58),least_upper_bound(X_58,identity)) != least_upper_bound(identity,inverse(X_58))
| inverse(multiply(inverse(X_58),least_upper_bound(X_58,identity))) != multiply(inverse(least_upper_bound(X_58,identity)),inverse(inverse(X_58)))
| inverse(least_upper_bound(identity,inverse(X_58))) = multiply(inverse(least_upper_bound(X_58,identity)),inverse(inverse(X_58))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X_58),least_upper_bound(X_58,identity))),multiply(inverse(least_upper_bound(X_58,identity)),inverse(inverse(X_58)))) ),[0,0],$fot(least_upper_bound(identity,inverse(X_58)))]]) ).
cnf(refute_0_1055,plain,
( inverse(multiply(inverse(X_58),least_upper_bound(X_58,identity))) != multiply(inverse(least_upper_bound(X_58,identity)),inverse(inverse(X_58)))
| inverse(least_upper_bound(identity,inverse(X_58))) = multiply(inverse(least_upper_bound(X_58,identity)),inverse(inverse(X_58))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_58),least_upper_bound(X_58,identity)),least_upper_bound(identity,inverse(X_58))) )],[refute_0_1053,refute_0_1054]) ).
cnf(refute_0_1056,plain,
inverse(least_upper_bound(identity,inverse(X_58))) = multiply(inverse(least_upper_bound(X_58,identity)),inverse(inverse(X_58))),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_58),least_upper_bound(X_58,identity))),multiply(inverse(least_upper_bound(X_58,identity)),inverse(inverse(X_58)))) )],[refute_0_1043,refute_0_1055]) ).
cnf(refute_0_1057,plain,
inverse(multiply(inverse(X_58),least_upper_bound(X_58,identity))) = multiply(inverse(least_upper_bound(X_58,identity)),X_58),
inference(subst,[],[refute_0_982:[bind(X,$fot(X_58)),bind(X_33,$fot(least_upper_bound(X_58,identity)))]]) ).
cnf(refute_0_1058,plain,
multiply(inverse(least_upper_bound(X_58,identity)),inverse(inverse(X_58))) = inverse(multiply(inverse(X_58),least_upper_bound(X_58,identity))),
inference(subst,[],[refute_0_370:[bind(X,$fot(inverse(X_58))),bind(Y,$fot(least_upper_bound(X_58,identity)))]]) ).
cnf(refute_0_1059,plain,
( multiply(inverse(least_upper_bound(X_58,identity)),inverse(inverse(X_58))) != inverse(multiply(inverse(X_58),least_upper_bound(X_58,identity)))
| inverse(multiply(inverse(X_58),least_upper_bound(X_58,identity))) != multiply(inverse(least_upper_bound(X_58,identity)),X_58)
| multiply(inverse(least_upper_bound(X_58,identity)),inverse(inverse(X_58))) = multiply(inverse(least_upper_bound(X_58,identity)),X_58) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(multiply(inverse(least_upper_bound(X_58,identity)),inverse(inverse(X_58))))),bind(Y0,$fot(inverse(multiply(inverse(X_58),least_upper_bound(X_58,identity))))),bind(Z0,$fot(multiply(inverse(least_upper_bound(X_58,identity)),X_58)))]]) ).
cnf(refute_0_1060,plain,
( inverse(multiply(inverse(X_58),least_upper_bound(X_58,identity))) != multiply(inverse(least_upper_bound(X_58,identity)),X_58)
| multiply(inverse(least_upper_bound(X_58,identity)),inverse(inverse(X_58))) = multiply(inverse(least_upper_bound(X_58,identity)),X_58) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_58,identity)),inverse(inverse(X_58))),inverse(multiply(inverse(X_58),least_upper_bound(X_58,identity)))) )],[refute_0_1058,refute_0_1059]) ).
cnf(refute_0_1061,plain,
multiply(inverse(least_upper_bound(X_58,identity)),inverse(inverse(X_58))) = multiply(inverse(least_upper_bound(X_58,identity)),X_58),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_58),least_upper_bound(X_58,identity))),multiply(inverse(least_upper_bound(X_58,identity)),X_58)) )],[refute_0_1057,refute_0_1060]) ).
cnf(refute_0_1062,plain,
( multiply(inverse(least_upper_bound(X_58,identity)),inverse(inverse(X_58))) != multiply(inverse(least_upper_bound(X_58,identity)),X_58)
| inverse(least_upper_bound(identity,inverse(X_58))) != multiply(inverse(least_upper_bound(X_58,identity)),inverse(inverse(X_58)))
| inverse(least_upper_bound(identity,inverse(X_58))) = multiply(inverse(least_upper_bound(X_58,identity)),X_58) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_58))),multiply(inverse(least_upper_bound(X_58,identity)),inverse(inverse(X_58)))) ),[1],$fot(multiply(inverse(least_upper_bound(X_58,identity)),X_58))]]) ).
cnf(refute_0_1063,plain,
( inverse(least_upper_bound(identity,inverse(X_58))) != multiply(inverse(least_upper_bound(X_58,identity)),inverse(inverse(X_58)))
| inverse(least_upper_bound(identity,inverse(X_58))) = multiply(inverse(least_upper_bound(X_58,identity)),X_58) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_58,identity)),inverse(inverse(X_58))),multiply(inverse(least_upper_bound(X_58,identity)),X_58)) )],[refute_0_1061,refute_0_1062]) ).
cnf(refute_0_1064,plain,
inverse(least_upper_bound(identity,inverse(X_58))) = multiply(inverse(least_upper_bound(X_58,identity)),X_58),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_58))),multiply(inverse(least_upper_bound(X_58,identity)),inverse(inverse(X_58)))) )],[refute_0_1056,refute_0_1063]) ).
cnf(refute_0_1065,plain,
inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197)))) = multiply(inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity)),greatest_lower_bound(identity,X_197)),
inference(subst,[],[refute_0_1064:[bind(X_58,$fot(greatest_lower_bound(identity,X_197)))]]) ).
cnf(refute_0_1066,plain,
( inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197)))) != multiply(inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity)),greatest_lower_bound(identity,X_197))
| multiply(inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity)),greatest_lower_bound(identity,X_197)) = inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197)))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197)))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity)),greatest_lower_bound(identity,X_197))))]]) ).
cnf(refute_0_1067,plain,
multiply(inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity)),greatest_lower_bound(identity,X_197)) = inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197)))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197)))),multiply(inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity)),greatest_lower_bound(identity,X_197))) )],[refute_0_1065,refute_0_1066]) ).
cnf(refute_0_1068,plain,
( multiply(inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity)),greatest_lower_bound(identity,X_197)) != inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197))))
| multiply(least_upper_bound(inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity)),inverse(X_197)),greatest_lower_bound(identity,X_197)) != least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),multiply(inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity)),greatest_lower_bound(identity,X_197)))
| multiply(least_upper_bound(inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity)),inverse(X_197)),greatest_lower_bound(identity,X_197)) = least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity)),inverse(X_197)),greatest_lower_bound(identity,X_197)),least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),multiply(inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity)),greatest_lower_bound(identity,X_197)))) ),[1,1],$fot(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197)))))]]) ).
cnf(refute_0_1069,plain,
( multiply(least_upper_bound(inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity)),inverse(X_197)),greatest_lower_bound(identity,X_197)) != least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),multiply(inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity)),greatest_lower_bound(identity,X_197)))
| multiply(least_upper_bound(inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity)),inverse(X_197)),greatest_lower_bound(identity,X_197)) = least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity)),greatest_lower_bound(identity,X_197)),inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197))))) )],[refute_0_1067,refute_0_1068]) ).
cnf(refute_0_1070,plain,
multiply(least_upper_bound(inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity)),inverse(X_197)),greatest_lower_bound(identity,X_197)) = least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197))))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity)),inverse(X_197)),greatest_lower_bound(identity,X_197)),least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),multiply(inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity)),greatest_lower_bound(identity,X_197)))) )],[refute_0_1042,refute_0_1069]) ).
cnf(refute_0_1071,plain,
multiply(greatest_lower_bound(X_106,identity),least_upper_bound(inverse(X_106),identity)) = least_upper_bound(greatest_lower_bound(X_106,identity),multiply(greatest_lower_bound(X_106,identity),inverse(X_106))),
inference(subst,[],[refute_0_736:[bind(X_53,$fot(greatest_lower_bound(X_106,identity))),bind(X_54,$fot(inverse(X_106)))]]) ).
cnf(refute_0_1072,plain,
( multiply(greatest_lower_bound(X_106,identity),inverse(X_106)) != greatest_lower_bound(identity,inverse(X_106))
| multiply(greatest_lower_bound(X_106,identity),least_upper_bound(inverse(X_106),identity)) != least_upper_bound(greatest_lower_bound(X_106,identity),multiply(greatest_lower_bound(X_106,identity),inverse(X_106)))
| multiply(greatest_lower_bound(X_106,identity),least_upper_bound(inverse(X_106),identity)) = least_upper_bound(greatest_lower_bound(X_106,identity),greatest_lower_bound(identity,inverse(X_106))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_106,identity),least_upper_bound(inverse(X_106),identity)),least_upper_bound(greatest_lower_bound(X_106,identity),multiply(greatest_lower_bound(X_106,identity),inverse(X_106)))) ),[1,1],$fot(greatest_lower_bound(identity,inverse(X_106)))]]) ).
cnf(refute_0_1073,plain,
( multiply(greatest_lower_bound(X_106,identity),least_upper_bound(inverse(X_106),identity)) != least_upper_bound(greatest_lower_bound(X_106,identity),multiply(greatest_lower_bound(X_106,identity),inverse(X_106)))
| multiply(greatest_lower_bound(X_106,identity),least_upper_bound(inverse(X_106),identity)) = least_upper_bound(greatest_lower_bound(X_106,identity),greatest_lower_bound(identity,inverse(X_106))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_106,identity),inverse(X_106)),greatest_lower_bound(identity,inverse(X_106))) )],[refute_0_783,refute_0_1072]) ).
cnf(refute_0_1074,plain,
multiply(greatest_lower_bound(X_106,identity),least_upper_bound(inverse(X_106),identity)) = least_upper_bound(greatest_lower_bound(X_106,identity),greatest_lower_bound(identity,inverse(X_106))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_106,identity),least_upper_bound(inverse(X_106),identity)),least_upper_bound(greatest_lower_bound(X_106,identity),multiply(greatest_lower_bound(X_106,identity),inverse(X_106)))) )],[refute_0_1071,refute_0_1073]) ).
cnf(refute_0_1075,plain,
multiply(greatest_lower_bound(X_106,identity),least_upper_bound(inverse(X_106),identity)) = multiply(greatest_lower_bound(X_106,identity),least_upper_bound(identity,inverse(X_106))),
inference(subst,[],[refute_0_950:[bind(X,$fot(greatest_lower_bound(X_106,identity))),bind(Y,$fot(identity)),bind(Z,$fot(inverse(X_106)))]]) ).
cnf(refute_0_1076,plain,
( multiply(greatest_lower_bound(X_106,identity),least_upper_bound(inverse(X_106),identity)) != multiply(greatest_lower_bound(X_106,identity),least_upper_bound(identity,inverse(X_106)))
| multiply(greatest_lower_bound(X_106,identity),least_upper_bound(inverse(X_106),identity)) != least_upper_bound(greatest_lower_bound(X_106,identity),greatest_lower_bound(identity,inverse(X_106)))
| multiply(greatest_lower_bound(X_106,identity),least_upper_bound(identity,inverse(X_106))) = least_upper_bound(greatest_lower_bound(X_106,identity),greatest_lower_bound(identity,inverse(X_106))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_106,identity),least_upper_bound(inverse(X_106),identity)),least_upper_bound(greatest_lower_bound(X_106,identity),greatest_lower_bound(identity,inverse(X_106)))) ),[0],$fot(multiply(greatest_lower_bound(X_106,identity),least_upper_bound(identity,inverse(X_106))))]]) ).
cnf(refute_0_1077,plain,
( multiply(greatest_lower_bound(X_106,identity),least_upper_bound(inverse(X_106),identity)) != least_upper_bound(greatest_lower_bound(X_106,identity),greatest_lower_bound(identity,inverse(X_106)))
| multiply(greatest_lower_bound(X_106,identity),least_upper_bound(identity,inverse(X_106))) = least_upper_bound(greatest_lower_bound(X_106,identity),greatest_lower_bound(identity,inverse(X_106))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_106,identity),least_upper_bound(inverse(X_106),identity)),multiply(greatest_lower_bound(X_106,identity),least_upper_bound(identity,inverse(X_106)))) )],[refute_0_1075,refute_0_1076]) ).
cnf(refute_0_1078,plain,
multiply(least_upper_bound(inverse(X_103),identity),greatest_lower_bound(X_103,identity)) = least_upper_bound(greatest_lower_bound(X_103,identity),multiply(inverse(X_103),greatest_lower_bound(X_103,identity))),
inference(subst,[],[refute_0_672:[bind(X_65,$fot(greatest_lower_bound(X_103,identity))),bind(X_66,$fot(inverse(X_103)))]]) ).
cnf(refute_0_1079,plain,
multiply(inverse(X_38),greatest_lower_bound(greatest_lower_bound(identity,X_38),X_38)) = greatest_lower_bound(identity,multiply(inverse(X_38),greatest_lower_bound(identity,X_38))),
inference(subst,[],[refute_0_462:[bind(X_37,$fot(greatest_lower_bound(identity,X_38)))]]) ).
cnf(refute_0_1080,plain,
multiply(inverse(X_38),greatest_lower_bound(identity,X_38)) = greatest_lower_bound(identity,inverse(X_38)),
inference(subst,[],[refute_0_469:[bind(X_51,$fot(X_38))]]) ).
cnf(refute_0_1081,plain,
( multiply(inverse(X_38),greatest_lower_bound(greatest_lower_bound(identity,X_38),X_38)) != greatest_lower_bound(identity,multiply(inverse(X_38),greatest_lower_bound(identity,X_38)))
| multiply(inverse(X_38),greatest_lower_bound(identity,X_38)) != greatest_lower_bound(identity,inverse(X_38))
| multiply(inverse(X_38),greatest_lower_bound(greatest_lower_bound(identity,X_38),X_38)) = greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_38))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_38),greatest_lower_bound(greatest_lower_bound(identity,X_38),X_38)),greatest_lower_bound(identity,multiply(inverse(X_38),greatest_lower_bound(identity,X_38)))) ),[1,1],$fot(greatest_lower_bound(identity,inverse(X_38)))]]) ).
cnf(refute_0_1082,plain,
( multiply(inverse(X_38),greatest_lower_bound(greatest_lower_bound(identity,X_38),X_38)) != greatest_lower_bound(identity,multiply(inverse(X_38),greatest_lower_bound(identity,X_38)))
| multiply(inverse(X_38),greatest_lower_bound(greatest_lower_bound(identity,X_38),X_38)) = greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_38))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_38),greatest_lower_bound(identity,X_38)),greatest_lower_bound(identity,inverse(X_38))) )],[refute_0_1080,refute_0_1081]) ).
cnf(refute_0_1083,plain,
multiply(inverse(X_38),greatest_lower_bound(greatest_lower_bound(identity,X_38),X_38)) = greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_38))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_38),greatest_lower_bound(greatest_lower_bound(identity,X_38),X_38)),greatest_lower_bound(identity,multiply(inverse(X_38),greatest_lower_bound(identity,X_38)))) )],[refute_0_1079,refute_0_1082]) ).
cnf(refute_0_1084,plain,
greatest_lower_bound(X_38,greatest_lower_bound(identity,X_38)) = greatest_lower_bound(X_38,identity),
inference(subst,[],[refute_0_182:[bind(Y,$fot(identity)),bind(X_15,$fot(X_38))]]) ).
cnf(refute_0_1085,plain,
multiply(inverse(X_38),greatest_lower_bound(X_38,greatest_lower_bound(identity,X_38))) = multiply(inverse(X_38),greatest_lower_bound(X_38,greatest_lower_bound(identity,X_38))),
introduced(tautology,[refl,[$fot(multiply(inverse(X_38),greatest_lower_bound(X_38,greatest_lower_bound(identity,X_38))))]]) ).
cnf(refute_0_1086,plain,
( multiply(inverse(X_38),greatest_lower_bound(X_38,greatest_lower_bound(identity,X_38))) != multiply(inverse(X_38),greatest_lower_bound(X_38,greatest_lower_bound(identity,X_38)))
| greatest_lower_bound(X_38,greatest_lower_bound(identity,X_38)) != greatest_lower_bound(X_38,identity)
| multiply(inverse(X_38),greatest_lower_bound(X_38,greatest_lower_bound(identity,X_38))) = multiply(inverse(X_38),greatest_lower_bound(X_38,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_38),greatest_lower_bound(X_38,greatest_lower_bound(identity,X_38))),multiply(inverse(X_38),greatest_lower_bound(X_38,greatest_lower_bound(identity,X_38)))) ),[1,1],$fot(greatest_lower_bound(X_38,identity))]]) ).
cnf(refute_0_1087,plain,
( greatest_lower_bound(X_38,greatest_lower_bound(identity,X_38)) != greatest_lower_bound(X_38,identity)
| multiply(inverse(X_38),greatest_lower_bound(X_38,greatest_lower_bound(identity,X_38))) = multiply(inverse(X_38),greatest_lower_bound(X_38,identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_38),greatest_lower_bound(X_38,greatest_lower_bound(identity,X_38))),multiply(inverse(X_38),greatest_lower_bound(X_38,greatest_lower_bound(identity,X_38)))) )],[refute_0_1085,refute_0_1086]) ).
cnf(refute_0_1088,plain,
multiply(inverse(X_38),greatest_lower_bound(X_38,greatest_lower_bound(identity,X_38))) = multiply(inverse(X_38),greatest_lower_bound(X_38,identity)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_38,greatest_lower_bound(identity,X_38)),greatest_lower_bound(X_38,identity)) )],[refute_0_1084,refute_0_1087]) ).
cnf(refute_0_1089,plain,
greatest_lower_bound(multiply(X_36,X_38),multiply(X_36,X_37)) = greatest_lower_bound(multiply(X_36,X_37),multiply(X_36,X_38)),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(multiply(X_36,X_38))),bind(Y,$fot(multiply(X_36,X_37)))]]) ).
cnf(refute_0_1090,plain,
multiply(X_36,greatest_lower_bound(X_37,X_38)) = greatest_lower_bound(multiply(X_36,X_37),multiply(X_36,X_38)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(X_36)),bind(Y,$fot(X_37)),bind(Z,$fot(X_38))]]) ).
cnf(refute_0_1091,plain,
( multiply(X_36,greatest_lower_bound(X_37,X_38)) != greatest_lower_bound(multiply(X_36,X_37),multiply(X_36,X_38))
| greatest_lower_bound(multiply(X_36,X_37),multiply(X_36,X_38)) = multiply(X_36,greatest_lower_bound(X_37,X_38)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X_36,greatest_lower_bound(X_37,X_38)))),bind(Y0,$fot(greatest_lower_bound(multiply(X_36,X_37),multiply(X_36,X_38))))]]) ).
cnf(refute_0_1092,plain,
greatest_lower_bound(multiply(X_36,X_37),multiply(X_36,X_38)) = multiply(X_36,greatest_lower_bound(X_37,X_38)),
inference(resolve,[$cnf( $equal(multiply(X_36,greatest_lower_bound(X_37,X_38)),greatest_lower_bound(multiply(X_36,X_37),multiply(X_36,X_38))) )],[refute_0_1090,refute_0_1091]) ).
cnf(refute_0_1093,plain,
( greatest_lower_bound(multiply(X_36,X_37),multiply(X_36,X_38)) != multiply(X_36,greatest_lower_bound(X_37,X_38))
| greatest_lower_bound(multiply(X_36,X_38),multiply(X_36,X_37)) != greatest_lower_bound(multiply(X_36,X_37),multiply(X_36,X_38))
| greatest_lower_bound(multiply(X_36,X_38),multiply(X_36,X_37)) = multiply(X_36,greatest_lower_bound(X_37,X_38)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_36,X_38),multiply(X_36,X_37)),greatest_lower_bound(multiply(X_36,X_37),multiply(X_36,X_38))) ),[1],$fot(multiply(X_36,greatest_lower_bound(X_37,X_38)))]]) ).
cnf(refute_0_1094,plain,
( greatest_lower_bound(multiply(X_36,X_38),multiply(X_36,X_37)) != greatest_lower_bound(multiply(X_36,X_37),multiply(X_36,X_38))
| greatest_lower_bound(multiply(X_36,X_38),multiply(X_36,X_37)) = multiply(X_36,greatest_lower_bound(X_37,X_38)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_36,X_37),multiply(X_36,X_38)),multiply(X_36,greatest_lower_bound(X_37,X_38))) )],[refute_0_1092,refute_0_1093]) ).
cnf(refute_0_1095,plain,
greatest_lower_bound(multiply(X_36,X_38),multiply(X_36,X_37)) = multiply(X_36,greatest_lower_bound(X_37,X_38)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_36,X_38),multiply(X_36,X_37)),greatest_lower_bound(multiply(X_36,X_37),multiply(X_36,X_38))) )],[refute_0_1089,refute_0_1094]) ).
cnf(refute_0_1096,plain,
greatest_lower_bound(multiply(X_36,X_38),multiply(X_36,X_37)) = multiply(X_36,greatest_lower_bound(X_38,X_37)),
inference(subst,[],[refute_0_239:[bind(X,$fot(X_36)),bind(Y,$fot(X_38)),bind(Z,$fot(X_37))]]) ).
cnf(refute_0_1097,plain,
( greatest_lower_bound(multiply(X_36,X_38),multiply(X_36,X_37)) != multiply(X_36,greatest_lower_bound(X_37,X_38))
| greatest_lower_bound(multiply(X_36,X_38),multiply(X_36,X_37)) != multiply(X_36,greatest_lower_bound(X_38,X_37))
| multiply(X_36,greatest_lower_bound(X_38,X_37)) = multiply(X_36,greatest_lower_bound(X_37,X_38)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_36,X_38),multiply(X_36,X_37)),multiply(X_36,greatest_lower_bound(X_37,X_38))) ),[0],$fot(multiply(X_36,greatest_lower_bound(X_38,X_37)))]]) ).
cnf(refute_0_1098,plain,
( greatest_lower_bound(multiply(X_36,X_38),multiply(X_36,X_37)) != multiply(X_36,greatest_lower_bound(X_37,X_38))
| multiply(X_36,greatest_lower_bound(X_38,X_37)) = multiply(X_36,greatest_lower_bound(X_37,X_38)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_36,X_38),multiply(X_36,X_37)),multiply(X_36,greatest_lower_bound(X_38,X_37))) )],[refute_0_1096,refute_0_1097]) ).
cnf(refute_0_1099,plain,
multiply(X_36,greatest_lower_bound(X_38,X_37)) = multiply(X_36,greatest_lower_bound(X_37,X_38)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_36,X_38),multiply(X_36,X_37)),multiply(X_36,greatest_lower_bound(X_37,X_38))) )],[refute_0_1095,refute_0_1098]) ).
cnf(refute_0_1100,plain,
( multiply(X_36,greatest_lower_bound(X_38,X_37)) != multiply(X_36,greatest_lower_bound(X_37,X_38))
| multiply(X_36,greatest_lower_bound(X_37,X_38)) = multiply(X_36,greatest_lower_bound(X_38,X_37)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X_36,greatest_lower_bound(X_38,X_37)))),bind(Y0,$fot(multiply(X_36,greatest_lower_bound(X_37,X_38))))]]) ).
cnf(refute_0_1101,plain,
multiply(X_36,greatest_lower_bound(X_37,X_38)) = multiply(X_36,greatest_lower_bound(X_38,X_37)),
inference(resolve,[$cnf( $equal(multiply(X_36,greatest_lower_bound(X_38,X_37)),multiply(X_36,greatest_lower_bound(X_37,X_38))) )],[refute_0_1099,refute_0_1100]) ).
cnf(refute_0_1102,plain,
multiply(inverse(X_38),greatest_lower_bound(greatest_lower_bound(identity,X_38),X_38)) = multiply(inverse(X_38),greatest_lower_bound(X_38,greatest_lower_bound(identity,X_38))),
inference(subst,[],[refute_0_1101:[bind(X_36,$fot(inverse(X_38))),bind(X_37,$fot(greatest_lower_bound(identity,X_38)))]]) ).
cnf(refute_0_1103,plain,
( multiply(inverse(X_38),greatest_lower_bound(X_38,greatest_lower_bound(identity,X_38))) != multiply(inverse(X_38),greatest_lower_bound(X_38,identity))
| multiply(inverse(X_38),greatest_lower_bound(greatest_lower_bound(identity,X_38),X_38)) != multiply(inverse(X_38),greatest_lower_bound(X_38,greatest_lower_bound(identity,X_38)))
| multiply(inverse(X_38),greatest_lower_bound(greatest_lower_bound(identity,X_38),X_38)) = multiply(inverse(X_38),greatest_lower_bound(X_38,identity)) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(multiply(inverse(X_38),greatest_lower_bound(greatest_lower_bound(identity,X_38),X_38)))),bind(Y0,$fot(multiply(inverse(X_38),greatest_lower_bound(X_38,greatest_lower_bound(identity,X_38))))),bind(Z0,$fot(multiply(inverse(X_38),greatest_lower_bound(X_38,identity))))]]) ).
cnf(refute_0_1104,plain,
( multiply(inverse(X_38),greatest_lower_bound(X_38,greatest_lower_bound(identity,X_38))) != multiply(inverse(X_38),greatest_lower_bound(X_38,identity))
| multiply(inverse(X_38),greatest_lower_bound(greatest_lower_bound(identity,X_38),X_38)) = multiply(inverse(X_38),greatest_lower_bound(X_38,identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_38),greatest_lower_bound(greatest_lower_bound(identity,X_38),X_38)),multiply(inverse(X_38),greatest_lower_bound(X_38,greatest_lower_bound(identity,X_38)))) )],[refute_0_1102,refute_0_1103]) ).
cnf(refute_0_1105,plain,
multiply(inverse(X_38),greatest_lower_bound(greatest_lower_bound(identity,X_38),X_38)) = multiply(inverse(X_38),greatest_lower_bound(X_38,identity)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_38),greatest_lower_bound(X_38,greatest_lower_bound(identity,X_38))),multiply(inverse(X_38),greatest_lower_bound(X_38,identity))) )],[refute_0_1088,refute_0_1104]) ).
cnf(refute_0_1106,plain,
( multiply(inverse(X_38),greatest_lower_bound(greatest_lower_bound(identity,X_38),X_38)) != multiply(inverse(X_38),greatest_lower_bound(X_38,identity))
| multiply(inverse(X_38),greatest_lower_bound(greatest_lower_bound(identity,X_38),X_38)) != greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_38)))
| multiply(inverse(X_38),greatest_lower_bound(X_38,identity)) = greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_38))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_38),greatest_lower_bound(greatest_lower_bound(identity,X_38),X_38)),greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_38)))) ),[0],$fot(multiply(inverse(X_38),greatest_lower_bound(X_38,identity)))]]) ).
cnf(refute_0_1107,plain,
( multiply(inverse(X_38),greatest_lower_bound(greatest_lower_bound(identity,X_38),X_38)) != greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_38)))
| multiply(inverse(X_38),greatest_lower_bound(X_38,identity)) = greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_38))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_38),greatest_lower_bound(greatest_lower_bound(identity,X_38),X_38)),multiply(inverse(X_38),greatest_lower_bound(X_38,identity))) )],[refute_0_1105,refute_0_1106]) ).
cnf(refute_0_1108,plain,
greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_38))) = greatest_lower_bound(identity,inverse(X_38)),
inference(subst,[],[refute_0_189:[bind(X_16,$fot(inverse(X_38))),bind(X_17,$fot(identity))]]) ).
cnf(refute_0_1109,plain,
( multiply(inverse(X_38),greatest_lower_bound(X_38,identity)) != greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_38)))
| greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_38))) != greatest_lower_bound(identity,inverse(X_38))
| multiply(inverse(X_38),greatest_lower_bound(X_38,identity)) = greatest_lower_bound(identity,inverse(X_38)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_38),greatest_lower_bound(X_38,identity)),greatest_lower_bound(identity,inverse(X_38))) ),[0],$fot(greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_38))))]]) ).
cnf(refute_0_1110,plain,
( multiply(inverse(X_38),greatest_lower_bound(X_38,identity)) != greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_38)))
| multiply(inverse(X_38),greatest_lower_bound(X_38,identity)) = greatest_lower_bound(identity,inverse(X_38)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_38))),greatest_lower_bound(identity,inverse(X_38))) )],[refute_0_1108,refute_0_1109]) ).
cnf(refute_0_1111,plain,
( multiply(inverse(X_38),greatest_lower_bound(greatest_lower_bound(identity,X_38),X_38)) != greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_38)))
| multiply(inverse(X_38),greatest_lower_bound(X_38,identity)) = greatest_lower_bound(identity,inverse(X_38)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_38),greatest_lower_bound(X_38,identity)),greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_38)))) )],[refute_0_1107,refute_0_1110]) ).
cnf(refute_0_1112,plain,
multiply(inverse(X_38),greatest_lower_bound(X_38,identity)) = greatest_lower_bound(identity,inverse(X_38)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_38),greatest_lower_bound(greatest_lower_bound(identity,X_38),X_38)),greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_38)))) )],[refute_0_1083,refute_0_1111]) ).
cnf(refute_0_1113,plain,
multiply(inverse(X_103),greatest_lower_bound(X_103,identity)) = greatest_lower_bound(identity,inverse(X_103)),
inference(subst,[],[refute_0_1112:[bind(X_38,$fot(X_103))]]) ).
cnf(refute_0_1114,plain,
( multiply(inverse(X_103),greatest_lower_bound(X_103,identity)) != greatest_lower_bound(identity,inverse(X_103))
| multiply(least_upper_bound(inverse(X_103),identity),greatest_lower_bound(X_103,identity)) != least_upper_bound(greatest_lower_bound(X_103,identity),multiply(inverse(X_103),greatest_lower_bound(X_103,identity)))
| multiply(least_upper_bound(inverse(X_103),identity),greatest_lower_bound(X_103,identity)) = least_upper_bound(greatest_lower_bound(X_103,identity),greatest_lower_bound(identity,inverse(X_103))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(X_103),identity),greatest_lower_bound(X_103,identity)),least_upper_bound(greatest_lower_bound(X_103,identity),multiply(inverse(X_103),greatest_lower_bound(X_103,identity)))) ),[1,1],$fot(greatest_lower_bound(identity,inverse(X_103)))]]) ).
cnf(refute_0_1115,plain,
( multiply(least_upper_bound(inverse(X_103),identity),greatest_lower_bound(X_103,identity)) != least_upper_bound(greatest_lower_bound(X_103,identity),multiply(inverse(X_103),greatest_lower_bound(X_103,identity)))
| multiply(least_upper_bound(inverse(X_103),identity),greatest_lower_bound(X_103,identity)) = least_upper_bound(greatest_lower_bound(X_103,identity),greatest_lower_bound(identity,inverse(X_103))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_103),greatest_lower_bound(X_103,identity)),greatest_lower_bound(identity,inverse(X_103))) )],[refute_0_1113,refute_0_1114]) ).
cnf(refute_0_1116,plain,
multiply(least_upper_bound(inverse(X_103),identity),greatest_lower_bound(X_103,identity)) = least_upper_bound(greatest_lower_bound(X_103,identity),greatest_lower_bound(identity,inverse(X_103))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_103),identity),greatest_lower_bound(X_103,identity)),least_upper_bound(greatest_lower_bound(X_103,identity),multiply(inverse(X_103),greatest_lower_bound(X_103,identity)))) )],[refute_0_1078,refute_0_1115]) ).
cnf(refute_0_1117,plain,
greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),least_upper_bound(multiply(Y,X),multiply(Z,X))) = least_upper_bound(multiply(Z,X),multiply(Y,X)),
inference(subst,[],[refute_0_917:[bind(Y,$fot(multiply(Y,X))),bind(X_22,$fot(multiply(Z,X)))]]) ).
cnf(refute_0_1118,plain,
( greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),least_upper_bound(multiply(Y,X),multiply(Z,X))) != least_upper_bound(multiply(Z,X),multiply(Y,X))
| least_upper_bound(multiply(Y,X),multiply(Z,X)) != multiply(least_upper_bound(Y,Z),X)
| greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) = least_upper_bound(multiply(Z,X),multiply(Y,X)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),least_upper_bound(multiply(Y,X),multiply(Z,X))),least_upper_bound(multiply(Z,X),multiply(Y,X))) ),[0,1],$fot(multiply(least_upper_bound(Y,Z),X))]]) ).
cnf(refute_0_1119,plain,
( greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),least_upper_bound(multiply(Y,X),multiply(Z,X))) != least_upper_bound(multiply(Z,X),multiply(Y,X))
| greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) = least_upper_bound(multiply(Z,X),multiply(Y,X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(Y,X),multiply(Z,X)),multiply(least_upper_bound(Y,Z),X)) )],[refute_0_697,refute_0_1118]) ).
cnf(refute_0_1120,plain,
greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) = least_upper_bound(multiply(Z,X),multiply(Y,X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),least_upper_bound(multiply(Y,X),multiply(Z,X))),least_upper_bound(multiply(Z,X),multiply(Y,X))) )],[refute_0_1117,refute_0_1119]) ).
cnf(refute_0_1121,plain,
multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X) = multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X))]]) ).
cnf(refute_0_1122,plain,
( multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X) != multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X)
| greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)) != least_upper_bound(Y,Z)
| multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X) = multiply(least_upper_bound(Y,Z),X) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X),multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X)) ),[1,0],$fot(least_upper_bound(Y,Z))]]) ).
cnf(refute_0_1123,plain,
( greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)) != least_upper_bound(Y,Z)
| multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X) = multiply(least_upper_bound(Y,Z),X) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X),multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X)) )],[refute_0_1121,refute_0_1122]) ).
cnf(refute_0_1124,plain,
multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X) = multiply(least_upper_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),least_upper_bound(Y,Z)) )],[refute_0_922,refute_0_1123]) ).
cnf(refute_0_1125,plain,
greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) = multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X),
inference(subst,[],[refute_0_806:[bind(Y,$fot(least_upper_bound(Y,Z))),bind(Z,$fot(least_upper_bound(Z,Y)))]]) ).
cnf(refute_0_1126,plain,
( multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X) != multiply(least_upper_bound(Y,Z),X)
| greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) != multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X)
| greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) = multiply(least_upper_bound(Y,Z),X) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)))),bind(Y0,$fot(multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X))),bind(Z0,$fot(multiply(least_upper_bound(Y,Z),X)))]]) ).
cnf(refute_0_1127,plain,
( multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X) != multiply(least_upper_bound(Y,Z),X)
| greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) = multiply(least_upper_bound(Y,Z),X) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)),multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X)) )],[refute_0_1125,refute_0_1126]) ).
cnf(refute_0_1128,plain,
greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) = multiply(least_upper_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X),multiply(least_upper_bound(Y,Z),X)) )],[refute_0_1124,refute_0_1127]) ).
cnf(refute_0_1129,plain,
least_upper_bound(multiply(Z,X),multiply(Y,X)) = multiply(least_upper_bound(Z,Y),X),
inference(subst,[],[refute_0_697:[bind(Y,$fot(Z)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_1130,plain,
greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) = greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))))]]) ).
cnf(refute_0_1131,plain,
( greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) != greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X)))
| least_upper_bound(multiply(Z,X),multiply(Y,X)) != multiply(least_upper_bound(Z,Y),X)
| greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) = greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))),greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X)))) ),[1,1],$fot(multiply(least_upper_bound(Z,Y),X))]]) ).
cnf(refute_0_1132,plain,
( least_upper_bound(multiply(Z,X),multiply(Y,X)) != multiply(least_upper_bound(Z,Y),X)
| greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) = greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))),greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X)))) )],[refute_0_1130,refute_0_1131]) ).
cnf(refute_0_1133,plain,
greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) = greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Z,Y),X)) )],[refute_0_1129,refute_0_1132]) ).
cnf(refute_0_1134,plain,
( greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) != multiply(least_upper_bound(Y,Z),X)
| greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) != greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X))
| greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) = multiply(least_upper_bound(Y,Z),X) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))))),bind(Y0,$fot(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)))),bind(Z0,$fot(multiply(least_upper_bound(Y,Z),X)))]]) ).
cnf(refute_0_1135,plain,
( greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) != multiply(least_upper_bound(Y,Z),X)
| greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) = multiply(least_upper_bound(Y,Z),X) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))),greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X))) )],[refute_0_1133,refute_0_1134]) ).
cnf(refute_0_1136,plain,
greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) = multiply(least_upper_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)),multiply(least_upper_bound(Y,Z),X)) )],[refute_0_1128,refute_0_1135]) ).
cnf(refute_0_1137,plain,
greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) = greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))),
inference(subst,[],[refute_0_122:[bind(X,$fot(multiply(least_upper_bound(Y,Z),X))),bind(Y,$fot(least_upper_bound(multiply(Z,X),multiply(Y,X))))]]) ).
cnf(refute_0_1138,plain,
( greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) != multiply(least_upper_bound(Y,Z),X)
| greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) != greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X)))
| greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) = multiply(least_upper_bound(Y,Z),X) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)))),bind(Y0,$fot(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))))),bind(Z0,$fot(multiply(least_upper_bound(Y,Z),X)))]]) ).
cnf(refute_0_1139,plain,
( greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) != multiply(least_upper_bound(Y,Z),X)
| greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) = multiply(least_upper_bound(Y,Z),X) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)),greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X)))) )],[refute_0_1137,refute_0_1138]) ).
cnf(refute_0_1140,plain,
greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) = multiply(least_upper_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))),multiply(least_upper_bound(Y,Z),X)) )],[refute_0_1136,refute_0_1139]) ).
cnf(refute_0_1141,plain,
( greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) != multiply(least_upper_bound(Y,Z),X)
| greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) != least_upper_bound(multiply(Z,X),multiply(Y,X))
| multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Z,X),multiply(Y,X)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)),least_upper_bound(multiply(Z,X),multiply(Y,X))) ),[0],$fot(multiply(least_upper_bound(Y,Z),X))]]) ).
cnf(refute_0_1142,plain,
( greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) != least_upper_bound(multiply(Z,X),multiply(Y,X))
| multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Z,X),multiply(Y,X)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)),multiply(least_upper_bound(Y,Z),X)) )],[refute_0_1140,refute_0_1141]) ).
cnf(refute_0_1143,plain,
( multiply(least_upper_bound(Y,Z),X) != least_upper_bound(multiply(Z,X),multiply(Y,X))
| least_upper_bound(multiply(Z,X),multiply(Y,X)) != multiply(least_upper_bound(Z,Y),X)
| multiply(least_upper_bound(Y,Z),X) = multiply(least_upper_bound(Z,Y),X) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) ),[0],$fot(least_upper_bound(multiply(Z,X),multiply(Y,X)))]]) ).
cnf(refute_0_1144,plain,
( multiply(least_upper_bound(Y,Z),X) != least_upper_bound(multiply(Z,X),multiply(Y,X))
| multiply(least_upper_bound(Y,Z),X) = multiply(least_upper_bound(Z,Y),X) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Z,Y),X)) )],[refute_0_1129,refute_0_1143]) ).
cnf(refute_0_1145,plain,
( greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) != least_upper_bound(multiply(Z,X),multiply(Y,X))
| multiply(least_upper_bound(Y,Z),X) = multiply(least_upper_bound(Z,Y),X) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) )],[refute_0_1142,refute_0_1144]) ).
cnf(refute_0_1146,plain,
multiply(least_upper_bound(Y,Z),X) = multiply(least_upper_bound(Z,Y),X),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)),least_upper_bound(multiply(Z,X),multiply(Y,X))) )],[refute_0_1120,refute_0_1145]) ).
cnf(refute_0_1147,plain,
( multiply(least_upper_bound(Y,Z),X) != multiply(least_upper_bound(Z,Y),X)
| multiply(least_upper_bound(Z,Y),X) = multiply(least_upper_bound(Y,Z),X) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(Y,Z),X))),bind(Y0,$fot(multiply(least_upper_bound(Z,Y),X)))]]) ).
cnf(refute_0_1148,plain,
multiply(least_upper_bound(Z,Y),X) = multiply(least_upper_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) )],[refute_0_1146,refute_0_1147]) ).
cnf(refute_0_1149,plain,
multiply(least_upper_bound(inverse(X_103),identity),greatest_lower_bound(X_103,identity)) = multiply(least_upper_bound(identity,inverse(X_103)),greatest_lower_bound(X_103,identity)),
inference(subst,[],[refute_0_1148:[bind(X,$fot(greatest_lower_bound(X_103,identity))),bind(Y,$fot(identity)),bind(Z,$fot(inverse(X_103)))]]) ).
cnf(refute_0_1150,plain,
( multiply(least_upper_bound(inverse(X_103),identity),greatest_lower_bound(X_103,identity)) != multiply(least_upper_bound(identity,inverse(X_103)),greatest_lower_bound(X_103,identity))
| multiply(least_upper_bound(inverse(X_103),identity),greatest_lower_bound(X_103,identity)) != least_upper_bound(greatest_lower_bound(X_103,identity),greatest_lower_bound(identity,inverse(X_103)))
| multiply(least_upper_bound(identity,inverse(X_103)),greatest_lower_bound(X_103,identity)) = least_upper_bound(greatest_lower_bound(X_103,identity),greatest_lower_bound(identity,inverse(X_103))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(X_103),identity),greatest_lower_bound(X_103,identity)),least_upper_bound(greatest_lower_bound(X_103,identity),greatest_lower_bound(identity,inverse(X_103)))) ),[0],$fot(multiply(least_upper_bound(identity,inverse(X_103)),greatest_lower_bound(X_103,identity)))]]) ).
cnf(refute_0_1151,plain,
( multiply(least_upper_bound(inverse(X_103),identity),greatest_lower_bound(X_103,identity)) != least_upper_bound(greatest_lower_bound(X_103,identity),greatest_lower_bound(identity,inverse(X_103)))
| multiply(least_upper_bound(identity,inverse(X_103)),greatest_lower_bound(X_103,identity)) = least_upper_bound(greatest_lower_bound(X_103,identity),greatest_lower_bound(identity,inverse(X_103))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_103),identity),greatest_lower_bound(X_103,identity)),multiply(least_upper_bound(identity,inverse(X_103)),greatest_lower_bound(X_103,identity))) )],[refute_0_1149,refute_0_1150]) ).
cnf(refute_0_1152,plain,
multiply(least_upper_bound(identity,inverse(X_103)),greatest_lower_bound(X_103,identity)) = least_upper_bound(greatest_lower_bound(X_103,identity),greatest_lower_bound(identity,inverse(X_103))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_103),identity),greatest_lower_bound(X_103,identity)),least_upper_bound(greatest_lower_bound(X_103,identity),greatest_lower_bound(identity,inverse(X_103)))) )],[refute_0_1116,refute_0_1151]) ).
cnf(refute_0_1153,plain,
( multiply(least_upper_bound(identity,inverse(X_103)),greatest_lower_bound(X_103,identity)) != least_upper_bound(greatest_lower_bound(X_103,identity),greatest_lower_bound(identity,inverse(X_103)))
| least_upper_bound(greatest_lower_bound(X_103,identity),greatest_lower_bound(identity,inverse(X_103))) = multiply(least_upper_bound(identity,inverse(X_103)),greatest_lower_bound(X_103,identity)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(identity,inverse(X_103)),greatest_lower_bound(X_103,identity)))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(X_103,identity),greatest_lower_bound(identity,inverse(X_103)))))]]) ).
cnf(refute_0_1154,plain,
least_upper_bound(greatest_lower_bound(X_103,identity),greatest_lower_bound(identity,inverse(X_103))) = multiply(least_upper_bound(identity,inverse(X_103)),greatest_lower_bound(X_103,identity)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_103)),greatest_lower_bound(X_103,identity)),least_upper_bound(greatest_lower_bound(X_103,identity),greatest_lower_bound(identity,inverse(X_103)))) )],[refute_0_1152,refute_0_1153]) ).
cnf(refute_0_1155,plain,
least_upper_bound(greatest_lower_bound(X_106,identity),greatest_lower_bound(identity,inverse(X_106))) = multiply(least_upper_bound(identity,inverse(X_106)),greatest_lower_bound(X_106,identity)),
inference(subst,[],[refute_0_1154:[bind(X_103,$fot(X_106))]]) ).
cnf(refute_0_1156,plain,
( multiply(greatest_lower_bound(X_106,identity),least_upper_bound(identity,inverse(X_106))) != least_upper_bound(greatest_lower_bound(X_106,identity),greatest_lower_bound(identity,inverse(X_106)))
| least_upper_bound(greatest_lower_bound(X_106,identity),greatest_lower_bound(identity,inverse(X_106))) != multiply(least_upper_bound(identity,inverse(X_106)),greatest_lower_bound(X_106,identity))
| multiply(greatest_lower_bound(X_106,identity),least_upper_bound(identity,inverse(X_106))) = multiply(least_upper_bound(identity,inverse(X_106)),greatest_lower_bound(X_106,identity)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_106,identity),least_upper_bound(identity,inverse(X_106))),multiply(least_upper_bound(identity,inverse(X_106)),greatest_lower_bound(X_106,identity))) ),[0],$fot(least_upper_bound(greatest_lower_bound(X_106,identity),greatest_lower_bound(identity,inverse(X_106))))]]) ).
cnf(refute_0_1157,plain,
( multiply(greatest_lower_bound(X_106,identity),least_upper_bound(identity,inverse(X_106))) != least_upper_bound(greatest_lower_bound(X_106,identity),greatest_lower_bound(identity,inverse(X_106)))
| multiply(greatest_lower_bound(X_106,identity),least_upper_bound(identity,inverse(X_106))) = multiply(least_upper_bound(identity,inverse(X_106)),greatest_lower_bound(X_106,identity)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_106,identity),greatest_lower_bound(identity,inverse(X_106))),multiply(least_upper_bound(identity,inverse(X_106)),greatest_lower_bound(X_106,identity))) )],[refute_0_1155,refute_0_1156]) ).
cnf(refute_0_1158,plain,
( multiply(greatest_lower_bound(X_106,identity),least_upper_bound(inverse(X_106),identity)) != least_upper_bound(greatest_lower_bound(X_106,identity),greatest_lower_bound(identity,inverse(X_106)))
| multiply(greatest_lower_bound(X_106,identity),least_upper_bound(identity,inverse(X_106))) = multiply(least_upper_bound(identity,inverse(X_106)),greatest_lower_bound(X_106,identity)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_106,identity),least_upper_bound(identity,inverse(X_106))),least_upper_bound(greatest_lower_bound(X_106,identity),greatest_lower_bound(identity,inverse(X_106)))) )],[refute_0_1077,refute_0_1157]) ).
cnf(refute_0_1159,plain,
multiply(greatest_lower_bound(X_106,identity),least_upper_bound(identity,inverse(X_106))) = multiply(least_upper_bound(identity,inverse(X_106)),greatest_lower_bound(X_106,identity)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_106,identity),least_upper_bound(inverse(X_106),identity)),least_upper_bound(greatest_lower_bound(X_106,identity),greatest_lower_bound(identity,inverse(X_106)))) )],[refute_0_1074,refute_0_1158]) ).
cnf(refute_0_1160,plain,
( multiply(greatest_lower_bound(X_106,identity),least_upper_bound(identity,inverse(X_106))) != multiply(least_upper_bound(identity,inverse(X_106)),greatest_lower_bound(X_106,identity))
| multiply(least_upper_bound(identity,inverse(X_106)),greatest_lower_bound(X_106,identity)) = multiply(greatest_lower_bound(X_106,identity),least_upper_bound(identity,inverse(X_106))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(greatest_lower_bound(X_106,identity),least_upper_bound(identity,inverse(X_106))))),bind(Y0,$fot(multiply(least_upper_bound(identity,inverse(X_106)),greatest_lower_bound(X_106,identity))))]]) ).
cnf(refute_0_1161,plain,
multiply(least_upper_bound(identity,inverse(X_106)),greatest_lower_bound(X_106,identity)) = multiply(greatest_lower_bound(X_106,identity),least_upper_bound(identity,inverse(X_106))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_106,identity),least_upper_bound(identity,inverse(X_106))),multiply(least_upper_bound(identity,inverse(X_106)),greatest_lower_bound(X_106,identity))) )],[refute_0_1159,refute_0_1160]) ).
cnf(refute_0_1162,plain,
multiply(least_upper_bound(identity,inverse(X_197)),greatest_lower_bound(X_197,identity)) = multiply(greatest_lower_bound(X_197,identity),least_upper_bound(identity,inverse(X_197))),
inference(subst,[],[refute_0_1161:[bind(X_106,$fot(X_197))]]) ).
cnf(refute_0_1163,plain,
multiply(X_53,least_upper_bound(inverse(X_53),X_55)) = least_upper_bound(multiply(X_53,inverse(X_53)),multiply(X_53,X_55)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(X_53)),bind(Y,$fot(inverse(X_53))),bind(Z,$fot(X_55))]]) ).
cnf(refute_0_1164,plain,
multiply(X_53,inverse(X_53)) = identity,
inference(subst,[],[refute_0_38:[bind(X_1,$fot(X_53))]]) ).
cnf(refute_0_1165,plain,
( multiply(X_53,inverse(X_53)) != identity
| multiply(X_53,least_upper_bound(inverse(X_53),X_55)) != least_upper_bound(multiply(X_53,inverse(X_53)),multiply(X_53,X_55))
| multiply(X_53,least_upper_bound(inverse(X_53),X_55)) = least_upper_bound(identity,multiply(X_53,X_55)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_53,least_upper_bound(inverse(X_53),X_55)),least_upper_bound(multiply(X_53,inverse(X_53)),multiply(X_53,X_55))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_1166,plain,
( multiply(X_53,least_upper_bound(inverse(X_53),X_55)) != least_upper_bound(multiply(X_53,inverse(X_53)),multiply(X_53,X_55))
| multiply(X_53,least_upper_bound(inverse(X_53),X_55)) = least_upper_bound(identity,multiply(X_53,X_55)) ),
inference(resolve,[$cnf( $equal(multiply(X_53,inverse(X_53)),identity) )],[refute_0_1164,refute_0_1165]) ).
cnf(refute_0_1167,plain,
multiply(X_53,least_upper_bound(inverse(X_53),X_55)) = least_upper_bound(identity,multiply(X_53,X_55)),
inference(resolve,[$cnf( $equal(multiply(X_53,least_upper_bound(inverse(X_53),X_55)),least_upper_bound(multiply(X_53,inverse(X_53)),multiply(X_53,X_55))) )],[refute_0_1163,refute_0_1166]) ).
cnf(refute_0_1168,plain,
multiply(X_61,least_upper_bound(inverse(X_61),multiply(inverse(X_61),X_54))) = least_upper_bound(identity,multiply(X_61,multiply(inverse(X_61),X_54))),
inference(subst,[],[refute_0_1167:[bind(X_53,$fot(X_61)),bind(X_55,$fot(multiply(inverse(X_61),X_54)))]]) ).
cnf(refute_0_1169,plain,
multiply(inverse(X_61),least_upper_bound(X_54,identity)) = least_upper_bound(inverse(X_61),multiply(inverse(X_61),X_54)),
inference(subst,[],[refute_0_736:[bind(X_53,$fot(inverse(X_61)))]]) ).
cnf(refute_0_1170,plain,
( multiply(inverse(X_61),least_upper_bound(X_54,identity)) != least_upper_bound(inverse(X_61),multiply(inverse(X_61),X_54))
| least_upper_bound(inverse(X_61),multiply(inverse(X_61),X_54)) = multiply(inverse(X_61),least_upper_bound(X_54,identity)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(inverse(X_61),least_upper_bound(X_54,identity)))),bind(Y0,$fot(least_upper_bound(inverse(X_61),multiply(inverse(X_61),X_54))))]]) ).
cnf(refute_0_1171,plain,
least_upper_bound(inverse(X_61),multiply(inverse(X_61),X_54)) = multiply(inverse(X_61),least_upper_bound(X_54,identity)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_61),least_upper_bound(X_54,identity)),least_upper_bound(inverse(X_61),multiply(inverse(X_61),X_54))) )],[refute_0_1169,refute_0_1170]) ).
cnf(refute_0_1172,plain,
( multiply(X_61,least_upper_bound(inverse(X_61),multiply(inverse(X_61),X_54))) != least_upper_bound(identity,multiply(X_61,multiply(inverse(X_61),X_54)))
| least_upper_bound(inverse(X_61),multiply(inverse(X_61),X_54)) != multiply(inverse(X_61),least_upper_bound(X_54,identity))
| multiply(X_61,multiply(inverse(X_61),least_upper_bound(X_54,identity))) = least_upper_bound(identity,multiply(X_61,multiply(inverse(X_61),X_54))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_61,least_upper_bound(inverse(X_61),multiply(inverse(X_61),X_54))),least_upper_bound(identity,multiply(X_61,multiply(inverse(X_61),X_54)))) ),[0,1],$fot(multiply(inverse(X_61),least_upper_bound(X_54,identity)))]]) ).
cnf(refute_0_1173,plain,
( multiply(X_61,least_upper_bound(inverse(X_61),multiply(inverse(X_61),X_54))) != least_upper_bound(identity,multiply(X_61,multiply(inverse(X_61),X_54)))
| multiply(X_61,multiply(inverse(X_61),least_upper_bound(X_54,identity))) = least_upper_bound(identity,multiply(X_61,multiply(inverse(X_61),X_54))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_61),multiply(inverse(X_61),X_54)),multiply(inverse(X_61),least_upper_bound(X_54,identity))) )],[refute_0_1171,refute_0_1172]) ).
cnf(refute_0_1174,plain,
multiply(X_61,multiply(inverse(X_61),least_upper_bound(X_54,identity))) = least_upper_bound(identity,multiply(X_61,multiply(inverse(X_61),X_54))),
inference(resolve,[$cnf( $equal(multiply(X_61,least_upper_bound(inverse(X_61),multiply(inverse(X_61),X_54))),least_upper_bound(identity,multiply(X_61,multiply(inverse(X_61),X_54)))) )],[refute_0_1168,refute_0_1173]) ).
cnf(refute_0_1175,plain,
multiply(X_61,multiply(inverse(X_61),least_upper_bound(X_54,identity))) = least_upper_bound(X_54,identity),
inference(subst,[],[refute_0_766:[bind(X_92,$fot(X_61)),bind(X_94,$fot(least_upper_bound(X_54,identity)))]]) ).
cnf(refute_0_1176,plain,
( multiply(X_61,multiply(inverse(X_61),least_upper_bound(X_54,identity))) != least_upper_bound(X_54,identity)
| multiply(X_61,multiply(inverse(X_61),least_upper_bound(X_54,identity))) != least_upper_bound(identity,multiply(X_61,multiply(inverse(X_61),X_54)))
| least_upper_bound(X_54,identity) = least_upper_bound(identity,multiply(X_61,multiply(inverse(X_61),X_54))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_61,multiply(inverse(X_61),least_upper_bound(X_54,identity))),least_upper_bound(identity,multiply(X_61,multiply(inverse(X_61),X_54)))) ),[0],$fot(least_upper_bound(X_54,identity))]]) ).
cnf(refute_0_1177,plain,
( multiply(X_61,multiply(inverse(X_61),least_upper_bound(X_54,identity))) != least_upper_bound(identity,multiply(X_61,multiply(inverse(X_61),X_54)))
| least_upper_bound(X_54,identity) = least_upper_bound(identity,multiply(X_61,multiply(inverse(X_61),X_54))) ),
inference(resolve,[$cnf( $equal(multiply(X_61,multiply(inverse(X_61),least_upper_bound(X_54,identity))),least_upper_bound(X_54,identity)) )],[refute_0_1175,refute_0_1176]) ).
cnf(refute_0_1178,plain,
multiply(X_61,multiply(inverse(X_61),X_54)) = X_54,
inference(subst,[],[refute_0_766:[bind(X_92,$fot(X_61)),bind(X_94,$fot(X_54))]]) ).
cnf(refute_0_1179,plain,
least_upper_bound(identity,multiply(X_61,multiply(inverse(X_61),X_54))) = least_upper_bound(identity,multiply(X_61,multiply(inverse(X_61),X_54))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,multiply(X_61,multiply(inverse(X_61),X_54))))]]) ).
cnf(refute_0_1180,plain,
( multiply(X_61,multiply(inverse(X_61),X_54)) != X_54
| least_upper_bound(identity,multiply(X_61,multiply(inverse(X_61),X_54))) != least_upper_bound(identity,multiply(X_61,multiply(inverse(X_61),X_54)))
| least_upper_bound(identity,multiply(X_61,multiply(inverse(X_61),X_54))) = least_upper_bound(identity,X_54) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(X_61,multiply(inverse(X_61),X_54))),least_upper_bound(identity,multiply(X_61,multiply(inverse(X_61),X_54)))) ),[1,1],$fot(X_54)]]) ).
cnf(refute_0_1181,plain,
( multiply(X_61,multiply(inverse(X_61),X_54)) != X_54
| least_upper_bound(identity,multiply(X_61,multiply(inverse(X_61),X_54))) = least_upper_bound(identity,X_54) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_61,multiply(inverse(X_61),X_54))),least_upper_bound(identity,multiply(X_61,multiply(inverse(X_61),X_54)))) )],[refute_0_1179,refute_0_1180]) ).
cnf(refute_0_1182,plain,
least_upper_bound(identity,multiply(X_61,multiply(inverse(X_61),X_54))) = least_upper_bound(identity,X_54),
inference(resolve,[$cnf( $equal(multiply(X_61,multiply(inverse(X_61),X_54)),X_54) )],[refute_0_1178,refute_0_1181]) ).
cnf(refute_0_1183,plain,
( least_upper_bound(X_54,identity) != least_upper_bound(identity,multiply(X_61,multiply(inverse(X_61),X_54)))
| least_upper_bound(identity,multiply(X_61,multiply(inverse(X_61),X_54))) != least_upper_bound(identity,X_54)
| least_upper_bound(X_54,identity) = least_upper_bound(identity,X_54) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_54,identity),least_upper_bound(identity,X_54)) ),[0],$fot(least_upper_bound(identity,multiply(X_61,multiply(inverse(X_61),X_54))))]]) ).
cnf(refute_0_1184,plain,
( least_upper_bound(X_54,identity) != least_upper_bound(identity,multiply(X_61,multiply(inverse(X_61),X_54)))
| least_upper_bound(X_54,identity) = least_upper_bound(identity,X_54) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_61,multiply(inverse(X_61),X_54))),least_upper_bound(identity,X_54)) )],[refute_0_1182,refute_0_1183]) ).
cnf(refute_0_1185,plain,
( multiply(X_61,multiply(inverse(X_61),least_upper_bound(X_54,identity))) != least_upper_bound(identity,multiply(X_61,multiply(inverse(X_61),X_54)))
| least_upper_bound(X_54,identity) = least_upper_bound(identity,X_54) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_54,identity),least_upper_bound(identity,multiply(X_61,multiply(inverse(X_61),X_54)))) )],[refute_0_1177,refute_0_1184]) ).
cnf(refute_0_1186,plain,
least_upper_bound(X_54,identity) = least_upper_bound(identity,X_54),
inference(resolve,[$cnf( $equal(multiply(X_61,multiply(inverse(X_61),least_upper_bound(X_54,identity))),least_upper_bound(identity,multiply(X_61,multiply(inverse(X_61),X_54)))) )],[refute_0_1174,refute_0_1185]) ).
cnf(refute_0_1187,plain,
least_upper_bound(inverse(X_197),identity) = least_upper_bound(identity,inverse(X_197)),
inference(subst,[],[refute_0_1186:[bind(X_54,$fot(inverse(X_197)))]]) ).
cnf(refute_0_1188,plain,
least_upper_bound(identity,greatest_lower_bound(identity,X_197)) = identity,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(identity)),bind(Y,$fot(X_197))]]) ).
cnf(refute_0_1189,plain,
inverse(least_upper_bound(identity,greatest_lower_bound(identity,X_197))) = inverse(least_upper_bound(identity,greatest_lower_bound(identity,X_197))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(identity,greatest_lower_bound(identity,X_197))))]]) ).
cnf(refute_0_1190,plain,
( inverse(least_upper_bound(identity,greatest_lower_bound(identity,X_197))) != inverse(least_upper_bound(identity,greatest_lower_bound(identity,X_197)))
| least_upper_bound(identity,greatest_lower_bound(identity,X_197)) != identity
| inverse(least_upper_bound(identity,greatest_lower_bound(identity,X_197))) = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,greatest_lower_bound(identity,X_197))),inverse(least_upper_bound(identity,greatest_lower_bound(identity,X_197)))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_1191,plain,
( least_upper_bound(identity,greatest_lower_bound(identity,X_197)) != identity
| inverse(least_upper_bound(identity,greatest_lower_bound(identity,X_197))) = inverse(identity) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,greatest_lower_bound(identity,X_197))),inverse(least_upper_bound(identity,greatest_lower_bound(identity,X_197)))) )],[refute_0_1189,refute_0_1190]) ).
cnf(refute_0_1192,plain,
inverse(least_upper_bound(identity,greatest_lower_bound(identity,X_197))) = inverse(identity),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(identity,X_197)),identity) )],[refute_0_1188,refute_0_1191]) ).
cnf(refute_0_1193,plain,
( inverse(identity) != identity
| inverse(least_upper_bound(identity,greatest_lower_bound(identity,X_197))) != inverse(identity)
| inverse(least_upper_bound(identity,greatest_lower_bound(identity,X_197))) = identity ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(inverse(least_upper_bound(identity,greatest_lower_bound(identity,X_197))))),bind(Y0,$fot(inverse(identity))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_1194,plain,
( inverse(identity) != identity
| inverse(least_upper_bound(identity,greatest_lower_bound(identity,X_197))) = identity ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,greatest_lower_bound(identity,X_197))),inverse(identity)) )],[refute_0_1192,refute_0_1193]) ).
cnf(refute_0_1195,plain,
inverse(least_upper_bound(identity,greatest_lower_bound(identity,X_197))) = identity,
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[p18_1,refute_0_1194]) ).
cnf(refute_0_1196,plain,
least_upper_bound(inverse(X_197),inverse(least_upper_bound(identity,greatest_lower_bound(identity,X_197)))) = least_upper_bound(inverse(X_197),inverse(least_upper_bound(identity,greatest_lower_bound(identity,X_197)))),
introduced(tautology,[refl,[$fot(least_upper_bound(inverse(X_197),inverse(least_upper_bound(identity,greatest_lower_bound(identity,X_197)))))]]) ).
cnf(refute_0_1197,plain,
( inverse(least_upper_bound(identity,greatest_lower_bound(identity,X_197))) != identity
| least_upper_bound(inverse(X_197),inverse(least_upper_bound(identity,greatest_lower_bound(identity,X_197)))) != least_upper_bound(inverse(X_197),inverse(least_upper_bound(identity,greatest_lower_bound(identity,X_197))))
| least_upper_bound(inverse(X_197),inverse(least_upper_bound(identity,greatest_lower_bound(identity,X_197)))) = least_upper_bound(inverse(X_197),identity) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(X_197),inverse(least_upper_bound(identity,greatest_lower_bound(identity,X_197)))),least_upper_bound(inverse(X_197),inverse(least_upper_bound(identity,greatest_lower_bound(identity,X_197))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_1198,plain,
( inverse(least_upper_bound(identity,greatest_lower_bound(identity,X_197))) != identity
| least_upper_bound(inverse(X_197),inverse(least_upper_bound(identity,greatest_lower_bound(identity,X_197)))) = least_upper_bound(inverse(X_197),identity) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_197),inverse(least_upper_bound(identity,greatest_lower_bound(identity,X_197)))),least_upper_bound(inverse(X_197),inverse(least_upper_bound(identity,greatest_lower_bound(identity,X_197))))) )],[refute_0_1196,refute_0_1197]) ).
cnf(refute_0_1199,plain,
least_upper_bound(inverse(X_197),inverse(least_upper_bound(identity,greatest_lower_bound(identity,X_197)))) = least_upper_bound(inverse(X_197),identity),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,greatest_lower_bound(identity,X_197))),identity) )],[refute_0_1195,refute_0_1198]) ).
cnf(refute_0_1200,plain,
( least_upper_bound(inverse(X_197),identity) != least_upper_bound(identity,inverse(X_197))
| least_upper_bound(inverse(X_197),inverse(least_upper_bound(identity,greatest_lower_bound(identity,X_197)))) != least_upper_bound(inverse(X_197),identity)
| least_upper_bound(inverse(X_197),inverse(least_upper_bound(identity,greatest_lower_bound(identity,X_197)))) = least_upper_bound(identity,inverse(X_197)) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(least_upper_bound(inverse(X_197),inverse(least_upper_bound(identity,greatest_lower_bound(identity,X_197)))))),bind(Y0,$fot(least_upper_bound(inverse(X_197),identity))),bind(Z0,$fot(least_upper_bound(identity,inverse(X_197))))]]) ).
cnf(refute_0_1201,plain,
( least_upper_bound(inverse(X_197),identity) != least_upper_bound(identity,inverse(X_197))
| least_upper_bound(inverse(X_197),inverse(least_upper_bound(identity,greatest_lower_bound(identity,X_197)))) = least_upper_bound(identity,inverse(X_197)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_197),inverse(least_upper_bound(identity,greatest_lower_bound(identity,X_197)))),least_upper_bound(inverse(X_197),identity)) )],[refute_0_1199,refute_0_1200]) ).
cnf(refute_0_1202,plain,
least_upper_bound(inverse(X_197),inverse(least_upper_bound(identity,greatest_lower_bound(identity,X_197)))) = least_upper_bound(identity,inverse(X_197)),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_197),identity),least_upper_bound(identity,inverse(X_197))) )],[refute_0_1187,refute_0_1201]) ).
cnf(refute_0_1203,plain,
multiply(least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122))),greatest_lower_bound(identity,least_upper_bound(identity,X_122))) = least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_122))),multiply(X_198,greatest_lower_bound(identity,least_upper_bound(identity,X_122)))),
inference(subst,[],[refute_0_1041:[bind(X_51,$fot(least_upper_bound(identity,X_122))),bind(X_66,$fot(X_198))]]) ).
cnf(refute_0_1204,plain,
inverse(multiply(inverse(X_97),least_upper_bound(inverse(inverse(X_97)),X_55))) = multiply(inverse(least_upper_bound(inverse(inverse(X_97)),X_55)),X_97),
inference(subst,[],[refute_0_982:[bind(X,$fot(X_97)),bind(X_33,$fot(least_upper_bound(inverse(inverse(X_97)),X_55)))]]) ).
cnf(refute_0_1205,plain,
multiply(inverse(X_97),least_upper_bound(inverse(inverse(X_97)),X_55)) = least_upper_bound(identity,multiply(inverse(X_97),X_55)),
inference(subst,[],[refute_0_1167:[bind(X_53,$fot(inverse(X_97)))]]) ).
cnf(refute_0_1206,plain,
( multiply(inverse(X_97),least_upper_bound(inverse(inverse(X_97)),X_55)) != least_upper_bound(identity,multiply(inverse(X_97),X_55))
| inverse(multiply(inverse(X_97),least_upper_bound(inverse(inverse(X_97)),X_55))) != multiply(inverse(least_upper_bound(inverse(inverse(X_97)),X_55)),X_97)
| inverse(least_upper_bound(identity,multiply(inverse(X_97),X_55))) = multiply(inverse(least_upper_bound(inverse(inverse(X_97)),X_55)),X_97) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X_97),least_upper_bound(inverse(inverse(X_97)),X_55))),multiply(inverse(least_upper_bound(inverse(inverse(X_97)),X_55)),X_97)) ),[0,0],$fot(least_upper_bound(identity,multiply(inverse(X_97),X_55)))]]) ).
cnf(refute_0_1207,plain,
( inverse(multiply(inverse(X_97),least_upper_bound(inverse(inverse(X_97)),X_55))) != multiply(inverse(least_upper_bound(inverse(inverse(X_97)),X_55)),X_97)
| inverse(least_upper_bound(identity,multiply(inverse(X_97),X_55))) = multiply(inverse(least_upper_bound(inverse(inverse(X_97)),X_55)),X_97) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_97),least_upper_bound(inverse(inverse(X_97)),X_55)),least_upper_bound(identity,multiply(inverse(X_97),X_55))) )],[refute_0_1205,refute_0_1206]) ).
cnf(refute_0_1208,plain,
inverse(least_upper_bound(identity,multiply(inverse(X_97),X_55))) = multiply(inverse(least_upper_bound(inverse(inverse(X_97)),X_55)),X_97),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_97),least_upper_bound(inverse(inverse(X_97)),X_55))),multiply(inverse(least_upper_bound(inverse(inverse(X_97)),X_55)),X_97)) )],[refute_0_1204,refute_0_1207]) ).
cnf(refute_0_1209,plain,
inverse(inverse(X_97)) = X_97,
inference(subst,[],[p18_2:[bind(X,$fot(X_97))]]) ).
cnf(refute_0_1210,plain,
least_upper_bound(inverse(inverse(X_97)),X_55) = least_upper_bound(inverse(inverse(X_97)),X_55),
introduced(tautology,[refl,[$fot(least_upper_bound(inverse(inverse(X_97)),X_55))]]) ).
cnf(refute_0_1211,plain,
( inverse(inverse(X_97)) != X_97
| least_upper_bound(inverse(inverse(X_97)),X_55) != least_upper_bound(inverse(inverse(X_97)),X_55)
| least_upper_bound(inverse(inverse(X_97)),X_55) = least_upper_bound(X_97,X_55) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(inverse(X_97)),X_55),least_upper_bound(inverse(inverse(X_97)),X_55)) ),[1,0],$fot(X_97)]]) ).
cnf(refute_0_1212,plain,
( inverse(inverse(X_97)) != X_97
| least_upper_bound(inverse(inverse(X_97)),X_55) = least_upper_bound(X_97,X_55) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(inverse(X_97)),X_55),least_upper_bound(inverse(inverse(X_97)),X_55)) )],[refute_0_1210,refute_0_1211]) ).
cnf(refute_0_1213,plain,
least_upper_bound(inverse(inverse(X_97)),X_55) = least_upper_bound(X_97,X_55),
inference(resolve,[$cnf( $equal(inverse(inverse(X_97)),X_97) )],[refute_0_1209,refute_0_1212]) ).
cnf(refute_0_1214,plain,
inverse(least_upper_bound(inverse(inverse(X_97)),X_55)) = inverse(least_upper_bound(inverse(inverse(X_97)),X_55)),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(inverse(inverse(X_97)),X_55)))]]) ).
cnf(refute_0_1215,plain,
( inverse(least_upper_bound(inverse(inverse(X_97)),X_55)) != inverse(least_upper_bound(inverse(inverse(X_97)),X_55))
| least_upper_bound(inverse(inverse(X_97)),X_55) != least_upper_bound(X_97,X_55)
| inverse(least_upper_bound(inverse(inverse(X_97)),X_55)) = inverse(least_upper_bound(X_97,X_55)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(inverse(inverse(X_97)),X_55)),inverse(least_upper_bound(inverse(inverse(X_97)),X_55))) ),[1,0],$fot(least_upper_bound(X_97,X_55))]]) ).
cnf(refute_0_1216,plain,
( least_upper_bound(inverse(inverse(X_97)),X_55) != least_upper_bound(X_97,X_55)
| inverse(least_upper_bound(inverse(inverse(X_97)),X_55)) = inverse(least_upper_bound(X_97,X_55)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(inverse(X_97)),X_55)),inverse(least_upper_bound(inverse(inverse(X_97)),X_55))) )],[refute_0_1214,refute_0_1215]) ).
cnf(refute_0_1217,plain,
inverse(least_upper_bound(inverse(inverse(X_97)),X_55)) = inverse(least_upper_bound(X_97,X_55)),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(inverse(X_97)),X_55),least_upper_bound(X_97,X_55)) )],[refute_0_1213,refute_0_1216]) ).
cnf(refute_0_1218,plain,
multiply(inverse(least_upper_bound(inverse(inverse(X_97)),X_55)),X_97) = multiply(inverse(least_upper_bound(inverse(inverse(X_97)),X_55)),X_97),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(inverse(inverse(X_97)),X_55)),X_97))]]) ).
cnf(refute_0_1219,plain,
( multiply(inverse(least_upper_bound(inverse(inverse(X_97)),X_55)),X_97) != multiply(inverse(least_upper_bound(inverse(inverse(X_97)),X_55)),X_97)
| inverse(least_upper_bound(inverse(inverse(X_97)),X_55)) != inverse(least_upper_bound(X_97,X_55))
| multiply(inverse(least_upper_bound(inverse(inverse(X_97)),X_55)),X_97) = multiply(inverse(least_upper_bound(X_97,X_55)),X_97) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(inverse(X_97)),X_55)),X_97),multiply(inverse(least_upper_bound(inverse(inverse(X_97)),X_55)),X_97)) ),[1,0],$fot(inverse(least_upper_bound(X_97,X_55)))]]) ).
cnf(refute_0_1220,plain,
( inverse(least_upper_bound(inverse(inverse(X_97)),X_55)) != inverse(least_upper_bound(X_97,X_55))
| multiply(inverse(least_upper_bound(inverse(inverse(X_97)),X_55)),X_97) = multiply(inverse(least_upper_bound(X_97,X_55)),X_97) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(inverse(X_97)),X_55)),X_97),multiply(inverse(least_upper_bound(inverse(inverse(X_97)),X_55)),X_97)) )],[refute_0_1218,refute_0_1219]) ).
cnf(refute_0_1221,plain,
multiply(inverse(least_upper_bound(inverse(inverse(X_97)),X_55)),X_97) = multiply(inverse(least_upper_bound(X_97,X_55)),X_97),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(inverse(X_97)),X_55)),inverse(least_upper_bound(X_97,X_55))) )],[refute_0_1217,refute_0_1220]) ).
cnf(refute_0_1222,plain,
( multiply(inverse(least_upper_bound(inverse(inverse(X_97)),X_55)),X_97) != multiply(inverse(least_upper_bound(X_97,X_55)),X_97)
| inverse(least_upper_bound(identity,multiply(inverse(X_97),X_55))) != multiply(inverse(least_upper_bound(inverse(inverse(X_97)),X_55)),X_97)
| inverse(least_upper_bound(identity,multiply(inverse(X_97),X_55))) = multiply(inverse(least_upper_bound(X_97,X_55)),X_97) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(X_97),X_55))),multiply(inverse(least_upper_bound(inverse(inverse(X_97)),X_55)),X_97)) ),[1],$fot(multiply(inverse(least_upper_bound(X_97,X_55)),X_97))]]) ).
cnf(refute_0_1223,plain,
( inverse(least_upper_bound(identity,multiply(inverse(X_97),X_55))) != multiply(inverse(least_upper_bound(inverse(inverse(X_97)),X_55)),X_97)
| inverse(least_upper_bound(identity,multiply(inverse(X_97),X_55))) = multiply(inverse(least_upper_bound(X_97,X_55)),X_97) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(inverse(X_97)),X_55)),X_97),multiply(inverse(least_upper_bound(X_97,X_55)),X_97)) )],[refute_0_1221,refute_0_1222]) ).
cnf(refute_0_1224,plain,
inverse(least_upper_bound(identity,multiply(inverse(X_97),X_55))) = multiply(inverse(least_upper_bound(X_97,X_55)),X_97),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(X_97),X_55))),multiply(inverse(least_upper_bound(inverse(inverse(X_97)),X_55)),X_97)) )],[refute_0_1208,refute_0_1223]) ).
cnf(refute_0_1225,plain,
inverse(least_upper_bound(identity,multiply(inverse(identity),X_122))) = multiply(inverse(least_upper_bound(identity,X_122)),identity),
inference(subst,[],[refute_0_1224:[bind(X_55,$fot(X_122)),bind(X_97,$fot(identity))]]) ).
cnf(refute_0_1226,plain,
( inverse(identity) != identity
| inverse(least_upper_bound(identity,multiply(inverse(identity),X_122))) != multiply(inverse(least_upper_bound(identity,X_122)),identity)
| inverse(least_upper_bound(identity,multiply(identity,X_122))) = multiply(inverse(least_upper_bound(identity,X_122)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(identity),X_122))),multiply(inverse(least_upper_bound(identity,X_122)),identity)) ),[0,0,1,0],$fot(identity)]]) ).
cnf(refute_0_1227,plain,
( inverse(least_upper_bound(identity,multiply(inverse(identity),X_122))) != multiply(inverse(least_upper_bound(identity,X_122)),identity)
| inverse(least_upper_bound(identity,multiply(identity,X_122))) = multiply(inverse(least_upper_bound(identity,X_122)),identity) ),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[p18_1,refute_0_1226]) ).
cnf(refute_0_1228,plain,
inverse(least_upper_bound(identity,multiply(identity,X_122))) = multiply(inverse(least_upper_bound(identity,X_122)),identity),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(identity),X_122))),multiply(inverse(least_upper_bound(identity,X_122)),identity)) )],[refute_0_1225,refute_0_1227]) ).
cnf(refute_0_1229,plain,
multiply(identity,least_upper_bound(X_122,identity)) = least_upper_bound(X_122,identity),
inference(subst,[],[left_identity:[bind(X,$fot(least_upper_bound(X_122,identity)))]]) ).
cnf(refute_0_1230,plain,
( multiply(X_53,least_upper_bound(X_54,identity)) != least_upper_bound(X_53,multiply(X_53,X_54))
| least_upper_bound(X_53,multiply(X_53,X_54)) = multiply(X_53,least_upper_bound(X_54,identity)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X_53,least_upper_bound(X_54,identity)))),bind(Y0,$fot(least_upper_bound(X_53,multiply(X_53,X_54))))]]) ).
cnf(refute_0_1231,plain,
least_upper_bound(X_53,multiply(X_53,X_54)) = multiply(X_53,least_upper_bound(X_54,identity)),
inference(resolve,[$cnf( $equal(multiply(X_53,least_upper_bound(X_54,identity)),least_upper_bound(X_53,multiply(X_53,X_54))) )],[refute_0_736,refute_0_1230]) ).
cnf(refute_0_1232,plain,
least_upper_bound(identity,multiply(identity,X_122)) = multiply(identity,least_upper_bound(X_122,identity)),
inference(subst,[],[refute_0_1231:[bind(X_53,$fot(identity)),bind(X_54,$fot(X_122))]]) ).
cnf(refute_0_1233,plain,
( multiply(identity,least_upper_bound(X_122,identity)) != least_upper_bound(X_122,identity)
| least_upper_bound(identity,multiply(identity,X_122)) != multiply(identity,least_upper_bound(X_122,identity))
| least_upper_bound(identity,multiply(identity,X_122)) = least_upper_bound(X_122,identity) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(least_upper_bound(identity,multiply(identity,X_122)))),bind(Y0,$fot(multiply(identity,least_upper_bound(X_122,identity)))),bind(Z0,$fot(least_upper_bound(X_122,identity)))]]) ).
cnf(refute_0_1234,plain,
( multiply(identity,least_upper_bound(X_122,identity)) != least_upper_bound(X_122,identity)
| least_upper_bound(identity,multiply(identity,X_122)) = least_upper_bound(X_122,identity) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(identity,X_122)),multiply(identity,least_upper_bound(X_122,identity))) )],[refute_0_1232,refute_0_1233]) ).
cnf(refute_0_1235,plain,
least_upper_bound(identity,multiply(identity,X_122)) = least_upper_bound(X_122,identity),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(X_122,identity)),least_upper_bound(X_122,identity)) )],[refute_0_1229,refute_0_1234]) ).
cnf(refute_0_1236,plain,
inverse(least_upper_bound(identity,multiply(identity,X_122))) = inverse(least_upper_bound(identity,multiply(identity,X_122))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(identity,multiply(identity,X_122))))]]) ).
cnf(refute_0_1237,plain,
( inverse(least_upper_bound(identity,multiply(identity,X_122))) != inverse(least_upper_bound(identity,multiply(identity,X_122)))
| least_upper_bound(identity,multiply(identity,X_122)) != least_upper_bound(X_122,identity)
| inverse(least_upper_bound(identity,multiply(identity,X_122))) = inverse(least_upper_bound(X_122,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(identity,X_122))),inverse(least_upper_bound(identity,multiply(identity,X_122)))) ),[1,0],$fot(least_upper_bound(X_122,identity))]]) ).
cnf(refute_0_1238,plain,
( least_upper_bound(identity,multiply(identity,X_122)) != least_upper_bound(X_122,identity)
| inverse(least_upper_bound(identity,multiply(identity,X_122))) = inverse(least_upper_bound(X_122,identity)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(identity,X_122))),inverse(least_upper_bound(identity,multiply(identity,X_122)))) )],[refute_0_1236,refute_0_1237]) ).
cnf(refute_0_1239,plain,
inverse(least_upper_bound(identity,multiply(identity,X_122))) = inverse(least_upper_bound(X_122,identity)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(identity,X_122)),least_upper_bound(X_122,identity)) )],[refute_0_1235,refute_0_1238]) ).
cnf(refute_0_1240,plain,
( inverse(least_upper_bound(identity,multiply(identity,X_122))) != multiply(inverse(least_upper_bound(identity,X_122)),identity)
| inverse(least_upper_bound(identity,multiply(identity,X_122))) != inverse(least_upper_bound(X_122,identity))
| inverse(least_upper_bound(X_122,identity)) = multiply(inverse(least_upper_bound(identity,X_122)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(identity,X_122))),multiply(inverse(least_upper_bound(identity,X_122)),identity)) ),[0],$fot(inverse(least_upper_bound(X_122,identity)))]]) ).
cnf(refute_0_1241,plain,
( inverse(least_upper_bound(identity,multiply(identity,X_122))) != multiply(inverse(least_upper_bound(identity,X_122)),identity)
| inverse(least_upper_bound(X_122,identity)) = multiply(inverse(least_upper_bound(identity,X_122)),identity) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(identity,X_122))),inverse(least_upper_bound(X_122,identity))) )],[refute_0_1239,refute_0_1240]) ).
cnf(refute_0_1242,plain,
multiply(inverse(least_upper_bound(identity,X_122)),identity) = inverse(least_upper_bound(identity,X_122)),
inference(subst,[],[refute_0_603:[bind(X,$fot(inverse(least_upper_bound(identity,X_122))))]]) ).
cnf(refute_0_1243,plain,
( multiply(inverse(least_upper_bound(identity,X_122)),identity) != inverse(least_upper_bound(identity,X_122))
| inverse(least_upper_bound(X_122,identity)) != multiply(inverse(least_upper_bound(identity,X_122)),identity)
| inverse(least_upper_bound(X_122,identity)) = inverse(least_upper_bound(identity,X_122)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_122,identity)),multiply(inverse(least_upper_bound(identity,X_122)),identity)) ),[1],$fot(inverse(least_upper_bound(identity,X_122)))]]) ).
cnf(refute_0_1244,plain,
( inverse(least_upper_bound(X_122,identity)) != multiply(inverse(least_upper_bound(identity,X_122)),identity)
| inverse(least_upper_bound(X_122,identity)) = inverse(least_upper_bound(identity,X_122)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_122)),identity),inverse(least_upper_bound(identity,X_122))) )],[refute_0_1242,refute_0_1243]) ).
cnf(refute_0_1245,plain,
( inverse(least_upper_bound(identity,multiply(identity,X_122))) != multiply(inverse(least_upper_bound(identity,X_122)),identity)
| inverse(least_upper_bound(X_122,identity)) = inverse(least_upper_bound(identity,X_122)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_122,identity)),multiply(inverse(least_upper_bound(identity,X_122)),identity)) )],[refute_0_1241,refute_0_1244]) ).
cnf(refute_0_1246,plain,
inverse(least_upper_bound(X_122,identity)) = inverse(least_upper_bound(identity,X_122)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(identity,X_122))),multiply(inverse(least_upper_bound(identity,X_122)),identity)) )],[refute_0_1228,refute_0_1245]) ).
cnf(refute_0_1247,plain,
( inverse(least_upper_bound(X_122,identity)) != inverse(least_upper_bound(identity,X_122))
| inverse(least_upper_bound(identity,X_122)) = inverse(least_upper_bound(X_122,identity)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(least_upper_bound(X_122,identity)))),bind(Y0,$fot(inverse(least_upper_bound(identity,X_122))))]]) ).
cnf(refute_0_1248,plain,
inverse(least_upper_bound(identity,X_122)) = inverse(least_upper_bound(X_122,identity)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_122,identity)),inverse(least_upper_bound(identity,X_122))) )],[refute_0_1246,refute_0_1247]) ).
