TSTP Solution File: GRP180-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP180-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n006.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 10:37:24 EDT 2022
% Result : Unsatisfiable 129.24s 129.38s
% Output : CNFRefutation 129.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 149
% Number of leaves : 649
% Syntax : Number of clauses : 3138 (1602 unt; 0 nHn;1506 RR)
% Number of literals : 5345 (5344 equ;2209 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 6007 ( 79 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(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(prove_p11,negated_conjecture,
multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)) != least_upper_bound(a,b) ).
cnf(refute_0_0,plain,
multiply(inverse(X_30),least_upper_bound(X_49,multiply(X_30,X_31))) = least_upper_bound(multiply(inverse(X_30),X_49),multiply(inverse(X_30),multiply(X_30,X_31))),
inference(subst,[],[monotony_lub1:[bind(X,$fot(inverse(X_30))),bind(Y,$fot(X_49)),bind(Z,$fot(multiply(X_30,X_31)))]]) ).
cnf(refute_0_1,plain,
multiply(multiply(inverse(X_30),X_30),X_31) = multiply(inverse(X_30),multiply(X_30,X_31)),
inference(subst,[],[associativity:[bind(X,$fot(inverse(X_30))),bind(Y,$fot(X_30)),bind(Z,$fot(X_31))]]) ).
cnf(refute_0_2,plain,
multiply(inverse(X_30),X_30) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_30))]]) ).
cnf(refute_0_3,plain,
( multiply(multiply(inverse(X_30),X_30),X_31) != multiply(inverse(X_30),multiply(X_30,X_31))
| multiply(inverse(X_30),X_30) != identity
| multiply(identity,X_31) = multiply(inverse(X_30),multiply(X_30,X_31)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_30),X_30),X_31),multiply(inverse(X_30),multiply(X_30,X_31))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_4,plain,
( multiply(multiply(inverse(X_30),X_30),X_31) != multiply(inverse(X_30),multiply(X_30,X_31))
| multiply(identity,X_31) = multiply(inverse(X_30),multiply(X_30,X_31)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_30),X_30),identity) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
multiply(identity,X_31) = multiply(inverse(X_30),multiply(X_30,X_31)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_30),X_30),X_31),multiply(inverse(X_30),multiply(X_30,X_31))) )],[refute_0_1,refute_0_4]) ).
cnf(refute_0_6,plain,
multiply(identity,X_31) = X_31,
inference(subst,[],[left_identity:[bind(X,$fot(X_31))]]) ).
cnf(refute_0_7,plain,
( multiply(identity,X_31) != X_31
| multiply(identity,X_31) != multiply(inverse(X_30),multiply(X_30,X_31))
| X_31 = multiply(inverse(X_30),multiply(X_30,X_31)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_31),multiply(inverse(X_30),multiply(X_30,X_31))) ),[0],$fot(X_31)]]) ).
cnf(refute_0_8,plain,
( multiply(identity,X_31) != multiply(inverse(X_30),multiply(X_30,X_31))
| X_31 = multiply(inverse(X_30),multiply(X_30,X_31)) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_31),X_31) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
X_31 = multiply(inverse(X_30),multiply(X_30,X_31)),
inference(resolve,[$cnf( $equal(multiply(identity,X_31),multiply(inverse(X_30),multiply(X_30,X_31))) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_11,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_12,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( X_31 != multiply(inverse(X_30),multiply(X_30,X_31))
| multiply(inverse(X_30),multiply(X_30,X_31)) = X_31 ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(X_31)),bind(Y0,$fot(multiply(inverse(X_30),multiply(X_30,X_31))))]]) ).
cnf(refute_0_14,plain,
multiply(inverse(X_30),multiply(X_30,X_31)) = X_31,
inference(resolve,[$cnf( $equal(X_31,multiply(inverse(X_30),multiply(X_30,X_31))) )],[refute_0_9,refute_0_13]) ).
cnf(refute_0_15,plain,
( multiply(inverse(X_30),multiply(X_30,X_31)) != X_31
| multiply(inverse(X_30),least_upper_bound(X_49,multiply(X_30,X_31))) != least_upper_bound(multiply(inverse(X_30),X_49),multiply(inverse(X_30),multiply(X_30,X_31)))
| multiply(inverse(X_30),least_upper_bound(X_49,multiply(X_30,X_31))) = least_upper_bound(multiply(inverse(X_30),X_49),X_31) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_30),least_upper_bound(X_49,multiply(X_30,X_31))),least_upper_bound(multiply(inverse(X_30),X_49),multiply(inverse(X_30),multiply(X_30,X_31)))) ),[1,1],$fot(X_31)]]) ).
cnf(refute_0_16,plain,
( multiply(inverse(X_30),least_upper_bound(X_49,multiply(X_30,X_31))) != least_upper_bound(multiply(inverse(X_30),X_49),multiply(inverse(X_30),multiply(X_30,X_31)))
| multiply(inverse(X_30),least_upper_bound(X_49,multiply(X_30,X_31))) = least_upper_bound(multiply(inverse(X_30),X_49),X_31) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_30),multiply(X_30,X_31)),X_31) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
multiply(inverse(X_30),least_upper_bound(X_49,multiply(X_30,X_31))) = least_upper_bound(multiply(inverse(X_30),X_49),X_31),
inference(resolve,[$cnf( $equal(multiply(inverse(X_30),least_upper_bound(X_49,multiply(X_30,X_31))),least_upper_bound(multiply(inverse(X_30),X_49),multiply(inverse(X_30),multiply(X_30,X_31)))) )],[refute_0_0,refute_0_16]) ).
cnf(refute_0_18,plain,
multiply(inverse(inverse(X_657)),least_upper_bound(identity,multiply(inverse(X_657),X_31))) = least_upper_bound(multiply(inverse(inverse(X_657)),identity),X_31),
inference(subst,[],[refute_0_17:[bind(X_30,$fot(inverse(X_657))),bind(X_49,$fot(identity))]]) ).
cnf(refute_0_19,plain,
multiply(inverse(X_50),least_upper_bound(X_49,X_50)) = least_upper_bound(multiply(inverse(X_50),X_49),multiply(inverse(X_50),X_50)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(inverse(X_50))),bind(Y,$fot(X_49)),bind(Z,$fot(X_50))]]) ).
cnf(refute_0_20,plain,
multiply(inverse(X_50),X_50) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_50))]]) ).
cnf(refute_0_21,plain,
( multiply(inverse(X_50),X_50) != identity
| multiply(inverse(X_50),least_upper_bound(X_49,X_50)) != least_upper_bound(multiply(inverse(X_50),X_49),multiply(inverse(X_50),X_50))
| multiply(inverse(X_50),least_upper_bound(X_49,X_50)) = least_upper_bound(multiply(inverse(X_50),X_49),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_50),least_upper_bound(X_49,X_50)),least_upper_bound(multiply(inverse(X_50),X_49),multiply(inverse(X_50),X_50))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_22,plain,
( multiply(inverse(X_50),least_upper_bound(X_49,X_50)) != least_upper_bound(multiply(inverse(X_50),X_49),multiply(inverse(X_50),X_50))
| multiply(inverse(X_50),least_upper_bound(X_49,X_50)) = least_upper_bound(multiply(inverse(X_50),X_49),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_50),X_50),identity) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
multiply(inverse(X_50),least_upper_bound(X_49,X_50)) = least_upper_bound(multiply(inverse(X_50),X_49),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_50),least_upper_bound(X_49,X_50)),least_upper_bound(multiply(inverse(X_50),X_49),multiply(inverse(X_50),X_50))) )],[refute_0_19,refute_0_22]) ).
cnf(refute_0_24,plain,
( least_upper_bound(X,Y) != least_upper_bound(Y,X)
| least_upper_bound(Y,X) = least_upper_bound(X,Y) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(least_upper_bound(X,Y))),bind(Y0,$fot(least_upper_bound(Y,X)))]]) ).
cnf(refute_0_25,plain,
least_upper_bound(Y,X) = least_upper_bound(X,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(X,Y),least_upper_bound(Y,X)) )],[symmetry_of_lub,refute_0_24]) ).
cnf(refute_0_26,plain,
least_upper_bound(multiply(inverse(X_50),X_49),identity) = least_upper_bound(identity,multiply(inverse(X_50),X_49)),
inference(subst,[],[refute_0_25:[bind(X,$fot(identity)),bind(Y,$fot(multiply(inverse(X_50),X_49)))]]) ).
cnf(refute_0_27,plain,
( multiply(inverse(X_50),least_upper_bound(X_49,X_50)) != least_upper_bound(multiply(inverse(X_50),X_49),identity)
| least_upper_bound(multiply(inverse(X_50),X_49),identity) != least_upper_bound(identity,multiply(inverse(X_50),X_49))
| multiply(inverse(X_50),least_upper_bound(X_49,X_50)) = least_upper_bound(identity,multiply(inverse(X_50),X_49)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_50),least_upper_bound(X_49,X_50)),least_upper_bound(identity,multiply(inverse(X_50),X_49))) ),[0],$fot(least_upper_bound(multiply(inverse(X_50),X_49),identity))]]) ).
cnf(refute_0_28,plain,
( multiply(inverse(X_50),least_upper_bound(X_49,X_50)) != least_upper_bound(multiply(inverse(X_50),X_49),identity)
| multiply(inverse(X_50),least_upper_bound(X_49,X_50)) = least_upper_bound(identity,multiply(inverse(X_50),X_49)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(X_50),X_49),identity),least_upper_bound(identity,multiply(inverse(X_50),X_49))) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
multiply(inverse(X_50),least_upper_bound(X_49,X_50)) = least_upper_bound(identity,multiply(inverse(X_50),X_49)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_50),least_upper_bound(X_49,X_50)),least_upper_bound(multiply(inverse(X_50),X_49),identity)) )],[refute_0_23,refute_0_28]) ).
cnf(refute_0_30,plain,
multiply(inverse(greatest_lower_bound(X_55,Y)),least_upper_bound(X_55,greatest_lower_bound(X_55,Y))) = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_55,Y)),X_55)),
inference(subst,[],[refute_0_29:[bind(X_49,$fot(X_55)),bind(X_50,$fot(greatest_lower_bound(X_55,Y)))]]) ).
cnf(refute_0_31,plain,
least_upper_bound(X_55,greatest_lower_bound(X_55,Y)) = X_55,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_55))]]) ).
cnf(refute_0_32,plain,
( multiply(inverse(greatest_lower_bound(X_55,Y)),least_upper_bound(X_55,greatest_lower_bound(X_55,Y))) != least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_55,Y)),X_55))
| least_upper_bound(X_55,greatest_lower_bound(X_55,Y)) != X_55
| multiply(inverse(greatest_lower_bound(X_55,Y)),X_55) = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_55,Y)),X_55)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_55,Y)),least_upper_bound(X_55,greatest_lower_bound(X_55,Y))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_55,Y)),X_55))) ),[0,1],$fot(X_55)]]) ).
cnf(refute_0_33,plain,
( multiply(inverse(greatest_lower_bound(X_55,Y)),least_upper_bound(X_55,greatest_lower_bound(X_55,Y))) != least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_55,Y)),X_55))
| multiply(inverse(greatest_lower_bound(X_55,Y)),X_55) = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_55,Y)),X_55)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_55,greatest_lower_bound(X_55,Y)),X_55) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
multiply(inverse(greatest_lower_bound(X_55,Y)),X_55) = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_55,Y)),X_55)),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_55,Y)),least_upper_bound(X_55,greatest_lower_bound(X_55,Y))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_55,Y)),X_55))) )],[refute_0_30,refute_0_33]) ).
cnf(refute_0_35,plain,
multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))),identity) = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))),identity)),
inference(subst,[],[refute_0_34:[bind(Y,$fot(multiply(inverse(X_106),X_105))),bind(X_55,$fot(identity))]]) ).
cnf(refute_0_36,plain,
multiply(inverse(X_106),greatest_lower_bound(X_105,X_106)) = greatest_lower_bound(multiply(inverse(X_106),X_105),multiply(inverse(X_106),X_106)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(inverse(X_106))),bind(Y,$fot(X_105)),bind(Z,$fot(X_106))]]) ).
cnf(refute_0_37,plain,
multiply(inverse(X_106),X_106) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_106))]]) ).
cnf(refute_0_38,plain,
( multiply(inverse(X_106),X_106) != identity
| multiply(inverse(X_106),greatest_lower_bound(X_105,X_106)) != greatest_lower_bound(multiply(inverse(X_106),X_105),multiply(inverse(X_106),X_106))
| multiply(inverse(X_106),greatest_lower_bound(X_105,X_106)) = greatest_lower_bound(multiply(inverse(X_106),X_105),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_106),greatest_lower_bound(X_105,X_106)),greatest_lower_bound(multiply(inverse(X_106),X_105),multiply(inverse(X_106),X_106))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_39,plain,
( multiply(inverse(X_106),greatest_lower_bound(X_105,X_106)) != greatest_lower_bound(multiply(inverse(X_106),X_105),multiply(inverse(X_106),X_106))
| multiply(inverse(X_106),greatest_lower_bound(X_105,X_106)) = greatest_lower_bound(multiply(inverse(X_106),X_105),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_106),X_106),identity) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
multiply(inverse(X_106),greatest_lower_bound(X_105,X_106)) = greatest_lower_bound(multiply(inverse(X_106),X_105),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_106),greatest_lower_bound(X_105,X_106)),greatest_lower_bound(multiply(inverse(X_106),X_105),multiply(inverse(X_106),X_106))) )],[refute_0_36,refute_0_39]) ).
cnf(refute_0_41,plain,
( greatest_lower_bound(X,Y) != greatest_lower_bound(Y,X)
| greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(greatest_lower_bound(X,Y))),bind(Y0,$fot(greatest_lower_bound(Y,X)))]]) ).
cnf(refute_0_42,plain,
greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X)) )],[symmetry_of_glb,refute_0_41]) ).
cnf(refute_0_43,plain,
greatest_lower_bound(multiply(inverse(X_106),X_105),identity) = greatest_lower_bound(identity,multiply(inverse(X_106),X_105)),
inference(subst,[],[refute_0_42:[bind(X,$fot(identity)),bind(Y,$fot(multiply(inverse(X_106),X_105)))]]) ).
cnf(refute_0_44,plain,
( multiply(inverse(X_106),greatest_lower_bound(X_105,X_106)) != greatest_lower_bound(multiply(inverse(X_106),X_105),identity)
| greatest_lower_bound(multiply(inverse(X_106),X_105),identity) != greatest_lower_bound(identity,multiply(inverse(X_106),X_105))
| multiply(inverse(X_106),greatest_lower_bound(X_105,X_106)) = greatest_lower_bound(identity,multiply(inverse(X_106),X_105)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_106),greatest_lower_bound(X_105,X_106)),greatest_lower_bound(identity,multiply(inverse(X_106),X_105))) ),[0],$fot(greatest_lower_bound(multiply(inverse(X_106),X_105),identity))]]) ).
cnf(refute_0_45,plain,
( multiply(inverse(X_106),greatest_lower_bound(X_105,X_106)) != greatest_lower_bound(multiply(inverse(X_106),X_105),identity)
| multiply(inverse(X_106),greatest_lower_bound(X_105,X_106)) = greatest_lower_bound(identity,multiply(inverse(X_106),X_105)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(inverse(X_106),X_105),identity),greatest_lower_bound(identity,multiply(inverse(X_106),X_105))) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
multiply(inverse(X_106),greatest_lower_bound(X_105,X_106)) = greatest_lower_bound(identity,multiply(inverse(X_106),X_105)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_106),greatest_lower_bound(X_105,X_106)),greatest_lower_bound(multiply(inverse(X_106),X_105),identity)) )],[refute_0_40,refute_0_45]) ).
cnf(refute_0_47,plain,
( multiply(inverse(X_106),greatest_lower_bound(X_105,X_106)) != greatest_lower_bound(identity,multiply(inverse(X_106),X_105))
| greatest_lower_bound(identity,multiply(inverse(X_106),X_105)) = multiply(inverse(X_106),greatest_lower_bound(X_105,X_106)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(inverse(X_106),greatest_lower_bound(X_105,X_106)))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))))]]) ).
cnf(refute_0_48,plain,
greatest_lower_bound(identity,multiply(inverse(X_106),X_105)) = multiply(inverse(X_106),greatest_lower_bound(X_105,X_106)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_106),greatest_lower_bound(X_105,X_106)),greatest_lower_bound(identity,multiply(inverse(X_106),X_105))) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
( multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))),identity) != least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))),identity))
| greatest_lower_bound(identity,multiply(inverse(X_106),X_105)) != multiply(inverse(X_106),greatest_lower_bound(X_105,X_106))
| multiply(inverse(multiply(inverse(X_106),greatest_lower_bound(X_105,X_106))),identity) = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))),identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))),identity),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))),identity))) ),[0,0,0],$fot(multiply(inverse(X_106),greatest_lower_bound(X_105,X_106)))]]) ).
cnf(refute_0_50,plain,
( multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))),identity) != least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))),identity))
| multiply(inverse(multiply(inverse(X_106),greatest_lower_bound(X_105,X_106))),identity) = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))),identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(X_106),X_105)),multiply(inverse(X_106),greatest_lower_bound(X_105,X_106))) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
multiply(inverse(multiply(inverse(X_106),greatest_lower_bound(X_105,X_106))),identity) = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))),identity)),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))),identity),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))),identity))) )],[refute_0_35,refute_0_50]) ).
cnf(refute_0_52,plain,
X_33 = multiply(inverse(multiply(X,Y)),multiply(multiply(X,Y),X_33)),
inference(subst,[],[refute_0_9:[bind(X_30,$fot(multiply(X,Y))),bind(X_31,$fot(X_33))]]) ).
cnf(refute_0_53,plain,
multiply(multiply(X,Y),X_33) = multiply(X,multiply(Y,X_33)),
inference(subst,[],[associativity:[bind(Z,$fot(X_33))]]) ).
cnf(refute_0_54,plain,
( X_33 != multiply(inverse(multiply(X,Y)),multiply(multiply(X,Y),X_33))
| multiply(multiply(X,Y),X_33) != multiply(X,multiply(Y,X_33))
| X_33 = multiply(inverse(multiply(X,Y)),multiply(X,multiply(Y,X_33))) ),
introduced(tautology,[equality,[$cnf( $equal(X_33,multiply(inverse(multiply(X,Y)),multiply(multiply(X,Y),X_33))) ),[1,1],$fot(multiply(X,multiply(Y,X_33)))]]) ).
cnf(refute_0_55,plain,
( X_33 != multiply(inverse(multiply(X,Y)),multiply(multiply(X,Y),X_33))
| X_33 = multiply(inverse(multiply(X,Y)),multiply(X,multiply(Y,X_33))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X,Y),X_33),multiply(X,multiply(Y,X_33))) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
X_33 = multiply(inverse(multiply(X,Y)),multiply(X,multiply(Y,X_33))),
inference(resolve,[$cnf( $equal(X_33,multiply(inverse(multiply(X,Y)),multiply(multiply(X,Y),X_33))) )],[refute_0_52,refute_0_55]) ).
cnf(refute_0_57,plain,
inverse(X_46) = multiply(inverse(multiply(X_45,X_46)),multiply(X_45,multiply(X_46,inverse(X_46)))),
inference(subst,[],[refute_0_56:[bind(X,$fot(X_45)),bind(Y,$fot(X_46)),bind(X_33,$fot(inverse(X_46)))]]) ).
cnf(refute_0_58,plain,
multiply(inverse(inverse(X_35)),inverse(X_35)) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(inverse(X_35)))]]) ).
cnf(refute_0_59,plain,
multiply(X_32,X_33) = multiply(inverse(inverse(X_32)),multiply(inverse(X_32),multiply(X_32,X_33))),
inference(subst,[],[refute_0_9:[bind(X_30,$fot(inverse(X_32))),bind(X_31,$fot(multiply(X_32,X_33)))]]) ).
cnf(refute_0_60,plain,
X_33 = multiply(inverse(X_32),multiply(X_32,X_33)),
inference(subst,[],[refute_0_9:[bind(X_30,$fot(X_32)),bind(X_31,$fot(X_33))]]) ).
cnf(refute_0_61,plain,
( X_33 != multiply(inverse(X_32),multiply(X_32,X_33))
| multiply(inverse(X_32),multiply(X_32,X_33)) = X_33 ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(X_33)),bind(Y0,$fot(multiply(inverse(X_32),multiply(X_32,X_33))))]]) ).
cnf(refute_0_62,plain,
multiply(inverse(X_32),multiply(X_32,X_33)) = X_33,
inference(resolve,[$cnf( $equal(X_33,multiply(inverse(X_32),multiply(X_32,X_33))) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
( multiply(X_32,X_33) != multiply(inverse(inverse(X_32)),multiply(inverse(X_32),multiply(X_32,X_33)))
| multiply(inverse(X_32),multiply(X_32,X_33)) != X_33
| multiply(X_32,X_33) = multiply(inverse(inverse(X_32)),X_33) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_32,X_33),multiply(inverse(inverse(X_32)),multiply(inverse(X_32),multiply(X_32,X_33)))) ),[1,1],$fot(X_33)]]) ).
cnf(refute_0_64,plain,
( multiply(X_32,X_33) != multiply(inverse(inverse(X_32)),multiply(inverse(X_32),multiply(X_32,X_33)))
| multiply(X_32,X_33) = multiply(inverse(inverse(X_32)),X_33) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_32),multiply(X_32,X_33)),X_33) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
multiply(X_32,X_33) = multiply(inverse(inverse(X_32)),X_33),
inference(resolve,[$cnf( $equal(multiply(X_32,X_33),multiply(inverse(inverse(X_32)),multiply(inverse(X_32),multiply(X_32,X_33)))) )],[refute_0_59,refute_0_64]) ).
cnf(refute_0_66,plain,
multiply(X_35,inverse(X_35)) = multiply(inverse(inverse(X_35)),inverse(X_35)),
inference(subst,[],[refute_0_65:[bind(X_32,$fot(X_35)),bind(X_33,$fot(inverse(X_35)))]]) ).
cnf(refute_0_67,plain,
( multiply(X_35,inverse(X_35)) != multiply(inverse(inverse(X_35)),inverse(X_35))
| multiply(inverse(inverse(X_35)),inverse(X_35)) = multiply(X_35,inverse(X_35)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(X_35,inverse(X_35)))),bind(Y0,$fot(multiply(inverse(inverse(X_35)),inverse(X_35))))]]) ).
cnf(refute_0_68,plain,
multiply(inverse(inverse(X_35)),inverse(X_35)) = multiply(X_35,inverse(X_35)),
inference(resolve,[$cnf( $equal(multiply(X_35,inverse(X_35)),multiply(inverse(inverse(X_35)),inverse(X_35))) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
( multiply(inverse(inverse(X_35)),inverse(X_35)) != multiply(X_35,inverse(X_35))
| multiply(inverse(inverse(X_35)),inverse(X_35)) != identity
| multiply(X_35,inverse(X_35)) = identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X_35)),inverse(X_35)),identity) ),[0],$fot(multiply(X_35,inverse(X_35)))]]) ).
cnf(refute_0_70,plain,
( multiply(inverse(inverse(X_35)),inverse(X_35)) != identity
| multiply(X_35,inverse(X_35)) = identity ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_35)),inverse(X_35)),multiply(X_35,inverse(X_35))) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
multiply(X_35,inverse(X_35)) = identity,
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_35)),inverse(X_35)),identity) )],[refute_0_58,refute_0_70]) ).
cnf(refute_0_72,plain,
multiply(X_46,inverse(X_46)) = identity,
inference(subst,[],[refute_0_71:[bind(X_35,$fot(X_46))]]) ).
cnf(refute_0_73,plain,
( multiply(X_46,inverse(X_46)) != identity
| inverse(X_46) != multiply(inverse(multiply(X_45,X_46)),multiply(X_45,multiply(X_46,inverse(X_46))))
| inverse(X_46) = multiply(inverse(multiply(X_45,X_46)),multiply(X_45,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(X_46),multiply(inverse(multiply(X_45,X_46)),multiply(X_45,multiply(X_46,inverse(X_46))))) ),[1,1,1],$fot(identity)]]) ).
cnf(refute_0_74,plain,
( inverse(X_46) != multiply(inverse(multiply(X_45,X_46)),multiply(X_45,multiply(X_46,inverse(X_46))))
| inverse(X_46) = multiply(inverse(multiply(X_45,X_46)),multiply(X_45,identity)) ),
inference(resolve,[$cnf( $equal(multiply(X_46,inverse(X_46)),identity) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
inverse(X_46) = multiply(inverse(multiply(X_45,X_46)),multiply(X_45,identity)),
inference(resolve,[$cnf( $equal(inverse(X_46),multiply(inverse(multiply(X_45,X_46)),multiply(X_45,multiply(X_46,inverse(X_46))))) )],[refute_0_57,refute_0_74]) ).
cnf(refute_0_76,plain,
X_33 = multiply(inverse(inverse(X_33)),multiply(inverse(X_33),X_33)),
inference(subst,[],[refute_0_9:[bind(X_30,$fot(inverse(X_33))),bind(X_31,$fot(X_33))]]) ).
cnf(refute_0_77,plain,
multiply(inverse(X_33),X_33) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_33))]]) ).
cnf(refute_0_78,plain,
( X_33 != multiply(inverse(inverse(X_33)),multiply(inverse(X_33),X_33))
| multiply(inverse(X_33),X_33) != identity
| X_33 = multiply(inverse(inverse(X_33)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(X_33,multiply(inverse(inverse(X_33)),multiply(inverse(X_33),X_33))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_79,plain,
( X_33 != multiply(inverse(inverse(X_33)),multiply(inverse(X_33),X_33))
| X_33 = multiply(inverse(inverse(X_33)),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_33),X_33),identity) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
X_33 = multiply(inverse(inverse(X_33)),identity),
inference(resolve,[$cnf( $equal(X_33,multiply(inverse(inverse(X_33)),multiply(inverse(X_33),X_33))) )],[refute_0_76,refute_0_79]) ).
cnf(refute_0_81,plain,
( multiply(X_32,X_33) != multiply(inverse(inverse(X_32)),X_33)
| multiply(inverse(inverse(X_32)),X_33) = multiply(X_32,X_33) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(X_32,X_33))),bind(Y0,$fot(multiply(inverse(inverse(X_32)),X_33)))]]) ).
cnf(refute_0_82,plain,
multiply(inverse(inverse(X_32)),X_33) = multiply(X_32,X_33),
inference(resolve,[$cnf( $equal(multiply(X_32,X_33),multiply(inverse(inverse(X_32)),X_33)) )],[refute_0_65,refute_0_81]) ).
cnf(refute_0_83,plain,
multiply(inverse(inverse(X_33)),identity) = multiply(X_33,identity),
inference(subst,[],[refute_0_82:[bind(X_32,$fot(X_33)),bind(X_33,$fot(identity))]]) ).
cnf(refute_0_84,plain,
( X_33 != multiply(inverse(inverse(X_33)),identity)
| multiply(inverse(inverse(X_33)),identity) != multiply(X_33,identity)
| X_33 = multiply(X_33,identity) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_33,multiply(X_33,identity)) ),[0],$fot(multiply(inverse(inverse(X_33)),identity))]]) ).
cnf(refute_0_85,plain,
( X_33 != multiply(inverse(inverse(X_33)),identity)
| X_33 = multiply(X_33,identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_33)),identity),multiply(X_33,identity)) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
X_33 = multiply(X_33,identity),
inference(resolve,[$cnf( $equal(X_33,multiply(inverse(inverse(X_33)),identity)) )],[refute_0_80,refute_0_85]) ).
cnf(refute_0_87,plain,
( X_33 != multiply(X_33,identity)
| multiply(X_33,identity) = X_33 ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(X_33)),bind(Y0,$fot(multiply(X_33,identity)))]]) ).
cnf(refute_0_88,plain,
multiply(X_33,identity) = X_33,
inference(resolve,[$cnf( $equal(X_33,multiply(X_33,identity)) )],[refute_0_86,refute_0_87]) ).
cnf(refute_0_89,plain,
multiply(X_45,identity) = X_45,
inference(subst,[],[refute_0_88:[bind(X_33,$fot(X_45))]]) ).
cnf(refute_0_90,plain,
multiply(inverse(multiply(X_45,X_46)),multiply(X_45,identity)) = multiply(inverse(multiply(X_45,X_46)),multiply(X_45,identity)),
introduced(tautology,[refl,[$fot(multiply(inverse(multiply(X_45,X_46)),multiply(X_45,identity)))]]) ).
cnf(refute_0_91,plain,
( multiply(X_45,identity) != X_45
| multiply(inverse(multiply(X_45,X_46)),multiply(X_45,identity)) != multiply(inverse(multiply(X_45,X_46)),multiply(X_45,identity))
| multiply(inverse(multiply(X_45,X_46)),multiply(X_45,identity)) = multiply(inverse(multiply(X_45,X_46)),X_45) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(X_45,X_46)),multiply(X_45,identity)),multiply(inverse(multiply(X_45,X_46)),multiply(X_45,identity))) ),[1,1],$fot(X_45)]]) ).
cnf(refute_0_92,plain,
( multiply(X_45,identity) != X_45
| multiply(inverse(multiply(X_45,X_46)),multiply(X_45,identity)) = multiply(inverse(multiply(X_45,X_46)),X_45) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_45,X_46)),multiply(X_45,identity)),multiply(inverse(multiply(X_45,X_46)),multiply(X_45,identity))) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
multiply(inverse(multiply(X_45,X_46)),multiply(X_45,identity)) = multiply(inverse(multiply(X_45,X_46)),X_45),
inference(resolve,[$cnf( $equal(multiply(X_45,identity),X_45) )],[refute_0_89,refute_0_92]) ).
cnf(refute_0_94,plain,
( multiply(inverse(multiply(X_45,X_46)),multiply(X_45,identity)) != multiply(inverse(multiply(X_45,X_46)),X_45)
| inverse(X_46) != multiply(inverse(multiply(X_45,X_46)),multiply(X_45,identity))
| inverse(X_46) = multiply(inverse(multiply(X_45,X_46)),X_45) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(X_46),multiply(inverse(multiply(X_45,X_46)),multiply(X_45,identity))) ),[1],$fot(multiply(inverse(multiply(X_45,X_46)),X_45))]]) ).
cnf(refute_0_95,plain,
( inverse(X_46) != multiply(inverse(multiply(X_45,X_46)),multiply(X_45,identity))
| inverse(X_46) = multiply(inverse(multiply(X_45,X_46)),X_45) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_45,X_46)),multiply(X_45,identity)),multiply(inverse(multiply(X_45,X_46)),X_45)) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
inverse(X_46) = multiply(inverse(multiply(X_45,X_46)),X_45),
inference(resolve,[$cnf( $equal(inverse(X_46),multiply(inverse(multiply(X_45,X_46)),multiply(X_45,identity))) )],[refute_0_75,refute_0_95]) ).
cnf(refute_0_97,plain,
inverse(multiply(inverse(X_145),X_31)) = multiply(inverse(multiply(X_145,multiply(inverse(X_145),X_31))),X_145),
inference(subst,[],[refute_0_96:[bind(X_45,$fot(X_145)),bind(X_46,$fot(multiply(inverse(X_145),X_31)))]]) ).
cnf(refute_0_98,plain,
X_31 = multiply(inverse(inverse(X_35)),multiply(inverse(X_35),X_31)),
inference(subst,[],[refute_0_9:[bind(X_30,$fot(inverse(X_35)))]]) ).
cnf(refute_0_99,plain,
multiply(X_35,multiply(inverse(X_35),X_31)) = multiply(inverse(inverse(X_35)),multiply(inverse(X_35),X_31)),
inference(subst,[],[refute_0_65:[bind(X_32,$fot(X_35)),bind(X_33,$fot(multiply(inverse(X_35),X_31)))]]) ).
cnf(refute_0_100,plain,
( multiply(X_35,multiply(inverse(X_35),X_31)) != multiply(inverse(inverse(X_35)),multiply(inverse(X_35),X_31))
| multiply(inverse(inverse(X_35)),multiply(inverse(X_35),X_31)) = multiply(X_35,multiply(inverse(X_35),X_31)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(X_35,multiply(inverse(X_35),X_31)))),bind(Y0,$fot(multiply(inverse(inverse(X_35)),multiply(inverse(X_35),X_31))))]]) ).
cnf(refute_0_101,plain,
multiply(inverse(inverse(X_35)),multiply(inverse(X_35),X_31)) = multiply(X_35,multiply(inverse(X_35),X_31)),
inference(resolve,[$cnf( $equal(multiply(X_35,multiply(inverse(X_35),X_31)),multiply(inverse(inverse(X_35)),multiply(inverse(X_35),X_31))) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
( X_31 != multiply(inverse(inverse(X_35)),multiply(inverse(X_35),X_31))
| multiply(inverse(inverse(X_35)),multiply(inverse(X_35),X_31)) != multiply(X_35,multiply(inverse(X_35),X_31))
| X_31 = multiply(X_35,multiply(inverse(X_35),X_31)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_31,multiply(X_35,multiply(inverse(X_35),X_31))) ),[0],$fot(multiply(inverse(inverse(X_35)),multiply(inverse(X_35),X_31)))]]) ).
cnf(refute_0_103,plain,
( X_31 != multiply(inverse(inverse(X_35)),multiply(inverse(X_35),X_31))
| X_31 = multiply(X_35,multiply(inverse(X_35),X_31)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_35)),multiply(inverse(X_35),X_31)),multiply(X_35,multiply(inverse(X_35),X_31))) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
X_31 = multiply(X_35,multiply(inverse(X_35),X_31)),
inference(resolve,[$cnf( $equal(X_31,multiply(inverse(inverse(X_35)),multiply(inverse(X_35),X_31))) )],[refute_0_98,refute_0_103]) ).
cnf(refute_0_105,plain,
X_31 = multiply(X_145,multiply(inverse(X_145),X_31)),
inference(subst,[],[refute_0_104:[bind(X_35,$fot(X_145))]]) ).
cnf(refute_0_106,plain,
( X_31 != multiply(X_145,multiply(inverse(X_145),X_31))
| multiply(X_145,multiply(inverse(X_145),X_31)) = X_31 ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(X_31)),bind(Y0,$fot(multiply(X_145,multiply(inverse(X_145),X_31))))]]) ).
cnf(refute_0_107,plain,
multiply(X_145,multiply(inverse(X_145),X_31)) = X_31,
inference(resolve,[$cnf( $equal(X_31,multiply(X_145,multiply(inverse(X_145),X_31))) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
( multiply(X_145,multiply(inverse(X_145),X_31)) != X_31
| inverse(multiply(inverse(X_145),X_31)) != multiply(inverse(multiply(X_145,multiply(inverse(X_145),X_31))),X_145)
| inverse(multiply(inverse(X_145),X_31)) = multiply(inverse(X_31),X_145) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X_145),X_31)),multiply(inverse(multiply(X_145,multiply(inverse(X_145),X_31))),X_145)) ),[1,0,0],$fot(X_31)]]) ).
cnf(refute_0_109,plain,
( inverse(multiply(inverse(X_145),X_31)) != multiply(inverse(multiply(X_145,multiply(inverse(X_145),X_31))),X_145)
| inverse(multiply(inverse(X_145),X_31)) = multiply(inverse(X_31),X_145) ),
inference(resolve,[$cnf( $equal(multiply(X_145,multiply(inverse(X_145),X_31)),X_31) )],[refute_0_107,refute_0_108]) ).
cnf(refute_0_110,plain,
inverse(multiply(inverse(X_145),X_31)) = multiply(inverse(X_31),X_145),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_145),X_31)),multiply(inverse(multiply(X_145,multiply(inverse(X_145),X_31))),X_145)) )],[refute_0_97,refute_0_109]) ).
cnf(refute_0_111,plain,
inverse(multiply(inverse(X_106),greatest_lower_bound(X_105,X_106))) = multiply(inverse(greatest_lower_bound(X_105,X_106)),X_106),
inference(subst,[],[refute_0_110:[bind(X_145,$fot(X_106)),bind(X_31,$fot(greatest_lower_bound(X_105,X_106)))]]) ).
cnf(refute_0_112,plain,
multiply(inverse(multiply(inverse(X_106),greatest_lower_bound(X_105,X_106))),identity) = inverse(multiply(inverse(X_106),greatest_lower_bound(X_105,X_106))),
inference(subst,[],[refute_0_88:[bind(X_33,$fot(inverse(multiply(inverse(X_106),greatest_lower_bound(X_105,X_106)))))]]) ).
cnf(refute_0_113,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_114,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_12,refute_0_113]) ).
cnf(refute_0_115,plain,
( multiply(inverse(multiply(inverse(X_106),greatest_lower_bound(X_105,X_106))),identity) != inverse(multiply(inverse(X_106),greatest_lower_bound(X_105,X_106)))
| inverse(multiply(inverse(X_106),greatest_lower_bound(X_105,X_106))) != multiply(inverse(greatest_lower_bound(X_105,X_106)),X_106)
| multiply(inverse(multiply(inverse(X_106),greatest_lower_bound(X_105,X_106))),identity) = multiply(inverse(greatest_lower_bound(X_105,X_106)),X_106) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(inverse(multiply(inverse(X_106),greatest_lower_bound(X_105,X_106))),identity))),bind(Y0,$fot(inverse(multiply(inverse(X_106),greatest_lower_bound(X_105,X_106))))),bind(Z0,$fot(multiply(inverse(greatest_lower_bound(X_105,X_106)),X_106)))]]) ).
cnf(refute_0_116,plain,
( inverse(multiply(inverse(X_106),greatest_lower_bound(X_105,X_106))) != multiply(inverse(greatest_lower_bound(X_105,X_106)),X_106)
| multiply(inverse(multiply(inverse(X_106),greatest_lower_bound(X_105,X_106))),identity) = multiply(inverse(greatest_lower_bound(X_105,X_106)),X_106) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(X_106),greatest_lower_bound(X_105,X_106))),identity),inverse(multiply(inverse(X_106),greatest_lower_bound(X_105,X_106)))) )],[refute_0_112,refute_0_115]) ).
cnf(refute_0_117,plain,
multiply(inverse(multiply(inverse(X_106),greatest_lower_bound(X_105,X_106))),identity) = multiply(inverse(greatest_lower_bound(X_105,X_106)),X_106),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_106),greatest_lower_bound(X_105,X_106))),multiply(inverse(greatest_lower_bound(X_105,X_106)),X_106)) )],[refute_0_111,refute_0_116]) ).
cnf(refute_0_118,plain,
( multiply(inverse(multiply(inverse(X_106),greatest_lower_bound(X_105,X_106))),identity) != multiply(inverse(greatest_lower_bound(X_105,X_106)),X_106)
| multiply(inverse(multiply(inverse(X_106),greatest_lower_bound(X_105,X_106))),identity) != least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))),identity))
| multiply(inverse(greatest_lower_bound(X_105,X_106)),X_106) = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))),identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(inverse(X_106),greatest_lower_bound(X_105,X_106))),identity),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))),identity))) ),[0],$fot(multiply(inverse(greatest_lower_bound(X_105,X_106)),X_106))]]) ).
cnf(refute_0_119,plain,
( multiply(inverse(multiply(inverse(X_106),greatest_lower_bound(X_105,X_106))),identity) != least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))),identity))
| multiply(inverse(greatest_lower_bound(X_105,X_106)),X_106) = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))),identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(X_106),greatest_lower_bound(X_105,X_106))),identity),multiply(inverse(greatest_lower_bound(X_105,X_106)),X_106)) )],[refute_0_117,refute_0_118]) ).
cnf(refute_0_120,plain,
multiply(inverse(X_56),least_upper_bound(identity,X_56)) = least_upper_bound(identity,multiply(inverse(X_56),identity)),
inference(subst,[],[refute_0_29:[bind(X_49,$fot(identity)),bind(X_50,$fot(X_56))]]) ).
cnf(refute_0_121,plain,
inverse(X_56) = multiply(inverse(X_56),identity),
inference(subst,[],[refute_0_86:[bind(X_33,$fot(inverse(X_56)))]]) ).
cnf(refute_0_122,plain,
( inverse(X_56) != multiply(inverse(X_56),identity)
| multiply(inverse(X_56),identity) = inverse(X_56) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(inverse(X_56))),bind(Y0,$fot(multiply(inverse(X_56),identity)))]]) ).
cnf(refute_0_123,plain,
multiply(inverse(X_56),identity) = inverse(X_56),
inference(resolve,[$cnf( $equal(inverse(X_56),multiply(inverse(X_56),identity)) )],[refute_0_121,refute_0_122]) ).
cnf(refute_0_124,plain,
( multiply(inverse(X_56),identity) != inverse(X_56)
| multiply(inverse(X_56),least_upper_bound(identity,X_56)) != least_upper_bound(identity,multiply(inverse(X_56),identity))
| multiply(inverse(X_56),least_upper_bound(identity,X_56)) = least_upper_bound(identity,inverse(X_56)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_56),least_upper_bound(identity,X_56)),least_upper_bound(identity,multiply(inverse(X_56),identity))) ),[1,1],$fot(inverse(X_56))]]) ).
cnf(refute_0_125,plain,
( multiply(inverse(X_56),least_upper_bound(identity,X_56)) != least_upper_bound(identity,multiply(inverse(X_56),identity))
| multiply(inverse(X_56),least_upper_bound(identity,X_56)) = least_upper_bound(identity,inverse(X_56)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_56),identity),inverse(X_56)) )],[refute_0_123,refute_0_124]) ).
cnf(refute_0_126,plain,
multiply(inverse(X_56),least_upper_bound(identity,X_56)) = least_upper_bound(identity,inverse(X_56)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_56),least_upper_bound(identity,X_56)),least_upper_bound(identity,multiply(inverse(X_56),identity))) )],[refute_0_120,refute_0_125]) ).
cnf(refute_0_127,plain,
multiply(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(identity,greatest_lower_bound(identity,Y))) = least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y))),
inference(subst,[],[refute_0_126:[bind(X_56,$fot(greatest_lower_bound(identity,Y)))]]) ).
cnf(refute_0_128,plain,
least_upper_bound(identity,greatest_lower_bound(identity,Y)) = identity,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(identity))]]) ).
cnf(refute_0_129,plain,
( multiply(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(identity,greatest_lower_bound(identity,Y))) != least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y)))
| least_upper_bound(identity,greatest_lower_bound(identity,Y)) != identity
| multiply(inverse(greatest_lower_bound(identity,Y)),identity) = least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(identity,greatest_lower_bound(identity,Y))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y)))) ),[0,1],$fot(identity)]]) ).
cnf(refute_0_130,plain,
( multiply(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(identity,greatest_lower_bound(identity,Y))) != least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y)))
| multiply(inverse(greatest_lower_bound(identity,Y)),identity) = least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(identity,Y)),identity) )],[refute_0_128,refute_0_129]) ).
cnf(refute_0_131,plain,
multiply(inverse(greatest_lower_bound(identity,Y)),identity) = least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y))),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(identity,greatest_lower_bound(identity,Y))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y)))) )],[refute_0_127,refute_0_130]) ).
cnf(refute_0_132,plain,
multiply(inverse(greatest_lower_bound(identity,Y)),identity) = inverse(greatest_lower_bound(identity,Y)),
inference(subst,[],[refute_0_88:[bind(X_33,$fot(inverse(greatest_lower_bound(identity,Y))))]]) ).
cnf(refute_0_133,plain,
( multiply(inverse(greatest_lower_bound(identity,Y)),identity) != inverse(greatest_lower_bound(identity,Y))
| multiply(inverse(greatest_lower_bound(identity,Y)),identity) != least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y)))
| inverse(greatest_lower_bound(identity,Y)) = least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,Y)),identity),least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y)))) ),[0],$fot(inverse(greatest_lower_bound(identity,Y)))]]) ).
cnf(refute_0_134,plain,
( multiply(inverse(greatest_lower_bound(identity,Y)),identity) != least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y)))
| inverse(greatest_lower_bound(identity,Y)) = least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,Y)),identity),inverse(greatest_lower_bound(identity,Y))) )],[refute_0_132,refute_0_133]) ).
cnf(refute_0_135,plain,
inverse(greatest_lower_bound(identity,Y)) = least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y))),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,Y)),identity),least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y)))) )],[refute_0_131,refute_0_134]) ).
cnf(refute_0_136,plain,
( inverse(greatest_lower_bound(identity,Y)) != least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y)))
| least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y))) = inverse(greatest_lower_bound(identity,Y)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(inverse(greatest_lower_bound(identity,Y)))),bind(Y0,$fot(least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y)))))]]) ).
cnf(refute_0_137,plain,
least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y))) = inverse(greatest_lower_bound(identity,Y)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y)))) )],[refute_0_135,refute_0_136]) ).
cnf(refute_0_138,plain,
least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))) = inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))),
inference(subst,[],[refute_0_137:[bind(Y,$fot(multiply(inverse(X_106),X_105)))]]) ).
cnf(refute_0_139,plain,
least_upper_bound(X_10,greatest_lower_bound(X_10,X_11)) = X_10,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_10)),bind(Y,$fot(X_11))]]) ).
cnf(refute_0_140,plain,
greatest_lower_bound(X_11,X_10) = greatest_lower_bound(X_10,X_11),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_11)),bind(Y,$fot(X_10))]]) ).
cnf(refute_0_141,plain,
( greatest_lower_bound(X_11,X_10) != greatest_lower_bound(X_10,X_11)
| greatest_lower_bound(X_10,X_11) = greatest_lower_bound(X_11,X_10) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(greatest_lower_bound(X_11,X_10))),bind(Y0,$fot(greatest_lower_bound(X_10,X_11)))]]) ).
cnf(refute_0_142,plain,
greatest_lower_bound(X_10,X_11) = greatest_lower_bound(X_11,X_10),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_11,X_10),greatest_lower_bound(X_10,X_11)) )],[refute_0_140,refute_0_141]) ).
cnf(refute_0_143,plain,
( greatest_lower_bound(X_10,X_11) != greatest_lower_bound(X_11,X_10)
| least_upper_bound(X_10,greatest_lower_bound(X_10,X_11)) != X_10
| least_upper_bound(X_10,greatest_lower_bound(X_11,X_10)) = X_10 ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_10,greatest_lower_bound(X_10,X_11)),X_10) ),[0,1],$fot(greatest_lower_bound(X_11,X_10))]]) ).
cnf(refute_0_144,plain,
( least_upper_bound(X_10,greatest_lower_bound(X_10,X_11)) != X_10
| least_upper_bound(X_10,greatest_lower_bound(X_11,X_10)) = X_10 ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_10,X_11),greatest_lower_bound(X_11,X_10)) )],[refute_0_142,refute_0_143]) ).
cnf(refute_0_145,plain,
least_upper_bound(X_10,greatest_lower_bound(X_11,X_10)) = X_10,
inference(resolve,[$cnf( $equal(least_upper_bound(X_10,greatest_lower_bound(X_10,X_11)),X_10) )],[refute_0_139,refute_0_144]) ).
cnf(refute_0_146,plain,
least_upper_bound(least_upper_bound(X_42,least_upper_bound(X_43,X_11)),greatest_lower_bound(X_11,least_upper_bound(X_42,least_upper_bound(X_43,X_11)))) = least_upper_bound(X_42,least_upper_bound(X_43,X_11)),
inference(subst,[],[refute_0_145:[bind(X_10,$fot(least_upper_bound(X_42,least_upper_bound(X_43,X_11))))]]) ).
cnf(refute_0_147,plain,
greatest_lower_bound(X_6,least_upper_bound(X_6,X_7)) = X_6,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_6)),bind(Y,$fot(X_7))]]) ).
cnf(refute_0_148,plain,
least_upper_bound(X_7,X_6) = least_upper_bound(X_6,X_7),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_7)),bind(Y,$fot(X_6))]]) ).
cnf(refute_0_149,plain,
( least_upper_bound(X_7,X_6) != least_upper_bound(X_6,X_7)
| least_upper_bound(X_6,X_7) = least_upper_bound(X_7,X_6) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(least_upper_bound(X_7,X_6))),bind(Y0,$fot(least_upper_bound(X_6,X_7)))]]) ).
cnf(refute_0_150,plain,
least_upper_bound(X_6,X_7) = least_upper_bound(X_7,X_6),
inference(resolve,[$cnf( $equal(least_upper_bound(X_7,X_6),least_upper_bound(X_6,X_7)) )],[refute_0_148,refute_0_149]) ).
cnf(refute_0_151,plain,
( greatest_lower_bound(X_6,least_upper_bound(X_6,X_7)) != X_6
| least_upper_bound(X_6,X_7) != least_upper_bound(X_7,X_6)
| greatest_lower_bound(X_6,least_upper_bound(X_7,X_6)) = X_6 ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_6,least_upper_bound(X_6,X_7)),X_6) ),[0,1],$fot(least_upper_bound(X_7,X_6))]]) ).
cnf(refute_0_152,plain,
( greatest_lower_bound(X_6,least_upper_bound(X_6,X_7)) != X_6
| greatest_lower_bound(X_6,least_upper_bound(X_7,X_6)) = X_6 ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_6,X_7),least_upper_bound(X_7,X_6)) )],[refute_0_150,refute_0_151]) ).
cnf(refute_0_153,plain,
greatest_lower_bound(X_6,least_upper_bound(X_7,X_6)) = X_6,
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_6,least_upper_bound(X_6,X_7)),X_6) )],[refute_0_147,refute_0_152]) ).
cnf(refute_0_154,plain,
greatest_lower_bound(X_6,least_upper_bound(least_upper_bound(X_39,X_40),X_6)) = X_6,
inference(subst,[],[refute_0_153:[bind(X_7,$fot(least_upper_bound(X_39,X_40)))]]) ).
cnf(refute_0_155,plain,
least_upper_bound(X_39,least_upper_bound(X_40,X_6)) = least_upper_bound(least_upper_bound(X_39,X_40),X_6),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_39)),bind(Y,$fot(X_40)),bind(Z,$fot(X_6))]]) ).
cnf(refute_0_156,plain,
( least_upper_bound(X_39,least_upper_bound(X_40,X_6)) != least_upper_bound(least_upper_bound(X_39,X_40),X_6)
| least_upper_bound(least_upper_bound(X_39,X_40),X_6) = least_upper_bound(X_39,least_upper_bound(X_40,X_6)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(least_upper_bound(X_39,least_upper_bound(X_40,X_6)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X_39,X_40),X_6)))]]) ).
cnf(refute_0_157,plain,
least_upper_bound(least_upper_bound(X_39,X_40),X_6) = least_upper_bound(X_39,least_upper_bound(X_40,X_6)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_39,least_upper_bound(X_40,X_6)),least_upper_bound(least_upper_bound(X_39,X_40),X_6)) )],[refute_0_155,refute_0_156]) ).
cnf(refute_0_158,plain,
( greatest_lower_bound(X_6,least_upper_bound(least_upper_bound(X_39,X_40),X_6)) != X_6
| least_upper_bound(least_upper_bound(X_39,X_40),X_6) != least_upper_bound(X_39,least_upper_bound(X_40,X_6))
| greatest_lower_bound(X_6,least_upper_bound(X_39,least_upper_bound(X_40,X_6))) = X_6 ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_6,least_upper_bound(least_upper_bound(X_39,X_40),X_6)),X_6) ),[0,1],$fot(least_upper_bound(X_39,least_upper_bound(X_40,X_6)))]]) ).
cnf(refute_0_159,plain,
( greatest_lower_bound(X_6,least_upper_bound(least_upper_bound(X_39,X_40),X_6)) != X_6
| greatest_lower_bound(X_6,least_upper_bound(X_39,least_upper_bound(X_40,X_6))) = X_6 ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_39,X_40),X_6),least_upper_bound(X_39,least_upper_bound(X_40,X_6))) )],[refute_0_157,refute_0_158]) ).
cnf(refute_0_160,plain,
greatest_lower_bound(X_6,least_upper_bound(X_39,least_upper_bound(X_40,X_6))) = X_6,
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_6,least_upper_bound(least_upper_bound(X_39,X_40),X_6)),X_6) )],[refute_0_154,refute_0_159]) ).
cnf(refute_0_161,plain,
greatest_lower_bound(X_11,least_upper_bound(X_42,least_upper_bound(X_43,X_11))) = X_11,
inference(subst,[],[refute_0_160:[bind(X_39,$fot(X_42)),bind(X_40,$fot(X_43)),bind(X_6,$fot(X_11))]]) ).
cnf(refute_0_162,plain,
( greatest_lower_bound(X_11,least_upper_bound(X_42,least_upper_bound(X_43,X_11))) != X_11
| least_upper_bound(least_upper_bound(X_42,least_upper_bound(X_43,X_11)),greatest_lower_bound(X_11,least_upper_bound(X_42,least_upper_bound(X_43,X_11)))) != least_upper_bound(X_42,least_upper_bound(X_43,X_11))
| least_upper_bound(least_upper_bound(X_42,least_upper_bound(X_43,X_11)),X_11) = least_upper_bound(X_42,least_upper_bound(X_43,X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_42,least_upper_bound(X_43,X_11)),greatest_lower_bound(X_11,least_upper_bound(X_42,least_upper_bound(X_43,X_11)))),least_upper_bound(X_42,least_upper_bound(X_43,X_11))) ),[0,1],$fot(X_11)]]) ).
cnf(refute_0_163,plain,
( least_upper_bound(least_upper_bound(X_42,least_upper_bound(X_43,X_11)),greatest_lower_bound(X_11,least_upper_bound(X_42,least_upper_bound(X_43,X_11)))) != least_upper_bound(X_42,least_upper_bound(X_43,X_11))
| least_upper_bound(least_upper_bound(X_42,least_upper_bound(X_43,X_11)),X_11) = least_upper_bound(X_42,least_upper_bound(X_43,X_11)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_11,least_upper_bound(X_42,least_upper_bound(X_43,X_11))),X_11) )],[refute_0_161,refute_0_162]) ).
cnf(refute_0_164,plain,
least_upper_bound(least_upper_bound(X_42,least_upper_bound(X_43,X_11)),X_11) = least_upper_bound(X_42,least_upper_bound(X_43,X_11)),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_42,least_upper_bound(X_43,X_11)),greatest_lower_bound(X_11,least_upper_bound(X_42,least_upper_bound(X_43,X_11)))),least_upper_bound(X_42,least_upper_bound(X_43,X_11))) )],[refute_0_146,refute_0_163]) ).
cnf(refute_0_165,plain,
least_upper_bound(least_upper_bound(X_15,Y),greatest_lower_bound(X_15,least_upper_bound(X_15,Y))) = least_upper_bound(X_15,Y),
inference(subst,[],[refute_0_145:[bind(X_10,$fot(least_upper_bound(X_15,Y))),bind(X_11,$fot(X_15))]]) ).
cnf(refute_0_166,plain,
greatest_lower_bound(X_15,least_upper_bound(X_15,Y)) = X_15,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_15))]]) ).
cnf(refute_0_167,plain,
( greatest_lower_bound(X_15,least_upper_bound(X_15,Y)) != X_15
| least_upper_bound(least_upper_bound(X_15,Y),greatest_lower_bound(X_15,least_upper_bound(X_15,Y))) != least_upper_bound(X_15,Y)
| least_upper_bound(least_upper_bound(X_15,Y),X_15) = least_upper_bound(X_15,Y) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_15,Y),greatest_lower_bound(X_15,least_upper_bound(X_15,Y))),least_upper_bound(X_15,Y)) ),[0,1],$fot(X_15)]]) ).
cnf(refute_0_168,plain,
( least_upper_bound(least_upper_bound(X_15,Y),greatest_lower_bound(X_15,least_upper_bound(X_15,Y))) != least_upper_bound(X_15,Y)
| least_upper_bound(least_upper_bound(X_15,Y),X_15) = least_upper_bound(X_15,Y) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_15,least_upper_bound(X_15,Y)),X_15) )],[refute_0_166,refute_0_167]) ).
cnf(refute_0_169,plain,
least_upper_bound(least_upper_bound(X_15,Y),X_15) = least_upper_bound(X_15,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_15,Y),greatest_lower_bound(X_15,least_upper_bound(X_15,Y))),least_upper_bound(X_15,Y)) )],[refute_0_165,refute_0_168]) ).
cnf(refute_0_170,plain,
( least_upper_bound(X,least_upper_bound(Y,Z)) != least_upper_bound(least_upper_bound(X,Y),Z)
| least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(Y,Z)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X,Y),Z)))]]) ).
cnf(refute_0_171,plain,
least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,Z)),least_upper_bound(least_upper_bound(X,Y),Z)) )],[associativity_of_lub,refute_0_170]) ).
cnf(refute_0_172,plain,
least_upper_bound(least_upper_bound(X_15,Y),X_15) = least_upper_bound(X_15,least_upper_bound(Y,X_15)),
inference(subst,[],[refute_0_171:[bind(X,$fot(X_15)),bind(Z,$fot(X_15))]]) ).
cnf(refute_0_173,plain,
( least_upper_bound(least_upper_bound(X_15,Y),X_15) != least_upper_bound(X_15,Y)
| least_upper_bound(least_upper_bound(X_15,Y),X_15) != least_upper_bound(X_15,least_upper_bound(Y,X_15))
| least_upper_bound(X_15,least_upper_bound(Y,X_15)) = least_upper_bound(X_15,Y) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_15,Y),X_15),least_upper_bound(X_15,Y)) ),[0],$fot(least_upper_bound(X_15,least_upper_bound(Y,X_15)))]]) ).
cnf(refute_0_174,plain,
( least_upper_bound(least_upper_bound(X_15,Y),X_15) != least_upper_bound(X_15,Y)
| least_upper_bound(X_15,least_upper_bound(Y,X_15)) = least_upper_bound(X_15,Y) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_15,Y),X_15),least_upper_bound(X_15,least_upper_bound(Y,X_15))) )],[refute_0_172,refute_0_173]) ).
cnf(refute_0_175,plain,
least_upper_bound(X_15,least_upper_bound(Y,X_15)) = least_upper_bound(X_15,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_15,Y),X_15),least_upper_bound(X_15,Y)) )],[refute_0_169,refute_0_174]) ).
cnf(refute_0_176,plain,
least_upper_bound(X_11,least_upper_bound(X_43,X_11)) = least_upper_bound(X_11,X_43),
inference(subst,[],[refute_0_175:[bind(Y,$fot(X_43)),bind(X_15,$fot(X_11))]]) ).
cnf(refute_0_177,plain,
least_upper_bound(X_42,least_upper_bound(X_11,least_upper_bound(X_43,X_11))) = least_upper_bound(X_42,least_upper_bound(X_11,least_upper_bound(X_43,X_11))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_42,least_upper_bound(X_11,least_upper_bound(X_43,X_11))))]]) ).
cnf(refute_0_178,plain,
( least_upper_bound(X_11,least_upper_bound(X_43,X_11)) != least_upper_bound(X_11,X_43)
| least_upper_bound(X_42,least_upper_bound(X_11,least_upper_bound(X_43,X_11))) != least_upper_bound(X_42,least_upper_bound(X_11,least_upper_bound(X_43,X_11)))
| least_upper_bound(X_42,least_upper_bound(X_11,least_upper_bound(X_43,X_11))) = least_upper_bound(X_42,least_upper_bound(X_11,X_43)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_42,least_upper_bound(X_11,least_upper_bound(X_43,X_11))),least_upper_bound(X_42,least_upper_bound(X_11,least_upper_bound(X_43,X_11)))) ),[1,1],$fot(least_upper_bound(X_11,X_43))]]) ).
cnf(refute_0_179,plain,
( least_upper_bound(X_11,least_upper_bound(X_43,X_11)) != least_upper_bound(X_11,X_43)
| least_upper_bound(X_42,least_upper_bound(X_11,least_upper_bound(X_43,X_11))) = least_upper_bound(X_42,least_upper_bound(X_11,X_43)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_42,least_upper_bound(X_11,least_upper_bound(X_43,X_11))),least_upper_bound(X_42,least_upper_bound(X_11,least_upper_bound(X_43,X_11)))) )],[refute_0_177,refute_0_178]) ).
cnf(refute_0_180,plain,
least_upper_bound(X_42,least_upper_bound(X_11,least_upper_bound(X_43,X_11))) = least_upper_bound(X_42,least_upper_bound(X_11,X_43)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_11,least_upper_bound(X_43,X_11)),least_upper_bound(X_11,X_43)) )],[refute_0_176,refute_0_179]) ).
cnf(refute_0_181,plain,
least_upper_bound(X_39,least_upper_bound(X_40,X_41)) = least_upper_bound(least_upper_bound(X_39,X_40),X_41),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_39)),bind(Y,$fot(X_40)),bind(Z,$fot(X_41))]]) ).
cnf(refute_0_182,plain,
least_upper_bound(X_41,X_40) = least_upper_bound(X_40,X_41),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_41)),bind(Y,$fot(X_40))]]) ).
cnf(refute_0_183,plain,
( least_upper_bound(X_41,X_40) != least_upper_bound(X_40,X_41)
| least_upper_bound(X_40,X_41) = least_upper_bound(X_41,X_40) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(least_upper_bound(X_41,X_40))),bind(Y0,$fot(least_upper_bound(X_40,X_41)))]]) ).
cnf(refute_0_184,plain,
least_upper_bound(X_40,X_41) = least_upper_bound(X_41,X_40),
inference(resolve,[$cnf( $equal(least_upper_bound(X_41,X_40),least_upper_bound(X_40,X_41)) )],[refute_0_182,refute_0_183]) ).
cnf(refute_0_185,plain,
( least_upper_bound(X_39,least_upper_bound(X_40,X_41)) != least_upper_bound(least_upper_bound(X_39,X_40),X_41)
| least_upper_bound(X_40,X_41) != least_upper_bound(X_41,X_40)
| least_upper_bound(X_39,least_upper_bound(X_41,X_40)) = least_upper_bound(least_upper_bound(X_39,X_40),X_41) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_39,least_upper_bound(X_40,X_41)),least_upper_bound(least_upper_bound(X_39,X_40),X_41)) ),[0,1],$fot(least_upper_bound(X_41,X_40))]]) ).
cnf(refute_0_186,plain,
( least_upper_bound(X_39,least_upper_bound(X_40,X_41)) != least_upper_bound(least_upper_bound(X_39,X_40),X_41)
| least_upper_bound(X_39,least_upper_bound(X_41,X_40)) = least_upper_bound(least_upper_bound(X_39,X_40),X_41) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_40,X_41),least_upper_bound(X_41,X_40)) )],[refute_0_184,refute_0_185]) ).
cnf(refute_0_187,plain,
least_upper_bound(X_39,least_upper_bound(X_41,X_40)) = least_upper_bound(least_upper_bound(X_39,X_40),X_41),
inference(resolve,[$cnf( $equal(least_upper_bound(X_39,least_upper_bound(X_40,X_41)),least_upper_bound(least_upper_bound(X_39,X_40),X_41)) )],[refute_0_181,refute_0_186]) ).
cnf(refute_0_188,plain,
least_upper_bound(least_upper_bound(X_39,X_40),X_41) = least_upper_bound(X_39,least_upper_bound(X_40,X_41)),
inference(subst,[],[refute_0_171:[bind(X,$fot(X_39)),bind(Y,$fot(X_40)),bind(Z,$fot(X_41))]]) ).
cnf(refute_0_189,plain,
( least_upper_bound(X_39,least_upper_bound(X_41,X_40)) != least_upper_bound(least_upper_bound(X_39,X_40),X_41)
| least_upper_bound(least_upper_bound(X_39,X_40),X_41) != least_upper_bound(X_39,least_upper_bound(X_40,X_41))
| least_upper_bound(X_39,least_upper_bound(X_41,X_40)) = least_upper_bound(X_39,least_upper_bound(X_40,X_41)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_39,least_upper_bound(X_41,X_40)),least_upper_bound(X_39,least_upper_bound(X_40,X_41))) ),[0],$fot(least_upper_bound(least_upper_bound(X_39,X_40),X_41))]]) ).
cnf(refute_0_190,plain,
( least_upper_bound(X_39,least_upper_bound(X_41,X_40)) != least_upper_bound(least_upper_bound(X_39,X_40),X_41)
| least_upper_bound(X_39,least_upper_bound(X_41,X_40)) = least_upper_bound(X_39,least_upper_bound(X_40,X_41)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_39,X_40),X_41),least_upper_bound(X_39,least_upper_bound(X_40,X_41))) )],[refute_0_188,refute_0_189]) ).
cnf(refute_0_191,plain,
least_upper_bound(X_39,least_upper_bound(X_41,X_40)) = least_upper_bound(X_39,least_upper_bound(X_40,X_41)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_39,least_upper_bound(X_41,X_40)),least_upper_bound(least_upper_bound(X_39,X_40),X_41)) )],[refute_0_187,refute_0_190]) ).
cnf(refute_0_192,plain,
( least_upper_bound(X_39,least_upper_bound(X_41,X_40)) != least_upper_bound(X_39,least_upper_bound(X_40,X_41))
| least_upper_bound(X_39,least_upper_bound(X_40,X_41)) = least_upper_bound(X_39,least_upper_bound(X_41,X_40)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(least_upper_bound(X_39,least_upper_bound(X_41,X_40)))),bind(Y0,$fot(least_upper_bound(X_39,least_upper_bound(X_40,X_41))))]]) ).
cnf(refute_0_193,plain,
least_upper_bound(X_39,least_upper_bound(X_40,X_41)) = least_upper_bound(X_39,least_upper_bound(X_41,X_40)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_39,least_upper_bound(X_41,X_40)),least_upper_bound(X_39,least_upper_bound(X_40,X_41))) )],[refute_0_191,refute_0_192]) ).
cnf(refute_0_194,plain,
least_upper_bound(X_42,least_upper_bound(least_upper_bound(X_43,X_11),X_11)) = least_upper_bound(X_42,least_upper_bound(X_11,least_upper_bound(X_43,X_11))),
inference(subst,[],[refute_0_193:[bind(X_39,$fot(X_42)),bind(X_40,$fot(least_upper_bound(X_43,X_11))),bind(X_41,$fot(X_11))]]) ).
cnf(refute_0_195,plain,
least_upper_bound(least_upper_bound(X_42,least_upper_bound(X_43,X_11)),X_11) = least_upper_bound(X_42,least_upper_bound(least_upper_bound(X_43,X_11),X_11)),
inference(subst,[],[refute_0_171:[bind(X,$fot(X_42)),bind(Y,$fot(least_upper_bound(X_43,X_11))),bind(Z,$fot(X_11))]]) ).
cnf(refute_0_196,plain,
( least_upper_bound(X_42,least_upper_bound(least_upper_bound(X_43,X_11),X_11)) != least_upper_bound(X_42,least_upper_bound(X_11,least_upper_bound(X_43,X_11)))
| least_upper_bound(least_upper_bound(X_42,least_upper_bound(X_43,X_11)),X_11) != least_upper_bound(X_42,least_upper_bound(least_upper_bound(X_43,X_11),X_11))
| least_upper_bound(least_upper_bound(X_42,least_upper_bound(X_43,X_11)),X_11) = least_upper_bound(X_42,least_upper_bound(X_11,least_upper_bound(X_43,X_11))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_42,least_upper_bound(X_43,X_11)),X_11))),bind(Y0,$fot(least_upper_bound(X_42,least_upper_bound(least_upper_bound(X_43,X_11),X_11)))),bind(Z0,$fot(least_upper_bound(X_42,least_upper_bound(X_11,least_upper_bound(X_43,X_11)))))]]) ).
cnf(refute_0_197,plain,
( least_upper_bound(X_42,least_upper_bound(least_upper_bound(X_43,X_11),X_11)) != least_upper_bound(X_42,least_upper_bound(X_11,least_upper_bound(X_43,X_11)))
| least_upper_bound(least_upper_bound(X_42,least_upper_bound(X_43,X_11)),X_11) = least_upper_bound(X_42,least_upper_bound(X_11,least_upper_bound(X_43,X_11))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_42,least_upper_bound(X_43,X_11)),X_11),least_upper_bound(X_42,least_upper_bound(least_upper_bound(X_43,X_11),X_11))) )],[refute_0_195,refute_0_196]) ).
cnf(refute_0_198,plain,
least_upper_bound(least_upper_bound(X_42,least_upper_bound(X_43,X_11)),X_11) = least_upper_bound(X_42,least_upper_bound(X_11,least_upper_bound(X_43,X_11))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_42,least_upper_bound(least_upper_bound(X_43,X_11),X_11)),least_upper_bound(X_42,least_upper_bound(X_11,least_upper_bound(X_43,X_11)))) )],[refute_0_194,refute_0_197]) ).
cnf(refute_0_199,plain,
( least_upper_bound(X_42,least_upper_bound(X_11,least_upper_bound(X_43,X_11))) != least_upper_bound(X_42,least_upper_bound(X_11,X_43))
| least_upper_bound(least_upper_bound(X_42,least_upper_bound(X_43,X_11)),X_11) != least_upper_bound(X_42,least_upper_bound(X_11,least_upper_bound(X_43,X_11)))
| least_upper_bound(least_upper_bound(X_42,least_upper_bound(X_43,X_11)),X_11) = least_upper_bound(X_42,least_upper_bound(X_11,X_43)) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_42,least_upper_bound(X_43,X_11)),X_11))),bind(Y0,$fot(least_upper_bound(X_42,least_upper_bound(X_11,least_upper_bound(X_43,X_11))))),bind(Z0,$fot(least_upper_bound(X_42,least_upper_bound(X_11,X_43))))]]) ).
cnf(refute_0_200,plain,
( least_upper_bound(X_42,least_upper_bound(X_11,least_upper_bound(X_43,X_11))) != least_upper_bound(X_42,least_upper_bound(X_11,X_43))
| least_upper_bound(least_upper_bound(X_42,least_upper_bound(X_43,X_11)),X_11) = least_upper_bound(X_42,least_upper_bound(X_11,X_43)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_42,least_upper_bound(X_43,X_11)),X_11),least_upper_bound(X_42,least_upper_bound(X_11,least_upper_bound(X_43,X_11)))) )],[refute_0_198,refute_0_199]) ).
cnf(refute_0_201,plain,
least_upper_bound(least_upper_bound(X_42,least_upper_bound(X_43,X_11)),X_11) = least_upper_bound(X_42,least_upper_bound(X_11,X_43)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_42,least_upper_bound(X_11,least_upper_bound(X_43,X_11))),least_upper_bound(X_42,least_upper_bound(X_11,X_43))) )],[refute_0_180,refute_0_200]) ).
cnf(refute_0_202,plain,
( least_upper_bound(least_upper_bound(X_42,least_upper_bound(X_43,X_11)),X_11) != least_upper_bound(X_42,least_upper_bound(X_11,X_43))
| least_upper_bound(least_upper_bound(X_42,least_upper_bound(X_43,X_11)),X_11) != least_upper_bound(X_42,least_upper_bound(X_43,X_11))
| least_upper_bound(X_42,least_upper_bound(X_11,X_43)) = least_upper_bound(X_42,least_upper_bound(X_43,X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_42,least_upper_bound(X_43,X_11)),X_11),least_upper_bound(X_42,least_upper_bound(X_43,X_11))) ),[0],$fot(least_upper_bound(X_42,least_upper_bound(X_11,X_43)))]]) ).
cnf(refute_0_203,plain,
( least_upper_bound(least_upper_bound(X_42,least_upper_bound(X_43,X_11)),X_11) != least_upper_bound(X_42,least_upper_bound(X_43,X_11))
| least_upper_bound(X_42,least_upper_bound(X_11,X_43)) = least_upper_bound(X_42,least_upper_bound(X_43,X_11)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_42,least_upper_bound(X_43,X_11)),X_11),least_upper_bound(X_42,least_upper_bound(X_11,X_43))) )],[refute_0_201,refute_0_202]) ).
cnf(refute_0_204,plain,
least_upper_bound(X_42,least_upper_bound(X_11,X_43)) = least_upper_bound(X_42,least_upper_bound(X_43,X_11)),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_42,least_upper_bound(X_43,X_11)),X_11),least_upper_bound(X_42,least_upper_bound(X_43,X_11))) )],[refute_0_164,refute_0_203]) ).
cnf(refute_0_205,plain,
least_upper_bound(X_42,least_upper_bound(inverse(greatest_lower_bound(identity,X_262)),identity)) = least_upper_bound(X_42,least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_262)))),
inference(subst,[],[refute_0_204:[bind(X_11,$fot(inverse(greatest_lower_bound(identity,X_262)))),bind(X_43,$fot(identity))]]) ).
cnf(refute_0_206,plain,
inverse(greatest_lower_bound(identity,X_262)) = least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_262))),
inference(subst,[],[refute_0_135:[bind(Y,$fot(X_262))]]) ).
cnf(refute_0_207,plain,
( inverse(greatest_lower_bound(identity,X_262)) != least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_262)))
| least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_262))) = inverse(greatest_lower_bound(identity,X_262)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(inverse(greatest_lower_bound(identity,X_262)))),bind(Y0,$fot(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_262)))))]]) ).
cnf(refute_0_208,plain,
least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_262))) = inverse(greatest_lower_bound(identity,X_262)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,X_262)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_262)))) )],[refute_0_206,refute_0_207]) ).
cnf(refute_0_209,plain,
( least_upper_bound(X_42,least_upper_bound(inverse(greatest_lower_bound(identity,X_262)),identity)) != least_upper_bound(X_42,least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_262))))
| least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_262))) != inverse(greatest_lower_bound(identity,X_262))
| least_upper_bound(X_42,least_upper_bound(inverse(greatest_lower_bound(identity,X_262)),identity)) = least_upper_bound(X_42,inverse(greatest_lower_bound(identity,X_262))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_42,least_upper_bound(inverse(greatest_lower_bound(identity,X_262)),identity)),least_upper_bound(X_42,least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_262))))) ),[1,1],$fot(inverse(greatest_lower_bound(identity,X_262)))]]) ).
cnf(refute_0_210,plain,
( least_upper_bound(X_42,least_upper_bound(inverse(greatest_lower_bound(identity,X_262)),identity)) != least_upper_bound(X_42,least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_262))))
| least_upper_bound(X_42,least_upper_bound(inverse(greatest_lower_bound(identity,X_262)),identity)) = least_upper_bound(X_42,inverse(greatest_lower_bound(identity,X_262))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_262))),inverse(greatest_lower_bound(identity,X_262))) )],[refute_0_208,refute_0_209]) ).
cnf(refute_0_211,plain,
least_upper_bound(X_42,least_upper_bound(inverse(greatest_lower_bound(identity,X_262)),identity)) = least_upper_bound(X_42,inverse(greatest_lower_bound(identity,X_262))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_42,least_upper_bound(inverse(greatest_lower_bound(identity,X_262)),identity)),least_upper_bound(X_42,least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_262))))) )],[refute_0_205,refute_0_210]) ).
cnf(refute_0_212,plain,
multiply(inverse(greatest_lower_bound(X_11,identity)),least_upper_bound(identity,greatest_lower_bound(X_11,identity))) = least_upper_bound(identity,inverse(greatest_lower_bound(X_11,identity))),
inference(subst,[],[refute_0_126:[bind(X_56,$fot(greatest_lower_bound(X_11,identity)))]]) ).
cnf(refute_0_213,plain,
least_upper_bound(identity,greatest_lower_bound(X_11,identity)) = identity,
inference(subst,[],[refute_0_145:[bind(X_10,$fot(identity))]]) ).
cnf(refute_0_214,plain,
( multiply(inverse(greatest_lower_bound(X_11,identity)),least_upper_bound(identity,greatest_lower_bound(X_11,identity))) != least_upper_bound(identity,inverse(greatest_lower_bound(X_11,identity)))
| least_upper_bound(identity,greatest_lower_bound(X_11,identity)) != identity
| multiply(inverse(greatest_lower_bound(X_11,identity)),identity) = least_upper_bound(identity,inverse(greatest_lower_bound(X_11,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_11,identity)),least_upper_bound(identity,greatest_lower_bound(X_11,identity))),least_upper_bound(identity,inverse(greatest_lower_bound(X_11,identity)))) ),[0,1],$fot(identity)]]) ).
cnf(refute_0_215,plain,
( multiply(inverse(greatest_lower_bound(X_11,identity)),least_upper_bound(identity,greatest_lower_bound(X_11,identity))) != least_upper_bound(identity,inverse(greatest_lower_bound(X_11,identity)))
| multiply(inverse(greatest_lower_bound(X_11,identity)),identity) = least_upper_bound(identity,inverse(greatest_lower_bound(X_11,identity))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(X_11,identity)),identity) )],[refute_0_213,refute_0_214]) ).
cnf(refute_0_216,plain,
multiply(inverse(greatest_lower_bound(X_11,identity)),identity) = least_upper_bound(identity,inverse(greatest_lower_bound(X_11,identity))),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_11,identity)),least_upper_bound(identity,greatest_lower_bound(X_11,identity))),least_upper_bound(identity,inverse(greatest_lower_bound(X_11,identity)))) )],[refute_0_212,refute_0_215]) ).
cnf(refute_0_217,plain,
multiply(inverse(greatest_lower_bound(X_11,identity)),identity) = inverse(greatest_lower_bound(X_11,identity)),
inference(subst,[],[refute_0_88:[bind(X_33,$fot(inverse(greatest_lower_bound(X_11,identity))))]]) ).
cnf(refute_0_218,plain,
( multiply(inverse(greatest_lower_bound(X_11,identity)),identity) != inverse(greatest_lower_bound(X_11,identity))
| multiply(inverse(greatest_lower_bound(X_11,identity)),identity) != least_upper_bound(identity,inverse(greatest_lower_bound(X_11,identity)))
| inverse(greatest_lower_bound(X_11,identity)) = least_upper_bound(identity,inverse(greatest_lower_bound(X_11,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_11,identity)),identity),least_upper_bound(identity,inverse(greatest_lower_bound(X_11,identity)))) ),[0],$fot(inverse(greatest_lower_bound(X_11,identity)))]]) ).
cnf(refute_0_219,plain,
( multiply(inverse(greatest_lower_bound(X_11,identity)),identity) != least_upper_bound(identity,inverse(greatest_lower_bound(X_11,identity)))
| inverse(greatest_lower_bound(X_11,identity)) = least_upper_bound(identity,inverse(greatest_lower_bound(X_11,identity))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_11,identity)),identity),inverse(greatest_lower_bound(X_11,identity))) )],[refute_0_217,refute_0_218]) ).
cnf(refute_0_220,plain,
inverse(greatest_lower_bound(X_11,identity)) = least_upper_bound(identity,inverse(greatest_lower_bound(X_11,identity))),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_11,identity)),identity),least_upper_bound(identity,inverse(greatest_lower_bound(X_11,identity)))) )],[refute_0_216,refute_0_219]) ).
cnf(refute_0_221,plain,
( inverse(greatest_lower_bound(X_11,identity)) != least_upper_bound(identity,inverse(greatest_lower_bound(X_11,identity)))
| least_upper_bound(identity,inverse(greatest_lower_bound(X_11,identity))) = inverse(greatest_lower_bound(X_11,identity)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(inverse(greatest_lower_bound(X_11,identity)))),bind(Y0,$fot(least_upper_bound(identity,inverse(greatest_lower_bound(X_11,identity)))))]]) ).
cnf(refute_0_222,plain,
least_upper_bound(identity,inverse(greatest_lower_bound(X_11,identity))) = inverse(greatest_lower_bound(X_11,identity)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_11,identity)),least_upper_bound(identity,inverse(greatest_lower_bound(X_11,identity)))) )],[refute_0_220,refute_0_221]) ).
cnf(refute_0_223,plain,
least_upper_bound(identity,inverse(greatest_lower_bound(X_262,identity))) = inverse(greatest_lower_bound(X_262,identity)),
inference(subst,[],[refute_0_222:[bind(X_11,$fot(X_262))]]) ).
cnf(refute_0_224,plain,
least_upper_bound(X_42,least_upper_bound(identity,inverse(greatest_lower_bound(X_262,identity)))) = least_upper_bound(X_42,least_upper_bound(identity,inverse(greatest_lower_bound(X_262,identity)))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_42,least_upper_bound(identity,inverse(greatest_lower_bound(X_262,identity)))))]]) ).
cnf(refute_0_225,plain,
( least_upper_bound(X_42,least_upper_bound(identity,inverse(greatest_lower_bound(X_262,identity)))) != least_upper_bound(X_42,least_upper_bound(identity,inverse(greatest_lower_bound(X_262,identity))))
| least_upper_bound(identity,inverse(greatest_lower_bound(X_262,identity))) != inverse(greatest_lower_bound(X_262,identity))
| least_upper_bound(X_42,least_upper_bound(identity,inverse(greatest_lower_bound(X_262,identity)))) = least_upper_bound(X_42,inverse(greatest_lower_bound(X_262,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_42,least_upper_bound(identity,inverse(greatest_lower_bound(X_262,identity)))),least_upper_bound(X_42,least_upper_bound(identity,inverse(greatest_lower_bound(X_262,identity))))) ),[1,1],$fot(inverse(greatest_lower_bound(X_262,identity)))]]) ).
cnf(refute_0_226,plain,
( least_upper_bound(identity,inverse(greatest_lower_bound(X_262,identity))) != inverse(greatest_lower_bound(X_262,identity))
| least_upper_bound(X_42,least_upper_bound(identity,inverse(greatest_lower_bound(X_262,identity)))) = least_upper_bound(X_42,inverse(greatest_lower_bound(X_262,identity))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_42,least_upper_bound(identity,inverse(greatest_lower_bound(X_262,identity)))),least_upper_bound(X_42,least_upper_bound(identity,inverse(greatest_lower_bound(X_262,identity))))) )],[refute_0_224,refute_0_225]) ).
cnf(refute_0_227,plain,
least_upper_bound(X_42,least_upper_bound(identity,inverse(greatest_lower_bound(X_262,identity)))) = least_upper_bound(X_42,inverse(greatest_lower_bound(X_262,identity))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(greatest_lower_bound(X_262,identity))),inverse(greatest_lower_bound(X_262,identity))) )],[refute_0_223,refute_0_226]) ).
cnf(refute_0_228,plain,
least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(Y,X_40))) = least_upper_bound(least_upper_bound(X_39,X_40),least_upper_bound(Y,X_40)),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_39)),bind(Y,$fot(X_40)),bind(Z,$fot(least_upper_bound(Y,X_40)))]]) ).
cnf(refute_0_229,plain,
least_upper_bound(X_40,least_upper_bound(Y,X_40)) = least_upper_bound(X_40,Y),
inference(subst,[],[refute_0_175:[bind(X_15,$fot(X_40))]]) ).
cnf(refute_0_230,plain,
( least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(Y,X_40))) != least_upper_bound(least_upper_bound(X_39,X_40),least_upper_bound(Y,X_40))
| least_upper_bound(X_40,least_upper_bound(Y,X_40)) != least_upper_bound(X_40,Y)
| least_upper_bound(X_39,least_upper_bound(X_40,Y)) = least_upper_bound(least_upper_bound(X_39,X_40),least_upper_bound(Y,X_40)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(Y,X_40))),least_upper_bound(least_upper_bound(X_39,X_40),least_upper_bound(Y,X_40))) ),[0,1],$fot(least_upper_bound(X_40,Y))]]) ).
cnf(refute_0_231,plain,
( least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(Y,X_40))) != least_upper_bound(least_upper_bound(X_39,X_40),least_upper_bound(Y,X_40))
| least_upper_bound(X_39,least_upper_bound(X_40,Y)) = least_upper_bound(least_upper_bound(X_39,X_40),least_upper_bound(Y,X_40)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_40,least_upper_bound(Y,X_40)),least_upper_bound(X_40,Y)) )],[refute_0_229,refute_0_230]) ).
cnf(refute_0_232,plain,
least_upper_bound(X_39,least_upper_bound(X_40,Y)) = least_upper_bound(least_upper_bound(X_39,X_40),least_upper_bound(Y,X_40)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(Y,X_40))),least_upper_bound(least_upper_bound(X_39,X_40),least_upper_bound(Y,X_40))) )],[refute_0_228,refute_0_231]) ).
cnf(refute_0_233,plain,
least_upper_bound(least_upper_bound(X_39,X_40),Y) = least_upper_bound(X_39,least_upper_bound(X_40,Y)),
inference(subst,[],[refute_0_171:[bind(X,$fot(X_39)),bind(Y,$fot(X_40)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_234,plain,
least_upper_bound(X_40,least_upper_bound(least_upper_bound(X_39,X_40),Y)) = least_upper_bound(X_40,least_upper_bound(least_upper_bound(X_39,X_40),Y)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_40,least_upper_bound(least_upper_bound(X_39,X_40),Y)))]]) ).
cnf(refute_0_235,plain,
( least_upper_bound(X_40,least_upper_bound(least_upper_bound(X_39,X_40),Y)) != least_upper_bound(X_40,least_upper_bound(least_upper_bound(X_39,X_40),Y))
| least_upper_bound(least_upper_bound(X_39,X_40),Y) != least_upper_bound(X_39,least_upper_bound(X_40,Y))
| least_upper_bound(X_40,least_upper_bound(least_upper_bound(X_39,X_40),Y)) = least_upper_bound(X_40,least_upper_bound(X_39,least_upper_bound(X_40,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_40,least_upper_bound(least_upper_bound(X_39,X_40),Y)),least_upper_bound(X_40,least_upper_bound(least_upper_bound(X_39,X_40),Y))) ),[1,1],$fot(least_upper_bound(X_39,least_upper_bound(X_40,Y)))]]) ).
cnf(refute_0_236,plain,
( least_upper_bound(least_upper_bound(X_39,X_40),Y) != least_upper_bound(X_39,least_upper_bound(X_40,Y))
| least_upper_bound(X_40,least_upper_bound(least_upper_bound(X_39,X_40),Y)) = least_upper_bound(X_40,least_upper_bound(X_39,least_upper_bound(X_40,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_40,least_upper_bound(least_upper_bound(X_39,X_40),Y)),least_upper_bound(X_40,least_upper_bound(least_upper_bound(X_39,X_40),Y))) )],[refute_0_234,refute_0_235]) ).
cnf(refute_0_237,plain,
least_upper_bound(X_40,least_upper_bound(least_upper_bound(X_39,X_40),Y)) = least_upper_bound(X_40,least_upper_bound(X_39,least_upper_bound(X_40,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_39,X_40),Y),least_upper_bound(X_39,least_upper_bound(X_40,Y))) )],[refute_0_233,refute_0_236]) ).