cnf(refute_0_1249,plain,
( multiply(least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122))),greatest_lower_bound(identity,least_upper_bound(identity,X_122))) != least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_122))),multiply(X_198,greatest_lower_bound(identity,least_upper_bound(identity,X_122))))
| inverse(least_upper_bound(identity,X_122)) != inverse(least_upper_bound(X_122,identity))
| multiply(least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_122))) = least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_122))),multiply(X_198,greatest_lower_bound(identity,least_upper_bound(identity,X_122)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122))),greatest_lower_bound(identity,least_upper_bound(identity,X_122))),least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_122))),multiply(X_198,greatest_lower_bound(identity,least_upper_bound(identity,X_122))))) ),[0,0,1],$fot(inverse(least_upper_bound(X_122,identity)))]]) ).
cnf(refute_0_1250,plain,
( multiply(least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122))),greatest_lower_bound(identity,least_upper_bound(identity,X_122))) != least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_122))),multiply(X_198,greatest_lower_bound(identity,least_upper_bound(identity,X_122))))
| multiply(least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_122))) = least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_122))),multiply(X_198,greatest_lower_bound(identity,least_upper_bound(identity,X_122)))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,X_122)),inverse(least_upper_bound(X_122,identity))) )],[refute_0_1248,refute_0_1249]) ).
cnf(refute_0_1251,plain,
multiply(least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_122))) = least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_122))),multiply(X_198,greatest_lower_bound(identity,least_upper_bound(identity,X_122)))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122))),greatest_lower_bound(identity,least_upper_bound(identity,X_122))),least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_122))),multiply(X_198,greatest_lower_bound(identity,least_upper_bound(identity,X_122))))) )],[refute_0_1203,refute_0_1250]) ).
cnf(refute_0_1252,plain,
multiply(least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity))),identity) = least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity))),
inference(subst,[],[refute_0_603:[bind(X,$fot(least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity)))))]]) ).
cnf(refute_0_1253,plain,
greatest_lower_bound(identity,least_upper_bound(identity,X_122)) = identity,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(identity)),bind(Y,$fot(X_122))]]) ).
cnf(refute_0_1254,plain,
multiply(least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_122))) = multiply(least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_122))),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_122))))]]) ).
cnf(refute_0_1255,plain,
( multiply(least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_122))) != multiply(least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_122)))
| greatest_lower_bound(identity,least_upper_bound(identity,X_122)) != identity
| multiply(least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_122))) = multiply(least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity))),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_122))),multiply(least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_122)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_1256,plain,
( greatest_lower_bound(identity,least_upper_bound(identity,X_122)) != identity
| multiply(least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_122))) = multiply(least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity))),identity) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_122))),multiply(least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_122)))) )],[refute_0_1254,refute_0_1255]) ).
cnf(refute_0_1257,plain,
multiply(least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_122))) = multiply(least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity))),identity),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(identity,X_122)),identity) )],[refute_0_1253,refute_0_1256]) ).
cnf(refute_0_1258,plain,
( multiply(least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_122))) != multiply(least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity))),identity)
| multiply(least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity))),identity) != least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity)))
| multiply(least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_122))) = least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity))) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(multiply(least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_122))))),bind(Y0,$fot(multiply(least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity))),identity))),bind(Z0,$fot(least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity)))))]]) ).
cnf(refute_0_1259,plain,
( multiply(least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity))),identity) != least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity)))
| multiply(least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_122))) = least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_122))),multiply(least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity))),identity)) )],[refute_0_1257,refute_0_1258]) ).
cnf(refute_0_1260,plain,
multiply(least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_122))) = least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity))),identity),least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity)))) )],[refute_0_1252,refute_0_1259]) ).
cnf(refute_0_1261,plain,
( multiply(least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_122))) != least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity)))
| multiply(least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_122))) != least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_122))),multiply(X_198,greatest_lower_bound(identity,least_upper_bound(identity,X_122))))
| least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity))) = least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_122))),multiply(X_198,greatest_lower_bound(identity,least_upper_bound(identity,X_122)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_122))),least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_122))),multiply(X_198,greatest_lower_bound(identity,least_upper_bound(identity,X_122))))) ),[0],$fot(least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity))))]]) ).
cnf(refute_0_1262,plain,
( multiply(least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_122))) != least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_122))),multiply(X_198,greatest_lower_bound(identity,least_upper_bound(identity,X_122))))
| least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity))) = least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_122))),multiply(X_198,greatest_lower_bound(identity,least_upper_bound(identity,X_122)))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_122))),least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity)))) )],[refute_0_1260,refute_0_1261]) ).
cnf(refute_0_1263,plain,
multiply(least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122))),identity) = least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122))),
inference(subst,[],[refute_0_603:[bind(X,$fot(least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122)))))]]) ).
cnf(refute_0_1264,plain,
multiply(least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122))),greatest_lower_bound(identity,least_upper_bound(identity,X_122))) = multiply(least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122))),greatest_lower_bound(identity,least_upper_bound(identity,X_122))),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122))),greatest_lower_bound(identity,least_upper_bound(identity,X_122))))]]) ).
cnf(refute_0_1265,plain,
( multiply(least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122))),greatest_lower_bound(identity,least_upper_bound(identity,X_122))) != multiply(least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122))),greatest_lower_bound(identity,least_upper_bound(identity,X_122)))
| greatest_lower_bound(identity,least_upper_bound(identity,X_122)) != identity
| multiply(least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122))),greatest_lower_bound(identity,least_upper_bound(identity,X_122))) = multiply(least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122))),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122))),greatest_lower_bound(identity,least_upper_bound(identity,X_122))),multiply(least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122))),greatest_lower_bound(identity,least_upper_bound(identity,X_122)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_1266,plain,
( greatest_lower_bound(identity,least_upper_bound(identity,X_122)) != identity
| multiply(least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122))),greatest_lower_bound(identity,least_upper_bound(identity,X_122))) = multiply(least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122))),identity) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122))),greatest_lower_bound(identity,least_upper_bound(identity,X_122))),multiply(least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122))),greatest_lower_bound(identity,least_upper_bound(identity,X_122)))) )],[refute_0_1264,refute_0_1265]) ).
cnf(refute_0_1267,plain,
multiply(least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122))),greatest_lower_bound(identity,least_upper_bound(identity,X_122))) = multiply(least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122))),identity),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(identity,X_122)),identity) )],[refute_0_1253,refute_0_1266]) ).
cnf(refute_0_1268,plain,
( multiply(least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122))),greatest_lower_bound(identity,least_upper_bound(identity,X_122))) != multiply(least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122))),identity)
| multiply(least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122))),identity) != least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122)))
| multiply(least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122))),greatest_lower_bound(identity,least_upper_bound(identity,X_122))) = least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122))) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(multiply(least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122))),greatest_lower_bound(identity,least_upper_bound(identity,X_122))))),bind(Y0,$fot(multiply(least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122))),identity))),bind(Z0,$fot(least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122)))))]]) ).
cnf(refute_0_1269,plain,
( multiply(least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122))),identity) != least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122)))
| multiply(least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122))),greatest_lower_bound(identity,least_upper_bound(identity,X_122))) = least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122))),greatest_lower_bound(identity,least_upper_bound(identity,X_122))),multiply(least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122))),identity)) )],[refute_0_1267,refute_0_1268]) ).
cnf(refute_0_1270,plain,
multiply(least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122))),greatest_lower_bound(identity,least_upper_bound(identity,X_122))) = least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122))),identity),least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122)))) )],[refute_0_1263,refute_0_1269]) ).
cnf(refute_0_1271,plain,
( multiply(least_upper_bound(X_66,inverse(X_51)),greatest_lower_bound(identity,X_51)) != least_upper_bound(greatest_lower_bound(identity,inverse(X_51)),multiply(X_66,greatest_lower_bound(identity,X_51)))
| least_upper_bound(greatest_lower_bound(identity,inverse(X_51)),multiply(X_66,greatest_lower_bound(identity,X_51))) = multiply(least_upper_bound(X_66,inverse(X_51)),greatest_lower_bound(identity,X_51)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(X_66,inverse(X_51)),greatest_lower_bound(identity,X_51)))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(identity,inverse(X_51)),multiply(X_66,greatest_lower_bound(identity,X_51)))))]]) ).
cnf(refute_0_1272,plain,
least_upper_bound(greatest_lower_bound(identity,inverse(X_51)),multiply(X_66,greatest_lower_bound(identity,X_51))) = multiply(least_upper_bound(X_66,inverse(X_51)),greatest_lower_bound(identity,X_51)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_66,inverse(X_51)),greatest_lower_bound(identity,X_51)),least_upper_bound(greatest_lower_bound(identity,inverse(X_51)),multiply(X_66,greatest_lower_bound(identity,X_51)))) )],[refute_0_1041,refute_0_1271]) ).
cnf(refute_0_1273,plain,
least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_122))),multiply(X_198,greatest_lower_bound(identity,least_upper_bound(identity,X_122)))) = multiply(least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122))),greatest_lower_bound(identity,least_upper_bound(identity,X_122))),
inference(subst,[],[refute_0_1272:[bind(X_51,$fot(least_upper_bound(identity,X_122))),bind(X_66,$fot(X_198))]]) ).
cnf(refute_0_1274,plain,
( multiply(least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122))),greatest_lower_bound(identity,least_upper_bound(identity,X_122))) != least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122)))
| least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_122))),multiply(X_198,greatest_lower_bound(identity,least_upper_bound(identity,X_122)))) != multiply(least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122))),greatest_lower_bound(identity,least_upper_bound(identity,X_122)))
| least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_122))),multiply(X_198,greatest_lower_bound(identity,least_upper_bound(identity,X_122)))) = least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122))) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_122))),multiply(X_198,greatest_lower_bound(identity,least_upper_bound(identity,X_122)))))),bind(Y0,$fot(multiply(least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122))),greatest_lower_bound(identity,least_upper_bound(identity,X_122))))),bind(Z0,$fot(least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122)))))]]) ).
cnf(refute_0_1275,plain,
( multiply(least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122))),greatest_lower_bound(identity,least_upper_bound(identity,X_122))) != least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122)))
| least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_122))),multiply(X_198,greatest_lower_bound(identity,least_upper_bound(identity,X_122)))) = least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_122))),multiply(X_198,greatest_lower_bound(identity,least_upper_bound(identity,X_122)))),multiply(least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122))),greatest_lower_bound(identity,least_upper_bound(identity,X_122)))) )],[refute_0_1273,refute_0_1274]) ).
cnf(refute_0_1276,plain,
least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_122))),multiply(X_198,greatest_lower_bound(identity,least_upper_bound(identity,X_122)))) = least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122))),greatest_lower_bound(identity,least_upper_bound(identity,X_122))),least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122)))) )],[refute_0_1270,refute_0_1275]) ).
cnf(refute_0_1277,plain,
( least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity))) != least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_122))),multiply(X_198,greatest_lower_bound(identity,least_upper_bound(identity,X_122))))
| least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_122))),multiply(X_198,greatest_lower_bound(identity,least_upper_bound(identity,X_122)))) != least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122)))
| least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity))) = least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity))),least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122)))) ),[0],$fot(least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_122))),multiply(X_198,greatest_lower_bound(identity,least_upper_bound(identity,X_122)))))]]) ).
cnf(refute_0_1278,plain,
( least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity))) != least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_122))),multiply(X_198,greatest_lower_bound(identity,least_upper_bound(identity,X_122))))
| least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity))) = least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_122))),multiply(X_198,greatest_lower_bound(identity,least_upper_bound(identity,X_122)))),least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122)))) )],[refute_0_1276,refute_0_1277]) ).
cnf(refute_0_1279,plain,
( multiply(least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_122))) != least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_122))),multiply(X_198,greatest_lower_bound(identity,least_upper_bound(identity,X_122))))
| least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity))) = least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity))),least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_122))),multiply(X_198,greatest_lower_bound(identity,least_upper_bound(identity,X_122))))) )],[refute_0_1262,refute_0_1278]) ).
cnf(refute_0_1280,plain,
least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity))) = least_upper_bound(X_198,inverse(least_upper_bound(identity,X_122))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_198,inverse(least_upper_bound(X_122,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_122))),least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_122))),multiply(X_198,greatest_lower_bound(identity,least_upper_bound(identity,X_122))))) )],[refute_0_1251,refute_0_1279]) ).
cnf(refute_0_1281,plain,
least_upper_bound(inverse(X_197),inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity))) = least_upper_bound(inverse(X_197),inverse(least_upper_bound(identity,greatest_lower_bound(identity,X_197)))),
inference(subst,[],[refute_0_1280:[bind(X_122,$fot(greatest_lower_bound(identity,X_197))),bind(X_198,$fot(inverse(X_197)))]]) ).
cnf(refute_0_1282,plain,
( least_upper_bound(inverse(X_197),inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity))) != least_upper_bound(inverse(X_197),inverse(least_upper_bound(identity,greatest_lower_bound(identity,X_197))))
| least_upper_bound(inverse(X_197),inverse(least_upper_bound(identity,greatest_lower_bound(identity,X_197)))) != least_upper_bound(identity,inverse(X_197))
| least_upper_bound(inverse(X_197),inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity))) = least_upper_bound(identity,inverse(X_197)) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(least_upper_bound(inverse(X_197),inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity))))),bind(Y0,$fot(least_upper_bound(inverse(X_197),inverse(least_upper_bound(identity,greatest_lower_bound(identity,X_197)))))),bind(Z0,$fot(least_upper_bound(identity,inverse(X_197))))]]) ).
cnf(refute_0_1283,plain,
( least_upper_bound(inverse(X_197),inverse(least_upper_bound(identity,greatest_lower_bound(identity,X_197)))) != least_upper_bound(identity,inverse(X_197))
| least_upper_bound(inverse(X_197),inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity))) = least_upper_bound(identity,inverse(X_197)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_197),inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity))),least_upper_bound(inverse(X_197),inverse(least_upper_bound(identity,greatest_lower_bound(identity,X_197))))) )],[refute_0_1281,refute_0_1282]) ).
cnf(refute_0_1284,plain,
least_upper_bound(inverse(X_197),inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity))) = least_upper_bound(identity,inverse(X_197)),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_197),inverse(least_upper_bound(identity,greatest_lower_bound(identity,X_197)))),least_upper_bound(identity,inverse(X_197))) )],[refute_0_1202,refute_0_1283]) ).
cnf(refute_0_1285,plain,
multiply(least_upper_bound(inverse(X_197),inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity))),greatest_lower_bound(X_197,identity)) = multiply(least_upper_bound(inverse(X_197),inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity))),greatest_lower_bound(X_197,identity)),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(inverse(X_197),inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity))),greatest_lower_bound(X_197,identity)))]]) ).
cnf(refute_0_1286,plain,
( multiply(least_upper_bound(inverse(X_197),inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity))),greatest_lower_bound(X_197,identity)) != multiply(least_upper_bound(inverse(X_197),inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity))),greatest_lower_bound(X_197,identity))
| least_upper_bound(inverse(X_197),inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity))) != least_upper_bound(identity,inverse(X_197))
| multiply(least_upper_bound(inverse(X_197),inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity))),greatest_lower_bound(X_197,identity)) = multiply(least_upper_bound(identity,inverse(X_197)),greatest_lower_bound(X_197,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(X_197),inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity))),greatest_lower_bound(X_197,identity)),multiply(least_upper_bound(inverse(X_197),inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity))),greatest_lower_bound(X_197,identity))) ),[1,0],$fot(least_upper_bound(identity,inverse(X_197)))]]) ).
cnf(refute_0_1287,plain,
( least_upper_bound(inverse(X_197),inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity))) != least_upper_bound(identity,inverse(X_197))
| multiply(least_upper_bound(inverse(X_197),inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity))),greatest_lower_bound(X_197,identity)) = multiply(least_upper_bound(identity,inverse(X_197)),greatest_lower_bound(X_197,identity)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_197),inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity))),greatest_lower_bound(X_197,identity)),multiply(least_upper_bound(inverse(X_197),inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity))),greatest_lower_bound(X_197,identity))) )],[refute_0_1285,refute_0_1286]) ).
cnf(refute_0_1288,plain,
multiply(least_upper_bound(inverse(X_197),inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity))),greatest_lower_bound(X_197,identity)) = multiply(least_upper_bound(identity,inverse(X_197)),greatest_lower_bound(X_197,identity)),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_197),inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity))),least_upper_bound(identity,inverse(X_197))) )],[refute_0_1284,refute_0_1287]) ).
cnf(refute_0_1289,plain,
( multiply(least_upper_bound(identity,inverse(X_197)),greatest_lower_bound(X_197,identity)) != multiply(greatest_lower_bound(X_197,identity),least_upper_bound(identity,inverse(X_197)))
| multiply(least_upper_bound(inverse(X_197),inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity))),greatest_lower_bound(X_197,identity)) != multiply(least_upper_bound(identity,inverse(X_197)),greatest_lower_bound(X_197,identity))
| multiply(least_upper_bound(inverse(X_197),inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity))),greatest_lower_bound(X_197,identity)) = multiply(greatest_lower_bound(X_197,identity),least_upper_bound(identity,inverse(X_197))) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(multiply(least_upper_bound(inverse(X_197),inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity))),greatest_lower_bound(X_197,identity)))),bind(Y0,$fot(multiply(least_upper_bound(identity,inverse(X_197)),greatest_lower_bound(X_197,identity)))),bind(Z0,$fot(multiply(greatest_lower_bound(X_197,identity),least_upper_bound(identity,inverse(X_197)))))]]) ).
cnf(refute_0_1290,plain,
( multiply(least_upper_bound(identity,inverse(X_197)),greatest_lower_bound(X_197,identity)) != multiply(greatest_lower_bound(X_197,identity),least_upper_bound(identity,inverse(X_197)))
| multiply(least_upper_bound(inverse(X_197),inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity))),greatest_lower_bound(X_197,identity)) = multiply(greatest_lower_bound(X_197,identity),least_upper_bound(identity,inverse(X_197))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_197),inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity))),greatest_lower_bound(X_197,identity)),multiply(least_upper_bound(identity,inverse(X_197)),greatest_lower_bound(X_197,identity))) )],[refute_0_1288,refute_0_1289]) ).
cnf(refute_0_1291,plain,
multiply(least_upper_bound(inverse(X_197),inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity))),greatest_lower_bound(X_197,identity)) = multiply(greatest_lower_bound(X_197,identity),least_upper_bound(identity,inverse(X_197))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_197)),greatest_lower_bound(X_197,identity)),multiply(greatest_lower_bound(X_197,identity),least_upper_bound(identity,inverse(X_197)))) )],[refute_0_1162,refute_0_1290]) ).
cnf(refute_0_1292,plain,
multiply(least_upper_bound(X_198,inverse(X_197)),greatest_lower_bound(identity,X_197)) = least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),multiply(X_198,greatest_lower_bound(identity,X_197))),
inference(subst,[],[refute_0_1041:[bind(X_51,$fot(X_197)),bind(X_66,$fot(X_198))]]) ).
cnf(refute_0_1293,plain,
greatest_lower_bound(X_197,identity) = greatest_lower_bound(identity,X_197),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_197)),bind(Y,$fot(identity))]]) ).
cnf(refute_0_1294,plain,
( greatest_lower_bound(X_197,identity) != greatest_lower_bound(identity,X_197)
| greatest_lower_bound(identity,X_197) = greatest_lower_bound(X_197,identity) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X_197,identity))),bind(Y0,$fot(greatest_lower_bound(identity,X_197)))]]) ).
cnf(refute_0_1295,plain,
greatest_lower_bound(identity,X_197) = greatest_lower_bound(X_197,identity),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_197,identity),greatest_lower_bound(identity,X_197)) )],[refute_0_1293,refute_0_1294]) ).
cnf(refute_0_1296,plain,
( multiply(least_upper_bound(X_198,inverse(X_197)),greatest_lower_bound(identity,X_197)) != least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),multiply(X_198,greatest_lower_bound(identity,X_197)))
| greatest_lower_bound(identity,X_197) != greatest_lower_bound(X_197,identity)
| multiply(least_upper_bound(X_198,inverse(X_197)),greatest_lower_bound(identity,X_197)) = least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),multiply(X_198,greatest_lower_bound(X_197,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_198,inverse(X_197)),greatest_lower_bound(identity,X_197)),least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),multiply(X_198,greatest_lower_bound(identity,X_197)))) ),[1,1,1],$fot(greatest_lower_bound(X_197,identity))]]) ).
cnf(refute_0_1297,plain,
( multiply(least_upper_bound(X_198,inverse(X_197)),greatest_lower_bound(identity,X_197)) != least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),multiply(X_198,greatest_lower_bound(identity,X_197)))
| multiply(least_upper_bound(X_198,inverse(X_197)),greatest_lower_bound(identity,X_197)) = least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),multiply(X_198,greatest_lower_bound(X_197,identity))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,X_197),greatest_lower_bound(X_197,identity)) )],[refute_0_1295,refute_0_1296]) ).
cnf(refute_0_1298,plain,
multiply(least_upper_bound(X_198,inverse(X_197)),greatest_lower_bound(identity,X_197)) = least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),multiply(X_198,greatest_lower_bound(X_197,identity))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_198,inverse(X_197)),greatest_lower_bound(identity,X_197)),least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),multiply(X_198,greatest_lower_bound(identity,X_197)))) )],[refute_0_1292,refute_0_1297]) ).
cnf(refute_0_1299,plain,
multiply(least_upper_bound(inverse(X_103),Z),greatest_lower_bound(X_103,identity)) = least_upper_bound(multiply(inverse(X_103),greatest_lower_bound(X_103,identity)),multiply(Z,greatest_lower_bound(X_103,identity))),
inference(subst,[],[monotony_lub2:[bind(X,$fot(greatest_lower_bound(X_103,identity))),bind(Y,$fot(inverse(X_103)))]]) ).
cnf(refute_0_1300,plain,
( multiply(inverse(X_103),greatest_lower_bound(X_103,identity)) != greatest_lower_bound(identity,inverse(X_103))
| multiply(least_upper_bound(inverse(X_103),Z),greatest_lower_bound(X_103,identity)) != least_upper_bound(multiply(inverse(X_103),greatest_lower_bound(X_103,identity)),multiply(Z,greatest_lower_bound(X_103,identity)))
| multiply(least_upper_bound(inverse(X_103),Z),greatest_lower_bound(X_103,identity)) = least_upper_bound(greatest_lower_bound(identity,inverse(X_103)),multiply(Z,greatest_lower_bound(X_103,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(X_103),Z),greatest_lower_bound(X_103,identity)),least_upper_bound(multiply(inverse(X_103),greatest_lower_bound(X_103,identity)),multiply(Z,greatest_lower_bound(X_103,identity)))) ),[1,0],$fot(greatest_lower_bound(identity,inverse(X_103)))]]) ).
cnf(refute_0_1301,plain,
( multiply(least_upper_bound(inverse(X_103),Z),greatest_lower_bound(X_103,identity)) != least_upper_bound(multiply(inverse(X_103),greatest_lower_bound(X_103,identity)),multiply(Z,greatest_lower_bound(X_103,identity)))
| multiply(least_upper_bound(inverse(X_103),Z),greatest_lower_bound(X_103,identity)) = least_upper_bound(greatest_lower_bound(identity,inverse(X_103)),multiply(Z,greatest_lower_bound(X_103,identity))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_103),greatest_lower_bound(X_103,identity)),greatest_lower_bound(identity,inverse(X_103))) )],[refute_0_1113,refute_0_1300]) ).
cnf(refute_0_1302,plain,
multiply(least_upper_bound(inverse(X_103),Z),greatest_lower_bound(X_103,identity)) = least_upper_bound(greatest_lower_bound(identity,inverse(X_103)),multiply(Z,greatest_lower_bound(X_103,identity))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_103),Z),greatest_lower_bound(X_103,identity)),least_upper_bound(multiply(inverse(X_103),greatest_lower_bound(X_103,identity)),multiply(Z,greatest_lower_bound(X_103,identity)))) )],[refute_0_1299,refute_0_1301]) ).
cnf(refute_0_1303,plain,
( multiply(least_upper_bound(inverse(X_103),Z),greatest_lower_bound(X_103,identity)) != least_upper_bound(greatest_lower_bound(identity,inverse(X_103)),multiply(Z,greatest_lower_bound(X_103,identity)))
| least_upper_bound(greatest_lower_bound(identity,inverse(X_103)),multiply(Z,greatest_lower_bound(X_103,identity))) = multiply(least_upper_bound(inverse(X_103),Z),greatest_lower_bound(X_103,identity)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(inverse(X_103),Z),greatest_lower_bound(X_103,identity)))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(identity,inverse(X_103)),multiply(Z,greatest_lower_bound(X_103,identity)))))]]) ).
cnf(refute_0_1304,plain,
least_upper_bound(greatest_lower_bound(identity,inverse(X_103)),multiply(Z,greatest_lower_bound(X_103,identity))) = multiply(least_upper_bound(inverse(X_103),Z),greatest_lower_bound(X_103,identity)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_103),Z),greatest_lower_bound(X_103,identity)),least_upper_bound(greatest_lower_bound(identity,inverse(X_103)),multiply(Z,greatest_lower_bound(X_103,identity)))) )],[refute_0_1302,refute_0_1303]) ).
cnf(refute_0_1305,plain,
least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),multiply(X_198,greatest_lower_bound(X_197,identity))) = multiply(least_upper_bound(inverse(X_197),X_198),greatest_lower_bound(X_197,identity)),
inference(subst,[],[refute_0_1304:[bind(Z,$fot(X_198)),bind(X_103,$fot(X_197))]]) ).
cnf(refute_0_1306,plain,
( multiply(least_upper_bound(X_198,inverse(X_197)),greatest_lower_bound(identity,X_197)) != least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),multiply(X_198,greatest_lower_bound(X_197,identity)))
| least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),multiply(X_198,greatest_lower_bound(X_197,identity))) != multiply(least_upper_bound(inverse(X_197),X_198),greatest_lower_bound(X_197,identity))
| multiply(least_upper_bound(X_198,inverse(X_197)),greatest_lower_bound(identity,X_197)) = multiply(least_upper_bound(inverse(X_197),X_198),greatest_lower_bound(X_197,identity)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_198,inverse(X_197)),greatest_lower_bound(identity,X_197)),multiply(least_upper_bound(inverse(X_197),X_198),greatest_lower_bound(X_197,identity))) ),[0],$fot(least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),multiply(X_198,greatest_lower_bound(X_197,identity))))]]) ).
cnf(refute_0_1307,plain,
( multiply(least_upper_bound(X_198,inverse(X_197)),greatest_lower_bound(identity,X_197)) != least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),multiply(X_198,greatest_lower_bound(X_197,identity)))
| multiply(least_upper_bound(X_198,inverse(X_197)),greatest_lower_bound(identity,X_197)) = multiply(least_upper_bound(inverse(X_197),X_198),greatest_lower_bound(X_197,identity)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),multiply(X_198,greatest_lower_bound(X_197,identity))),multiply(least_upper_bound(inverse(X_197),X_198),greatest_lower_bound(X_197,identity))) )],[refute_0_1305,refute_0_1306]) ).
cnf(refute_0_1308,plain,
multiply(least_upper_bound(X_198,inverse(X_197)),greatest_lower_bound(identity,X_197)) = multiply(least_upper_bound(inverse(X_197),X_198),greatest_lower_bound(X_197,identity)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_198,inverse(X_197)),greatest_lower_bound(identity,X_197)),least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),multiply(X_198,greatest_lower_bound(X_197,identity)))) )],[refute_0_1298,refute_0_1307]) ).
cnf(refute_0_1309,plain,
multiply(least_upper_bound(inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity)),inverse(X_197)),greatest_lower_bound(identity,X_197)) = multiply(least_upper_bound(inverse(X_197),inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity))),greatest_lower_bound(X_197,identity)),
inference(subst,[],[refute_0_1308:[bind(X_198,$fot(inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity))))]]) ).
cnf(refute_0_1310,plain,
( multiply(least_upper_bound(inverse(X_197),inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity))),greatest_lower_bound(X_197,identity)) != multiply(greatest_lower_bound(X_197,identity),least_upper_bound(identity,inverse(X_197)))
| multiply(least_upper_bound(inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity)),inverse(X_197)),greatest_lower_bound(identity,X_197)) != multiply(least_upper_bound(inverse(X_197),inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity))),greatest_lower_bound(X_197,identity))
| multiply(least_upper_bound(inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity)),inverse(X_197)),greatest_lower_bound(identity,X_197)) = multiply(greatest_lower_bound(X_197,identity),least_upper_bound(identity,inverse(X_197))) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(multiply(least_upper_bound(inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity)),inverse(X_197)),greatest_lower_bound(identity,X_197)))),bind(Y0,$fot(multiply(least_upper_bound(inverse(X_197),inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity))),greatest_lower_bound(X_197,identity)))),bind(Z0,$fot(multiply(greatest_lower_bound(X_197,identity),least_upper_bound(identity,inverse(X_197)))))]]) ).
cnf(refute_0_1311,plain,
( multiply(least_upper_bound(inverse(X_197),inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity))),greatest_lower_bound(X_197,identity)) != multiply(greatest_lower_bound(X_197,identity),least_upper_bound(identity,inverse(X_197)))
| multiply(least_upper_bound(inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity)),inverse(X_197)),greatest_lower_bound(identity,X_197)) = multiply(greatest_lower_bound(X_197,identity),least_upper_bound(identity,inverse(X_197))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity)),inverse(X_197)),greatest_lower_bound(identity,X_197)),multiply(least_upper_bound(inverse(X_197),inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity))),greatest_lower_bound(X_197,identity))) )],[refute_0_1309,refute_0_1310]) ).
cnf(refute_0_1312,plain,
multiply(least_upper_bound(inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity)),inverse(X_197)),greatest_lower_bound(identity,X_197)) = multiply(greatest_lower_bound(X_197,identity),least_upper_bound(identity,inverse(X_197))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_197),inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity))),greatest_lower_bound(X_197,identity)),multiply(greatest_lower_bound(X_197,identity),least_upper_bound(identity,inverse(X_197)))) )],[refute_0_1291,refute_0_1311]) ).
cnf(refute_0_1313,plain,
( multiply(least_upper_bound(inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity)),inverse(X_197)),greatest_lower_bound(identity,X_197)) != multiply(greatest_lower_bound(X_197,identity),least_upper_bound(identity,inverse(X_197)))
| multiply(least_upper_bound(inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity)),inverse(X_197)),greatest_lower_bound(identity,X_197)) != least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197)))))
| multiply(greatest_lower_bound(X_197,identity),least_upper_bound(identity,inverse(X_197))) = least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity)),inverse(X_197)),greatest_lower_bound(identity,X_197)),least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197)))))) ),[0],$fot(multiply(greatest_lower_bound(X_197,identity),least_upper_bound(identity,inverse(X_197))))]]) ).
cnf(refute_0_1314,plain,
( multiply(least_upper_bound(inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity)),inverse(X_197)),greatest_lower_bound(identity,X_197)) != least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197)))))
| multiply(greatest_lower_bound(X_197,identity),least_upper_bound(identity,inverse(X_197))) = least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197))))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity)),inverse(X_197)),greatest_lower_bound(identity,X_197)),multiply(greatest_lower_bound(X_197,identity),least_upper_bound(identity,inverse(X_197)))) )],[refute_0_1312,refute_0_1313]) ).
cnf(refute_0_1315,plain,
least_upper_bound(greatest_lower_bound(identity,X_197),greatest_lower_bound(identity,inverse(X_197))) = multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197))),
inference(subst,[],[refute_0_968:[bind(X_51,$fot(X_197))]]) ).
cnf(refute_0_1316,plain,
multiply(greatest_lower_bound(inverse(X_45),X_47),X_45) = greatest_lower_bound(multiply(inverse(X_45),X_45),multiply(X_47,X_45)),
inference(subst,[],[monotony_glb2:[bind(X,$fot(X_45)),bind(Y,$fot(inverse(X_45))),bind(Z,$fot(X_47))]]) ).
cnf(refute_0_1317,plain,
( multiply(greatest_lower_bound(inverse(X_45),X_47),X_45) != greatest_lower_bound(multiply(inverse(X_45),X_45),multiply(X_47,X_45))
| multiply(inverse(X_45),X_45) != identity
| multiply(greatest_lower_bound(inverse(X_45),X_47),X_45) = greatest_lower_bound(identity,multiply(X_47,X_45)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_45),X_47),X_45),greatest_lower_bound(multiply(inverse(X_45),X_45),multiply(X_47,X_45))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_1318,plain,
( multiply(greatest_lower_bound(inverse(X_45),X_47),X_45) != greatest_lower_bound(multiply(inverse(X_45),X_45),multiply(X_47,X_45))
| multiply(greatest_lower_bound(inverse(X_45),X_47),X_45) = greatest_lower_bound(identity,multiply(X_47,X_45)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_45),X_45),identity) )],[refute_0_117,refute_0_1317]) ).
cnf(refute_0_1319,plain,
multiply(greatest_lower_bound(inverse(X_45),X_47),X_45) = greatest_lower_bound(identity,multiply(X_47,X_45)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_45),X_47),X_45),greatest_lower_bound(multiply(inverse(X_45),X_45),multiply(X_47,X_45))) )],[refute_0_1316,refute_0_1318]) ).
cnf(refute_0_1320,plain,
multiply(greatest_lower_bound(inverse(greatest_lower_bound(X_148,identity)),inverse(greatest_lower_bound(identity,inverse(X_148)))),greatest_lower_bound(X_148,identity)) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X_148))),greatest_lower_bound(X_148,identity))),
inference(subst,[],[refute_0_1319:[bind(X_45,$fot(greatest_lower_bound(X_148,identity))),bind(X_47,$fot(inverse(greatest_lower_bound(identity,inverse(X_148)))))]]) ).
cnf(refute_0_1321,plain,
multiply(greatest_lower_bound(X_46,identity),inverse(greatest_lower_bound(X_46,identity))) = greatest_lower_bound(inverse(greatest_lower_bound(X_46,identity)),multiply(X_46,inverse(greatest_lower_bound(X_46,identity)))),
inference(subst,[],[refute_0_746:[bind(X_45,$fot(inverse(greatest_lower_bound(X_46,identity))))]]) ).
cnf(refute_0_1322,plain,
inverse(greatest_lower_bound(identity,multiply(X_46,inverse(multiply(X_105,X_46))))) = multiply(multiply(X_105,X_46),inverse(greatest_lower_bound(X_46,multiply(X_105,X_46)))),
inference(subst,[],[refute_0_146:[bind(X_99,$fot(multiply(X_105,X_46)))]]) ).
cnf(refute_0_1323,plain,
multiply(greatest_lower_bound(X_105,identity),X_46) = greatest_lower_bound(X_46,multiply(X_105,X_46)),
inference(subst,[],[refute_0_746:[bind(X_45,$fot(X_46)),bind(X_46,$fot(X_105))]]) ).
cnf(refute_0_1324,plain,
( multiply(greatest_lower_bound(X_105,identity),X_46) != greatest_lower_bound(X_46,multiply(X_105,X_46))
| greatest_lower_bound(X_46,multiply(X_105,X_46)) = multiply(greatest_lower_bound(X_105,identity),X_46) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(greatest_lower_bound(X_105,identity),X_46))),bind(Y0,$fot(greatest_lower_bound(X_46,multiply(X_105,X_46))))]]) ).
cnf(refute_0_1325,plain,
greatest_lower_bound(X_46,multiply(X_105,X_46)) = multiply(greatest_lower_bound(X_105,identity),X_46),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_105,identity),X_46),greatest_lower_bound(X_46,multiply(X_105,X_46))) )],[refute_0_1323,refute_0_1324]) ).
cnf(refute_0_1326,plain,
( greatest_lower_bound(X_46,multiply(X_105,X_46)) != multiply(greatest_lower_bound(X_105,identity),X_46)
| inverse(greatest_lower_bound(identity,multiply(X_46,inverse(multiply(X_105,X_46))))) != multiply(multiply(X_105,X_46),inverse(greatest_lower_bound(X_46,multiply(X_105,X_46))))
| inverse(greatest_lower_bound(identity,multiply(X_46,inverse(multiply(X_105,X_46))))) = multiply(multiply(X_105,X_46),inverse(multiply(greatest_lower_bound(X_105,identity),X_46))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(X_46,inverse(multiply(X_105,X_46))))),multiply(multiply(X_105,X_46),inverse(greatest_lower_bound(X_46,multiply(X_105,X_46))))) ),[1,1,0],$fot(multiply(greatest_lower_bound(X_105,identity),X_46))]]) ).
cnf(refute_0_1327,plain,
( inverse(greatest_lower_bound(identity,multiply(X_46,inverse(multiply(X_105,X_46))))) != multiply(multiply(X_105,X_46),inverse(greatest_lower_bound(X_46,multiply(X_105,X_46))))
| inverse(greatest_lower_bound(identity,multiply(X_46,inverse(multiply(X_105,X_46))))) = multiply(multiply(X_105,X_46),inverse(multiply(greatest_lower_bound(X_105,identity),X_46))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_46,multiply(X_105,X_46)),multiply(greatest_lower_bound(X_105,identity),X_46)) )],[refute_0_1325,refute_0_1326]) ).
cnf(refute_0_1328,plain,
inverse(greatest_lower_bound(identity,multiply(X_46,inverse(multiply(X_105,X_46))))) = multiply(multiply(X_105,X_46),inverse(multiply(greatest_lower_bound(X_105,identity),X_46))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(X_46,inverse(multiply(X_105,X_46))))),multiply(multiply(X_105,X_46),inverse(greatest_lower_bound(X_46,multiply(X_105,X_46))))) )],[refute_0_1322,refute_0_1327]) ).
cnf(refute_0_1329,plain,
multiply(X_46,inverse(multiply(X_105,X_46))) = inverse(X_105),
inference(subst,[],[refute_0_383:[bind(X,$fot(X_105)),bind(Y,$fot(X_46))]]) ).
cnf(refute_0_1330,plain,
greatest_lower_bound(identity,multiply(X_46,inverse(multiply(X_105,X_46)))) = greatest_lower_bound(identity,multiply(X_46,inverse(multiply(X_105,X_46)))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,multiply(X_46,inverse(multiply(X_105,X_46)))))]]) ).
cnf(refute_0_1331,plain,
( multiply(X_46,inverse(multiply(X_105,X_46))) != inverse(X_105)
| greatest_lower_bound(identity,multiply(X_46,inverse(multiply(X_105,X_46)))) != greatest_lower_bound(identity,multiply(X_46,inverse(multiply(X_105,X_46))))
| greatest_lower_bound(identity,multiply(X_46,inverse(multiply(X_105,X_46)))) = greatest_lower_bound(identity,inverse(X_105)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_46,inverse(multiply(X_105,X_46)))),greatest_lower_bound(identity,multiply(X_46,inverse(multiply(X_105,X_46))))) ),[1,1],$fot(inverse(X_105))]]) ).
cnf(refute_0_1332,plain,
( multiply(X_46,inverse(multiply(X_105,X_46))) != inverse(X_105)
| greatest_lower_bound(identity,multiply(X_46,inverse(multiply(X_105,X_46)))) = greatest_lower_bound(identity,inverse(X_105)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_46,inverse(multiply(X_105,X_46)))),greatest_lower_bound(identity,multiply(X_46,inverse(multiply(X_105,X_46))))) )],[refute_0_1330,refute_0_1331]) ).
cnf(refute_0_1333,plain,
greatest_lower_bound(identity,multiply(X_46,inverse(multiply(X_105,X_46)))) = greatest_lower_bound(identity,inverse(X_105)),
inference(resolve,[$cnf( $equal(multiply(X_46,inverse(multiply(X_105,X_46))),inverse(X_105)) )],[refute_0_1329,refute_0_1332]) ).
cnf(refute_0_1334,plain,
inverse(greatest_lower_bound(identity,multiply(X_46,inverse(multiply(X_105,X_46))))) = inverse(greatest_lower_bound(identity,multiply(X_46,inverse(multiply(X_105,X_46))))),
introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(identity,multiply(X_46,inverse(multiply(X_105,X_46))))))]]) ).
cnf(refute_0_1335,plain,
( greatest_lower_bound(identity,multiply(X_46,inverse(multiply(X_105,X_46)))) != greatest_lower_bound(identity,inverse(X_105))
| inverse(greatest_lower_bound(identity,multiply(X_46,inverse(multiply(X_105,X_46))))) != inverse(greatest_lower_bound(identity,multiply(X_46,inverse(multiply(X_105,X_46)))))
| inverse(greatest_lower_bound(identity,multiply(X_46,inverse(multiply(X_105,X_46))))) = inverse(greatest_lower_bound(identity,inverse(X_105))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(X_46,inverse(multiply(X_105,X_46))))),inverse(greatest_lower_bound(identity,multiply(X_46,inverse(multiply(X_105,X_46)))))) ),[1,0],$fot(greatest_lower_bound(identity,inverse(X_105)))]]) ).
cnf(refute_0_1336,plain,
( greatest_lower_bound(identity,multiply(X_46,inverse(multiply(X_105,X_46)))) != greatest_lower_bound(identity,inverse(X_105))
| inverse(greatest_lower_bound(identity,multiply(X_46,inverse(multiply(X_105,X_46))))) = inverse(greatest_lower_bound(identity,inverse(X_105))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(X_46,inverse(multiply(X_105,X_46))))),inverse(greatest_lower_bound(identity,multiply(X_46,inverse(multiply(X_105,X_46)))))) )],[refute_0_1334,refute_0_1335]) ).
cnf(refute_0_1337,plain,
inverse(greatest_lower_bound(identity,multiply(X_46,inverse(multiply(X_105,X_46))))) = inverse(greatest_lower_bound(identity,inverse(X_105))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_46,inverse(multiply(X_105,X_46)))),greatest_lower_bound(identity,inverse(X_105))) )],[refute_0_1333,refute_0_1336]) ).
cnf(refute_0_1338,plain,
( inverse(greatest_lower_bound(identity,multiply(X_46,inverse(multiply(X_105,X_46))))) != multiply(multiply(X_105,X_46),inverse(multiply(greatest_lower_bound(X_105,identity),X_46)))
| inverse(greatest_lower_bound(identity,multiply(X_46,inverse(multiply(X_105,X_46))))) != inverse(greatest_lower_bound(identity,inverse(X_105)))
| inverse(greatest_lower_bound(identity,inverse(X_105))) = multiply(multiply(X_105,X_46),inverse(multiply(greatest_lower_bound(X_105,identity),X_46))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(X_46,inverse(multiply(X_105,X_46))))),multiply(multiply(X_105,X_46),inverse(multiply(greatest_lower_bound(X_105,identity),X_46)))) ),[0],$fot(inverse(greatest_lower_bound(identity,inverse(X_105))))]]) ).
cnf(refute_0_1339,plain,
( inverse(greatest_lower_bound(identity,multiply(X_46,inverse(multiply(X_105,X_46))))) != multiply(multiply(X_105,X_46),inverse(multiply(greatest_lower_bound(X_105,identity),X_46)))
| inverse(greatest_lower_bound(identity,inverse(X_105))) = multiply(multiply(X_105,X_46),inverse(multiply(greatest_lower_bound(X_105,identity),X_46))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(X_46,inverse(multiply(X_105,X_46))))),inverse(greatest_lower_bound(identity,inverse(X_105)))) )],[refute_0_1337,refute_0_1338]) ).
cnf(refute_0_1340,plain,
multiply(X_46,inverse(multiply(greatest_lower_bound(X_105,identity),X_46))) = inverse(greatest_lower_bound(X_105,identity)),
inference(subst,[],[refute_0_383:[bind(X,$fot(greatest_lower_bound(X_105,identity))),bind(Y,$fot(X_46))]]) ).
cnf(refute_0_1341,plain,
multiply(X_105,multiply(X_46,inverse(multiply(greatest_lower_bound(X_105,identity),X_46)))) = multiply(X_105,multiply(X_46,inverse(multiply(greatest_lower_bound(X_105,identity),X_46)))),
introduced(tautology,[refl,[$fot(multiply(X_105,multiply(X_46,inverse(multiply(greatest_lower_bound(X_105,identity),X_46)))))]]) ).
cnf(refute_0_1342,plain,
( multiply(X_105,multiply(X_46,inverse(multiply(greatest_lower_bound(X_105,identity),X_46)))) != multiply(X_105,multiply(X_46,inverse(multiply(greatest_lower_bound(X_105,identity),X_46))))
| multiply(X_46,inverse(multiply(greatest_lower_bound(X_105,identity),X_46))) != inverse(greatest_lower_bound(X_105,identity))
| multiply(X_105,multiply(X_46,inverse(multiply(greatest_lower_bound(X_105,identity),X_46)))) = multiply(X_105,inverse(greatest_lower_bound(X_105,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_105,multiply(X_46,inverse(multiply(greatest_lower_bound(X_105,identity),X_46)))),multiply(X_105,multiply(X_46,inverse(multiply(greatest_lower_bound(X_105,identity),X_46))))) ),[1,1],$fot(inverse(greatest_lower_bound(X_105,identity)))]]) ).
cnf(refute_0_1343,plain,
( multiply(X_46,inverse(multiply(greatest_lower_bound(X_105,identity),X_46))) != inverse(greatest_lower_bound(X_105,identity))
| multiply(X_105,multiply(X_46,inverse(multiply(greatest_lower_bound(X_105,identity),X_46)))) = multiply(X_105,inverse(greatest_lower_bound(X_105,identity))) ),
inference(resolve,[$cnf( $equal(multiply(X_105,multiply(X_46,inverse(multiply(greatest_lower_bound(X_105,identity),X_46)))),multiply(X_105,multiply(X_46,inverse(multiply(greatest_lower_bound(X_105,identity),X_46))))) )],[refute_0_1341,refute_0_1342]) ).
cnf(refute_0_1344,plain,
multiply(X_105,multiply(X_46,inverse(multiply(greatest_lower_bound(X_105,identity),X_46)))) = multiply(X_105,inverse(greatest_lower_bound(X_105,identity))),
inference(resolve,[$cnf( $equal(multiply(X_46,inverse(multiply(greatest_lower_bound(X_105,identity),X_46))),inverse(greatest_lower_bound(X_105,identity))) )],[refute_0_1340,refute_0_1343]) ).
cnf(refute_0_1345,plain,
multiply(multiply(X_105,X_46),inverse(multiply(greatest_lower_bound(X_105,identity),X_46))) = multiply(X_105,multiply(X_46,inverse(multiply(greatest_lower_bound(X_105,identity),X_46)))),
inference(subst,[],[associativity:[bind(X,$fot(X_105)),bind(Y,$fot(X_46)),bind(Z,$fot(inverse(multiply(greatest_lower_bound(X_105,identity),X_46))))]]) ).
cnf(refute_0_1346,plain,
( multiply(X_105,multiply(X_46,inverse(multiply(greatest_lower_bound(X_105,identity),X_46)))) != multiply(X_105,inverse(greatest_lower_bound(X_105,identity)))
| multiply(multiply(X_105,X_46),inverse(multiply(greatest_lower_bound(X_105,identity),X_46))) != multiply(X_105,multiply(X_46,inverse(multiply(greatest_lower_bound(X_105,identity),X_46))))
| multiply(multiply(X_105,X_46),inverse(multiply(greatest_lower_bound(X_105,identity),X_46))) = multiply(X_105,inverse(greatest_lower_bound(X_105,identity))) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(multiply(multiply(X_105,X_46),inverse(multiply(greatest_lower_bound(X_105,identity),X_46))))),bind(Y0,$fot(multiply(X_105,multiply(X_46,inverse(multiply(greatest_lower_bound(X_105,identity),X_46)))))),bind(Z0,$fot(multiply(X_105,inverse(greatest_lower_bound(X_105,identity)))))]]) ).
cnf(refute_0_1347,plain,
( multiply(X_105,multiply(X_46,inverse(multiply(greatest_lower_bound(X_105,identity),X_46)))) != multiply(X_105,inverse(greatest_lower_bound(X_105,identity)))
| multiply(multiply(X_105,X_46),inverse(multiply(greatest_lower_bound(X_105,identity),X_46))) = multiply(X_105,inverse(greatest_lower_bound(X_105,identity))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_105,X_46),inverse(multiply(greatest_lower_bound(X_105,identity),X_46))),multiply(X_105,multiply(X_46,inverse(multiply(greatest_lower_bound(X_105,identity),X_46))))) )],[refute_0_1345,refute_0_1346]) ).
cnf(refute_0_1348,plain,
multiply(multiply(X_105,X_46),inverse(multiply(greatest_lower_bound(X_105,identity),X_46))) = multiply(X_105,inverse(greatest_lower_bound(X_105,identity))),
inference(resolve,[$cnf( $equal(multiply(X_105,multiply(X_46,inverse(multiply(greatest_lower_bound(X_105,identity),X_46)))),multiply(X_105,inverse(greatest_lower_bound(X_105,identity)))) )],[refute_0_1344,refute_0_1347]) ).
cnf(refute_0_1349,plain,
( multiply(multiply(X_105,X_46),inverse(multiply(greatest_lower_bound(X_105,identity),X_46))) != multiply(X_105,inverse(greatest_lower_bound(X_105,identity)))
| inverse(greatest_lower_bound(identity,inverse(X_105))) != multiply(multiply(X_105,X_46),inverse(multiply(greatest_lower_bound(X_105,identity),X_46)))
| inverse(greatest_lower_bound(identity,inverse(X_105))) = multiply(X_105,inverse(greatest_lower_bound(X_105,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_105))),multiply(multiply(X_105,X_46),inverse(multiply(greatest_lower_bound(X_105,identity),X_46)))) ),[1],$fot(multiply(X_105,inverse(greatest_lower_bound(X_105,identity))))]]) ).
cnf(refute_0_1350,plain,
( inverse(greatest_lower_bound(identity,inverse(X_105))) != multiply(multiply(X_105,X_46),inverse(multiply(greatest_lower_bound(X_105,identity),X_46)))
| inverse(greatest_lower_bound(identity,inverse(X_105))) = multiply(X_105,inverse(greatest_lower_bound(X_105,identity))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_105,X_46),inverse(multiply(greatest_lower_bound(X_105,identity),X_46))),multiply(X_105,inverse(greatest_lower_bound(X_105,identity)))) )],[refute_0_1348,refute_0_1349]) ).
cnf(refute_0_1351,plain,
( inverse(greatest_lower_bound(identity,multiply(X_46,inverse(multiply(X_105,X_46))))) != multiply(multiply(X_105,X_46),inverse(multiply(greatest_lower_bound(X_105,identity),X_46)))
| inverse(greatest_lower_bound(identity,inverse(X_105))) = multiply(X_105,inverse(greatest_lower_bound(X_105,identity))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_105))),multiply(multiply(X_105,X_46),inverse(multiply(greatest_lower_bound(X_105,identity),X_46)))) )],[refute_0_1339,refute_0_1350]) ).
cnf(refute_0_1352,plain,
inverse(greatest_lower_bound(identity,inverse(X_105))) = multiply(X_105,inverse(greatest_lower_bound(X_105,identity))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(X_46,inverse(multiply(X_105,X_46))))),multiply(multiply(X_105,X_46),inverse(multiply(greatest_lower_bound(X_105,identity),X_46)))) )],[refute_0_1328,refute_0_1351]) ).
cnf(refute_0_1353,plain,
inverse(greatest_lower_bound(identity,inverse(X_46))) = multiply(X_46,inverse(greatest_lower_bound(X_46,identity))),
inference(subst,[],[refute_0_1352:[bind(X_105,$fot(X_46))]]) ).
cnf(refute_0_1354,plain,
( inverse(greatest_lower_bound(identity,inverse(X_46))) != multiply(X_46,inverse(greatest_lower_bound(X_46,identity)))
| multiply(X_46,inverse(greatest_lower_bound(X_46,identity))) = inverse(greatest_lower_bound(identity,inverse(X_46))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(greatest_lower_bound(identity,inverse(X_46))))),bind(Y0,$fot(multiply(X_46,inverse(greatest_lower_bound(X_46,identity)))))]]) ).
cnf(refute_0_1355,plain,
multiply(X_46,inverse(greatest_lower_bound(X_46,identity))) = inverse(greatest_lower_bound(identity,inverse(X_46))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_46))),multiply(X_46,inverse(greatest_lower_bound(X_46,identity)))) )],[refute_0_1353,refute_0_1354]) ).
cnf(refute_0_1356,plain,
( multiply(X_46,inverse(greatest_lower_bound(X_46,identity))) != inverse(greatest_lower_bound(identity,inverse(X_46)))
| multiply(greatest_lower_bound(X_46,identity),inverse(greatest_lower_bound(X_46,identity))) != greatest_lower_bound(inverse(greatest_lower_bound(X_46,identity)),multiply(X_46,inverse(greatest_lower_bound(X_46,identity))))
| multiply(greatest_lower_bound(X_46,identity),inverse(greatest_lower_bound(X_46,identity))) = greatest_lower_bound(inverse(greatest_lower_bound(X_46,identity)),inverse(greatest_lower_bound(identity,inverse(X_46)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_46,identity),inverse(greatest_lower_bound(X_46,identity))),greatest_lower_bound(inverse(greatest_lower_bound(X_46,identity)),multiply(X_46,inverse(greatest_lower_bound(X_46,identity))))) ),[1,1],$fot(inverse(greatest_lower_bound(identity,inverse(X_46))))]]) ).
cnf(refute_0_1357,plain,
( multiply(greatest_lower_bound(X_46,identity),inverse(greatest_lower_bound(X_46,identity))) != greatest_lower_bound(inverse(greatest_lower_bound(X_46,identity)),multiply(X_46,inverse(greatest_lower_bound(X_46,identity))))
| multiply(greatest_lower_bound(X_46,identity),inverse(greatest_lower_bound(X_46,identity))) = greatest_lower_bound(inverse(greatest_lower_bound(X_46,identity)),inverse(greatest_lower_bound(identity,inverse(X_46)))) ),
inference(resolve,[$cnf( $equal(multiply(X_46,inverse(greatest_lower_bound(X_46,identity))),inverse(greatest_lower_bound(identity,inverse(X_46)))) )],[refute_0_1355,refute_0_1356]) ).
cnf(refute_0_1358,plain,
multiply(greatest_lower_bound(X_46,identity),inverse(greatest_lower_bound(X_46,identity))) = greatest_lower_bound(inverse(greatest_lower_bound(X_46,identity)),inverse(greatest_lower_bound(identity,inverse(X_46)))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_46,identity),inverse(greatest_lower_bound(X_46,identity))),greatest_lower_bound(inverse(greatest_lower_bound(X_46,identity)),multiply(X_46,inverse(greatest_lower_bound(X_46,identity))))) )],[refute_0_1321,refute_0_1357]) ).
cnf(refute_0_1359,plain,
multiply(greatest_lower_bound(X_46,identity),inverse(greatest_lower_bound(X_46,identity))) = identity,
inference(subst,[],[refute_0_38:[bind(X_1,$fot(greatest_lower_bound(X_46,identity)))]]) ).
cnf(refute_0_1360,plain,
( multiply(greatest_lower_bound(X_46,identity),inverse(greatest_lower_bound(X_46,identity))) != greatest_lower_bound(inverse(greatest_lower_bound(X_46,identity)),inverse(greatest_lower_bound(identity,inverse(X_46))))
| multiply(greatest_lower_bound(X_46,identity),inverse(greatest_lower_bound(X_46,identity))) != identity
| identity = greatest_lower_bound(inverse(greatest_lower_bound(X_46,identity)),inverse(greatest_lower_bound(identity,inverse(X_46)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_46,identity),inverse(greatest_lower_bound(X_46,identity))),greatest_lower_bound(inverse(greatest_lower_bound(X_46,identity)),inverse(greatest_lower_bound(identity,inverse(X_46))))) ),[0],$fot(identity)]]) ).
cnf(refute_0_1361,plain,
( multiply(greatest_lower_bound(X_46,identity),inverse(greatest_lower_bound(X_46,identity))) != greatest_lower_bound(inverse(greatest_lower_bound(X_46,identity)),inverse(greatest_lower_bound(identity,inverse(X_46))))
| identity = greatest_lower_bound(inverse(greatest_lower_bound(X_46,identity)),inverse(greatest_lower_bound(identity,inverse(X_46)))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_46,identity),inverse(greatest_lower_bound(X_46,identity))),identity) )],[refute_0_1359,refute_0_1360]) ).
cnf(refute_0_1362,plain,
identity = greatest_lower_bound(inverse(greatest_lower_bound(X_46,identity)),inverse(greatest_lower_bound(identity,inverse(X_46)))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_46,identity),inverse(greatest_lower_bound(X_46,identity))),greatest_lower_bound(inverse(greatest_lower_bound(X_46,identity)),inverse(greatest_lower_bound(identity,inverse(X_46))))) )],[refute_0_1358,refute_0_1361]) ).
cnf(refute_0_1363,plain,
identity = greatest_lower_bound(inverse(greatest_lower_bound(X_148,identity)),inverse(greatest_lower_bound(identity,inverse(X_148)))),
inference(subst,[],[refute_0_1362:[bind(X_46,$fot(X_148))]]) ).
cnf(refute_0_1364,plain,
( identity != greatest_lower_bound(inverse(greatest_lower_bound(X_148,identity)),inverse(greatest_lower_bound(identity,inverse(X_148))))
| greatest_lower_bound(inverse(greatest_lower_bound(X_148,identity)),inverse(greatest_lower_bound(identity,inverse(X_148)))) = identity ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(identity)),bind(Y0,$fot(greatest_lower_bound(inverse(greatest_lower_bound(X_148,identity)),inverse(greatest_lower_bound(identity,inverse(X_148))))))]]) ).
cnf(refute_0_1365,plain,
greatest_lower_bound(inverse(greatest_lower_bound(X_148,identity)),inverse(greatest_lower_bound(identity,inverse(X_148)))) = identity,
inference(resolve,[$cnf( $equal(identity,greatest_lower_bound(inverse(greatest_lower_bound(X_148,identity)),inverse(greatest_lower_bound(identity,inverse(X_148))))) )],[refute_0_1363,refute_0_1364]) ).
cnf(refute_0_1366,plain,
( multiply(greatest_lower_bound(inverse(greatest_lower_bound(X_148,identity)),inverse(greatest_lower_bound(identity,inverse(X_148)))),greatest_lower_bound(X_148,identity)) != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X_148))),greatest_lower_bound(X_148,identity)))
| greatest_lower_bound(inverse(greatest_lower_bound(X_148,identity)),inverse(greatest_lower_bound(identity,inverse(X_148)))) != identity
| multiply(identity,greatest_lower_bound(X_148,identity)) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X_148))),greatest_lower_bound(X_148,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(inverse(greatest_lower_bound(X_148,identity)),inverse(greatest_lower_bound(identity,inverse(X_148)))),greatest_lower_bound(X_148,identity)),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X_148))),greatest_lower_bound(X_148,identity)))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_1367,plain,
( multiply(greatest_lower_bound(inverse(greatest_lower_bound(X_148,identity)),inverse(greatest_lower_bound(identity,inverse(X_148)))),greatest_lower_bound(X_148,identity)) != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X_148))),greatest_lower_bound(X_148,identity)))
| multiply(identity,greatest_lower_bound(X_148,identity)) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X_148))),greatest_lower_bound(X_148,identity))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(greatest_lower_bound(X_148,identity)),inverse(greatest_lower_bound(identity,inverse(X_148)))),identity) )],[refute_0_1365,refute_0_1366]) ).
cnf(refute_0_1368,plain,
multiply(identity,greatest_lower_bound(X_148,identity)) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X_148))),greatest_lower_bound(X_148,identity))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(greatest_lower_bound(X_148,identity)),inverse(greatest_lower_bound(identity,inverse(X_148)))),greatest_lower_bound(X_148,identity)),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X_148))),greatest_lower_bound(X_148,identity)))) )],[refute_0_1320,refute_0_1367]) ).
cnf(refute_0_1369,plain,
multiply(identity,greatest_lower_bound(X_148,identity)) = greatest_lower_bound(X_148,identity),
inference(subst,[],[left_identity:[bind(X,$fot(greatest_lower_bound(X_148,identity)))]]) ).
cnf(refute_0_1370,plain,
( multiply(identity,greatest_lower_bound(X_148,identity)) != greatest_lower_bound(X_148,identity)
| multiply(identity,greatest_lower_bound(X_148,identity)) != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X_148))),greatest_lower_bound(X_148,identity)))
| greatest_lower_bound(X_148,identity) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X_148))),greatest_lower_bound(X_148,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,greatest_lower_bound(X_148,identity)),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X_148))),greatest_lower_bound(X_148,identity)))) ),[0],$fot(greatest_lower_bound(X_148,identity))]]) ).
cnf(refute_0_1371,plain,
( multiply(identity,greatest_lower_bound(X_148,identity)) != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X_148))),greatest_lower_bound(X_148,identity)))
| greatest_lower_bound(X_148,identity) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X_148))),greatest_lower_bound(X_148,identity))) ),
inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(X_148,identity)),greatest_lower_bound(X_148,identity)) )],[refute_0_1369,refute_0_1370]) ).
cnf(refute_0_1372,plain,
greatest_lower_bound(X_148,identity) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X_148))),greatest_lower_bound(X_148,identity))),
inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(X_148,identity)),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X_148))),greatest_lower_bound(X_148,identity)))) )],[refute_0_1368,refute_0_1371]) ).
cnf(refute_0_1373,plain,
X_94 = multiply(inverse(greatest_lower_bound(inverse(X_94),X_131)),multiply(greatest_lower_bound(inverse(X_94),X_131),X_94)),
inference(subst,[],[refute_0_17:[bind(X_93,$fot(greatest_lower_bound(inverse(X_94),X_131)))]]) ).
cnf(refute_0_1374,plain,
multiply(greatest_lower_bound(inverse(X_94),X_131),X_94) = greatest_lower_bound(identity,multiply(X_131,X_94)),
inference(subst,[],[refute_0_1319:[bind(X_45,$fot(X_94)),bind(X_47,$fot(X_131))]]) ).
cnf(refute_0_1375,plain,
( X_94 != multiply(inverse(greatest_lower_bound(inverse(X_94),X_131)),multiply(greatest_lower_bound(inverse(X_94),X_131),X_94))
| multiply(greatest_lower_bound(inverse(X_94),X_131),X_94) != greatest_lower_bound(identity,multiply(X_131,X_94))
| X_94 = multiply(inverse(greatest_lower_bound(inverse(X_94),X_131)),greatest_lower_bound(identity,multiply(X_131,X_94))) ),
introduced(tautology,[equality,[$cnf( $equal(X_94,multiply(inverse(greatest_lower_bound(inverse(X_94),X_131)),multiply(greatest_lower_bound(inverse(X_94),X_131),X_94))) ),[1,1],$fot(greatest_lower_bound(identity,multiply(X_131,X_94)))]]) ).
cnf(refute_0_1376,plain,
( X_94 != multiply(inverse(greatest_lower_bound(inverse(X_94),X_131)),multiply(greatest_lower_bound(inverse(X_94),X_131),X_94))
| X_94 = multiply(inverse(greatest_lower_bound(inverse(X_94),X_131)),greatest_lower_bound(identity,multiply(X_131,X_94))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_94),X_131),X_94),greatest_lower_bound(identity,multiply(X_131,X_94))) )],[refute_0_1374,refute_0_1375]) ).
cnf(refute_0_1377,plain,
X_94 = multiply(inverse(greatest_lower_bound(inverse(X_94),X_131)),greatest_lower_bound(identity,multiply(X_131,X_94))),
inference(resolve,[$cnf( $equal(X_94,multiply(inverse(greatest_lower_bound(inverse(X_94),X_131)),multiply(greatest_lower_bound(inverse(X_94),X_131),X_94))) )],[refute_0_1373,refute_0_1376]) ).
cnf(refute_0_1378,plain,
X_171 = multiply(inverse(greatest_lower_bound(inverse(X_171),identity)),greatest_lower_bound(identity,multiply(identity,X_171))),
inference(subst,[],[refute_0_1377:[bind(X_131,$fot(identity)),bind(X_94,$fot(X_171))]]) ).
cnf(refute_0_1379,plain,
multiply(identity,greatest_lower_bound(X_171,identity)) = greatest_lower_bound(identity,multiply(identity,X_171)),
inference(subst,[],[refute_0_220:[bind(X_36,$fot(identity)),bind(X_37,$fot(X_171))]]) ).
cnf(refute_0_1380,plain,
( multiply(identity,greatest_lower_bound(X_171,identity)) != greatest_lower_bound(identity,multiply(identity,X_171))
| greatest_lower_bound(identity,multiply(identity,X_171)) = multiply(identity,greatest_lower_bound(X_171,identity)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(identity,greatest_lower_bound(X_171,identity)))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(identity,X_171))))]]) ).
cnf(refute_0_1381,plain,
greatest_lower_bound(identity,multiply(identity,X_171)) = multiply(identity,greatest_lower_bound(X_171,identity)),
inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(X_171,identity)),greatest_lower_bound(identity,multiply(identity,X_171))) )],[refute_0_1379,refute_0_1380]) ).
cnf(refute_0_1382,plain,
( X_171 != multiply(inverse(greatest_lower_bound(inverse(X_171),identity)),greatest_lower_bound(identity,multiply(identity,X_171)))
| greatest_lower_bound(identity,multiply(identity,X_171)) != multiply(identity,greatest_lower_bound(X_171,identity))
| X_171 = multiply(inverse(greatest_lower_bound(inverse(X_171),identity)),multiply(identity,greatest_lower_bound(X_171,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(X_171,multiply(inverse(greatest_lower_bound(inverse(X_171),identity)),greatest_lower_bound(identity,multiply(identity,X_171)))) ),[1,1],$fot(multiply(identity,greatest_lower_bound(X_171,identity)))]]) ).
cnf(refute_0_1383,plain,
( X_171 != multiply(inverse(greatest_lower_bound(inverse(X_171),identity)),greatest_lower_bound(identity,multiply(identity,X_171)))
| X_171 = multiply(inverse(greatest_lower_bound(inverse(X_171),identity)),multiply(identity,greatest_lower_bound(X_171,identity))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(identity,X_171)),multiply(identity,greatest_lower_bound(X_171,identity))) )],[refute_0_1381,refute_0_1382]) ).
cnf(refute_0_1384,plain,
X_171 = multiply(inverse(greatest_lower_bound(inverse(X_171),identity)),multiply(identity,greatest_lower_bound(X_171,identity))),
inference(resolve,[$cnf( $equal(X_171,multiply(inverse(greatest_lower_bound(inverse(X_171),identity)),greatest_lower_bound(identity,multiply(identity,X_171)))) )],[refute_0_1378,refute_0_1383]) ).
cnf(refute_0_1385,plain,
multiply(identity,greatest_lower_bound(X_171,identity)) = greatest_lower_bound(X_171,identity),
inference(subst,[],[left_identity:[bind(X,$fot(greatest_lower_bound(X_171,identity)))]]) ).
cnf(refute_0_1386,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X_171))),multiply(identity,greatest_lower_bound(X_171,identity))) = multiply(inverse(greatest_lower_bound(identity,inverse(X_171))),multiply(identity,greatest_lower_bound(X_171,identity))),
introduced(tautology,[refl,[$fot(multiply(inverse(greatest_lower_bound(identity,inverse(X_171))),multiply(identity,greatest_lower_bound(X_171,identity))))]]) ).
cnf(refute_0_1387,plain,
( multiply(identity,greatest_lower_bound(X_171,identity)) != greatest_lower_bound(X_171,identity)
| multiply(inverse(greatest_lower_bound(identity,inverse(X_171))),multiply(identity,greatest_lower_bound(X_171,identity))) != multiply(inverse(greatest_lower_bound(identity,inverse(X_171))),multiply(identity,greatest_lower_bound(X_171,identity)))
| multiply(inverse(greatest_lower_bound(identity,inverse(X_171))),multiply(identity,greatest_lower_bound(X_171,identity))) = multiply(inverse(greatest_lower_bound(identity,inverse(X_171))),greatest_lower_bound(X_171,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X_171))),multiply(identity,greatest_lower_bound(X_171,identity))),multiply(inverse(greatest_lower_bound(identity,inverse(X_171))),multiply(identity,greatest_lower_bound(X_171,identity)))) ),[1,1],$fot(greatest_lower_bound(X_171,identity))]]) ).
cnf(refute_0_1388,plain,
( multiply(identity,greatest_lower_bound(X_171,identity)) != greatest_lower_bound(X_171,identity)
| multiply(inverse(greatest_lower_bound(identity,inverse(X_171))),multiply(identity,greatest_lower_bound(X_171,identity))) = multiply(inverse(greatest_lower_bound(identity,inverse(X_171))),greatest_lower_bound(X_171,identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X_171))),multiply(identity,greatest_lower_bound(X_171,identity))),multiply(inverse(greatest_lower_bound(identity,inverse(X_171))),multiply(identity,greatest_lower_bound(X_171,identity)))) )],[refute_0_1386,refute_0_1387]) ).
cnf(refute_0_1389,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X_171))),multiply(identity,greatest_lower_bound(X_171,identity))) = multiply(inverse(greatest_lower_bound(identity,inverse(X_171))),greatest_lower_bound(X_171,identity)),
inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(X_171,identity)),greatest_lower_bound(X_171,identity)) )],[refute_0_1385,refute_0_1388]) ).
cnf(refute_0_1390,plain,
inverse(multiply(inverse(X),greatest_lower_bound(identity,X_132))) = multiply(inverse(greatest_lower_bound(identity,X_132)),X),
inference(subst,[],[refute_0_982:[bind(X_33,$fot(greatest_lower_bound(identity,X_132)))]]) ).
cnf(refute_0_1391,plain,
inverse(greatest_lower_bound(identity,multiply(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))))) = multiply(inverse(greatest_lower_bound(X_73,identity)),inverse(greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity))))),
inference(subst,[],[refute_0_146:[bind(X_46,$fot(identity)),bind(X_99,$fot(inverse(greatest_lower_bound(X_73,identity))))]]) ).
cnf(refute_0_1392,plain,
greatest_lower_bound(X_73,identity) = greatest_lower_bound(identity,X_73),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_73)),bind(Y,$fot(identity))]]) ).
cnf(refute_0_1393,plain,
( greatest_lower_bound(X_73,identity) != greatest_lower_bound(identity,X_73)
| greatest_lower_bound(identity,X_73) = greatest_lower_bound(X_73,identity) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X_73,identity))),bind(Y0,$fot(greatest_lower_bound(identity,X_73)))]]) ).
cnf(refute_0_1394,plain,
greatest_lower_bound(identity,X_73) = greatest_lower_bound(X_73,identity),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_73,identity),greatest_lower_bound(identity,X_73)) )],[refute_0_1392,refute_0_1393]) ).
cnf(refute_0_1395,plain,
( greatest_lower_bound(identity,X_73) != greatest_lower_bound(X_73,identity)
| identity != greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_73)))
| identity = greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(identity,greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_73)))) ),[1,1,0],$fot(greatest_lower_bound(X_73,identity))]]) ).
cnf(refute_0_1396,plain,
( identity != greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_73)))
| identity = greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,X_73),greatest_lower_bound(X_73,identity)) )],[refute_0_1394,refute_0_1395]) ).
cnf(refute_0_1397,plain,
identity = greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity))),
inference(resolve,[$cnf( $equal(identity,greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_73)))) )],[refute_0_479,refute_0_1396]) ).
cnf(refute_0_1398,plain,
( identity != greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))
| greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity))) = identity ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(identity)),bind(Y0,$fot(greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))))]]) ).
cnf(refute_0_1399,plain,
greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity))) = identity,
inference(resolve,[$cnf( $equal(identity,greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))) )],[refute_0_1397,refute_0_1398]) ).
cnf(refute_0_1400,plain,
( greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity))) != identity
| inverse(greatest_lower_bound(identity,multiply(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))))) != multiply(inverse(greatest_lower_bound(X_73,identity)),inverse(greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))))
| inverse(greatest_lower_bound(identity,multiply(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))))) = multiply(inverse(greatest_lower_bound(X_73,identity)),inverse(identity)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))))),multiply(inverse(greatest_lower_bound(X_73,identity)),inverse(greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))))) ),[1,1,0],$fot(identity)]]) ).
cnf(refute_0_1401,plain,
( inverse(greatest_lower_bound(identity,multiply(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))))) != multiply(inverse(greatest_lower_bound(X_73,identity)),inverse(greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))))
| inverse(greatest_lower_bound(identity,multiply(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))))) = multiply(inverse(greatest_lower_bound(X_73,identity)),inverse(identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity))),identity) )],[refute_0_1399,refute_0_1400]) ).
cnf(refute_0_1402,plain,
inverse(greatest_lower_bound(identity,multiply(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))))) = multiply(inverse(greatest_lower_bound(X_73,identity)),inverse(identity)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))))),multiply(inverse(greatest_lower_bound(X_73,identity)),inverse(greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))))) )],[refute_0_1391,refute_0_1401]) ).
cnf(refute_0_1403,plain,
greatest_lower_bound(identity,greatest_lower_bound(X_73,identity)) = greatest_lower_bound(identity,X_73),
inference(subst,[],[refute_0_182:[bind(Y,$fot(X_73)),bind(X_15,$fot(identity))]]) ).
cnf(refute_0_1404,plain,
inverse(inverse(greatest_lower_bound(X_73,identity))) = greatest_lower_bound(X_73,identity),
inference(subst,[],[p18_2:[bind(X,$fot(greatest_lower_bound(X_73,identity)))]]) ).
cnf(refute_0_1405,plain,
greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))) = greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))))]]) ).
cnf(refute_0_1406,plain,
( greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))) != greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity))))
| inverse(inverse(greatest_lower_bound(X_73,identity))) != greatest_lower_bound(X_73,identity)
| greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))) = greatest_lower_bound(identity,greatest_lower_bound(X_73,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))),greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity))))) ),[1,1],$fot(greatest_lower_bound(X_73,identity))]]) ).
cnf(refute_0_1407,plain,
( inverse(inverse(greatest_lower_bound(X_73,identity))) != greatest_lower_bound(X_73,identity)
| greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))) = greatest_lower_bound(identity,greatest_lower_bound(X_73,identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))),greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity))))) )],[refute_0_1405,refute_0_1406]) ).
cnf(refute_0_1408,plain,
greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))) = greatest_lower_bound(identity,greatest_lower_bound(X_73,identity)),
inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(X_73,identity))),greatest_lower_bound(X_73,identity)) )],[refute_0_1404,refute_0_1407]) ).
cnf(refute_0_1409,plain,
( greatest_lower_bound(identity,greatest_lower_bound(X_73,identity)) != greatest_lower_bound(identity,X_73)
| greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))) != greatest_lower_bound(identity,greatest_lower_bound(X_73,identity))
| greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))) = greatest_lower_bound(identity,X_73) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))))),bind(Y0,$fot(greatest_lower_bound(identity,greatest_lower_bound(X_73,identity)))),bind(Z0,$fot(greatest_lower_bound(identity,X_73)))]]) ).
cnf(refute_0_1410,plain,
( greatest_lower_bound(identity,greatest_lower_bound(X_73,identity)) != greatest_lower_bound(identity,X_73)
| greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))) = greatest_lower_bound(identity,X_73) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))),greatest_lower_bound(identity,greatest_lower_bound(X_73,identity))) )],[refute_0_1408,refute_0_1409]) ).
cnf(refute_0_1411,plain,
greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))) = greatest_lower_bound(identity,X_73),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_73,identity)),greatest_lower_bound(identity,X_73)) )],[refute_0_1403,refute_0_1410]) ).
cnf(refute_0_1412,plain,
multiply(identity,greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity))))) = greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))),
inference(subst,[],[left_identity:[bind(X,$fot(greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity))))))]]) ).
cnf(refute_0_1413,plain,
multiply(identity,greatest_lower_bound(inverse(inverse(greatest_lower_bound(X_73,identity))),identity)) = multiply(identity,greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity))))),
inference(subst,[],[refute_0_350:[bind(X_17,$fot(identity)),bind(X_91,$fot(inverse(inverse(greatest_lower_bound(X_73,identity)))))]]) ).
cnf(refute_0_1414,plain,
( multiply(identity,greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity))))) != greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity))))
| multiply(identity,greatest_lower_bound(inverse(inverse(greatest_lower_bound(X_73,identity))),identity)) != multiply(identity,greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))))
| multiply(identity,greatest_lower_bound(inverse(inverse(greatest_lower_bound(X_73,identity))),identity)) = greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(multiply(identity,greatest_lower_bound(inverse(inverse(greatest_lower_bound(X_73,identity))),identity)))),bind(Y0,$fot(multiply(identity,greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity))))))),bind(Z0,$fot(greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity))))))]]) ).
cnf(refute_0_1415,plain,
( multiply(identity,greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity))))) != greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity))))
| multiply(identity,greatest_lower_bound(inverse(inverse(greatest_lower_bound(X_73,identity))),identity)) = greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))) ),
inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(inverse(inverse(greatest_lower_bound(X_73,identity))),identity)),multiply(identity,greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))))) )],[refute_0_1413,refute_0_1414]) ).
cnf(refute_0_1416,plain,
multiply(identity,greatest_lower_bound(inverse(inverse(greatest_lower_bound(X_73,identity))),identity)) = greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))),
inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity))))),greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity))))) )],[refute_0_1412,refute_0_1415]) ).
cnf(refute_0_1417,plain,
greatest_lower_bound(identity,multiply(identity,inverse(inverse(greatest_lower_bound(X_73,identity))))) = multiply(identity,greatest_lower_bound(inverse(inverse(greatest_lower_bound(X_73,identity))),identity)),
inference(subst,[],[refute_0_276:[bind(X_36,$fot(identity)),bind(X_37,$fot(inverse(inverse(greatest_lower_bound(X_73,identity)))))]]) ).
cnf(refute_0_1418,plain,
( multiply(identity,greatest_lower_bound(inverse(inverse(greatest_lower_bound(X_73,identity))),identity)) != greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity))))
| greatest_lower_bound(identity,multiply(identity,inverse(inverse(greatest_lower_bound(X_73,identity))))) != multiply(identity,greatest_lower_bound(inverse(inverse(greatest_lower_bound(X_73,identity))),identity))
| greatest_lower_bound(identity,multiply(identity,inverse(inverse(greatest_lower_bound(X_73,identity))))) = greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(greatest_lower_bound(identity,multiply(identity,inverse(inverse(greatest_lower_bound(X_73,identity))))))),bind(Y0,$fot(multiply(identity,greatest_lower_bound(inverse(inverse(greatest_lower_bound(X_73,identity))),identity)))),bind(Z0,$fot(greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity))))))]]) ).
cnf(refute_0_1419,plain,
( multiply(identity,greatest_lower_bound(inverse(inverse(greatest_lower_bound(X_73,identity))),identity)) != greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity))))
| greatest_lower_bound(identity,multiply(identity,inverse(inverse(greatest_lower_bound(X_73,identity))))) = greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(identity,inverse(inverse(greatest_lower_bound(X_73,identity))))),multiply(identity,greatest_lower_bound(inverse(inverse(greatest_lower_bound(X_73,identity))),identity))) )],[refute_0_1417,refute_0_1418]) ).
cnf(refute_0_1420,plain,
greatest_lower_bound(identity,multiply(identity,inverse(inverse(greatest_lower_bound(X_73,identity))))) = greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))),
inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(inverse(inverse(greatest_lower_bound(X_73,identity))),identity)),greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity))))) )],[refute_0_1416,refute_0_1419]) ).
cnf(refute_0_1421,plain,
( greatest_lower_bound(identity,multiply(identity,inverse(inverse(greatest_lower_bound(X_73,identity))))) != greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity))))
| greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))) != greatest_lower_bound(identity,X_73)
| greatest_lower_bound(identity,multiply(identity,inverse(inverse(greatest_lower_bound(X_73,identity))))) = greatest_lower_bound(identity,X_73) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(greatest_lower_bound(identity,multiply(identity,inverse(inverse(greatest_lower_bound(X_73,identity))))))),bind(Y0,$fot(greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))))),bind(Z0,$fot(greatest_lower_bound(identity,X_73)))]]) ).
cnf(refute_0_1422,plain,
( greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))) != greatest_lower_bound(identity,X_73)
| greatest_lower_bound(identity,multiply(identity,inverse(inverse(greatest_lower_bound(X_73,identity))))) = greatest_lower_bound(identity,X_73) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(identity,inverse(inverse(greatest_lower_bound(X_73,identity))))),greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity))))) )],[refute_0_1420,refute_0_1421]) ).
cnf(refute_0_1423,plain,
greatest_lower_bound(identity,multiply(identity,inverse(inverse(greatest_lower_bound(X_73,identity))))) = greatest_lower_bound(identity,X_73),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))),greatest_lower_bound(identity,X_73)) )],[refute_0_1411,refute_0_1422]) ).
cnf(refute_0_1424,plain,
inverse(greatest_lower_bound(identity,multiply(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))))) = inverse(greatest_lower_bound(identity,multiply(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))))),
introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(identity,multiply(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))))))]]) ).
cnf(refute_0_1425,plain,
( greatest_lower_bound(identity,multiply(identity,inverse(inverse(greatest_lower_bound(X_73,identity))))) != greatest_lower_bound(identity,X_73)
| inverse(greatest_lower_bound(identity,multiply(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))))) != inverse(greatest_lower_bound(identity,multiply(identity,inverse(inverse(greatest_lower_bound(X_73,identity))))))
| inverse(greatest_lower_bound(identity,multiply(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))))) = inverse(greatest_lower_bound(identity,X_73)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))))),inverse(greatest_lower_bound(identity,multiply(identity,inverse(inverse(greatest_lower_bound(X_73,identity))))))) ),[1,0],$fot(greatest_lower_bound(identity,X_73))]]) ).
cnf(refute_0_1426,plain,
( greatest_lower_bound(identity,multiply(identity,inverse(inverse(greatest_lower_bound(X_73,identity))))) != greatest_lower_bound(identity,X_73)
| inverse(greatest_lower_bound(identity,multiply(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))))) = inverse(greatest_lower_bound(identity,X_73)) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))))),inverse(greatest_lower_bound(identity,multiply(identity,inverse(inverse(greatest_lower_bound(X_73,identity))))))) )],[refute_0_1424,refute_0_1425]) ).
cnf(refute_0_1427,plain,
inverse(greatest_lower_bound(identity,multiply(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))))) = inverse(greatest_lower_bound(identity,X_73)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(identity,inverse(inverse(greatest_lower_bound(X_73,identity))))),greatest_lower_bound(identity,X_73)) )],[refute_0_1423,refute_0_1426]) ).
cnf(refute_0_1428,plain,
( inverse(greatest_lower_bound(identity,multiply(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))))) != multiply(inverse(greatest_lower_bound(X_73,identity)),inverse(identity))
| inverse(greatest_lower_bound(identity,multiply(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))))) != inverse(greatest_lower_bound(identity,X_73))
| inverse(greatest_lower_bound(identity,X_73)) = multiply(inverse(greatest_lower_bound(X_73,identity)),inverse(identity)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))))),multiply(inverse(greatest_lower_bound(X_73,identity)),inverse(identity))) ),[0],$fot(inverse(greatest_lower_bound(identity,X_73)))]]) ).
cnf(refute_0_1429,plain,
( inverse(greatest_lower_bound(identity,multiply(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))))) != multiply(inverse(greatest_lower_bound(X_73,identity)),inverse(identity))
| inverse(greatest_lower_bound(identity,X_73)) = multiply(inverse(greatest_lower_bound(X_73,identity)),inverse(identity)) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))))),inverse(greatest_lower_bound(identity,X_73))) )],[refute_0_1427,refute_0_1428]) ).
cnf(refute_0_1430,plain,
multiply(identity,greatest_lower_bound(X_73,identity)) = greatest_lower_bound(X_73,identity),
inference(subst,[],[left_identity:[bind(X,$fot(greatest_lower_bound(X_73,identity)))]]) ).
cnf(refute_0_1431,plain,
inverse(multiply(identity,greatest_lower_bound(X_73,identity))) = inverse(multiply(identity,greatest_lower_bound(X_73,identity))),
introduced(tautology,[refl,[$fot(inverse(multiply(identity,greatest_lower_bound(X_73,identity))))]]) ).
cnf(refute_0_1432,plain,
( multiply(identity,greatest_lower_bound(X_73,identity)) != greatest_lower_bound(X_73,identity)
| inverse(multiply(identity,greatest_lower_bound(X_73,identity))) != inverse(multiply(identity,greatest_lower_bound(X_73,identity)))
| inverse(multiply(identity,greatest_lower_bound(X_73,identity))) = inverse(greatest_lower_bound(X_73,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(identity,greatest_lower_bound(X_73,identity))),inverse(multiply(identity,greatest_lower_bound(X_73,identity)))) ),[1,0],$fot(greatest_lower_bound(X_73,identity))]]) ).
cnf(refute_0_1433,plain,
( multiply(identity,greatest_lower_bound(X_73,identity)) != greatest_lower_bound(X_73,identity)
| inverse(multiply(identity,greatest_lower_bound(X_73,identity))) = inverse(greatest_lower_bound(X_73,identity)) ),
inference(resolve,[$cnf( $equal(inverse(multiply(identity,greatest_lower_bound(X_73,identity))),inverse(multiply(identity,greatest_lower_bound(X_73,identity)))) )],[refute_0_1431,refute_0_1432]) ).
cnf(refute_0_1434,plain,
inverse(multiply(identity,greatest_lower_bound(X_73,identity))) = inverse(greatest_lower_bound(X_73,identity)),
inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(X_73,identity)),greatest_lower_bound(X_73,identity)) )],[refute_0_1430,refute_0_1433]) ).
cnf(refute_0_1435,plain,
multiply(inverse(greatest_lower_bound(X_73,identity)),inverse(identity)) = inverse(multiply(identity,greatest_lower_bound(X_73,identity))),
inference(subst,[],[refute_0_370:[bind(X,$fot(identity)),bind(Y,$fot(greatest_lower_bound(X_73,identity)))]]) ).
cnf(refute_0_1436,plain,
( multiply(inverse(greatest_lower_bound(X_73,identity)),inverse(identity)) != inverse(multiply(identity,greatest_lower_bound(X_73,identity)))
| inverse(multiply(identity,greatest_lower_bound(X_73,identity))) != inverse(greatest_lower_bound(X_73,identity))
| multiply(inverse(greatest_lower_bound(X_73,identity)),inverse(identity)) = inverse(greatest_lower_bound(X_73,identity)) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(X_73,identity)),inverse(identity)))),bind(Y0,$fot(inverse(multiply(identity,greatest_lower_bound(X_73,identity))))),bind(Z0,$fot(inverse(greatest_lower_bound(X_73,identity))))]]) ).
cnf(refute_0_1437,plain,
( inverse(multiply(identity,greatest_lower_bound(X_73,identity))) != inverse(greatest_lower_bound(X_73,identity))
| multiply(inverse(greatest_lower_bound(X_73,identity)),inverse(identity)) = inverse(greatest_lower_bound(X_73,identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_73,identity)),inverse(identity)),inverse(multiply(identity,greatest_lower_bound(X_73,identity)))) )],[refute_0_1435,refute_0_1436]) ).
cnf(refute_0_1438,plain,
multiply(inverse(greatest_lower_bound(X_73,identity)),inverse(identity)) = inverse(greatest_lower_bound(X_73,identity)),
inference(resolve,[$cnf( $equal(inverse(multiply(identity,greatest_lower_bound(X_73,identity))),inverse(greatest_lower_bound(X_73,identity))) )],[refute_0_1434,refute_0_1437]) ).
cnf(refute_0_1439,plain,
( multiply(inverse(greatest_lower_bound(X_73,identity)),inverse(identity)) != inverse(greatest_lower_bound(X_73,identity))
| inverse(greatest_lower_bound(identity,X_73)) != multiply(inverse(greatest_lower_bound(X_73,identity)),inverse(identity))
| inverse(greatest_lower_bound(identity,X_73)) = inverse(greatest_lower_bound(X_73,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,X_73)),multiply(inverse(greatest_lower_bound(X_73,identity)),inverse(identity))) ),[1],$fot(inverse(greatest_lower_bound(X_73,identity)))]]) ).
cnf(refute_0_1440,plain,
( inverse(greatest_lower_bound(identity,X_73)) != multiply(inverse(greatest_lower_bound(X_73,identity)),inverse(identity))
| inverse(greatest_lower_bound(identity,X_73)) = inverse(greatest_lower_bound(X_73,identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_73,identity)),inverse(identity)),inverse(greatest_lower_bound(X_73,identity))) )],[refute_0_1438,refute_0_1439]) ).
cnf(refute_0_1441,plain,
( inverse(greatest_lower_bound(identity,multiply(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))))) != multiply(inverse(greatest_lower_bound(X_73,identity)),inverse(identity))
| inverse(greatest_lower_bound(identity,X_73)) = inverse(greatest_lower_bound(X_73,identity)) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,X_73)),multiply(inverse(greatest_lower_bound(X_73,identity)),inverse(identity))) )],[refute_0_1429,refute_0_1440]) ).
cnf(refute_0_1442,plain,
inverse(greatest_lower_bound(identity,X_73)) = inverse(greatest_lower_bound(X_73,identity)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))))),multiply(inverse(greatest_lower_bound(X_73,identity)),inverse(identity))) )],[refute_0_1402,refute_0_1441]) ).
cnf(refute_0_1443,plain,
inverse(greatest_lower_bound(identity,X_132)) = inverse(greatest_lower_bound(X_132,identity)),
inference(subst,[],[refute_0_1442:[bind(X_73,$fot(X_132))]]) ).
cnf(refute_0_1444,plain,
( inverse(multiply(inverse(X),greatest_lower_bound(identity,X_132))) != multiply(inverse(greatest_lower_bound(identity,X_132)),X)
| inverse(greatest_lower_bound(identity,X_132)) != inverse(greatest_lower_bound(X_132,identity))
| inverse(multiply(inverse(X),greatest_lower_bound(identity,X_132))) = multiply(inverse(greatest_lower_bound(X_132,identity)),X) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X),greatest_lower_bound(identity,X_132))),multiply(inverse(greatest_lower_bound(identity,X_132)),X)) ),[1,0],$fot(inverse(greatest_lower_bound(X_132,identity)))]]) ).
cnf(refute_0_1445,plain,
( inverse(multiply(inverse(X),greatest_lower_bound(identity,X_132))) != multiply(inverse(greatest_lower_bound(identity,X_132)),X)
| inverse(multiply(inverse(X),greatest_lower_bound(identity,X_132))) = multiply(inverse(greatest_lower_bound(X_132,identity)),X) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,X_132)),inverse(greatest_lower_bound(X_132,identity))) )],[refute_0_1443,refute_0_1444]) ).
cnf(refute_0_1446,plain,
inverse(multiply(inverse(X),greatest_lower_bound(identity,X_132))) = multiply(inverse(greatest_lower_bound(X_132,identity)),X),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X),greatest_lower_bound(identity,X_132))),multiply(inverse(greatest_lower_bound(identity,X_132)),X)) )],[refute_0_1390,refute_0_1445]) ).
cnf(refute_0_1447,plain,
( inverse(multiply(inverse(X),greatest_lower_bound(identity,X_132))) != multiply(inverse(greatest_lower_bound(X_132,identity)),X)
| inverse(multiply(inverse(X),greatest_lower_bound(identity,X_132))) != multiply(inverse(greatest_lower_bound(identity,X_132)),X)
| multiply(inverse(greatest_lower_bound(identity,X_132)),X) = multiply(inverse(greatest_lower_bound(X_132,identity)),X) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X),greatest_lower_bound(identity,X_132))),multiply(inverse(greatest_lower_bound(X_132,identity)),X)) ),[0],$fot(multiply(inverse(greatest_lower_bound(identity,X_132)),X))]]) ).
cnf(refute_0_1448,plain,
( inverse(multiply(inverse(X),greatest_lower_bound(identity,X_132))) != multiply(inverse(greatest_lower_bound(X_132,identity)),X)
| multiply(inverse(greatest_lower_bound(identity,X_132)),X) = multiply(inverse(greatest_lower_bound(X_132,identity)),X) ),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X),greatest_lower_bound(identity,X_132))),multiply(inverse(greatest_lower_bound(identity,X_132)),X)) )],[refute_0_1390,refute_0_1447]) ).
cnf(refute_0_1449,plain,
multiply(inverse(greatest_lower_bound(identity,X_132)),X) = multiply(inverse(greatest_lower_bound(X_132,identity)),X),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X),greatest_lower_bound(identity,X_132))),multiply(inverse(greatest_lower_bound(X_132,identity)),X)) )],[refute_0_1446,refute_0_1448]) ).
cnf(refute_0_1450,plain,
( multiply(inverse(greatest_lower_bound(identity,X_132)),X) != multiply(inverse(greatest_lower_bound(X_132,identity)),X)
| multiply(inverse(greatest_lower_bound(X_132,identity)),X) = multiply(inverse(greatest_lower_bound(identity,X_132)),X) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(identity,X_132)),X))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(X_132,identity)),X)))]]) ).
cnf(refute_0_1451,plain,
multiply(inverse(greatest_lower_bound(X_132,identity)),X) = multiply(inverse(greatest_lower_bound(identity,X_132)),X),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_132)),X),multiply(inverse(greatest_lower_bound(X_132,identity)),X)) )],[refute_0_1449,refute_0_1450]) ).
cnf(refute_0_1452,plain,
multiply(inverse(greatest_lower_bound(inverse(X_171),identity)),multiply(identity,greatest_lower_bound(X_171,identity))) = multiply(inverse(greatest_lower_bound(identity,inverse(X_171))),multiply(identity,greatest_lower_bound(X_171,identity))),
inference(subst,[],[refute_0_1451:[bind(X,$fot(multiply(identity,greatest_lower_bound(X_171,identity)))),bind(X_132,$fot(inverse(X_171)))]]) ).
cnf(refute_0_1453,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(X_171))),multiply(identity,greatest_lower_bound(X_171,identity))) != multiply(inverse(greatest_lower_bound(identity,inverse(X_171))),greatest_lower_bound(X_171,identity))
| multiply(inverse(greatest_lower_bound(inverse(X_171),identity)),multiply(identity,greatest_lower_bound(X_171,identity))) != multiply(inverse(greatest_lower_bound(identity,inverse(X_171))),multiply(identity,greatest_lower_bound(X_171,identity)))
| multiply(inverse(greatest_lower_bound(inverse(X_171),identity)),multiply(identity,greatest_lower_bound(X_171,identity))) = multiply(inverse(greatest_lower_bound(identity,inverse(X_171))),greatest_lower_bound(X_171,identity)) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(inverse(X_171),identity)),multiply(identity,greatest_lower_bound(X_171,identity))))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(identity,inverse(X_171))),multiply(identity,greatest_lower_bound(X_171,identity))))),bind(Z0,$fot(multiply(inverse(greatest_lower_bound(identity,inverse(X_171))),greatest_lower_bound(X_171,identity))))]]) ).
cnf(refute_0_1454,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(X_171))),multiply(identity,greatest_lower_bound(X_171,identity))) != multiply(inverse(greatest_lower_bound(identity,inverse(X_171))),greatest_lower_bound(X_171,identity))
| multiply(inverse(greatest_lower_bound(inverse(X_171),identity)),multiply(identity,greatest_lower_bound(X_171,identity))) = multiply(inverse(greatest_lower_bound(identity,inverse(X_171))),greatest_lower_bound(X_171,identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(X_171),identity)),multiply(identity,greatest_lower_bound(X_171,identity))),multiply(inverse(greatest_lower_bound(identity,inverse(X_171))),multiply(identity,greatest_lower_bound(X_171,identity)))) )],[refute_0_1452,refute_0_1453]) ).
cnf(refute_0_1455,plain,
multiply(inverse(greatest_lower_bound(inverse(X_171),identity)),multiply(identity,greatest_lower_bound(X_171,identity))) = multiply(inverse(greatest_lower_bound(identity,inverse(X_171))),greatest_lower_bound(X_171,identity)),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X_171))),multiply(identity,greatest_lower_bound(X_171,identity))),multiply(inverse(greatest_lower_bound(identity,inverse(X_171))),greatest_lower_bound(X_171,identity))) )],[refute_0_1389,refute_0_1454]) ).
cnf(refute_0_1456,plain,
( X_171 != multiply(inverse(greatest_lower_bound(inverse(X_171),identity)),multiply(identity,greatest_lower_bound(X_171,identity)))
| multiply(inverse(greatest_lower_bound(inverse(X_171),identity)),multiply(identity,greatest_lower_bound(X_171,identity))) != multiply(inverse(greatest_lower_bound(identity,inverse(X_171))),greatest_lower_bound(X_171,identity))
| X_171 = multiply(inverse(greatest_lower_bound(identity,inverse(X_171))),greatest_lower_bound(X_171,identity)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_171,multiply(inverse(greatest_lower_bound(identity,inverse(X_171))),greatest_lower_bound(X_171,identity))) ),[0],$fot(multiply(inverse(greatest_lower_bound(inverse(X_171),identity)),multiply(identity,greatest_lower_bound(X_171,identity))))]]) ).
cnf(refute_0_1457,plain,
( X_171 != multiply(inverse(greatest_lower_bound(inverse(X_171),identity)),multiply(identity,greatest_lower_bound(X_171,identity)))
| X_171 = multiply(inverse(greatest_lower_bound(identity,inverse(X_171))),greatest_lower_bound(X_171,identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(X_171),identity)),multiply(identity,greatest_lower_bound(X_171,identity))),multiply(inverse(greatest_lower_bound(identity,inverse(X_171))),greatest_lower_bound(X_171,identity))) )],[refute_0_1455,refute_0_1456]) ).
cnf(refute_0_1458,plain,
X_171 = multiply(inverse(greatest_lower_bound(identity,inverse(X_171))),greatest_lower_bound(X_171,identity)),
inference(resolve,[$cnf( $equal(X_171,multiply(inverse(greatest_lower_bound(inverse(X_171),identity)),multiply(identity,greatest_lower_bound(X_171,identity)))) )],[refute_0_1384,refute_0_1457]) ).
cnf(refute_0_1459,plain,
( X_171 != multiply(inverse(greatest_lower_bound(identity,inverse(X_171))),greatest_lower_bound(X_171,identity))
| multiply(inverse(greatest_lower_bound(identity,inverse(X_171))),greatest_lower_bound(X_171,identity)) = X_171 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_171)),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(identity,inverse(X_171))),greatest_lower_bound(X_171,identity))))]]) ).
cnf(refute_0_1460,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X_171))),greatest_lower_bound(X_171,identity)) = X_171,
inference(resolve,[$cnf( $equal(X_171,multiply(inverse(greatest_lower_bound(identity,inverse(X_171))),greatest_lower_bound(X_171,identity))) )],[refute_0_1458,refute_0_1459]) ).
cnf(refute_0_1461,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X_148))),greatest_lower_bound(X_148,identity)) = X_148,
inference(subst,[],[refute_0_1460:[bind(X_171,$fot(X_148))]]) ).
cnf(refute_0_1462,plain,
greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X_148))),greatest_lower_bound(X_148,identity))) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X_148))),greatest_lower_bound(X_148,identity))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X_148))),greatest_lower_bound(X_148,identity))))]]) ).
cnf(refute_0_1463,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(X_148))),greatest_lower_bound(X_148,identity)) != X_148
| greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X_148))),greatest_lower_bound(X_148,identity))) != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X_148))),greatest_lower_bound(X_148,identity)))
| greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X_148))),greatest_lower_bound(X_148,identity))) = greatest_lower_bound(identity,X_148) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X_148))),greatest_lower_bound(X_148,identity))),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X_148))),greatest_lower_bound(X_148,identity)))) ),[1,1],$fot(X_148)]]) ).
cnf(refute_0_1464,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(X_148))),greatest_lower_bound(X_148,identity)) != X_148
| greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X_148))),greatest_lower_bound(X_148,identity))) = greatest_lower_bound(identity,X_148) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X_148))),greatest_lower_bound(X_148,identity))),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X_148))),greatest_lower_bound(X_148,identity)))) )],[refute_0_1462,refute_0_1463]) ).
cnf(refute_0_1465,plain,
greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X_148))),greatest_lower_bound(X_148,identity))) = greatest_lower_bound(identity,X_148),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X_148))),greatest_lower_bound(X_148,identity)),X_148) )],[refute_0_1461,refute_0_1464]) ).
cnf(refute_0_1466,plain,
( greatest_lower_bound(X_148,identity) != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X_148))),greatest_lower_bound(X_148,identity)))
| greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X_148))),greatest_lower_bound(X_148,identity))) != greatest_lower_bound(identity,X_148)
| greatest_lower_bound(X_148,identity) = greatest_lower_bound(identity,X_148) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_148,identity),greatest_lower_bound(identity,X_148)) ),[0],$fot(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X_148))),greatest_lower_bound(X_148,identity))))]]) ).
cnf(refute_0_1467,plain,
( greatest_lower_bound(X_148,identity) != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X_148))),greatest_lower_bound(X_148,identity)))
| greatest_lower_bound(X_148,identity) = greatest_lower_bound(identity,X_148) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X_148))),greatest_lower_bound(X_148,identity))),greatest_lower_bound(identity,X_148)) )],[refute_0_1465,refute_0_1466]) ).
cnf(refute_0_1468,plain,
greatest_lower_bound(X_148,identity) = greatest_lower_bound(identity,X_148),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_148,identity),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X_148))),greatest_lower_bound(X_148,identity)))) )],[refute_0_1372,refute_0_1467]) ).
cnf(refute_0_1469,plain,
greatest_lower_bound(inverse(X_197),identity) = greatest_lower_bound(identity,inverse(X_197)),
inference(subst,[],[refute_0_1468:[bind(X_148,$fot(inverse(X_197)))]]) ).
cnf(refute_0_1470,plain,
least_upper_bound(greatest_lower_bound(identity,X_197),greatest_lower_bound(inverse(X_197),identity)) = least_upper_bound(greatest_lower_bound(identity,X_197),greatest_lower_bound(inverse(X_197),identity)),
introduced(tautology,[refl,[$fot(least_upper_bound(greatest_lower_bound(identity,X_197),greatest_lower_bound(inverse(X_197),identity)))]]) ).
cnf(refute_0_1471,plain,
( greatest_lower_bound(inverse(X_197),identity) != greatest_lower_bound(identity,inverse(X_197))
| least_upper_bound(greatest_lower_bound(identity,X_197),greatest_lower_bound(inverse(X_197),identity)) != least_upper_bound(greatest_lower_bound(identity,X_197),greatest_lower_bound(inverse(X_197),identity))
| least_upper_bound(greatest_lower_bound(identity,X_197),greatest_lower_bound(inverse(X_197),identity)) = least_upper_bound(greatest_lower_bound(identity,X_197),greatest_lower_bound(identity,inverse(X_197))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,X_197),greatest_lower_bound(inverse(X_197),identity)),least_upper_bound(greatest_lower_bound(identity,X_197),greatest_lower_bound(inverse(X_197),identity))) ),[1,1],$fot(greatest_lower_bound(identity,inverse(X_197)))]]) ).
cnf(refute_0_1472,plain,
( greatest_lower_bound(inverse(X_197),identity) != greatest_lower_bound(identity,inverse(X_197))
| least_upper_bound(greatest_lower_bound(identity,X_197),greatest_lower_bound(inverse(X_197),identity)) = least_upper_bound(greatest_lower_bound(identity,X_197),greatest_lower_bound(identity,inverse(X_197))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,X_197),greatest_lower_bound(inverse(X_197),identity)),least_upper_bound(greatest_lower_bound(identity,X_197),greatest_lower_bound(inverse(X_197),identity))) )],[refute_0_1470,refute_0_1471]) ).
cnf(refute_0_1473,plain,
least_upper_bound(greatest_lower_bound(identity,X_197),greatest_lower_bound(inverse(X_197),identity)) = least_upper_bound(greatest_lower_bound(identity,X_197),greatest_lower_bound(identity,inverse(X_197))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_197),identity),greatest_lower_bound(identity,inverse(X_197))) )],[refute_0_1469,refute_0_1472]) ).
cnf(refute_0_1474,plain,
( least_upper_bound(greatest_lower_bound(identity,X_197),greatest_lower_bound(identity,inverse(X_197))) != multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197)))
| least_upper_bound(greatest_lower_bound(identity,X_197),greatest_lower_bound(inverse(X_197),identity)) != least_upper_bound(greatest_lower_bound(identity,X_197),greatest_lower_bound(identity,inverse(X_197)))
| least_upper_bound(greatest_lower_bound(identity,X_197),greatest_lower_bound(inverse(X_197),identity)) = multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197))) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(identity,X_197),greatest_lower_bound(inverse(X_197),identity)))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(identity,X_197),greatest_lower_bound(identity,inverse(X_197))))),bind(Z0,$fot(multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197)))))]]) ).
cnf(refute_0_1475,plain,
( least_upper_bound(greatest_lower_bound(identity,X_197),greatest_lower_bound(identity,inverse(X_197))) != multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197)))
| least_upper_bound(greatest_lower_bound(identity,X_197),greatest_lower_bound(inverse(X_197),identity)) = multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,X_197),greatest_lower_bound(inverse(X_197),identity)),least_upper_bound(greatest_lower_bound(identity,X_197),greatest_lower_bound(identity,inverse(X_197)))) )],[refute_0_1473,refute_0_1474]) ).
cnf(refute_0_1476,plain,
least_upper_bound(greatest_lower_bound(identity,X_197),greatest_lower_bound(inverse(X_197),identity)) = multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197))),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,X_197),greatest_lower_bound(identity,inverse(X_197))),multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197)))) )],[refute_0_1315,refute_0_1475]) ).
cnf(refute_0_1477,plain,
multiply(least_upper_bound(X_198,inverse(inverse(greatest_lower_bound(X_73,identity)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))) = least_upper_bound(greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))),multiply(X_198,greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity))))),
inference(subst,[],[refute_0_1041:[bind(X_51,$fot(inverse(greatest_lower_bound(X_73,identity)))),bind(X_66,$fot(X_198))]]) ).
cnf(refute_0_1478,plain,
( multiply(least_upper_bound(X_198,inverse(inverse(greatest_lower_bound(X_73,identity)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))) != least_upper_bound(greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))),multiply(X_198,greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))))
| greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity))) != identity
| multiply(least_upper_bound(X_198,inverse(inverse(greatest_lower_bound(X_73,identity)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))) = least_upper_bound(greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))),multiply(X_198,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_198,inverse(inverse(greatest_lower_bound(X_73,identity)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))),least_upper_bound(greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))),multiply(X_198,greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))))) ),[1,1,1],$fot(identity)]]) ).
cnf(refute_0_1479,plain,
( multiply(least_upper_bound(X_198,inverse(inverse(greatest_lower_bound(X_73,identity)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))) != least_upper_bound(greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))),multiply(X_198,greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))))
| multiply(least_upper_bound(X_198,inverse(inverse(greatest_lower_bound(X_73,identity)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))) = least_upper_bound(greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))),multiply(X_198,identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity))),identity) )],[refute_0_1399,refute_0_1478]) ).
cnf(refute_0_1480,plain,
multiply(least_upper_bound(X_198,inverse(inverse(greatest_lower_bound(X_73,identity)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))) = least_upper_bound(greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))),multiply(X_198,identity)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_198,inverse(inverse(greatest_lower_bound(X_73,identity)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))),least_upper_bound(greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))),multiply(X_198,greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))))) )],[refute_0_1477,refute_0_1479]) ).
cnf(refute_0_1481,plain,
multiply(least_upper_bound(X_198,greatest_lower_bound(X_73,identity)),identity) = least_upper_bound(X_198,greatest_lower_bound(X_73,identity)),
inference(subst,[],[refute_0_603:[bind(X,$fot(least_upper_bound(X_198,greatest_lower_bound(X_73,identity))))]]) ).
cnf(refute_0_1482,plain,
multiply(least_upper_bound(X_198,greatest_lower_bound(X_73,identity)),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))) = multiply(least_upper_bound(X_198,greatest_lower_bound(X_73,identity)),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(X_198,greatest_lower_bound(X_73,identity)),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))))]]) ).
cnf(refute_0_1483,plain,
( multiply(least_upper_bound(X_198,greatest_lower_bound(X_73,identity)),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))) != multiply(least_upper_bound(X_198,greatest_lower_bound(X_73,identity)),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity))))
| greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity))) != identity
| multiply(least_upper_bound(X_198,greatest_lower_bound(X_73,identity)),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))) = multiply(least_upper_bound(X_198,greatest_lower_bound(X_73,identity)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_198,greatest_lower_bound(X_73,identity)),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))),multiply(least_upper_bound(X_198,greatest_lower_bound(X_73,identity)),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_1484,plain,
( greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity))) != identity
| multiply(least_upper_bound(X_198,greatest_lower_bound(X_73,identity)),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))) = multiply(least_upper_bound(X_198,greatest_lower_bound(X_73,identity)),identity) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_198,greatest_lower_bound(X_73,identity)),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))),multiply(least_upper_bound(X_198,greatest_lower_bound(X_73,identity)),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity))))) )],[refute_0_1482,refute_0_1483]) ).
cnf(refute_0_1485,plain,
multiply(least_upper_bound(X_198,greatest_lower_bound(X_73,identity)),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))) = multiply(least_upper_bound(X_198,greatest_lower_bound(X_73,identity)),identity),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity))),identity) )],[refute_0_1399,refute_0_1484]) ).
cnf(refute_0_1486,plain,
least_upper_bound(X_198,inverse(inverse(greatest_lower_bound(X_73,identity)))) = least_upper_bound(X_198,inverse(inverse(greatest_lower_bound(X_73,identity)))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_198,inverse(inverse(greatest_lower_bound(X_73,identity)))))]]) ).
cnf(refute_0_1487,plain,
( inverse(inverse(greatest_lower_bound(X_73,identity))) != greatest_lower_bound(X_73,identity)
| least_upper_bound(X_198,inverse(inverse(greatest_lower_bound(X_73,identity)))) != least_upper_bound(X_198,inverse(inverse(greatest_lower_bound(X_73,identity))))
| least_upper_bound(X_198,inverse(inverse(greatest_lower_bound(X_73,identity)))) = least_upper_bound(X_198,greatest_lower_bound(X_73,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_198,inverse(inverse(greatest_lower_bound(X_73,identity)))),least_upper_bound(X_198,inverse(inverse(greatest_lower_bound(X_73,identity))))) ),[1,1],$fot(greatest_lower_bound(X_73,identity))]]) ).
cnf(refute_0_1488,plain,
( inverse(inverse(greatest_lower_bound(X_73,identity))) != greatest_lower_bound(X_73,identity)
| least_upper_bound(X_198,inverse(inverse(greatest_lower_bound(X_73,identity)))) = least_upper_bound(X_198,greatest_lower_bound(X_73,identity)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_198,inverse(inverse(greatest_lower_bound(X_73,identity)))),least_upper_bound(X_198,inverse(inverse(greatest_lower_bound(X_73,identity))))) )],[refute_0_1486,refute_0_1487]) ).
cnf(refute_0_1489,plain,
least_upper_bound(X_198,inverse(inverse(greatest_lower_bound(X_73,identity)))) = least_upper_bound(X_198,greatest_lower_bound(X_73,identity)),
inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(X_73,identity))),greatest_lower_bound(X_73,identity)) )],[refute_0_1404,refute_0_1488]) ).
cnf(refute_0_1490,plain,
multiply(least_upper_bound(X_198,inverse(inverse(greatest_lower_bound(X_73,identity)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))) = multiply(least_upper_bound(X_198,inverse(inverse(greatest_lower_bound(X_73,identity)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(X_198,inverse(inverse(greatest_lower_bound(X_73,identity)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))))]]) ).
cnf(refute_0_1491,plain,
( multiply(least_upper_bound(X_198,inverse(inverse(greatest_lower_bound(X_73,identity)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))) != multiply(least_upper_bound(X_198,inverse(inverse(greatest_lower_bound(X_73,identity)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity))))
| least_upper_bound(X_198,inverse(inverse(greatest_lower_bound(X_73,identity)))) != least_upper_bound(X_198,greatest_lower_bound(X_73,identity))
| multiply(least_upper_bound(X_198,inverse(inverse(greatest_lower_bound(X_73,identity)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))) = multiply(least_upper_bound(X_198,greatest_lower_bound(X_73,identity)),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_198,inverse(inverse(greatest_lower_bound(X_73,identity)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))),multiply(least_upper_bound(X_198,inverse(inverse(greatest_lower_bound(X_73,identity)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity))))) ),[1,0],$fot(least_upper_bound(X_198,greatest_lower_bound(X_73,identity)))]]) ).
cnf(refute_0_1492,plain,
( least_upper_bound(X_198,inverse(inverse(greatest_lower_bound(X_73,identity)))) != least_upper_bound(X_198,greatest_lower_bound(X_73,identity))
| multiply(least_upper_bound(X_198,inverse(inverse(greatest_lower_bound(X_73,identity)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))) = multiply(least_upper_bound(X_198,greatest_lower_bound(X_73,identity)),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_198,inverse(inverse(greatest_lower_bound(X_73,identity)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))),multiply(least_upper_bound(X_198,inverse(inverse(greatest_lower_bound(X_73,identity)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity))))) )],[refute_0_1490,refute_0_1491]) ).
cnf(refute_0_1493,plain,
multiply(least_upper_bound(X_198,inverse(inverse(greatest_lower_bound(X_73,identity)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))) = multiply(least_upper_bound(X_198,greatest_lower_bound(X_73,identity)),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_198,inverse(inverse(greatest_lower_bound(X_73,identity)))),least_upper_bound(X_198,greatest_lower_bound(X_73,identity))) )],[refute_0_1489,refute_0_1492]) ).
cnf(refute_0_1494,plain,
( multiply(least_upper_bound(X_198,greatest_lower_bound(X_73,identity)),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))) != multiply(least_upper_bound(X_198,greatest_lower_bound(X_73,identity)),identity)
| multiply(least_upper_bound(X_198,inverse(inverse(greatest_lower_bound(X_73,identity)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))) != multiply(least_upper_bound(X_198,greatest_lower_bound(X_73,identity)),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity))))
| multiply(least_upper_bound(X_198,inverse(inverse(greatest_lower_bound(X_73,identity)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))) = multiply(least_upper_bound(X_198,greatest_lower_bound(X_73,identity)),identity) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(multiply(least_upper_bound(X_198,inverse(inverse(greatest_lower_bound(X_73,identity)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))))),bind(Y0,$fot(multiply(least_upper_bound(X_198,greatest_lower_bound(X_73,identity)),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))))),bind(Z0,$fot(multiply(least_upper_bound(X_198,greatest_lower_bound(X_73,identity)),identity)))]]) ).
cnf(refute_0_1495,plain,
( multiply(least_upper_bound(X_198,greatest_lower_bound(X_73,identity)),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))) != multiply(least_upper_bound(X_198,greatest_lower_bound(X_73,identity)),identity)
| multiply(least_upper_bound(X_198,inverse(inverse(greatest_lower_bound(X_73,identity)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))) = multiply(least_upper_bound(X_198,greatest_lower_bound(X_73,identity)),identity) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_198,inverse(inverse(greatest_lower_bound(X_73,identity)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))),multiply(least_upper_bound(X_198,greatest_lower_bound(X_73,identity)),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity))))) )],[refute_0_1493,refute_0_1494]) ).
cnf(refute_0_1496,plain,
multiply(least_upper_bound(X_198,inverse(inverse(greatest_lower_bound(X_73,identity)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))) = multiply(least_upper_bound(X_198,greatest_lower_bound(X_73,identity)),identity),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_198,greatest_lower_bound(X_73,identity)),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))),multiply(least_upper_bound(X_198,greatest_lower_bound(X_73,identity)),identity)) )],[refute_0_1485,refute_0_1495]) ).
cnf(refute_0_1497,plain,
( multiply(least_upper_bound(X_198,greatest_lower_bound(X_73,identity)),identity) != least_upper_bound(X_198,greatest_lower_bound(X_73,identity))
| multiply(least_upper_bound(X_198,inverse(inverse(greatest_lower_bound(X_73,identity)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))) != multiply(least_upper_bound(X_198,greatest_lower_bound(X_73,identity)),identity)
| multiply(least_upper_bound(X_198,inverse(inverse(greatest_lower_bound(X_73,identity)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))) = least_upper_bound(X_198,greatest_lower_bound(X_73,identity)) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(multiply(least_upper_bound(X_198,inverse(inverse(greatest_lower_bound(X_73,identity)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))))),bind(Y0,$fot(multiply(least_upper_bound(X_198,greatest_lower_bound(X_73,identity)),identity))),bind(Z0,$fot(least_upper_bound(X_198,greatest_lower_bound(X_73,identity))))]]) ).
cnf(refute_0_1498,plain,
( multiply(least_upper_bound(X_198,greatest_lower_bound(X_73,identity)),identity) != least_upper_bound(X_198,greatest_lower_bound(X_73,identity))
| multiply(least_upper_bound(X_198,inverse(inverse(greatest_lower_bound(X_73,identity)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))) = least_upper_bound(X_198,greatest_lower_bound(X_73,identity)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_198,inverse(inverse(greatest_lower_bound(X_73,identity)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))),multiply(least_upper_bound(X_198,greatest_lower_bound(X_73,identity)),identity)) )],[refute_0_1496,refute_0_1497]) ).
cnf(refute_0_1499,plain,
multiply(least_upper_bound(X_198,inverse(inverse(greatest_lower_bound(X_73,identity)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))) = least_upper_bound(X_198,greatest_lower_bound(X_73,identity)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_198,greatest_lower_bound(X_73,identity)),identity),least_upper_bound(X_198,greatest_lower_bound(X_73,identity))) )],[refute_0_1481,refute_0_1498]) ).
cnf(refute_0_1500,plain,
( multiply(least_upper_bound(X_198,inverse(inverse(greatest_lower_bound(X_73,identity)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))) != least_upper_bound(X_198,greatest_lower_bound(X_73,identity))
| multiply(least_upper_bound(X_198,inverse(inverse(greatest_lower_bound(X_73,identity)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))) != least_upper_bound(greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))),multiply(X_198,identity))
| least_upper_bound(X_198,greatest_lower_bound(X_73,identity)) = least_upper_bound(greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))),multiply(X_198,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_198,inverse(inverse(greatest_lower_bound(X_73,identity)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))),least_upper_bound(greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))),multiply(X_198,identity))) ),[0],$fot(least_upper_bound(X_198,greatest_lower_bound(X_73,identity)))]]) ).
cnf(refute_0_1501,plain,
( multiply(least_upper_bound(X_198,inverse(inverse(greatest_lower_bound(X_73,identity)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))) != least_upper_bound(greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))),multiply(X_198,identity))
| least_upper_bound(X_198,greatest_lower_bound(X_73,identity)) = least_upper_bound(greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))),multiply(X_198,identity)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_198,inverse(inverse(greatest_lower_bound(X_73,identity)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))),least_upper_bound(X_198,greatest_lower_bound(X_73,identity))) )],[refute_0_1499,refute_0_1500]) ).
cnf(refute_0_1502,plain,
multiply(X_198,identity) = X_198,
inference(subst,[],[refute_0_603:[bind(X,$fot(X_198))]]) ).
cnf(refute_0_1503,plain,
least_upper_bound(greatest_lower_bound(identity,X_73),multiply(X_198,identity)) = least_upper_bound(greatest_lower_bound(identity,X_73),multiply(X_198,identity)),
introduced(tautology,[refl,[$fot(least_upper_bound(greatest_lower_bound(identity,X_73),multiply(X_198,identity)))]]) ).
cnf(refute_0_1504,plain,
( multiply(X_198,identity) != X_198
| least_upper_bound(greatest_lower_bound(identity,X_73),multiply(X_198,identity)) != least_upper_bound(greatest_lower_bound(identity,X_73),multiply(X_198,identity))
| least_upper_bound(greatest_lower_bound(identity,X_73),multiply(X_198,identity)) = least_upper_bound(greatest_lower_bound(identity,X_73),X_198) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,X_73),multiply(X_198,identity)),least_upper_bound(greatest_lower_bound(identity,X_73),multiply(X_198,identity))) ),[1,1],$fot(X_198)]]) ).
cnf(refute_0_1505,plain,
( multiply(X_198,identity) != X_198
| least_upper_bound(greatest_lower_bound(identity,X_73),multiply(X_198,identity)) = least_upper_bound(greatest_lower_bound(identity,X_73),X_198) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,X_73),multiply(X_198,identity)),least_upper_bound(greatest_lower_bound(identity,X_73),multiply(X_198,identity))) )],[refute_0_1503,refute_0_1504]) ).
cnf(refute_0_1506,plain,
least_upper_bound(greatest_lower_bound(identity,X_73),multiply(X_198,identity)) = least_upper_bound(greatest_lower_bound(identity,X_73),X_198),
inference(resolve,[$cnf( $equal(multiply(X_198,identity),X_198) )],[refute_0_1502,refute_0_1505]) ).
cnf(refute_0_1507,plain,
least_upper_bound(greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))),multiply(X_198,identity)) = least_upper_bound(greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))),multiply(X_198,identity)),
introduced(tautology,[refl,[$fot(least_upper_bound(greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))),multiply(X_198,identity)))]]) ).
cnf(refute_0_1508,plain,
( greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))) != greatest_lower_bound(identity,X_73)
| least_upper_bound(greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))),multiply(X_198,identity)) != least_upper_bound(greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))),multiply(X_198,identity))
| least_upper_bound(greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))),multiply(X_198,identity)) = least_upper_bound(greatest_lower_bound(identity,X_73),multiply(X_198,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))),multiply(X_198,identity)),least_upper_bound(greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))),multiply(X_198,identity))) ),[1,0],$fot(greatest_lower_bound(identity,X_73))]]) ).
cnf(refute_0_1509,plain,
( greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))) != greatest_lower_bound(identity,X_73)
| least_upper_bound(greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))),multiply(X_198,identity)) = least_upper_bound(greatest_lower_bound(identity,X_73),multiply(X_198,identity)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))),multiply(X_198,identity)),least_upper_bound(greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))),multiply(X_198,identity))) )],[refute_0_1507,refute_0_1508]) ).
cnf(refute_0_1510,plain,
least_upper_bound(greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))),multiply(X_198,identity)) = least_upper_bound(greatest_lower_bound(identity,X_73),multiply(X_198,identity)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))),greatest_lower_bound(identity,X_73)) )],[refute_0_1411,refute_0_1509]) ).
cnf(refute_0_1511,plain,
( least_upper_bound(greatest_lower_bound(identity,X_73),multiply(X_198,identity)) != least_upper_bound(greatest_lower_bound(identity,X_73),X_198)
| least_upper_bound(greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))),multiply(X_198,identity)) != least_upper_bound(greatest_lower_bound(identity,X_73),multiply(X_198,identity))
| least_upper_bound(greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))),multiply(X_198,identity)) = least_upper_bound(greatest_lower_bound(identity,X_73),X_198) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))),multiply(X_198,identity)))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(identity,X_73),multiply(X_198,identity)))),bind(Z0,$fot(least_upper_bound(greatest_lower_bound(identity,X_73),X_198)))]]) ).
cnf(refute_0_1512,plain,
( least_upper_bound(greatest_lower_bound(identity,X_73),multiply(X_198,identity)) != least_upper_bound(greatest_lower_bound(identity,X_73),X_198)
| least_upper_bound(greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))),multiply(X_198,identity)) = least_upper_bound(greatest_lower_bound(identity,X_73),X_198) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))),multiply(X_198,identity)),least_upper_bound(greatest_lower_bound(identity,X_73),multiply(X_198,identity))) )],[refute_0_1510,refute_0_1511]) ).
cnf(refute_0_1513,plain,
least_upper_bound(greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))),multiply(X_198,identity)) = least_upper_bound(greatest_lower_bound(identity,X_73),X_198),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,X_73),multiply(X_198,identity)),least_upper_bound(greatest_lower_bound(identity,X_73),X_198)) )],[refute_0_1506,refute_0_1512]) ).
cnf(refute_0_1514,plain,
( least_upper_bound(X_198,greatest_lower_bound(X_73,identity)) != least_upper_bound(greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))),multiply(X_198,identity))
| least_upper_bound(greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))),multiply(X_198,identity)) != least_upper_bound(greatest_lower_bound(identity,X_73),X_198)
| least_upper_bound(X_198,greatest_lower_bound(X_73,identity)) = least_upper_bound(greatest_lower_bound(identity,X_73),X_198) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_198,greatest_lower_bound(X_73,identity)),least_upper_bound(greatest_lower_bound(identity,X_73),X_198)) ),[0],$fot(least_upper_bound(greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))),multiply(X_198,identity)))]]) ).
cnf(refute_0_1515,plain,
( least_upper_bound(X_198,greatest_lower_bound(X_73,identity)) != least_upper_bound(greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))),multiply(X_198,identity))
| least_upper_bound(X_198,greatest_lower_bound(X_73,identity)) = least_upper_bound(greatest_lower_bound(identity,X_73),X_198) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))),multiply(X_198,identity)),least_upper_bound(greatest_lower_bound(identity,X_73),X_198)) )],[refute_0_1513,refute_0_1514]) ).
cnf(refute_0_1516,plain,
( multiply(least_upper_bound(X_198,inverse(inverse(greatest_lower_bound(X_73,identity)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))) != least_upper_bound(greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))),multiply(X_198,identity))
| least_upper_bound(X_198,greatest_lower_bound(X_73,identity)) = least_upper_bound(greatest_lower_bound(identity,X_73),X_198) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_198,greatest_lower_bound(X_73,identity)),least_upper_bound(greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))),multiply(X_198,identity))) )],[refute_0_1501,refute_0_1515]) ).
cnf(refute_0_1517,plain,
least_upper_bound(X_198,greatest_lower_bound(X_73,identity)) = least_upper_bound(greatest_lower_bound(identity,X_73),X_198),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_198,inverse(inverse(greatest_lower_bound(X_73,identity)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_73,identity)))),least_upper_bound(greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_73,identity)))),multiply(X_198,identity))) )],[refute_0_1480,refute_0_1516]) ).
cnf(refute_0_1518,plain,
( least_upper_bound(X_198,greatest_lower_bound(X_73,identity)) != least_upper_bound(greatest_lower_bound(identity,X_73),X_198)
| least_upper_bound(greatest_lower_bound(identity,X_73),X_198) = least_upper_bound(X_198,greatest_lower_bound(X_73,identity)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X_198,greatest_lower_bound(X_73,identity)))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(identity,X_73),X_198)))]]) ).
cnf(refute_0_1519,plain,
least_upper_bound(greatest_lower_bound(identity,X_73),X_198) = least_upper_bound(X_198,greatest_lower_bound(X_73,identity)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_198,greatest_lower_bound(X_73,identity)),least_upper_bound(greatest_lower_bound(identity,X_73),X_198)) )],[refute_0_1517,refute_0_1518]) ).
cnf(refute_0_1520,plain,
least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),greatest_lower_bound(identity,X_197)) = least_upper_bound(greatest_lower_bound(identity,X_197),greatest_lower_bound(inverse(X_197),identity)),
inference(subst,[],[refute_0_1519:[bind(X_198,$fot(greatest_lower_bound(identity,X_197))),bind(X_73,$fot(inverse(X_197)))]]) ).
cnf(refute_0_1521,plain,
( least_upper_bound(greatest_lower_bound(identity,X_197),greatest_lower_bound(inverse(X_197),identity)) != multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197)))
| least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),greatest_lower_bound(identity,X_197)) != least_upper_bound(greatest_lower_bound(identity,X_197),greatest_lower_bound(inverse(X_197),identity))
| least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),greatest_lower_bound(identity,X_197)) = multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197))) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),greatest_lower_bound(identity,X_197)))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(identity,X_197),greatest_lower_bound(inverse(X_197),identity)))),bind(Z0,$fot(multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197)))))]]) ).
cnf(refute_0_1522,plain,
( least_upper_bound(greatest_lower_bound(identity,X_197),greatest_lower_bound(inverse(X_197),identity)) != multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197)))
| least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),greatest_lower_bound(identity,X_197)) = multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),greatest_lower_bound(identity,X_197)),least_upper_bound(greatest_lower_bound(identity,X_197),greatest_lower_bound(inverse(X_197),identity))) )],[refute_0_1520,refute_0_1521]) ).
cnf(refute_0_1523,plain,
least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),greatest_lower_bound(identity,X_197)) = multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197))),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,X_197),greatest_lower_bound(inverse(X_197),identity)),multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197)))) )],[refute_0_1476,refute_0_1522]) ).
cnf(refute_0_1524,plain,
inverse(inverse(greatest_lower_bound(identity,X_197))) = greatest_lower_bound(identity,X_197),
inference(subst,[],[p18_2:[bind(X,$fot(greatest_lower_bound(identity,X_197)))]]) ).
cnf(refute_0_1525,plain,
least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197))) = inverse(greatest_lower_bound(identity,X_197)),
inference(subst,[],[refute_0_488:[bind(X_73,$fot(X_197))]]) ).
cnf(refute_0_1526,plain,
inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197)))) = inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197)))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197)))))]]) ).
cnf(refute_0_1527,plain,
( inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197)))) != inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197))))
| least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197))) != inverse(greatest_lower_bound(identity,X_197))
| inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197)))) = inverse(inverse(greatest_lower_bound(identity,X_197))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197)))),inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197))))) ),[1,0],$fot(inverse(greatest_lower_bound(identity,X_197)))]]) ).
cnf(refute_0_1528,plain,
( least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197))) != inverse(greatest_lower_bound(identity,X_197))
| inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197)))) = inverse(inverse(greatest_lower_bound(identity,X_197))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197)))),inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197))))) )],[refute_0_1526,refute_0_1527]) ).
cnf(refute_0_1529,plain,
inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197)))) = inverse(inverse(greatest_lower_bound(identity,X_197))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197))),inverse(greatest_lower_bound(identity,X_197))) )],[refute_0_1525,refute_0_1528]) ).
cnf(refute_0_1530,plain,
( inverse(inverse(greatest_lower_bound(identity,X_197))) != greatest_lower_bound(identity,X_197)
| inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197)))) != inverse(inverse(greatest_lower_bound(identity,X_197)))
| inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197)))) = greatest_lower_bound(identity,X_197) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197)))))),bind(Y0,$fot(inverse(inverse(greatest_lower_bound(identity,X_197))))),bind(Z0,$fot(greatest_lower_bound(identity,X_197)))]]) ).
cnf(refute_0_1531,plain,
( inverse(inverse(greatest_lower_bound(identity,X_197))) != greatest_lower_bound(identity,X_197)
| inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197)))) = greatest_lower_bound(identity,X_197) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197)))),inverse(inverse(greatest_lower_bound(identity,X_197)))) )],[refute_0_1529,refute_0_1530]) ).
cnf(refute_0_1532,plain,
inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197)))) = greatest_lower_bound(identity,X_197),
inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(identity,X_197))),greatest_lower_bound(identity,X_197)) )],[refute_0_1524,refute_0_1531]) ).
cnf(refute_0_1533,plain,
least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197))))) = least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197))))),
introduced(tautology,[refl,[$fot(least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197))))))]]) ).
cnf(refute_0_1534,plain,
( inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197)))) != greatest_lower_bound(identity,X_197)
| least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197))))) != least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197)))))
| least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197))))) = least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),greatest_lower_bound(identity,X_197)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197))))),least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197)))))) ),[1,1],$fot(greatest_lower_bound(identity,X_197))]]) ).
cnf(refute_0_1535,plain,
( inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197)))) != greatest_lower_bound(identity,X_197)
| least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197))))) = least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),greatest_lower_bound(identity,X_197)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197))))),least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197)))))) )],[refute_0_1533,refute_0_1534]) ).
cnf(refute_0_1536,plain,
least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197))))) = least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),greatest_lower_bound(identity,X_197)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197)))),greatest_lower_bound(identity,X_197)) )],[refute_0_1532,refute_0_1535]) ).
cnf(refute_0_1537,plain,
( least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),greatest_lower_bound(identity,X_197)) != multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197)))
| least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197))))) != least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),greatest_lower_bound(identity,X_197))
| least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197))))) = multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197))) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197))))))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),greatest_lower_bound(identity,X_197)))),bind(Z0,$fot(multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197)))))]]) ).
cnf(refute_0_1538,plain,
( least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),greatest_lower_bound(identity,X_197)) != multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197)))
| least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197))))) = multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197))))),least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),greatest_lower_bound(identity,X_197))) )],[refute_0_1536,refute_0_1537]) ).
cnf(refute_0_1539,plain,
least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197))))) = multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197))),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),greatest_lower_bound(identity,X_197)),multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197)))) )],[refute_0_1523,refute_0_1538]) ).
cnf(refute_0_1540,plain,
( multiply(greatest_lower_bound(X_197,identity),least_upper_bound(identity,inverse(X_197))) != least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197)))))
| least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197))))) != multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197)))
| multiply(greatest_lower_bound(X_197,identity),least_upper_bound(identity,inverse(X_197))) = multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_197,identity),least_upper_bound(identity,inverse(X_197))),multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197)))) ),[0],$fot(least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197))))))]]) ).
cnf(refute_0_1541,plain,
( multiply(greatest_lower_bound(X_197,identity),least_upper_bound(identity,inverse(X_197))) != least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197)))))
| multiply(greatest_lower_bound(X_197,identity),least_upper_bound(identity,inverse(X_197))) = multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197))))),multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197)))) )],[refute_0_1539,refute_0_1540]) ).
cnf(refute_0_1542,plain,
( multiply(least_upper_bound(inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity)),inverse(X_197)),greatest_lower_bound(identity,X_197)) != least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197)))))
| multiply(greatest_lower_bound(X_197,identity),least_upper_bound(identity,inverse(X_197))) = multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_197,identity),least_upper_bound(identity,inverse(X_197))),least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197)))))) )],[refute_0_1314,refute_0_1541]) ).
cnf(refute_0_1543,plain,
multiply(greatest_lower_bound(X_197,identity),least_upper_bound(identity,inverse(X_197))) = multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(least_upper_bound(greatest_lower_bound(identity,X_197),identity)),inverse(X_197)),greatest_lower_bound(identity,X_197)),least_upper_bound(greatest_lower_bound(identity,inverse(X_197)),inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_197)))))) )],[refute_0_1070,refute_0_1542]) ).
cnf(refute_0_1544,plain,
multiply(inverse(least_upper_bound(Y,X_50)),greatest_lower_bound(X_50,least_upper_bound(Y,X_50))) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(Y,X_50)),X_50)),
inference(subst,[],[refute_0_462:[bind(X_37,$fot(X_50)),bind(X_38,$fot(least_upper_bound(Y,X_50)))]]) ).
cnf(refute_0_1545,plain,
greatest_lower_bound(X_50,least_upper_bound(Y,X_50)) = X_50,
inference(subst,[],[refute_0_171:[bind(X,$fot(X_50))]]) ).
cnf(refute_0_1546,plain,
( multiply(inverse(least_upper_bound(Y,X_50)),greatest_lower_bound(X_50,least_upper_bound(Y,X_50))) != greatest_lower_bound(identity,multiply(inverse(least_upper_bound(Y,X_50)),X_50))
| greatest_lower_bound(X_50,least_upper_bound(Y,X_50)) != X_50
| multiply(inverse(least_upper_bound(Y,X_50)),X_50) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(Y,X_50)),X_50)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(Y,X_50)),greatest_lower_bound(X_50,least_upper_bound(Y,X_50))),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(Y,X_50)),X_50))) ),[0,1],$fot(X_50)]]) ).
cnf(refute_0_1547,plain,
( multiply(inverse(least_upper_bound(Y,X_50)),greatest_lower_bound(X_50,least_upper_bound(Y,X_50))) != greatest_lower_bound(identity,multiply(inverse(least_upper_bound(Y,X_50)),X_50))
| multiply(inverse(least_upper_bound(Y,X_50)),X_50) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(Y,X_50)),X_50)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_50,least_upper_bound(Y,X_50)),X_50) )],[refute_0_1545,refute_0_1546]) ).
cnf(refute_0_1548,plain,
multiply(inverse(least_upper_bound(Y,X_50)),X_50) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(Y,X_50)),X_50)),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(Y,X_50)),greatest_lower_bound(X_50,least_upper_bound(Y,X_50))),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(Y,X_50)),X_50))) )],[refute_0_1544,refute_0_1547]) ).
cnf(refute_0_1549,plain,
multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_397)),greatest_lower_bound(identity,inverse(X_397)))),greatest_lower_bound(identity,inverse(X_397))) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_397)),greatest_lower_bound(identity,inverse(X_397)))),greatest_lower_bound(identity,inverse(X_397)))),
inference(subst,[],[refute_0_1548:[bind(Y,$fot(inverse(least_upper_bound(identity,X_397)))),bind(X_50,$fot(greatest_lower_bound(identity,inverse(X_397))))]]) ).
cnf(refute_0_1550,plain,
multiply(X_56,least_upper_bound(greatest_lower_bound(inverse(X_56),X_38),identity)) = least_upper_bound(X_56,multiply(X_56,greatest_lower_bound(inverse(X_56),X_38))),
inference(subst,[],[refute_0_736:[bind(X_53,$fot(X_56)),bind(X_54,$fot(greatest_lower_bound(inverse(X_56),X_38)))]]) ).
cnf(refute_0_1551,plain,
multiply(X_56,greatest_lower_bound(inverse(X_56),X_38)) = greatest_lower_bound(identity,multiply(X_56,X_38)),
inference(subst,[],[refute_0_757:[bind(X_36,$fot(X_56))]]) ).
cnf(refute_0_1552,plain,
( multiply(X_56,greatest_lower_bound(inverse(X_56),X_38)) != greatest_lower_bound(identity,multiply(X_56,X_38))
| multiply(X_56,least_upper_bound(greatest_lower_bound(inverse(X_56),X_38),identity)) != least_upper_bound(X_56,multiply(X_56,greatest_lower_bound(inverse(X_56),X_38)))
| multiply(X_56,least_upper_bound(greatest_lower_bound(inverse(X_56),X_38),identity)) = least_upper_bound(X_56,greatest_lower_bound(identity,multiply(X_56,X_38))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_56,least_upper_bound(greatest_lower_bound(inverse(X_56),X_38),identity)),least_upper_bound(X_56,multiply(X_56,greatest_lower_bound(inverse(X_56),X_38)))) ),[1,1],$fot(greatest_lower_bound(identity,multiply(X_56,X_38)))]]) ).
cnf(refute_0_1553,plain,
( multiply(X_56,least_upper_bound(greatest_lower_bound(inverse(X_56),X_38),identity)) != least_upper_bound(X_56,multiply(X_56,greatest_lower_bound(inverse(X_56),X_38)))
| multiply(X_56,least_upper_bound(greatest_lower_bound(inverse(X_56),X_38),identity)) = least_upper_bound(X_56,greatest_lower_bound(identity,multiply(X_56,X_38))) ),
inference(resolve,[$cnf( $equal(multiply(X_56,greatest_lower_bound(inverse(X_56),X_38)),greatest_lower_bound(identity,multiply(X_56,X_38))) )],[refute_0_1551,refute_0_1552]) ).
cnf(refute_0_1554,plain,
multiply(X_56,least_upper_bound(greatest_lower_bound(inverse(X_56),X_38),identity)) = least_upper_bound(X_56,greatest_lower_bound(identity,multiply(X_56,X_38))),
inference(resolve,[$cnf( $equal(multiply(X_56,least_upper_bound(greatest_lower_bound(inverse(X_56),X_38),identity)),least_upper_bound(X_56,multiply(X_56,greatest_lower_bound(inverse(X_56),X_38)))) )],[refute_0_1550,refute_0_1553]) ).
cnf(refute_0_1555,plain,
least_upper_bound(X_23,least_upper_bound(X_23,multiply(X_23,X_57))) = least_upper_bound(X_23,multiply(X_23,X_57)),
inference(subst,[],[refute_0_71:[bind(X_22,$fot(multiply(X_23,X_57)))]]) ).
cnf(refute_0_1556,plain,
multiply(X_23,least_upper_bound(X_57,identity)) = least_upper_bound(X_23,multiply(X_23,X_57)),
inference(subst,[],[refute_0_736:[bind(X_53,$fot(X_23)),bind(X_54,$fot(X_57))]]) ).
cnf(refute_0_1557,plain,
( multiply(X_23,least_upper_bound(X_57,identity)) != least_upper_bound(X_23,multiply(X_23,X_57))
| least_upper_bound(X_23,multiply(X_23,X_57)) = multiply(X_23,least_upper_bound(X_57,identity)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X_23,least_upper_bound(X_57,identity)))),bind(Y0,$fot(least_upper_bound(X_23,multiply(X_23,X_57))))]]) ).
cnf(refute_0_1558,plain,
least_upper_bound(X_23,multiply(X_23,X_57)) = multiply(X_23,least_upper_bound(X_57,identity)),
inference(resolve,[$cnf( $equal(multiply(X_23,least_upper_bound(X_57,identity)),least_upper_bound(X_23,multiply(X_23,X_57))) )],[refute_0_1556,refute_0_1557]) ).
cnf(refute_0_1559,plain,
( least_upper_bound(X_23,multiply(X_23,X_57)) != multiply(X_23,least_upper_bound(X_57,identity))
| least_upper_bound(X_23,least_upper_bound(X_23,multiply(X_23,X_57))) != least_upper_bound(X_23,multiply(X_23,X_57))
| least_upper_bound(X_23,multiply(X_23,least_upper_bound(X_57,identity))) = least_upper_bound(X_23,multiply(X_23,X_57)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_23,least_upper_bound(X_23,multiply(X_23,X_57))),least_upper_bound(X_23,multiply(X_23,X_57))) ),[0,1],$fot(multiply(X_23,least_upper_bound(X_57,identity)))]]) ).
cnf(refute_0_1560,plain,
( least_upper_bound(X_23,least_upper_bound(X_23,multiply(X_23,X_57))) != least_upper_bound(X_23,multiply(X_23,X_57))
| least_upper_bound(X_23,multiply(X_23,least_upper_bound(X_57,identity))) = least_upper_bound(X_23,multiply(X_23,X_57)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_23,multiply(X_23,X_57)),multiply(X_23,least_upper_bound(X_57,identity))) )],[refute_0_1558,refute_0_1559]) ).
cnf(refute_0_1561,plain,
least_upper_bound(X_23,multiply(X_23,least_upper_bound(X_57,identity))) = least_upper_bound(X_23,multiply(X_23,X_57)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_23,least_upper_bound(X_23,multiply(X_23,X_57))),least_upper_bound(X_23,multiply(X_23,X_57))) )],[refute_0_1555,refute_0_1560]) ).
cnf(refute_0_1562,plain,
least_upper_bound(identity,least_upper_bound(X_57,identity)) = least_upper_bound(identity,X_57),
inference(subst,[],[refute_0_64:[bind(Y,$fot(X_57)),bind(X_21,$fot(identity))]]) ).
cnf(refute_0_1563,plain,
multiply(X_23,least_upper_bound(identity,least_upper_bound(X_57,identity))) = multiply(X_23,least_upper_bound(identity,least_upper_bound(X_57,identity))),
introduced(tautology,[refl,[$fot(multiply(X_23,least_upper_bound(identity,least_upper_bound(X_57,identity))))]]) ).
cnf(refute_0_1564,plain,
( multiply(X_23,least_upper_bound(identity,least_upper_bound(X_57,identity))) != multiply(X_23,least_upper_bound(identity,least_upper_bound(X_57,identity)))
| least_upper_bound(identity,least_upper_bound(X_57,identity)) != least_upper_bound(identity,X_57)
| multiply(X_23,least_upper_bound(identity,least_upper_bound(X_57,identity))) = multiply(X_23,least_upper_bound(identity,X_57)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_23,least_upper_bound(identity,least_upper_bound(X_57,identity))),multiply(X_23,least_upper_bound(identity,least_upper_bound(X_57,identity)))) ),[1,1],$fot(least_upper_bound(identity,X_57))]]) ).
cnf(refute_0_1565,plain,
( least_upper_bound(identity,least_upper_bound(X_57,identity)) != least_upper_bound(identity,X_57)
| multiply(X_23,least_upper_bound(identity,least_upper_bound(X_57,identity))) = multiply(X_23,least_upper_bound(identity,X_57)) ),
inference(resolve,[$cnf( $equal(multiply(X_23,least_upper_bound(identity,least_upper_bound(X_57,identity))),multiply(X_23,least_upper_bound(identity,least_upper_bound(X_57,identity)))) )],[refute_0_1563,refute_0_1564]) ).
cnf(refute_0_1566,plain,
multiply(X_23,least_upper_bound(identity,least_upper_bound(X_57,identity))) = multiply(X_23,least_upper_bound(identity,X_57)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_57,identity)),least_upper_bound(identity,X_57)) )],[refute_0_1562,refute_0_1565]) ).
cnf(refute_0_1567,plain,
least_upper_bound(multiply(X_53,X_55),multiply(X_53,X_54)) = least_upper_bound(multiply(X_53,X_54),multiply(X_53,X_55)),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(multiply(X_53,X_55))),bind(Y,$fot(multiply(X_53,X_54)))]]) ).
cnf(refute_0_1568,plain,
multiply(X_53,least_upper_bound(X_54,X_55)) = least_upper_bound(multiply(X_53,X_54),multiply(X_53,X_55)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(X_53)),bind(Y,$fot(X_54)),bind(Z,$fot(X_55))]]) ).
cnf(refute_0_1569,plain,
( multiply(X_53,least_upper_bound(X_54,X_55)) != least_upper_bound(multiply(X_53,X_54),multiply(X_53,X_55))
| least_upper_bound(multiply(X_53,X_54),multiply(X_53,X_55)) = multiply(X_53,least_upper_bound(X_54,X_55)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X_53,least_upper_bound(X_54,X_55)))),bind(Y0,$fot(least_upper_bound(multiply(X_53,X_54),multiply(X_53,X_55))))]]) ).
cnf(refute_0_1570,plain,
least_upper_bound(multiply(X_53,X_54),multiply(X_53,X_55)) = multiply(X_53,least_upper_bound(X_54,X_55)),
inference(resolve,[$cnf( $equal(multiply(X_53,least_upper_bound(X_54,X_55)),least_upper_bound(multiply(X_53,X_54),multiply(X_53,X_55))) )],[refute_0_1568,refute_0_1569]) ).
cnf(refute_0_1571,plain,
( least_upper_bound(multiply(X_53,X_54),multiply(X_53,X_55)) != multiply(X_53,least_upper_bound(X_54,X_55))
| least_upper_bound(multiply(X_53,X_55),multiply(X_53,X_54)) != least_upper_bound(multiply(X_53,X_54),multiply(X_53,X_55))
| least_upper_bound(multiply(X_53,X_55),multiply(X_53,X_54)) = multiply(X_53,least_upper_bound(X_54,X_55)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_53,X_55),multiply(X_53,X_54)),least_upper_bound(multiply(X_53,X_54),multiply(X_53,X_55))) ),[1],$fot(multiply(X_53,least_upper_bound(X_54,X_55)))]]) ).
cnf(refute_0_1572,plain,
( least_upper_bound(multiply(X_53,X_55),multiply(X_53,X_54)) != least_upper_bound(multiply(X_53,X_54),multiply(X_53,X_55))
| least_upper_bound(multiply(X_53,X_55),multiply(X_53,X_54)) = multiply(X_53,least_upper_bound(X_54,X_55)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_53,X_54),multiply(X_53,X_55)),multiply(X_53,least_upper_bound(X_54,X_55))) )],[refute_0_1570,refute_0_1571]) ).
cnf(refute_0_1573,plain,
least_upper_bound(multiply(X_53,X_55),multiply(X_53,X_54)) = multiply(X_53,least_upper_bound(X_54,X_55)),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_53,X_55),multiply(X_53,X_54)),least_upper_bound(multiply(X_53,X_54),multiply(X_53,X_55))) )],[refute_0_1567,refute_0_1572]) ).
cnf(refute_0_1574,plain,
least_upper_bound(multiply(X_53,X_55),multiply(X_53,X_54)) = multiply(X_53,least_upper_bound(X_55,X_54)),
inference(subst,[],[refute_0_249:[bind(X,$fot(X_53)),bind(Y,$fot(X_55)),bind(Z,$fot(X_54))]]) ).
cnf(refute_0_1575,plain,
( least_upper_bound(multiply(X_53,X_55),multiply(X_53,X_54)) != multiply(X_53,least_upper_bound(X_54,X_55))
| least_upper_bound(multiply(X_53,X_55),multiply(X_53,X_54)) != multiply(X_53,least_upper_bound(X_55,X_54))
| multiply(X_53,least_upper_bound(X_55,X_54)) = multiply(X_53,least_upper_bound(X_54,X_55)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_53,X_55),multiply(X_53,X_54)),multiply(X_53,least_upper_bound(X_54,X_55))) ),[0],$fot(multiply(X_53,least_upper_bound(X_55,X_54)))]]) ).
cnf(refute_0_1576,plain,
( least_upper_bound(multiply(X_53,X_55),multiply(X_53,X_54)) != multiply(X_53,least_upper_bound(X_54,X_55))
| multiply(X_53,least_upper_bound(X_55,X_54)) = multiply(X_53,least_upper_bound(X_54,X_55)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_53,X_55),multiply(X_53,X_54)),multiply(X_53,least_upper_bound(X_55,X_54))) )],[refute_0_1574,refute_0_1575]) ).
cnf(refute_0_1577,plain,
multiply(X_53,least_upper_bound(X_55,X_54)) = multiply(X_53,least_upper_bound(X_54,X_55)),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_53,X_55),multiply(X_53,X_54)),multiply(X_53,least_upper_bound(X_54,X_55))) )],[refute_0_1573,refute_0_1576]) ).
cnf(refute_0_1578,plain,
( multiply(X_53,least_upper_bound(X_55,X_54)) != multiply(X_53,least_upper_bound(X_54,X_55))
| multiply(X_53,least_upper_bound(X_54,X_55)) = multiply(X_53,least_upper_bound(X_55,X_54)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X_53,least_upper_bound(X_55,X_54)))),bind(Y0,$fot(multiply(X_53,least_upper_bound(X_54,X_55))))]]) ).
cnf(refute_0_1579,plain,
multiply(X_53,least_upper_bound(X_54,X_55)) = multiply(X_53,least_upper_bound(X_55,X_54)),
inference(resolve,[$cnf( $equal(multiply(X_53,least_upper_bound(X_55,X_54)),multiply(X_53,least_upper_bound(X_54,X_55))) )],[refute_0_1577,refute_0_1578]) ).
cnf(refute_0_1580,plain,
multiply(X_23,least_upper_bound(least_upper_bound(X_57,identity),identity)) = multiply(X_23,least_upper_bound(identity,least_upper_bound(X_57,identity))),
inference(subst,[],[refute_0_1579:[bind(X_53,$fot(X_23)),bind(X_54,$fot(least_upper_bound(X_57,identity))),bind(X_55,$fot(identity))]]) ).
cnf(refute_0_1581,plain,
least_upper_bound(X_23,multiply(X_23,least_upper_bound(X_57,identity))) = multiply(X_23,least_upper_bound(least_upper_bound(X_57,identity),identity)),
inference(subst,[],[refute_0_1231:[bind(X_53,$fot(X_23)),bind(X_54,$fot(least_upper_bound(X_57,identity)))]]) ).
cnf(refute_0_1582,plain,
( multiply(X_23,least_upper_bound(least_upper_bound(X_57,identity),identity)) != multiply(X_23,least_upper_bound(identity,least_upper_bound(X_57,identity)))
| least_upper_bound(X_23,multiply(X_23,least_upper_bound(X_57,identity))) != multiply(X_23,least_upper_bound(least_upper_bound(X_57,identity),identity))
| least_upper_bound(X_23,multiply(X_23,least_upper_bound(X_57,identity))) = multiply(X_23,least_upper_bound(identity,least_upper_bound(X_57,identity))) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(least_upper_bound(X_23,multiply(X_23,least_upper_bound(X_57,identity))))),bind(Y0,$fot(multiply(X_23,least_upper_bound(least_upper_bound(X_57,identity),identity)))),bind(Z0,$fot(multiply(X_23,least_upper_bound(identity,least_upper_bound(X_57,identity)))))]]) ).
cnf(refute_0_1583,plain,
( multiply(X_23,least_upper_bound(least_upper_bound(X_57,identity),identity)) != multiply(X_23,least_upper_bound(identity,least_upper_bound(X_57,identity)))
| least_upper_bound(X_23,multiply(X_23,least_upper_bound(X_57,identity))) = multiply(X_23,least_upper_bound(identity,least_upper_bound(X_57,identity))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_23,multiply(X_23,least_upper_bound(X_57,identity))),multiply(X_23,least_upper_bound(least_upper_bound(X_57,identity),identity))) )],[refute_0_1581,refute_0_1582]) ).
cnf(refute_0_1584,plain,
least_upper_bound(X_23,multiply(X_23,least_upper_bound(X_57,identity))) = multiply(X_23,least_upper_bound(identity,least_upper_bound(X_57,identity))),
inference(resolve,[$cnf( $equal(multiply(X_23,least_upper_bound(least_upper_bound(X_57,identity),identity)),multiply(X_23,least_upper_bound(identity,least_upper_bound(X_57,identity)))) )],[refute_0_1580,refute_0_1583]) ).
cnf(refute_0_1585,plain,
( multiply(X_23,least_upper_bound(identity,least_upper_bound(X_57,identity))) != multiply(X_23,least_upper_bound(identity,X_57))
| least_upper_bound(X_23,multiply(X_23,least_upper_bound(X_57,identity))) != multiply(X_23,least_upper_bound(identity,least_upper_bound(X_57,identity)))
| least_upper_bound(X_23,multiply(X_23,least_upper_bound(X_57,identity))) = multiply(X_23,least_upper_bound(identity,X_57)) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(least_upper_bound(X_23,multiply(X_23,least_upper_bound(X_57,identity))))),bind(Y0,$fot(multiply(X_23,least_upper_bound(identity,least_upper_bound(X_57,identity))))),bind(Z0,$fot(multiply(X_23,least_upper_bound(identity,X_57))))]]) ).
cnf(refute_0_1586,plain,
( multiply(X_23,least_upper_bound(identity,least_upper_bound(X_57,identity))) != multiply(X_23,least_upper_bound(identity,X_57))
| least_upper_bound(X_23,multiply(X_23,least_upper_bound(X_57,identity))) = multiply(X_23,least_upper_bound(identity,X_57)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_23,multiply(X_23,least_upper_bound(X_57,identity))),multiply(X_23,least_upper_bound(identity,least_upper_bound(X_57,identity)))) )],[refute_0_1584,refute_0_1585]) ).
cnf(refute_0_1587,plain,
least_upper_bound(X_23,multiply(X_23,least_upper_bound(X_57,identity))) = multiply(X_23,least_upper_bound(identity,X_57)),
inference(resolve,[$cnf( $equal(multiply(X_23,least_upper_bound(identity,least_upper_bound(X_57,identity))),multiply(X_23,least_upper_bound(identity,X_57))) )],[refute_0_1566,refute_0_1586]) ).
cnf(refute_0_1588,plain,
( least_upper_bound(X_23,multiply(X_23,least_upper_bound(X_57,identity))) != multiply(X_23,least_upper_bound(identity,X_57))
| least_upper_bound(X_23,multiply(X_23,least_upper_bound(X_57,identity))) != least_upper_bound(X_23,multiply(X_23,X_57))
| multiply(X_23,least_upper_bound(identity,X_57)) = least_upper_bound(X_23,multiply(X_23,X_57)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_23,multiply(X_23,least_upper_bound(X_57,identity))),least_upper_bound(X_23,multiply(X_23,X_57))) ),[0],$fot(multiply(X_23,least_upper_bound(identity,X_57)))]]) ).
cnf(refute_0_1589,plain,
( least_upper_bound(X_23,multiply(X_23,least_upper_bound(X_57,identity))) != least_upper_bound(X_23,multiply(X_23,X_57))
| multiply(X_23,least_upper_bound(identity,X_57)) = least_upper_bound(X_23,multiply(X_23,X_57)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_23,multiply(X_23,least_upper_bound(X_57,identity))),multiply(X_23,least_upper_bound(identity,X_57))) )],[refute_0_1587,refute_0_1588]) ).
cnf(refute_0_1590,plain,
( multiply(X_23,least_upper_bound(identity,X_57)) != least_upper_bound(X_23,multiply(X_23,X_57))
| least_upper_bound(X_23,multiply(X_23,X_57)) != multiply(X_23,least_upper_bound(X_57,identity))
| multiply(X_23,least_upper_bound(identity,X_57)) = multiply(X_23,least_upper_bound(X_57,identity)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_23,least_upper_bound(identity,X_57)),multiply(X_23,least_upper_bound(X_57,identity))) ),[0],$fot(least_upper_bound(X_23,multiply(X_23,X_57)))]]) ).
cnf(refute_0_1591,plain,
( multiply(X_23,least_upper_bound(identity,X_57)) != least_upper_bound(X_23,multiply(X_23,X_57))
| multiply(X_23,least_upper_bound(identity,X_57)) = multiply(X_23,least_upper_bound(X_57,identity)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_23,multiply(X_23,X_57)),multiply(X_23,least_upper_bound(X_57,identity))) )],[refute_0_1558,refute_0_1590]) ).
cnf(refute_0_1592,plain,
( least_upper_bound(X_23,multiply(X_23,least_upper_bound(X_57,identity))) != least_upper_bound(X_23,multiply(X_23,X_57))
| multiply(X_23,least_upper_bound(identity,X_57)) = multiply(X_23,least_upper_bound(X_57,identity)) ),
inference(resolve,[$cnf( $equal(multiply(X_23,least_upper_bound(identity,X_57)),least_upper_bound(X_23,multiply(X_23,X_57))) )],[refute_0_1589,refute_0_1591]) ).
cnf(refute_0_1593,plain,
multiply(X_23,least_upper_bound(identity,X_57)) = multiply(X_23,least_upper_bound(X_57,identity)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_23,multiply(X_23,least_upper_bound(X_57,identity))),least_upper_bound(X_23,multiply(X_23,X_57))) )],[refute_0_1561,refute_0_1592]) ).
cnf(refute_0_1594,plain,
( multiply(X_23,least_upper_bound(identity,X_57)) != multiply(X_23,least_upper_bound(X_57,identity))
| multiply(X_23,least_upper_bound(X_57,identity)) = multiply(X_23,least_upper_bound(identity,X_57)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X_23,least_upper_bound(identity,X_57)))),bind(Y0,$fot(multiply(X_23,least_upper_bound(X_57,identity))))]]) ).
cnf(refute_0_1595,plain,
multiply(X_23,least_upper_bound(X_57,identity)) = multiply(X_23,least_upper_bound(identity,X_57)),
inference(resolve,[$cnf( $equal(multiply(X_23,least_upper_bound(identity,X_57)),multiply(X_23,least_upper_bound(X_57,identity))) )],[refute_0_1593,refute_0_1594]) ).
cnf(refute_0_1596,plain,
multiply(X_56,least_upper_bound(greatest_lower_bound(inverse(X_56),X_38),identity)) = multiply(X_56,least_upper_bound(identity,greatest_lower_bound(inverse(X_56),X_38))),
inference(subst,[],[refute_0_1595:[bind(X_23,$fot(X_56)),bind(X_57,$fot(greatest_lower_bound(inverse(X_56),X_38)))]]) ).
cnf(refute_0_1597,plain,
( multiply(X_56,least_upper_bound(greatest_lower_bound(inverse(X_56),X_38),identity)) != multiply(X_56,least_upper_bound(identity,greatest_lower_bound(inverse(X_56),X_38)))
| multiply(X_56,least_upper_bound(greatest_lower_bound(inverse(X_56),X_38),identity)) != least_upper_bound(X_56,greatest_lower_bound(identity,multiply(X_56,X_38)))
| multiply(X_56,least_upper_bound(identity,greatest_lower_bound(inverse(X_56),X_38))) = least_upper_bound(X_56,greatest_lower_bound(identity,multiply(X_56,X_38))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_56,least_upper_bound(greatest_lower_bound(inverse(X_56),X_38),identity)),least_upper_bound(X_56,greatest_lower_bound(identity,multiply(X_56,X_38)))) ),[0],$fot(multiply(X_56,least_upper_bound(identity,greatest_lower_bound(inverse(X_56),X_38))))]]) ).
cnf(refute_0_1598,plain,
( multiply(X_56,least_upper_bound(greatest_lower_bound(inverse(X_56),X_38),identity)) != least_upper_bound(X_56,greatest_lower_bound(identity,multiply(X_56,X_38)))
| multiply(X_56,least_upper_bound(identity,greatest_lower_bound(inverse(X_56),X_38))) = least_upper_bound(X_56,greatest_lower_bound(identity,multiply(X_56,X_38))) ),
inference(resolve,[$cnf( $equal(multiply(X_56,least_upper_bound(greatest_lower_bound(inverse(X_56),X_38),identity)),multiply(X_56,least_upper_bound(identity,greatest_lower_bound(inverse(X_56),X_38)))) )],[refute_0_1596,refute_0_1597]) ).
cnf(refute_0_1599,plain,
multiply(X_56,least_upper_bound(identity,greatest_lower_bound(inverse(X_56),X_38))) = least_upper_bound(X_56,greatest_lower_bound(identity,multiply(X_56,X_38))),
inference(resolve,[$cnf( $equal(multiply(X_56,least_upper_bound(greatest_lower_bound(inverse(X_56),X_38),identity)),least_upper_bound(X_56,greatest_lower_bound(identity,multiply(X_56,X_38)))) )],[refute_0_1554,refute_0_1598]) ).
cnf(refute_0_1600,plain,
multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(least_upper_bound(identity,X_114))),least_upper_bound(identity,inverse(X_114))))) = least_upper_bound(inverse(least_upper_bound(identity,X_114)),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,inverse(X_114))))),
inference(subst,[],[refute_0_1599:[bind(X_38,$fot(least_upper_bound(identity,inverse(X_114)))),bind(X_56,$fot(inverse(least_upper_bound(identity,X_114))))]]) ).
cnf(refute_0_1601,plain,
inverse(X_69) = multiply(inverse(least_upper_bound(X_69,identity)),multiply(least_upper_bound(X_69,identity),inverse(X_69))),
inference(subst,[],[refute_0_17:[bind(X_93,$fot(least_upper_bound(X_69,identity))),bind(X_94,$fot(inverse(X_69)))]]) ).
cnf(refute_0_1602,plain,
multiply(least_upper_bound(X_69,identity),inverse(X_69)) = least_upper_bound(inverse(X_69),multiply(X_69,inverse(X_69))),
inference(subst,[],[refute_0_672:[bind(X_65,$fot(inverse(X_69))),bind(X_66,$fot(X_69))]]) ).
cnf(refute_0_1603,plain,
multiply(X_69,inverse(X_69)) = identity,
inference(subst,[],[refute_0_38:[bind(X_1,$fot(X_69))]]) ).
cnf(refute_0_1604,plain,
( multiply(X_69,inverse(X_69)) != identity
| multiply(least_upper_bound(X_69,identity),inverse(X_69)) != least_upper_bound(inverse(X_69),multiply(X_69,inverse(X_69)))
| multiply(least_upper_bound(X_69,identity),inverse(X_69)) = least_upper_bound(inverse(X_69),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_69,identity),inverse(X_69)),least_upper_bound(inverse(X_69),multiply(X_69,inverse(X_69)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_1605,plain,
( multiply(least_upper_bound(X_69,identity),inverse(X_69)) != least_upper_bound(inverse(X_69),multiply(X_69,inverse(X_69)))
| multiply(least_upper_bound(X_69,identity),inverse(X_69)) = least_upper_bound(inverse(X_69),identity) ),
inference(resolve,[$cnf( $equal(multiply(X_69,inverse(X_69)),identity) )],[refute_0_1603,refute_0_1604]) ).
cnf(refute_0_1606,plain,
multiply(least_upper_bound(X_69,identity),inverse(X_69)) = least_upper_bound(inverse(X_69),identity),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_69,identity),inverse(X_69)),least_upper_bound(inverse(X_69),multiply(X_69,inverse(X_69)))) )],[refute_0_1602,refute_0_1605]) ).
cnf(refute_0_1607,plain,
least_upper_bound(inverse(X_69),identity) = least_upper_bound(identity,inverse(X_69)),
inference(subst,[],[refute_0_4:[bind(X,$fot(identity)),bind(Y,$fot(inverse(X_69)))]]) ).
cnf(refute_0_1608,plain,
( multiply(least_upper_bound(X_69,identity),inverse(X_69)) != least_upper_bound(inverse(X_69),identity)
| least_upper_bound(inverse(X_69),identity) != least_upper_bound(identity,inverse(X_69))
| multiply(least_upper_bound(X_69,identity),inverse(X_69)) = least_upper_bound(identity,inverse(X_69)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_69,identity),inverse(X_69)),least_upper_bound(identity,inverse(X_69))) ),[0],$fot(least_upper_bound(inverse(X_69),identity))]]) ).
cnf(refute_0_1609,plain,
( multiply(least_upper_bound(X_69,identity),inverse(X_69)) != least_upper_bound(inverse(X_69),identity)
| multiply(least_upper_bound(X_69,identity),inverse(X_69)) = least_upper_bound(identity,inverse(X_69)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_69),identity),least_upper_bound(identity,inverse(X_69))) )],[refute_0_1607,refute_0_1608]) ).
cnf(refute_0_1610,plain,
multiply(least_upper_bound(X_69,identity),inverse(X_69)) = least_upper_bound(identity,inverse(X_69)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_69,identity),inverse(X_69)),least_upper_bound(inverse(X_69),identity)) )],[refute_0_1606,refute_0_1609]) ).
cnf(refute_0_1611,plain,
( multiply(least_upper_bound(X_69,identity),inverse(X_69)) != least_upper_bound(identity,inverse(X_69))
| inverse(X_69) != multiply(inverse(least_upper_bound(X_69,identity)),multiply(least_upper_bound(X_69,identity),inverse(X_69)))
| inverse(X_69) = multiply(inverse(least_upper_bound(X_69,identity)),least_upper_bound(identity,inverse(X_69))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(X_69),multiply(inverse(least_upper_bound(X_69,identity)),multiply(least_upper_bound(X_69,identity),inverse(X_69)))) ),[1,1],$fot(least_upper_bound(identity,inverse(X_69)))]]) ).
cnf(refute_0_1612,plain,
( inverse(X_69) != multiply(inverse(least_upper_bound(X_69,identity)),multiply(least_upper_bound(X_69,identity),inverse(X_69)))
| inverse(X_69) = multiply(inverse(least_upper_bound(X_69,identity)),least_upper_bound(identity,inverse(X_69))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_69,identity),inverse(X_69)),least_upper_bound(identity,inverse(X_69))) )],[refute_0_1610,refute_0_1611]) ).
cnf(refute_0_1613,plain,
inverse(X_69) = multiply(inverse(least_upper_bound(X_69,identity)),least_upper_bound(identity,inverse(X_69))),
inference(resolve,[$cnf( $equal(inverse(X_69),multiply(inverse(least_upper_bound(X_69,identity)),multiply(least_upper_bound(X_69,identity),inverse(X_69)))) )],[refute_0_1601,refute_0_1612]) ).
cnf(refute_0_1614,plain,
inverse(X_114) = multiply(inverse(least_upper_bound(X_114,identity)),least_upper_bound(identity,inverse(X_114))),
inference(subst,[],[refute_0_1613:[bind(X_69,$fot(X_114))]]) ).
cnf(refute_0_1615,plain,
least_upper_bound(identity,X_114) = least_upper_bound(X_114,identity),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(identity)),bind(Y,$fot(X_114))]]) ).
cnf(refute_0_1616,plain,
( least_upper_bound(identity,X_114) != least_upper_bound(X_114,identity)
| least_upper_bound(X_114,identity) = least_upper_bound(identity,X_114) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(identity,X_114))),bind(Y0,$fot(least_upper_bound(X_114,identity)))]]) ).
cnf(refute_0_1617,plain,
least_upper_bound(X_114,identity) = least_upper_bound(identity,X_114),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,X_114),least_upper_bound(X_114,identity)) )],[refute_0_1615,refute_0_1616]) ).
cnf(refute_0_1618,plain,
( inverse(X_114) != multiply(inverse(least_upper_bound(X_114,identity)),least_upper_bound(identity,inverse(X_114)))
| least_upper_bound(X_114,identity) != least_upper_bound(identity,X_114)
| inverse(X_114) = multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,inverse(X_114))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(X_114),multiply(inverse(least_upper_bound(X_114,identity)),least_upper_bound(identity,inverse(X_114)))) ),[1,0,0],$fot(least_upper_bound(identity,X_114))]]) ).