cnf(refute_0_238,plain,
least_upper_bound(X,least_upper_bound(X_39,X_40)) = least_upper_bound(least_upper_bound(X_39,X_40),X),
inference(subst,[],[symmetry_of_lub:[bind(Y,$fot(least_upper_bound(X_39,X_40)))]]) ).
cnf(refute_0_239,plain,
least_upper_bound(X_39,least_upper_bound(X_40,X)) = least_upper_bound(least_upper_bound(X_39,X_40),X),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_39)),bind(Y,$fot(X_40)),bind(Z,$fot(X))]]) ).
cnf(refute_0_240,plain,
( least_upper_bound(X_39,least_upper_bound(X_40,X)) != least_upper_bound(least_upper_bound(X_39,X_40),X)
| least_upper_bound(least_upper_bound(X_39,X_40),X) = least_upper_bound(X_39,least_upper_bound(X_40,X)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(least_upper_bound(X_39,least_upper_bound(X_40,X)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X_39,X_40),X)))]]) ).
cnf(refute_0_241,plain,
least_upper_bound(least_upper_bound(X_39,X_40),X) = least_upper_bound(X_39,least_upper_bound(X_40,X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_39,least_upper_bound(X_40,X)),least_upper_bound(least_upper_bound(X_39,X_40),X)) )],[refute_0_239,refute_0_240]) ).
cnf(refute_0_242,plain,
( least_upper_bound(X,least_upper_bound(X_39,X_40)) != least_upper_bound(least_upper_bound(X_39,X_40),X)
| least_upper_bound(least_upper_bound(X_39,X_40),X) != least_upper_bound(X_39,least_upper_bound(X_40,X))
| least_upper_bound(X,least_upper_bound(X_39,X_40)) = least_upper_bound(X_39,least_upper_bound(X_40,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,least_upper_bound(X_39,X_40)),least_upper_bound(X_39,least_upper_bound(X_40,X))) ),[0],$fot(least_upper_bound(least_upper_bound(X_39,X_40),X))]]) ).
cnf(refute_0_243,plain,
( least_upper_bound(X,least_upper_bound(X_39,X_40)) != least_upper_bound(least_upper_bound(X_39,X_40),X)
| least_upper_bound(X,least_upper_bound(X_39,X_40)) = least_upper_bound(X_39,least_upper_bound(X_40,X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_39,X_40),X),least_upper_bound(X_39,least_upper_bound(X_40,X))) )],[refute_0_241,refute_0_242]) ).
cnf(refute_0_244,plain,
least_upper_bound(X,least_upper_bound(X_39,X_40)) = least_upper_bound(X_39,least_upper_bound(X_40,X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_39,X_40)),least_upper_bound(least_upper_bound(X_39,X_40),X)) )],[refute_0_238,refute_0_243]) ).
cnf(refute_0_245,plain,
( least_upper_bound(X,least_upper_bound(X_39,X_40)) != least_upper_bound(X_39,least_upper_bound(X_40,X))
| least_upper_bound(X_39,least_upper_bound(X_40,X)) = least_upper_bound(X,least_upper_bound(X_39,X_40)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(X_39,X_40)))),bind(Y0,$fot(least_upper_bound(X_39,least_upper_bound(X_40,X))))]]) ).
cnf(refute_0_246,plain,
least_upper_bound(X_39,least_upper_bound(X_40,X)) = least_upper_bound(X,least_upper_bound(X_39,X_40)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_39,X_40)),least_upper_bound(X_39,least_upper_bound(X_40,X))) )],[refute_0_244,refute_0_245]) ).
cnf(refute_0_247,plain,
least_upper_bound(least_upper_bound(X_39,X_40),least_upper_bound(Y,X_40)) = least_upper_bound(X_40,least_upper_bound(least_upper_bound(X_39,X_40),Y)),
inference(subst,[],[refute_0_246:[bind(X,$fot(X_40)),bind(X_39,$fot(least_upper_bound(X_39,X_40))),bind(X_40,$fot(Y))]]) ).
cnf(refute_0_248,plain,
( least_upper_bound(X_40,least_upper_bound(least_upper_bound(X_39,X_40),Y)) != least_upper_bound(X_40,least_upper_bound(X_39,least_upper_bound(X_40,Y)))
| least_upper_bound(least_upper_bound(X_39,X_40),least_upper_bound(Y,X_40)) != least_upper_bound(X_40,least_upper_bound(least_upper_bound(X_39,X_40),Y))
| least_upper_bound(least_upper_bound(X_39,X_40),least_upper_bound(Y,X_40)) = least_upper_bound(X_40,least_upper_bound(X_39,least_upper_bound(X_40,Y))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_39,X_40),least_upper_bound(Y,X_40)))),bind(Y0,$fot(least_upper_bound(X_40,least_upper_bound(least_upper_bound(X_39,X_40),Y)))),bind(Z0,$fot(least_upper_bound(X_40,least_upper_bound(X_39,least_upper_bound(X_40,Y)))))]]) ).
cnf(refute_0_249,plain,
( least_upper_bound(X_40,least_upper_bound(least_upper_bound(X_39,X_40),Y)) != least_upper_bound(X_40,least_upper_bound(X_39,least_upper_bound(X_40,Y)))
| least_upper_bound(least_upper_bound(X_39,X_40),least_upper_bound(Y,X_40)) = least_upper_bound(X_40,least_upper_bound(X_39,least_upper_bound(X_40,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_39,X_40),least_upper_bound(Y,X_40)),least_upper_bound(X_40,least_upper_bound(least_upper_bound(X_39,X_40),Y))) )],[refute_0_247,refute_0_248]) ).
cnf(refute_0_250,plain,
least_upper_bound(least_upper_bound(X_39,X_40),least_upper_bound(Y,X_40)) = least_upper_bound(X_40,least_upper_bound(X_39,least_upper_bound(X_40,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_40,least_upper_bound(least_upper_bound(X_39,X_40),Y)),least_upper_bound(X_40,least_upper_bound(X_39,least_upper_bound(X_40,Y)))) )],[refute_0_237,refute_0_249]) ).
cnf(refute_0_251,plain,
( least_upper_bound(X_39,least_upper_bound(X_40,Y)) != least_upper_bound(least_upper_bound(X_39,X_40),least_upper_bound(Y,X_40))
| least_upper_bound(least_upper_bound(X_39,X_40),least_upper_bound(Y,X_40)) != least_upper_bound(X_40,least_upper_bound(X_39,least_upper_bound(X_40,Y)))
| least_upper_bound(X_39,least_upper_bound(X_40,Y)) = least_upper_bound(X_40,least_upper_bound(X_39,least_upper_bound(X_40,Y))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_39,least_upper_bound(X_40,Y)),least_upper_bound(X_40,least_upper_bound(X_39,least_upper_bound(X_40,Y)))) ),[0],$fot(least_upper_bound(least_upper_bound(X_39,X_40),least_upper_bound(Y,X_40)))]]) ).
cnf(refute_0_252,plain,
( least_upper_bound(X_39,least_upper_bound(X_40,Y)) != least_upper_bound(least_upper_bound(X_39,X_40),least_upper_bound(Y,X_40))
| least_upper_bound(X_39,least_upper_bound(X_40,Y)) = least_upper_bound(X_40,least_upper_bound(X_39,least_upper_bound(X_40,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_39,X_40),least_upper_bound(Y,X_40)),least_upper_bound(X_40,least_upper_bound(X_39,least_upper_bound(X_40,Y)))) )],[refute_0_250,refute_0_251]) ).
cnf(refute_0_253,plain,
least_upper_bound(X_39,least_upper_bound(X_40,Y)) = least_upper_bound(X_40,least_upper_bound(X_39,least_upper_bound(X_40,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_39,least_upper_bound(X_40,Y)),least_upper_bound(least_upper_bound(X_39,X_40),least_upper_bound(Y,X_40))) )],[refute_0_232,refute_0_252]) ).
cnf(refute_0_254,plain,
least_upper_bound(X_39,least_upper_bound(X_40,inverse(greatest_lower_bound(X_260,identity)))) = least_upper_bound(X_40,least_upper_bound(X_39,least_upper_bound(X_40,inverse(greatest_lower_bound(X_260,identity))))),
inference(subst,[],[refute_0_253:[bind(Y,$fot(inverse(greatest_lower_bound(X_260,identity))))]]) ).
cnf(refute_0_255,plain,
multiply(least_upper_bound(X_68,inverse(X_57)),least_upper_bound(X_57,identity)) = least_upper_bound(multiply(X_68,least_upper_bound(X_57,identity)),multiply(inverse(X_57),least_upper_bound(X_57,identity))),
inference(subst,[],[monotony_lub2:[bind(X,$fot(least_upper_bound(X_57,identity))),bind(Y,$fot(X_68)),bind(Z,$fot(inverse(X_57)))]]) ).
cnf(refute_0_256,plain,
multiply(inverse(X_49),least_upper_bound(X_49,X_50)) = least_upper_bound(multiply(inverse(X_49),X_49),multiply(inverse(X_49),X_50)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(inverse(X_49))),bind(Y,$fot(X_49)),bind(Z,$fot(X_50))]]) ).
cnf(refute_0_257,plain,
multiply(inverse(X_49),X_49) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_49))]]) ).
cnf(refute_0_258,plain,
( multiply(inverse(X_49),X_49) != identity
| multiply(inverse(X_49),least_upper_bound(X_49,X_50)) != least_upper_bound(multiply(inverse(X_49),X_49),multiply(inverse(X_49),X_50))
| multiply(inverse(X_49),least_upper_bound(X_49,X_50)) = least_upper_bound(identity,multiply(inverse(X_49),X_50)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_49),least_upper_bound(X_49,X_50)),least_upper_bound(multiply(inverse(X_49),X_49),multiply(inverse(X_49),X_50))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_259,plain,
( multiply(inverse(X_49),least_upper_bound(X_49,X_50)) != least_upper_bound(multiply(inverse(X_49),X_49),multiply(inverse(X_49),X_50))
| multiply(inverse(X_49),least_upper_bound(X_49,X_50)) = least_upper_bound(identity,multiply(inverse(X_49),X_50)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_49),X_49),identity) )],[refute_0_257,refute_0_258]) ).
cnf(refute_0_260,plain,
multiply(inverse(X_49),least_upper_bound(X_49,X_50)) = least_upper_bound(identity,multiply(inverse(X_49),X_50)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_49),least_upper_bound(X_49,X_50)),least_upper_bound(multiply(inverse(X_49),X_49),multiply(inverse(X_49),X_50))) )],[refute_0_256,refute_0_259]) ).
cnf(refute_0_261,plain,
multiply(inverse(X_57),least_upper_bound(X_57,identity)) = least_upper_bound(identity,multiply(inverse(X_57),identity)),
inference(subst,[],[refute_0_260:[bind(X_49,$fot(X_57)),bind(X_50,$fot(identity))]]) ).
cnf(refute_0_262,plain,
inverse(X_57) = multiply(inverse(X_57),identity),
inference(subst,[],[refute_0_86:[bind(X_33,$fot(inverse(X_57)))]]) ).
cnf(refute_0_263,plain,
( inverse(X_57) != multiply(inverse(X_57),identity)
| multiply(inverse(X_57),identity) = inverse(X_57) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(inverse(X_57))),bind(Y0,$fot(multiply(inverse(X_57),identity)))]]) ).
cnf(refute_0_264,plain,
multiply(inverse(X_57),identity) = inverse(X_57),
inference(resolve,[$cnf( $equal(inverse(X_57),multiply(inverse(X_57),identity)) )],[refute_0_262,refute_0_263]) ).
cnf(refute_0_265,plain,
( multiply(inverse(X_57),identity) != inverse(X_57)
| multiply(inverse(X_57),least_upper_bound(X_57,identity)) != least_upper_bound(identity,multiply(inverse(X_57),identity))
| multiply(inverse(X_57),least_upper_bound(X_57,identity)) = least_upper_bound(identity,inverse(X_57)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_57),least_upper_bound(X_57,identity)),least_upper_bound(identity,multiply(inverse(X_57),identity))) ),[1,1],$fot(inverse(X_57))]]) ).
cnf(refute_0_266,plain,
( multiply(inverse(X_57),least_upper_bound(X_57,identity)) != least_upper_bound(identity,multiply(inverse(X_57),identity))
| multiply(inverse(X_57),least_upper_bound(X_57,identity)) = least_upper_bound(identity,inverse(X_57)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_57),identity),inverse(X_57)) )],[refute_0_264,refute_0_265]) ).
cnf(refute_0_267,plain,
multiply(inverse(X_57),least_upper_bound(X_57,identity)) = least_upper_bound(identity,inverse(X_57)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_57),least_upper_bound(X_57,identity)),least_upper_bound(identity,multiply(inverse(X_57),identity))) )],[refute_0_261,refute_0_266]) ).
cnf(refute_0_268,plain,
( multiply(inverse(X_57),least_upper_bound(X_57,identity)) != least_upper_bound(identity,inverse(X_57))
| multiply(least_upper_bound(X_68,inverse(X_57)),least_upper_bound(X_57,identity)) != least_upper_bound(multiply(X_68,least_upper_bound(X_57,identity)),multiply(inverse(X_57),least_upper_bound(X_57,identity)))
| multiply(least_upper_bound(X_68,inverse(X_57)),least_upper_bound(X_57,identity)) = least_upper_bound(multiply(X_68,least_upper_bound(X_57,identity)),least_upper_bound(identity,inverse(X_57))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_68,inverse(X_57)),least_upper_bound(X_57,identity)),least_upper_bound(multiply(X_68,least_upper_bound(X_57,identity)),multiply(inverse(X_57),least_upper_bound(X_57,identity)))) ),[1,1],$fot(least_upper_bound(identity,inverse(X_57)))]]) ).
cnf(refute_0_269,plain,
( multiply(least_upper_bound(X_68,inverse(X_57)),least_upper_bound(X_57,identity)) != least_upper_bound(multiply(X_68,least_upper_bound(X_57,identity)),multiply(inverse(X_57),least_upper_bound(X_57,identity)))
| multiply(least_upper_bound(X_68,inverse(X_57)),least_upper_bound(X_57,identity)) = least_upper_bound(multiply(X_68,least_upper_bound(X_57,identity)),least_upper_bound(identity,inverse(X_57))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_57),least_upper_bound(X_57,identity)),least_upper_bound(identity,inverse(X_57))) )],[refute_0_267,refute_0_268]) ).
cnf(refute_0_270,plain,
multiply(least_upper_bound(X_68,inverse(X_57)),least_upper_bound(X_57,identity)) = least_upper_bound(multiply(X_68,least_upper_bound(X_57,identity)),least_upper_bound(identity,inverse(X_57))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_68,inverse(X_57)),least_upper_bound(X_57,identity)),least_upper_bound(multiply(X_68,least_upper_bound(X_57,identity)),multiply(inverse(X_57),least_upper_bound(X_57,identity)))) )],[refute_0_255,refute_0_269]) ).
cnf(refute_0_271,plain,
( least_upper_bound(X_42,least_upper_bound(X_11,X_43)) != least_upper_bound(X_42,least_upper_bound(X_43,X_11))
| least_upper_bound(X_42,least_upper_bound(X_43,X_11)) = least_upper_bound(X_42,least_upper_bound(X_11,X_43)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(least_upper_bound(X_42,least_upper_bound(X_11,X_43)))),bind(Y0,$fot(least_upper_bound(X_42,least_upper_bound(X_43,X_11))))]]) ).
cnf(refute_0_272,plain,
least_upper_bound(X_42,least_upper_bound(X_43,X_11)) = least_upper_bound(X_42,least_upper_bound(X_11,X_43)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_42,least_upper_bound(X_11,X_43)),least_upper_bound(X_42,least_upper_bound(X_43,X_11))) )],[refute_0_204,refute_0_271]) ).
cnf(refute_0_273,plain,
least_upper_bound(identity,least_upper_bound(multiply(X_68,least_upper_bound(X_57,identity)),inverse(X_57))) = least_upper_bound(identity,least_upper_bound(inverse(X_57),multiply(X_68,least_upper_bound(X_57,identity)))),
inference(subst,[],[refute_0_272:[bind(X_11,$fot(inverse(X_57))),bind(X_42,$fot(identity)),bind(X_43,$fot(multiply(X_68,least_upper_bound(X_57,identity))))]]) ).
cnf(refute_0_274,plain,
least_upper_bound(X_39,least_upper_bound(least_upper_bound(Y,X_39),X_41)) = least_upper_bound(least_upper_bound(X_39,least_upper_bound(Y,X_39)),X_41),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_39)),bind(Y,$fot(least_upper_bound(Y,X_39))),bind(Z,$fot(X_41))]]) ).
cnf(refute_0_275,plain,
least_upper_bound(X_39,least_upper_bound(Y,X_39)) = least_upper_bound(X_39,Y),
inference(subst,[],[refute_0_175:[bind(X_15,$fot(X_39))]]) ).
cnf(refute_0_276,plain,
( least_upper_bound(X_39,least_upper_bound(Y,X_39)) != least_upper_bound(X_39,Y)
| least_upper_bound(X_39,least_upper_bound(least_upper_bound(Y,X_39),X_41)) != least_upper_bound(least_upper_bound(X_39,least_upper_bound(Y,X_39)),X_41)
| least_upper_bound(X_39,least_upper_bound(least_upper_bound(Y,X_39),X_41)) = least_upper_bound(least_upper_bound(X_39,Y),X_41) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_39,least_upper_bound(least_upper_bound(Y,X_39),X_41)),least_upper_bound(least_upper_bound(X_39,least_upper_bound(Y,X_39)),X_41)) ),[1,0],$fot(least_upper_bound(X_39,Y))]]) ).
cnf(refute_0_277,plain,
( least_upper_bound(X_39,least_upper_bound(least_upper_bound(Y,X_39),X_41)) != least_upper_bound(least_upper_bound(X_39,least_upper_bound(Y,X_39)),X_41)
| least_upper_bound(X_39,least_upper_bound(least_upper_bound(Y,X_39),X_41)) = least_upper_bound(least_upper_bound(X_39,Y),X_41) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_39,least_upper_bound(Y,X_39)),least_upper_bound(X_39,Y)) )],[refute_0_275,refute_0_276]) ).
cnf(refute_0_278,plain,
least_upper_bound(X_39,least_upper_bound(least_upper_bound(Y,X_39),X_41)) = least_upper_bound(least_upper_bound(X_39,Y),X_41),
inference(resolve,[$cnf( $equal(least_upper_bound(X_39,least_upper_bound(least_upper_bound(Y,X_39),X_41)),least_upper_bound(least_upper_bound(X_39,least_upper_bound(Y,X_39)),X_41)) )],[refute_0_274,refute_0_277]) ).
cnf(refute_0_279,plain,
( least_upper_bound(X_39,least_upper_bound(X_40,Y)) != least_upper_bound(X_40,least_upper_bound(X_39,least_upper_bound(X_40,Y)))
| least_upper_bound(X_40,least_upper_bound(X_39,least_upper_bound(X_40,Y))) = least_upper_bound(X_39,least_upper_bound(X_40,Y)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(least_upper_bound(X_39,least_upper_bound(X_40,Y)))),bind(Y0,$fot(least_upper_bound(X_40,least_upper_bound(X_39,least_upper_bound(X_40,Y)))))]]) ).
cnf(refute_0_280,plain,
least_upper_bound(X_40,least_upper_bound(X_39,least_upper_bound(X_40,Y))) = least_upper_bound(X_39,least_upper_bound(X_40,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_39,least_upper_bound(X_40,Y)),least_upper_bound(X_40,least_upper_bound(X_39,least_upper_bound(X_40,Y)))) )],[refute_0_253,refute_0_279]) ).
cnf(refute_0_281,plain,
least_upper_bound(X_39,least_upper_bound(Y,least_upper_bound(X_39,X_41))) = least_upper_bound(Y,least_upper_bound(X_39,X_41)),
inference(subst,[],[refute_0_280:[bind(Y,$fot(X_41)),bind(X_39,$fot(Y)),bind(X_40,$fot(X_39))]]) ).
cnf(refute_0_282,plain,
least_upper_bound(least_upper_bound(Y,X_39),X_41) = least_upper_bound(Y,least_upper_bound(X_39,X_41)),
inference(subst,[],[refute_0_171:[bind(X,$fot(Y)),bind(Y,$fot(X_39)),bind(Z,$fot(X_41))]]) ).
cnf(refute_0_283,plain,
least_upper_bound(X_39,least_upper_bound(least_upper_bound(Y,X_39),X_41)) = least_upper_bound(X_39,least_upper_bound(least_upper_bound(Y,X_39),X_41)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_39,least_upper_bound(least_upper_bound(Y,X_39),X_41)))]]) ).
cnf(refute_0_284,plain,
( least_upper_bound(X_39,least_upper_bound(least_upper_bound(Y,X_39),X_41)) != least_upper_bound(X_39,least_upper_bound(least_upper_bound(Y,X_39),X_41))
| least_upper_bound(least_upper_bound(Y,X_39),X_41) != least_upper_bound(Y,least_upper_bound(X_39,X_41))
| least_upper_bound(X_39,least_upper_bound(least_upper_bound(Y,X_39),X_41)) = least_upper_bound(X_39,least_upper_bound(Y,least_upper_bound(X_39,X_41))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_39,least_upper_bound(least_upper_bound(Y,X_39),X_41)),least_upper_bound(X_39,least_upper_bound(least_upper_bound(Y,X_39),X_41))) ),[1,1],$fot(least_upper_bound(Y,least_upper_bound(X_39,X_41)))]]) ).
cnf(refute_0_285,plain,
( least_upper_bound(least_upper_bound(Y,X_39),X_41) != least_upper_bound(Y,least_upper_bound(X_39,X_41))
| least_upper_bound(X_39,least_upper_bound(least_upper_bound(Y,X_39),X_41)) = least_upper_bound(X_39,least_upper_bound(Y,least_upper_bound(X_39,X_41))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_39,least_upper_bound(least_upper_bound(Y,X_39),X_41)),least_upper_bound(X_39,least_upper_bound(least_upper_bound(Y,X_39),X_41))) )],[refute_0_283,refute_0_284]) ).
cnf(refute_0_286,plain,
least_upper_bound(X_39,least_upper_bound(least_upper_bound(Y,X_39),X_41)) = least_upper_bound(X_39,least_upper_bound(Y,least_upper_bound(X_39,X_41))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_39),X_41),least_upper_bound(Y,least_upper_bound(X_39,X_41))) )],[refute_0_282,refute_0_285]) ).
cnf(refute_0_287,plain,
( least_upper_bound(X_39,least_upper_bound(Y,least_upper_bound(X_39,X_41))) != least_upper_bound(Y,least_upper_bound(X_39,X_41))
| least_upper_bound(X_39,least_upper_bound(least_upper_bound(Y,X_39),X_41)) != least_upper_bound(X_39,least_upper_bound(Y,least_upper_bound(X_39,X_41)))
| least_upper_bound(X_39,least_upper_bound(least_upper_bound(Y,X_39),X_41)) = least_upper_bound(Y,least_upper_bound(X_39,X_41)) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(least_upper_bound(X_39,least_upper_bound(least_upper_bound(Y,X_39),X_41)))),bind(Y0,$fot(least_upper_bound(X_39,least_upper_bound(Y,least_upper_bound(X_39,X_41))))),bind(Z0,$fot(least_upper_bound(Y,least_upper_bound(X_39,X_41))))]]) ).
cnf(refute_0_288,plain,
( least_upper_bound(X_39,least_upper_bound(Y,least_upper_bound(X_39,X_41))) != least_upper_bound(Y,least_upper_bound(X_39,X_41))
| least_upper_bound(X_39,least_upper_bound(least_upper_bound(Y,X_39),X_41)) = least_upper_bound(Y,least_upper_bound(X_39,X_41)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_39,least_upper_bound(least_upper_bound(Y,X_39),X_41)),least_upper_bound(X_39,least_upper_bound(Y,least_upper_bound(X_39,X_41)))) )],[refute_0_286,refute_0_287]) ).
cnf(refute_0_289,plain,
least_upper_bound(X_39,least_upper_bound(least_upper_bound(Y,X_39),X_41)) = least_upper_bound(Y,least_upper_bound(X_39,X_41)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_39,least_upper_bound(Y,least_upper_bound(X_39,X_41))),least_upper_bound(Y,least_upper_bound(X_39,X_41))) )],[refute_0_281,refute_0_288]) ).
cnf(refute_0_290,plain,
( least_upper_bound(X_39,least_upper_bound(least_upper_bound(Y,X_39),X_41)) != least_upper_bound(Y,least_upper_bound(X_39,X_41))
| least_upper_bound(X_39,least_upper_bound(least_upper_bound(Y,X_39),X_41)) != least_upper_bound(least_upper_bound(X_39,Y),X_41)
| least_upper_bound(Y,least_upper_bound(X_39,X_41)) = least_upper_bound(least_upper_bound(X_39,Y),X_41) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_39,least_upper_bound(least_upper_bound(Y,X_39),X_41)),least_upper_bound(least_upper_bound(X_39,Y),X_41)) ),[0],$fot(least_upper_bound(Y,least_upper_bound(X_39,X_41)))]]) ).
cnf(refute_0_291,plain,
( least_upper_bound(X_39,least_upper_bound(least_upper_bound(Y,X_39),X_41)) != least_upper_bound(least_upper_bound(X_39,Y),X_41)
| least_upper_bound(Y,least_upper_bound(X_39,X_41)) = least_upper_bound(least_upper_bound(X_39,Y),X_41) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_39,least_upper_bound(least_upper_bound(Y,X_39),X_41)),least_upper_bound(Y,least_upper_bound(X_39,X_41))) )],[refute_0_289,refute_0_290]) ).
cnf(refute_0_292,plain,
least_upper_bound(least_upper_bound(X_39,Y),X_41) = least_upper_bound(X_39,least_upper_bound(Y,X_41)),
inference(subst,[],[refute_0_171:[bind(X,$fot(X_39)),bind(Z,$fot(X_41))]]) ).
cnf(refute_0_293,plain,
( least_upper_bound(Y,least_upper_bound(X_39,X_41)) != least_upper_bound(least_upper_bound(X_39,Y),X_41)
| least_upper_bound(least_upper_bound(X_39,Y),X_41) != least_upper_bound(X_39,least_upper_bound(Y,X_41))
| least_upper_bound(Y,least_upper_bound(X_39,X_41)) = least_upper_bound(X_39,least_upper_bound(Y,X_41)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(Y,least_upper_bound(X_39,X_41)),least_upper_bound(X_39,least_upper_bound(Y,X_41))) ),[0],$fot(least_upper_bound(least_upper_bound(X_39,Y),X_41))]]) ).
cnf(refute_0_294,plain,
( least_upper_bound(Y,least_upper_bound(X_39,X_41)) != least_upper_bound(least_upper_bound(X_39,Y),X_41)
| least_upper_bound(Y,least_upper_bound(X_39,X_41)) = least_upper_bound(X_39,least_upper_bound(Y,X_41)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_39,Y),X_41),least_upper_bound(X_39,least_upper_bound(Y,X_41))) )],[refute_0_292,refute_0_293]) ).
cnf(refute_0_295,plain,
( least_upper_bound(X_39,least_upper_bound(least_upper_bound(Y,X_39),X_41)) != least_upper_bound(least_upper_bound(X_39,Y),X_41)
| least_upper_bound(Y,least_upper_bound(X_39,X_41)) = least_upper_bound(X_39,least_upper_bound(Y,X_41)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_39,X_41)),least_upper_bound(least_upper_bound(X_39,Y),X_41)) )],[refute_0_291,refute_0_294]) ).
cnf(refute_0_296,plain,
least_upper_bound(Y,least_upper_bound(X_39,X_41)) = least_upper_bound(X_39,least_upper_bound(Y,X_41)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_39,least_upper_bound(least_upper_bound(Y,X_39),X_41)),least_upper_bound(least_upper_bound(X_39,Y),X_41)) )],[refute_0_278,refute_0_295]) ).
cnf(refute_0_297,plain,
( least_upper_bound(Y,least_upper_bound(X_39,X_41)) != least_upper_bound(X_39,least_upper_bound(Y,X_41))
| least_upper_bound(X_39,least_upper_bound(Y,X_41)) = least_upper_bound(Y,least_upper_bound(X_39,X_41)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(least_upper_bound(Y,least_upper_bound(X_39,X_41)))),bind(Y0,$fot(least_upper_bound(X_39,least_upper_bound(Y,X_41))))]]) ).
cnf(refute_0_298,plain,
least_upper_bound(X_39,least_upper_bound(Y,X_41)) = least_upper_bound(Y,least_upper_bound(X_39,X_41)),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_39,X_41)),least_upper_bound(X_39,least_upper_bound(Y,X_41))) )],[refute_0_296,refute_0_297]) ).
cnf(refute_0_299,plain,
least_upper_bound(multiply(X_68,least_upper_bound(X_57,identity)),least_upper_bound(identity,inverse(X_57))) = least_upper_bound(identity,least_upper_bound(multiply(X_68,least_upper_bound(X_57,identity)),inverse(X_57))),
inference(subst,[],[refute_0_298:[bind(Y,$fot(identity)),bind(X_39,$fot(multiply(X_68,least_upper_bound(X_57,identity)))),bind(X_41,$fot(inverse(X_57)))]]) ).
cnf(refute_0_300,plain,
( least_upper_bound(multiply(X_68,least_upper_bound(X_57,identity)),least_upper_bound(identity,inverse(X_57))) != least_upper_bound(identity,least_upper_bound(multiply(X_68,least_upper_bound(X_57,identity)),inverse(X_57)))
| least_upper_bound(identity,least_upper_bound(multiply(X_68,least_upper_bound(X_57,identity)),inverse(X_57))) != least_upper_bound(identity,least_upper_bound(inverse(X_57),multiply(X_68,least_upper_bound(X_57,identity))))
| least_upper_bound(multiply(X_68,least_upper_bound(X_57,identity)),least_upper_bound(identity,inverse(X_57))) = least_upper_bound(identity,least_upper_bound(inverse(X_57),multiply(X_68,least_upper_bound(X_57,identity)))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(least_upper_bound(multiply(X_68,least_upper_bound(X_57,identity)),least_upper_bound(identity,inverse(X_57))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(multiply(X_68,least_upper_bound(X_57,identity)),inverse(X_57))))),bind(Z0,$fot(least_upper_bound(identity,least_upper_bound(inverse(X_57),multiply(X_68,least_upper_bound(X_57,identity))))))]]) ).
cnf(refute_0_301,plain,
( least_upper_bound(identity,least_upper_bound(multiply(X_68,least_upper_bound(X_57,identity)),inverse(X_57))) != least_upper_bound(identity,least_upper_bound(inverse(X_57),multiply(X_68,least_upper_bound(X_57,identity))))
| least_upper_bound(multiply(X_68,least_upper_bound(X_57,identity)),least_upper_bound(identity,inverse(X_57))) = least_upper_bound(identity,least_upper_bound(inverse(X_57),multiply(X_68,least_upper_bound(X_57,identity)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_68,least_upper_bound(X_57,identity)),least_upper_bound(identity,inverse(X_57))),least_upper_bound(identity,least_upper_bound(multiply(X_68,least_upper_bound(X_57,identity)),inverse(X_57)))) )],[refute_0_299,refute_0_300]) ).
cnf(refute_0_302,plain,
least_upper_bound(multiply(X_68,least_upper_bound(X_57,identity)),least_upper_bound(identity,inverse(X_57))) = least_upper_bound(identity,least_upper_bound(inverse(X_57),multiply(X_68,least_upper_bound(X_57,identity)))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(X_68,least_upper_bound(X_57,identity)),inverse(X_57))),least_upper_bound(identity,least_upper_bound(inverse(X_57),multiply(X_68,least_upper_bound(X_57,identity))))) )],[refute_0_273,refute_0_301]) ).
cnf(refute_0_303,plain,
( multiply(least_upper_bound(X_68,inverse(X_57)),least_upper_bound(X_57,identity)) != least_upper_bound(multiply(X_68,least_upper_bound(X_57,identity)),least_upper_bound(identity,inverse(X_57)))
| least_upper_bound(multiply(X_68,least_upper_bound(X_57,identity)),least_upper_bound(identity,inverse(X_57))) != least_upper_bound(identity,least_upper_bound(inverse(X_57),multiply(X_68,least_upper_bound(X_57,identity))))
| multiply(least_upper_bound(X_68,inverse(X_57)),least_upper_bound(X_57,identity)) = least_upper_bound(identity,least_upper_bound(inverse(X_57),multiply(X_68,least_upper_bound(X_57,identity)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_68,inverse(X_57)),least_upper_bound(X_57,identity)),least_upper_bound(identity,least_upper_bound(inverse(X_57),multiply(X_68,least_upper_bound(X_57,identity))))) ),[0],$fot(least_upper_bound(multiply(X_68,least_upper_bound(X_57,identity)),least_upper_bound(identity,inverse(X_57))))]]) ).
cnf(refute_0_304,plain,
( multiply(least_upper_bound(X_68,inverse(X_57)),least_upper_bound(X_57,identity)) != least_upper_bound(multiply(X_68,least_upper_bound(X_57,identity)),least_upper_bound(identity,inverse(X_57)))
| multiply(least_upper_bound(X_68,inverse(X_57)),least_upper_bound(X_57,identity)) = least_upper_bound(identity,least_upper_bound(inverse(X_57),multiply(X_68,least_upper_bound(X_57,identity)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_68,least_upper_bound(X_57,identity)),least_upper_bound(identity,inverse(X_57))),least_upper_bound(identity,least_upper_bound(inverse(X_57),multiply(X_68,least_upper_bound(X_57,identity))))) )],[refute_0_302,refute_0_303]) ).
cnf(refute_0_305,plain,
multiply(least_upper_bound(X_68,inverse(X_57)),least_upper_bound(X_57,identity)) = least_upper_bound(identity,least_upper_bound(inverse(X_57),multiply(X_68,least_upper_bound(X_57,identity)))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_68,inverse(X_57)),least_upper_bound(X_57,identity)),least_upper_bound(multiply(X_68,least_upper_bound(X_57,identity)),least_upper_bound(identity,inverse(X_57)))) )],[refute_0_270,refute_0_304]) ).
cnf(refute_0_306,plain,
multiply(least_upper_bound(X_190,inverse(greatest_lower_bound(identity,X_150))),least_upper_bound(greatest_lower_bound(identity,X_150),identity)) = least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(greatest_lower_bound(identity,X_150),identity)))),
inference(subst,[],[refute_0_305:[bind(X_57,$fot(greatest_lower_bound(identity,X_150))),bind(X_68,$fot(X_190))]]) ).
cnf(refute_0_307,plain,
inverse(greatest_lower_bound(identity,X_150)) = multiply(inverse(multiply(inverse(greatest_lower_bound(identity,inverse(X_150))),greatest_lower_bound(identity,X_150))),inverse(greatest_lower_bound(identity,inverse(X_150)))),
inference(subst,[],[refute_0_96:[bind(X_45,$fot(inverse(greatest_lower_bound(identity,inverse(X_150))))),bind(X_46,$fot(greatest_lower_bound(identity,X_150)))]]) ).
cnf(refute_0_308,plain,
inverse(inverse(X_125)) = multiply(inverse(multiply(greatest_lower_bound(identity,X_125),inverse(X_125))),greatest_lower_bound(identity,X_125)),
inference(subst,[],[refute_0_96:[bind(X_45,$fot(greatest_lower_bound(identity,X_125))),bind(X_46,$fot(inverse(X_125)))]]) ).
cnf(refute_0_309,plain,
multiply(X_104,greatest_lower_bound(X_105,identity)) = greatest_lower_bound(multiply(X_104,X_105),multiply(X_104,identity)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(X_104)),bind(Y,$fot(X_105)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_310,plain,
X_104 = multiply(X_104,identity),
inference(subst,[],[refute_0_86:[bind(X_33,$fot(X_104))]]) ).
cnf(refute_0_311,plain,
( X_104 != multiply(X_104,identity)
| multiply(X_104,identity) = X_104 ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(X_104)),bind(Y0,$fot(multiply(X_104,identity)))]]) ).
cnf(refute_0_312,plain,
multiply(X_104,identity) = X_104,
inference(resolve,[$cnf( $equal(X_104,multiply(X_104,identity)) )],[refute_0_310,refute_0_311]) ).
cnf(refute_0_313,plain,
( multiply(X_104,greatest_lower_bound(X_105,identity)) != greatest_lower_bound(multiply(X_104,X_105),multiply(X_104,identity))
| multiply(X_104,identity) != X_104
| multiply(X_104,greatest_lower_bound(X_105,identity)) = greatest_lower_bound(multiply(X_104,X_105),X_104) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_104,greatest_lower_bound(X_105,identity)),greatest_lower_bound(multiply(X_104,X_105),multiply(X_104,identity))) ),[1,1],$fot(X_104)]]) ).
cnf(refute_0_314,plain,
( multiply(X_104,greatest_lower_bound(X_105,identity)) != greatest_lower_bound(multiply(X_104,X_105),multiply(X_104,identity))
| multiply(X_104,greatest_lower_bound(X_105,identity)) = greatest_lower_bound(multiply(X_104,X_105),X_104) ),
inference(resolve,[$cnf( $equal(multiply(X_104,identity),X_104) )],[refute_0_312,refute_0_313]) ).
cnf(refute_0_315,plain,
multiply(X_104,greatest_lower_bound(X_105,identity)) = greatest_lower_bound(multiply(X_104,X_105),X_104),
inference(resolve,[$cnf( $equal(multiply(X_104,greatest_lower_bound(X_105,identity)),greatest_lower_bound(multiply(X_104,X_105),multiply(X_104,identity))) )],[refute_0_309,refute_0_314]) ).
cnf(refute_0_316,plain,
greatest_lower_bound(multiply(X_104,X_105),X_104) = greatest_lower_bound(X_104,multiply(X_104,X_105)),
inference(subst,[],[refute_0_42:[bind(X,$fot(X_104)),bind(Y,$fot(multiply(X_104,X_105)))]]) ).
cnf(refute_0_317,plain,
( multiply(X_104,greatest_lower_bound(X_105,identity)) != greatest_lower_bound(multiply(X_104,X_105),X_104)
| greatest_lower_bound(multiply(X_104,X_105),X_104) != greatest_lower_bound(X_104,multiply(X_104,X_105))
| multiply(X_104,greatest_lower_bound(X_105,identity)) = greatest_lower_bound(X_104,multiply(X_104,X_105)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_104,greatest_lower_bound(X_105,identity)),greatest_lower_bound(X_104,multiply(X_104,X_105))) ),[0],$fot(greatest_lower_bound(multiply(X_104,X_105),X_104))]]) ).
cnf(refute_0_318,plain,
( multiply(X_104,greatest_lower_bound(X_105,identity)) != greatest_lower_bound(multiply(X_104,X_105),X_104)
| multiply(X_104,greatest_lower_bound(X_105,identity)) = greatest_lower_bound(X_104,multiply(X_104,X_105)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_104,X_105),X_104),greatest_lower_bound(X_104,multiply(X_104,X_105))) )],[refute_0_316,refute_0_317]) ).
cnf(refute_0_319,plain,
multiply(X_104,greatest_lower_bound(X_105,identity)) = greatest_lower_bound(X_104,multiply(X_104,X_105)),
inference(resolve,[$cnf( $equal(multiply(X_104,greatest_lower_bound(X_105,identity)),greatest_lower_bound(multiply(X_104,X_105),X_104)) )],[refute_0_315,refute_0_318]) ).
cnf(refute_0_320,plain,
multiply(identity,greatest_lower_bound(inverse(X_125),identity)) = greatest_lower_bound(identity,multiply(identity,inverse(X_125))),
inference(subst,[],[refute_0_319:[bind(X_104,$fot(identity)),bind(X_105,$fot(inverse(X_125)))]]) ).
cnf(refute_0_321,plain,
multiply(greatest_lower_bound(X_120,X_121),inverse(X_121)) = greatest_lower_bound(multiply(X_120,inverse(X_121)),multiply(X_121,inverse(X_121))),
inference(subst,[],[monotony_glb2:[bind(X,$fot(inverse(X_121))),bind(Y,$fot(X_120)),bind(Z,$fot(X_121))]]) ).
cnf(refute_0_322,plain,
multiply(X_121,inverse(X_121)) = identity,
inference(subst,[],[refute_0_71:[bind(X_35,$fot(X_121))]]) ).
cnf(refute_0_323,plain,
( multiply(X_121,inverse(X_121)) != identity
| multiply(greatest_lower_bound(X_120,X_121),inverse(X_121)) != greatest_lower_bound(multiply(X_120,inverse(X_121)),multiply(X_121,inverse(X_121)))
| multiply(greatest_lower_bound(X_120,X_121),inverse(X_121)) = greatest_lower_bound(multiply(X_120,inverse(X_121)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_120,X_121),inverse(X_121)),greatest_lower_bound(multiply(X_120,inverse(X_121)),multiply(X_121,inverse(X_121)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_324,plain,
( multiply(greatest_lower_bound(X_120,X_121),inverse(X_121)) != greatest_lower_bound(multiply(X_120,inverse(X_121)),multiply(X_121,inverse(X_121)))
| multiply(greatest_lower_bound(X_120,X_121),inverse(X_121)) = greatest_lower_bound(multiply(X_120,inverse(X_121)),identity) ),
inference(resolve,[$cnf( $equal(multiply(X_121,inverse(X_121)),identity) )],[refute_0_322,refute_0_323]) ).
cnf(refute_0_325,plain,
multiply(greatest_lower_bound(X_120,X_121),inverse(X_121)) = greatest_lower_bound(multiply(X_120,inverse(X_121)),identity),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_120,X_121),inverse(X_121)),greatest_lower_bound(multiply(X_120,inverse(X_121)),multiply(X_121,inverse(X_121)))) )],[refute_0_321,refute_0_324]) ).
cnf(refute_0_326,plain,
greatest_lower_bound(multiply(X_120,inverse(X_121)),identity) = greatest_lower_bound(identity,multiply(X_120,inverse(X_121))),
inference(subst,[],[refute_0_42:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_120,inverse(X_121))))]]) ).
cnf(refute_0_327,plain,
( multiply(greatest_lower_bound(X_120,X_121),inverse(X_121)) != greatest_lower_bound(multiply(X_120,inverse(X_121)),identity)
| greatest_lower_bound(multiply(X_120,inverse(X_121)),identity) != greatest_lower_bound(identity,multiply(X_120,inverse(X_121)))
| multiply(greatest_lower_bound(X_120,X_121),inverse(X_121)) = greatest_lower_bound(identity,multiply(X_120,inverse(X_121))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_120,X_121),inverse(X_121)),greatest_lower_bound(identity,multiply(X_120,inverse(X_121)))) ),[0],$fot(greatest_lower_bound(multiply(X_120,inverse(X_121)),identity))]]) ).
cnf(refute_0_328,plain,
( multiply(greatest_lower_bound(X_120,X_121),inverse(X_121)) != greatest_lower_bound(multiply(X_120,inverse(X_121)),identity)
| multiply(greatest_lower_bound(X_120,X_121),inverse(X_121)) = greatest_lower_bound(identity,multiply(X_120,inverse(X_121))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_120,inverse(X_121)),identity),greatest_lower_bound(identity,multiply(X_120,inverse(X_121)))) )],[refute_0_326,refute_0_327]) ).
cnf(refute_0_329,plain,
multiply(greatest_lower_bound(X_120,X_121),inverse(X_121)) = greatest_lower_bound(identity,multiply(X_120,inverse(X_121))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_120,X_121),inverse(X_121)),greatest_lower_bound(multiply(X_120,inverse(X_121)),identity)) )],[refute_0_325,refute_0_328]) ).
cnf(refute_0_330,plain,
multiply(greatest_lower_bound(identity,X_125),inverse(X_125)) = greatest_lower_bound(identity,multiply(identity,inverse(X_125))),
inference(subst,[],[refute_0_329:[bind(X_120,$fot(identity)),bind(X_121,$fot(X_125))]]) ).
cnf(refute_0_331,plain,
( multiply(greatest_lower_bound(identity,X_125),inverse(X_125)) != greatest_lower_bound(identity,multiply(identity,inverse(X_125)))
| greatest_lower_bound(identity,multiply(identity,inverse(X_125))) = multiply(greatest_lower_bound(identity,X_125),inverse(X_125)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(greatest_lower_bound(identity,X_125),inverse(X_125)))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(identity,inverse(X_125)))))]]) ).
cnf(refute_0_332,plain,
greatest_lower_bound(identity,multiply(identity,inverse(X_125))) = multiply(greatest_lower_bound(identity,X_125),inverse(X_125)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_125),inverse(X_125)),greatest_lower_bound(identity,multiply(identity,inverse(X_125)))) )],[refute_0_330,refute_0_331]) ).
cnf(refute_0_333,plain,
( multiply(identity,greatest_lower_bound(inverse(X_125),identity)) != greatest_lower_bound(identity,multiply(identity,inverse(X_125)))
| greatest_lower_bound(identity,multiply(identity,inverse(X_125))) != multiply(greatest_lower_bound(identity,X_125),inverse(X_125))
| multiply(identity,greatest_lower_bound(inverse(X_125),identity)) = multiply(greatest_lower_bound(identity,X_125),inverse(X_125)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(identity,greatest_lower_bound(inverse(X_125),identity)),multiply(greatest_lower_bound(identity,X_125),inverse(X_125))) ),[0],$fot(greatest_lower_bound(identity,multiply(identity,inverse(X_125))))]]) ).
cnf(refute_0_334,plain,
( multiply(identity,greatest_lower_bound(inverse(X_125),identity)) != greatest_lower_bound(identity,multiply(identity,inverse(X_125)))
| multiply(identity,greatest_lower_bound(inverse(X_125),identity)) = multiply(greatest_lower_bound(identity,X_125),inverse(X_125)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(identity,inverse(X_125))),multiply(greatest_lower_bound(identity,X_125),inverse(X_125))) )],[refute_0_332,refute_0_333]) ).
cnf(refute_0_335,plain,
multiply(identity,greatest_lower_bound(inverse(X_125),identity)) = multiply(greatest_lower_bound(identity,X_125),inverse(X_125)),
inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(inverse(X_125),identity)),greatest_lower_bound(identity,multiply(identity,inverse(X_125)))) )],[refute_0_320,refute_0_334]) ).
cnf(refute_0_336,plain,
multiply(identity,greatest_lower_bound(identity,inverse(X_125))) = greatest_lower_bound(identity,inverse(X_125)),
inference(subst,[],[left_identity:[bind(X,$fot(greatest_lower_bound(identity,inverse(X_125))))]]) ).
cnf(refute_0_337,plain,
greatest_lower_bound(greatest_lower_bound(X_13,Y),least_upper_bound(X_13,greatest_lower_bound(X_13,Y))) = greatest_lower_bound(X_13,Y),
inference(subst,[],[refute_0_153:[bind(X_6,$fot(greatest_lower_bound(X_13,Y))),bind(X_7,$fot(X_13))]]) ).
cnf(refute_0_338,plain,
least_upper_bound(X_13,greatest_lower_bound(X_13,Y)) = X_13,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_13))]]) ).
cnf(refute_0_339,plain,
( greatest_lower_bound(greatest_lower_bound(X_13,Y),least_upper_bound(X_13,greatest_lower_bound(X_13,Y))) != greatest_lower_bound(X_13,Y)
| least_upper_bound(X_13,greatest_lower_bound(X_13,Y)) != X_13
| greatest_lower_bound(greatest_lower_bound(X_13,Y),X_13) = greatest_lower_bound(X_13,Y) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_13,Y),least_upper_bound(X_13,greatest_lower_bound(X_13,Y))),greatest_lower_bound(X_13,Y)) ),[0,1],$fot(X_13)]]) ).
cnf(refute_0_340,plain,
( greatest_lower_bound(greatest_lower_bound(X_13,Y),least_upper_bound(X_13,greatest_lower_bound(X_13,Y))) != greatest_lower_bound(X_13,Y)
| greatest_lower_bound(greatest_lower_bound(X_13,Y),X_13) = greatest_lower_bound(X_13,Y) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_13,greatest_lower_bound(X_13,Y)),X_13) )],[refute_0_338,refute_0_339]) ).
cnf(refute_0_341,plain,
greatest_lower_bound(greatest_lower_bound(X_13,Y),X_13) = greatest_lower_bound(X_13,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_13,Y),least_upper_bound(X_13,greatest_lower_bound(X_13,Y))),greatest_lower_bound(X_13,Y)) )],[refute_0_337,refute_0_340]) ).
cnf(refute_0_342,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,Z)) != greatest_lower_bound(greatest_lower_bound(X,Y),Z)
| greatest_lower_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(Y,Z)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X,Y),Z)))]]) ).
cnf(refute_0_343,plain,
greatest_lower_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(greatest_lower_bound(X,Y),Z)) )],[associativity_of_glb,refute_0_342]) ).
cnf(refute_0_344,plain,
greatest_lower_bound(greatest_lower_bound(X_13,Y),X_13) = greatest_lower_bound(X_13,greatest_lower_bound(Y,X_13)),
inference(subst,[],[refute_0_343:[bind(X,$fot(X_13)),bind(Z,$fot(X_13))]]) ).
cnf(refute_0_345,plain,
( greatest_lower_bound(greatest_lower_bound(X_13,Y),X_13) != greatest_lower_bound(X_13,Y)
| greatest_lower_bound(greatest_lower_bound(X_13,Y),X_13) != greatest_lower_bound(X_13,greatest_lower_bound(Y,X_13))
| greatest_lower_bound(X_13,greatest_lower_bound(Y,X_13)) = greatest_lower_bound(X_13,Y) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_13,Y),X_13),greatest_lower_bound(X_13,Y)) ),[0],$fot(greatest_lower_bound(X_13,greatest_lower_bound(Y,X_13)))]]) ).
cnf(refute_0_346,plain,
( greatest_lower_bound(greatest_lower_bound(X_13,Y),X_13) != greatest_lower_bound(X_13,Y)
| greatest_lower_bound(X_13,greatest_lower_bound(Y,X_13)) = greatest_lower_bound(X_13,Y) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_13,Y),X_13),greatest_lower_bound(X_13,greatest_lower_bound(Y,X_13))) )],[refute_0_344,refute_0_345]) ).
cnf(refute_0_347,plain,
greatest_lower_bound(X_13,greatest_lower_bound(Y,X_13)) = greatest_lower_bound(X_13,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_13,Y),X_13),greatest_lower_bound(X_13,Y)) )],[refute_0_341,refute_0_346]) ).
cnf(refute_0_348,plain,
greatest_lower_bound(X_17,greatest_lower_bound(X_16,X_17)) = greatest_lower_bound(X_17,X_16),
inference(subst,[],[refute_0_347:[bind(Y,$fot(X_16)),bind(X_13,$fot(X_17))]]) ).
cnf(refute_0_349,plain,
greatest_lower_bound(X_17,X_16) = greatest_lower_bound(X_16,X_17),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_17)),bind(Y,$fot(X_16))]]) ).
cnf(refute_0_350,plain,
( greatest_lower_bound(X_17,X_16) != greatest_lower_bound(X_16,X_17)
| greatest_lower_bound(X_16,X_17) = greatest_lower_bound(X_17,X_16) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(greatest_lower_bound(X_17,X_16))),bind(Y0,$fot(greatest_lower_bound(X_16,X_17)))]]) ).
cnf(refute_0_351,plain,
greatest_lower_bound(X_16,X_17) = greatest_lower_bound(X_17,X_16),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,X_16),greatest_lower_bound(X_16,X_17)) )],[refute_0_349,refute_0_350]) ).
cnf(refute_0_352,plain,
( greatest_lower_bound(X_16,X_17) != greatest_lower_bound(X_17,X_16)
| greatest_lower_bound(X_17,greatest_lower_bound(X_16,X_17)) != greatest_lower_bound(X_17,X_16)
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_16)) = greatest_lower_bound(X_17,X_16) ),
introduced(tautology,[equality,[$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_353,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( $equal(greatest_lower_bound(X_16,X_17),greatest_lower_bound(X_17,X_16)) )],[refute_0_351,refute_0_352]) ).
cnf(refute_0_354,plain,
greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_16)) = greatest_lower_bound(X_17,X_16),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,greatest_lower_bound(X_16,X_17)),greatest_lower_bound(X_17,X_16)) )],[refute_0_348,refute_0_353]) ).
cnf(refute_0_355,plain,
greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_17,X_108))) = greatest_lower_bound(X_17,multiply(X_17,X_108)),
inference(subst,[],[refute_0_354:[bind(X_16,$fot(multiply(X_17,X_108)))]]) ).
cnf(refute_0_356,plain,
multiply(X_17,greatest_lower_bound(X_108,identity)) = greatest_lower_bound(X_17,multiply(X_17,X_108)),
inference(subst,[],[refute_0_319:[bind(X_104,$fot(X_17)),bind(X_105,$fot(X_108))]]) ).
cnf(refute_0_357,plain,
( multiply(X_17,greatest_lower_bound(X_108,identity)) != greatest_lower_bound(X_17,multiply(X_17,X_108))
| greatest_lower_bound(X_17,multiply(X_17,X_108)) = multiply(X_17,greatest_lower_bound(X_108,identity)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(X_17,greatest_lower_bound(X_108,identity)))),bind(Y0,$fot(greatest_lower_bound(X_17,multiply(X_17,X_108))))]]) ).
cnf(refute_0_358,plain,
greatest_lower_bound(X_17,multiply(X_17,X_108)) = multiply(X_17,greatest_lower_bound(X_108,identity)),
inference(resolve,[$cnf( $equal(multiply(X_17,greatest_lower_bound(X_108,identity)),greatest_lower_bound(X_17,multiply(X_17,X_108))) )],[refute_0_356,refute_0_357]) ).
cnf(refute_0_359,plain,
( greatest_lower_bound(X_17,multiply(X_17,X_108)) != multiply(X_17,greatest_lower_bound(X_108,identity))
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_17,X_108))) != greatest_lower_bound(X_17,multiply(X_17,X_108))
| greatest_lower_bound(X_17,multiply(X_17,greatest_lower_bound(X_108,identity))) = greatest_lower_bound(X_17,multiply(X_17,X_108)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_17,X_108))),greatest_lower_bound(X_17,multiply(X_17,X_108))) ),[0,1],$fot(multiply(X_17,greatest_lower_bound(X_108,identity)))]]) ).
cnf(refute_0_360,plain,
( greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_17,X_108))) != greatest_lower_bound(X_17,multiply(X_17,X_108))
| greatest_lower_bound(X_17,multiply(X_17,greatest_lower_bound(X_108,identity))) = greatest_lower_bound(X_17,multiply(X_17,X_108)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,multiply(X_17,X_108)),multiply(X_17,greatest_lower_bound(X_108,identity))) )],[refute_0_358,refute_0_359]) ).
cnf(refute_0_361,plain,
greatest_lower_bound(X_17,multiply(X_17,greatest_lower_bound(X_108,identity))) = greatest_lower_bound(X_17,multiply(X_17,X_108)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_17,X_108))),greatest_lower_bound(X_17,multiply(X_17,X_108))) )],[refute_0_355,refute_0_360]) ).
cnf(refute_0_362,plain,
greatest_lower_bound(identity,greatest_lower_bound(X_108,identity)) = greatest_lower_bound(identity,X_108),
inference(subst,[],[refute_0_347:[bind(Y,$fot(X_108)),bind(X_13,$fot(identity))]]) ).
cnf(refute_0_363,plain,
multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_108,identity))) = multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_108,identity))),
introduced(tautology,[refl,[$fot(multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_108,identity))))]]) ).
cnf(refute_0_364,plain,
( multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_108,identity))) != multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_108,identity)))
| greatest_lower_bound(identity,greatest_lower_bound(X_108,identity)) != greatest_lower_bound(identity,X_108)
| multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_108,identity))) = multiply(X_17,greatest_lower_bound(identity,X_108)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_108,identity))),multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_108,identity)))) ),[1,1],$fot(greatest_lower_bound(identity,X_108))]]) ).
cnf(refute_0_365,plain,
( greatest_lower_bound(identity,greatest_lower_bound(X_108,identity)) != greatest_lower_bound(identity,X_108)
| multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_108,identity))) = multiply(X_17,greatest_lower_bound(identity,X_108)) ),
inference(resolve,[$cnf( $equal(multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_108,identity))),multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_108,identity)))) )],[refute_0_363,refute_0_364]) ).
cnf(refute_0_366,plain,
multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_108,identity))) = multiply(X_17,greatest_lower_bound(identity,X_108)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_108,identity)),greatest_lower_bound(identity,X_108)) )],[refute_0_362,refute_0_365]) ).
cnf(refute_0_367,plain,
least_upper_bound(greatest_lower_bound(X_16,X_11),greatest_lower_bound(X_11,greatest_lower_bound(X_16,X_11))) = greatest_lower_bound(X_16,X_11),
inference(subst,[],[refute_0_145:[bind(X_10,$fot(greatest_lower_bound(X_16,X_11)))]]) ).
cnf(refute_0_368,plain,
greatest_lower_bound(X_11,greatest_lower_bound(X_16,X_11)) = greatest_lower_bound(X_11,X_16),
inference(subst,[],[refute_0_347:[bind(Y,$fot(X_16)),bind(X_13,$fot(X_11))]]) ).
cnf(refute_0_369,plain,
( greatest_lower_bound(X_11,greatest_lower_bound(X_16,X_11)) != greatest_lower_bound(X_11,X_16)
| least_upper_bound(greatest_lower_bound(X_16,X_11),greatest_lower_bound(X_11,greatest_lower_bound(X_16,X_11))) != greatest_lower_bound(X_16,X_11)
| least_upper_bound(greatest_lower_bound(X_16,X_11),greatest_lower_bound(X_11,X_16)) = greatest_lower_bound(X_16,X_11) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_16,X_11),greatest_lower_bound(X_11,greatest_lower_bound(X_16,X_11))),greatest_lower_bound(X_16,X_11)) ),[0,1],$fot(greatest_lower_bound(X_11,X_16))]]) ).
cnf(refute_0_370,plain,
( least_upper_bound(greatest_lower_bound(X_16,X_11),greatest_lower_bound(X_11,greatest_lower_bound(X_16,X_11))) != greatest_lower_bound(X_16,X_11)
| least_upper_bound(greatest_lower_bound(X_16,X_11),greatest_lower_bound(X_11,X_16)) = greatest_lower_bound(X_16,X_11) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_11,greatest_lower_bound(X_16,X_11)),greatest_lower_bound(X_11,X_16)) )],[refute_0_368,refute_0_369]) ).
cnf(refute_0_371,plain,
least_upper_bound(greatest_lower_bound(X_16,X_11),greatest_lower_bound(X_11,X_16)) = greatest_lower_bound(X_16,X_11),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_16,X_11),greatest_lower_bound(X_11,greatest_lower_bound(X_16,X_11))),greatest_lower_bound(X_16,X_11)) )],[refute_0_367,refute_0_370]) ).
cnf(refute_0_372,plain,
least_upper_bound(greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105)),greatest_lower_bound(multiply(X_104,X_105),multiply(X_104,X_106))) = greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105)),
inference(subst,[],[refute_0_371:[bind(X_11,$fot(multiply(X_104,X_105))),bind(X_16,$fot(multiply(X_104,X_106)))]]) ).
cnf(refute_0_373,plain,
multiply(X_104,greatest_lower_bound(X_105,X_106)) = greatest_lower_bound(multiply(X_104,X_105),multiply(X_104,X_106)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(X_104)),bind(Y,$fot(X_105)),bind(Z,$fot(X_106))]]) ).
cnf(refute_0_374,plain,
( multiply(X_104,greatest_lower_bound(X_105,X_106)) != greatest_lower_bound(multiply(X_104,X_105),multiply(X_104,X_106))
| greatest_lower_bound(multiply(X_104,X_105),multiply(X_104,X_106)) = multiply(X_104,greatest_lower_bound(X_105,X_106)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(X_104,greatest_lower_bound(X_105,X_106)))),bind(Y0,$fot(greatest_lower_bound(multiply(X_104,X_105),multiply(X_104,X_106))))]]) ).
cnf(refute_0_375,plain,
greatest_lower_bound(multiply(X_104,X_105),multiply(X_104,X_106)) = multiply(X_104,greatest_lower_bound(X_105,X_106)),
inference(resolve,[$cnf( $equal(multiply(X_104,greatest_lower_bound(X_105,X_106)),greatest_lower_bound(multiply(X_104,X_105),multiply(X_104,X_106))) )],[refute_0_373,refute_0_374]) ).
cnf(refute_0_376,plain,
( greatest_lower_bound(multiply(X_104,X_105),multiply(X_104,X_106)) != multiply(X_104,greatest_lower_bound(X_105,X_106))
| least_upper_bound(greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105)),greatest_lower_bound(multiply(X_104,X_105),multiply(X_104,X_106))) != greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105))
| least_upper_bound(greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105)),multiply(X_104,greatest_lower_bound(X_105,X_106))) = greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105)),greatest_lower_bound(multiply(X_104,X_105),multiply(X_104,X_106))),greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105))) ),[0,1],$fot(multiply(X_104,greatest_lower_bound(X_105,X_106)))]]) ).
cnf(refute_0_377,plain,
( least_upper_bound(greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105)),greatest_lower_bound(multiply(X_104,X_105),multiply(X_104,X_106))) != greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105))
| least_upper_bound(greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105)),multiply(X_104,greatest_lower_bound(X_105,X_106))) = greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_104,X_105),multiply(X_104,X_106)),multiply(X_104,greatest_lower_bound(X_105,X_106))) )],[refute_0_375,refute_0_376]) ).
cnf(refute_0_378,plain,
least_upper_bound(greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105)),multiply(X_104,greatest_lower_bound(X_105,X_106))) = greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105)),greatest_lower_bound(multiply(X_104,X_105),multiply(X_104,X_106))),greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105))) )],[refute_0_372,refute_0_377]) ).
cnf(refute_0_379,plain,
least_upper_bound(greatest_lower_bound(X_105,X_106),greatest_lower_bound(X_106,X_105)) = greatest_lower_bound(X_105,X_106),
inference(subst,[],[refute_0_371:[bind(X_11,$fot(X_106)),bind(X_16,$fot(X_105))]]) ).
cnf(refute_0_380,plain,
multiply(X_104,least_upper_bound(greatest_lower_bound(X_105,X_106),greatest_lower_bound(X_106,X_105))) = multiply(X_104,least_upper_bound(greatest_lower_bound(X_105,X_106),greatest_lower_bound(X_106,X_105))),
introduced(tautology,[refl,[$fot(multiply(X_104,least_upper_bound(greatest_lower_bound(X_105,X_106),greatest_lower_bound(X_106,X_105))))]]) ).
cnf(refute_0_381,plain,
( multiply(X_104,least_upper_bound(greatest_lower_bound(X_105,X_106),greatest_lower_bound(X_106,X_105))) != multiply(X_104,least_upper_bound(greatest_lower_bound(X_105,X_106),greatest_lower_bound(X_106,X_105)))
| least_upper_bound(greatest_lower_bound(X_105,X_106),greatest_lower_bound(X_106,X_105)) != greatest_lower_bound(X_105,X_106)
| multiply(X_104,least_upper_bound(greatest_lower_bound(X_105,X_106),greatest_lower_bound(X_106,X_105))) = multiply(X_104,greatest_lower_bound(X_105,X_106)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_104,least_upper_bound(greatest_lower_bound(X_105,X_106),greatest_lower_bound(X_106,X_105))),multiply(X_104,least_upper_bound(greatest_lower_bound(X_105,X_106),greatest_lower_bound(X_106,X_105)))) ),[1,1],$fot(greatest_lower_bound(X_105,X_106))]]) ).
cnf(refute_0_382,plain,
( least_upper_bound(greatest_lower_bound(X_105,X_106),greatest_lower_bound(X_106,X_105)) != greatest_lower_bound(X_105,X_106)
| multiply(X_104,least_upper_bound(greatest_lower_bound(X_105,X_106),greatest_lower_bound(X_106,X_105))) = multiply(X_104,greatest_lower_bound(X_105,X_106)) ),
inference(resolve,[$cnf( $equal(multiply(X_104,least_upper_bound(greatest_lower_bound(X_105,X_106),greatest_lower_bound(X_106,X_105))),multiply(X_104,least_upper_bound(greatest_lower_bound(X_105,X_106),greatest_lower_bound(X_106,X_105)))) )],[refute_0_380,refute_0_381]) ).
cnf(refute_0_383,plain,
multiply(X_104,least_upper_bound(greatest_lower_bound(X_105,X_106),greatest_lower_bound(X_106,X_105))) = multiply(X_104,greatest_lower_bound(X_105,X_106)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_105,X_106),greatest_lower_bound(X_106,X_105)),greatest_lower_bound(X_105,X_106)) )],[refute_0_379,refute_0_382]) ).
cnf(refute_0_384,plain,
( multiply(X,least_upper_bound(Y,Z)) != least_upper_bound(multiply(X,Y),multiply(X,Z))
| least_upper_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(X,least_upper_bound(Y,Z)))),bind(Y0,$fot(least_upper_bound(multiply(X,Y),multiply(X,Z))))]]) ).
cnf(refute_0_385,plain,
least_upper_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Y),multiply(X,Z))) )],[monotony_lub1,refute_0_384]) ).
cnf(refute_0_386,plain,
least_upper_bound(multiply(X_104,greatest_lower_bound(X_105,X_106)),multiply(X_104,greatest_lower_bound(X_106,X_105))) = multiply(X_104,least_upper_bound(greatest_lower_bound(X_105,X_106),greatest_lower_bound(X_106,X_105))),
inference(subst,[],[refute_0_385:[bind(X,$fot(X_104)),bind(Y,$fot(greatest_lower_bound(X_105,X_106))),bind(Z,$fot(greatest_lower_bound(X_106,X_105)))]]) ).
cnf(refute_0_387,plain,
( multiply(X_104,least_upper_bound(greatest_lower_bound(X_105,X_106),greatest_lower_bound(X_106,X_105))) != multiply(X_104,greatest_lower_bound(X_105,X_106))
| least_upper_bound(multiply(X_104,greatest_lower_bound(X_105,X_106)),multiply(X_104,greatest_lower_bound(X_106,X_105))) != multiply(X_104,least_upper_bound(greatest_lower_bound(X_105,X_106),greatest_lower_bound(X_106,X_105)))
| least_upper_bound(multiply(X_104,greatest_lower_bound(X_105,X_106)),multiply(X_104,greatest_lower_bound(X_106,X_105))) = multiply(X_104,greatest_lower_bound(X_105,X_106)) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(least_upper_bound(multiply(X_104,greatest_lower_bound(X_105,X_106)),multiply(X_104,greatest_lower_bound(X_106,X_105))))),bind(Y0,$fot(multiply(X_104,least_upper_bound(greatest_lower_bound(X_105,X_106),greatest_lower_bound(X_106,X_105))))),bind(Z0,$fot(multiply(X_104,greatest_lower_bound(X_105,X_106))))]]) ).
cnf(refute_0_388,plain,
( multiply(X_104,least_upper_bound(greatest_lower_bound(X_105,X_106),greatest_lower_bound(X_106,X_105))) != multiply(X_104,greatest_lower_bound(X_105,X_106))
| least_upper_bound(multiply(X_104,greatest_lower_bound(X_105,X_106)),multiply(X_104,greatest_lower_bound(X_106,X_105))) = multiply(X_104,greatest_lower_bound(X_105,X_106)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_104,greatest_lower_bound(X_105,X_106)),multiply(X_104,greatest_lower_bound(X_106,X_105))),multiply(X_104,least_upper_bound(greatest_lower_bound(X_105,X_106),greatest_lower_bound(X_106,X_105)))) )],[refute_0_386,refute_0_387]) ).
cnf(refute_0_389,plain,
least_upper_bound(multiply(X_104,greatest_lower_bound(X_105,X_106)),multiply(X_104,greatest_lower_bound(X_106,X_105))) = multiply(X_104,greatest_lower_bound(X_105,X_106)),
inference(resolve,[$cnf( $equal(multiply(X_104,least_upper_bound(greatest_lower_bound(X_105,X_106),greatest_lower_bound(X_106,X_105))),multiply(X_104,greatest_lower_bound(X_105,X_106))) )],[refute_0_383,refute_0_388]) ).
cnf(refute_0_390,plain,
( multiply(X,greatest_lower_bound(Y,Z)) != greatest_lower_bound(multiply(X,Y),multiply(X,Z))
| greatest_lower_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,greatest_lower_bound(Y,Z)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(X,greatest_lower_bound(Y,Z)))),bind(Y0,$fot(greatest_lower_bound(multiply(X,Y),multiply(X,Z))))]]) ).
cnf(refute_0_391,plain,
greatest_lower_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) )],[monotony_glb1,refute_0_390]) ).
cnf(refute_0_392,plain,
greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105)) = multiply(X_104,greatest_lower_bound(X_106,X_105)),
inference(subst,[],[refute_0_391:[bind(X,$fot(X_104)),bind(Y,$fot(X_106)),bind(Z,$fot(X_105))]]) ).
cnf(refute_0_393,plain,
least_upper_bound(multiply(X_104,greatest_lower_bound(X_105,X_106)),greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105))) = least_upper_bound(multiply(X_104,greatest_lower_bound(X_105,X_106)),greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105))),
introduced(tautology,[refl,[$fot(least_upper_bound(multiply(X_104,greatest_lower_bound(X_105,X_106)),greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105))))]]) ).
cnf(refute_0_394,plain,
( greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105)) != multiply(X_104,greatest_lower_bound(X_106,X_105))
| least_upper_bound(multiply(X_104,greatest_lower_bound(X_105,X_106)),greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105))) != least_upper_bound(multiply(X_104,greatest_lower_bound(X_105,X_106)),greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105)))
| least_upper_bound(multiply(X_104,greatest_lower_bound(X_105,X_106)),greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105))) = least_upper_bound(multiply(X_104,greatest_lower_bound(X_105,X_106)),multiply(X_104,greatest_lower_bound(X_106,X_105))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_104,greatest_lower_bound(X_105,X_106)),greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105))),least_upper_bound(multiply(X_104,greatest_lower_bound(X_105,X_106)),greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105)))) ),[1,1],$fot(multiply(X_104,greatest_lower_bound(X_106,X_105)))]]) ).
cnf(refute_0_395,plain,
( greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105)) != multiply(X_104,greatest_lower_bound(X_106,X_105))
| least_upper_bound(multiply(X_104,greatest_lower_bound(X_105,X_106)),greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105))) = least_upper_bound(multiply(X_104,greatest_lower_bound(X_105,X_106)),multiply(X_104,greatest_lower_bound(X_106,X_105))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_104,greatest_lower_bound(X_105,X_106)),greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105))),least_upper_bound(multiply(X_104,greatest_lower_bound(X_105,X_106)),greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105)))) )],[refute_0_393,refute_0_394]) ).
cnf(refute_0_396,plain,
least_upper_bound(multiply(X_104,greatest_lower_bound(X_105,X_106)),greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105))) = least_upper_bound(multiply(X_104,greatest_lower_bound(X_105,X_106)),multiply(X_104,greatest_lower_bound(X_106,X_105))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105)),multiply(X_104,greatest_lower_bound(X_106,X_105))) )],[refute_0_392,refute_0_395]) ).
cnf(refute_0_397,plain,
( least_upper_bound(multiply(X_104,greatest_lower_bound(X_105,X_106)),multiply(X_104,greatest_lower_bound(X_106,X_105))) != multiply(X_104,greatest_lower_bound(X_105,X_106))
| least_upper_bound(multiply(X_104,greatest_lower_bound(X_105,X_106)),greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105))) != least_upper_bound(multiply(X_104,greatest_lower_bound(X_105,X_106)),multiply(X_104,greatest_lower_bound(X_106,X_105)))
| least_upper_bound(multiply(X_104,greatest_lower_bound(X_105,X_106)),greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105))) = multiply(X_104,greatest_lower_bound(X_105,X_106)) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(least_upper_bound(multiply(X_104,greatest_lower_bound(X_105,X_106)),greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105))))),bind(Y0,$fot(least_upper_bound(multiply(X_104,greatest_lower_bound(X_105,X_106)),multiply(X_104,greatest_lower_bound(X_106,X_105))))),bind(Z0,$fot(multiply(X_104,greatest_lower_bound(X_105,X_106))))]]) ).
cnf(refute_0_398,plain,
( least_upper_bound(multiply(X_104,greatest_lower_bound(X_105,X_106)),multiply(X_104,greatest_lower_bound(X_106,X_105))) != multiply(X_104,greatest_lower_bound(X_105,X_106))
| least_upper_bound(multiply(X_104,greatest_lower_bound(X_105,X_106)),greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105))) = multiply(X_104,greatest_lower_bound(X_105,X_106)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_104,greatest_lower_bound(X_105,X_106)),greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105))),least_upper_bound(multiply(X_104,greatest_lower_bound(X_105,X_106)),multiply(X_104,greatest_lower_bound(X_106,X_105)))) )],[refute_0_396,refute_0_397]) ).
cnf(refute_0_399,plain,
least_upper_bound(multiply(X_104,greatest_lower_bound(X_105,X_106)),greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105))) = multiply(X_104,greatest_lower_bound(X_105,X_106)),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_104,greatest_lower_bound(X_105,X_106)),multiply(X_104,greatest_lower_bound(X_106,X_105))),multiply(X_104,greatest_lower_bound(X_105,X_106))) )],[refute_0_389,refute_0_398]) ).
cnf(refute_0_400,plain,
least_upper_bound(greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105)),multiply(X_104,greatest_lower_bound(X_105,X_106))) = least_upper_bound(multiply(X_104,greatest_lower_bound(X_105,X_106)),greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105))),
inference(subst,[],[refute_0_25:[bind(X,$fot(multiply(X_104,greatest_lower_bound(X_105,X_106)))),bind(Y,$fot(greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105))))]]) ).
cnf(refute_0_401,plain,
( least_upper_bound(multiply(X_104,greatest_lower_bound(X_105,X_106)),greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105))) != multiply(X_104,greatest_lower_bound(X_105,X_106))
| least_upper_bound(greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105)),multiply(X_104,greatest_lower_bound(X_105,X_106))) != least_upper_bound(multiply(X_104,greatest_lower_bound(X_105,X_106)),greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105)))
| least_upper_bound(greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105)),multiply(X_104,greatest_lower_bound(X_105,X_106))) = multiply(X_104,greatest_lower_bound(X_105,X_106)) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105)),multiply(X_104,greatest_lower_bound(X_105,X_106))))),bind(Y0,$fot(least_upper_bound(multiply(X_104,greatest_lower_bound(X_105,X_106)),greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105))))),bind(Z0,$fot(multiply(X_104,greatest_lower_bound(X_105,X_106))))]]) ).
cnf(refute_0_402,plain,
( least_upper_bound(multiply(X_104,greatest_lower_bound(X_105,X_106)),greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105))) != multiply(X_104,greatest_lower_bound(X_105,X_106))
| least_upper_bound(greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105)),multiply(X_104,greatest_lower_bound(X_105,X_106))) = multiply(X_104,greatest_lower_bound(X_105,X_106)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105)),multiply(X_104,greatest_lower_bound(X_105,X_106))),least_upper_bound(multiply(X_104,greatest_lower_bound(X_105,X_106)),greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105)))) )],[refute_0_400,refute_0_401]) ).
cnf(refute_0_403,plain,
least_upper_bound(greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105)),multiply(X_104,greatest_lower_bound(X_105,X_106))) = multiply(X_104,greatest_lower_bound(X_105,X_106)),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_104,greatest_lower_bound(X_105,X_106)),greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105))),multiply(X_104,greatest_lower_bound(X_105,X_106))) )],[refute_0_399,refute_0_402]) ).
cnf(refute_0_404,plain,
( least_upper_bound(greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105)),multiply(X_104,greatest_lower_bound(X_105,X_106))) != multiply(X_104,greatest_lower_bound(X_105,X_106))
| least_upper_bound(greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105)),multiply(X_104,greatest_lower_bound(X_105,X_106))) != greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105))
| multiply(X_104,greatest_lower_bound(X_105,X_106)) = greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105)),multiply(X_104,greatest_lower_bound(X_105,X_106))),greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105))) ),[0],$fot(multiply(X_104,greatest_lower_bound(X_105,X_106)))]]) ).
cnf(refute_0_405,plain,
( least_upper_bound(greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105)),multiply(X_104,greatest_lower_bound(X_105,X_106))) != greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105))
| multiply(X_104,greatest_lower_bound(X_105,X_106)) = greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105)),multiply(X_104,greatest_lower_bound(X_105,X_106))),multiply(X_104,greatest_lower_bound(X_105,X_106))) )],[refute_0_403,refute_0_404]) ).
cnf(refute_0_406,plain,
( multiply(X_104,greatest_lower_bound(X_105,X_106)) != greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105))
| greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105)) != multiply(X_104,greatest_lower_bound(X_106,X_105))
| multiply(X_104,greatest_lower_bound(X_105,X_106)) = multiply(X_104,greatest_lower_bound(X_106,X_105)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_104,greatest_lower_bound(X_105,X_106)),multiply(X_104,greatest_lower_bound(X_106,X_105))) ),[0],$fot(greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105)))]]) ).
cnf(refute_0_407,plain,
( multiply(X_104,greatest_lower_bound(X_105,X_106)) != greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105))
| multiply(X_104,greatest_lower_bound(X_105,X_106)) = multiply(X_104,greatest_lower_bound(X_106,X_105)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105)),multiply(X_104,greatest_lower_bound(X_106,X_105))) )],[refute_0_392,refute_0_406]) ).
cnf(refute_0_408,plain,
( least_upper_bound(greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105)),multiply(X_104,greatest_lower_bound(X_105,X_106))) != greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105))
| multiply(X_104,greatest_lower_bound(X_105,X_106)) = multiply(X_104,greatest_lower_bound(X_106,X_105)) ),
inference(resolve,[$cnf( $equal(multiply(X_104,greatest_lower_bound(X_105,X_106)),greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105))) )],[refute_0_405,refute_0_407]) ).
cnf(refute_0_409,plain,
multiply(X_104,greatest_lower_bound(X_105,X_106)) = multiply(X_104,greatest_lower_bound(X_106,X_105)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105)),multiply(X_104,greatest_lower_bound(X_105,X_106))),greatest_lower_bound(multiply(X_104,X_106),multiply(X_104,X_105))) )],[refute_0_378,refute_0_408]) ).
cnf(refute_0_410,plain,
( multiply(X_104,greatest_lower_bound(X_105,X_106)) != multiply(X_104,greatest_lower_bound(X_106,X_105))
| multiply(X_104,greatest_lower_bound(X_106,X_105)) = multiply(X_104,greatest_lower_bound(X_105,X_106)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(X_104,greatest_lower_bound(X_105,X_106)))),bind(Y0,$fot(multiply(X_104,greatest_lower_bound(X_106,X_105))))]]) ).
cnf(refute_0_411,plain,
multiply(X_104,greatest_lower_bound(X_106,X_105)) = multiply(X_104,greatest_lower_bound(X_105,X_106)),
inference(resolve,[$cnf( $equal(multiply(X_104,greatest_lower_bound(X_105,X_106)),multiply(X_104,greatest_lower_bound(X_106,X_105))) )],[refute_0_409,refute_0_410]) ).
cnf(refute_0_412,plain,
multiply(X_17,greatest_lower_bound(greatest_lower_bound(X_108,identity),identity)) = multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_108,identity))),
inference(subst,[],[refute_0_411:[bind(X_104,$fot(X_17)),bind(X_105,$fot(identity)),bind(X_106,$fot(greatest_lower_bound(X_108,identity)))]]) ).
cnf(refute_0_413,plain,
( multiply(X_104,greatest_lower_bound(X_105,identity)) != greatest_lower_bound(X_104,multiply(X_104,X_105))
| greatest_lower_bound(X_104,multiply(X_104,X_105)) = multiply(X_104,greatest_lower_bound(X_105,identity)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(X_104,greatest_lower_bound(X_105,identity)))),bind(Y0,$fot(greatest_lower_bound(X_104,multiply(X_104,X_105))))]]) ).
cnf(refute_0_414,plain,
greatest_lower_bound(X_104,multiply(X_104,X_105)) = multiply(X_104,greatest_lower_bound(X_105,identity)),
inference(resolve,[$cnf( $equal(multiply(X_104,greatest_lower_bound(X_105,identity)),greatest_lower_bound(X_104,multiply(X_104,X_105))) )],[refute_0_319,refute_0_413]) ).
cnf(refute_0_415,plain,
greatest_lower_bound(X_17,multiply(X_17,greatest_lower_bound(X_108,identity))) = multiply(X_17,greatest_lower_bound(greatest_lower_bound(X_108,identity),identity)),
inference(subst,[],[refute_0_414:[bind(X_104,$fot(X_17)),bind(X_105,$fot(greatest_lower_bound(X_108,identity)))]]) ).
cnf(refute_0_416,plain,
( multiply(X_17,greatest_lower_bound(greatest_lower_bound(X_108,identity),identity)) != multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_108,identity)))
| greatest_lower_bound(X_17,multiply(X_17,greatest_lower_bound(X_108,identity))) != multiply(X_17,greatest_lower_bound(greatest_lower_bound(X_108,identity),identity))
| greatest_lower_bound(X_17,multiply(X_17,greatest_lower_bound(X_108,identity))) = multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_108,identity))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(greatest_lower_bound(X_17,multiply(X_17,greatest_lower_bound(X_108,identity))))),bind(Y0,$fot(multiply(X_17,greatest_lower_bound(greatest_lower_bound(X_108,identity),identity)))),bind(Z0,$fot(multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_108,identity)))))]]) ).
cnf(refute_0_417,plain,
( multiply(X_17,greatest_lower_bound(greatest_lower_bound(X_108,identity),identity)) != multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_108,identity)))
| greatest_lower_bound(X_17,multiply(X_17,greatest_lower_bound(X_108,identity))) = multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_108,identity))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,multiply(X_17,greatest_lower_bound(X_108,identity))),multiply(X_17,greatest_lower_bound(greatest_lower_bound(X_108,identity),identity))) )],[refute_0_415,refute_0_416]) ).
cnf(refute_0_418,plain,
greatest_lower_bound(X_17,multiply(X_17,greatest_lower_bound(X_108,identity))) = multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_108,identity))),
inference(resolve,[$cnf( $equal(multiply(X_17,greatest_lower_bound(greatest_lower_bound(X_108,identity),identity)),multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_108,identity)))) )],[refute_0_412,refute_0_417]) ).
cnf(refute_0_419,plain,
( multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_108,identity))) != multiply(X_17,greatest_lower_bound(identity,X_108))
| greatest_lower_bound(X_17,multiply(X_17,greatest_lower_bound(X_108,identity))) != multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_108,identity)))
| greatest_lower_bound(X_17,multiply(X_17,greatest_lower_bound(X_108,identity))) = multiply(X_17,greatest_lower_bound(identity,X_108)) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(greatest_lower_bound(X_17,multiply(X_17,greatest_lower_bound(X_108,identity))))),bind(Y0,$fot(multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_108,identity))))),bind(Z0,$fot(multiply(X_17,greatest_lower_bound(identity,X_108))))]]) ).
cnf(refute_0_420,plain,
( multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_108,identity))) != multiply(X_17,greatest_lower_bound(identity,X_108))
| greatest_lower_bound(X_17,multiply(X_17,greatest_lower_bound(X_108,identity))) = multiply(X_17,greatest_lower_bound(identity,X_108)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,multiply(X_17,greatest_lower_bound(X_108,identity))),multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_108,identity)))) )],[refute_0_418,refute_0_419]) ).
cnf(refute_0_421,plain,
greatest_lower_bound(X_17,multiply(X_17,greatest_lower_bound(X_108,identity))) = multiply(X_17,greatest_lower_bound(identity,X_108)),
inference(resolve,[$cnf( $equal(multiply(X_17,greatest_lower_bound(identity,greatest_lower_bound(X_108,identity))),multiply(X_17,greatest_lower_bound(identity,X_108))) )],[refute_0_366,refute_0_420]) ).
cnf(refute_0_422,plain,
( greatest_lower_bound(X_17,multiply(X_17,greatest_lower_bound(X_108,identity))) != multiply(X_17,greatest_lower_bound(identity,X_108))
| greatest_lower_bound(X_17,multiply(X_17,greatest_lower_bound(X_108,identity))) != greatest_lower_bound(X_17,multiply(X_17,X_108))
| multiply(X_17,greatest_lower_bound(identity,X_108)) = greatest_lower_bound(X_17,multiply(X_17,X_108)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_17,multiply(X_17,greatest_lower_bound(X_108,identity))),greatest_lower_bound(X_17,multiply(X_17,X_108))) ),[0],$fot(multiply(X_17,greatest_lower_bound(identity,X_108)))]]) ).
cnf(refute_0_423,plain,
( greatest_lower_bound(X_17,multiply(X_17,greatest_lower_bound(X_108,identity))) != greatest_lower_bound(X_17,multiply(X_17,X_108))
| multiply(X_17,greatest_lower_bound(identity,X_108)) = greatest_lower_bound(X_17,multiply(X_17,X_108)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,multiply(X_17,greatest_lower_bound(X_108,identity))),multiply(X_17,greatest_lower_bound(identity,X_108))) )],[refute_0_421,refute_0_422]) ).
cnf(refute_0_424,plain,
( multiply(X_17,greatest_lower_bound(identity,X_108)) != greatest_lower_bound(X_17,multiply(X_17,X_108))
| greatest_lower_bound(X_17,multiply(X_17,X_108)) != multiply(X_17,greatest_lower_bound(X_108,identity))
| multiply(X_17,greatest_lower_bound(identity,X_108)) = multiply(X_17,greatest_lower_bound(X_108,identity)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_17,greatest_lower_bound(identity,X_108)),multiply(X_17,greatest_lower_bound(X_108,identity))) ),[0],$fot(greatest_lower_bound(X_17,multiply(X_17,X_108)))]]) ).