cnf(refute_0_1619,plain,
( inverse(X_114) != multiply(inverse(least_upper_bound(X_114,identity)),least_upper_bound(identity,inverse(X_114)))
| inverse(X_114) = multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,inverse(X_114))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_114,identity),least_upper_bound(identity,X_114)) )],[refute_0_1617,refute_0_1618]) ).
cnf(refute_0_1620,plain,
inverse(X_114) = multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,inverse(X_114))),
inference(resolve,[$cnf( $equal(inverse(X_114),multiply(inverse(least_upper_bound(X_114,identity)),least_upper_bound(identity,inverse(X_114)))) )],[refute_0_1614,refute_0_1619]) ).
cnf(refute_0_1621,plain,
( inverse(X_114) != multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,inverse(X_114)))
| multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,inverse(X_114))) = inverse(X_114) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(X_114))),bind(Y0,$fot(multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,inverse(X_114)))))]]) ).
cnf(refute_0_1622,plain,
multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,inverse(X_114))) = inverse(X_114),
inference(resolve,[$cnf( $equal(inverse(X_114),multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,inverse(X_114)))) )],[refute_0_1620,refute_0_1621]) ).
cnf(refute_0_1623,plain,
( multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(least_upper_bound(identity,X_114))),least_upper_bound(identity,inverse(X_114))))) != least_upper_bound(inverse(least_upper_bound(identity,X_114)),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,inverse(X_114)))))
| multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,inverse(X_114))) != inverse(X_114)
| multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(least_upper_bound(identity,X_114))),least_upper_bound(identity,inverse(X_114))))) = least_upper_bound(inverse(least_upper_bound(identity,X_114)),greatest_lower_bound(identity,inverse(X_114))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(least_upper_bound(identity,X_114))),least_upper_bound(identity,inverse(X_114))))),least_upper_bound(inverse(least_upper_bound(identity,X_114)),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,inverse(X_114)))))) ),[1,1,1],$fot(inverse(X_114))]]) ).
cnf(refute_0_1624,plain,
( multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(least_upper_bound(identity,X_114))),least_upper_bound(identity,inverse(X_114))))) != least_upper_bound(inverse(least_upper_bound(identity,X_114)),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,inverse(X_114)))))
| multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(least_upper_bound(identity,X_114))),least_upper_bound(identity,inverse(X_114))))) = least_upper_bound(inverse(least_upper_bound(identity,X_114)),greatest_lower_bound(identity,inverse(X_114))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,inverse(X_114))),inverse(X_114)) )],[refute_0_1622,refute_0_1623]) ).
cnf(refute_0_1625,plain,
multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(least_upper_bound(identity,X_114))),least_upper_bound(identity,inverse(X_114))))) = least_upper_bound(inverse(least_upper_bound(identity,X_114)),greatest_lower_bound(identity,inverse(X_114))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(least_upper_bound(identity,X_114))),least_upper_bound(identity,inverse(X_114))))),least_upper_bound(inverse(least_upper_bound(identity,X_114)),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,inverse(X_114)))))) )],[refute_0_1600,refute_0_1624]) ).
cnf(refute_0_1626,plain,
multiply(inverse(least_upper_bound(identity,X_114)),identity) = inverse(least_upper_bound(identity,X_114)),
inference(subst,[],[refute_0_603:[bind(X,$fot(inverse(least_upper_bound(identity,X_114))))]]) ).
cnf(refute_0_1627,plain,
least_upper_bound(identity,greatest_lower_bound(X_114,identity)) = identity,
inference(subst,[],[refute_0_53:[bind(X_12,$fot(identity)),bind(X_13,$fot(X_114))]]) ).
cnf(refute_0_1628,plain,
multiply(least_upper_bound(identity,greatest_lower_bound(X_114,identity)),identity) = least_upper_bound(identity,greatest_lower_bound(X_114,identity)),
inference(subst,[],[refute_0_603:[bind(X,$fot(least_upper_bound(identity,greatest_lower_bound(X_114,identity))))]]) ).
cnf(refute_0_1629,plain,
( multiply(least_upper_bound(identity,greatest_lower_bound(X_114,identity)),identity) != least_upper_bound(identity,greatest_lower_bound(X_114,identity))
| least_upper_bound(identity,greatest_lower_bound(X_114,identity)) != identity
| multiply(least_upper_bound(identity,greatest_lower_bound(X_114,identity)),identity) = identity ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(multiply(least_upper_bound(identity,greatest_lower_bound(X_114,identity)),identity))),bind(Y0,$fot(least_upper_bound(identity,greatest_lower_bound(X_114,identity)))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_1630,plain,
( least_upper_bound(identity,greatest_lower_bound(X_114,identity)) != identity
| multiply(least_upper_bound(identity,greatest_lower_bound(X_114,identity)),identity) = identity ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(X_114,identity)),identity),least_upper_bound(identity,greatest_lower_bound(X_114,identity))) )],[refute_0_1628,refute_0_1629]) ).
cnf(refute_0_1631,plain,
multiply(least_upper_bound(identity,greatest_lower_bound(X_114,identity)),identity) = identity,
inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(X_114,identity)),identity) )],[refute_0_1627,refute_0_1630]) ).
cnf(refute_0_1632,plain,
X_141 = multiply(least_upper_bound(identity,X_122),multiply(inverse(least_upper_bound(identity,X_122)),X_141)),
inference(subst,[],[refute_0_419:[bind(X_92,$fot(least_upper_bound(identity,X_122))),bind(X_94,$fot(X_141))]]) ).
cnf(refute_0_1633,plain,
( X_141 != multiply(least_upper_bound(identity,X_122),multiply(inverse(least_upper_bound(identity,X_122)),X_141))
| inverse(least_upper_bound(identity,X_122)) != inverse(least_upper_bound(X_122,identity))
| X_141 = multiply(least_upper_bound(identity,X_122),multiply(inverse(least_upper_bound(X_122,identity)),X_141)) ),
introduced(tautology,[equality,[$cnf( $equal(X_141,multiply(least_upper_bound(identity,X_122),multiply(inverse(least_upper_bound(identity,X_122)),X_141))) ),[1,1,0],$fot(inverse(least_upper_bound(X_122,identity)))]]) ).
cnf(refute_0_1634,plain,
( X_141 != multiply(least_upper_bound(identity,X_122),multiply(inverse(least_upper_bound(identity,X_122)),X_141))
| X_141 = multiply(least_upper_bound(identity,X_122),multiply(inverse(least_upper_bound(X_122,identity)),X_141)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,X_122)),inverse(least_upper_bound(X_122,identity))) )],[refute_0_1248,refute_0_1633]) ).
cnf(refute_0_1635,plain,
X_141 = multiply(least_upper_bound(identity,X_122),multiply(inverse(least_upper_bound(X_122,identity)),X_141)),
inference(resolve,[$cnf( $equal(X_141,multiply(least_upper_bound(identity,X_122),multiply(inverse(least_upper_bound(identity,X_122)),X_141))) )],[refute_0_1632,refute_0_1634]) ).
cnf(refute_0_1636,plain,
multiply(inverse(inverse(least_upper_bound(X_180,identity))),X_94) = multiply(least_upper_bound(identity,X_180),multiply(inverse(least_upper_bound(X_180,identity)),multiply(inverse(inverse(least_upper_bound(X_180,identity))),X_94))),
inference(subst,[],[refute_0_1635:[bind(X_122,$fot(X_180)),bind(X_141,$fot(multiply(inverse(inverse(least_upper_bound(X_180,identity))),X_94)))]]) ).
cnf(refute_0_1637,plain,
X_94 = multiply(inverse(least_upper_bound(X_180,identity)),multiply(inverse(inverse(least_upper_bound(X_180,identity))),X_94)),
inference(subst,[],[refute_0_419:[bind(X_92,$fot(inverse(least_upper_bound(X_180,identity))))]]) ).
cnf(refute_0_1638,plain,
( X_94 != multiply(inverse(least_upper_bound(X_180,identity)),multiply(inverse(inverse(least_upper_bound(X_180,identity))),X_94))
| multiply(inverse(least_upper_bound(X_180,identity)),multiply(inverse(inverse(least_upper_bound(X_180,identity))),X_94)) = X_94 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_94)),bind(Y0,$fot(multiply(inverse(least_upper_bound(X_180,identity)),multiply(inverse(inverse(least_upper_bound(X_180,identity))),X_94))))]]) ).
cnf(refute_0_1639,plain,
multiply(inverse(least_upper_bound(X_180,identity)),multiply(inverse(inverse(least_upper_bound(X_180,identity))),X_94)) = X_94,
inference(resolve,[$cnf( $equal(X_94,multiply(inverse(least_upper_bound(X_180,identity)),multiply(inverse(inverse(least_upper_bound(X_180,identity))),X_94))) )],[refute_0_1637,refute_0_1638]) ).
cnf(refute_0_1640,plain,
( multiply(inverse(inverse(least_upper_bound(X_180,identity))),X_94) != multiply(least_upper_bound(identity,X_180),multiply(inverse(least_upper_bound(X_180,identity)),multiply(inverse(inverse(least_upper_bound(X_180,identity))),X_94)))
| multiply(inverse(least_upper_bound(X_180,identity)),multiply(inverse(inverse(least_upper_bound(X_180,identity))),X_94)) != X_94
| multiply(inverse(inverse(least_upper_bound(X_180,identity))),X_94) = multiply(least_upper_bound(identity,X_180),X_94) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(X_180,identity))),X_94),multiply(least_upper_bound(identity,X_180),multiply(inverse(least_upper_bound(X_180,identity)),multiply(inverse(inverse(least_upper_bound(X_180,identity))),X_94)))) ),[1,1],$fot(X_94)]]) ).
cnf(refute_0_1641,plain,
( multiply(inverse(inverse(least_upper_bound(X_180,identity))),X_94) != multiply(least_upper_bound(identity,X_180),multiply(inverse(least_upper_bound(X_180,identity)),multiply(inverse(inverse(least_upper_bound(X_180,identity))),X_94)))
| multiply(inverse(inverse(least_upper_bound(X_180,identity))),X_94) = multiply(least_upper_bound(identity,X_180),X_94) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_180,identity)),multiply(inverse(inverse(least_upper_bound(X_180,identity))),X_94)),X_94) )],[refute_0_1639,refute_0_1640]) ).
cnf(refute_0_1642,plain,
multiply(inverse(inverse(least_upper_bound(X_180,identity))),X_94) = multiply(least_upper_bound(identity,X_180),X_94),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(X_180,identity))),X_94),multiply(least_upper_bound(identity,X_180),multiply(inverse(least_upper_bound(X_180,identity)),multiply(inverse(inverse(least_upper_bound(X_180,identity))),X_94)))) )],[refute_0_1636,refute_0_1641]) ).
cnf(refute_0_1643,plain,
inverse(inverse(least_upper_bound(X_180,identity))) = least_upper_bound(X_180,identity),
inference(subst,[],[p18_2:[bind(X,$fot(least_upper_bound(X_180,identity)))]]) ).
cnf(refute_0_1644,plain,
multiply(inverse(inverse(least_upper_bound(X_180,identity))),X_94) = multiply(inverse(inverse(least_upper_bound(X_180,identity))),X_94),
introduced(tautology,[refl,[$fot(multiply(inverse(inverse(least_upper_bound(X_180,identity))),X_94))]]) ).
cnf(refute_0_1645,plain,
( multiply(inverse(inverse(least_upper_bound(X_180,identity))),X_94) != multiply(inverse(inverse(least_upper_bound(X_180,identity))),X_94)
| inverse(inverse(least_upper_bound(X_180,identity))) != least_upper_bound(X_180,identity)
| multiply(inverse(inverse(least_upper_bound(X_180,identity))),X_94) = multiply(least_upper_bound(X_180,identity),X_94) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(X_180,identity))),X_94),multiply(inverse(inverse(least_upper_bound(X_180,identity))),X_94)) ),[1,0],$fot(least_upper_bound(X_180,identity))]]) ).
cnf(refute_0_1646,plain,
( inverse(inverse(least_upper_bound(X_180,identity))) != least_upper_bound(X_180,identity)
| multiply(inverse(inverse(least_upper_bound(X_180,identity))),X_94) = multiply(least_upper_bound(X_180,identity),X_94) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(X_180,identity))),X_94),multiply(inverse(inverse(least_upper_bound(X_180,identity))),X_94)) )],[refute_0_1644,refute_0_1645]) ).
cnf(refute_0_1647,plain,
multiply(inverse(inverse(least_upper_bound(X_180,identity))),X_94) = multiply(least_upper_bound(X_180,identity),X_94),
inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(X_180,identity))),least_upper_bound(X_180,identity)) )],[refute_0_1643,refute_0_1646]) ).
cnf(refute_0_1648,plain,
( multiply(inverse(inverse(least_upper_bound(X_180,identity))),X_94) != multiply(least_upper_bound(X_180,identity),X_94)
| multiply(inverse(inverse(least_upper_bound(X_180,identity))),X_94) != multiply(least_upper_bound(identity,X_180),X_94)
| multiply(least_upper_bound(X_180,identity),X_94) = multiply(least_upper_bound(identity,X_180),X_94) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(X_180,identity))),X_94),multiply(least_upper_bound(identity,X_180),X_94)) ),[0],$fot(multiply(least_upper_bound(X_180,identity),X_94))]]) ).
cnf(refute_0_1649,plain,
( multiply(inverse(inverse(least_upper_bound(X_180,identity))),X_94) != multiply(least_upper_bound(identity,X_180),X_94)
| multiply(least_upper_bound(X_180,identity),X_94) = multiply(least_upper_bound(identity,X_180),X_94) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(X_180,identity))),X_94),multiply(least_upper_bound(X_180,identity),X_94)) )],[refute_0_1647,refute_0_1648]) ).
cnf(refute_0_1650,plain,
multiply(least_upper_bound(X_180,identity),X_94) = multiply(least_upper_bound(identity,X_180),X_94),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(X_180,identity))),X_94),multiply(least_upper_bound(identity,X_180),X_94)) )],[refute_0_1642,refute_0_1649]) ).
cnf(refute_0_1651,plain,
multiply(least_upper_bound(greatest_lower_bound(X_114,identity),identity),identity) = multiply(least_upper_bound(identity,greatest_lower_bound(X_114,identity)),identity),
inference(subst,[],[refute_0_1650:[bind(X_180,$fot(greatest_lower_bound(X_114,identity))),bind(X_94,$fot(identity))]]) ).
cnf(refute_0_1652,plain,
( multiply(least_upper_bound(greatest_lower_bound(X_114,identity),identity),identity) != multiply(least_upper_bound(identity,greatest_lower_bound(X_114,identity)),identity)
| multiply(least_upper_bound(identity,greatest_lower_bound(X_114,identity)),identity) != identity
| multiply(least_upper_bound(greatest_lower_bound(X_114,identity),identity),identity) = identity ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(multiply(least_upper_bound(greatest_lower_bound(X_114,identity),identity),identity))),bind(Y0,$fot(multiply(least_upper_bound(identity,greatest_lower_bound(X_114,identity)),identity))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_1653,plain,
( multiply(least_upper_bound(identity,greatest_lower_bound(X_114,identity)),identity) != identity
| multiply(least_upper_bound(greatest_lower_bound(X_114,identity),identity),identity) = identity ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(X_114,identity),identity),identity),multiply(least_upper_bound(identity,greatest_lower_bound(X_114,identity)),identity)) )],[refute_0_1651,refute_0_1652]) ).
cnf(refute_0_1654,plain,
multiply(least_upper_bound(greatest_lower_bound(X_114,identity),identity),identity) = identity,
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(X_114,identity)),identity),identity) )],[refute_0_1631,refute_0_1653]) ).
cnf(refute_0_1655,plain,
least_upper_bound(identity,multiply(greatest_lower_bound(X_114,identity),identity)) = multiply(least_upper_bound(greatest_lower_bound(X_114,identity),identity),identity),
inference(subst,[],[refute_0_706:[bind(X_65,$fot(identity)),bind(X_66,$fot(greatest_lower_bound(X_114,identity)))]]) ).
cnf(refute_0_1656,plain,
( multiply(least_upper_bound(greatest_lower_bound(X_114,identity),identity),identity) != identity
| least_upper_bound(identity,multiply(greatest_lower_bound(X_114,identity),identity)) != multiply(least_upper_bound(greatest_lower_bound(X_114,identity),identity),identity)
| least_upper_bound(identity,multiply(greatest_lower_bound(X_114,identity),identity)) = identity ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(least_upper_bound(identity,multiply(greatest_lower_bound(X_114,identity),identity)))),bind(Y0,$fot(multiply(least_upper_bound(greatest_lower_bound(X_114,identity),identity),identity))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_1657,plain,
( multiply(least_upper_bound(greatest_lower_bound(X_114,identity),identity),identity) != identity
| least_upper_bound(identity,multiply(greatest_lower_bound(X_114,identity),identity)) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(greatest_lower_bound(X_114,identity),identity)),multiply(least_upper_bound(greatest_lower_bound(X_114,identity),identity),identity)) )],[refute_0_1655,refute_0_1656]) ).
cnf(refute_0_1658,plain,
least_upper_bound(identity,multiply(greatest_lower_bound(X_114,identity),identity)) = identity,
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(X_114,identity),identity),identity),identity) )],[refute_0_1654,refute_0_1657]) ).
cnf(refute_0_1659,plain,
multiply(inverse(X_55),least_upper_bound(X_54,X_55)) = least_upper_bound(multiply(inverse(X_55),X_54),multiply(inverse(X_55),X_55)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(inverse(X_55))),bind(Y,$fot(X_54)),bind(Z,$fot(X_55))]]) ).
cnf(refute_0_1660,plain,
multiply(inverse(X_55),X_55) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_55))]]) ).
cnf(refute_0_1661,plain,
( multiply(inverse(X_55),X_55) != identity
| multiply(inverse(X_55),least_upper_bound(X_54,X_55)) != least_upper_bound(multiply(inverse(X_55),X_54),multiply(inverse(X_55),X_55))
| multiply(inverse(X_55),least_upper_bound(X_54,X_55)) = least_upper_bound(multiply(inverse(X_55),X_54),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_55),least_upper_bound(X_54,X_55)),least_upper_bound(multiply(inverse(X_55),X_54),multiply(inverse(X_55),X_55))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_1662,plain,
( multiply(inverse(X_55),least_upper_bound(X_54,X_55)) != least_upper_bound(multiply(inverse(X_55),X_54),multiply(inverse(X_55),X_55))
| multiply(inverse(X_55),least_upper_bound(X_54,X_55)) = least_upper_bound(multiply(inverse(X_55),X_54),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_55),X_55),identity) )],[refute_0_1660,refute_0_1661]) ).
cnf(refute_0_1663,plain,
multiply(inverse(X_55),least_upper_bound(X_54,X_55)) = least_upper_bound(multiply(inverse(X_55),X_54),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_55),least_upper_bound(X_54,X_55)),least_upper_bound(multiply(inverse(X_55),X_54),multiply(inverse(X_55),X_55))) )],[refute_0_1659,refute_0_1662]) ).
cnf(refute_0_1664,plain,
least_upper_bound(multiply(inverse(X_55),X_54),identity) = least_upper_bound(identity,multiply(inverse(X_55),X_54)),
inference(subst,[],[refute_0_4:[bind(X,$fot(identity)),bind(Y,$fot(multiply(inverse(X_55),X_54)))]]) ).
cnf(refute_0_1665,plain,
( multiply(inverse(X_55),least_upper_bound(X_54,X_55)) != least_upper_bound(multiply(inverse(X_55),X_54),identity)
| least_upper_bound(multiply(inverse(X_55),X_54),identity) != least_upper_bound(identity,multiply(inverse(X_55),X_54))
| multiply(inverse(X_55),least_upper_bound(X_54,X_55)) = least_upper_bound(identity,multiply(inverse(X_55),X_54)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_55),least_upper_bound(X_54,X_55)),least_upper_bound(identity,multiply(inverse(X_55),X_54))) ),[0],$fot(least_upper_bound(multiply(inverse(X_55),X_54),identity))]]) ).
cnf(refute_0_1666,plain,
( multiply(inverse(X_55),least_upper_bound(X_54,X_55)) != least_upper_bound(multiply(inverse(X_55),X_54),identity)
| multiply(inverse(X_55),least_upper_bound(X_54,X_55)) = least_upper_bound(identity,multiply(inverse(X_55),X_54)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(X_55),X_54),identity),least_upper_bound(identity,multiply(inverse(X_55),X_54))) )],[refute_0_1664,refute_0_1665]) ).
cnf(refute_0_1667,plain,
multiply(inverse(X_55),least_upper_bound(X_54,X_55)) = least_upper_bound(identity,multiply(inverse(X_55),X_54)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_55),least_upper_bound(X_54,X_55)),least_upper_bound(multiply(inverse(X_55),X_54),identity)) )],[refute_0_1663,refute_0_1666]) ).
cnf(refute_0_1668,plain,
multiply(inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))),least_upper_bound(X_54,least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283))))) = least_upper_bound(identity,multiply(inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))),X_54)),
inference(subst,[],[refute_0_1667:[bind(X_55,$fot(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))))]]) ).
cnf(refute_0_1669,plain,
X_94 = multiply(inverse(least_upper_bound(inverse(X_94),X_173)),multiply(least_upper_bound(inverse(X_94),X_173),X_94)),
inference(subst,[],[refute_0_17:[bind(X_93,$fot(least_upper_bound(inverse(X_94),X_173)))]]) ).
cnf(refute_0_1670,plain,
multiply(least_upper_bound(inverse(X_94),X_173),X_94) = least_upper_bound(identity,multiply(X_173,X_94)),
inference(subst,[],[refute_0_509:[bind(X_65,$fot(X_94)),bind(X_67,$fot(X_173))]]) ).
cnf(refute_0_1671,plain,
( X_94 != multiply(inverse(least_upper_bound(inverse(X_94),X_173)),multiply(least_upper_bound(inverse(X_94),X_173),X_94))
| multiply(least_upper_bound(inverse(X_94),X_173),X_94) != least_upper_bound(identity,multiply(X_173,X_94))
| X_94 = multiply(inverse(least_upper_bound(inverse(X_94),X_173)),least_upper_bound(identity,multiply(X_173,X_94))) ),
introduced(tautology,[equality,[$cnf( $equal(X_94,multiply(inverse(least_upper_bound(inverse(X_94),X_173)),multiply(least_upper_bound(inverse(X_94),X_173),X_94))) ),[1,1],$fot(least_upper_bound(identity,multiply(X_173,X_94)))]]) ).
cnf(refute_0_1672,plain,
( X_94 != multiply(inverse(least_upper_bound(inverse(X_94),X_173)),multiply(least_upper_bound(inverse(X_94),X_173),X_94))
| X_94 = multiply(inverse(least_upper_bound(inverse(X_94),X_173)),least_upper_bound(identity,multiply(X_173,X_94))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_94),X_173),X_94),least_upper_bound(identity,multiply(X_173,X_94))) )],[refute_0_1670,refute_0_1671]) ).
cnf(refute_0_1673,plain,
X_94 = multiply(inverse(least_upper_bound(inverse(X_94),X_173)),least_upper_bound(identity,multiply(X_173,X_94))),
inference(resolve,[$cnf( $equal(X_94,multiply(inverse(least_upper_bound(inverse(X_94),X_173)),multiply(least_upper_bound(inverse(X_94),X_173),X_94))) )],[refute_0_1669,refute_0_1672]) ).
cnf(refute_0_1674,plain,
greatest_lower_bound(X_256,X_257) = multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_256,X_257)),inverse(X_256))),least_upper_bound(identity,multiply(inverse(X_256),greatest_lower_bound(X_256,X_257)))),
inference(subst,[],[refute_0_1673:[bind(X_173,$fot(inverse(X_256))),bind(X_94,$fot(greatest_lower_bound(X_256,X_257)))]]) ).
cnf(refute_0_1675,plain,
multiply(inverse(X),greatest_lower_bound(inverse(inverse(X)),X_42)) = greatest_lower_bound(identity,multiply(inverse(X),X_42)),
inference(subst,[],[refute_0_757:[bind(X_36,$fot(inverse(X))),bind(X_38,$fot(X_42))]]) ).
cnf(refute_0_1676,plain,
( multiply(inverse(X),greatest_lower_bound(inverse(inverse(X)),X_42)) != greatest_lower_bound(identity,multiply(inverse(X),X_42))
| inverse(inverse(X)) != X
| multiply(inverse(X),greatest_lower_bound(X,X_42)) = greatest_lower_bound(identity,multiply(inverse(X),X_42)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X),greatest_lower_bound(inverse(inverse(X)),X_42)),greatest_lower_bound(identity,multiply(inverse(X),X_42))) ),[0,1,0],$fot(X)]]) ).
cnf(refute_0_1677,plain,
( multiply(inverse(X),greatest_lower_bound(inverse(inverse(X)),X_42)) != greatest_lower_bound(identity,multiply(inverse(X),X_42))
| multiply(inverse(X),greatest_lower_bound(X,X_42)) = greatest_lower_bound(identity,multiply(inverse(X),X_42)) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p18_2,refute_0_1676]) ).
cnf(refute_0_1678,plain,
multiply(inverse(X),greatest_lower_bound(X,X_42)) = greatest_lower_bound(identity,multiply(inverse(X),X_42)),
inference(resolve,[$cnf( $equal(multiply(inverse(X),greatest_lower_bound(inverse(inverse(X)),X_42)),greatest_lower_bound(identity,multiply(inverse(X),X_42))) )],[refute_0_1675,refute_0_1677]) ).
cnf(refute_0_1679,plain,
multiply(inverse(X_256),greatest_lower_bound(X_256,X_257)) = greatest_lower_bound(identity,multiply(inverse(X_256),X_257)),
inference(subst,[],[refute_0_1678:[bind(X,$fot(X_256)),bind(X_42,$fot(X_257))]]) ).
cnf(refute_0_1680,plain,
( multiply(inverse(X_256),greatest_lower_bound(X_256,X_257)) != greatest_lower_bound(identity,multiply(inverse(X_256),X_257))
| greatest_lower_bound(X_256,X_257) != multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_256,X_257)),inverse(X_256))),least_upper_bound(identity,multiply(inverse(X_256),greatest_lower_bound(X_256,X_257))))
| greatest_lower_bound(X_256,X_257) = multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_256,X_257)),inverse(X_256))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257)))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_256,X_257),multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_256,X_257)),inverse(X_256))),least_upper_bound(identity,multiply(inverse(X_256),greatest_lower_bound(X_256,X_257))))) ),[1,1,1],$fot(greatest_lower_bound(identity,multiply(inverse(X_256),X_257)))]]) ).
cnf(refute_0_1681,plain,
( greatest_lower_bound(X_256,X_257) != multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_256,X_257)),inverse(X_256))),least_upper_bound(identity,multiply(inverse(X_256),greatest_lower_bound(X_256,X_257))))
| greatest_lower_bound(X_256,X_257) = multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_256,X_257)),inverse(X_256))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_256),greatest_lower_bound(X_256,X_257)),greatest_lower_bound(identity,multiply(inverse(X_256),X_257))) )],[refute_0_1679,refute_0_1680]) ).
cnf(refute_0_1682,plain,
greatest_lower_bound(X_256,X_257) = multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_256,X_257)),inverse(X_256))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257)))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_256,X_257),multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_256,X_257)),inverse(X_256))),least_upper_bound(identity,multiply(inverse(X_256),greatest_lower_bound(X_256,X_257))))) )],[refute_0_1674,refute_0_1681]) ).
cnf(refute_0_1683,plain,
multiply(inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257)))),identity) = inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257)))),
inference(subst,[],[refute_0_603:[bind(X,$fot(inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257))))))]]) ).
cnf(refute_0_1684,plain,
least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257))) = identity,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(identity)),bind(Y,$fot(multiply(inverse(X_256),X_257)))]]) ).
cnf(refute_0_1685,plain,
multiply(inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257)))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257)))) = multiply(inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257)))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257)))),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257)))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257)))))]]) ).
cnf(refute_0_1686,plain,
( multiply(inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257)))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257)))) != multiply(inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257)))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257))))
| least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257))) != identity
| multiply(inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257)))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257)))) = multiply(inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257)))),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257)))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257)))),multiply(inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257)))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_1687,plain,
( least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257))) != identity
| multiply(inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257)))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257)))) = multiply(inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257)))),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257)))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257)))),multiply(inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257)))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257))))) )],[refute_0_1685,refute_0_1686]) ).
cnf(refute_0_1688,plain,
multiply(inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257)))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257)))) = multiply(inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257)))),identity),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257))),identity) )],[refute_0_1684,refute_0_1687]) ).
cnf(refute_0_1689,plain,
least_upper_bound(inverse(greatest_lower_bound(X_256,X_257)),inverse(X_256)) = least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257))),
inference(subst,[],[refute_0_4:[bind(X,$fot(inverse(X_256))),bind(Y,$fot(inverse(greatest_lower_bound(X_256,X_257))))]]) ).
cnf(refute_0_1690,plain,
inverse(least_upper_bound(inverse(greatest_lower_bound(X_256,X_257)),inverse(X_256))) = inverse(least_upper_bound(inverse(greatest_lower_bound(X_256,X_257)),inverse(X_256))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(inverse(greatest_lower_bound(X_256,X_257)),inverse(X_256))))]]) ).
cnf(refute_0_1691,plain,
( inverse(least_upper_bound(inverse(greatest_lower_bound(X_256,X_257)),inverse(X_256))) != inverse(least_upper_bound(inverse(greatest_lower_bound(X_256,X_257)),inverse(X_256)))
| least_upper_bound(inverse(greatest_lower_bound(X_256,X_257)),inverse(X_256)) != least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257)))
| inverse(least_upper_bound(inverse(greatest_lower_bound(X_256,X_257)),inverse(X_256))) = inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(inverse(greatest_lower_bound(X_256,X_257)),inverse(X_256))),inverse(least_upper_bound(inverse(greatest_lower_bound(X_256,X_257)),inverse(X_256)))) ),[1,0],$fot(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257))))]]) ).
cnf(refute_0_1692,plain,
( least_upper_bound(inverse(greatest_lower_bound(X_256,X_257)),inverse(X_256)) != least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257)))
| inverse(least_upper_bound(inverse(greatest_lower_bound(X_256,X_257)),inverse(X_256))) = inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257)))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(greatest_lower_bound(X_256,X_257)),inverse(X_256))),inverse(least_upper_bound(inverse(greatest_lower_bound(X_256,X_257)),inverse(X_256)))) )],[refute_0_1690,refute_0_1691]) ).
cnf(refute_0_1693,plain,
inverse(least_upper_bound(inverse(greatest_lower_bound(X_256,X_257)),inverse(X_256))) = inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257)))),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(X_256,X_257)),inverse(X_256)),least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257)))) )],[refute_0_1689,refute_0_1692]) ).
cnf(refute_0_1694,plain,
multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_256,X_257)),inverse(X_256))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257)))) = multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_256,X_257)),inverse(X_256))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257)))),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_256,X_257)),inverse(X_256))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257)))))]]) ).
cnf(refute_0_1695,plain,
( multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_256,X_257)),inverse(X_256))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257)))) != multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_256,X_257)),inverse(X_256))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257))))
| inverse(least_upper_bound(inverse(greatest_lower_bound(X_256,X_257)),inverse(X_256))) != inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257))))
| multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_256,X_257)),inverse(X_256))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257)))) = multiply(inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257)))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_256,X_257)),inverse(X_256))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257)))),multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_256,X_257)),inverse(X_256))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257))))) ),[1,0],$fot(inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257)))))]]) ).
cnf(refute_0_1696,plain,
( inverse(least_upper_bound(inverse(greatest_lower_bound(X_256,X_257)),inverse(X_256))) != inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257))))
| multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_256,X_257)),inverse(X_256))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257)))) = multiply(inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257)))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_256,X_257)),inverse(X_256))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257)))),multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_256,X_257)),inverse(X_256))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257))))) )],[refute_0_1694,refute_0_1695]) ).
cnf(refute_0_1697,plain,
multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_256,X_257)),inverse(X_256))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257)))) = multiply(inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257)))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257)))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(greatest_lower_bound(X_256,X_257)),inverse(X_256))),inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257))))) )],[refute_0_1693,refute_0_1696]) ).
cnf(refute_0_1698,plain,
( multiply(inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257)))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257)))) != multiply(inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257)))),identity)
| multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_256,X_257)),inverse(X_256))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257)))) != multiply(inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257)))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257))))
| multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_256,X_257)),inverse(X_256))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257)))) = multiply(inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257)))),identity) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_256,X_257)),inverse(X_256))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257)))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257)))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257)))))),bind(Z0,$fot(multiply(inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257)))),identity)))]]) ).
cnf(refute_0_1699,plain,
( multiply(inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257)))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257)))) != multiply(inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257)))),identity)
| multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_256,X_257)),inverse(X_256))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257)))) = multiply(inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257)))),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_256,X_257)),inverse(X_256))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257)))),multiply(inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257)))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257))))) )],[refute_0_1697,refute_0_1698]) ).
cnf(refute_0_1700,plain,
multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_256,X_257)),inverse(X_256))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257)))) = multiply(inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257)))),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257)))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257)))),multiply(inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257)))),identity)) )],[refute_0_1688,refute_0_1699]) ).
cnf(refute_0_1701,plain,
( multiply(inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257)))),identity) != inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257))))
| multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_256,X_257)),inverse(X_256))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257)))) != multiply(inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257)))),identity)
| multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_256,X_257)),inverse(X_256))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257)))) = inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257)))) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_256,X_257)),inverse(X_256))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257)))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257)))),identity))),bind(Z0,$fot(inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257))))))]]) ).
cnf(refute_0_1702,plain,
( multiply(inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257)))),identity) != inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257))))
| multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_256,X_257)),inverse(X_256))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257)))) = inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_256,X_257)),inverse(X_256))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257)))),multiply(inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257)))),identity)) )],[refute_0_1700,refute_0_1701]) ).
cnf(refute_0_1703,plain,
multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_256,X_257)),inverse(X_256))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257)))) = inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257)))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257)))),identity),inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257))))) )],[refute_0_1683,refute_0_1702]) ).
cnf(refute_0_1704,plain,
( multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_256,X_257)),inverse(X_256))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257)))) != inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257))))
| greatest_lower_bound(X_256,X_257) != multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_256,X_257)),inverse(X_256))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257))))
| greatest_lower_bound(X_256,X_257) = inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257)))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_256,X_257),multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_256,X_257)),inverse(X_256))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257))))) ),[1],$fot(inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257)))))]]) ).
cnf(refute_0_1705,plain,
( greatest_lower_bound(X_256,X_257) != multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_256,X_257)),inverse(X_256))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257))))
| greatest_lower_bound(X_256,X_257) = inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_256,X_257)),inverse(X_256))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257)))),inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257))))) )],[refute_0_1703,refute_0_1704]) ).
cnf(refute_0_1706,plain,
greatest_lower_bound(X_256,X_257) = inverse(least_upper_bound(inverse(X_256),inverse(greatest_lower_bound(X_256,X_257)))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_256,X_257),multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_256,X_257)),inverse(X_256))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_256),X_257))))) )],[refute_0_1682,refute_0_1705]) ).
cnf(refute_0_1707,plain,
greatest_lower_bound(X_282,X_283) = inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))),
inference(subst,[],[refute_0_1706:[bind(X_256,$fot(X_282)),bind(X_257,$fot(X_283))]]) ).
cnf(refute_0_1708,plain,
( greatest_lower_bound(X_282,X_283) != inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283))))
| inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))) = greatest_lower_bound(X_282,X_283) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X_282,X_283))),bind(Y0,$fot(inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283))))))]]) ).
cnf(refute_0_1709,plain,
inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))) = greatest_lower_bound(X_282,X_283),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_282,X_283),inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283))))) )],[refute_0_1707,refute_0_1708]) ).
cnf(refute_0_1710,plain,
( multiply(inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))),least_upper_bound(X_54,least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283))))) != least_upper_bound(identity,multiply(inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))),X_54))
| inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))) != greatest_lower_bound(X_282,X_283)
| multiply(greatest_lower_bound(X_282,X_283),least_upper_bound(X_54,least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283))))) = least_upper_bound(identity,multiply(inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))),X_54)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))),least_upper_bound(X_54,least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283))))),least_upper_bound(identity,multiply(inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))),X_54))) ),[0,0],$fot(greatest_lower_bound(X_282,X_283))]]) ).
cnf(refute_0_1711,plain,
( multiply(inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))),least_upper_bound(X_54,least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283))))) != least_upper_bound(identity,multiply(inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))),X_54))
| multiply(greatest_lower_bound(X_282,X_283),least_upper_bound(X_54,least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283))))) = least_upper_bound(identity,multiply(inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))),X_54)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))),greatest_lower_bound(X_282,X_283)) )],[refute_0_1709,refute_0_1710]) ).
cnf(refute_0_1712,plain,
multiply(greatest_lower_bound(X_282,X_283),least_upper_bound(X_54,least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283))))) = least_upper_bound(identity,multiply(inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))),X_54)),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))),least_upper_bound(X_54,least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283))))),least_upper_bound(identity,multiply(inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))),X_54))) )],[refute_0_1668,refute_0_1711]) ).
cnf(refute_0_1713,plain,
multiply(X,least_upper_bound(Y,least_upper_bound(X_60,inverse(X)))) = least_upper_bound(multiply(X,Y),multiply(X,least_upper_bound(X_60,inverse(X)))),
inference(subst,[],[monotony_lub1:[bind(Z,$fot(least_upper_bound(X_60,inverse(X))))]]) ).
cnf(refute_0_1714,plain,
multiply(X_53,least_upper_bound(X_54,inverse(X_53))) = least_upper_bound(multiply(X_53,X_54),multiply(X_53,inverse(X_53))),
inference(subst,[],[monotony_lub1:[bind(X,$fot(X_53)),bind(Y,$fot(X_54)),bind(Z,$fot(inverse(X_53)))]]) ).
cnf(refute_0_1715,plain,
( multiply(X_53,inverse(X_53)) != identity
| multiply(X_53,least_upper_bound(X_54,inverse(X_53))) != least_upper_bound(multiply(X_53,X_54),multiply(X_53,inverse(X_53)))
| multiply(X_53,least_upper_bound(X_54,inverse(X_53))) = least_upper_bound(multiply(X_53,X_54),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_53,least_upper_bound(X_54,inverse(X_53))),least_upper_bound(multiply(X_53,X_54),multiply(X_53,inverse(X_53)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_1716,plain,
( multiply(X_53,least_upper_bound(X_54,inverse(X_53))) != least_upper_bound(multiply(X_53,X_54),multiply(X_53,inverse(X_53)))
| multiply(X_53,least_upper_bound(X_54,inverse(X_53))) = least_upper_bound(multiply(X_53,X_54),identity) ),
inference(resolve,[$cnf( $equal(multiply(X_53,inverse(X_53)),identity) )],[refute_0_1164,refute_0_1715]) ).
cnf(refute_0_1717,plain,
multiply(X_53,least_upper_bound(X_54,inverse(X_53))) = least_upper_bound(multiply(X_53,X_54),identity),
inference(resolve,[$cnf( $equal(multiply(X_53,least_upper_bound(X_54,inverse(X_53))),least_upper_bound(multiply(X_53,X_54),multiply(X_53,inverse(X_53)))) )],[refute_0_1714,refute_0_1716]) ).
cnf(refute_0_1718,plain,
least_upper_bound(multiply(X_53,X_54),identity) = least_upper_bound(identity,multiply(X_53,X_54)),
inference(subst,[],[refute_0_4:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_53,X_54)))]]) ).
cnf(refute_0_1719,plain,
( multiply(X_53,least_upper_bound(X_54,inverse(X_53))) != least_upper_bound(multiply(X_53,X_54),identity)
| least_upper_bound(multiply(X_53,X_54),identity) != least_upper_bound(identity,multiply(X_53,X_54))
| multiply(X_53,least_upper_bound(X_54,inverse(X_53))) = least_upper_bound(identity,multiply(X_53,X_54)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_53,least_upper_bound(X_54,inverse(X_53))),least_upper_bound(identity,multiply(X_53,X_54))) ),[0],$fot(least_upper_bound(multiply(X_53,X_54),identity))]]) ).
cnf(refute_0_1720,plain,
( multiply(X_53,least_upper_bound(X_54,inverse(X_53))) != least_upper_bound(multiply(X_53,X_54),identity)
| multiply(X_53,least_upper_bound(X_54,inverse(X_53))) = least_upper_bound(identity,multiply(X_53,X_54)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_53,X_54),identity),least_upper_bound(identity,multiply(X_53,X_54))) )],[refute_0_1718,refute_0_1719]) ).
cnf(refute_0_1721,plain,
multiply(X_53,least_upper_bound(X_54,inverse(X_53))) = least_upper_bound(identity,multiply(X_53,X_54)),
inference(resolve,[$cnf( $equal(multiply(X_53,least_upper_bound(X_54,inverse(X_53))),least_upper_bound(multiply(X_53,X_54),identity)) )],[refute_0_1717,refute_0_1720]) ).
cnf(refute_0_1722,plain,
multiply(X,least_upper_bound(X_60,inverse(X))) = least_upper_bound(identity,multiply(X,X_60)),
inference(subst,[],[refute_0_1721:[bind(X_53,$fot(X)),bind(X_54,$fot(X_60))]]) ).
cnf(refute_0_1723,plain,
( multiply(X,least_upper_bound(Y,least_upper_bound(X_60,inverse(X)))) != least_upper_bound(multiply(X,Y),multiply(X,least_upper_bound(X_60,inverse(X))))
| multiply(X,least_upper_bound(X_60,inverse(X))) != least_upper_bound(identity,multiply(X,X_60))
| multiply(X,least_upper_bound(Y,least_upper_bound(X_60,inverse(X)))) = least_upper_bound(multiply(X,Y),least_upper_bound(identity,multiply(X,X_60))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X,least_upper_bound(Y,least_upper_bound(X_60,inverse(X)))),least_upper_bound(multiply(X,Y),multiply(X,least_upper_bound(X_60,inverse(X))))) ),[1,1],$fot(least_upper_bound(identity,multiply(X,X_60)))]]) ).
cnf(refute_0_1724,plain,
( multiply(X,least_upper_bound(Y,least_upper_bound(X_60,inverse(X)))) != least_upper_bound(multiply(X,Y),multiply(X,least_upper_bound(X_60,inverse(X))))
| multiply(X,least_upper_bound(Y,least_upper_bound(X_60,inverse(X)))) = least_upper_bound(multiply(X,Y),least_upper_bound(identity,multiply(X,X_60))) ),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(X_60,inverse(X))),least_upper_bound(identity,multiply(X,X_60))) )],[refute_0_1722,refute_0_1723]) ).
cnf(refute_0_1725,plain,
multiply(X,least_upper_bound(Y,least_upper_bound(X_60,inverse(X)))) = least_upper_bound(multiply(X,Y),least_upper_bound(identity,multiply(X,X_60))),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(Y,least_upper_bound(X_60,inverse(X)))),least_upper_bound(multiply(X,Y),multiply(X,least_upper_bound(X_60,inverse(X))))) )],[refute_0_1713,refute_0_1724]) ).
cnf(refute_0_1726,plain,
least_upper_bound(multiply(X,Y),multiply(X,X_60)) = multiply(X,least_upper_bound(Y,X_60)),
inference(subst,[],[refute_0_249:[bind(Z,$fot(X_60))]]) ).
cnf(refute_0_1727,plain,
least_upper_bound(identity,least_upper_bound(multiply(X,Y),multiply(X,X_60))) = least_upper_bound(identity,least_upper_bound(multiply(X,Y),multiply(X,X_60))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,least_upper_bound(multiply(X,Y),multiply(X,X_60))))]]) ).
cnf(refute_0_1728,plain,
( least_upper_bound(multiply(X,Y),multiply(X,X_60)) != multiply(X,least_upper_bound(Y,X_60))
| least_upper_bound(identity,least_upper_bound(multiply(X,Y),multiply(X,X_60))) != least_upper_bound(identity,least_upper_bound(multiply(X,Y),multiply(X,X_60)))
| least_upper_bound(identity,least_upper_bound(multiply(X,Y),multiply(X,X_60))) = least_upper_bound(identity,multiply(X,least_upper_bound(Y,X_60))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(X,Y),multiply(X,X_60))),least_upper_bound(identity,least_upper_bound(multiply(X,Y),multiply(X,X_60)))) ),[1,1],$fot(multiply(X,least_upper_bound(Y,X_60)))]]) ).
cnf(refute_0_1729,plain,
( least_upper_bound(multiply(X,Y),multiply(X,X_60)) != multiply(X,least_upper_bound(Y,X_60))
| least_upper_bound(identity,least_upper_bound(multiply(X,Y),multiply(X,X_60))) = least_upper_bound(identity,multiply(X,least_upper_bound(Y,X_60))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(X,Y),multiply(X,X_60))),least_upper_bound(identity,least_upper_bound(multiply(X,Y),multiply(X,X_60)))) )],[refute_0_1727,refute_0_1728]) ).
cnf(refute_0_1730,plain,
least_upper_bound(identity,least_upper_bound(multiply(X,Y),multiply(X,X_60))) = least_upper_bound(identity,multiply(X,least_upper_bound(Y,X_60))),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,Y),multiply(X,X_60)),multiply(X,least_upper_bound(Y,X_60))) )],[refute_0_1726,refute_0_1729]) ).
cnf(refute_0_1731,plain,
least_upper_bound(X_29,least_upper_bound(least_upper_bound(Y,X_29),X_31)) = least_upper_bound(least_upper_bound(X_29,least_upper_bound(Y,X_29)),X_31),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_29)),bind(Y,$fot(least_upper_bound(Y,X_29))),bind(Z,$fot(X_31))]]) ).
cnf(refute_0_1732,plain,
least_upper_bound(X_29,least_upper_bound(Y,X_29)) = least_upper_bound(X_29,Y),
inference(subst,[],[refute_0_64:[bind(X_21,$fot(X_29))]]) ).
cnf(refute_0_1733,plain,
( least_upper_bound(X_29,least_upper_bound(Y,X_29)) != least_upper_bound(X_29,Y)
| least_upper_bound(X_29,least_upper_bound(least_upper_bound(Y,X_29),X_31)) != least_upper_bound(least_upper_bound(X_29,least_upper_bound(Y,X_29)),X_31)
| least_upper_bound(X_29,least_upper_bound(least_upper_bound(Y,X_29),X_31)) = least_upper_bound(least_upper_bound(X_29,Y),X_31) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_29,least_upper_bound(least_upper_bound(Y,X_29),X_31)),least_upper_bound(least_upper_bound(X_29,least_upper_bound(Y,X_29)),X_31)) ),[1,0],$fot(least_upper_bound(X_29,Y))]]) ).
cnf(refute_0_1734,plain,
( least_upper_bound(X_29,least_upper_bound(least_upper_bound(Y,X_29),X_31)) != least_upper_bound(least_upper_bound(X_29,least_upper_bound(Y,X_29)),X_31)
| least_upper_bound(X_29,least_upper_bound(least_upper_bound(Y,X_29),X_31)) = least_upper_bound(least_upper_bound(X_29,Y),X_31) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_29,least_upper_bound(Y,X_29)),least_upper_bound(X_29,Y)) )],[refute_0_1732,refute_0_1733]) ).
cnf(refute_0_1735,plain,
least_upper_bound(X_29,least_upper_bound(least_upper_bound(Y,X_29),X_31)) = least_upper_bound(least_upper_bound(X_29,Y),X_31),
inference(resolve,[$cnf( $equal(least_upper_bound(X_29,least_upper_bound(least_upper_bound(Y,X_29),X_31)),least_upper_bound(least_upper_bound(X_29,least_upper_bound(Y,X_29)),X_31)) )],[refute_0_1731,refute_0_1734]) ).
cnf(refute_0_1736,plain,
least_upper_bound(X_29,least_upper_bound(X_30,least_upper_bound(Y,X_30))) = least_upper_bound(least_upper_bound(X_29,X_30),least_upper_bound(Y,X_30)),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_29)),bind(Y,$fot(X_30)),bind(Z,$fot(least_upper_bound(Y,X_30)))]]) ).
cnf(refute_0_1737,plain,
least_upper_bound(X_30,least_upper_bound(Y,X_30)) = least_upper_bound(X_30,Y),
inference(subst,[],[refute_0_64:[bind(X_21,$fot(X_30))]]) ).
cnf(refute_0_1738,plain,
( least_upper_bound(X_29,least_upper_bound(X_30,least_upper_bound(Y,X_30))) != least_upper_bound(least_upper_bound(X_29,X_30),least_upper_bound(Y,X_30))
| least_upper_bound(X_30,least_upper_bound(Y,X_30)) != least_upper_bound(X_30,Y)
| least_upper_bound(X_29,least_upper_bound(X_30,Y)) = least_upper_bound(least_upper_bound(X_29,X_30),least_upper_bound(Y,X_30)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_29,least_upper_bound(X_30,least_upper_bound(Y,X_30))),least_upper_bound(least_upper_bound(X_29,X_30),least_upper_bound(Y,X_30))) ),[0,1],$fot(least_upper_bound(X_30,Y))]]) ).
cnf(refute_0_1739,plain,
( least_upper_bound(X_29,least_upper_bound(X_30,least_upper_bound(Y,X_30))) != least_upper_bound(least_upper_bound(X_29,X_30),least_upper_bound(Y,X_30))
| least_upper_bound(X_29,least_upper_bound(X_30,Y)) = least_upper_bound(least_upper_bound(X_29,X_30),least_upper_bound(Y,X_30)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_30,least_upper_bound(Y,X_30)),least_upper_bound(X_30,Y)) )],[refute_0_1737,refute_0_1738]) ).
cnf(refute_0_1740,plain,
least_upper_bound(X_29,least_upper_bound(X_30,Y)) = least_upper_bound(least_upper_bound(X_29,X_30),least_upper_bound(Y,X_30)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_29,least_upper_bound(X_30,least_upper_bound(Y,X_30))),least_upper_bound(least_upper_bound(X_29,X_30),least_upper_bound(Y,X_30))) )],[refute_0_1736,refute_0_1739]) ).
cnf(refute_0_1741,plain,
least_upper_bound(least_upper_bound(X_29,X_30),Y) = least_upper_bound(X_29,least_upper_bound(X_30,Y)),
inference(subst,[],[refute_0_60:[bind(X,$fot(X_29)),bind(Y,$fot(X_30)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_1742,plain,
least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_29,X_30),Y)) = least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_29,X_30),Y)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_29,X_30),Y)))]]) ).
cnf(refute_0_1743,plain,
( least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_29,X_30),Y)) != least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_29,X_30),Y))
| least_upper_bound(least_upper_bound(X_29,X_30),Y) != least_upper_bound(X_29,least_upper_bound(X_30,Y))
| least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_29,X_30),Y)) = least_upper_bound(X_30,least_upper_bound(X_29,least_upper_bound(X_30,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_29,X_30),Y)),least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_29,X_30),Y))) ),[1,1],$fot(least_upper_bound(X_29,least_upper_bound(X_30,Y)))]]) ).
cnf(refute_0_1744,plain,
( least_upper_bound(least_upper_bound(X_29,X_30),Y) != least_upper_bound(X_29,least_upper_bound(X_30,Y))
| least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_29,X_30),Y)) = least_upper_bound(X_30,least_upper_bound(X_29,least_upper_bound(X_30,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_29,X_30),Y)),least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_29,X_30),Y))) )],[refute_0_1742,refute_0_1743]) ).
cnf(refute_0_1745,plain,
least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_29,X_30),Y)) = least_upper_bound(X_30,least_upper_bound(X_29,least_upper_bound(X_30,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_29,X_30),Y),least_upper_bound(X_29,least_upper_bound(X_30,Y))) )],[refute_0_1741,refute_0_1744]) ).
cnf(refute_0_1746,plain,
least_upper_bound(X,least_upper_bound(X_29,X_30)) = least_upper_bound(least_upper_bound(X_29,X_30),X),
inference(subst,[],[symmetry_of_lub:[bind(Y,$fot(least_upper_bound(X_29,X_30)))]]) ).
cnf(refute_0_1747,plain,
least_upper_bound(X_29,least_upper_bound(X_30,X)) = least_upper_bound(least_upper_bound(X_29,X_30),X),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_29)),bind(Y,$fot(X_30)),bind(Z,$fot(X))]]) ).
cnf(refute_0_1748,plain,
( least_upper_bound(X_29,least_upper_bound(X_30,X)) != least_upper_bound(least_upper_bound(X_29,X_30),X)
| least_upper_bound(least_upper_bound(X_29,X_30),X) = least_upper_bound(X_29,least_upper_bound(X_30,X)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X_29,least_upper_bound(X_30,X)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X_29,X_30),X)))]]) ).
cnf(refute_0_1749,plain,
least_upper_bound(least_upper_bound(X_29,X_30),X) = least_upper_bound(X_29,least_upper_bound(X_30,X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_29,least_upper_bound(X_30,X)),least_upper_bound(least_upper_bound(X_29,X_30),X)) )],[refute_0_1747,refute_0_1748]) ).
cnf(refute_0_1750,plain,
( least_upper_bound(X,least_upper_bound(X_29,X_30)) != least_upper_bound(least_upper_bound(X_29,X_30),X)
| least_upper_bound(least_upper_bound(X_29,X_30),X) != least_upper_bound(X_29,least_upper_bound(X_30,X))
| least_upper_bound(X,least_upper_bound(X_29,X_30)) = least_upper_bound(X_29,least_upper_bound(X_30,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,least_upper_bound(X_29,X_30)),least_upper_bound(X_29,least_upper_bound(X_30,X))) ),[0],$fot(least_upper_bound(least_upper_bound(X_29,X_30),X))]]) ).
cnf(refute_0_1751,plain,
( least_upper_bound(X,least_upper_bound(X_29,X_30)) != least_upper_bound(least_upper_bound(X_29,X_30),X)
| least_upper_bound(X,least_upper_bound(X_29,X_30)) = least_upper_bound(X_29,least_upper_bound(X_30,X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_29,X_30),X),least_upper_bound(X_29,least_upper_bound(X_30,X))) )],[refute_0_1749,refute_0_1750]) ).
cnf(refute_0_1752,plain,
least_upper_bound(X,least_upper_bound(X_29,X_30)) = least_upper_bound(X_29,least_upper_bound(X_30,X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_29,X_30)),least_upper_bound(least_upper_bound(X_29,X_30),X)) )],[refute_0_1746,refute_0_1751]) ).
cnf(refute_0_1753,plain,
( least_upper_bound(X,least_upper_bound(X_29,X_30)) != least_upper_bound(X_29,least_upper_bound(X_30,X))
| least_upper_bound(X_29,least_upper_bound(X_30,X)) = least_upper_bound(X,least_upper_bound(X_29,X_30)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(X_29,X_30)))),bind(Y0,$fot(least_upper_bound(X_29,least_upper_bound(X_30,X))))]]) ).
cnf(refute_0_1754,plain,
least_upper_bound(X_29,least_upper_bound(X_30,X)) = least_upper_bound(X,least_upper_bound(X_29,X_30)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_29,X_30)),least_upper_bound(X_29,least_upper_bound(X_30,X))) )],[refute_0_1752,refute_0_1753]) ).
cnf(refute_0_1755,plain,
least_upper_bound(least_upper_bound(X_29,X_30),least_upper_bound(Y,X_30)) = least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_29,X_30),Y)),
inference(subst,[],[refute_0_1754:[bind(X,$fot(X_30)),bind(X_29,$fot(least_upper_bound(X_29,X_30))),bind(X_30,$fot(Y))]]) ).
cnf(refute_0_1756,plain,
( least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_29,X_30),Y)) != least_upper_bound(X_30,least_upper_bound(X_29,least_upper_bound(X_30,Y)))
| least_upper_bound(least_upper_bound(X_29,X_30),least_upper_bound(Y,X_30)) != least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_29,X_30),Y))
| least_upper_bound(least_upper_bound(X_29,X_30),least_upper_bound(Y,X_30)) = least_upper_bound(X_30,least_upper_bound(X_29,least_upper_bound(X_30,Y))) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_29,X_30),least_upper_bound(Y,X_30)))),bind(Y0,$fot(least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_29,X_30),Y)))),bind(Z0,$fot(least_upper_bound(X_30,least_upper_bound(X_29,least_upper_bound(X_30,Y)))))]]) ).
cnf(refute_0_1757,plain,
( least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_29,X_30),Y)) != least_upper_bound(X_30,least_upper_bound(X_29,least_upper_bound(X_30,Y)))
| least_upper_bound(least_upper_bound(X_29,X_30),least_upper_bound(Y,X_30)) = least_upper_bound(X_30,least_upper_bound(X_29,least_upper_bound(X_30,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_29,X_30),least_upper_bound(Y,X_30)),least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_29,X_30),Y))) )],[refute_0_1755,refute_0_1756]) ).
cnf(refute_0_1758,plain,
least_upper_bound(least_upper_bound(X_29,X_30),least_upper_bound(Y,X_30)) = least_upper_bound(X_30,least_upper_bound(X_29,least_upper_bound(X_30,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_29,X_30),Y)),least_upper_bound(X_30,least_upper_bound(X_29,least_upper_bound(X_30,Y)))) )],[refute_0_1745,refute_0_1757]) ).
cnf(refute_0_1759,plain,
( least_upper_bound(X_29,least_upper_bound(X_30,Y)) != least_upper_bound(least_upper_bound(X_29,X_30),least_upper_bound(Y,X_30))
| least_upper_bound(least_upper_bound(X_29,X_30),least_upper_bound(Y,X_30)) != least_upper_bound(X_30,least_upper_bound(X_29,least_upper_bound(X_30,Y)))
| least_upper_bound(X_29,least_upper_bound(X_30,Y)) = least_upper_bound(X_30,least_upper_bound(X_29,least_upper_bound(X_30,Y))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_29,least_upper_bound(X_30,Y)),least_upper_bound(X_30,least_upper_bound(X_29,least_upper_bound(X_30,Y)))) ),[0],$fot(least_upper_bound(least_upper_bound(X_29,X_30),least_upper_bound(Y,X_30)))]]) ).
cnf(refute_0_1760,plain,
( least_upper_bound(X_29,least_upper_bound(X_30,Y)) != least_upper_bound(least_upper_bound(X_29,X_30),least_upper_bound(Y,X_30))
| least_upper_bound(X_29,least_upper_bound(X_30,Y)) = least_upper_bound(X_30,least_upper_bound(X_29,least_upper_bound(X_30,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_29,X_30),least_upper_bound(Y,X_30)),least_upper_bound(X_30,least_upper_bound(X_29,least_upper_bound(X_30,Y)))) )],[refute_0_1758,refute_0_1759]) ).
cnf(refute_0_1761,plain,
least_upper_bound(X_29,least_upper_bound(X_30,Y)) = least_upper_bound(X_30,least_upper_bound(X_29,least_upper_bound(X_30,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_29,least_upper_bound(X_30,Y)),least_upper_bound(least_upper_bound(X_29,X_30),least_upper_bound(Y,X_30))) )],[refute_0_1740,refute_0_1760]) ).
cnf(refute_0_1762,plain,
( least_upper_bound(X_29,least_upper_bound(X_30,Y)) != least_upper_bound(X_30,least_upper_bound(X_29,least_upper_bound(X_30,Y)))
| least_upper_bound(X_30,least_upper_bound(X_29,least_upper_bound(X_30,Y))) = least_upper_bound(X_29,least_upper_bound(X_30,Y)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X_29,least_upper_bound(X_30,Y)))),bind(Y0,$fot(least_upper_bound(X_30,least_upper_bound(X_29,least_upper_bound(X_30,Y)))))]]) ).
cnf(refute_0_1763,plain,
least_upper_bound(X_30,least_upper_bound(X_29,least_upper_bound(X_30,Y))) = least_upper_bound(X_29,least_upper_bound(X_30,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_29,least_upper_bound(X_30,Y)),least_upper_bound(X_30,least_upper_bound(X_29,least_upper_bound(X_30,Y)))) )],[refute_0_1761,refute_0_1762]) ).
cnf(refute_0_1764,plain,
least_upper_bound(X_29,least_upper_bound(Y,least_upper_bound(X_29,X_31))) = least_upper_bound(Y,least_upper_bound(X_29,X_31)),
inference(subst,[],[refute_0_1763:[bind(Y,$fot(X_31)),bind(X_29,$fot(Y)),bind(X_30,$fot(X_29))]]) ).
cnf(refute_0_1765,plain,
least_upper_bound(least_upper_bound(Y,X_29),X_31) = least_upper_bound(Y,least_upper_bound(X_29,X_31)),
inference(subst,[],[refute_0_60:[bind(X,$fot(Y)),bind(Y,$fot(X_29)),bind(Z,$fot(X_31))]]) ).
cnf(refute_0_1766,plain,
least_upper_bound(X_29,least_upper_bound(least_upper_bound(Y,X_29),X_31)) = least_upper_bound(X_29,least_upper_bound(least_upper_bound(Y,X_29),X_31)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_29,least_upper_bound(least_upper_bound(Y,X_29),X_31)))]]) ).
cnf(refute_0_1767,plain,
( least_upper_bound(X_29,least_upper_bound(least_upper_bound(Y,X_29),X_31)) != least_upper_bound(X_29,least_upper_bound(least_upper_bound(Y,X_29),X_31))
| least_upper_bound(least_upper_bound(Y,X_29),X_31) != least_upper_bound(Y,least_upper_bound(X_29,X_31))
| least_upper_bound(X_29,least_upper_bound(least_upper_bound(Y,X_29),X_31)) = least_upper_bound(X_29,least_upper_bound(Y,least_upper_bound(X_29,X_31))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_29,least_upper_bound(least_upper_bound(Y,X_29),X_31)),least_upper_bound(X_29,least_upper_bound(least_upper_bound(Y,X_29),X_31))) ),[1,1],$fot(least_upper_bound(Y,least_upper_bound(X_29,X_31)))]]) ).
cnf(refute_0_1768,plain,
( least_upper_bound(least_upper_bound(Y,X_29),X_31) != least_upper_bound(Y,least_upper_bound(X_29,X_31))
| least_upper_bound(X_29,least_upper_bound(least_upper_bound(Y,X_29),X_31)) = least_upper_bound(X_29,least_upper_bound(Y,least_upper_bound(X_29,X_31))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_29,least_upper_bound(least_upper_bound(Y,X_29),X_31)),least_upper_bound(X_29,least_upper_bound(least_upper_bound(Y,X_29),X_31))) )],[refute_0_1766,refute_0_1767]) ).
cnf(refute_0_1769,plain,
least_upper_bound(X_29,least_upper_bound(least_upper_bound(Y,X_29),X_31)) = least_upper_bound(X_29,least_upper_bound(Y,least_upper_bound(X_29,X_31))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_29),X_31),least_upper_bound(Y,least_upper_bound(X_29,X_31))) )],[refute_0_1765,refute_0_1768]) ).
cnf(refute_0_1770,plain,
( least_upper_bound(X_29,least_upper_bound(Y,least_upper_bound(X_29,X_31))) != least_upper_bound(Y,least_upper_bound(X_29,X_31))
| least_upper_bound(X_29,least_upper_bound(least_upper_bound(Y,X_29),X_31)) != least_upper_bound(X_29,least_upper_bound(Y,least_upper_bound(X_29,X_31)))
| least_upper_bound(X_29,least_upper_bound(least_upper_bound(Y,X_29),X_31)) = least_upper_bound(Y,least_upper_bound(X_29,X_31)) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(least_upper_bound(X_29,least_upper_bound(least_upper_bound(Y,X_29),X_31)))),bind(Y0,$fot(least_upper_bound(X_29,least_upper_bound(Y,least_upper_bound(X_29,X_31))))),bind(Z0,$fot(least_upper_bound(Y,least_upper_bound(X_29,X_31))))]]) ).
cnf(refute_0_1771,plain,
( least_upper_bound(X_29,least_upper_bound(Y,least_upper_bound(X_29,X_31))) != least_upper_bound(Y,least_upper_bound(X_29,X_31))
| least_upper_bound(X_29,least_upper_bound(least_upper_bound(Y,X_29),X_31)) = least_upper_bound(Y,least_upper_bound(X_29,X_31)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_29,least_upper_bound(least_upper_bound(Y,X_29),X_31)),least_upper_bound(X_29,least_upper_bound(Y,least_upper_bound(X_29,X_31)))) )],[refute_0_1769,refute_0_1770]) ).
cnf(refute_0_1772,plain,
least_upper_bound(X_29,least_upper_bound(least_upper_bound(Y,X_29),X_31)) = least_upper_bound(Y,least_upper_bound(X_29,X_31)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_29,least_upper_bound(Y,least_upper_bound(X_29,X_31))),least_upper_bound(Y,least_upper_bound(X_29,X_31))) )],[refute_0_1764,refute_0_1771]) ).
cnf(refute_0_1773,plain,
( least_upper_bound(X_29,least_upper_bound(least_upper_bound(Y,X_29),X_31)) != least_upper_bound(Y,least_upper_bound(X_29,X_31))
| least_upper_bound(X_29,least_upper_bound(least_upper_bound(Y,X_29),X_31)) != least_upper_bound(least_upper_bound(X_29,Y),X_31)
| least_upper_bound(Y,least_upper_bound(X_29,X_31)) = least_upper_bound(least_upper_bound(X_29,Y),X_31) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_29,least_upper_bound(least_upper_bound(Y,X_29),X_31)),least_upper_bound(least_upper_bound(X_29,Y),X_31)) ),[0],$fot(least_upper_bound(Y,least_upper_bound(X_29,X_31)))]]) ).
cnf(refute_0_1774,plain,
( least_upper_bound(X_29,least_upper_bound(least_upper_bound(Y,X_29),X_31)) != least_upper_bound(least_upper_bound(X_29,Y),X_31)
| least_upper_bound(Y,least_upper_bound(X_29,X_31)) = least_upper_bound(least_upper_bound(X_29,Y),X_31) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_29,least_upper_bound(least_upper_bound(Y,X_29),X_31)),least_upper_bound(Y,least_upper_bound(X_29,X_31))) )],[refute_0_1772,refute_0_1773]) ).
cnf(refute_0_1775,plain,
least_upper_bound(least_upper_bound(X_29,Y),X_31) = least_upper_bound(X_29,least_upper_bound(Y,X_31)),
inference(subst,[],[refute_0_60:[bind(X,$fot(X_29)),bind(Z,$fot(X_31))]]) ).
cnf(refute_0_1776,plain,
( least_upper_bound(Y,least_upper_bound(X_29,X_31)) != least_upper_bound(least_upper_bound(X_29,Y),X_31)
| least_upper_bound(least_upper_bound(X_29,Y),X_31) != least_upper_bound(X_29,least_upper_bound(Y,X_31))
| least_upper_bound(Y,least_upper_bound(X_29,X_31)) = least_upper_bound(X_29,least_upper_bound(Y,X_31)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(Y,least_upper_bound(X_29,X_31)),least_upper_bound(X_29,least_upper_bound(Y,X_31))) ),[0],$fot(least_upper_bound(least_upper_bound(X_29,Y),X_31))]]) ).
cnf(refute_0_1777,plain,
( least_upper_bound(Y,least_upper_bound(X_29,X_31)) != least_upper_bound(least_upper_bound(X_29,Y),X_31)
| least_upper_bound(Y,least_upper_bound(X_29,X_31)) = least_upper_bound(X_29,least_upper_bound(Y,X_31)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_29,Y),X_31),least_upper_bound(X_29,least_upper_bound(Y,X_31))) )],[refute_0_1775,refute_0_1776]) ).
cnf(refute_0_1778,plain,
( least_upper_bound(X_29,least_upper_bound(least_upper_bound(Y,X_29),X_31)) != least_upper_bound(least_upper_bound(X_29,Y),X_31)
| least_upper_bound(Y,least_upper_bound(X_29,X_31)) = least_upper_bound(X_29,least_upper_bound(Y,X_31)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_29,X_31)),least_upper_bound(least_upper_bound(X_29,Y),X_31)) )],[refute_0_1774,refute_0_1777]) ).
cnf(refute_0_1779,plain,
least_upper_bound(Y,least_upper_bound(X_29,X_31)) = least_upper_bound(X_29,least_upper_bound(Y,X_31)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_29,least_upper_bound(least_upper_bound(Y,X_29),X_31)),least_upper_bound(least_upper_bound(X_29,Y),X_31)) )],[refute_0_1735,refute_0_1778]) ).
cnf(refute_0_1780,plain,
( least_upper_bound(Y,least_upper_bound(X_29,X_31)) != least_upper_bound(X_29,least_upper_bound(Y,X_31))
| least_upper_bound(X_29,least_upper_bound(Y,X_31)) = least_upper_bound(Y,least_upper_bound(X_29,X_31)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(Y,least_upper_bound(X_29,X_31)))),bind(Y0,$fot(least_upper_bound(X_29,least_upper_bound(Y,X_31))))]]) ).
cnf(refute_0_1781,plain,
least_upper_bound(X_29,least_upper_bound(Y,X_31)) = least_upper_bound(Y,least_upper_bound(X_29,X_31)),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_29,X_31)),least_upper_bound(X_29,least_upper_bound(Y,X_31))) )],[refute_0_1779,refute_0_1780]) ).
cnf(refute_0_1782,plain,
least_upper_bound(multiply(X,Y),least_upper_bound(identity,multiply(X,X_60))) = least_upper_bound(identity,least_upper_bound(multiply(X,Y),multiply(X,X_60))),
inference(subst,[],[refute_0_1781:[bind(Y,$fot(identity)),bind(X_29,$fot(multiply(X,Y))),bind(X_31,$fot(multiply(X,X_60)))]]) ).
cnf(refute_0_1783,plain,
( least_upper_bound(multiply(X,Y),least_upper_bound(identity,multiply(X,X_60))) != least_upper_bound(identity,least_upper_bound(multiply(X,Y),multiply(X,X_60)))
| least_upper_bound(identity,least_upper_bound(multiply(X,Y),multiply(X,X_60))) != least_upper_bound(identity,multiply(X,least_upper_bound(Y,X_60)))
| least_upper_bound(multiply(X,Y),least_upper_bound(identity,multiply(X,X_60))) = least_upper_bound(identity,multiply(X,least_upper_bound(Y,X_60))) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(least_upper_bound(multiply(X,Y),least_upper_bound(identity,multiply(X,X_60))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(multiply(X,Y),multiply(X,X_60))))),bind(Z0,$fot(least_upper_bound(identity,multiply(X,least_upper_bound(Y,X_60)))))]]) ).
cnf(refute_0_1784,plain,
( least_upper_bound(identity,least_upper_bound(multiply(X,Y),multiply(X,X_60))) != least_upper_bound(identity,multiply(X,least_upper_bound(Y,X_60)))
| least_upper_bound(multiply(X,Y),least_upper_bound(identity,multiply(X,X_60))) = least_upper_bound(identity,multiply(X,least_upper_bound(Y,X_60))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,Y),least_upper_bound(identity,multiply(X,X_60))),least_upper_bound(identity,least_upper_bound(multiply(X,Y),multiply(X,X_60)))) )],[refute_0_1782,refute_0_1783]) ).
cnf(refute_0_1785,plain,
least_upper_bound(multiply(X,Y),least_upper_bound(identity,multiply(X,X_60))) = least_upper_bound(identity,multiply(X,least_upper_bound(Y,X_60))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(X,Y),multiply(X,X_60))),least_upper_bound(identity,multiply(X,least_upper_bound(Y,X_60)))) )],[refute_0_1730,refute_0_1784]) ).
cnf(refute_0_1786,plain,
( multiply(X,least_upper_bound(Y,least_upper_bound(X_60,inverse(X)))) != least_upper_bound(multiply(X,Y),least_upper_bound(identity,multiply(X,X_60)))
| least_upper_bound(multiply(X,Y),least_upper_bound(identity,multiply(X,X_60))) != least_upper_bound(identity,multiply(X,least_upper_bound(Y,X_60)))
| multiply(X,least_upper_bound(Y,least_upper_bound(X_60,inverse(X)))) = least_upper_bound(identity,multiply(X,least_upper_bound(Y,X_60))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X,least_upper_bound(Y,least_upper_bound(X_60,inverse(X)))),least_upper_bound(identity,multiply(X,least_upper_bound(Y,X_60)))) ),[0],$fot(least_upper_bound(multiply(X,Y),least_upper_bound(identity,multiply(X,X_60))))]]) ).
cnf(refute_0_1787,plain,
( multiply(X,least_upper_bound(Y,least_upper_bound(X_60,inverse(X)))) != least_upper_bound(multiply(X,Y),least_upper_bound(identity,multiply(X,X_60)))
| multiply(X,least_upper_bound(Y,least_upper_bound(X_60,inverse(X)))) = least_upper_bound(identity,multiply(X,least_upper_bound(Y,X_60))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,Y),least_upper_bound(identity,multiply(X,X_60))),least_upper_bound(identity,multiply(X,least_upper_bound(Y,X_60)))) )],[refute_0_1785,refute_0_1786]) ).
cnf(refute_0_1788,plain,
multiply(X,least_upper_bound(Y,least_upper_bound(X_60,inverse(X)))) = least_upper_bound(identity,multiply(X,least_upper_bound(Y,X_60))),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(Y,least_upper_bound(X_60,inverse(X)))),least_upper_bound(multiply(X,Y),least_upper_bound(identity,multiply(X,X_60)))) )],[refute_0_1725,refute_0_1787]) ).
cnf(refute_0_1789,plain,
multiply(greatest_lower_bound(X_282,X_283),least_upper_bound(X_54,least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283))))) = least_upper_bound(identity,multiply(greatest_lower_bound(X_282,X_283),least_upper_bound(X_54,inverse(X_282)))),
inference(subst,[],[refute_0_1788:[bind(X,$fot(greatest_lower_bound(X_282,X_283))),bind(Y,$fot(X_54)),bind(X_60,$fot(inverse(X_282)))]]) ).
cnf(refute_0_1790,plain,
( multiply(greatest_lower_bound(X_282,X_283),least_upper_bound(X_54,least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283))))) != least_upper_bound(identity,multiply(greatest_lower_bound(X_282,X_283),least_upper_bound(X_54,inverse(X_282))))
| multiply(greatest_lower_bound(X_282,X_283),least_upper_bound(X_54,least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283))))) != least_upper_bound(identity,multiply(inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))),X_54))
| least_upper_bound(identity,multiply(greatest_lower_bound(X_282,X_283),least_upper_bound(X_54,inverse(X_282)))) = least_upper_bound(identity,multiply(inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))),X_54)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_282,X_283),least_upper_bound(X_54,least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283))))),least_upper_bound(identity,multiply(inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))),X_54))) ),[0],$fot(least_upper_bound(identity,multiply(greatest_lower_bound(X_282,X_283),least_upper_bound(X_54,inverse(X_282)))))]]) ).
cnf(refute_0_1791,plain,
( multiply(greatest_lower_bound(X_282,X_283),least_upper_bound(X_54,least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283))))) != least_upper_bound(identity,multiply(inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))),X_54))
| least_upper_bound(identity,multiply(greatest_lower_bound(X_282,X_283),least_upper_bound(X_54,inverse(X_282)))) = least_upper_bound(identity,multiply(inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))),X_54)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_282,X_283),least_upper_bound(X_54,least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283))))),least_upper_bound(identity,multiply(greatest_lower_bound(X_282,X_283),least_upper_bound(X_54,inverse(X_282))))) )],[refute_0_1789,refute_0_1790]) ).
cnf(refute_0_1792,plain,
multiply(inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))),X_54) = multiply(inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))),X_54),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))),X_54))]]) ).
cnf(refute_0_1793,plain,
( multiply(inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))),X_54) != multiply(inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))),X_54)
| inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))) != greatest_lower_bound(X_282,X_283)
| multiply(inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))),X_54) = multiply(greatest_lower_bound(X_282,X_283),X_54) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))),X_54),multiply(inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))),X_54)) ),[1,0],$fot(greatest_lower_bound(X_282,X_283))]]) ).
cnf(refute_0_1794,plain,
( inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))) != greatest_lower_bound(X_282,X_283)
| multiply(inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))),X_54) = multiply(greatest_lower_bound(X_282,X_283),X_54) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))),X_54),multiply(inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))),X_54)) )],[refute_0_1792,refute_0_1793]) ).
cnf(refute_0_1795,plain,
multiply(inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))),X_54) = multiply(greatest_lower_bound(X_282,X_283),X_54),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))),greatest_lower_bound(X_282,X_283)) )],[refute_0_1709,refute_0_1794]) ).
cnf(refute_0_1796,plain,
least_upper_bound(identity,multiply(inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))),X_54)) = least_upper_bound(identity,multiply(inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))),X_54)),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,multiply(inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))),X_54)))]]) ).
cnf(refute_0_1797,plain,
( multiply(inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))),X_54) != multiply(greatest_lower_bound(X_282,X_283),X_54)
| least_upper_bound(identity,multiply(inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))),X_54)) != least_upper_bound(identity,multiply(inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))),X_54))
| least_upper_bound(identity,multiply(inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))),X_54)) = least_upper_bound(identity,multiply(greatest_lower_bound(X_282,X_283),X_54)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))),X_54)),least_upper_bound(identity,multiply(inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))),X_54))) ),[1,1],$fot(multiply(greatest_lower_bound(X_282,X_283),X_54))]]) ).
cnf(refute_0_1798,plain,
( multiply(inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))),X_54) != multiply(greatest_lower_bound(X_282,X_283),X_54)
| least_upper_bound(identity,multiply(inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))),X_54)) = least_upper_bound(identity,multiply(greatest_lower_bound(X_282,X_283),X_54)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))),X_54)),least_upper_bound(identity,multiply(inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))),X_54))) )],[refute_0_1796,refute_0_1797]) ).
cnf(refute_0_1799,plain,
least_upper_bound(identity,multiply(inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))),X_54)) = least_upper_bound(identity,multiply(greatest_lower_bound(X_282,X_283),X_54)),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))),X_54),multiply(greatest_lower_bound(X_282,X_283),X_54)) )],[refute_0_1795,refute_0_1798]) ).
cnf(refute_0_1800,plain,
( least_upper_bound(identity,multiply(greatest_lower_bound(X_282,X_283),least_upper_bound(X_54,inverse(X_282)))) != least_upper_bound(identity,multiply(inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))),X_54))
| least_upper_bound(identity,multiply(inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))),X_54)) != least_upper_bound(identity,multiply(greatest_lower_bound(X_282,X_283),X_54))
| least_upper_bound(identity,multiply(greatest_lower_bound(X_282,X_283),least_upper_bound(X_54,inverse(X_282)))) = least_upper_bound(identity,multiply(greatest_lower_bound(X_282,X_283),X_54)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(identity,multiply(greatest_lower_bound(X_282,X_283),least_upper_bound(X_54,inverse(X_282)))),least_upper_bound(identity,multiply(greatest_lower_bound(X_282,X_283),X_54))) ),[0],$fot(least_upper_bound(identity,multiply(inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))),X_54)))]]) ).
cnf(refute_0_1801,plain,
( least_upper_bound(identity,multiply(greatest_lower_bound(X_282,X_283),least_upper_bound(X_54,inverse(X_282)))) != least_upper_bound(identity,multiply(inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))),X_54))
| least_upper_bound(identity,multiply(greatest_lower_bound(X_282,X_283),least_upper_bound(X_54,inverse(X_282)))) = least_upper_bound(identity,multiply(greatest_lower_bound(X_282,X_283),X_54)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))),X_54)),least_upper_bound(identity,multiply(greatest_lower_bound(X_282,X_283),X_54))) )],[refute_0_1799,refute_0_1800]) ).
cnf(refute_0_1802,plain,
( multiply(greatest_lower_bound(X_282,X_283),least_upper_bound(X_54,least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283))))) != least_upper_bound(identity,multiply(inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))),X_54))
| least_upper_bound(identity,multiply(greatest_lower_bound(X_282,X_283),least_upper_bound(X_54,inverse(X_282)))) = least_upper_bound(identity,multiply(greatest_lower_bound(X_282,X_283),X_54)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(greatest_lower_bound(X_282,X_283),least_upper_bound(X_54,inverse(X_282)))),least_upper_bound(identity,multiply(inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))),X_54))) )],[refute_0_1791,refute_0_1801]) ).
cnf(refute_0_1803,plain,
least_upper_bound(identity,multiply(greatest_lower_bound(X_282,X_283),least_upper_bound(X_54,inverse(X_282)))) = least_upper_bound(identity,multiply(greatest_lower_bound(X_282,X_283),X_54)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_282,X_283),least_upper_bound(X_54,least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283))))),least_upper_bound(identity,multiply(inverse(least_upper_bound(inverse(X_282),inverse(greatest_lower_bound(X_282,X_283)))),X_54))) )],[refute_0_1712,refute_0_1802]) ).
cnf(refute_0_1804,plain,
least_upper_bound(identity,multiply(greatest_lower_bound(X_114,identity),least_upper_bound(identity,inverse(X_114)))) = least_upper_bound(identity,multiply(greatest_lower_bound(X_114,identity),identity)),
inference(subst,[],[refute_0_1803:[bind(X_282,$fot(X_114)),bind(X_283,$fot(identity)),bind(X_54,$fot(identity))]]) ).
cnf(refute_0_1805,plain,
( least_upper_bound(identity,multiply(greatest_lower_bound(X_114,identity),identity)) != identity
| least_upper_bound(identity,multiply(greatest_lower_bound(X_114,identity),least_upper_bound(identity,inverse(X_114)))) != least_upper_bound(identity,multiply(greatest_lower_bound(X_114,identity),identity))
| least_upper_bound(identity,multiply(greatest_lower_bound(X_114,identity),least_upper_bound(identity,inverse(X_114)))) = identity ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(least_upper_bound(identity,multiply(greatest_lower_bound(X_114,identity),least_upper_bound(identity,inverse(X_114)))))),bind(Y0,$fot(least_upper_bound(identity,multiply(greatest_lower_bound(X_114,identity),identity)))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_1806,plain,
( least_upper_bound(identity,multiply(greatest_lower_bound(X_114,identity),identity)) != identity
| least_upper_bound(identity,multiply(greatest_lower_bound(X_114,identity),least_upper_bound(identity,inverse(X_114)))) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(greatest_lower_bound(X_114,identity),least_upper_bound(identity,inverse(X_114)))),least_upper_bound(identity,multiply(greatest_lower_bound(X_114,identity),identity))) )],[refute_0_1804,refute_0_1805]) ).
cnf(refute_0_1807,plain,
least_upper_bound(identity,multiply(greatest_lower_bound(X_114,identity),least_upper_bound(identity,inverse(X_114)))) = identity,
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(greatest_lower_bound(X_114,identity),identity)),identity) )],[refute_0_1658,refute_0_1806]) ).
cnf(refute_0_1808,plain,
multiply(greatest_lower_bound(inverse(X_121),identity),least_upper_bound(identity,X_121)) = greatest_lower_bound(least_upper_bound(identity,X_121),multiply(inverse(X_121),least_upper_bound(identity,X_121))),
inference(subst,[],[refute_0_746:[bind(X_45,$fot(least_upper_bound(identity,X_121))),bind(X_46,$fot(inverse(X_121)))]]) ).
cnf(refute_0_1809,plain,
multiply(inverse(X_58),least_upper_bound(least_upper_bound(X_58,identity),identity)) = least_upper_bound(inverse(X_58),multiply(inverse(X_58),least_upper_bound(X_58,identity))),
inference(subst,[],[refute_0_736:[bind(X_53,$fot(inverse(X_58))),bind(X_54,$fot(least_upper_bound(X_58,identity)))]]) ).
cnf(refute_0_1810,plain,
( multiply(inverse(X_58),least_upper_bound(X_58,identity)) != least_upper_bound(identity,inverse(X_58))
| multiply(inverse(X_58),least_upper_bound(least_upper_bound(X_58,identity),identity)) != least_upper_bound(inverse(X_58),multiply(inverse(X_58),least_upper_bound(X_58,identity)))
| multiply(inverse(X_58),least_upper_bound(least_upper_bound(X_58,identity),identity)) = least_upper_bound(inverse(X_58),least_upper_bound(identity,inverse(X_58))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_58),least_upper_bound(least_upper_bound(X_58,identity),identity)),least_upper_bound(inverse(X_58),multiply(inverse(X_58),least_upper_bound(X_58,identity)))) ),[1,1],$fot(least_upper_bound(identity,inverse(X_58)))]]) ).
cnf(refute_0_1811,plain,
( multiply(inverse(X_58),least_upper_bound(least_upper_bound(X_58,identity),identity)) != least_upper_bound(inverse(X_58),multiply(inverse(X_58),least_upper_bound(X_58,identity)))
| multiply(inverse(X_58),least_upper_bound(least_upper_bound(X_58,identity),identity)) = least_upper_bound(inverse(X_58),least_upper_bound(identity,inverse(X_58))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_58),least_upper_bound(X_58,identity)),least_upper_bound(identity,inverse(X_58))) )],[refute_0_1053,refute_0_1810]) ).
cnf(refute_0_1812,plain,
multiply(inverse(X_58),least_upper_bound(least_upper_bound(X_58,identity),identity)) = least_upper_bound(inverse(X_58),least_upper_bound(identity,inverse(X_58))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_58),least_upper_bound(least_upper_bound(X_58,identity),identity)),least_upper_bound(inverse(X_58),multiply(inverse(X_58),least_upper_bound(X_58,identity)))) )],[refute_0_1809,refute_0_1811]) ).
cnf(refute_0_1813,plain,
least_upper_bound(identity,least_upper_bound(X_58,identity)) = least_upper_bound(identity,X_58),
inference(subst,[],[refute_0_64:[bind(Y,$fot(X_58)),bind(X_21,$fot(identity))]]) ).
cnf(refute_0_1814,plain,
multiply(inverse(X_58),least_upper_bound(identity,least_upper_bound(X_58,identity))) = multiply(inverse(X_58),least_upper_bound(identity,least_upper_bound(X_58,identity))),
introduced(tautology,[refl,[$fot(multiply(inverse(X_58),least_upper_bound(identity,least_upper_bound(X_58,identity))))]]) ).
cnf(refute_0_1815,plain,
( multiply(inverse(X_58),least_upper_bound(identity,least_upper_bound(X_58,identity))) != multiply(inverse(X_58),least_upper_bound(identity,least_upper_bound(X_58,identity)))
| least_upper_bound(identity,least_upper_bound(X_58,identity)) != least_upper_bound(identity,X_58)
| multiply(inverse(X_58),least_upper_bound(identity,least_upper_bound(X_58,identity))) = multiply(inverse(X_58),least_upper_bound(identity,X_58)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_58),least_upper_bound(identity,least_upper_bound(X_58,identity))),multiply(inverse(X_58),least_upper_bound(identity,least_upper_bound(X_58,identity)))) ),[1,1],$fot(least_upper_bound(identity,X_58))]]) ).
cnf(refute_0_1816,plain,
( least_upper_bound(identity,least_upper_bound(X_58,identity)) != least_upper_bound(identity,X_58)
| multiply(inverse(X_58),least_upper_bound(identity,least_upper_bound(X_58,identity))) = multiply(inverse(X_58),least_upper_bound(identity,X_58)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_58),least_upper_bound(identity,least_upper_bound(X_58,identity))),multiply(inverse(X_58),least_upper_bound(identity,least_upper_bound(X_58,identity)))) )],[refute_0_1814,refute_0_1815]) ).
cnf(refute_0_1817,plain,
multiply(inverse(X_58),least_upper_bound(identity,least_upper_bound(X_58,identity))) = multiply(inverse(X_58),least_upper_bound(identity,X_58)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_58,identity)),least_upper_bound(identity,X_58)) )],[refute_0_1813,refute_0_1816]) ).
cnf(refute_0_1818,plain,
multiply(inverse(X_58),least_upper_bound(least_upper_bound(X_58,identity),identity)) = multiply(inverse(X_58),least_upper_bound(identity,least_upper_bound(X_58,identity))),
inference(subst,[],[refute_0_1595:[bind(X_23,$fot(inverse(X_58))),bind(X_57,$fot(least_upper_bound(X_58,identity)))]]) ).
cnf(refute_0_1819,plain,
( multiply(inverse(X_58),least_upper_bound(identity,least_upper_bound(X_58,identity))) != multiply(inverse(X_58),least_upper_bound(identity,X_58))
| multiply(inverse(X_58),least_upper_bound(least_upper_bound(X_58,identity),identity)) != multiply(inverse(X_58),least_upper_bound(identity,least_upper_bound(X_58,identity)))
| multiply(inverse(X_58),least_upper_bound(least_upper_bound(X_58,identity),identity)) = multiply(inverse(X_58),least_upper_bound(identity,X_58)) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(multiply(inverse(X_58),least_upper_bound(least_upper_bound(X_58,identity),identity)))),bind(Y0,$fot(multiply(inverse(X_58),least_upper_bound(identity,least_upper_bound(X_58,identity))))),bind(Z0,$fot(multiply(inverse(X_58),least_upper_bound(identity,X_58))))]]) ).
cnf(refute_0_1820,plain,
( multiply(inverse(X_58),least_upper_bound(identity,least_upper_bound(X_58,identity))) != multiply(inverse(X_58),least_upper_bound(identity,X_58))
| multiply(inverse(X_58),least_upper_bound(least_upper_bound(X_58,identity),identity)) = multiply(inverse(X_58),least_upper_bound(identity,X_58)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_58),least_upper_bound(least_upper_bound(X_58,identity),identity)),multiply(inverse(X_58),least_upper_bound(identity,least_upper_bound(X_58,identity)))) )],[refute_0_1818,refute_0_1819]) ).
cnf(refute_0_1821,plain,
multiply(inverse(X_58),least_upper_bound(least_upper_bound(X_58,identity),identity)) = multiply(inverse(X_58),least_upper_bound(identity,X_58)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_58),least_upper_bound(identity,least_upper_bound(X_58,identity))),multiply(inverse(X_58),least_upper_bound(identity,X_58))) )],[refute_0_1817,refute_0_1820]) ).
cnf(refute_0_1822,plain,
( multiply(inverse(X_58),least_upper_bound(least_upper_bound(X_58,identity),identity)) != multiply(inverse(X_58),least_upper_bound(identity,X_58))
| multiply(inverse(X_58),least_upper_bound(least_upper_bound(X_58,identity),identity)) != least_upper_bound(inverse(X_58),least_upper_bound(identity,inverse(X_58)))
| multiply(inverse(X_58),least_upper_bound(identity,X_58)) = least_upper_bound(inverse(X_58),least_upper_bound(identity,inverse(X_58))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_58),least_upper_bound(least_upper_bound(X_58,identity),identity)),least_upper_bound(inverse(X_58),least_upper_bound(identity,inverse(X_58)))) ),[0],$fot(multiply(inverse(X_58),least_upper_bound(identity,X_58)))]]) ).
cnf(refute_0_1823,plain,
( multiply(inverse(X_58),least_upper_bound(least_upper_bound(X_58,identity),identity)) != least_upper_bound(inverse(X_58),least_upper_bound(identity,inverse(X_58)))
| multiply(inverse(X_58),least_upper_bound(identity,X_58)) = least_upper_bound(inverse(X_58),least_upper_bound(identity,inverse(X_58))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_58),least_upper_bound(least_upper_bound(X_58,identity),identity)),multiply(inverse(X_58),least_upper_bound(identity,X_58))) )],[refute_0_1821,refute_0_1822]) ).
cnf(refute_0_1824,plain,
least_upper_bound(inverse(X_58),inverse(X_58)) = inverse(X_58),
inference(subst,[],[idempotence_of_lub:[bind(X,$fot(inverse(X_58)))]]) ).
cnf(refute_0_1825,plain,
least_upper_bound(identity,least_upper_bound(inverse(X_58),inverse(X_58))) = least_upper_bound(identity,least_upper_bound(inverse(X_58),inverse(X_58))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,least_upper_bound(inverse(X_58),inverse(X_58))))]]) ).
cnf(refute_0_1826,plain,
( least_upper_bound(identity,least_upper_bound(inverse(X_58),inverse(X_58))) != least_upper_bound(identity,least_upper_bound(inverse(X_58),inverse(X_58)))
| least_upper_bound(inverse(X_58),inverse(X_58)) != inverse(X_58)
| least_upper_bound(identity,least_upper_bound(inverse(X_58),inverse(X_58))) = least_upper_bound(identity,inverse(X_58)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_58),inverse(X_58))),least_upper_bound(identity,least_upper_bound(inverse(X_58),inverse(X_58)))) ),[1,1],$fot(inverse(X_58))]]) ).
cnf(refute_0_1827,plain,
( least_upper_bound(inverse(X_58),inverse(X_58)) != inverse(X_58)
| least_upper_bound(identity,least_upper_bound(inverse(X_58),inverse(X_58))) = least_upper_bound(identity,inverse(X_58)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_58),inverse(X_58))),least_upper_bound(identity,least_upper_bound(inverse(X_58),inverse(X_58)))) )],[refute_0_1825,refute_0_1826]) ).
cnf(refute_0_1828,plain,
least_upper_bound(identity,least_upper_bound(inverse(X_58),inverse(X_58))) = least_upper_bound(identity,inverse(X_58)),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_58),inverse(X_58)),inverse(X_58)) )],[refute_0_1824,refute_0_1827]) ).
cnf(refute_0_1829,plain,
least_upper_bound(inverse(X_58),least_upper_bound(identity,inverse(X_58))) = least_upper_bound(identity,least_upper_bound(inverse(X_58),inverse(X_58))),
inference(subst,[],[refute_0_1781:[bind(Y,$fot(identity)),bind(X_29,$fot(inverse(X_58))),bind(X_31,$fot(inverse(X_58)))]]) ).
cnf(refute_0_1830,plain,
( least_upper_bound(identity,least_upper_bound(inverse(X_58),inverse(X_58))) != least_upper_bound(identity,inverse(X_58))
| least_upper_bound(inverse(X_58),least_upper_bound(identity,inverse(X_58))) != least_upper_bound(identity,least_upper_bound(inverse(X_58),inverse(X_58)))
| least_upper_bound(inverse(X_58),least_upper_bound(identity,inverse(X_58))) = least_upper_bound(identity,inverse(X_58)) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(least_upper_bound(inverse(X_58),least_upper_bound(identity,inverse(X_58))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(inverse(X_58),inverse(X_58))))),bind(Z0,$fot(least_upper_bound(identity,inverse(X_58))))]]) ).
cnf(refute_0_1831,plain,
( least_upper_bound(identity,least_upper_bound(inverse(X_58),inverse(X_58))) != least_upper_bound(identity,inverse(X_58))
| least_upper_bound(inverse(X_58),least_upper_bound(identity,inverse(X_58))) = least_upper_bound(identity,inverse(X_58)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_58),least_upper_bound(identity,inverse(X_58))),least_upper_bound(identity,least_upper_bound(inverse(X_58),inverse(X_58)))) )],[refute_0_1829,refute_0_1830]) ).
cnf(refute_0_1832,plain,
least_upper_bound(inverse(X_58),least_upper_bound(identity,inverse(X_58))) = least_upper_bound(identity,inverse(X_58)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_58),inverse(X_58))),least_upper_bound(identity,inverse(X_58))) )],[refute_0_1828,refute_0_1831]) ).
cnf(refute_0_1833,plain,
( multiply(inverse(X_58),least_upper_bound(identity,X_58)) != least_upper_bound(inverse(X_58),least_upper_bound(identity,inverse(X_58)))
| least_upper_bound(inverse(X_58),least_upper_bound(identity,inverse(X_58))) != least_upper_bound(identity,inverse(X_58))
| multiply(inverse(X_58),least_upper_bound(identity,X_58)) = least_upper_bound(identity,inverse(X_58)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_58),least_upper_bound(identity,X_58)),least_upper_bound(identity,inverse(X_58))) ),[0],$fot(least_upper_bound(inverse(X_58),least_upper_bound(identity,inverse(X_58))))]]) ).
cnf(refute_0_1834,plain,
( multiply(inverse(X_58),least_upper_bound(identity,X_58)) != least_upper_bound(inverse(X_58),least_upper_bound(identity,inverse(X_58)))
| multiply(inverse(X_58),least_upper_bound(identity,X_58)) = least_upper_bound(identity,inverse(X_58)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_58),least_upper_bound(identity,inverse(X_58))),least_upper_bound(identity,inverse(X_58))) )],[refute_0_1832,refute_0_1833]) ).
cnf(refute_0_1835,plain,
( multiply(inverse(X_58),least_upper_bound(least_upper_bound(X_58,identity),identity)) != least_upper_bound(inverse(X_58),least_upper_bound(identity,inverse(X_58)))
| multiply(inverse(X_58),least_upper_bound(identity,X_58)) = least_upper_bound(identity,inverse(X_58)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_58),least_upper_bound(identity,X_58)),least_upper_bound(inverse(X_58),least_upper_bound(identity,inverse(X_58)))) )],[refute_0_1823,refute_0_1834]) ).
cnf(refute_0_1836,plain,
multiply(inverse(X_58),least_upper_bound(identity,X_58)) = least_upper_bound(identity,inverse(X_58)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_58),least_upper_bound(least_upper_bound(X_58,identity),identity)),least_upper_bound(inverse(X_58),least_upper_bound(identity,inverse(X_58)))) )],[refute_0_1812,refute_0_1835]) ).
cnf(refute_0_1837,plain,
multiply(inverse(X_121),least_upper_bound(identity,X_121)) = least_upper_bound(identity,inverse(X_121)),
inference(subst,[],[refute_0_1836:[bind(X_58,$fot(X_121))]]) ).
cnf(refute_0_1838,plain,
( multiply(greatest_lower_bound(inverse(X_121),identity),least_upper_bound(identity,X_121)) != greatest_lower_bound(least_upper_bound(identity,X_121),multiply(inverse(X_121),least_upper_bound(identity,X_121)))
| multiply(inverse(X_121),least_upper_bound(identity,X_121)) != least_upper_bound(identity,inverse(X_121))
| multiply(greatest_lower_bound(inverse(X_121),identity),least_upper_bound(identity,X_121)) = greatest_lower_bound(least_upper_bound(identity,X_121),least_upper_bound(identity,inverse(X_121))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_121),identity),least_upper_bound(identity,X_121)),greatest_lower_bound(least_upper_bound(identity,X_121),multiply(inverse(X_121),least_upper_bound(identity,X_121)))) ),[1,1],$fot(least_upper_bound(identity,inverse(X_121)))]]) ).
cnf(refute_0_1839,plain,
( multiply(greatest_lower_bound(inverse(X_121),identity),least_upper_bound(identity,X_121)) != greatest_lower_bound(least_upper_bound(identity,X_121),multiply(inverse(X_121),least_upper_bound(identity,X_121)))
| multiply(greatest_lower_bound(inverse(X_121),identity),least_upper_bound(identity,X_121)) = greatest_lower_bound(least_upper_bound(identity,X_121),least_upper_bound(identity,inverse(X_121))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_121),least_upper_bound(identity,X_121)),least_upper_bound(identity,inverse(X_121))) )],[refute_0_1837,refute_0_1838]) ).
cnf(refute_0_1840,plain,
multiply(greatest_lower_bound(inverse(X_121),identity),least_upper_bound(identity,X_121)) = greatest_lower_bound(least_upper_bound(identity,X_121),least_upper_bound(identity,inverse(X_121))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_121),identity),least_upper_bound(identity,X_121)),greatest_lower_bound(least_upper_bound(identity,X_121),multiply(inverse(X_121),least_upper_bound(identity,X_121)))) )],[refute_0_1808,refute_0_1839]) ).
cnf(refute_0_1841,plain,
multiply(greatest_lower_bound(inverse(X_121),identity),least_upper_bound(identity,X_121)) = multiply(greatest_lower_bound(identity,inverse(X_121)),least_upper_bound(identity,X_121)),
inference(subst,[],[refute_0_867:[bind(X_105,$fot(inverse(X_121))),bind(X_17,$fot(least_upper_bound(identity,X_121)))]]) ).
cnf(refute_0_1842,plain,
( multiply(greatest_lower_bound(inverse(X_121),identity),least_upper_bound(identity,X_121)) != multiply(greatest_lower_bound(identity,inverse(X_121)),least_upper_bound(identity,X_121))
| multiply(greatest_lower_bound(inverse(X_121),identity),least_upper_bound(identity,X_121)) != greatest_lower_bound(least_upper_bound(identity,X_121),least_upper_bound(identity,inverse(X_121)))
| multiply(greatest_lower_bound(identity,inverse(X_121)),least_upper_bound(identity,X_121)) = greatest_lower_bound(least_upper_bound(identity,X_121),least_upper_bound(identity,inverse(X_121))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_121),identity),least_upper_bound(identity,X_121)),greatest_lower_bound(least_upper_bound(identity,X_121),least_upper_bound(identity,inverse(X_121)))) ),[0],$fot(multiply(greatest_lower_bound(identity,inverse(X_121)),least_upper_bound(identity,X_121)))]]) ).
cnf(refute_0_1843,plain,
( multiply(greatest_lower_bound(inverse(X_121),identity),least_upper_bound(identity,X_121)) != greatest_lower_bound(least_upper_bound(identity,X_121),least_upper_bound(identity,inverse(X_121)))
| multiply(greatest_lower_bound(identity,inverse(X_121)),least_upper_bound(identity,X_121)) = greatest_lower_bound(least_upper_bound(identity,X_121),least_upper_bound(identity,inverse(X_121))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_121),identity),least_upper_bound(identity,X_121)),multiply(greatest_lower_bound(identity,inverse(X_121)),least_upper_bound(identity,X_121))) )],[refute_0_1841,refute_0_1842]) ).
cnf(refute_0_1844,plain,
multiply(greatest_lower_bound(identity,inverse(X_121)),least_upper_bound(identity,X_121)) = greatest_lower_bound(least_upper_bound(identity,X_121),least_upper_bound(identity,inverse(X_121))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_121),identity),least_upper_bound(identity,X_121)),greatest_lower_bound(least_upper_bound(identity,X_121),least_upper_bound(identity,inverse(X_121)))) )],[refute_0_1840,refute_0_1843]) ).
cnf(refute_0_1845,plain,
multiply(least_upper_bound(identity,X_157),greatest_lower_bound(inverse(X_157),identity)) = greatest_lower_bound(least_upper_bound(identity,X_157),multiply(least_upper_bound(identity,X_157),inverse(X_157))),
inference(subst,[],[refute_0_220:[bind(X_36,$fot(least_upper_bound(identity,X_157))),bind(X_37,$fot(inverse(X_157)))]]) ).
cnf(refute_0_1846,plain,
multiply(least_upper_bound(least_upper_bound(X_72,identity),identity),inverse(X_72)) = least_upper_bound(inverse(X_72),multiply(least_upper_bound(X_72,identity),inverse(X_72))),
inference(subst,[],[refute_0_672:[bind(X_65,$fot(inverse(X_72))),bind(X_66,$fot(least_upper_bound(X_72,identity)))]]) ).
cnf(refute_0_1847,plain,
multiply(least_upper_bound(X_72,identity),inverse(X_72)) = least_upper_bound(identity,inverse(X_72)),
inference(subst,[],[refute_0_1610:[bind(X_69,$fot(X_72))]]) ).
cnf(refute_0_1848,plain,
( multiply(least_upper_bound(X_72,identity),inverse(X_72)) != least_upper_bound(identity,inverse(X_72))
| multiply(least_upper_bound(least_upper_bound(X_72,identity),identity),inverse(X_72)) != least_upper_bound(inverse(X_72),multiply(least_upper_bound(X_72,identity),inverse(X_72)))
| multiply(least_upper_bound(least_upper_bound(X_72,identity),identity),inverse(X_72)) = least_upper_bound(inverse(X_72),least_upper_bound(identity,inverse(X_72))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_72,identity),identity),inverse(X_72)),least_upper_bound(inverse(X_72),multiply(least_upper_bound(X_72,identity),inverse(X_72)))) ),[1,1],$fot(least_upper_bound(identity,inverse(X_72)))]]) ).
cnf(refute_0_1849,plain,
( multiply(least_upper_bound(least_upper_bound(X_72,identity),identity),inverse(X_72)) != least_upper_bound(inverse(X_72),multiply(least_upper_bound(X_72,identity),inverse(X_72)))
| multiply(least_upper_bound(least_upper_bound(X_72,identity),identity),inverse(X_72)) = least_upper_bound(inverse(X_72),least_upper_bound(identity,inverse(X_72))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_72,identity),inverse(X_72)),least_upper_bound(identity,inverse(X_72))) )],[refute_0_1847,refute_0_1848]) ).
cnf(refute_0_1850,plain,
multiply(least_upper_bound(least_upper_bound(X_72,identity),identity),inverse(X_72)) = least_upper_bound(inverse(X_72),least_upper_bound(identity,inverse(X_72))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_72,identity),identity),inverse(X_72)),least_upper_bound(inverse(X_72),multiply(least_upper_bound(X_72,identity),inverse(X_72)))) )],[refute_0_1846,refute_0_1849]) ).
cnf(refute_0_1851,plain,
least_upper_bound(identity,least_upper_bound(X_72,identity)) = least_upper_bound(identity,X_72),
inference(subst,[],[refute_0_64:[bind(Y,$fot(X_72)),bind(X_21,$fot(identity))]]) ).
cnf(refute_0_1852,plain,
multiply(least_upper_bound(identity,least_upper_bound(X_72,identity)),inverse(X_72)) = multiply(least_upper_bound(identity,least_upper_bound(X_72,identity)),inverse(X_72)),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(identity,least_upper_bound(X_72,identity)),inverse(X_72)))]]) ).
cnf(refute_0_1853,plain,
( multiply(least_upper_bound(identity,least_upper_bound(X_72,identity)),inverse(X_72)) != multiply(least_upper_bound(identity,least_upper_bound(X_72,identity)),inverse(X_72))
| least_upper_bound(identity,least_upper_bound(X_72,identity)) != least_upper_bound(identity,X_72)
| multiply(least_upper_bound(identity,least_upper_bound(X_72,identity)),inverse(X_72)) = multiply(least_upper_bound(identity,X_72),inverse(X_72)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(X_72,identity)),inverse(X_72)),multiply(least_upper_bound(identity,least_upper_bound(X_72,identity)),inverse(X_72))) ),[1,0],$fot(least_upper_bound(identity,X_72))]]) ).
cnf(refute_0_1854,plain,
( least_upper_bound(identity,least_upper_bound(X_72,identity)) != least_upper_bound(identity,X_72)
| multiply(least_upper_bound(identity,least_upper_bound(X_72,identity)),inverse(X_72)) = multiply(least_upper_bound(identity,X_72),inverse(X_72)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(X_72,identity)),inverse(X_72)),multiply(least_upper_bound(identity,least_upper_bound(X_72,identity)),inverse(X_72))) )],[refute_0_1852,refute_0_1853]) ).
cnf(refute_0_1855,plain,
multiply(least_upper_bound(identity,least_upper_bound(X_72,identity)),inverse(X_72)) = multiply(least_upper_bound(identity,X_72),inverse(X_72)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_72,identity)),least_upper_bound(identity,X_72)) )],[refute_0_1851,refute_0_1854]) ).
cnf(refute_0_1856,plain,
multiply(least_upper_bound(least_upper_bound(X_72,identity),identity),inverse(X_72)) = multiply(least_upper_bound(identity,least_upper_bound(X_72,identity)),inverse(X_72)),
inference(subst,[],[refute_0_721:[bind(X_23,$fot(inverse(X_72))),bind(X_69,$fot(least_upper_bound(X_72,identity)))]]) ).
cnf(refute_0_1857,plain,
( multiply(least_upper_bound(identity,least_upper_bound(X_72,identity)),inverse(X_72)) != multiply(least_upper_bound(identity,X_72),inverse(X_72))
| multiply(least_upper_bound(least_upper_bound(X_72,identity),identity),inverse(X_72)) != multiply(least_upper_bound(identity,least_upper_bound(X_72,identity)),inverse(X_72))
| multiply(least_upper_bound(least_upper_bound(X_72,identity),identity),inverse(X_72)) = multiply(least_upper_bound(identity,X_72),inverse(X_72)) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(multiply(least_upper_bound(least_upper_bound(X_72,identity),identity),inverse(X_72)))),bind(Y0,$fot(multiply(least_upper_bound(identity,least_upper_bound(X_72,identity)),inverse(X_72)))),bind(Z0,$fot(multiply(least_upper_bound(identity,X_72),inverse(X_72))))]]) ).
cnf(refute_0_1858,plain,
( multiply(least_upper_bound(identity,least_upper_bound(X_72,identity)),inverse(X_72)) != multiply(least_upper_bound(identity,X_72),inverse(X_72))
| multiply(least_upper_bound(least_upper_bound(X_72,identity),identity),inverse(X_72)) = multiply(least_upper_bound(identity,X_72),inverse(X_72)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_72,identity),identity),inverse(X_72)),multiply(least_upper_bound(identity,least_upper_bound(X_72,identity)),inverse(X_72))) )],[refute_0_1856,refute_0_1857]) ).
cnf(refute_0_1859,plain,
multiply(least_upper_bound(least_upper_bound(X_72,identity),identity),inverse(X_72)) = multiply(least_upper_bound(identity,X_72),inverse(X_72)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(X_72,identity)),inverse(X_72)),multiply(least_upper_bound(identity,X_72),inverse(X_72))) )],[refute_0_1855,refute_0_1858]) ).
cnf(refute_0_1860,plain,
( multiply(least_upper_bound(least_upper_bound(X_72,identity),identity),inverse(X_72)) != multiply(least_upper_bound(identity,X_72),inverse(X_72))
| multiply(least_upper_bound(least_upper_bound(X_72,identity),identity),inverse(X_72)) != least_upper_bound(inverse(X_72),least_upper_bound(identity,inverse(X_72)))
| multiply(least_upper_bound(identity,X_72),inverse(X_72)) = least_upper_bound(inverse(X_72),least_upper_bound(identity,inverse(X_72))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_72,identity),identity),inverse(X_72)),least_upper_bound(inverse(X_72),least_upper_bound(identity,inverse(X_72)))) ),[0],$fot(multiply(least_upper_bound(identity,X_72),inverse(X_72)))]]) ).
cnf(refute_0_1861,plain,
( multiply(least_upper_bound(least_upper_bound(X_72,identity),identity),inverse(X_72)) != least_upper_bound(inverse(X_72),least_upper_bound(identity,inverse(X_72)))
| multiply(least_upper_bound(identity,X_72),inverse(X_72)) = least_upper_bound(inverse(X_72),least_upper_bound(identity,inverse(X_72))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_72,identity),identity),inverse(X_72)),multiply(least_upper_bound(identity,X_72),inverse(X_72))) )],[refute_0_1859,refute_0_1860]) ).
cnf(refute_0_1862,plain,
least_upper_bound(inverse(X_72),inverse(X_72)) = inverse(X_72),
inference(subst,[],[idempotence_of_lub:[bind(X,$fot(inverse(X_72)))]]) ).
cnf(refute_0_1863,plain,
least_upper_bound(identity,least_upper_bound(inverse(X_72),inverse(X_72))) = least_upper_bound(identity,least_upper_bound(inverse(X_72),inverse(X_72))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,least_upper_bound(inverse(X_72),inverse(X_72))))]]) ).
cnf(refute_0_1864,plain,
( least_upper_bound(identity,least_upper_bound(inverse(X_72),inverse(X_72))) != least_upper_bound(identity,least_upper_bound(inverse(X_72),inverse(X_72)))
| least_upper_bound(inverse(X_72),inverse(X_72)) != inverse(X_72)
| least_upper_bound(identity,least_upper_bound(inverse(X_72),inverse(X_72))) = least_upper_bound(identity,inverse(X_72)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_72),inverse(X_72))),least_upper_bound(identity,least_upper_bound(inverse(X_72),inverse(X_72)))) ),[1,1],$fot(inverse(X_72))]]) ).
cnf(refute_0_1865,plain,
( least_upper_bound(inverse(X_72),inverse(X_72)) != inverse(X_72)
| least_upper_bound(identity,least_upper_bound(inverse(X_72),inverse(X_72))) = least_upper_bound(identity,inverse(X_72)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_72),inverse(X_72))),least_upper_bound(identity,least_upper_bound(inverse(X_72),inverse(X_72)))) )],[refute_0_1863,refute_0_1864]) ).
cnf(refute_0_1866,plain,
least_upper_bound(identity,least_upper_bound(inverse(X_72),inverse(X_72))) = least_upper_bound(identity,inverse(X_72)),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_72),inverse(X_72)),inverse(X_72)) )],[refute_0_1862,refute_0_1865]) ).
cnf(refute_0_1867,plain,
least_upper_bound(inverse(X_72),least_upper_bound(identity,inverse(X_72))) = least_upper_bound(identity,least_upper_bound(inverse(X_72),inverse(X_72))),
inference(subst,[],[refute_0_1781:[bind(Y,$fot(identity)),bind(X_29,$fot(inverse(X_72))),bind(X_31,$fot(inverse(X_72)))]]) ).
cnf(refute_0_1868,plain,
( least_upper_bound(identity,least_upper_bound(inverse(X_72),inverse(X_72))) != least_upper_bound(identity,inverse(X_72))
| least_upper_bound(inverse(X_72),least_upper_bound(identity,inverse(X_72))) != least_upper_bound(identity,least_upper_bound(inverse(X_72),inverse(X_72)))
| least_upper_bound(inverse(X_72),least_upper_bound(identity,inverse(X_72))) = least_upper_bound(identity,inverse(X_72)) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(least_upper_bound(inverse(X_72),least_upper_bound(identity,inverse(X_72))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(inverse(X_72),inverse(X_72))))),bind(Z0,$fot(least_upper_bound(identity,inverse(X_72))))]]) ).
cnf(refute_0_1869,plain,
( least_upper_bound(identity,least_upper_bound(inverse(X_72),inverse(X_72))) != least_upper_bound(identity,inverse(X_72))
| least_upper_bound(inverse(X_72),least_upper_bound(identity,inverse(X_72))) = least_upper_bound(identity,inverse(X_72)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_72),least_upper_bound(identity,inverse(X_72))),least_upper_bound(identity,least_upper_bound(inverse(X_72),inverse(X_72)))) )],[refute_0_1867,refute_0_1868]) ).
cnf(refute_0_1870,plain,
least_upper_bound(inverse(X_72),least_upper_bound(identity,inverse(X_72))) = least_upper_bound(identity,inverse(X_72)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_72),inverse(X_72))),least_upper_bound(identity,inverse(X_72))) )],[refute_0_1866,refute_0_1869]) ).
cnf(refute_0_1871,plain,
( multiply(least_upper_bound(identity,X_72),inverse(X_72)) != least_upper_bound(inverse(X_72),least_upper_bound(identity,inverse(X_72)))
| least_upper_bound(inverse(X_72),least_upper_bound(identity,inverse(X_72))) != least_upper_bound(identity,inverse(X_72))
| multiply(least_upper_bound(identity,X_72),inverse(X_72)) = least_upper_bound(identity,inverse(X_72)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(identity,X_72),inverse(X_72)),least_upper_bound(identity,inverse(X_72))) ),[0],$fot(least_upper_bound(inverse(X_72),least_upper_bound(identity,inverse(X_72))))]]) ).
cnf(refute_0_1872,plain,
( multiply(least_upper_bound(identity,X_72),inverse(X_72)) != least_upper_bound(inverse(X_72),least_upper_bound(identity,inverse(X_72)))
| multiply(least_upper_bound(identity,X_72),inverse(X_72)) = least_upper_bound(identity,inverse(X_72)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_72),least_upper_bound(identity,inverse(X_72))),least_upper_bound(identity,inverse(X_72))) )],[refute_0_1870,refute_0_1871]) ).
cnf(refute_0_1873,plain,
( multiply(least_upper_bound(least_upper_bound(X_72,identity),identity),inverse(X_72)) != least_upper_bound(inverse(X_72),least_upper_bound(identity,inverse(X_72)))
| multiply(least_upper_bound(identity,X_72),inverse(X_72)) = least_upper_bound(identity,inverse(X_72)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_72),inverse(X_72)),least_upper_bound(inverse(X_72),least_upper_bound(identity,inverse(X_72)))) )],[refute_0_1861,refute_0_1872]) ).
cnf(refute_0_1874,plain,
multiply(least_upper_bound(identity,X_72),inverse(X_72)) = least_upper_bound(identity,inverse(X_72)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_72,identity),identity),inverse(X_72)),least_upper_bound(inverse(X_72),least_upper_bound(identity,inverse(X_72)))) )],[refute_0_1850,refute_0_1873]) ).
cnf(refute_0_1875,plain,
multiply(least_upper_bound(identity,X_157),inverse(X_157)) = least_upper_bound(identity,inverse(X_157)),
inference(subst,[],[refute_0_1874:[bind(X_72,$fot(X_157))]]) ).
cnf(refute_0_1876,plain,
( multiply(least_upper_bound(identity,X_157),greatest_lower_bound(inverse(X_157),identity)) != greatest_lower_bound(least_upper_bound(identity,X_157),multiply(least_upper_bound(identity,X_157),inverse(X_157)))
| multiply(least_upper_bound(identity,X_157),inverse(X_157)) != least_upper_bound(identity,inverse(X_157))
| multiply(least_upper_bound(identity,X_157),greatest_lower_bound(inverse(X_157),identity)) = greatest_lower_bound(least_upper_bound(identity,X_157),least_upper_bound(identity,inverse(X_157))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,X_157),greatest_lower_bound(inverse(X_157),identity)),greatest_lower_bound(least_upper_bound(identity,X_157),multiply(least_upper_bound(identity,X_157),inverse(X_157)))) ),[1,1],$fot(least_upper_bound(identity,inverse(X_157)))]]) ).
cnf(refute_0_1877,plain,
( multiply(least_upper_bound(identity,X_157),greatest_lower_bound(inverse(X_157),identity)) != greatest_lower_bound(least_upper_bound(identity,X_157),multiply(least_upper_bound(identity,X_157),inverse(X_157)))
| multiply(least_upper_bound(identity,X_157),greatest_lower_bound(inverse(X_157),identity)) = greatest_lower_bound(least_upper_bound(identity,X_157),least_upper_bound(identity,inverse(X_157))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_157),inverse(X_157)),least_upper_bound(identity,inverse(X_157))) )],[refute_0_1875,refute_0_1876]) ).
cnf(refute_0_1878,plain,
multiply(least_upper_bound(identity,X_157),greatest_lower_bound(inverse(X_157),identity)) = greatest_lower_bound(least_upper_bound(identity,X_157),least_upper_bound(identity,inverse(X_157))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_157),greatest_lower_bound(inverse(X_157),identity)),greatest_lower_bound(least_upper_bound(identity,X_157),multiply(least_upper_bound(identity,X_157),inverse(X_157)))) )],[refute_0_1845,refute_0_1877]) ).
cnf(refute_0_1879,plain,
multiply(least_upper_bound(identity,X_157),greatest_lower_bound(inverse(X_157),identity)) = multiply(least_upper_bound(identity,X_157),greatest_lower_bound(identity,inverse(X_157))),
inference(subst,[],[refute_0_350:[bind(X_17,$fot(least_upper_bound(identity,X_157))),bind(X_91,$fot(inverse(X_157)))]]) ).
cnf(refute_0_1880,plain,
( multiply(least_upper_bound(identity,X_157),greatest_lower_bound(inverse(X_157),identity)) != multiply(least_upper_bound(identity,X_157),greatest_lower_bound(identity,inverse(X_157)))
| multiply(least_upper_bound(identity,X_157),greatest_lower_bound(inverse(X_157),identity)) != greatest_lower_bound(least_upper_bound(identity,X_157),least_upper_bound(identity,inverse(X_157)))
| multiply(least_upper_bound(identity,X_157),greatest_lower_bound(identity,inverse(X_157))) = greatest_lower_bound(least_upper_bound(identity,X_157),least_upper_bound(identity,inverse(X_157))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,X_157),greatest_lower_bound(inverse(X_157),identity)),greatest_lower_bound(least_upper_bound(identity,X_157),least_upper_bound(identity,inverse(X_157)))) ),[0],$fot(multiply(least_upper_bound(identity,X_157),greatest_lower_bound(identity,inverse(X_157))))]]) ).
cnf(refute_0_1881,plain,
( multiply(least_upper_bound(identity,X_157),greatest_lower_bound(inverse(X_157),identity)) != greatest_lower_bound(least_upper_bound(identity,X_157),least_upper_bound(identity,inverse(X_157)))
| multiply(least_upper_bound(identity,X_157),greatest_lower_bound(identity,inverse(X_157))) = greatest_lower_bound(least_upper_bound(identity,X_157),least_upper_bound(identity,inverse(X_157))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_157),greatest_lower_bound(inverse(X_157),identity)),multiply(least_upper_bound(identity,X_157),greatest_lower_bound(identity,inverse(X_157)))) )],[refute_0_1879,refute_0_1880]) ).
cnf(refute_0_1882,plain,
( multiply(greatest_lower_bound(identity,inverse(X_121)),least_upper_bound(identity,X_121)) != greatest_lower_bound(least_upper_bound(identity,X_121),least_upper_bound(identity,inverse(X_121)))
| greatest_lower_bound(least_upper_bound(identity,X_121),least_upper_bound(identity,inverse(X_121))) = multiply(greatest_lower_bound(identity,inverse(X_121)),least_upper_bound(identity,X_121)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(greatest_lower_bound(identity,inverse(X_121)),least_upper_bound(identity,X_121)))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(identity,X_121),least_upper_bound(identity,inverse(X_121)))))]]) ).
cnf(refute_0_1883,plain,
greatest_lower_bound(least_upper_bound(identity,X_121),least_upper_bound(identity,inverse(X_121))) = multiply(greatest_lower_bound(identity,inverse(X_121)),least_upper_bound(identity,X_121)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(X_121)),least_upper_bound(identity,X_121)),greatest_lower_bound(least_upper_bound(identity,X_121),least_upper_bound(identity,inverse(X_121)))) )],[refute_0_1844,refute_0_1882]) ).
cnf(refute_0_1884,plain,
greatest_lower_bound(least_upper_bound(identity,X_157),least_upper_bound(identity,inverse(X_157))) = multiply(greatest_lower_bound(identity,inverse(X_157)),least_upper_bound(identity,X_157)),
inference(subst,[],[refute_0_1883:[bind(X_121,$fot(X_157))]]) ).
cnf(refute_0_1885,plain,
( multiply(least_upper_bound(identity,X_157),greatest_lower_bound(identity,inverse(X_157))) != greatest_lower_bound(least_upper_bound(identity,X_157),least_upper_bound(identity,inverse(X_157)))
| greatest_lower_bound(least_upper_bound(identity,X_157),least_upper_bound(identity,inverse(X_157))) != multiply(greatest_lower_bound(identity,inverse(X_157)),least_upper_bound(identity,X_157))
| multiply(least_upper_bound(identity,X_157),greatest_lower_bound(identity,inverse(X_157))) = multiply(greatest_lower_bound(identity,inverse(X_157)),least_upper_bound(identity,X_157)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(identity,X_157),greatest_lower_bound(identity,inverse(X_157))),multiply(greatest_lower_bound(identity,inverse(X_157)),least_upper_bound(identity,X_157))) ),[0],$fot(greatest_lower_bound(least_upper_bound(identity,X_157),least_upper_bound(identity,inverse(X_157))))]]) ).
cnf(refute_0_1886,plain,
( multiply(least_upper_bound(identity,X_157),greatest_lower_bound(identity,inverse(X_157))) != greatest_lower_bound(least_upper_bound(identity,X_157),least_upper_bound(identity,inverse(X_157)))
| multiply(least_upper_bound(identity,X_157),greatest_lower_bound(identity,inverse(X_157))) = multiply(greatest_lower_bound(identity,inverse(X_157)),least_upper_bound(identity,X_157)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,X_157),least_upper_bound(identity,inverse(X_157))),multiply(greatest_lower_bound(identity,inverse(X_157)),least_upper_bound(identity,X_157))) )],[refute_0_1884,refute_0_1885]) ).
cnf(refute_0_1887,plain,
( multiply(least_upper_bound(identity,X_157),greatest_lower_bound(inverse(X_157),identity)) != greatest_lower_bound(least_upper_bound(identity,X_157),least_upper_bound(identity,inverse(X_157)))
| multiply(least_upper_bound(identity,X_157),greatest_lower_bound(identity,inverse(X_157))) = multiply(greatest_lower_bound(identity,inverse(X_157)),least_upper_bound(identity,X_157)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_157),greatest_lower_bound(identity,inverse(X_157))),greatest_lower_bound(least_upper_bound(identity,X_157),least_upper_bound(identity,inverse(X_157)))) )],[refute_0_1881,refute_0_1886]) ).
cnf(refute_0_1888,plain,
multiply(least_upper_bound(identity,X_157),greatest_lower_bound(identity,inverse(X_157))) = multiply(greatest_lower_bound(identity,inverse(X_157)),least_upper_bound(identity,X_157)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_157),greatest_lower_bound(inverse(X_157),identity)),greatest_lower_bound(least_upper_bound(identity,X_157),least_upper_bound(identity,inverse(X_157)))) )],[refute_0_1878,refute_0_1887]) ).
cnf(refute_0_1889,plain,
( multiply(least_upper_bound(identity,X_157),greatest_lower_bound(identity,inverse(X_157))) != multiply(greatest_lower_bound(identity,inverse(X_157)),least_upper_bound(identity,X_157))
| multiply(greatest_lower_bound(identity,inverse(X_157)),least_upper_bound(identity,X_157)) = multiply(least_upper_bound(identity,X_157),greatest_lower_bound(identity,inverse(X_157))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(identity,X_157),greatest_lower_bound(identity,inverse(X_157))))),bind(Y0,$fot(multiply(greatest_lower_bound(identity,inverse(X_157)),least_upper_bound(identity,X_157))))]]) ).
cnf(refute_0_1890,plain,
multiply(greatest_lower_bound(identity,inverse(X_157)),least_upper_bound(identity,X_157)) = multiply(least_upper_bound(identity,X_157),greatest_lower_bound(identity,inverse(X_157))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_157),greatest_lower_bound(identity,inverse(X_157))),multiply(greatest_lower_bound(identity,inverse(X_157)),least_upper_bound(identity,X_157))) )],[refute_0_1888,refute_0_1889]) ).
cnf(refute_0_1891,plain,
multiply(greatest_lower_bound(identity,inverse(X_121)),least_upper_bound(identity,X_121)) = multiply(least_upper_bound(identity,X_121),greatest_lower_bound(identity,inverse(X_121))),
inference(subst,[],[refute_0_1890:[bind(X_157,$fot(X_121))]]) ).
cnf(refute_0_1892,plain,
( multiply(greatest_lower_bound(identity,inverse(X_121)),least_upper_bound(identity,X_121)) != multiply(least_upper_bound(identity,X_121),greatest_lower_bound(identity,inverse(X_121)))
| multiply(greatest_lower_bound(identity,inverse(X_121)),least_upper_bound(identity,X_121)) != greatest_lower_bound(least_upper_bound(identity,X_121),least_upper_bound(identity,inverse(X_121)))
| multiply(least_upper_bound(identity,X_121),greatest_lower_bound(identity,inverse(X_121))) = greatest_lower_bound(least_upper_bound(identity,X_121),least_upper_bound(identity,inverse(X_121))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(X_121)),least_upper_bound(identity,X_121)),greatest_lower_bound(least_upper_bound(identity,X_121),least_upper_bound(identity,inverse(X_121)))) ),[0],$fot(multiply(least_upper_bound(identity,X_121),greatest_lower_bound(identity,inverse(X_121))))]]) ).
cnf(refute_0_1893,plain,
( multiply(greatest_lower_bound(identity,inverse(X_121)),least_upper_bound(identity,X_121)) != greatest_lower_bound(least_upper_bound(identity,X_121),least_upper_bound(identity,inverse(X_121)))
| multiply(least_upper_bound(identity,X_121),greatest_lower_bound(identity,inverse(X_121))) = greatest_lower_bound(least_upper_bound(identity,X_121),least_upper_bound(identity,inverse(X_121))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(X_121)),least_upper_bound(identity,X_121)),multiply(least_upper_bound(identity,X_121),greatest_lower_bound(identity,inverse(X_121)))) )],[refute_0_1891,refute_0_1892]) ).
cnf(refute_0_1894,plain,
multiply(least_upper_bound(identity,X_121),greatest_lower_bound(identity,inverse(X_121))) = greatest_lower_bound(least_upper_bound(identity,X_121),least_upper_bound(identity,inverse(X_121))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(X_121)),least_upper_bound(identity,X_121)),greatest_lower_bound(least_upper_bound(identity,X_121),least_upper_bound(identity,inverse(X_121)))) )],[refute_0_1844,refute_0_1893]) ).
cnf(refute_0_1895,plain,
multiply(greatest_lower_bound(identity,inverse(X)),least_upper_bound(identity,inverse(inverse(X)))) = least_upper_bound(greatest_lower_bound(identity,inverse(X)),greatest_lower_bound(identity,inverse(inverse(X)))),
inference(subst,[],[refute_0_966:[bind(X_51,$fot(inverse(X)))]]) ).
cnf(refute_0_1896,plain,
( multiply(greatest_lower_bound(identity,inverse(X)),least_upper_bound(identity,inverse(inverse(X)))) != least_upper_bound(greatest_lower_bound(identity,inverse(X)),greatest_lower_bound(identity,inverse(inverse(X))))
| inverse(inverse(X)) != X
| multiply(greatest_lower_bound(identity,inverse(X)),least_upper_bound(identity,inverse(inverse(X)))) = least_upper_bound(greatest_lower_bound(identity,inverse(X)),greatest_lower_bound(identity,X)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(X)),least_upper_bound(identity,inverse(inverse(X)))),least_upper_bound(greatest_lower_bound(identity,inverse(X)),greatest_lower_bound(identity,inverse(inverse(X))))) ),[1,1,1],$fot(X)]]) ).
cnf(refute_0_1897,plain,
( multiply(greatest_lower_bound(identity,inverse(X)),least_upper_bound(identity,inverse(inverse(X)))) != least_upper_bound(greatest_lower_bound(identity,inverse(X)),greatest_lower_bound(identity,inverse(inverse(X))))
| multiply(greatest_lower_bound(identity,inverse(X)),least_upper_bound(identity,inverse(inverse(X)))) = least_upper_bound(greatest_lower_bound(identity,inverse(X)),greatest_lower_bound(identity,X)) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p18_2,refute_0_1896]) ).
cnf(refute_0_1898,plain,
multiply(greatest_lower_bound(identity,inverse(X)),least_upper_bound(identity,inverse(inverse(X)))) = least_upper_bound(greatest_lower_bound(identity,inverse(X)),greatest_lower_bound(identity,X)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(X)),least_upper_bound(identity,inverse(inverse(X)))),least_upper_bound(greatest_lower_bound(identity,inverse(X)),greatest_lower_bound(identity,inverse(inverse(X))))) )],[refute_0_1895,refute_0_1897]) ).
cnf(refute_0_1899,plain,
multiply(greatest_lower_bound(identity,inverse(X)),least_upper_bound(identity,X)) = multiply(least_upper_bound(identity,X),greatest_lower_bound(identity,inverse(X))),
inference(subst,[],[refute_0_1890:[bind(X_157,$fot(X))]]) ).
cnf(refute_0_1900,plain,
least_upper_bound(identity,inverse(inverse(X))) = least_upper_bound(identity,inverse(inverse(X))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,inverse(inverse(X))))]]) ).
cnf(refute_0_1901,plain,
( inverse(inverse(X)) != X
| least_upper_bound(identity,inverse(inverse(X))) != least_upper_bound(identity,inverse(inverse(X)))
| least_upper_bound(identity,inverse(inverse(X))) = least_upper_bound(identity,X) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,inverse(inverse(X))),least_upper_bound(identity,inverse(inverse(X)))) ),[1,1],$fot(X)]]) ).
cnf(refute_0_1902,plain,
( inverse(inverse(X)) != X
| least_upper_bound(identity,inverse(inverse(X))) = least_upper_bound(identity,X) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(inverse(X))),least_upper_bound(identity,inverse(inverse(X)))) )],[refute_0_1900,refute_0_1901]) ).
cnf(refute_0_1903,plain,
least_upper_bound(identity,inverse(inverse(X))) = least_upper_bound(identity,X),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p18_2,refute_0_1902]) ).
cnf(refute_0_1904,plain,
multiply(greatest_lower_bound(identity,inverse(X)),least_upper_bound(identity,inverse(inverse(X)))) = multiply(greatest_lower_bound(identity,inverse(X)),least_upper_bound(identity,inverse(inverse(X)))),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(identity,inverse(X)),least_upper_bound(identity,inverse(inverse(X)))))]]) ).
cnf(refute_0_1905,plain,
( multiply(greatest_lower_bound(identity,inverse(X)),least_upper_bound(identity,inverse(inverse(X)))) != multiply(greatest_lower_bound(identity,inverse(X)),least_upper_bound(identity,inverse(inverse(X))))
| least_upper_bound(identity,inverse(inverse(X))) != least_upper_bound(identity,X)
| multiply(greatest_lower_bound(identity,inverse(X)),least_upper_bound(identity,inverse(inverse(X)))) = multiply(greatest_lower_bound(identity,inverse(X)),least_upper_bound(identity,X)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(X)),least_upper_bound(identity,inverse(inverse(X)))),multiply(greatest_lower_bound(identity,inverse(X)),least_upper_bound(identity,inverse(inverse(X))))) ),[1,1],$fot(least_upper_bound(identity,X))]]) ).
cnf(refute_0_1906,plain,
( least_upper_bound(identity,inverse(inverse(X))) != least_upper_bound(identity,X)
| multiply(greatest_lower_bound(identity,inverse(X)),least_upper_bound(identity,inverse(inverse(X)))) = multiply(greatest_lower_bound(identity,inverse(X)),least_upper_bound(identity,X)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(X)),least_upper_bound(identity,inverse(inverse(X)))),multiply(greatest_lower_bound(identity,inverse(X)),least_upper_bound(identity,inverse(inverse(X))))) )],[refute_0_1904,refute_0_1905]) ).
cnf(refute_0_1907,plain,
multiply(greatest_lower_bound(identity,inverse(X)),least_upper_bound(identity,inverse(inverse(X)))) = multiply(greatest_lower_bound(identity,inverse(X)),least_upper_bound(identity,X)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(inverse(X))),least_upper_bound(identity,X)) )],[refute_0_1903,refute_0_1906]) ).
cnf(refute_0_1908,plain,
( multiply(greatest_lower_bound(identity,inverse(X)),least_upper_bound(identity,X)) != multiply(least_upper_bound(identity,X),greatest_lower_bound(identity,inverse(X)))
| multiply(greatest_lower_bound(identity,inverse(X)),least_upper_bound(identity,inverse(inverse(X)))) != multiply(greatest_lower_bound(identity,inverse(X)),least_upper_bound(identity,X))
| multiply(greatest_lower_bound(identity,inverse(X)),least_upper_bound(identity,inverse(inverse(X)))) = multiply(least_upper_bound(identity,X),greatest_lower_bound(identity,inverse(X))) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(multiply(greatest_lower_bound(identity,inverse(X)),least_upper_bound(identity,inverse(inverse(X)))))),bind(Y0,$fot(multiply(greatest_lower_bound(identity,inverse(X)),least_upper_bound(identity,X)))),bind(Z0,$fot(multiply(least_upper_bound(identity,X),greatest_lower_bound(identity,inverse(X)))))]]) ).
cnf(refute_0_1909,plain,
( multiply(greatest_lower_bound(identity,inverse(X)),least_upper_bound(identity,X)) != multiply(least_upper_bound(identity,X),greatest_lower_bound(identity,inverse(X)))
| multiply(greatest_lower_bound(identity,inverse(X)),least_upper_bound(identity,inverse(inverse(X)))) = multiply(least_upper_bound(identity,X),greatest_lower_bound(identity,inverse(X))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(X)),least_upper_bound(identity,inverse(inverse(X)))),multiply(greatest_lower_bound(identity,inverse(X)),least_upper_bound(identity,X))) )],[refute_0_1907,refute_0_1908]) ).
cnf(refute_0_1910,plain,
multiply(greatest_lower_bound(identity,inverse(X)),least_upper_bound(identity,inverse(inverse(X)))) = multiply(least_upper_bound(identity,X),greatest_lower_bound(identity,inverse(X))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(X)),least_upper_bound(identity,X)),multiply(least_upper_bound(identity,X),greatest_lower_bound(identity,inverse(X)))) )],[refute_0_1899,refute_0_1909]) ).
cnf(refute_0_1911,plain,
( multiply(greatest_lower_bound(identity,inverse(X)),least_upper_bound(identity,inverse(inverse(X)))) != multiply(least_upper_bound(identity,X),greatest_lower_bound(identity,inverse(X)))
| multiply(greatest_lower_bound(identity,inverse(X)),least_upper_bound(identity,inverse(inverse(X)))) != least_upper_bound(greatest_lower_bound(identity,inverse(X)),greatest_lower_bound(identity,X))
| multiply(least_upper_bound(identity,X),greatest_lower_bound(identity,inverse(X))) = least_upper_bound(greatest_lower_bound(identity,inverse(X)),greatest_lower_bound(identity,X)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(X)),least_upper_bound(identity,inverse(inverse(X)))),least_upper_bound(greatest_lower_bound(identity,inverse(X)),greatest_lower_bound(identity,X))) ),[0],$fot(multiply(least_upper_bound(identity,X),greatest_lower_bound(identity,inverse(X))))]]) ).
cnf(refute_0_1912,plain,
( multiply(greatest_lower_bound(identity,inverse(X)),least_upper_bound(identity,inverse(inverse(X)))) != least_upper_bound(greatest_lower_bound(identity,inverse(X)),greatest_lower_bound(identity,X))
| multiply(least_upper_bound(identity,X),greatest_lower_bound(identity,inverse(X))) = least_upper_bound(greatest_lower_bound(identity,inverse(X)),greatest_lower_bound(identity,X)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(X)),least_upper_bound(identity,inverse(inverse(X)))),multiply(least_upper_bound(identity,X),greatest_lower_bound(identity,inverse(X)))) )],[refute_0_1910,refute_0_1911]) ).
cnf(refute_0_1913,plain,
multiply(least_upper_bound(identity,inverse(X_103)),greatest_lower_bound(X_103,identity)) = multiply(greatest_lower_bound(X_103,identity),least_upper_bound(identity,inverse(X_103))),
inference(subst,[],[refute_0_1161:[bind(X_106,$fot(X_103))]]) ).
cnf(refute_0_1914,plain,
( multiply(least_upper_bound(identity,inverse(X_103)),greatest_lower_bound(X_103,identity)) != multiply(greatest_lower_bound(X_103,identity),least_upper_bound(identity,inverse(X_103)))
| multiply(least_upper_bound(identity,inverse(X_103)),greatest_lower_bound(X_103,identity)) != least_upper_bound(greatest_lower_bound(X_103,identity),greatest_lower_bound(identity,inverse(X_103)))
| multiply(greatest_lower_bound(X_103,identity),least_upper_bound(identity,inverse(X_103))) = least_upper_bound(greatest_lower_bound(X_103,identity),greatest_lower_bound(identity,inverse(X_103))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_103)),greatest_lower_bound(X_103,identity)),least_upper_bound(greatest_lower_bound(X_103,identity),greatest_lower_bound(identity,inverse(X_103)))) ),[0],$fot(multiply(greatest_lower_bound(X_103,identity),least_upper_bound(identity,inverse(X_103))))]]) ).
cnf(refute_0_1915,plain,
( multiply(least_upper_bound(identity,inverse(X_103)),greatest_lower_bound(X_103,identity)) != least_upper_bound(greatest_lower_bound(X_103,identity),greatest_lower_bound(identity,inverse(X_103)))
| multiply(greatest_lower_bound(X_103,identity),least_upper_bound(identity,inverse(X_103))) = least_upper_bound(greatest_lower_bound(X_103,identity),greatest_lower_bound(identity,inverse(X_103))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_103)),greatest_lower_bound(X_103,identity)),multiply(greatest_lower_bound(X_103,identity),least_upper_bound(identity,inverse(X_103)))) )],[refute_0_1913,refute_0_1914]) ).
cnf(refute_0_1916,plain,
multiply(greatest_lower_bound(X_103,identity),least_upper_bound(identity,inverse(X_103))) = least_upper_bound(greatest_lower_bound(X_103,identity),greatest_lower_bound(identity,inverse(X_103))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_103)),greatest_lower_bound(X_103,identity)),least_upper_bound(greatest_lower_bound(X_103,identity),greatest_lower_bound(identity,inverse(X_103)))) )],[refute_0_1152,refute_0_1915]) ).
cnf(refute_0_1917,plain,
( multiply(greatest_lower_bound(X_103,identity),least_upper_bound(identity,inverse(X_103))) != least_upper_bound(greatest_lower_bound(X_103,identity),greatest_lower_bound(identity,inverse(X_103)))
| least_upper_bound(greatest_lower_bound(X_103,identity),greatest_lower_bound(identity,inverse(X_103))) = multiply(greatest_lower_bound(X_103,identity),least_upper_bound(identity,inverse(X_103))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(greatest_lower_bound(X_103,identity),least_upper_bound(identity,inverse(X_103))))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(X_103,identity),greatest_lower_bound(identity,inverse(X_103)))))]]) ).
cnf(refute_0_1918,plain,
least_upper_bound(greatest_lower_bound(X_103,identity),greatest_lower_bound(identity,inverse(X_103))) = multiply(greatest_lower_bound(X_103,identity),least_upper_bound(identity,inverse(X_103))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_103,identity),least_upper_bound(identity,inverse(X_103))),least_upper_bound(greatest_lower_bound(X_103,identity),greatest_lower_bound(identity,inverse(X_103)))) )],[refute_0_1916,refute_0_1917]) ).
cnf(refute_0_1919,plain,
least_upper_bound(greatest_lower_bound(X,identity),greatest_lower_bound(identity,inverse(X))) = multiply(greatest_lower_bound(X,identity),least_upper_bound(identity,inverse(X))),
inference(subst,[],[refute_0_1918:[bind(X_103,$fot(X))]]) ).
cnf(refute_0_1920,plain,
least_upper_bound(greatest_lower_bound(X_79,X_80),least_upper_bound(greatest_lower_bound(X_80,X_79),Z)) = least_upper_bound(least_upper_bound(greatest_lower_bound(X_79,X_80),greatest_lower_bound(X_80,X_79)),Z),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(greatest_lower_bound(X_79,X_80))),bind(Y,$fot(greatest_lower_bound(X_80,X_79)))]]) ).
cnf(refute_0_1921,plain,
least_upper_bound(greatest_lower_bound(X_79,X_80),greatest_lower_bound(X_80,X_79)) = greatest_lower_bound(X_79,X_80),
inference(subst,[],[refute_0_236:[bind(Y,$fot(X_79)),bind(X_21,$fot(X_80))]]) ).
cnf(refute_0_1922,plain,
( least_upper_bound(greatest_lower_bound(X_79,X_80),greatest_lower_bound(X_80,X_79)) != greatest_lower_bound(X_79,X_80)
| least_upper_bound(greatest_lower_bound(X_79,X_80),least_upper_bound(greatest_lower_bound(X_80,X_79),Z)) != least_upper_bound(least_upper_bound(greatest_lower_bound(X_79,X_80),greatest_lower_bound(X_80,X_79)),Z)
| least_upper_bound(greatest_lower_bound(X_79,X_80),least_upper_bound(greatest_lower_bound(X_80,X_79),Z)) = least_upper_bound(greatest_lower_bound(X_79,X_80),Z) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_79,X_80),least_upper_bound(greatest_lower_bound(X_80,X_79),Z)),least_upper_bound(least_upper_bound(greatest_lower_bound(X_79,X_80),greatest_lower_bound(X_80,X_79)),Z)) ),[1,0],$fot(greatest_lower_bound(X_79,X_80))]]) ).
cnf(refute_0_1923,plain,
( least_upper_bound(greatest_lower_bound(X_79,X_80),least_upper_bound(greatest_lower_bound(X_80,X_79),Z)) != least_upper_bound(least_upper_bound(greatest_lower_bound(X_79,X_80),greatest_lower_bound(X_80,X_79)),Z)
| least_upper_bound(greatest_lower_bound(X_79,X_80),least_upper_bound(greatest_lower_bound(X_80,X_79),Z)) = least_upper_bound(greatest_lower_bound(X_79,X_80),Z) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_79,X_80),greatest_lower_bound(X_80,X_79)),greatest_lower_bound(X_79,X_80)) )],[refute_0_1921,refute_0_1922]) ).
cnf(refute_0_1924,plain,
least_upper_bound(greatest_lower_bound(X_79,X_80),least_upper_bound(greatest_lower_bound(X_80,X_79),Z)) = least_upper_bound(greatest_lower_bound(X_79,X_80),Z),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_79,X_80),least_upper_bound(greatest_lower_bound(X_80,X_79),Z)),least_upper_bound(least_upper_bound(greatest_lower_bound(X_79,X_80),greatest_lower_bound(X_80,X_79)),Z)) )],[refute_0_1920,refute_0_1923]) ).
cnf(refute_0_1925,plain,
least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),greatest_lower_bound(X_13,least_upper_bound(X_134,least_upper_bound(X_135,X_13)))) = least_upper_bound(X_134,least_upper_bound(X_135,X_13)),
inference(subst,[],[refute_0_53:[bind(X_12,$fot(least_upper_bound(X_134,least_upper_bound(X_135,X_13))))]]) ).
cnf(refute_0_1926,plain,
greatest_lower_bound(X,least_upper_bound(least_upper_bound(X_29,X_30),X)) = X,
inference(subst,[],[refute_0_171:[bind(Y,$fot(least_upper_bound(X_29,X_30)))]]) ).
cnf(refute_0_1927,plain,
( greatest_lower_bound(X,least_upper_bound(least_upper_bound(X_29,X_30),X)) != X
| least_upper_bound(least_upper_bound(X_29,X_30),X) != least_upper_bound(X_29,least_upper_bound(X_30,X))
| greatest_lower_bound(X,least_upper_bound(X_29,least_upper_bound(X_30,X))) = X ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X,least_upper_bound(least_upper_bound(X_29,X_30),X)),X) ),[0,1],$fot(least_upper_bound(X_29,least_upper_bound(X_30,X)))]]) ).
cnf(refute_0_1928,plain,
( greatest_lower_bound(X,least_upper_bound(least_upper_bound(X_29,X_30),X)) != X
| greatest_lower_bound(X,least_upper_bound(X_29,least_upper_bound(X_30,X))) = X ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_29,X_30),X),least_upper_bound(X_29,least_upper_bound(X_30,X))) )],[refute_0_1749,refute_0_1927]) ).
cnf(refute_0_1929,plain,
greatest_lower_bound(X,least_upper_bound(X_29,least_upper_bound(X_30,X))) = X,
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,least_upper_bound(least_upper_bound(X_29,X_30),X)),X) )],[refute_0_1926,refute_0_1928]) ).
cnf(refute_0_1930,plain,
greatest_lower_bound(X_13,least_upper_bound(X_134,least_upper_bound(X_135,X_13))) = X_13,
inference(subst,[],[refute_0_1929:[bind(X,$fot(X_13)),bind(X_29,$fot(X_134)),bind(X_30,$fot(X_135))]]) ).
cnf(refute_0_1931,plain,
( greatest_lower_bound(X_13,least_upper_bound(X_134,least_upper_bound(X_135,X_13))) != X_13
| least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),greatest_lower_bound(X_13,least_upper_bound(X_134,least_upper_bound(X_135,X_13)))) != least_upper_bound(X_134,least_upper_bound(X_135,X_13))
| least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_13) = least_upper_bound(X_134,least_upper_bound(X_135,X_13)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),greatest_lower_bound(X_13,least_upper_bound(X_134,least_upper_bound(X_135,X_13)))),least_upper_bound(X_134,least_upper_bound(X_135,X_13))) ),[0,1],$fot(X_13)]]) ).
cnf(refute_0_1932,plain,
( least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),greatest_lower_bound(X_13,least_upper_bound(X_134,least_upper_bound(X_135,X_13)))) != least_upper_bound(X_134,least_upper_bound(X_135,X_13))
| least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_13) = least_upper_bound(X_134,least_upper_bound(X_135,X_13)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_13,least_upper_bound(X_134,least_upper_bound(X_135,X_13))),X_13) )],[refute_0_1930,refute_0_1931]) ).
cnf(refute_0_1933,plain,
least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_13) = least_upper_bound(X_134,least_upper_bound(X_135,X_13)),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),greatest_lower_bound(X_13,least_upper_bound(X_134,least_upper_bound(X_135,X_13)))),least_upper_bound(X_134,least_upper_bound(X_135,X_13))) )],[refute_0_1925,refute_0_1932]) ).
cnf(refute_0_1934,plain,
least_upper_bound(X_13,least_upper_bound(X_135,X_13)) = least_upper_bound(X_13,X_135),
inference(subst,[],[refute_0_64:[bind(Y,$fot(X_135)),bind(X_21,$fot(X_13))]]) ).
cnf(refute_0_1935,plain,
least_upper_bound(X_134,least_upper_bound(X_13,least_upper_bound(X_135,X_13))) = least_upper_bound(X_134,least_upper_bound(X_13,least_upper_bound(X_135,X_13))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_134,least_upper_bound(X_13,least_upper_bound(X_135,X_13))))]]) ).
cnf(refute_0_1936,plain,
( least_upper_bound(X_13,least_upper_bound(X_135,X_13)) != least_upper_bound(X_13,X_135)
| least_upper_bound(X_134,least_upper_bound(X_13,least_upper_bound(X_135,X_13))) != least_upper_bound(X_134,least_upper_bound(X_13,least_upper_bound(X_135,X_13)))
| least_upper_bound(X_134,least_upper_bound(X_13,least_upper_bound(X_135,X_13))) = least_upper_bound(X_134,least_upper_bound(X_13,X_135)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_134,least_upper_bound(X_13,least_upper_bound(X_135,X_13))),least_upper_bound(X_134,least_upper_bound(X_13,least_upper_bound(X_135,X_13)))) ),[1,1],$fot(least_upper_bound(X_13,X_135))]]) ).
cnf(refute_0_1937,plain,
( least_upper_bound(X_13,least_upper_bound(X_135,X_13)) != least_upper_bound(X_13,X_135)
| least_upper_bound(X_134,least_upper_bound(X_13,least_upper_bound(X_135,X_13))) = least_upper_bound(X_134,least_upper_bound(X_13,X_135)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_134,least_upper_bound(X_13,least_upper_bound(X_135,X_13))),least_upper_bound(X_134,least_upper_bound(X_13,least_upper_bound(X_135,X_13)))) )],[refute_0_1935,refute_0_1936]) ).
cnf(refute_0_1938,plain,
least_upper_bound(X_134,least_upper_bound(X_13,least_upper_bound(X_135,X_13))) = least_upper_bound(X_134,least_upper_bound(X_13,X_135)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_13,least_upper_bound(X_135,X_13)),least_upper_bound(X_13,X_135)) )],[refute_0_1934,refute_0_1937]) ).
cnf(refute_0_1939,plain,
least_upper_bound(X_29,least_upper_bound(X_30,X_31)) = least_upper_bound(least_upper_bound(X_29,X_30),X_31),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_29)),bind(Y,$fot(X_30)),bind(Z,$fot(X_31))]]) ).
cnf(refute_0_1940,plain,
least_upper_bound(X_31,X_30) = least_upper_bound(X_30,X_31),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_31)),bind(Y,$fot(X_30))]]) ).
cnf(refute_0_1941,plain,
( least_upper_bound(X_31,X_30) != least_upper_bound(X_30,X_31)
| least_upper_bound(X_30,X_31) = least_upper_bound(X_31,X_30) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X_31,X_30))),bind(Y0,$fot(least_upper_bound(X_30,X_31)))]]) ).
cnf(refute_0_1942,plain,
least_upper_bound(X_30,X_31) = least_upper_bound(X_31,X_30),
inference(resolve,[$cnf( $equal(least_upper_bound(X_31,X_30),least_upper_bound(X_30,X_31)) )],[refute_0_1940,refute_0_1941]) ).
cnf(refute_0_1943,plain,
( least_upper_bound(X_29,least_upper_bound(X_30,X_31)) != least_upper_bound(least_upper_bound(X_29,X_30),X_31)
| least_upper_bound(X_30,X_31) != least_upper_bound(X_31,X_30)
| least_upper_bound(X_29,least_upper_bound(X_31,X_30)) = least_upper_bound(least_upper_bound(X_29,X_30),X_31) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_29,least_upper_bound(X_30,X_31)),least_upper_bound(least_upper_bound(X_29,X_30),X_31)) ),[0,1],$fot(least_upper_bound(X_31,X_30))]]) ).
cnf(refute_0_1944,plain,
( least_upper_bound(X_29,least_upper_bound(X_30,X_31)) != least_upper_bound(least_upper_bound(X_29,X_30),X_31)
| least_upper_bound(X_29,least_upper_bound(X_31,X_30)) = least_upper_bound(least_upper_bound(X_29,X_30),X_31) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_30,X_31),least_upper_bound(X_31,X_30)) )],[refute_0_1942,refute_0_1943]) ).
cnf(refute_0_1945,plain,
least_upper_bound(X_29,least_upper_bound(X_31,X_30)) = least_upper_bound(least_upper_bound(X_29,X_30),X_31),
inference(resolve,[$cnf( $equal(least_upper_bound(X_29,least_upper_bound(X_30,X_31)),least_upper_bound(least_upper_bound(X_29,X_30),X_31)) )],[refute_0_1939,refute_0_1944]) ).
cnf(refute_0_1946,plain,
least_upper_bound(least_upper_bound(X_29,X_30),X_31) = least_upper_bound(X_29,least_upper_bound(X_30,X_31)),
inference(subst,[],[refute_0_60:[bind(X,$fot(X_29)),bind(Y,$fot(X_30)),bind(Z,$fot(X_31))]]) ).
cnf(refute_0_1947,plain,
( least_upper_bound(X_29,least_upper_bound(X_31,X_30)) != least_upper_bound(least_upper_bound(X_29,X_30),X_31)
| least_upper_bound(least_upper_bound(X_29,X_30),X_31) != least_upper_bound(X_29,least_upper_bound(X_30,X_31))
| least_upper_bound(X_29,least_upper_bound(X_31,X_30)) = least_upper_bound(X_29,least_upper_bound(X_30,X_31)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_29,least_upper_bound(X_31,X_30)),least_upper_bound(X_29,least_upper_bound(X_30,X_31))) ),[0],$fot(least_upper_bound(least_upper_bound(X_29,X_30),X_31))]]) ).
cnf(refute_0_1948,plain,
( least_upper_bound(X_29,least_upper_bound(X_31,X_30)) != least_upper_bound(least_upper_bound(X_29,X_30),X_31)
| least_upper_bound(X_29,least_upper_bound(X_31,X_30)) = least_upper_bound(X_29,least_upper_bound(X_30,X_31)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_29,X_30),X_31),least_upper_bound(X_29,least_upper_bound(X_30,X_31))) )],[refute_0_1946,refute_0_1947]) ).
cnf(refute_0_1949,plain,
least_upper_bound(X_29,least_upper_bound(X_31,X_30)) = least_upper_bound(X_29,least_upper_bound(X_30,X_31)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_29,least_upper_bound(X_31,X_30)),least_upper_bound(least_upper_bound(X_29,X_30),X_31)) )],[refute_0_1945,refute_0_1948]) ).
cnf(refute_0_1950,plain,
( least_upper_bound(X_29,least_upper_bound(X_31,X_30)) != least_upper_bound(X_29,least_upper_bound(X_30,X_31))
| least_upper_bound(X_29,least_upper_bound(X_30,X_31)) = least_upper_bound(X_29,least_upper_bound(X_31,X_30)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X_29,least_upper_bound(X_31,X_30)))),bind(Y0,$fot(least_upper_bound(X_29,least_upper_bound(X_30,X_31))))]]) ).
cnf(refute_0_1951,plain,
least_upper_bound(X_29,least_upper_bound(X_30,X_31)) = least_upper_bound(X_29,least_upper_bound(X_31,X_30)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_29,least_upper_bound(X_31,X_30)),least_upper_bound(X_29,least_upper_bound(X_30,X_31))) )],[refute_0_1949,refute_0_1950]) ).
cnf(refute_0_1952,plain,
least_upper_bound(X_134,least_upper_bound(least_upper_bound(X_135,X_13),X_13)) = least_upper_bound(X_134,least_upper_bound(X_13,least_upper_bound(X_135,X_13))),
inference(subst,[],[refute_0_1951:[bind(X_29,$fot(X_134)),bind(X_30,$fot(least_upper_bound(X_135,X_13))),bind(X_31,$fot(X_13))]]) ).
cnf(refute_0_1953,plain,
least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_13) = least_upper_bound(X_134,least_upper_bound(least_upper_bound(X_135,X_13),X_13)),
inference(subst,[],[refute_0_60:[bind(X,$fot(X_134)),bind(Y,$fot(least_upper_bound(X_135,X_13))),bind(Z,$fot(X_13))]]) ).
cnf(refute_0_1954,plain,
( least_upper_bound(X_134,least_upper_bound(least_upper_bound(X_135,X_13),X_13)) != least_upper_bound(X_134,least_upper_bound(X_13,least_upper_bound(X_135,X_13)))
| least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_13) != least_upper_bound(X_134,least_upper_bound(least_upper_bound(X_135,X_13),X_13))
| least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_13) = least_upper_bound(X_134,least_upper_bound(X_13,least_upper_bound(X_135,X_13))) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_13))),bind(Y0,$fot(least_upper_bound(X_134,least_upper_bound(least_upper_bound(X_135,X_13),X_13)))),bind(Z0,$fot(least_upper_bound(X_134,least_upper_bound(X_13,least_upper_bound(X_135,X_13)))))]]) ).
cnf(refute_0_1955,plain,
( least_upper_bound(X_134,least_upper_bound(least_upper_bound(X_135,X_13),X_13)) != least_upper_bound(X_134,least_upper_bound(X_13,least_upper_bound(X_135,X_13)))
| least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_13) = least_upper_bound(X_134,least_upper_bound(X_13,least_upper_bound(X_135,X_13))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_13),least_upper_bound(X_134,least_upper_bound(least_upper_bound(X_135,X_13),X_13))) )],[refute_0_1953,refute_0_1954]) ).
cnf(refute_0_1956,plain,
least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_13) = least_upper_bound(X_134,least_upper_bound(X_13,least_upper_bound(X_135,X_13))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_134,least_upper_bound(least_upper_bound(X_135,X_13),X_13)),least_upper_bound(X_134,least_upper_bound(X_13,least_upper_bound(X_135,X_13)))) )],[refute_0_1952,refute_0_1955]) ).
cnf(refute_0_1957,plain,
( least_upper_bound(X_134,least_upper_bound(X_13,least_upper_bound(X_135,X_13))) != least_upper_bound(X_134,least_upper_bound(X_13,X_135))
| least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_13) != least_upper_bound(X_134,least_upper_bound(X_13,least_upper_bound(X_135,X_13)))
| least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_13) = least_upper_bound(X_134,least_upper_bound(X_13,X_135)) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_13))),bind(Y0,$fot(least_upper_bound(X_134,least_upper_bound(X_13,least_upper_bound(X_135,X_13))))),bind(Z0,$fot(least_upper_bound(X_134,least_upper_bound(X_13,X_135))))]]) ).
cnf(refute_0_1958,plain,
( least_upper_bound(X_134,least_upper_bound(X_13,least_upper_bound(X_135,X_13))) != least_upper_bound(X_134,least_upper_bound(X_13,X_135))
| least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_13) = least_upper_bound(X_134,least_upper_bound(X_13,X_135)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_13),least_upper_bound(X_134,least_upper_bound(X_13,least_upper_bound(X_135,X_13)))) )],[refute_0_1956,refute_0_1957]) ).
cnf(refute_0_1959,plain,
least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_13) = least_upper_bound(X_134,least_upper_bound(X_13,X_135)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_134,least_upper_bound(X_13,least_upper_bound(X_135,X_13))),least_upper_bound(X_134,least_upper_bound(X_13,X_135))) )],[refute_0_1938,refute_0_1958]) ).
cnf(refute_0_1960,plain,
( least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_13) != least_upper_bound(X_134,least_upper_bound(X_13,X_135))
| least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_13) != least_upper_bound(X_134,least_upper_bound(X_135,X_13))
| least_upper_bound(X_134,least_upper_bound(X_13,X_135)) = least_upper_bound(X_134,least_upper_bound(X_135,X_13)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_13),least_upper_bound(X_134,least_upper_bound(X_135,X_13))) ),[0],$fot(least_upper_bound(X_134,least_upper_bound(X_13,X_135)))]]) ).
cnf(refute_0_1961,plain,
( least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_13) != least_upper_bound(X_134,least_upper_bound(X_135,X_13))
| least_upper_bound(X_134,least_upper_bound(X_13,X_135)) = least_upper_bound(X_134,least_upper_bound(X_135,X_13)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_13),least_upper_bound(X_134,least_upper_bound(X_13,X_135))) )],[refute_0_1959,refute_0_1960]) ).
cnf(refute_0_1962,plain,
least_upper_bound(X_134,least_upper_bound(X_13,X_135)) = least_upper_bound(X_134,least_upper_bound(X_135,X_13)),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_13),least_upper_bound(X_134,least_upper_bound(X_135,X_13))) )],[refute_0_1933,refute_0_1961]) ).
cnf(refute_0_1963,plain,
least_upper_bound(greatest_lower_bound(X_79,X_80),least_upper_bound(greatest_lower_bound(X_80,X_79),Z)) = least_upper_bound(greatest_lower_bound(X_79,X_80),least_upper_bound(Z,greatest_lower_bound(X_80,X_79))),
inference(subst,[],[refute_0_1962:[bind(X_13,$fot(greatest_lower_bound(X_80,X_79))),bind(X_134,$fot(greatest_lower_bound(X_79,X_80))),bind(X_135,$fot(Z))]]) ).
cnf(refute_0_1964,plain,
( least_upper_bound(greatest_lower_bound(X_79,X_80),least_upper_bound(greatest_lower_bound(X_80,X_79),Z)) != least_upper_bound(greatest_lower_bound(X_79,X_80),Z)
| least_upper_bound(greatest_lower_bound(X_79,X_80),least_upper_bound(greatest_lower_bound(X_80,X_79),Z)) != least_upper_bound(greatest_lower_bound(X_79,X_80),least_upper_bound(Z,greatest_lower_bound(X_80,X_79)))
| least_upper_bound(greatest_lower_bound(X_79,X_80),least_upper_bound(Z,greatest_lower_bound(X_80,X_79))) = least_upper_bound(greatest_lower_bound(X_79,X_80),Z) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_79,X_80),least_upper_bound(greatest_lower_bound(X_80,X_79),Z)),least_upper_bound(greatest_lower_bound(X_79,X_80),Z)) ),[0],$fot(least_upper_bound(greatest_lower_bound(X_79,X_80),least_upper_bound(Z,greatest_lower_bound(X_80,X_79))))]]) ).
cnf(refute_0_1965,plain,
( least_upper_bound(greatest_lower_bound(X_79,X_80),least_upper_bound(greatest_lower_bound(X_80,X_79),Z)) != least_upper_bound(greatest_lower_bound(X_79,X_80),Z)
| least_upper_bound(greatest_lower_bound(X_79,X_80),least_upper_bound(Z,greatest_lower_bound(X_80,X_79))) = least_upper_bound(greatest_lower_bound(X_79,X_80),Z) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_79,X_80),least_upper_bound(greatest_lower_bound(X_80,X_79),Z)),least_upper_bound(greatest_lower_bound(X_79,X_80),least_upper_bound(Z,greatest_lower_bound(X_80,X_79)))) )],[refute_0_1963,refute_0_1964]) ).
cnf(refute_0_1966,plain,
least_upper_bound(greatest_lower_bound(X_79,X_80),least_upper_bound(Z,greatest_lower_bound(X_80,X_79))) = least_upper_bound(greatest_lower_bound(X_79,X_80),Z),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_79,X_80),least_upper_bound(greatest_lower_bound(X_80,X_79),Z)),least_upper_bound(greatest_lower_bound(X_79,X_80),Z)) )],[refute_0_1924,refute_0_1965]) ).
cnf(refute_0_1967,plain,
least_upper_bound(greatest_lower_bound(X_21,Y),least_upper_bound(X_146,greatest_lower_bound(Y,X_21))) = least_upper_bound(X_146,least_upper_bound(greatest_lower_bound(Y,X_21),greatest_lower_bound(X_21,Y))),
inference(subst,[],[refute_0_1752:[bind(X,$fot(greatest_lower_bound(X_21,Y))),bind(X_29,$fot(X_146)),bind(X_30,$fot(greatest_lower_bound(Y,X_21)))]]) ).
cnf(refute_0_1968,plain,
( least_upper_bound(greatest_lower_bound(Y,X_21),greatest_lower_bound(X_21,Y)) != greatest_lower_bound(Y,X_21)
| least_upper_bound(greatest_lower_bound(X_21,Y),least_upper_bound(X_146,greatest_lower_bound(Y,X_21))) != least_upper_bound(X_146,least_upper_bound(greatest_lower_bound(Y,X_21),greatest_lower_bound(X_21,Y)))
| least_upper_bound(greatest_lower_bound(X_21,Y),least_upper_bound(X_146,greatest_lower_bound(Y,X_21))) = least_upper_bound(X_146,greatest_lower_bound(Y,X_21)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_21,Y),least_upper_bound(X_146,greatest_lower_bound(Y,X_21))),least_upper_bound(X_146,least_upper_bound(greatest_lower_bound(Y,X_21),greatest_lower_bound(X_21,Y)))) ),[1,1],$fot(greatest_lower_bound(Y,X_21))]]) ).
cnf(refute_0_1969,plain,
( least_upper_bound(greatest_lower_bound(X_21,Y),least_upper_bound(X_146,greatest_lower_bound(Y,X_21))) != least_upper_bound(X_146,least_upper_bound(greatest_lower_bound(Y,X_21),greatest_lower_bound(X_21,Y)))
| least_upper_bound(greatest_lower_bound(X_21,Y),least_upper_bound(X_146,greatest_lower_bound(Y,X_21))) = least_upper_bound(X_146,greatest_lower_bound(Y,X_21)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(Y,X_21),greatest_lower_bound(X_21,Y)),greatest_lower_bound(Y,X_21)) )],[refute_0_236,refute_0_1968]) ).
cnf(refute_0_1970,plain,
least_upper_bound(greatest_lower_bound(X_21,Y),least_upper_bound(X_146,greatest_lower_bound(Y,X_21))) = least_upper_bound(X_146,greatest_lower_bound(Y,X_21)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_21,Y),least_upper_bound(X_146,greatest_lower_bound(Y,X_21))),least_upper_bound(X_146,least_upper_bound(greatest_lower_bound(Y,X_21),greatest_lower_bound(X_21,Y)))) )],[refute_0_1967,refute_0_1969]) ).
cnf(refute_0_1971,plain,
least_upper_bound(greatest_lower_bound(X_79,X_80),least_upper_bound(Z,greatest_lower_bound(X_80,X_79))) = least_upper_bound(Z,greatest_lower_bound(X_80,X_79)),
inference(subst,[],[refute_0_1970:[bind(Y,$fot(X_80)),bind(X_146,$fot(Z)),bind(X_21,$fot(X_79))]]) ).
cnf(refute_0_1972,plain,
( least_upper_bound(greatest_lower_bound(X_79,X_80),least_upper_bound(Z,greatest_lower_bound(X_80,X_79))) != least_upper_bound(Z,greatest_lower_bound(X_80,X_79))
| least_upper_bound(greatest_lower_bound(X_79,X_80),least_upper_bound(Z,greatest_lower_bound(X_80,X_79))) != least_upper_bound(greatest_lower_bound(X_79,X_80),Z)
| least_upper_bound(Z,greatest_lower_bound(X_80,X_79)) = least_upper_bound(greatest_lower_bound(X_79,X_80),Z) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_79,X_80),least_upper_bound(Z,greatest_lower_bound(X_80,X_79))),least_upper_bound(greatest_lower_bound(X_79,X_80),Z)) ),[0],$fot(least_upper_bound(Z,greatest_lower_bound(X_80,X_79)))]]) ).
cnf(refute_0_1973,plain,
( least_upper_bound(greatest_lower_bound(X_79,X_80),least_upper_bound(Z,greatest_lower_bound(X_80,X_79))) != least_upper_bound(greatest_lower_bound(X_79,X_80),Z)
| least_upper_bound(Z,greatest_lower_bound(X_80,X_79)) = least_upper_bound(greatest_lower_bound(X_79,X_80),Z) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_79,X_80),least_upper_bound(Z,greatest_lower_bound(X_80,X_79))),least_upper_bound(Z,greatest_lower_bound(X_80,X_79))) )],[refute_0_1971,refute_0_1972]) ).
cnf(refute_0_1974,plain,
least_upper_bound(Z,greatest_lower_bound(X_80,X_79)) = least_upper_bound(greatest_lower_bound(X_79,X_80),Z),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_79,X_80),least_upper_bound(Z,greatest_lower_bound(X_80,X_79))),least_upper_bound(greatest_lower_bound(X_79,X_80),Z)) )],[refute_0_1966,refute_0_1973]) ).