cnf(refute_0_425,plain,
( multiply(X_17,greatest_lower_bound(identity,X_108)) != greatest_lower_bound(X_17,multiply(X_17,X_108))
| multiply(X_17,greatest_lower_bound(identity,X_108)) = multiply(X_17,greatest_lower_bound(X_108,identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,multiply(X_17,X_108)),multiply(X_17,greatest_lower_bound(X_108,identity))) )],[refute_0_358,refute_0_424]) ).
cnf(refute_0_426,plain,
( greatest_lower_bound(X_17,multiply(X_17,greatest_lower_bound(X_108,identity))) != greatest_lower_bound(X_17,multiply(X_17,X_108))
| multiply(X_17,greatest_lower_bound(identity,X_108)) = multiply(X_17,greatest_lower_bound(X_108,identity)) ),
inference(resolve,[$cnf( $equal(multiply(X_17,greatest_lower_bound(identity,X_108)),greatest_lower_bound(X_17,multiply(X_17,X_108))) )],[refute_0_423,refute_0_425]) ).
cnf(refute_0_427,plain,
multiply(X_17,greatest_lower_bound(identity,X_108)) = multiply(X_17,greatest_lower_bound(X_108,identity)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,multiply(X_17,greatest_lower_bound(X_108,identity))),greatest_lower_bound(X_17,multiply(X_17,X_108))) )],[refute_0_361,refute_0_426]) ).
cnf(refute_0_428,plain,
( multiply(X_17,greatest_lower_bound(identity,X_108)) != multiply(X_17,greatest_lower_bound(X_108,identity))
| multiply(X_17,greatest_lower_bound(X_108,identity)) = multiply(X_17,greatest_lower_bound(identity,X_108)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(X_17,greatest_lower_bound(identity,X_108)))),bind(Y0,$fot(multiply(X_17,greatest_lower_bound(X_108,identity))))]]) ).
cnf(refute_0_429,plain,
multiply(X_17,greatest_lower_bound(X_108,identity)) = multiply(X_17,greatest_lower_bound(identity,X_108)),
inference(resolve,[$cnf( $equal(multiply(X_17,greatest_lower_bound(identity,X_108)),multiply(X_17,greatest_lower_bound(X_108,identity))) )],[refute_0_427,refute_0_428]) ).
cnf(refute_0_430,plain,
multiply(identity,greatest_lower_bound(inverse(X_125),identity)) = multiply(identity,greatest_lower_bound(identity,inverse(X_125))),
inference(subst,[],[refute_0_429:[bind(X_108,$fot(inverse(X_125))),bind(X_17,$fot(identity))]]) ).
cnf(refute_0_431,plain,
( multiply(identity,greatest_lower_bound(identity,inverse(X_125))) != greatest_lower_bound(identity,inverse(X_125))
| multiply(identity,greatest_lower_bound(inverse(X_125),identity)) != multiply(identity,greatest_lower_bound(identity,inverse(X_125)))
| multiply(identity,greatest_lower_bound(inverse(X_125),identity)) = greatest_lower_bound(identity,inverse(X_125)) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(identity,greatest_lower_bound(inverse(X_125),identity)))),bind(Y0,$fot(multiply(identity,greatest_lower_bound(identity,inverse(X_125))))),bind(Z0,$fot(greatest_lower_bound(identity,inverse(X_125))))]]) ).
cnf(refute_0_432,plain,
( multiply(identity,greatest_lower_bound(identity,inverse(X_125))) != greatest_lower_bound(identity,inverse(X_125))
| multiply(identity,greatest_lower_bound(inverse(X_125),identity)) = greatest_lower_bound(identity,inverse(X_125)) ),
inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(inverse(X_125),identity)),multiply(identity,greatest_lower_bound(identity,inverse(X_125)))) )],[refute_0_430,refute_0_431]) ).
cnf(refute_0_433,plain,
multiply(identity,greatest_lower_bound(inverse(X_125),identity)) = greatest_lower_bound(identity,inverse(X_125)),
inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(identity,inverse(X_125))),greatest_lower_bound(identity,inverse(X_125))) )],[refute_0_336,refute_0_432]) ).
cnf(refute_0_434,plain,
( multiply(identity,greatest_lower_bound(inverse(X_125),identity)) != multiply(greatest_lower_bound(identity,X_125),inverse(X_125))
| multiply(identity,greatest_lower_bound(inverse(X_125),identity)) != greatest_lower_bound(identity,inverse(X_125))
| greatest_lower_bound(identity,inverse(X_125)) = multiply(greatest_lower_bound(identity,X_125),inverse(X_125)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,greatest_lower_bound(inverse(X_125),identity)),multiply(greatest_lower_bound(identity,X_125),inverse(X_125))) ),[0],$fot(greatest_lower_bound(identity,inverse(X_125)))]]) ).
cnf(refute_0_435,plain,
( multiply(identity,greatest_lower_bound(inverse(X_125),identity)) != multiply(greatest_lower_bound(identity,X_125),inverse(X_125))
| greatest_lower_bound(identity,inverse(X_125)) = multiply(greatest_lower_bound(identity,X_125),inverse(X_125)) ),
inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(inverse(X_125),identity)),greatest_lower_bound(identity,inverse(X_125))) )],[refute_0_433,refute_0_434]) ).
cnf(refute_0_436,plain,
greatest_lower_bound(identity,inverse(X_125)) = multiply(greatest_lower_bound(identity,X_125),inverse(X_125)),
inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(inverse(X_125),identity)),multiply(greatest_lower_bound(identity,X_125),inverse(X_125))) )],[refute_0_335,refute_0_435]) ).
cnf(refute_0_437,plain,
( greatest_lower_bound(identity,inverse(X_125)) != multiply(greatest_lower_bound(identity,X_125),inverse(X_125))
| multiply(greatest_lower_bound(identity,X_125),inverse(X_125)) = greatest_lower_bound(identity,inverse(X_125)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(greatest_lower_bound(identity,inverse(X_125)))),bind(Y0,$fot(multiply(greatest_lower_bound(identity,X_125),inverse(X_125))))]]) ).
cnf(refute_0_438,plain,
multiply(greatest_lower_bound(identity,X_125),inverse(X_125)) = greatest_lower_bound(identity,inverse(X_125)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(X_125)),multiply(greatest_lower_bound(identity,X_125),inverse(X_125))) )],[refute_0_436,refute_0_437]) ).
cnf(refute_0_439,plain,
( multiply(greatest_lower_bound(identity,X_125),inverse(X_125)) != greatest_lower_bound(identity,inverse(X_125))
| inverse(inverse(X_125)) != multiply(inverse(multiply(greatest_lower_bound(identity,X_125),inverse(X_125))),greatest_lower_bound(identity,X_125))
| inverse(inverse(X_125)) = multiply(inverse(greatest_lower_bound(identity,inverse(X_125))),greatest_lower_bound(identity,X_125)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_125)),multiply(inverse(multiply(greatest_lower_bound(identity,X_125),inverse(X_125))),greatest_lower_bound(identity,X_125))) ),[1,0,0],$fot(greatest_lower_bound(identity,inverse(X_125)))]]) ).
cnf(refute_0_440,plain,
( inverse(inverse(X_125)) != multiply(inverse(multiply(greatest_lower_bound(identity,X_125),inverse(X_125))),greatest_lower_bound(identity,X_125))
| inverse(inverse(X_125)) = multiply(inverse(greatest_lower_bound(identity,inverse(X_125))),greatest_lower_bound(identity,X_125)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_125),inverse(X_125)),greatest_lower_bound(identity,inverse(X_125))) )],[refute_0_438,refute_0_439]) ).
cnf(refute_0_441,plain,
inverse(inverse(X_125)) = multiply(inverse(greatest_lower_bound(identity,inverse(X_125))),greatest_lower_bound(identity,X_125)),
inference(resolve,[$cnf( $equal(inverse(inverse(X_125)),multiply(inverse(multiply(greatest_lower_bound(identity,X_125),inverse(X_125))),greatest_lower_bound(identity,X_125))) )],[refute_0_308,refute_0_440]) ).
cnf(refute_0_442,plain,
inverse(inverse(X_35)) = multiply(inverse(inverse(X_35)),identity),
inference(subst,[],[refute_0_86:[bind(X_33,$fot(inverse(inverse(X_35))))]]) ).
cnf(refute_0_443,plain,
multiply(X_35,identity) = multiply(inverse(inverse(X_35)),identity),
inference(subst,[],[refute_0_65:[bind(X_32,$fot(X_35)),bind(X_33,$fot(identity))]]) ).
cnf(refute_0_444,plain,
( multiply(X_35,identity) != multiply(inverse(inverse(X_35)),identity)
| multiply(inverse(inverse(X_35)),identity) = multiply(X_35,identity) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(X_35,identity))),bind(Y0,$fot(multiply(inverse(inverse(X_35)),identity)))]]) ).
cnf(refute_0_445,plain,
multiply(inverse(inverse(X_35)),identity) = multiply(X_35,identity),
inference(resolve,[$cnf( $equal(multiply(X_35,identity),multiply(inverse(inverse(X_35)),identity)) )],[refute_0_443,refute_0_444]) ).
cnf(refute_0_446,plain,
( multiply(inverse(inverse(X_35)),identity) != multiply(X_35,identity)
| inverse(inverse(X_35)) != multiply(inverse(inverse(X_35)),identity)
| inverse(inverse(X_35)) = multiply(X_35,identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_35)),multiply(inverse(inverse(X_35)),identity)) ),[1],$fot(multiply(X_35,identity))]]) ).
cnf(refute_0_447,plain,
( inverse(inverse(X_35)) != multiply(inverse(inverse(X_35)),identity)
| inverse(inverse(X_35)) = multiply(X_35,identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_35)),identity),multiply(X_35,identity)) )],[refute_0_445,refute_0_446]) ).
cnf(refute_0_448,plain,
inverse(inverse(X_35)) = multiply(X_35,identity),
inference(resolve,[$cnf( $equal(inverse(inverse(X_35)),multiply(inverse(inverse(X_35)),identity)) )],[refute_0_442,refute_0_447]) ).
cnf(refute_0_449,plain,
multiply(X_35,identity) = X_35,
inference(subst,[],[refute_0_88:[bind(X_33,$fot(X_35))]]) ).
cnf(refute_0_450,plain,
( multiply(X_35,identity) != X_35
| inverse(inverse(X_35)) != multiply(X_35,identity)
| inverse(inverse(X_35)) = X_35 ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_35)),multiply(X_35,identity)) ),[1],$fot(X_35)]]) ).
cnf(refute_0_451,plain,
( inverse(inverse(X_35)) != multiply(X_35,identity)
| inverse(inverse(X_35)) = X_35 ),
inference(resolve,[$cnf( $equal(multiply(X_35,identity),X_35) )],[refute_0_449,refute_0_450]) ).
cnf(refute_0_452,plain,
inverse(inverse(X_35)) = X_35,
inference(resolve,[$cnf( $equal(inverse(inverse(X_35)),multiply(X_35,identity)) )],[refute_0_448,refute_0_451]) ).
cnf(refute_0_453,plain,
inverse(inverse(X_125)) = X_125,
inference(subst,[],[refute_0_452:[bind(X_35,$fot(X_125))]]) ).
cnf(refute_0_454,plain,
( inverse(inverse(X_125)) != X_125
| inverse(inverse(X_125)) != multiply(inverse(greatest_lower_bound(identity,inverse(X_125))),greatest_lower_bound(identity,X_125))
| X_125 = multiply(inverse(greatest_lower_bound(identity,inverse(X_125))),greatest_lower_bound(identity,X_125)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_125)),multiply(inverse(greatest_lower_bound(identity,inverse(X_125))),greatest_lower_bound(identity,X_125))) ),[0],$fot(X_125)]]) ).
cnf(refute_0_455,plain,
( inverse(inverse(X_125)) != multiply(inverse(greatest_lower_bound(identity,inverse(X_125))),greatest_lower_bound(identity,X_125))
| X_125 = multiply(inverse(greatest_lower_bound(identity,inverse(X_125))),greatest_lower_bound(identity,X_125)) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_125)),X_125) )],[refute_0_453,refute_0_454]) ).
cnf(refute_0_456,plain,
X_125 = multiply(inverse(greatest_lower_bound(identity,inverse(X_125))),greatest_lower_bound(identity,X_125)),
inference(resolve,[$cnf( $equal(inverse(inverse(X_125)),multiply(inverse(greatest_lower_bound(identity,inverse(X_125))),greatest_lower_bound(identity,X_125))) )],[refute_0_441,refute_0_455]) ).
cnf(refute_0_457,plain,
X_150 = multiply(inverse(greatest_lower_bound(identity,inverse(X_150))),greatest_lower_bound(identity,X_150)),
inference(subst,[],[refute_0_456:[bind(X_125,$fot(X_150))]]) ).
cnf(refute_0_458,plain,
( X_150 != multiply(inverse(greatest_lower_bound(identity,inverse(X_150))),greatest_lower_bound(identity,X_150))
| multiply(inverse(greatest_lower_bound(identity,inverse(X_150))),greatest_lower_bound(identity,X_150)) = X_150 ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(X_150)),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(identity,inverse(X_150))),greatest_lower_bound(identity,X_150))))]]) ).
cnf(refute_0_459,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X_150))),greatest_lower_bound(identity,X_150)) = X_150,
inference(resolve,[$cnf( $equal(X_150,multiply(inverse(greatest_lower_bound(identity,inverse(X_150))),greatest_lower_bound(identity,X_150))) )],[refute_0_457,refute_0_458]) ).
cnf(refute_0_460,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(X_150))),greatest_lower_bound(identity,X_150)) != X_150
| inverse(greatest_lower_bound(identity,X_150)) != multiply(inverse(multiply(inverse(greatest_lower_bound(identity,inverse(X_150))),greatest_lower_bound(identity,X_150))),inverse(greatest_lower_bound(identity,inverse(X_150))))
| inverse(greatest_lower_bound(identity,X_150)) = multiply(inverse(X_150),inverse(greatest_lower_bound(identity,inverse(X_150)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,X_150)),multiply(inverse(multiply(inverse(greatest_lower_bound(identity,inverse(X_150))),greatest_lower_bound(identity,X_150))),inverse(greatest_lower_bound(identity,inverse(X_150))))) ),[1,0,0],$fot(X_150)]]) ).
cnf(refute_0_461,plain,
( inverse(greatest_lower_bound(identity,X_150)) != multiply(inverse(multiply(inverse(greatest_lower_bound(identity,inverse(X_150))),greatest_lower_bound(identity,X_150))),inverse(greatest_lower_bound(identity,inverse(X_150))))
| inverse(greatest_lower_bound(identity,X_150)) = multiply(inverse(X_150),inverse(greatest_lower_bound(identity,inverse(X_150)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X_150))),greatest_lower_bound(identity,X_150)),X_150) )],[refute_0_459,refute_0_460]) ).
cnf(refute_0_462,plain,
inverse(greatest_lower_bound(identity,X_150)) = multiply(inverse(X_150),inverse(greatest_lower_bound(identity,inverse(X_150)))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,X_150)),multiply(inverse(multiply(inverse(greatest_lower_bound(identity,inverse(X_150))),greatest_lower_bound(identity,X_150))),inverse(greatest_lower_bound(identity,inverse(X_150))))) )],[refute_0_307,refute_0_461]) ).
cnf(refute_0_463,plain,
multiply(identity,greatest_lower_bound(X_150,identity)) = greatest_lower_bound(X_150,identity),
inference(subst,[],[left_identity:[bind(X,$fot(greatest_lower_bound(X_150,identity)))]]) ).
cnf(refute_0_464,plain,
greatest_lower_bound(identity,multiply(identity,X_150)) = multiply(identity,greatest_lower_bound(X_150,identity)),
inference(subst,[],[refute_0_414:[bind(X_104,$fot(identity)),bind(X_105,$fot(X_150))]]) ).
cnf(refute_0_465,plain,
( multiply(identity,greatest_lower_bound(X_150,identity)) != greatest_lower_bound(X_150,identity)
| greatest_lower_bound(identity,multiply(identity,X_150)) != multiply(identity,greatest_lower_bound(X_150,identity))
| greatest_lower_bound(identity,multiply(identity,X_150)) = greatest_lower_bound(X_150,identity) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(greatest_lower_bound(identity,multiply(identity,X_150)))),bind(Y0,$fot(multiply(identity,greatest_lower_bound(X_150,identity)))),bind(Z0,$fot(greatest_lower_bound(X_150,identity)))]]) ).
cnf(refute_0_466,plain,
( multiply(identity,greatest_lower_bound(X_150,identity)) != greatest_lower_bound(X_150,identity)
| greatest_lower_bound(identity,multiply(identity,X_150)) = greatest_lower_bound(X_150,identity) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(identity,X_150)),multiply(identity,greatest_lower_bound(X_150,identity))) )],[refute_0_464,refute_0_465]) ).
cnf(refute_0_467,plain,
greatest_lower_bound(identity,multiply(identity,X_150)) = greatest_lower_bound(X_150,identity),
inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(X_150,identity)),greatest_lower_bound(X_150,identity)) )],[refute_0_463,refute_0_466]) ).
cnf(refute_0_468,plain,
multiply(greatest_lower_bound(X_120,inverse(X_119)),X_119) = greatest_lower_bound(multiply(X_120,X_119),multiply(inverse(X_119),X_119)),
inference(subst,[],[monotony_glb2:[bind(X,$fot(X_119)),bind(Y,$fot(X_120)),bind(Z,$fot(inverse(X_119)))]]) ).
cnf(refute_0_469,plain,
multiply(inverse(X_119),X_119) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_119))]]) ).
cnf(refute_0_470,plain,
( multiply(greatest_lower_bound(X_120,inverse(X_119)),X_119) != greatest_lower_bound(multiply(X_120,X_119),multiply(inverse(X_119),X_119))
| multiply(inverse(X_119),X_119) != identity
| multiply(greatest_lower_bound(X_120,inverse(X_119)),X_119) = greatest_lower_bound(multiply(X_120,X_119),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_120,inverse(X_119)),X_119),greatest_lower_bound(multiply(X_120,X_119),multiply(inverse(X_119),X_119))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_471,plain,
( multiply(greatest_lower_bound(X_120,inverse(X_119)),X_119) != greatest_lower_bound(multiply(X_120,X_119),multiply(inverse(X_119),X_119))
| multiply(greatest_lower_bound(X_120,inverse(X_119)),X_119) = greatest_lower_bound(multiply(X_120,X_119),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_119),X_119),identity) )],[refute_0_469,refute_0_470]) ).
cnf(refute_0_472,plain,
multiply(greatest_lower_bound(X_120,inverse(X_119)),X_119) = greatest_lower_bound(multiply(X_120,X_119),identity),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_120,inverse(X_119)),X_119),greatest_lower_bound(multiply(X_120,X_119),multiply(inverse(X_119),X_119))) )],[refute_0_468,refute_0_471]) ).
cnf(refute_0_473,plain,
greatest_lower_bound(multiply(X_120,X_119),identity) = greatest_lower_bound(identity,multiply(X_120,X_119)),
inference(subst,[],[refute_0_42:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_120,X_119)))]]) ).
cnf(refute_0_474,plain,
( multiply(greatest_lower_bound(X_120,inverse(X_119)),X_119) != greatest_lower_bound(multiply(X_120,X_119),identity)
| greatest_lower_bound(multiply(X_120,X_119),identity) != greatest_lower_bound(identity,multiply(X_120,X_119))
| multiply(greatest_lower_bound(X_120,inverse(X_119)),X_119) = greatest_lower_bound(identity,multiply(X_120,X_119)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_120,inverse(X_119)),X_119),greatest_lower_bound(identity,multiply(X_120,X_119))) ),[0],$fot(greatest_lower_bound(multiply(X_120,X_119),identity))]]) ).
cnf(refute_0_475,plain,
( multiply(greatest_lower_bound(X_120,inverse(X_119)),X_119) != greatest_lower_bound(multiply(X_120,X_119),identity)
| multiply(greatest_lower_bound(X_120,inverse(X_119)),X_119) = greatest_lower_bound(identity,multiply(X_120,X_119)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_120,X_119),identity),greatest_lower_bound(identity,multiply(X_120,X_119))) )],[refute_0_473,refute_0_474]) ).
cnf(refute_0_476,plain,
multiply(greatest_lower_bound(X_120,inverse(X_119)),X_119) = greatest_lower_bound(identity,multiply(X_120,X_119)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_120,inverse(X_119)),X_119),greatest_lower_bound(multiply(X_120,X_119),identity)) )],[refute_0_472,refute_0_475]) ).
cnf(refute_0_477,plain,
multiply(greatest_lower_bound(identity,inverse(X_150)),X_150) = greatest_lower_bound(identity,multiply(identity,X_150)),
inference(subst,[],[refute_0_476:[bind(X_119,$fot(X_150)),bind(X_120,$fot(identity))]]) ).
cnf(refute_0_478,plain,
( multiply(greatest_lower_bound(identity,inverse(X_150)),X_150) != greatest_lower_bound(identity,multiply(identity,X_150))
| greatest_lower_bound(identity,multiply(identity,X_150)) != greatest_lower_bound(X_150,identity)
| multiply(greatest_lower_bound(identity,inverse(X_150)),X_150) = greatest_lower_bound(X_150,identity) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(greatest_lower_bound(identity,inverse(X_150)),X_150))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(identity,X_150)))),bind(Z0,$fot(greatest_lower_bound(X_150,identity)))]]) ).
cnf(refute_0_479,plain,
( greatest_lower_bound(identity,multiply(identity,X_150)) != greatest_lower_bound(X_150,identity)
| multiply(greatest_lower_bound(identity,inverse(X_150)),X_150) = greatest_lower_bound(X_150,identity) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(X_150)),X_150),greatest_lower_bound(identity,multiply(identity,X_150))) )],[refute_0_477,refute_0_478]) ).
cnf(refute_0_480,plain,
multiply(greatest_lower_bound(identity,inverse(X_150)),X_150) = greatest_lower_bound(X_150,identity),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(identity,X_150)),greatest_lower_bound(X_150,identity)) )],[refute_0_467,refute_0_479]) ).
cnf(refute_0_481,plain,
inverse(multiply(greatest_lower_bound(identity,inverse(X_150)),X_150)) = inverse(multiply(greatest_lower_bound(identity,inverse(X_150)),X_150)),
introduced(tautology,[refl,[$fot(inverse(multiply(greatest_lower_bound(identity,inverse(X_150)),X_150)))]]) ).
cnf(refute_0_482,plain,
( multiply(greatest_lower_bound(identity,inverse(X_150)),X_150) != greatest_lower_bound(X_150,identity)
| inverse(multiply(greatest_lower_bound(identity,inverse(X_150)),X_150)) != inverse(multiply(greatest_lower_bound(identity,inverse(X_150)),X_150))
| inverse(multiply(greatest_lower_bound(identity,inverse(X_150)),X_150)) = inverse(greatest_lower_bound(X_150,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(greatest_lower_bound(identity,inverse(X_150)),X_150)),inverse(multiply(greatest_lower_bound(identity,inverse(X_150)),X_150))) ),[1,0],$fot(greatest_lower_bound(X_150,identity))]]) ).
cnf(refute_0_483,plain,
( multiply(greatest_lower_bound(identity,inverse(X_150)),X_150) != greatest_lower_bound(X_150,identity)
| inverse(multiply(greatest_lower_bound(identity,inverse(X_150)),X_150)) = inverse(greatest_lower_bound(X_150,identity)) ),
inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(identity,inverse(X_150)),X_150)),inverse(multiply(greatest_lower_bound(identity,inverse(X_150)),X_150))) )],[refute_0_481,refute_0_482]) ).
cnf(refute_0_484,plain,
inverse(multiply(greatest_lower_bound(identity,inverse(X_150)),X_150)) = inverse(greatest_lower_bound(X_150,identity)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(X_150)),X_150),greatest_lower_bound(X_150,identity)) )],[refute_0_480,refute_0_483]) ).
cnf(refute_0_485,plain,
inverse(multiply(X_30,X_31)) = multiply(inverse(multiply(inverse(X_30),multiply(X_30,X_31))),inverse(X_30)),
inference(subst,[],[refute_0_96:[bind(X_45,$fot(inverse(X_30))),bind(X_46,$fot(multiply(X_30,X_31)))]]) ).
cnf(refute_0_486,plain,
( multiply(inverse(X_30),multiply(X_30,X_31)) != X_31
| inverse(multiply(X_30,X_31)) != multiply(inverse(multiply(inverse(X_30),multiply(X_30,X_31))),inverse(X_30))
| inverse(multiply(X_30,X_31)) = multiply(inverse(X_31),inverse(X_30)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_30,X_31)),multiply(inverse(multiply(inverse(X_30),multiply(X_30,X_31))),inverse(X_30))) ),[1,0,0],$fot(X_31)]]) ).
cnf(refute_0_487,plain,
( inverse(multiply(X_30,X_31)) != multiply(inverse(multiply(inverse(X_30),multiply(X_30,X_31))),inverse(X_30))
| inverse(multiply(X_30,X_31)) = multiply(inverse(X_31),inverse(X_30)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_30),multiply(X_30,X_31)),X_31) )],[refute_0_14,refute_0_486]) ).
cnf(refute_0_488,plain,
inverse(multiply(X_30,X_31)) = multiply(inverse(X_31),inverse(X_30)),
inference(resolve,[$cnf( $equal(inverse(multiply(X_30,X_31)),multiply(inverse(multiply(inverse(X_30),multiply(X_30,X_31))),inverse(X_30))) )],[refute_0_485,refute_0_487]) ).
cnf(refute_0_489,plain,
( inverse(multiply(X_30,X_31)) != multiply(inverse(X_31),inverse(X_30))
| multiply(inverse(X_31),inverse(X_30)) = inverse(multiply(X_30,X_31)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(inverse(multiply(X_30,X_31)))),bind(Y0,$fot(multiply(inverse(X_31),inverse(X_30))))]]) ).
cnf(refute_0_490,plain,
multiply(inverse(X_31),inverse(X_30)) = inverse(multiply(X_30,X_31)),
inference(resolve,[$cnf( $equal(inverse(multiply(X_30,X_31)),multiply(inverse(X_31),inverse(X_30))) )],[refute_0_488,refute_0_489]) ).
cnf(refute_0_491,plain,
multiply(inverse(X_150),inverse(greatest_lower_bound(identity,inverse(X_150)))) = inverse(multiply(greatest_lower_bound(identity,inverse(X_150)),X_150)),
inference(subst,[],[refute_0_490:[bind(X_30,$fot(greatest_lower_bound(identity,inverse(X_150)))),bind(X_31,$fot(X_150))]]) ).
cnf(refute_0_492,plain,
( multiply(inverse(X_150),inverse(greatest_lower_bound(identity,inverse(X_150)))) != inverse(multiply(greatest_lower_bound(identity,inverse(X_150)),X_150))
| inverse(multiply(greatest_lower_bound(identity,inverse(X_150)),X_150)) != inverse(greatest_lower_bound(X_150,identity))
| multiply(inverse(X_150),inverse(greatest_lower_bound(identity,inverse(X_150)))) = inverse(greatest_lower_bound(X_150,identity)) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(inverse(X_150),inverse(greatest_lower_bound(identity,inverse(X_150)))))),bind(Y0,$fot(inverse(multiply(greatest_lower_bound(identity,inverse(X_150)),X_150)))),bind(Z0,$fot(inverse(greatest_lower_bound(X_150,identity))))]]) ).
cnf(refute_0_493,plain,
( inverse(multiply(greatest_lower_bound(identity,inverse(X_150)),X_150)) != inverse(greatest_lower_bound(X_150,identity))
| multiply(inverse(X_150),inverse(greatest_lower_bound(identity,inverse(X_150)))) = inverse(greatest_lower_bound(X_150,identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_150),inverse(greatest_lower_bound(identity,inverse(X_150)))),inverse(multiply(greatest_lower_bound(identity,inverse(X_150)),X_150))) )],[refute_0_491,refute_0_492]) ).
cnf(refute_0_494,plain,
multiply(inverse(X_150),inverse(greatest_lower_bound(identity,inverse(X_150)))) = inverse(greatest_lower_bound(X_150,identity)),
inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(identity,inverse(X_150)),X_150)),inverse(greatest_lower_bound(X_150,identity))) )],[refute_0_484,refute_0_493]) ).
cnf(refute_0_495,plain,
( multiply(inverse(X_150),inverse(greatest_lower_bound(identity,inverse(X_150)))) != inverse(greatest_lower_bound(X_150,identity))
| inverse(greatest_lower_bound(identity,X_150)) != multiply(inverse(X_150),inverse(greatest_lower_bound(identity,inverse(X_150))))
| inverse(greatest_lower_bound(identity,X_150)) = inverse(greatest_lower_bound(X_150,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,X_150)),multiply(inverse(X_150),inverse(greatest_lower_bound(identity,inverse(X_150))))) ),[1],$fot(inverse(greatest_lower_bound(X_150,identity)))]]) ).
cnf(refute_0_496,plain,
( inverse(greatest_lower_bound(identity,X_150)) != multiply(inverse(X_150),inverse(greatest_lower_bound(identity,inverse(X_150))))
| inverse(greatest_lower_bound(identity,X_150)) = inverse(greatest_lower_bound(X_150,identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_150),inverse(greatest_lower_bound(identity,inverse(X_150)))),inverse(greatest_lower_bound(X_150,identity))) )],[refute_0_494,refute_0_495]) ).
cnf(refute_0_497,plain,
inverse(greatest_lower_bound(identity,X_150)) = inverse(greatest_lower_bound(X_150,identity)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,X_150)),multiply(inverse(X_150),inverse(greatest_lower_bound(identity,inverse(X_150))))) )],[refute_0_462,refute_0_496]) ).
cnf(refute_0_498,plain,
( multiply(least_upper_bound(X_190,inverse(greatest_lower_bound(identity,X_150))),least_upper_bound(greatest_lower_bound(identity,X_150),identity)) != least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(greatest_lower_bound(identity,X_150),identity))))
| inverse(greatest_lower_bound(identity,X_150)) != inverse(greatest_lower_bound(X_150,identity))
| multiply(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))),least_upper_bound(greatest_lower_bound(identity,X_150),identity)) = least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(greatest_lower_bound(identity,X_150),identity)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_190,inverse(greatest_lower_bound(identity,X_150))),least_upper_bound(greatest_lower_bound(identity,X_150),identity)),least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(greatest_lower_bound(identity,X_150),identity))))) ),[0,0,1],$fot(inverse(greatest_lower_bound(X_150,identity)))]]) ).
cnf(refute_0_499,plain,
( multiply(least_upper_bound(X_190,inverse(greatest_lower_bound(identity,X_150))),least_upper_bound(greatest_lower_bound(identity,X_150),identity)) != least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(greatest_lower_bound(identity,X_150),identity))))
| multiply(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))),least_upper_bound(greatest_lower_bound(identity,X_150),identity)) = least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(greatest_lower_bound(identity,X_150),identity)))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,X_150)),inverse(greatest_lower_bound(X_150,identity))) )],[refute_0_497,refute_0_498]) ).
cnf(refute_0_500,plain,
multiply(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))),least_upper_bound(greatest_lower_bound(identity,X_150),identity)) = least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(greatest_lower_bound(identity,X_150),identity)))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_190,inverse(greatest_lower_bound(identity,X_150))),least_upper_bound(greatest_lower_bound(identity,X_150),identity)),least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(greatest_lower_bound(identity,X_150),identity))))) )],[refute_0_306,refute_0_499]) ).
cnf(refute_0_501,plain,
multiply(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))),identity) = least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))),
inference(subst,[],[refute_0_88:[bind(X_33,$fot(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity)))))]]) ).
cnf(refute_0_502,plain,
least_upper_bound(identity,greatest_lower_bound(identity,X_150)) = identity,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(identity)),bind(Y,$fot(X_150))]]) ).
cnf(refute_0_503,plain,
multiply(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))),least_upper_bound(identity,greatest_lower_bound(identity,X_150))) = multiply(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))),least_upper_bound(identity,greatest_lower_bound(identity,X_150))),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))),least_upper_bound(identity,greatest_lower_bound(identity,X_150))))]]) ).
cnf(refute_0_504,plain,
( multiply(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))),least_upper_bound(identity,greatest_lower_bound(identity,X_150))) != multiply(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))),least_upper_bound(identity,greatest_lower_bound(identity,X_150)))
| least_upper_bound(identity,greatest_lower_bound(identity,X_150)) != identity
| multiply(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))),least_upper_bound(identity,greatest_lower_bound(identity,X_150))) = multiply(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))),least_upper_bound(identity,greatest_lower_bound(identity,X_150))),multiply(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))),least_upper_bound(identity,greatest_lower_bound(identity,X_150)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_505,plain,
( least_upper_bound(identity,greatest_lower_bound(identity,X_150)) != identity
| multiply(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))),least_upper_bound(identity,greatest_lower_bound(identity,X_150))) = multiply(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))),identity) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))),least_upper_bound(identity,greatest_lower_bound(identity,X_150))),multiply(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))),least_upper_bound(identity,greatest_lower_bound(identity,X_150)))) )],[refute_0_503,refute_0_504]) ).
cnf(refute_0_506,plain,
multiply(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))),least_upper_bound(identity,greatest_lower_bound(identity,X_150))) = multiply(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))),identity),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),identity) )],[refute_0_502,refute_0_505]) ).
cnf(refute_0_507,plain,
( multiply(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))),identity) != least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity)))
| multiply(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))),least_upper_bound(identity,greatest_lower_bound(identity,X_150))) != multiply(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))),identity)
| multiply(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))),least_upper_bound(identity,greatest_lower_bound(identity,X_150))) = least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))),least_upper_bound(identity,greatest_lower_bound(identity,X_150))))),bind(Y0,$fot(multiply(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))),identity))),bind(Z0,$fot(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity)))))]]) ).
cnf(refute_0_508,plain,
( multiply(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))),identity) != least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity)))
| multiply(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))),least_upper_bound(identity,greatest_lower_bound(identity,X_150))) = least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))),least_upper_bound(identity,greatest_lower_bound(identity,X_150))),multiply(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))),identity)) )],[refute_0_506,refute_0_507]) ).
cnf(refute_0_509,plain,
multiply(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))),least_upper_bound(identity,greatest_lower_bound(identity,X_150))) = least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))),identity),least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity)))) )],[refute_0_501,refute_0_508]) ).
cnf(refute_0_510,plain,
least_upper_bound(X_19,least_upper_bound(X_18,X_19)) = least_upper_bound(X_19,X_18),
inference(subst,[],[refute_0_175:[bind(Y,$fot(X_18)),bind(X_15,$fot(X_19))]]) ).
cnf(refute_0_511,plain,
least_upper_bound(X_19,X_18) = least_upper_bound(X_18,X_19),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_19)),bind(Y,$fot(X_18))]]) ).
cnf(refute_0_512,plain,
( least_upper_bound(X_19,X_18) != least_upper_bound(X_18,X_19)
| least_upper_bound(X_18,X_19) = least_upper_bound(X_19,X_18) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(least_upper_bound(X_19,X_18))),bind(Y0,$fot(least_upper_bound(X_18,X_19)))]]) ).
cnf(refute_0_513,plain,
least_upper_bound(X_18,X_19) = least_upper_bound(X_19,X_18),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,X_18),least_upper_bound(X_18,X_19)) )],[refute_0_511,refute_0_512]) ).
cnf(refute_0_514,plain,
( least_upper_bound(X_18,X_19) != least_upper_bound(X_19,X_18)
| least_upper_bound(X_19,least_upper_bound(X_18,X_19)) != least_upper_bound(X_19,X_18)
| least_upper_bound(X_19,least_upper_bound(X_19,X_18)) = least_upper_bound(X_19,X_18) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_19,least_upper_bound(X_18,X_19)),least_upper_bound(X_19,X_18)) ),[0,1],$fot(least_upper_bound(X_19,X_18))]]) ).
cnf(refute_0_515,plain,
( least_upper_bound(X_19,least_upper_bound(X_18,X_19)) != least_upper_bound(X_19,X_18)
| least_upper_bound(X_19,least_upper_bound(X_19,X_18)) = least_upper_bound(X_19,X_18) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,X_19),least_upper_bound(X_19,X_18)) )],[refute_0_513,refute_0_514]) ).
cnf(refute_0_516,plain,
least_upper_bound(X_19,least_upper_bound(X_19,X_18)) = least_upper_bound(X_19,X_18),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,least_upper_bound(X_18,X_19)),least_upper_bound(X_19,X_18)) )],[refute_0_510,refute_0_515]) ).
cnf(refute_0_517,plain,
least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_19,X_88))) = least_upper_bound(X_19,multiply(X_19,X_88)),
inference(subst,[],[refute_0_516:[bind(X_18,$fot(multiply(X_19,X_88)))]]) ).
cnf(refute_0_518,plain,
multiply(X_48,least_upper_bound(X_49,identity)) = least_upper_bound(multiply(X_48,X_49),multiply(X_48,identity)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(X_48)),bind(Y,$fot(X_49)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_519,plain,
X_48 = multiply(X_48,identity),
inference(subst,[],[refute_0_86:[bind(X_33,$fot(X_48))]]) ).
cnf(refute_0_520,plain,
( X_48 != multiply(X_48,identity)
| multiply(X_48,identity) = X_48 ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(X_48)),bind(Y0,$fot(multiply(X_48,identity)))]]) ).
cnf(refute_0_521,plain,
multiply(X_48,identity) = X_48,
inference(resolve,[$cnf( $equal(X_48,multiply(X_48,identity)) )],[refute_0_519,refute_0_520]) ).
cnf(refute_0_522,plain,
( multiply(X_48,identity) != X_48
| multiply(X_48,least_upper_bound(X_49,identity)) != least_upper_bound(multiply(X_48,X_49),multiply(X_48,identity))
| multiply(X_48,least_upper_bound(X_49,identity)) = least_upper_bound(multiply(X_48,X_49),X_48) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_48,least_upper_bound(X_49,identity)),least_upper_bound(multiply(X_48,X_49),multiply(X_48,identity))) ),[1,1],$fot(X_48)]]) ).
cnf(refute_0_523,plain,
( multiply(X_48,least_upper_bound(X_49,identity)) != least_upper_bound(multiply(X_48,X_49),multiply(X_48,identity))
| multiply(X_48,least_upper_bound(X_49,identity)) = least_upper_bound(multiply(X_48,X_49),X_48) ),
inference(resolve,[$cnf( $equal(multiply(X_48,identity),X_48) )],[refute_0_521,refute_0_522]) ).
cnf(refute_0_524,plain,
multiply(X_48,least_upper_bound(X_49,identity)) = least_upper_bound(multiply(X_48,X_49),X_48),
inference(resolve,[$cnf( $equal(multiply(X_48,least_upper_bound(X_49,identity)),least_upper_bound(multiply(X_48,X_49),multiply(X_48,identity))) )],[refute_0_518,refute_0_523]) ).
cnf(refute_0_525,plain,
least_upper_bound(multiply(X_48,X_49),X_48) = least_upper_bound(X_48,multiply(X_48,X_49)),
inference(subst,[],[refute_0_25:[bind(X,$fot(X_48)),bind(Y,$fot(multiply(X_48,X_49)))]]) ).
cnf(refute_0_526,plain,
( multiply(X_48,least_upper_bound(X_49,identity)) != least_upper_bound(multiply(X_48,X_49),X_48)
| least_upper_bound(multiply(X_48,X_49),X_48) != least_upper_bound(X_48,multiply(X_48,X_49))
| multiply(X_48,least_upper_bound(X_49,identity)) = least_upper_bound(X_48,multiply(X_48,X_49)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_48,least_upper_bound(X_49,identity)),least_upper_bound(X_48,multiply(X_48,X_49))) ),[0],$fot(least_upper_bound(multiply(X_48,X_49),X_48))]]) ).
cnf(refute_0_527,plain,
( multiply(X_48,least_upper_bound(X_49,identity)) != least_upper_bound(multiply(X_48,X_49),X_48)
| multiply(X_48,least_upper_bound(X_49,identity)) = least_upper_bound(X_48,multiply(X_48,X_49)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_48,X_49),X_48),least_upper_bound(X_48,multiply(X_48,X_49))) )],[refute_0_525,refute_0_526]) ).
cnf(refute_0_528,plain,
multiply(X_48,least_upper_bound(X_49,identity)) = least_upper_bound(X_48,multiply(X_48,X_49)),
inference(resolve,[$cnf( $equal(multiply(X_48,least_upper_bound(X_49,identity)),least_upper_bound(multiply(X_48,X_49),X_48)) )],[refute_0_524,refute_0_527]) ).
cnf(refute_0_529,plain,
multiply(X_19,least_upper_bound(X_88,identity)) = least_upper_bound(X_19,multiply(X_19,X_88)),
inference(subst,[],[refute_0_528:[bind(X_48,$fot(X_19)),bind(X_49,$fot(X_88))]]) ).
cnf(refute_0_530,plain,
( multiply(X_19,least_upper_bound(X_88,identity)) != least_upper_bound(X_19,multiply(X_19,X_88))
| least_upper_bound(X_19,multiply(X_19,X_88)) = multiply(X_19,least_upper_bound(X_88,identity)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(X_19,least_upper_bound(X_88,identity)))),bind(Y0,$fot(least_upper_bound(X_19,multiply(X_19,X_88))))]]) ).
cnf(refute_0_531,plain,
least_upper_bound(X_19,multiply(X_19,X_88)) = multiply(X_19,least_upper_bound(X_88,identity)),
inference(resolve,[$cnf( $equal(multiply(X_19,least_upper_bound(X_88,identity)),least_upper_bound(X_19,multiply(X_19,X_88))) )],[refute_0_529,refute_0_530]) ).
cnf(refute_0_532,plain,
( least_upper_bound(X_19,multiply(X_19,X_88)) != multiply(X_19,least_upper_bound(X_88,identity))
| least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_19,X_88))) != least_upper_bound(X_19,multiply(X_19,X_88))
| least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_88,identity))) = least_upper_bound(X_19,multiply(X_19,X_88)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_19,X_88))),least_upper_bound(X_19,multiply(X_19,X_88))) ),[0,1],$fot(multiply(X_19,least_upper_bound(X_88,identity)))]]) ).
cnf(refute_0_533,plain,
( least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_19,X_88))) != least_upper_bound(X_19,multiply(X_19,X_88))
| least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_88,identity))) = least_upper_bound(X_19,multiply(X_19,X_88)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,multiply(X_19,X_88)),multiply(X_19,least_upper_bound(X_88,identity))) )],[refute_0_531,refute_0_532]) ).
cnf(refute_0_534,plain,
least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_88,identity))) = least_upper_bound(X_19,multiply(X_19,X_88)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_19,X_88))),least_upper_bound(X_19,multiply(X_19,X_88))) )],[refute_0_517,refute_0_533]) ).
cnf(refute_0_535,plain,
least_upper_bound(identity,least_upper_bound(X_88,identity)) = least_upper_bound(identity,X_88),
inference(subst,[],[refute_0_175:[bind(Y,$fot(X_88)),bind(X_15,$fot(identity))]]) ).
cnf(refute_0_536,plain,
multiply(X_19,least_upper_bound(identity,least_upper_bound(X_88,identity))) = multiply(X_19,least_upper_bound(identity,least_upper_bound(X_88,identity))),
introduced(tautology,[refl,[$fot(multiply(X_19,least_upper_bound(identity,least_upper_bound(X_88,identity))))]]) ).
cnf(refute_0_537,plain,
( multiply(X_19,least_upper_bound(identity,least_upper_bound(X_88,identity))) != multiply(X_19,least_upper_bound(identity,least_upper_bound(X_88,identity)))
| least_upper_bound(identity,least_upper_bound(X_88,identity)) != least_upper_bound(identity,X_88)
| multiply(X_19,least_upper_bound(identity,least_upper_bound(X_88,identity))) = multiply(X_19,least_upper_bound(identity,X_88)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_19,least_upper_bound(identity,least_upper_bound(X_88,identity))),multiply(X_19,least_upper_bound(identity,least_upper_bound(X_88,identity)))) ),[1,1],$fot(least_upper_bound(identity,X_88))]]) ).
cnf(refute_0_538,plain,
( least_upper_bound(identity,least_upper_bound(X_88,identity)) != least_upper_bound(identity,X_88)
| multiply(X_19,least_upper_bound(identity,least_upper_bound(X_88,identity))) = multiply(X_19,least_upper_bound(identity,X_88)) ),
inference(resolve,[$cnf( $equal(multiply(X_19,least_upper_bound(identity,least_upper_bound(X_88,identity))),multiply(X_19,least_upper_bound(identity,least_upper_bound(X_88,identity)))) )],[refute_0_536,refute_0_537]) ).
cnf(refute_0_539,plain,
multiply(X_19,least_upper_bound(identity,least_upper_bound(X_88,identity))) = multiply(X_19,least_upper_bound(identity,X_88)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_88,identity)),least_upper_bound(identity,X_88)) )],[refute_0_535,refute_0_538]) ).
cnf(refute_0_540,plain,
greatest_lower_bound(least_upper_bound(X_18,X_7),least_upper_bound(X_7,least_upper_bound(X_18,X_7))) = least_upper_bound(X_18,X_7),
inference(subst,[],[refute_0_153:[bind(X_6,$fot(least_upper_bound(X_18,X_7)))]]) ).
cnf(refute_0_541,plain,
least_upper_bound(X_7,least_upper_bound(X_18,X_7)) = least_upper_bound(X_7,X_18),
inference(subst,[],[refute_0_175:[bind(Y,$fot(X_18)),bind(X_15,$fot(X_7))]]) ).
cnf(refute_0_542,plain,
( greatest_lower_bound(least_upper_bound(X_18,X_7),least_upper_bound(X_7,least_upper_bound(X_18,X_7))) != least_upper_bound(X_18,X_7)
| least_upper_bound(X_7,least_upper_bound(X_18,X_7)) != least_upper_bound(X_7,X_18)
| greatest_lower_bound(least_upper_bound(X_18,X_7),least_upper_bound(X_7,X_18)) = least_upper_bound(X_18,X_7) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_18,X_7),least_upper_bound(X_7,least_upper_bound(X_18,X_7))),least_upper_bound(X_18,X_7)) ),[0,1],$fot(least_upper_bound(X_7,X_18))]]) ).
cnf(refute_0_543,plain,
( greatest_lower_bound(least_upper_bound(X_18,X_7),least_upper_bound(X_7,least_upper_bound(X_18,X_7))) != least_upper_bound(X_18,X_7)
| greatest_lower_bound(least_upper_bound(X_18,X_7),least_upper_bound(X_7,X_18)) = least_upper_bound(X_18,X_7) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_7,least_upper_bound(X_18,X_7)),least_upper_bound(X_7,X_18)) )],[refute_0_541,refute_0_542]) ).
cnf(refute_0_544,plain,
greatest_lower_bound(least_upper_bound(X_18,X_7),least_upper_bound(X_7,X_18)) = least_upper_bound(X_18,X_7),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_18,X_7),least_upper_bound(X_7,least_upper_bound(X_18,X_7))),least_upper_bound(X_18,X_7)) )],[refute_0_540,refute_0_543]) ).
cnf(refute_0_545,plain,
greatest_lower_bound(least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49)),least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50))) = least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49)),
inference(subst,[],[refute_0_544:[bind(X_18,$fot(multiply(X_48,X_50))),bind(X_7,$fot(multiply(X_48,X_49)))]]) ).
cnf(refute_0_546,plain,
multiply(X_48,least_upper_bound(X_49,X_50)) = least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(X_48)),bind(Y,$fot(X_49)),bind(Z,$fot(X_50))]]) ).
cnf(refute_0_547,plain,
( multiply(X_48,least_upper_bound(X_49,X_50)) != least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50))
| least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50)) = multiply(X_48,least_upper_bound(X_49,X_50)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(X_48,least_upper_bound(X_49,X_50)))),bind(Y0,$fot(least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50))))]]) ).
cnf(refute_0_548,plain,
least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50)) = multiply(X_48,least_upper_bound(X_49,X_50)),
inference(resolve,[$cnf( $equal(multiply(X_48,least_upper_bound(X_49,X_50)),least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50))) )],[refute_0_546,refute_0_547]) ).
cnf(refute_0_549,plain,
( greatest_lower_bound(least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49)),least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50))) != least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49))
| least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50)) != multiply(X_48,least_upper_bound(X_49,X_50))
| greatest_lower_bound(least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49)),multiply(X_48,least_upper_bound(X_49,X_50))) = least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49)),least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50))),least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49))) ),[0,1],$fot(multiply(X_48,least_upper_bound(X_49,X_50)))]]) ).
cnf(refute_0_550,plain,
( greatest_lower_bound(least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49)),least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50))) != least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49))
| greatest_lower_bound(least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49)),multiply(X_48,least_upper_bound(X_49,X_50))) = least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50)),multiply(X_48,least_upper_bound(X_49,X_50))) )],[refute_0_548,refute_0_549]) ).
cnf(refute_0_551,plain,
greatest_lower_bound(least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49)),multiply(X_48,least_upper_bound(X_49,X_50))) = least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49)),least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50))),least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49))) )],[refute_0_545,refute_0_550]) ).
cnf(refute_0_552,plain,
greatest_lower_bound(least_upper_bound(X_49,X_50),least_upper_bound(X_50,X_49)) = least_upper_bound(X_49,X_50),
inference(subst,[],[refute_0_544:[bind(X_18,$fot(X_49)),bind(X_7,$fot(X_50))]]) ).
cnf(refute_0_553,plain,
multiply(X_48,greatest_lower_bound(least_upper_bound(X_49,X_50),least_upper_bound(X_50,X_49))) = multiply(X_48,greatest_lower_bound(least_upper_bound(X_49,X_50),least_upper_bound(X_50,X_49))),
introduced(tautology,[refl,[$fot(multiply(X_48,greatest_lower_bound(least_upper_bound(X_49,X_50),least_upper_bound(X_50,X_49))))]]) ).
cnf(refute_0_554,plain,
( multiply(X_48,greatest_lower_bound(least_upper_bound(X_49,X_50),least_upper_bound(X_50,X_49))) != multiply(X_48,greatest_lower_bound(least_upper_bound(X_49,X_50),least_upper_bound(X_50,X_49)))
| greatest_lower_bound(least_upper_bound(X_49,X_50),least_upper_bound(X_50,X_49)) != least_upper_bound(X_49,X_50)
| multiply(X_48,greatest_lower_bound(least_upper_bound(X_49,X_50),least_upper_bound(X_50,X_49))) = multiply(X_48,least_upper_bound(X_49,X_50)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_48,greatest_lower_bound(least_upper_bound(X_49,X_50),least_upper_bound(X_50,X_49))),multiply(X_48,greatest_lower_bound(least_upper_bound(X_49,X_50),least_upper_bound(X_50,X_49)))) ),[1,1],$fot(least_upper_bound(X_49,X_50))]]) ).
cnf(refute_0_555,plain,
( greatest_lower_bound(least_upper_bound(X_49,X_50),least_upper_bound(X_50,X_49)) != least_upper_bound(X_49,X_50)
| multiply(X_48,greatest_lower_bound(least_upper_bound(X_49,X_50),least_upper_bound(X_50,X_49))) = multiply(X_48,least_upper_bound(X_49,X_50)) ),
inference(resolve,[$cnf( $equal(multiply(X_48,greatest_lower_bound(least_upper_bound(X_49,X_50),least_upper_bound(X_50,X_49))),multiply(X_48,greatest_lower_bound(least_upper_bound(X_49,X_50),least_upper_bound(X_50,X_49)))) )],[refute_0_553,refute_0_554]) ).
cnf(refute_0_556,plain,
multiply(X_48,greatest_lower_bound(least_upper_bound(X_49,X_50),least_upper_bound(X_50,X_49))) = multiply(X_48,least_upper_bound(X_49,X_50)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_49,X_50),least_upper_bound(X_50,X_49)),least_upper_bound(X_49,X_50)) )],[refute_0_552,refute_0_555]) ).
cnf(refute_0_557,plain,
greatest_lower_bound(multiply(X_48,least_upper_bound(X_49,X_50)),multiply(X_48,least_upper_bound(X_50,X_49))) = multiply(X_48,greatest_lower_bound(least_upper_bound(X_49,X_50),least_upper_bound(X_50,X_49))),
inference(subst,[],[refute_0_391:[bind(X,$fot(X_48)),bind(Y,$fot(least_upper_bound(X_49,X_50))),bind(Z,$fot(least_upper_bound(X_50,X_49)))]]) ).
cnf(refute_0_558,plain,
( multiply(X_48,greatest_lower_bound(least_upper_bound(X_49,X_50),least_upper_bound(X_50,X_49))) != multiply(X_48,least_upper_bound(X_49,X_50))
| greatest_lower_bound(multiply(X_48,least_upper_bound(X_49,X_50)),multiply(X_48,least_upper_bound(X_50,X_49))) != multiply(X_48,greatest_lower_bound(least_upper_bound(X_49,X_50),least_upper_bound(X_50,X_49)))
| greatest_lower_bound(multiply(X_48,least_upper_bound(X_49,X_50)),multiply(X_48,least_upper_bound(X_50,X_49))) = multiply(X_48,least_upper_bound(X_49,X_50)) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(greatest_lower_bound(multiply(X_48,least_upper_bound(X_49,X_50)),multiply(X_48,least_upper_bound(X_50,X_49))))),bind(Y0,$fot(multiply(X_48,greatest_lower_bound(least_upper_bound(X_49,X_50),least_upper_bound(X_50,X_49))))),bind(Z0,$fot(multiply(X_48,least_upper_bound(X_49,X_50))))]]) ).
cnf(refute_0_559,plain,
( multiply(X_48,greatest_lower_bound(least_upper_bound(X_49,X_50),least_upper_bound(X_50,X_49))) != multiply(X_48,least_upper_bound(X_49,X_50))
| greatest_lower_bound(multiply(X_48,least_upper_bound(X_49,X_50)),multiply(X_48,least_upper_bound(X_50,X_49))) = multiply(X_48,least_upper_bound(X_49,X_50)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_48,least_upper_bound(X_49,X_50)),multiply(X_48,least_upper_bound(X_50,X_49))),multiply(X_48,greatest_lower_bound(least_upper_bound(X_49,X_50),least_upper_bound(X_50,X_49)))) )],[refute_0_557,refute_0_558]) ).
cnf(refute_0_560,plain,
greatest_lower_bound(multiply(X_48,least_upper_bound(X_49,X_50)),multiply(X_48,least_upper_bound(X_50,X_49))) = multiply(X_48,least_upper_bound(X_49,X_50)),
inference(resolve,[$cnf( $equal(multiply(X_48,greatest_lower_bound(least_upper_bound(X_49,X_50),least_upper_bound(X_50,X_49))),multiply(X_48,least_upper_bound(X_49,X_50))) )],[refute_0_556,refute_0_559]) ).
cnf(refute_0_561,plain,
least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49)) = multiply(X_48,least_upper_bound(X_50,X_49)),
inference(subst,[],[refute_0_385:[bind(X,$fot(X_48)),bind(Y,$fot(X_50)),bind(Z,$fot(X_49))]]) ).
cnf(refute_0_562,plain,
greatest_lower_bound(multiply(X_48,least_upper_bound(X_49,X_50)),least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49))) = greatest_lower_bound(multiply(X_48,least_upper_bound(X_49,X_50)),least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(multiply(X_48,least_upper_bound(X_49,X_50)),least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49))))]]) ).
cnf(refute_0_563,plain,
( greatest_lower_bound(multiply(X_48,least_upper_bound(X_49,X_50)),least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49))) != greatest_lower_bound(multiply(X_48,least_upper_bound(X_49,X_50)),least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49)))
| least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49)) != multiply(X_48,least_upper_bound(X_50,X_49))
| greatest_lower_bound(multiply(X_48,least_upper_bound(X_49,X_50)),least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49))) = greatest_lower_bound(multiply(X_48,least_upper_bound(X_49,X_50)),multiply(X_48,least_upper_bound(X_50,X_49))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_48,least_upper_bound(X_49,X_50)),least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49))),greatest_lower_bound(multiply(X_48,least_upper_bound(X_49,X_50)),least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49)))) ),[1,1],$fot(multiply(X_48,least_upper_bound(X_50,X_49)))]]) ).
cnf(refute_0_564,plain,
( least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49)) != multiply(X_48,least_upper_bound(X_50,X_49))
| greatest_lower_bound(multiply(X_48,least_upper_bound(X_49,X_50)),least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49))) = greatest_lower_bound(multiply(X_48,least_upper_bound(X_49,X_50)),multiply(X_48,least_upper_bound(X_50,X_49))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_48,least_upper_bound(X_49,X_50)),least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49))),greatest_lower_bound(multiply(X_48,least_upper_bound(X_49,X_50)),least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49)))) )],[refute_0_562,refute_0_563]) ).
cnf(refute_0_565,plain,
greatest_lower_bound(multiply(X_48,least_upper_bound(X_49,X_50)),least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49))) = greatest_lower_bound(multiply(X_48,least_upper_bound(X_49,X_50)),multiply(X_48,least_upper_bound(X_50,X_49))),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49)),multiply(X_48,least_upper_bound(X_50,X_49))) )],[refute_0_561,refute_0_564]) ).
cnf(refute_0_566,plain,
( greatest_lower_bound(multiply(X_48,least_upper_bound(X_49,X_50)),multiply(X_48,least_upper_bound(X_50,X_49))) != multiply(X_48,least_upper_bound(X_49,X_50))
| greatest_lower_bound(multiply(X_48,least_upper_bound(X_49,X_50)),least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49))) != greatest_lower_bound(multiply(X_48,least_upper_bound(X_49,X_50)),multiply(X_48,least_upper_bound(X_50,X_49)))
| greatest_lower_bound(multiply(X_48,least_upper_bound(X_49,X_50)),least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49))) = multiply(X_48,least_upper_bound(X_49,X_50)) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(greatest_lower_bound(multiply(X_48,least_upper_bound(X_49,X_50)),least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49))))),bind(Y0,$fot(greatest_lower_bound(multiply(X_48,least_upper_bound(X_49,X_50)),multiply(X_48,least_upper_bound(X_50,X_49))))),bind(Z0,$fot(multiply(X_48,least_upper_bound(X_49,X_50))))]]) ).
cnf(refute_0_567,plain,
( greatest_lower_bound(multiply(X_48,least_upper_bound(X_49,X_50)),multiply(X_48,least_upper_bound(X_50,X_49))) != multiply(X_48,least_upper_bound(X_49,X_50))
| greatest_lower_bound(multiply(X_48,least_upper_bound(X_49,X_50)),least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49))) = multiply(X_48,least_upper_bound(X_49,X_50)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_48,least_upper_bound(X_49,X_50)),least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49))),greatest_lower_bound(multiply(X_48,least_upper_bound(X_49,X_50)),multiply(X_48,least_upper_bound(X_50,X_49)))) )],[refute_0_565,refute_0_566]) ).
cnf(refute_0_568,plain,
greatest_lower_bound(multiply(X_48,least_upper_bound(X_49,X_50)),least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49))) = multiply(X_48,least_upper_bound(X_49,X_50)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_48,least_upper_bound(X_49,X_50)),multiply(X_48,least_upper_bound(X_50,X_49))),multiply(X_48,least_upper_bound(X_49,X_50))) )],[refute_0_560,refute_0_567]) ).
cnf(refute_0_569,plain,
greatest_lower_bound(least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49)),multiply(X_48,least_upper_bound(X_49,X_50))) = greatest_lower_bound(multiply(X_48,least_upper_bound(X_49,X_50)),least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49))),
inference(subst,[],[refute_0_42:[bind(X,$fot(multiply(X_48,least_upper_bound(X_49,X_50)))),bind(Y,$fot(least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49))))]]) ).
cnf(refute_0_570,plain,
( greatest_lower_bound(multiply(X_48,least_upper_bound(X_49,X_50)),least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49))) != multiply(X_48,least_upper_bound(X_49,X_50))
| greatest_lower_bound(least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49)),multiply(X_48,least_upper_bound(X_49,X_50))) != greatest_lower_bound(multiply(X_48,least_upper_bound(X_49,X_50)),least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49)))
| greatest_lower_bound(least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49)),multiply(X_48,least_upper_bound(X_49,X_50))) = multiply(X_48,least_upper_bound(X_49,X_50)) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49)),multiply(X_48,least_upper_bound(X_49,X_50))))),bind(Y0,$fot(greatest_lower_bound(multiply(X_48,least_upper_bound(X_49,X_50)),least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49))))),bind(Z0,$fot(multiply(X_48,least_upper_bound(X_49,X_50))))]]) ).
cnf(refute_0_571,plain,
( greatest_lower_bound(multiply(X_48,least_upper_bound(X_49,X_50)),least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49))) != multiply(X_48,least_upper_bound(X_49,X_50))
| greatest_lower_bound(least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49)),multiply(X_48,least_upper_bound(X_49,X_50))) = multiply(X_48,least_upper_bound(X_49,X_50)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49)),multiply(X_48,least_upper_bound(X_49,X_50))),greatest_lower_bound(multiply(X_48,least_upper_bound(X_49,X_50)),least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49)))) )],[refute_0_569,refute_0_570]) ).
cnf(refute_0_572,plain,
greatest_lower_bound(least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49)),multiply(X_48,least_upper_bound(X_49,X_50))) = multiply(X_48,least_upper_bound(X_49,X_50)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_48,least_upper_bound(X_49,X_50)),least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49))),multiply(X_48,least_upper_bound(X_49,X_50))) )],[refute_0_568,refute_0_571]) ).
cnf(refute_0_573,plain,
( greatest_lower_bound(least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49)),multiply(X_48,least_upper_bound(X_49,X_50))) != multiply(X_48,least_upper_bound(X_49,X_50))
| greatest_lower_bound(least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49)),multiply(X_48,least_upper_bound(X_49,X_50))) != least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49))
| multiply(X_48,least_upper_bound(X_49,X_50)) = least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49)),multiply(X_48,least_upper_bound(X_49,X_50))),least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49))) ),[0],$fot(multiply(X_48,least_upper_bound(X_49,X_50)))]]) ).
cnf(refute_0_574,plain,
( greatest_lower_bound(least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49)),multiply(X_48,least_upper_bound(X_49,X_50))) != least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49))
| multiply(X_48,least_upper_bound(X_49,X_50)) = least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49)),multiply(X_48,least_upper_bound(X_49,X_50))),multiply(X_48,least_upper_bound(X_49,X_50))) )],[refute_0_572,refute_0_573]) ).
cnf(refute_0_575,plain,
( multiply(X_48,least_upper_bound(X_49,X_50)) != least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49))
| least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49)) != multiply(X_48,least_upper_bound(X_50,X_49))
| multiply(X_48,least_upper_bound(X_49,X_50)) = multiply(X_48,least_upper_bound(X_50,X_49)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_48,least_upper_bound(X_49,X_50)),multiply(X_48,least_upper_bound(X_50,X_49))) ),[0],$fot(least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49)))]]) ).
cnf(refute_0_576,plain,
( multiply(X_48,least_upper_bound(X_49,X_50)) != least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49))
| multiply(X_48,least_upper_bound(X_49,X_50)) = multiply(X_48,least_upper_bound(X_50,X_49)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49)),multiply(X_48,least_upper_bound(X_50,X_49))) )],[refute_0_561,refute_0_575]) ).
cnf(refute_0_577,plain,
( greatest_lower_bound(least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49)),multiply(X_48,least_upper_bound(X_49,X_50))) != least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49))
| multiply(X_48,least_upper_bound(X_49,X_50)) = multiply(X_48,least_upper_bound(X_50,X_49)) ),
inference(resolve,[$cnf( $equal(multiply(X_48,least_upper_bound(X_49,X_50)),least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49))) )],[refute_0_574,refute_0_576]) ).
cnf(refute_0_578,plain,
multiply(X_48,least_upper_bound(X_49,X_50)) = multiply(X_48,least_upper_bound(X_50,X_49)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49)),multiply(X_48,least_upper_bound(X_49,X_50))),least_upper_bound(multiply(X_48,X_50),multiply(X_48,X_49))) )],[refute_0_551,refute_0_577]) ).
cnf(refute_0_579,plain,
( multiply(X_48,least_upper_bound(X_49,X_50)) != multiply(X_48,least_upper_bound(X_50,X_49))
| multiply(X_48,least_upper_bound(X_50,X_49)) = multiply(X_48,least_upper_bound(X_49,X_50)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(X_48,least_upper_bound(X_49,X_50)))),bind(Y0,$fot(multiply(X_48,least_upper_bound(X_50,X_49))))]]) ).
cnf(refute_0_580,plain,
multiply(X_48,least_upper_bound(X_50,X_49)) = multiply(X_48,least_upper_bound(X_49,X_50)),
inference(resolve,[$cnf( $equal(multiply(X_48,least_upper_bound(X_49,X_50)),multiply(X_48,least_upper_bound(X_50,X_49))) )],[refute_0_578,refute_0_579]) ).
cnf(refute_0_581,plain,
multiply(X_19,least_upper_bound(least_upper_bound(X_88,identity),identity)) = multiply(X_19,least_upper_bound(identity,least_upper_bound(X_88,identity))),
inference(subst,[],[refute_0_580:[bind(X_48,$fot(X_19)),bind(X_49,$fot(identity)),bind(X_50,$fot(least_upper_bound(X_88,identity)))]]) ).
cnf(refute_0_582,plain,
( multiply(X_48,least_upper_bound(X_49,identity)) != least_upper_bound(X_48,multiply(X_48,X_49))
| least_upper_bound(X_48,multiply(X_48,X_49)) = multiply(X_48,least_upper_bound(X_49,identity)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(X_48,least_upper_bound(X_49,identity)))),bind(Y0,$fot(least_upper_bound(X_48,multiply(X_48,X_49))))]]) ).
cnf(refute_0_583,plain,
least_upper_bound(X_48,multiply(X_48,X_49)) = multiply(X_48,least_upper_bound(X_49,identity)),
inference(resolve,[$cnf( $equal(multiply(X_48,least_upper_bound(X_49,identity)),least_upper_bound(X_48,multiply(X_48,X_49))) )],[refute_0_528,refute_0_582]) ).
cnf(refute_0_584,plain,
least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_88,identity))) = multiply(X_19,least_upper_bound(least_upper_bound(X_88,identity),identity)),
inference(subst,[],[refute_0_583:[bind(X_48,$fot(X_19)),bind(X_49,$fot(least_upper_bound(X_88,identity)))]]) ).
cnf(refute_0_585,plain,
( multiply(X_19,least_upper_bound(least_upper_bound(X_88,identity),identity)) != multiply(X_19,least_upper_bound(identity,least_upper_bound(X_88,identity)))
| least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_88,identity))) != multiply(X_19,least_upper_bound(least_upper_bound(X_88,identity),identity))
| least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_88,identity))) = multiply(X_19,least_upper_bound(identity,least_upper_bound(X_88,identity))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_88,identity))))),bind(Y0,$fot(multiply(X_19,least_upper_bound(least_upper_bound(X_88,identity),identity)))),bind(Z0,$fot(multiply(X_19,least_upper_bound(identity,least_upper_bound(X_88,identity)))))]]) ).
cnf(refute_0_586,plain,
( multiply(X_19,least_upper_bound(least_upper_bound(X_88,identity),identity)) != multiply(X_19,least_upper_bound(identity,least_upper_bound(X_88,identity)))
| least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_88,identity))) = multiply(X_19,least_upper_bound(identity,least_upper_bound(X_88,identity))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_88,identity))),multiply(X_19,least_upper_bound(least_upper_bound(X_88,identity),identity))) )],[refute_0_584,refute_0_585]) ).
cnf(refute_0_587,plain,
least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_88,identity))) = multiply(X_19,least_upper_bound(identity,least_upper_bound(X_88,identity))),
inference(resolve,[$cnf( $equal(multiply(X_19,least_upper_bound(least_upper_bound(X_88,identity),identity)),multiply(X_19,least_upper_bound(identity,least_upper_bound(X_88,identity)))) )],[refute_0_581,refute_0_586]) ).
cnf(refute_0_588,plain,
( multiply(X_19,least_upper_bound(identity,least_upper_bound(X_88,identity))) != multiply(X_19,least_upper_bound(identity,X_88))
| least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_88,identity))) != multiply(X_19,least_upper_bound(identity,least_upper_bound(X_88,identity)))
| least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_88,identity))) = multiply(X_19,least_upper_bound(identity,X_88)) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_88,identity))))),bind(Y0,$fot(multiply(X_19,least_upper_bound(identity,least_upper_bound(X_88,identity))))),bind(Z0,$fot(multiply(X_19,least_upper_bound(identity,X_88))))]]) ).
cnf(refute_0_589,plain,
( multiply(X_19,least_upper_bound(identity,least_upper_bound(X_88,identity))) != multiply(X_19,least_upper_bound(identity,X_88))
| least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_88,identity))) = multiply(X_19,least_upper_bound(identity,X_88)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_88,identity))),multiply(X_19,least_upper_bound(identity,least_upper_bound(X_88,identity)))) )],[refute_0_587,refute_0_588]) ).
cnf(refute_0_590,plain,
least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_88,identity))) = multiply(X_19,least_upper_bound(identity,X_88)),
inference(resolve,[$cnf( $equal(multiply(X_19,least_upper_bound(identity,least_upper_bound(X_88,identity))),multiply(X_19,least_upper_bound(identity,X_88))) )],[refute_0_539,refute_0_589]) ).
cnf(refute_0_591,plain,
( least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_88,identity))) != multiply(X_19,least_upper_bound(identity,X_88))
| least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_88,identity))) != least_upper_bound(X_19,multiply(X_19,X_88))
| multiply(X_19,least_upper_bound(identity,X_88)) = least_upper_bound(X_19,multiply(X_19,X_88)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_88,identity))),least_upper_bound(X_19,multiply(X_19,X_88))) ),[0],$fot(multiply(X_19,least_upper_bound(identity,X_88)))]]) ).
cnf(refute_0_592,plain,
( least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_88,identity))) != least_upper_bound(X_19,multiply(X_19,X_88))
| multiply(X_19,least_upper_bound(identity,X_88)) = least_upper_bound(X_19,multiply(X_19,X_88)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_88,identity))),multiply(X_19,least_upper_bound(identity,X_88))) )],[refute_0_590,refute_0_591]) ).
cnf(refute_0_593,plain,
( multiply(X_19,least_upper_bound(identity,X_88)) != least_upper_bound(X_19,multiply(X_19,X_88))
| least_upper_bound(X_19,multiply(X_19,X_88)) != multiply(X_19,least_upper_bound(X_88,identity))
| multiply(X_19,least_upper_bound(identity,X_88)) = multiply(X_19,least_upper_bound(X_88,identity)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_19,least_upper_bound(identity,X_88)),multiply(X_19,least_upper_bound(X_88,identity))) ),[0],$fot(least_upper_bound(X_19,multiply(X_19,X_88)))]]) ).
cnf(refute_0_594,plain,
( multiply(X_19,least_upper_bound(identity,X_88)) != least_upper_bound(X_19,multiply(X_19,X_88))
| multiply(X_19,least_upper_bound(identity,X_88)) = multiply(X_19,least_upper_bound(X_88,identity)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,multiply(X_19,X_88)),multiply(X_19,least_upper_bound(X_88,identity))) )],[refute_0_531,refute_0_593]) ).
cnf(refute_0_595,plain,
( least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_88,identity))) != least_upper_bound(X_19,multiply(X_19,X_88))
| multiply(X_19,least_upper_bound(identity,X_88)) = multiply(X_19,least_upper_bound(X_88,identity)) ),
inference(resolve,[$cnf( $equal(multiply(X_19,least_upper_bound(identity,X_88)),least_upper_bound(X_19,multiply(X_19,X_88))) )],[refute_0_592,refute_0_594]) ).
cnf(refute_0_596,plain,
multiply(X_19,least_upper_bound(identity,X_88)) = multiply(X_19,least_upper_bound(X_88,identity)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_88,identity))),least_upper_bound(X_19,multiply(X_19,X_88))) )],[refute_0_534,refute_0_595]) ).
cnf(refute_0_597,plain,
( multiply(X_19,least_upper_bound(identity,X_88)) != multiply(X_19,least_upper_bound(X_88,identity))
| multiply(X_19,least_upper_bound(X_88,identity)) = multiply(X_19,least_upper_bound(identity,X_88)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(X_19,least_upper_bound(identity,X_88)))),bind(Y0,$fot(multiply(X_19,least_upper_bound(X_88,identity))))]]) ).
cnf(refute_0_598,plain,
multiply(X_19,least_upper_bound(X_88,identity)) = multiply(X_19,least_upper_bound(identity,X_88)),
inference(resolve,[$cnf( $equal(multiply(X_19,least_upper_bound(identity,X_88)),multiply(X_19,least_upper_bound(X_88,identity))) )],[refute_0_596,refute_0_597]) ).
cnf(refute_0_599,plain,
multiply(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))),least_upper_bound(greatest_lower_bound(identity,X_150),identity)) = multiply(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))),least_upper_bound(identity,greatest_lower_bound(identity,X_150))),
inference(subst,[],[refute_0_598:[bind(X_19,$fot(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))))),bind(X_88,$fot(greatest_lower_bound(identity,X_150)))]]) ).
cnf(refute_0_600,plain,
( multiply(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))),least_upper_bound(greatest_lower_bound(identity,X_150),identity)) != multiply(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))),least_upper_bound(identity,greatest_lower_bound(identity,X_150)))
| multiply(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))),least_upper_bound(identity,greatest_lower_bound(identity,X_150))) != least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity)))
| multiply(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))),least_upper_bound(greatest_lower_bound(identity,X_150),identity)) = least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))),least_upper_bound(greatest_lower_bound(identity,X_150),identity)))),bind(Y0,$fot(multiply(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))),least_upper_bound(identity,greatest_lower_bound(identity,X_150))))),bind(Z0,$fot(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity)))))]]) ).
cnf(refute_0_601,plain,
( multiply(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))),least_upper_bound(identity,greatest_lower_bound(identity,X_150))) != least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity)))
| multiply(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))),least_upper_bound(greatest_lower_bound(identity,X_150),identity)) = least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))),least_upper_bound(greatest_lower_bound(identity,X_150),identity)),multiply(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))),least_upper_bound(identity,greatest_lower_bound(identity,X_150)))) )],[refute_0_599,refute_0_600]) ).
cnf(refute_0_602,plain,
multiply(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))),least_upper_bound(greatest_lower_bound(identity,X_150),identity)) = least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))),least_upper_bound(identity,greatest_lower_bound(identity,X_150))),least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity)))) )],[refute_0_509,refute_0_601]) ).
cnf(refute_0_603,plain,
( multiply(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))),least_upper_bound(greatest_lower_bound(identity,X_150),identity)) != least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity)))
| multiply(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))),least_upper_bound(greatest_lower_bound(identity,X_150),identity)) != least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(greatest_lower_bound(identity,X_150),identity))))
| least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))) = least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(greatest_lower_bound(identity,X_150),identity)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))),least_upper_bound(greatest_lower_bound(identity,X_150),identity)),least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(greatest_lower_bound(identity,X_150),identity))))) ),[0],$fot(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))))]]) ).
cnf(refute_0_604,plain,
( multiply(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))),least_upper_bound(greatest_lower_bound(identity,X_150),identity)) != least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(greatest_lower_bound(identity,X_150),identity))))
| least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))) = least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(greatest_lower_bound(identity,X_150),identity)))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))),least_upper_bound(greatest_lower_bound(identity,X_150),identity)),least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity)))) )],[refute_0_602,refute_0_603]) ).
cnf(refute_0_605,plain,
multiply(X_190,identity) = X_190,
inference(subst,[],[refute_0_88:[bind(X_33,$fot(X_190))]]) ).
cnf(refute_0_606,plain,
multiply(X_190,least_upper_bound(identity,greatest_lower_bound(identity,X_150))) = multiply(X_190,least_upper_bound(identity,greatest_lower_bound(identity,X_150))),
introduced(tautology,[refl,[$fot(multiply(X_190,least_upper_bound(identity,greatest_lower_bound(identity,X_150))))]]) ).
cnf(refute_0_607,plain,
( multiply(X_190,least_upper_bound(identity,greatest_lower_bound(identity,X_150))) != multiply(X_190,least_upper_bound(identity,greatest_lower_bound(identity,X_150)))
| least_upper_bound(identity,greatest_lower_bound(identity,X_150)) != identity
| multiply(X_190,least_upper_bound(identity,greatest_lower_bound(identity,X_150))) = multiply(X_190,identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_190,least_upper_bound(identity,greatest_lower_bound(identity,X_150))),multiply(X_190,least_upper_bound(identity,greatest_lower_bound(identity,X_150)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_608,plain,
( least_upper_bound(identity,greatest_lower_bound(identity,X_150)) != identity
| multiply(X_190,least_upper_bound(identity,greatest_lower_bound(identity,X_150))) = multiply(X_190,identity) ),
inference(resolve,[$cnf( $equal(multiply(X_190,least_upper_bound(identity,greatest_lower_bound(identity,X_150))),multiply(X_190,least_upper_bound(identity,greatest_lower_bound(identity,X_150)))) )],[refute_0_606,refute_0_607]) ).
cnf(refute_0_609,plain,
multiply(X_190,least_upper_bound(identity,greatest_lower_bound(identity,X_150))) = multiply(X_190,identity),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),identity) )],[refute_0_502,refute_0_608]) ).
cnf(refute_0_610,plain,
( multiply(X_190,identity) != X_190
| multiply(X_190,least_upper_bound(identity,greatest_lower_bound(identity,X_150))) != multiply(X_190,identity)
| multiply(X_190,least_upper_bound(identity,greatest_lower_bound(identity,X_150))) = X_190 ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(X_190,least_upper_bound(identity,greatest_lower_bound(identity,X_150))))),bind(Y0,$fot(multiply(X_190,identity))),bind(Z0,$fot(X_190))]]) ).
cnf(refute_0_611,plain,
( multiply(X_190,identity) != X_190
| multiply(X_190,least_upper_bound(identity,greatest_lower_bound(identity,X_150))) = X_190 ),
inference(resolve,[$cnf( $equal(multiply(X_190,least_upper_bound(identity,greatest_lower_bound(identity,X_150))),multiply(X_190,identity)) )],[refute_0_609,refute_0_610]) ).
cnf(refute_0_612,plain,
multiply(X_190,least_upper_bound(identity,greatest_lower_bound(identity,X_150))) = X_190,
inference(resolve,[$cnf( $equal(multiply(X_190,identity),X_190) )],[refute_0_605,refute_0_611]) ).
cnf(refute_0_613,plain,
least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(identity,greatest_lower_bound(identity,X_150)))) = least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(identity,greatest_lower_bound(identity,X_150)))),
introduced(tautology,[refl,[$fot(least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(identity,greatest_lower_bound(identity,X_150)))))]]) ).
cnf(refute_0_614,plain,
( multiply(X_190,least_upper_bound(identity,greatest_lower_bound(identity,X_150))) != X_190
| least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(identity,greatest_lower_bound(identity,X_150)))) != least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(identity,greatest_lower_bound(identity,X_150))))
| least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(identity,greatest_lower_bound(identity,X_150)))) = least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),X_190) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(identity,greatest_lower_bound(identity,X_150)))),least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(identity,greatest_lower_bound(identity,X_150))))) ),[1,1],$fot(X_190)]]) ).
cnf(refute_0_615,plain,
( multiply(X_190,least_upper_bound(identity,greatest_lower_bound(identity,X_150))) != X_190
| least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(identity,greatest_lower_bound(identity,X_150)))) = least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),X_190) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(identity,greatest_lower_bound(identity,X_150)))),least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(identity,greatest_lower_bound(identity,X_150))))) )],[refute_0_613,refute_0_614]) ).
cnf(refute_0_616,plain,
least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(identity,greatest_lower_bound(identity,X_150)))) = least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),X_190),
inference(resolve,[$cnf( $equal(multiply(X_190,least_upper_bound(identity,greatest_lower_bound(identity,X_150))),X_190) )],[refute_0_612,refute_0_615]) ).
cnf(refute_0_617,plain,
least_upper_bound(X_167,least_upper_bound(multiply(X,Y),multiply(X,Z))) = least_upper_bound(X_167,least_upper_bound(multiply(X,Z),multiply(X,Y))),
inference(subst,[],[refute_0_204:[bind(X_11,$fot(multiply(X,Y))),bind(X_42,$fot(X_167)),bind(X_43,$fot(multiply(X,Z)))]]) ).
cnf(refute_0_618,plain,
( least_upper_bound(X_167,least_upper_bound(multiply(X,Y),multiply(X,Z))) != least_upper_bound(X_167,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))
| least_upper_bound(X_167,multiply(X,least_upper_bound(Y,Z))) = least_upper_bound(X_167,least_upper_bound(multiply(X,Z),multiply(X,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_167,least_upper_bound(multiply(X,Y),multiply(X,Z))),least_upper_bound(X_167,least_upper_bound(multiply(X,Z),multiply(X,Y)))) ),[0,1],$fot(multiply(X,least_upper_bound(Y,Z)))]]) ).
cnf(refute_0_619,plain,
( least_upper_bound(X_167,least_upper_bound(multiply(X,Y),multiply(X,Z))) != least_upper_bound(X_167,least_upper_bound(multiply(X,Z),multiply(X,Y)))
| least_upper_bound(X_167,multiply(X,least_upper_bound(Y,Z))) = least_upper_bound(X_167,least_upper_bound(multiply(X,Z),multiply(X,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,Y),multiply(X,Z)),multiply(X,least_upper_bound(Y,Z))) )],[refute_0_385,refute_0_618]) ).
cnf(refute_0_620,plain,
least_upper_bound(X_167,multiply(X,least_upper_bound(Y,Z))) = least_upper_bound(X_167,least_upper_bound(multiply(X,Z),multiply(X,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_167,least_upper_bound(multiply(X,Y),multiply(X,Z))),least_upper_bound(X_167,least_upper_bound(multiply(X,Z),multiply(X,Y)))) )],[refute_0_617,refute_0_619]) ).
cnf(refute_0_621,plain,
least_upper_bound(multiply(X,Z),multiply(X,Y)) = multiply(X,least_upper_bound(Z,Y)),
inference(subst,[],[refute_0_385:[bind(Y,$fot(Z)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_622,plain,
least_upper_bound(X_167,least_upper_bound(multiply(X,Z),multiply(X,Y))) = least_upper_bound(X_167,least_upper_bound(multiply(X,Z),multiply(X,Y))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_167,least_upper_bound(multiply(X,Z),multiply(X,Y))))]]) ).
cnf(refute_0_623,plain,
( least_upper_bound(X_167,least_upper_bound(multiply(X,Z),multiply(X,Y))) != least_upper_bound(X_167,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))
| least_upper_bound(X_167,least_upper_bound(multiply(X,Z),multiply(X,Y))) = least_upper_bound(X_167,multiply(X,least_upper_bound(Z,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_167,least_upper_bound(multiply(X,Z),multiply(X,Y))),least_upper_bound(X_167,least_upper_bound(multiply(X,Z),multiply(X,Y)))) ),[1,1],$fot(multiply(X,least_upper_bound(Z,Y)))]]) ).
cnf(refute_0_624,plain,
( least_upper_bound(multiply(X,Z),multiply(X,Y)) != multiply(X,least_upper_bound(Z,Y))
| least_upper_bound(X_167,least_upper_bound(multiply(X,Z),multiply(X,Y))) = least_upper_bound(X_167,multiply(X,least_upper_bound(Z,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_167,least_upper_bound(multiply(X,Z),multiply(X,Y))),least_upper_bound(X_167,least_upper_bound(multiply(X,Z),multiply(X,Y)))) )],[refute_0_622,refute_0_623]) ).
cnf(refute_0_625,plain,
least_upper_bound(X_167,least_upper_bound(multiply(X,Z),multiply(X,Y))) = least_upper_bound(X_167,multiply(X,least_upper_bound(Z,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Z,Y))) )],[refute_0_621,refute_0_624]) ).
cnf(refute_0_626,plain,
( least_upper_bound(X_167,multiply(X,least_upper_bound(Y,Z))) != least_upper_bound(X_167,least_upper_bound(multiply(X,Z),multiply(X,Y)))
| least_upper_bound(X_167,least_upper_bound(multiply(X,Z),multiply(X,Y))) != least_upper_bound(X_167,multiply(X,least_upper_bound(Z,Y)))
| least_upper_bound(X_167,multiply(X,least_upper_bound(Y,Z))) = least_upper_bound(X_167,multiply(X,least_upper_bound(Z,Y))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_167,multiply(X,least_upper_bound(Y,Z))),least_upper_bound(X_167,multiply(X,least_upper_bound(Z,Y)))) ),[0],$fot(least_upper_bound(X_167,least_upper_bound(multiply(X,Z),multiply(X,Y))))]]) ).
cnf(refute_0_627,plain,
( least_upper_bound(X_167,multiply(X,least_upper_bound(Y,Z))) != least_upper_bound(X_167,least_upper_bound(multiply(X,Z),multiply(X,Y)))
| least_upper_bound(X_167,multiply(X,least_upper_bound(Y,Z))) = least_upper_bound(X_167,multiply(X,least_upper_bound(Z,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_167,least_upper_bound(multiply(X,Z),multiply(X,Y))),least_upper_bound(X_167,multiply(X,least_upper_bound(Z,Y)))) )],[refute_0_625,refute_0_626]) ).
cnf(refute_0_628,plain,
least_upper_bound(X_167,multiply(X,least_upper_bound(Y,Z))) = least_upper_bound(X_167,multiply(X,least_upper_bound(Z,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_167,multiply(X,least_upper_bound(Y,Z))),least_upper_bound(X_167,least_upper_bound(multiply(X,Z),multiply(X,Y)))) )],[refute_0_620,refute_0_627]) ).