cnf(refute_0_1975,plain,
least_upper_bound(greatest_lower_bound(identity,inverse(X)),greatest_lower_bound(identity,X)) = least_upper_bound(greatest_lower_bound(X,identity),greatest_lower_bound(identity,inverse(X))),
inference(subst,[],[refute_0_1974:[bind(Z,$fot(greatest_lower_bound(identity,inverse(X)))),bind(X_79,$fot(X)),bind(X_80,$fot(identity))]]) ).
cnf(refute_0_1976,plain,
( least_upper_bound(greatest_lower_bound(X,identity),greatest_lower_bound(identity,inverse(X))) != multiply(greatest_lower_bound(X,identity),least_upper_bound(identity,inverse(X)))
| least_upper_bound(greatest_lower_bound(identity,inverse(X)),greatest_lower_bound(identity,X)) != least_upper_bound(greatest_lower_bound(X,identity),greatest_lower_bound(identity,inverse(X)))
| least_upper_bound(greatest_lower_bound(identity,inverse(X)),greatest_lower_bound(identity,X)) = multiply(greatest_lower_bound(X,identity),least_upper_bound(identity,inverse(X))) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(identity,inverse(X)),greatest_lower_bound(identity,X)))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(X,identity),greatest_lower_bound(identity,inverse(X))))),bind(Z0,$fot(multiply(greatest_lower_bound(X,identity),least_upper_bound(identity,inverse(X)))))]]) ).
cnf(refute_0_1977,plain,
( least_upper_bound(greatest_lower_bound(X,identity),greatest_lower_bound(identity,inverse(X))) != multiply(greatest_lower_bound(X,identity),least_upper_bound(identity,inverse(X)))
| least_upper_bound(greatest_lower_bound(identity,inverse(X)),greatest_lower_bound(identity,X)) = multiply(greatest_lower_bound(X,identity),least_upper_bound(identity,inverse(X))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,inverse(X)),greatest_lower_bound(identity,X)),least_upper_bound(greatest_lower_bound(X,identity),greatest_lower_bound(identity,inverse(X)))) )],[refute_0_1975,refute_0_1976]) ).
cnf(refute_0_1978,plain,
least_upper_bound(greatest_lower_bound(identity,inverse(X)),greatest_lower_bound(identity,X)) = multiply(greatest_lower_bound(X,identity),least_upper_bound(identity,inverse(X))),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X,identity),greatest_lower_bound(identity,inverse(X))),multiply(greatest_lower_bound(X,identity),least_upper_bound(identity,inverse(X)))) )],[refute_0_1919,refute_0_1977]) ).
cnf(refute_0_1979,plain,
( multiply(least_upper_bound(identity,X),greatest_lower_bound(identity,inverse(X))) != least_upper_bound(greatest_lower_bound(identity,inverse(X)),greatest_lower_bound(identity,X))
| least_upper_bound(greatest_lower_bound(identity,inverse(X)),greatest_lower_bound(identity,X)) != multiply(greatest_lower_bound(X,identity),least_upper_bound(identity,inverse(X)))
| multiply(least_upper_bound(identity,X),greatest_lower_bound(identity,inverse(X))) = multiply(greatest_lower_bound(X,identity),least_upper_bound(identity,inverse(X))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(identity,X),greatest_lower_bound(identity,inverse(X))),multiply(greatest_lower_bound(X,identity),least_upper_bound(identity,inverse(X)))) ),[0],$fot(least_upper_bound(greatest_lower_bound(identity,inverse(X)),greatest_lower_bound(identity,X)))]]) ).
cnf(refute_0_1980,plain,
( multiply(least_upper_bound(identity,X),greatest_lower_bound(identity,inverse(X))) != least_upper_bound(greatest_lower_bound(identity,inverse(X)),greatest_lower_bound(identity,X))
| multiply(least_upper_bound(identity,X),greatest_lower_bound(identity,inverse(X))) = multiply(greatest_lower_bound(X,identity),least_upper_bound(identity,inverse(X))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,inverse(X)),greatest_lower_bound(identity,X)),multiply(greatest_lower_bound(X,identity),least_upper_bound(identity,inverse(X)))) )],[refute_0_1978,refute_0_1979]) ).
cnf(refute_0_1981,plain,
( multiply(greatest_lower_bound(identity,inverse(X)),least_upper_bound(identity,inverse(inverse(X)))) != least_upper_bound(greatest_lower_bound(identity,inverse(X)),greatest_lower_bound(identity,X))
| multiply(least_upper_bound(identity,X),greatest_lower_bound(identity,inverse(X))) = multiply(greatest_lower_bound(X,identity),least_upper_bound(identity,inverse(X))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X),greatest_lower_bound(identity,inverse(X))),least_upper_bound(greatest_lower_bound(identity,inverse(X)),greatest_lower_bound(identity,X))) )],[refute_0_1912,refute_0_1980]) ).
cnf(refute_0_1982,plain,
multiply(least_upper_bound(identity,X),greatest_lower_bound(identity,inverse(X))) = multiply(greatest_lower_bound(X,identity),least_upper_bound(identity,inverse(X))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(X)),least_upper_bound(identity,inverse(inverse(X)))),least_upper_bound(greatest_lower_bound(identity,inverse(X)),greatest_lower_bound(identity,X))) )],[refute_0_1898,refute_0_1981]) ).
cnf(refute_0_1983,plain,
multiply(least_upper_bound(identity,X_121),greatest_lower_bound(identity,inverse(X_121))) = multiply(greatest_lower_bound(X_121,identity),least_upper_bound(identity,inverse(X_121))),
inference(subst,[],[refute_0_1982:[bind(X,$fot(X_121))]]) ).
cnf(refute_0_1984,plain,
( multiply(least_upper_bound(identity,X_121),greatest_lower_bound(identity,inverse(X_121))) != multiply(greatest_lower_bound(X_121,identity),least_upper_bound(identity,inverse(X_121)))
| multiply(least_upper_bound(identity,X_121),greatest_lower_bound(identity,inverse(X_121))) != greatest_lower_bound(least_upper_bound(identity,X_121),least_upper_bound(identity,inverse(X_121)))
| multiply(greatest_lower_bound(X_121,identity),least_upper_bound(identity,inverse(X_121))) = greatest_lower_bound(least_upper_bound(identity,X_121),least_upper_bound(identity,inverse(X_121))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,X_121),greatest_lower_bound(identity,inverse(X_121))),greatest_lower_bound(least_upper_bound(identity,X_121),least_upper_bound(identity,inverse(X_121)))) ),[0],$fot(multiply(greatest_lower_bound(X_121,identity),least_upper_bound(identity,inverse(X_121))))]]) ).
cnf(refute_0_1985,plain,
( multiply(least_upper_bound(identity,X_121),greatest_lower_bound(identity,inverse(X_121))) != greatest_lower_bound(least_upper_bound(identity,X_121),least_upper_bound(identity,inverse(X_121)))
| multiply(greatest_lower_bound(X_121,identity),least_upper_bound(identity,inverse(X_121))) = greatest_lower_bound(least_upper_bound(identity,X_121),least_upper_bound(identity,inverse(X_121))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_121),greatest_lower_bound(identity,inverse(X_121))),multiply(greatest_lower_bound(X_121,identity),least_upper_bound(identity,inverse(X_121)))) )],[refute_0_1983,refute_0_1984]) ).
cnf(refute_0_1986,plain,
multiply(greatest_lower_bound(X_121,identity),least_upper_bound(identity,inverse(X_121))) = greatest_lower_bound(least_upper_bound(identity,X_121),least_upper_bound(identity,inverse(X_121))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_121),greatest_lower_bound(identity,inverse(X_121))),greatest_lower_bound(least_upper_bound(identity,X_121),least_upper_bound(identity,inverse(X_121)))) )],[refute_0_1894,refute_0_1985]) ).
cnf(refute_0_1987,plain,
( multiply(greatest_lower_bound(X_121,identity),least_upper_bound(identity,inverse(X_121))) != greatest_lower_bound(least_upper_bound(identity,X_121),least_upper_bound(identity,inverse(X_121)))
| greatest_lower_bound(least_upper_bound(identity,X_121),least_upper_bound(identity,inverse(X_121))) = multiply(greatest_lower_bound(X_121,identity),least_upper_bound(identity,inverse(X_121))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(greatest_lower_bound(X_121,identity),least_upper_bound(identity,inverse(X_121))))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(identity,X_121),least_upper_bound(identity,inverse(X_121)))))]]) ).
cnf(refute_0_1988,plain,
greatest_lower_bound(least_upper_bound(identity,X_121),least_upper_bound(identity,inverse(X_121))) = multiply(greatest_lower_bound(X_121,identity),least_upper_bound(identity,inverse(X_121))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_121,identity),least_upper_bound(identity,inverse(X_121))),greatest_lower_bound(least_upper_bound(identity,X_121),least_upper_bound(identity,inverse(X_121)))) )],[refute_0_1986,refute_0_1987]) ).
cnf(refute_0_1989,plain,
greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114))) = multiply(greatest_lower_bound(X_114,identity),least_upper_bound(identity,inverse(X_114))),
inference(subst,[],[refute_0_1988:[bind(X_121,$fot(X_114))]]) ).
cnf(refute_0_1990,plain,
least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114)))) = least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114)))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114)))))]]) ).
cnf(refute_0_1991,plain,
( greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114))) != multiply(greatest_lower_bound(X_114,identity),least_upper_bound(identity,inverse(X_114)))
| least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114)))) != least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114))))
| least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114)))) = least_upper_bound(identity,multiply(greatest_lower_bound(X_114,identity),least_upper_bound(identity,inverse(X_114)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114)))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114))))) ),[1,1],$fot(multiply(greatest_lower_bound(X_114,identity),least_upper_bound(identity,inverse(X_114))))]]) ).
cnf(refute_0_1992,plain,
( greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114))) != multiply(greatest_lower_bound(X_114,identity),least_upper_bound(identity,inverse(X_114)))
| least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114)))) = least_upper_bound(identity,multiply(greatest_lower_bound(X_114,identity),least_upper_bound(identity,inverse(X_114)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114)))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114))))) )],[refute_0_1990,refute_0_1991]) ).
cnf(refute_0_1993,plain,
least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114)))) = least_upper_bound(identity,multiply(greatest_lower_bound(X_114,identity),least_upper_bound(identity,inverse(X_114)))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114))),multiply(greatest_lower_bound(X_114,identity),least_upper_bound(identity,inverse(X_114)))) )],[refute_0_1989,refute_0_1992]) ).
cnf(refute_0_1994,plain,
( least_upper_bound(identity,multiply(greatest_lower_bound(X_114,identity),least_upper_bound(identity,inverse(X_114)))) != identity
| least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114)))) != least_upper_bound(identity,multiply(greatest_lower_bound(X_114,identity),least_upper_bound(identity,inverse(X_114))))
| least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114)))) = identity ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114)))))),bind(Y0,$fot(least_upper_bound(identity,multiply(greatest_lower_bound(X_114,identity),least_upper_bound(identity,inverse(X_114)))))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_1995,plain,
( least_upper_bound(identity,multiply(greatest_lower_bound(X_114,identity),least_upper_bound(identity,inverse(X_114)))) != identity
| least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114)))) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114)))),least_upper_bound(identity,multiply(greatest_lower_bound(X_114,identity),least_upper_bound(identity,inverse(X_114))))) )],[refute_0_1993,refute_0_1994]) ).
cnf(refute_0_1996,plain,
least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114)))) = identity,
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(greatest_lower_bound(X_114,identity),least_upper_bound(identity,inverse(X_114)))),identity) )],[refute_0_1807,refute_0_1995]) ).
cnf(refute_0_1997,plain,
multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114))))) = multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114))))),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114))))))]]) ).
cnf(refute_0_1998,plain,
( multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114))))) != multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114)))))
| least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114)))) != identity
| multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114))))) = multiply(inverse(least_upper_bound(identity,X_114)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114))))),multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114)))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_1999,plain,
( least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114)))) != identity
| multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114))))) = multiply(inverse(least_upper_bound(identity,X_114)),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114))))),multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114)))))) )],[refute_0_1997,refute_0_1998]) ).
cnf(refute_0_2000,plain,
multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114))))) = multiply(inverse(least_upper_bound(identity,X_114)),identity),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114)))),identity) )],[refute_0_1996,refute_0_1999]) ).
cnf(refute_0_2001,plain,
( multiply(inverse(least_upper_bound(identity,X_114)),identity) != inverse(least_upper_bound(identity,X_114))
| multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114))))) != multiply(inverse(least_upper_bound(identity,X_114)),identity)
| multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114))))) = inverse(least_upper_bound(identity,X_114)) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114))))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(identity,X_114)),identity))),bind(Z0,$fot(inverse(least_upper_bound(identity,X_114))))]]) ).
cnf(refute_0_2002,plain,
( multiply(inverse(least_upper_bound(identity,X_114)),identity) != inverse(least_upper_bound(identity,X_114))
| multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114))))) = inverse(least_upper_bound(identity,X_114)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114))))),multiply(inverse(least_upper_bound(identity,X_114)),identity)) )],[refute_0_2000,refute_0_2001]) ).
cnf(refute_0_2003,plain,
multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114))))) = inverse(least_upper_bound(identity,X_114)),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_114)),identity),inverse(least_upper_bound(identity,X_114))) )],[refute_0_1626,refute_0_2002]) ).
cnf(refute_0_2004,plain,
multiply(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,X_51),X_55)) = least_upper_bound(multiply(inverse(X_51),greatest_lower_bound(identity,X_51)),multiply(inverse(X_51),X_55)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(inverse(X_51))),bind(Y,$fot(greatest_lower_bound(identity,X_51))),bind(Z,$fot(X_55))]]) ).
cnf(refute_0_2005,plain,
( multiply(inverse(X_51),greatest_lower_bound(identity,X_51)) != greatest_lower_bound(identity,inverse(X_51))
| multiply(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,X_51),X_55)) != least_upper_bound(multiply(inverse(X_51),greatest_lower_bound(identity,X_51)),multiply(inverse(X_51),X_55))
| multiply(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,X_51),X_55)) = least_upper_bound(greatest_lower_bound(identity,inverse(X_51)),multiply(inverse(X_51),X_55)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,X_51),X_55)),least_upper_bound(multiply(inverse(X_51),greatest_lower_bound(identity,X_51)),multiply(inverse(X_51),X_55))) ),[1,0],$fot(greatest_lower_bound(identity,inverse(X_51)))]]) ).
cnf(refute_0_2006,plain,
( multiply(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,X_51),X_55)) != least_upper_bound(multiply(inverse(X_51),greatest_lower_bound(identity,X_51)),multiply(inverse(X_51),X_55))
| multiply(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,X_51),X_55)) = least_upper_bound(greatest_lower_bound(identity,inverse(X_51)),multiply(inverse(X_51),X_55)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_51),greatest_lower_bound(identity,X_51)),greatest_lower_bound(identity,inverse(X_51))) )],[refute_0_469,refute_0_2005]) ).
cnf(refute_0_2007,plain,
multiply(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,X_51),X_55)) = least_upper_bound(greatest_lower_bound(identity,inverse(X_51)),multiply(inverse(X_51),X_55)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,X_51),X_55)),least_upper_bound(multiply(inverse(X_51),greatest_lower_bound(identity,X_51)),multiply(inverse(X_51),X_55))) )],[refute_0_2004,refute_0_2006]) ).
cnf(refute_0_2008,plain,
multiply(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,X_51),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(X_51)),X_330)))) = least_upper_bound(greatest_lower_bound(identity,inverse(X_51)),multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(X_51)),X_330)))),
inference(subst,[],[refute_0_2007:[bind(X_55,$fot(least_upper_bound(identity,greatest_lower_bound(inverse(inverse(X_51)),X_330))))]]) ).
cnf(refute_0_2009,plain,
multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(X_51)),X_330))) = least_upper_bound(inverse(X_51),greatest_lower_bound(identity,multiply(inverse(X_51),X_330))),
inference(subst,[],[refute_0_1599:[bind(X_38,$fot(X_330)),bind(X_56,$fot(inverse(X_51)))]]) ).
cnf(refute_0_2010,plain,
( multiply(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,X_51),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(X_51)),X_330)))) != least_upper_bound(greatest_lower_bound(identity,inverse(X_51)),multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(X_51)),X_330))))
| multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(X_51)),X_330))) != least_upper_bound(inverse(X_51),greatest_lower_bound(identity,multiply(inverse(X_51),X_330)))
| multiply(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,X_51),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(X_51)),X_330)))) = least_upper_bound(greatest_lower_bound(identity,inverse(X_51)),least_upper_bound(inverse(X_51),greatest_lower_bound(identity,multiply(inverse(X_51),X_330)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,X_51),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(X_51)),X_330)))),least_upper_bound(greatest_lower_bound(identity,inverse(X_51)),multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(X_51)),X_330))))) ),[1,1],$fot(least_upper_bound(inverse(X_51),greatest_lower_bound(identity,multiply(inverse(X_51),X_330))))]]) ).
cnf(refute_0_2011,plain,
( multiply(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,X_51),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(X_51)),X_330)))) != least_upper_bound(greatest_lower_bound(identity,inverse(X_51)),multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(X_51)),X_330))))
| multiply(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,X_51),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(X_51)),X_330)))) = least_upper_bound(greatest_lower_bound(identity,inverse(X_51)),least_upper_bound(inverse(X_51),greatest_lower_bound(identity,multiply(inverse(X_51),X_330)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(X_51)),X_330))),least_upper_bound(inverse(X_51),greatest_lower_bound(identity,multiply(inverse(X_51),X_330)))) )],[refute_0_2009,refute_0_2010]) ).
cnf(refute_0_2012,plain,
multiply(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,X_51),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(X_51)),X_330)))) = least_upper_bound(greatest_lower_bound(identity,inverse(X_51)),least_upper_bound(inverse(X_51),greatest_lower_bound(identity,multiply(inverse(X_51),X_330)))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,X_51),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(X_51)),X_330)))),least_upper_bound(greatest_lower_bound(identity,inverse(X_51)),multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(X_51)),X_330))))) )],[refute_0_2008,refute_0_2011]) ).
cnf(refute_0_2013,plain,
inverse(inverse(X_51)) = X_51,
inference(subst,[],[p18_2:[bind(X,$fot(X_51))]]) ).
cnf(refute_0_2014,plain,
greatest_lower_bound(inverse(inverse(X_51)),X_330) = greatest_lower_bound(inverse(inverse(X_51)),X_330),
introduced(tautology,[refl,[$fot(greatest_lower_bound(inverse(inverse(X_51)),X_330))]]) ).
cnf(refute_0_2015,plain,
( greatest_lower_bound(inverse(inverse(X_51)),X_330) != greatest_lower_bound(inverse(inverse(X_51)),X_330)
| inverse(inverse(X_51)) != X_51
| greatest_lower_bound(inverse(inverse(X_51)),X_330) = greatest_lower_bound(X_51,X_330) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(inverse(inverse(X_51)),X_330),greatest_lower_bound(inverse(inverse(X_51)),X_330)) ),[1,0],$fot(X_51)]]) ).
cnf(refute_0_2016,plain,
( inverse(inverse(X_51)) != X_51
| greatest_lower_bound(inverse(inverse(X_51)),X_330) = greatest_lower_bound(X_51,X_330) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(inverse(X_51)),X_330),greatest_lower_bound(inverse(inverse(X_51)),X_330)) )],[refute_0_2014,refute_0_2015]) ).
cnf(refute_0_2017,plain,
greatest_lower_bound(inverse(inverse(X_51)),X_330) = greatest_lower_bound(X_51,X_330),
inference(resolve,[$cnf( $equal(inverse(inverse(X_51)),X_51) )],[refute_0_2013,refute_0_2016]) ).
cnf(refute_0_2018,plain,
least_upper_bound(identity,greatest_lower_bound(inverse(inverse(X_51)),X_330)) = least_upper_bound(identity,greatest_lower_bound(inverse(inverse(X_51)),X_330)),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,greatest_lower_bound(inverse(inverse(X_51)),X_330)))]]) ).
cnf(refute_0_2019,plain,
( greatest_lower_bound(inverse(inverse(X_51)),X_330) != greatest_lower_bound(X_51,X_330)
| least_upper_bound(identity,greatest_lower_bound(inverse(inverse(X_51)),X_330)) != least_upper_bound(identity,greatest_lower_bound(inverse(inverse(X_51)),X_330))
| least_upper_bound(identity,greatest_lower_bound(inverse(inverse(X_51)),X_330)) = least_upper_bound(identity,greatest_lower_bound(X_51,X_330)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(inverse(inverse(X_51)),X_330)),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(X_51)),X_330))) ),[1,1],$fot(greatest_lower_bound(X_51,X_330))]]) ).
cnf(refute_0_2020,plain,
( greatest_lower_bound(inverse(inverse(X_51)),X_330) != greatest_lower_bound(X_51,X_330)
| least_upper_bound(identity,greatest_lower_bound(inverse(inverse(X_51)),X_330)) = least_upper_bound(identity,greatest_lower_bound(X_51,X_330)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(inverse(inverse(X_51)),X_330)),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(X_51)),X_330))) )],[refute_0_2018,refute_0_2019]) ).
cnf(refute_0_2021,plain,
least_upper_bound(identity,greatest_lower_bound(inverse(inverse(X_51)),X_330)) = least_upper_bound(identity,greatest_lower_bound(X_51,X_330)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(inverse(X_51)),X_330),greatest_lower_bound(X_51,X_330)) )],[refute_0_2017,refute_0_2020]) ).
cnf(refute_0_2022,plain,
least_upper_bound(X_29,least_upper_bound(greatest_lower_bound(X_29,Y),X_31)) = least_upper_bound(least_upper_bound(X_29,greatest_lower_bound(X_29,Y)),X_31),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_29)),bind(Y,$fot(greatest_lower_bound(X_29,Y))),bind(Z,$fot(X_31))]]) ).
cnf(refute_0_2023,plain,
least_upper_bound(X_29,greatest_lower_bound(X_29,Y)) = X_29,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_29))]]) ).
cnf(refute_0_2024,plain,
( least_upper_bound(X_29,greatest_lower_bound(X_29,Y)) != X_29
| least_upper_bound(X_29,least_upper_bound(greatest_lower_bound(X_29,Y),X_31)) != least_upper_bound(least_upper_bound(X_29,greatest_lower_bound(X_29,Y)),X_31)
| least_upper_bound(X_29,least_upper_bound(greatest_lower_bound(X_29,Y),X_31)) = least_upper_bound(X_29,X_31) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_29,least_upper_bound(greatest_lower_bound(X_29,Y),X_31)),least_upper_bound(least_upper_bound(X_29,greatest_lower_bound(X_29,Y)),X_31)) ),[1,0],$fot(X_29)]]) ).
cnf(refute_0_2025,plain,
( least_upper_bound(X_29,least_upper_bound(greatest_lower_bound(X_29,Y),X_31)) != least_upper_bound(least_upper_bound(X_29,greatest_lower_bound(X_29,Y)),X_31)
| least_upper_bound(X_29,least_upper_bound(greatest_lower_bound(X_29,Y),X_31)) = least_upper_bound(X_29,X_31) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_29,greatest_lower_bound(X_29,Y)),X_29) )],[refute_0_2023,refute_0_2024]) ).
cnf(refute_0_2026,plain,
least_upper_bound(X_29,least_upper_bound(greatest_lower_bound(X_29,Y),X_31)) = least_upper_bound(X_29,X_31),
inference(resolve,[$cnf( $equal(least_upper_bound(X_29,least_upper_bound(greatest_lower_bound(X_29,Y),X_31)),least_upper_bound(least_upper_bound(X_29,greatest_lower_bound(X_29,Y)),X_31)) )],[refute_0_2022,refute_0_2025]) ).
cnf(refute_0_2027,plain,
least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(inverse(inverse(X_51)),X_330))) = least_upper_bound(identity,greatest_lower_bound(inverse(inverse(X_51)),X_330)),
inference(subst,[],[refute_0_2026:[bind(Y,$fot(X_51)),bind(X_29,$fot(identity)),bind(X_31,$fot(greatest_lower_bound(inverse(inverse(X_51)),X_330)))]]) ).
cnf(refute_0_2028,plain,
( least_upper_bound(identity,greatest_lower_bound(inverse(inverse(X_51)),X_330)) != least_upper_bound(identity,greatest_lower_bound(X_51,X_330))
| least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(inverse(inverse(X_51)),X_330))) != least_upper_bound(identity,greatest_lower_bound(inverse(inverse(X_51)),X_330))
| least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(inverse(inverse(X_51)),X_330))) = least_upper_bound(identity,greatest_lower_bound(X_51,X_330)) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(inverse(inverse(X_51)),X_330))))),bind(Y0,$fot(least_upper_bound(identity,greatest_lower_bound(inverse(inverse(X_51)),X_330)))),bind(Z0,$fot(least_upper_bound(identity,greatest_lower_bound(X_51,X_330))))]]) ).
cnf(refute_0_2029,plain,
( least_upper_bound(identity,greatest_lower_bound(inverse(inverse(X_51)),X_330)) != least_upper_bound(identity,greatest_lower_bound(X_51,X_330))
| least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(inverse(inverse(X_51)),X_330))) = least_upper_bound(identity,greatest_lower_bound(X_51,X_330)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(inverse(inverse(X_51)),X_330))),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(X_51)),X_330))) )],[refute_0_2027,refute_0_2028]) ).
cnf(refute_0_2030,plain,
least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(inverse(inverse(X_51)),X_330))) = least_upper_bound(identity,greatest_lower_bound(X_51,X_330)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(inverse(inverse(X_51)),X_330)),least_upper_bound(identity,greatest_lower_bound(X_51,X_330))) )],[refute_0_2021,refute_0_2029]) ).
cnf(refute_0_2031,plain,
multiply(inverse(X_51),least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(inverse(inverse(X_51)),X_330)))) = multiply(inverse(X_51),least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(inverse(inverse(X_51)),X_330)))),
introduced(tautology,[refl,[$fot(multiply(inverse(X_51),least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(inverse(inverse(X_51)),X_330)))))]]) ).
cnf(refute_0_2032,plain,
( multiply(inverse(X_51),least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(inverse(inverse(X_51)),X_330)))) != multiply(inverse(X_51),least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(inverse(inverse(X_51)),X_330))))
| least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(inverse(inverse(X_51)),X_330))) != least_upper_bound(identity,greatest_lower_bound(X_51,X_330))
| multiply(inverse(X_51),least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(inverse(inverse(X_51)),X_330)))) = multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_51,X_330))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_51),least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(inverse(inverse(X_51)),X_330)))),multiply(inverse(X_51),least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(inverse(inverse(X_51)),X_330))))) ),[1,1],$fot(least_upper_bound(identity,greatest_lower_bound(X_51,X_330)))]]) ).
cnf(refute_0_2033,plain,
( least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(inverse(inverse(X_51)),X_330))) != least_upper_bound(identity,greatest_lower_bound(X_51,X_330))
| multiply(inverse(X_51),least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(inverse(inverse(X_51)),X_330)))) = multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_51,X_330))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_51),least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(inverse(inverse(X_51)),X_330)))),multiply(inverse(X_51),least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(inverse(inverse(X_51)),X_330))))) )],[refute_0_2031,refute_0_2032]) ).
cnf(refute_0_2034,plain,
multiply(inverse(X_51),least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(inverse(inverse(X_51)),X_330)))) = multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_51,X_330))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(inverse(inverse(X_51)),X_330))),least_upper_bound(identity,greatest_lower_bound(X_51,X_330))) )],[refute_0_2030,refute_0_2033]) ).
cnf(refute_0_2035,plain,
multiply(X,least_upper_bound(Y,least_upper_bound(X_254,X_255))) = least_upper_bound(multiply(X,Y),multiply(X,least_upper_bound(X_254,X_255))),
inference(subst,[],[monotony_lub1:[bind(Z,$fot(least_upper_bound(X_254,X_255)))]]) ).
cnf(refute_0_2036,plain,
least_upper_bound(Y,least_upper_bound(X_254,X_255)) = least_upper_bound(X_254,least_upper_bound(Y,X_255)),
inference(subst,[],[refute_0_1779:[bind(X_29,$fot(X_254)),bind(X_31,$fot(X_255))]]) ).
cnf(refute_0_2037,plain,
( multiply(X,least_upper_bound(Y,least_upper_bound(X_254,X_255))) != least_upper_bound(multiply(X,Y),multiply(X,least_upper_bound(X_254,X_255)))
| least_upper_bound(Y,least_upper_bound(X_254,X_255)) != least_upper_bound(X_254,least_upper_bound(Y,X_255))
| multiply(X,least_upper_bound(X_254,least_upper_bound(Y,X_255))) = least_upper_bound(multiply(X,Y),multiply(X,least_upper_bound(X_254,X_255))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X,least_upper_bound(Y,least_upper_bound(X_254,X_255))),least_upper_bound(multiply(X,Y),multiply(X,least_upper_bound(X_254,X_255)))) ),[0,1],$fot(least_upper_bound(X_254,least_upper_bound(Y,X_255)))]]) ).
cnf(refute_0_2038,plain,
( multiply(X,least_upper_bound(Y,least_upper_bound(X_254,X_255))) != least_upper_bound(multiply(X,Y),multiply(X,least_upper_bound(X_254,X_255)))
| multiply(X,least_upper_bound(X_254,least_upper_bound(Y,X_255))) = least_upper_bound(multiply(X,Y),multiply(X,least_upper_bound(X_254,X_255))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_254,X_255)),least_upper_bound(X_254,least_upper_bound(Y,X_255))) )],[refute_0_2036,refute_0_2037]) ).
cnf(refute_0_2039,plain,
multiply(X,least_upper_bound(X_254,least_upper_bound(Y,X_255))) = least_upper_bound(multiply(X,Y),multiply(X,least_upper_bound(X_254,X_255))),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(Y,least_upper_bound(X_254,X_255))),least_upper_bound(multiply(X,Y),multiply(X,least_upper_bound(X_254,X_255)))) )],[refute_0_2035,refute_0_2038]) ).
cnf(refute_0_2040,plain,
least_upper_bound(multiply(X,Y),multiply(X,least_upper_bound(X_254,X_255))) = multiply(X,least_upper_bound(Y,least_upper_bound(X_254,X_255))),
inference(subst,[],[refute_0_249:[bind(Z,$fot(least_upper_bound(X_254,X_255)))]]) ).
cnf(refute_0_2041,plain,
( multiply(X,least_upper_bound(X_254,least_upper_bound(Y,X_255))) != least_upper_bound(multiply(X,Y),multiply(X,least_upper_bound(X_254,X_255)))
| least_upper_bound(multiply(X,Y),multiply(X,least_upper_bound(X_254,X_255))) != multiply(X,least_upper_bound(Y,least_upper_bound(X_254,X_255)))
| multiply(X,least_upper_bound(X_254,least_upper_bound(Y,X_255))) = multiply(X,least_upper_bound(Y,least_upper_bound(X_254,X_255))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X,least_upper_bound(X_254,least_upper_bound(Y,X_255))),multiply(X,least_upper_bound(Y,least_upper_bound(X_254,X_255)))) ),[0],$fot(least_upper_bound(multiply(X,Y),multiply(X,least_upper_bound(X_254,X_255))))]]) ).
cnf(refute_0_2042,plain,
( multiply(X,least_upper_bound(X_254,least_upper_bound(Y,X_255))) != least_upper_bound(multiply(X,Y),multiply(X,least_upper_bound(X_254,X_255)))
| multiply(X,least_upper_bound(X_254,least_upper_bound(Y,X_255))) = multiply(X,least_upper_bound(Y,least_upper_bound(X_254,X_255))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,Y),multiply(X,least_upper_bound(X_254,X_255))),multiply(X,least_upper_bound(Y,least_upper_bound(X_254,X_255)))) )],[refute_0_2040,refute_0_2041]) ).
cnf(refute_0_2043,plain,
multiply(X,least_upper_bound(X_254,least_upper_bound(Y,X_255))) = multiply(X,least_upper_bound(Y,least_upper_bound(X_254,X_255))),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(X_254,least_upper_bound(Y,X_255))),least_upper_bound(multiply(X,Y),multiply(X,least_upper_bound(X_254,X_255)))) )],[refute_0_2039,refute_0_2042]) ).
cnf(refute_0_2044,plain,
( multiply(X,least_upper_bound(X_254,least_upper_bound(Y,X_255))) != multiply(X,least_upper_bound(Y,least_upper_bound(X_254,X_255)))
| multiply(X,least_upper_bound(Y,least_upper_bound(X_254,X_255))) = multiply(X,least_upper_bound(X_254,least_upper_bound(Y,X_255))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X,least_upper_bound(X_254,least_upper_bound(Y,X_255))))),bind(Y0,$fot(multiply(X,least_upper_bound(Y,least_upper_bound(X_254,X_255)))))]]) ).
cnf(refute_0_2045,plain,
multiply(X,least_upper_bound(Y,least_upper_bound(X_254,X_255))) = multiply(X,least_upper_bound(X_254,least_upper_bound(Y,X_255))),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(X_254,least_upper_bound(Y,X_255))),multiply(X,least_upper_bound(Y,least_upper_bound(X_254,X_255)))) )],[refute_0_2043,refute_0_2044]) ).
cnf(refute_0_2046,plain,
multiply(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,X_51),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(X_51)),X_330)))) = multiply(inverse(X_51),least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(inverse(inverse(X_51)),X_330)))),
inference(subst,[],[refute_0_2045:[bind(X,$fot(inverse(X_51))),bind(Y,$fot(greatest_lower_bound(identity,X_51))),bind(X_254,$fot(identity)),bind(X_255,$fot(greatest_lower_bound(inverse(inverse(X_51)),X_330)))]]) ).
cnf(refute_0_2047,plain,
( multiply(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,X_51),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(X_51)),X_330)))) != multiply(inverse(X_51),least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(inverse(inverse(X_51)),X_330))))
| multiply(inverse(X_51),least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(inverse(inverse(X_51)),X_330)))) != multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_51,X_330)))
| multiply(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,X_51),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(X_51)),X_330)))) = multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_51,X_330))) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(multiply(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,X_51),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(X_51)),X_330)))))),bind(Y0,$fot(multiply(inverse(X_51),least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(inverse(inverse(X_51)),X_330)))))),bind(Z0,$fot(multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_51,X_330)))))]]) ).
cnf(refute_0_2048,plain,
( multiply(inverse(X_51),least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(inverse(inverse(X_51)),X_330)))) != multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_51,X_330)))
| multiply(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,X_51),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(X_51)),X_330)))) = multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_51,X_330))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,X_51),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(X_51)),X_330)))),multiply(inverse(X_51),least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(inverse(inverse(X_51)),X_330))))) )],[refute_0_2046,refute_0_2047]) ).
cnf(refute_0_2049,plain,
multiply(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,X_51),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(X_51)),X_330)))) = multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_51,X_330))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_51),least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_51),greatest_lower_bound(inverse(inverse(X_51)),X_330)))),multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_51,X_330)))) )],[refute_0_2034,refute_0_2048]) ).
cnf(refute_0_2050,plain,
( multiply(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,X_51),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(X_51)),X_330)))) != multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_51,X_330)))
| multiply(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,X_51),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(X_51)),X_330)))) != least_upper_bound(greatest_lower_bound(identity,inverse(X_51)),least_upper_bound(inverse(X_51),greatest_lower_bound(identity,multiply(inverse(X_51),X_330))))
| multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_51,X_330))) = least_upper_bound(greatest_lower_bound(identity,inverse(X_51)),least_upper_bound(inverse(X_51),greatest_lower_bound(identity,multiply(inverse(X_51),X_330)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,X_51),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(X_51)),X_330)))),least_upper_bound(greatest_lower_bound(identity,inverse(X_51)),least_upper_bound(inverse(X_51),greatest_lower_bound(identity,multiply(inverse(X_51),X_330))))) ),[0],$fot(multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_51,X_330))))]]) ).
cnf(refute_0_2051,plain,
( multiply(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,X_51),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(X_51)),X_330)))) != least_upper_bound(greatest_lower_bound(identity,inverse(X_51)),least_upper_bound(inverse(X_51),greatest_lower_bound(identity,multiply(inverse(X_51),X_330))))
| multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_51,X_330))) = least_upper_bound(greatest_lower_bound(identity,inverse(X_51)),least_upper_bound(inverse(X_51),greatest_lower_bound(identity,multiply(inverse(X_51),X_330)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,X_51),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(X_51)),X_330)))),multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_51,X_330)))) )],[refute_0_2049,refute_0_2050]) ).
cnf(refute_0_2052,plain,
multiply(inverse(X_38),least_upper_bound(greatest_lower_bound(X_37,X_38),identity)) = least_upper_bound(inverse(X_38),multiply(inverse(X_38),greatest_lower_bound(X_37,X_38))),
inference(subst,[],[refute_0_736:[bind(X_53,$fot(inverse(X_38))),bind(X_54,$fot(greatest_lower_bound(X_37,X_38)))]]) ).
cnf(refute_0_2053,plain,
( multiply(inverse(X_38),greatest_lower_bound(X_37,X_38)) != greatest_lower_bound(identity,multiply(inverse(X_38),X_37))
| multiply(inverse(X_38),least_upper_bound(greatest_lower_bound(X_37,X_38),identity)) != least_upper_bound(inverse(X_38),multiply(inverse(X_38),greatest_lower_bound(X_37,X_38)))
| multiply(inverse(X_38),least_upper_bound(greatest_lower_bound(X_37,X_38),identity)) = least_upper_bound(inverse(X_38),greatest_lower_bound(identity,multiply(inverse(X_38),X_37))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_38),least_upper_bound(greatest_lower_bound(X_37,X_38),identity)),least_upper_bound(inverse(X_38),multiply(inverse(X_38),greatest_lower_bound(X_37,X_38)))) ),[1,1],$fot(greatest_lower_bound(identity,multiply(inverse(X_38),X_37)))]]) ).
cnf(refute_0_2054,plain,
( multiply(inverse(X_38),least_upper_bound(greatest_lower_bound(X_37,X_38),identity)) != least_upper_bound(inverse(X_38),multiply(inverse(X_38),greatest_lower_bound(X_37,X_38)))
| multiply(inverse(X_38),least_upper_bound(greatest_lower_bound(X_37,X_38),identity)) = least_upper_bound(inverse(X_38),greatest_lower_bound(identity,multiply(inverse(X_38),X_37))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_38),greatest_lower_bound(X_37,X_38)),greatest_lower_bound(identity,multiply(inverse(X_38),X_37))) )],[refute_0_462,refute_0_2053]) ).
cnf(refute_0_2055,plain,
multiply(inverse(X_38),least_upper_bound(greatest_lower_bound(X_37,X_38),identity)) = least_upper_bound(inverse(X_38),greatest_lower_bound(identity,multiply(inverse(X_38),X_37))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_38),least_upper_bound(greatest_lower_bound(X_37,X_38),identity)),least_upper_bound(inverse(X_38),multiply(inverse(X_38),greatest_lower_bound(X_37,X_38)))) )],[refute_0_2052,refute_0_2054]) ).
cnf(refute_0_2056,plain,
multiply(inverse(X_38),least_upper_bound(greatest_lower_bound(X_37,X_38),identity)) = multiply(inverse(X_38),least_upper_bound(identity,greatest_lower_bound(X_37,X_38))),
inference(subst,[],[refute_0_1595:[bind(X_23,$fot(inverse(X_38))),bind(X_57,$fot(greatest_lower_bound(X_37,X_38)))]]) ).
cnf(refute_0_2057,plain,
( multiply(inverse(X_38),least_upper_bound(greatest_lower_bound(X_37,X_38),identity)) != multiply(inverse(X_38),least_upper_bound(identity,greatest_lower_bound(X_37,X_38)))
| multiply(inverse(X_38),least_upper_bound(greatest_lower_bound(X_37,X_38),identity)) != least_upper_bound(inverse(X_38),greatest_lower_bound(identity,multiply(inverse(X_38),X_37)))
| multiply(inverse(X_38),least_upper_bound(identity,greatest_lower_bound(X_37,X_38))) = least_upper_bound(inverse(X_38),greatest_lower_bound(identity,multiply(inverse(X_38),X_37))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_38),least_upper_bound(greatest_lower_bound(X_37,X_38),identity)),least_upper_bound(inverse(X_38),greatest_lower_bound(identity,multiply(inverse(X_38),X_37)))) ),[0],$fot(multiply(inverse(X_38),least_upper_bound(identity,greatest_lower_bound(X_37,X_38))))]]) ).
cnf(refute_0_2058,plain,
( multiply(inverse(X_38),least_upper_bound(greatest_lower_bound(X_37,X_38),identity)) != least_upper_bound(inverse(X_38),greatest_lower_bound(identity,multiply(inverse(X_38),X_37)))
| multiply(inverse(X_38),least_upper_bound(identity,greatest_lower_bound(X_37,X_38))) = least_upper_bound(inverse(X_38),greatest_lower_bound(identity,multiply(inverse(X_38),X_37))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_38),least_upper_bound(greatest_lower_bound(X_37,X_38),identity)),multiply(inverse(X_38),least_upper_bound(identity,greatest_lower_bound(X_37,X_38)))) )],[refute_0_2056,refute_0_2057]) ).
cnf(refute_0_2059,plain,
multiply(inverse(X_38),least_upper_bound(identity,greatest_lower_bound(X_37,X_38))) = least_upper_bound(inverse(X_38),greatest_lower_bound(identity,multiply(inverse(X_38),X_37))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_38),least_upper_bound(greatest_lower_bound(X_37,X_38),identity)),least_upper_bound(inverse(X_38),greatest_lower_bound(identity,multiply(inverse(X_38),X_37)))) )],[refute_0_2055,refute_0_2058]) ).
cnf(refute_0_2060,plain,
( multiply(inverse(X_38),least_upper_bound(identity,greatest_lower_bound(X_37,X_38))) != least_upper_bound(inverse(X_38),greatest_lower_bound(identity,multiply(inverse(X_38),X_37)))
| least_upper_bound(inverse(X_38),greatest_lower_bound(identity,multiply(inverse(X_38),X_37))) = multiply(inverse(X_38),least_upper_bound(identity,greatest_lower_bound(X_37,X_38))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(inverse(X_38),least_upper_bound(identity,greatest_lower_bound(X_37,X_38))))),bind(Y0,$fot(least_upper_bound(inverse(X_38),greatest_lower_bound(identity,multiply(inverse(X_38),X_37)))))]]) ).
cnf(refute_0_2061,plain,
least_upper_bound(inverse(X_38),greatest_lower_bound(identity,multiply(inverse(X_38),X_37))) = multiply(inverse(X_38),least_upper_bound(identity,greatest_lower_bound(X_37,X_38))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_38),least_upper_bound(identity,greatest_lower_bound(X_37,X_38))),least_upper_bound(inverse(X_38),greatest_lower_bound(identity,multiply(inverse(X_38),X_37)))) )],[refute_0_2059,refute_0_2060]) ).
cnf(refute_0_2062,plain,
least_upper_bound(inverse(X_51),greatest_lower_bound(identity,multiply(inverse(X_51),X_330))) = multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_330,X_51))),
inference(subst,[],[refute_0_2061:[bind(X_37,$fot(X_330)),bind(X_38,$fot(X_51))]]) ).
cnf(refute_0_2063,plain,
least_upper_bound(X_29,least_upper_bound(greatest_lower_bound(X_13,X_29),X_31)) = least_upper_bound(least_upper_bound(X_29,greatest_lower_bound(X_13,X_29)),X_31),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_29)),bind(Y,$fot(greatest_lower_bound(X_13,X_29))),bind(Z,$fot(X_31))]]) ).
cnf(refute_0_2064,plain,
least_upper_bound(X_29,greatest_lower_bound(X_13,X_29)) = X_29,
inference(subst,[],[refute_0_53:[bind(X_12,$fot(X_29))]]) ).
cnf(refute_0_2065,plain,
( least_upper_bound(X_29,greatest_lower_bound(X_13,X_29)) != X_29
| least_upper_bound(X_29,least_upper_bound(greatest_lower_bound(X_13,X_29),X_31)) != least_upper_bound(least_upper_bound(X_29,greatest_lower_bound(X_13,X_29)),X_31)
| least_upper_bound(X_29,least_upper_bound(greatest_lower_bound(X_13,X_29),X_31)) = least_upper_bound(X_29,X_31) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_29,least_upper_bound(greatest_lower_bound(X_13,X_29),X_31)),least_upper_bound(least_upper_bound(X_29,greatest_lower_bound(X_13,X_29)),X_31)) ),[1,0],$fot(X_29)]]) ).
cnf(refute_0_2066,plain,
( least_upper_bound(X_29,least_upper_bound(greatest_lower_bound(X_13,X_29),X_31)) != least_upper_bound(least_upper_bound(X_29,greatest_lower_bound(X_13,X_29)),X_31)
| least_upper_bound(X_29,least_upper_bound(greatest_lower_bound(X_13,X_29),X_31)) = least_upper_bound(X_29,X_31) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_29,greatest_lower_bound(X_13,X_29)),X_29) )],[refute_0_2064,refute_0_2065]) ).
cnf(refute_0_2067,plain,
least_upper_bound(X_29,least_upper_bound(greatest_lower_bound(X_13,X_29),X_31)) = least_upper_bound(X_29,X_31),
inference(resolve,[$cnf( $equal(least_upper_bound(X_29,least_upper_bound(greatest_lower_bound(X_13,X_29),X_31)),least_upper_bound(least_upper_bound(X_29,greatest_lower_bound(X_13,X_29)),X_31)) )],[refute_0_2063,refute_0_2066]) ).
cnf(refute_0_2068,plain,
least_upper_bound(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,inverse(X_51)),greatest_lower_bound(identity,multiply(inverse(X_51),X_330)))) = least_upper_bound(inverse(X_51),greatest_lower_bound(identity,multiply(inverse(X_51),X_330))),
inference(subst,[],[refute_0_2067:[bind(X_13,$fot(identity)),bind(X_29,$fot(inverse(X_51))),bind(X_31,$fot(greatest_lower_bound(identity,multiply(inverse(X_51),X_330))))]]) ).
cnf(refute_0_2069,plain,
( least_upper_bound(inverse(X_51),greatest_lower_bound(identity,multiply(inverse(X_51),X_330))) != multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_330,X_51)))
| least_upper_bound(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,inverse(X_51)),greatest_lower_bound(identity,multiply(inverse(X_51),X_330)))) != least_upper_bound(inverse(X_51),greatest_lower_bound(identity,multiply(inverse(X_51),X_330)))
| least_upper_bound(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,inverse(X_51)),greatest_lower_bound(identity,multiply(inverse(X_51),X_330)))) = multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_330,X_51))) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(least_upper_bound(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,inverse(X_51)),greatest_lower_bound(identity,multiply(inverse(X_51),X_330)))))),bind(Y0,$fot(least_upper_bound(inverse(X_51),greatest_lower_bound(identity,multiply(inverse(X_51),X_330))))),bind(Z0,$fot(multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_330,X_51)))))]]) ).
cnf(refute_0_2070,plain,
( least_upper_bound(inverse(X_51),greatest_lower_bound(identity,multiply(inverse(X_51),X_330))) != multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_330,X_51)))
| least_upper_bound(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,inverse(X_51)),greatest_lower_bound(identity,multiply(inverse(X_51),X_330)))) = multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_330,X_51))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,inverse(X_51)),greatest_lower_bound(identity,multiply(inverse(X_51),X_330)))),least_upper_bound(inverse(X_51),greatest_lower_bound(identity,multiply(inverse(X_51),X_330)))) )],[refute_0_2068,refute_0_2069]) ).
cnf(refute_0_2071,plain,
least_upper_bound(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,inverse(X_51)),greatest_lower_bound(identity,multiply(inverse(X_51),X_330)))) = multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_330,X_51))),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_51),greatest_lower_bound(identity,multiply(inverse(X_51),X_330))),multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_330,X_51)))) )],[refute_0_2062,refute_0_2070]) ).
cnf(refute_0_2072,plain,
least_upper_bound(X_29,least_upper_bound(greatest_lower_bound(X_29,Y),least_upper_bound(X_254,X_255))) = least_upper_bound(X_29,least_upper_bound(X_254,X_255)),
inference(subst,[],[refute_0_2026:[bind(X_31,$fot(least_upper_bound(X_254,X_255)))]]) ).
cnf(refute_0_2073,plain,
least_upper_bound(greatest_lower_bound(X_29,Y),least_upper_bound(X_254,X_255)) = least_upper_bound(X_254,least_upper_bound(greatest_lower_bound(X_29,Y),X_255)),
inference(subst,[],[refute_0_1779:[bind(Y,$fot(greatest_lower_bound(X_29,Y))),bind(X_29,$fot(X_254)),bind(X_31,$fot(X_255))]]) ).
cnf(refute_0_2074,plain,
( least_upper_bound(X_29,least_upper_bound(greatest_lower_bound(X_29,Y),least_upper_bound(X_254,X_255))) != least_upper_bound(X_29,least_upper_bound(X_254,X_255))
| least_upper_bound(greatest_lower_bound(X_29,Y),least_upper_bound(X_254,X_255)) != least_upper_bound(X_254,least_upper_bound(greatest_lower_bound(X_29,Y),X_255))
| least_upper_bound(X_29,least_upper_bound(X_254,least_upper_bound(greatest_lower_bound(X_29,Y),X_255))) = least_upper_bound(X_29,least_upper_bound(X_254,X_255)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_29,least_upper_bound(greatest_lower_bound(X_29,Y),least_upper_bound(X_254,X_255))),least_upper_bound(X_29,least_upper_bound(X_254,X_255))) ),[0,1],$fot(least_upper_bound(X_254,least_upper_bound(greatest_lower_bound(X_29,Y),X_255)))]]) ).
cnf(refute_0_2075,plain,
( least_upper_bound(X_29,least_upper_bound(greatest_lower_bound(X_29,Y),least_upper_bound(X_254,X_255))) != least_upper_bound(X_29,least_upper_bound(X_254,X_255))
| least_upper_bound(X_29,least_upper_bound(X_254,least_upper_bound(greatest_lower_bound(X_29,Y),X_255))) = least_upper_bound(X_29,least_upper_bound(X_254,X_255)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_29,Y),least_upper_bound(X_254,X_255)),least_upper_bound(X_254,least_upper_bound(greatest_lower_bound(X_29,Y),X_255))) )],[refute_0_2073,refute_0_2074]) ).
cnf(refute_0_2076,plain,
least_upper_bound(X_29,least_upper_bound(X_254,least_upper_bound(greatest_lower_bound(X_29,Y),X_255))) = least_upper_bound(X_29,least_upper_bound(X_254,X_255)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_29,least_upper_bound(greatest_lower_bound(X_29,Y),least_upper_bound(X_254,X_255))),least_upper_bound(X_29,least_upper_bound(X_254,X_255))) )],[refute_0_2072,refute_0_2075]) ).
cnf(refute_0_2077,plain,
least_upper_bound(X_21,least_upper_bound(least_upper_bound(X_29,X_30),X_21)) = least_upper_bound(X_21,least_upper_bound(X_29,X_30)),
inference(subst,[],[refute_0_64:[bind(Y,$fot(least_upper_bound(X_29,X_30)))]]) ).
cnf(refute_0_2078,plain,
least_upper_bound(X_29,least_upper_bound(X_30,X_21)) = least_upper_bound(least_upper_bound(X_29,X_30),X_21),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_29)),bind(Y,$fot(X_30)),bind(Z,$fot(X_21))]]) ).
cnf(refute_0_2079,plain,
( least_upper_bound(X_29,least_upper_bound(X_30,X_21)) != least_upper_bound(least_upper_bound(X_29,X_30),X_21)
| least_upper_bound(least_upper_bound(X_29,X_30),X_21) = least_upper_bound(X_29,least_upper_bound(X_30,X_21)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X_29,least_upper_bound(X_30,X_21)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X_29,X_30),X_21)))]]) ).
cnf(refute_0_2080,plain,
least_upper_bound(least_upper_bound(X_29,X_30),X_21) = least_upper_bound(X_29,least_upper_bound(X_30,X_21)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_29,least_upper_bound(X_30,X_21)),least_upper_bound(least_upper_bound(X_29,X_30),X_21)) )],[refute_0_2078,refute_0_2079]) ).
cnf(refute_0_2081,plain,
( least_upper_bound(X_21,least_upper_bound(least_upper_bound(X_29,X_30),X_21)) != least_upper_bound(X_21,least_upper_bound(X_29,X_30))
| least_upper_bound(least_upper_bound(X_29,X_30),X_21) != least_upper_bound(X_29,least_upper_bound(X_30,X_21))
| least_upper_bound(X_21,least_upper_bound(X_29,least_upper_bound(X_30,X_21))) = least_upper_bound(X_21,least_upper_bound(X_29,X_30)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_21,least_upper_bound(least_upper_bound(X_29,X_30),X_21)),least_upper_bound(X_21,least_upper_bound(X_29,X_30))) ),[0,1],$fot(least_upper_bound(X_29,least_upper_bound(X_30,X_21)))]]) ).
cnf(refute_0_2082,plain,
( least_upper_bound(X_21,least_upper_bound(least_upper_bound(X_29,X_30),X_21)) != least_upper_bound(X_21,least_upper_bound(X_29,X_30))
| least_upper_bound(X_21,least_upper_bound(X_29,least_upper_bound(X_30,X_21))) = least_upper_bound(X_21,least_upper_bound(X_29,X_30)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_29,X_30),X_21),least_upper_bound(X_29,least_upper_bound(X_30,X_21))) )],[refute_0_2080,refute_0_2081]) ).
cnf(refute_0_2083,plain,
least_upper_bound(X_21,least_upper_bound(X_29,least_upper_bound(X_30,X_21))) = least_upper_bound(X_21,least_upper_bound(X_29,X_30)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_21,least_upper_bound(least_upper_bound(X_29,X_30),X_21)),least_upper_bound(X_21,least_upper_bound(X_29,X_30))) )],[refute_0_2077,refute_0_2082]) ).
cnf(refute_0_2084,plain,
least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),least_upper_bound(X_29,least_upper_bound(X_30,least_upper_bound(greatest_lower_bound(X_30,X_246),X_248)))) = least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),least_upper_bound(X_29,X_30)),
inference(subst,[],[refute_0_2083:[bind(X_21,$fot(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248)))]]) ).
cnf(refute_0_2085,plain,
least_upper_bound(X_30,least_upper_bound(greatest_lower_bound(X_30,X_246),X_248)) = least_upper_bound(X_30,X_248),
inference(subst,[],[refute_0_2026:[bind(Y,$fot(X_246)),bind(X_29,$fot(X_30)),bind(X_31,$fot(X_248))]]) ).
cnf(refute_0_2086,plain,
( least_upper_bound(X_30,least_upper_bound(greatest_lower_bound(X_30,X_246),X_248)) != least_upper_bound(X_30,X_248)
| least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),least_upper_bound(X_29,least_upper_bound(X_30,least_upper_bound(greatest_lower_bound(X_30,X_246),X_248)))) != least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),least_upper_bound(X_29,X_30))
| least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),least_upper_bound(X_29,least_upper_bound(X_30,X_248))) = least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),least_upper_bound(X_29,X_30)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),least_upper_bound(X_29,least_upper_bound(X_30,least_upper_bound(greatest_lower_bound(X_30,X_246),X_248)))),least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),least_upper_bound(X_29,X_30))) ),[0,1,1],$fot(least_upper_bound(X_30,X_248))]]) ).
cnf(refute_0_2087,plain,
( least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),least_upper_bound(X_29,least_upper_bound(X_30,least_upper_bound(greatest_lower_bound(X_30,X_246),X_248)))) != least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),least_upper_bound(X_29,X_30))
| least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),least_upper_bound(X_29,least_upper_bound(X_30,X_248))) = least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),least_upper_bound(X_29,X_30)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_30,least_upper_bound(greatest_lower_bound(X_30,X_246),X_248)),least_upper_bound(X_30,X_248)) )],[refute_0_2085,refute_0_2086]) ).
cnf(refute_0_2088,plain,
least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),least_upper_bound(X_29,least_upper_bound(X_30,X_248))) = least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),least_upper_bound(X_29,X_30)),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),least_upper_bound(X_29,least_upper_bound(X_30,least_upper_bound(greatest_lower_bound(X_30,X_246),X_248)))),least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),least_upper_bound(X_29,X_30))) )],[refute_0_2084,refute_0_2087]) ).
cnf(refute_0_2089,plain,
least_upper_bound(X_30,least_upper_bound(greatest_lower_bound(X_30,X_246),least_upper_bound(X_248,X_29))) = least_upper_bound(X_30,least_upper_bound(X_248,X_29)),
inference(subst,[],[refute_0_2026:[bind(Y,$fot(X_246)),bind(X_29,$fot(X_30)),bind(X_31,$fot(least_upper_bound(X_248,X_29)))]]) ).
cnf(refute_0_2090,plain,
least_upper_bound(X_248,least_upper_bound(greatest_lower_bound(X_30,X_246),least_upper_bound(X_248,X_29))) = least_upper_bound(greatest_lower_bound(X_30,X_246),least_upper_bound(X_248,X_29)),
inference(subst,[],[refute_0_1763:[bind(Y,$fot(X_29)),bind(X_29,$fot(greatest_lower_bound(X_30,X_246))),bind(X_30,$fot(X_248))]]) ).
cnf(refute_0_2091,plain,
least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),X_29) = least_upper_bound(greatest_lower_bound(X_30,X_246),least_upper_bound(X_248,X_29)),
inference(subst,[],[refute_0_60:[bind(X,$fot(greatest_lower_bound(X_30,X_246))),bind(Y,$fot(X_248)),bind(Z,$fot(X_29))]]) ).
cnf(refute_0_2092,plain,
least_upper_bound(X_248,least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),X_29)) = least_upper_bound(X_248,least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),X_29)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_248,least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),X_29)))]]) ).
cnf(refute_0_2093,plain,
( least_upper_bound(X_248,least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),X_29)) != least_upper_bound(X_248,least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),X_29))
| least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),X_29) != least_upper_bound(greatest_lower_bound(X_30,X_246),least_upper_bound(X_248,X_29))
| least_upper_bound(X_248,least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),X_29)) = least_upper_bound(X_248,least_upper_bound(greatest_lower_bound(X_30,X_246),least_upper_bound(X_248,X_29))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_248,least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),X_29)),least_upper_bound(X_248,least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),X_29))) ),[1,1],$fot(least_upper_bound(greatest_lower_bound(X_30,X_246),least_upper_bound(X_248,X_29)))]]) ).
cnf(refute_0_2094,plain,
( least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),X_29) != least_upper_bound(greatest_lower_bound(X_30,X_246),least_upper_bound(X_248,X_29))
| least_upper_bound(X_248,least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),X_29)) = least_upper_bound(X_248,least_upper_bound(greatest_lower_bound(X_30,X_246),least_upper_bound(X_248,X_29))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_248,least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),X_29)),least_upper_bound(X_248,least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),X_29))) )],[refute_0_2092,refute_0_2093]) ).
cnf(refute_0_2095,plain,
least_upper_bound(X_248,least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),X_29)) = least_upper_bound(X_248,least_upper_bound(greatest_lower_bound(X_30,X_246),least_upper_bound(X_248,X_29))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),X_29),least_upper_bound(greatest_lower_bound(X_30,X_246),least_upper_bound(X_248,X_29))) )],[refute_0_2091,refute_0_2094]) ).
cnf(refute_0_2096,plain,
( least_upper_bound(X_248,least_upper_bound(greatest_lower_bound(X_30,X_246),least_upper_bound(X_248,X_29))) != least_upper_bound(greatest_lower_bound(X_30,X_246),least_upper_bound(X_248,X_29))
| least_upper_bound(X_248,least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),X_29)) != least_upper_bound(X_248,least_upper_bound(greatest_lower_bound(X_30,X_246),least_upper_bound(X_248,X_29)))
| least_upper_bound(X_248,least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),X_29)) = least_upper_bound(greatest_lower_bound(X_30,X_246),least_upper_bound(X_248,X_29)) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(least_upper_bound(X_248,least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),X_29)))),bind(Y0,$fot(least_upper_bound(X_248,least_upper_bound(greatest_lower_bound(X_30,X_246),least_upper_bound(X_248,X_29))))),bind(Z0,$fot(least_upper_bound(greatest_lower_bound(X_30,X_246),least_upper_bound(X_248,X_29))))]]) ).
cnf(refute_0_2097,plain,
( least_upper_bound(X_248,least_upper_bound(greatest_lower_bound(X_30,X_246),least_upper_bound(X_248,X_29))) != least_upper_bound(greatest_lower_bound(X_30,X_246),least_upper_bound(X_248,X_29))
| least_upper_bound(X_248,least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),X_29)) = least_upper_bound(greatest_lower_bound(X_30,X_246),least_upper_bound(X_248,X_29)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_248,least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),X_29)),least_upper_bound(X_248,least_upper_bound(greatest_lower_bound(X_30,X_246),least_upper_bound(X_248,X_29)))) )],[refute_0_2095,refute_0_2096]) ).
cnf(refute_0_2098,plain,
least_upper_bound(X_248,least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),X_29)) = least_upper_bound(greatest_lower_bound(X_30,X_246),least_upper_bound(X_248,X_29)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_248,least_upper_bound(greatest_lower_bound(X_30,X_246),least_upper_bound(X_248,X_29))),least_upper_bound(greatest_lower_bound(X_30,X_246),least_upper_bound(X_248,X_29))) )],[refute_0_2090,refute_0_2097]) ).
cnf(refute_0_2099,plain,
least_upper_bound(X_30,least_upper_bound(X_248,least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),X_29))) = least_upper_bound(X_30,least_upper_bound(X_248,least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),X_29))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_30,least_upper_bound(X_248,least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),X_29))))]]) ).
cnf(refute_0_2100,plain,
( least_upper_bound(X_248,least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),X_29)) != least_upper_bound(greatest_lower_bound(X_30,X_246),least_upper_bound(X_248,X_29))
| least_upper_bound(X_30,least_upper_bound(X_248,least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),X_29))) != least_upper_bound(X_30,least_upper_bound(X_248,least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),X_29)))
| least_upper_bound(X_30,least_upper_bound(X_248,least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),X_29))) = least_upper_bound(X_30,least_upper_bound(greatest_lower_bound(X_30,X_246),least_upper_bound(X_248,X_29))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_30,least_upper_bound(X_248,least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),X_29))),least_upper_bound(X_30,least_upper_bound(X_248,least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),X_29)))) ),[1,1],$fot(least_upper_bound(greatest_lower_bound(X_30,X_246),least_upper_bound(X_248,X_29)))]]) ).
cnf(refute_0_2101,plain,
( least_upper_bound(X_248,least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),X_29)) != least_upper_bound(greatest_lower_bound(X_30,X_246),least_upper_bound(X_248,X_29))
| least_upper_bound(X_30,least_upper_bound(X_248,least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),X_29))) = least_upper_bound(X_30,least_upper_bound(greatest_lower_bound(X_30,X_246),least_upper_bound(X_248,X_29))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_30,least_upper_bound(X_248,least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),X_29))),least_upper_bound(X_30,least_upper_bound(X_248,least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),X_29)))) )],[refute_0_2099,refute_0_2100]) ).
cnf(refute_0_2102,plain,
least_upper_bound(X_30,least_upper_bound(X_248,least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),X_29))) = least_upper_bound(X_30,least_upper_bound(greatest_lower_bound(X_30,X_246),least_upper_bound(X_248,X_29))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_248,least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),X_29)),least_upper_bound(greatest_lower_bound(X_30,X_246),least_upper_bound(X_248,X_29))) )],[refute_0_2098,refute_0_2101]) ).
cnf(refute_0_2103,plain,
( least_upper_bound(X_30,least_upper_bound(X_248,least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),X_29))) != least_upper_bound(X_30,least_upper_bound(greatest_lower_bound(X_30,X_246),least_upper_bound(X_248,X_29)))
| least_upper_bound(X_30,least_upper_bound(greatest_lower_bound(X_30,X_246),least_upper_bound(X_248,X_29))) != least_upper_bound(X_30,least_upper_bound(X_248,X_29))
| least_upper_bound(X_30,least_upper_bound(X_248,least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),X_29))) = least_upper_bound(X_30,least_upper_bound(X_248,X_29)) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(least_upper_bound(X_30,least_upper_bound(X_248,least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),X_29))))),bind(Y0,$fot(least_upper_bound(X_30,least_upper_bound(greatest_lower_bound(X_30,X_246),least_upper_bound(X_248,X_29))))),bind(Z0,$fot(least_upper_bound(X_30,least_upper_bound(X_248,X_29))))]]) ).
cnf(refute_0_2104,plain,
( least_upper_bound(X_30,least_upper_bound(greatest_lower_bound(X_30,X_246),least_upper_bound(X_248,X_29))) != least_upper_bound(X_30,least_upper_bound(X_248,X_29))
| least_upper_bound(X_30,least_upper_bound(X_248,least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),X_29))) = least_upper_bound(X_30,least_upper_bound(X_248,X_29)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_30,least_upper_bound(X_248,least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),X_29))),least_upper_bound(X_30,least_upper_bound(greatest_lower_bound(X_30,X_246),least_upper_bound(X_248,X_29)))) )],[refute_0_2102,refute_0_2103]) ).
cnf(refute_0_2105,plain,
least_upper_bound(X_30,least_upper_bound(X_248,least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),X_29))) = least_upper_bound(X_30,least_upper_bound(X_248,X_29)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_30,least_upper_bound(greatest_lower_bound(X_30,X_246),least_upper_bound(X_248,X_29))),least_upper_bound(X_30,least_upper_bound(X_248,X_29))) )],[refute_0_2089,refute_0_2104]) ).
cnf(refute_0_2106,plain,
least_upper_bound(X_231,least_upper_bound(X_232,least_upper_bound(least_upper_bound(X,Y),X_231))) = least_upper_bound(X_231,least_upper_bound(X_232,least_upper_bound(X,Y))),
inference(subst,[],[refute_0_2083:[bind(X_21,$fot(X_231)),bind(X_29,$fot(X_232)),bind(X_30,$fot(least_upper_bound(X,Y)))]]) ).
cnf(refute_0_2107,plain,
least_upper_bound(X,least_upper_bound(Y,X_231)) = least_upper_bound(least_upper_bound(X,Y),X_231),
inference(subst,[],[associativity_of_lub:[bind(Z,$fot(X_231))]]) ).
cnf(refute_0_2108,plain,
( least_upper_bound(X,least_upper_bound(Y,X_231)) != least_upper_bound(least_upper_bound(X,Y),X_231)
| least_upper_bound(least_upper_bound(X,Y),X_231) = least_upper_bound(X,least_upper_bound(Y,X_231)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(Y,X_231)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X,Y),X_231)))]]) ).
cnf(refute_0_2109,plain,
least_upper_bound(least_upper_bound(X,Y),X_231) = least_upper_bound(X,least_upper_bound(Y,X_231)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,X_231)),least_upper_bound(least_upper_bound(X,Y),X_231)) )],[refute_0_2107,refute_0_2108]) ).
cnf(refute_0_2110,plain,
( least_upper_bound(X_231,least_upper_bound(X_232,least_upper_bound(least_upper_bound(X,Y),X_231))) != least_upper_bound(X_231,least_upper_bound(X_232,least_upper_bound(X,Y)))
| least_upper_bound(least_upper_bound(X,Y),X_231) != least_upper_bound(X,least_upper_bound(Y,X_231))
| least_upper_bound(X_231,least_upper_bound(X_232,least_upper_bound(X,least_upper_bound(Y,X_231)))) = least_upper_bound(X_231,least_upper_bound(X_232,least_upper_bound(X,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_231,least_upper_bound(X_232,least_upper_bound(least_upper_bound(X,Y),X_231))),least_upper_bound(X_231,least_upper_bound(X_232,least_upper_bound(X,Y)))) ),[0,1,1],$fot(least_upper_bound(X,least_upper_bound(Y,X_231)))]]) ).
cnf(refute_0_2111,plain,
( least_upper_bound(X_231,least_upper_bound(X_232,least_upper_bound(least_upper_bound(X,Y),X_231))) != least_upper_bound(X_231,least_upper_bound(X_232,least_upper_bound(X,Y)))
| least_upper_bound(X_231,least_upper_bound(X_232,least_upper_bound(X,least_upper_bound(Y,X_231)))) = least_upper_bound(X_231,least_upper_bound(X_232,least_upper_bound(X,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X,Y),X_231),least_upper_bound(X,least_upper_bound(Y,X_231))) )],[refute_0_2109,refute_0_2110]) ).
cnf(refute_0_2112,plain,
least_upper_bound(X_231,least_upper_bound(X_232,least_upper_bound(X,least_upper_bound(Y,X_231)))) = least_upper_bound(X_231,least_upper_bound(X_232,least_upper_bound(X,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_231,least_upper_bound(X_232,least_upper_bound(least_upper_bound(X,Y),X_231))),least_upper_bound(X_231,least_upper_bound(X_232,least_upper_bound(X,Y)))) )],[refute_0_2106,refute_0_2111]) ).
cnf(refute_0_2113,plain,
least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),least_upper_bound(X_29,least_upper_bound(X_30,least_upper_bound(X_232,least_upper_bound(X_233,X_30))))) = least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),least_upper_bound(X_29,X_30)),
inference(subst,[],[refute_0_2083:[bind(X_21,$fot(least_upper_bound(X_232,least_upper_bound(X_233,X_30))))]]) ).
cnf(refute_0_2114,plain,
least_upper_bound(X_30,least_upper_bound(X_232,least_upper_bound(X_233,X_30))) = least_upper_bound(X_30,least_upper_bound(X_232,X_233)),
inference(subst,[],[refute_0_2083:[bind(X_21,$fot(X_30)),bind(X_29,$fot(X_232)),bind(X_30,$fot(X_233))]]) ).
cnf(refute_0_2115,plain,
( least_upper_bound(X_30,least_upper_bound(X_232,least_upper_bound(X_233,X_30))) != least_upper_bound(X_30,least_upper_bound(X_232,X_233))
| least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),least_upper_bound(X_29,least_upper_bound(X_30,least_upper_bound(X_232,least_upper_bound(X_233,X_30))))) != least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),least_upper_bound(X_29,X_30))
| least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),least_upper_bound(X_29,least_upper_bound(X_30,least_upper_bound(X_232,X_233)))) = least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),least_upper_bound(X_29,X_30)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),least_upper_bound(X_29,least_upper_bound(X_30,least_upper_bound(X_232,least_upper_bound(X_233,X_30))))),least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),least_upper_bound(X_29,X_30))) ),[0,1,1],$fot(least_upper_bound(X_30,least_upper_bound(X_232,X_233)))]]) ).
cnf(refute_0_2116,plain,
( least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),least_upper_bound(X_29,least_upper_bound(X_30,least_upper_bound(X_232,least_upper_bound(X_233,X_30))))) != least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),least_upper_bound(X_29,X_30))
| least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),least_upper_bound(X_29,least_upper_bound(X_30,least_upper_bound(X_232,X_233)))) = least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),least_upper_bound(X_29,X_30)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_30,least_upper_bound(X_232,least_upper_bound(X_233,X_30))),least_upper_bound(X_30,least_upper_bound(X_232,X_233))) )],[refute_0_2114,refute_0_2115]) ).
cnf(refute_0_2117,plain,
least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),least_upper_bound(X_29,least_upper_bound(X_30,least_upper_bound(X_232,X_233)))) = least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),least_upper_bound(X_29,X_30)),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),least_upper_bound(X_29,least_upper_bound(X_30,least_upper_bound(X_232,least_upper_bound(X_233,X_30))))),least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),least_upper_bound(X_29,X_30))) )],[refute_0_2113,refute_0_2116]) ).
cnf(refute_0_2118,plain,
least_upper_bound(X_232,least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29)))) = least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29))),
inference(subst,[],[refute_0_71:[bind(X_22,$fot(least_upper_bound(X_233,least_upper_bound(X_30,X_29)))),bind(X_23,$fot(X_232))]]) ).
cnf(refute_0_2119,plain,
least_upper_bound(X_233,least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29)))) = least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29))),
inference(subst,[],[refute_0_1763:[bind(Y,$fot(least_upper_bound(X_30,X_29))),bind(X_29,$fot(X_232)),bind(X_30,$fot(X_233))]]) ).
cnf(refute_0_2120,plain,
least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),least_upper_bound(greatest_lower_bound(X_13,least_upper_bound(X_134,least_upper_bound(X_135,X_13))),X_31)) = least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_31),
inference(subst,[],[refute_0_2067:[bind(X_29,$fot(least_upper_bound(X_134,least_upper_bound(X_135,X_13))))]]) ).
cnf(refute_0_2121,plain,
( greatest_lower_bound(X_13,least_upper_bound(X_134,least_upper_bound(X_135,X_13))) != X_13
| least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),least_upper_bound(greatest_lower_bound(X_13,least_upper_bound(X_134,least_upper_bound(X_135,X_13))),X_31)) != least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_31)
| least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),least_upper_bound(X_13,X_31)) = least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_31) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),least_upper_bound(greatest_lower_bound(X_13,least_upper_bound(X_134,least_upper_bound(X_135,X_13))),X_31)),least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_31)) ),[0,1,0],$fot(X_13)]]) ).
cnf(refute_0_2122,plain,
( least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),least_upper_bound(greatest_lower_bound(X_13,least_upper_bound(X_134,least_upper_bound(X_135,X_13))),X_31)) != least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_31)
| least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),least_upper_bound(X_13,X_31)) = least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_31) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_13,least_upper_bound(X_134,least_upper_bound(X_135,X_13))),X_13) )],[refute_0_1930,refute_0_2121]) ).
cnf(refute_0_2123,plain,
least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),least_upper_bound(X_13,X_31)) = least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_31),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),least_upper_bound(greatest_lower_bound(X_13,least_upper_bound(X_134,least_upper_bound(X_135,X_13))),X_31)),least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_31)) )],[refute_0_2120,refute_0_2122]) ).
cnf(refute_0_2124,plain,
least_upper_bound(least_upper_bound(X_135,X_13),X_31) = least_upper_bound(X_135,least_upper_bound(X_13,X_31)),
inference(subst,[],[refute_0_60:[bind(X,$fot(X_135)),bind(Y,$fot(X_13)),bind(Z,$fot(X_31))]]) ).
cnf(refute_0_2125,plain,
least_upper_bound(X_134,least_upper_bound(least_upper_bound(X_135,X_13),X_31)) = least_upper_bound(X_134,least_upper_bound(least_upper_bound(X_135,X_13),X_31)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_134,least_upper_bound(least_upper_bound(X_135,X_13),X_31)))]]) ).
cnf(refute_0_2126,plain,
( least_upper_bound(X_134,least_upper_bound(least_upper_bound(X_135,X_13),X_31)) != least_upper_bound(X_134,least_upper_bound(least_upper_bound(X_135,X_13),X_31))
| least_upper_bound(least_upper_bound(X_135,X_13),X_31) != least_upper_bound(X_135,least_upper_bound(X_13,X_31))
| least_upper_bound(X_134,least_upper_bound(least_upper_bound(X_135,X_13),X_31)) = least_upper_bound(X_134,least_upper_bound(X_135,least_upper_bound(X_13,X_31))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_134,least_upper_bound(least_upper_bound(X_135,X_13),X_31)),least_upper_bound(X_134,least_upper_bound(least_upper_bound(X_135,X_13),X_31))) ),[1,1],$fot(least_upper_bound(X_135,least_upper_bound(X_13,X_31)))]]) ).
cnf(refute_0_2127,plain,
( least_upper_bound(least_upper_bound(X_135,X_13),X_31) != least_upper_bound(X_135,least_upper_bound(X_13,X_31))
| least_upper_bound(X_134,least_upper_bound(least_upper_bound(X_135,X_13),X_31)) = least_upper_bound(X_134,least_upper_bound(X_135,least_upper_bound(X_13,X_31))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_134,least_upper_bound(least_upper_bound(X_135,X_13),X_31)),least_upper_bound(X_134,least_upper_bound(least_upper_bound(X_135,X_13),X_31))) )],[refute_0_2125,refute_0_2126]) ).
cnf(refute_0_2128,plain,
least_upper_bound(X_134,least_upper_bound(least_upper_bound(X_135,X_13),X_31)) = least_upper_bound(X_134,least_upper_bound(X_135,least_upper_bound(X_13,X_31))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_135,X_13),X_31),least_upper_bound(X_135,least_upper_bound(X_13,X_31))) )],[refute_0_2124,refute_0_2127]) ).
cnf(refute_0_2129,plain,
least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_31) = least_upper_bound(X_134,least_upper_bound(least_upper_bound(X_135,X_13),X_31)),
inference(subst,[],[refute_0_60:[bind(X,$fot(X_134)),bind(Y,$fot(least_upper_bound(X_135,X_13))),bind(Z,$fot(X_31))]]) ).
cnf(refute_0_2130,plain,
( least_upper_bound(X_134,least_upper_bound(least_upper_bound(X_135,X_13),X_31)) != least_upper_bound(X_134,least_upper_bound(X_135,least_upper_bound(X_13,X_31)))
| least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_31) != least_upper_bound(X_134,least_upper_bound(least_upper_bound(X_135,X_13),X_31))
| least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_31) = least_upper_bound(X_134,least_upper_bound(X_135,least_upper_bound(X_13,X_31))) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_31))),bind(Y0,$fot(least_upper_bound(X_134,least_upper_bound(least_upper_bound(X_135,X_13),X_31)))),bind(Z0,$fot(least_upper_bound(X_134,least_upper_bound(X_135,least_upper_bound(X_13,X_31)))))]]) ).
cnf(refute_0_2131,plain,
( least_upper_bound(X_134,least_upper_bound(least_upper_bound(X_135,X_13),X_31)) != least_upper_bound(X_134,least_upper_bound(X_135,least_upper_bound(X_13,X_31)))
| least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_31) = least_upper_bound(X_134,least_upper_bound(X_135,least_upper_bound(X_13,X_31))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_31),least_upper_bound(X_134,least_upper_bound(least_upper_bound(X_135,X_13),X_31))) )],[refute_0_2129,refute_0_2130]) ).
cnf(refute_0_2132,plain,
least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_31) = least_upper_bound(X_134,least_upper_bound(X_135,least_upper_bound(X_13,X_31))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_134,least_upper_bound(least_upper_bound(X_135,X_13),X_31)),least_upper_bound(X_134,least_upper_bound(X_135,least_upper_bound(X_13,X_31)))) )],[refute_0_2128,refute_0_2131]) ).
cnf(refute_0_2133,plain,
least_upper_bound(X_13,least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_31)) = least_upper_bound(X_13,least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_31)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_13,least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_31)))]]) ).
cnf(refute_0_2134,plain,
( least_upper_bound(X_13,least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_31)) != least_upper_bound(X_13,least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_31))
| least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_31) != least_upper_bound(X_134,least_upper_bound(X_135,least_upper_bound(X_13,X_31)))
| least_upper_bound(X_13,least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_31)) = least_upper_bound(X_13,least_upper_bound(X_134,least_upper_bound(X_135,least_upper_bound(X_13,X_31)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_13,least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_31)),least_upper_bound(X_13,least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_31))) ),[1,1],$fot(least_upper_bound(X_134,least_upper_bound(X_135,least_upper_bound(X_13,X_31))))]]) ).
cnf(refute_0_2135,plain,
( least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_31) != least_upper_bound(X_134,least_upper_bound(X_135,least_upper_bound(X_13,X_31)))
| least_upper_bound(X_13,least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_31)) = least_upper_bound(X_13,least_upper_bound(X_134,least_upper_bound(X_135,least_upper_bound(X_13,X_31)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_13,least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_31)),least_upper_bound(X_13,least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_31))) )],[refute_0_2133,refute_0_2134]) ).
cnf(refute_0_2136,plain,
least_upper_bound(X_13,least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_31)) = least_upper_bound(X_13,least_upper_bound(X_134,least_upper_bound(X_135,least_upper_bound(X_13,X_31)))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_31),least_upper_bound(X_134,least_upper_bound(X_135,least_upper_bound(X_13,X_31)))) )],[refute_0_2132,refute_0_2135]) ).
cnf(refute_0_2137,plain,
least_upper_bound(least_upper_bound(Y,X_22),least_upper_bound(greatest_lower_bound(least_upper_bound(X_22,Y),least_upper_bound(Y,X_22)),X_89)) = least_upper_bound(least_upper_bound(Y,X_22),X_89),
inference(subst,[],[refute_0_2067:[bind(X_13,$fot(least_upper_bound(X_22,Y))),bind(X_29,$fot(least_upper_bound(Y,X_22))),bind(X_31,$fot(X_89))]]) ).
cnf(refute_0_2138,plain,
( greatest_lower_bound(least_upper_bound(X_22,Y),least_upper_bound(Y,X_22)) != least_upper_bound(X_22,Y)
| least_upper_bound(least_upper_bound(Y,X_22),least_upper_bound(greatest_lower_bound(least_upper_bound(X_22,Y),least_upper_bound(Y,X_22)),X_89)) != least_upper_bound(least_upper_bound(Y,X_22),X_89)
| least_upper_bound(least_upper_bound(Y,X_22),least_upper_bound(least_upper_bound(X_22,Y),X_89)) = least_upper_bound(least_upper_bound(Y,X_22),X_89) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_22),least_upper_bound(greatest_lower_bound(least_upper_bound(X_22,Y),least_upper_bound(Y,X_22)),X_89)),least_upper_bound(least_upper_bound(Y,X_22),X_89)) ),[0,1,0],$fot(least_upper_bound(X_22,Y))]]) ).
cnf(refute_0_2139,plain,
( least_upper_bound(least_upper_bound(Y,X_22),least_upper_bound(greatest_lower_bound(least_upper_bound(X_22,Y),least_upper_bound(Y,X_22)),X_89)) != least_upper_bound(least_upper_bound(Y,X_22),X_89)
| least_upper_bound(least_upper_bound(Y,X_22),least_upper_bound(least_upper_bound(X_22,Y),X_89)) = least_upper_bound(least_upper_bound(Y,X_22),X_89) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_22,Y),least_upper_bound(Y,X_22)),least_upper_bound(X_22,Y)) )],[refute_0_917,refute_0_2138]) ).
cnf(refute_0_2140,plain,
least_upper_bound(least_upper_bound(Y,X_22),least_upper_bound(least_upper_bound(X_22,Y),X_89)) = least_upper_bound(least_upper_bound(Y,X_22),X_89),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_22),least_upper_bound(greatest_lower_bound(least_upper_bound(X_22,Y),least_upper_bound(Y,X_22)),X_89)),least_upper_bound(least_upper_bound(Y,X_22),X_89)) )],[refute_0_2137,refute_0_2139]) ).
cnf(refute_0_2141,plain,
least_upper_bound(Y,least_upper_bound(X_22,least_upper_bound(Y,X_89))) = least_upper_bound(X_22,least_upper_bound(Y,X_89)),
inference(subst,[],[refute_0_1763:[bind(Y,$fot(X_89)),bind(X_29,$fot(X_22)),bind(X_30,$fot(Y))]]) ).
cnf(refute_0_2142,plain,
least_upper_bound(X_22,least_upper_bound(X_22,least_upper_bound(Y,X_89))) = least_upper_bound(X_22,least_upper_bound(Y,X_89)),
inference(subst,[],[refute_0_71:[bind(X_22,$fot(least_upper_bound(Y,X_89))),bind(X_23,$fot(X_22))]]) ).
cnf(refute_0_2143,plain,
least_upper_bound(least_upper_bound(X_22,Y),X_89) = least_upper_bound(X_22,least_upper_bound(Y,X_89)),
inference(subst,[],[refute_0_60:[bind(X,$fot(X_22)),bind(Z,$fot(X_89))]]) ).
cnf(refute_0_2144,plain,
least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_22,Y),X_89)) = least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_22,Y),X_89)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_22,Y),X_89)))]]) ).
cnf(refute_0_2145,plain,
( least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_22,Y),X_89)) != least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_22,Y),X_89))
| least_upper_bound(least_upper_bound(X_22,Y),X_89) != least_upper_bound(X_22,least_upper_bound(Y,X_89))
| least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_22,Y),X_89)) = least_upper_bound(X_22,least_upper_bound(X_22,least_upper_bound(Y,X_89))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_22,Y),X_89)),least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_22,Y),X_89))) ),[1,1],$fot(least_upper_bound(X_22,least_upper_bound(Y,X_89)))]]) ).
cnf(refute_0_2146,plain,
( least_upper_bound(least_upper_bound(X_22,Y),X_89) != least_upper_bound(X_22,least_upper_bound(Y,X_89))
| least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_22,Y),X_89)) = least_upper_bound(X_22,least_upper_bound(X_22,least_upper_bound(Y,X_89))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_22,Y),X_89)),least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_22,Y),X_89))) )],[refute_0_2144,refute_0_2145]) ).
cnf(refute_0_2147,plain,
least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_22,Y),X_89)) = least_upper_bound(X_22,least_upper_bound(X_22,least_upper_bound(Y,X_89))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_22,Y),X_89),least_upper_bound(X_22,least_upper_bound(Y,X_89))) )],[refute_0_2143,refute_0_2146]) ).
cnf(refute_0_2148,plain,
( least_upper_bound(X_22,least_upper_bound(X_22,least_upper_bound(Y,X_89))) != least_upper_bound(X_22,least_upper_bound(Y,X_89))
| least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_22,Y),X_89)) != least_upper_bound(X_22,least_upper_bound(X_22,least_upper_bound(Y,X_89)))
| least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_22,Y),X_89)) = least_upper_bound(X_22,least_upper_bound(Y,X_89)) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_22,Y),X_89)))),bind(Y0,$fot(least_upper_bound(X_22,least_upper_bound(X_22,least_upper_bound(Y,X_89))))),bind(Z0,$fot(least_upper_bound(X_22,least_upper_bound(Y,X_89))))]]) ).
cnf(refute_0_2149,plain,
( least_upper_bound(X_22,least_upper_bound(X_22,least_upper_bound(Y,X_89))) != least_upper_bound(X_22,least_upper_bound(Y,X_89))
| least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_22,Y),X_89)) = least_upper_bound(X_22,least_upper_bound(Y,X_89)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_22,Y),X_89)),least_upper_bound(X_22,least_upper_bound(X_22,least_upper_bound(Y,X_89)))) )],[refute_0_2147,refute_0_2148]) ).
cnf(refute_0_2150,plain,
least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_22,Y),X_89)) = least_upper_bound(X_22,least_upper_bound(Y,X_89)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(X_22,least_upper_bound(Y,X_89))),least_upper_bound(X_22,least_upper_bound(Y,X_89))) )],[refute_0_2142,refute_0_2149]) ).
cnf(refute_0_2151,plain,
least_upper_bound(Y,least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_22,Y),X_89))) = least_upper_bound(Y,least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_22,Y),X_89))),
introduced(tautology,[refl,[$fot(least_upper_bound(Y,least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_22,Y),X_89))))]]) ).
cnf(refute_0_2152,plain,
( least_upper_bound(Y,least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_22,Y),X_89))) != least_upper_bound(Y,least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_22,Y),X_89)))
| least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_22,Y),X_89)) != least_upper_bound(X_22,least_upper_bound(Y,X_89))
| least_upper_bound(Y,least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_22,Y),X_89))) = least_upper_bound(Y,least_upper_bound(X_22,least_upper_bound(Y,X_89))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_22,Y),X_89))),least_upper_bound(Y,least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_22,Y),X_89)))) ),[1,1],$fot(least_upper_bound(X_22,least_upper_bound(Y,X_89)))]]) ).
cnf(refute_0_2153,plain,
( least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_22,Y),X_89)) != least_upper_bound(X_22,least_upper_bound(Y,X_89))
| least_upper_bound(Y,least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_22,Y),X_89))) = least_upper_bound(Y,least_upper_bound(X_22,least_upper_bound(Y,X_89))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_22,Y),X_89))),least_upper_bound(Y,least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_22,Y),X_89)))) )],[refute_0_2151,refute_0_2152]) ).
cnf(refute_0_2154,plain,
least_upper_bound(Y,least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_22,Y),X_89))) = least_upper_bound(Y,least_upper_bound(X_22,least_upper_bound(Y,X_89))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_22,Y),X_89)),least_upper_bound(X_22,least_upper_bound(Y,X_89))) )],[refute_0_2150,refute_0_2153]) ).
cnf(refute_0_2155,plain,
( least_upper_bound(Y,least_upper_bound(X_22,least_upper_bound(Y,X_89))) != least_upper_bound(X_22,least_upper_bound(Y,X_89))
| least_upper_bound(Y,least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_22,Y),X_89))) != least_upper_bound(Y,least_upper_bound(X_22,least_upper_bound(Y,X_89)))
| least_upper_bound(Y,least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_22,Y),X_89))) = least_upper_bound(X_22,least_upper_bound(Y,X_89)) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(least_upper_bound(Y,least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_22,Y),X_89))))),bind(Y0,$fot(least_upper_bound(Y,least_upper_bound(X_22,least_upper_bound(Y,X_89))))),bind(Z0,$fot(least_upper_bound(X_22,least_upper_bound(Y,X_89))))]]) ).
cnf(refute_0_2156,plain,
( least_upper_bound(Y,least_upper_bound(X_22,least_upper_bound(Y,X_89))) != least_upper_bound(X_22,least_upper_bound(Y,X_89))
| least_upper_bound(Y,least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_22,Y),X_89))) = least_upper_bound(X_22,least_upper_bound(Y,X_89)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_22,Y),X_89))),least_upper_bound(Y,least_upper_bound(X_22,least_upper_bound(Y,X_89)))) )],[refute_0_2154,refute_0_2155]) ).
cnf(refute_0_2157,plain,
least_upper_bound(Y,least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_22,Y),X_89))) = least_upper_bound(X_22,least_upper_bound(Y,X_89)),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_22,least_upper_bound(Y,X_89))),least_upper_bound(X_22,least_upper_bound(Y,X_89))) )],[refute_0_2141,refute_0_2156]) ).
cnf(refute_0_2158,plain,
least_upper_bound(least_upper_bound(Y,X_22),least_upper_bound(least_upper_bound(X_22,Y),X_89)) = least_upper_bound(Y,least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_22,Y),X_89))),
inference(subst,[],[refute_0_60:[bind(X,$fot(Y)),bind(Y,$fot(X_22)),bind(Z,$fot(least_upper_bound(least_upper_bound(X_22,Y),X_89)))]]) ).
cnf(refute_0_2159,plain,
( least_upper_bound(Y,least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_22,Y),X_89))) != least_upper_bound(X_22,least_upper_bound(Y,X_89))
| least_upper_bound(least_upper_bound(Y,X_22),least_upper_bound(least_upper_bound(X_22,Y),X_89)) != least_upper_bound(Y,least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_22,Y),X_89)))
| least_upper_bound(least_upper_bound(Y,X_22),least_upper_bound(least_upper_bound(X_22,Y),X_89)) = least_upper_bound(X_22,least_upper_bound(Y,X_89)) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(least_upper_bound(least_upper_bound(Y,X_22),least_upper_bound(least_upper_bound(X_22,Y),X_89)))),bind(Y0,$fot(least_upper_bound(Y,least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_22,Y),X_89))))),bind(Z0,$fot(least_upper_bound(X_22,least_upper_bound(Y,X_89))))]]) ).
cnf(refute_0_2160,plain,
( least_upper_bound(Y,least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_22,Y),X_89))) != least_upper_bound(X_22,least_upper_bound(Y,X_89))
| least_upper_bound(least_upper_bound(Y,X_22),least_upper_bound(least_upper_bound(X_22,Y),X_89)) = least_upper_bound(X_22,least_upper_bound(Y,X_89)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_22),least_upper_bound(least_upper_bound(X_22,Y),X_89)),least_upper_bound(Y,least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_22,Y),X_89)))) )],[refute_0_2158,refute_0_2159]) ).
cnf(refute_0_2161,plain,
least_upper_bound(least_upper_bound(Y,X_22),least_upper_bound(least_upper_bound(X_22,Y),X_89)) = least_upper_bound(X_22,least_upper_bound(Y,X_89)),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_22,Y),X_89))),least_upper_bound(X_22,least_upper_bound(Y,X_89))) )],[refute_0_2157,refute_0_2160]) ).
cnf(refute_0_2162,plain,
( least_upper_bound(least_upper_bound(Y,X_22),least_upper_bound(least_upper_bound(X_22,Y),X_89)) != least_upper_bound(X_22,least_upper_bound(Y,X_89))
| least_upper_bound(least_upper_bound(Y,X_22),least_upper_bound(least_upper_bound(X_22,Y),X_89)) != least_upper_bound(least_upper_bound(Y,X_22),X_89)
| least_upper_bound(X_22,least_upper_bound(Y,X_89)) = least_upper_bound(least_upper_bound(Y,X_22),X_89) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_22),least_upper_bound(least_upper_bound(X_22,Y),X_89)),least_upper_bound(least_upper_bound(Y,X_22),X_89)) ),[0],$fot(least_upper_bound(X_22,least_upper_bound(Y,X_89)))]]) ).
cnf(refute_0_2163,plain,
( least_upper_bound(least_upper_bound(Y,X_22),least_upper_bound(least_upper_bound(X_22,Y),X_89)) != least_upper_bound(least_upper_bound(Y,X_22),X_89)
| least_upper_bound(X_22,least_upper_bound(Y,X_89)) = least_upper_bound(least_upper_bound(Y,X_22),X_89) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_22),least_upper_bound(least_upper_bound(X_22,Y),X_89)),least_upper_bound(X_22,least_upper_bound(Y,X_89))) )],[refute_0_2161,refute_0_2162]) ).
cnf(refute_0_2164,plain,
least_upper_bound(least_upper_bound(Y,X_22),X_89) = least_upper_bound(Y,least_upper_bound(X_22,X_89)),
inference(subst,[],[refute_0_60:[bind(X,$fot(Y)),bind(Y,$fot(X_22)),bind(Z,$fot(X_89))]]) ).
cnf(refute_0_2165,plain,
( least_upper_bound(X_22,least_upper_bound(Y,X_89)) != least_upper_bound(least_upper_bound(Y,X_22),X_89)
| least_upper_bound(least_upper_bound(Y,X_22),X_89) != least_upper_bound(Y,least_upper_bound(X_22,X_89))
| least_upper_bound(X_22,least_upper_bound(Y,X_89)) = least_upper_bound(Y,least_upper_bound(X_22,X_89)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_22,least_upper_bound(Y,X_89)),least_upper_bound(Y,least_upper_bound(X_22,X_89))) ),[0],$fot(least_upper_bound(least_upper_bound(Y,X_22),X_89))]]) ).
cnf(refute_0_2166,plain,
( least_upper_bound(X_22,least_upper_bound(Y,X_89)) != least_upper_bound(least_upper_bound(Y,X_22),X_89)
| least_upper_bound(X_22,least_upper_bound(Y,X_89)) = least_upper_bound(Y,least_upper_bound(X_22,X_89)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_22),X_89),least_upper_bound(Y,least_upper_bound(X_22,X_89))) )],[refute_0_2164,refute_0_2165]) ).
cnf(refute_0_2167,plain,
( least_upper_bound(least_upper_bound(Y,X_22),least_upper_bound(least_upper_bound(X_22,Y),X_89)) != least_upper_bound(least_upper_bound(Y,X_22),X_89)
| least_upper_bound(X_22,least_upper_bound(Y,X_89)) = least_upper_bound(Y,least_upper_bound(X_22,X_89)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(Y,X_89)),least_upper_bound(least_upper_bound(Y,X_22),X_89)) )],[refute_0_2163,refute_0_2166]) ).
cnf(refute_0_2168,plain,
least_upper_bound(X_22,least_upper_bound(Y,X_89)) = least_upper_bound(Y,least_upper_bound(X_22,X_89)),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_22),least_upper_bound(least_upper_bound(X_22,Y),X_89)),least_upper_bound(least_upper_bound(Y,X_22),X_89)) )],[refute_0_2140,refute_0_2167]) ).
cnf(refute_0_2169,plain,
( least_upper_bound(X_22,least_upper_bound(Y,X_89)) != least_upper_bound(Y,least_upper_bound(X_22,X_89))
| least_upper_bound(Y,least_upper_bound(X_22,X_89)) = least_upper_bound(X_22,least_upper_bound(Y,X_89)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X_22,least_upper_bound(Y,X_89)))),bind(Y0,$fot(least_upper_bound(Y,least_upper_bound(X_22,X_89))))]]) ).
cnf(refute_0_2170,plain,
least_upper_bound(Y,least_upper_bound(X_22,X_89)) = least_upper_bound(X_22,least_upper_bound(Y,X_89)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(Y,X_89)),least_upper_bound(Y,least_upper_bound(X_22,X_89))) )],[refute_0_2168,refute_0_2169]) ).
cnf(refute_0_2171,plain,
least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),least_upper_bound(X_13,X_31)) = least_upper_bound(X_13,least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_31)),
inference(subst,[],[refute_0_2170:[bind(Y,$fot(least_upper_bound(X_134,least_upper_bound(X_135,X_13)))),bind(X_22,$fot(X_13)),bind(X_89,$fot(X_31))]]) ).
cnf(refute_0_2172,plain,
( least_upper_bound(X_13,least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_31)) != least_upper_bound(X_13,least_upper_bound(X_134,least_upper_bound(X_135,least_upper_bound(X_13,X_31))))
| least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),least_upper_bound(X_13,X_31)) != least_upper_bound(X_13,least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_31))
| least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),least_upper_bound(X_13,X_31)) = least_upper_bound(X_13,least_upper_bound(X_134,least_upper_bound(X_135,least_upper_bound(X_13,X_31)))) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),least_upper_bound(X_13,X_31)))),bind(Y0,$fot(least_upper_bound(X_13,least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_31)))),bind(Z0,$fot(least_upper_bound(X_13,least_upper_bound(X_134,least_upper_bound(X_135,least_upper_bound(X_13,X_31))))))]]) ).
cnf(refute_0_2173,plain,
( least_upper_bound(X_13,least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_31)) != least_upper_bound(X_13,least_upper_bound(X_134,least_upper_bound(X_135,least_upper_bound(X_13,X_31))))
| least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),least_upper_bound(X_13,X_31)) = least_upper_bound(X_13,least_upper_bound(X_134,least_upper_bound(X_135,least_upper_bound(X_13,X_31)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),least_upper_bound(X_13,X_31)),least_upper_bound(X_13,least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_31))) )],[refute_0_2171,refute_0_2172]) ).
cnf(refute_0_2174,plain,
least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),least_upper_bound(X_13,X_31)) = least_upper_bound(X_13,least_upper_bound(X_134,least_upper_bound(X_135,least_upper_bound(X_13,X_31)))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_13,least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_31)),least_upper_bound(X_13,least_upper_bound(X_134,least_upper_bound(X_135,least_upper_bound(X_13,X_31))))) )],[refute_0_2136,refute_0_2173]) ).
cnf(refute_0_2175,plain,
( least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),least_upper_bound(X_13,X_31)) != least_upper_bound(X_13,least_upper_bound(X_134,least_upper_bound(X_135,least_upper_bound(X_13,X_31))))
| least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),least_upper_bound(X_13,X_31)) != least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_31)
| least_upper_bound(X_13,least_upper_bound(X_134,least_upper_bound(X_135,least_upper_bound(X_13,X_31)))) = least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_31) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),least_upper_bound(X_13,X_31)),least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_31)) ),[0],$fot(least_upper_bound(X_13,least_upper_bound(X_134,least_upper_bound(X_135,least_upper_bound(X_13,X_31)))))]]) ).
cnf(refute_0_2176,plain,
( least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),least_upper_bound(X_13,X_31)) != least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_31)
| least_upper_bound(X_13,least_upper_bound(X_134,least_upper_bound(X_135,least_upper_bound(X_13,X_31)))) = least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_31) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),least_upper_bound(X_13,X_31)),least_upper_bound(X_13,least_upper_bound(X_134,least_upper_bound(X_135,least_upper_bound(X_13,X_31))))) )],[refute_0_2174,refute_0_2175]) ).
cnf(refute_0_2177,plain,
( least_upper_bound(X_13,least_upper_bound(X_134,least_upper_bound(X_135,least_upper_bound(X_13,X_31)))) != least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_31)
| least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_31) != least_upper_bound(X_134,least_upper_bound(X_135,least_upper_bound(X_13,X_31)))
| least_upper_bound(X_13,least_upper_bound(X_134,least_upper_bound(X_135,least_upper_bound(X_13,X_31)))) = least_upper_bound(X_134,least_upper_bound(X_135,least_upper_bound(X_13,X_31))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_13,least_upper_bound(X_134,least_upper_bound(X_135,least_upper_bound(X_13,X_31)))),least_upper_bound(X_134,least_upper_bound(X_135,least_upper_bound(X_13,X_31)))) ),[0],$fot(least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_31))]]) ).
cnf(refute_0_2178,plain,
( least_upper_bound(X_13,least_upper_bound(X_134,least_upper_bound(X_135,least_upper_bound(X_13,X_31)))) != least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_31)
| least_upper_bound(X_13,least_upper_bound(X_134,least_upper_bound(X_135,least_upper_bound(X_13,X_31)))) = least_upper_bound(X_134,least_upper_bound(X_135,least_upper_bound(X_13,X_31))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_31),least_upper_bound(X_134,least_upper_bound(X_135,least_upper_bound(X_13,X_31)))) )],[refute_0_2132,refute_0_2177]) ).
cnf(refute_0_2179,plain,
( least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),least_upper_bound(X_13,X_31)) != least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_31)
| least_upper_bound(X_13,least_upper_bound(X_134,least_upper_bound(X_135,least_upper_bound(X_13,X_31)))) = least_upper_bound(X_134,least_upper_bound(X_135,least_upper_bound(X_13,X_31))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_13,least_upper_bound(X_134,least_upper_bound(X_135,least_upper_bound(X_13,X_31)))),least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_31)) )],[refute_0_2176,refute_0_2178]) ).
cnf(refute_0_2180,plain,
least_upper_bound(X_13,least_upper_bound(X_134,least_upper_bound(X_135,least_upper_bound(X_13,X_31)))) = least_upper_bound(X_134,least_upper_bound(X_135,least_upper_bound(X_13,X_31))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),least_upper_bound(X_13,X_31)),least_upper_bound(least_upper_bound(X_134,least_upper_bound(X_135,X_13)),X_31)) )],[refute_0_2123,refute_0_2179]) ).
cnf(refute_0_2181,plain,
least_upper_bound(X_30,least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29)))) = least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29))),
inference(subst,[],[refute_0_2180:[bind(X_13,$fot(X_30)),bind(X_134,$fot(X_232)),bind(X_135,$fot(X_233)),bind(X_31,$fot(X_29))]]) ).
cnf(refute_0_2182,plain,
least_upper_bound(least_upper_bound(X_233,X_30),X_29) = least_upper_bound(X_233,least_upper_bound(X_30,X_29)),
inference(subst,[],[refute_0_60:[bind(X,$fot(X_233)),bind(Y,$fot(X_30)),bind(Z,$fot(X_29))]]) ).
cnf(refute_0_2183,plain,
least_upper_bound(X_232,least_upper_bound(least_upper_bound(X_233,X_30),X_29)) = least_upper_bound(X_232,least_upper_bound(least_upper_bound(X_233,X_30),X_29)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_232,least_upper_bound(least_upper_bound(X_233,X_30),X_29)))]]) ).
cnf(refute_0_2184,plain,
( least_upper_bound(X_232,least_upper_bound(least_upper_bound(X_233,X_30),X_29)) != least_upper_bound(X_232,least_upper_bound(least_upper_bound(X_233,X_30),X_29))
| least_upper_bound(least_upper_bound(X_233,X_30),X_29) != least_upper_bound(X_233,least_upper_bound(X_30,X_29))
| least_upper_bound(X_232,least_upper_bound(least_upper_bound(X_233,X_30),X_29)) = least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_232,least_upper_bound(least_upper_bound(X_233,X_30),X_29)),least_upper_bound(X_232,least_upper_bound(least_upper_bound(X_233,X_30),X_29))) ),[1,1],$fot(least_upper_bound(X_233,least_upper_bound(X_30,X_29)))]]) ).
cnf(refute_0_2185,plain,
( least_upper_bound(least_upper_bound(X_233,X_30),X_29) != least_upper_bound(X_233,least_upper_bound(X_30,X_29))
| least_upper_bound(X_232,least_upper_bound(least_upper_bound(X_233,X_30),X_29)) = least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_232,least_upper_bound(least_upper_bound(X_233,X_30),X_29)),least_upper_bound(X_232,least_upper_bound(least_upper_bound(X_233,X_30),X_29))) )],[refute_0_2183,refute_0_2184]) ).
cnf(refute_0_2186,plain,
least_upper_bound(X_232,least_upper_bound(least_upper_bound(X_233,X_30),X_29)) = least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_233,X_30),X_29),least_upper_bound(X_233,least_upper_bound(X_30,X_29))) )],[refute_0_2182,refute_0_2185]) ).
cnf(refute_0_2187,plain,
least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29) = least_upper_bound(X_232,least_upper_bound(least_upper_bound(X_233,X_30),X_29)),
inference(subst,[],[refute_0_60:[bind(X,$fot(X_232)),bind(Y,$fot(least_upper_bound(X_233,X_30))),bind(Z,$fot(X_29))]]) ).
cnf(refute_0_2188,plain,
( least_upper_bound(X_232,least_upper_bound(least_upper_bound(X_233,X_30),X_29)) != least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29)))
| least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29) != least_upper_bound(X_232,least_upper_bound(least_upper_bound(X_233,X_30),X_29))
| least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29) = least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29))) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29))),bind(Y0,$fot(least_upper_bound(X_232,least_upper_bound(least_upper_bound(X_233,X_30),X_29)))),bind(Z0,$fot(least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29)))))]]) ).
cnf(refute_0_2189,plain,
( least_upper_bound(X_232,least_upper_bound(least_upper_bound(X_233,X_30),X_29)) != least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29)))
| least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29) = least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29),least_upper_bound(X_232,least_upper_bound(least_upper_bound(X_233,X_30),X_29))) )],[refute_0_2187,refute_0_2188]) ).
cnf(refute_0_2190,plain,
least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29) = least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_232,least_upper_bound(least_upper_bound(X_233,X_30),X_29)),least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29)))) )],[refute_0_2186,refute_0_2189]) ).
cnf(refute_0_2191,plain,
least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29)) = least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29)))]]) ).
cnf(refute_0_2192,plain,
( least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29)) != least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29))
| least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29) != least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29)))
| least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29)) = least_upper_bound(X_30,least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29)),least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29))) ),[1,1],$fot(least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29))))]]) ).
cnf(refute_0_2193,plain,
( least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29) != least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29)))
| least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29)) = least_upper_bound(X_30,least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29)),least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29))) )],[refute_0_2191,refute_0_2192]) ).
cnf(refute_0_2194,plain,
least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29)) = least_upper_bound(X_30,least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29)))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29),least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29)))) )],[refute_0_2190,refute_0_2193]) ).
cnf(refute_0_2195,plain,
( least_upper_bound(X_30,least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29)))) != least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29)))
| least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29)) != least_upper_bound(X_30,least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29))))
| least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29)) = least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29))) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29)))),bind(Y0,$fot(least_upper_bound(X_30,least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29)))))),bind(Z0,$fot(least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29)))))]]) ).
cnf(refute_0_2196,plain,
( least_upper_bound(X_30,least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29)))) != least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29)))
| least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29)) = least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29)),least_upper_bound(X_30,least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29))))) )],[refute_0_2194,refute_0_2195]) ).
cnf(refute_0_2197,plain,
least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29)) = least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_30,least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29)))),least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29)))) )],[refute_0_2181,refute_0_2196]) ).
cnf(refute_0_2198,plain,
least_upper_bound(X_233,least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29))) = least_upper_bound(X_233,least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_233,least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29))))]]) ).
cnf(refute_0_2199,plain,
( least_upper_bound(X_233,least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29))) != least_upper_bound(X_233,least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29)))
| least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29)) != least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29)))
| least_upper_bound(X_233,least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29))) = least_upper_bound(X_233,least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_233,least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29))),least_upper_bound(X_233,least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29)))) ),[1,1],$fot(least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29))))]]) ).
cnf(refute_0_2200,plain,
( least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29)) != least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29)))
| least_upper_bound(X_233,least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29))) = least_upper_bound(X_233,least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_233,least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29))),least_upper_bound(X_233,least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29)))) )],[refute_0_2198,refute_0_2199]) ).
cnf(refute_0_2201,plain,
least_upper_bound(X_233,least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29))) = least_upper_bound(X_233,least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29)))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29)),least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29)))) )],[refute_0_2197,refute_0_2200]) ).
cnf(refute_0_2202,plain,
( least_upper_bound(X_233,least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29)))) != least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29)))
| least_upper_bound(X_233,least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29))) != least_upper_bound(X_233,least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29))))
| least_upper_bound(X_233,least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29))) = least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29))) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(least_upper_bound(X_233,least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29))))),bind(Y0,$fot(least_upper_bound(X_233,least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29)))))),bind(Z0,$fot(least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29)))))]]) ).
cnf(refute_0_2203,plain,
( least_upper_bound(X_233,least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29)))) != least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29)))
| least_upper_bound(X_233,least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29))) = least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_233,least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29))),least_upper_bound(X_233,least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29))))) )],[refute_0_2201,refute_0_2202]) ).
cnf(refute_0_2204,plain,
least_upper_bound(X_233,least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29))) = least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_233,least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29)))),least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29)))) )],[refute_0_2119,refute_0_2203]) ).
cnf(refute_0_2205,plain,
least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29)))) = least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29)))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29)))))]]) ).
cnf(refute_0_2206,plain,
( least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29)))) != least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29))))
| least_upper_bound(X_233,least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29))) != least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29)))
| least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29)))) = least_upper_bound(X_232,least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29)))),least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29))))) ),[1,1],$fot(least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29))))]]) ).
cnf(refute_0_2207,plain,
( least_upper_bound(X_233,least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29))) != least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29)))
| least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29)))) = least_upper_bound(X_232,least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29)))),least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29))))) )],[refute_0_2205,refute_0_2206]) ).
cnf(refute_0_2208,plain,
least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29)))) = least_upper_bound(X_232,least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29)))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_233,least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29))),least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29)))) )],[refute_0_2204,refute_0_2207]) ).
cnf(refute_0_2209,plain,
( least_upper_bound(X_232,least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29)))) != least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29)))
| least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29)))) != least_upper_bound(X_232,least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29))))
| least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29)))) = least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29))) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29)))))),bind(Y0,$fot(least_upper_bound(X_232,least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29)))))),bind(Z0,$fot(least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29)))))]]) ).
cnf(refute_0_2210,plain,
( least_upper_bound(X_232,least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29)))) != least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29)))
| least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29)))) = least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29)))),least_upper_bound(X_232,least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29))))) )],[refute_0_2208,refute_0_2209]) ).
cnf(refute_0_2211,plain,
least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29)))) = least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_232,least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29)))),least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29)))) )],[refute_0_2118,refute_0_2210]) ).
cnf(refute_0_2212,plain,
least_upper_bound(least_upper_bound(X_232,X_233),least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29))) = least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29)))),
inference(subst,[],[refute_0_60:[bind(X,$fot(X_232)),bind(Y,$fot(X_233)),bind(Z,$fot(least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29))))]]) ).
cnf(refute_0_2213,plain,
least_upper_bound(X,least_upper_bound(X_29,least_upper_bound(X_147,X_145))) = least_upper_bound(X_29,least_upper_bound(least_upper_bound(X_147,X_145),X)),
inference(subst,[],[refute_0_1752:[bind(X_30,$fot(least_upper_bound(X_147,X_145)))]]) ).
cnf(refute_0_2214,plain,
least_upper_bound(X_145,least_upper_bound(X_29,X_147)) = least_upper_bound(X_29,least_upper_bound(X_147,X_145)),
inference(subst,[],[refute_0_1752:[bind(X,$fot(X_145)),bind(X_30,$fot(X_147))]]) ).
cnf(refute_0_2215,plain,
( least_upper_bound(X_145,least_upper_bound(X_29,X_147)) != least_upper_bound(X_29,least_upper_bound(X_147,X_145))
| least_upper_bound(X_29,least_upper_bound(X_147,X_145)) = least_upper_bound(X_145,least_upper_bound(X_29,X_147)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X_145,least_upper_bound(X_29,X_147)))),bind(Y0,$fot(least_upper_bound(X_29,least_upper_bound(X_147,X_145))))]]) ).
cnf(refute_0_2216,plain,
least_upper_bound(X_29,least_upper_bound(X_147,X_145)) = least_upper_bound(X_145,least_upper_bound(X_29,X_147)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_145,least_upper_bound(X_29,X_147)),least_upper_bound(X_29,least_upper_bound(X_147,X_145))) )],[refute_0_2214,refute_0_2215]) ).
cnf(refute_0_2217,plain,
( least_upper_bound(X,least_upper_bound(X_29,least_upper_bound(X_147,X_145))) != least_upper_bound(X_29,least_upper_bound(least_upper_bound(X_147,X_145),X))
| least_upper_bound(X_29,least_upper_bound(X_147,X_145)) != least_upper_bound(X_145,least_upper_bound(X_29,X_147))
| least_upper_bound(X,least_upper_bound(X_145,least_upper_bound(X_29,X_147))) = least_upper_bound(X_29,least_upper_bound(least_upper_bound(X_147,X_145),X)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_29,least_upper_bound(X_147,X_145))),least_upper_bound(X_29,least_upper_bound(least_upper_bound(X_147,X_145),X))) ),[0,1],$fot(least_upper_bound(X_145,least_upper_bound(X_29,X_147)))]]) ).
cnf(refute_0_2218,plain,
( least_upper_bound(X,least_upper_bound(X_29,least_upper_bound(X_147,X_145))) != least_upper_bound(X_29,least_upper_bound(least_upper_bound(X_147,X_145),X))
| least_upper_bound(X,least_upper_bound(X_145,least_upper_bound(X_29,X_147))) = least_upper_bound(X_29,least_upper_bound(least_upper_bound(X_147,X_145),X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_29,least_upper_bound(X_147,X_145)),least_upper_bound(X_145,least_upper_bound(X_29,X_147))) )],[refute_0_2216,refute_0_2217]) ).
cnf(refute_0_2219,plain,
least_upper_bound(X,least_upper_bound(X_145,least_upper_bound(X_29,X_147))) = least_upper_bound(X_29,least_upper_bound(least_upper_bound(X_147,X_145),X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_29,least_upper_bound(X_147,X_145))),least_upper_bound(X_29,least_upper_bound(least_upper_bound(X_147,X_145),X))) )],[refute_0_2213,refute_0_2218]) ).
cnf(refute_0_2220,plain,
least_upper_bound(least_upper_bound(X_147,X_145),X) = least_upper_bound(X_147,least_upper_bound(X_145,X)),
inference(subst,[],[refute_0_60:[bind(X,$fot(X_147)),bind(Y,$fot(X_145)),bind(Z,$fot(X))]]) ).
cnf(refute_0_2221,plain,
least_upper_bound(X_29,least_upper_bound(least_upper_bound(X_147,X_145),X)) = least_upper_bound(X_29,least_upper_bound(least_upper_bound(X_147,X_145),X)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_29,least_upper_bound(least_upper_bound(X_147,X_145),X)))]]) ).
cnf(refute_0_2222,plain,
( least_upper_bound(X_29,least_upper_bound(least_upper_bound(X_147,X_145),X)) != least_upper_bound(X_29,least_upper_bound(least_upper_bound(X_147,X_145),X))
| least_upper_bound(least_upper_bound(X_147,X_145),X) != least_upper_bound(X_147,least_upper_bound(X_145,X))
| least_upper_bound(X_29,least_upper_bound(least_upper_bound(X_147,X_145),X)) = least_upper_bound(X_29,least_upper_bound(X_147,least_upper_bound(X_145,X))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_29,least_upper_bound(least_upper_bound(X_147,X_145),X)),least_upper_bound(X_29,least_upper_bound(least_upper_bound(X_147,X_145),X))) ),[1,1],$fot(least_upper_bound(X_147,least_upper_bound(X_145,X)))]]) ).
cnf(refute_0_2223,plain,
( least_upper_bound(least_upper_bound(X_147,X_145),X) != least_upper_bound(X_147,least_upper_bound(X_145,X))
| least_upper_bound(X_29,least_upper_bound(least_upper_bound(X_147,X_145),X)) = least_upper_bound(X_29,least_upper_bound(X_147,least_upper_bound(X_145,X))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_29,least_upper_bound(least_upper_bound(X_147,X_145),X)),least_upper_bound(X_29,least_upper_bound(least_upper_bound(X_147,X_145),X))) )],[refute_0_2221,refute_0_2222]) ).
cnf(refute_0_2224,plain,
least_upper_bound(X_29,least_upper_bound(least_upper_bound(X_147,X_145),X)) = least_upper_bound(X_29,least_upper_bound(X_147,least_upper_bound(X_145,X))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_147,X_145),X),least_upper_bound(X_147,least_upper_bound(X_145,X))) )],[refute_0_2220,refute_0_2223]) ).
cnf(refute_0_2225,plain,
( least_upper_bound(X,least_upper_bound(X_145,least_upper_bound(X_29,X_147))) != least_upper_bound(X_29,least_upper_bound(least_upper_bound(X_147,X_145),X))
| least_upper_bound(X_29,least_upper_bound(least_upper_bound(X_147,X_145),X)) != least_upper_bound(X_29,least_upper_bound(X_147,least_upper_bound(X_145,X)))
| least_upper_bound(X,least_upper_bound(X_145,least_upper_bound(X_29,X_147))) = least_upper_bound(X_29,least_upper_bound(X_147,least_upper_bound(X_145,X))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,least_upper_bound(X_145,least_upper_bound(X_29,X_147))),least_upper_bound(X_29,least_upper_bound(X_147,least_upper_bound(X_145,X)))) ),[0],$fot(least_upper_bound(X_29,least_upper_bound(least_upper_bound(X_147,X_145),X)))]]) ).
cnf(refute_0_2226,plain,
( least_upper_bound(X,least_upper_bound(X_145,least_upper_bound(X_29,X_147))) != least_upper_bound(X_29,least_upper_bound(least_upper_bound(X_147,X_145),X))
| least_upper_bound(X,least_upper_bound(X_145,least_upper_bound(X_29,X_147))) = least_upper_bound(X_29,least_upper_bound(X_147,least_upper_bound(X_145,X))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_29,least_upper_bound(least_upper_bound(X_147,X_145),X)),least_upper_bound(X_29,least_upper_bound(X_147,least_upper_bound(X_145,X)))) )],[refute_0_2224,refute_0_2225]) ).
cnf(refute_0_2227,plain,
least_upper_bound(X,least_upper_bound(X_145,least_upper_bound(X_29,X_147))) = least_upper_bound(X_29,least_upper_bound(X_147,least_upper_bound(X_145,X))),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_145,least_upper_bound(X_29,X_147))),least_upper_bound(X_29,least_upper_bound(least_upper_bound(X_147,X_145),X))) )],[refute_0_2219,refute_0_2226]) ).
cnf(refute_0_2228,plain,
( least_upper_bound(X,least_upper_bound(X_145,least_upper_bound(X_29,X_147))) != least_upper_bound(X_29,least_upper_bound(X_147,least_upper_bound(X_145,X)))
| least_upper_bound(X_29,least_upper_bound(X_147,least_upper_bound(X_145,X))) = least_upper_bound(X,least_upper_bound(X_145,least_upper_bound(X_29,X_147))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(X_145,least_upper_bound(X_29,X_147))))),bind(Y0,$fot(least_upper_bound(X_29,least_upper_bound(X_147,least_upper_bound(X_145,X)))))]]) ).
cnf(refute_0_2229,plain,
least_upper_bound(X_29,least_upper_bound(X_147,least_upper_bound(X_145,X))) = least_upper_bound(X,least_upper_bound(X_145,least_upper_bound(X_29,X_147))),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_145,least_upper_bound(X_29,X_147))),least_upper_bound(X_29,least_upper_bound(X_147,least_upper_bound(X_145,X)))) )],[refute_0_2227,refute_0_2228]) ).
cnf(refute_0_2230,plain,
least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),least_upper_bound(X_29,least_upper_bound(X_30,least_upper_bound(X_232,X_233)))) = least_upper_bound(least_upper_bound(X_232,X_233),least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29))),
inference(subst,[],[refute_0_2229:[bind(X,$fot(least_upper_bound(X_232,X_233))),bind(X_145,$fot(X_30)),bind(X_147,$fot(X_29)),bind(X_29,$fot(least_upper_bound(X_232,least_upper_bound(X_233,X_30))))]]) ).
cnf(refute_0_2231,plain,
( least_upper_bound(least_upper_bound(X_232,X_233),least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29))) != least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29))))
| least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),least_upper_bound(X_29,least_upper_bound(X_30,least_upper_bound(X_232,X_233)))) != least_upper_bound(least_upper_bound(X_232,X_233),least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29)))
| least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),least_upper_bound(X_29,least_upper_bound(X_30,least_upper_bound(X_232,X_233)))) = least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29)))) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),least_upper_bound(X_29,least_upper_bound(X_30,least_upper_bound(X_232,X_233)))))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X_232,X_233),least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29))))),bind(Z0,$fot(least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29))))))]]) ).
cnf(refute_0_2232,plain,
( least_upper_bound(least_upper_bound(X_232,X_233),least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29))) != least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29))))
| least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),least_upper_bound(X_29,least_upper_bound(X_30,least_upper_bound(X_232,X_233)))) = least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),least_upper_bound(X_29,least_upper_bound(X_30,least_upper_bound(X_232,X_233)))),least_upper_bound(least_upper_bound(X_232,X_233),least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29)))) )],[refute_0_2230,refute_0_2231]) ).
cnf(refute_0_2233,plain,
least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),least_upper_bound(X_29,least_upper_bound(X_30,least_upper_bound(X_232,X_233)))) = least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29)))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_232,X_233),least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29))),least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29))))) )],[refute_0_2212,refute_0_2232]) ).
cnf(refute_0_2234,plain,
( least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29)))) != least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29)))
| least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),least_upper_bound(X_29,least_upper_bound(X_30,least_upper_bound(X_232,X_233)))) != least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29))))
| least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),least_upper_bound(X_29,least_upper_bound(X_30,least_upper_bound(X_232,X_233)))) = least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29))) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),least_upper_bound(X_29,least_upper_bound(X_30,least_upper_bound(X_232,X_233)))))),bind(Y0,$fot(least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29)))))),bind(Z0,$fot(least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29)))))]]) ).
cnf(refute_0_2235,plain,
( least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29)))) != least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29)))
| least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),least_upper_bound(X_29,least_upper_bound(X_30,least_upper_bound(X_232,X_233)))) = least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),least_upper_bound(X_29,least_upper_bound(X_30,least_upper_bound(X_232,X_233)))),least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29))))) )],[refute_0_2233,refute_0_2234]) ).
cnf(refute_0_2236,plain,
least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),least_upper_bound(X_29,least_upper_bound(X_30,least_upper_bound(X_232,X_233)))) = least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),X_29)))),least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29)))) )],[refute_0_2211,refute_0_2235]) ).
cnf(refute_0_2237,plain,
( least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),least_upper_bound(X_29,least_upper_bound(X_30,least_upper_bound(X_232,X_233)))) != least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29)))
| least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),least_upper_bound(X_29,least_upper_bound(X_30,least_upper_bound(X_232,X_233)))) != least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),least_upper_bound(X_29,X_30))
| least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29))) = least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),least_upper_bound(X_29,X_30)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),least_upper_bound(X_29,least_upper_bound(X_30,least_upper_bound(X_232,X_233)))),least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),least_upper_bound(X_29,X_30))) ),[0],$fot(least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29))))]]) ).
cnf(refute_0_2238,plain,
( least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),least_upper_bound(X_29,least_upper_bound(X_30,least_upper_bound(X_232,X_233)))) != least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),least_upper_bound(X_29,X_30))
| least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29))) = least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),least_upper_bound(X_29,X_30)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),least_upper_bound(X_29,least_upper_bound(X_30,least_upper_bound(X_232,X_233)))),least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29)))) )],[refute_0_2236,refute_0_2237]) ).
cnf(refute_0_2239,plain,
least_upper_bound(X_145,least_upper_bound(X_146,least_upper_bound(Y,X_146))) = least_upper_bound(X_146,least_upper_bound(least_upper_bound(Y,X_146),X_145)),
inference(subst,[],[refute_0_1752:[bind(X,$fot(X_145)),bind(X_29,$fot(X_146)),bind(X_30,$fot(least_upper_bound(Y,X_146)))]]) ).
cnf(refute_0_2240,plain,
least_upper_bound(X_146,least_upper_bound(Y,X_146)) = least_upper_bound(X_146,Y),
inference(subst,[],[refute_0_64:[bind(X_21,$fot(X_146))]]) ).
cnf(refute_0_2241,plain,
( least_upper_bound(X_145,least_upper_bound(X_146,least_upper_bound(Y,X_146))) != least_upper_bound(X_146,least_upper_bound(least_upper_bound(Y,X_146),X_145))
| least_upper_bound(X_146,least_upper_bound(Y,X_146)) != least_upper_bound(X_146,Y)
| least_upper_bound(X_145,least_upper_bound(X_146,Y)) = least_upper_bound(X_146,least_upper_bound(least_upper_bound(Y,X_146),X_145)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_145,least_upper_bound(X_146,least_upper_bound(Y,X_146))),least_upper_bound(X_146,least_upper_bound(least_upper_bound(Y,X_146),X_145))) ),[0,1],$fot(least_upper_bound(X_146,Y))]]) ).
cnf(refute_0_2242,plain,
( least_upper_bound(X_145,least_upper_bound(X_146,least_upper_bound(Y,X_146))) != least_upper_bound(X_146,least_upper_bound(least_upper_bound(Y,X_146),X_145))
| least_upper_bound(X_145,least_upper_bound(X_146,Y)) = least_upper_bound(X_146,least_upper_bound(least_upper_bound(Y,X_146),X_145)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_146,least_upper_bound(Y,X_146)),least_upper_bound(X_146,Y)) )],[refute_0_2240,refute_0_2241]) ).
cnf(refute_0_2243,plain,
least_upper_bound(X_145,least_upper_bound(X_146,Y)) = least_upper_bound(X_146,least_upper_bound(least_upper_bound(Y,X_146),X_145)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_145,least_upper_bound(X_146,least_upper_bound(Y,X_146))),least_upper_bound(X_146,least_upper_bound(least_upper_bound(Y,X_146),X_145))) )],[refute_0_2239,refute_0_2242]) ).
cnf(refute_0_2244,plain,
least_upper_bound(X_146,least_upper_bound(Y,least_upper_bound(X_146,X_145))) = least_upper_bound(Y,least_upper_bound(X_146,X_145)),
inference(subst,[],[refute_0_1763:[bind(Y,$fot(X_145)),bind(X_29,$fot(Y)),bind(X_30,$fot(X_146))]]) ).
cnf(refute_0_2245,plain,
least_upper_bound(least_upper_bound(Y,X_146),X_145) = least_upper_bound(Y,least_upper_bound(X_146,X_145)),
inference(subst,[],[refute_0_60:[bind(X,$fot(Y)),bind(Y,$fot(X_146)),bind(Z,$fot(X_145))]]) ).
cnf(refute_0_2246,plain,
least_upper_bound(X_146,least_upper_bound(least_upper_bound(Y,X_146),X_145)) = least_upper_bound(X_146,least_upper_bound(least_upper_bound(Y,X_146),X_145)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_146,least_upper_bound(least_upper_bound(Y,X_146),X_145)))]]) ).
cnf(refute_0_2247,plain,
( least_upper_bound(X_146,least_upper_bound(least_upper_bound(Y,X_146),X_145)) != least_upper_bound(X_146,least_upper_bound(least_upper_bound(Y,X_146),X_145))
| least_upper_bound(least_upper_bound(Y,X_146),X_145) != least_upper_bound(Y,least_upper_bound(X_146,X_145))
| least_upper_bound(X_146,least_upper_bound(least_upper_bound(Y,X_146),X_145)) = least_upper_bound(X_146,least_upper_bound(Y,least_upper_bound(X_146,X_145))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_146,least_upper_bound(least_upper_bound(Y,X_146),X_145)),least_upper_bound(X_146,least_upper_bound(least_upper_bound(Y,X_146),X_145))) ),[1,1],$fot(least_upper_bound(Y,least_upper_bound(X_146,X_145)))]]) ).
cnf(refute_0_2248,plain,
( least_upper_bound(least_upper_bound(Y,X_146),X_145) != least_upper_bound(Y,least_upper_bound(X_146,X_145))
| least_upper_bound(X_146,least_upper_bound(least_upper_bound(Y,X_146),X_145)) = least_upper_bound(X_146,least_upper_bound(Y,least_upper_bound(X_146,X_145))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_146,least_upper_bound(least_upper_bound(Y,X_146),X_145)),least_upper_bound(X_146,least_upper_bound(least_upper_bound(Y,X_146),X_145))) )],[refute_0_2246,refute_0_2247]) ).
cnf(refute_0_2249,plain,
least_upper_bound(X_146,least_upper_bound(least_upper_bound(Y,X_146),X_145)) = least_upper_bound(X_146,least_upper_bound(Y,least_upper_bound(X_146,X_145))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_146),X_145),least_upper_bound(Y,least_upper_bound(X_146,X_145))) )],[refute_0_2245,refute_0_2248]) ).
cnf(refute_0_2250,plain,
( least_upper_bound(X_146,least_upper_bound(Y,least_upper_bound(X_146,X_145))) != least_upper_bound(Y,least_upper_bound(X_146,X_145))
| least_upper_bound(X_146,least_upper_bound(least_upper_bound(Y,X_146),X_145)) != least_upper_bound(X_146,least_upper_bound(Y,least_upper_bound(X_146,X_145)))
| least_upper_bound(X_146,least_upper_bound(least_upper_bound(Y,X_146),X_145)) = least_upper_bound(Y,least_upper_bound(X_146,X_145)) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(least_upper_bound(X_146,least_upper_bound(least_upper_bound(Y,X_146),X_145)))),bind(Y0,$fot(least_upper_bound(X_146,least_upper_bound(Y,least_upper_bound(X_146,X_145))))),bind(Z0,$fot(least_upper_bound(Y,least_upper_bound(X_146,X_145))))]]) ).
cnf(refute_0_2251,plain,
( least_upper_bound(X_146,least_upper_bound(Y,least_upper_bound(X_146,X_145))) != least_upper_bound(Y,least_upper_bound(X_146,X_145))
| least_upper_bound(X_146,least_upper_bound(least_upper_bound(Y,X_146),X_145)) = least_upper_bound(Y,least_upper_bound(X_146,X_145)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_146,least_upper_bound(least_upper_bound(Y,X_146),X_145)),least_upper_bound(X_146,least_upper_bound(Y,least_upper_bound(X_146,X_145)))) )],[refute_0_2249,refute_0_2250]) ).
cnf(refute_0_2252,plain,
least_upper_bound(X_146,least_upper_bound(least_upper_bound(Y,X_146),X_145)) = least_upper_bound(Y,least_upper_bound(X_146,X_145)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_146,least_upper_bound(Y,least_upper_bound(X_146,X_145))),least_upper_bound(Y,least_upper_bound(X_146,X_145))) )],[refute_0_2244,refute_0_2251]) ).
cnf(refute_0_2253,plain,
( least_upper_bound(X_145,least_upper_bound(X_146,Y)) != least_upper_bound(X_146,least_upper_bound(least_upper_bound(Y,X_146),X_145))
| least_upper_bound(X_146,least_upper_bound(least_upper_bound(Y,X_146),X_145)) != least_upper_bound(Y,least_upper_bound(X_146,X_145))
| least_upper_bound(X_145,least_upper_bound(X_146,Y)) = least_upper_bound(Y,least_upper_bound(X_146,X_145)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_145,least_upper_bound(X_146,Y)),least_upper_bound(Y,least_upper_bound(X_146,X_145))) ),[0],$fot(least_upper_bound(X_146,least_upper_bound(least_upper_bound(Y,X_146),X_145)))]]) ).
cnf(refute_0_2254,plain,
( least_upper_bound(X_145,least_upper_bound(X_146,Y)) != least_upper_bound(X_146,least_upper_bound(least_upper_bound(Y,X_146),X_145))
| least_upper_bound(X_145,least_upper_bound(X_146,Y)) = least_upper_bound(Y,least_upper_bound(X_146,X_145)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_146,least_upper_bound(least_upper_bound(Y,X_146),X_145)),least_upper_bound(Y,least_upper_bound(X_146,X_145))) )],[refute_0_2252,refute_0_2253]) ).
cnf(refute_0_2255,plain,
least_upper_bound(X_145,least_upper_bound(X_146,Y)) = least_upper_bound(Y,least_upper_bound(X_146,X_145)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_145,least_upper_bound(X_146,Y)),least_upper_bound(X_146,least_upper_bound(least_upper_bound(Y,X_146),X_145))) )],[refute_0_2243,refute_0_2254]) ).
cnf(refute_0_2256,plain,
( least_upper_bound(X_145,least_upper_bound(X_146,Y)) != least_upper_bound(Y,least_upper_bound(X_146,X_145))
| least_upper_bound(Y,least_upper_bound(X_146,X_145)) = least_upper_bound(X_145,least_upper_bound(X_146,Y)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X_145,least_upper_bound(X_146,Y)))),bind(Y0,$fot(least_upper_bound(Y,least_upper_bound(X_146,X_145))))]]) ).
cnf(refute_0_2257,plain,
least_upper_bound(Y,least_upper_bound(X_146,X_145)) = least_upper_bound(X_145,least_upper_bound(X_146,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_145,least_upper_bound(X_146,Y)),least_upper_bound(Y,least_upper_bound(X_146,X_145))) )],[refute_0_2255,refute_0_2256]) ).
cnf(refute_0_2258,plain,
least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),least_upper_bound(X_29,X_30)) = least_upper_bound(X_30,least_upper_bound(X_29,least_upper_bound(X_232,least_upper_bound(X_233,X_30)))),
inference(subst,[],[refute_0_2257:[bind(Y,$fot(least_upper_bound(X_232,least_upper_bound(X_233,X_30)))),bind(X_145,$fot(X_30)),bind(X_146,$fot(X_29))]]) ).
cnf(refute_0_2259,plain,
( least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29))) != least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),least_upper_bound(X_29,X_30))
| least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),least_upper_bound(X_29,X_30)) != least_upper_bound(X_30,least_upper_bound(X_29,least_upper_bound(X_232,least_upper_bound(X_233,X_30))))
| least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29))) = least_upper_bound(X_30,least_upper_bound(X_29,least_upper_bound(X_232,least_upper_bound(X_233,X_30)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29))),least_upper_bound(X_30,least_upper_bound(X_29,least_upper_bound(X_232,least_upper_bound(X_233,X_30))))) ),[0],$fot(least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),least_upper_bound(X_29,X_30)))]]) ).
cnf(refute_0_2260,plain,
( least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29))) != least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),least_upper_bound(X_29,X_30))
| least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29))) = least_upper_bound(X_30,least_upper_bound(X_29,least_upper_bound(X_232,least_upper_bound(X_233,X_30)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),least_upper_bound(X_29,X_30)),least_upper_bound(X_30,least_upper_bound(X_29,least_upper_bound(X_232,least_upper_bound(X_233,X_30))))) )],[refute_0_2258,refute_0_2259]) ).
cnf(refute_0_2261,plain,
( least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),least_upper_bound(X_29,least_upper_bound(X_30,least_upper_bound(X_232,X_233)))) != least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),least_upper_bound(X_29,X_30))
| least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29))) = least_upper_bound(X_30,least_upper_bound(X_29,least_upper_bound(X_232,least_upper_bound(X_233,X_30)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29))),least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),least_upper_bound(X_29,X_30))) )],[refute_0_2238,refute_0_2260]) ).
cnf(refute_0_2262,plain,
least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29))) = least_upper_bound(X_30,least_upper_bound(X_29,least_upper_bound(X_232,least_upper_bound(X_233,X_30)))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),least_upper_bound(X_29,least_upper_bound(X_30,least_upper_bound(X_232,X_233)))),least_upper_bound(least_upper_bound(X_232,least_upper_bound(X_233,X_30)),least_upper_bound(X_29,X_30))) )],[refute_0_2117,refute_0_2261]) ).
cnf(refute_0_2263,plain,
( least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29))) != least_upper_bound(X_30,least_upper_bound(X_29,least_upper_bound(X_232,least_upper_bound(X_233,X_30))))
| least_upper_bound(X_30,least_upper_bound(X_29,least_upper_bound(X_232,least_upper_bound(X_233,X_30)))) = least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29))))),bind(Y0,$fot(least_upper_bound(X_30,least_upper_bound(X_29,least_upper_bound(X_232,least_upper_bound(X_233,X_30))))))]]) ).
cnf(refute_0_2264,plain,
least_upper_bound(X_30,least_upper_bound(X_29,least_upper_bound(X_232,least_upper_bound(X_233,X_30)))) = least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_232,least_upper_bound(X_233,least_upper_bound(X_30,X_29))),least_upper_bound(X_30,least_upper_bound(X_29,least_upper_bound(X_232,least_upper_bound(X_233,X_30))))) )],[refute_0_2262,refute_0_2263]) ).
cnf(refute_0_2265,plain,
least_upper_bound(X_231,least_upper_bound(X_232,least_upper_bound(X,least_upper_bound(Y,X_231)))) = least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_231,X_232))),
inference(subst,[],[refute_0_2264:[bind(X_232,$fot(X)),bind(X_233,$fot(Y)),bind(X_29,$fot(X_232)),bind(X_30,$fot(X_231))]]) ).
cnf(refute_0_2266,plain,
( least_upper_bound(X_231,least_upper_bound(X_232,least_upper_bound(X,least_upper_bound(Y,X_231)))) != least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_231,X_232)))
| least_upper_bound(X_231,least_upper_bound(X_232,least_upper_bound(X,least_upper_bound(Y,X_231)))) != least_upper_bound(X_231,least_upper_bound(X_232,least_upper_bound(X,Y)))
| least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_231,X_232))) = least_upper_bound(X_231,least_upper_bound(X_232,least_upper_bound(X,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_231,least_upper_bound(X_232,least_upper_bound(X,least_upper_bound(Y,X_231)))),least_upper_bound(X_231,least_upper_bound(X_232,least_upper_bound(X,Y)))) ),[0],$fot(least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_231,X_232))))]]) ).
cnf(refute_0_2267,plain,
( least_upper_bound(X_231,least_upper_bound(X_232,least_upper_bound(X,least_upper_bound(Y,X_231)))) != least_upper_bound(X_231,least_upper_bound(X_232,least_upper_bound(X,Y)))
| least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_231,X_232))) = least_upper_bound(X_231,least_upper_bound(X_232,least_upper_bound(X,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_231,least_upper_bound(X_232,least_upper_bound(X,least_upper_bound(Y,X_231)))),least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_231,X_232)))) )],[refute_0_2265,refute_0_2266]) ).
cnf(refute_0_2268,plain,
least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_231,X_232))) = least_upper_bound(X_231,least_upper_bound(X_232,least_upper_bound(X,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_231,least_upper_bound(X_232,least_upper_bound(X,least_upper_bound(Y,X_231)))),least_upper_bound(X_231,least_upper_bound(X_232,least_upper_bound(X,Y)))) )],[refute_0_2112,refute_0_2267]) ).
cnf(refute_0_2269,plain,
( least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_231,X_232))) != least_upper_bound(X_231,least_upper_bound(X_232,least_upper_bound(X,Y)))
| least_upper_bound(X_231,least_upper_bound(X_232,least_upper_bound(X,Y))) = least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_231,X_232))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_231,X_232))))),bind(Y0,$fot(least_upper_bound(X_231,least_upper_bound(X_232,least_upper_bound(X,Y)))))]]) ).
cnf(refute_0_2270,plain,
least_upper_bound(X_231,least_upper_bound(X_232,least_upper_bound(X,Y))) = least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_231,X_232))),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_231,X_232))),least_upper_bound(X_231,least_upper_bound(X_232,least_upper_bound(X,Y)))) )],[refute_0_2268,refute_0_2269]) ).
cnf(refute_0_2271,plain,
least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),least_upper_bound(X_29,least_upper_bound(X_30,X_248))) = least_upper_bound(X_30,least_upper_bound(X_248,least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),X_29))),
inference(subst,[],[refute_0_2270:[bind(X,$fot(X_30)),bind(Y,$fot(X_248)),bind(X_231,$fot(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248))),bind(X_232,$fot(X_29))]]) ).
cnf(refute_0_2272,plain,
( least_upper_bound(X_30,least_upper_bound(X_248,least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),X_29))) != least_upper_bound(X_30,least_upper_bound(X_248,X_29))
| least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),least_upper_bound(X_29,least_upper_bound(X_30,X_248))) != least_upper_bound(X_30,least_upper_bound(X_248,least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),X_29)))
| least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),least_upper_bound(X_29,least_upper_bound(X_30,X_248))) = least_upper_bound(X_30,least_upper_bound(X_248,X_29)) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),least_upper_bound(X_29,least_upper_bound(X_30,X_248))))),bind(Y0,$fot(least_upper_bound(X_30,least_upper_bound(X_248,least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),X_29))))),bind(Z0,$fot(least_upper_bound(X_30,least_upper_bound(X_248,X_29))))]]) ).
cnf(refute_0_2273,plain,
( least_upper_bound(X_30,least_upper_bound(X_248,least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),X_29))) != least_upper_bound(X_30,least_upper_bound(X_248,X_29))
| least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),least_upper_bound(X_29,least_upper_bound(X_30,X_248))) = least_upper_bound(X_30,least_upper_bound(X_248,X_29)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),least_upper_bound(X_29,least_upper_bound(X_30,X_248))),least_upper_bound(X_30,least_upper_bound(X_248,least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),X_29)))) )],[refute_0_2271,refute_0_2272]) ).
cnf(refute_0_2274,plain,
least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),least_upper_bound(X_29,least_upper_bound(X_30,X_248))) = least_upper_bound(X_30,least_upper_bound(X_248,X_29)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_30,least_upper_bound(X_248,least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),X_29))),least_upper_bound(X_30,least_upper_bound(X_248,X_29))) )],[refute_0_2105,refute_0_2273]) ).
cnf(refute_0_2275,plain,
( least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),least_upper_bound(X_29,least_upper_bound(X_30,X_248))) != least_upper_bound(X_30,least_upper_bound(X_248,X_29))
| least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),least_upper_bound(X_29,least_upper_bound(X_30,X_248))) != least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),least_upper_bound(X_29,X_30))
| least_upper_bound(X_30,least_upper_bound(X_248,X_29)) = least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),least_upper_bound(X_29,X_30)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),least_upper_bound(X_29,least_upper_bound(X_30,X_248))),least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),least_upper_bound(X_29,X_30))) ),[0],$fot(least_upper_bound(X_30,least_upper_bound(X_248,X_29)))]]) ).
cnf(refute_0_2276,plain,
( least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),least_upper_bound(X_29,least_upper_bound(X_30,X_248))) != least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),least_upper_bound(X_29,X_30))
| least_upper_bound(X_30,least_upper_bound(X_248,X_29)) = least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),least_upper_bound(X_29,X_30)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),least_upper_bound(X_29,least_upper_bound(X_30,X_248))),least_upper_bound(X_30,least_upper_bound(X_248,X_29))) )],[refute_0_2274,refute_0_2275]) ).
cnf(refute_0_2277,plain,
least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),least_upper_bound(X_29,X_30)) = least_upper_bound(X_30,least_upper_bound(X_29,least_upper_bound(greatest_lower_bound(X_30,X_246),X_248))),
inference(subst,[],[refute_0_2257:[bind(Y,$fot(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248))),bind(X_145,$fot(X_30)),bind(X_146,$fot(X_29))]]) ).
cnf(refute_0_2278,plain,
( least_upper_bound(X_30,least_upper_bound(X_248,X_29)) != least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),least_upper_bound(X_29,X_30))
| least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),least_upper_bound(X_29,X_30)) != least_upper_bound(X_30,least_upper_bound(X_29,least_upper_bound(greatest_lower_bound(X_30,X_246),X_248)))
| least_upper_bound(X_30,least_upper_bound(X_248,X_29)) = least_upper_bound(X_30,least_upper_bound(X_29,least_upper_bound(greatest_lower_bound(X_30,X_246),X_248))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_30,least_upper_bound(X_248,X_29)),least_upper_bound(X_30,least_upper_bound(X_29,least_upper_bound(greatest_lower_bound(X_30,X_246),X_248)))) ),[0],$fot(least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),least_upper_bound(X_29,X_30)))]]) ).
cnf(refute_0_2279,plain,
( least_upper_bound(X_30,least_upper_bound(X_248,X_29)) != least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),least_upper_bound(X_29,X_30))
| least_upper_bound(X_30,least_upper_bound(X_248,X_29)) = least_upper_bound(X_30,least_upper_bound(X_29,least_upper_bound(greatest_lower_bound(X_30,X_246),X_248))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),least_upper_bound(X_29,X_30)),least_upper_bound(X_30,least_upper_bound(X_29,least_upper_bound(greatest_lower_bound(X_30,X_246),X_248)))) )],[refute_0_2277,refute_0_2278]) ).
cnf(refute_0_2280,plain,
( least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),least_upper_bound(X_29,least_upper_bound(X_30,X_248))) != least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),least_upper_bound(X_29,X_30))
| least_upper_bound(X_30,least_upper_bound(X_248,X_29)) = least_upper_bound(X_30,least_upper_bound(X_29,least_upper_bound(greatest_lower_bound(X_30,X_246),X_248))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_30,least_upper_bound(X_248,X_29)),least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),least_upper_bound(X_29,X_30))) )],[refute_0_2276,refute_0_2279]) ).
cnf(refute_0_2281,plain,
least_upper_bound(X_30,least_upper_bound(X_248,X_29)) = least_upper_bound(X_30,least_upper_bound(X_29,least_upper_bound(greatest_lower_bound(X_30,X_246),X_248))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),least_upper_bound(X_29,least_upper_bound(X_30,X_248))),least_upper_bound(least_upper_bound(greatest_lower_bound(X_30,X_246),X_248),least_upper_bound(X_29,X_30))) )],[refute_0_2088,refute_0_2280]) ).
cnf(refute_0_2282,plain,
( least_upper_bound(X_30,least_upper_bound(X_248,X_29)) != least_upper_bound(X_30,least_upper_bound(X_29,least_upper_bound(greatest_lower_bound(X_30,X_246),X_248)))
| least_upper_bound(X_30,least_upper_bound(X_29,least_upper_bound(greatest_lower_bound(X_30,X_246),X_248))) = least_upper_bound(X_30,least_upper_bound(X_248,X_29)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X_30,least_upper_bound(X_248,X_29)))),bind(Y0,$fot(least_upper_bound(X_30,least_upper_bound(X_29,least_upper_bound(greatest_lower_bound(X_30,X_246),X_248)))))]]) ).
cnf(refute_0_2283,plain,
least_upper_bound(X_30,least_upper_bound(X_29,least_upper_bound(greatest_lower_bound(X_30,X_246),X_248))) = least_upper_bound(X_30,least_upper_bound(X_248,X_29)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_30,least_upper_bound(X_248,X_29)),least_upper_bound(X_30,least_upper_bound(X_29,least_upper_bound(greatest_lower_bound(X_30,X_246),X_248)))) )],[refute_0_2281,refute_0_2282]) ).
cnf(refute_0_2284,plain,
least_upper_bound(X_29,least_upper_bound(X_254,least_upper_bound(greatest_lower_bound(X_29,Y),X_255))) = least_upper_bound(X_29,least_upper_bound(X_255,X_254)),
inference(subst,[],[refute_0_2283:[bind(X_246,$fot(Y)),bind(X_248,$fot(X_255)),bind(X_29,$fot(X_254)),bind(X_30,$fot(X_29))]]) ).
cnf(refute_0_2285,plain,
( least_upper_bound(X_29,least_upper_bound(X_254,least_upper_bound(greatest_lower_bound(X_29,Y),X_255))) != least_upper_bound(X_29,least_upper_bound(X_254,X_255))
| least_upper_bound(X_29,least_upper_bound(X_254,least_upper_bound(greatest_lower_bound(X_29,Y),X_255))) != least_upper_bound(X_29,least_upper_bound(X_255,X_254))
| least_upper_bound(X_29,least_upper_bound(X_255,X_254)) = least_upper_bound(X_29,least_upper_bound(X_254,X_255)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_29,least_upper_bound(X_254,least_upper_bound(greatest_lower_bound(X_29,Y),X_255))),least_upper_bound(X_29,least_upper_bound(X_254,X_255))) ),[0],$fot(least_upper_bound(X_29,least_upper_bound(X_255,X_254)))]]) ).
cnf(refute_0_2286,plain,
( least_upper_bound(X_29,least_upper_bound(X_254,least_upper_bound(greatest_lower_bound(X_29,Y),X_255))) != least_upper_bound(X_29,least_upper_bound(X_254,X_255))
| least_upper_bound(X_29,least_upper_bound(X_255,X_254)) = least_upper_bound(X_29,least_upper_bound(X_254,X_255)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_29,least_upper_bound(X_254,least_upper_bound(greatest_lower_bound(X_29,Y),X_255))),least_upper_bound(X_29,least_upper_bound(X_255,X_254))) )],[refute_0_2284,refute_0_2285]) ).
cnf(refute_0_2287,plain,
least_upper_bound(X_29,least_upper_bound(X_255,X_254)) = least_upper_bound(X_29,least_upper_bound(X_254,X_255)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_29,least_upper_bound(X_254,least_upper_bound(greatest_lower_bound(X_29,Y),X_255))),least_upper_bound(X_29,least_upper_bound(X_254,X_255))) )],[refute_0_2076,refute_0_2286]) ).
cnf(refute_0_2288,plain,
( least_upper_bound(X_29,least_upper_bound(X_255,X_254)) != least_upper_bound(X_29,least_upper_bound(X_254,X_255))
| least_upper_bound(X_29,least_upper_bound(X_254,X_255)) = least_upper_bound(X_29,least_upper_bound(X_255,X_254)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X_29,least_upper_bound(X_255,X_254)))),bind(Y0,$fot(least_upper_bound(X_29,least_upper_bound(X_254,X_255))))]]) ).
cnf(refute_0_2289,plain,
least_upper_bound(X_29,least_upper_bound(X_254,X_255)) = least_upper_bound(X_29,least_upper_bound(X_255,X_254)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_29,least_upper_bound(X_255,X_254)),least_upper_bound(X_29,least_upper_bound(X_254,X_255))) )],[refute_0_2287,refute_0_2288]) ).
cnf(refute_0_2290,plain,
least_upper_bound(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X_51),X_330)),greatest_lower_bound(identity,inverse(X_51)))) = least_upper_bound(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,inverse(X_51)),greatest_lower_bound(identity,multiply(inverse(X_51),X_330)))),
inference(subst,[],[refute_0_2289:[bind(X_254,$fot(greatest_lower_bound(identity,multiply(inverse(X_51),X_330)))),bind(X_255,$fot(greatest_lower_bound(identity,inverse(X_51)))),bind(X_29,$fot(inverse(X_51)))]]) ).
cnf(refute_0_2291,plain,
( least_upper_bound(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X_51),X_330)),greatest_lower_bound(identity,inverse(X_51)))) != least_upper_bound(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,inverse(X_51)),greatest_lower_bound(identity,multiply(inverse(X_51),X_330))))
| least_upper_bound(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,inverse(X_51)),greatest_lower_bound(identity,multiply(inverse(X_51),X_330)))) != multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_330,X_51)))
| least_upper_bound(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X_51),X_330)),greatest_lower_bound(identity,inverse(X_51)))) = multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_330,X_51))) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(least_upper_bound(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X_51),X_330)),greatest_lower_bound(identity,inverse(X_51)))))),bind(Y0,$fot(least_upper_bound(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,inverse(X_51)),greatest_lower_bound(identity,multiply(inverse(X_51),X_330)))))),bind(Z0,$fot(multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_330,X_51)))))]]) ).
cnf(refute_0_2292,plain,
( least_upper_bound(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,inverse(X_51)),greatest_lower_bound(identity,multiply(inverse(X_51),X_330)))) != multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_330,X_51)))
| least_upper_bound(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X_51),X_330)),greatest_lower_bound(identity,inverse(X_51)))) = multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_330,X_51))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X_51),X_330)),greatest_lower_bound(identity,inverse(X_51)))),least_upper_bound(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,inverse(X_51)),greatest_lower_bound(identity,multiply(inverse(X_51),X_330))))) )],[refute_0_2290,refute_0_2291]) ).
cnf(refute_0_2293,plain,
least_upper_bound(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X_51),X_330)),greatest_lower_bound(identity,inverse(X_51)))) = multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_330,X_51))),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,inverse(X_51)),greatest_lower_bound(identity,multiply(inverse(X_51),X_330)))),multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_330,X_51)))) )],[refute_0_2071,refute_0_2292]) ).
cnf(refute_0_2294,plain,
least_upper_bound(X_289,least_upper_bound(greatest_lower_bound(identity,X_73),X_290)) = least_upper_bound(X_289,least_upper_bound(X_290,greatest_lower_bound(identity,X_73))),
inference(subst,[],[refute_0_1962:[bind(X_13,$fot(greatest_lower_bound(identity,X_73))),bind(X_134,$fot(X_289)),bind(X_135,$fot(X_290))]]) ).
cnf(refute_0_2295,plain,
least_upper_bound(X_290,greatest_lower_bound(X_73,identity)) = least_upper_bound(greatest_lower_bound(identity,X_73),X_290),
inference(subst,[],[refute_0_1517:[bind(X_198,$fot(X_290))]]) ).
cnf(refute_0_2296,plain,
( least_upper_bound(X_290,greatest_lower_bound(X_73,identity)) != least_upper_bound(greatest_lower_bound(identity,X_73),X_290)
| least_upper_bound(greatest_lower_bound(identity,X_73),X_290) = least_upper_bound(X_290,greatest_lower_bound(X_73,identity)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X_290,greatest_lower_bound(X_73,identity)))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(identity,X_73),X_290)))]]) ).
cnf(refute_0_2297,plain,
least_upper_bound(greatest_lower_bound(identity,X_73),X_290) = least_upper_bound(X_290,greatest_lower_bound(X_73,identity)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_290,greatest_lower_bound(X_73,identity)),least_upper_bound(greatest_lower_bound(identity,X_73),X_290)) )],[refute_0_2295,refute_0_2296]) ).
cnf(refute_0_2298,plain,
( least_upper_bound(X_289,least_upper_bound(greatest_lower_bound(identity,X_73),X_290)) != least_upper_bound(X_289,least_upper_bound(X_290,greatest_lower_bound(identity,X_73)))
| least_upper_bound(greatest_lower_bound(identity,X_73),X_290) != least_upper_bound(X_290,greatest_lower_bound(X_73,identity))
| least_upper_bound(X_289,least_upper_bound(X_290,greatest_lower_bound(X_73,identity))) = least_upper_bound(X_289,least_upper_bound(X_290,greatest_lower_bound(identity,X_73))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_289,least_upper_bound(greatest_lower_bound(identity,X_73),X_290)),least_upper_bound(X_289,least_upper_bound(X_290,greatest_lower_bound(identity,X_73)))) ),[0,1],$fot(least_upper_bound(X_290,greatest_lower_bound(X_73,identity)))]]) ).
cnf(refute_0_2299,plain,
( least_upper_bound(X_289,least_upper_bound(greatest_lower_bound(identity,X_73),X_290)) != least_upper_bound(X_289,least_upper_bound(X_290,greatest_lower_bound(identity,X_73)))
| least_upper_bound(X_289,least_upper_bound(X_290,greatest_lower_bound(X_73,identity))) = least_upper_bound(X_289,least_upper_bound(X_290,greatest_lower_bound(identity,X_73))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,X_73),X_290),least_upper_bound(X_290,greatest_lower_bound(X_73,identity))) )],[refute_0_2297,refute_0_2298]) ).
cnf(refute_0_2300,plain,
least_upper_bound(X_289,least_upper_bound(X_290,greatest_lower_bound(X_73,identity))) = least_upper_bound(X_289,least_upper_bound(X_290,greatest_lower_bound(identity,X_73))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_289,least_upper_bound(greatest_lower_bound(identity,X_73),X_290)),least_upper_bound(X_289,least_upper_bound(X_290,greatest_lower_bound(identity,X_73)))) )],[refute_0_2294,refute_0_2299]) ).
cnf(refute_0_2301,plain,
least_upper_bound(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X_51),X_330)),greatest_lower_bound(inverse(X_51),identity))) = least_upper_bound(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X_51),X_330)),greatest_lower_bound(identity,inverse(X_51)))),
inference(subst,[],[refute_0_2300:[bind(X_289,$fot(inverse(X_51))),bind(X_290,$fot(greatest_lower_bound(identity,multiply(inverse(X_51),X_330)))),bind(X_73,$fot(inverse(X_51)))]]) ).
cnf(refute_0_2302,plain,
( least_upper_bound(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X_51),X_330)),greatest_lower_bound(identity,inverse(X_51)))) != multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_330,X_51)))
| least_upper_bound(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X_51),X_330)),greatest_lower_bound(inverse(X_51),identity))) != least_upper_bound(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X_51),X_330)),greatest_lower_bound(identity,inverse(X_51))))
| least_upper_bound(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X_51),X_330)),greatest_lower_bound(inverse(X_51),identity))) = multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_330,X_51))) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(least_upper_bound(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X_51),X_330)),greatest_lower_bound(inverse(X_51),identity))))),bind(Y0,$fot(least_upper_bound(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X_51),X_330)),greatest_lower_bound(identity,inverse(X_51)))))),bind(Z0,$fot(multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_330,X_51)))))]]) ).
cnf(refute_0_2303,plain,
( least_upper_bound(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X_51),X_330)),greatest_lower_bound(identity,inverse(X_51)))) != multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_330,X_51)))
| least_upper_bound(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X_51),X_330)),greatest_lower_bound(inverse(X_51),identity))) = multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_330,X_51))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X_51),X_330)),greatest_lower_bound(inverse(X_51),identity))),least_upper_bound(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X_51),X_330)),greatest_lower_bound(identity,inverse(X_51))))) )],[refute_0_2301,refute_0_2302]) ).
cnf(refute_0_2304,plain,
least_upper_bound(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X_51),X_330)),greatest_lower_bound(inverse(X_51),identity))) = multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_330,X_51))),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X_51),X_330)),greatest_lower_bound(identity,inverse(X_51)))),multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_330,X_51)))) )],[refute_0_2293,refute_0_2303]) ).
cnf(refute_0_2305,plain,
least_upper_bound(X_253,least_upper_bound(greatest_lower_bound(identity,X_73),X_255)) = least_upper_bound(greatest_lower_bound(identity,X_73),least_upper_bound(X_253,X_255)),
inference(subst,[],[refute_0_1779:[bind(Y,$fot(X_253)),bind(X_29,$fot(greatest_lower_bound(identity,X_73))),bind(X_31,$fot(X_255))]]) ).
cnf(refute_0_2306,plain,
least_upper_bound(X_255,greatest_lower_bound(X_73,identity)) = least_upper_bound(greatest_lower_bound(identity,X_73),X_255),
inference(subst,[],[refute_0_1517:[bind(X_198,$fot(X_255))]]) ).
cnf(refute_0_2307,plain,
( least_upper_bound(X_255,greatest_lower_bound(X_73,identity)) != least_upper_bound(greatest_lower_bound(identity,X_73),X_255)
| least_upper_bound(greatest_lower_bound(identity,X_73),X_255) = least_upper_bound(X_255,greatest_lower_bound(X_73,identity)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X_255,greatest_lower_bound(X_73,identity)))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(identity,X_73),X_255)))]]) ).
cnf(refute_0_2308,plain,
least_upper_bound(greatest_lower_bound(identity,X_73),X_255) = least_upper_bound(X_255,greatest_lower_bound(X_73,identity)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_255,greatest_lower_bound(X_73,identity)),least_upper_bound(greatest_lower_bound(identity,X_73),X_255)) )],[refute_0_2306,refute_0_2307]) ).
cnf(refute_0_2309,plain,
( least_upper_bound(X_253,least_upper_bound(greatest_lower_bound(identity,X_73),X_255)) != least_upper_bound(greatest_lower_bound(identity,X_73),least_upper_bound(X_253,X_255))
| least_upper_bound(greatest_lower_bound(identity,X_73),X_255) != least_upper_bound(X_255,greatest_lower_bound(X_73,identity))
| least_upper_bound(X_253,least_upper_bound(X_255,greatest_lower_bound(X_73,identity))) = least_upper_bound(greatest_lower_bound(identity,X_73),least_upper_bound(X_253,X_255)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_253,least_upper_bound(greatest_lower_bound(identity,X_73),X_255)),least_upper_bound(greatest_lower_bound(identity,X_73),least_upper_bound(X_253,X_255))) ),[0,1],$fot(least_upper_bound(X_255,greatest_lower_bound(X_73,identity)))]]) ).
cnf(refute_0_2310,plain,
( least_upper_bound(X_253,least_upper_bound(greatest_lower_bound(identity,X_73),X_255)) != least_upper_bound(greatest_lower_bound(identity,X_73),least_upper_bound(X_253,X_255))
| least_upper_bound(X_253,least_upper_bound(X_255,greatest_lower_bound(X_73,identity))) = least_upper_bound(greatest_lower_bound(identity,X_73),least_upper_bound(X_253,X_255)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,X_73),X_255),least_upper_bound(X_255,greatest_lower_bound(X_73,identity))) )],[refute_0_2308,refute_0_2309]) ).
cnf(refute_0_2311,plain,
least_upper_bound(X_253,least_upper_bound(X_255,greatest_lower_bound(X_73,identity))) = least_upper_bound(greatest_lower_bound(identity,X_73),least_upper_bound(X_253,X_255)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_253,least_upper_bound(greatest_lower_bound(identity,X_73),X_255)),least_upper_bound(greatest_lower_bound(identity,X_73),least_upper_bound(X_253,X_255))) )],[refute_0_2305,refute_0_2310]) ).
cnf(refute_0_2312,plain,
( least_upper_bound(X_253,least_upper_bound(X_255,greatest_lower_bound(X_73,identity))) != least_upper_bound(greatest_lower_bound(identity,X_73),least_upper_bound(X_253,X_255))
| least_upper_bound(greatest_lower_bound(identity,X_73),least_upper_bound(X_253,X_255)) = least_upper_bound(X_253,least_upper_bound(X_255,greatest_lower_bound(X_73,identity))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X_253,least_upper_bound(X_255,greatest_lower_bound(X_73,identity))))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(identity,X_73),least_upper_bound(X_253,X_255))))]]) ).
cnf(refute_0_2313,plain,
least_upper_bound(greatest_lower_bound(identity,X_73),least_upper_bound(X_253,X_255)) = least_upper_bound(X_253,least_upper_bound(X_255,greatest_lower_bound(X_73,identity))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_253,least_upper_bound(X_255,greatest_lower_bound(X_73,identity))),least_upper_bound(greatest_lower_bound(identity,X_73),least_upper_bound(X_253,X_255))) )],[refute_0_2311,refute_0_2312]) ).
cnf(refute_0_2314,plain,
least_upper_bound(greatest_lower_bound(identity,inverse(X_51)),least_upper_bound(inverse(X_51),greatest_lower_bound(identity,multiply(inverse(X_51),X_330)))) = least_upper_bound(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X_51),X_330)),greatest_lower_bound(inverse(X_51),identity))),
inference(subst,[],[refute_0_2313:[bind(X_253,$fot(inverse(X_51))),bind(X_255,$fot(greatest_lower_bound(identity,multiply(inverse(X_51),X_330)))),bind(X_73,$fot(inverse(X_51)))]]) ).
cnf(refute_0_2315,plain,
( least_upper_bound(greatest_lower_bound(identity,inverse(X_51)),least_upper_bound(inverse(X_51),greatest_lower_bound(identity,multiply(inverse(X_51),X_330)))) != least_upper_bound(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X_51),X_330)),greatest_lower_bound(inverse(X_51),identity)))
| least_upper_bound(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X_51),X_330)),greatest_lower_bound(inverse(X_51),identity))) != multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_330,X_51)))
| least_upper_bound(greatest_lower_bound(identity,inverse(X_51)),least_upper_bound(inverse(X_51),greatest_lower_bound(identity,multiply(inverse(X_51),X_330)))) = multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_330,X_51))) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(identity,inverse(X_51)),least_upper_bound(inverse(X_51),greatest_lower_bound(identity,multiply(inverse(X_51),X_330)))))),bind(Y0,$fot(least_upper_bound(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X_51),X_330)),greatest_lower_bound(inverse(X_51),identity))))),bind(Z0,$fot(multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_330,X_51)))))]]) ).
cnf(refute_0_2316,plain,
( least_upper_bound(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X_51),X_330)),greatest_lower_bound(inverse(X_51),identity))) != multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_330,X_51)))
| least_upper_bound(greatest_lower_bound(identity,inverse(X_51)),least_upper_bound(inverse(X_51),greatest_lower_bound(identity,multiply(inverse(X_51),X_330)))) = multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_330,X_51))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,inverse(X_51)),least_upper_bound(inverse(X_51),greatest_lower_bound(identity,multiply(inverse(X_51),X_330)))),least_upper_bound(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X_51),X_330)),greatest_lower_bound(inverse(X_51),identity)))) )],[refute_0_2314,refute_0_2315]) ).
cnf(refute_0_2317,plain,
least_upper_bound(greatest_lower_bound(identity,inverse(X_51)),least_upper_bound(inverse(X_51),greatest_lower_bound(identity,multiply(inverse(X_51),X_330)))) = multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_330,X_51))),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X_51),X_330)),greatest_lower_bound(inverse(X_51),identity))),multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_330,X_51)))) )],[refute_0_2304,refute_0_2316]) ).
cnf(refute_0_2318,plain,
( multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_51,X_330))) != least_upper_bound(greatest_lower_bound(identity,inverse(X_51)),least_upper_bound(inverse(X_51),greatest_lower_bound(identity,multiply(inverse(X_51),X_330))))
| least_upper_bound(greatest_lower_bound(identity,inverse(X_51)),least_upper_bound(inverse(X_51),greatest_lower_bound(identity,multiply(inverse(X_51),X_330)))) != multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_330,X_51)))
| multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_51,X_330))) = multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_330,X_51))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_51,X_330))),multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_330,X_51)))) ),[0],$fot(least_upper_bound(greatest_lower_bound(identity,inverse(X_51)),least_upper_bound(inverse(X_51),greatest_lower_bound(identity,multiply(inverse(X_51),X_330)))))]]) ).
cnf(refute_0_2319,plain,
( multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_51,X_330))) != least_upper_bound(greatest_lower_bound(identity,inverse(X_51)),least_upper_bound(inverse(X_51),greatest_lower_bound(identity,multiply(inverse(X_51),X_330))))
| multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_51,X_330))) = multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_330,X_51))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,inverse(X_51)),least_upper_bound(inverse(X_51),greatest_lower_bound(identity,multiply(inverse(X_51),X_330)))),multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_330,X_51)))) )],[refute_0_2317,refute_0_2318]) ).
cnf(refute_0_2320,plain,
( multiply(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,X_51),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(X_51)),X_330)))) != least_upper_bound(greatest_lower_bound(identity,inverse(X_51)),least_upper_bound(inverse(X_51),greatest_lower_bound(identity,multiply(inverse(X_51),X_330))))
| multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_51,X_330))) = multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_330,X_51))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_51,X_330))),least_upper_bound(greatest_lower_bound(identity,inverse(X_51)),least_upper_bound(inverse(X_51),greatest_lower_bound(identity,multiply(inverse(X_51),X_330))))) )],[refute_0_2051,refute_0_2319]) ).
cnf(refute_0_2321,plain,
multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_51,X_330))) = multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_330,X_51))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_51),least_upper_bound(greatest_lower_bound(identity,X_51),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(X_51)),X_330)))),least_upper_bound(greatest_lower_bound(identity,inverse(X_51)),least_upper_bound(inverse(X_51),greatest_lower_bound(identity,multiply(inverse(X_51),X_330))))) )],[refute_0_2012,refute_0_2320]) ).
cnf(refute_0_2322,plain,
( multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_51,X_330))) != multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_330,X_51)))
| multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_330,X_51))) = multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_51,X_330))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_51,X_330))))),bind(Y0,$fot(multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_330,X_51)))))]]) ).
cnf(refute_0_2323,plain,
multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_330,X_51))) = multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_51,X_330))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_51,X_330))),multiply(inverse(X_51),least_upper_bound(identity,greatest_lower_bound(X_330,X_51)))) )],[refute_0_2321,refute_0_2322]) ).