cnf(refute_0_629,plain,
( least_upper_bound(X_167,multiply(X,least_upper_bound(Y,Z))) != least_upper_bound(X_167,multiply(X,least_upper_bound(Z,Y)))
| least_upper_bound(X_167,multiply(X,least_upper_bound(Z,Y))) = least_upper_bound(X_167,multiply(X,least_upper_bound(Y,Z))) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(least_upper_bound(X_167,multiply(X,least_upper_bound(Y,Z))))),bind(Y0,$fot(least_upper_bound(X_167,multiply(X,least_upper_bound(Z,Y)))))]]) ).
cnf(refute_0_630,plain,
least_upper_bound(X_167,multiply(X,least_upper_bound(Z,Y))) = least_upper_bound(X_167,multiply(X,least_upper_bound(Y,Z))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_167,multiply(X,least_upper_bound(Y,Z))),least_upper_bound(X_167,multiply(X,least_upper_bound(Z,Y)))) )],[refute_0_628,refute_0_629]) ).
cnf(refute_0_631,plain,
least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(greatest_lower_bound(identity,X_150),identity))) = least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(identity,greatest_lower_bound(identity,X_150)))),
inference(subst,[],[refute_0_630:[bind(X,$fot(X_190)),bind(Y,$fot(identity)),bind(Z,$fot(greatest_lower_bound(identity,X_150))),bind(X_167,$fot(inverse(greatest_lower_bound(identity,X_150))))]]) ).
cnf(refute_0_632,plain,
least_upper_bound(X_39,least_upper_bound(greatest_lower_bound(X_11,X_39),X_41)) = least_upper_bound(least_upper_bound(X_39,greatest_lower_bound(X_11,X_39)),X_41),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_39)),bind(Y,$fot(greatest_lower_bound(X_11,X_39))),bind(Z,$fot(X_41))]]) ).
cnf(refute_0_633,plain,
least_upper_bound(X_39,greatest_lower_bound(X_11,X_39)) = X_39,
inference(subst,[],[refute_0_145:[bind(X_10,$fot(X_39))]]) ).
cnf(refute_0_634,plain,
( least_upper_bound(X_39,greatest_lower_bound(X_11,X_39)) != X_39
| least_upper_bound(X_39,least_upper_bound(greatest_lower_bound(X_11,X_39),X_41)) != least_upper_bound(least_upper_bound(X_39,greatest_lower_bound(X_11,X_39)),X_41)
| least_upper_bound(X_39,least_upper_bound(greatest_lower_bound(X_11,X_39),X_41)) = least_upper_bound(X_39,X_41) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_39,least_upper_bound(greatest_lower_bound(X_11,X_39),X_41)),least_upper_bound(least_upper_bound(X_39,greatest_lower_bound(X_11,X_39)),X_41)) ),[1,0],$fot(X_39)]]) ).
cnf(refute_0_635,plain,
( least_upper_bound(X_39,least_upper_bound(greatest_lower_bound(X_11,X_39),X_41)) != least_upper_bound(least_upper_bound(X_39,greatest_lower_bound(X_11,X_39)),X_41)
| least_upper_bound(X_39,least_upper_bound(greatest_lower_bound(X_11,X_39),X_41)) = least_upper_bound(X_39,X_41) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_39,greatest_lower_bound(X_11,X_39)),X_39) )],[refute_0_633,refute_0_634]) ).
cnf(refute_0_636,plain,
least_upper_bound(X_39,least_upper_bound(greatest_lower_bound(X_11,X_39),X_41)) = least_upper_bound(X_39,X_41),
inference(resolve,[$cnf( $equal(least_upper_bound(X_39,least_upper_bound(greatest_lower_bound(X_11,X_39),X_41)),least_upper_bound(least_upper_bound(X_39,greatest_lower_bound(X_11,X_39)),X_41)) )],[refute_0_632,refute_0_635]) ).
cnf(refute_0_637,plain,
least_upper_bound(inverse(greatest_lower_bound(identity,X_16)),least_upper_bound(greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_16))),X_139)) = least_upper_bound(inverse(greatest_lower_bound(identity,X_16)),X_139),
inference(subst,[],[refute_0_636:[bind(X_11,$fot(identity)),bind(X_39,$fot(inverse(greatest_lower_bound(identity,X_16)))),bind(X_41,$fot(X_139))]]) ).
cnf(refute_0_638,plain,
multiply(inverse(X_114),greatest_lower_bound(identity,X_114)) = greatest_lower_bound(identity,multiply(inverse(X_114),identity)),
inference(subst,[],[refute_0_46:[bind(X_105,$fot(identity)),bind(X_106,$fot(X_114))]]) ).
cnf(refute_0_639,plain,
inverse(X_114) = multiply(inverse(X_114),identity),
inference(subst,[],[refute_0_86:[bind(X_33,$fot(inverse(X_114)))]]) ).
cnf(refute_0_640,plain,
( inverse(X_114) != multiply(inverse(X_114),identity)
| multiply(inverse(X_114),identity) = inverse(X_114) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(inverse(X_114))),bind(Y0,$fot(multiply(inverse(X_114),identity)))]]) ).
cnf(refute_0_641,plain,
multiply(inverse(X_114),identity) = inverse(X_114),
inference(resolve,[$cnf( $equal(inverse(X_114),multiply(inverse(X_114),identity)) )],[refute_0_639,refute_0_640]) ).
cnf(refute_0_642,plain,
( multiply(inverse(X_114),greatest_lower_bound(identity,X_114)) != greatest_lower_bound(identity,multiply(inverse(X_114),identity))
| multiply(inverse(X_114),identity) != inverse(X_114)
| multiply(inverse(X_114),greatest_lower_bound(identity,X_114)) = greatest_lower_bound(identity,inverse(X_114)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_114),greatest_lower_bound(identity,X_114)),greatest_lower_bound(identity,multiply(inverse(X_114),identity))) ),[1,1],$fot(inverse(X_114))]]) ).
cnf(refute_0_643,plain,
( multiply(inverse(X_114),greatest_lower_bound(identity,X_114)) != greatest_lower_bound(identity,multiply(inverse(X_114),identity))
| multiply(inverse(X_114),greatest_lower_bound(identity,X_114)) = greatest_lower_bound(identity,inverse(X_114)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_114),identity),inverse(X_114)) )],[refute_0_641,refute_0_642]) ).
cnf(refute_0_644,plain,
multiply(inverse(X_114),greatest_lower_bound(identity,X_114)) = greatest_lower_bound(identity,inverse(X_114)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_114),greatest_lower_bound(identity,X_114)),greatest_lower_bound(identity,multiply(inverse(X_114),identity))) )],[refute_0_638,refute_0_643]) ).
cnf(refute_0_645,plain,
multiply(inverse(greatest_lower_bound(identity,X_16)),greatest_lower_bound(identity,greatest_lower_bound(identity,X_16))) = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_16))),
inference(subst,[],[refute_0_644:[bind(X_114,$fot(greatest_lower_bound(identity,X_16)))]]) ).
cnf(refute_0_646,plain,
greatest_lower_bound(identity,greatest_lower_bound(identity,X_16)) = greatest_lower_bound(identity,X_16),
inference(subst,[],[refute_0_354:[bind(X_17,$fot(identity))]]) ).
cnf(refute_0_647,plain,
( multiply(inverse(greatest_lower_bound(identity,X_16)),greatest_lower_bound(identity,greatest_lower_bound(identity,X_16))) != greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_16)))
| greatest_lower_bound(identity,greatest_lower_bound(identity,X_16)) != greatest_lower_bound(identity,X_16)
| multiply(inverse(greatest_lower_bound(identity,X_16)),greatest_lower_bound(identity,X_16)) = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_16))) ),
introduced(tautology,[equality,[$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_648,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( $equal(greatest_lower_bound(identity,greatest_lower_bound(identity,X_16)),greatest_lower_bound(identity,X_16)) )],[refute_0_646,refute_0_647]) ).
cnf(refute_0_649,plain,
multiply(inverse(greatest_lower_bound(identity,X_16)),greatest_lower_bound(identity,X_16)) = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_16))),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_16)),greatest_lower_bound(identity,greatest_lower_bound(identity,X_16))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_16)))) )],[refute_0_645,refute_0_648]) ).
cnf(refute_0_650,plain,
multiply(inverse(greatest_lower_bound(identity,X_16)),greatest_lower_bound(identity,X_16)) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(greatest_lower_bound(identity,X_16)))]]) ).
cnf(refute_0_651,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_652,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( $equal(multiply(inverse(greatest_lower_bound(identity,X_16)),greatest_lower_bound(identity,X_16)),identity) )],[refute_0_650,refute_0_651]) ).
cnf(refute_0_653,plain,
identity = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_16))),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_16)),greatest_lower_bound(identity,X_16)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_16)))) )],[refute_0_649,refute_0_652]) ).
cnf(refute_0_654,plain,
( identity != greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_16)))
| greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_16))) = identity ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(identity)),bind(Y0,$fot(greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_16)))))]]) ).
cnf(refute_0_655,plain,
greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_16))) = identity,
inference(resolve,[$cnf( $equal(identity,greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_16)))) )],[refute_0_653,refute_0_654]) ).
cnf(refute_0_656,plain,
( greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_16))) != identity
| least_upper_bound(inverse(greatest_lower_bound(identity,X_16)),least_upper_bound(greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_16))),X_139)) != least_upper_bound(inverse(greatest_lower_bound(identity,X_16)),X_139)
| least_upper_bound(inverse(greatest_lower_bound(identity,X_16)),least_upper_bound(identity,X_139)) = least_upper_bound(inverse(greatest_lower_bound(identity,X_16)),X_139) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(identity,X_16)),least_upper_bound(greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_16))),X_139)),least_upper_bound(inverse(greatest_lower_bound(identity,X_16)),X_139)) ),[0,1,0],$fot(identity)]]) ).
cnf(refute_0_657,plain,
( least_upper_bound(inverse(greatest_lower_bound(identity,X_16)),least_upper_bound(greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_16))),X_139)) != least_upper_bound(inverse(greatest_lower_bound(identity,X_16)),X_139)
| least_upper_bound(inverse(greatest_lower_bound(identity,X_16)),least_upper_bound(identity,X_139)) = least_upper_bound(inverse(greatest_lower_bound(identity,X_16)),X_139) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_16))),identity) )],[refute_0_655,refute_0_656]) ).
cnf(refute_0_658,plain,
least_upper_bound(inverse(greatest_lower_bound(identity,X_16)),least_upper_bound(identity,X_139)) = least_upper_bound(inverse(greatest_lower_bound(identity,X_16)),X_139),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(identity,X_16)),least_upper_bound(greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_16))),X_139)),least_upper_bound(inverse(greatest_lower_bound(identity,X_16)),X_139)) )],[refute_0_637,refute_0_657]) ).
cnf(refute_0_659,plain,
least_upper_bound(least_upper_bound(Y,X_136),least_upper_bound(X_135,X_136)) = least_upper_bound(X_135,least_upper_bound(X_136,least_upper_bound(Y,X_136))),
inference(subst,[],[refute_0_244:[bind(X,$fot(least_upper_bound(Y,X_136))),bind(X_39,$fot(X_135)),bind(X_40,$fot(X_136))]]) ).
cnf(refute_0_660,plain,
least_upper_bound(X_136,least_upper_bound(Y,X_136)) = least_upper_bound(X_136,Y),
inference(subst,[],[refute_0_175:[bind(X_15,$fot(X_136))]]) ).
cnf(refute_0_661,plain,
( least_upper_bound(X_136,least_upper_bound(Y,X_136)) != least_upper_bound(X_136,Y)
| least_upper_bound(least_upper_bound(Y,X_136),least_upper_bound(X_135,X_136)) != least_upper_bound(X_135,least_upper_bound(X_136,least_upper_bound(Y,X_136)))
| least_upper_bound(least_upper_bound(Y,X_136),least_upper_bound(X_135,X_136)) = least_upper_bound(X_135,least_upper_bound(X_136,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_136),least_upper_bound(X_135,X_136)),least_upper_bound(X_135,least_upper_bound(X_136,least_upper_bound(Y,X_136)))) ),[1,1],$fot(least_upper_bound(X_136,Y))]]) ).
cnf(refute_0_662,plain,
( least_upper_bound(least_upper_bound(Y,X_136),least_upper_bound(X_135,X_136)) != least_upper_bound(X_135,least_upper_bound(X_136,least_upper_bound(Y,X_136)))
| least_upper_bound(least_upper_bound(Y,X_136),least_upper_bound(X_135,X_136)) = least_upper_bound(X_135,least_upper_bound(X_136,Y)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_136,least_upper_bound(Y,X_136)),least_upper_bound(X_136,Y)) )],[refute_0_660,refute_0_661]) ).
cnf(refute_0_663,plain,
least_upper_bound(least_upper_bound(Y,X_136),least_upper_bound(X_135,X_136)) = least_upper_bound(X_135,least_upper_bound(X_136,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_136),least_upper_bound(X_135,X_136)),least_upper_bound(X_135,least_upper_bound(X_136,least_upper_bound(Y,X_136)))) )],[refute_0_659,refute_0_662]) ).
cnf(refute_0_664,plain,
least_upper_bound(X_15,least_upper_bound(least_upper_bound(X_39,X_40),X_15)) = least_upper_bound(X_15,least_upper_bound(X_39,X_40)),
inference(subst,[],[refute_0_175:[bind(Y,$fot(least_upper_bound(X_39,X_40)))]]) ).
cnf(refute_0_665,plain,
least_upper_bound(X_39,least_upper_bound(X_40,X_15)) = least_upper_bound(least_upper_bound(X_39,X_40),X_15),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_39)),bind(Y,$fot(X_40)),bind(Z,$fot(X_15))]]) ).
cnf(refute_0_666,plain,
( least_upper_bound(X_39,least_upper_bound(X_40,X_15)) != least_upper_bound(least_upper_bound(X_39,X_40),X_15)
| least_upper_bound(least_upper_bound(X_39,X_40),X_15) = least_upper_bound(X_39,least_upper_bound(X_40,X_15)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(least_upper_bound(X_39,least_upper_bound(X_40,X_15)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X_39,X_40),X_15)))]]) ).
cnf(refute_0_667,plain,
least_upper_bound(least_upper_bound(X_39,X_40),X_15) = least_upper_bound(X_39,least_upper_bound(X_40,X_15)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_39,least_upper_bound(X_40,X_15)),least_upper_bound(least_upper_bound(X_39,X_40),X_15)) )],[refute_0_665,refute_0_666]) ).
cnf(refute_0_668,plain,
( least_upper_bound(X_15,least_upper_bound(least_upper_bound(X_39,X_40),X_15)) != least_upper_bound(X_15,least_upper_bound(X_39,X_40))
| least_upper_bound(least_upper_bound(X_39,X_40),X_15) != least_upper_bound(X_39,least_upper_bound(X_40,X_15))
| least_upper_bound(X_15,least_upper_bound(X_39,least_upper_bound(X_40,X_15))) = least_upper_bound(X_15,least_upper_bound(X_39,X_40)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_15,least_upper_bound(least_upper_bound(X_39,X_40),X_15)),least_upper_bound(X_15,least_upper_bound(X_39,X_40))) ),[0,1],$fot(least_upper_bound(X_39,least_upper_bound(X_40,X_15)))]]) ).
cnf(refute_0_669,plain,
( least_upper_bound(X_15,least_upper_bound(least_upper_bound(X_39,X_40),X_15)) != least_upper_bound(X_15,least_upper_bound(X_39,X_40))
| least_upper_bound(X_15,least_upper_bound(X_39,least_upper_bound(X_40,X_15))) = least_upper_bound(X_15,least_upper_bound(X_39,X_40)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_39,X_40),X_15),least_upper_bound(X_39,least_upper_bound(X_40,X_15))) )],[refute_0_667,refute_0_668]) ).
cnf(refute_0_670,plain,
least_upper_bound(X_15,least_upper_bound(X_39,least_upper_bound(X_40,X_15))) = least_upper_bound(X_15,least_upper_bound(X_39,X_40)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_15,least_upper_bound(least_upper_bound(X_39,X_40),X_15)),least_upper_bound(X_15,least_upper_bound(X_39,X_40))) )],[refute_0_664,refute_0_669]) ).
cnf(refute_0_671,plain,
least_upper_bound(X_136,least_upper_bound(X_135,least_upper_bound(Y,X_136))) = least_upper_bound(X_136,least_upper_bound(X_135,Y)),
inference(subst,[],[refute_0_670:[bind(X_15,$fot(X_136)),bind(X_39,$fot(X_135)),bind(X_40,$fot(Y))]]) ).
cnf(refute_0_672,plain,
least_upper_bound(X_134,least_upper_bound(X_135,least_upper_bound(Y,X_135))) = least_upper_bound(X_135,least_upper_bound(least_upper_bound(Y,X_135),X_134)),
inference(subst,[],[refute_0_244:[bind(X,$fot(X_134)),bind(X_39,$fot(X_135)),bind(X_40,$fot(least_upper_bound(Y,X_135)))]]) ).
cnf(refute_0_673,plain,
least_upper_bound(X_135,least_upper_bound(Y,X_135)) = least_upper_bound(X_135,Y),
inference(subst,[],[refute_0_175:[bind(X_15,$fot(X_135))]]) ).
cnf(refute_0_674,plain,
( least_upper_bound(X_134,least_upper_bound(X_135,least_upper_bound(Y,X_135))) != least_upper_bound(X_135,least_upper_bound(least_upper_bound(Y,X_135),X_134))
| least_upper_bound(X_135,least_upper_bound(Y,X_135)) != least_upper_bound(X_135,Y)
| least_upper_bound(X_134,least_upper_bound(X_135,Y)) = least_upper_bound(X_135,least_upper_bound(least_upper_bound(Y,X_135),X_134)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_134,least_upper_bound(X_135,least_upper_bound(Y,X_135))),least_upper_bound(X_135,least_upper_bound(least_upper_bound(Y,X_135),X_134))) ),[0,1],$fot(least_upper_bound(X_135,Y))]]) ).
cnf(refute_0_675,plain,
( least_upper_bound(X_134,least_upper_bound(X_135,least_upper_bound(Y,X_135))) != least_upper_bound(X_135,least_upper_bound(least_upper_bound(Y,X_135),X_134))
| least_upper_bound(X_134,least_upper_bound(X_135,Y)) = least_upper_bound(X_135,least_upper_bound(least_upper_bound(Y,X_135),X_134)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_135,least_upper_bound(Y,X_135)),least_upper_bound(X_135,Y)) )],[refute_0_673,refute_0_674]) ).
cnf(refute_0_676,plain,
least_upper_bound(X_134,least_upper_bound(X_135,Y)) = least_upper_bound(X_135,least_upper_bound(least_upper_bound(Y,X_135),X_134)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_134,least_upper_bound(X_135,least_upper_bound(Y,X_135))),least_upper_bound(X_135,least_upper_bound(least_upper_bound(Y,X_135),X_134))) )],[refute_0_672,refute_0_675]) ).
cnf(refute_0_677,plain,
least_upper_bound(X_135,least_upper_bound(Y,least_upper_bound(X_135,X_134))) = least_upper_bound(Y,least_upper_bound(X_135,X_134)),
inference(subst,[],[refute_0_280:[bind(Y,$fot(X_134)),bind(X_39,$fot(Y)),bind(X_40,$fot(X_135))]]) ).
cnf(refute_0_678,plain,
least_upper_bound(least_upper_bound(Y,X_135),X_134) = least_upper_bound(Y,least_upper_bound(X_135,X_134)),
inference(subst,[],[refute_0_171:[bind(X,$fot(Y)),bind(Y,$fot(X_135)),bind(Z,$fot(X_134))]]) ).
cnf(refute_0_679,plain,
least_upper_bound(X_135,least_upper_bound(least_upper_bound(Y,X_135),X_134)) = least_upper_bound(X_135,least_upper_bound(least_upper_bound(Y,X_135),X_134)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_135,least_upper_bound(least_upper_bound(Y,X_135),X_134)))]]) ).
cnf(refute_0_680,plain,
( least_upper_bound(X_135,least_upper_bound(least_upper_bound(Y,X_135),X_134)) != least_upper_bound(X_135,least_upper_bound(least_upper_bound(Y,X_135),X_134))
| least_upper_bound(least_upper_bound(Y,X_135),X_134) != least_upper_bound(Y,least_upper_bound(X_135,X_134))
| least_upper_bound(X_135,least_upper_bound(least_upper_bound(Y,X_135),X_134)) = least_upper_bound(X_135,least_upper_bound(Y,least_upper_bound(X_135,X_134))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_135,least_upper_bound(least_upper_bound(Y,X_135),X_134)),least_upper_bound(X_135,least_upper_bound(least_upper_bound(Y,X_135),X_134))) ),[1,1],$fot(least_upper_bound(Y,least_upper_bound(X_135,X_134)))]]) ).
cnf(refute_0_681,plain,
( least_upper_bound(least_upper_bound(Y,X_135),X_134) != least_upper_bound(Y,least_upper_bound(X_135,X_134))
| least_upper_bound(X_135,least_upper_bound(least_upper_bound(Y,X_135),X_134)) = least_upper_bound(X_135,least_upper_bound(Y,least_upper_bound(X_135,X_134))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_135,least_upper_bound(least_upper_bound(Y,X_135),X_134)),least_upper_bound(X_135,least_upper_bound(least_upper_bound(Y,X_135),X_134))) )],[refute_0_679,refute_0_680]) ).
cnf(refute_0_682,plain,
least_upper_bound(X_135,least_upper_bound(least_upper_bound(Y,X_135),X_134)) = least_upper_bound(X_135,least_upper_bound(Y,least_upper_bound(X_135,X_134))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_135),X_134),least_upper_bound(Y,least_upper_bound(X_135,X_134))) )],[refute_0_678,refute_0_681]) ).
cnf(refute_0_683,plain,
( least_upper_bound(X_135,least_upper_bound(Y,least_upper_bound(X_135,X_134))) != least_upper_bound(Y,least_upper_bound(X_135,X_134))
| least_upper_bound(X_135,least_upper_bound(least_upper_bound(Y,X_135),X_134)) != least_upper_bound(X_135,least_upper_bound(Y,least_upper_bound(X_135,X_134)))
| least_upper_bound(X_135,least_upper_bound(least_upper_bound(Y,X_135),X_134)) = least_upper_bound(Y,least_upper_bound(X_135,X_134)) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(least_upper_bound(X_135,least_upper_bound(least_upper_bound(Y,X_135),X_134)))),bind(Y0,$fot(least_upper_bound(X_135,least_upper_bound(Y,least_upper_bound(X_135,X_134))))),bind(Z0,$fot(least_upper_bound(Y,least_upper_bound(X_135,X_134))))]]) ).
cnf(refute_0_684,plain,
( least_upper_bound(X_135,least_upper_bound(Y,least_upper_bound(X_135,X_134))) != least_upper_bound(Y,least_upper_bound(X_135,X_134))
| least_upper_bound(X_135,least_upper_bound(least_upper_bound(Y,X_135),X_134)) = least_upper_bound(Y,least_upper_bound(X_135,X_134)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_135,least_upper_bound(least_upper_bound(Y,X_135),X_134)),least_upper_bound(X_135,least_upper_bound(Y,least_upper_bound(X_135,X_134)))) )],[refute_0_682,refute_0_683]) ).
cnf(refute_0_685,plain,
least_upper_bound(X_135,least_upper_bound(least_upper_bound(Y,X_135),X_134)) = least_upper_bound(Y,least_upper_bound(X_135,X_134)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_135,least_upper_bound(Y,least_upper_bound(X_135,X_134))),least_upper_bound(Y,least_upper_bound(X_135,X_134))) )],[refute_0_677,refute_0_684]) ).
cnf(refute_0_686,plain,
( least_upper_bound(X_134,least_upper_bound(X_135,Y)) != least_upper_bound(X_135,least_upper_bound(least_upper_bound(Y,X_135),X_134))
| least_upper_bound(X_135,least_upper_bound(least_upper_bound(Y,X_135),X_134)) != least_upper_bound(Y,least_upper_bound(X_135,X_134))
| least_upper_bound(X_134,least_upper_bound(X_135,Y)) = least_upper_bound(Y,least_upper_bound(X_135,X_134)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_134,least_upper_bound(X_135,Y)),least_upper_bound(Y,least_upper_bound(X_135,X_134))) ),[0],$fot(least_upper_bound(X_135,least_upper_bound(least_upper_bound(Y,X_135),X_134)))]]) ).
cnf(refute_0_687,plain,
( least_upper_bound(X_134,least_upper_bound(X_135,Y)) != least_upper_bound(X_135,least_upper_bound(least_upper_bound(Y,X_135),X_134))
| least_upper_bound(X_134,least_upper_bound(X_135,Y)) = least_upper_bound(Y,least_upper_bound(X_135,X_134)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_135,least_upper_bound(least_upper_bound(Y,X_135),X_134)),least_upper_bound(Y,least_upper_bound(X_135,X_134))) )],[refute_0_685,refute_0_686]) ).
cnf(refute_0_688,plain,
least_upper_bound(X_134,least_upper_bound(X_135,Y)) = least_upper_bound(Y,least_upper_bound(X_135,X_134)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_134,least_upper_bound(X_135,Y)),least_upper_bound(X_135,least_upper_bound(least_upper_bound(Y,X_135),X_134))) )],[refute_0_676,refute_0_687]) ).
cnf(refute_0_689,plain,
( least_upper_bound(X_134,least_upper_bound(X_135,Y)) != least_upper_bound(Y,least_upper_bound(X_135,X_134))
| least_upper_bound(Y,least_upper_bound(X_135,X_134)) = least_upper_bound(X_134,least_upper_bound(X_135,Y)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(least_upper_bound(X_134,least_upper_bound(X_135,Y)))),bind(Y0,$fot(least_upper_bound(Y,least_upper_bound(X_135,X_134))))]]) ).
cnf(refute_0_690,plain,
least_upper_bound(Y,least_upper_bound(X_135,X_134)) = least_upper_bound(X_134,least_upper_bound(X_135,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_134,least_upper_bound(X_135,Y)),least_upper_bound(Y,least_upper_bound(X_135,X_134))) )],[refute_0_688,refute_0_689]) ).
cnf(refute_0_691,plain,
least_upper_bound(least_upper_bound(Y,X_136),least_upper_bound(X_135,X_136)) = least_upper_bound(X_136,least_upper_bound(X_135,least_upper_bound(Y,X_136))),
inference(subst,[],[refute_0_690:[bind(Y,$fot(least_upper_bound(Y,X_136))),bind(X_134,$fot(X_136))]]) ).
cnf(refute_0_692,plain,
( least_upper_bound(X_136,least_upper_bound(X_135,least_upper_bound(Y,X_136))) != least_upper_bound(X_136,least_upper_bound(X_135,Y))
| least_upper_bound(least_upper_bound(Y,X_136),least_upper_bound(X_135,X_136)) != least_upper_bound(X_136,least_upper_bound(X_135,least_upper_bound(Y,X_136)))
| least_upper_bound(least_upper_bound(Y,X_136),least_upper_bound(X_135,X_136)) = least_upper_bound(X_136,least_upper_bound(X_135,Y)) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(least_upper_bound(least_upper_bound(Y,X_136),least_upper_bound(X_135,X_136)))),bind(Y0,$fot(least_upper_bound(X_136,least_upper_bound(X_135,least_upper_bound(Y,X_136))))),bind(Z0,$fot(least_upper_bound(X_136,least_upper_bound(X_135,Y))))]]) ).
cnf(refute_0_693,plain,
( least_upper_bound(X_136,least_upper_bound(X_135,least_upper_bound(Y,X_136))) != least_upper_bound(X_136,least_upper_bound(X_135,Y))
| least_upper_bound(least_upper_bound(Y,X_136),least_upper_bound(X_135,X_136)) = least_upper_bound(X_136,least_upper_bound(X_135,Y)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_136),least_upper_bound(X_135,X_136)),least_upper_bound(X_136,least_upper_bound(X_135,least_upper_bound(Y,X_136)))) )],[refute_0_691,refute_0_692]) ).
cnf(refute_0_694,plain,
least_upper_bound(least_upper_bound(Y,X_136),least_upper_bound(X_135,X_136)) = least_upper_bound(X_136,least_upper_bound(X_135,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_136,least_upper_bound(X_135,least_upper_bound(Y,X_136))),least_upper_bound(X_136,least_upper_bound(X_135,Y))) )],[refute_0_671,refute_0_693]) ).
cnf(refute_0_695,plain,
( least_upper_bound(least_upper_bound(Y,X_136),least_upper_bound(X_135,X_136)) != least_upper_bound(X_135,least_upper_bound(X_136,Y))
| least_upper_bound(least_upper_bound(Y,X_136),least_upper_bound(X_135,X_136)) != least_upper_bound(X_136,least_upper_bound(X_135,Y))
| least_upper_bound(X_136,least_upper_bound(X_135,Y)) = least_upper_bound(X_135,least_upper_bound(X_136,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_136),least_upper_bound(X_135,X_136)),least_upper_bound(X_135,least_upper_bound(X_136,Y))) ),[0],$fot(least_upper_bound(X_136,least_upper_bound(X_135,Y)))]]) ).
cnf(refute_0_696,plain,
( least_upper_bound(least_upper_bound(Y,X_136),least_upper_bound(X_135,X_136)) != least_upper_bound(X_135,least_upper_bound(X_136,Y))
| least_upper_bound(X_136,least_upper_bound(X_135,Y)) = least_upper_bound(X_135,least_upper_bound(X_136,Y)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_136),least_upper_bound(X_135,X_136)),least_upper_bound(X_136,least_upper_bound(X_135,Y))) )],[refute_0_694,refute_0_695]) ).
cnf(refute_0_697,plain,
least_upper_bound(X_136,least_upper_bound(X_135,Y)) = least_upper_bound(X_135,least_upper_bound(X_136,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_136),least_upper_bound(X_135,X_136)),least_upper_bound(X_135,least_upper_bound(X_136,Y))) )],[refute_0_663,refute_0_696]) ).
cnf(refute_0_698,plain,
( least_upper_bound(X_136,least_upper_bound(X_135,Y)) != least_upper_bound(X_135,least_upper_bound(X_136,Y))
| least_upper_bound(X_135,least_upper_bound(X_136,Y)) = least_upper_bound(X_136,least_upper_bound(X_135,Y)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(least_upper_bound(X_136,least_upper_bound(X_135,Y)))),bind(Y0,$fot(least_upper_bound(X_135,least_upper_bound(X_136,Y))))]]) ).
cnf(refute_0_699,plain,
least_upper_bound(X_135,least_upper_bound(X_136,Y)) = least_upper_bound(X_136,least_upper_bound(X_135,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_136,least_upper_bound(X_135,Y)),least_upper_bound(X_135,least_upper_bound(X_136,Y))) )],[refute_0_697,refute_0_698]) ).
cnf(refute_0_700,plain,
least_upper_bound(inverse(greatest_lower_bound(identity,X_16)),least_upper_bound(identity,X_139)) = least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_16)),X_139)),
inference(subst,[],[refute_0_699:[bind(Y,$fot(X_139)),bind(X_135,$fot(inverse(greatest_lower_bound(identity,X_16)))),bind(X_136,$fot(identity))]]) ).
cnf(refute_0_701,plain,
( least_upper_bound(inverse(greatest_lower_bound(identity,X_16)),least_upper_bound(identity,X_139)) != least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_16)),X_139))
| least_upper_bound(inverse(greatest_lower_bound(identity,X_16)),least_upper_bound(identity,X_139)) != least_upper_bound(inverse(greatest_lower_bound(identity,X_16)),X_139)
| least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_16)),X_139)) = least_upper_bound(inverse(greatest_lower_bound(identity,X_16)),X_139) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(identity,X_16)),least_upper_bound(identity,X_139)),least_upper_bound(inverse(greatest_lower_bound(identity,X_16)),X_139)) ),[0],$fot(least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_16)),X_139)))]]) ).
cnf(refute_0_702,plain,
( least_upper_bound(inverse(greatest_lower_bound(identity,X_16)),least_upper_bound(identity,X_139)) != least_upper_bound(inverse(greatest_lower_bound(identity,X_16)),X_139)
| least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_16)),X_139)) = least_upper_bound(inverse(greatest_lower_bound(identity,X_16)),X_139) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(identity,X_16)),least_upper_bound(identity,X_139)),least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_16)),X_139))) )],[refute_0_700,refute_0_701]) ).
cnf(refute_0_703,plain,
least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_16)),X_139)) = least_upper_bound(inverse(greatest_lower_bound(identity,X_16)),X_139),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(identity,X_16)),least_upper_bound(identity,X_139)),least_upper_bound(inverse(greatest_lower_bound(identity,X_16)),X_139)) )],[refute_0_658,refute_0_702]) ).
cnf(refute_0_704,plain,
least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(greatest_lower_bound(identity,X_150),identity)))) = least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(greatest_lower_bound(identity,X_150),identity))),
inference(subst,[],[refute_0_703:[bind(X_139,$fot(multiply(X_190,least_upper_bound(greatest_lower_bound(identity,X_150),identity)))),bind(X_16,$fot(X_150))]]) ).
cnf(refute_0_705,plain,
( least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(greatest_lower_bound(identity,X_150),identity)))) != least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(greatest_lower_bound(identity,X_150),identity)))
| least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(greatest_lower_bound(identity,X_150),identity))) != least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(identity,greatest_lower_bound(identity,X_150))))
| least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(greatest_lower_bound(identity,X_150),identity)))) = least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(identity,greatest_lower_bound(identity,X_150)))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(greatest_lower_bound(identity,X_150),identity)))))),bind(Y0,$fot(least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(greatest_lower_bound(identity,X_150),identity))))),bind(Z0,$fot(least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(identity,greatest_lower_bound(identity,X_150))))))]]) ).
cnf(refute_0_706,plain,
( least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(greatest_lower_bound(identity,X_150),identity))) != least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(identity,greatest_lower_bound(identity,X_150))))
| least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(greatest_lower_bound(identity,X_150),identity)))) = least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(identity,greatest_lower_bound(identity,X_150)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(greatest_lower_bound(identity,X_150),identity)))),least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(greatest_lower_bound(identity,X_150),identity)))) )],[refute_0_704,refute_0_705]) ).
cnf(refute_0_707,plain,
least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(greatest_lower_bound(identity,X_150),identity)))) = least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(identity,greatest_lower_bound(identity,X_150)))),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(greatest_lower_bound(identity,X_150),identity))),least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(identity,greatest_lower_bound(identity,X_150))))) )],[refute_0_631,refute_0_706]) ).
cnf(refute_0_708,plain,
( least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(greatest_lower_bound(identity,X_150),identity)))) != least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(identity,greatest_lower_bound(identity,X_150))))
| least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(identity,greatest_lower_bound(identity,X_150)))) != least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),X_190)
| least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(greatest_lower_bound(identity,X_150),identity)))) = least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),X_190) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(greatest_lower_bound(identity,X_150),identity)))))),bind(Y0,$fot(least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(identity,greatest_lower_bound(identity,X_150)))))),bind(Z0,$fot(least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),X_190)))]]) ).
cnf(refute_0_709,plain,
( least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(identity,greatest_lower_bound(identity,X_150)))) != least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),X_190)
| least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(greatest_lower_bound(identity,X_150),identity)))) = least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),X_190) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(greatest_lower_bound(identity,X_150),identity)))),least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(identity,greatest_lower_bound(identity,X_150))))) )],[refute_0_707,refute_0_708]) ).
cnf(refute_0_710,plain,
least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(greatest_lower_bound(identity,X_150),identity)))) = least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),X_190),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(identity,greatest_lower_bound(identity,X_150)))),least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),X_190)) )],[refute_0_616,refute_0_709]) ).
cnf(refute_0_711,plain,
( least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))) != least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(greatest_lower_bound(identity,X_150),identity))))
| least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(greatest_lower_bound(identity,X_150),identity)))) != least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),X_190)
| least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))) = least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),X_190) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))),least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),X_190)) ),[0],$fot(least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(greatest_lower_bound(identity,X_150),identity)))))]]) ).
cnf(refute_0_712,plain,
( least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))) != least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(greatest_lower_bound(identity,X_150),identity))))
| least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))) = least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),X_190) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(greatest_lower_bound(identity,X_150),identity)))),least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),X_190)) )],[refute_0_710,refute_0_711]) ).
cnf(refute_0_713,plain,
( multiply(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))),least_upper_bound(greatest_lower_bound(identity,X_150),identity)) != least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(greatest_lower_bound(identity,X_150),identity))))
| least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))) = least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),X_190) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))),least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(greatest_lower_bound(identity,X_150),identity))))) )],[refute_0_604,refute_0_712]) ).
cnf(refute_0_714,plain,
least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))) = least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),X_190),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_190,inverse(greatest_lower_bound(X_150,identity))),least_upper_bound(greatest_lower_bound(identity,X_150),identity)),least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_150)),multiply(X_190,least_upper_bound(greatest_lower_bound(identity,X_150),identity))))) )],[refute_0_500,refute_0_713]) ).
cnf(refute_0_715,plain,
least_upper_bound(X_40,inverse(greatest_lower_bound(X_260,identity))) = least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),X_40),
inference(subst,[],[refute_0_714:[bind(X_150,$fot(X_260)),bind(X_190,$fot(X_40))]]) ).
cnf(refute_0_716,plain,
( least_upper_bound(X_39,least_upper_bound(X_40,inverse(greatest_lower_bound(X_260,identity)))) != least_upper_bound(X_40,least_upper_bound(X_39,least_upper_bound(X_40,inverse(greatest_lower_bound(X_260,identity)))))
| least_upper_bound(X_40,inverse(greatest_lower_bound(X_260,identity))) != least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),X_40)
| least_upper_bound(X_39,least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),X_40)) = least_upper_bound(X_40,least_upper_bound(X_39,least_upper_bound(X_40,inverse(greatest_lower_bound(X_260,identity))))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_39,least_upper_bound(X_40,inverse(greatest_lower_bound(X_260,identity)))),least_upper_bound(X_40,least_upper_bound(X_39,least_upper_bound(X_40,inverse(greatest_lower_bound(X_260,identity)))))) ),[0,1],$fot(least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),X_40))]]) ).
cnf(refute_0_717,plain,
( least_upper_bound(X_39,least_upper_bound(X_40,inverse(greatest_lower_bound(X_260,identity)))) != least_upper_bound(X_40,least_upper_bound(X_39,least_upper_bound(X_40,inverse(greatest_lower_bound(X_260,identity)))))
| least_upper_bound(X_39,least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),X_40)) = least_upper_bound(X_40,least_upper_bound(X_39,least_upper_bound(X_40,inverse(greatest_lower_bound(X_260,identity))))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_40,inverse(greatest_lower_bound(X_260,identity))),least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),X_40)) )],[refute_0_715,refute_0_716]) ).
cnf(refute_0_718,plain,
least_upper_bound(X_39,least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),X_40)) = least_upper_bound(X_40,least_upper_bound(X_39,least_upper_bound(X_40,inverse(greatest_lower_bound(X_260,identity))))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_39,least_upper_bound(X_40,inverse(greatest_lower_bound(X_260,identity)))),least_upper_bound(X_40,least_upper_bound(X_39,least_upper_bound(X_40,inverse(greatest_lower_bound(X_260,identity)))))) )],[refute_0_254,refute_0_717]) ).
cnf(refute_0_719,plain,
least_upper_bound(X_40,least_upper_bound(X_39,least_upper_bound(X_40,inverse(greatest_lower_bound(X_260,identity))))) = least_upper_bound(X_39,least_upper_bound(X_40,inverse(greatest_lower_bound(X_260,identity)))),
inference(subst,[],[refute_0_280:[bind(Y,$fot(inverse(greatest_lower_bound(X_260,identity))))]]) ).
cnf(refute_0_720,plain,
( least_upper_bound(X_39,least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),X_40)) != least_upper_bound(X_40,least_upper_bound(X_39,least_upper_bound(X_40,inverse(greatest_lower_bound(X_260,identity)))))
| least_upper_bound(X_40,least_upper_bound(X_39,least_upper_bound(X_40,inverse(greatest_lower_bound(X_260,identity))))) != least_upper_bound(X_39,least_upper_bound(X_40,inverse(greatest_lower_bound(X_260,identity))))
| least_upper_bound(X_39,least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),X_40)) = least_upper_bound(X_39,least_upper_bound(X_40,inverse(greatest_lower_bound(X_260,identity)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_39,least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),X_40)),least_upper_bound(X_39,least_upper_bound(X_40,inverse(greatest_lower_bound(X_260,identity))))) ),[0],$fot(least_upper_bound(X_40,least_upper_bound(X_39,least_upper_bound(X_40,inverse(greatest_lower_bound(X_260,identity))))))]]) ).
cnf(refute_0_721,plain,
( least_upper_bound(X_39,least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),X_40)) != least_upper_bound(X_40,least_upper_bound(X_39,least_upper_bound(X_40,inverse(greatest_lower_bound(X_260,identity)))))
| least_upper_bound(X_39,least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),X_40)) = least_upper_bound(X_39,least_upper_bound(X_40,inverse(greatest_lower_bound(X_260,identity)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_40,least_upper_bound(X_39,least_upper_bound(X_40,inverse(greatest_lower_bound(X_260,identity))))),least_upper_bound(X_39,least_upper_bound(X_40,inverse(greatest_lower_bound(X_260,identity))))) )],[refute_0_719,refute_0_720]) ).
cnf(refute_0_722,plain,
least_upper_bound(X_39,least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),X_40)) = least_upper_bound(X_39,least_upper_bound(X_40,inverse(greatest_lower_bound(X_260,identity)))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_39,least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),X_40)),least_upper_bound(X_40,least_upper_bound(X_39,least_upper_bound(X_40,inverse(greatest_lower_bound(X_260,identity)))))) )],[refute_0_718,refute_0_721]) ).
cnf(refute_0_723,plain,
least_upper_bound(X_42,least_upper_bound(inverse(greatest_lower_bound(identity,X_262)),identity)) = least_upper_bound(X_42,least_upper_bound(identity,inverse(greatest_lower_bound(X_262,identity)))),
inference(subst,[],[refute_0_722:[bind(X_260,$fot(X_262)),bind(X_39,$fot(X_42)),bind(X_40,$fot(identity))]]) ).
cnf(refute_0_724,plain,
( least_upper_bound(X_42,least_upper_bound(identity,inverse(greatest_lower_bound(X_262,identity)))) != least_upper_bound(X_42,inverse(greatest_lower_bound(X_262,identity)))
| least_upper_bound(X_42,least_upper_bound(inverse(greatest_lower_bound(identity,X_262)),identity)) != least_upper_bound(X_42,least_upper_bound(identity,inverse(greatest_lower_bound(X_262,identity))))
| least_upper_bound(X_42,least_upper_bound(inverse(greatest_lower_bound(identity,X_262)),identity)) = least_upper_bound(X_42,inverse(greatest_lower_bound(X_262,identity))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(least_upper_bound(X_42,least_upper_bound(inverse(greatest_lower_bound(identity,X_262)),identity)))),bind(Y0,$fot(least_upper_bound(X_42,least_upper_bound(identity,inverse(greatest_lower_bound(X_262,identity)))))),bind(Z0,$fot(least_upper_bound(X_42,inverse(greatest_lower_bound(X_262,identity)))))]]) ).
cnf(refute_0_725,plain,
( least_upper_bound(X_42,least_upper_bound(identity,inverse(greatest_lower_bound(X_262,identity)))) != least_upper_bound(X_42,inverse(greatest_lower_bound(X_262,identity)))
| least_upper_bound(X_42,least_upper_bound(inverse(greatest_lower_bound(identity,X_262)),identity)) = least_upper_bound(X_42,inverse(greatest_lower_bound(X_262,identity))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_42,least_upper_bound(inverse(greatest_lower_bound(identity,X_262)),identity)),least_upper_bound(X_42,least_upper_bound(identity,inverse(greatest_lower_bound(X_262,identity))))) )],[refute_0_723,refute_0_724]) ).
cnf(refute_0_726,plain,
least_upper_bound(X_42,least_upper_bound(inverse(greatest_lower_bound(identity,X_262)),identity)) = least_upper_bound(X_42,inverse(greatest_lower_bound(X_262,identity))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_42,least_upper_bound(identity,inverse(greatest_lower_bound(X_262,identity)))),least_upper_bound(X_42,inverse(greatest_lower_bound(X_262,identity)))) )],[refute_0_227,refute_0_725]) ).
cnf(refute_0_727,plain,
( least_upper_bound(X_42,least_upper_bound(inverse(greatest_lower_bound(identity,X_262)),identity)) != least_upper_bound(X_42,inverse(greatest_lower_bound(X_262,identity)))
| least_upper_bound(X_42,least_upper_bound(inverse(greatest_lower_bound(identity,X_262)),identity)) != least_upper_bound(X_42,inverse(greatest_lower_bound(identity,X_262)))
| least_upper_bound(X_42,inverse(greatest_lower_bound(X_262,identity))) = least_upper_bound(X_42,inverse(greatest_lower_bound(identity,X_262))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_42,least_upper_bound(inverse(greatest_lower_bound(identity,X_262)),identity)),least_upper_bound(X_42,inverse(greatest_lower_bound(identity,X_262)))) ),[0],$fot(least_upper_bound(X_42,inverse(greatest_lower_bound(X_262,identity))))]]) ).
cnf(refute_0_728,plain,
( least_upper_bound(X_42,least_upper_bound(inverse(greatest_lower_bound(identity,X_262)),identity)) != least_upper_bound(X_42,inverse(greatest_lower_bound(identity,X_262)))
| least_upper_bound(X_42,inverse(greatest_lower_bound(X_262,identity))) = least_upper_bound(X_42,inverse(greatest_lower_bound(identity,X_262))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_42,least_upper_bound(inverse(greatest_lower_bound(identity,X_262)),identity)),least_upper_bound(X_42,inverse(greatest_lower_bound(X_262,identity)))) )],[refute_0_726,refute_0_727]) ).
cnf(refute_0_729,plain,
least_upper_bound(X_42,inverse(greatest_lower_bound(X_262,identity))) = least_upper_bound(X_42,inverse(greatest_lower_bound(identity,X_262))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_42,least_upper_bound(inverse(greatest_lower_bound(identity,X_262)),identity)),least_upper_bound(X_42,inverse(greatest_lower_bound(identity,X_262)))) )],[refute_0_211,refute_0_728]) ).
cnf(refute_0_730,plain,
least_upper_bound(identity,inverse(greatest_lower_bound(multiply(inverse(X_106),X_105),identity))) = least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))),
inference(subst,[],[refute_0_729:[bind(X_262,$fot(multiply(inverse(X_106),X_105))),bind(X_42,$fot(identity))]]) ).
cnf(refute_0_731,plain,
( least_upper_bound(identity,inverse(greatest_lower_bound(multiply(inverse(X_106),X_105),identity))) != least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))))
| least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))) != inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))
| least_upper_bound(identity,inverse(greatest_lower_bound(multiply(inverse(X_106),X_105),identity))) = inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(least_upper_bound(identity,inverse(greatest_lower_bound(multiply(inverse(X_106),X_105),identity))))),bind(Y0,$fot(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))))),bind(Z0,$fot(inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))))]]) ).
cnf(refute_0_732,plain,
( least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))) != inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))
| least_upper_bound(identity,inverse(greatest_lower_bound(multiply(inverse(X_106),X_105),identity))) = inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(greatest_lower_bound(multiply(inverse(X_106),X_105),identity))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))))) )],[refute_0_730,refute_0_731]) ).
cnf(refute_0_733,plain,
least_upper_bound(identity,inverse(greatest_lower_bound(multiply(inverse(X_106),X_105),identity))) = inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))),inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))) )],[refute_0_138,refute_0_732]) ).
cnf(refute_0_734,plain,
multiply(least_upper_bound(identity,inverse(greatest_lower_bound(multiply(inverse(X_106),X_105),identity))),identity) = least_upper_bound(identity,inverse(greatest_lower_bound(multiply(inverse(X_106),X_105),identity))),
inference(subst,[],[refute_0_88:[bind(X_33,$fot(least_upper_bound(identity,inverse(greatest_lower_bound(multiply(inverse(X_106),X_105),identity)))))]]) ).
cnf(refute_0_735,plain,
( multiply(least_upper_bound(identity,inverse(greatest_lower_bound(multiply(inverse(X_106),X_105),identity))),identity) != least_upper_bound(identity,inverse(greatest_lower_bound(multiply(inverse(X_106),X_105),identity)))
| least_upper_bound(identity,inverse(greatest_lower_bound(multiply(inverse(X_106),X_105),identity))) != inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))
| multiply(least_upper_bound(identity,inverse(greatest_lower_bound(multiply(inverse(X_106),X_105),identity))),identity) = inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(least_upper_bound(identity,inverse(greatest_lower_bound(multiply(inverse(X_106),X_105),identity))),identity))),bind(Y0,$fot(least_upper_bound(identity,inverse(greatest_lower_bound(multiply(inverse(X_106),X_105),identity))))),bind(Z0,$fot(inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))))]]) ).
cnf(refute_0_736,plain,
( least_upper_bound(identity,inverse(greatest_lower_bound(multiply(inverse(X_106),X_105),identity))) != inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))
| multiply(least_upper_bound(identity,inverse(greatest_lower_bound(multiply(inverse(X_106),X_105),identity))),identity) = inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(greatest_lower_bound(multiply(inverse(X_106),X_105),identity))),identity),least_upper_bound(identity,inverse(greatest_lower_bound(multiply(inverse(X_106),X_105),identity)))) )],[refute_0_734,refute_0_735]) ).
cnf(refute_0_737,plain,
multiply(least_upper_bound(identity,inverse(greatest_lower_bound(multiply(inverse(X_106),X_105),identity))),identity) = inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(greatest_lower_bound(multiply(inverse(X_106),X_105),identity))),inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))) )],[refute_0_733,refute_0_736]) ).
cnf(refute_0_738,plain,
multiply(least_upper_bound(Y,inverse(greatest_lower_bound(X_260,identity))),X) = least_upper_bound(multiply(Y,X),multiply(inverse(greatest_lower_bound(X_260,identity)),X)),
inference(subst,[],[monotony_lub2:[bind(Z,$fot(inverse(greatest_lower_bound(X_260,identity))))]]) ).
cnf(refute_0_739,plain,
least_upper_bound(Y,inverse(greatest_lower_bound(X_260,identity))) = least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),Y),
inference(subst,[],[refute_0_714:[bind(X_150,$fot(X_260)),bind(X_190,$fot(Y))]]) ).
cnf(refute_0_740,plain,
( multiply(least_upper_bound(Y,inverse(greatest_lower_bound(X_260,identity))),X) != least_upper_bound(multiply(Y,X),multiply(inverse(greatest_lower_bound(X_260,identity)),X))
| least_upper_bound(Y,inverse(greatest_lower_bound(X_260,identity))) != least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),Y)
| multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),Y),X) = least_upper_bound(multiply(Y,X),multiply(inverse(greatest_lower_bound(X_260,identity)),X)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(Y,inverse(greatest_lower_bound(X_260,identity))),X),least_upper_bound(multiply(Y,X),multiply(inverse(greatest_lower_bound(X_260,identity)),X))) ),[0,0],$fot(least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),Y))]]) ).
cnf(refute_0_741,plain,
( multiply(least_upper_bound(Y,inverse(greatest_lower_bound(X_260,identity))),X) != least_upper_bound(multiply(Y,X),multiply(inverse(greatest_lower_bound(X_260,identity)),X))
| multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),Y),X) = least_upper_bound(multiply(Y,X),multiply(inverse(greatest_lower_bound(X_260,identity)),X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,inverse(greatest_lower_bound(X_260,identity))),least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),Y)) )],[refute_0_739,refute_0_740]) ).
cnf(refute_0_742,plain,
multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),Y),X) = least_upper_bound(multiply(Y,X),multiply(inverse(greatest_lower_bound(X_260,identity)),X)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,inverse(greatest_lower_bound(X_260,identity))),X),least_upper_bound(multiply(Y,X),multiply(inverse(greatest_lower_bound(X_260,identity)),X))) )],[refute_0_738,refute_0_741]) ).
cnf(refute_0_743,plain,
( multiply(least_upper_bound(Y,Z),X) != least_upper_bound(multiply(Y,X),multiply(Z,X))
| least_upper_bound(multiply(Y,X),multiply(Z,X)) = multiply(least_upper_bound(Y,Z),X) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(least_upper_bound(Y,Z),X))),bind(Y0,$fot(least_upper_bound(multiply(Y,X),multiply(Z,X))))]]) ).
cnf(refute_0_744,plain,
least_upper_bound(multiply(Y,X),multiply(Z,X)) = multiply(least_upper_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Y,X),multiply(Z,X))) )],[monotony_lub2,refute_0_743]) ).
cnf(refute_0_745,plain,
least_upper_bound(multiply(Y,X),multiply(inverse(greatest_lower_bound(X_260,identity)),X)) = multiply(least_upper_bound(Y,inverse(greatest_lower_bound(X_260,identity))),X),
inference(subst,[],[refute_0_744:[bind(Z,$fot(inverse(greatest_lower_bound(X_260,identity))))]]) ).
cnf(refute_0_746,plain,
( multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),Y),X) != least_upper_bound(multiply(Y,X),multiply(inverse(greatest_lower_bound(X_260,identity)),X))
| least_upper_bound(multiply(Y,X),multiply(inverse(greatest_lower_bound(X_260,identity)),X)) != multiply(least_upper_bound(Y,inverse(greatest_lower_bound(X_260,identity))),X)
| multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),Y),X) = multiply(least_upper_bound(Y,inverse(greatest_lower_bound(X_260,identity))),X) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),Y),X),multiply(least_upper_bound(Y,inverse(greatest_lower_bound(X_260,identity))),X)) ),[0],$fot(least_upper_bound(multiply(Y,X),multiply(inverse(greatest_lower_bound(X_260,identity)),X)))]]) ).
cnf(refute_0_747,plain,
( multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),Y),X) != least_upper_bound(multiply(Y,X),multiply(inverse(greatest_lower_bound(X_260,identity)),X))
| multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),Y),X) = multiply(least_upper_bound(Y,inverse(greatest_lower_bound(X_260,identity))),X) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(Y,X),multiply(inverse(greatest_lower_bound(X_260,identity)),X)),multiply(least_upper_bound(Y,inverse(greatest_lower_bound(X_260,identity))),X)) )],[refute_0_745,refute_0_746]) ).
cnf(refute_0_748,plain,
multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),Y),X) = multiply(least_upper_bound(Y,inverse(greatest_lower_bound(X_260,identity))),X),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),Y),X),least_upper_bound(multiply(Y,X),multiply(inverse(greatest_lower_bound(X_260,identity)),X))) )],[refute_0_742,refute_0_747]) ).
cnf(refute_0_749,plain,
multiply(least_upper_bound(inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))),identity),identity) = multiply(least_upper_bound(identity,inverse(greatest_lower_bound(multiply(inverse(X_106),X_105),identity))),identity),
inference(subst,[],[refute_0_748:[bind(X,$fot(identity)),bind(Y,$fot(identity)),bind(X_260,$fot(multiply(inverse(X_106),X_105)))]]) ).
cnf(refute_0_750,plain,
( multiply(least_upper_bound(identity,inverse(greatest_lower_bound(multiply(inverse(X_106),X_105),identity))),identity) != inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))
| multiply(least_upper_bound(inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))),identity),identity) != multiply(least_upper_bound(identity,inverse(greatest_lower_bound(multiply(inverse(X_106),X_105),identity))),identity)
| multiply(least_upper_bound(inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))),identity),identity) = inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(least_upper_bound(inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))),identity),identity))),bind(Y0,$fot(multiply(least_upper_bound(identity,inverse(greatest_lower_bound(multiply(inverse(X_106),X_105),identity))),identity))),bind(Z0,$fot(inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))))]]) ).
cnf(refute_0_751,plain,
( multiply(least_upper_bound(identity,inverse(greatest_lower_bound(multiply(inverse(X_106),X_105),identity))),identity) != inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))
| multiply(least_upper_bound(inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))),identity),identity) = inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))),identity),identity),multiply(least_upper_bound(identity,inverse(greatest_lower_bound(multiply(inverse(X_106),X_105),identity))),identity)) )],[refute_0_749,refute_0_750]) ).
cnf(refute_0_752,plain,
multiply(least_upper_bound(inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))),identity),identity) = inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(greatest_lower_bound(multiply(inverse(X_106),X_105),identity))),identity),inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))) )],[refute_0_737,refute_0_751]) ).
cnf(refute_0_753,plain,
multiply(least_upper_bound(X_68,identity),X_67) = least_upper_bound(multiply(X_68,X_67),multiply(identity,X_67)),
inference(subst,[],[monotony_lub2:[bind(X,$fot(X_67)),bind(Y,$fot(X_68)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_754,plain,
multiply(identity,X_67) = X_67,
inference(subst,[],[left_identity:[bind(X,$fot(X_67))]]) ).
cnf(refute_0_755,plain,
( multiply(identity,X_67) != X_67
| multiply(least_upper_bound(X_68,identity),X_67) != least_upper_bound(multiply(X_68,X_67),multiply(identity,X_67))
| multiply(least_upper_bound(X_68,identity),X_67) = least_upper_bound(multiply(X_68,X_67),X_67) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_68,identity),X_67),least_upper_bound(multiply(X_68,X_67),multiply(identity,X_67))) ),[1,1],$fot(X_67)]]) ).
cnf(refute_0_756,plain,
( multiply(least_upper_bound(X_68,identity),X_67) != least_upper_bound(multiply(X_68,X_67),multiply(identity,X_67))
| multiply(least_upper_bound(X_68,identity),X_67) = least_upper_bound(multiply(X_68,X_67),X_67) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_67),X_67) )],[refute_0_754,refute_0_755]) ).
cnf(refute_0_757,plain,
multiply(least_upper_bound(X_68,identity),X_67) = least_upper_bound(multiply(X_68,X_67),X_67),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_68,identity),X_67),least_upper_bound(multiply(X_68,X_67),multiply(identity,X_67))) )],[refute_0_753,refute_0_756]) ).
cnf(refute_0_758,plain,
least_upper_bound(multiply(X_68,X_67),X_67) = least_upper_bound(X_67,multiply(X_68,X_67)),
inference(subst,[],[refute_0_25:[bind(X,$fot(X_67)),bind(Y,$fot(multiply(X_68,X_67)))]]) ).
cnf(refute_0_759,plain,
( multiply(least_upper_bound(X_68,identity),X_67) != least_upper_bound(multiply(X_68,X_67),X_67)
| least_upper_bound(multiply(X_68,X_67),X_67) != least_upper_bound(X_67,multiply(X_68,X_67))
| multiply(least_upper_bound(X_68,identity),X_67) = least_upper_bound(X_67,multiply(X_68,X_67)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_68,identity),X_67),least_upper_bound(X_67,multiply(X_68,X_67))) ),[0],$fot(least_upper_bound(multiply(X_68,X_67),X_67))]]) ).
cnf(refute_0_760,plain,
( multiply(least_upper_bound(X_68,identity),X_67) != least_upper_bound(multiply(X_68,X_67),X_67)
| multiply(least_upper_bound(X_68,identity),X_67) = least_upper_bound(X_67,multiply(X_68,X_67)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_68,X_67),X_67),least_upper_bound(X_67,multiply(X_68,X_67))) )],[refute_0_758,refute_0_759]) ).
cnf(refute_0_761,plain,
multiply(least_upper_bound(X_68,identity),X_67) = least_upper_bound(X_67,multiply(X_68,X_67)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_68,identity),X_67),least_upper_bound(multiply(X_68,X_67),X_67)) )],[refute_0_757,refute_0_760]) ).
cnf(refute_0_762,plain,
( multiply(least_upper_bound(X_68,identity),X_67) != least_upper_bound(X_67,multiply(X_68,X_67))
| least_upper_bound(X_67,multiply(X_68,X_67)) = multiply(least_upper_bound(X_68,identity),X_67) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(least_upper_bound(X_68,identity),X_67))),bind(Y0,$fot(least_upper_bound(X_67,multiply(X_68,X_67))))]]) ).
cnf(refute_0_763,plain,
least_upper_bound(X_67,multiply(X_68,X_67)) = multiply(least_upper_bound(X_68,identity),X_67),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_68,identity),X_67),least_upper_bound(X_67,multiply(X_68,X_67))) )],[refute_0_761,refute_0_762]) ).
cnf(refute_0_764,plain,
least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))),identity)) = multiply(least_upper_bound(inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))),identity),identity),
inference(subst,[],[refute_0_763:[bind(X_67,$fot(identity)),bind(X_68,$fot(inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))))]]) ).
cnf(refute_0_765,plain,
( multiply(least_upper_bound(inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))),identity),identity) != inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))
| least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))),identity)) != multiply(least_upper_bound(inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))),identity),identity)
| least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))),identity)) = inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))),identity)))),bind(Y0,$fot(multiply(least_upper_bound(inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))),identity),identity))),bind(Z0,$fot(inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))))]]) ).
cnf(refute_0_766,plain,
( multiply(least_upper_bound(inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))),identity),identity) != inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))
| least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))),identity)) = inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))),identity)),multiply(least_upper_bound(inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))),identity),identity)) )],[refute_0_764,refute_0_765]) ).
cnf(refute_0_767,plain,
least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))),identity)) = inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))),identity),identity),inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))) )],[refute_0_752,refute_0_766]) ).
cnf(refute_0_768,plain,
( multiply(inverse(greatest_lower_bound(X_105,X_106)),X_106) != least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))),identity))
| least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))),identity)) != inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))
| multiply(inverse(greatest_lower_bound(X_105,X_106)),X_106) = inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(greatest_lower_bound(X_105,X_106)),X_106),inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))) ),[0],$fot(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))),identity)))]]) ).
cnf(refute_0_769,plain,
( multiply(inverse(greatest_lower_bound(X_105,X_106)),X_106) != least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))),identity))
| multiply(inverse(greatest_lower_bound(X_105,X_106)),X_106) = inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))),identity)),inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))) )],[refute_0_767,refute_0_768]) ).
cnf(refute_0_770,plain,
( multiply(inverse(multiply(inverse(X_106),greatest_lower_bound(X_105,X_106))),identity) != least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))),identity))
| multiply(inverse(greatest_lower_bound(X_105,X_106)),X_106) = inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_105,X_106)),X_106),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))),identity))) )],[refute_0_119,refute_0_769]) ).
cnf(refute_0_771,plain,
multiply(inverse(greatest_lower_bound(X_105,X_106)),X_106) = inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(X_106),greatest_lower_bound(X_105,X_106))),identity),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))),identity))) )],[refute_0_51,refute_0_770]) ).
cnf(refute_0_772,plain,
multiply(least_upper_bound(X_68,X_69),inverse(X_69)) = least_upper_bound(multiply(X_68,inverse(X_69)),multiply(X_69,inverse(X_69))),
inference(subst,[],[monotony_lub2:[bind(X,$fot(inverse(X_69))),bind(Y,$fot(X_68)),bind(Z,$fot(X_69))]]) ).
cnf(refute_0_773,plain,
multiply(X_69,inverse(X_69)) = identity,
inference(subst,[],[refute_0_71:[bind(X_35,$fot(X_69))]]) ).
cnf(refute_0_774,plain,
( multiply(X_69,inverse(X_69)) != identity
| multiply(least_upper_bound(X_68,X_69),inverse(X_69)) != least_upper_bound(multiply(X_68,inverse(X_69)),multiply(X_69,inverse(X_69)))
| multiply(least_upper_bound(X_68,X_69),inverse(X_69)) = least_upper_bound(multiply(X_68,inverse(X_69)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_68,X_69),inverse(X_69)),least_upper_bound(multiply(X_68,inverse(X_69)),multiply(X_69,inverse(X_69)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_775,plain,
( multiply(least_upper_bound(X_68,X_69),inverse(X_69)) != least_upper_bound(multiply(X_68,inverse(X_69)),multiply(X_69,inverse(X_69)))
| multiply(least_upper_bound(X_68,X_69),inverse(X_69)) = least_upper_bound(multiply(X_68,inverse(X_69)),identity) ),
inference(resolve,[$cnf( $equal(multiply(X_69,inverse(X_69)),identity) )],[refute_0_773,refute_0_774]) ).
cnf(refute_0_776,plain,
multiply(least_upper_bound(X_68,X_69),inverse(X_69)) = least_upper_bound(multiply(X_68,inverse(X_69)),identity),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_68,X_69),inverse(X_69)),least_upper_bound(multiply(X_68,inverse(X_69)),multiply(X_69,inverse(X_69)))) )],[refute_0_772,refute_0_775]) ).
cnf(refute_0_777,plain,
least_upper_bound(multiply(X_68,inverse(X_69)),identity) = least_upper_bound(identity,multiply(X_68,inverse(X_69))),
inference(subst,[],[refute_0_25:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_68,inverse(X_69))))]]) ).
cnf(refute_0_778,plain,
( multiply(least_upper_bound(X_68,X_69),inverse(X_69)) != least_upper_bound(multiply(X_68,inverse(X_69)),identity)
| least_upper_bound(multiply(X_68,inverse(X_69)),identity) != least_upper_bound(identity,multiply(X_68,inverse(X_69)))
| multiply(least_upper_bound(X_68,X_69),inverse(X_69)) = least_upper_bound(identity,multiply(X_68,inverse(X_69))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_68,X_69),inverse(X_69)),least_upper_bound(identity,multiply(X_68,inverse(X_69)))) ),[0],$fot(least_upper_bound(multiply(X_68,inverse(X_69)),identity))]]) ).
cnf(refute_0_779,plain,
( multiply(least_upper_bound(X_68,X_69),inverse(X_69)) != least_upper_bound(multiply(X_68,inverse(X_69)),identity)
| multiply(least_upper_bound(X_68,X_69),inverse(X_69)) = least_upper_bound(identity,multiply(X_68,inverse(X_69))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_68,inverse(X_69)),identity),least_upper_bound(identity,multiply(X_68,inverse(X_69)))) )],[refute_0_777,refute_0_778]) ).
cnf(refute_0_780,plain,
multiply(least_upper_bound(X_68,X_69),inverse(X_69)) = least_upper_bound(identity,multiply(X_68,inverse(X_69))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_68,X_69),inverse(X_69)),least_upper_bound(multiply(X_68,inverse(X_69)),identity)) )],[refute_0_776,refute_0_779]) ).
cnf(refute_0_781,plain,
multiply(least_upper_bound(identity,X_75),inverse(X_75)) = least_upper_bound(identity,multiply(identity,inverse(X_75))),
inference(subst,[],[refute_0_780:[bind(X_68,$fot(identity)),bind(X_69,$fot(X_75))]]) ).
cnf(refute_0_782,plain,
multiply(identity,inverse(X_75)) = inverse(X_75),
inference(subst,[],[left_identity:[bind(X,$fot(inverse(X_75)))]]) ).
cnf(refute_0_783,plain,
( multiply(identity,inverse(X_75)) != inverse(X_75)
| multiply(least_upper_bound(identity,X_75),inverse(X_75)) != least_upper_bound(identity,multiply(identity,inverse(X_75)))
| multiply(least_upper_bound(identity,X_75),inverse(X_75)) = least_upper_bound(identity,inverse(X_75)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,X_75),inverse(X_75)),least_upper_bound(identity,multiply(identity,inverse(X_75)))) ),[1,1],$fot(inverse(X_75))]]) ).
cnf(refute_0_784,plain,
( multiply(least_upper_bound(identity,X_75),inverse(X_75)) != least_upper_bound(identity,multiply(identity,inverse(X_75)))
| multiply(least_upper_bound(identity,X_75),inverse(X_75)) = least_upper_bound(identity,inverse(X_75)) ),
inference(resolve,[$cnf( $equal(multiply(identity,inverse(X_75)),inverse(X_75)) )],[refute_0_782,refute_0_783]) ).
cnf(refute_0_785,plain,
multiply(least_upper_bound(identity,X_75),inverse(X_75)) = least_upper_bound(identity,inverse(X_75)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_75),inverse(X_75)),least_upper_bound(identity,multiply(identity,inverse(X_75)))) )],[refute_0_781,refute_0_784]) ).
cnf(refute_0_786,plain,
inverse(X_146) = multiply(inverse(multiply(least_upper_bound(X_68,inverse(X_146)),X_146)),least_upper_bound(X_68,inverse(X_146))),
inference(subst,[],[refute_0_96:[bind(X_45,$fot(least_upper_bound(X_68,inverse(X_146)))),bind(X_46,$fot(X_146))]]) ).
cnf(refute_0_787,plain,
multiply(least_upper_bound(X_68,inverse(X_67)),X_67) = least_upper_bound(multiply(X_68,X_67),multiply(inverse(X_67),X_67)),
inference(subst,[],[monotony_lub2:[bind(X,$fot(X_67)),bind(Y,$fot(X_68)),bind(Z,$fot(inverse(X_67)))]]) ).
cnf(refute_0_788,plain,
multiply(inverse(X_67),X_67) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_67))]]) ).
cnf(refute_0_789,plain,
( multiply(inverse(X_67),X_67) != identity
| multiply(least_upper_bound(X_68,inverse(X_67)),X_67) != least_upper_bound(multiply(X_68,X_67),multiply(inverse(X_67),X_67))
| multiply(least_upper_bound(X_68,inverse(X_67)),X_67) = least_upper_bound(multiply(X_68,X_67),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_68,inverse(X_67)),X_67),least_upper_bound(multiply(X_68,X_67),multiply(inverse(X_67),X_67))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_790,plain,
( multiply(least_upper_bound(X_68,inverse(X_67)),X_67) != least_upper_bound(multiply(X_68,X_67),multiply(inverse(X_67),X_67))
| multiply(least_upper_bound(X_68,inverse(X_67)),X_67) = least_upper_bound(multiply(X_68,X_67),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_67),X_67),identity) )],[refute_0_788,refute_0_789]) ).
cnf(refute_0_791,plain,
multiply(least_upper_bound(X_68,inverse(X_67)),X_67) = least_upper_bound(multiply(X_68,X_67),identity),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_68,inverse(X_67)),X_67),least_upper_bound(multiply(X_68,X_67),multiply(inverse(X_67),X_67))) )],[refute_0_787,refute_0_790]) ).
cnf(refute_0_792,plain,
least_upper_bound(multiply(X_68,X_67),identity) = least_upper_bound(identity,multiply(X_68,X_67)),
inference(subst,[],[refute_0_25:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_68,X_67)))]]) ).
cnf(refute_0_793,plain,
( multiply(least_upper_bound(X_68,inverse(X_67)),X_67) != least_upper_bound(multiply(X_68,X_67),identity)
| least_upper_bound(multiply(X_68,X_67),identity) != least_upper_bound(identity,multiply(X_68,X_67))
| multiply(least_upper_bound(X_68,inverse(X_67)),X_67) = least_upper_bound(identity,multiply(X_68,X_67)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_68,inverse(X_67)),X_67),least_upper_bound(identity,multiply(X_68,X_67))) ),[0],$fot(least_upper_bound(multiply(X_68,X_67),identity))]]) ).
cnf(refute_0_794,plain,
( multiply(least_upper_bound(X_68,inverse(X_67)),X_67) != least_upper_bound(multiply(X_68,X_67),identity)
| multiply(least_upper_bound(X_68,inverse(X_67)),X_67) = least_upper_bound(identity,multiply(X_68,X_67)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_68,X_67),identity),least_upper_bound(identity,multiply(X_68,X_67))) )],[refute_0_792,refute_0_793]) ).
cnf(refute_0_795,plain,
multiply(least_upper_bound(X_68,inverse(X_67)),X_67) = least_upper_bound(identity,multiply(X_68,X_67)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_68,inverse(X_67)),X_67),least_upper_bound(multiply(X_68,X_67),identity)) )],[refute_0_791,refute_0_794]) ).
cnf(refute_0_796,plain,
multiply(least_upper_bound(X_68,inverse(X_146)),X_146) = least_upper_bound(identity,multiply(X_68,X_146)),
inference(subst,[],[refute_0_795:[bind(X_67,$fot(X_146))]]) ).
cnf(refute_0_797,plain,
( multiply(least_upper_bound(X_68,inverse(X_146)),X_146) != least_upper_bound(identity,multiply(X_68,X_146))
| inverse(X_146) != multiply(inverse(multiply(least_upper_bound(X_68,inverse(X_146)),X_146)),least_upper_bound(X_68,inverse(X_146)))
| inverse(X_146) = multiply(inverse(least_upper_bound(identity,multiply(X_68,X_146))),least_upper_bound(X_68,inverse(X_146))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(X_146),multiply(inverse(multiply(least_upper_bound(X_68,inverse(X_146)),X_146)),least_upper_bound(X_68,inverse(X_146)))) ),[1,0,0],$fot(least_upper_bound(identity,multiply(X_68,X_146)))]]) ).
cnf(refute_0_798,plain,
( inverse(X_146) != multiply(inverse(multiply(least_upper_bound(X_68,inverse(X_146)),X_146)),least_upper_bound(X_68,inverse(X_146)))
| inverse(X_146) = multiply(inverse(least_upper_bound(identity,multiply(X_68,X_146))),least_upper_bound(X_68,inverse(X_146))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_68,inverse(X_146)),X_146),least_upper_bound(identity,multiply(X_68,X_146))) )],[refute_0_796,refute_0_797]) ).
cnf(refute_0_799,plain,
inverse(X_146) = multiply(inverse(least_upper_bound(identity,multiply(X_68,X_146))),least_upper_bound(X_68,inverse(X_146))),
inference(resolve,[$cnf( $equal(inverse(X_146),multiply(inverse(multiply(least_upper_bound(X_68,inverse(X_146)),X_146)),least_upper_bound(X_68,inverse(X_146)))) )],[refute_0_786,refute_0_798]) ).
cnf(refute_0_800,plain,
inverse(greatest_lower_bound(identity,X_125)) = multiply(inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X_125))),greatest_lower_bound(identity,X_125)))),least_upper_bound(inverse(greatest_lower_bound(identity,inverse(X_125))),inverse(greatest_lower_bound(identity,X_125)))),
inference(subst,[],[refute_0_799:[bind(X_146,$fot(greatest_lower_bound(identity,X_125))),bind(X_68,$fot(inverse(greatest_lower_bound(identity,inverse(X_125)))))]]) ).
cnf(refute_0_801,plain,
( X_125 != multiply(inverse(greatest_lower_bound(identity,inverse(X_125))),greatest_lower_bound(identity,X_125))
| multiply(inverse(greatest_lower_bound(identity,inverse(X_125))),greatest_lower_bound(identity,X_125)) = X_125 ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(X_125)),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(identity,inverse(X_125))),greatest_lower_bound(identity,X_125))))]]) ).
cnf(refute_0_802,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X_125))),greatest_lower_bound(identity,X_125)) = X_125,
inference(resolve,[$cnf( $equal(X_125,multiply(inverse(greatest_lower_bound(identity,inverse(X_125))),greatest_lower_bound(identity,X_125))) )],[refute_0_456,refute_0_801]) ).
cnf(refute_0_803,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(X_125))),greatest_lower_bound(identity,X_125)) != X_125
| inverse(greatest_lower_bound(identity,X_125)) != multiply(inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X_125))),greatest_lower_bound(identity,X_125)))),least_upper_bound(inverse(greatest_lower_bound(identity,inverse(X_125))),inverse(greatest_lower_bound(identity,X_125))))
| inverse(greatest_lower_bound(identity,X_125)) = multiply(inverse(least_upper_bound(identity,X_125)),least_upper_bound(inverse(greatest_lower_bound(identity,inverse(X_125))),inverse(greatest_lower_bound(identity,X_125)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,X_125)),multiply(inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X_125))),greatest_lower_bound(identity,X_125)))),least_upper_bound(inverse(greatest_lower_bound(identity,inverse(X_125))),inverse(greatest_lower_bound(identity,X_125))))) ),[1,0,0,1],$fot(X_125)]]) ).
cnf(refute_0_804,plain,
( inverse(greatest_lower_bound(identity,X_125)) != multiply(inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X_125))),greatest_lower_bound(identity,X_125)))),least_upper_bound(inverse(greatest_lower_bound(identity,inverse(X_125))),inverse(greatest_lower_bound(identity,X_125))))
| inverse(greatest_lower_bound(identity,X_125)) = multiply(inverse(least_upper_bound(identity,X_125)),least_upper_bound(inverse(greatest_lower_bound(identity,inverse(X_125))),inverse(greatest_lower_bound(identity,X_125)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X_125))),greatest_lower_bound(identity,X_125)),X_125) )],[refute_0_802,refute_0_803]) ).
cnf(refute_0_805,plain,
inverse(greatest_lower_bound(identity,X_125)) = multiply(inverse(least_upper_bound(identity,X_125)),least_upper_bound(inverse(greatest_lower_bound(identity,inverse(X_125))),inverse(greatest_lower_bound(identity,X_125)))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,X_125)),multiply(inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X_125))),greatest_lower_bound(identity,X_125)))),least_upper_bound(inverse(greatest_lower_bound(identity,inverse(X_125))),inverse(greatest_lower_bound(identity,X_125))))) )],[refute_0_800,refute_0_804]) ).
cnf(refute_0_806,plain,
inverse(multiply(inverse(multiply(inverse(X_148),X_149)),X_31)) = multiply(inverse(X_31),multiply(inverse(X_148),X_149)),
inference(subst,[],[refute_0_110:[bind(X_145,$fot(multiply(inverse(X_148),X_149)))]]) ).
cnf(refute_0_807,plain,
inverse(multiply(inverse(X_148),X_149)) = multiply(inverse(X_149),X_148),
inference(subst,[],[refute_0_110:[bind(X_145,$fot(X_148)),bind(X_31,$fot(X_149))]]) ).
cnf(refute_0_808,plain,
( inverse(multiply(inverse(X_148),X_149)) != multiply(inverse(X_149),X_148)
| inverse(multiply(inverse(multiply(inverse(X_148),X_149)),X_31)) != multiply(inverse(X_31),multiply(inverse(X_148),X_149))
| inverse(multiply(multiply(inverse(X_149),X_148),X_31)) = multiply(inverse(X_31),multiply(inverse(X_148),X_149)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(multiply(inverse(X_148),X_149)),X_31)),multiply(inverse(X_31),multiply(inverse(X_148),X_149))) ),[0,0,0],$fot(multiply(inverse(X_149),X_148))]]) ).
cnf(refute_0_809,plain,
( inverse(multiply(inverse(multiply(inverse(X_148),X_149)),X_31)) != multiply(inverse(X_31),multiply(inverse(X_148),X_149))
| inverse(multiply(multiply(inverse(X_149),X_148),X_31)) = multiply(inverse(X_31),multiply(inverse(X_148),X_149)) ),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_148),X_149)),multiply(inverse(X_149),X_148)) )],[refute_0_807,refute_0_808]) ).
cnf(refute_0_810,plain,
inverse(multiply(multiply(inverse(X_149),X_148),X_31)) = multiply(inverse(X_31),multiply(inverse(X_148),X_149)),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(multiply(inverse(X_148),X_149)),X_31)),multiply(inverse(X_31),multiply(inverse(X_148),X_149))) )],[refute_0_806,refute_0_809]) ).
cnf(refute_0_811,plain,
inverse(multiply(inverse(X_149),multiply(X_148,X_31))) = multiply(inverse(multiply(X_148,X_31)),X_149),
inference(subst,[],[refute_0_110:[bind(X_145,$fot(X_149)),bind(X_31,$fot(multiply(X_148,X_31)))]]) ).
cnf(refute_0_812,plain,
multiply(multiply(inverse(X_149),X_148),X_31) = multiply(inverse(X_149),multiply(X_148,X_31)),
inference(subst,[],[associativity:[bind(X,$fot(inverse(X_149))),bind(Y,$fot(X_148)),bind(Z,$fot(X_31))]]) ).
cnf(refute_0_813,plain,
inverse(multiply(multiply(inverse(X_149),X_148),X_31)) = inverse(multiply(multiply(inverse(X_149),X_148),X_31)),
introduced(tautology,[refl,[$fot(inverse(multiply(multiply(inverse(X_149),X_148),X_31)))]]) ).
cnf(refute_0_814,plain,
( multiply(multiply(inverse(X_149),X_148),X_31) != multiply(inverse(X_149),multiply(X_148,X_31))
| inverse(multiply(multiply(inverse(X_149),X_148),X_31)) != inverse(multiply(multiply(inverse(X_149),X_148),X_31))
| inverse(multiply(multiply(inverse(X_149),X_148),X_31)) = inverse(multiply(inverse(X_149),multiply(X_148,X_31))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(multiply(inverse(X_149),X_148),X_31)),inverse(multiply(multiply(inverse(X_149),X_148),X_31))) ),[1,0],$fot(multiply(inverse(X_149),multiply(X_148,X_31)))]]) ).
cnf(refute_0_815,plain,
( multiply(multiply(inverse(X_149),X_148),X_31) != multiply(inverse(X_149),multiply(X_148,X_31))
| inverse(multiply(multiply(inverse(X_149),X_148),X_31)) = inverse(multiply(inverse(X_149),multiply(X_148,X_31))) ),
inference(resolve,[$cnf( $equal(inverse(multiply(multiply(inverse(X_149),X_148),X_31)),inverse(multiply(multiply(inverse(X_149),X_148),X_31))) )],[refute_0_813,refute_0_814]) ).
cnf(refute_0_816,plain,
inverse(multiply(multiply(inverse(X_149),X_148),X_31)) = inverse(multiply(inverse(X_149),multiply(X_148,X_31))),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_149),X_148),X_31),multiply(inverse(X_149),multiply(X_148,X_31))) )],[refute_0_812,refute_0_815]) ).
cnf(refute_0_817,plain,
( inverse(multiply(multiply(inverse(X_149),X_148),X_31)) != inverse(multiply(inverse(X_149),multiply(X_148,X_31)))
| inverse(multiply(inverse(X_149),multiply(X_148,X_31))) != multiply(inverse(multiply(X_148,X_31)),X_149)
| inverse(multiply(multiply(inverse(X_149),X_148),X_31)) = multiply(inverse(multiply(X_148,X_31)),X_149) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(inverse(multiply(multiply(inverse(X_149),X_148),X_31)))),bind(Y0,$fot(inverse(multiply(inverse(X_149),multiply(X_148,X_31))))),bind(Z0,$fot(multiply(inverse(multiply(X_148,X_31)),X_149)))]]) ).
cnf(refute_0_818,plain,
( inverse(multiply(inverse(X_149),multiply(X_148,X_31))) != multiply(inverse(multiply(X_148,X_31)),X_149)
| inverse(multiply(multiply(inverse(X_149),X_148),X_31)) = multiply(inverse(multiply(X_148,X_31)),X_149) ),
inference(resolve,[$cnf( $equal(inverse(multiply(multiply(inverse(X_149),X_148),X_31)),inverse(multiply(inverse(X_149),multiply(X_148,X_31)))) )],[refute_0_816,refute_0_817]) ).
cnf(refute_0_819,plain,
inverse(multiply(multiply(inverse(X_149),X_148),X_31)) = multiply(inverse(multiply(X_148,X_31)),X_149),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_149),multiply(X_148,X_31))),multiply(inverse(multiply(X_148,X_31)),X_149)) )],[refute_0_811,refute_0_818]) ).
cnf(refute_0_820,plain,
( inverse(multiply(multiply(inverse(X_149),X_148),X_31)) != multiply(inverse(X_31),multiply(inverse(X_148),X_149))
| inverse(multiply(multiply(inverse(X_149),X_148),X_31)) != multiply(inverse(multiply(X_148,X_31)),X_149)
| multiply(inverse(multiply(X_148,X_31)),X_149) = multiply(inverse(X_31),multiply(inverse(X_148),X_149)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(multiply(inverse(X_149),X_148),X_31)),multiply(inverse(X_31),multiply(inverse(X_148),X_149))) ),[0],$fot(multiply(inverse(multiply(X_148,X_31)),X_149))]]) ).
cnf(refute_0_821,plain,
( inverse(multiply(multiply(inverse(X_149),X_148),X_31)) != multiply(inverse(X_31),multiply(inverse(X_148),X_149))
| multiply(inverse(multiply(X_148,X_31)),X_149) = multiply(inverse(X_31),multiply(inverse(X_148),X_149)) ),
inference(resolve,[$cnf( $equal(inverse(multiply(multiply(inverse(X_149),X_148),X_31)),multiply(inverse(multiply(X_148,X_31)),X_149)) )],[refute_0_819,refute_0_820]) ).
cnf(refute_0_822,plain,
multiply(inverse(multiply(X_148,X_31)),X_149) = multiply(inverse(X_31),multiply(inverse(X_148),X_149)),
inference(resolve,[$cnf( $equal(inverse(multiply(multiply(inverse(X_149),X_148),X_31)),multiply(inverse(X_31),multiply(inverse(X_148),X_149))) )],[refute_0_810,refute_0_821]) ).
cnf(refute_0_823,plain,
( multiply(inverse(multiply(X_148,X_31)),X_149) != multiply(inverse(X_31),multiply(inverse(X_148),X_149))
| multiply(inverse(X_31),multiply(inverse(X_148),X_149)) = multiply(inverse(multiply(X_148,X_31)),X_149) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(inverse(multiply(X_148,X_31)),X_149))),bind(Y0,$fot(multiply(inverse(X_31),multiply(inverse(X_148),X_149))))]]) ).
cnf(refute_0_824,plain,
multiply(inverse(X_31),multiply(inverse(X_148),X_149)) = multiply(inverse(multiply(X_148,X_31)),X_149),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_148,X_31)),X_149),multiply(inverse(X_31),multiply(inverse(X_148),X_149))) )],[refute_0_822,refute_0_823]) ).
cnf(refute_0_825,plain,
multiply(inverse(least_upper_bound(identity,X_125)),multiply(inverse(greatest_lower_bound(identity,X_125)),least_upper_bound(X_125,identity))) = multiply(inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125))),least_upper_bound(X_125,identity)),
inference(subst,[],[refute_0_824:[bind(X_148,$fot(greatest_lower_bound(identity,X_125))),bind(X_149,$fot(least_upper_bound(X_125,identity))),bind(X_31,$fot(least_upper_bound(identity,X_125)))]]) ).