cnf(refute_0_2324,plain,
multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,inverse(X_114)),least_upper_bound(identity,X_114)))) = multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114))))),
inference(subst,[],[refute_0_2323:[bind(X_330,$fot(least_upper_bound(identity,inverse(X_114)))),bind(X_51,$fot(least_upper_bound(identity,X_114)))]]) ).
cnf(refute_0_2325,plain,
least_upper_bound(inverse(least_upper_bound(identity,X_114)),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,inverse(X_114))))) = multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,inverse(X_114)),least_upper_bound(identity,X_114)))),
inference(subst,[],[refute_0_2061:[bind(X_37,$fot(least_upper_bound(identity,inverse(X_114)))),bind(X_38,$fot(least_upper_bound(identity,X_114)))]]) ).
cnf(refute_0_2326,plain,
( multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,inverse(X_114)),least_upper_bound(identity,X_114)))) != multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114)))))
| least_upper_bound(inverse(least_upper_bound(identity,X_114)),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,inverse(X_114))))) != multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,inverse(X_114)),least_upper_bound(identity,X_114))))
| least_upper_bound(inverse(least_upper_bound(identity,X_114)),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,inverse(X_114))))) = multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114))))) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(least_upper_bound(inverse(least_upper_bound(identity,X_114)),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,inverse(X_114))))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,inverse(X_114)),least_upper_bound(identity,X_114)))))),bind(Z0,$fot(multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114)))))))]]) ).
cnf(refute_0_2327,plain,
( multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,inverse(X_114)),least_upper_bound(identity,X_114)))) != multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114)))))
| least_upper_bound(inverse(least_upper_bound(identity,X_114)),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,inverse(X_114))))) = multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114))))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(identity,X_114)),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,inverse(X_114))))),multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,inverse(X_114)),least_upper_bound(identity,X_114))))) )],[refute_0_2325,refute_0_2326]) ).
cnf(refute_0_2328,plain,
least_upper_bound(inverse(least_upper_bound(identity,X_114)),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,inverse(X_114))))) = multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114))))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,inverse(X_114)),least_upper_bound(identity,X_114)))),multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114)))))) )],[refute_0_2324,refute_0_2327]) ).
cnf(refute_0_2329,plain,
( multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(least_upper_bound(identity,X_114))),least_upper_bound(identity,inverse(X_114))))) != least_upper_bound(inverse(least_upper_bound(identity,X_114)),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,inverse(X_114)))))
| least_upper_bound(inverse(least_upper_bound(identity,X_114)),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,inverse(X_114))))) != multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114)))))
| multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(least_upper_bound(identity,X_114))),least_upper_bound(identity,inverse(X_114))))) = multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114))))) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(least_upper_bound(identity,X_114))),least_upper_bound(identity,inverse(X_114))))))),bind(Y0,$fot(least_upper_bound(inverse(least_upper_bound(identity,X_114)),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,inverse(X_114))))))),bind(Z0,$fot(multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114)))))))]]) ).
cnf(refute_0_2330,plain,
( least_upper_bound(inverse(least_upper_bound(identity,X_114)),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,inverse(X_114))))) != multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114)))))
| multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(least_upper_bound(identity,X_114))),least_upper_bound(identity,inverse(X_114))))) = multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(least_upper_bound(identity,X_114))),least_upper_bound(identity,inverse(X_114))))),least_upper_bound(inverse(least_upper_bound(identity,X_114)),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,inverse(X_114)))))) )],[refute_0_1600,refute_0_2329]) ).
cnf(refute_0_2331,plain,
multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(least_upper_bound(identity,X_114))),least_upper_bound(identity,inverse(X_114))))) = multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114))))),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(identity,X_114)),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,inverse(X_114))))),multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114)))))) )],[refute_0_2328,refute_0_2330]) ).
cnf(refute_0_2332,plain,
( multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(least_upper_bound(identity,X_114))),least_upper_bound(identity,inverse(X_114))))) != multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114)))))
| multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114))))) != inverse(least_upper_bound(identity,X_114))
| multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(least_upper_bound(identity,X_114))),least_upper_bound(identity,inverse(X_114))))) = inverse(least_upper_bound(identity,X_114)) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(least_upper_bound(identity,X_114))),least_upper_bound(identity,inverse(X_114))))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114))))))),bind(Z0,$fot(inverse(least_upper_bound(identity,X_114))))]]) ).
cnf(refute_0_2333,plain,
( multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114))))) != inverse(least_upper_bound(identity,X_114))
| multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(least_upper_bound(identity,X_114))),least_upper_bound(identity,inverse(X_114))))) = inverse(least_upper_bound(identity,X_114)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(least_upper_bound(identity,X_114))),least_upper_bound(identity,inverse(X_114))))),multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114)))))) )],[refute_0_2331,refute_0_2332]) ).
cnf(refute_0_2334,plain,
multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(least_upper_bound(identity,X_114))),least_upper_bound(identity,inverse(X_114))))) = inverse(least_upper_bound(identity,X_114)),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_114),least_upper_bound(identity,inverse(X_114))))),inverse(least_upper_bound(identity,X_114))) )],[refute_0_2003,refute_0_2333]) ).
cnf(refute_0_2335,plain,
( multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(least_upper_bound(identity,X_114))),least_upper_bound(identity,inverse(X_114))))) != inverse(least_upper_bound(identity,X_114))
| multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(least_upper_bound(identity,X_114))),least_upper_bound(identity,inverse(X_114))))) != least_upper_bound(inverse(least_upper_bound(identity,X_114)),greatest_lower_bound(identity,inverse(X_114)))
| inverse(least_upper_bound(identity,X_114)) = least_upper_bound(inverse(least_upper_bound(identity,X_114)),greatest_lower_bound(identity,inverse(X_114))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(least_upper_bound(identity,X_114))),least_upper_bound(identity,inverse(X_114))))),least_upper_bound(inverse(least_upper_bound(identity,X_114)),greatest_lower_bound(identity,inverse(X_114)))) ),[0],$fot(inverse(least_upper_bound(identity,X_114)))]]) ).
cnf(refute_0_2336,plain,
( multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(least_upper_bound(identity,X_114))),least_upper_bound(identity,inverse(X_114))))) != least_upper_bound(inverse(least_upper_bound(identity,X_114)),greatest_lower_bound(identity,inverse(X_114)))
| inverse(least_upper_bound(identity,X_114)) = least_upper_bound(inverse(least_upper_bound(identity,X_114)),greatest_lower_bound(identity,inverse(X_114))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(least_upper_bound(identity,X_114))),least_upper_bound(identity,inverse(X_114))))),inverse(least_upper_bound(identity,X_114))) )],[refute_0_2334,refute_0_2335]) ).
cnf(refute_0_2337,plain,
inverse(least_upper_bound(identity,X_114)) = least_upper_bound(inverse(least_upper_bound(identity,X_114)),greatest_lower_bound(identity,inverse(X_114))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_114)),least_upper_bound(identity,greatest_lower_bound(inverse(inverse(least_upper_bound(identity,X_114))),least_upper_bound(identity,inverse(X_114))))),least_upper_bound(inverse(least_upper_bound(identity,X_114)),greatest_lower_bound(identity,inverse(X_114)))) )],[refute_0_1625,refute_0_2336]) ).
cnf(refute_0_2338,plain,
inverse(least_upper_bound(identity,X_397)) = least_upper_bound(inverse(least_upper_bound(identity,X_397)),greatest_lower_bound(identity,inverse(X_397))),
inference(subst,[],[refute_0_2337:[bind(X_114,$fot(X_397))]]) ).
cnf(refute_0_2339,plain,
( inverse(least_upper_bound(identity,X_397)) != least_upper_bound(inverse(least_upper_bound(identity,X_397)),greatest_lower_bound(identity,inverse(X_397)))
| least_upper_bound(inverse(least_upper_bound(identity,X_397)),greatest_lower_bound(identity,inverse(X_397))) = inverse(least_upper_bound(identity,X_397)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(least_upper_bound(identity,X_397)))),bind(Y0,$fot(least_upper_bound(inverse(least_upper_bound(identity,X_397)),greatest_lower_bound(identity,inverse(X_397)))))]]) ).
cnf(refute_0_2340,plain,
least_upper_bound(inverse(least_upper_bound(identity,X_397)),greatest_lower_bound(identity,inverse(X_397))) = inverse(least_upper_bound(identity,X_397)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,X_397)),least_upper_bound(inverse(least_upper_bound(identity,X_397)),greatest_lower_bound(identity,inverse(X_397)))) )],[refute_0_2338,refute_0_2339]) ).
cnf(refute_0_2341,plain,
( multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_397)),greatest_lower_bound(identity,inverse(X_397)))),greatest_lower_bound(identity,inverse(X_397))) != greatest_lower_bound(identity,multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_397)),greatest_lower_bound(identity,inverse(X_397)))),greatest_lower_bound(identity,inverse(X_397))))
| least_upper_bound(inverse(least_upper_bound(identity,X_397)),greatest_lower_bound(identity,inverse(X_397))) != inverse(least_upper_bound(identity,X_397))
| multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_397)),greatest_lower_bound(identity,inverse(X_397)))),greatest_lower_bound(identity,inverse(X_397))) = greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,X_397))),greatest_lower_bound(identity,inverse(X_397)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_397)),greatest_lower_bound(identity,inverse(X_397)))),greatest_lower_bound(identity,inverse(X_397))),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_397)),greatest_lower_bound(identity,inverse(X_397)))),greatest_lower_bound(identity,inverse(X_397))))) ),[1,1,0,0],$fot(inverse(least_upper_bound(identity,X_397)))]]) ).
cnf(refute_0_2342,plain,
( multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_397)),greatest_lower_bound(identity,inverse(X_397)))),greatest_lower_bound(identity,inverse(X_397))) != greatest_lower_bound(identity,multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_397)),greatest_lower_bound(identity,inverse(X_397)))),greatest_lower_bound(identity,inverse(X_397))))
| multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_397)),greatest_lower_bound(identity,inverse(X_397)))),greatest_lower_bound(identity,inverse(X_397))) = greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,X_397))),greatest_lower_bound(identity,inverse(X_397)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(identity,X_397)),greatest_lower_bound(identity,inverse(X_397))),inverse(least_upper_bound(identity,X_397))) )],[refute_0_2340,refute_0_2341]) ).
cnf(refute_0_2343,plain,
multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_397)),greatest_lower_bound(identity,inverse(X_397)))),greatest_lower_bound(identity,inverse(X_397))) = greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,X_397))),greatest_lower_bound(identity,inverse(X_397)))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_397)),greatest_lower_bound(identity,inverse(X_397)))),greatest_lower_bound(identity,inverse(X_397))),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_397)),greatest_lower_bound(identity,inverse(X_397)))),greatest_lower_bound(identity,inverse(X_397))))) )],[refute_0_1549,refute_0_2342]) ).
cnf(refute_0_2344,plain,
inverse(least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,X_397)),inverse(greatest_lower_bound(identity,inverse(X_397)))))) = multiply(greatest_lower_bound(identity,inverse(X_397)),inverse(least_upper_bound(inverse(least_upper_bound(identity,X_397)),greatest_lower_bound(identity,inverse(X_397))))),
inference(subst,[],[refute_0_564:[bind(X_66,$fot(inverse(least_upper_bound(identity,X_397)))),bind(X_99,$fot(greatest_lower_bound(identity,inverse(X_397))))]]) ).
cnf(refute_0_2345,plain,
( inverse(least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,X_397)),inverse(greatest_lower_bound(identity,inverse(X_397)))))) != multiply(greatest_lower_bound(identity,inverse(X_397)),inverse(least_upper_bound(inverse(least_upper_bound(identity,X_397)),greatest_lower_bound(identity,inverse(X_397)))))
| least_upper_bound(inverse(least_upper_bound(identity,X_397)),greatest_lower_bound(identity,inverse(X_397))) != inverse(least_upper_bound(identity,X_397))
| inverse(least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,X_397)),inverse(greatest_lower_bound(identity,inverse(X_397)))))) = multiply(greatest_lower_bound(identity,inverse(X_397)),inverse(inverse(least_upper_bound(identity,X_397)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,X_397)),inverse(greatest_lower_bound(identity,inverse(X_397)))))),multiply(greatest_lower_bound(identity,inverse(X_397)),inverse(least_upper_bound(inverse(least_upper_bound(identity,X_397)),greatest_lower_bound(identity,inverse(X_397)))))) ),[1,1,0],$fot(inverse(least_upper_bound(identity,X_397)))]]) ).
cnf(refute_0_2346,plain,
( inverse(least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,X_397)),inverse(greatest_lower_bound(identity,inverse(X_397)))))) != multiply(greatest_lower_bound(identity,inverse(X_397)),inverse(least_upper_bound(inverse(least_upper_bound(identity,X_397)),greatest_lower_bound(identity,inverse(X_397)))))
| inverse(least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,X_397)),inverse(greatest_lower_bound(identity,inverse(X_397)))))) = multiply(greatest_lower_bound(identity,inverse(X_397)),inverse(inverse(least_upper_bound(identity,X_397)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(identity,X_397)),greatest_lower_bound(identity,inverse(X_397))),inverse(least_upper_bound(identity,X_397))) )],[refute_0_2340,refute_0_2345]) ).
cnf(refute_0_2347,plain,
inverse(least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,X_397)),inverse(greatest_lower_bound(identity,inverse(X_397)))))) = multiply(greatest_lower_bound(identity,inverse(X_397)),inverse(inverse(least_upper_bound(identity,X_397)))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,X_397)),inverse(greatest_lower_bound(identity,inverse(X_397)))))),multiply(greatest_lower_bound(identity,inverse(X_397)),inverse(least_upper_bound(inverse(least_upper_bound(identity,X_397)),greatest_lower_bound(identity,inverse(X_397)))))) )],[refute_0_2344,refute_0_2346]) ).
cnf(refute_0_2348,plain,
multiply(least_upper_bound(identity,X_157),greatest_lower_bound(identity,inverse(X_157))) = multiply(greatest_lower_bound(X_157,identity),least_upper_bound(identity,inverse(X_157))),
inference(subst,[],[refute_0_1982:[bind(X,$fot(X_157))]]) ).
cnf(refute_0_2349,plain,
( multiply(least_upper_bound(identity,X_157),greatest_lower_bound(identity,inverse(X_157))) != multiply(greatest_lower_bound(X_157,identity),least_upper_bound(identity,inverse(X_157)))
| multiply(least_upper_bound(identity,X_157),greatest_lower_bound(identity,inverse(X_157))) != multiply(greatest_lower_bound(identity,inverse(X_157)),least_upper_bound(identity,X_157))
| multiply(greatest_lower_bound(X_157,identity),least_upper_bound(identity,inverse(X_157))) = multiply(greatest_lower_bound(identity,inverse(X_157)),least_upper_bound(identity,X_157)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,X_157),greatest_lower_bound(identity,inverse(X_157))),multiply(greatest_lower_bound(identity,inverse(X_157)),least_upper_bound(identity,X_157))) ),[0],$fot(multiply(greatest_lower_bound(X_157,identity),least_upper_bound(identity,inverse(X_157))))]]) ).
cnf(refute_0_2350,plain,
( multiply(least_upper_bound(identity,X_157),greatest_lower_bound(identity,inverse(X_157))) != multiply(greatest_lower_bound(identity,inverse(X_157)),least_upper_bound(identity,X_157))
| multiply(greatest_lower_bound(X_157,identity),least_upper_bound(identity,inverse(X_157))) = multiply(greatest_lower_bound(identity,inverse(X_157)),least_upper_bound(identity,X_157)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_157),greatest_lower_bound(identity,inverse(X_157))),multiply(greatest_lower_bound(X_157,identity),least_upper_bound(identity,inverse(X_157)))) )],[refute_0_2348,refute_0_2349]) ).
cnf(refute_0_2351,plain,
multiply(greatest_lower_bound(X_157,identity),least_upper_bound(identity,inverse(X_157))) = multiply(greatest_lower_bound(identity,inverse(X_157)),least_upper_bound(identity,X_157)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_157),greatest_lower_bound(identity,inverse(X_157))),multiply(greatest_lower_bound(identity,inverse(X_157)),least_upper_bound(identity,X_157))) )],[refute_0_1888,refute_0_2350]) ).
cnf(refute_0_2352,plain,
( multiply(greatest_lower_bound(X_157,identity),least_upper_bound(identity,inverse(X_157))) != multiply(greatest_lower_bound(identity,inverse(X_157)),least_upper_bound(identity,X_157))
| multiply(greatest_lower_bound(identity,inverse(X_157)),least_upper_bound(identity,X_157)) = multiply(greatest_lower_bound(X_157,identity),least_upper_bound(identity,inverse(X_157))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(greatest_lower_bound(X_157,identity),least_upper_bound(identity,inverse(X_157))))),bind(Y0,$fot(multiply(greatest_lower_bound(identity,inverse(X_157)),least_upper_bound(identity,X_157))))]]) ).
cnf(refute_0_2353,plain,
multiply(greatest_lower_bound(identity,inverse(X_157)),least_upper_bound(identity,X_157)) = multiply(greatest_lower_bound(X_157,identity),least_upper_bound(identity,inverse(X_157))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_157,identity),least_upper_bound(identity,inverse(X_157))),multiply(greatest_lower_bound(identity,inverse(X_157)),least_upper_bound(identity,X_157))) )],[refute_0_2351,refute_0_2352]) ).
cnf(refute_0_2354,plain,
multiply(greatest_lower_bound(identity,inverse(X_397)),least_upper_bound(identity,X_397)) = multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397))),
inference(subst,[],[refute_0_2353:[bind(X_157,$fot(X_397))]]) ).
cnf(refute_0_2355,plain,
inverse(multiply(greatest_lower_bound(identity,inverse(X_397)),least_upper_bound(identity,X_397))) = inverse(multiply(greatest_lower_bound(identity,inverse(X_397)),least_upper_bound(identity,X_397))),
introduced(tautology,[refl,[$fot(inverse(multiply(greatest_lower_bound(identity,inverse(X_397)),least_upper_bound(identity,X_397))))]]) ).
cnf(refute_0_2356,plain,
( multiply(greatest_lower_bound(identity,inverse(X_397)),least_upper_bound(identity,X_397)) != multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))
| inverse(multiply(greatest_lower_bound(identity,inverse(X_397)),least_upper_bound(identity,X_397))) != inverse(multiply(greatest_lower_bound(identity,inverse(X_397)),least_upper_bound(identity,X_397)))
| inverse(multiply(greatest_lower_bound(identity,inverse(X_397)),least_upper_bound(identity,X_397))) = inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(greatest_lower_bound(identity,inverse(X_397)),least_upper_bound(identity,X_397))),inverse(multiply(greatest_lower_bound(identity,inverse(X_397)),least_upper_bound(identity,X_397)))) ),[1,0],$fot(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397))))]]) ).
cnf(refute_0_2357,plain,
( multiply(greatest_lower_bound(identity,inverse(X_397)),least_upper_bound(identity,X_397)) != multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))
| inverse(multiply(greatest_lower_bound(identity,inverse(X_397)),least_upper_bound(identity,X_397))) = inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))) ),
inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(identity,inverse(X_397)),least_upper_bound(identity,X_397))),inverse(multiply(greatest_lower_bound(identity,inverse(X_397)),least_upper_bound(identity,X_397)))) )],[refute_0_2355,refute_0_2356]) ).
cnf(refute_0_2358,plain,
inverse(multiply(greatest_lower_bound(identity,inverse(X_397)),least_upper_bound(identity,X_397))) = inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(X_397)),least_upper_bound(identity,X_397)),multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))) )],[refute_0_2354,refute_0_2357]) ).
cnf(refute_0_2359,plain,
multiply(inverse(least_upper_bound(identity,X_397)),inverse(greatest_lower_bound(identity,inverse(X_397)))) = inverse(multiply(greatest_lower_bound(identity,inverse(X_397)),least_upper_bound(identity,X_397))),
inference(subst,[],[refute_0_370:[bind(X,$fot(greatest_lower_bound(identity,inverse(X_397)))),bind(Y,$fot(least_upper_bound(identity,X_397)))]]) ).
cnf(refute_0_2360,plain,
( multiply(inverse(least_upper_bound(identity,X_397)),inverse(greatest_lower_bound(identity,inverse(X_397)))) != inverse(multiply(greatest_lower_bound(identity,inverse(X_397)),least_upper_bound(identity,X_397)))
| inverse(multiply(greatest_lower_bound(identity,inverse(X_397)),least_upper_bound(identity,X_397))) != inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397))))
| multiply(inverse(least_upper_bound(identity,X_397)),inverse(greatest_lower_bound(identity,inverse(X_397)))) = inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(multiply(inverse(least_upper_bound(identity,X_397)),inverse(greatest_lower_bound(identity,inverse(X_397)))))),bind(Y0,$fot(inverse(multiply(greatest_lower_bound(identity,inverse(X_397)),least_upper_bound(identity,X_397))))),bind(Z0,$fot(inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397))))))]]) ).
cnf(refute_0_2361,plain,
( inverse(multiply(greatest_lower_bound(identity,inverse(X_397)),least_upper_bound(identity,X_397))) != inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397))))
| multiply(inverse(least_upper_bound(identity,X_397)),inverse(greatest_lower_bound(identity,inverse(X_397)))) = inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_397)),inverse(greatest_lower_bound(identity,inverse(X_397)))),inverse(multiply(greatest_lower_bound(identity,inverse(X_397)),least_upper_bound(identity,X_397)))) )],[refute_0_2359,refute_0_2360]) ).
cnf(refute_0_2362,plain,
multiply(inverse(least_upper_bound(identity,X_397)),inverse(greatest_lower_bound(identity,inverse(X_397)))) = inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))),
inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(identity,inverse(X_397)),least_upper_bound(identity,X_397))),inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397))))) )],[refute_0_2358,refute_0_2361]) ).
cnf(refute_0_2363,plain,
least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,X_397)),inverse(greatest_lower_bound(identity,inverse(X_397))))) = least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,X_397)),inverse(greatest_lower_bound(identity,inverse(X_397))))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,X_397)),inverse(greatest_lower_bound(identity,inverse(X_397))))))]]) ).
cnf(refute_0_2364,plain,
( multiply(inverse(least_upper_bound(identity,X_397)),inverse(greatest_lower_bound(identity,inverse(X_397)))) != inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397))))
| least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,X_397)),inverse(greatest_lower_bound(identity,inverse(X_397))))) != least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,X_397)),inverse(greatest_lower_bound(identity,inverse(X_397)))))
| least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,X_397)),inverse(greatest_lower_bound(identity,inverse(X_397))))) = least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397))))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,X_397)),inverse(greatest_lower_bound(identity,inverse(X_397))))),least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,X_397)),inverse(greatest_lower_bound(identity,inverse(X_397)))))) ),[1,1],$fot(inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))))]]) ).
cnf(refute_0_2365,plain,
( multiply(inverse(least_upper_bound(identity,X_397)),inverse(greatest_lower_bound(identity,inverse(X_397)))) != inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397))))
| least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,X_397)),inverse(greatest_lower_bound(identity,inverse(X_397))))) = least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397))))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,X_397)),inverse(greatest_lower_bound(identity,inverse(X_397))))),least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,X_397)),inverse(greatest_lower_bound(identity,inverse(X_397)))))) )],[refute_0_2363,refute_0_2364]) ).
cnf(refute_0_2366,plain,
least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,X_397)),inverse(greatest_lower_bound(identity,inverse(X_397))))) = least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397))))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_397)),inverse(greatest_lower_bound(identity,inverse(X_397)))),inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397))))) )],[refute_0_2362,refute_0_2365]) ).
cnf(refute_0_2367,plain,
inverse(least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,X_397)),inverse(greatest_lower_bound(identity,inverse(X_397)))))) = inverse(least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,X_397)),inverse(greatest_lower_bound(identity,inverse(X_397)))))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,X_397)),inverse(greatest_lower_bound(identity,inverse(X_397)))))))]]) ).
cnf(refute_0_2368,plain,
( inverse(least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,X_397)),inverse(greatest_lower_bound(identity,inverse(X_397)))))) != inverse(least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,X_397)),inverse(greatest_lower_bound(identity,inverse(X_397))))))
| least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,X_397)),inverse(greatest_lower_bound(identity,inverse(X_397))))) != least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))))
| inverse(least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,X_397)),inverse(greatest_lower_bound(identity,inverse(X_397)))))) = inverse(least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,X_397)),inverse(greatest_lower_bound(identity,inverse(X_397)))))),inverse(least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,X_397)),inverse(greatest_lower_bound(identity,inverse(X_397))))))) ),[1,0],$fot(least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397))))))]]) ).
cnf(refute_0_2369,plain,
( least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,X_397)),inverse(greatest_lower_bound(identity,inverse(X_397))))) != least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))))
| inverse(least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,X_397)),inverse(greatest_lower_bound(identity,inverse(X_397)))))) = inverse(least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,X_397)),inverse(greatest_lower_bound(identity,inverse(X_397)))))),inverse(least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,X_397)),inverse(greatest_lower_bound(identity,inverse(X_397))))))) )],[refute_0_2367,refute_0_2368]) ).
cnf(refute_0_2370,plain,
inverse(least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,X_397)),inverse(greatest_lower_bound(identity,inverse(X_397)))))) = inverse(least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,X_397)),inverse(greatest_lower_bound(identity,inverse(X_397))))),least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))))) )],[refute_0_2366,refute_0_2369]) ).
cnf(refute_0_2371,plain,
( inverse(least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,X_397)),inverse(greatest_lower_bound(identity,inverse(X_397)))))) != multiply(greatest_lower_bound(identity,inverse(X_397)),inverse(inverse(least_upper_bound(identity,X_397))))
| inverse(least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,X_397)),inverse(greatest_lower_bound(identity,inverse(X_397)))))) != inverse(least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397))))))
| inverse(least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))))) = multiply(greatest_lower_bound(identity,inverse(X_397)),inverse(inverse(least_upper_bound(identity,X_397)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,X_397)),inverse(greatest_lower_bound(identity,inverse(X_397)))))),multiply(greatest_lower_bound(identity,inverse(X_397)),inverse(inverse(least_upper_bound(identity,X_397))))) ),[0],$fot(inverse(least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))))))]]) ).
cnf(refute_0_2372,plain,
( inverse(least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,X_397)),inverse(greatest_lower_bound(identity,inverse(X_397)))))) != multiply(greatest_lower_bound(identity,inverse(X_397)),inverse(inverse(least_upper_bound(identity,X_397))))
| inverse(least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))))) = multiply(greatest_lower_bound(identity,inverse(X_397)),inverse(inverse(least_upper_bound(identity,X_397)))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,X_397)),inverse(greatest_lower_bound(identity,inverse(X_397)))))),inverse(least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397))))))) )],[refute_0_2370,refute_0_2371]) ).
cnf(refute_0_2373,plain,
inverse(inverse(least_upper_bound(identity,X_397))) = least_upper_bound(identity,X_397),
inference(subst,[],[p18_2:[bind(X,$fot(least_upper_bound(identity,X_397)))]]) ).
cnf(refute_0_2374,plain,
multiply(greatest_lower_bound(identity,inverse(X_397)),inverse(inverse(least_upper_bound(identity,X_397)))) = multiply(greatest_lower_bound(identity,inverse(X_397)),inverse(inverse(least_upper_bound(identity,X_397)))),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(identity,inverse(X_397)),inverse(inverse(least_upper_bound(identity,X_397)))))]]) ).
cnf(refute_0_2375,plain,
( multiply(greatest_lower_bound(identity,inverse(X_397)),inverse(inverse(least_upper_bound(identity,X_397)))) != multiply(greatest_lower_bound(identity,inverse(X_397)),inverse(inverse(least_upper_bound(identity,X_397))))
| inverse(inverse(least_upper_bound(identity,X_397))) != least_upper_bound(identity,X_397)
| multiply(greatest_lower_bound(identity,inverse(X_397)),inverse(inverse(least_upper_bound(identity,X_397)))) = multiply(greatest_lower_bound(identity,inverse(X_397)),least_upper_bound(identity,X_397)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(X_397)),inverse(inverse(least_upper_bound(identity,X_397)))),multiply(greatest_lower_bound(identity,inverse(X_397)),inverse(inverse(least_upper_bound(identity,X_397))))) ),[1,1],$fot(least_upper_bound(identity,X_397))]]) ).
cnf(refute_0_2376,plain,
( inverse(inverse(least_upper_bound(identity,X_397))) != least_upper_bound(identity,X_397)
| multiply(greatest_lower_bound(identity,inverse(X_397)),inverse(inverse(least_upper_bound(identity,X_397)))) = multiply(greatest_lower_bound(identity,inverse(X_397)),least_upper_bound(identity,X_397)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(X_397)),inverse(inverse(least_upper_bound(identity,X_397)))),multiply(greatest_lower_bound(identity,inverse(X_397)),inverse(inverse(least_upper_bound(identity,X_397))))) )],[refute_0_2374,refute_0_2375]) ).
cnf(refute_0_2377,plain,
multiply(greatest_lower_bound(identity,inverse(X_397)),inverse(inverse(least_upper_bound(identity,X_397)))) = multiply(greatest_lower_bound(identity,inverse(X_397)),least_upper_bound(identity,X_397)),
inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(identity,X_397))),least_upper_bound(identity,X_397)) )],[refute_0_2373,refute_0_2376]) ).
cnf(refute_0_2378,plain,
( multiply(greatest_lower_bound(identity,inverse(X_397)),inverse(inverse(least_upper_bound(identity,X_397)))) != multiply(greatest_lower_bound(identity,inverse(X_397)),least_upper_bound(identity,X_397))
| multiply(greatest_lower_bound(identity,inverse(X_397)),least_upper_bound(identity,X_397)) != multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))
| multiply(greatest_lower_bound(identity,inverse(X_397)),inverse(inverse(least_upper_bound(identity,X_397)))) = multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397))) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(multiply(greatest_lower_bound(identity,inverse(X_397)),inverse(inverse(least_upper_bound(identity,X_397)))))),bind(Y0,$fot(multiply(greatest_lower_bound(identity,inverse(X_397)),least_upper_bound(identity,X_397)))),bind(Z0,$fot(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))))]]) ).
cnf(refute_0_2379,plain,
( multiply(greatest_lower_bound(identity,inverse(X_397)),least_upper_bound(identity,X_397)) != multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))
| multiply(greatest_lower_bound(identity,inverse(X_397)),inverse(inverse(least_upper_bound(identity,X_397)))) = multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(X_397)),inverse(inverse(least_upper_bound(identity,X_397)))),multiply(greatest_lower_bound(identity,inverse(X_397)),least_upper_bound(identity,X_397))) )],[refute_0_2377,refute_0_2378]) ).
cnf(refute_0_2380,plain,
multiply(greatest_lower_bound(identity,inverse(X_397)),inverse(inverse(least_upper_bound(identity,X_397)))) = multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(X_397)),least_upper_bound(identity,X_397)),multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))) )],[refute_0_2354,refute_0_2379]) ).
cnf(refute_0_2381,plain,
( multiply(greatest_lower_bound(identity,inverse(X_397)),inverse(inverse(least_upper_bound(identity,X_397)))) != multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))
| inverse(least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))))) != multiply(greatest_lower_bound(identity,inverse(X_397)),inverse(inverse(least_upper_bound(identity,X_397))))
| inverse(least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))))) = multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))))),multiply(greatest_lower_bound(identity,inverse(X_397)),inverse(inverse(least_upper_bound(identity,X_397))))) ),[1],$fot(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397))))]]) ).
cnf(refute_0_2382,plain,
( inverse(least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))))) != multiply(greatest_lower_bound(identity,inverse(X_397)),inverse(inverse(least_upper_bound(identity,X_397))))
| inverse(least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))))) = multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(X_397)),inverse(inverse(least_upper_bound(identity,X_397)))),multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))) )],[refute_0_2380,refute_0_2381]) ).
cnf(refute_0_2383,plain,
( inverse(least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,X_397)),inverse(greatest_lower_bound(identity,inverse(X_397)))))) != multiply(greatest_lower_bound(identity,inverse(X_397)),inverse(inverse(least_upper_bound(identity,X_397))))
| inverse(least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))))) = multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))))),multiply(greatest_lower_bound(identity,inverse(X_397)),inverse(inverse(least_upper_bound(identity,X_397))))) )],[refute_0_2372,refute_0_2382]) ).
cnf(refute_0_2384,plain,
inverse(least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))))) = multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,X_397)),inverse(greatest_lower_bound(identity,inverse(X_397)))))),multiply(greatest_lower_bound(identity,inverse(X_397)),inverse(inverse(least_upper_bound(identity,X_397))))) )],[refute_0_2347,refute_0_2383]) ).
cnf(refute_0_2385,plain,
multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397))) = multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397))),
inference(subst,[],[refute_0_1982:[bind(X,$fot(X_397))]]) ).
cnf(refute_0_2386,plain,
inverse(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397)))) = inverse(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397)))),
introduced(tautology,[refl,[$fot(inverse(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397)))))]]) ).
cnf(refute_0_2387,plain,
( multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397))) != multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))
| inverse(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397)))) != inverse(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397))))
| inverse(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397)))) = inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397)))),inverse(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397))))) ),[1,0],$fot(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397))))]]) ).
cnf(refute_0_2388,plain,
( multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397))) != multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))
| inverse(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397)))) = inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))) ),
inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397)))),inverse(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397))))) )],[refute_0_2386,refute_0_2387]) ).
cnf(refute_0_2389,plain,
inverse(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397)))) = inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397))),multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))) )],[refute_0_2385,refute_0_2388]) ).
cnf(refute_0_2390,plain,
least_upper_bound(identity,inverse(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397))))) = least_upper_bound(identity,inverse(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397))))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,inverse(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397))))))]]) ).
cnf(refute_0_2391,plain,
( inverse(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397)))) != inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397))))
| least_upper_bound(identity,inverse(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397))))) != least_upper_bound(identity,inverse(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397)))))
| least_upper_bound(identity,inverse(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397))))) = least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397))))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,inverse(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397))))),least_upper_bound(identity,inverse(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397)))))) ),[1,1],$fot(inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))))]]) ).
cnf(refute_0_2392,plain,
( inverse(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397)))) != inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397))))
| least_upper_bound(identity,inverse(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397))))) = least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397))))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397))))),least_upper_bound(identity,inverse(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397)))))) )],[refute_0_2390,refute_0_2391]) ).
cnf(refute_0_2393,plain,
least_upper_bound(identity,inverse(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397))))) = least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397))))),
inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397)))),inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397))))) )],[refute_0_2389,refute_0_2392]) ).
cnf(refute_0_2394,plain,
inverse(least_upper_bound(identity,inverse(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397)))))) = inverse(least_upper_bound(identity,inverse(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397)))))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(identity,inverse(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397)))))))]]) ).
cnf(refute_0_2395,plain,
( inverse(least_upper_bound(identity,inverse(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397)))))) != inverse(least_upper_bound(identity,inverse(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397))))))
| least_upper_bound(identity,inverse(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397))))) != least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))))
| inverse(least_upper_bound(identity,inverse(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397)))))) = inverse(least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397)))))),inverse(least_upper_bound(identity,inverse(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397))))))) ),[1,0],$fot(least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397))))))]]) ).
cnf(refute_0_2396,plain,
( least_upper_bound(identity,inverse(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397))))) != least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))))
| inverse(least_upper_bound(identity,inverse(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397)))))) = inverse(least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397)))))),inverse(least_upper_bound(identity,inverse(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397))))))) )],[refute_0_2394,refute_0_2395]) ).
cnf(refute_0_2397,plain,
inverse(least_upper_bound(identity,inverse(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397)))))) = inverse(least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397))))),least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))))) )],[refute_0_2393,refute_0_2396]) ).
cnf(refute_0_2398,plain,
( inverse(least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))))) != multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))
| inverse(least_upper_bound(identity,inverse(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397)))))) != inverse(least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397))))))
| inverse(least_upper_bound(identity,inverse(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397)))))) = multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397))) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(inverse(least_upper_bound(identity,inverse(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397)))))))),bind(Y0,$fot(inverse(least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))))))),bind(Z0,$fot(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))))]]) ).
cnf(refute_0_2399,plain,
( inverse(least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))))) != multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))
| inverse(least_upper_bound(identity,inverse(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397)))))) = multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397)))))),inverse(least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397))))))) )],[refute_0_2397,refute_0_2398]) ).
cnf(refute_0_2400,plain,
inverse(least_upper_bound(identity,inverse(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397)))))) = multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))))),multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))) )],[refute_0_2384,refute_0_2399]) ).
cnf(refute_0_2401,plain,
inverse(multiply(inverse(X_97),least_upper_bound(X_54,inverse(inverse(X_97))))) = multiply(inverse(least_upper_bound(X_54,inverse(inverse(X_97)))),X_97),
inference(subst,[],[refute_0_982:[bind(X,$fot(X_97)),bind(X_33,$fot(least_upper_bound(X_54,inverse(inverse(X_97)))))]]) ).
cnf(refute_0_2402,plain,
multiply(inverse(X_97),least_upper_bound(X_54,inverse(inverse(X_97)))) = least_upper_bound(identity,multiply(inverse(X_97),X_54)),
inference(subst,[],[refute_0_1721:[bind(X_53,$fot(inverse(X_97)))]]) ).
cnf(refute_0_2403,plain,
( multiply(inverse(X_97),least_upper_bound(X_54,inverse(inverse(X_97)))) != least_upper_bound(identity,multiply(inverse(X_97),X_54))
| inverse(multiply(inverse(X_97),least_upper_bound(X_54,inverse(inverse(X_97))))) != multiply(inverse(least_upper_bound(X_54,inverse(inverse(X_97)))),X_97)
| inverse(least_upper_bound(identity,multiply(inverse(X_97),X_54))) = multiply(inverse(least_upper_bound(X_54,inverse(inverse(X_97)))),X_97) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X_97),least_upper_bound(X_54,inverse(inverse(X_97))))),multiply(inverse(least_upper_bound(X_54,inverse(inverse(X_97)))),X_97)) ),[0,0],$fot(least_upper_bound(identity,multiply(inverse(X_97),X_54)))]]) ).
cnf(refute_0_2404,plain,
( inverse(multiply(inverse(X_97),least_upper_bound(X_54,inverse(inverse(X_97))))) != multiply(inverse(least_upper_bound(X_54,inverse(inverse(X_97)))),X_97)
| inverse(least_upper_bound(identity,multiply(inverse(X_97),X_54))) = multiply(inverse(least_upper_bound(X_54,inverse(inverse(X_97)))),X_97) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_97),least_upper_bound(X_54,inverse(inverse(X_97)))),least_upper_bound(identity,multiply(inverse(X_97),X_54))) )],[refute_0_2402,refute_0_2403]) ).
cnf(refute_0_2405,plain,
inverse(least_upper_bound(identity,multiply(inverse(X_97),X_54))) = multiply(inverse(least_upper_bound(X_54,inverse(inverse(X_97)))),X_97),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_97),least_upper_bound(X_54,inverse(inverse(X_97))))),multiply(inverse(least_upper_bound(X_54,inverse(inverse(X_97)))),X_97)) )],[refute_0_2401,refute_0_2404]) ).
cnf(refute_0_2406,plain,
least_upper_bound(X_54,inverse(inverse(X_97))) = least_upper_bound(X_54,inverse(inverse(X_97))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_54,inverse(inverse(X_97))))]]) ).
cnf(refute_0_2407,plain,
( inverse(inverse(X_97)) != X_97
| least_upper_bound(X_54,inverse(inverse(X_97))) != least_upper_bound(X_54,inverse(inverse(X_97)))
| least_upper_bound(X_54,inverse(inverse(X_97))) = least_upper_bound(X_54,X_97) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_54,inverse(inverse(X_97))),least_upper_bound(X_54,inverse(inverse(X_97)))) ),[1,1],$fot(X_97)]]) ).
cnf(refute_0_2408,plain,
( inverse(inverse(X_97)) != X_97
| least_upper_bound(X_54,inverse(inverse(X_97))) = least_upper_bound(X_54,X_97) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_54,inverse(inverse(X_97))),least_upper_bound(X_54,inverse(inverse(X_97)))) )],[refute_0_2406,refute_0_2407]) ).
cnf(refute_0_2409,plain,
least_upper_bound(X_54,inverse(inverse(X_97))) = least_upper_bound(X_54,X_97),
inference(resolve,[$cnf( $equal(inverse(inverse(X_97)),X_97) )],[refute_0_1209,refute_0_2408]) ).
cnf(refute_0_2410,plain,
inverse(least_upper_bound(X_54,inverse(inverse(X_97)))) = inverse(least_upper_bound(X_54,inverse(inverse(X_97)))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(X_54,inverse(inverse(X_97)))))]]) ).
cnf(refute_0_2411,plain,
( inverse(least_upper_bound(X_54,inverse(inverse(X_97)))) != inverse(least_upper_bound(X_54,inverse(inverse(X_97))))
| least_upper_bound(X_54,inverse(inverse(X_97))) != least_upper_bound(X_54,X_97)
| inverse(least_upper_bound(X_54,inverse(inverse(X_97)))) = inverse(least_upper_bound(X_54,X_97)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_54,inverse(inverse(X_97)))),inverse(least_upper_bound(X_54,inverse(inverse(X_97))))) ),[1,0],$fot(least_upper_bound(X_54,X_97))]]) ).
cnf(refute_0_2412,plain,
( least_upper_bound(X_54,inverse(inverse(X_97))) != least_upper_bound(X_54,X_97)
| inverse(least_upper_bound(X_54,inverse(inverse(X_97)))) = inverse(least_upper_bound(X_54,X_97)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_54,inverse(inverse(X_97)))),inverse(least_upper_bound(X_54,inverse(inverse(X_97))))) )],[refute_0_2410,refute_0_2411]) ).
cnf(refute_0_2413,plain,
inverse(least_upper_bound(X_54,inverse(inverse(X_97)))) = inverse(least_upper_bound(X_54,X_97)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_54,inverse(inverse(X_97))),least_upper_bound(X_54,X_97)) )],[refute_0_2409,refute_0_2412]) ).
cnf(refute_0_2414,plain,
multiply(inverse(least_upper_bound(X_54,inverse(inverse(X_97)))),X_97) = multiply(inverse(least_upper_bound(X_54,inverse(inverse(X_97)))),X_97),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(X_54,inverse(inverse(X_97)))),X_97))]]) ).
cnf(refute_0_2415,plain,
( multiply(inverse(least_upper_bound(X_54,inverse(inverse(X_97)))),X_97) != multiply(inverse(least_upper_bound(X_54,inverse(inverse(X_97)))),X_97)
| inverse(least_upper_bound(X_54,inverse(inverse(X_97)))) != inverse(least_upper_bound(X_54,X_97))
| multiply(inverse(least_upper_bound(X_54,inverse(inverse(X_97)))),X_97) = multiply(inverse(least_upper_bound(X_54,X_97)),X_97) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(X_54,inverse(inverse(X_97)))),X_97),multiply(inverse(least_upper_bound(X_54,inverse(inverse(X_97)))),X_97)) ),[1,0],$fot(inverse(least_upper_bound(X_54,X_97)))]]) ).
cnf(refute_0_2416,plain,
( inverse(least_upper_bound(X_54,inverse(inverse(X_97)))) != inverse(least_upper_bound(X_54,X_97))
| multiply(inverse(least_upper_bound(X_54,inverse(inverse(X_97)))),X_97) = multiply(inverse(least_upper_bound(X_54,X_97)),X_97) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_54,inverse(inverse(X_97)))),X_97),multiply(inverse(least_upper_bound(X_54,inverse(inverse(X_97)))),X_97)) )],[refute_0_2414,refute_0_2415]) ).
cnf(refute_0_2417,plain,
multiply(inverse(least_upper_bound(X_54,inverse(inverse(X_97)))),X_97) = multiply(inverse(least_upper_bound(X_54,X_97)),X_97),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_54,inverse(inverse(X_97)))),inverse(least_upper_bound(X_54,X_97))) )],[refute_0_2413,refute_0_2416]) ).
cnf(refute_0_2418,plain,
( multiply(inverse(least_upper_bound(X_54,inverse(inverse(X_97)))),X_97) != multiply(inverse(least_upper_bound(X_54,X_97)),X_97)
| inverse(least_upper_bound(identity,multiply(inverse(X_97),X_54))) != multiply(inverse(least_upper_bound(X_54,inverse(inverse(X_97)))),X_97)
| inverse(least_upper_bound(identity,multiply(inverse(X_97),X_54))) = multiply(inverse(least_upper_bound(X_54,X_97)),X_97) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(X_97),X_54))),multiply(inverse(least_upper_bound(X_54,inverse(inverse(X_97)))),X_97)) ),[1],$fot(multiply(inverse(least_upper_bound(X_54,X_97)),X_97))]]) ).
cnf(refute_0_2419,plain,
( inverse(least_upper_bound(identity,multiply(inverse(X_97),X_54))) != multiply(inverse(least_upper_bound(X_54,inverse(inverse(X_97)))),X_97)
| inverse(least_upper_bound(identity,multiply(inverse(X_97),X_54))) = multiply(inverse(least_upper_bound(X_54,X_97)),X_97) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_54,inverse(inverse(X_97)))),X_97),multiply(inverse(least_upper_bound(X_54,X_97)),X_97)) )],[refute_0_2417,refute_0_2418]) ).
cnf(refute_0_2420,plain,
inverse(least_upper_bound(identity,multiply(inverse(X_97),X_54))) = multiply(inverse(least_upper_bound(X_54,X_97)),X_97),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(X_97),X_54))),multiply(inverse(least_upper_bound(X_54,inverse(inverse(X_97)))),X_97)) )],[refute_0_2405,refute_0_2419]) ).
cnf(refute_0_2421,plain,
inverse(least_upper_bound(identity,multiply(inverse(X_126),inverse(X)))) = multiply(inverse(least_upper_bound(inverse(X),X_126)),X_126),
inference(subst,[],[refute_0_2420:[bind(X_54,$fot(inverse(X))),bind(X_97,$fot(X_126))]]) ).
cnf(refute_0_2422,plain,
inverse(multiply(X,X_126)) = multiply(inverse(X_126),inverse(X)),
inference(subst,[],[p18_3:[bind(Y,$fot(X_126))]]) ).
cnf(refute_0_2423,plain,
( inverse(multiply(X,X_126)) != multiply(inverse(X_126),inverse(X))
| multiply(inverse(X_126),inverse(X)) = inverse(multiply(X,X_126)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(multiply(X,X_126)))),bind(Y0,$fot(multiply(inverse(X_126),inverse(X))))]]) ).
cnf(refute_0_2424,plain,
multiply(inverse(X_126),inverse(X)) = inverse(multiply(X,X_126)),
inference(resolve,[$cnf( $equal(inverse(multiply(X,X_126)),multiply(inverse(X_126),inverse(X))) )],[refute_0_2422,refute_0_2423]) ).
cnf(refute_0_2425,plain,
( multiply(inverse(X_126),inverse(X)) != inverse(multiply(X,X_126))
| inverse(least_upper_bound(identity,multiply(inverse(X_126),inverse(X)))) != multiply(inverse(least_upper_bound(inverse(X),X_126)),X_126)
| inverse(least_upper_bound(identity,inverse(multiply(X,X_126)))) = multiply(inverse(least_upper_bound(inverse(X),X_126)),X_126) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(X_126),inverse(X)))),multiply(inverse(least_upper_bound(inverse(X),X_126)),X_126)) ),[0,0,1],$fot(inverse(multiply(X,X_126)))]]) ).
cnf(refute_0_2426,plain,
( inverse(least_upper_bound(identity,multiply(inverse(X_126),inverse(X)))) != multiply(inverse(least_upper_bound(inverse(X),X_126)),X_126)
| inverse(least_upper_bound(identity,inverse(multiply(X,X_126)))) = multiply(inverse(least_upper_bound(inverse(X),X_126)),X_126) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_126),inverse(X)),inverse(multiply(X,X_126))) )],[refute_0_2424,refute_0_2425]) ).
cnf(refute_0_2427,plain,
inverse(least_upper_bound(identity,inverse(multiply(X,X_126)))) = multiply(inverse(least_upper_bound(inverse(X),X_126)),X_126),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(X_126),inverse(X)))),multiply(inverse(least_upper_bound(inverse(X),X_126)),X_126)) )],[refute_0_2421,refute_0_2426]) ).
cnf(refute_0_2428,plain,
( inverse(least_upper_bound(identity,inverse(multiply(X,X_126)))) != multiply(inverse(least_upper_bound(inverse(X),X_126)),X_126)
| multiply(inverse(least_upper_bound(inverse(X),X_126)),X_126) = inverse(least_upper_bound(identity,inverse(multiply(X,X_126)))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(least_upper_bound(identity,inverse(multiply(X,X_126)))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(inverse(X),X_126)),X_126)))]]) ).
cnf(refute_0_2429,plain,
multiply(inverse(least_upper_bound(inverse(X),X_126)),X_126) = inverse(least_upper_bound(identity,inverse(multiply(X,X_126)))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(multiply(X,X_126)))),multiply(inverse(least_upper_bound(inverse(X),X_126)),X_126)) )],[refute_0_2427,refute_0_2428]) ).
cnf(refute_0_2430,plain,
multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_397)),greatest_lower_bound(identity,inverse(X_397)))),greatest_lower_bound(identity,inverse(X_397))) = inverse(least_upper_bound(identity,inverse(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397)))))),
inference(subst,[],[refute_0_2429:[bind(X,$fot(least_upper_bound(identity,X_397))),bind(X_126,$fot(greatest_lower_bound(identity,inverse(X_397))))]]) ).
cnf(refute_0_2431,plain,
( multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_397)),greatest_lower_bound(identity,inverse(X_397)))),greatest_lower_bound(identity,inverse(X_397))) != inverse(least_upper_bound(identity,inverse(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397))))))
| inverse(least_upper_bound(identity,inverse(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397)))))) != multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))
| multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_397)),greatest_lower_bound(identity,inverse(X_397)))),greatest_lower_bound(identity,inverse(X_397))) = multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397))) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_397)),greatest_lower_bound(identity,inverse(X_397)))),greatest_lower_bound(identity,inverse(X_397))))),bind(Y0,$fot(inverse(least_upper_bound(identity,inverse(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397)))))))),bind(Z0,$fot(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))))]]) ).
cnf(refute_0_2432,plain,
( inverse(least_upper_bound(identity,inverse(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397)))))) != multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))
| multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_397)),greatest_lower_bound(identity,inverse(X_397)))),greatest_lower_bound(identity,inverse(X_397))) = multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_397)),greatest_lower_bound(identity,inverse(X_397)))),greatest_lower_bound(identity,inverse(X_397))),inverse(least_upper_bound(identity,inverse(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397))))))) )],[refute_0_2430,refute_0_2431]) ).
cnf(refute_0_2433,plain,
multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_397)),greatest_lower_bound(identity,inverse(X_397)))),greatest_lower_bound(identity,inverse(X_397))) = multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397)))))),multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))) )],[refute_0_2400,refute_0_2432]) ).
cnf(refute_0_2434,plain,
( multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_397)),greatest_lower_bound(identity,inverse(X_397)))),greatest_lower_bound(identity,inverse(X_397))) != multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))
| multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_397)),greatest_lower_bound(identity,inverse(X_397)))),greatest_lower_bound(identity,inverse(X_397))) != greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,X_397))),greatest_lower_bound(identity,inverse(X_397))))
| multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397))) = greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,X_397))),greatest_lower_bound(identity,inverse(X_397)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_397)),greatest_lower_bound(identity,inverse(X_397)))),greatest_lower_bound(identity,inverse(X_397))),greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,X_397))),greatest_lower_bound(identity,inverse(X_397))))) ),[0],$fot(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397))))]]) ).
cnf(refute_0_2435,plain,
( multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_397)),greatest_lower_bound(identity,inverse(X_397)))),greatest_lower_bound(identity,inverse(X_397))) != greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,X_397))),greatest_lower_bound(identity,inverse(X_397))))
| multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397))) = greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,X_397))),greatest_lower_bound(identity,inverse(X_397)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_397)),greatest_lower_bound(identity,inverse(X_397)))),greatest_lower_bound(identity,inverse(X_397))),multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))) )],[refute_0_2433,refute_0_2434]) ).
cnf(refute_0_2436,plain,
greatest_lower_bound(identity,least_upper_bound(X_397,identity)) = identity,
inference(subst,[],[refute_0_171:[bind(X,$fot(identity)),bind(Y,$fot(X_397))]]) ).
cnf(refute_0_2437,plain,
multiply(least_upper_bound(X_397,identity),identity) = least_upper_bound(X_397,identity),
inference(subst,[],[refute_0_603:[bind(X,$fot(least_upper_bound(X_397,identity)))]]) ).
cnf(refute_0_2438,plain,
least_upper_bound(identity,multiply(X_397,identity)) = multiply(least_upper_bound(X_397,identity),identity),
inference(subst,[],[refute_0_706:[bind(X_65,$fot(identity)),bind(X_66,$fot(X_397))]]) ).
cnf(refute_0_2439,plain,
( multiply(least_upper_bound(X_397,identity),identity) != least_upper_bound(X_397,identity)
| least_upper_bound(identity,multiply(X_397,identity)) != multiply(least_upper_bound(X_397,identity),identity)
| least_upper_bound(identity,multiply(X_397,identity)) = least_upper_bound(X_397,identity) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(least_upper_bound(identity,multiply(X_397,identity)))),bind(Y0,$fot(multiply(least_upper_bound(X_397,identity),identity))),bind(Z0,$fot(least_upper_bound(X_397,identity)))]]) ).
cnf(refute_0_2440,plain,
( multiply(least_upper_bound(X_397,identity),identity) != least_upper_bound(X_397,identity)
| least_upper_bound(identity,multiply(X_397,identity)) = least_upper_bound(X_397,identity) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_397,identity)),multiply(least_upper_bound(X_397,identity),identity)) )],[refute_0_2438,refute_0_2439]) ).
cnf(refute_0_2441,plain,
least_upper_bound(identity,multiply(X_397,identity)) = least_upper_bound(X_397,identity),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_397,identity),identity),least_upper_bound(X_397,identity)) )],[refute_0_2437,refute_0_2440]) ).
cnf(refute_0_2442,plain,
multiply(X_397,least_upper_bound(identity,inverse(X_397))) = least_upper_bound(identity,multiply(X_397,identity)),
inference(subst,[],[refute_0_1721:[bind(X_53,$fot(X_397)),bind(X_54,$fot(identity))]]) ).
cnf(refute_0_2443,plain,
( multiply(X_397,least_upper_bound(identity,inverse(X_397))) != least_upper_bound(identity,multiply(X_397,identity))
| least_upper_bound(identity,multiply(X_397,identity)) != least_upper_bound(X_397,identity)
| multiply(X_397,least_upper_bound(identity,inverse(X_397))) = least_upper_bound(X_397,identity) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(multiply(X_397,least_upper_bound(identity,inverse(X_397))))),bind(Y0,$fot(least_upper_bound(identity,multiply(X_397,identity)))),bind(Z0,$fot(least_upper_bound(X_397,identity)))]]) ).
cnf(refute_0_2444,plain,
( least_upper_bound(identity,multiply(X_397,identity)) != least_upper_bound(X_397,identity)
| multiply(X_397,least_upper_bound(identity,inverse(X_397))) = least_upper_bound(X_397,identity) ),
inference(resolve,[$cnf( $equal(multiply(X_397,least_upper_bound(identity,inverse(X_397))),least_upper_bound(identity,multiply(X_397,identity))) )],[refute_0_2442,refute_0_2443]) ).
cnf(refute_0_2445,plain,
multiply(X_397,least_upper_bound(identity,inverse(X_397))) = least_upper_bound(X_397,identity),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_397,identity)),least_upper_bound(X_397,identity)) )],[refute_0_2441,refute_0_2444]) ).
cnf(refute_0_2446,plain,
greatest_lower_bound(identity,multiply(X_397,least_upper_bound(identity,inverse(X_397)))) = greatest_lower_bound(identity,multiply(X_397,least_upper_bound(identity,inverse(X_397)))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,multiply(X_397,least_upper_bound(identity,inverse(X_397)))))]]) ).
cnf(refute_0_2447,plain,
( multiply(X_397,least_upper_bound(identity,inverse(X_397))) != least_upper_bound(X_397,identity)
| greatest_lower_bound(identity,multiply(X_397,least_upper_bound(identity,inverse(X_397)))) != greatest_lower_bound(identity,multiply(X_397,least_upper_bound(identity,inverse(X_397))))
| greatest_lower_bound(identity,multiply(X_397,least_upper_bound(identity,inverse(X_397)))) = greatest_lower_bound(identity,least_upper_bound(X_397,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_397,least_upper_bound(identity,inverse(X_397)))),greatest_lower_bound(identity,multiply(X_397,least_upper_bound(identity,inverse(X_397))))) ),[1,1],$fot(least_upper_bound(X_397,identity))]]) ).
cnf(refute_0_2448,plain,
( multiply(X_397,least_upper_bound(identity,inverse(X_397))) != least_upper_bound(X_397,identity)
| greatest_lower_bound(identity,multiply(X_397,least_upper_bound(identity,inverse(X_397)))) = greatest_lower_bound(identity,least_upper_bound(X_397,identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_397,least_upper_bound(identity,inverse(X_397)))),greatest_lower_bound(identity,multiply(X_397,least_upper_bound(identity,inverse(X_397))))) )],[refute_0_2446,refute_0_2447]) ).
cnf(refute_0_2449,plain,
greatest_lower_bound(identity,multiply(X_397,least_upper_bound(identity,inverse(X_397)))) = greatest_lower_bound(identity,least_upper_bound(X_397,identity)),
inference(resolve,[$cnf( $equal(multiply(X_397,least_upper_bound(identity,inverse(X_397))),least_upper_bound(X_397,identity)) )],[refute_0_2445,refute_0_2448]) ).
cnf(refute_0_2450,plain,
( greatest_lower_bound(identity,multiply(X_397,least_upper_bound(identity,inverse(X_397)))) != greatest_lower_bound(identity,least_upper_bound(X_397,identity))
| greatest_lower_bound(identity,least_upper_bound(X_397,identity)) != identity
| greatest_lower_bound(identity,multiply(X_397,least_upper_bound(identity,inverse(X_397)))) = identity ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(greatest_lower_bound(identity,multiply(X_397,least_upper_bound(identity,inverse(X_397)))))),bind(Y0,$fot(greatest_lower_bound(identity,least_upper_bound(X_397,identity)))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_2451,plain,
( greatest_lower_bound(identity,least_upper_bound(X_397,identity)) != identity
| greatest_lower_bound(identity,multiply(X_397,least_upper_bound(identity,inverse(X_397)))) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_397,least_upper_bound(identity,inverse(X_397)))),greatest_lower_bound(identity,least_upper_bound(X_397,identity))) )],[refute_0_2449,refute_0_2450]) ).
cnf(refute_0_2452,plain,
greatest_lower_bound(identity,multiply(X_397,least_upper_bound(identity,inverse(X_397)))) = identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(X_397,identity)),identity) )],[refute_0_2436,refute_0_2451]) ).
cnf(refute_0_2453,plain,
greatest_lower_bound(X_26,greatest_lower_bound(least_upper_bound(X_26,Y),X_28)) = greatest_lower_bound(greatest_lower_bound(X_26,least_upper_bound(X_26,Y)),X_28),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_26)),bind(Y,$fot(least_upper_bound(X_26,Y))),bind(Z,$fot(X_28))]]) ).
cnf(refute_0_2454,plain,
greatest_lower_bound(X_26,least_upper_bound(X_26,Y)) = X_26,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_26))]]) ).
cnf(refute_0_2455,plain,
( greatest_lower_bound(X_26,greatest_lower_bound(least_upper_bound(X_26,Y),X_28)) != greatest_lower_bound(greatest_lower_bound(X_26,least_upper_bound(X_26,Y)),X_28)
| greatest_lower_bound(X_26,least_upper_bound(X_26,Y)) != X_26
| greatest_lower_bound(X_26,greatest_lower_bound(least_upper_bound(X_26,Y),X_28)) = greatest_lower_bound(X_26,X_28) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_26,greatest_lower_bound(least_upper_bound(X_26,Y),X_28)),greatest_lower_bound(greatest_lower_bound(X_26,least_upper_bound(X_26,Y)),X_28)) ),[1,0],$fot(X_26)]]) ).
cnf(refute_0_2456,plain,
( greatest_lower_bound(X_26,greatest_lower_bound(least_upper_bound(X_26,Y),X_28)) != greatest_lower_bound(greatest_lower_bound(X_26,least_upper_bound(X_26,Y)),X_28)
| greatest_lower_bound(X_26,greatest_lower_bound(least_upper_bound(X_26,Y),X_28)) = greatest_lower_bound(X_26,X_28) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_26,least_upper_bound(X_26,Y)),X_26) )],[refute_0_2454,refute_0_2455]) ).
cnf(refute_0_2457,plain,
greatest_lower_bound(X_26,greatest_lower_bound(least_upper_bound(X_26,Y),X_28)) = greatest_lower_bound(X_26,X_28),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_26,greatest_lower_bound(least_upper_bound(X_26,Y),X_28)),greatest_lower_bound(greatest_lower_bound(X_26,least_upper_bound(X_26,Y)),X_28)) )],[refute_0_2453,refute_0_2456]) ).
cnf(refute_0_2458,plain,
greatest_lower_bound(X_26,greatest_lower_bound(least_upper_bound(X_26,Y),multiply(X_105,least_upper_bound(X_26,Y)))) = greatest_lower_bound(X_26,multiply(X_105,least_upper_bound(X_26,Y))),
inference(subst,[],[refute_0_2457:[bind(X_28,$fot(multiply(X_105,least_upper_bound(X_26,Y))))]]) ).
cnf(refute_0_2459,plain,
multiply(greatest_lower_bound(X_105,identity),least_upper_bound(X_26,Y)) = greatest_lower_bound(least_upper_bound(X_26,Y),multiply(X_105,least_upper_bound(X_26,Y))),
inference(subst,[],[refute_0_746:[bind(X_45,$fot(least_upper_bound(X_26,Y))),bind(X_46,$fot(X_105))]]) ).
cnf(refute_0_2460,plain,
( multiply(greatest_lower_bound(X_105,identity),least_upper_bound(X_26,Y)) != greatest_lower_bound(least_upper_bound(X_26,Y),multiply(X_105,least_upper_bound(X_26,Y)))
| greatest_lower_bound(least_upper_bound(X_26,Y),multiply(X_105,least_upper_bound(X_26,Y))) = multiply(greatest_lower_bound(X_105,identity),least_upper_bound(X_26,Y)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(greatest_lower_bound(X_105,identity),least_upper_bound(X_26,Y)))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(X_26,Y),multiply(X_105,least_upper_bound(X_26,Y)))))]]) ).
cnf(refute_0_2461,plain,
greatest_lower_bound(least_upper_bound(X_26,Y),multiply(X_105,least_upper_bound(X_26,Y))) = multiply(greatest_lower_bound(X_105,identity),least_upper_bound(X_26,Y)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_105,identity),least_upper_bound(X_26,Y)),greatest_lower_bound(least_upper_bound(X_26,Y),multiply(X_105,least_upper_bound(X_26,Y)))) )],[refute_0_2459,refute_0_2460]) ).
cnf(refute_0_2462,plain,
( greatest_lower_bound(X_26,greatest_lower_bound(least_upper_bound(X_26,Y),multiply(X_105,least_upper_bound(X_26,Y)))) != greatest_lower_bound(X_26,multiply(X_105,least_upper_bound(X_26,Y)))
| greatest_lower_bound(least_upper_bound(X_26,Y),multiply(X_105,least_upper_bound(X_26,Y))) != multiply(greatest_lower_bound(X_105,identity),least_upper_bound(X_26,Y))
| greatest_lower_bound(X_26,multiply(greatest_lower_bound(X_105,identity),least_upper_bound(X_26,Y))) = greatest_lower_bound(X_26,multiply(X_105,least_upper_bound(X_26,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_26,greatest_lower_bound(least_upper_bound(X_26,Y),multiply(X_105,least_upper_bound(X_26,Y)))),greatest_lower_bound(X_26,multiply(X_105,least_upper_bound(X_26,Y)))) ),[0,1],$fot(multiply(greatest_lower_bound(X_105,identity),least_upper_bound(X_26,Y)))]]) ).
cnf(refute_0_2463,plain,
( greatest_lower_bound(X_26,greatest_lower_bound(least_upper_bound(X_26,Y),multiply(X_105,least_upper_bound(X_26,Y)))) != greatest_lower_bound(X_26,multiply(X_105,least_upper_bound(X_26,Y)))
| greatest_lower_bound(X_26,multiply(greatest_lower_bound(X_105,identity),least_upper_bound(X_26,Y))) = greatest_lower_bound(X_26,multiply(X_105,least_upper_bound(X_26,Y))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_26,Y),multiply(X_105,least_upper_bound(X_26,Y))),multiply(greatest_lower_bound(X_105,identity),least_upper_bound(X_26,Y))) )],[refute_0_2461,refute_0_2462]) ).
cnf(refute_0_2464,plain,
greatest_lower_bound(X_26,multiply(greatest_lower_bound(X_105,identity),least_upper_bound(X_26,Y))) = greatest_lower_bound(X_26,multiply(X_105,least_upper_bound(X_26,Y))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_26,greatest_lower_bound(least_upper_bound(X_26,Y),multiply(X_105,least_upper_bound(X_26,Y)))),greatest_lower_bound(X_26,multiply(X_105,least_upper_bound(X_26,Y)))) )],[refute_0_2458,refute_0_2463]) ).
cnf(refute_0_2465,plain,
greatest_lower_bound(identity,multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))) = greatest_lower_bound(identity,multiply(X_397,least_upper_bound(identity,inverse(X_397)))),
inference(subst,[],[refute_0_2464:[bind(Y,$fot(inverse(X_397))),bind(X_105,$fot(X_397)),bind(X_26,$fot(identity))]]) ).
cnf(refute_0_2466,plain,
( greatest_lower_bound(identity,multiply(X_397,least_upper_bound(identity,inverse(X_397)))) != identity
| greatest_lower_bound(identity,multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))) != greatest_lower_bound(identity,multiply(X_397,least_upper_bound(identity,inverse(X_397))))
| greatest_lower_bound(identity,multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))) = identity ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(greatest_lower_bound(identity,multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(X_397,least_upper_bound(identity,inverse(X_397)))))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_2467,plain,
( greatest_lower_bound(identity,multiply(X_397,least_upper_bound(identity,inverse(X_397)))) != identity
| greatest_lower_bound(identity,multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))),greatest_lower_bound(identity,multiply(X_397,least_upper_bound(identity,inverse(X_397))))) )],[refute_0_2465,refute_0_2466]) ).
cnf(refute_0_2468,plain,
greatest_lower_bound(identity,multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))) = identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_397,least_upper_bound(identity,inverse(X_397)))),identity) )],[refute_0_2452,refute_0_2467]) ).
cnf(refute_0_2469,plain,
multiply(inverse(inverse(least_upper_bound(identity,X_397))),greatest_lower_bound(identity,inverse(X_397))) = multiply(inverse(inverse(least_upper_bound(identity,X_397))),greatest_lower_bound(identity,inverse(X_397))),
introduced(tautology,[refl,[$fot(multiply(inverse(inverse(least_upper_bound(identity,X_397))),greatest_lower_bound(identity,inverse(X_397))))]]) ).
cnf(refute_0_2470,plain,
( multiply(inverse(inverse(least_upper_bound(identity,X_397))),greatest_lower_bound(identity,inverse(X_397))) != multiply(inverse(inverse(least_upper_bound(identity,X_397))),greatest_lower_bound(identity,inverse(X_397)))
| inverse(inverse(least_upper_bound(identity,X_397))) != least_upper_bound(identity,X_397)
| multiply(inverse(inverse(least_upper_bound(identity,X_397))),greatest_lower_bound(identity,inverse(X_397))) = multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(identity,X_397))),greatest_lower_bound(identity,inverse(X_397))),multiply(inverse(inverse(least_upper_bound(identity,X_397))),greatest_lower_bound(identity,inverse(X_397)))) ),[1,0],$fot(least_upper_bound(identity,X_397))]]) ).
cnf(refute_0_2471,plain,
( inverse(inverse(least_upper_bound(identity,X_397))) != least_upper_bound(identity,X_397)
| multiply(inverse(inverse(least_upper_bound(identity,X_397))),greatest_lower_bound(identity,inverse(X_397))) = multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(identity,X_397))),greatest_lower_bound(identity,inverse(X_397))),multiply(inverse(inverse(least_upper_bound(identity,X_397))),greatest_lower_bound(identity,inverse(X_397)))) )],[refute_0_2469,refute_0_2470]) ).
cnf(refute_0_2472,plain,
multiply(inverse(inverse(least_upper_bound(identity,X_397))),greatest_lower_bound(identity,inverse(X_397))) = multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397))),
inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(identity,X_397))),least_upper_bound(identity,X_397)) )],[refute_0_2373,refute_0_2471]) ).
cnf(refute_0_2473,plain,
( multiply(inverse(inverse(least_upper_bound(identity,X_397))),greatest_lower_bound(identity,inverse(X_397))) != multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397)))
| multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397))) != multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))
| multiply(inverse(inverse(least_upper_bound(identity,X_397))),greatest_lower_bound(identity,inverse(X_397))) = multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397))) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(multiply(inverse(inverse(least_upper_bound(identity,X_397))),greatest_lower_bound(identity,inverse(X_397))))),bind(Y0,$fot(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397))))),bind(Z0,$fot(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))))]]) ).
cnf(refute_0_2474,plain,
( multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397))) != multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))
| multiply(inverse(inverse(least_upper_bound(identity,X_397))),greatest_lower_bound(identity,inverse(X_397))) = multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(identity,X_397))),greatest_lower_bound(identity,inverse(X_397))),multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397)))) )],[refute_0_2472,refute_0_2473]) ).
cnf(refute_0_2475,plain,
multiply(inverse(inverse(least_upper_bound(identity,X_397))),greatest_lower_bound(identity,inverse(X_397))) = multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_397),greatest_lower_bound(identity,inverse(X_397))),multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))) )],[refute_0_2385,refute_0_2474]) ).
cnf(refute_0_2476,plain,
greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,X_397))),greatest_lower_bound(identity,inverse(X_397)))) = greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,X_397))),greatest_lower_bound(identity,inverse(X_397)))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,X_397))),greatest_lower_bound(identity,inverse(X_397)))))]]) ).
cnf(refute_0_2477,plain,
( multiply(inverse(inverse(least_upper_bound(identity,X_397))),greatest_lower_bound(identity,inverse(X_397))) != multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))
| greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,X_397))),greatest_lower_bound(identity,inverse(X_397)))) != greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,X_397))),greatest_lower_bound(identity,inverse(X_397))))
| greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,X_397))),greatest_lower_bound(identity,inverse(X_397)))) = greatest_lower_bound(identity,multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,X_397))),greatest_lower_bound(identity,inverse(X_397)))),greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,X_397))),greatest_lower_bound(identity,inverse(X_397))))) ),[1,1],$fot(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397))))]]) ).
cnf(refute_0_2478,plain,
( multiply(inverse(inverse(least_upper_bound(identity,X_397))),greatest_lower_bound(identity,inverse(X_397))) != multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))
| greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,X_397))),greatest_lower_bound(identity,inverse(X_397)))) = greatest_lower_bound(identity,multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,X_397))),greatest_lower_bound(identity,inverse(X_397)))),greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,X_397))),greatest_lower_bound(identity,inverse(X_397))))) )],[refute_0_2476,refute_0_2477]) ).
cnf(refute_0_2479,plain,
greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,X_397))),greatest_lower_bound(identity,inverse(X_397)))) = greatest_lower_bound(identity,multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(identity,X_397))),greatest_lower_bound(identity,inverse(X_397))),multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))) )],[refute_0_2475,refute_0_2478]) ).
cnf(refute_0_2480,plain,
( greatest_lower_bound(identity,multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))) != identity
| greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,X_397))),greatest_lower_bound(identity,inverse(X_397)))) != greatest_lower_bound(identity,multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397))))
| greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,X_397))),greatest_lower_bound(identity,inverse(X_397)))) = identity ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,X_397))),greatest_lower_bound(identity,inverse(X_397)))))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_2481,plain,
( greatest_lower_bound(identity,multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))) != identity
| greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,X_397))),greatest_lower_bound(identity,inverse(X_397)))) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,X_397))),greatest_lower_bound(identity,inverse(X_397)))),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397))))) )],[refute_0_2479,refute_0_2480]) ).
cnf(refute_0_2482,plain,
greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,X_397))),greatest_lower_bound(identity,inverse(X_397)))) = identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397)))),identity) )],[refute_0_2468,refute_0_2481]) ).
cnf(refute_0_2483,plain,
( multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397))) != greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,X_397))),greatest_lower_bound(identity,inverse(X_397))))
| greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,X_397))),greatest_lower_bound(identity,inverse(X_397)))) != identity
| multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397))) = identity ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397))),identity) ),[0],$fot(greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,X_397))),greatest_lower_bound(identity,inverse(X_397)))))]]) ).
cnf(refute_0_2484,plain,
( multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397))) != greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,X_397))),greatest_lower_bound(identity,inverse(X_397))))
| multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397))) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,X_397))),greatest_lower_bound(identity,inverse(X_397)))),identity) )],[refute_0_2482,refute_0_2483]) ).
cnf(refute_0_2485,plain,
( multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_397)),greatest_lower_bound(identity,inverse(X_397)))),greatest_lower_bound(identity,inverse(X_397))) != greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,X_397))),greatest_lower_bound(identity,inverse(X_397))))
| multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397))) = identity ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397))),greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,X_397))),greatest_lower_bound(identity,inverse(X_397))))) )],[refute_0_2435,refute_0_2484]) ).
cnf(refute_0_2486,plain,
multiply(greatest_lower_bound(X_397,identity),least_upper_bound(identity,inverse(X_397))) = identity,
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_397)),greatest_lower_bound(identity,inverse(X_397)))),greatest_lower_bound(identity,inverse(X_397))),greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,X_397))),greatest_lower_bound(identity,inverse(X_397))))) )],[refute_0_2343,refute_0_2485]) ).
cnf(refute_0_2487,plain,
multiply(greatest_lower_bound(X_197,identity),least_upper_bound(identity,inverse(X_197))) = identity,
inference(subst,[],[refute_0_2486:[bind(X_397,$fot(X_197))]]) ).
cnf(refute_0_2488,plain,
( multiply(greatest_lower_bound(X_197,identity),least_upper_bound(identity,inverse(X_197))) != multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197)))
| multiply(greatest_lower_bound(X_197,identity),least_upper_bound(identity,inverse(X_197))) != identity
| identity = multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_197,identity),least_upper_bound(identity,inverse(X_197))),multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197)))) ),[0],$fot(identity)]]) ).
cnf(refute_0_2489,plain,
( multiply(greatest_lower_bound(X_197,identity),least_upper_bound(identity,inverse(X_197))) != multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197)))
| identity = multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_197,identity),least_upper_bound(identity,inverse(X_197))),identity) )],[refute_0_2487,refute_0_2488]) ).
cnf(refute_0_2490,plain,
identity = multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_197,identity),least_upper_bound(identity,inverse(X_197))),multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197)))) )],[refute_0_1543,refute_0_2489]) ).
cnf(refute_0_2491,plain,
( identity != multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197)))
| multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197))) = identity ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(identity)),bind(Y0,$fot(multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197)))))]]) ).
cnf(refute_0_2492,plain,
multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197))) = identity,
inference(resolve,[$cnf( $equal(identity,multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197)))) )],[refute_0_2490,refute_0_2491]) ).
cnf(refute_0_2493,plain,
multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51))) = identity,
inference(subst,[],[refute_0_2492:[bind(X_197,$fot(X_51))]]) ).
cnf(refute_0_2494,plain,
inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))) = inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),
introduced(tautology,[refl,[$fot(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))))]]) ).
cnf(refute_0_2495,plain,
( multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51))) != identity
| inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))) != inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51))))
| inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))) = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51))))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_2496,plain,
( multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51))) != identity
| inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))) = inverse(identity) ),
inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51))))) )],[refute_0_2494,refute_0_2495]) ).
cnf(refute_0_2497,plain,
inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))) = inverse(identity),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51))),identity) )],[refute_0_2493,refute_0_2496]) ).
cnf(refute_0_2498,plain,
( inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))) != inverse(identity)
| inverse(identity) != identity
| inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))) = identity ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))))),bind(Y0,$fot(inverse(identity))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_2499,plain,
( inverse(identity) != identity
| inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))) = identity ),
inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),inverse(identity)) )],[refute_0_2497,refute_0_2498]) ).
cnf(refute_0_2500,plain,
inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))) = identity,
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[p18_1,refute_0_2499]) ).
cnf(refute_0_2501,plain,
multiply(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),least_upper_bound(identity,inverse(X_51))) = multiply(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),least_upper_bound(identity,inverse(X_51))),
introduced(tautology,[refl,[$fot(multiply(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),least_upper_bound(identity,inverse(X_51))))]]) ).
cnf(refute_0_2502,plain,
( multiply(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),least_upper_bound(identity,inverse(X_51))) != multiply(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),least_upper_bound(identity,inverse(X_51)))
| inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))) != identity
| multiply(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),least_upper_bound(identity,inverse(X_51))) = multiply(identity,least_upper_bound(identity,inverse(X_51))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),least_upper_bound(identity,inverse(X_51))),multiply(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),least_upper_bound(identity,inverse(X_51)))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_2503,plain,
( inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))) != identity
| multiply(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),least_upper_bound(identity,inverse(X_51))) = multiply(identity,least_upper_bound(identity,inverse(X_51))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),least_upper_bound(identity,inverse(X_51))),multiply(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),least_upper_bound(identity,inverse(X_51)))) )],[refute_0_2501,refute_0_2502]) ).
cnf(refute_0_2504,plain,
multiply(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),least_upper_bound(identity,inverse(X_51))) = multiply(identity,least_upper_bound(identity,inverse(X_51))),
inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),identity) )],[refute_0_2500,refute_0_2503]) ).
cnf(refute_0_2505,plain,
( multiply(identity,least_upper_bound(identity,inverse(X_51))) != least_upper_bound(identity,inverse(X_51))
| multiply(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),least_upper_bound(identity,inverse(X_51))) != multiply(identity,least_upper_bound(identity,inverse(X_51)))
| multiply(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),least_upper_bound(identity,inverse(X_51))) = least_upper_bound(identity,inverse(X_51)) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(multiply(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),least_upper_bound(identity,inverse(X_51))))),bind(Y0,$fot(multiply(identity,least_upper_bound(identity,inverse(X_51))))),bind(Z0,$fot(least_upper_bound(identity,inverse(X_51))))]]) ).
cnf(refute_0_2506,plain,
( multiply(identity,least_upper_bound(identity,inverse(X_51))) != least_upper_bound(identity,inverse(X_51))
| multiply(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),least_upper_bound(identity,inverse(X_51))) = least_upper_bound(identity,inverse(X_51)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),least_upper_bound(identity,inverse(X_51))),multiply(identity,least_upper_bound(identity,inverse(X_51)))) )],[refute_0_2504,refute_0_2505]) ).
cnf(refute_0_2507,plain,
multiply(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),least_upper_bound(identity,inverse(X_51))) = least_upper_bound(identity,inverse(X_51)),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(identity,inverse(X_51))),least_upper_bound(identity,inverse(X_51))) )],[refute_0_1033,refute_0_2506]) ).
cnf(refute_0_2508,plain,
( multiply(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),least_upper_bound(identity,inverse(X_51))) != least_upper_bound(identity,inverse(X_51))
| inverse(greatest_lower_bound(identity,X_51)) != multiply(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),least_upper_bound(identity,inverse(X_51)))
| inverse(greatest_lower_bound(identity,X_51)) = least_upper_bound(identity,inverse(X_51)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,X_51)),multiply(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),least_upper_bound(identity,inverse(X_51)))) ),[1],$fot(least_upper_bound(identity,inverse(X_51)))]]) ).
cnf(refute_0_2509,plain,
( inverse(greatest_lower_bound(identity,X_51)) != multiply(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),least_upper_bound(identity,inverse(X_51)))
| inverse(greatest_lower_bound(identity,X_51)) = least_upper_bound(identity,inverse(X_51)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),least_upper_bound(identity,inverse(X_51))),least_upper_bound(identity,inverse(X_51))) )],[refute_0_2507,refute_0_2508]) ).
cnf(refute_0_2510,plain,
inverse(greatest_lower_bound(identity,X_51)) = least_upper_bound(identity,inverse(X_51)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,X_51)),multiply(inverse(multiply(greatest_lower_bound(identity,X_51),least_upper_bound(identity,inverse(X_51)))),least_upper_bound(identity,inverse(X_51)))) )],[refute_0_1032,refute_0_2509]) ).
cnf(refute_0_2511,plain,
( inverse(greatest_lower_bound(identity,X_51)) != least_upper_bound(identity,inverse(X_51))
| least_upper_bound(identity,inverse(X_51)) = inverse(greatest_lower_bound(identity,X_51)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(greatest_lower_bound(identity,X_51)))),bind(Y0,$fot(least_upper_bound(identity,inverse(X_51))))]]) ).
cnf(refute_0_2512,plain,
least_upper_bound(identity,inverse(X_51)) = inverse(greatest_lower_bound(identity,X_51)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,X_51)),least_upper_bound(identity,inverse(X_51))) )],[refute_0_2510,refute_0_2511]) ).
cnf(refute_0_2513,plain,
least_upper_bound(identity,inverse(a)) = inverse(greatest_lower_bound(identity,a)),
inference(subst,[],[refute_0_2512:[bind(X_51,$fot(a))]]) ).
cnf(refute_0_2514,plain,
( inverse(greatest_lower_bound(identity,a)) != inverse(greatest_lower_bound(a,identity))
| least_upper_bound(identity,inverse(a)) != inverse(greatest_lower_bound(identity,a))
| least_upper_bound(identity,inverse(a)) = inverse(greatest_lower_bound(a,identity)) ),
inference(subst,[],[refute_0_88:[bind(X0,$fot(least_upper_bound(identity,inverse(a)))),bind(Y0,$fot(inverse(greatest_lower_bound(identity,a)))),bind(Z0,$fot(inverse(greatest_lower_bound(a,identity))))]]) ).
cnf(refute_0_2515,plain,
( inverse(greatest_lower_bound(identity,a)) != inverse(greatest_lower_bound(a,identity))
| least_upper_bound(identity,inverse(a)) = inverse(greatest_lower_bound(a,identity)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(a)),inverse(greatest_lower_bound(identity,a))) )],[refute_0_2513,refute_0_2514]) ).
cnf(refute_0_2516,plain,
least_upper_bound(identity,inverse(a)) = inverse(greatest_lower_bound(a,identity)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,a)),inverse(greatest_lower_bound(a,identity))) )],[refute_0_662,refute_0_2515]) ).
cnf(refute_0_2517,plain,
( inverse(greatest_lower_bound(a,identity)) != inverse(greatest_lower_bound(a,identity))
| least_upper_bound(identity,inverse(a)) != inverse(greatest_lower_bound(a,identity))
| least_upper_bound(identity,inverse(a)) = inverse(greatest_lower_bound(a,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,inverse(a)),inverse(greatest_lower_bound(a,identity))) ),[1],$fot(inverse(greatest_lower_bound(a,identity)))]]) ).
cnf(refute_0_2518,plain,
( inverse(greatest_lower_bound(a,identity)) != inverse(greatest_lower_bound(a,identity))
| least_upper_bound(identity,inverse(a)) = inverse(greatest_lower_bound(a,identity)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(a)),inverse(greatest_lower_bound(a,identity))) )],[refute_0_2516,refute_0_2517]) ).
cnf(refute_0_2519,plain,
inverse(greatest_lower_bound(a,identity)) != inverse(greatest_lower_bound(a,identity)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(a)),inverse(greatest_lower_bound(a,identity))) )],[refute_0_2518,refute_0_8]) ).
cnf(refute_0_2520,plain,
inverse(greatest_lower_bound(a,identity)) = inverse(greatest_lower_bound(a,identity)),
introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(a,identity)))]]) ).
cnf(refute_0_2521,plain,
$false,
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(a,identity)),inverse(greatest_lower_bound(a,identity))) )],[refute_0_2520,refute_0_2519]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP179-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jun 14 03:34:10 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 24.84/25.04 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.84/25.04
% 24.84/25.04 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 25.16/25.37
%------------------------------------------------------------------------------