cnf(refute_0_826,plain,
multiply(inverse(greatest_lower_bound(identity,X_49)),least_upper_bound(X_49,identity)) = least_upper_bound(inverse(greatest_lower_bound(identity,X_49)),multiply(inverse(greatest_lower_bound(identity,X_49)),X_49)),
inference(subst,[],[refute_0_528:[bind(X_48,$fot(inverse(greatest_lower_bound(identity,X_49))))]]) ).
cnf(refute_0_827,plain,
inverse(multiply(inverse(X_148),greatest_lower_bound(identity,X_148))) = multiply(inverse(greatest_lower_bound(identity,X_148)),X_148),
inference(subst,[],[refute_0_110:[bind(X_145,$fot(X_148)),bind(X_31,$fot(greatest_lower_bound(identity,X_148)))]]) ).
cnf(refute_0_828,plain,
multiply(inverse(X_148),greatest_lower_bound(identity,X_148)) = greatest_lower_bound(identity,inverse(X_148)),
inference(subst,[],[refute_0_644:[bind(X_114,$fot(X_148))]]) ).
cnf(refute_0_829,plain,
( multiply(inverse(X_148),greatest_lower_bound(identity,X_148)) != greatest_lower_bound(identity,inverse(X_148))
| inverse(multiply(inverse(X_148),greatest_lower_bound(identity,X_148))) != multiply(inverse(greatest_lower_bound(identity,X_148)),X_148)
| inverse(greatest_lower_bound(identity,inverse(X_148))) = multiply(inverse(greatest_lower_bound(identity,X_148)),X_148) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X_148),greatest_lower_bound(identity,X_148))),multiply(inverse(greatest_lower_bound(identity,X_148)),X_148)) ),[0,0],$fot(greatest_lower_bound(identity,inverse(X_148)))]]) ).
cnf(refute_0_830,plain,
( inverse(multiply(inverse(X_148),greatest_lower_bound(identity,X_148))) != multiply(inverse(greatest_lower_bound(identity,X_148)),X_148)
| inverse(greatest_lower_bound(identity,inverse(X_148))) = multiply(inverse(greatest_lower_bound(identity,X_148)),X_148) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_148),greatest_lower_bound(identity,X_148)),greatest_lower_bound(identity,inverse(X_148))) )],[refute_0_828,refute_0_829]) ).
cnf(refute_0_831,plain,
inverse(greatest_lower_bound(identity,inverse(X_148))) = multiply(inverse(greatest_lower_bound(identity,X_148)),X_148),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_148),greatest_lower_bound(identity,X_148))),multiply(inverse(greatest_lower_bound(identity,X_148)),X_148)) )],[refute_0_827,refute_0_830]) ).
cnf(refute_0_832,plain,
inverse(greatest_lower_bound(identity,inverse(X_49))) = multiply(inverse(greatest_lower_bound(identity,X_49)),X_49),
inference(subst,[],[refute_0_831:[bind(X_148,$fot(X_49))]]) ).
cnf(refute_0_833,plain,
( inverse(greatest_lower_bound(identity,inverse(X_49))) != multiply(inverse(greatest_lower_bound(identity,X_49)),X_49)
| multiply(inverse(greatest_lower_bound(identity,X_49)),X_49) = inverse(greatest_lower_bound(identity,inverse(X_49))) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(inverse(greatest_lower_bound(identity,inverse(X_49))))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(identity,X_49)),X_49)))]]) ).
cnf(refute_0_834,plain,
multiply(inverse(greatest_lower_bound(identity,X_49)),X_49) = inverse(greatest_lower_bound(identity,inverse(X_49))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_49))),multiply(inverse(greatest_lower_bound(identity,X_49)),X_49)) )],[refute_0_832,refute_0_833]) ).
cnf(refute_0_835,plain,
( multiply(inverse(greatest_lower_bound(identity,X_49)),X_49) != inverse(greatest_lower_bound(identity,inverse(X_49)))
| multiply(inverse(greatest_lower_bound(identity,X_49)),least_upper_bound(X_49,identity)) != least_upper_bound(inverse(greatest_lower_bound(identity,X_49)),multiply(inverse(greatest_lower_bound(identity,X_49)),X_49))
| multiply(inverse(greatest_lower_bound(identity,X_49)),least_upper_bound(X_49,identity)) = least_upper_bound(inverse(greatest_lower_bound(identity,X_49)),inverse(greatest_lower_bound(identity,inverse(X_49)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_49)),least_upper_bound(X_49,identity)),least_upper_bound(inverse(greatest_lower_bound(identity,X_49)),multiply(inverse(greatest_lower_bound(identity,X_49)),X_49))) ),[1,1],$fot(inverse(greatest_lower_bound(identity,inverse(X_49))))]]) ).
cnf(refute_0_836,plain,
( multiply(inverse(greatest_lower_bound(identity,X_49)),least_upper_bound(X_49,identity)) != least_upper_bound(inverse(greatest_lower_bound(identity,X_49)),multiply(inverse(greatest_lower_bound(identity,X_49)),X_49))
| multiply(inverse(greatest_lower_bound(identity,X_49)),least_upper_bound(X_49,identity)) = least_upper_bound(inverse(greatest_lower_bound(identity,X_49)),inverse(greatest_lower_bound(identity,inverse(X_49)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_49)),X_49),inverse(greatest_lower_bound(identity,inverse(X_49)))) )],[refute_0_834,refute_0_835]) ).
cnf(refute_0_837,plain,
multiply(inverse(greatest_lower_bound(identity,X_49)),least_upper_bound(X_49,identity)) = least_upper_bound(inverse(greatest_lower_bound(identity,X_49)),inverse(greatest_lower_bound(identity,inverse(X_49)))),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_49)),least_upper_bound(X_49,identity)),least_upper_bound(inverse(greatest_lower_bound(identity,X_49)),multiply(inverse(greatest_lower_bound(identity,X_49)),X_49))) )],[refute_0_826,refute_0_836]) ).
cnf(refute_0_838,plain,
( multiply(inverse(greatest_lower_bound(identity,X_49)),least_upper_bound(X_49,identity)) != least_upper_bound(inverse(greatest_lower_bound(identity,X_49)),inverse(greatest_lower_bound(identity,inverse(X_49))))
| least_upper_bound(inverse(greatest_lower_bound(identity,X_49)),inverse(greatest_lower_bound(identity,inverse(X_49)))) = multiply(inverse(greatest_lower_bound(identity,X_49)),least_upper_bound(X_49,identity)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(identity,X_49)),least_upper_bound(X_49,identity)))),bind(Y0,$fot(least_upper_bound(inverse(greatest_lower_bound(identity,X_49)),inverse(greatest_lower_bound(identity,inverse(X_49))))))]]) ).
cnf(refute_0_839,plain,
least_upper_bound(inverse(greatest_lower_bound(identity,X_49)),inverse(greatest_lower_bound(identity,inverse(X_49)))) = multiply(inverse(greatest_lower_bound(identity,X_49)),least_upper_bound(X_49,identity)),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_49)),least_upper_bound(X_49,identity)),least_upper_bound(inverse(greatest_lower_bound(identity,X_49)),inverse(greatest_lower_bound(identity,inverse(X_49))))) )],[refute_0_837,refute_0_838]) ).
cnf(refute_0_840,plain,
least_upper_bound(inverse(greatest_lower_bound(identity,X_125)),inverse(greatest_lower_bound(identity,inverse(X_125)))) = multiply(inverse(greatest_lower_bound(identity,X_125)),least_upper_bound(X_125,identity)),
inference(subst,[],[refute_0_839:[bind(X_49,$fot(X_125))]]) ).
cnf(refute_0_841,plain,
least_upper_bound(X_213,least_upper_bound(X_214,least_upper_bound(Y,X_214))) = least_upper_bound(X_214,least_upper_bound(X_213,least_upper_bound(X_214,least_upper_bound(Y,X_214)))),
inference(subst,[],[refute_0_253:[bind(Y,$fot(least_upper_bound(Y,X_214))),bind(X_39,$fot(X_213)),bind(X_40,$fot(X_214))]]) ).
cnf(refute_0_842,plain,
least_upper_bound(X_214,least_upper_bound(Y,X_214)) = least_upper_bound(X_214,Y),
inference(subst,[],[refute_0_175:[bind(X_15,$fot(X_214))]]) ).
cnf(refute_0_843,plain,
( least_upper_bound(X_213,least_upper_bound(X_214,least_upper_bound(Y,X_214))) != least_upper_bound(X_214,least_upper_bound(X_213,least_upper_bound(X_214,least_upper_bound(Y,X_214))))
| least_upper_bound(X_214,least_upper_bound(Y,X_214)) != least_upper_bound(X_214,Y)
| least_upper_bound(X_213,least_upper_bound(X_214,Y)) = least_upper_bound(X_214,least_upper_bound(X_213,least_upper_bound(X_214,least_upper_bound(Y,X_214)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_213,least_upper_bound(X_214,least_upper_bound(Y,X_214))),least_upper_bound(X_214,least_upper_bound(X_213,least_upper_bound(X_214,least_upper_bound(Y,X_214))))) ),[0,1],$fot(least_upper_bound(X_214,Y))]]) ).
cnf(refute_0_844,plain,
( least_upper_bound(X_213,least_upper_bound(X_214,least_upper_bound(Y,X_214))) != least_upper_bound(X_214,least_upper_bound(X_213,least_upper_bound(X_214,least_upper_bound(Y,X_214))))
| least_upper_bound(X_213,least_upper_bound(X_214,Y)) = least_upper_bound(X_214,least_upper_bound(X_213,least_upper_bound(X_214,least_upper_bound(Y,X_214)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_214,least_upper_bound(Y,X_214)),least_upper_bound(X_214,Y)) )],[refute_0_842,refute_0_843]) ).
cnf(refute_0_845,plain,
least_upper_bound(X_213,least_upper_bound(X_214,Y)) = least_upper_bound(X_214,least_upper_bound(X_213,least_upper_bound(X_214,least_upper_bound(Y,X_214)))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_213,least_upper_bound(X_214,least_upper_bound(Y,X_214))),least_upper_bound(X_214,least_upper_bound(X_213,least_upper_bound(X_214,least_upper_bound(Y,X_214))))) )],[refute_0_841,refute_0_844]) ).
cnf(refute_0_846,plain,
least_upper_bound(X_214,least_upper_bound(X_214,X_213)) = least_upper_bound(X_214,X_213),
inference(subst,[],[refute_0_516:[bind(X_18,$fot(X_213)),bind(X_19,$fot(X_214))]]) ).
cnf(refute_0_847,plain,
least_upper_bound(Y,least_upper_bound(X_214,least_upper_bound(X_214,X_213))) = least_upper_bound(Y,least_upper_bound(X_214,least_upper_bound(X_214,X_213))),
introduced(tautology,[refl,[$fot(least_upper_bound(Y,least_upper_bound(X_214,least_upper_bound(X_214,X_213))))]]) ).
cnf(refute_0_848,plain,
( least_upper_bound(Y,least_upper_bound(X_214,least_upper_bound(X_214,X_213))) != least_upper_bound(Y,least_upper_bound(X_214,least_upper_bound(X_214,X_213)))
| least_upper_bound(X_214,least_upper_bound(X_214,X_213)) != least_upper_bound(X_214,X_213)
| least_upper_bound(Y,least_upper_bound(X_214,least_upper_bound(X_214,X_213))) = least_upper_bound(Y,least_upper_bound(X_214,X_213)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_214,least_upper_bound(X_214,X_213))),least_upper_bound(Y,least_upper_bound(X_214,least_upper_bound(X_214,X_213)))) ),[1,1],$fot(least_upper_bound(X_214,X_213))]]) ).
cnf(refute_0_849,plain,
( least_upper_bound(X_214,least_upper_bound(X_214,X_213)) != least_upper_bound(X_214,X_213)
| least_upper_bound(Y,least_upper_bound(X_214,least_upper_bound(X_214,X_213))) = least_upper_bound(Y,least_upper_bound(X_214,X_213)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_214,least_upper_bound(X_214,X_213))),least_upper_bound(Y,least_upper_bound(X_214,least_upper_bound(X_214,X_213)))) )],[refute_0_847,refute_0_848]) ).
cnf(refute_0_850,plain,
least_upper_bound(Y,least_upper_bound(X_214,least_upper_bound(X_214,X_213))) = least_upper_bound(Y,least_upper_bound(X_214,X_213)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_214,least_upper_bound(X_214,X_213)),least_upper_bound(X_214,X_213)) )],[refute_0_846,refute_0_849]) ).
cnf(refute_0_851,plain,
least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_213,least_upper_bound(Y,X_212)))) = least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_213,least_upper_bound(Y,X_212))),
inference(subst,[],[associativity_of_lub:[bind(Z,$fot(least_upper_bound(X_213,least_upper_bound(Y,X_212))))]]) ).
cnf(refute_0_852,plain,
least_upper_bound(X_213,least_upper_bound(Y,X_212)) = least_upper_bound(Y,least_upper_bound(X_213,least_upper_bound(Y,X_212))),
inference(subst,[],[refute_0_253:[bind(Y,$fot(X_212)),bind(X_39,$fot(X_213)),bind(X_40,$fot(Y))]]) ).
cnf(refute_0_853,plain,
( least_upper_bound(X_213,least_upper_bound(Y,X_212)) != least_upper_bound(Y,least_upper_bound(X_213,least_upper_bound(Y,X_212)))
| least_upper_bound(Y,least_upper_bound(X_213,least_upper_bound(Y,X_212))) = least_upper_bound(X_213,least_upper_bound(Y,X_212)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(least_upper_bound(X_213,least_upper_bound(Y,X_212)))),bind(Y0,$fot(least_upper_bound(Y,least_upper_bound(X_213,least_upper_bound(Y,X_212)))))]]) ).
cnf(refute_0_854,plain,
least_upper_bound(Y,least_upper_bound(X_213,least_upper_bound(Y,X_212))) = least_upper_bound(X_213,least_upper_bound(Y,X_212)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_213,least_upper_bound(Y,X_212)),least_upper_bound(Y,least_upper_bound(X_213,least_upper_bound(Y,X_212)))) )],[refute_0_852,refute_0_853]) ).
cnf(refute_0_855,plain,
( least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_213,least_upper_bound(Y,X_212)))) != least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_213,least_upper_bound(Y,X_212)))
| least_upper_bound(Y,least_upper_bound(X_213,least_upper_bound(Y,X_212))) != least_upper_bound(X_213,least_upper_bound(Y,X_212))
| least_upper_bound(X,least_upper_bound(X_213,least_upper_bound(Y,X_212))) = least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_213,least_upper_bound(Y,X_212))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_213,least_upper_bound(Y,X_212)))),least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_213,least_upper_bound(Y,X_212)))) ),[0,1],$fot(least_upper_bound(X_213,least_upper_bound(Y,X_212)))]]) ).
cnf(refute_0_856,plain,
( least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_213,least_upper_bound(Y,X_212)))) != least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_213,least_upper_bound(Y,X_212)))
| least_upper_bound(X,least_upper_bound(X_213,least_upper_bound(Y,X_212))) = least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_213,least_upper_bound(Y,X_212))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_213,least_upper_bound(Y,X_212))),least_upper_bound(X_213,least_upper_bound(Y,X_212))) )],[refute_0_854,refute_0_855]) ).
cnf(refute_0_857,plain,
least_upper_bound(X,least_upper_bound(X_213,least_upper_bound(Y,X_212))) = least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_213,least_upper_bound(Y,X_212))),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_213,least_upper_bound(Y,X_212)))),least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_213,least_upper_bound(Y,X_212)))) )],[refute_0_851,refute_0_856]) ).
cnf(refute_0_858,plain,
least_upper_bound(least_upper_bound(X_166,X_168),least_upper_bound(X_39,X_40)) = least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_166,X_168))),
inference(subst,[],[refute_0_244:[bind(X,$fot(least_upper_bound(X_166,X_168)))]]) ).
cnf(refute_0_859,plain,
least_upper_bound(X_40,least_upper_bound(X_166,X_168)) = least_upper_bound(X_40,least_upper_bound(X_168,X_166)),
inference(subst,[],[refute_0_204:[bind(X_11,$fot(X_166)),bind(X_42,$fot(X_40)),bind(X_43,$fot(X_168))]]) ).
cnf(refute_0_860,plain,
( least_upper_bound(X_40,least_upper_bound(X_166,X_168)) != least_upper_bound(X_40,least_upper_bound(X_168,X_166))
| least_upper_bound(least_upper_bound(X_166,X_168),least_upper_bound(X_39,X_40)) != least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_166,X_168)))
| least_upper_bound(least_upper_bound(X_166,X_168),least_upper_bound(X_39,X_40)) = least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_168,X_166))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_166,X_168),least_upper_bound(X_39,X_40)),least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_166,X_168)))) ),[1,1],$fot(least_upper_bound(X_40,least_upper_bound(X_168,X_166)))]]) ).
cnf(refute_0_861,plain,
( least_upper_bound(least_upper_bound(X_166,X_168),least_upper_bound(X_39,X_40)) != least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_166,X_168)))
| least_upper_bound(least_upper_bound(X_166,X_168),least_upper_bound(X_39,X_40)) = least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_168,X_166))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_40,least_upper_bound(X_166,X_168)),least_upper_bound(X_40,least_upper_bound(X_168,X_166))) )],[refute_0_859,refute_0_860]) ).
cnf(refute_0_862,plain,
least_upper_bound(least_upper_bound(X_166,X_168),least_upper_bound(X_39,X_40)) = least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_168,X_166))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_166,X_168),least_upper_bound(X_39,X_40)),least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_166,X_168)))) )],[refute_0_858,refute_0_861]) ).
cnf(refute_0_863,plain,
least_upper_bound(least_upper_bound(X_166,X_168),least_upper_bound(X_39,X_40)) = least_upper_bound(X_166,least_upper_bound(X_168,least_upper_bound(X_39,X_40))),
inference(subst,[],[refute_0_171:[bind(X,$fot(X_166)),bind(Y,$fot(X_168)),bind(Z,$fot(least_upper_bound(X_39,X_40)))]]) ).
cnf(refute_0_864,plain,
( least_upper_bound(least_upper_bound(X_166,X_168),least_upper_bound(X_39,X_40)) != least_upper_bound(X_166,least_upper_bound(X_168,least_upper_bound(X_39,X_40)))
| least_upper_bound(least_upper_bound(X_166,X_168),least_upper_bound(X_39,X_40)) != least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_168,X_166)))
| least_upper_bound(X_166,least_upper_bound(X_168,least_upper_bound(X_39,X_40))) = least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_168,X_166))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_166,X_168),least_upper_bound(X_39,X_40)),least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_168,X_166)))) ),[0],$fot(least_upper_bound(X_166,least_upper_bound(X_168,least_upper_bound(X_39,X_40))))]]) ).
cnf(refute_0_865,plain,
( least_upper_bound(least_upper_bound(X_166,X_168),least_upper_bound(X_39,X_40)) != least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_168,X_166)))
| least_upper_bound(X_166,least_upper_bound(X_168,least_upper_bound(X_39,X_40))) = least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_168,X_166))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_166,X_168),least_upper_bound(X_39,X_40)),least_upper_bound(X_166,least_upper_bound(X_168,least_upper_bound(X_39,X_40)))) )],[refute_0_863,refute_0_864]) ).
cnf(refute_0_866,plain,
least_upper_bound(X_166,least_upper_bound(X_168,least_upper_bound(X_39,X_40))) = least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_168,X_166))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_166,X_168),least_upper_bound(X_39,X_40)),least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_168,X_166)))) )],[refute_0_862,refute_0_865]) ).
cnf(refute_0_867,plain,
least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_213,least_upper_bound(Y,X_212))) = least_upper_bound(Y,least_upper_bound(X_212,least_upper_bound(X_213,least_upper_bound(X,Y)))),
inference(subst,[],[refute_0_866:[bind(X_166,$fot(least_upper_bound(X,Y))),bind(X_168,$fot(X_213)),bind(X_39,$fot(Y)),bind(X_40,$fot(X_212))]]) ).
cnf(refute_0_868,plain,
( least_upper_bound(X,least_upper_bound(X_213,least_upper_bound(Y,X_212))) != least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_213,least_upper_bound(Y,X_212)))
| least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_213,least_upper_bound(Y,X_212))) != least_upper_bound(Y,least_upper_bound(X_212,least_upper_bound(X_213,least_upper_bound(X,Y))))
| least_upper_bound(X,least_upper_bound(X_213,least_upper_bound(Y,X_212))) = least_upper_bound(Y,least_upper_bound(X_212,least_upper_bound(X_213,least_upper_bound(X,Y)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,least_upper_bound(X_213,least_upper_bound(Y,X_212))),least_upper_bound(Y,least_upper_bound(X_212,least_upper_bound(X_213,least_upper_bound(X,Y))))) ),[0],$fot(least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_213,least_upper_bound(Y,X_212))))]]) ).
cnf(refute_0_869,plain,
( least_upper_bound(X,least_upper_bound(X_213,least_upper_bound(Y,X_212))) != least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_213,least_upper_bound(Y,X_212)))
| least_upper_bound(X,least_upper_bound(X_213,least_upper_bound(Y,X_212))) = least_upper_bound(Y,least_upper_bound(X_212,least_upper_bound(X_213,least_upper_bound(X,Y)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_213,least_upper_bound(Y,X_212))),least_upper_bound(Y,least_upper_bound(X_212,least_upper_bound(X_213,least_upper_bound(X,Y))))) )],[refute_0_867,refute_0_868]) ).
cnf(refute_0_870,plain,
least_upper_bound(X,least_upper_bound(X_213,least_upper_bound(Y,X_212))) = least_upper_bound(Y,least_upper_bound(X_212,least_upper_bound(X_213,least_upper_bound(X,Y)))),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_213,least_upper_bound(Y,X_212))),least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_213,least_upper_bound(Y,X_212)))) )],[refute_0_857,refute_0_869]) ).
cnf(refute_0_871,plain,
( least_upper_bound(X,least_upper_bound(X_213,least_upper_bound(Y,X_212))) != least_upper_bound(Y,least_upper_bound(X_212,least_upper_bound(X_213,least_upper_bound(X,Y))))
| least_upper_bound(Y,least_upper_bound(X_212,least_upper_bound(X_213,least_upper_bound(X,Y)))) = least_upper_bound(X,least_upper_bound(X_213,least_upper_bound(Y,X_212))) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(X_213,least_upper_bound(Y,X_212))))),bind(Y0,$fot(least_upper_bound(Y,least_upper_bound(X_212,least_upper_bound(X_213,least_upper_bound(X,Y))))))]]) ).
cnf(refute_0_872,plain,
least_upper_bound(Y,least_upper_bound(X_212,least_upper_bound(X_213,least_upper_bound(X,Y)))) = least_upper_bound(X,least_upper_bound(X_213,least_upper_bound(Y,X_212))),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_213,least_upper_bound(Y,X_212))),least_upper_bound(Y,least_upper_bound(X_212,least_upper_bound(X_213,least_upper_bound(X,Y))))) )],[refute_0_870,refute_0_871]) ).
cnf(refute_0_873,plain,
least_upper_bound(X_214,least_upper_bound(X_213,least_upper_bound(X_214,least_upper_bound(Y,X_214)))) = least_upper_bound(Y,least_upper_bound(X_214,least_upper_bound(X_214,X_213))),
inference(subst,[],[refute_0_872:[bind(X,$fot(Y)),bind(Y,$fot(X_214)),bind(X_212,$fot(X_213)),bind(X_213,$fot(X_214))]]) ).
cnf(refute_0_874,plain,
( least_upper_bound(Y,least_upper_bound(X_214,least_upper_bound(X_214,X_213))) != least_upper_bound(Y,least_upper_bound(X_214,X_213))
| least_upper_bound(X_214,least_upper_bound(X_213,least_upper_bound(X_214,least_upper_bound(Y,X_214)))) != least_upper_bound(Y,least_upper_bound(X_214,least_upper_bound(X_214,X_213)))
| least_upper_bound(X_214,least_upper_bound(X_213,least_upper_bound(X_214,least_upper_bound(Y,X_214)))) = least_upper_bound(Y,least_upper_bound(X_214,X_213)) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(least_upper_bound(X_214,least_upper_bound(X_213,least_upper_bound(X_214,least_upper_bound(Y,X_214)))))),bind(Y0,$fot(least_upper_bound(Y,least_upper_bound(X_214,least_upper_bound(X_214,X_213))))),bind(Z0,$fot(least_upper_bound(Y,least_upper_bound(X_214,X_213))))]]) ).
cnf(refute_0_875,plain,
( least_upper_bound(Y,least_upper_bound(X_214,least_upper_bound(X_214,X_213))) != least_upper_bound(Y,least_upper_bound(X_214,X_213))
| least_upper_bound(X_214,least_upper_bound(X_213,least_upper_bound(X_214,least_upper_bound(Y,X_214)))) = least_upper_bound(Y,least_upper_bound(X_214,X_213)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_214,least_upper_bound(X_213,least_upper_bound(X_214,least_upper_bound(Y,X_214)))),least_upper_bound(Y,least_upper_bound(X_214,least_upper_bound(X_214,X_213)))) )],[refute_0_873,refute_0_874]) ).
cnf(refute_0_876,plain,
least_upper_bound(X_214,least_upper_bound(X_213,least_upper_bound(X_214,least_upper_bound(Y,X_214)))) = least_upper_bound(Y,least_upper_bound(X_214,X_213)),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_214,least_upper_bound(X_214,X_213))),least_upper_bound(Y,least_upper_bound(X_214,X_213))) )],[refute_0_850,refute_0_875]) ).
cnf(refute_0_877,plain,
( least_upper_bound(X_213,least_upper_bound(X_214,Y)) != least_upper_bound(X_214,least_upper_bound(X_213,least_upper_bound(X_214,least_upper_bound(Y,X_214))))
| least_upper_bound(X_214,least_upper_bound(X_213,least_upper_bound(X_214,least_upper_bound(Y,X_214)))) != least_upper_bound(Y,least_upper_bound(X_214,X_213))
| least_upper_bound(X_213,least_upper_bound(X_214,Y)) = least_upper_bound(Y,least_upper_bound(X_214,X_213)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_213,least_upper_bound(X_214,Y)),least_upper_bound(Y,least_upper_bound(X_214,X_213))) ),[0],$fot(least_upper_bound(X_214,least_upper_bound(X_213,least_upper_bound(X_214,least_upper_bound(Y,X_214)))))]]) ).
cnf(refute_0_878,plain,
( least_upper_bound(X_213,least_upper_bound(X_214,Y)) != least_upper_bound(X_214,least_upper_bound(X_213,least_upper_bound(X_214,least_upper_bound(Y,X_214))))
| least_upper_bound(X_213,least_upper_bound(X_214,Y)) = least_upper_bound(Y,least_upper_bound(X_214,X_213)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_214,least_upper_bound(X_213,least_upper_bound(X_214,least_upper_bound(Y,X_214)))),least_upper_bound(Y,least_upper_bound(X_214,X_213))) )],[refute_0_876,refute_0_877]) ).
cnf(refute_0_879,plain,
least_upper_bound(X_213,least_upper_bound(X_214,Y)) = least_upper_bound(Y,least_upper_bound(X_214,X_213)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_213,least_upper_bound(X_214,Y)),least_upper_bound(X_214,least_upper_bound(X_213,least_upper_bound(X_214,least_upper_bound(Y,X_214))))) )],[refute_0_845,refute_0_878]) ).
cnf(refute_0_880,plain,
least_upper_bound(X_278,least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y)))) = least_upper_bound(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(identity,X_278)),
inference(subst,[],[refute_0_879:[bind(Y,$fot(inverse(greatest_lower_bound(identity,Y)))),bind(X_213,$fot(X_278)),bind(X_214,$fot(identity))]]) ).
cnf(refute_0_881,plain,
( least_upper_bound(X_278,least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y)))) != least_upper_bound(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(identity,X_278))
| least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y))) != inverse(greatest_lower_bound(identity,Y))
| least_upper_bound(X_278,inverse(greatest_lower_bound(identity,Y))) = least_upper_bound(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(identity,X_278)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_278,least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y)))),least_upper_bound(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(identity,X_278))) ),[0,1],$fot(inverse(greatest_lower_bound(identity,Y)))]]) ).
cnf(refute_0_882,plain,
( least_upper_bound(X_278,least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y)))) != least_upper_bound(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(identity,X_278))
| least_upper_bound(X_278,inverse(greatest_lower_bound(identity,Y))) = least_upper_bound(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(identity,X_278)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y))),inverse(greatest_lower_bound(identity,Y))) )],[refute_0_137,refute_0_881]) ).
cnf(refute_0_883,plain,
least_upper_bound(X_278,inverse(greatest_lower_bound(identity,Y))) = least_upper_bound(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(identity,X_278)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_278,least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y)))),least_upper_bound(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(identity,X_278))) )],[refute_0_880,refute_0_882]) ).
cnf(refute_0_884,plain,
least_upper_bound(X,least_upper_bound(identity,inverse(greatest_lower_bound(X_154,identity)))) = least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(X_154,identity)),X)),
inference(subst,[],[refute_0_244:[bind(X_39,$fot(identity)),bind(X_40,$fot(inverse(greatest_lower_bound(X_154,identity))))]]) ).
cnf(refute_0_885,plain,
inverse(greatest_lower_bound(X_154,identity)) = least_upper_bound(identity,inverse(greatest_lower_bound(X_154,identity))),
inference(subst,[],[refute_0_220:[bind(X_11,$fot(X_154))]]) ).
cnf(refute_0_886,plain,
( inverse(greatest_lower_bound(X_154,identity)) != least_upper_bound(identity,inverse(greatest_lower_bound(X_154,identity)))
| least_upper_bound(identity,inverse(greatest_lower_bound(X_154,identity))) = inverse(greatest_lower_bound(X_154,identity)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(inverse(greatest_lower_bound(X_154,identity)))),bind(Y0,$fot(least_upper_bound(identity,inverse(greatest_lower_bound(X_154,identity)))))]]) ).
cnf(refute_0_887,plain,
least_upper_bound(identity,inverse(greatest_lower_bound(X_154,identity))) = inverse(greatest_lower_bound(X_154,identity)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_154,identity)),least_upper_bound(identity,inverse(greatest_lower_bound(X_154,identity)))) )],[refute_0_885,refute_0_886]) ).
cnf(refute_0_888,plain,
( least_upper_bound(X,least_upper_bound(identity,inverse(greatest_lower_bound(X_154,identity)))) != least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(X_154,identity)),X))
| least_upper_bound(identity,inverse(greatest_lower_bound(X_154,identity))) != inverse(greatest_lower_bound(X_154,identity))
| least_upper_bound(X,inverse(greatest_lower_bound(X_154,identity))) = least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(X_154,identity)),X)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(identity,inverse(greatest_lower_bound(X_154,identity)))),least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(X_154,identity)),X))) ),[0,1],$fot(inverse(greatest_lower_bound(X_154,identity)))]]) ).
cnf(refute_0_889,plain,
( least_upper_bound(X,least_upper_bound(identity,inverse(greatest_lower_bound(X_154,identity)))) != least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(X_154,identity)),X))
| least_upper_bound(X,inverse(greatest_lower_bound(X_154,identity))) = least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(X_154,identity)),X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(greatest_lower_bound(X_154,identity))),inverse(greatest_lower_bound(X_154,identity))) )],[refute_0_887,refute_0_888]) ).
cnf(refute_0_890,plain,
least_upper_bound(X,inverse(greatest_lower_bound(X_154,identity))) = least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(X_154,identity)),X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(identity,inverse(greatest_lower_bound(X_154,identity)))),least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(X_154,identity)),X))) )],[refute_0_884,refute_0_889]) ).
cnf(refute_0_891,plain,
( least_upper_bound(X,inverse(greatest_lower_bound(X_154,identity))) != least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(X_154,identity)),X))
| least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(X_154,identity)),X)) = least_upper_bound(X,inverse(greatest_lower_bound(X_154,identity))) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(least_upper_bound(X,inverse(greatest_lower_bound(X_154,identity))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(X_154,identity)),X))))]]) ).
cnf(refute_0_892,plain,
least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(X_154,identity)),X)) = least_upper_bound(X,inverse(greatest_lower_bound(X_154,identity))),
inference(resolve,[$cnf( $equal(least_upper_bound(X,inverse(greatest_lower_bound(X_154,identity))),least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(X_154,identity)),X))) )],[refute_0_890,refute_0_891]) ).
cnf(refute_0_893,plain,
least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(Y,identity)),X_278)) = least_upper_bound(X_278,inverse(greatest_lower_bound(Y,identity))),
inference(subst,[],[refute_0_892:[bind(X,$fot(X_278)),bind(X_154,$fot(Y))]]) ).
cnf(refute_0_894,plain,
least_upper_bound(X,least_upper_bound(inverse(greatest_lower_bound(X_260,identity)),Z)) = least_upper_bound(least_upper_bound(X,inverse(greatest_lower_bound(X_260,identity))),Z),
inference(subst,[],[associativity_of_lub:[bind(Y,$fot(inverse(greatest_lower_bound(X_260,identity))))]]) ).
cnf(refute_0_895,plain,
least_upper_bound(X,inverse(greatest_lower_bound(X_260,identity))) = least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),X),
inference(subst,[],[refute_0_714:[bind(X_150,$fot(X_260)),bind(X_190,$fot(X))]]) ).
cnf(refute_0_896,plain,
( least_upper_bound(X,inverse(greatest_lower_bound(X_260,identity))) != least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),X)
| least_upper_bound(X,least_upper_bound(inverse(greatest_lower_bound(X_260,identity)),Z)) != least_upper_bound(least_upper_bound(X,inverse(greatest_lower_bound(X_260,identity))),Z)
| least_upper_bound(X,least_upper_bound(inverse(greatest_lower_bound(X_260,identity)),Z)) = least_upper_bound(least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),X),Z) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(inverse(greatest_lower_bound(X_260,identity)),Z)),least_upper_bound(least_upper_bound(X,inverse(greatest_lower_bound(X_260,identity))),Z)) ),[1,0],$fot(least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),X))]]) ).
cnf(refute_0_897,plain,
( least_upper_bound(X,least_upper_bound(inverse(greatest_lower_bound(X_260,identity)),Z)) != least_upper_bound(least_upper_bound(X,inverse(greatest_lower_bound(X_260,identity))),Z)
| least_upper_bound(X,least_upper_bound(inverse(greatest_lower_bound(X_260,identity)),Z)) = least_upper_bound(least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),X),Z) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X,inverse(greatest_lower_bound(X_260,identity))),least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),X)) )],[refute_0_895,refute_0_896]) ).
cnf(refute_0_898,plain,
least_upper_bound(X,least_upper_bound(inverse(greatest_lower_bound(X_260,identity)),Z)) = least_upper_bound(least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),X),Z),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(inverse(greatest_lower_bound(X_260,identity)),Z)),least_upper_bound(least_upper_bound(X,inverse(greatest_lower_bound(X_260,identity))),Z)) )],[refute_0_894,refute_0_897]) ).
cnf(refute_0_899,plain,
least_upper_bound(least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),X),Z) = least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),least_upper_bound(X,Z)),
inference(subst,[],[refute_0_171:[bind(X,$fot(inverse(greatest_lower_bound(identity,X_260)))),bind(Y,$fot(X))]]) ).
cnf(refute_0_900,plain,
( least_upper_bound(X,least_upper_bound(inverse(greatest_lower_bound(X_260,identity)),Z)) != least_upper_bound(least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),X),Z)
| least_upper_bound(least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),X),Z) != least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),least_upper_bound(X,Z))
| least_upper_bound(X,least_upper_bound(inverse(greatest_lower_bound(X_260,identity)),Z)) = least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),least_upper_bound(X,Z)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,least_upper_bound(inverse(greatest_lower_bound(X_260,identity)),Z)),least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),least_upper_bound(X,Z))) ),[0],$fot(least_upper_bound(least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),X),Z))]]) ).
cnf(refute_0_901,plain,
( least_upper_bound(X,least_upper_bound(inverse(greatest_lower_bound(X_260,identity)),Z)) != least_upper_bound(least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),X),Z)
| least_upper_bound(X,least_upper_bound(inverse(greatest_lower_bound(X_260,identity)),Z)) = least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),least_upper_bound(X,Z)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),X),Z),least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),least_upper_bound(X,Z))) )],[refute_0_899,refute_0_900]) ).
cnf(refute_0_902,plain,
least_upper_bound(X,least_upper_bound(inverse(greatest_lower_bound(X_260,identity)),Z)) = least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),least_upper_bound(X,Z)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(inverse(greatest_lower_bound(X_260,identity)),Z)),least_upper_bound(least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),X),Z)) )],[refute_0_898,refute_0_901]) ).
cnf(refute_0_903,plain,
( least_upper_bound(X,least_upper_bound(inverse(greatest_lower_bound(X_260,identity)),Z)) != least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),least_upper_bound(X,Z))
| least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),least_upper_bound(X,Z)) = least_upper_bound(X,least_upper_bound(inverse(greatest_lower_bound(X_260,identity)),Z)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(inverse(greatest_lower_bound(X_260,identity)),Z)))),bind(Y0,$fot(least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),least_upper_bound(X,Z))))]]) ).
cnf(refute_0_904,plain,
least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),least_upper_bound(X,Z)) = least_upper_bound(X,least_upper_bound(inverse(greatest_lower_bound(X_260,identity)),Z)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(inverse(greatest_lower_bound(X_260,identity)),Z)),least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),least_upper_bound(X,Z))) )],[refute_0_902,refute_0_903]) ).
cnf(refute_0_905,plain,
least_upper_bound(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(identity,X_278)) = least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(Y,identity)),X_278)),
inference(subst,[],[refute_0_904:[bind(X,$fot(identity)),bind(Z,$fot(X_278)),bind(X_260,$fot(Y))]]) ).
cnf(refute_0_906,plain,
( least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(Y,identity)),X_278)) != least_upper_bound(X_278,inverse(greatest_lower_bound(Y,identity)))
| least_upper_bound(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(identity,X_278)) != least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(Y,identity)),X_278))
| least_upper_bound(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(identity,X_278)) = least_upper_bound(X_278,inverse(greatest_lower_bound(Y,identity))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(least_upper_bound(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(identity,X_278)))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(Y,identity)),X_278)))),bind(Z0,$fot(least_upper_bound(X_278,inverse(greatest_lower_bound(Y,identity)))))]]) ).
cnf(refute_0_907,plain,
( least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(Y,identity)),X_278)) != least_upper_bound(X_278,inverse(greatest_lower_bound(Y,identity)))
| least_upper_bound(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(identity,X_278)) = least_upper_bound(X_278,inverse(greatest_lower_bound(Y,identity))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(identity,X_278)),least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(Y,identity)),X_278))) )],[refute_0_905,refute_0_906]) ).
cnf(refute_0_908,plain,
least_upper_bound(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(identity,X_278)) = least_upper_bound(X_278,inverse(greatest_lower_bound(Y,identity))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(Y,identity)),X_278)),least_upper_bound(X_278,inverse(greatest_lower_bound(Y,identity)))) )],[refute_0_893,refute_0_907]) ).
cnf(refute_0_909,plain,
( least_upper_bound(X_278,inverse(greatest_lower_bound(identity,Y))) != least_upper_bound(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(identity,X_278))
| least_upper_bound(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(identity,X_278)) != least_upper_bound(X_278,inverse(greatest_lower_bound(Y,identity)))
| least_upper_bound(X_278,inverse(greatest_lower_bound(identity,Y))) = least_upper_bound(X_278,inverse(greatest_lower_bound(Y,identity))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_278,inverse(greatest_lower_bound(identity,Y))),least_upper_bound(X_278,inverse(greatest_lower_bound(Y,identity)))) ),[0],$fot(least_upper_bound(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(identity,X_278)))]]) ).
cnf(refute_0_910,plain,
( least_upper_bound(X_278,inverse(greatest_lower_bound(identity,Y))) != least_upper_bound(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(identity,X_278))
| least_upper_bound(X_278,inverse(greatest_lower_bound(identity,Y))) = least_upper_bound(X_278,inverse(greatest_lower_bound(Y,identity))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(identity,X_278)),least_upper_bound(X_278,inverse(greatest_lower_bound(Y,identity)))) )],[refute_0_908,refute_0_909]) ).
cnf(refute_0_911,plain,
least_upper_bound(X_278,inverse(greatest_lower_bound(identity,Y))) = least_upper_bound(X_278,inverse(greatest_lower_bound(Y,identity))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_278,inverse(greatest_lower_bound(identity,Y))),least_upper_bound(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(identity,X_278))) )],[refute_0_883,refute_0_910]) ).
cnf(refute_0_912,plain,
( least_upper_bound(X_278,inverse(greatest_lower_bound(identity,Y))) != least_upper_bound(X_278,inverse(greatest_lower_bound(Y,identity)))
| least_upper_bound(X_278,inverse(greatest_lower_bound(Y,identity))) = least_upper_bound(X_278,inverse(greatest_lower_bound(identity,Y))) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(least_upper_bound(X_278,inverse(greatest_lower_bound(identity,Y))))),bind(Y0,$fot(least_upper_bound(X_278,inverse(greatest_lower_bound(Y,identity)))))]]) ).
cnf(refute_0_913,plain,
least_upper_bound(X_278,inverse(greatest_lower_bound(Y,identity))) = least_upper_bound(X_278,inverse(greatest_lower_bound(identity,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_278,inverse(greatest_lower_bound(identity,Y))),least_upper_bound(X_278,inverse(greatest_lower_bound(Y,identity)))) )],[refute_0_911,refute_0_912]) ).
cnf(refute_0_914,plain,
least_upper_bound(inverse(greatest_lower_bound(identity,X_125)),inverse(greatest_lower_bound(inverse(X_125),identity))) = least_upper_bound(inverse(greatest_lower_bound(identity,X_125)),inverse(greatest_lower_bound(identity,inverse(X_125)))),
inference(subst,[],[refute_0_913:[bind(Y,$fot(inverse(X_125))),bind(X_278,$fot(inverse(greatest_lower_bound(identity,X_125))))]]) ).
cnf(refute_0_915,plain,
( least_upper_bound(inverse(greatest_lower_bound(identity,X_125)),inverse(greatest_lower_bound(identity,inverse(X_125)))) != multiply(inverse(greatest_lower_bound(identity,X_125)),least_upper_bound(X_125,identity))
| least_upper_bound(inverse(greatest_lower_bound(identity,X_125)),inverse(greatest_lower_bound(inverse(X_125),identity))) != least_upper_bound(inverse(greatest_lower_bound(identity,X_125)),inverse(greatest_lower_bound(identity,inverse(X_125))))
| least_upper_bound(inverse(greatest_lower_bound(identity,X_125)),inverse(greatest_lower_bound(inverse(X_125),identity))) = multiply(inverse(greatest_lower_bound(identity,X_125)),least_upper_bound(X_125,identity)) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(least_upper_bound(inverse(greatest_lower_bound(identity,X_125)),inverse(greatest_lower_bound(inverse(X_125),identity))))),bind(Y0,$fot(least_upper_bound(inverse(greatest_lower_bound(identity,X_125)),inverse(greatest_lower_bound(identity,inverse(X_125)))))),bind(Z0,$fot(multiply(inverse(greatest_lower_bound(identity,X_125)),least_upper_bound(X_125,identity))))]]) ).
cnf(refute_0_916,plain,
( least_upper_bound(inverse(greatest_lower_bound(identity,X_125)),inverse(greatest_lower_bound(identity,inverse(X_125)))) != multiply(inverse(greatest_lower_bound(identity,X_125)),least_upper_bound(X_125,identity))
| least_upper_bound(inverse(greatest_lower_bound(identity,X_125)),inverse(greatest_lower_bound(inverse(X_125),identity))) = multiply(inverse(greatest_lower_bound(identity,X_125)),least_upper_bound(X_125,identity)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(identity,X_125)),inverse(greatest_lower_bound(inverse(X_125),identity))),least_upper_bound(inverse(greatest_lower_bound(identity,X_125)),inverse(greatest_lower_bound(identity,inverse(X_125))))) )],[refute_0_914,refute_0_915]) ).
cnf(refute_0_917,plain,
least_upper_bound(inverse(greatest_lower_bound(identity,X_125)),inverse(greatest_lower_bound(inverse(X_125),identity))) = multiply(inverse(greatest_lower_bound(identity,X_125)),least_upper_bound(X_125,identity)),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(identity,X_125)),inverse(greatest_lower_bound(identity,inverse(X_125)))),multiply(inverse(greatest_lower_bound(identity,X_125)),least_upper_bound(X_125,identity))) )],[refute_0_840,refute_0_916]) ).
cnf(refute_0_918,plain,
multiply(inverse(least_upper_bound(identity,X_125)),least_upper_bound(inverse(greatest_lower_bound(identity,X_125)),inverse(greatest_lower_bound(inverse(X_125),identity)))) = multiply(inverse(least_upper_bound(identity,X_125)),least_upper_bound(inverse(greatest_lower_bound(identity,X_125)),inverse(greatest_lower_bound(inverse(X_125),identity)))),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(identity,X_125)),least_upper_bound(inverse(greatest_lower_bound(identity,X_125)),inverse(greatest_lower_bound(inverse(X_125),identity)))))]]) ).
cnf(refute_0_919,plain,
( multiply(inverse(least_upper_bound(identity,X_125)),least_upper_bound(inverse(greatest_lower_bound(identity,X_125)),inverse(greatest_lower_bound(inverse(X_125),identity)))) != multiply(inverse(least_upper_bound(identity,X_125)),least_upper_bound(inverse(greatest_lower_bound(identity,X_125)),inverse(greatest_lower_bound(inverse(X_125),identity))))
| least_upper_bound(inverse(greatest_lower_bound(identity,X_125)),inverse(greatest_lower_bound(inverse(X_125),identity))) != multiply(inverse(greatest_lower_bound(identity,X_125)),least_upper_bound(X_125,identity))
| multiply(inverse(least_upper_bound(identity,X_125)),least_upper_bound(inverse(greatest_lower_bound(identity,X_125)),inverse(greatest_lower_bound(inverse(X_125),identity)))) = multiply(inverse(least_upper_bound(identity,X_125)),multiply(inverse(greatest_lower_bound(identity,X_125)),least_upper_bound(X_125,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_125)),least_upper_bound(inverse(greatest_lower_bound(identity,X_125)),inverse(greatest_lower_bound(inverse(X_125),identity)))),multiply(inverse(least_upper_bound(identity,X_125)),least_upper_bound(inverse(greatest_lower_bound(identity,X_125)),inverse(greatest_lower_bound(inverse(X_125),identity))))) ),[1,1],$fot(multiply(inverse(greatest_lower_bound(identity,X_125)),least_upper_bound(X_125,identity)))]]) ).
cnf(refute_0_920,plain,
( least_upper_bound(inverse(greatest_lower_bound(identity,X_125)),inverse(greatest_lower_bound(inverse(X_125),identity))) != multiply(inverse(greatest_lower_bound(identity,X_125)),least_upper_bound(X_125,identity))
| multiply(inverse(least_upper_bound(identity,X_125)),least_upper_bound(inverse(greatest_lower_bound(identity,X_125)),inverse(greatest_lower_bound(inverse(X_125),identity)))) = multiply(inverse(least_upper_bound(identity,X_125)),multiply(inverse(greatest_lower_bound(identity,X_125)),least_upper_bound(X_125,identity))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_125)),least_upper_bound(inverse(greatest_lower_bound(identity,X_125)),inverse(greatest_lower_bound(inverse(X_125),identity)))),multiply(inverse(least_upper_bound(identity,X_125)),least_upper_bound(inverse(greatest_lower_bound(identity,X_125)),inverse(greatest_lower_bound(inverse(X_125),identity))))) )],[refute_0_918,refute_0_919]) ).
cnf(refute_0_921,plain,
multiply(inverse(least_upper_bound(identity,X_125)),least_upper_bound(inverse(greatest_lower_bound(identity,X_125)),inverse(greatest_lower_bound(inverse(X_125),identity)))) = multiply(inverse(least_upper_bound(identity,X_125)),multiply(inverse(greatest_lower_bound(identity,X_125)),least_upper_bound(X_125,identity))),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(identity,X_125)),inverse(greatest_lower_bound(inverse(X_125),identity))),multiply(inverse(greatest_lower_bound(identity,X_125)),least_upper_bound(X_125,identity))) )],[refute_0_917,refute_0_920]) ).
cnf(refute_0_922,plain,
( multiply(inverse(least_upper_bound(identity,X_125)),multiply(inverse(greatest_lower_bound(identity,X_125)),least_upper_bound(X_125,identity))) != multiply(inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125))),least_upper_bound(X_125,identity))
| multiply(inverse(least_upper_bound(identity,X_125)),least_upper_bound(inverse(greatest_lower_bound(identity,X_125)),inverse(greatest_lower_bound(inverse(X_125),identity)))) != multiply(inverse(least_upper_bound(identity,X_125)),multiply(inverse(greatest_lower_bound(identity,X_125)),least_upper_bound(X_125,identity)))
| multiply(inverse(least_upper_bound(identity,X_125)),least_upper_bound(inverse(greatest_lower_bound(identity,X_125)),inverse(greatest_lower_bound(inverse(X_125),identity)))) = multiply(inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125))),least_upper_bound(X_125,identity)) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(inverse(least_upper_bound(identity,X_125)),least_upper_bound(inverse(greatest_lower_bound(identity,X_125)),inverse(greatest_lower_bound(inverse(X_125),identity)))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(identity,X_125)),multiply(inverse(greatest_lower_bound(identity,X_125)),least_upper_bound(X_125,identity))))),bind(Z0,$fot(multiply(inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125))),least_upper_bound(X_125,identity))))]]) ).
cnf(refute_0_923,plain,
( multiply(inverse(least_upper_bound(identity,X_125)),multiply(inverse(greatest_lower_bound(identity,X_125)),least_upper_bound(X_125,identity))) != multiply(inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125))),least_upper_bound(X_125,identity))
| multiply(inverse(least_upper_bound(identity,X_125)),least_upper_bound(inverse(greatest_lower_bound(identity,X_125)),inverse(greatest_lower_bound(inverse(X_125),identity)))) = multiply(inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125))),least_upper_bound(X_125,identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_125)),least_upper_bound(inverse(greatest_lower_bound(identity,X_125)),inverse(greatest_lower_bound(inverse(X_125),identity)))),multiply(inverse(least_upper_bound(identity,X_125)),multiply(inverse(greatest_lower_bound(identity,X_125)),least_upper_bound(X_125,identity)))) )],[refute_0_921,refute_0_922]) ).
cnf(refute_0_924,plain,
multiply(inverse(least_upper_bound(identity,X_125)),least_upper_bound(inverse(greatest_lower_bound(identity,X_125)),inverse(greatest_lower_bound(inverse(X_125),identity)))) = multiply(inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125))),least_upper_bound(X_125,identity)),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_125)),multiply(inverse(greatest_lower_bound(identity,X_125)),least_upper_bound(X_125,identity))),multiply(inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125))),least_upper_bound(X_125,identity))) )],[refute_0_825,refute_0_923]) ).
cnf(refute_0_925,plain,
multiply(X,least_upper_bound(Y,inverse(greatest_lower_bound(X_260,identity)))) = least_upper_bound(multiply(X,Y),multiply(X,inverse(greatest_lower_bound(X_260,identity)))),
inference(subst,[],[monotony_lub1:[bind(Z,$fot(inverse(greatest_lower_bound(X_260,identity))))]]) ).
cnf(refute_0_926,plain,
( multiply(X,least_upper_bound(Y,inverse(greatest_lower_bound(X_260,identity)))) != least_upper_bound(multiply(X,Y),multiply(X,inverse(greatest_lower_bound(X_260,identity))))
| least_upper_bound(Y,inverse(greatest_lower_bound(X_260,identity))) != least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),Y)
| multiply(X,least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),Y)) = least_upper_bound(multiply(X,Y),multiply(X,inverse(greatest_lower_bound(X_260,identity)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X,least_upper_bound(Y,inverse(greatest_lower_bound(X_260,identity)))),least_upper_bound(multiply(X,Y),multiply(X,inverse(greatest_lower_bound(X_260,identity))))) ),[0,1],$fot(least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),Y))]]) ).
cnf(refute_0_927,plain,
( multiply(X,least_upper_bound(Y,inverse(greatest_lower_bound(X_260,identity)))) != least_upper_bound(multiply(X,Y),multiply(X,inverse(greatest_lower_bound(X_260,identity))))
| multiply(X,least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),Y)) = least_upper_bound(multiply(X,Y),multiply(X,inverse(greatest_lower_bound(X_260,identity)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,inverse(greatest_lower_bound(X_260,identity))),least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),Y)) )],[refute_0_739,refute_0_926]) ).
cnf(refute_0_928,plain,
multiply(X,least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),Y)) = least_upper_bound(multiply(X,Y),multiply(X,inverse(greatest_lower_bound(X_260,identity)))),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(Y,inverse(greatest_lower_bound(X_260,identity)))),least_upper_bound(multiply(X,Y),multiply(X,inverse(greatest_lower_bound(X_260,identity))))) )],[refute_0_925,refute_0_927]) ).
cnf(refute_0_929,plain,
least_upper_bound(multiply(X,Y),multiply(X,inverse(greatest_lower_bound(X_260,identity)))) = multiply(X,least_upper_bound(Y,inverse(greatest_lower_bound(X_260,identity)))),
inference(subst,[],[refute_0_385:[bind(Z,$fot(inverse(greatest_lower_bound(X_260,identity))))]]) ).
cnf(refute_0_930,plain,
( multiply(X,least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),Y)) != least_upper_bound(multiply(X,Y),multiply(X,inverse(greatest_lower_bound(X_260,identity))))
| least_upper_bound(multiply(X,Y),multiply(X,inverse(greatest_lower_bound(X_260,identity)))) != multiply(X,least_upper_bound(Y,inverse(greatest_lower_bound(X_260,identity))))
| multiply(X,least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),Y)) = multiply(X,least_upper_bound(Y,inverse(greatest_lower_bound(X_260,identity)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X,least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),Y)),multiply(X,least_upper_bound(Y,inverse(greatest_lower_bound(X_260,identity))))) ),[0],$fot(least_upper_bound(multiply(X,Y),multiply(X,inverse(greatest_lower_bound(X_260,identity)))))]]) ).
cnf(refute_0_931,plain,
( multiply(X,least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),Y)) != least_upper_bound(multiply(X,Y),multiply(X,inverse(greatest_lower_bound(X_260,identity))))
| multiply(X,least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),Y)) = multiply(X,least_upper_bound(Y,inverse(greatest_lower_bound(X_260,identity)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,Y),multiply(X,inverse(greatest_lower_bound(X_260,identity)))),multiply(X,least_upper_bound(Y,inverse(greatest_lower_bound(X_260,identity))))) )],[refute_0_929,refute_0_930]) ).
cnf(refute_0_932,plain,
multiply(X,least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),Y)) = multiply(X,least_upper_bound(Y,inverse(greatest_lower_bound(X_260,identity)))),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(inverse(greatest_lower_bound(identity,X_260)),Y)),least_upper_bound(multiply(X,Y),multiply(X,inverse(greatest_lower_bound(X_260,identity))))) )],[refute_0_928,refute_0_931]) ).
cnf(refute_0_933,plain,
multiply(inverse(least_upper_bound(identity,X_125)),least_upper_bound(inverse(greatest_lower_bound(identity,inverse(X_125))),inverse(greatest_lower_bound(identity,X_125)))) = multiply(inverse(least_upper_bound(identity,X_125)),least_upper_bound(inverse(greatest_lower_bound(identity,X_125)),inverse(greatest_lower_bound(inverse(X_125),identity)))),
inference(subst,[],[refute_0_932:[bind(X,$fot(inverse(least_upper_bound(identity,X_125)))),bind(Y,$fot(inverse(greatest_lower_bound(identity,X_125)))),bind(X_260,$fot(inverse(X_125)))]]) ).
cnf(refute_0_934,plain,
( multiply(inverse(least_upper_bound(identity,X_125)),least_upper_bound(inverse(greatest_lower_bound(identity,X_125)),inverse(greatest_lower_bound(inverse(X_125),identity)))) != multiply(inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125))),least_upper_bound(X_125,identity))
| multiply(inverse(least_upper_bound(identity,X_125)),least_upper_bound(inverse(greatest_lower_bound(identity,inverse(X_125))),inverse(greatest_lower_bound(identity,X_125)))) != multiply(inverse(least_upper_bound(identity,X_125)),least_upper_bound(inverse(greatest_lower_bound(identity,X_125)),inverse(greatest_lower_bound(inverse(X_125),identity))))
| multiply(inverse(least_upper_bound(identity,X_125)),least_upper_bound(inverse(greatest_lower_bound(identity,inverse(X_125))),inverse(greatest_lower_bound(identity,X_125)))) = multiply(inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125))),least_upper_bound(X_125,identity)) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(inverse(least_upper_bound(identity,X_125)),least_upper_bound(inverse(greatest_lower_bound(identity,inverse(X_125))),inverse(greatest_lower_bound(identity,X_125)))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(identity,X_125)),least_upper_bound(inverse(greatest_lower_bound(identity,X_125)),inverse(greatest_lower_bound(inverse(X_125),identity)))))),bind(Z0,$fot(multiply(inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125))),least_upper_bound(X_125,identity))))]]) ).
cnf(refute_0_935,plain,
( multiply(inverse(least_upper_bound(identity,X_125)),least_upper_bound(inverse(greatest_lower_bound(identity,X_125)),inverse(greatest_lower_bound(inverse(X_125),identity)))) != multiply(inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125))),least_upper_bound(X_125,identity))
| multiply(inverse(least_upper_bound(identity,X_125)),least_upper_bound(inverse(greatest_lower_bound(identity,inverse(X_125))),inverse(greatest_lower_bound(identity,X_125)))) = multiply(inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125))),least_upper_bound(X_125,identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_125)),least_upper_bound(inverse(greatest_lower_bound(identity,inverse(X_125))),inverse(greatest_lower_bound(identity,X_125)))),multiply(inverse(least_upper_bound(identity,X_125)),least_upper_bound(inverse(greatest_lower_bound(identity,X_125)),inverse(greatest_lower_bound(inverse(X_125),identity))))) )],[refute_0_933,refute_0_934]) ).
cnf(refute_0_936,plain,
multiply(inverse(least_upper_bound(identity,X_125)),least_upper_bound(inverse(greatest_lower_bound(identity,inverse(X_125))),inverse(greatest_lower_bound(identity,X_125)))) = multiply(inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125))),least_upper_bound(X_125,identity)),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_125)),least_upper_bound(inverse(greatest_lower_bound(identity,X_125)),inverse(greatest_lower_bound(inverse(X_125),identity)))),multiply(inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125))),least_upper_bound(X_125,identity))) )],[refute_0_924,refute_0_935]) ).
cnf(refute_0_937,plain,
( multiply(inverse(least_upper_bound(identity,X_125)),least_upper_bound(inverse(greatest_lower_bound(identity,inverse(X_125))),inverse(greatest_lower_bound(identity,X_125)))) != multiply(inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125))),least_upper_bound(X_125,identity))
| inverse(greatest_lower_bound(identity,X_125)) != multiply(inverse(least_upper_bound(identity,X_125)),least_upper_bound(inverse(greatest_lower_bound(identity,inverse(X_125))),inverse(greatest_lower_bound(identity,X_125))))
| inverse(greatest_lower_bound(identity,X_125)) = multiply(inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125))),least_upper_bound(X_125,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,X_125)),multiply(inverse(least_upper_bound(identity,X_125)),least_upper_bound(inverse(greatest_lower_bound(identity,inverse(X_125))),inverse(greatest_lower_bound(identity,X_125))))) ),[1],$fot(multiply(inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125))),least_upper_bound(X_125,identity)))]]) ).
cnf(refute_0_938,plain,
( inverse(greatest_lower_bound(identity,X_125)) != multiply(inverse(least_upper_bound(identity,X_125)),least_upper_bound(inverse(greatest_lower_bound(identity,inverse(X_125))),inverse(greatest_lower_bound(identity,X_125))))
| inverse(greatest_lower_bound(identity,X_125)) = multiply(inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125))),least_upper_bound(X_125,identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_125)),least_upper_bound(inverse(greatest_lower_bound(identity,inverse(X_125))),inverse(greatest_lower_bound(identity,X_125)))),multiply(inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125))),least_upper_bound(X_125,identity))) )],[refute_0_936,refute_0_937]) ).
cnf(refute_0_939,plain,
inverse(greatest_lower_bound(identity,X_125)) = multiply(inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125))),least_upper_bound(X_125,identity)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,X_125)),multiply(inverse(least_upper_bound(identity,X_125)),least_upper_bound(inverse(greatest_lower_bound(identity,inverse(X_125))),inverse(greatest_lower_bound(identity,X_125))))) )],[refute_0_805,refute_0_938]) ).
cnf(refute_0_940,plain,
multiply(inverse(X_125),least_upper_bound(X_125,identity)) = least_upper_bound(identity,inverse(X_125)),
inference(subst,[],[refute_0_267:[bind(X_57,$fot(X_125))]]) ).
cnf(refute_0_941,plain,
X_31 = multiply(inverse(least_upper_bound(inverse(X_31),X_73)),multiply(least_upper_bound(inverse(X_31),X_73),X_31)),
inference(subst,[],[refute_0_9:[bind(X_30,$fot(least_upper_bound(inverse(X_31),X_73)))]]) ).
cnf(refute_0_942,plain,
multiply(least_upper_bound(inverse(X_67),X_69),X_67) = least_upper_bound(multiply(inverse(X_67),X_67),multiply(X_69,X_67)),
inference(subst,[],[monotony_lub2:[bind(X,$fot(X_67)),bind(Y,$fot(inverse(X_67))),bind(Z,$fot(X_69))]]) ).
cnf(refute_0_943,plain,
( multiply(inverse(X_67),X_67) != identity
| multiply(least_upper_bound(inverse(X_67),X_69),X_67) != least_upper_bound(multiply(inverse(X_67),X_67),multiply(X_69,X_67))
| multiply(least_upper_bound(inverse(X_67),X_69),X_67) = least_upper_bound(identity,multiply(X_69,X_67)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(X_67),X_69),X_67),least_upper_bound(multiply(inverse(X_67),X_67),multiply(X_69,X_67))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_944,plain,
( multiply(least_upper_bound(inverse(X_67),X_69),X_67) != least_upper_bound(multiply(inverse(X_67),X_67),multiply(X_69,X_67))
| multiply(least_upper_bound(inverse(X_67),X_69),X_67) = least_upper_bound(identity,multiply(X_69,X_67)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_67),X_67),identity) )],[refute_0_788,refute_0_943]) ).
cnf(refute_0_945,plain,
multiply(least_upper_bound(inverse(X_67),X_69),X_67) = least_upper_bound(identity,multiply(X_69,X_67)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_67),X_69),X_67),least_upper_bound(multiply(inverse(X_67),X_67),multiply(X_69,X_67))) )],[refute_0_942,refute_0_944]) ).
cnf(refute_0_946,plain,
multiply(least_upper_bound(inverse(X_31),X_73),X_31) = least_upper_bound(identity,multiply(X_73,X_31)),
inference(subst,[],[refute_0_945:[bind(X_67,$fot(X_31)),bind(X_69,$fot(X_73))]]) ).
cnf(refute_0_947,plain,
( X_31 != multiply(inverse(least_upper_bound(inverse(X_31),X_73)),multiply(least_upper_bound(inverse(X_31),X_73),X_31))
| multiply(least_upper_bound(inverse(X_31),X_73),X_31) != least_upper_bound(identity,multiply(X_73,X_31))
| X_31 = multiply(inverse(least_upper_bound(inverse(X_31),X_73)),least_upper_bound(identity,multiply(X_73,X_31))) ),
introduced(tautology,[equality,[$cnf( $equal(X_31,multiply(inverse(least_upper_bound(inverse(X_31),X_73)),multiply(least_upper_bound(inverse(X_31),X_73),X_31))) ),[1,1],$fot(least_upper_bound(identity,multiply(X_73,X_31)))]]) ).
cnf(refute_0_948,plain,
( X_31 != multiply(inverse(least_upper_bound(inverse(X_31),X_73)),multiply(least_upper_bound(inverse(X_31),X_73),X_31))
| X_31 = multiply(inverse(least_upper_bound(inverse(X_31),X_73)),least_upper_bound(identity,multiply(X_73,X_31))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_31),X_73),X_31),least_upper_bound(identity,multiply(X_73,X_31))) )],[refute_0_946,refute_0_947]) ).
cnf(refute_0_949,plain,
X_31 = multiply(inverse(least_upper_bound(inverse(X_31),X_73)),least_upper_bound(identity,multiply(X_73,X_31))),
inference(resolve,[$cnf( $equal(X_31,multiply(inverse(least_upper_bound(inverse(X_31),X_73)),multiply(least_upper_bound(inverse(X_31),X_73),X_31))) )],[refute_0_941,refute_0_948]) ).
cnf(refute_0_950,plain,
X_31 = multiply(inverse(least_upper_bound(inverse(X_31),inverse(greatest_lower_bound(identity,X_31)))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_31)),X_31))),
inference(subst,[],[refute_0_949:[bind(X_73,$fot(inverse(greatest_lower_bound(identity,X_31))))]]) ).
cnf(refute_0_951,plain,
inverse(greatest_lower_bound(identity,inverse(X_31))) = multiply(inverse(greatest_lower_bound(identity,X_31)),X_31),
inference(subst,[],[refute_0_831:[bind(X_148,$fot(X_31))]]) ).
cnf(refute_0_952,plain,
( inverse(greatest_lower_bound(identity,inverse(X_31))) != multiply(inverse(greatest_lower_bound(identity,X_31)),X_31)
| multiply(inverse(greatest_lower_bound(identity,X_31)),X_31) = inverse(greatest_lower_bound(identity,inverse(X_31))) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(inverse(greatest_lower_bound(identity,inverse(X_31))))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(identity,X_31)),X_31)))]]) ).
cnf(refute_0_953,plain,
multiply(inverse(greatest_lower_bound(identity,X_31)),X_31) = inverse(greatest_lower_bound(identity,inverse(X_31))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_31))),multiply(inverse(greatest_lower_bound(identity,X_31)),X_31)) )],[refute_0_951,refute_0_952]) ).
cnf(refute_0_954,plain,
( X_31 != multiply(inverse(least_upper_bound(inverse(X_31),inverse(greatest_lower_bound(identity,X_31)))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_31)),X_31)))
| multiply(inverse(greatest_lower_bound(identity,X_31)),X_31) != inverse(greatest_lower_bound(identity,inverse(X_31)))
| X_31 = multiply(inverse(least_upper_bound(inverse(X_31),inverse(greatest_lower_bound(identity,X_31)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_31))))) ),
introduced(tautology,[equality,[$cnf( $equal(X_31,multiply(inverse(least_upper_bound(inverse(X_31),inverse(greatest_lower_bound(identity,X_31)))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_31)),X_31)))) ),[1,1,1],$fot(inverse(greatest_lower_bound(identity,inverse(X_31))))]]) ).
cnf(refute_0_955,plain,
( X_31 != multiply(inverse(least_upper_bound(inverse(X_31),inverse(greatest_lower_bound(identity,X_31)))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_31)),X_31)))
| X_31 = multiply(inverse(least_upper_bound(inverse(X_31),inverse(greatest_lower_bound(identity,X_31)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_31))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_31)),X_31),inverse(greatest_lower_bound(identity,inverse(X_31)))) )],[refute_0_953,refute_0_954]) ).
cnf(refute_0_956,plain,
X_31 = multiply(inverse(least_upper_bound(inverse(X_31),inverse(greatest_lower_bound(identity,X_31)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_31))))),
inference(resolve,[$cnf( $equal(X_31,multiply(inverse(least_upper_bound(inverse(X_31),inverse(greatest_lower_bound(identity,X_31)))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_31)),X_31)))) )],[refute_0_950,refute_0_955]) ).
cnf(refute_0_957,plain,
least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_31)))) = inverse(greatest_lower_bound(identity,inverse(X_31))),
inference(subst,[],[refute_0_137:[bind(Y,$fot(inverse(X_31)))]]) ).
cnf(refute_0_958,plain,
multiply(greatest_lower_bound(identity,X_31),least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_31))))) = multiply(greatest_lower_bound(identity,X_31),least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_31))))),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(identity,X_31),least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_31))))))]]) ).
cnf(refute_0_959,plain,
( multiply(greatest_lower_bound(identity,X_31),least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_31))))) != multiply(greatest_lower_bound(identity,X_31),least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_31)))))
| least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_31)))) != inverse(greatest_lower_bound(identity,inverse(X_31)))
| multiply(greatest_lower_bound(identity,X_31),least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_31))))) = multiply(greatest_lower_bound(identity,X_31),inverse(greatest_lower_bound(identity,inverse(X_31)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_31),least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_31))))),multiply(greatest_lower_bound(identity,X_31),least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_31)))))) ),[1,1],$fot(inverse(greatest_lower_bound(identity,inverse(X_31))))]]) ).
cnf(refute_0_960,plain,
( least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_31)))) != inverse(greatest_lower_bound(identity,inverse(X_31)))
| multiply(greatest_lower_bound(identity,X_31),least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_31))))) = multiply(greatest_lower_bound(identity,X_31),inverse(greatest_lower_bound(identity,inverse(X_31)))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_31),least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_31))))),multiply(greatest_lower_bound(identity,X_31),least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_31)))))) )],[refute_0_958,refute_0_959]) ).
cnf(refute_0_961,plain,
multiply(greatest_lower_bound(identity,X_31),least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_31))))) = multiply(greatest_lower_bound(identity,X_31),inverse(greatest_lower_bound(identity,inverse(X_31)))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_31)))),inverse(greatest_lower_bound(identity,inverse(X_31)))) )],[refute_0_957,refute_0_960]) ).
cnf(refute_0_962,plain,
greatest_lower_bound(X_105,X_106) = multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_105,X_106)),inverse(X_106))),least_upper_bound(identity,multiply(inverse(X_106),greatest_lower_bound(X_105,X_106)))),
inference(subst,[],[refute_0_949:[bind(X_31,$fot(greatest_lower_bound(X_105,X_106))),bind(X_73,$fot(inverse(X_106)))]]) ).
cnf(refute_0_963,plain,
( multiply(inverse(X_106),greatest_lower_bound(X_105,X_106)) != greatest_lower_bound(identity,multiply(inverse(X_106),X_105))
| greatest_lower_bound(X_105,X_106) != multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_105,X_106)),inverse(X_106))),least_upper_bound(identity,multiply(inverse(X_106),greatest_lower_bound(X_105,X_106))))
| greatest_lower_bound(X_105,X_106) = multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_105,X_106)),inverse(X_106))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_105,X_106),multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_105,X_106)),inverse(X_106))),least_upper_bound(identity,multiply(inverse(X_106),greatest_lower_bound(X_105,X_106))))) ),[1,1,1],$fot(greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))]]) ).
cnf(refute_0_964,plain,
( greatest_lower_bound(X_105,X_106) != multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_105,X_106)),inverse(X_106))),least_upper_bound(identity,multiply(inverse(X_106),greatest_lower_bound(X_105,X_106))))
| greatest_lower_bound(X_105,X_106) = multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_105,X_106)),inverse(X_106))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_106),greatest_lower_bound(X_105,X_106)),greatest_lower_bound(identity,multiply(inverse(X_106),X_105))) )],[refute_0_46,refute_0_963]) ).
cnf(refute_0_965,plain,
greatest_lower_bound(X_105,X_106) = multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_105,X_106)),inverse(X_106))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_105,X_106),multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_105,X_106)),inverse(X_106))),least_upper_bound(identity,multiply(inverse(X_106),greatest_lower_bound(X_105,X_106))))) )],[refute_0_962,refute_0_964]) ).
cnf(refute_0_966,plain,
multiply(inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106)))),identity) = inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106)))),
inference(subst,[],[refute_0_88:[bind(X_33,$fot(inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106))))))]]) ).
cnf(refute_0_967,plain,
least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105))) = identity,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(identity)),bind(Y,$fot(multiply(inverse(X_106),X_105)))]]) ).
cnf(refute_0_968,plain,
multiply(inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106)))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))) = multiply(inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106)))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106)))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))))]]) ).
cnf(refute_0_969,plain,
( multiply(inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106)))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))) != multiply(inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106)))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105))))
| least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105))) != identity
| multiply(inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106)))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))) = multiply(inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106)))),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106)))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))),multiply(inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106)))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_970,plain,
( least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105))) != identity
| multiply(inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106)))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))) = multiply(inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106)))),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106)))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))),multiply(inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106)))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105))))) )],[refute_0_968,refute_0_969]) ).
cnf(refute_0_971,plain,
multiply(inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106)))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))) = multiply(inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106)))),identity),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105))),identity) )],[refute_0_967,refute_0_970]) ).
cnf(refute_0_972,plain,
inverse(least_upper_bound(X_49,X_50)) = multiply(inverse(multiply(inverse(X_50),least_upper_bound(X_49,X_50))),inverse(X_50)),
inference(subst,[],[refute_0_96:[bind(X_45,$fot(inverse(X_50))),bind(X_46,$fot(least_upper_bound(X_49,X_50)))]]) ).
cnf(refute_0_973,plain,
( multiply(inverse(X_50),least_upper_bound(X_49,X_50)) != least_upper_bound(identity,multiply(inverse(X_50),X_49))
| inverse(least_upper_bound(X_49,X_50)) != multiply(inverse(multiply(inverse(X_50),least_upper_bound(X_49,X_50))),inverse(X_50))
| inverse(least_upper_bound(X_49,X_50)) = multiply(inverse(least_upper_bound(identity,multiply(inverse(X_50),X_49))),inverse(X_50)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_49,X_50)),multiply(inverse(multiply(inverse(X_50),least_upper_bound(X_49,X_50))),inverse(X_50))) ),[1,0,0],$fot(least_upper_bound(identity,multiply(inverse(X_50),X_49)))]]) ).
cnf(refute_0_974,plain,
( inverse(least_upper_bound(X_49,X_50)) != multiply(inverse(multiply(inverse(X_50),least_upper_bound(X_49,X_50))),inverse(X_50))
| inverse(least_upper_bound(X_49,X_50)) = multiply(inverse(least_upper_bound(identity,multiply(inverse(X_50),X_49))),inverse(X_50)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_50),least_upper_bound(X_49,X_50)),least_upper_bound(identity,multiply(inverse(X_50),X_49))) )],[refute_0_29,refute_0_973]) ).
cnf(refute_0_975,plain,
inverse(least_upper_bound(X_49,X_50)) = multiply(inverse(least_upper_bound(identity,multiply(inverse(X_50),X_49))),inverse(X_50)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_49,X_50)),multiply(inverse(multiply(inverse(X_50),least_upper_bound(X_49,X_50))),inverse(X_50))) )],[refute_0_972,refute_0_974]) ).
cnf(refute_0_976,plain,
multiply(X_50,identity) = X_50,
inference(subst,[],[refute_0_88:[bind(X_33,$fot(X_50))]]) ).
cnf(refute_0_977,plain,
least_upper_bound(multiply(X_50,identity),X_49) = least_upper_bound(multiply(X_50,identity),X_49),
introduced(tautology,[refl,[$fot(least_upper_bound(multiply(X_50,identity),X_49))]]) ).
cnf(refute_0_978,plain,
( multiply(X_50,identity) != X_50
| least_upper_bound(multiply(X_50,identity),X_49) != least_upper_bound(multiply(X_50,identity),X_49)
| least_upper_bound(multiply(X_50,identity),X_49) = least_upper_bound(X_50,X_49) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_50,identity),X_49),least_upper_bound(multiply(X_50,identity),X_49)) ),[1,0],$fot(X_50)]]) ).
cnf(refute_0_979,plain,
( multiply(X_50,identity) != X_50
| least_upper_bound(multiply(X_50,identity),X_49) = least_upper_bound(X_50,X_49) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_50,identity),X_49),least_upper_bound(multiply(X_50,identity),X_49)) )],[refute_0_977,refute_0_978]) ).
cnf(refute_0_980,plain,
least_upper_bound(multiply(X_50,identity),X_49) = least_upper_bound(X_50,X_49),
inference(resolve,[$cnf( $equal(multiply(X_50,identity),X_50) )],[refute_0_976,refute_0_979]) ).
cnf(refute_0_981,plain,
multiply(X,least_upper_bound(Y,multiply(inverse(X),X_81))) = least_upper_bound(multiply(X,Y),multiply(X,multiply(inverse(X),X_81))),
inference(subst,[],[monotony_lub1:[bind(Z,$fot(multiply(inverse(X),X_81)))]]) ).
cnf(refute_0_982,plain,
X_81 = multiply(X,multiply(inverse(X),X_81)),
inference(subst,[],[refute_0_104:[bind(X_31,$fot(X_81)),bind(X_35,$fot(X))]]) ).
cnf(refute_0_983,plain,
( X_81 != multiply(X,multiply(inverse(X),X_81))
| multiply(X,multiply(inverse(X),X_81)) = X_81 ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(X_81)),bind(Y0,$fot(multiply(X,multiply(inverse(X),X_81))))]]) ).
cnf(refute_0_984,plain,
multiply(X,multiply(inverse(X),X_81)) = X_81,
inference(resolve,[$cnf( $equal(X_81,multiply(X,multiply(inverse(X),X_81))) )],[refute_0_982,refute_0_983]) ).
cnf(refute_0_985,plain,
( multiply(X,multiply(inverse(X),X_81)) != X_81
| multiply(X,least_upper_bound(Y,multiply(inverse(X),X_81))) != least_upper_bound(multiply(X,Y),multiply(X,multiply(inverse(X),X_81)))
| multiply(X,least_upper_bound(Y,multiply(inverse(X),X_81))) = least_upper_bound(multiply(X,Y),X_81) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X,least_upper_bound(Y,multiply(inverse(X),X_81))),least_upper_bound(multiply(X,Y),multiply(X,multiply(inverse(X),X_81)))) ),[1,1],$fot(X_81)]]) ).
cnf(refute_0_986,plain,
( multiply(X,least_upper_bound(Y,multiply(inverse(X),X_81))) != least_upper_bound(multiply(X,Y),multiply(X,multiply(inverse(X),X_81)))
| multiply(X,least_upper_bound(Y,multiply(inverse(X),X_81))) = least_upper_bound(multiply(X,Y),X_81) ),
inference(resolve,[$cnf( $equal(multiply(X,multiply(inverse(X),X_81)),X_81) )],[refute_0_984,refute_0_985]) ).
cnf(refute_0_987,plain,
multiply(X,least_upper_bound(Y,multiply(inverse(X),X_81))) = least_upper_bound(multiply(X,Y),X_81),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(Y,multiply(inverse(X),X_81))),least_upper_bound(multiply(X,Y),multiply(X,multiply(inverse(X),X_81)))) )],[refute_0_981,refute_0_986]) ).
cnf(refute_0_988,plain,
multiply(X_50,least_upper_bound(identity,multiply(inverse(X_50),X_49))) = least_upper_bound(multiply(X_50,identity),X_49),
inference(subst,[],[refute_0_987:[bind(X,$fot(X_50)),bind(Y,$fot(identity)),bind(X_81,$fot(X_49))]]) ).
cnf(refute_0_989,plain,
( multiply(X_50,least_upper_bound(identity,multiply(inverse(X_50),X_49))) != least_upper_bound(multiply(X_50,identity),X_49)
| least_upper_bound(multiply(X_50,identity),X_49) != least_upper_bound(X_50,X_49)
| multiply(X_50,least_upper_bound(identity,multiply(inverse(X_50),X_49))) = least_upper_bound(X_50,X_49) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(X_50,least_upper_bound(identity,multiply(inverse(X_50),X_49))))),bind(Y0,$fot(least_upper_bound(multiply(X_50,identity),X_49))),bind(Z0,$fot(least_upper_bound(X_50,X_49)))]]) ).
cnf(refute_0_990,plain,
( least_upper_bound(multiply(X_50,identity),X_49) != least_upper_bound(X_50,X_49)
| multiply(X_50,least_upper_bound(identity,multiply(inverse(X_50),X_49))) = least_upper_bound(X_50,X_49) ),
inference(resolve,[$cnf( $equal(multiply(X_50,least_upper_bound(identity,multiply(inverse(X_50),X_49))),least_upper_bound(multiply(X_50,identity),X_49)) )],[refute_0_988,refute_0_989]) ).
cnf(refute_0_991,plain,
multiply(X_50,least_upper_bound(identity,multiply(inverse(X_50),X_49))) = least_upper_bound(X_50,X_49),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_50,identity),X_49),least_upper_bound(X_50,X_49)) )],[refute_0_980,refute_0_990]) ).
cnf(refute_0_992,plain,
inverse(multiply(X_50,least_upper_bound(identity,multiply(inverse(X_50),X_49)))) = inverse(multiply(X_50,least_upper_bound(identity,multiply(inverse(X_50),X_49)))),
introduced(tautology,[refl,[$fot(inverse(multiply(X_50,least_upper_bound(identity,multiply(inverse(X_50),X_49)))))]]) ).
cnf(refute_0_993,plain,
( multiply(X_50,least_upper_bound(identity,multiply(inverse(X_50),X_49))) != least_upper_bound(X_50,X_49)
| inverse(multiply(X_50,least_upper_bound(identity,multiply(inverse(X_50),X_49)))) != inverse(multiply(X_50,least_upper_bound(identity,multiply(inverse(X_50),X_49))))
| inverse(multiply(X_50,least_upper_bound(identity,multiply(inverse(X_50),X_49)))) = inverse(least_upper_bound(X_50,X_49)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_50,least_upper_bound(identity,multiply(inverse(X_50),X_49)))),inverse(multiply(X_50,least_upper_bound(identity,multiply(inverse(X_50),X_49))))) ),[1,0],$fot(least_upper_bound(X_50,X_49))]]) ).
cnf(refute_0_994,plain,
( multiply(X_50,least_upper_bound(identity,multiply(inverse(X_50),X_49))) != least_upper_bound(X_50,X_49)
| inverse(multiply(X_50,least_upper_bound(identity,multiply(inverse(X_50),X_49)))) = inverse(least_upper_bound(X_50,X_49)) ),
inference(resolve,[$cnf( $equal(inverse(multiply(X_50,least_upper_bound(identity,multiply(inverse(X_50),X_49)))),inverse(multiply(X_50,least_upper_bound(identity,multiply(inverse(X_50),X_49))))) )],[refute_0_992,refute_0_993]) ).
cnf(refute_0_995,plain,
inverse(multiply(X_50,least_upper_bound(identity,multiply(inverse(X_50),X_49)))) = inverse(least_upper_bound(X_50,X_49)),
inference(resolve,[$cnf( $equal(multiply(X_50,least_upper_bound(identity,multiply(inverse(X_50),X_49))),least_upper_bound(X_50,X_49)) )],[refute_0_991,refute_0_994]) ).
cnf(refute_0_996,plain,
multiply(inverse(least_upper_bound(identity,multiply(inverse(X_50),X_49))),inverse(X_50)) = inverse(multiply(X_50,least_upper_bound(identity,multiply(inverse(X_50),X_49)))),
inference(subst,[],[refute_0_490:[bind(X_30,$fot(X_50)),bind(X_31,$fot(least_upper_bound(identity,multiply(inverse(X_50),X_49))))]]) ).
cnf(refute_0_997,plain,
( multiply(inverse(least_upper_bound(identity,multiply(inverse(X_50),X_49))),inverse(X_50)) != inverse(multiply(X_50,least_upper_bound(identity,multiply(inverse(X_50),X_49))))
| inverse(multiply(X_50,least_upper_bound(identity,multiply(inverse(X_50),X_49)))) != inverse(least_upper_bound(X_50,X_49))
| multiply(inverse(least_upper_bound(identity,multiply(inverse(X_50),X_49))),inverse(X_50)) = inverse(least_upper_bound(X_50,X_49)) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(inverse(least_upper_bound(identity,multiply(inverse(X_50),X_49))),inverse(X_50)))),bind(Y0,$fot(inverse(multiply(X_50,least_upper_bound(identity,multiply(inverse(X_50),X_49)))))),bind(Z0,$fot(inverse(least_upper_bound(X_50,X_49))))]]) ).
cnf(refute_0_998,plain,
( inverse(multiply(X_50,least_upper_bound(identity,multiply(inverse(X_50),X_49)))) != inverse(least_upper_bound(X_50,X_49))
| multiply(inverse(least_upper_bound(identity,multiply(inverse(X_50),X_49))),inverse(X_50)) = inverse(least_upper_bound(X_50,X_49)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,multiply(inverse(X_50),X_49))),inverse(X_50)),inverse(multiply(X_50,least_upper_bound(identity,multiply(inverse(X_50),X_49))))) )],[refute_0_996,refute_0_997]) ).
cnf(refute_0_999,plain,
multiply(inverse(least_upper_bound(identity,multiply(inverse(X_50),X_49))),inverse(X_50)) = inverse(least_upper_bound(X_50,X_49)),
inference(resolve,[$cnf( $equal(inverse(multiply(X_50,least_upper_bound(identity,multiply(inverse(X_50),X_49)))),inverse(least_upper_bound(X_50,X_49))) )],[refute_0_995,refute_0_998]) ).
cnf(refute_0_1000,plain,
( multiply(inverse(least_upper_bound(identity,multiply(inverse(X_50),X_49))),inverse(X_50)) != inverse(least_upper_bound(X_50,X_49))
| inverse(least_upper_bound(X_49,X_50)) != multiply(inverse(least_upper_bound(identity,multiply(inverse(X_50),X_49))),inverse(X_50))
| inverse(least_upper_bound(X_49,X_50)) = inverse(least_upper_bound(X_50,X_49)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_49,X_50)),multiply(inverse(least_upper_bound(identity,multiply(inverse(X_50),X_49))),inverse(X_50))) ),[1],$fot(inverse(least_upper_bound(X_50,X_49)))]]) ).
cnf(refute_0_1001,plain,
( inverse(least_upper_bound(X_49,X_50)) != multiply(inverse(least_upper_bound(identity,multiply(inverse(X_50),X_49))),inverse(X_50))
| inverse(least_upper_bound(X_49,X_50)) = inverse(least_upper_bound(X_50,X_49)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,multiply(inverse(X_50),X_49))),inverse(X_50)),inverse(least_upper_bound(X_50,X_49))) )],[refute_0_999,refute_0_1000]) ).
cnf(refute_0_1002,plain,
inverse(least_upper_bound(X_49,X_50)) = inverse(least_upper_bound(X_50,X_49)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_49,X_50)),multiply(inverse(least_upper_bound(identity,multiply(inverse(X_50),X_49))),inverse(X_50))) )],[refute_0_975,refute_0_1001]) ).
cnf(refute_0_1003,plain,
( inverse(least_upper_bound(X_49,X_50)) != inverse(least_upper_bound(X_50,X_49))
| inverse(least_upper_bound(X_50,X_49)) = inverse(least_upper_bound(X_49,X_50)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(inverse(least_upper_bound(X_49,X_50)))),bind(Y0,$fot(inverse(least_upper_bound(X_50,X_49))))]]) ).
cnf(refute_0_1004,plain,
inverse(least_upper_bound(X_50,X_49)) = inverse(least_upper_bound(X_49,X_50)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_49,X_50)),inverse(least_upper_bound(X_50,X_49))) )],[refute_0_1002,refute_0_1003]) ).
cnf(refute_0_1005,plain,
inverse(least_upper_bound(inverse(greatest_lower_bound(X_105,X_106)),inverse(X_106))) = inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106)))),
inference(subst,[],[refute_0_1004:[bind(X_49,$fot(inverse(X_106))),bind(X_50,$fot(inverse(greatest_lower_bound(X_105,X_106))))]]) ).
cnf(refute_0_1006,plain,
multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_105,X_106)),inverse(X_106))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))) = multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_105,X_106)),inverse(X_106))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_105,X_106)),inverse(X_106))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))))]]) ).
cnf(refute_0_1007,plain,
( multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_105,X_106)),inverse(X_106))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))) != multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_105,X_106)),inverse(X_106))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105))))
| inverse(least_upper_bound(inverse(greatest_lower_bound(X_105,X_106)),inverse(X_106))) != inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106))))
| multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_105,X_106)),inverse(X_106))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))) = multiply(inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106)))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_105,X_106)),inverse(X_106))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))),multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_105,X_106)),inverse(X_106))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105))))) ),[1,0],$fot(inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106)))))]]) ).
cnf(refute_0_1008,plain,
( inverse(least_upper_bound(inverse(greatest_lower_bound(X_105,X_106)),inverse(X_106))) != inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106))))
| multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_105,X_106)),inverse(X_106))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))) = multiply(inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106)))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_105,X_106)),inverse(X_106))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))),multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_105,X_106)),inverse(X_106))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105))))) )],[refute_0_1006,refute_0_1007]) ).
cnf(refute_0_1009,plain,
multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_105,X_106)),inverse(X_106))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))) = multiply(inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106)))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(greatest_lower_bound(X_105,X_106)),inverse(X_106))),inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106))))) )],[refute_0_1005,refute_0_1008]) ).
cnf(refute_0_1010,plain,
( multiply(inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106)))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))) != multiply(inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106)))),identity)
| multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_105,X_106)),inverse(X_106))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))) != multiply(inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106)))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105))))
| multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_105,X_106)),inverse(X_106))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))) = multiply(inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106)))),identity) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_105,X_106)),inverse(X_106))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106)))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))))),bind(Z0,$fot(multiply(inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106)))),identity)))]]) ).
cnf(refute_0_1011,plain,
( multiply(inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106)))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))) != multiply(inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106)))),identity)
| multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_105,X_106)),inverse(X_106))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))) = multiply(inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106)))),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_105,X_106)),inverse(X_106))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))),multiply(inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106)))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105))))) )],[refute_0_1009,refute_0_1010]) ).
cnf(refute_0_1012,plain,
multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_105,X_106)),inverse(X_106))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))) = multiply(inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106)))),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106)))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))),multiply(inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106)))),identity)) )],[refute_0_971,refute_0_1011]) ).
cnf(refute_0_1013,plain,
( multiply(inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106)))),identity) != inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106))))
| multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_105,X_106)),inverse(X_106))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))) != multiply(inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106)))),identity)
| multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_105,X_106)),inverse(X_106))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))) = inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106)))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_105,X_106)),inverse(X_106))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106)))),identity))),bind(Z0,$fot(inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106))))))]]) ).
cnf(refute_0_1014,plain,
( multiply(inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106)))),identity) != inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106))))
| multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_105,X_106)),inverse(X_106))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))) = inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_105,X_106)),inverse(X_106))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))),multiply(inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106)))),identity)) )],[refute_0_1012,refute_0_1013]) ).
cnf(refute_0_1015,plain,
multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_105,X_106)),inverse(X_106))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))) = inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106)))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106)))),identity),inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106))))) )],[refute_0_966,refute_0_1014]) ).
cnf(refute_0_1016,plain,
( multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_105,X_106)),inverse(X_106))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))) != inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106))))
| greatest_lower_bound(X_105,X_106) != multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_105,X_106)),inverse(X_106))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105))))
| greatest_lower_bound(X_105,X_106) = inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106)))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_105,X_106),multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_105,X_106)),inverse(X_106))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105))))) ),[1],$fot(inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106)))))]]) ).
cnf(refute_0_1017,plain,
( greatest_lower_bound(X_105,X_106) != multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_105,X_106)),inverse(X_106))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105))))
| greatest_lower_bound(X_105,X_106) = inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_105,X_106)),inverse(X_106))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))),inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106))))) )],[refute_0_1015,refute_0_1016]) ).
cnf(refute_0_1018,plain,
greatest_lower_bound(X_105,X_106) = inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106)))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_105,X_106),multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_105,X_106)),inverse(X_106))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_106),X_105))))) )],[refute_0_965,refute_0_1017]) ).
cnf(refute_0_1019,plain,
( greatest_lower_bound(X_105,X_106) != inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106))))
| inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106)))) = greatest_lower_bound(X_105,X_106) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(greatest_lower_bound(X_105,X_106))),bind(Y0,$fot(inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106))))))]]) ).
cnf(refute_0_1020,plain,
inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106)))) = greatest_lower_bound(X_105,X_106),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_105,X_106),inverse(least_upper_bound(inverse(X_106),inverse(greatest_lower_bound(X_105,X_106))))) )],[refute_0_1018,refute_0_1019]) ).
cnf(refute_0_1021,plain,
inverse(least_upper_bound(inverse(X_31),inverse(greatest_lower_bound(identity,X_31)))) = greatest_lower_bound(identity,X_31),
inference(subst,[],[refute_0_1020:[bind(X_105,$fot(identity)),bind(X_106,$fot(X_31))]]) ).
cnf(refute_0_1022,plain,
multiply(inverse(least_upper_bound(inverse(X_31),inverse(greatest_lower_bound(identity,X_31)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_31))))) = multiply(inverse(least_upper_bound(inverse(X_31),inverse(greatest_lower_bound(identity,X_31)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_31))))),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(inverse(X_31),inverse(greatest_lower_bound(identity,X_31)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_31))))))]]) ).
cnf(refute_0_1023,plain,
( multiply(inverse(least_upper_bound(inverse(X_31),inverse(greatest_lower_bound(identity,X_31)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_31))))) != multiply(inverse(least_upper_bound(inverse(X_31),inverse(greatest_lower_bound(identity,X_31)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_31)))))
| inverse(least_upper_bound(inverse(X_31),inverse(greatest_lower_bound(identity,X_31)))) != greatest_lower_bound(identity,X_31)
| multiply(inverse(least_upper_bound(inverse(X_31),inverse(greatest_lower_bound(identity,X_31)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_31))))) = multiply(greatest_lower_bound(identity,X_31),least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_31))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_31),inverse(greatest_lower_bound(identity,X_31)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_31))))),multiply(inverse(least_upper_bound(inverse(X_31),inverse(greatest_lower_bound(identity,X_31)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_31)))))) ),[1,0],$fot(greatest_lower_bound(identity,X_31))]]) ).
cnf(refute_0_1024,plain,
( inverse(least_upper_bound(inverse(X_31),inverse(greatest_lower_bound(identity,X_31)))) != greatest_lower_bound(identity,X_31)
| multiply(inverse(least_upper_bound(inverse(X_31),inverse(greatest_lower_bound(identity,X_31)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_31))))) = multiply(greatest_lower_bound(identity,X_31),least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_31))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_31),inverse(greatest_lower_bound(identity,X_31)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_31))))),multiply(inverse(least_upper_bound(inverse(X_31),inverse(greatest_lower_bound(identity,X_31)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_31)))))) )],[refute_0_1022,refute_0_1023]) ).
cnf(refute_0_1025,plain,
multiply(inverse(least_upper_bound(inverse(X_31),inverse(greatest_lower_bound(identity,X_31)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_31))))) = multiply(greatest_lower_bound(identity,X_31),least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_31))))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(X_31),inverse(greatest_lower_bound(identity,X_31)))),greatest_lower_bound(identity,X_31)) )],[refute_0_1021,refute_0_1024]) ).
cnf(refute_0_1026,plain,
( multiply(greatest_lower_bound(identity,X_31),least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_31))))) != multiply(greatest_lower_bound(identity,X_31),inverse(greatest_lower_bound(identity,inverse(X_31))))
| multiply(inverse(least_upper_bound(inverse(X_31),inverse(greatest_lower_bound(identity,X_31)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_31))))) != multiply(greatest_lower_bound(identity,X_31),least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_31)))))
| multiply(inverse(least_upper_bound(inverse(X_31),inverse(greatest_lower_bound(identity,X_31)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_31))))) = multiply(greatest_lower_bound(identity,X_31),inverse(greatest_lower_bound(identity,inverse(X_31)))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(inverse(least_upper_bound(inverse(X_31),inverse(greatest_lower_bound(identity,X_31)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_31))))))),bind(Y0,$fot(multiply(greatest_lower_bound(identity,X_31),least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_31))))))),bind(Z0,$fot(multiply(greatest_lower_bound(identity,X_31),inverse(greatest_lower_bound(identity,inverse(X_31))))))]]) ).
cnf(refute_0_1027,plain,
( multiply(greatest_lower_bound(identity,X_31),least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_31))))) != multiply(greatest_lower_bound(identity,X_31),inverse(greatest_lower_bound(identity,inverse(X_31))))
| multiply(inverse(least_upper_bound(inverse(X_31),inverse(greatest_lower_bound(identity,X_31)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_31))))) = multiply(greatest_lower_bound(identity,X_31),inverse(greatest_lower_bound(identity,inverse(X_31)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_31),inverse(greatest_lower_bound(identity,X_31)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_31))))),multiply(greatest_lower_bound(identity,X_31),least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_31)))))) )],[refute_0_1025,refute_0_1026]) ).
cnf(refute_0_1028,plain,
multiply(inverse(least_upper_bound(inverse(X_31),inverse(greatest_lower_bound(identity,X_31)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_31))))) = multiply(greatest_lower_bound(identity,X_31),inverse(greatest_lower_bound(identity,inverse(X_31)))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_31),least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_31))))),multiply(greatest_lower_bound(identity,X_31),inverse(greatest_lower_bound(identity,inverse(X_31))))) )],[refute_0_961,refute_0_1027]) ).
cnf(refute_0_1029,plain,
( X_31 != multiply(inverse(least_upper_bound(inverse(X_31),inverse(greatest_lower_bound(identity,X_31)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_31)))))
| multiply(inverse(least_upper_bound(inverse(X_31),inverse(greatest_lower_bound(identity,X_31)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_31))))) != multiply(greatest_lower_bound(identity,X_31),inverse(greatest_lower_bound(identity,inverse(X_31))))
| X_31 = multiply(greatest_lower_bound(identity,X_31),inverse(greatest_lower_bound(identity,inverse(X_31)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_31,multiply(greatest_lower_bound(identity,X_31),inverse(greatest_lower_bound(identity,inverse(X_31))))) ),[0],$fot(multiply(inverse(least_upper_bound(inverse(X_31),inverse(greatest_lower_bound(identity,X_31)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_31))))))]]) ).
cnf(refute_0_1030,plain,
( X_31 != multiply(inverse(least_upper_bound(inverse(X_31),inverse(greatest_lower_bound(identity,X_31)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_31)))))
| X_31 = multiply(greatest_lower_bound(identity,X_31),inverse(greatest_lower_bound(identity,inverse(X_31)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_31),inverse(greatest_lower_bound(identity,X_31)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_31))))),multiply(greatest_lower_bound(identity,X_31),inverse(greatest_lower_bound(identity,inverse(X_31))))) )],[refute_0_1028,refute_0_1029]) ).
cnf(refute_0_1031,plain,
X_31 = multiply(greatest_lower_bound(identity,X_31),inverse(greatest_lower_bound(identity,inverse(X_31)))),
inference(resolve,[$cnf( $equal(X_31,multiply(inverse(least_upper_bound(inverse(X_31),inverse(greatest_lower_bound(identity,X_31)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_31)))))) )],[refute_0_956,refute_0_1030]) ).
cnf(refute_0_1032,plain,
inverse(inverse(least_upper_bound(identity,X_31))) = least_upper_bound(identity,X_31),
inference(subst,[],[refute_0_452:[bind(X_35,$fot(least_upper_bound(identity,X_31)))]]) ).
cnf(refute_0_1033,plain,
X_31 = multiply(inverse(greatest_lower_bound(X_123,inverse(X_31))),multiply(greatest_lower_bound(X_123,inverse(X_31)),X_31)),
inference(subst,[],[refute_0_9:[bind(X_30,$fot(greatest_lower_bound(X_123,inverse(X_31))))]]) ).
cnf(refute_0_1034,plain,
multiply(greatest_lower_bound(X_123,inverse(X_31)),X_31) = greatest_lower_bound(identity,multiply(X_123,X_31)),
inference(subst,[],[refute_0_476:[bind(X_119,$fot(X_31)),bind(X_120,$fot(X_123))]]) ).
cnf(refute_0_1035,plain,
( X_31 != multiply(inverse(greatest_lower_bound(X_123,inverse(X_31))),multiply(greatest_lower_bound(X_123,inverse(X_31)),X_31))
| multiply(greatest_lower_bound(X_123,inverse(X_31)),X_31) != greatest_lower_bound(identity,multiply(X_123,X_31))
| X_31 = multiply(inverse(greatest_lower_bound(X_123,inverse(X_31))),greatest_lower_bound(identity,multiply(X_123,X_31))) ),
introduced(tautology,[equality,[$cnf( $equal(X_31,multiply(inverse(greatest_lower_bound(X_123,inverse(X_31))),multiply(greatest_lower_bound(X_123,inverse(X_31)),X_31))) ),[1,1],$fot(greatest_lower_bound(identity,multiply(X_123,X_31)))]]) ).
cnf(refute_0_1036,plain,
( X_31 != multiply(inverse(greatest_lower_bound(X_123,inverse(X_31))),multiply(greatest_lower_bound(X_123,inverse(X_31)),X_31))
| X_31 = multiply(inverse(greatest_lower_bound(X_123,inverse(X_31))),greatest_lower_bound(identity,multiply(X_123,X_31))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_123,inverse(X_31)),X_31),greatest_lower_bound(identity,multiply(X_123,X_31))) )],[refute_0_1034,refute_0_1035]) ).
cnf(refute_0_1037,plain,
X_31 = multiply(inverse(greatest_lower_bound(X_123,inverse(X_31))),greatest_lower_bound(identity,multiply(X_123,X_31))),
inference(resolve,[$cnf( $equal(X_31,multiply(inverse(greatest_lower_bound(X_123,inverse(X_31))),multiply(greatest_lower_bound(X_123,inverse(X_31)),X_31))) )],[refute_0_1033,refute_0_1036]) ).
cnf(refute_0_1038,plain,
inverse(least_upper_bound(identity,X_316)) = multiply(inverse(greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316))))),greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X_316)),inverse(least_upper_bound(identity,X_316))))),
inference(subst,[],[refute_0_1037:[bind(X_123,$fot(least_upper_bound(identity,inverse(X_316)))),bind(X_31,$fot(inverse(least_upper_bound(identity,X_316))))]]) ).
cnf(refute_0_1039,plain,
inverse(X_146) = multiply(inverse(multiply(greatest_lower_bound(X_120,inverse(X_146)),X_146)),greatest_lower_bound(X_120,inverse(X_146))),
inference(subst,[],[refute_0_96:[bind(X_45,$fot(greatest_lower_bound(X_120,inverse(X_146)))),bind(X_46,$fot(X_146))]]) ).
cnf(refute_0_1040,plain,
multiply(greatest_lower_bound(X_120,inverse(X_146)),X_146) = greatest_lower_bound(identity,multiply(X_120,X_146)),
inference(subst,[],[refute_0_476:[bind(X_119,$fot(X_146))]]) ).
cnf(refute_0_1041,plain,
( multiply(greatest_lower_bound(X_120,inverse(X_146)),X_146) != greatest_lower_bound(identity,multiply(X_120,X_146))
| inverse(X_146) != multiply(inverse(multiply(greatest_lower_bound(X_120,inverse(X_146)),X_146)),greatest_lower_bound(X_120,inverse(X_146)))
| inverse(X_146) = multiply(inverse(greatest_lower_bound(identity,multiply(X_120,X_146))),greatest_lower_bound(X_120,inverse(X_146))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(X_146),multiply(inverse(multiply(greatest_lower_bound(X_120,inverse(X_146)),X_146)),greatest_lower_bound(X_120,inverse(X_146)))) ),[1,0,0],$fot(greatest_lower_bound(identity,multiply(X_120,X_146)))]]) ).
cnf(refute_0_1042,plain,
( inverse(X_146) != multiply(inverse(multiply(greatest_lower_bound(X_120,inverse(X_146)),X_146)),greatest_lower_bound(X_120,inverse(X_146)))
| inverse(X_146) = multiply(inverse(greatest_lower_bound(identity,multiply(X_120,X_146))),greatest_lower_bound(X_120,inverse(X_146))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_120,inverse(X_146)),X_146),greatest_lower_bound(identity,multiply(X_120,X_146))) )],[refute_0_1040,refute_0_1041]) ).
cnf(refute_0_1043,plain,
inverse(X_146) = multiply(inverse(greatest_lower_bound(identity,multiply(X_120,X_146))),greatest_lower_bound(X_120,inverse(X_146))),
inference(resolve,[$cnf( $equal(inverse(X_146),multiply(inverse(multiply(greatest_lower_bound(X_120,inverse(X_146)),X_146)),greatest_lower_bound(X_120,inverse(X_146)))) )],[refute_0_1039,refute_0_1042]) ).
cnf(refute_0_1044,plain,
inverse(X_286) = multiply(inverse(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,X_286)),X_286))),greatest_lower_bound(inverse(least_upper_bound(identity,X_286)),inverse(X_286))),
inference(subst,[],[refute_0_1043:[bind(X_120,$fot(inverse(least_upper_bound(identity,X_286)))),bind(X_146,$fot(X_286))]]) ).
cnf(refute_0_1045,plain,
inverse(multiply(inverse(X_148),least_upper_bound(identity,X_148))) = multiply(inverse(least_upper_bound(identity,X_148)),X_148),
inference(subst,[],[refute_0_110:[bind(X_145,$fot(X_148)),bind(X_31,$fot(least_upper_bound(identity,X_148)))]]) ).
cnf(refute_0_1046,plain,
multiply(inverse(X_148),least_upper_bound(identity,X_148)) = least_upper_bound(identity,inverse(X_148)),
inference(subst,[],[refute_0_126:[bind(X_56,$fot(X_148))]]) ).
cnf(refute_0_1047,plain,
( multiply(inverse(X_148),least_upper_bound(identity,X_148)) != least_upper_bound(identity,inverse(X_148))
| inverse(multiply(inverse(X_148),least_upper_bound(identity,X_148))) != multiply(inverse(least_upper_bound(identity,X_148)),X_148)
| inverse(least_upper_bound(identity,inverse(X_148))) = multiply(inverse(least_upper_bound(identity,X_148)),X_148) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X_148),least_upper_bound(identity,X_148))),multiply(inverse(least_upper_bound(identity,X_148)),X_148)) ),[0,0],$fot(least_upper_bound(identity,inverse(X_148)))]]) ).
cnf(refute_0_1048,plain,
( inverse(multiply(inverse(X_148),least_upper_bound(identity,X_148))) != multiply(inverse(least_upper_bound(identity,X_148)),X_148)
| inverse(least_upper_bound(identity,inverse(X_148))) = multiply(inverse(least_upper_bound(identity,X_148)),X_148) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_148),least_upper_bound(identity,X_148)),least_upper_bound(identity,inverse(X_148))) )],[refute_0_1046,refute_0_1047]) ).
cnf(refute_0_1049,plain,
inverse(least_upper_bound(identity,inverse(X_148))) = multiply(inverse(least_upper_bound(identity,X_148)),X_148),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_148),least_upper_bound(identity,X_148))),multiply(inverse(least_upper_bound(identity,X_148)),X_148)) )],[refute_0_1045,refute_0_1048]) ).
cnf(refute_0_1050,plain,
inverse(least_upper_bound(identity,inverse(X_286))) = multiply(inverse(least_upper_bound(identity,X_286)),X_286),
inference(subst,[],[refute_0_1049:[bind(X_148,$fot(X_286))]]) ).
cnf(refute_0_1051,plain,
( inverse(least_upper_bound(identity,inverse(X_286))) != multiply(inverse(least_upper_bound(identity,X_286)),X_286)
| multiply(inverse(least_upper_bound(identity,X_286)),X_286) = inverse(least_upper_bound(identity,inverse(X_286))) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(inverse(least_upper_bound(identity,inverse(X_286))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(identity,X_286)),X_286)))]]) ).
cnf(refute_0_1052,plain,
multiply(inverse(least_upper_bound(identity,X_286)),X_286) = inverse(least_upper_bound(identity,inverse(X_286))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_286))),multiply(inverse(least_upper_bound(identity,X_286)),X_286)) )],[refute_0_1050,refute_0_1051]) ).
cnf(refute_0_1053,plain,
( multiply(inverse(least_upper_bound(identity,X_286)),X_286) != inverse(least_upper_bound(identity,inverse(X_286)))
| inverse(X_286) != multiply(inverse(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,X_286)),X_286))),greatest_lower_bound(inverse(least_upper_bound(identity,X_286)),inverse(X_286)))
| inverse(X_286) = multiply(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))),greatest_lower_bound(inverse(least_upper_bound(identity,X_286)),inverse(X_286))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(X_286),multiply(inverse(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,X_286)),X_286))),greatest_lower_bound(inverse(least_upper_bound(identity,X_286)),inverse(X_286)))) ),[1,0,0,1],$fot(inverse(least_upper_bound(identity,inverse(X_286))))]]) ).
cnf(refute_0_1054,plain,
( inverse(X_286) != multiply(inverse(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,X_286)),X_286))),greatest_lower_bound(inverse(least_upper_bound(identity,X_286)),inverse(X_286)))
| inverse(X_286) = multiply(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))),greatest_lower_bound(inverse(least_upper_bound(identity,X_286)),inverse(X_286))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_286)),X_286),inverse(least_upper_bound(identity,inverse(X_286)))) )],[refute_0_1052,refute_0_1053]) ).
cnf(refute_0_1055,plain,
inverse(X_286) = multiply(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))),greatest_lower_bound(inverse(least_upper_bound(identity,X_286)),inverse(X_286))),
inference(resolve,[$cnf( $equal(inverse(X_286),multiply(inverse(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,X_286)),X_286))),greatest_lower_bound(inverse(least_upper_bound(identity,X_286)),inverse(X_286)))) )],[refute_0_1044,refute_0_1054]) ).
cnf(refute_0_1056,plain,
multiply(inverse(least_upper_bound(identity,X_208)),greatest_lower_bound(least_upper_bound(identity,inverse(X_208)),identity)) = greatest_lower_bound(inverse(least_upper_bound(identity,X_208)),multiply(inverse(least_upper_bound(identity,X_208)),least_upper_bound(identity,inverse(X_208)))),
inference(subst,[],[refute_0_319:[bind(X_104,$fot(inverse(least_upper_bound(identity,X_208)))),bind(X_105,$fot(least_upper_bound(identity,inverse(X_208))))]]) ).
cnf(refute_0_1057,plain,
inverse(X_78) = multiply(inverse(least_upper_bound(identity,X_78)),multiply(least_upper_bound(identity,X_78),inverse(X_78))),
inference(subst,[],[refute_0_9:[bind(X_30,$fot(least_upper_bound(identity,X_78))),bind(X_31,$fot(inverse(X_78)))]]) ).
cnf(refute_0_1058,plain,
multiply(least_upper_bound(identity,X_78),inverse(X_78)) = least_upper_bound(identity,inverse(X_78)),
inference(subst,[],[refute_0_785:[bind(X_75,$fot(X_78))]]) ).
cnf(refute_0_1059,plain,
( multiply(least_upper_bound(identity,X_78),inverse(X_78)) != least_upper_bound(identity,inverse(X_78))
| inverse(X_78) != multiply(inverse(least_upper_bound(identity,X_78)),multiply(least_upper_bound(identity,X_78),inverse(X_78)))
| inverse(X_78) = multiply(inverse(least_upper_bound(identity,X_78)),least_upper_bound(identity,inverse(X_78))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(X_78),multiply(inverse(least_upper_bound(identity,X_78)),multiply(least_upper_bound(identity,X_78),inverse(X_78)))) ),[1,1],$fot(least_upper_bound(identity,inverse(X_78)))]]) ).
cnf(refute_0_1060,plain,
( inverse(X_78) != multiply(inverse(least_upper_bound(identity,X_78)),multiply(least_upper_bound(identity,X_78),inverse(X_78)))
| inverse(X_78) = multiply(inverse(least_upper_bound(identity,X_78)),least_upper_bound(identity,inverse(X_78))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_78),inverse(X_78)),least_upper_bound(identity,inverse(X_78))) )],[refute_0_1058,refute_0_1059]) ).
cnf(refute_0_1061,plain,
inverse(X_78) = multiply(inverse(least_upper_bound(identity,X_78)),least_upper_bound(identity,inverse(X_78))),
inference(resolve,[$cnf( $equal(inverse(X_78),multiply(inverse(least_upper_bound(identity,X_78)),multiply(least_upper_bound(identity,X_78),inverse(X_78)))) )],[refute_0_1057,refute_0_1060]) ).
cnf(refute_0_1062,plain,
inverse(X_208) = multiply(inverse(least_upper_bound(identity,X_208)),least_upper_bound(identity,inverse(X_208))),
inference(subst,[],[refute_0_1061:[bind(X_78,$fot(X_208))]]) ).
cnf(refute_0_1063,plain,
( inverse(X_208) != multiply(inverse(least_upper_bound(identity,X_208)),least_upper_bound(identity,inverse(X_208)))
| multiply(inverse(least_upper_bound(identity,X_208)),least_upper_bound(identity,inverse(X_208))) = inverse(X_208) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(inverse(X_208))),bind(Y0,$fot(multiply(inverse(least_upper_bound(identity,X_208)),least_upper_bound(identity,inverse(X_208)))))]]) ).
cnf(refute_0_1064,plain,
multiply(inverse(least_upper_bound(identity,X_208)),least_upper_bound(identity,inverse(X_208))) = inverse(X_208),
inference(resolve,[$cnf( $equal(inverse(X_208),multiply(inverse(least_upper_bound(identity,X_208)),least_upper_bound(identity,inverse(X_208)))) )],[refute_0_1062,refute_0_1063]) ).
cnf(refute_0_1065,plain,
( multiply(inverse(least_upper_bound(identity,X_208)),greatest_lower_bound(least_upper_bound(identity,inverse(X_208)),identity)) != greatest_lower_bound(inverse(least_upper_bound(identity,X_208)),multiply(inverse(least_upper_bound(identity,X_208)),least_upper_bound(identity,inverse(X_208))))
| multiply(inverse(least_upper_bound(identity,X_208)),least_upper_bound(identity,inverse(X_208))) != inverse(X_208)
| multiply(inverse(least_upper_bound(identity,X_208)),greatest_lower_bound(least_upper_bound(identity,inverse(X_208)),identity)) = greatest_lower_bound(inverse(least_upper_bound(identity,X_208)),inverse(X_208)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_208)),greatest_lower_bound(least_upper_bound(identity,inverse(X_208)),identity)),greatest_lower_bound(inverse(least_upper_bound(identity,X_208)),multiply(inverse(least_upper_bound(identity,X_208)),least_upper_bound(identity,inverse(X_208))))) ),[1,1],$fot(inverse(X_208))]]) ).
cnf(refute_0_1066,plain,
( multiply(inverse(least_upper_bound(identity,X_208)),greatest_lower_bound(least_upper_bound(identity,inverse(X_208)),identity)) != greatest_lower_bound(inverse(least_upper_bound(identity,X_208)),multiply(inverse(least_upper_bound(identity,X_208)),least_upper_bound(identity,inverse(X_208))))
| multiply(inverse(least_upper_bound(identity,X_208)),greatest_lower_bound(least_upper_bound(identity,inverse(X_208)),identity)) = greatest_lower_bound(inverse(least_upper_bound(identity,X_208)),inverse(X_208)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_208)),least_upper_bound(identity,inverse(X_208))),inverse(X_208)) )],[refute_0_1064,refute_0_1065]) ).
cnf(refute_0_1067,plain,
multiply(inverse(least_upper_bound(identity,X_208)),greatest_lower_bound(least_upper_bound(identity,inverse(X_208)),identity)) = greatest_lower_bound(inverse(least_upper_bound(identity,X_208)),inverse(X_208)),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_208)),greatest_lower_bound(least_upper_bound(identity,inverse(X_208)),identity)),greatest_lower_bound(inverse(least_upper_bound(identity,X_208)),multiply(inverse(least_upper_bound(identity,X_208)),least_upper_bound(identity,inverse(X_208))))) )],[refute_0_1056,refute_0_1066]) ).
cnf(refute_0_1068,plain,
multiply(inverse(least_upper_bound(identity,X_208)),identity) = inverse(least_upper_bound(identity,X_208)),
inference(subst,[],[refute_0_88:[bind(X_33,$fot(inverse(least_upper_bound(identity,X_208))))]]) ).
cnf(refute_0_1069,plain,
greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_208))) = identity,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(identity)),bind(Y,$fot(inverse(X_208)))]]) ).
cnf(refute_0_1070,plain,
multiply(inverse(least_upper_bound(identity,X_208)),greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_208)))) = multiply(inverse(least_upper_bound(identity,X_208)),greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_208)))),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(identity,X_208)),greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_208)))))]]) ).
cnf(refute_0_1071,plain,
( multiply(inverse(least_upper_bound(identity,X_208)),greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_208)))) != multiply(inverse(least_upper_bound(identity,X_208)),greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_208))))
| greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_208))) != identity
| multiply(inverse(least_upper_bound(identity,X_208)),greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_208)))) = multiply(inverse(least_upper_bound(identity,X_208)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_208)),greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_208)))),multiply(inverse(least_upper_bound(identity,X_208)),greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_208))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_1072,plain,
( greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_208))) != identity
| multiply(inverse(least_upper_bound(identity,X_208)),greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_208)))) = multiply(inverse(least_upper_bound(identity,X_208)),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_208)),greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_208)))),multiply(inverse(least_upper_bound(identity,X_208)),greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_208))))) )],[refute_0_1070,refute_0_1071]) ).
cnf(refute_0_1073,plain,
multiply(inverse(least_upper_bound(identity,X_208)),greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_208)))) = multiply(inverse(least_upper_bound(identity,X_208)),identity),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_208))),identity) )],[refute_0_1069,refute_0_1072]) ).
cnf(refute_0_1074,plain,
( multiply(inverse(least_upper_bound(identity,X_208)),greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_208)))) != multiply(inverse(least_upper_bound(identity,X_208)),identity)
| multiply(inverse(least_upper_bound(identity,X_208)),identity) != inverse(least_upper_bound(identity,X_208))
| multiply(inverse(least_upper_bound(identity,X_208)),greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_208)))) = inverse(least_upper_bound(identity,X_208)) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(inverse(least_upper_bound(identity,X_208)),greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_208)))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(identity,X_208)),identity))),bind(Z0,$fot(inverse(least_upper_bound(identity,X_208))))]]) ).
cnf(refute_0_1075,plain,
( multiply(inverse(least_upper_bound(identity,X_208)),identity) != inverse(least_upper_bound(identity,X_208))
| multiply(inverse(least_upper_bound(identity,X_208)),greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_208)))) = inverse(least_upper_bound(identity,X_208)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_208)),greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_208)))),multiply(inverse(least_upper_bound(identity,X_208)),identity)) )],[refute_0_1073,refute_0_1074]) ).
cnf(refute_0_1076,plain,
multiply(inverse(least_upper_bound(identity,X_208)),greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_208)))) = inverse(least_upper_bound(identity,X_208)),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_208)),identity),inverse(least_upper_bound(identity,X_208))) )],[refute_0_1068,refute_0_1075]) ).
cnf(refute_0_1077,plain,
greatest_lower_bound(X_22,greatest_lower_bound(least_upper_bound(X_7,X_22),X_24)) = greatest_lower_bound(greatest_lower_bound(X_22,least_upper_bound(X_7,X_22)),X_24),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_22)),bind(Y,$fot(least_upper_bound(X_7,X_22))),bind(Z,$fot(X_24))]]) ).
cnf(refute_0_1078,plain,
greatest_lower_bound(X_22,least_upper_bound(X_7,X_22)) = X_22,
inference(subst,[],[refute_0_153:[bind(X_6,$fot(X_22))]]) ).
cnf(refute_0_1079,plain,
( greatest_lower_bound(X_22,greatest_lower_bound(least_upper_bound(X_7,X_22),X_24)) != greatest_lower_bound(greatest_lower_bound(X_22,least_upper_bound(X_7,X_22)),X_24)
| greatest_lower_bound(X_22,least_upper_bound(X_7,X_22)) != X_22
| greatest_lower_bound(X_22,greatest_lower_bound(least_upper_bound(X_7,X_22),X_24)) = greatest_lower_bound(X_22,X_24) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_22,greatest_lower_bound(least_upper_bound(X_7,X_22),X_24)),greatest_lower_bound(greatest_lower_bound(X_22,least_upper_bound(X_7,X_22)),X_24)) ),[1,0],$fot(X_22)]]) ).
cnf(refute_0_1080,plain,
( greatest_lower_bound(X_22,greatest_lower_bound(least_upper_bound(X_7,X_22),X_24)) != greatest_lower_bound(greatest_lower_bound(X_22,least_upper_bound(X_7,X_22)),X_24)
| greatest_lower_bound(X_22,greatest_lower_bound(least_upper_bound(X_7,X_22),X_24)) = greatest_lower_bound(X_22,X_24) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_22,least_upper_bound(X_7,X_22)),X_22) )],[refute_0_1078,refute_0_1079]) ).
cnf(refute_0_1081,plain,
greatest_lower_bound(X_22,greatest_lower_bound(least_upper_bound(X_7,X_22),X_24)) = greatest_lower_bound(X_22,X_24),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_22,greatest_lower_bound(least_upper_bound(X_7,X_22),X_24)),greatest_lower_bound(greatest_lower_bound(X_22,least_upper_bound(X_7,X_22)),X_24)) )],[refute_0_1077,refute_0_1080]) ).
cnf(refute_0_1082,plain,
greatest_lower_bound(inverse(X_56),greatest_lower_bound(least_upper_bound(identity,inverse(X_56)),multiply(inverse(X_56),X_106))) = greatest_lower_bound(inverse(X_56),multiply(inverse(X_56),X_106)),
inference(subst,[],[refute_0_1081:[bind(X_22,$fot(inverse(X_56))),bind(X_24,$fot(multiply(inverse(X_56),X_106))),bind(X_7,$fot(identity))]]) ).
cnf(refute_0_1083,plain,
multiply(inverse(X_56),greatest_lower_bound(least_upper_bound(identity,X_56),X_106)) = greatest_lower_bound(multiply(inverse(X_56),least_upper_bound(identity,X_56)),multiply(inverse(X_56),X_106)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(inverse(X_56))),bind(Y,$fot(least_upper_bound(identity,X_56))),bind(Z,$fot(X_106))]]) ).
cnf(refute_0_1084,plain,
( multiply(inverse(X_56),greatest_lower_bound(least_upper_bound(identity,X_56),X_106)) != greatest_lower_bound(multiply(inverse(X_56),least_upper_bound(identity,X_56)),multiply(inverse(X_56),X_106))
| multiply(inverse(X_56),least_upper_bound(identity,X_56)) != least_upper_bound(identity,inverse(X_56))
| multiply(inverse(X_56),greatest_lower_bound(least_upper_bound(identity,X_56),X_106)) = greatest_lower_bound(least_upper_bound(identity,inverse(X_56)),multiply(inverse(X_56),X_106)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_56),greatest_lower_bound(least_upper_bound(identity,X_56),X_106)),greatest_lower_bound(multiply(inverse(X_56),least_upper_bound(identity,X_56)),multiply(inverse(X_56),X_106))) ),[1,0],$fot(least_upper_bound(identity,inverse(X_56)))]]) ).
cnf(refute_0_1085,plain,
( multiply(inverse(X_56),greatest_lower_bound(least_upper_bound(identity,X_56),X_106)) != greatest_lower_bound(multiply(inverse(X_56),least_upper_bound(identity,X_56)),multiply(inverse(X_56),X_106))
| multiply(inverse(X_56),greatest_lower_bound(least_upper_bound(identity,X_56),X_106)) = greatest_lower_bound(least_upper_bound(identity,inverse(X_56)),multiply(inverse(X_56),X_106)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_56),least_upper_bound(identity,X_56)),least_upper_bound(identity,inverse(X_56))) )],[refute_0_126,refute_0_1084]) ).
cnf(refute_0_1086,plain,
multiply(inverse(X_56),greatest_lower_bound(least_upper_bound(identity,X_56),X_106)) = greatest_lower_bound(least_upper_bound(identity,inverse(X_56)),multiply(inverse(X_56),X_106)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_56),greatest_lower_bound(least_upper_bound(identity,X_56),X_106)),greatest_lower_bound(multiply(inverse(X_56),least_upper_bound(identity,X_56)),multiply(inverse(X_56),X_106))) )],[refute_0_1083,refute_0_1085]) ).
cnf(refute_0_1087,plain,
( multiply(inverse(X_56),greatest_lower_bound(least_upper_bound(identity,X_56),X_106)) != greatest_lower_bound(least_upper_bound(identity,inverse(X_56)),multiply(inverse(X_56),X_106))
| greatest_lower_bound(least_upper_bound(identity,inverse(X_56)),multiply(inverse(X_56),X_106)) = multiply(inverse(X_56),greatest_lower_bound(least_upper_bound(identity,X_56),X_106)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(inverse(X_56),greatest_lower_bound(least_upper_bound(identity,X_56),X_106)))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(identity,inverse(X_56)),multiply(inverse(X_56),X_106))))]]) ).
cnf(refute_0_1088,plain,
greatest_lower_bound(least_upper_bound(identity,inverse(X_56)),multiply(inverse(X_56),X_106)) = multiply(inverse(X_56),greatest_lower_bound(least_upper_bound(identity,X_56),X_106)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_56),greatest_lower_bound(least_upper_bound(identity,X_56),X_106)),greatest_lower_bound(least_upper_bound(identity,inverse(X_56)),multiply(inverse(X_56),X_106))) )],[refute_0_1086,refute_0_1087]) ).
cnf(refute_0_1089,plain,
( greatest_lower_bound(inverse(X_56),greatest_lower_bound(least_upper_bound(identity,inverse(X_56)),multiply(inverse(X_56),X_106))) != greatest_lower_bound(inverse(X_56),multiply(inverse(X_56),X_106))
| greatest_lower_bound(least_upper_bound(identity,inverse(X_56)),multiply(inverse(X_56),X_106)) != multiply(inverse(X_56),greatest_lower_bound(least_upper_bound(identity,X_56),X_106))
| greatest_lower_bound(inverse(X_56),multiply(inverse(X_56),greatest_lower_bound(least_upper_bound(identity,X_56),X_106))) = greatest_lower_bound(inverse(X_56),multiply(inverse(X_56),X_106)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(inverse(X_56),greatest_lower_bound(least_upper_bound(identity,inverse(X_56)),multiply(inverse(X_56),X_106))),greatest_lower_bound(inverse(X_56),multiply(inverse(X_56),X_106))) ),[0,1],$fot(multiply(inverse(X_56),greatest_lower_bound(least_upper_bound(identity,X_56),X_106)))]]) ).
cnf(refute_0_1090,plain,
( greatest_lower_bound(inverse(X_56),greatest_lower_bound(least_upper_bound(identity,inverse(X_56)),multiply(inverse(X_56),X_106))) != greatest_lower_bound(inverse(X_56),multiply(inverse(X_56),X_106))
| greatest_lower_bound(inverse(X_56),multiply(inverse(X_56),greatest_lower_bound(least_upper_bound(identity,X_56),X_106))) = greatest_lower_bound(inverse(X_56),multiply(inverse(X_56),X_106)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,inverse(X_56)),multiply(inverse(X_56),X_106)),multiply(inverse(X_56),greatest_lower_bound(least_upper_bound(identity,X_56),X_106))) )],[refute_0_1088,refute_0_1089]) ).
cnf(refute_0_1091,plain,
greatest_lower_bound(inverse(X_56),multiply(inverse(X_56),greatest_lower_bound(least_upper_bound(identity,X_56),X_106))) = greatest_lower_bound(inverse(X_56),multiply(inverse(X_56),X_106)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_56),greatest_lower_bound(least_upper_bound(identity,inverse(X_56)),multiply(inverse(X_56),X_106))),greatest_lower_bound(inverse(X_56),multiply(inverse(X_56),X_106))) )],[refute_0_1082,refute_0_1090]) ).
cnf(refute_0_1092,plain,
greatest_lower_bound(X_22,greatest_lower_bound(least_upper_bound(X_22,Y),X_24)) = greatest_lower_bound(greatest_lower_bound(X_22,least_upper_bound(X_22,Y)),X_24),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_22)),bind(Y,$fot(least_upper_bound(X_22,Y))),bind(Z,$fot(X_24))]]) ).
cnf(refute_0_1093,plain,
greatest_lower_bound(X_22,least_upper_bound(X_22,Y)) = X_22,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_22))]]) ).
cnf(refute_0_1094,plain,
( greatest_lower_bound(X_22,greatest_lower_bound(least_upper_bound(X_22,Y),X_24)) != greatest_lower_bound(greatest_lower_bound(X_22,least_upper_bound(X_22,Y)),X_24)
| greatest_lower_bound(X_22,least_upper_bound(X_22,Y)) != X_22
| greatest_lower_bound(X_22,greatest_lower_bound(least_upper_bound(X_22,Y),X_24)) = greatest_lower_bound(X_22,X_24) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_22,greatest_lower_bound(least_upper_bound(X_22,Y),X_24)),greatest_lower_bound(greatest_lower_bound(X_22,least_upper_bound(X_22,Y)),X_24)) ),[1,0],$fot(X_22)]]) ).
cnf(refute_0_1095,plain,
( greatest_lower_bound(X_22,greatest_lower_bound(least_upper_bound(X_22,Y),X_24)) != greatest_lower_bound(greatest_lower_bound(X_22,least_upper_bound(X_22,Y)),X_24)
| greatest_lower_bound(X_22,greatest_lower_bound(least_upper_bound(X_22,Y),X_24)) = greatest_lower_bound(X_22,X_24) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_22,least_upper_bound(X_22,Y)),X_22) )],[refute_0_1093,refute_0_1094]) ).
cnf(refute_0_1096,plain,
greatest_lower_bound(X_22,greatest_lower_bound(least_upper_bound(X_22,Y),X_24)) = greatest_lower_bound(X_22,X_24),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_22,greatest_lower_bound(least_upper_bound(X_22,Y),X_24)),greatest_lower_bound(greatest_lower_bound(X_22,least_upper_bound(X_22,Y)),X_24)) )],[refute_0_1092,refute_0_1095]) ).
cnf(refute_0_1097,plain,
greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_56),X_106)) = greatest_lower_bound(identity,X_106),
inference(subst,[],[refute_0_1096:[bind(Y,$fot(X_56)),bind(X_22,$fot(identity)),bind(X_24,$fot(X_106))]]) ).
cnf(refute_0_1098,plain,
multiply(inverse(X_56),greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_56),X_106))) = multiply(inverse(X_56),greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_56),X_106))),
introduced(tautology,[refl,[$fot(multiply(inverse(X_56),greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_56),X_106))))]]) ).
cnf(refute_0_1099,plain,
( multiply(inverse(X_56),greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_56),X_106))) != multiply(inverse(X_56),greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_56),X_106)))
| greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_56),X_106)) != greatest_lower_bound(identity,X_106)
| multiply(inverse(X_56),greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_56),X_106))) = multiply(inverse(X_56),greatest_lower_bound(identity,X_106)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_56),greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_56),X_106))),multiply(inverse(X_56),greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_56),X_106)))) ),[1,1],$fot(greatest_lower_bound(identity,X_106))]]) ).
cnf(refute_0_1100,plain,
( greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_56),X_106)) != greatest_lower_bound(identity,X_106)
| multiply(inverse(X_56),greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_56),X_106))) = multiply(inverse(X_56),greatest_lower_bound(identity,X_106)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_56),greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_56),X_106))),multiply(inverse(X_56),greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_56),X_106)))) )],[refute_0_1098,refute_0_1099]) ).
cnf(refute_0_1101,plain,
multiply(inverse(X_56),greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_56),X_106))) = multiply(inverse(X_56),greatest_lower_bound(identity,X_106)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_56),X_106)),greatest_lower_bound(identity,X_106)) )],[refute_0_1097,refute_0_1100]) ).
cnf(refute_0_1102,plain,
inverse(multiply(inverse(greatest_lower_bound(identity,X_151)),X_31)) = multiply(inverse(X_31),greatest_lower_bound(identity,X_151)),
inference(subst,[],[refute_0_110:[bind(X_145,$fot(greatest_lower_bound(identity,X_151)))]]) ).
cnf(refute_0_1103,plain,
inverse(greatest_lower_bound(identity,X_151)) = inverse(greatest_lower_bound(X_151,identity)),
inference(subst,[],[refute_0_497:[bind(X_150,$fot(X_151))]]) ).
cnf(refute_0_1104,plain,
( inverse(multiply(inverse(greatest_lower_bound(identity,X_151)),X_31)) != multiply(inverse(X_31),greatest_lower_bound(identity,X_151))
| inverse(greatest_lower_bound(identity,X_151)) != inverse(greatest_lower_bound(X_151,identity))
| inverse(multiply(inverse(greatest_lower_bound(X_151,identity)),X_31)) = multiply(inverse(X_31),greatest_lower_bound(identity,X_151)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(greatest_lower_bound(identity,X_151)),X_31)),multiply(inverse(X_31),greatest_lower_bound(identity,X_151))) ),[0,0,0],$fot(inverse(greatest_lower_bound(X_151,identity)))]]) ).
cnf(refute_0_1105,plain,
( inverse(multiply(inverse(greatest_lower_bound(identity,X_151)),X_31)) != multiply(inverse(X_31),greatest_lower_bound(identity,X_151))
| inverse(multiply(inverse(greatest_lower_bound(X_151,identity)),X_31)) = multiply(inverse(X_31),greatest_lower_bound(identity,X_151)) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,X_151)),inverse(greatest_lower_bound(X_151,identity))) )],[refute_0_1103,refute_0_1104]) ).
cnf(refute_0_1106,plain,
inverse(multiply(inverse(greatest_lower_bound(X_151,identity)),X_31)) = multiply(inverse(X_31),greatest_lower_bound(identity,X_151)),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(greatest_lower_bound(identity,X_151)),X_31)),multiply(inverse(X_31),greatest_lower_bound(identity,X_151))) )],[refute_0_1102,refute_0_1105]) ).
cnf(refute_0_1107,plain,
inverse(multiply(inverse(greatest_lower_bound(X_151,identity)),X_31)) = multiply(inverse(X_31),greatest_lower_bound(X_151,identity)),
inference(subst,[],[refute_0_110:[bind(X_145,$fot(greatest_lower_bound(X_151,identity)))]]) ).
cnf(refute_0_1108,plain,
( inverse(multiply(inverse(greatest_lower_bound(X_151,identity)),X_31)) != multiply(inverse(X_31),greatest_lower_bound(X_151,identity))
| inverse(multiply(inverse(greatest_lower_bound(X_151,identity)),X_31)) != multiply(inverse(X_31),greatest_lower_bound(identity,X_151))
| multiply(inverse(X_31),greatest_lower_bound(X_151,identity)) = multiply(inverse(X_31),greatest_lower_bound(identity,X_151)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(greatest_lower_bound(X_151,identity)),X_31)),multiply(inverse(X_31),greatest_lower_bound(identity,X_151))) ),[0],$fot(multiply(inverse(X_31),greatest_lower_bound(X_151,identity)))]]) ).
cnf(refute_0_1109,plain,
( inverse(multiply(inverse(greatest_lower_bound(X_151,identity)),X_31)) != multiply(inverse(X_31),greatest_lower_bound(identity,X_151))
| multiply(inverse(X_31),greatest_lower_bound(X_151,identity)) = multiply(inverse(X_31),greatest_lower_bound(identity,X_151)) ),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(greatest_lower_bound(X_151,identity)),X_31)),multiply(inverse(X_31),greatest_lower_bound(X_151,identity))) )],[refute_0_1107,refute_0_1108]) ).
cnf(refute_0_1110,plain,
multiply(inverse(X_31),greatest_lower_bound(X_151,identity)) = multiply(inverse(X_31),greatest_lower_bound(identity,X_151)),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(greatest_lower_bound(X_151,identity)),X_31)),multiply(inverse(X_31),greatest_lower_bound(identity,X_151))) )],[refute_0_1106,refute_0_1109]) ).
cnf(refute_0_1111,plain,
multiply(inverse(X_56),greatest_lower_bound(greatest_lower_bound(least_upper_bound(identity,X_56),X_106),identity)) = multiply(inverse(X_56),greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_56),X_106))),
inference(subst,[],[refute_0_1110:[bind(X_151,$fot(greatest_lower_bound(least_upper_bound(identity,X_56),X_106))),bind(X_31,$fot(X_56))]]) ).
cnf(refute_0_1112,plain,
greatest_lower_bound(inverse(X_56),multiply(inverse(X_56),greatest_lower_bound(least_upper_bound(identity,X_56),X_106))) = multiply(inverse(X_56),greatest_lower_bound(greatest_lower_bound(least_upper_bound(identity,X_56),X_106),identity)),
inference(subst,[],[refute_0_414:[bind(X_104,$fot(inverse(X_56))),bind(X_105,$fot(greatest_lower_bound(least_upper_bound(identity,X_56),X_106)))]]) ).
cnf(refute_0_1113,plain,
( multiply(inverse(X_56),greatest_lower_bound(greatest_lower_bound(least_upper_bound(identity,X_56),X_106),identity)) != multiply(inverse(X_56),greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_56),X_106)))
| greatest_lower_bound(inverse(X_56),multiply(inverse(X_56),greatest_lower_bound(least_upper_bound(identity,X_56),X_106))) != multiply(inverse(X_56),greatest_lower_bound(greatest_lower_bound(least_upper_bound(identity,X_56),X_106),identity))
| greatest_lower_bound(inverse(X_56),multiply(inverse(X_56),greatest_lower_bound(least_upper_bound(identity,X_56),X_106))) = multiply(inverse(X_56),greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_56),X_106))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(greatest_lower_bound(inverse(X_56),multiply(inverse(X_56),greatest_lower_bound(least_upper_bound(identity,X_56),X_106))))),bind(Y0,$fot(multiply(inverse(X_56),greatest_lower_bound(greatest_lower_bound(least_upper_bound(identity,X_56),X_106),identity)))),bind(Z0,$fot(multiply(inverse(X_56),greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_56),X_106)))))]]) ).
cnf(refute_0_1114,plain,
( multiply(inverse(X_56),greatest_lower_bound(greatest_lower_bound(least_upper_bound(identity,X_56),X_106),identity)) != multiply(inverse(X_56),greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_56),X_106)))
| greatest_lower_bound(inverse(X_56),multiply(inverse(X_56),greatest_lower_bound(least_upper_bound(identity,X_56),X_106))) = multiply(inverse(X_56),greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_56),X_106))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_56),multiply(inverse(X_56),greatest_lower_bound(least_upper_bound(identity,X_56),X_106))),multiply(inverse(X_56),greatest_lower_bound(greatest_lower_bound(least_upper_bound(identity,X_56),X_106),identity))) )],[refute_0_1112,refute_0_1113]) ).
cnf(refute_0_1115,plain,
greatest_lower_bound(inverse(X_56),multiply(inverse(X_56),greatest_lower_bound(least_upper_bound(identity,X_56),X_106))) = multiply(inverse(X_56),greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_56),X_106))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_56),greatest_lower_bound(greatest_lower_bound(least_upper_bound(identity,X_56),X_106),identity)),multiply(inverse(X_56),greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_56),X_106)))) )],[refute_0_1111,refute_0_1114]) ).
cnf(refute_0_1116,plain,
( multiply(inverse(X_56),greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_56),X_106))) != multiply(inverse(X_56),greatest_lower_bound(identity,X_106))
| greatest_lower_bound(inverse(X_56),multiply(inverse(X_56),greatest_lower_bound(least_upper_bound(identity,X_56),X_106))) != multiply(inverse(X_56),greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_56),X_106)))
| greatest_lower_bound(inverse(X_56),multiply(inverse(X_56),greatest_lower_bound(least_upper_bound(identity,X_56),X_106))) = multiply(inverse(X_56),greatest_lower_bound(identity,X_106)) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(greatest_lower_bound(inverse(X_56),multiply(inverse(X_56),greatest_lower_bound(least_upper_bound(identity,X_56),X_106))))),bind(Y0,$fot(multiply(inverse(X_56),greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_56),X_106))))),bind(Z0,$fot(multiply(inverse(X_56),greatest_lower_bound(identity,X_106))))]]) ).
cnf(refute_0_1117,plain,
( multiply(inverse(X_56),greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_56),X_106))) != multiply(inverse(X_56),greatest_lower_bound(identity,X_106))
| greatest_lower_bound(inverse(X_56),multiply(inverse(X_56),greatest_lower_bound(least_upper_bound(identity,X_56),X_106))) = multiply(inverse(X_56),greatest_lower_bound(identity,X_106)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_56),multiply(inverse(X_56),greatest_lower_bound(least_upper_bound(identity,X_56),X_106))),multiply(inverse(X_56),greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_56),X_106)))) )],[refute_0_1115,refute_0_1116]) ).
cnf(refute_0_1118,plain,
greatest_lower_bound(inverse(X_56),multiply(inverse(X_56),greatest_lower_bound(least_upper_bound(identity,X_56),X_106))) = multiply(inverse(X_56),greatest_lower_bound(identity,X_106)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_56),greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_56),X_106))),multiply(inverse(X_56),greatest_lower_bound(identity,X_106))) )],[refute_0_1101,refute_0_1117]) ).
cnf(refute_0_1119,plain,
( greatest_lower_bound(inverse(X_56),multiply(inverse(X_56),greatest_lower_bound(least_upper_bound(identity,X_56),X_106))) != multiply(inverse(X_56),greatest_lower_bound(identity,X_106))
| greatest_lower_bound(inverse(X_56),multiply(inverse(X_56),greatest_lower_bound(least_upper_bound(identity,X_56),X_106))) != greatest_lower_bound(inverse(X_56),multiply(inverse(X_56),X_106))
| multiply(inverse(X_56),greatest_lower_bound(identity,X_106)) = greatest_lower_bound(inverse(X_56),multiply(inverse(X_56),X_106)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(inverse(X_56),multiply(inverse(X_56),greatest_lower_bound(least_upper_bound(identity,X_56),X_106))),greatest_lower_bound(inverse(X_56),multiply(inverse(X_56),X_106))) ),[0],$fot(multiply(inverse(X_56),greatest_lower_bound(identity,X_106)))]]) ).
cnf(refute_0_1120,plain,
( greatest_lower_bound(inverse(X_56),multiply(inverse(X_56),greatest_lower_bound(least_upper_bound(identity,X_56),X_106))) != greatest_lower_bound(inverse(X_56),multiply(inverse(X_56),X_106))
| multiply(inverse(X_56),greatest_lower_bound(identity,X_106)) = greatest_lower_bound(inverse(X_56),multiply(inverse(X_56),X_106)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_56),multiply(inverse(X_56),greatest_lower_bound(least_upper_bound(identity,X_56),X_106))),multiply(inverse(X_56),greatest_lower_bound(identity,X_106))) )],[refute_0_1118,refute_0_1119]) ).
cnf(refute_0_1121,plain,
greatest_lower_bound(inverse(X_56),multiply(inverse(X_56),X_106)) = multiply(inverse(X_56),greatest_lower_bound(X_106,identity)),
inference(subst,[],[refute_0_414:[bind(X_104,$fot(inverse(X_56))),bind(X_105,$fot(X_106))]]) ).
cnf(refute_0_1122,plain,
( multiply(inverse(X_56),greatest_lower_bound(identity,X_106)) != greatest_lower_bound(inverse(X_56),multiply(inverse(X_56),X_106))
| greatest_lower_bound(inverse(X_56),multiply(inverse(X_56),X_106)) != multiply(inverse(X_56),greatest_lower_bound(X_106,identity))
| multiply(inverse(X_56),greatest_lower_bound(identity,X_106)) = multiply(inverse(X_56),greatest_lower_bound(X_106,identity)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_56),greatest_lower_bound(identity,X_106)),multiply(inverse(X_56),greatest_lower_bound(X_106,identity))) ),[0],$fot(greatest_lower_bound(inverse(X_56),multiply(inverse(X_56),X_106)))]]) ).
cnf(refute_0_1123,plain,
( multiply(inverse(X_56),greatest_lower_bound(identity,X_106)) != greatest_lower_bound(inverse(X_56),multiply(inverse(X_56),X_106))
| multiply(inverse(X_56),greatest_lower_bound(identity,X_106)) = multiply(inverse(X_56),greatest_lower_bound(X_106,identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_56),multiply(inverse(X_56),X_106)),multiply(inverse(X_56),greatest_lower_bound(X_106,identity))) )],[refute_0_1121,refute_0_1122]) ).
cnf(refute_0_1124,plain,
( greatest_lower_bound(inverse(X_56),multiply(inverse(X_56),greatest_lower_bound(least_upper_bound(identity,X_56),X_106))) != greatest_lower_bound(inverse(X_56),multiply(inverse(X_56),X_106))
| multiply(inverse(X_56),greatest_lower_bound(identity,X_106)) = multiply(inverse(X_56),greatest_lower_bound(X_106,identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_56),greatest_lower_bound(identity,X_106)),greatest_lower_bound(inverse(X_56),multiply(inverse(X_56),X_106))) )],[refute_0_1120,refute_0_1123]) ).
cnf(refute_0_1125,plain,
multiply(inverse(X_56),greatest_lower_bound(identity,X_106)) = multiply(inverse(X_56),greatest_lower_bound(X_106,identity)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_56),multiply(inverse(X_56),greatest_lower_bound(least_upper_bound(identity,X_56),X_106))),greatest_lower_bound(inverse(X_56),multiply(inverse(X_56),X_106))) )],[refute_0_1091,refute_0_1124]) ).
cnf(refute_0_1126,plain,
( multiply(inverse(X_56),greatest_lower_bound(identity,X_106)) != multiply(inverse(X_56),greatest_lower_bound(X_106,identity))
| multiply(inverse(X_56),greatest_lower_bound(X_106,identity)) = multiply(inverse(X_56),greatest_lower_bound(identity,X_106)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(inverse(X_56),greatest_lower_bound(identity,X_106)))),bind(Y0,$fot(multiply(inverse(X_56),greatest_lower_bound(X_106,identity))))]]) ).
cnf(refute_0_1127,plain,
multiply(inverse(X_56),greatest_lower_bound(X_106,identity)) = multiply(inverse(X_56),greatest_lower_bound(identity,X_106)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_56),greatest_lower_bound(identity,X_106)),multiply(inverse(X_56),greatest_lower_bound(X_106,identity))) )],[refute_0_1125,refute_0_1126]) ).
cnf(refute_0_1128,plain,
multiply(inverse(least_upper_bound(identity,X_208)),greatest_lower_bound(least_upper_bound(identity,inverse(X_208)),identity)) = multiply(inverse(least_upper_bound(identity,X_208)),greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_208)))),
inference(subst,[],[refute_0_1127:[bind(X_106,$fot(least_upper_bound(identity,inverse(X_208)))),bind(X_56,$fot(least_upper_bound(identity,X_208)))]]) ).
cnf(refute_0_1129,plain,
( multiply(inverse(least_upper_bound(identity,X_208)),greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_208)))) != inverse(least_upper_bound(identity,X_208))
| multiply(inverse(least_upper_bound(identity,X_208)),greatest_lower_bound(least_upper_bound(identity,inverse(X_208)),identity)) != multiply(inverse(least_upper_bound(identity,X_208)),greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_208))))
| multiply(inverse(least_upper_bound(identity,X_208)),greatest_lower_bound(least_upper_bound(identity,inverse(X_208)),identity)) = inverse(least_upper_bound(identity,X_208)) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(inverse(least_upper_bound(identity,X_208)),greatest_lower_bound(least_upper_bound(identity,inverse(X_208)),identity)))),bind(Y0,$fot(multiply(inverse(least_upper_bound(identity,X_208)),greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_208)))))),bind(Z0,$fot(inverse(least_upper_bound(identity,X_208))))]]) ).
cnf(refute_0_1130,plain,
( multiply(inverse(least_upper_bound(identity,X_208)),greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_208)))) != inverse(least_upper_bound(identity,X_208))
| multiply(inverse(least_upper_bound(identity,X_208)),greatest_lower_bound(least_upper_bound(identity,inverse(X_208)),identity)) = inverse(least_upper_bound(identity,X_208)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_208)),greatest_lower_bound(least_upper_bound(identity,inverse(X_208)),identity)),multiply(inverse(least_upper_bound(identity,X_208)),greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_208))))) )],[refute_0_1128,refute_0_1129]) ).
cnf(refute_0_1131,plain,
multiply(inverse(least_upper_bound(identity,X_208)),greatest_lower_bound(least_upper_bound(identity,inverse(X_208)),identity)) = inverse(least_upper_bound(identity,X_208)),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_208)),greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_208)))),inverse(least_upper_bound(identity,X_208))) )],[refute_0_1076,refute_0_1130]) ).
cnf(refute_0_1132,plain,
( multiply(inverse(least_upper_bound(identity,X_208)),greatest_lower_bound(least_upper_bound(identity,inverse(X_208)),identity)) != greatest_lower_bound(inverse(least_upper_bound(identity,X_208)),inverse(X_208))
| multiply(inverse(least_upper_bound(identity,X_208)),greatest_lower_bound(least_upper_bound(identity,inverse(X_208)),identity)) != inverse(least_upper_bound(identity,X_208))
| inverse(least_upper_bound(identity,X_208)) = greatest_lower_bound(inverse(least_upper_bound(identity,X_208)),inverse(X_208)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_208)),greatest_lower_bound(least_upper_bound(identity,inverse(X_208)),identity)),greatest_lower_bound(inverse(least_upper_bound(identity,X_208)),inverse(X_208))) ),[0],$fot(inverse(least_upper_bound(identity,X_208)))]]) ).
cnf(refute_0_1133,plain,
( multiply(inverse(least_upper_bound(identity,X_208)),greatest_lower_bound(least_upper_bound(identity,inverse(X_208)),identity)) != greatest_lower_bound(inverse(least_upper_bound(identity,X_208)),inverse(X_208))
| inverse(least_upper_bound(identity,X_208)) = greatest_lower_bound(inverse(least_upper_bound(identity,X_208)),inverse(X_208)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_208)),greatest_lower_bound(least_upper_bound(identity,inverse(X_208)),identity)),inverse(least_upper_bound(identity,X_208))) )],[refute_0_1131,refute_0_1132]) ).
cnf(refute_0_1134,plain,
greatest_lower_bound(inverse(least_upper_bound(identity,X_208)),inverse(X_208)) = greatest_lower_bound(inverse(X_208),inverse(least_upper_bound(identity,X_208))),
inference(subst,[],[refute_0_42:[bind(X,$fot(inverse(X_208))),bind(Y,$fot(inverse(least_upper_bound(identity,X_208))))]]) ).
cnf(refute_0_1135,plain,
( greatest_lower_bound(inverse(least_upper_bound(identity,X_208)),inverse(X_208)) != greatest_lower_bound(inverse(X_208),inverse(least_upper_bound(identity,X_208)))
| inverse(least_upper_bound(identity,X_208)) != greatest_lower_bound(inverse(least_upper_bound(identity,X_208)),inverse(X_208))
| inverse(least_upper_bound(identity,X_208)) = greatest_lower_bound(inverse(X_208),inverse(least_upper_bound(identity,X_208))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,X_208)),greatest_lower_bound(inverse(least_upper_bound(identity,X_208)),inverse(X_208))) ),[1],$fot(greatest_lower_bound(inverse(X_208),inverse(least_upper_bound(identity,X_208))))]]) ).
cnf(refute_0_1136,plain,
( inverse(least_upper_bound(identity,X_208)) != greatest_lower_bound(inverse(least_upper_bound(identity,X_208)),inverse(X_208))
| inverse(least_upper_bound(identity,X_208)) = greatest_lower_bound(inverse(X_208),inverse(least_upper_bound(identity,X_208))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(least_upper_bound(identity,X_208)),inverse(X_208)),greatest_lower_bound(inverse(X_208),inverse(least_upper_bound(identity,X_208)))) )],[refute_0_1134,refute_0_1135]) ).
cnf(refute_0_1137,plain,
( multiply(inverse(least_upper_bound(identity,X_208)),greatest_lower_bound(least_upper_bound(identity,inverse(X_208)),identity)) != greatest_lower_bound(inverse(least_upper_bound(identity,X_208)),inverse(X_208))
| inverse(least_upper_bound(identity,X_208)) = greatest_lower_bound(inverse(X_208),inverse(least_upper_bound(identity,X_208))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,X_208)),greatest_lower_bound(inverse(least_upper_bound(identity,X_208)),inverse(X_208))) )],[refute_0_1133,refute_0_1136]) ).
cnf(refute_0_1138,plain,
inverse(least_upper_bound(identity,X_208)) = greatest_lower_bound(inverse(X_208),inverse(least_upper_bound(identity,X_208))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_208)),greatest_lower_bound(least_upper_bound(identity,inverse(X_208)),identity)),greatest_lower_bound(inverse(least_upper_bound(identity,X_208)),inverse(X_208))) )],[refute_0_1067,refute_0_1137]) ).
cnf(refute_0_1139,plain,
( inverse(least_upper_bound(identity,X_208)) != greatest_lower_bound(inverse(X_208),inverse(least_upper_bound(identity,X_208)))
| greatest_lower_bound(inverse(X_208),inverse(least_upper_bound(identity,X_208))) = inverse(least_upper_bound(identity,X_208)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(inverse(least_upper_bound(identity,X_208)))),bind(Y0,$fot(greatest_lower_bound(inverse(X_208),inverse(least_upper_bound(identity,X_208)))))]]) ).
cnf(refute_0_1140,plain,
greatest_lower_bound(inverse(X_208),inverse(least_upper_bound(identity,X_208))) = inverse(least_upper_bound(identity,X_208)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,X_208)),greatest_lower_bound(inverse(X_208),inverse(least_upper_bound(identity,X_208)))) )],[refute_0_1138,refute_0_1139]) ).
cnf(refute_0_1141,plain,
greatest_lower_bound(inverse(X_286),inverse(least_upper_bound(identity,X_286))) = inverse(least_upper_bound(identity,X_286)),
inference(subst,[],[refute_0_1140:[bind(X_208,$fot(X_286))]]) ).
cnf(refute_0_1142,plain,
multiply(least_upper_bound(identity,inverse(X_286)),greatest_lower_bound(inverse(X_286),inverse(least_upper_bound(identity,X_286)))) = multiply(least_upper_bound(identity,inverse(X_286)),greatest_lower_bound(inverse(X_286),inverse(least_upper_bound(identity,X_286)))),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(identity,inverse(X_286)),greatest_lower_bound(inverse(X_286),inverse(least_upper_bound(identity,X_286)))))]]) ).
cnf(refute_0_1143,plain,
( multiply(least_upper_bound(identity,inverse(X_286)),greatest_lower_bound(inverse(X_286),inverse(least_upper_bound(identity,X_286)))) != multiply(least_upper_bound(identity,inverse(X_286)),greatest_lower_bound(inverse(X_286),inverse(least_upper_bound(identity,X_286))))
| greatest_lower_bound(inverse(X_286),inverse(least_upper_bound(identity,X_286))) != inverse(least_upper_bound(identity,X_286))
| multiply(least_upper_bound(identity,inverse(X_286)),greatest_lower_bound(inverse(X_286),inverse(least_upper_bound(identity,X_286)))) = multiply(least_upper_bound(identity,inverse(X_286)),inverse(least_upper_bound(identity,X_286))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_286)),greatest_lower_bound(inverse(X_286),inverse(least_upper_bound(identity,X_286)))),multiply(least_upper_bound(identity,inverse(X_286)),greatest_lower_bound(inverse(X_286),inverse(least_upper_bound(identity,X_286))))) ),[1,1],$fot(inverse(least_upper_bound(identity,X_286)))]]) ).
cnf(refute_0_1144,plain,
( greatest_lower_bound(inverse(X_286),inverse(least_upper_bound(identity,X_286))) != inverse(least_upper_bound(identity,X_286))
| multiply(least_upper_bound(identity,inverse(X_286)),greatest_lower_bound(inverse(X_286),inverse(least_upper_bound(identity,X_286)))) = multiply(least_upper_bound(identity,inverse(X_286)),inverse(least_upper_bound(identity,X_286))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_286)),greatest_lower_bound(inverse(X_286),inverse(least_upper_bound(identity,X_286)))),multiply(least_upper_bound(identity,inverse(X_286)),greatest_lower_bound(inverse(X_286),inverse(least_upper_bound(identity,X_286))))) )],[refute_0_1142,refute_0_1143]) ).
cnf(refute_0_1145,plain,
multiply(least_upper_bound(identity,inverse(X_286)),greatest_lower_bound(inverse(X_286),inverse(least_upper_bound(identity,X_286)))) = multiply(least_upper_bound(identity,inverse(X_286)),inverse(least_upper_bound(identity,X_286))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_286),inverse(least_upper_bound(identity,X_286))),inverse(least_upper_bound(identity,X_286))) )],[refute_0_1141,refute_0_1144]) ).
cnf(refute_0_1146,plain,
inverse(inverse(least_upper_bound(identity,inverse(X_286)))) = least_upper_bound(identity,inverse(X_286)),
inference(subst,[],[refute_0_452:[bind(X_35,$fot(least_upper_bound(identity,inverse(X_286))))]]) ).
cnf(refute_0_1147,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_644:[bind(X_114,$fot(least_upper_bound(identity,Y)))]]) ).
cnf(refute_0_1148,plain,
greatest_lower_bound(identity,least_upper_bound(identity,Y)) = identity,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(identity))]]) ).
cnf(refute_0_1149,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_1150,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( $equal(greatest_lower_bound(identity,least_upper_bound(identity,Y)),identity) )],[refute_0_1148,refute_0_1149]) ).
cnf(refute_0_1151,plain,
multiply(inverse(least_upper_bound(identity,Y)),identity) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,Y)),greatest_lower_bound(identity,least_upper_bound(identity,Y))),greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y)))) )],[refute_0_1147,refute_0_1150]) ).
cnf(refute_0_1152,plain,
multiply(inverse(least_upper_bound(identity,Y)),identity) = inverse(least_upper_bound(identity,Y)),
inference(subst,[],[refute_0_88:[bind(X_33,$fot(inverse(least_upper_bound(identity,Y))))]]) ).
cnf(refute_0_1153,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_1154,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( $equal(multiply(inverse(least_upper_bound(identity,Y)),identity),inverse(least_upper_bound(identity,Y))) )],[refute_0_1152,refute_0_1153]) ).
cnf(refute_0_1155,plain,
inverse(least_upper_bound(identity,Y)) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,Y)),identity),greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y)))) )],[refute_0_1151,refute_0_1154]) ).
cnf(refute_0_1156,plain,
( inverse(least_upper_bound(identity,Y)) != greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y)))
| greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y))) = inverse(least_upper_bound(identity,Y)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(inverse(least_upper_bound(identity,Y)))),bind(Y0,$fot(greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y)))))]]) ).
cnf(refute_0_1157,plain,
greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y))) = inverse(least_upper_bound(identity,Y)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,Y)),greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y)))) )],[refute_0_1155,refute_0_1156]) ).
cnf(refute_0_1158,plain,
greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286)))) = inverse(least_upper_bound(identity,inverse(X_286))),
inference(subst,[],[refute_0_1157:[bind(Y,$fot(inverse(X_286)))]]) ).
cnf(refute_0_1159,plain,
inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))) = inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))),
introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))))]]) ).
cnf(refute_0_1160,plain,
( greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286)))) != inverse(least_upper_bound(identity,inverse(X_286)))
| inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))) != inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286)))))
| inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))) = inverse(inverse(least_upper_bound(identity,inverse(X_286)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))),inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286)))))) ),[1,0],$fot(inverse(least_upper_bound(identity,inverse(X_286))))]]) ).
cnf(refute_0_1161,plain,
( greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286)))) != inverse(least_upper_bound(identity,inverse(X_286)))
| inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))) = inverse(inverse(least_upper_bound(identity,inverse(X_286)))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))),inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286)))))) )],[refute_0_1159,refute_0_1160]) ).
cnf(refute_0_1162,plain,
inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))) = inverse(inverse(least_upper_bound(identity,inverse(X_286)))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286)))),inverse(least_upper_bound(identity,inverse(X_286)))) )],[refute_0_1158,refute_0_1161]) ).
cnf(refute_0_1163,plain,
( inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))) != inverse(inverse(least_upper_bound(identity,inverse(X_286))))
| inverse(inverse(least_upper_bound(identity,inverse(X_286)))) != least_upper_bound(identity,inverse(X_286))
| inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))) = least_upper_bound(identity,inverse(X_286)) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))))),bind(Y0,$fot(inverse(inverse(least_upper_bound(identity,inverse(X_286)))))),bind(Z0,$fot(least_upper_bound(identity,inverse(X_286))))]]) ).
cnf(refute_0_1164,plain,
( inverse(inverse(least_upper_bound(identity,inverse(X_286)))) != least_upper_bound(identity,inverse(X_286))
| inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))) = least_upper_bound(identity,inverse(X_286)) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))),inverse(inverse(least_upper_bound(identity,inverse(X_286))))) )],[refute_0_1162,refute_0_1163]) ).
cnf(refute_0_1165,plain,
inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))) = least_upper_bound(identity,inverse(X_286)),
inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(identity,inverse(X_286)))),least_upper_bound(identity,inverse(X_286))) )],[refute_0_1146,refute_0_1164]) ).
cnf(refute_0_1166,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))),greatest_lower_bound(inverse(X_286),inverse(least_upper_bound(identity,X_286)))) = multiply(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))),greatest_lower_bound(inverse(X_286),inverse(least_upper_bound(identity,X_286)))),
introduced(tautology,[refl,[$fot(multiply(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))),greatest_lower_bound(inverse(X_286),inverse(least_upper_bound(identity,X_286)))))]]) ).
cnf(refute_0_1167,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))),greatest_lower_bound(inverse(X_286),inverse(least_upper_bound(identity,X_286)))) != multiply(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))),greatest_lower_bound(inverse(X_286),inverse(least_upper_bound(identity,X_286))))
| inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))) != least_upper_bound(identity,inverse(X_286))
| multiply(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))),greatest_lower_bound(inverse(X_286),inverse(least_upper_bound(identity,X_286)))) = multiply(least_upper_bound(identity,inverse(X_286)),greatest_lower_bound(inverse(X_286),inverse(least_upper_bound(identity,X_286)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))),greatest_lower_bound(inverse(X_286),inverse(least_upper_bound(identity,X_286)))),multiply(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))),greatest_lower_bound(inverse(X_286),inverse(least_upper_bound(identity,X_286))))) ),[1,0],$fot(least_upper_bound(identity,inverse(X_286)))]]) ).
cnf(refute_0_1168,plain,
( inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))) != least_upper_bound(identity,inverse(X_286))
| multiply(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))),greatest_lower_bound(inverse(X_286),inverse(least_upper_bound(identity,X_286)))) = multiply(least_upper_bound(identity,inverse(X_286)),greatest_lower_bound(inverse(X_286),inverse(least_upper_bound(identity,X_286)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))),greatest_lower_bound(inverse(X_286),inverse(least_upper_bound(identity,X_286)))),multiply(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))),greatest_lower_bound(inverse(X_286),inverse(least_upper_bound(identity,X_286))))) )],[refute_0_1166,refute_0_1167]) ).
cnf(refute_0_1169,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))),greatest_lower_bound(inverse(X_286),inverse(least_upper_bound(identity,X_286)))) = multiply(least_upper_bound(identity,inverse(X_286)),greatest_lower_bound(inverse(X_286),inverse(least_upper_bound(identity,X_286)))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))),least_upper_bound(identity,inverse(X_286))) )],[refute_0_1165,refute_0_1168]) ).
cnf(refute_0_1170,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))),greatest_lower_bound(inverse(X_286),inverse(least_upper_bound(identity,X_286)))) != multiply(least_upper_bound(identity,inverse(X_286)),greatest_lower_bound(inverse(X_286),inverse(least_upper_bound(identity,X_286))))
| multiply(least_upper_bound(identity,inverse(X_286)),greatest_lower_bound(inverse(X_286),inverse(least_upper_bound(identity,X_286)))) != multiply(least_upper_bound(identity,inverse(X_286)),inverse(least_upper_bound(identity,X_286)))
| multiply(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))),greatest_lower_bound(inverse(X_286),inverse(least_upper_bound(identity,X_286)))) = multiply(least_upper_bound(identity,inverse(X_286)),inverse(least_upper_bound(identity,X_286))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))),greatest_lower_bound(inverse(X_286),inverse(least_upper_bound(identity,X_286)))))),bind(Y0,$fot(multiply(least_upper_bound(identity,inverse(X_286)),greatest_lower_bound(inverse(X_286),inverse(least_upper_bound(identity,X_286)))))),bind(Z0,$fot(multiply(least_upper_bound(identity,inverse(X_286)),inverse(least_upper_bound(identity,X_286)))))]]) ).
cnf(refute_0_1171,plain,
( multiply(least_upper_bound(identity,inverse(X_286)),greatest_lower_bound(inverse(X_286),inverse(least_upper_bound(identity,X_286)))) != multiply(least_upper_bound(identity,inverse(X_286)),inverse(least_upper_bound(identity,X_286)))
| multiply(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))),greatest_lower_bound(inverse(X_286),inverse(least_upper_bound(identity,X_286)))) = multiply(least_upper_bound(identity,inverse(X_286)),inverse(least_upper_bound(identity,X_286))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))),greatest_lower_bound(inverse(X_286),inverse(least_upper_bound(identity,X_286)))),multiply(least_upper_bound(identity,inverse(X_286)),greatest_lower_bound(inverse(X_286),inverse(least_upper_bound(identity,X_286))))) )],[refute_0_1169,refute_0_1170]) ).
cnf(refute_0_1172,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))),greatest_lower_bound(inverse(X_286),inverse(least_upper_bound(identity,X_286)))) = multiply(least_upper_bound(identity,inverse(X_286)),inverse(least_upper_bound(identity,X_286))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_286)),greatest_lower_bound(inverse(X_286),inverse(least_upper_bound(identity,X_286)))),multiply(least_upper_bound(identity,inverse(X_286)),inverse(least_upper_bound(identity,X_286)))) )],[refute_0_1145,refute_0_1171]) ).
cnf(refute_0_1173,plain,
inverse(multiply(inverse(greatest_lower_bound(X_249,X_250)),X_31)) = multiply(inverse(X_31),greatest_lower_bound(X_249,X_250)),
inference(subst,[],[refute_0_110:[bind(X_145,$fot(greatest_lower_bound(X_249,X_250)))]]) ).
cnf(refute_0_1174,plain,
X_31 = multiply(inverse(least_upper_bound(X_71,inverse(X_31))),multiply(least_upper_bound(X_71,inverse(X_31)),X_31)),
inference(subst,[],[refute_0_9:[bind(X_30,$fot(least_upper_bound(X_71,inverse(X_31))))]]) ).
cnf(refute_0_1175,plain,
multiply(least_upper_bound(X_71,inverse(X_31)),X_31) = least_upper_bound(identity,multiply(X_71,X_31)),
inference(subst,[],[refute_0_795:[bind(X_67,$fot(X_31)),bind(X_68,$fot(X_71))]]) ).
cnf(refute_0_1176,plain,
( X_31 != multiply(inverse(least_upper_bound(X_71,inverse(X_31))),multiply(least_upper_bound(X_71,inverse(X_31)),X_31))
| multiply(least_upper_bound(X_71,inverse(X_31)),X_31) != least_upper_bound(identity,multiply(X_71,X_31))
| X_31 = multiply(inverse(least_upper_bound(X_71,inverse(X_31))),least_upper_bound(identity,multiply(X_71,X_31))) ),
introduced(tautology,[equality,[$cnf( $equal(X_31,multiply(inverse(least_upper_bound(X_71,inverse(X_31))),multiply(least_upper_bound(X_71,inverse(X_31)),X_31))) ),[1,1],$fot(least_upper_bound(identity,multiply(X_71,X_31)))]]) ).
cnf(refute_0_1177,plain,
( X_31 != multiply(inverse(least_upper_bound(X_71,inverse(X_31))),multiply(least_upper_bound(X_71,inverse(X_31)),X_31))
| X_31 = multiply(inverse(least_upper_bound(X_71,inverse(X_31))),least_upper_bound(identity,multiply(X_71,X_31))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_71,inverse(X_31)),X_31),least_upper_bound(identity,multiply(X_71,X_31))) )],[refute_0_1175,refute_0_1176]) ).
cnf(refute_0_1178,plain,
X_31 = multiply(inverse(least_upper_bound(X_71,inverse(X_31))),least_upper_bound(identity,multiply(X_71,X_31))),
inference(resolve,[$cnf( $equal(X_31,multiply(inverse(least_upper_bound(X_71,inverse(X_31))),multiply(least_upper_bound(X_71,inverse(X_31)),X_31))) )],[refute_0_1174,refute_0_1177]) ).
cnf(refute_0_1179,plain,
inverse(greatest_lower_bound(X_247,X_248)) = multiply(inverse(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248))))),least_upper_bound(identity,multiply(greatest_lower_bound(X_248,X_247),inverse(greatest_lower_bound(X_247,X_248))))),
inference(subst,[],[refute_0_1178:[bind(X_31,$fot(inverse(greatest_lower_bound(X_247,X_248)))),bind(X_71,$fot(greatest_lower_bound(X_248,X_247)))]]) ).
cnf(refute_0_1180,plain,
multiply(least_upper_bound(greatest_lower_bound(X_84,X_83),greatest_lower_bound(X_83,X_84)),inverse(greatest_lower_bound(X_83,X_84))) = least_upper_bound(identity,multiply(greatest_lower_bound(X_84,X_83),inverse(greatest_lower_bound(X_83,X_84)))),
inference(subst,[],[refute_0_780:[bind(X_68,$fot(greatest_lower_bound(X_84,X_83))),bind(X_69,$fot(greatest_lower_bound(X_83,X_84)))]]) ).
cnf(refute_0_1181,plain,
least_upper_bound(greatest_lower_bound(X_84,X_83),greatest_lower_bound(X_83,X_84)) = greatest_lower_bound(X_84,X_83),
inference(subst,[],[refute_0_371:[bind(X_11,$fot(X_83)),bind(X_16,$fot(X_84))]]) ).
cnf(refute_0_1182,plain,
( multiply(least_upper_bound(greatest_lower_bound(X_84,X_83),greatest_lower_bound(X_83,X_84)),inverse(greatest_lower_bound(X_83,X_84))) != least_upper_bound(identity,multiply(greatest_lower_bound(X_84,X_83),inverse(greatest_lower_bound(X_83,X_84))))
| least_upper_bound(greatest_lower_bound(X_84,X_83),greatest_lower_bound(X_83,X_84)) != greatest_lower_bound(X_84,X_83)
| multiply(greatest_lower_bound(X_84,X_83),inverse(greatest_lower_bound(X_83,X_84))) = least_upper_bound(identity,multiply(greatest_lower_bound(X_84,X_83),inverse(greatest_lower_bound(X_83,X_84)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(X_84,X_83),greatest_lower_bound(X_83,X_84)),inverse(greatest_lower_bound(X_83,X_84))),least_upper_bound(identity,multiply(greatest_lower_bound(X_84,X_83),inverse(greatest_lower_bound(X_83,X_84))))) ),[0,0],$fot(greatest_lower_bound(X_84,X_83))]]) ).
cnf(refute_0_1183,plain,
( multiply(least_upper_bound(greatest_lower_bound(X_84,X_83),greatest_lower_bound(X_83,X_84)),inverse(greatest_lower_bound(X_83,X_84))) != least_upper_bound(identity,multiply(greatest_lower_bound(X_84,X_83),inverse(greatest_lower_bound(X_83,X_84))))
| multiply(greatest_lower_bound(X_84,X_83),inverse(greatest_lower_bound(X_83,X_84))) = least_upper_bound(identity,multiply(greatest_lower_bound(X_84,X_83),inverse(greatest_lower_bound(X_83,X_84)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_84,X_83),greatest_lower_bound(X_83,X_84)),greatest_lower_bound(X_84,X_83)) )],[refute_0_1181,refute_0_1182]) ).
cnf(refute_0_1184,plain,
multiply(greatest_lower_bound(X_84,X_83),inverse(greatest_lower_bound(X_83,X_84))) = least_upper_bound(identity,multiply(greatest_lower_bound(X_84,X_83),inverse(greatest_lower_bound(X_83,X_84)))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(X_84,X_83),greatest_lower_bound(X_83,X_84)),inverse(greatest_lower_bound(X_83,X_84))),least_upper_bound(identity,multiply(greatest_lower_bound(X_84,X_83),inverse(greatest_lower_bound(X_83,X_84))))) )],[refute_0_1180,refute_0_1183]) ).
cnf(refute_0_1185,plain,
multiply(least_upper_bound(X_68,X_69),inverse(X_68)) = least_upper_bound(multiply(X_68,inverse(X_68)),multiply(X_69,inverse(X_68))),
inference(subst,[],[monotony_lub2:[bind(X,$fot(inverse(X_68))),bind(Y,$fot(X_68)),bind(Z,$fot(X_69))]]) ).
cnf(refute_0_1186,plain,
multiply(X_68,inverse(X_68)) = identity,
inference(subst,[],[refute_0_71:[bind(X_35,$fot(X_68))]]) ).
cnf(refute_0_1187,plain,
( multiply(X_68,inverse(X_68)) != identity
| multiply(least_upper_bound(X_68,X_69),inverse(X_68)) != least_upper_bound(multiply(X_68,inverse(X_68)),multiply(X_69,inverse(X_68)))
| multiply(least_upper_bound(X_68,X_69),inverse(X_68)) = least_upper_bound(identity,multiply(X_69,inverse(X_68))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_68,X_69),inverse(X_68)),least_upper_bound(multiply(X_68,inverse(X_68)),multiply(X_69,inverse(X_68)))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_1188,plain,
( multiply(least_upper_bound(X_68,X_69),inverse(X_68)) != least_upper_bound(multiply(X_68,inverse(X_68)),multiply(X_69,inverse(X_68)))
| multiply(least_upper_bound(X_68,X_69),inverse(X_68)) = least_upper_bound(identity,multiply(X_69,inverse(X_68))) ),
inference(resolve,[$cnf( $equal(multiply(X_68,inverse(X_68)),identity) )],[refute_0_1186,refute_0_1187]) ).
cnf(refute_0_1189,plain,
multiply(least_upper_bound(X_68,X_69),inverse(X_68)) = least_upper_bound(identity,multiply(X_69,inverse(X_68))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_68,X_69),inverse(X_68)),least_upper_bound(multiply(X_68,inverse(X_68)),multiply(X_69,inverse(X_68)))) )],[refute_0_1185,refute_0_1188]) ).
cnf(refute_0_1190,plain,
multiply(least_upper_bound(greatest_lower_bound(X_84,X_83),greatest_lower_bound(X_83,X_84)),inverse(greatest_lower_bound(X_84,X_83))) = least_upper_bound(identity,multiply(greatest_lower_bound(X_83,X_84),inverse(greatest_lower_bound(X_84,X_83)))),
inference(subst,[],[refute_0_1189:[bind(X_68,$fot(greatest_lower_bound(X_84,X_83))),bind(X_69,$fot(greatest_lower_bound(X_83,X_84)))]]) ).
cnf(refute_0_1191,plain,
( multiply(least_upper_bound(greatest_lower_bound(X_84,X_83),greatest_lower_bound(X_83,X_84)),inverse(greatest_lower_bound(X_84,X_83))) != least_upper_bound(identity,multiply(greatest_lower_bound(X_83,X_84),inverse(greatest_lower_bound(X_84,X_83))))
| least_upper_bound(greatest_lower_bound(X_84,X_83),greatest_lower_bound(X_83,X_84)) != greatest_lower_bound(X_84,X_83)
| multiply(greatest_lower_bound(X_84,X_83),inverse(greatest_lower_bound(X_84,X_83))) = least_upper_bound(identity,multiply(greatest_lower_bound(X_83,X_84),inverse(greatest_lower_bound(X_84,X_83)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(X_84,X_83),greatest_lower_bound(X_83,X_84)),inverse(greatest_lower_bound(X_84,X_83))),least_upper_bound(identity,multiply(greatest_lower_bound(X_83,X_84),inverse(greatest_lower_bound(X_84,X_83))))) ),[0,0],$fot(greatest_lower_bound(X_84,X_83))]]) ).
cnf(refute_0_1192,plain,
( multiply(least_upper_bound(greatest_lower_bound(X_84,X_83),greatest_lower_bound(X_83,X_84)),inverse(greatest_lower_bound(X_84,X_83))) != least_upper_bound(identity,multiply(greatest_lower_bound(X_83,X_84),inverse(greatest_lower_bound(X_84,X_83))))
| multiply(greatest_lower_bound(X_84,X_83),inverse(greatest_lower_bound(X_84,X_83))) = least_upper_bound(identity,multiply(greatest_lower_bound(X_83,X_84),inverse(greatest_lower_bound(X_84,X_83)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_84,X_83),greatest_lower_bound(X_83,X_84)),greatest_lower_bound(X_84,X_83)) )],[refute_0_1181,refute_0_1191]) ).
cnf(refute_0_1193,plain,
multiply(greatest_lower_bound(X_84,X_83),inverse(greatest_lower_bound(X_84,X_83))) = least_upper_bound(identity,multiply(greatest_lower_bound(X_83,X_84),inverse(greatest_lower_bound(X_84,X_83)))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(X_84,X_83),greatest_lower_bound(X_83,X_84)),inverse(greatest_lower_bound(X_84,X_83))),least_upper_bound(identity,multiply(greatest_lower_bound(X_83,X_84),inverse(greatest_lower_bound(X_84,X_83))))) )],[refute_0_1190,refute_0_1192]) ).
cnf(refute_0_1194,plain,
multiply(greatest_lower_bound(X_84,X_83),inverse(greatest_lower_bound(X_84,X_83))) = identity,
inference(subst,[],[refute_0_71:[bind(X_35,$fot(greatest_lower_bound(X_84,X_83)))]]) ).
cnf(refute_0_1195,plain,
( multiply(greatest_lower_bound(X_84,X_83),inverse(greatest_lower_bound(X_84,X_83))) != identity
| multiply(greatest_lower_bound(X_84,X_83),inverse(greatest_lower_bound(X_84,X_83))) != least_upper_bound(identity,multiply(greatest_lower_bound(X_83,X_84),inverse(greatest_lower_bound(X_84,X_83))))
| identity = least_upper_bound(identity,multiply(greatest_lower_bound(X_83,X_84),inverse(greatest_lower_bound(X_84,X_83)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_84,X_83),inverse(greatest_lower_bound(X_84,X_83))),least_upper_bound(identity,multiply(greatest_lower_bound(X_83,X_84),inverse(greatest_lower_bound(X_84,X_83))))) ),[0],$fot(identity)]]) ).
cnf(refute_0_1196,plain,
( multiply(greatest_lower_bound(X_84,X_83),inverse(greatest_lower_bound(X_84,X_83))) != least_upper_bound(identity,multiply(greatest_lower_bound(X_83,X_84),inverse(greatest_lower_bound(X_84,X_83))))
| identity = least_upper_bound(identity,multiply(greatest_lower_bound(X_83,X_84),inverse(greatest_lower_bound(X_84,X_83)))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_84,X_83),inverse(greatest_lower_bound(X_84,X_83))),identity) )],[refute_0_1194,refute_0_1195]) ).
cnf(refute_0_1197,plain,
identity = least_upper_bound(identity,multiply(greatest_lower_bound(X_83,X_84),inverse(greatest_lower_bound(X_84,X_83)))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_84,X_83),inverse(greatest_lower_bound(X_84,X_83))),least_upper_bound(identity,multiply(greatest_lower_bound(X_83,X_84),inverse(greatest_lower_bound(X_84,X_83))))) )],[refute_0_1193,refute_0_1196]) ).
cnf(refute_0_1198,plain,
( identity != least_upper_bound(identity,multiply(greatest_lower_bound(X_83,X_84),inverse(greatest_lower_bound(X_84,X_83))))
| least_upper_bound(identity,multiply(greatest_lower_bound(X_83,X_84),inverse(greatest_lower_bound(X_84,X_83)))) = identity ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(identity)),bind(Y0,$fot(least_upper_bound(identity,multiply(greatest_lower_bound(X_83,X_84),inverse(greatest_lower_bound(X_84,X_83))))))]]) ).
cnf(refute_0_1199,plain,
least_upper_bound(identity,multiply(greatest_lower_bound(X_83,X_84),inverse(greatest_lower_bound(X_84,X_83)))) = identity,
inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,multiply(greatest_lower_bound(X_83,X_84),inverse(greatest_lower_bound(X_84,X_83))))) )],[refute_0_1197,refute_0_1198]) ).
cnf(refute_0_1200,plain,
least_upper_bound(identity,multiply(greatest_lower_bound(X_84,X_83),inverse(greatest_lower_bound(X_83,X_84)))) = identity,
inference(subst,[],[refute_0_1199:[bind(X_83,$fot(X_84)),bind(X_84,$fot(X_83))]]) ).
cnf(refute_0_1201,plain,
( multiply(greatest_lower_bound(X_84,X_83),inverse(greatest_lower_bound(X_83,X_84))) != least_upper_bound(identity,multiply(greatest_lower_bound(X_84,X_83),inverse(greatest_lower_bound(X_83,X_84))))
| least_upper_bound(identity,multiply(greatest_lower_bound(X_84,X_83),inverse(greatest_lower_bound(X_83,X_84)))) != identity
| multiply(greatest_lower_bound(X_84,X_83),inverse(greatest_lower_bound(X_83,X_84))) = identity ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_84,X_83),inverse(greatest_lower_bound(X_83,X_84))),identity) ),[0],$fot(least_upper_bound(identity,multiply(greatest_lower_bound(X_84,X_83),inverse(greatest_lower_bound(X_83,X_84)))))]]) ).
cnf(refute_0_1202,plain,
( multiply(greatest_lower_bound(X_84,X_83),inverse(greatest_lower_bound(X_83,X_84))) != least_upper_bound(identity,multiply(greatest_lower_bound(X_84,X_83),inverse(greatest_lower_bound(X_83,X_84))))
| multiply(greatest_lower_bound(X_84,X_83),inverse(greatest_lower_bound(X_83,X_84))) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(greatest_lower_bound(X_84,X_83),inverse(greatest_lower_bound(X_83,X_84)))),identity) )],[refute_0_1200,refute_0_1201]) ).
cnf(refute_0_1203,plain,
multiply(greatest_lower_bound(X_84,X_83),inverse(greatest_lower_bound(X_83,X_84))) = identity,
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_84,X_83),inverse(greatest_lower_bound(X_83,X_84))),least_upper_bound(identity,multiply(greatest_lower_bound(X_84,X_83),inverse(greatest_lower_bound(X_83,X_84))))) )],[refute_0_1184,refute_0_1202]) ).
cnf(refute_0_1204,plain,
multiply(greatest_lower_bound(X_248,X_247),inverse(greatest_lower_bound(X_247,X_248))) = identity,
inference(subst,[],[refute_0_1203:[bind(X_83,$fot(X_247)),bind(X_84,$fot(X_248))]]) ).
cnf(refute_0_1205,plain,
( multiply(greatest_lower_bound(X_248,X_247),inverse(greatest_lower_bound(X_247,X_248))) != identity
| inverse(greatest_lower_bound(X_247,X_248)) != multiply(inverse(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248))))),least_upper_bound(identity,multiply(greatest_lower_bound(X_248,X_247),inverse(greatest_lower_bound(X_247,X_248)))))
| inverse(greatest_lower_bound(X_247,X_248)) = multiply(inverse(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248))))),least_upper_bound(identity,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X_247,X_248)),multiply(inverse(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248))))),least_upper_bound(identity,multiply(greatest_lower_bound(X_248,X_247),inverse(greatest_lower_bound(X_247,X_248)))))) ),[1,1,1],$fot(identity)]]) ).
cnf(refute_0_1206,plain,
( inverse(greatest_lower_bound(X_247,X_248)) != multiply(inverse(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248))))),least_upper_bound(identity,multiply(greatest_lower_bound(X_248,X_247),inverse(greatest_lower_bound(X_247,X_248)))))
| inverse(greatest_lower_bound(X_247,X_248)) = multiply(inverse(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248))))),least_upper_bound(identity,identity)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_248,X_247),inverse(greatest_lower_bound(X_247,X_248))),identity) )],[refute_0_1204,refute_0_1205]) ).
cnf(refute_0_1207,plain,
inverse(greatest_lower_bound(X_247,X_248)) = multiply(inverse(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248))))),least_upper_bound(identity,identity)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_247,X_248)),multiply(inverse(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248))))),least_upper_bound(identity,multiply(greatest_lower_bound(X_248,X_247),inverse(greatest_lower_bound(X_247,X_248)))))) )],[refute_0_1179,refute_0_1206]) ).
cnf(refute_0_1208,plain,
multiply(inverse(greatest_lower_bound(X_248,X_247)),identity) = inverse(greatest_lower_bound(X_248,X_247)),
inference(subst,[],[refute_0_88:[bind(X_33,$fot(inverse(greatest_lower_bound(X_248,X_247))))]]) ).
cnf(refute_0_1209,plain,
least_upper_bound(identity,identity) = identity,
inference(subst,[],[idempotence_of_lub:[bind(X,$fot(identity))]]) ).
cnf(refute_0_1210,plain,
multiply(inverse(greatest_lower_bound(X_248,X_247)),least_upper_bound(identity,identity)) = multiply(inverse(greatest_lower_bound(X_248,X_247)),least_upper_bound(identity,identity)),
introduced(tautology,[refl,[$fot(multiply(inverse(greatest_lower_bound(X_248,X_247)),least_upper_bound(identity,identity)))]]) ).
cnf(refute_0_1211,plain,
( multiply(inverse(greatest_lower_bound(X_248,X_247)),least_upper_bound(identity,identity)) != multiply(inverse(greatest_lower_bound(X_248,X_247)),least_upper_bound(identity,identity))
| least_upper_bound(identity,identity) != identity
| multiply(inverse(greatest_lower_bound(X_248,X_247)),least_upper_bound(identity,identity)) = multiply(inverse(greatest_lower_bound(X_248,X_247)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_248,X_247)),least_upper_bound(identity,identity)),multiply(inverse(greatest_lower_bound(X_248,X_247)),least_upper_bound(identity,identity))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_1212,plain,
( least_upper_bound(identity,identity) != identity
| multiply(inverse(greatest_lower_bound(X_248,X_247)),least_upper_bound(identity,identity)) = multiply(inverse(greatest_lower_bound(X_248,X_247)),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_248,X_247)),least_upper_bound(identity,identity)),multiply(inverse(greatest_lower_bound(X_248,X_247)),least_upper_bound(identity,identity))) )],[refute_0_1210,refute_0_1211]) ).
cnf(refute_0_1213,plain,
multiply(inverse(greatest_lower_bound(X_248,X_247)),least_upper_bound(identity,identity)) = multiply(inverse(greatest_lower_bound(X_248,X_247)),identity),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,identity),identity) )],[refute_0_1209,refute_0_1212]) ).
cnf(refute_0_1214,plain,
least_upper_bound(greatest_lower_bound(X_248,X_247),greatest_lower_bound(X_247,X_248)) = greatest_lower_bound(X_248,X_247),
inference(subst,[],[refute_0_371:[bind(X_11,$fot(X_247)),bind(X_16,$fot(X_248))]]) ).
cnf(refute_0_1215,plain,
inverse(inverse(greatest_lower_bound(X_247,X_248))) = greatest_lower_bound(X_247,X_248),
inference(subst,[],[refute_0_452:[bind(X_35,$fot(greatest_lower_bound(X_247,X_248)))]]) ).
cnf(refute_0_1216,plain,
least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248)))) = least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248)))),
introduced(tautology,[refl,[$fot(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248)))))]]) ).
cnf(refute_0_1217,plain,
( inverse(inverse(greatest_lower_bound(X_247,X_248))) != greatest_lower_bound(X_247,X_248)
| least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248)))) != least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248))))
| least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248)))) = least_upper_bound(greatest_lower_bound(X_248,X_247),greatest_lower_bound(X_247,X_248)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248)))),least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248))))) ),[1,1],$fot(greatest_lower_bound(X_247,X_248))]]) ).
cnf(refute_0_1218,plain,
( inverse(inverse(greatest_lower_bound(X_247,X_248))) != greatest_lower_bound(X_247,X_248)
| least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248)))) = least_upper_bound(greatest_lower_bound(X_248,X_247),greatest_lower_bound(X_247,X_248)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248)))),least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248))))) )],[refute_0_1216,refute_0_1217]) ).
cnf(refute_0_1219,plain,
least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248)))) = least_upper_bound(greatest_lower_bound(X_248,X_247),greatest_lower_bound(X_247,X_248)),
inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(X_247,X_248))),greatest_lower_bound(X_247,X_248)) )],[refute_0_1215,refute_0_1218]) ).
cnf(refute_0_1220,plain,
( least_upper_bound(greatest_lower_bound(X_248,X_247),greatest_lower_bound(X_247,X_248)) != greatest_lower_bound(X_248,X_247)
| least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248)))) != least_upper_bound(greatest_lower_bound(X_248,X_247),greatest_lower_bound(X_247,X_248))
| least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248)))) = greatest_lower_bound(X_248,X_247) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248)))))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(X_248,X_247),greatest_lower_bound(X_247,X_248)))),bind(Z0,$fot(greatest_lower_bound(X_248,X_247)))]]) ).
cnf(refute_0_1221,plain,
( least_upper_bound(greatest_lower_bound(X_248,X_247),greatest_lower_bound(X_247,X_248)) != greatest_lower_bound(X_248,X_247)
| least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248)))) = greatest_lower_bound(X_248,X_247) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248)))),least_upper_bound(greatest_lower_bound(X_248,X_247),greatest_lower_bound(X_247,X_248))) )],[refute_0_1219,refute_0_1220]) ).
cnf(refute_0_1222,plain,
least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248)))) = greatest_lower_bound(X_248,X_247),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_248,X_247),greatest_lower_bound(X_247,X_248)),greatest_lower_bound(X_248,X_247)) )],[refute_0_1214,refute_0_1221]) ).
cnf(refute_0_1223,plain,
inverse(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248))))) = inverse(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248))))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248))))))]]) ).
cnf(refute_0_1224,plain,
( inverse(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248))))) != inverse(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248)))))
| least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248)))) != greatest_lower_bound(X_248,X_247)
| inverse(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248))))) = inverse(greatest_lower_bound(X_248,X_247)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248))))),inverse(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248)))))) ),[1,0],$fot(greatest_lower_bound(X_248,X_247))]]) ).
cnf(refute_0_1225,plain,
( least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248)))) != greatest_lower_bound(X_248,X_247)
| inverse(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248))))) = inverse(greatest_lower_bound(X_248,X_247)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248))))),inverse(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248)))))) )],[refute_0_1223,refute_0_1224]) ).
cnf(refute_0_1226,plain,
inverse(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248))))) = inverse(greatest_lower_bound(X_248,X_247)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248)))),greatest_lower_bound(X_248,X_247)) )],[refute_0_1222,refute_0_1225]) ).
cnf(refute_0_1227,plain,
multiply(inverse(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248))))),least_upper_bound(identity,identity)) = multiply(inverse(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248))))),least_upper_bound(identity,identity)),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248))))),least_upper_bound(identity,identity)))]]) ).
cnf(refute_0_1228,plain,
( multiply(inverse(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248))))),least_upper_bound(identity,identity)) != multiply(inverse(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248))))),least_upper_bound(identity,identity))
| inverse(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248))))) != inverse(greatest_lower_bound(X_248,X_247))
| multiply(inverse(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248))))),least_upper_bound(identity,identity)) = multiply(inverse(greatest_lower_bound(X_248,X_247)),least_upper_bound(identity,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248))))),least_upper_bound(identity,identity)),multiply(inverse(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248))))),least_upper_bound(identity,identity))) ),[1,0],$fot(inverse(greatest_lower_bound(X_248,X_247)))]]) ).
cnf(refute_0_1229,plain,
( inverse(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248))))) != inverse(greatest_lower_bound(X_248,X_247))
| multiply(inverse(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248))))),least_upper_bound(identity,identity)) = multiply(inverse(greatest_lower_bound(X_248,X_247)),least_upper_bound(identity,identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248))))),least_upper_bound(identity,identity)),multiply(inverse(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248))))),least_upper_bound(identity,identity))) )],[refute_0_1227,refute_0_1228]) ).
cnf(refute_0_1230,plain,
multiply(inverse(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248))))),least_upper_bound(identity,identity)) = multiply(inverse(greatest_lower_bound(X_248,X_247)),least_upper_bound(identity,identity)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248))))),inverse(greatest_lower_bound(X_248,X_247))) )],[refute_0_1226,refute_0_1229]) ).
cnf(refute_0_1231,plain,
( multiply(inverse(greatest_lower_bound(X_248,X_247)),least_upper_bound(identity,identity)) != multiply(inverse(greatest_lower_bound(X_248,X_247)),identity)
| multiply(inverse(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248))))),least_upper_bound(identity,identity)) != multiply(inverse(greatest_lower_bound(X_248,X_247)),least_upper_bound(identity,identity))
| multiply(inverse(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248))))),least_upper_bound(identity,identity)) = multiply(inverse(greatest_lower_bound(X_248,X_247)),identity) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(inverse(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248))))),least_upper_bound(identity,identity)))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(X_248,X_247)),least_upper_bound(identity,identity)))),bind(Z0,$fot(multiply(inverse(greatest_lower_bound(X_248,X_247)),identity)))]]) ).
cnf(refute_0_1232,plain,
( multiply(inverse(greatest_lower_bound(X_248,X_247)),least_upper_bound(identity,identity)) != multiply(inverse(greatest_lower_bound(X_248,X_247)),identity)
| multiply(inverse(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248))))),least_upper_bound(identity,identity)) = multiply(inverse(greatest_lower_bound(X_248,X_247)),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248))))),least_upper_bound(identity,identity)),multiply(inverse(greatest_lower_bound(X_248,X_247)),least_upper_bound(identity,identity))) )],[refute_0_1230,refute_0_1231]) ).
cnf(refute_0_1233,plain,
multiply(inverse(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248))))),least_upper_bound(identity,identity)) = multiply(inverse(greatest_lower_bound(X_248,X_247)),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_248,X_247)),least_upper_bound(identity,identity)),multiply(inverse(greatest_lower_bound(X_248,X_247)),identity)) )],[refute_0_1213,refute_0_1232]) ).
cnf(refute_0_1234,plain,
( multiply(inverse(greatest_lower_bound(X_248,X_247)),identity) != inverse(greatest_lower_bound(X_248,X_247))
| multiply(inverse(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248))))),least_upper_bound(identity,identity)) != multiply(inverse(greatest_lower_bound(X_248,X_247)),identity)
| multiply(inverse(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248))))),least_upper_bound(identity,identity)) = inverse(greatest_lower_bound(X_248,X_247)) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(inverse(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248))))),least_upper_bound(identity,identity)))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(X_248,X_247)),identity))),bind(Z0,$fot(inverse(greatest_lower_bound(X_248,X_247))))]]) ).
cnf(refute_0_1235,plain,
( multiply(inverse(greatest_lower_bound(X_248,X_247)),identity) != inverse(greatest_lower_bound(X_248,X_247))
| multiply(inverse(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248))))),least_upper_bound(identity,identity)) = inverse(greatest_lower_bound(X_248,X_247)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248))))),least_upper_bound(identity,identity)),multiply(inverse(greatest_lower_bound(X_248,X_247)),identity)) )],[refute_0_1233,refute_0_1234]) ).
cnf(refute_0_1236,plain,
multiply(inverse(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248))))),least_upper_bound(identity,identity)) = inverse(greatest_lower_bound(X_248,X_247)),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_248,X_247)),identity),inverse(greatest_lower_bound(X_248,X_247))) )],[refute_0_1208,refute_0_1235]) ).
cnf(refute_0_1237,plain,
( multiply(inverse(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248))))),least_upper_bound(identity,identity)) != inverse(greatest_lower_bound(X_248,X_247))
| inverse(greatest_lower_bound(X_247,X_248)) != multiply(inverse(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248))))),least_upper_bound(identity,identity))
| inverse(greatest_lower_bound(X_247,X_248)) = inverse(greatest_lower_bound(X_248,X_247)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X_247,X_248)),multiply(inverse(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248))))),least_upper_bound(identity,identity))) ),[1],$fot(inverse(greatest_lower_bound(X_248,X_247)))]]) ).
cnf(refute_0_1238,plain,
( inverse(greatest_lower_bound(X_247,X_248)) != multiply(inverse(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248))))),least_upper_bound(identity,identity))
| inverse(greatest_lower_bound(X_247,X_248)) = inverse(greatest_lower_bound(X_248,X_247)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248))))),least_upper_bound(identity,identity)),inverse(greatest_lower_bound(X_248,X_247))) )],[refute_0_1236,refute_0_1237]) ).
cnf(refute_0_1239,plain,
inverse(greatest_lower_bound(X_247,X_248)) = inverse(greatest_lower_bound(X_248,X_247)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_247,X_248)),multiply(inverse(least_upper_bound(greatest_lower_bound(X_248,X_247),inverse(inverse(greatest_lower_bound(X_247,X_248))))),least_upper_bound(identity,identity))) )],[refute_0_1207,refute_0_1238]) ).
cnf(refute_0_1240,plain,
inverse(greatest_lower_bound(X_249,X_250)) = inverse(greatest_lower_bound(X_250,X_249)),
inference(subst,[],[refute_0_1239:[bind(X_247,$fot(X_249)),bind(X_248,$fot(X_250))]]) ).
cnf(refute_0_1241,plain,
( inverse(multiply(inverse(greatest_lower_bound(X_249,X_250)),X_31)) != multiply(inverse(X_31),greatest_lower_bound(X_249,X_250))
| inverse(greatest_lower_bound(X_249,X_250)) != inverse(greatest_lower_bound(X_250,X_249))
| inverse(multiply(inverse(greatest_lower_bound(X_250,X_249)),X_31)) = multiply(inverse(X_31),greatest_lower_bound(X_249,X_250)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(greatest_lower_bound(X_249,X_250)),X_31)),multiply(inverse(X_31),greatest_lower_bound(X_249,X_250))) ),[0,0,0],$fot(inverse(greatest_lower_bound(X_250,X_249)))]]) ).
cnf(refute_0_1242,plain,
( inverse(multiply(inverse(greatest_lower_bound(X_249,X_250)),X_31)) != multiply(inverse(X_31),greatest_lower_bound(X_249,X_250))
| inverse(multiply(inverse(greatest_lower_bound(X_250,X_249)),X_31)) = multiply(inverse(X_31),greatest_lower_bound(X_249,X_250)) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_249,X_250)),inverse(greatest_lower_bound(X_250,X_249))) )],[refute_0_1240,refute_0_1241]) ).
cnf(refute_0_1243,plain,
inverse(multiply(inverse(greatest_lower_bound(X_250,X_249)),X_31)) = multiply(inverse(X_31),greatest_lower_bound(X_249,X_250)),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(greatest_lower_bound(X_249,X_250)),X_31)),multiply(inverse(X_31),greatest_lower_bound(X_249,X_250))) )],[refute_0_1173,refute_0_1242]) ).
cnf(refute_0_1244,plain,
inverse(multiply(inverse(greatest_lower_bound(X_250,X_249)),X_31)) = multiply(inverse(X_31),greatest_lower_bound(X_250,X_249)),
inference(subst,[],[refute_0_110:[bind(X_145,$fot(greatest_lower_bound(X_250,X_249)))]]) ).
cnf(refute_0_1245,plain,
( inverse(multiply(inverse(greatest_lower_bound(X_250,X_249)),X_31)) != multiply(inverse(X_31),greatest_lower_bound(X_249,X_250))
| inverse(multiply(inverse(greatest_lower_bound(X_250,X_249)),X_31)) != multiply(inverse(X_31),greatest_lower_bound(X_250,X_249))
| multiply(inverse(X_31),greatest_lower_bound(X_250,X_249)) = multiply(inverse(X_31),greatest_lower_bound(X_249,X_250)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(greatest_lower_bound(X_250,X_249)),X_31)),multiply(inverse(X_31),greatest_lower_bound(X_249,X_250))) ),[0],$fot(multiply(inverse(X_31),greatest_lower_bound(X_250,X_249)))]]) ).
cnf(refute_0_1246,plain,
( inverse(multiply(inverse(greatest_lower_bound(X_250,X_249)),X_31)) != multiply(inverse(X_31),greatest_lower_bound(X_249,X_250))
| multiply(inverse(X_31),greatest_lower_bound(X_250,X_249)) = multiply(inverse(X_31),greatest_lower_bound(X_249,X_250)) ),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(greatest_lower_bound(X_250,X_249)),X_31)),multiply(inverse(X_31),greatest_lower_bound(X_250,X_249))) )],[refute_0_1244,refute_0_1245]) ).
cnf(refute_0_1247,plain,
multiply(inverse(X_31),greatest_lower_bound(X_250,X_249)) = multiply(inverse(X_31),greatest_lower_bound(X_249,X_250)),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(greatest_lower_bound(X_250,X_249)),X_31)),multiply(inverse(X_31),greatest_lower_bound(X_249,X_250))) )],[refute_0_1243,refute_0_1246]) ).
cnf(refute_0_1248,plain,
( multiply(inverse(X_31),greatest_lower_bound(X_250,X_249)) != multiply(inverse(X_31),greatest_lower_bound(X_249,X_250))
| multiply(inverse(X_31),greatest_lower_bound(X_249,X_250)) = multiply(inverse(X_31),greatest_lower_bound(X_250,X_249)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(inverse(X_31),greatest_lower_bound(X_250,X_249)))),bind(Y0,$fot(multiply(inverse(X_31),greatest_lower_bound(X_249,X_250))))]]) ).
cnf(refute_0_1249,plain,
multiply(inverse(X_31),greatest_lower_bound(X_249,X_250)) = multiply(inverse(X_31),greatest_lower_bound(X_250,X_249)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_31),greatest_lower_bound(X_250,X_249)),multiply(inverse(X_31),greatest_lower_bound(X_249,X_250))) )],[refute_0_1247,refute_0_1248]) ).
cnf(refute_0_1250,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))),greatest_lower_bound(inverse(least_upper_bound(identity,X_286)),inverse(X_286))) = multiply(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))),greatest_lower_bound(inverse(X_286),inverse(least_upper_bound(identity,X_286)))),
inference(subst,[],[refute_0_1249:[bind(X_249,$fot(inverse(least_upper_bound(identity,X_286)))),bind(X_250,$fot(inverse(X_286))),bind(X_31,$fot(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))))]]) ).
cnf(refute_0_1251,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))),greatest_lower_bound(inverse(X_286),inverse(least_upper_bound(identity,X_286)))) != multiply(least_upper_bound(identity,inverse(X_286)),inverse(least_upper_bound(identity,X_286)))
| multiply(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))),greatest_lower_bound(inverse(least_upper_bound(identity,X_286)),inverse(X_286))) != multiply(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))),greatest_lower_bound(inverse(X_286),inverse(least_upper_bound(identity,X_286))))
| multiply(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))),greatest_lower_bound(inverse(least_upper_bound(identity,X_286)),inverse(X_286))) = multiply(least_upper_bound(identity,inverse(X_286)),inverse(least_upper_bound(identity,X_286))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))),greatest_lower_bound(inverse(least_upper_bound(identity,X_286)),inverse(X_286))))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))),greatest_lower_bound(inverse(X_286),inverse(least_upper_bound(identity,X_286)))))),bind(Z0,$fot(multiply(least_upper_bound(identity,inverse(X_286)),inverse(least_upper_bound(identity,X_286)))))]]) ).
cnf(refute_0_1252,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))),greatest_lower_bound(inverse(X_286),inverse(least_upper_bound(identity,X_286)))) != multiply(least_upper_bound(identity,inverse(X_286)),inverse(least_upper_bound(identity,X_286)))
| multiply(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))),greatest_lower_bound(inverse(least_upper_bound(identity,X_286)),inverse(X_286))) = multiply(least_upper_bound(identity,inverse(X_286)),inverse(least_upper_bound(identity,X_286))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))),greatest_lower_bound(inverse(least_upper_bound(identity,X_286)),inverse(X_286))),multiply(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))),greatest_lower_bound(inverse(X_286),inverse(least_upper_bound(identity,X_286))))) )],[refute_0_1250,refute_0_1251]) ).
cnf(refute_0_1253,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))),greatest_lower_bound(inverse(least_upper_bound(identity,X_286)),inverse(X_286))) = multiply(least_upper_bound(identity,inverse(X_286)),inverse(least_upper_bound(identity,X_286))),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))),greatest_lower_bound(inverse(X_286),inverse(least_upper_bound(identity,X_286)))),multiply(least_upper_bound(identity,inverse(X_286)),inverse(least_upper_bound(identity,X_286)))) )],[refute_0_1172,refute_0_1252]) ).
cnf(refute_0_1254,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))),greatest_lower_bound(inverse(least_upper_bound(identity,X_286)),inverse(X_286))) != multiply(least_upper_bound(identity,inverse(X_286)),inverse(least_upper_bound(identity,X_286)))
| inverse(X_286) != multiply(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))),greatest_lower_bound(inverse(least_upper_bound(identity,X_286)),inverse(X_286)))
| inverse(X_286) = multiply(least_upper_bound(identity,inverse(X_286)),inverse(least_upper_bound(identity,X_286))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(X_286),multiply(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))),greatest_lower_bound(inverse(least_upper_bound(identity,X_286)),inverse(X_286)))) ),[1],$fot(multiply(least_upper_bound(identity,inverse(X_286)),inverse(least_upper_bound(identity,X_286))))]]) ).
cnf(refute_0_1255,plain,
( inverse(X_286) != multiply(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))),greatest_lower_bound(inverse(least_upper_bound(identity,X_286)),inverse(X_286)))
| inverse(X_286) = multiply(least_upper_bound(identity,inverse(X_286)),inverse(least_upper_bound(identity,X_286))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))),greatest_lower_bound(inverse(least_upper_bound(identity,X_286)),inverse(X_286))),multiply(least_upper_bound(identity,inverse(X_286)),inverse(least_upper_bound(identity,X_286)))) )],[refute_0_1253,refute_0_1254]) ).
cnf(refute_0_1256,plain,
inverse(X_286) = multiply(least_upper_bound(identity,inverse(X_286)),inverse(least_upper_bound(identity,X_286))),
inference(resolve,[$cnf( $equal(inverse(X_286),multiply(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_286))))),greatest_lower_bound(inverse(least_upper_bound(identity,X_286)),inverse(X_286)))) )],[refute_0_1055,refute_0_1255]) ).
cnf(refute_0_1257,plain,
inverse(X_316) = multiply(least_upper_bound(identity,inverse(X_316)),inverse(least_upper_bound(identity,X_316))),
inference(subst,[],[refute_0_1256:[bind(X_286,$fot(X_316))]]) ).
cnf(refute_0_1258,plain,
( inverse(X_316) != multiply(least_upper_bound(identity,inverse(X_316)),inverse(least_upper_bound(identity,X_316)))
| multiply(least_upper_bound(identity,inverse(X_316)),inverse(least_upper_bound(identity,X_316))) = inverse(X_316) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(inverse(X_316))),bind(Y0,$fot(multiply(least_upper_bound(identity,inverse(X_316)),inverse(least_upper_bound(identity,X_316)))))]]) ).
cnf(refute_0_1259,plain,
multiply(least_upper_bound(identity,inverse(X_316)),inverse(least_upper_bound(identity,X_316))) = inverse(X_316),
inference(resolve,[$cnf( $equal(inverse(X_316),multiply(least_upper_bound(identity,inverse(X_316)),inverse(least_upper_bound(identity,X_316)))) )],[refute_0_1257,refute_0_1258]) ).
cnf(refute_0_1260,plain,
( multiply(least_upper_bound(identity,inverse(X_316)),inverse(least_upper_bound(identity,X_316))) != inverse(X_316)
| inverse(least_upper_bound(identity,X_316)) != multiply(inverse(greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316))))),greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X_316)),inverse(least_upper_bound(identity,X_316)))))
| inverse(least_upper_bound(identity,X_316)) = multiply(inverse(greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316))))),greatest_lower_bound(identity,inverse(X_316))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,X_316)),multiply(inverse(greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316))))),greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X_316)),inverse(least_upper_bound(identity,X_316)))))) ),[1,1,1],$fot(inverse(X_316))]]) ).
cnf(refute_0_1261,plain,
( inverse(least_upper_bound(identity,X_316)) != multiply(inverse(greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316))))),greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X_316)),inverse(least_upper_bound(identity,X_316)))))
| inverse(least_upper_bound(identity,X_316)) = multiply(inverse(greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316))))),greatest_lower_bound(identity,inverse(X_316))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_316)),inverse(least_upper_bound(identity,X_316))),inverse(X_316)) )],[refute_0_1259,refute_0_1260]) ).
cnf(refute_0_1262,plain,
inverse(least_upper_bound(identity,X_316)) = multiply(inverse(greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316))))),greatest_lower_bound(identity,inverse(X_316))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,X_316)),multiply(inverse(greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316))))),greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X_316)),inverse(least_upper_bound(identity,X_316)))))) )],[refute_0_1038,refute_0_1261]) ).
cnf(refute_0_1263,plain,
multiply(least_upper_bound(X_76,identity),greatest_lower_bound(inverse(X_76),identity)) = greatest_lower_bound(least_upper_bound(X_76,identity),multiply(least_upper_bound(X_76,identity),inverse(X_76))),
inference(subst,[],[refute_0_319:[bind(X_104,$fot(least_upper_bound(X_76,identity))),bind(X_105,$fot(inverse(X_76)))]]) ).
cnf(refute_0_1264,plain,
multiply(least_upper_bound(X_76,identity),inverse(X_76)) = least_upper_bound(identity,multiply(identity,inverse(X_76))),
inference(subst,[],[refute_0_1189:[bind(X_68,$fot(X_76)),bind(X_69,$fot(identity))]]) ).
cnf(refute_0_1265,plain,
multiply(identity,inverse(X_76)) = inverse(X_76),
inference(subst,[],[left_identity:[bind(X,$fot(inverse(X_76)))]]) ).
cnf(refute_0_1266,plain,
( multiply(identity,inverse(X_76)) != inverse(X_76)
| multiply(least_upper_bound(X_76,identity),inverse(X_76)) != least_upper_bound(identity,multiply(identity,inverse(X_76)))
| multiply(least_upper_bound(X_76,identity),inverse(X_76)) = least_upper_bound(identity,inverse(X_76)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_76,identity),inverse(X_76)),least_upper_bound(identity,multiply(identity,inverse(X_76)))) ),[1,1],$fot(inverse(X_76))]]) ).
cnf(refute_0_1267,plain,
( multiply(least_upper_bound(X_76,identity),inverse(X_76)) != least_upper_bound(identity,multiply(identity,inverse(X_76)))
| multiply(least_upper_bound(X_76,identity),inverse(X_76)) = least_upper_bound(identity,inverse(X_76)) ),
inference(resolve,[$cnf( $equal(multiply(identity,inverse(X_76)),inverse(X_76)) )],[refute_0_1265,refute_0_1266]) ).
cnf(refute_0_1268,plain,
multiply(least_upper_bound(X_76,identity),inverse(X_76)) = least_upper_bound(identity,inverse(X_76)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_76,identity),inverse(X_76)),least_upper_bound(identity,multiply(identity,inverse(X_76)))) )],[refute_0_1264,refute_0_1267]) ).
cnf(refute_0_1269,plain,
( multiply(least_upper_bound(X_76,identity),greatest_lower_bound(inverse(X_76),identity)) != greatest_lower_bound(least_upper_bound(X_76,identity),multiply(least_upper_bound(X_76,identity),inverse(X_76)))
| multiply(least_upper_bound(X_76,identity),inverse(X_76)) != least_upper_bound(identity,inverse(X_76))
| multiply(least_upper_bound(X_76,identity),greatest_lower_bound(inverse(X_76),identity)) = greatest_lower_bound(least_upper_bound(X_76,identity),least_upper_bound(identity,inverse(X_76))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_76,identity),greatest_lower_bound(inverse(X_76),identity)),greatest_lower_bound(least_upper_bound(X_76,identity),multiply(least_upper_bound(X_76,identity),inverse(X_76)))) ),[1,1],$fot(least_upper_bound(identity,inverse(X_76)))]]) ).
cnf(refute_0_1270,plain,
( multiply(least_upper_bound(X_76,identity),greatest_lower_bound(inverse(X_76),identity)) != greatest_lower_bound(least_upper_bound(X_76,identity),multiply(least_upper_bound(X_76,identity),inverse(X_76)))
| multiply(least_upper_bound(X_76,identity),greatest_lower_bound(inverse(X_76),identity)) = greatest_lower_bound(least_upper_bound(X_76,identity),least_upper_bound(identity,inverse(X_76))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_76,identity),inverse(X_76)),least_upper_bound(identity,inverse(X_76))) )],[refute_0_1268,refute_0_1269]) ).
cnf(refute_0_1271,plain,
multiply(least_upper_bound(X_76,identity),greatest_lower_bound(inverse(X_76),identity)) = greatest_lower_bound(least_upper_bound(X_76,identity),least_upper_bound(identity,inverse(X_76))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_76,identity),greatest_lower_bound(inverse(X_76),identity)),greatest_lower_bound(least_upper_bound(X_76,identity),multiply(least_upper_bound(X_76,identity),inverse(X_76)))) )],[refute_0_1263,refute_0_1270]) ).
cnf(refute_0_1272,plain,
multiply(least_upper_bound(X_76,identity),greatest_lower_bound(inverse(X_76),identity)) = multiply(least_upper_bound(X_76,identity),greatest_lower_bound(identity,inverse(X_76))),
inference(subst,[],[refute_0_429:[bind(X_108,$fot(inverse(X_76))),bind(X_17,$fot(least_upper_bound(X_76,identity)))]]) ).
cnf(refute_0_1273,plain,
( multiply(least_upper_bound(X_76,identity),greatest_lower_bound(inverse(X_76),identity)) != multiply(least_upper_bound(X_76,identity),greatest_lower_bound(identity,inverse(X_76)))
| multiply(least_upper_bound(X_76,identity),greatest_lower_bound(inverse(X_76),identity)) != greatest_lower_bound(least_upper_bound(X_76,identity),least_upper_bound(identity,inverse(X_76)))
| multiply(least_upper_bound(X_76,identity),greatest_lower_bound(identity,inverse(X_76))) = greatest_lower_bound(least_upper_bound(X_76,identity),least_upper_bound(identity,inverse(X_76))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_76,identity),greatest_lower_bound(inverse(X_76),identity)),greatest_lower_bound(least_upper_bound(X_76,identity),least_upper_bound(identity,inverse(X_76)))) ),[0],$fot(multiply(least_upper_bound(X_76,identity),greatest_lower_bound(identity,inverse(X_76))))]]) ).
cnf(refute_0_1274,plain,
( multiply(least_upper_bound(X_76,identity),greatest_lower_bound(inverse(X_76),identity)) != greatest_lower_bound(least_upper_bound(X_76,identity),least_upper_bound(identity,inverse(X_76)))
| multiply(least_upper_bound(X_76,identity),greatest_lower_bound(identity,inverse(X_76))) = greatest_lower_bound(least_upper_bound(X_76,identity),least_upper_bound(identity,inverse(X_76))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_76,identity),greatest_lower_bound(inverse(X_76),identity)),multiply(least_upper_bound(X_76,identity),greatest_lower_bound(identity,inverse(X_76)))) )],[refute_0_1272,refute_0_1273]) ).
cnf(refute_0_1275,plain,
multiply(least_upper_bound(X_76,identity),greatest_lower_bound(identity,inverse(X_76))) = greatest_lower_bound(least_upper_bound(X_76,identity),least_upper_bound(identity,inverse(X_76))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_76,identity),greatest_lower_bound(inverse(X_76),identity)),greatest_lower_bound(least_upper_bound(X_76,identity),least_upper_bound(identity,inverse(X_76)))) )],[refute_0_1271,refute_0_1274]) ).
cnf(refute_0_1276,plain,
multiply(least_upper_bound(identity,X_75),greatest_lower_bound(inverse(X_75),identity)) = greatest_lower_bound(least_upper_bound(identity,X_75),multiply(least_upper_bound(identity,X_75),inverse(X_75))),
inference(subst,[],[refute_0_319:[bind(X_104,$fot(least_upper_bound(identity,X_75))),bind(X_105,$fot(inverse(X_75)))]]) ).
cnf(refute_0_1277,plain,
( multiply(least_upper_bound(identity,X_75),greatest_lower_bound(inverse(X_75),identity)) != greatest_lower_bound(least_upper_bound(identity,X_75),multiply(least_upper_bound(identity,X_75),inverse(X_75)))
| multiply(least_upper_bound(identity,X_75),inverse(X_75)) != least_upper_bound(identity,inverse(X_75))
| multiply(least_upper_bound(identity,X_75),greatest_lower_bound(inverse(X_75),identity)) = greatest_lower_bound(least_upper_bound(identity,X_75),least_upper_bound(identity,inverse(X_75))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,X_75),greatest_lower_bound(inverse(X_75),identity)),greatest_lower_bound(least_upper_bound(identity,X_75),multiply(least_upper_bound(identity,X_75),inverse(X_75)))) ),[1,1],$fot(least_upper_bound(identity,inverse(X_75)))]]) ).
cnf(refute_0_1278,plain,
( multiply(least_upper_bound(identity,X_75),greatest_lower_bound(inverse(X_75),identity)) != greatest_lower_bound(least_upper_bound(identity,X_75),multiply(least_upper_bound(identity,X_75),inverse(X_75)))
| multiply(least_upper_bound(identity,X_75),greatest_lower_bound(inverse(X_75),identity)) = greatest_lower_bound(least_upper_bound(identity,X_75),least_upper_bound(identity,inverse(X_75))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_75),inverse(X_75)),least_upper_bound(identity,inverse(X_75))) )],[refute_0_785,refute_0_1277]) ).
cnf(refute_0_1279,plain,
multiply(least_upper_bound(identity,X_75),greatest_lower_bound(inverse(X_75),identity)) = greatest_lower_bound(least_upper_bound(identity,X_75),least_upper_bound(identity,inverse(X_75))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_75),greatest_lower_bound(inverse(X_75),identity)),greatest_lower_bound(least_upper_bound(identity,X_75),multiply(least_upper_bound(identity,X_75),inverse(X_75)))) )],[refute_0_1276,refute_0_1278]) ).
cnf(refute_0_1280,plain,
multiply(least_upper_bound(identity,X_75),greatest_lower_bound(inverse(X_75),identity)) = multiply(least_upper_bound(identity,X_75),greatest_lower_bound(identity,inverse(X_75))),
inference(subst,[],[refute_0_429:[bind(X_108,$fot(inverse(X_75))),bind(X_17,$fot(least_upper_bound(identity,X_75)))]]) ).
cnf(refute_0_1281,plain,
( multiply(least_upper_bound(identity,X_75),greatest_lower_bound(inverse(X_75),identity)) != multiply(least_upper_bound(identity,X_75),greatest_lower_bound(identity,inverse(X_75)))
| multiply(least_upper_bound(identity,X_75),greatest_lower_bound(inverse(X_75),identity)) != greatest_lower_bound(least_upper_bound(identity,X_75),least_upper_bound(identity,inverse(X_75)))
| multiply(least_upper_bound(identity,X_75),greatest_lower_bound(identity,inverse(X_75))) = greatest_lower_bound(least_upper_bound(identity,X_75),least_upper_bound(identity,inverse(X_75))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,X_75),greatest_lower_bound(inverse(X_75),identity)),greatest_lower_bound(least_upper_bound(identity,X_75),least_upper_bound(identity,inverse(X_75)))) ),[0],$fot(multiply(least_upper_bound(identity,X_75),greatest_lower_bound(identity,inverse(X_75))))]]) ).
cnf(refute_0_1282,plain,
( multiply(least_upper_bound(identity,X_75),greatest_lower_bound(inverse(X_75),identity)) != greatest_lower_bound(least_upper_bound(identity,X_75),least_upper_bound(identity,inverse(X_75)))
| multiply(least_upper_bound(identity,X_75),greatest_lower_bound(identity,inverse(X_75))) = greatest_lower_bound(least_upper_bound(identity,X_75),least_upper_bound(identity,inverse(X_75))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_75),greatest_lower_bound(inverse(X_75),identity)),multiply(least_upper_bound(identity,X_75),greatest_lower_bound(identity,inverse(X_75)))) )],[refute_0_1280,refute_0_1281]) ).
cnf(refute_0_1283,plain,
multiply(least_upper_bound(identity,X_75),greatest_lower_bound(identity,inverse(X_75))) = greatest_lower_bound(least_upper_bound(identity,X_75),least_upper_bound(identity,inverse(X_75))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_75),greatest_lower_bound(inverse(X_75),identity)),greatest_lower_bound(least_upper_bound(identity,X_75),least_upper_bound(identity,inverse(X_75)))) )],[refute_0_1279,refute_0_1282]) ).
cnf(refute_0_1284,plain,
multiply(least_upper_bound(identity,multiply(X_68,identity)),greatest_lower_bound(identity,inverse(multiply(X_68,identity)))) = greatest_lower_bound(least_upper_bound(identity,multiply(X_68,identity)),least_upper_bound(identity,inverse(multiply(X_68,identity)))),
inference(subst,[],[refute_0_1283:[bind(X_75,$fot(multiply(X_68,identity)))]]) ).
cnf(refute_0_1285,plain,
multiply(least_upper_bound(X_68,identity),identity) = least_upper_bound(identity,multiply(X_68,identity)),
inference(subst,[],[refute_0_761:[bind(X_67,$fot(identity))]]) ).
cnf(refute_0_1286,plain,
( multiply(least_upper_bound(X_68,identity),identity) != least_upper_bound(identity,multiply(X_68,identity))
| least_upper_bound(identity,multiply(X_68,identity)) = multiply(least_upper_bound(X_68,identity),identity) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(least_upper_bound(X_68,identity),identity))),bind(Y0,$fot(least_upper_bound(identity,multiply(X_68,identity))))]]) ).
cnf(refute_0_1287,plain,
least_upper_bound(identity,multiply(X_68,identity)) = multiply(least_upper_bound(X_68,identity),identity),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_68,identity),identity),least_upper_bound(identity,multiply(X_68,identity))) )],[refute_0_1285,refute_0_1286]) ).
cnf(refute_0_1288,plain,
( multiply(least_upper_bound(identity,multiply(X_68,identity)),greatest_lower_bound(identity,inverse(multiply(X_68,identity)))) != greatest_lower_bound(least_upper_bound(identity,multiply(X_68,identity)),least_upper_bound(identity,inverse(multiply(X_68,identity))))
| least_upper_bound(identity,multiply(X_68,identity)) != multiply(least_upper_bound(X_68,identity),identity)
| multiply(least_upper_bound(identity,multiply(X_68,identity)),greatest_lower_bound(identity,inverse(multiply(X_68,identity)))) = greatest_lower_bound(multiply(least_upper_bound(X_68,identity),identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(X_68,identity)),greatest_lower_bound(identity,inverse(multiply(X_68,identity)))),greatest_lower_bound(least_upper_bound(identity,multiply(X_68,identity)),least_upper_bound(identity,inverse(multiply(X_68,identity))))) ),[1,0],$fot(multiply(least_upper_bound(X_68,identity),identity))]]) ).
cnf(refute_0_1289,plain,
( multiply(least_upper_bound(identity,multiply(X_68,identity)),greatest_lower_bound(identity,inverse(multiply(X_68,identity)))) != greatest_lower_bound(least_upper_bound(identity,multiply(X_68,identity)),least_upper_bound(identity,inverse(multiply(X_68,identity))))
| multiply(least_upper_bound(identity,multiply(X_68,identity)),greatest_lower_bound(identity,inverse(multiply(X_68,identity)))) = greatest_lower_bound(multiply(least_upper_bound(X_68,identity),identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_68,identity)),multiply(least_upper_bound(X_68,identity),identity)) )],[refute_0_1287,refute_0_1288]) ).
cnf(refute_0_1290,plain,
multiply(least_upper_bound(identity,multiply(X_68,identity)),greatest_lower_bound(identity,inverse(multiply(X_68,identity)))) = greatest_lower_bound(multiply(least_upper_bound(X_68,identity),identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(X_68,identity)),greatest_lower_bound(identity,inverse(multiply(X_68,identity)))),greatest_lower_bound(least_upper_bound(identity,multiply(X_68,identity)),least_upper_bound(identity,inverse(multiply(X_68,identity))))) )],[refute_0_1284,refute_0_1289]) ).
cnf(refute_0_1291,plain,
multiply(X_68,identity) = X_68,
inference(subst,[],[refute_0_88:[bind(X_33,$fot(X_68))]]) ).
cnf(refute_0_1292,plain,
inverse(multiply(X_68,identity)) = inverse(multiply(X_68,identity)),
introduced(tautology,[refl,[$fot(inverse(multiply(X_68,identity)))]]) ).
cnf(refute_0_1293,plain,
( multiply(X_68,identity) != X_68
| inverse(multiply(X_68,identity)) != inverse(multiply(X_68,identity))
| inverse(multiply(X_68,identity)) = inverse(X_68) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_68,identity)),inverse(multiply(X_68,identity))) ),[1,0],$fot(X_68)]]) ).
cnf(refute_0_1294,plain,
( multiply(X_68,identity) != X_68
| inverse(multiply(X_68,identity)) = inverse(X_68) ),
inference(resolve,[$cnf( $equal(inverse(multiply(X_68,identity)),inverse(multiply(X_68,identity))) )],[refute_0_1292,refute_0_1293]) ).
cnf(refute_0_1295,plain,
inverse(multiply(X_68,identity)) = inverse(X_68),
inference(resolve,[$cnf( $equal(multiply(X_68,identity),X_68) )],[refute_0_1291,refute_0_1294]) ).
cnf(refute_0_1296,plain,
least_upper_bound(identity,inverse(multiply(X_68,identity))) = least_upper_bound(identity,inverse(multiply(X_68,identity))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,inverse(multiply(X_68,identity))))]]) ).
cnf(refute_0_1297,plain,
( inverse(multiply(X_68,identity)) != inverse(X_68)
| least_upper_bound(identity,inverse(multiply(X_68,identity))) != least_upper_bound(identity,inverse(multiply(X_68,identity)))
| least_upper_bound(identity,inverse(multiply(X_68,identity))) = least_upper_bound(identity,inverse(X_68)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,inverse(multiply(X_68,identity))),least_upper_bound(identity,inverse(multiply(X_68,identity)))) ),[1,1],$fot(inverse(X_68))]]) ).
cnf(refute_0_1298,plain,
( inverse(multiply(X_68,identity)) != inverse(X_68)
| least_upper_bound(identity,inverse(multiply(X_68,identity))) = least_upper_bound(identity,inverse(X_68)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(multiply(X_68,identity))),least_upper_bound(identity,inverse(multiply(X_68,identity)))) )],[refute_0_1296,refute_0_1297]) ).
cnf(refute_0_1299,plain,
least_upper_bound(identity,inverse(multiply(X_68,identity))) = least_upper_bound(identity,inverse(X_68)),
inference(resolve,[$cnf( $equal(inverse(multiply(X_68,identity)),inverse(X_68)) )],[refute_0_1295,refute_0_1298]) ).
cnf(refute_0_1300,plain,
multiply(greatest_lower_bound(X_68,identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))) = multiply(greatest_lower_bound(X_68,identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(X_68,identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))))]]) ).
cnf(refute_0_1301,plain,
( multiply(greatest_lower_bound(X_68,identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))) != multiply(greatest_lower_bound(X_68,identity),least_upper_bound(identity,inverse(multiply(X_68,identity))))
| least_upper_bound(identity,inverse(multiply(X_68,identity))) != least_upper_bound(identity,inverse(X_68))
| multiply(greatest_lower_bound(X_68,identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))) = multiply(greatest_lower_bound(X_68,identity),least_upper_bound(identity,inverse(X_68))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_68,identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))),multiply(greatest_lower_bound(X_68,identity),least_upper_bound(identity,inverse(multiply(X_68,identity))))) ),[1,1],$fot(least_upper_bound(identity,inverse(X_68)))]]) ).
cnf(refute_0_1302,plain,
( least_upper_bound(identity,inverse(multiply(X_68,identity))) != least_upper_bound(identity,inverse(X_68))
| multiply(greatest_lower_bound(X_68,identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))) = multiply(greatest_lower_bound(X_68,identity),least_upper_bound(identity,inverse(X_68))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_68,identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))),multiply(greatest_lower_bound(X_68,identity),least_upper_bound(identity,inverse(multiply(X_68,identity))))) )],[refute_0_1300,refute_0_1301]) ).
cnf(refute_0_1303,plain,
multiply(greatest_lower_bound(X_68,identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))) = multiply(greatest_lower_bound(X_68,identity),least_upper_bound(identity,inverse(X_68))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(multiply(X_68,identity))),least_upper_bound(identity,inverse(X_68))) )],[refute_0_1299,refute_0_1302]) ).
cnf(refute_0_1304,plain,
multiply(greatest_lower_bound(X_68,identity),identity) = greatest_lower_bound(X_68,identity),
inference(subst,[],[refute_0_88:[bind(X_33,$fot(greatest_lower_bound(X_68,identity)))]]) ).
cnf(refute_0_1305,plain,
multiply(greatest_lower_bound(X_120,identity),X_119) = greatest_lower_bound(multiply(X_120,X_119),multiply(identity,X_119)),
inference(subst,[],[monotony_glb2:[bind(X,$fot(X_119)),bind(Y,$fot(X_120)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_1306,plain,
multiply(identity,X_119) = X_119,
inference(subst,[],[left_identity:[bind(X,$fot(X_119))]]) ).
cnf(refute_0_1307,plain,
( multiply(greatest_lower_bound(X_120,identity),X_119) != greatest_lower_bound(multiply(X_120,X_119),multiply(identity,X_119))
| multiply(identity,X_119) != X_119
| multiply(greatest_lower_bound(X_120,identity),X_119) = greatest_lower_bound(multiply(X_120,X_119),X_119) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_120,identity),X_119),greatest_lower_bound(multiply(X_120,X_119),multiply(identity,X_119))) ),[1,1],$fot(X_119)]]) ).
cnf(refute_0_1308,plain,
( multiply(greatest_lower_bound(X_120,identity),X_119) != greatest_lower_bound(multiply(X_120,X_119),multiply(identity,X_119))
| multiply(greatest_lower_bound(X_120,identity),X_119) = greatest_lower_bound(multiply(X_120,X_119),X_119) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_119),X_119) )],[refute_0_1306,refute_0_1307]) ).
cnf(refute_0_1309,plain,
multiply(greatest_lower_bound(X_120,identity),X_119) = greatest_lower_bound(multiply(X_120,X_119),X_119),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_120,identity),X_119),greatest_lower_bound(multiply(X_120,X_119),multiply(identity,X_119))) )],[refute_0_1305,refute_0_1308]) ).
cnf(refute_0_1310,plain,
greatest_lower_bound(multiply(X_120,X_119),X_119) = greatest_lower_bound(X_119,multiply(X_120,X_119)),
inference(subst,[],[refute_0_42:[bind(X,$fot(X_119)),bind(Y,$fot(multiply(X_120,X_119)))]]) ).
cnf(refute_0_1311,plain,
( multiply(greatest_lower_bound(X_120,identity),X_119) != greatest_lower_bound(multiply(X_120,X_119),X_119)
| greatest_lower_bound(multiply(X_120,X_119),X_119) != greatest_lower_bound(X_119,multiply(X_120,X_119))
| multiply(greatest_lower_bound(X_120,identity),X_119) = greatest_lower_bound(X_119,multiply(X_120,X_119)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_120,identity),X_119),greatest_lower_bound(X_119,multiply(X_120,X_119))) ),[0],$fot(greatest_lower_bound(multiply(X_120,X_119),X_119))]]) ).
cnf(refute_0_1312,plain,
( multiply(greatest_lower_bound(X_120,identity),X_119) != greatest_lower_bound(multiply(X_120,X_119),X_119)
| multiply(greatest_lower_bound(X_120,identity),X_119) = greatest_lower_bound(X_119,multiply(X_120,X_119)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_120,X_119),X_119),greatest_lower_bound(X_119,multiply(X_120,X_119))) )],[refute_0_1310,refute_0_1311]) ).
cnf(refute_0_1313,plain,
multiply(greatest_lower_bound(X_120,identity),X_119) = greatest_lower_bound(X_119,multiply(X_120,X_119)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_120,identity),X_119),greatest_lower_bound(multiply(X_120,X_119),X_119)) )],[refute_0_1309,refute_0_1312]) ).
cnf(refute_0_1314,plain,
( multiply(greatest_lower_bound(X_120,identity),X_119) != greatest_lower_bound(X_119,multiply(X_120,X_119))
| greatest_lower_bound(X_119,multiply(X_120,X_119)) = multiply(greatest_lower_bound(X_120,identity),X_119) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(greatest_lower_bound(X_120,identity),X_119))),bind(Y0,$fot(greatest_lower_bound(X_119,multiply(X_120,X_119))))]]) ).
cnf(refute_0_1315,plain,
greatest_lower_bound(X_119,multiply(X_120,X_119)) = multiply(greatest_lower_bound(X_120,identity),X_119),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_120,identity),X_119),greatest_lower_bound(X_119,multiply(X_120,X_119))) )],[refute_0_1313,refute_0_1314]) ).
cnf(refute_0_1316,plain,
greatest_lower_bound(identity,multiply(X_68,identity)) = multiply(greatest_lower_bound(X_68,identity),identity),
inference(subst,[],[refute_0_1315:[bind(X_119,$fot(identity)),bind(X_120,$fot(X_68))]]) ).
cnf(refute_0_1317,plain,
( multiply(greatest_lower_bound(X_68,identity),identity) != greatest_lower_bound(X_68,identity)
| greatest_lower_bound(identity,multiply(X_68,identity)) != multiply(greatest_lower_bound(X_68,identity),identity)
| greatest_lower_bound(identity,multiply(X_68,identity)) = greatest_lower_bound(X_68,identity) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(greatest_lower_bound(identity,multiply(X_68,identity)))),bind(Y0,$fot(multiply(greatest_lower_bound(X_68,identity),identity))),bind(Z0,$fot(greatest_lower_bound(X_68,identity)))]]) ).
cnf(refute_0_1318,plain,
( multiply(greatest_lower_bound(X_68,identity),identity) != greatest_lower_bound(X_68,identity)
| greatest_lower_bound(identity,multiply(X_68,identity)) = greatest_lower_bound(X_68,identity) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_68,identity)),multiply(greatest_lower_bound(X_68,identity),identity)) )],[refute_0_1316,refute_0_1317]) ).
cnf(refute_0_1319,plain,
greatest_lower_bound(identity,multiply(X_68,identity)) = greatest_lower_bound(X_68,identity),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_68,identity),identity),greatest_lower_bound(X_68,identity)) )],[refute_0_1304,refute_0_1318]) ).
cnf(refute_0_1320,plain,
multiply(greatest_lower_bound(identity,multiply(X_68,identity)),least_upper_bound(identity,inverse(multiply(X_68,identity)))) = multiply(greatest_lower_bound(identity,multiply(X_68,identity)),least_upper_bound(identity,inverse(multiply(X_68,identity)))),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(identity,multiply(X_68,identity)),least_upper_bound(identity,inverse(multiply(X_68,identity)))))]]) ).
cnf(refute_0_1321,plain,
( multiply(greatest_lower_bound(identity,multiply(X_68,identity)),least_upper_bound(identity,inverse(multiply(X_68,identity)))) != multiply(greatest_lower_bound(identity,multiply(X_68,identity)),least_upper_bound(identity,inverse(multiply(X_68,identity))))
| greatest_lower_bound(identity,multiply(X_68,identity)) != greatest_lower_bound(X_68,identity)
| multiply(greatest_lower_bound(identity,multiply(X_68,identity)),least_upper_bound(identity,inverse(multiply(X_68,identity)))) = multiply(greatest_lower_bound(X_68,identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(X_68,identity)),least_upper_bound(identity,inverse(multiply(X_68,identity)))),multiply(greatest_lower_bound(identity,multiply(X_68,identity)),least_upper_bound(identity,inverse(multiply(X_68,identity))))) ),[1,0],$fot(greatest_lower_bound(X_68,identity))]]) ).
cnf(refute_0_1322,plain,
( greatest_lower_bound(identity,multiply(X_68,identity)) != greatest_lower_bound(X_68,identity)
| multiply(greatest_lower_bound(identity,multiply(X_68,identity)),least_upper_bound(identity,inverse(multiply(X_68,identity)))) = multiply(greatest_lower_bound(X_68,identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(X_68,identity)),least_upper_bound(identity,inverse(multiply(X_68,identity)))),multiply(greatest_lower_bound(identity,multiply(X_68,identity)),least_upper_bound(identity,inverse(multiply(X_68,identity))))) )],[refute_0_1320,refute_0_1321]) ).
cnf(refute_0_1323,plain,
multiply(greatest_lower_bound(identity,multiply(X_68,identity)),least_upper_bound(identity,inverse(multiply(X_68,identity)))) = multiply(greatest_lower_bound(X_68,identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_68,identity)),greatest_lower_bound(X_68,identity)) )],[refute_0_1319,refute_0_1322]) ).
cnf(refute_0_1324,plain,
( multiply(greatest_lower_bound(X_68,identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))) != multiply(greatest_lower_bound(X_68,identity),least_upper_bound(identity,inverse(X_68)))
| multiply(greatest_lower_bound(identity,multiply(X_68,identity)),least_upper_bound(identity,inverse(multiply(X_68,identity)))) != multiply(greatest_lower_bound(X_68,identity),least_upper_bound(identity,inverse(multiply(X_68,identity))))
| multiply(greatest_lower_bound(identity,multiply(X_68,identity)),least_upper_bound(identity,inverse(multiply(X_68,identity)))) = multiply(greatest_lower_bound(X_68,identity),least_upper_bound(identity,inverse(X_68))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(greatest_lower_bound(identity,multiply(X_68,identity)),least_upper_bound(identity,inverse(multiply(X_68,identity)))))),bind(Y0,$fot(multiply(greatest_lower_bound(X_68,identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))))),bind(Z0,$fot(multiply(greatest_lower_bound(X_68,identity),least_upper_bound(identity,inverse(X_68)))))]]) ).
cnf(refute_0_1325,plain,
( multiply(greatest_lower_bound(X_68,identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))) != multiply(greatest_lower_bound(X_68,identity),least_upper_bound(identity,inverse(X_68)))
| multiply(greatest_lower_bound(identity,multiply(X_68,identity)),least_upper_bound(identity,inverse(multiply(X_68,identity)))) = multiply(greatest_lower_bound(X_68,identity),least_upper_bound(identity,inverse(X_68))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(X_68,identity)),least_upper_bound(identity,inverse(multiply(X_68,identity)))),multiply(greatest_lower_bound(X_68,identity),least_upper_bound(identity,inverse(multiply(X_68,identity))))) )],[refute_0_1323,refute_0_1324]) ).
cnf(refute_0_1326,plain,
multiply(greatest_lower_bound(identity,multiply(X_68,identity)),least_upper_bound(identity,inverse(multiply(X_68,identity)))) = multiply(greatest_lower_bound(X_68,identity),least_upper_bound(identity,inverse(X_68))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_68,identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))),multiply(greatest_lower_bound(X_68,identity),least_upper_bound(identity,inverse(X_68)))) )],[refute_0_1303,refute_0_1325]) ).
cnf(refute_0_1327,plain,
multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(identity,inverse(inverse(X_35)))) = greatest_lower_bound(least_upper_bound(identity,inverse(X_35)),least_upper_bound(identity,inverse(inverse(X_35)))),
inference(subst,[],[refute_0_1283:[bind(X_75,$fot(inverse(X_35)))]]) ).
cnf(refute_0_1328,plain,
( multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(identity,inverse(inverse(X_35)))) != greatest_lower_bound(least_upper_bound(identity,inverse(X_35)),least_upper_bound(identity,inverse(inverse(X_35))))
| inverse(inverse(X_35)) != X_35
| multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(identity,inverse(inverse(X_35)))) = greatest_lower_bound(least_upper_bound(identity,inverse(X_35)),least_upper_bound(identity,X_35)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(identity,inverse(inverse(X_35)))),greatest_lower_bound(least_upper_bound(identity,inverse(X_35)),least_upper_bound(identity,inverse(inverse(X_35))))) ),[1,1,1],$fot(X_35)]]) ).
cnf(refute_0_1329,plain,
( multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(identity,inverse(inverse(X_35)))) != greatest_lower_bound(least_upper_bound(identity,inverse(X_35)),least_upper_bound(identity,inverse(inverse(X_35))))
| multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(identity,inverse(inverse(X_35)))) = greatest_lower_bound(least_upper_bound(identity,inverse(X_35)),least_upper_bound(identity,X_35)) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_35)),X_35) )],[refute_0_452,refute_0_1328]) ).
cnf(refute_0_1330,plain,
multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(identity,inverse(inverse(X_35)))) = greatest_lower_bound(least_upper_bound(identity,inverse(X_35)),least_upper_bound(identity,X_35)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(identity,inverse(inverse(X_35)))),greatest_lower_bound(least_upper_bound(identity,inverse(X_35)),least_upper_bound(identity,inverse(inverse(X_35))))) )],[refute_0_1327,refute_0_1329]) ).
cnf(refute_0_1331,plain,
multiply(least_upper_bound(inverse(X_114),identity),greatest_lower_bound(identity,X_114)) = least_upper_bound(greatest_lower_bound(identity,X_114),multiply(inverse(X_114),greatest_lower_bound(identity,X_114))),
inference(subst,[],[refute_0_761:[bind(X_67,$fot(greatest_lower_bound(identity,X_114))),bind(X_68,$fot(inverse(X_114)))]]) ).
cnf(refute_0_1332,plain,
( multiply(inverse(X_114),greatest_lower_bound(identity,X_114)) != greatest_lower_bound(identity,inverse(X_114))
| multiply(least_upper_bound(inverse(X_114),identity),greatest_lower_bound(identity,X_114)) != least_upper_bound(greatest_lower_bound(identity,X_114),multiply(inverse(X_114),greatest_lower_bound(identity,X_114)))
| multiply(least_upper_bound(inverse(X_114),identity),greatest_lower_bound(identity,X_114)) = least_upper_bound(greatest_lower_bound(identity,X_114),greatest_lower_bound(identity,inverse(X_114))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(X_114),identity),greatest_lower_bound(identity,X_114)),least_upper_bound(greatest_lower_bound(identity,X_114),multiply(inverse(X_114),greatest_lower_bound(identity,X_114)))) ),[1,1],$fot(greatest_lower_bound(identity,inverse(X_114)))]]) ).
cnf(refute_0_1333,plain,
( multiply(least_upper_bound(inverse(X_114),identity),greatest_lower_bound(identity,X_114)) != least_upper_bound(greatest_lower_bound(identity,X_114),multiply(inverse(X_114),greatest_lower_bound(identity,X_114)))
| multiply(least_upper_bound(inverse(X_114),identity),greatest_lower_bound(identity,X_114)) = least_upper_bound(greatest_lower_bound(identity,X_114),greatest_lower_bound(identity,inverse(X_114))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_114),greatest_lower_bound(identity,X_114)),greatest_lower_bound(identity,inverse(X_114))) )],[refute_0_644,refute_0_1332]) ).
cnf(refute_0_1334,plain,
multiply(least_upper_bound(inverse(X_114),identity),greatest_lower_bound(identity,X_114)) = least_upper_bound(greatest_lower_bound(identity,X_114),greatest_lower_bound(identity,inverse(X_114))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_114),identity),greatest_lower_bound(identity,X_114)),least_upper_bound(greatest_lower_bound(identity,X_114),multiply(inverse(X_114),greatest_lower_bound(identity,X_114)))) )],[refute_0_1331,refute_0_1333]) ).
cnf(refute_0_1335,plain,
least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_133,X_19))) = least_upper_bound(X_19,multiply(X_133,X_19)),
inference(subst,[],[refute_0_516:[bind(X_18,$fot(multiply(X_133,X_19)))]]) ).
cnf(refute_0_1336,plain,
multiply(least_upper_bound(X_133,identity),X_19) = least_upper_bound(X_19,multiply(X_133,X_19)),
inference(subst,[],[refute_0_761:[bind(X_67,$fot(X_19)),bind(X_68,$fot(X_133))]]) ).
cnf(refute_0_1337,plain,
( multiply(least_upper_bound(X_133,identity),X_19) != least_upper_bound(X_19,multiply(X_133,X_19))
| least_upper_bound(X_19,multiply(X_133,X_19)) = multiply(least_upper_bound(X_133,identity),X_19) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(least_upper_bound(X_133,identity),X_19))),bind(Y0,$fot(least_upper_bound(X_19,multiply(X_133,X_19))))]]) ).
cnf(refute_0_1338,plain,
least_upper_bound(X_19,multiply(X_133,X_19)) = multiply(least_upper_bound(X_133,identity),X_19),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_133,identity),X_19),least_upper_bound(X_19,multiply(X_133,X_19))) )],[refute_0_1336,refute_0_1337]) ).
cnf(refute_0_1339,plain,
( least_upper_bound(X_19,multiply(X_133,X_19)) != multiply(least_upper_bound(X_133,identity),X_19)
| least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_133,X_19))) != least_upper_bound(X_19,multiply(X_133,X_19))
| least_upper_bound(X_19,multiply(least_upper_bound(X_133,identity),X_19)) = least_upper_bound(X_19,multiply(X_133,X_19)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_133,X_19))),least_upper_bound(X_19,multiply(X_133,X_19))) ),[0,1],$fot(multiply(least_upper_bound(X_133,identity),X_19))]]) ).
cnf(refute_0_1340,plain,
( least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_133,X_19))) != least_upper_bound(X_19,multiply(X_133,X_19))
| least_upper_bound(X_19,multiply(least_upper_bound(X_133,identity),X_19)) = least_upper_bound(X_19,multiply(X_133,X_19)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,multiply(X_133,X_19)),multiply(least_upper_bound(X_133,identity),X_19)) )],[refute_0_1338,refute_0_1339]) ).
cnf(refute_0_1341,plain,
least_upper_bound(X_19,multiply(least_upper_bound(X_133,identity),X_19)) = least_upper_bound(X_19,multiply(X_133,X_19)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_133,X_19))),least_upper_bound(X_19,multiply(X_133,X_19))) )],[refute_0_1335,refute_0_1340]) ).
cnf(refute_0_1342,plain,
least_upper_bound(identity,least_upper_bound(X_133,identity)) = least_upper_bound(identity,X_133),
inference(subst,[],[refute_0_175:[bind(Y,$fot(X_133)),bind(X_15,$fot(identity))]]) ).
cnf(refute_0_1343,plain,
multiply(least_upper_bound(identity,least_upper_bound(X_133,identity)),X_19) = multiply(least_upper_bound(identity,least_upper_bound(X_133,identity)),X_19),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(identity,least_upper_bound(X_133,identity)),X_19))]]) ).
cnf(refute_0_1344,plain,
( multiply(least_upper_bound(identity,least_upper_bound(X_133,identity)),X_19) != multiply(least_upper_bound(identity,least_upper_bound(X_133,identity)),X_19)
| least_upper_bound(identity,least_upper_bound(X_133,identity)) != least_upper_bound(identity,X_133)
| multiply(least_upper_bound(identity,least_upper_bound(X_133,identity)),X_19) = multiply(least_upper_bound(identity,X_133),X_19) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(X_133,identity)),X_19),multiply(least_upper_bound(identity,least_upper_bound(X_133,identity)),X_19)) ),[1,0],$fot(least_upper_bound(identity,X_133))]]) ).
cnf(refute_0_1345,plain,
( least_upper_bound(identity,least_upper_bound(X_133,identity)) != least_upper_bound(identity,X_133)
| multiply(least_upper_bound(identity,least_upper_bound(X_133,identity)),X_19) = multiply(least_upper_bound(identity,X_133),X_19) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(X_133,identity)),X_19),multiply(least_upper_bound(identity,least_upper_bound(X_133,identity)),X_19)) )],[refute_0_1343,refute_0_1344]) ).
cnf(refute_0_1346,plain,
multiply(least_upper_bound(identity,least_upper_bound(X_133,identity)),X_19) = multiply(least_upper_bound(identity,X_133),X_19),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_133,identity)),least_upper_bound(identity,X_133)) )],[refute_0_1342,refute_0_1345]) ).
cnf(refute_0_1347,plain,
greatest_lower_bound(least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67)),least_upper_bound(multiply(X_68,X_67),multiply(X_69,X_67))) = least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67)),
inference(subst,[],[refute_0_544:[bind(X_18,$fot(multiply(X_69,X_67))),bind(X_7,$fot(multiply(X_68,X_67)))]]) ).
cnf(refute_0_1348,plain,
multiply(least_upper_bound(X_68,X_69),X_67) = least_upper_bound(multiply(X_68,X_67),multiply(X_69,X_67)),
inference(subst,[],[monotony_lub2:[bind(X,$fot(X_67)),bind(Y,$fot(X_68)),bind(Z,$fot(X_69))]]) ).
cnf(refute_0_1349,plain,
( multiply(least_upper_bound(X_68,X_69),X_67) != least_upper_bound(multiply(X_68,X_67),multiply(X_69,X_67))
| least_upper_bound(multiply(X_68,X_67),multiply(X_69,X_67)) = multiply(least_upper_bound(X_68,X_69),X_67) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(least_upper_bound(X_68,X_69),X_67))),bind(Y0,$fot(least_upper_bound(multiply(X_68,X_67),multiply(X_69,X_67))))]]) ).
cnf(refute_0_1350,plain,
least_upper_bound(multiply(X_68,X_67),multiply(X_69,X_67)) = multiply(least_upper_bound(X_68,X_69),X_67),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_68,X_69),X_67),least_upper_bound(multiply(X_68,X_67),multiply(X_69,X_67))) )],[refute_0_1348,refute_0_1349]) ).
cnf(refute_0_1351,plain,
( greatest_lower_bound(least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67)),least_upper_bound(multiply(X_68,X_67),multiply(X_69,X_67))) != least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67))
| least_upper_bound(multiply(X_68,X_67),multiply(X_69,X_67)) != multiply(least_upper_bound(X_68,X_69),X_67)
| greatest_lower_bound(least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67)),multiply(least_upper_bound(X_68,X_69),X_67)) = least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67)),least_upper_bound(multiply(X_68,X_67),multiply(X_69,X_67))),least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67))) ),[0,1],$fot(multiply(least_upper_bound(X_68,X_69),X_67))]]) ).
cnf(refute_0_1352,plain,
( greatest_lower_bound(least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67)),least_upper_bound(multiply(X_68,X_67),multiply(X_69,X_67))) != least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67))
| greatest_lower_bound(least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67)),multiply(least_upper_bound(X_68,X_69),X_67)) = least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_68,X_67),multiply(X_69,X_67)),multiply(least_upper_bound(X_68,X_69),X_67)) )],[refute_0_1350,refute_0_1351]) ).
cnf(refute_0_1353,plain,
greatest_lower_bound(least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67)),multiply(least_upper_bound(X_68,X_69),X_67)) = least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67)),least_upper_bound(multiply(X_68,X_67),multiply(X_69,X_67))),least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67))) )],[refute_0_1347,refute_0_1352]) ).
cnf(refute_0_1354,plain,
greatest_lower_bound(least_upper_bound(X_68,X_69),least_upper_bound(X_69,X_68)) = least_upper_bound(X_68,X_69),
inference(subst,[],[refute_0_544:[bind(X_18,$fot(X_68)),bind(X_7,$fot(X_69))]]) ).
cnf(refute_0_1355,plain,
multiply(greatest_lower_bound(least_upper_bound(X_68,X_69),least_upper_bound(X_69,X_68)),X_67) = multiply(greatest_lower_bound(least_upper_bound(X_68,X_69),least_upper_bound(X_69,X_68)),X_67),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(least_upper_bound(X_68,X_69),least_upper_bound(X_69,X_68)),X_67))]]) ).
cnf(refute_0_1356,plain,
( multiply(greatest_lower_bound(least_upper_bound(X_68,X_69),least_upper_bound(X_69,X_68)),X_67) != multiply(greatest_lower_bound(least_upper_bound(X_68,X_69),least_upper_bound(X_69,X_68)),X_67)
| greatest_lower_bound(least_upper_bound(X_68,X_69),least_upper_bound(X_69,X_68)) != least_upper_bound(X_68,X_69)
| multiply(greatest_lower_bound(least_upper_bound(X_68,X_69),least_upper_bound(X_69,X_68)),X_67) = multiply(least_upper_bound(X_68,X_69),X_67) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(X_68,X_69),least_upper_bound(X_69,X_68)),X_67),multiply(greatest_lower_bound(least_upper_bound(X_68,X_69),least_upper_bound(X_69,X_68)),X_67)) ),[1,0],$fot(least_upper_bound(X_68,X_69))]]) ).
cnf(refute_0_1357,plain,
( greatest_lower_bound(least_upper_bound(X_68,X_69),least_upper_bound(X_69,X_68)) != least_upper_bound(X_68,X_69)
| multiply(greatest_lower_bound(least_upper_bound(X_68,X_69),least_upper_bound(X_69,X_68)),X_67) = multiply(least_upper_bound(X_68,X_69),X_67) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(X_68,X_69),least_upper_bound(X_69,X_68)),X_67),multiply(greatest_lower_bound(least_upper_bound(X_68,X_69),least_upper_bound(X_69,X_68)),X_67)) )],[refute_0_1355,refute_0_1356]) ).
cnf(refute_0_1358,plain,
multiply(greatest_lower_bound(least_upper_bound(X_68,X_69),least_upper_bound(X_69,X_68)),X_67) = multiply(least_upper_bound(X_68,X_69),X_67),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_68,X_69),least_upper_bound(X_69,X_68)),least_upper_bound(X_68,X_69)) )],[refute_0_1354,refute_0_1357]) ).
cnf(refute_0_1359,plain,
( multiply(greatest_lower_bound(Y,Z),X) != greatest_lower_bound(multiply(Y,X),multiply(Z,X))
| greatest_lower_bound(multiply(Y,X),multiply(Z,X)) = multiply(greatest_lower_bound(Y,Z),X) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(greatest_lower_bound(Y,Z),X))),bind(Y0,$fot(greatest_lower_bound(multiply(Y,X),multiply(Z,X))))]]) ).
cnf(refute_0_1360,plain,
greatest_lower_bound(multiply(Y,X),multiply(Z,X)) = multiply(greatest_lower_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Y,X),multiply(Z,X))) )],[monotony_glb2,refute_0_1359]) ).
cnf(refute_0_1361,plain,
greatest_lower_bound(multiply(least_upper_bound(X_68,X_69),X_67),multiply(least_upper_bound(X_69,X_68),X_67)) = multiply(greatest_lower_bound(least_upper_bound(X_68,X_69),least_upper_bound(X_69,X_68)),X_67),
inference(subst,[],[refute_0_1360:[bind(X,$fot(X_67)),bind(Y,$fot(least_upper_bound(X_68,X_69))),bind(Z,$fot(least_upper_bound(X_69,X_68)))]]) ).
cnf(refute_0_1362,plain,
( multiply(greatest_lower_bound(least_upper_bound(X_68,X_69),least_upper_bound(X_69,X_68)),X_67) != multiply(least_upper_bound(X_68,X_69),X_67)
| greatest_lower_bound(multiply(least_upper_bound(X_68,X_69),X_67),multiply(least_upper_bound(X_69,X_68),X_67)) != multiply(greatest_lower_bound(least_upper_bound(X_68,X_69),least_upper_bound(X_69,X_68)),X_67)
| greatest_lower_bound(multiply(least_upper_bound(X_68,X_69),X_67),multiply(least_upper_bound(X_69,X_68),X_67)) = multiply(least_upper_bound(X_68,X_69),X_67) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(greatest_lower_bound(multiply(least_upper_bound(X_68,X_69),X_67),multiply(least_upper_bound(X_69,X_68),X_67)))),bind(Y0,$fot(multiply(greatest_lower_bound(least_upper_bound(X_68,X_69),least_upper_bound(X_69,X_68)),X_67))),bind(Z0,$fot(multiply(least_upper_bound(X_68,X_69),X_67)))]]) ).
cnf(refute_0_1363,plain,
( multiply(greatest_lower_bound(least_upper_bound(X_68,X_69),least_upper_bound(X_69,X_68)),X_67) != multiply(least_upper_bound(X_68,X_69),X_67)
| greatest_lower_bound(multiply(least_upper_bound(X_68,X_69),X_67),multiply(least_upper_bound(X_69,X_68),X_67)) = multiply(least_upper_bound(X_68,X_69),X_67) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(X_68,X_69),X_67),multiply(least_upper_bound(X_69,X_68),X_67)),multiply(greatest_lower_bound(least_upper_bound(X_68,X_69),least_upper_bound(X_69,X_68)),X_67)) )],[refute_0_1361,refute_0_1362]) ).
cnf(refute_0_1364,plain,
greatest_lower_bound(multiply(least_upper_bound(X_68,X_69),X_67),multiply(least_upper_bound(X_69,X_68),X_67)) = multiply(least_upper_bound(X_68,X_69),X_67),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(X_68,X_69),least_upper_bound(X_69,X_68)),X_67),multiply(least_upper_bound(X_68,X_69),X_67)) )],[refute_0_1358,refute_0_1363]) ).
cnf(refute_0_1365,plain,
least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67)) = multiply(least_upper_bound(X_69,X_68),X_67),
inference(subst,[],[refute_0_744:[bind(X,$fot(X_67)),bind(Y,$fot(X_69)),bind(Z,$fot(X_68))]]) ).
cnf(refute_0_1366,plain,
greatest_lower_bound(multiply(least_upper_bound(X_68,X_69),X_67),least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67))) = greatest_lower_bound(multiply(least_upper_bound(X_68,X_69),X_67),least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(multiply(least_upper_bound(X_68,X_69),X_67),least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67))))]]) ).
cnf(refute_0_1367,plain,
( greatest_lower_bound(multiply(least_upper_bound(X_68,X_69),X_67),least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67))) != greatest_lower_bound(multiply(least_upper_bound(X_68,X_69),X_67),least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67)))
| least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67)) != multiply(least_upper_bound(X_69,X_68),X_67)
| greatest_lower_bound(multiply(least_upper_bound(X_68,X_69),X_67),least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67))) = greatest_lower_bound(multiply(least_upper_bound(X_68,X_69),X_67),multiply(least_upper_bound(X_69,X_68),X_67)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(X_68,X_69),X_67),least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67))),greatest_lower_bound(multiply(least_upper_bound(X_68,X_69),X_67),least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67)))) ),[1,1],$fot(multiply(least_upper_bound(X_69,X_68),X_67))]]) ).
cnf(refute_0_1368,plain,
( least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67)) != multiply(least_upper_bound(X_69,X_68),X_67)
| greatest_lower_bound(multiply(least_upper_bound(X_68,X_69),X_67),least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67))) = greatest_lower_bound(multiply(least_upper_bound(X_68,X_69),X_67),multiply(least_upper_bound(X_69,X_68),X_67)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(X_68,X_69),X_67),least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67))),greatest_lower_bound(multiply(least_upper_bound(X_68,X_69),X_67),least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67)))) )],[refute_0_1366,refute_0_1367]) ).
cnf(refute_0_1369,plain,
greatest_lower_bound(multiply(least_upper_bound(X_68,X_69),X_67),least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67))) = greatest_lower_bound(multiply(least_upper_bound(X_68,X_69),X_67),multiply(least_upper_bound(X_69,X_68),X_67)),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67)),multiply(least_upper_bound(X_69,X_68),X_67)) )],[refute_0_1365,refute_0_1368]) ).
cnf(refute_0_1370,plain,
( greatest_lower_bound(multiply(least_upper_bound(X_68,X_69),X_67),multiply(least_upper_bound(X_69,X_68),X_67)) != multiply(least_upper_bound(X_68,X_69),X_67)
| greatest_lower_bound(multiply(least_upper_bound(X_68,X_69),X_67),least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67))) != greatest_lower_bound(multiply(least_upper_bound(X_68,X_69),X_67),multiply(least_upper_bound(X_69,X_68),X_67))
| greatest_lower_bound(multiply(least_upper_bound(X_68,X_69),X_67),least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67))) = multiply(least_upper_bound(X_68,X_69),X_67) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(greatest_lower_bound(multiply(least_upper_bound(X_68,X_69),X_67),least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67))))),bind(Y0,$fot(greatest_lower_bound(multiply(least_upper_bound(X_68,X_69),X_67),multiply(least_upper_bound(X_69,X_68),X_67)))),bind(Z0,$fot(multiply(least_upper_bound(X_68,X_69),X_67)))]]) ).
cnf(refute_0_1371,plain,
( greatest_lower_bound(multiply(least_upper_bound(X_68,X_69),X_67),multiply(least_upper_bound(X_69,X_68),X_67)) != multiply(least_upper_bound(X_68,X_69),X_67)
| greatest_lower_bound(multiply(least_upper_bound(X_68,X_69),X_67),least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67))) = multiply(least_upper_bound(X_68,X_69),X_67) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(X_68,X_69),X_67),least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67))),greatest_lower_bound(multiply(least_upper_bound(X_68,X_69),X_67),multiply(least_upper_bound(X_69,X_68),X_67))) )],[refute_0_1369,refute_0_1370]) ).
cnf(refute_0_1372,plain,
greatest_lower_bound(multiply(least_upper_bound(X_68,X_69),X_67),least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67))) = multiply(least_upper_bound(X_68,X_69),X_67),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(X_68,X_69),X_67),multiply(least_upper_bound(X_69,X_68),X_67)),multiply(least_upper_bound(X_68,X_69),X_67)) )],[refute_0_1364,refute_0_1371]) ).
cnf(refute_0_1373,plain,
greatest_lower_bound(least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67)),multiply(least_upper_bound(X_68,X_69),X_67)) = greatest_lower_bound(multiply(least_upper_bound(X_68,X_69),X_67),least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67))),
inference(subst,[],[refute_0_42:[bind(X,$fot(multiply(least_upper_bound(X_68,X_69),X_67))),bind(Y,$fot(least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67))))]]) ).
cnf(refute_0_1374,plain,
( greatest_lower_bound(multiply(least_upper_bound(X_68,X_69),X_67),least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67))) != multiply(least_upper_bound(X_68,X_69),X_67)
| greatest_lower_bound(least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67)),multiply(least_upper_bound(X_68,X_69),X_67)) != greatest_lower_bound(multiply(least_upper_bound(X_68,X_69),X_67),least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67)))
| greatest_lower_bound(least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67)),multiply(least_upper_bound(X_68,X_69),X_67)) = multiply(least_upper_bound(X_68,X_69),X_67) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67)),multiply(least_upper_bound(X_68,X_69),X_67)))),bind(Y0,$fot(greatest_lower_bound(multiply(least_upper_bound(X_68,X_69),X_67),least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67))))),bind(Z0,$fot(multiply(least_upper_bound(X_68,X_69),X_67)))]]) ).
cnf(refute_0_1375,plain,
( greatest_lower_bound(multiply(least_upper_bound(X_68,X_69),X_67),least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67))) != multiply(least_upper_bound(X_68,X_69),X_67)
| greatest_lower_bound(least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67)),multiply(least_upper_bound(X_68,X_69),X_67)) = multiply(least_upper_bound(X_68,X_69),X_67) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67)),multiply(least_upper_bound(X_68,X_69),X_67)),greatest_lower_bound(multiply(least_upper_bound(X_68,X_69),X_67),least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67)))) )],[refute_0_1373,refute_0_1374]) ).
cnf(refute_0_1376,plain,
greatest_lower_bound(least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67)),multiply(least_upper_bound(X_68,X_69),X_67)) = multiply(least_upper_bound(X_68,X_69),X_67),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(X_68,X_69),X_67),least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67))),multiply(least_upper_bound(X_68,X_69),X_67)) )],[refute_0_1372,refute_0_1375]) ).
cnf(refute_0_1377,plain,
( greatest_lower_bound(least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67)),multiply(least_upper_bound(X_68,X_69),X_67)) != multiply(least_upper_bound(X_68,X_69),X_67)
| greatest_lower_bound(least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67)),multiply(least_upper_bound(X_68,X_69),X_67)) != least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67))
| multiply(least_upper_bound(X_68,X_69),X_67) = least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67)),multiply(least_upper_bound(X_68,X_69),X_67)),least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67))) ),[0],$fot(multiply(least_upper_bound(X_68,X_69),X_67))]]) ).
cnf(refute_0_1378,plain,
( greatest_lower_bound(least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67)),multiply(least_upper_bound(X_68,X_69),X_67)) != least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67))
| multiply(least_upper_bound(X_68,X_69),X_67) = least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67)),multiply(least_upper_bound(X_68,X_69),X_67)),multiply(least_upper_bound(X_68,X_69),X_67)) )],[refute_0_1376,refute_0_1377]) ).
cnf(refute_0_1379,plain,
( multiply(least_upper_bound(X_68,X_69),X_67) != least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67))
| least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67)) != multiply(least_upper_bound(X_69,X_68),X_67)
| multiply(least_upper_bound(X_68,X_69),X_67) = multiply(least_upper_bound(X_69,X_68),X_67) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_68,X_69),X_67),multiply(least_upper_bound(X_69,X_68),X_67)) ),[0],$fot(least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67)))]]) ).
cnf(refute_0_1380,plain,
( multiply(least_upper_bound(X_68,X_69),X_67) != least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67))
| multiply(least_upper_bound(X_68,X_69),X_67) = multiply(least_upper_bound(X_69,X_68),X_67) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67)),multiply(least_upper_bound(X_69,X_68),X_67)) )],[refute_0_1365,refute_0_1379]) ).
cnf(refute_0_1381,plain,
( greatest_lower_bound(least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67)),multiply(least_upper_bound(X_68,X_69),X_67)) != least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67))
| multiply(least_upper_bound(X_68,X_69),X_67) = multiply(least_upper_bound(X_69,X_68),X_67) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_68,X_69),X_67),least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67))) )],[refute_0_1378,refute_0_1380]) ).
cnf(refute_0_1382,plain,
multiply(least_upper_bound(X_68,X_69),X_67) = multiply(least_upper_bound(X_69,X_68),X_67),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67)),multiply(least_upper_bound(X_68,X_69),X_67)),least_upper_bound(multiply(X_69,X_67),multiply(X_68,X_67))) )],[refute_0_1353,refute_0_1381]) ).
cnf(refute_0_1383,plain,
( multiply(least_upper_bound(X_68,X_69),X_67) != multiply(least_upper_bound(X_69,X_68),X_67)
| multiply(least_upper_bound(X_69,X_68),X_67) = multiply(least_upper_bound(X_68,X_69),X_67) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(least_upper_bound(X_68,X_69),X_67))),bind(Y0,$fot(multiply(least_upper_bound(X_69,X_68),X_67)))]]) ).
cnf(refute_0_1384,plain,
multiply(least_upper_bound(X_69,X_68),X_67) = multiply(least_upper_bound(X_68,X_69),X_67),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_68,X_69),X_67),multiply(least_upper_bound(X_69,X_68),X_67)) )],[refute_0_1382,refute_0_1383]) ).
cnf(refute_0_1385,plain,
multiply(least_upper_bound(least_upper_bound(X_133,identity),identity),X_19) = multiply(least_upper_bound(identity,least_upper_bound(X_133,identity)),X_19),
inference(subst,[],[refute_0_1384:[bind(X_67,$fot(X_19)),bind(X_68,$fot(identity)),bind(X_69,$fot(least_upper_bound(X_133,identity)))]]) ).
cnf(refute_0_1386,plain,
least_upper_bound(X_19,multiply(least_upper_bound(X_133,identity),X_19)) = multiply(least_upper_bound(least_upper_bound(X_133,identity),identity),X_19),
inference(subst,[],[refute_0_763:[bind(X_67,$fot(X_19)),bind(X_68,$fot(least_upper_bound(X_133,identity)))]]) ).
cnf(refute_0_1387,plain,
( multiply(least_upper_bound(least_upper_bound(X_133,identity),identity),X_19) != multiply(least_upper_bound(identity,least_upper_bound(X_133,identity)),X_19)
| least_upper_bound(X_19,multiply(least_upper_bound(X_133,identity),X_19)) != multiply(least_upper_bound(least_upper_bound(X_133,identity),identity),X_19)
| least_upper_bound(X_19,multiply(least_upper_bound(X_133,identity),X_19)) = multiply(least_upper_bound(identity,least_upper_bound(X_133,identity)),X_19) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(least_upper_bound(X_19,multiply(least_upper_bound(X_133,identity),X_19)))),bind(Y0,$fot(multiply(least_upper_bound(least_upper_bound(X_133,identity),identity),X_19))),bind(Z0,$fot(multiply(least_upper_bound(identity,least_upper_bound(X_133,identity)),X_19)))]]) ).
cnf(refute_0_1388,plain,
( multiply(least_upper_bound(least_upper_bound(X_133,identity),identity),X_19) != multiply(least_upper_bound(identity,least_upper_bound(X_133,identity)),X_19)
| least_upper_bound(X_19,multiply(least_upper_bound(X_133,identity),X_19)) = multiply(least_upper_bound(identity,least_upper_bound(X_133,identity)),X_19) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,multiply(least_upper_bound(X_133,identity),X_19)),multiply(least_upper_bound(least_upper_bound(X_133,identity),identity),X_19)) )],[refute_0_1386,refute_0_1387]) ).
cnf(refute_0_1389,plain,
least_upper_bound(X_19,multiply(least_upper_bound(X_133,identity),X_19)) = multiply(least_upper_bound(identity,least_upper_bound(X_133,identity)),X_19),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_133,identity),identity),X_19),multiply(least_upper_bound(identity,least_upper_bound(X_133,identity)),X_19)) )],[refute_0_1385,refute_0_1388]) ).
cnf(refute_0_1390,plain,
( multiply(least_upper_bound(identity,least_upper_bound(X_133,identity)),X_19) != multiply(least_upper_bound(identity,X_133),X_19)
| least_upper_bound(X_19,multiply(least_upper_bound(X_133,identity),X_19)) != multiply(least_upper_bound(identity,least_upper_bound(X_133,identity)),X_19)
| least_upper_bound(X_19,multiply(least_upper_bound(X_133,identity),X_19)) = multiply(least_upper_bound(identity,X_133),X_19) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(least_upper_bound(X_19,multiply(least_upper_bound(X_133,identity),X_19)))),bind(Y0,$fot(multiply(least_upper_bound(identity,least_upper_bound(X_133,identity)),X_19))),bind(Z0,$fot(multiply(least_upper_bound(identity,X_133),X_19)))]]) ).
cnf(refute_0_1391,plain,
( multiply(least_upper_bound(identity,least_upper_bound(X_133,identity)),X_19) != multiply(least_upper_bound(identity,X_133),X_19)
| least_upper_bound(X_19,multiply(least_upper_bound(X_133,identity),X_19)) = multiply(least_upper_bound(identity,X_133),X_19) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,multiply(least_upper_bound(X_133,identity),X_19)),multiply(least_upper_bound(identity,least_upper_bound(X_133,identity)),X_19)) )],[refute_0_1389,refute_0_1390]) ).
cnf(refute_0_1392,plain,
least_upper_bound(X_19,multiply(least_upper_bound(X_133,identity),X_19)) = multiply(least_upper_bound(identity,X_133),X_19),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(X_133,identity)),X_19),multiply(least_upper_bound(identity,X_133),X_19)) )],[refute_0_1346,refute_0_1391]) ).
cnf(refute_0_1393,plain,
( least_upper_bound(X_19,multiply(least_upper_bound(X_133,identity),X_19)) != multiply(least_upper_bound(identity,X_133),X_19)
| least_upper_bound(X_19,multiply(least_upper_bound(X_133,identity),X_19)) != least_upper_bound(X_19,multiply(X_133,X_19))
| multiply(least_upper_bound(identity,X_133),X_19) = least_upper_bound(X_19,multiply(X_133,X_19)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_19,multiply(least_upper_bound(X_133,identity),X_19)),least_upper_bound(X_19,multiply(X_133,X_19))) ),[0],$fot(multiply(least_upper_bound(identity,X_133),X_19))]]) ).
cnf(refute_0_1394,plain,
( least_upper_bound(X_19,multiply(least_upper_bound(X_133,identity),X_19)) != least_upper_bound(X_19,multiply(X_133,X_19))
| multiply(least_upper_bound(identity,X_133),X_19) = least_upper_bound(X_19,multiply(X_133,X_19)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,multiply(least_upper_bound(X_133,identity),X_19)),multiply(least_upper_bound(identity,X_133),X_19)) )],[refute_0_1392,refute_0_1393]) ).
cnf(refute_0_1395,plain,
( multiply(least_upper_bound(identity,X_133),X_19) != least_upper_bound(X_19,multiply(X_133,X_19))
| least_upper_bound(X_19,multiply(X_133,X_19)) != multiply(least_upper_bound(X_133,identity),X_19)
| multiply(least_upper_bound(identity,X_133),X_19) = multiply(least_upper_bound(X_133,identity),X_19) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(identity,X_133),X_19),multiply(least_upper_bound(X_133,identity),X_19)) ),[0],$fot(least_upper_bound(X_19,multiply(X_133,X_19)))]]) ).
cnf(refute_0_1396,plain,
( multiply(least_upper_bound(identity,X_133),X_19) != least_upper_bound(X_19,multiply(X_133,X_19))
| multiply(least_upper_bound(identity,X_133),X_19) = multiply(least_upper_bound(X_133,identity),X_19) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,multiply(X_133,X_19)),multiply(least_upper_bound(X_133,identity),X_19)) )],[refute_0_1338,refute_0_1395]) ).
cnf(refute_0_1397,plain,
( least_upper_bound(X_19,multiply(least_upper_bound(X_133,identity),X_19)) != least_upper_bound(X_19,multiply(X_133,X_19))
| multiply(least_upper_bound(identity,X_133),X_19) = multiply(least_upper_bound(X_133,identity),X_19) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_133),X_19),least_upper_bound(X_19,multiply(X_133,X_19))) )],[refute_0_1394,refute_0_1396]) ).
cnf(refute_0_1398,plain,
multiply(least_upper_bound(identity,X_133),X_19) = multiply(least_upper_bound(X_133,identity),X_19),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,multiply(least_upper_bound(X_133,identity),X_19)),least_upper_bound(X_19,multiply(X_133,X_19))) )],[refute_0_1341,refute_0_1397]) ).
cnf(refute_0_1399,plain,
( multiply(least_upper_bound(identity,X_133),X_19) != multiply(least_upper_bound(X_133,identity),X_19)
| multiply(least_upper_bound(X_133,identity),X_19) = multiply(least_upper_bound(identity,X_133),X_19) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(least_upper_bound(identity,X_133),X_19))),bind(Y0,$fot(multiply(least_upper_bound(X_133,identity),X_19)))]]) ).
cnf(refute_0_1400,plain,
multiply(least_upper_bound(X_133,identity),X_19) = multiply(least_upper_bound(identity,X_133),X_19),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_133),X_19),multiply(least_upper_bound(X_133,identity),X_19)) )],[refute_0_1398,refute_0_1399]) ).
cnf(refute_0_1401,plain,
multiply(least_upper_bound(inverse(X_114),identity),greatest_lower_bound(identity,X_114)) = multiply(least_upper_bound(identity,inverse(X_114)),greatest_lower_bound(identity,X_114)),
inference(subst,[],[refute_0_1400:[bind(X_133,$fot(inverse(X_114))),bind(X_19,$fot(greatest_lower_bound(identity,X_114)))]]) ).
cnf(refute_0_1402,plain,
( multiply(least_upper_bound(inverse(X_114),identity),greatest_lower_bound(identity,X_114)) != multiply(least_upper_bound(identity,inverse(X_114)),greatest_lower_bound(identity,X_114))
| multiply(least_upper_bound(inverse(X_114),identity),greatest_lower_bound(identity,X_114)) != least_upper_bound(greatest_lower_bound(identity,X_114),greatest_lower_bound(identity,inverse(X_114)))
| multiply(least_upper_bound(identity,inverse(X_114)),greatest_lower_bound(identity,X_114)) = least_upper_bound(greatest_lower_bound(identity,X_114),greatest_lower_bound(identity,inverse(X_114))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(X_114),identity),greatest_lower_bound(identity,X_114)),least_upper_bound(greatest_lower_bound(identity,X_114),greatest_lower_bound(identity,inverse(X_114)))) ),[0],$fot(multiply(least_upper_bound(identity,inverse(X_114)),greatest_lower_bound(identity,X_114)))]]) ).
cnf(refute_0_1403,plain,
( multiply(least_upper_bound(inverse(X_114),identity),greatest_lower_bound(identity,X_114)) != least_upper_bound(greatest_lower_bound(identity,X_114),greatest_lower_bound(identity,inverse(X_114)))
| multiply(least_upper_bound(identity,inverse(X_114)),greatest_lower_bound(identity,X_114)) = least_upper_bound(greatest_lower_bound(identity,X_114),greatest_lower_bound(identity,inverse(X_114))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_114),identity),greatest_lower_bound(identity,X_114)),multiply(least_upper_bound(identity,inverse(X_114)),greatest_lower_bound(identity,X_114))) )],[refute_0_1401,refute_0_1402]) ).
cnf(refute_0_1404,plain,
multiply(greatest_lower_bound(identity,X_126),least_upper_bound(inverse(X_126),identity)) = least_upper_bound(greatest_lower_bound(identity,X_126),multiply(greatest_lower_bound(identity,X_126),inverse(X_126))),
inference(subst,[],[refute_0_528:[bind(X_48,$fot(greatest_lower_bound(identity,X_126))),bind(X_49,$fot(inverse(X_126)))]]) ).
cnf(refute_0_1405,plain,
greatest_lower_bound(identity,inverse(X_126)) = multiply(greatest_lower_bound(identity,X_126),inverse(X_126)),
inference(subst,[],[refute_0_436:[bind(X_125,$fot(X_126))]]) ).
cnf(refute_0_1406,plain,
( greatest_lower_bound(identity,inverse(X_126)) != multiply(greatest_lower_bound(identity,X_126),inverse(X_126))
| multiply(greatest_lower_bound(identity,X_126),inverse(X_126)) = greatest_lower_bound(identity,inverse(X_126)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(greatest_lower_bound(identity,inverse(X_126)))),bind(Y0,$fot(multiply(greatest_lower_bound(identity,X_126),inverse(X_126))))]]) ).
cnf(refute_0_1407,plain,
multiply(greatest_lower_bound(identity,X_126),inverse(X_126)) = greatest_lower_bound(identity,inverse(X_126)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(X_126)),multiply(greatest_lower_bound(identity,X_126),inverse(X_126))) )],[refute_0_1405,refute_0_1406]) ).
cnf(refute_0_1408,plain,
( multiply(greatest_lower_bound(identity,X_126),inverse(X_126)) != greatest_lower_bound(identity,inverse(X_126))
| multiply(greatest_lower_bound(identity,X_126),least_upper_bound(inverse(X_126),identity)) != least_upper_bound(greatest_lower_bound(identity,X_126),multiply(greatest_lower_bound(identity,X_126),inverse(X_126)))
| multiply(greatest_lower_bound(identity,X_126),least_upper_bound(inverse(X_126),identity)) = least_upper_bound(greatest_lower_bound(identity,X_126),greatest_lower_bound(identity,inverse(X_126))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_126),least_upper_bound(inverse(X_126),identity)),least_upper_bound(greatest_lower_bound(identity,X_126),multiply(greatest_lower_bound(identity,X_126),inverse(X_126)))) ),[1,1],$fot(greatest_lower_bound(identity,inverse(X_126)))]]) ).
cnf(refute_0_1409,plain,
( multiply(greatest_lower_bound(identity,X_126),least_upper_bound(inverse(X_126),identity)) != least_upper_bound(greatest_lower_bound(identity,X_126),multiply(greatest_lower_bound(identity,X_126),inverse(X_126)))
| multiply(greatest_lower_bound(identity,X_126),least_upper_bound(inverse(X_126),identity)) = least_upper_bound(greatest_lower_bound(identity,X_126),greatest_lower_bound(identity,inverse(X_126))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_126),inverse(X_126)),greatest_lower_bound(identity,inverse(X_126))) )],[refute_0_1407,refute_0_1408]) ).
cnf(refute_0_1410,plain,
multiply(greatest_lower_bound(identity,X_126),least_upper_bound(inverse(X_126),identity)) = least_upper_bound(greatest_lower_bound(identity,X_126),greatest_lower_bound(identity,inverse(X_126))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_126),least_upper_bound(inverse(X_126),identity)),least_upper_bound(greatest_lower_bound(identity,X_126),multiply(greatest_lower_bound(identity,X_126),inverse(X_126)))) )],[refute_0_1404,refute_0_1409]) ).
cnf(refute_0_1411,plain,
multiply(greatest_lower_bound(identity,X_126),least_upper_bound(inverse(X_126),identity)) = multiply(greatest_lower_bound(identity,X_126),least_upper_bound(identity,inverse(X_126))),
inference(subst,[],[refute_0_598:[bind(X_19,$fot(greatest_lower_bound(identity,X_126))),bind(X_88,$fot(inverse(X_126)))]]) ).
cnf(refute_0_1412,plain,
( multiply(greatest_lower_bound(identity,X_126),least_upper_bound(inverse(X_126),identity)) != multiply(greatest_lower_bound(identity,X_126),least_upper_bound(identity,inverse(X_126)))
| multiply(greatest_lower_bound(identity,X_126),least_upper_bound(inverse(X_126),identity)) != least_upper_bound(greatest_lower_bound(identity,X_126),greatest_lower_bound(identity,inverse(X_126)))
| multiply(greatest_lower_bound(identity,X_126),least_upper_bound(identity,inverse(X_126))) = least_upper_bound(greatest_lower_bound(identity,X_126),greatest_lower_bound(identity,inverse(X_126))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_126),least_upper_bound(inverse(X_126),identity)),least_upper_bound(greatest_lower_bound(identity,X_126),greatest_lower_bound(identity,inverse(X_126)))) ),[0],$fot(multiply(greatest_lower_bound(identity,X_126),least_upper_bound(identity,inverse(X_126))))]]) ).
cnf(refute_0_1413,plain,
( multiply(greatest_lower_bound(identity,X_126),least_upper_bound(inverse(X_126),identity)) != least_upper_bound(greatest_lower_bound(identity,X_126),greatest_lower_bound(identity,inverse(X_126)))
| multiply(greatest_lower_bound(identity,X_126),least_upper_bound(identity,inverse(X_126))) = least_upper_bound(greatest_lower_bound(identity,X_126),greatest_lower_bound(identity,inverse(X_126))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_126),least_upper_bound(inverse(X_126),identity)),multiply(greatest_lower_bound(identity,X_126),least_upper_bound(identity,inverse(X_126)))) )],[refute_0_1411,refute_0_1412]) ).
cnf(refute_0_1414,plain,
multiply(greatest_lower_bound(identity,X_126),least_upper_bound(identity,inverse(X_126))) = least_upper_bound(greatest_lower_bound(identity,X_126),greatest_lower_bound(identity,inverse(X_126))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_126),least_upper_bound(inverse(X_126),identity)),least_upper_bound(greatest_lower_bound(identity,X_126),greatest_lower_bound(identity,inverse(X_126)))) )],[refute_0_1410,refute_0_1413]) ).
cnf(refute_0_1415,plain,
( multiply(greatest_lower_bound(identity,X_126),least_upper_bound(identity,inverse(X_126))) != least_upper_bound(greatest_lower_bound(identity,X_126),greatest_lower_bound(identity,inverse(X_126)))
| least_upper_bound(greatest_lower_bound(identity,X_126),greatest_lower_bound(identity,inverse(X_126))) = multiply(greatest_lower_bound(identity,X_126),least_upper_bound(identity,inverse(X_126))) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(greatest_lower_bound(identity,X_126),least_upper_bound(identity,inverse(X_126))))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(identity,X_126),greatest_lower_bound(identity,inverse(X_126)))))]]) ).
cnf(refute_0_1416,plain,
least_upper_bound(greatest_lower_bound(identity,X_126),greatest_lower_bound(identity,inverse(X_126))) = multiply(greatest_lower_bound(identity,X_126),least_upper_bound(identity,inverse(X_126))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_126),least_upper_bound(identity,inverse(X_126))),least_upper_bound(greatest_lower_bound(identity,X_126),greatest_lower_bound(identity,inverse(X_126)))) )],[refute_0_1414,refute_0_1415]) ).
cnf(refute_0_1417,plain,
least_upper_bound(greatest_lower_bound(identity,X_114),greatest_lower_bound(identity,inverse(X_114))) = multiply(greatest_lower_bound(identity,X_114),least_upper_bound(identity,inverse(X_114))),
inference(subst,[],[refute_0_1416:[bind(X_126,$fot(X_114))]]) ).
cnf(refute_0_1418,plain,
( multiply(least_upper_bound(identity,inverse(X_114)),greatest_lower_bound(identity,X_114)) != least_upper_bound(greatest_lower_bound(identity,X_114),greatest_lower_bound(identity,inverse(X_114)))
| least_upper_bound(greatest_lower_bound(identity,X_114),greatest_lower_bound(identity,inverse(X_114))) != multiply(greatest_lower_bound(identity,X_114),least_upper_bound(identity,inverse(X_114)))
| multiply(least_upper_bound(identity,inverse(X_114)),greatest_lower_bound(identity,X_114)) = multiply(greatest_lower_bound(identity,X_114),least_upper_bound(identity,inverse(X_114))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(identity,inverse(X_114)),greatest_lower_bound(identity,X_114)),multiply(greatest_lower_bound(identity,X_114),least_upper_bound(identity,inverse(X_114)))) ),[0],$fot(least_upper_bound(greatest_lower_bound(identity,X_114),greatest_lower_bound(identity,inverse(X_114))))]]) ).
cnf(refute_0_1419,plain,
( multiply(least_upper_bound(identity,inverse(X_114)),greatest_lower_bound(identity,X_114)) != least_upper_bound(greatest_lower_bound(identity,X_114),greatest_lower_bound(identity,inverse(X_114)))
| multiply(least_upper_bound(identity,inverse(X_114)),greatest_lower_bound(identity,X_114)) = multiply(greatest_lower_bound(identity,X_114),least_upper_bound(identity,inverse(X_114))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,X_114),greatest_lower_bound(identity,inverse(X_114))),multiply(greatest_lower_bound(identity,X_114),least_upper_bound(identity,inverse(X_114)))) )],[refute_0_1417,refute_0_1418]) ).
cnf(refute_0_1420,plain,
( multiply(least_upper_bound(inverse(X_114),identity),greatest_lower_bound(identity,X_114)) != least_upper_bound(greatest_lower_bound(identity,X_114),greatest_lower_bound(identity,inverse(X_114)))
| multiply(least_upper_bound(identity,inverse(X_114)),greatest_lower_bound(identity,X_114)) = multiply(greatest_lower_bound(identity,X_114),least_upper_bound(identity,inverse(X_114))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_114)),greatest_lower_bound(identity,X_114)),least_upper_bound(greatest_lower_bound(identity,X_114),greatest_lower_bound(identity,inverse(X_114)))) )],[refute_0_1403,refute_0_1419]) ).
cnf(refute_0_1421,plain,
multiply(least_upper_bound(identity,inverse(X_114)),greatest_lower_bound(identity,X_114)) = multiply(greatest_lower_bound(identity,X_114),least_upper_bound(identity,inverse(X_114))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_114),identity),greatest_lower_bound(identity,X_114)),least_upper_bound(greatest_lower_bound(identity,X_114),greatest_lower_bound(identity,inverse(X_114)))) )],[refute_0_1334,refute_0_1420]) ).
cnf(refute_0_1422,plain,
multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(identity,X_35)) = multiply(greatest_lower_bound(identity,X_35),least_upper_bound(identity,inverse(X_35))),
inference(subst,[],[refute_0_1421:[bind(X_114,$fot(X_35))]]) ).
cnf(refute_0_1423,plain,
greatest_lower_bound(identity,inverse(inverse(X_35))) = greatest_lower_bound(identity,inverse(inverse(X_35))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,inverse(inverse(X_35))))]]) ).
cnf(refute_0_1424,plain,
( greatest_lower_bound(identity,inverse(inverse(X_35))) != greatest_lower_bound(identity,inverse(inverse(X_35)))
| inverse(inverse(X_35)) != X_35
| greatest_lower_bound(identity,inverse(inverse(X_35))) = greatest_lower_bound(identity,X_35) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,inverse(inverse(X_35))),greatest_lower_bound(identity,inverse(inverse(X_35)))) ),[1,1],$fot(X_35)]]) ).
cnf(refute_0_1425,plain,
( inverse(inverse(X_35)) != X_35
| greatest_lower_bound(identity,inverse(inverse(X_35))) = greatest_lower_bound(identity,X_35) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(inverse(X_35))),greatest_lower_bound(identity,inverse(inverse(X_35)))) )],[refute_0_1423,refute_0_1424]) ).
cnf(refute_0_1426,plain,
greatest_lower_bound(identity,inverse(inverse(X_35))) = greatest_lower_bound(identity,X_35),
inference(resolve,[$cnf( $equal(inverse(inverse(X_35)),X_35) )],[refute_0_452,refute_0_1425]) ).
cnf(refute_0_1427,plain,
multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(identity,inverse(inverse(X_35)))) = multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(identity,inverse(inverse(X_35)))),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(identity,inverse(inverse(X_35)))))]]) ).
cnf(refute_0_1428,plain,
( multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(identity,inverse(inverse(X_35)))) != multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(identity,inverse(inverse(X_35))))
| greatest_lower_bound(identity,inverse(inverse(X_35))) != greatest_lower_bound(identity,X_35)
| multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(identity,inverse(inverse(X_35)))) = multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(identity,X_35)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(identity,inverse(inverse(X_35)))),multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(identity,inverse(inverse(X_35))))) ),[1,1],$fot(greatest_lower_bound(identity,X_35))]]) ).
cnf(refute_0_1429,plain,
( greatest_lower_bound(identity,inverse(inverse(X_35))) != greatest_lower_bound(identity,X_35)
| multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(identity,inverse(inverse(X_35)))) = multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(identity,X_35)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(identity,inverse(inverse(X_35)))),multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(identity,inverse(inverse(X_35))))) )],[refute_0_1427,refute_0_1428]) ).
cnf(refute_0_1430,plain,
multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(identity,inverse(inverse(X_35)))) = multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(identity,X_35)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(inverse(X_35))),greatest_lower_bound(identity,X_35)) )],[refute_0_1426,refute_0_1429]) ).
cnf(refute_0_1431,plain,
( multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(identity,X_35)) != multiply(greatest_lower_bound(identity,X_35),least_upper_bound(identity,inverse(X_35)))
| multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(identity,inverse(inverse(X_35)))) != multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(identity,X_35))
| multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(identity,inverse(inverse(X_35)))) = multiply(greatest_lower_bound(identity,X_35),least_upper_bound(identity,inverse(X_35))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(identity,inverse(inverse(X_35)))))),bind(Y0,$fot(multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(identity,X_35)))),bind(Z0,$fot(multiply(greatest_lower_bound(identity,X_35),least_upper_bound(identity,inverse(X_35)))))]]) ).
cnf(refute_0_1432,plain,
( multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(identity,X_35)) != multiply(greatest_lower_bound(identity,X_35),least_upper_bound(identity,inverse(X_35)))
| multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(identity,inverse(inverse(X_35)))) = multiply(greatest_lower_bound(identity,X_35),least_upper_bound(identity,inverse(X_35))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(identity,inverse(inverse(X_35)))),multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(identity,X_35))) )],[refute_0_1430,refute_0_1431]) ).
cnf(refute_0_1433,plain,
multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(identity,inverse(inverse(X_35)))) = multiply(greatest_lower_bound(identity,X_35),least_upper_bound(identity,inverse(X_35))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(identity,X_35)),multiply(greatest_lower_bound(identity,X_35),least_upper_bound(identity,inverse(X_35)))) )],[refute_0_1422,refute_0_1432]) ).
cnf(refute_0_1434,plain,
( multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(identity,inverse(inverse(X_35)))) != multiply(greatest_lower_bound(identity,X_35),least_upper_bound(identity,inverse(X_35)))
| multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(identity,inverse(inverse(X_35)))) != greatest_lower_bound(least_upper_bound(identity,inverse(X_35)),least_upper_bound(identity,X_35))
| multiply(greatest_lower_bound(identity,X_35),least_upper_bound(identity,inverse(X_35))) = greatest_lower_bound(least_upper_bound(identity,inverse(X_35)),least_upper_bound(identity,X_35)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(identity,inverse(inverse(X_35)))),greatest_lower_bound(least_upper_bound(identity,inverse(X_35)),least_upper_bound(identity,X_35))) ),[0],$fot(multiply(greatest_lower_bound(identity,X_35),least_upper_bound(identity,inverse(X_35))))]]) ).
cnf(refute_0_1435,plain,
( multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(identity,inverse(inverse(X_35)))) != greatest_lower_bound(least_upper_bound(identity,inverse(X_35)),least_upper_bound(identity,X_35))
| multiply(greatest_lower_bound(identity,X_35),least_upper_bound(identity,inverse(X_35))) = greatest_lower_bound(least_upper_bound(identity,inverse(X_35)),least_upper_bound(identity,X_35)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(identity,inverse(inverse(X_35)))),multiply(greatest_lower_bound(identity,X_35),least_upper_bound(identity,inverse(X_35)))) )],[refute_0_1433,refute_0_1434]) ).
cnf(refute_0_1436,plain,
( multiply(least_upper_bound(identity,X_75),greatest_lower_bound(identity,inverse(X_75))) != greatest_lower_bound(least_upper_bound(identity,X_75),least_upper_bound(identity,inverse(X_75)))
| greatest_lower_bound(least_upper_bound(identity,X_75),least_upper_bound(identity,inverse(X_75))) = multiply(least_upper_bound(identity,X_75),greatest_lower_bound(identity,inverse(X_75))) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(least_upper_bound(identity,X_75),greatest_lower_bound(identity,inverse(X_75))))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(identity,X_75),least_upper_bound(identity,inverse(X_75)))))]]) ).
cnf(refute_0_1437,plain,
greatest_lower_bound(least_upper_bound(identity,X_75),least_upper_bound(identity,inverse(X_75))) = multiply(least_upper_bound(identity,X_75),greatest_lower_bound(identity,inverse(X_75))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_75),greatest_lower_bound(identity,inverse(X_75))),greatest_lower_bound(least_upper_bound(identity,X_75),least_upper_bound(identity,inverse(X_75)))) )],[refute_0_1283,refute_0_1436]) ).
cnf(refute_0_1438,plain,
greatest_lower_bound(least_upper_bound(identity,X_35),least_upper_bound(identity,inverse(X_35))) = multiply(least_upper_bound(identity,X_35),greatest_lower_bound(identity,inverse(X_35))),
inference(subst,[],[refute_0_1437:[bind(X_75,$fot(X_35))]]) ).
cnf(refute_0_1439,plain,
greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(Y,X_22),X_24)) = greatest_lower_bound(greatest_lower_bound(X_22,greatest_lower_bound(Y,X_22)),X_24),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_22)),bind(Y,$fot(greatest_lower_bound(Y,X_22))),bind(Z,$fot(X_24))]]) ).
cnf(refute_0_1440,plain,
greatest_lower_bound(X_22,greatest_lower_bound(Y,X_22)) = greatest_lower_bound(X_22,Y),
inference(subst,[],[refute_0_347:[bind(X_13,$fot(X_22))]]) ).
cnf(refute_0_1441,plain,
( greatest_lower_bound(X_22,greatest_lower_bound(Y,X_22)) != greatest_lower_bound(X_22,Y)
| greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(Y,X_22),X_24)) != greatest_lower_bound(greatest_lower_bound(X_22,greatest_lower_bound(Y,X_22)),X_24)
| greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(Y,X_22),X_24)) = greatest_lower_bound(greatest_lower_bound(X_22,Y),X_24) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(Y,X_22),X_24)),greatest_lower_bound(greatest_lower_bound(X_22,greatest_lower_bound(Y,X_22)),X_24)) ),[1,0],$fot(greatest_lower_bound(X_22,Y))]]) ).
cnf(refute_0_1442,plain,
( greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(Y,X_22),X_24)) != greatest_lower_bound(greatest_lower_bound(X_22,greatest_lower_bound(Y,X_22)),X_24)
| greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(Y,X_22),X_24)) = greatest_lower_bound(greatest_lower_bound(X_22,Y),X_24) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_22,greatest_lower_bound(Y,X_22)),greatest_lower_bound(X_22,Y)) )],[refute_0_1440,refute_0_1441]) ).
cnf(refute_0_1443,plain,
greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(Y,X_22),X_24)) = greatest_lower_bound(greatest_lower_bound(X_22,Y),X_24),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(Y,X_22),X_24)),greatest_lower_bound(greatest_lower_bound(X_22,greatest_lower_bound(Y,X_22)),X_24)) )],[refute_0_1439,refute_0_1442]) ).
cnf(refute_0_1444,plain,
greatest_lower_bound(X_22,greatest_lower_bound(X_23,greatest_lower_bound(Y,X_23))) = greatest_lower_bound(greatest_lower_bound(X_22,X_23),greatest_lower_bound(Y,X_23)),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_22)),bind(Y,$fot(X_23)),bind(Z,$fot(greatest_lower_bound(Y,X_23)))]]) ).
cnf(refute_0_1445,plain,
greatest_lower_bound(X_23,greatest_lower_bound(Y,X_23)) = greatest_lower_bound(X_23,Y),
inference(subst,[],[refute_0_347:[bind(X_13,$fot(X_23))]]) ).
cnf(refute_0_1446,plain,
( greatest_lower_bound(X_22,greatest_lower_bound(X_23,greatest_lower_bound(Y,X_23))) != greatest_lower_bound(greatest_lower_bound(X_22,X_23),greatest_lower_bound(Y,X_23))
| greatest_lower_bound(X_23,greatest_lower_bound(Y,X_23)) != greatest_lower_bound(X_23,Y)
| greatest_lower_bound(X_22,greatest_lower_bound(X_23,Y)) = greatest_lower_bound(greatest_lower_bound(X_22,X_23),greatest_lower_bound(Y,X_23)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_22,greatest_lower_bound(X_23,greatest_lower_bound(Y,X_23))),greatest_lower_bound(greatest_lower_bound(X_22,X_23),greatest_lower_bound(Y,X_23))) ),[0,1],$fot(greatest_lower_bound(X_23,Y))]]) ).
cnf(refute_0_1447,plain,
( greatest_lower_bound(X_22,greatest_lower_bound(X_23,greatest_lower_bound(Y,X_23))) != greatest_lower_bound(greatest_lower_bound(X_22,X_23),greatest_lower_bound(Y,X_23))
| greatest_lower_bound(X_22,greatest_lower_bound(X_23,Y)) = greatest_lower_bound(greatest_lower_bound(X_22,X_23),greatest_lower_bound(Y,X_23)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_23,greatest_lower_bound(Y,X_23)),greatest_lower_bound(X_23,Y)) )],[refute_0_1445,refute_0_1446]) ).
cnf(refute_0_1448,plain,
greatest_lower_bound(X_22,greatest_lower_bound(X_23,Y)) = greatest_lower_bound(greatest_lower_bound(X_22,X_23),greatest_lower_bound(Y,X_23)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_22,greatest_lower_bound(X_23,greatest_lower_bound(Y,X_23))),greatest_lower_bound(greatest_lower_bound(X_22,X_23),greatest_lower_bound(Y,X_23))) )],[refute_0_1444,refute_0_1447]) ).
cnf(refute_0_1449,plain,
greatest_lower_bound(greatest_lower_bound(X_22,X_23),Y) = greatest_lower_bound(X_22,greatest_lower_bound(X_23,Y)),
inference(subst,[],[refute_0_343:[bind(X,$fot(X_22)),bind(Y,$fot(X_23)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_1450,plain,
greatest_lower_bound(X_23,greatest_lower_bound(greatest_lower_bound(X_22,X_23),Y)) = greatest_lower_bound(X_23,greatest_lower_bound(greatest_lower_bound(X_22,X_23),Y)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X_23,greatest_lower_bound(greatest_lower_bound(X_22,X_23),Y)))]]) ).
cnf(refute_0_1451,plain,
( greatest_lower_bound(X_23,greatest_lower_bound(greatest_lower_bound(X_22,X_23),Y)) != greatest_lower_bound(X_23,greatest_lower_bound(greatest_lower_bound(X_22,X_23),Y))
| greatest_lower_bound(greatest_lower_bound(X_22,X_23),Y) != greatest_lower_bound(X_22,greatest_lower_bound(X_23,Y))
| greatest_lower_bound(X_23,greatest_lower_bound(greatest_lower_bound(X_22,X_23),Y)) = greatest_lower_bound(X_23,greatest_lower_bound(X_22,greatest_lower_bound(X_23,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_23,greatest_lower_bound(greatest_lower_bound(X_22,X_23),Y)),greatest_lower_bound(X_23,greatest_lower_bound(greatest_lower_bound(X_22,X_23),Y))) ),[1,1],$fot(greatest_lower_bound(X_22,greatest_lower_bound(X_23,Y)))]]) ).
cnf(refute_0_1452,plain,
( greatest_lower_bound(greatest_lower_bound(X_22,X_23),Y) != greatest_lower_bound(X_22,greatest_lower_bound(X_23,Y))
| greatest_lower_bound(X_23,greatest_lower_bound(greatest_lower_bound(X_22,X_23),Y)) = greatest_lower_bound(X_23,greatest_lower_bound(X_22,greatest_lower_bound(X_23,Y))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_23,greatest_lower_bound(greatest_lower_bound(X_22,X_23),Y)),greatest_lower_bound(X_23,greatest_lower_bound(greatest_lower_bound(X_22,X_23),Y))) )],[refute_0_1450,refute_0_1451]) ).
cnf(refute_0_1453,plain,
greatest_lower_bound(X_23,greatest_lower_bound(greatest_lower_bound(X_22,X_23),Y)) = greatest_lower_bound(X_23,greatest_lower_bound(X_22,greatest_lower_bound(X_23,Y))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_22,X_23),Y),greatest_lower_bound(X_22,greatest_lower_bound(X_23,Y))) )],[refute_0_1449,refute_0_1452]) ).
cnf(refute_0_1454,plain,
greatest_lower_bound(X,greatest_lower_bound(X_22,X_23)) = greatest_lower_bound(greatest_lower_bound(X_22,X_23),X),
inference(subst,[],[symmetry_of_glb:[bind(Y,$fot(greatest_lower_bound(X_22,X_23)))]]) ).
cnf(refute_0_1455,plain,
greatest_lower_bound(X_22,greatest_lower_bound(X_23,X)) = greatest_lower_bound(greatest_lower_bound(X_22,X_23),X),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_22)),bind(Y,$fot(X_23)),bind(Z,$fot(X))]]) ).
cnf(refute_0_1456,plain,
( greatest_lower_bound(X_22,greatest_lower_bound(X_23,X)) != greatest_lower_bound(greatest_lower_bound(X_22,X_23),X)
| greatest_lower_bound(greatest_lower_bound(X_22,X_23),X) = greatest_lower_bound(X_22,greatest_lower_bound(X_23,X)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(greatest_lower_bound(X_22,greatest_lower_bound(X_23,X)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X_22,X_23),X)))]]) ).
cnf(refute_0_1457,plain,
greatest_lower_bound(greatest_lower_bound(X_22,X_23),X) = greatest_lower_bound(X_22,greatest_lower_bound(X_23,X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_22,greatest_lower_bound(X_23,X)),greatest_lower_bound(greatest_lower_bound(X_22,X_23),X)) )],[refute_0_1455,refute_0_1456]) ).
cnf(refute_0_1458,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_22,X_23)) != greatest_lower_bound(greatest_lower_bound(X_22,X_23),X)
| greatest_lower_bound(greatest_lower_bound(X_22,X_23),X) != greatest_lower_bound(X_22,greatest_lower_bound(X_23,X))
| greatest_lower_bound(X,greatest_lower_bound(X_22,X_23)) = greatest_lower_bound(X_22,greatest_lower_bound(X_23,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X,greatest_lower_bound(X_22,X_23)),greatest_lower_bound(X_22,greatest_lower_bound(X_23,X))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_22,X_23),X))]]) ).
cnf(refute_0_1459,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_22,X_23)) != greatest_lower_bound(greatest_lower_bound(X_22,X_23),X)
| greatest_lower_bound(X,greatest_lower_bound(X_22,X_23)) = greatest_lower_bound(X_22,greatest_lower_bound(X_23,X)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_22,X_23),X),greatest_lower_bound(X_22,greatest_lower_bound(X_23,X))) )],[refute_0_1457,refute_0_1458]) ).
cnf(refute_0_1460,plain,
greatest_lower_bound(X,greatest_lower_bound(X_22,X_23)) = greatest_lower_bound(X_22,greatest_lower_bound(X_23,X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_22,X_23)),greatest_lower_bound(greatest_lower_bound(X_22,X_23),X)) )],[refute_0_1454,refute_0_1459]) ).
cnf(refute_0_1461,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_22,X_23)) != greatest_lower_bound(X_22,greatest_lower_bound(X_23,X))
| greatest_lower_bound(X_22,greatest_lower_bound(X_23,X)) = greatest_lower_bound(X,greatest_lower_bound(X_22,X_23)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(X_22,X_23)))),bind(Y0,$fot(greatest_lower_bound(X_22,greatest_lower_bound(X_23,X))))]]) ).
cnf(refute_0_1462,plain,
greatest_lower_bound(X_22,greatest_lower_bound(X_23,X)) = greatest_lower_bound(X,greatest_lower_bound(X_22,X_23)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_22,X_23)),greatest_lower_bound(X_22,greatest_lower_bound(X_23,X))) )],[refute_0_1460,refute_0_1461]) ).
cnf(refute_0_1463,plain,
greatest_lower_bound(greatest_lower_bound(X_22,X_23),greatest_lower_bound(Y,X_23)) = greatest_lower_bound(X_23,greatest_lower_bound(greatest_lower_bound(X_22,X_23),Y)),
inference(subst,[],[refute_0_1462:[bind(X,$fot(X_23)),bind(X_22,$fot(greatest_lower_bound(X_22,X_23))),bind(X_23,$fot(Y))]]) ).
cnf(refute_0_1464,plain,
( greatest_lower_bound(X_23,greatest_lower_bound(greatest_lower_bound(X_22,X_23),Y)) != greatest_lower_bound(X_23,greatest_lower_bound(X_22,greatest_lower_bound(X_23,Y)))
| greatest_lower_bound(greatest_lower_bound(X_22,X_23),greatest_lower_bound(Y,X_23)) != greatest_lower_bound(X_23,greatest_lower_bound(greatest_lower_bound(X_22,X_23),Y))
| greatest_lower_bound(greatest_lower_bound(X_22,X_23),greatest_lower_bound(Y,X_23)) = greatest_lower_bound(X_23,greatest_lower_bound(X_22,greatest_lower_bound(X_23,Y))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(X_22,X_23),greatest_lower_bound(Y,X_23)))),bind(Y0,$fot(greatest_lower_bound(X_23,greatest_lower_bound(greatest_lower_bound(X_22,X_23),Y)))),bind(Z0,$fot(greatest_lower_bound(X_23,greatest_lower_bound(X_22,greatest_lower_bound(X_23,Y)))))]]) ).
cnf(refute_0_1465,plain,
( greatest_lower_bound(X_23,greatest_lower_bound(greatest_lower_bound(X_22,X_23),Y)) != greatest_lower_bound(X_23,greatest_lower_bound(X_22,greatest_lower_bound(X_23,Y)))
| greatest_lower_bound(greatest_lower_bound(X_22,X_23),greatest_lower_bound(Y,X_23)) = greatest_lower_bound(X_23,greatest_lower_bound(X_22,greatest_lower_bound(X_23,Y))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_22,X_23),greatest_lower_bound(Y,X_23)),greatest_lower_bound(X_23,greatest_lower_bound(greatest_lower_bound(X_22,X_23),Y))) )],[refute_0_1463,refute_0_1464]) ).
cnf(refute_0_1466,plain,
greatest_lower_bound(greatest_lower_bound(X_22,X_23),greatest_lower_bound(Y,X_23)) = greatest_lower_bound(X_23,greatest_lower_bound(X_22,greatest_lower_bound(X_23,Y))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_23,greatest_lower_bound(greatest_lower_bound(X_22,X_23),Y)),greatest_lower_bound(X_23,greatest_lower_bound(X_22,greatest_lower_bound(X_23,Y)))) )],[refute_0_1453,refute_0_1465]) ).
cnf(refute_0_1467,plain,
( greatest_lower_bound(X_22,greatest_lower_bound(X_23,Y)) != greatest_lower_bound(greatest_lower_bound(X_22,X_23),greatest_lower_bound(Y,X_23))
| greatest_lower_bound(greatest_lower_bound(X_22,X_23),greatest_lower_bound(Y,X_23)) != greatest_lower_bound(X_23,greatest_lower_bound(X_22,greatest_lower_bound(X_23,Y)))
| greatest_lower_bound(X_22,greatest_lower_bound(X_23,Y)) = greatest_lower_bound(X_23,greatest_lower_bound(X_22,greatest_lower_bound(X_23,Y))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_22,greatest_lower_bound(X_23,Y)),greatest_lower_bound(X_23,greatest_lower_bound(X_22,greatest_lower_bound(X_23,Y)))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_22,X_23),greatest_lower_bound(Y,X_23)))]]) ).
cnf(refute_0_1468,plain,
( greatest_lower_bound(X_22,greatest_lower_bound(X_23,Y)) != greatest_lower_bound(greatest_lower_bound(X_22,X_23),greatest_lower_bound(Y,X_23))
| greatest_lower_bound(X_22,greatest_lower_bound(X_23,Y)) = greatest_lower_bound(X_23,greatest_lower_bound(X_22,greatest_lower_bound(X_23,Y))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_22,X_23),greatest_lower_bound(Y,X_23)),greatest_lower_bound(X_23,greatest_lower_bound(X_22,greatest_lower_bound(X_23,Y)))) )],[refute_0_1466,refute_0_1467]) ).
cnf(refute_0_1469,plain,
greatest_lower_bound(X_22,greatest_lower_bound(X_23,Y)) = greatest_lower_bound(X_23,greatest_lower_bound(X_22,greatest_lower_bound(X_23,Y))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_22,greatest_lower_bound(X_23,Y)),greatest_lower_bound(greatest_lower_bound(X_22,X_23),greatest_lower_bound(Y,X_23))) )],[refute_0_1448,refute_0_1468]) ).
cnf(refute_0_1470,plain,
( greatest_lower_bound(X_22,greatest_lower_bound(X_23,Y)) != greatest_lower_bound(X_23,greatest_lower_bound(X_22,greatest_lower_bound(X_23,Y)))
| greatest_lower_bound(X_23,greatest_lower_bound(X_22,greatest_lower_bound(X_23,Y))) = greatest_lower_bound(X_22,greatest_lower_bound(X_23,Y)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(greatest_lower_bound(X_22,greatest_lower_bound(X_23,Y)))),bind(Y0,$fot(greatest_lower_bound(X_23,greatest_lower_bound(X_22,greatest_lower_bound(X_23,Y)))))]]) ).
cnf(refute_0_1471,plain,
greatest_lower_bound(X_23,greatest_lower_bound(X_22,greatest_lower_bound(X_23,Y))) = greatest_lower_bound(X_22,greatest_lower_bound(X_23,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_22,greatest_lower_bound(X_23,Y)),greatest_lower_bound(X_23,greatest_lower_bound(X_22,greatest_lower_bound(X_23,Y)))) )],[refute_0_1469,refute_0_1470]) ).
cnf(refute_0_1472,plain,
greatest_lower_bound(X_22,greatest_lower_bound(Y,greatest_lower_bound(X_22,X_24))) = greatest_lower_bound(Y,greatest_lower_bound(X_22,X_24)),
inference(subst,[],[refute_0_1471:[bind(Y,$fot(X_24)),bind(X_22,$fot(Y)),bind(X_23,$fot(X_22))]]) ).
cnf(refute_0_1473,plain,
greatest_lower_bound(greatest_lower_bound(Y,X_22),X_24) = greatest_lower_bound(Y,greatest_lower_bound(X_22,X_24)),
inference(subst,[],[refute_0_343:[bind(X,$fot(Y)),bind(Y,$fot(X_22)),bind(Z,$fot(X_24))]]) ).
cnf(refute_0_1474,plain,
greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(Y,X_22),X_24)) = greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(Y,X_22),X_24)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(Y,X_22),X_24)))]]) ).
cnf(refute_0_1475,plain,
( greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(Y,X_22),X_24)) != greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(Y,X_22),X_24))
| greatest_lower_bound(greatest_lower_bound(Y,X_22),X_24) != greatest_lower_bound(Y,greatest_lower_bound(X_22,X_24))
| greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(Y,X_22),X_24)) = greatest_lower_bound(X_22,greatest_lower_bound(Y,greatest_lower_bound(X_22,X_24))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(Y,X_22),X_24)),greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(Y,X_22),X_24))) ),[1,1],$fot(greatest_lower_bound(Y,greatest_lower_bound(X_22,X_24)))]]) ).
cnf(refute_0_1476,plain,
( greatest_lower_bound(greatest_lower_bound(Y,X_22),X_24) != greatest_lower_bound(Y,greatest_lower_bound(X_22,X_24))
| greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(Y,X_22),X_24)) = greatest_lower_bound(X_22,greatest_lower_bound(Y,greatest_lower_bound(X_22,X_24))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(Y,X_22),X_24)),greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(Y,X_22),X_24))) )],[refute_0_1474,refute_0_1475]) ).
cnf(refute_0_1477,plain,
greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(Y,X_22),X_24)) = greatest_lower_bound(X_22,greatest_lower_bound(Y,greatest_lower_bound(X_22,X_24))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(Y,X_22),X_24),greatest_lower_bound(Y,greatest_lower_bound(X_22,X_24))) )],[refute_0_1473,refute_0_1476]) ).
cnf(refute_0_1478,plain,
( greatest_lower_bound(X_22,greatest_lower_bound(Y,greatest_lower_bound(X_22,X_24))) != greatest_lower_bound(Y,greatest_lower_bound(X_22,X_24))
| greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(Y,X_22),X_24)) != greatest_lower_bound(X_22,greatest_lower_bound(Y,greatest_lower_bound(X_22,X_24)))
| greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(Y,X_22),X_24)) = greatest_lower_bound(Y,greatest_lower_bound(X_22,X_24)) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(Y,X_22),X_24)))),bind(Y0,$fot(greatest_lower_bound(X_22,greatest_lower_bound(Y,greatest_lower_bound(X_22,X_24))))),bind(Z0,$fot(greatest_lower_bound(Y,greatest_lower_bound(X_22,X_24))))]]) ).
cnf(refute_0_1479,plain,
( greatest_lower_bound(X_22,greatest_lower_bound(Y,greatest_lower_bound(X_22,X_24))) != greatest_lower_bound(Y,greatest_lower_bound(X_22,X_24))
| greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(Y,X_22),X_24)) = greatest_lower_bound(Y,greatest_lower_bound(X_22,X_24)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(Y,X_22),X_24)),greatest_lower_bound(X_22,greatest_lower_bound(Y,greatest_lower_bound(X_22,X_24)))) )],[refute_0_1477,refute_0_1478]) ).
cnf(refute_0_1480,plain,
greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(Y,X_22),X_24)) = greatest_lower_bound(Y,greatest_lower_bound(X_22,X_24)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_22,greatest_lower_bound(Y,greatest_lower_bound(X_22,X_24))),greatest_lower_bound(Y,greatest_lower_bound(X_22,X_24))) )],[refute_0_1472,refute_0_1479]) ).
cnf(refute_0_1481,plain,
( greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(Y,X_22),X_24)) != greatest_lower_bound(Y,greatest_lower_bound(X_22,X_24))
| greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(Y,X_22),X_24)) != greatest_lower_bound(greatest_lower_bound(X_22,Y),X_24)
| greatest_lower_bound(Y,greatest_lower_bound(X_22,X_24)) = greatest_lower_bound(greatest_lower_bound(X_22,Y),X_24) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(Y,X_22),X_24)),greatest_lower_bound(greatest_lower_bound(X_22,Y),X_24)) ),[0],$fot(greatest_lower_bound(Y,greatest_lower_bound(X_22,X_24)))]]) ).
cnf(refute_0_1482,plain,
( greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(Y,X_22),X_24)) != greatest_lower_bound(greatest_lower_bound(X_22,Y),X_24)
| greatest_lower_bound(Y,greatest_lower_bound(X_22,X_24)) = greatest_lower_bound(greatest_lower_bound(X_22,Y),X_24) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(Y,X_22),X_24)),greatest_lower_bound(Y,greatest_lower_bound(X_22,X_24))) )],[refute_0_1480,refute_0_1481]) ).
cnf(refute_0_1483,plain,
greatest_lower_bound(greatest_lower_bound(X_22,Y),X_24) = greatest_lower_bound(X_22,greatest_lower_bound(Y,X_24)),
inference(subst,[],[refute_0_343:[bind(X,$fot(X_22)),bind(Z,$fot(X_24))]]) ).
cnf(refute_0_1484,plain,
( greatest_lower_bound(Y,greatest_lower_bound(X_22,X_24)) != greatest_lower_bound(greatest_lower_bound(X_22,Y),X_24)
| greatest_lower_bound(greatest_lower_bound(X_22,Y),X_24) != greatest_lower_bound(X_22,greatest_lower_bound(Y,X_24))
| greatest_lower_bound(Y,greatest_lower_bound(X_22,X_24)) = greatest_lower_bound(X_22,greatest_lower_bound(Y,X_24)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(Y,greatest_lower_bound(X_22,X_24)),greatest_lower_bound(X_22,greatest_lower_bound(Y,X_24))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_22,Y),X_24))]]) ).
cnf(refute_0_1485,plain,
( greatest_lower_bound(Y,greatest_lower_bound(X_22,X_24)) != greatest_lower_bound(greatest_lower_bound(X_22,Y),X_24)
| greatest_lower_bound(Y,greatest_lower_bound(X_22,X_24)) = greatest_lower_bound(X_22,greatest_lower_bound(Y,X_24)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_22,Y),X_24),greatest_lower_bound(X_22,greatest_lower_bound(Y,X_24))) )],[refute_0_1483,refute_0_1484]) ).
cnf(refute_0_1486,plain,
( greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(Y,X_22),X_24)) != greatest_lower_bound(greatest_lower_bound(X_22,Y),X_24)
| greatest_lower_bound(Y,greatest_lower_bound(X_22,X_24)) = greatest_lower_bound(X_22,greatest_lower_bound(Y,X_24)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(X_22,X_24)),greatest_lower_bound(greatest_lower_bound(X_22,Y),X_24)) )],[refute_0_1482,refute_0_1485]) ).
cnf(refute_0_1487,plain,
greatest_lower_bound(Y,greatest_lower_bound(X_22,X_24)) = greatest_lower_bound(X_22,greatest_lower_bound(Y,X_24)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(Y,X_22),X_24)),greatest_lower_bound(greatest_lower_bound(X_22,Y),X_24)) )],[refute_0_1443,refute_0_1486]) ).
cnf(refute_0_1488,plain,
greatest_lower_bound(X_196,greatest_lower_bound(least_upper_bound(X_18,X_7),least_upper_bound(X_7,X_18))) = greatest_lower_bound(least_upper_bound(X_18,X_7),greatest_lower_bound(X_196,least_upper_bound(X_7,X_18))),
inference(subst,[],[refute_0_1487:[bind(Y,$fot(X_196)),bind(X_22,$fot(least_upper_bound(X_18,X_7))),bind(X_24,$fot(least_upper_bound(X_7,X_18)))]]) ).
cnf(refute_0_1489,plain,
( greatest_lower_bound(X_196,greatest_lower_bound(least_upper_bound(X_18,X_7),least_upper_bound(X_7,X_18))) != greatest_lower_bound(least_upper_bound(X_18,X_7),greatest_lower_bound(X_196,least_upper_bound(X_7,X_18)))
| greatest_lower_bound(least_upper_bound(X_18,X_7),least_upper_bound(X_7,X_18)) != least_upper_bound(X_18,X_7)
| greatest_lower_bound(X_196,least_upper_bound(X_18,X_7)) = greatest_lower_bound(least_upper_bound(X_18,X_7),greatest_lower_bound(X_196,least_upper_bound(X_7,X_18))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_196,greatest_lower_bound(least_upper_bound(X_18,X_7),least_upper_bound(X_7,X_18))),greatest_lower_bound(least_upper_bound(X_18,X_7),greatest_lower_bound(X_196,least_upper_bound(X_7,X_18)))) ),[0,1],$fot(least_upper_bound(X_18,X_7))]]) ).
cnf(refute_0_1490,plain,
( greatest_lower_bound(X_196,greatest_lower_bound(least_upper_bound(X_18,X_7),least_upper_bound(X_7,X_18))) != greatest_lower_bound(least_upper_bound(X_18,X_7),greatest_lower_bound(X_196,least_upper_bound(X_7,X_18)))
| greatest_lower_bound(X_196,least_upper_bound(X_18,X_7)) = greatest_lower_bound(least_upper_bound(X_18,X_7),greatest_lower_bound(X_196,least_upper_bound(X_7,X_18))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_18,X_7),least_upper_bound(X_7,X_18)),least_upper_bound(X_18,X_7)) )],[refute_0_544,refute_0_1489]) ).
cnf(refute_0_1491,plain,
greatest_lower_bound(X_196,least_upper_bound(X_18,X_7)) = greatest_lower_bound(least_upper_bound(X_18,X_7),greatest_lower_bound(X_196,least_upper_bound(X_7,X_18))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_196,greatest_lower_bound(least_upper_bound(X_18,X_7),least_upper_bound(X_7,X_18))),greatest_lower_bound(least_upper_bound(X_18,X_7),greatest_lower_bound(X_196,least_upper_bound(X_7,X_18)))) )],[refute_0_1488,refute_0_1490]) ).
cnf(refute_0_1492,plain,
greatest_lower_bound(least_upper_bound(X_7,X_18),greatest_lower_bound(X_129,least_upper_bound(X_18,X_7))) = greatest_lower_bound(X_129,greatest_lower_bound(least_upper_bound(X_18,X_7),least_upper_bound(X_7,X_18))),
inference(subst,[],[refute_0_1460:[bind(X,$fot(least_upper_bound(X_7,X_18))),bind(X_22,$fot(X_129)),bind(X_23,$fot(least_upper_bound(X_18,X_7)))]]) ).
cnf(refute_0_1493,plain,
( greatest_lower_bound(least_upper_bound(X_18,X_7),least_upper_bound(X_7,X_18)) != least_upper_bound(X_18,X_7)
| greatest_lower_bound(least_upper_bound(X_7,X_18),greatest_lower_bound(X_129,least_upper_bound(X_18,X_7))) != greatest_lower_bound(X_129,greatest_lower_bound(least_upper_bound(X_18,X_7),least_upper_bound(X_7,X_18)))
| greatest_lower_bound(least_upper_bound(X_7,X_18),greatest_lower_bound(X_129,least_upper_bound(X_18,X_7))) = greatest_lower_bound(X_129,least_upper_bound(X_18,X_7)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_7,X_18),greatest_lower_bound(X_129,least_upper_bound(X_18,X_7))),greatest_lower_bound(X_129,greatest_lower_bound(least_upper_bound(X_18,X_7),least_upper_bound(X_7,X_18)))) ),[1,1],$fot(least_upper_bound(X_18,X_7))]]) ).
cnf(refute_0_1494,plain,
( greatest_lower_bound(least_upper_bound(X_7,X_18),greatest_lower_bound(X_129,least_upper_bound(X_18,X_7))) != greatest_lower_bound(X_129,greatest_lower_bound(least_upper_bound(X_18,X_7),least_upper_bound(X_7,X_18)))
| greatest_lower_bound(least_upper_bound(X_7,X_18),greatest_lower_bound(X_129,least_upper_bound(X_18,X_7))) = greatest_lower_bound(X_129,least_upper_bound(X_18,X_7)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_18,X_7),least_upper_bound(X_7,X_18)),least_upper_bound(X_18,X_7)) )],[refute_0_544,refute_0_1493]) ).
cnf(refute_0_1495,plain,
greatest_lower_bound(least_upper_bound(X_7,X_18),greatest_lower_bound(X_129,least_upper_bound(X_18,X_7))) = greatest_lower_bound(X_129,least_upper_bound(X_18,X_7)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_7,X_18),greatest_lower_bound(X_129,least_upper_bound(X_18,X_7))),greatest_lower_bound(X_129,greatest_lower_bound(least_upper_bound(X_18,X_7),least_upper_bound(X_7,X_18)))) )],[refute_0_1492,refute_0_1494]) ).
cnf(refute_0_1496,plain,
greatest_lower_bound(least_upper_bound(X_18,X_7),greatest_lower_bound(X_196,least_upper_bound(X_7,X_18))) = greatest_lower_bound(X_196,least_upper_bound(X_7,X_18)),
inference(subst,[],[refute_0_1495:[bind(X_129,$fot(X_196)),bind(X_18,$fot(X_7)),bind(X_7,$fot(X_18))]]) ).
cnf(refute_0_1497,plain,
( greatest_lower_bound(X_196,least_upper_bound(X_18,X_7)) != greatest_lower_bound(least_upper_bound(X_18,X_7),greatest_lower_bound(X_196,least_upper_bound(X_7,X_18)))
| greatest_lower_bound(least_upper_bound(X_18,X_7),greatest_lower_bound(X_196,least_upper_bound(X_7,X_18))) != greatest_lower_bound(X_196,least_upper_bound(X_7,X_18))
| greatest_lower_bound(X_196,least_upper_bound(X_18,X_7)) = greatest_lower_bound(X_196,least_upper_bound(X_7,X_18)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_196,least_upper_bound(X_18,X_7)),greatest_lower_bound(X_196,least_upper_bound(X_7,X_18))) ),[0],$fot(greatest_lower_bound(least_upper_bound(X_18,X_7),greatest_lower_bound(X_196,least_upper_bound(X_7,X_18))))]]) ).
cnf(refute_0_1498,plain,
( greatest_lower_bound(X_196,least_upper_bound(X_18,X_7)) != greatest_lower_bound(least_upper_bound(X_18,X_7),greatest_lower_bound(X_196,least_upper_bound(X_7,X_18)))
| greatest_lower_bound(X_196,least_upper_bound(X_18,X_7)) = greatest_lower_bound(X_196,least_upper_bound(X_7,X_18)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_18,X_7),greatest_lower_bound(X_196,least_upper_bound(X_7,X_18))),greatest_lower_bound(X_196,least_upper_bound(X_7,X_18))) )],[refute_0_1496,refute_0_1497]) ).
cnf(refute_0_1499,plain,
greatest_lower_bound(X_196,least_upper_bound(X_18,X_7)) = greatest_lower_bound(X_196,least_upper_bound(X_7,X_18)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_196,least_upper_bound(X_18,X_7)),greatest_lower_bound(least_upper_bound(X_18,X_7),greatest_lower_bound(X_196,least_upper_bound(X_7,X_18)))) )],[refute_0_1491,refute_0_1498]) ).
cnf(refute_0_1500,plain,
( greatest_lower_bound(X_196,least_upper_bound(X_18,X_7)) != greatest_lower_bound(X_196,least_upper_bound(X_7,X_18))
| greatest_lower_bound(X_196,least_upper_bound(X_7,X_18)) = greatest_lower_bound(X_196,least_upper_bound(X_18,X_7)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(greatest_lower_bound(X_196,least_upper_bound(X_18,X_7)))),bind(Y0,$fot(greatest_lower_bound(X_196,least_upper_bound(X_7,X_18))))]]) ).
cnf(refute_0_1501,plain,
greatest_lower_bound(X_196,least_upper_bound(X_7,X_18)) = greatest_lower_bound(X_196,least_upper_bound(X_18,X_7)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_196,least_upper_bound(X_18,X_7)),greatest_lower_bound(X_196,least_upper_bound(X_7,X_18))) )],[refute_0_1499,refute_0_1500]) ).
cnf(refute_0_1502,plain,
greatest_lower_bound(least_upper_bound(identity,X_35),least_upper_bound(inverse(X_35),identity)) = greatest_lower_bound(least_upper_bound(identity,X_35),least_upper_bound(identity,inverse(X_35))),
inference(subst,[],[refute_0_1501:[bind(X_18,$fot(identity)),bind(X_196,$fot(least_upper_bound(identity,X_35))),bind(X_7,$fot(inverse(X_35)))]]) ).
cnf(refute_0_1503,plain,
( greatest_lower_bound(least_upper_bound(identity,X_35),least_upper_bound(identity,inverse(X_35))) != multiply(least_upper_bound(identity,X_35),greatest_lower_bound(identity,inverse(X_35)))
| greatest_lower_bound(least_upper_bound(identity,X_35),least_upper_bound(inverse(X_35),identity)) != greatest_lower_bound(least_upper_bound(identity,X_35),least_upper_bound(identity,inverse(X_35)))
| greatest_lower_bound(least_upper_bound(identity,X_35),least_upper_bound(inverse(X_35),identity)) = multiply(least_upper_bound(identity,X_35),greatest_lower_bound(identity,inverse(X_35))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(identity,X_35),least_upper_bound(inverse(X_35),identity)))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(identity,X_35),least_upper_bound(identity,inverse(X_35))))),bind(Z0,$fot(multiply(least_upper_bound(identity,X_35),greatest_lower_bound(identity,inverse(X_35)))))]]) ).
cnf(refute_0_1504,plain,
( greatest_lower_bound(least_upper_bound(identity,X_35),least_upper_bound(identity,inverse(X_35))) != multiply(least_upper_bound(identity,X_35),greatest_lower_bound(identity,inverse(X_35)))
| greatest_lower_bound(least_upper_bound(identity,X_35),least_upper_bound(inverse(X_35),identity)) = multiply(least_upper_bound(identity,X_35),greatest_lower_bound(identity,inverse(X_35))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,X_35),least_upper_bound(inverse(X_35),identity)),greatest_lower_bound(least_upper_bound(identity,X_35),least_upper_bound(identity,inverse(X_35)))) )],[refute_0_1502,refute_0_1503]) ).
cnf(refute_0_1505,plain,
greatest_lower_bound(least_upper_bound(identity,X_35),least_upper_bound(inverse(X_35),identity)) = multiply(least_upper_bound(identity,X_35),greatest_lower_bound(identity,inverse(X_35))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,X_35),least_upper_bound(identity,inverse(X_35))),multiply(least_upper_bound(identity,X_35),greatest_lower_bound(identity,inverse(X_35)))) )],[refute_0_1438,refute_0_1504]) ).
cnf(refute_0_1506,plain,
multiply(greatest_lower_bound(X_120,inverse(X_56)),least_upper_bound(identity,X_56)) = greatest_lower_bound(multiply(X_120,least_upper_bound(identity,X_56)),multiply(inverse(X_56),least_upper_bound(identity,X_56))),
inference(subst,[],[monotony_glb2:[bind(X,$fot(least_upper_bound(identity,X_56))),bind(Y,$fot(X_120)),bind(Z,$fot(inverse(X_56)))]]) ).
cnf(refute_0_1507,plain,
( multiply(greatest_lower_bound(X_120,inverse(X_56)),least_upper_bound(identity,X_56)) != greatest_lower_bound(multiply(X_120,least_upper_bound(identity,X_56)),multiply(inverse(X_56),least_upper_bound(identity,X_56)))
| multiply(inverse(X_56),least_upper_bound(identity,X_56)) != least_upper_bound(identity,inverse(X_56))
| multiply(greatest_lower_bound(X_120,inverse(X_56)),least_upper_bound(identity,X_56)) = greatest_lower_bound(multiply(X_120,least_upper_bound(identity,X_56)),least_upper_bound(identity,inverse(X_56))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_120,inverse(X_56)),least_upper_bound(identity,X_56)),greatest_lower_bound(multiply(X_120,least_upper_bound(identity,X_56)),multiply(inverse(X_56),least_upper_bound(identity,X_56)))) ),[1,1],$fot(least_upper_bound(identity,inverse(X_56)))]]) ).
cnf(refute_0_1508,plain,
( multiply(greatest_lower_bound(X_120,inverse(X_56)),least_upper_bound(identity,X_56)) != greatest_lower_bound(multiply(X_120,least_upper_bound(identity,X_56)),multiply(inverse(X_56),least_upper_bound(identity,X_56)))
| multiply(greatest_lower_bound(X_120,inverse(X_56)),least_upper_bound(identity,X_56)) = greatest_lower_bound(multiply(X_120,least_upper_bound(identity,X_56)),least_upper_bound(identity,inverse(X_56))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_56),least_upper_bound(identity,X_56)),least_upper_bound(identity,inverse(X_56))) )],[refute_0_126,refute_0_1507]) ).
cnf(refute_0_1509,plain,
multiply(greatest_lower_bound(X_120,inverse(X_56)),least_upper_bound(identity,X_56)) = greatest_lower_bound(multiply(X_120,least_upper_bound(identity,X_56)),least_upper_bound(identity,inverse(X_56))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_120,inverse(X_56)),least_upper_bound(identity,X_56)),greatest_lower_bound(multiply(X_120,least_upper_bound(identity,X_56)),multiply(inverse(X_56),least_upper_bound(identity,X_56)))) )],[refute_0_1506,refute_0_1508]) ).
cnf(refute_0_1510,plain,
greatest_lower_bound(multiply(X_120,least_upper_bound(identity,X_56)),least_upper_bound(identity,inverse(X_56))) = greatest_lower_bound(least_upper_bound(identity,inverse(X_56)),multiply(X_120,least_upper_bound(identity,X_56))),
inference(subst,[],[refute_0_42:[bind(X,$fot(least_upper_bound(identity,inverse(X_56)))),bind(Y,$fot(multiply(X_120,least_upper_bound(identity,X_56))))]]) ).
cnf(refute_0_1511,plain,
( multiply(greatest_lower_bound(X_120,inverse(X_56)),least_upper_bound(identity,X_56)) != greatest_lower_bound(multiply(X_120,least_upper_bound(identity,X_56)),least_upper_bound(identity,inverse(X_56)))
| greatest_lower_bound(multiply(X_120,least_upper_bound(identity,X_56)),least_upper_bound(identity,inverse(X_56))) != greatest_lower_bound(least_upper_bound(identity,inverse(X_56)),multiply(X_120,least_upper_bound(identity,X_56)))
| multiply(greatest_lower_bound(X_120,inverse(X_56)),least_upper_bound(identity,X_56)) = greatest_lower_bound(least_upper_bound(identity,inverse(X_56)),multiply(X_120,least_upper_bound(identity,X_56))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_120,inverse(X_56)),least_upper_bound(identity,X_56)),greatest_lower_bound(least_upper_bound(identity,inverse(X_56)),multiply(X_120,least_upper_bound(identity,X_56)))) ),[0],$fot(greatest_lower_bound(multiply(X_120,least_upper_bound(identity,X_56)),least_upper_bound(identity,inverse(X_56))))]]) ).
cnf(refute_0_1512,plain,
( multiply(greatest_lower_bound(X_120,inverse(X_56)),least_upper_bound(identity,X_56)) != greatest_lower_bound(multiply(X_120,least_upper_bound(identity,X_56)),least_upper_bound(identity,inverse(X_56)))
| multiply(greatest_lower_bound(X_120,inverse(X_56)),least_upper_bound(identity,X_56)) = greatest_lower_bound(least_upper_bound(identity,inverse(X_56)),multiply(X_120,least_upper_bound(identity,X_56))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_120,least_upper_bound(identity,X_56)),least_upper_bound(identity,inverse(X_56))),greatest_lower_bound(least_upper_bound(identity,inverse(X_56)),multiply(X_120,least_upper_bound(identity,X_56)))) )],[refute_0_1510,refute_0_1511]) ).
cnf(refute_0_1513,plain,
multiply(greatest_lower_bound(X_120,inverse(X_56)),least_upper_bound(identity,X_56)) = greatest_lower_bound(least_upper_bound(identity,inverse(X_56)),multiply(X_120,least_upper_bound(identity,X_56))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_120,inverse(X_56)),least_upper_bound(identity,X_56)),greatest_lower_bound(multiply(X_120,least_upper_bound(identity,X_56)),least_upper_bound(identity,inverse(X_56)))) )],[refute_0_1509,refute_0_1512]) ).
cnf(refute_0_1514,plain,
multiply(greatest_lower_bound(X_120,inverse(inverse(least_upper_bound(X_293,identity)))),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))) = greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity)))),multiply(X_120,least_upper_bound(identity,inverse(least_upper_bound(X_293,identity))))),
inference(subst,[],[refute_0_1513:[bind(X_56,$fot(inverse(least_upper_bound(X_293,identity))))]]) ).
cnf(refute_0_1515,plain,
multiply(inverse(least_upper_bound(Y,identity)),least_upper_bound(identity,least_upper_bound(Y,identity))) = least_upper_bound(identity,inverse(least_upper_bound(Y,identity))),
inference(subst,[],[refute_0_126:[bind(X_56,$fot(least_upper_bound(Y,identity)))]]) ).
cnf(refute_0_1516,plain,
least_upper_bound(identity,least_upper_bound(Y,identity)) = least_upper_bound(identity,Y),
inference(subst,[],[refute_0_175:[bind(X_15,$fot(identity))]]) ).
cnf(refute_0_1517,plain,
( multiply(inverse(least_upper_bound(Y,identity)),least_upper_bound(identity,least_upper_bound(Y,identity))) != least_upper_bound(identity,inverse(least_upper_bound(Y,identity)))
| least_upper_bound(identity,least_upper_bound(Y,identity)) != least_upper_bound(identity,Y)
| multiply(inverse(least_upper_bound(Y,identity)),least_upper_bound(identity,Y)) = least_upper_bound(identity,inverse(least_upper_bound(Y,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(Y,identity)),least_upper_bound(identity,least_upper_bound(Y,identity))),least_upper_bound(identity,inverse(least_upper_bound(Y,identity)))) ),[0,1],$fot(least_upper_bound(identity,Y))]]) ).
cnf(refute_0_1518,plain,
( multiply(inverse(least_upper_bound(Y,identity)),least_upper_bound(identity,least_upper_bound(Y,identity))) != least_upper_bound(identity,inverse(least_upper_bound(Y,identity)))
| multiply(inverse(least_upper_bound(Y,identity)),least_upper_bound(identity,Y)) = least_upper_bound(identity,inverse(least_upper_bound(Y,identity))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(Y,identity)),least_upper_bound(identity,Y)) )],[refute_0_1516,refute_0_1517]) ).
cnf(refute_0_1519,plain,
multiply(inverse(least_upper_bound(Y,identity)),least_upper_bound(identity,Y)) = least_upper_bound(identity,inverse(least_upper_bound(Y,identity))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(Y,identity)),least_upper_bound(identity,least_upper_bound(Y,identity))),least_upper_bound(identity,inverse(least_upper_bound(Y,identity)))) )],[refute_0_1515,refute_0_1518]) ).
cnf(refute_0_1520,plain,
multiply(inverse(least_upper_bound(Y,X_55)),least_upper_bound(X_55,least_upper_bound(Y,X_55))) = least_upper_bound(identity,multiply(inverse(least_upper_bound(Y,X_55)),X_55)),
inference(subst,[],[refute_0_29:[bind(X_49,$fot(X_55)),bind(X_50,$fot(least_upper_bound(Y,X_55)))]]) ).
cnf(refute_0_1521,plain,
least_upper_bound(X_55,least_upper_bound(Y,X_55)) = least_upper_bound(X_55,Y),
inference(subst,[],[refute_0_175:[bind(X_15,$fot(X_55))]]) ).
cnf(refute_0_1522,plain,
( multiply(inverse(least_upper_bound(Y,X_55)),least_upper_bound(X_55,least_upper_bound(Y,X_55))) != least_upper_bound(identity,multiply(inverse(least_upper_bound(Y,X_55)),X_55))
| least_upper_bound(X_55,least_upper_bound(Y,X_55)) != least_upper_bound(X_55,Y)
| multiply(inverse(least_upper_bound(Y,X_55)),least_upper_bound(X_55,Y)) = least_upper_bound(identity,multiply(inverse(least_upper_bound(Y,X_55)),X_55)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(Y,X_55)),least_upper_bound(X_55,least_upper_bound(Y,X_55))),least_upper_bound(identity,multiply(inverse(least_upper_bound(Y,X_55)),X_55))) ),[0,1],$fot(least_upper_bound(X_55,Y))]]) ).
cnf(refute_0_1523,plain,
( multiply(inverse(least_upper_bound(Y,X_55)),least_upper_bound(X_55,least_upper_bound(Y,X_55))) != least_upper_bound(identity,multiply(inverse(least_upper_bound(Y,X_55)),X_55))
| multiply(inverse(least_upper_bound(Y,X_55)),least_upper_bound(X_55,Y)) = least_upper_bound(identity,multiply(inverse(least_upper_bound(Y,X_55)),X_55)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_55,least_upper_bound(Y,X_55)),least_upper_bound(X_55,Y)) )],[refute_0_1521,refute_0_1522]) ).
cnf(refute_0_1524,plain,
multiply(inverse(least_upper_bound(Y,X_55)),least_upper_bound(X_55,Y)) = least_upper_bound(identity,multiply(inverse(least_upper_bound(Y,X_55)),X_55)),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(Y,X_55)),least_upper_bound(X_55,least_upper_bound(Y,X_55))),least_upper_bound(identity,multiply(inverse(least_upper_bound(Y,X_55)),X_55))) )],[refute_0_1520,refute_0_1523]) ).
cnf(refute_0_1525,plain,
multiply(inverse(least_upper_bound(X_55,X_18)),least_upper_bound(X_55,least_upper_bound(X_55,X_18))) = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_55,X_18)),X_55)),
inference(subst,[],[refute_0_29:[bind(X_49,$fot(X_55)),bind(X_50,$fot(least_upper_bound(X_55,X_18)))]]) ).
cnf(refute_0_1526,plain,
least_upper_bound(X_55,least_upper_bound(X_55,X_18)) = least_upper_bound(X_55,X_18),
inference(subst,[],[refute_0_516:[bind(X_19,$fot(X_55))]]) ).
cnf(refute_0_1527,plain,
( multiply(inverse(least_upper_bound(X_55,X_18)),least_upper_bound(X_55,least_upper_bound(X_55,X_18))) != least_upper_bound(identity,multiply(inverse(least_upper_bound(X_55,X_18)),X_55))
| least_upper_bound(X_55,least_upper_bound(X_55,X_18)) != least_upper_bound(X_55,X_18)
| multiply(inverse(least_upper_bound(X_55,X_18)),least_upper_bound(X_55,X_18)) = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_55,X_18)),X_55)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(X_55,X_18)),least_upper_bound(X_55,least_upper_bound(X_55,X_18))),least_upper_bound(identity,multiply(inverse(least_upper_bound(X_55,X_18)),X_55))) ),[0,1],$fot(least_upper_bound(X_55,X_18))]]) ).
cnf(refute_0_1528,plain,
( multiply(inverse(least_upper_bound(X_55,X_18)),least_upper_bound(X_55,least_upper_bound(X_55,X_18))) != least_upper_bound(identity,multiply(inverse(least_upper_bound(X_55,X_18)),X_55))
| multiply(inverse(least_upper_bound(X_55,X_18)),least_upper_bound(X_55,X_18)) = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_55,X_18)),X_55)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_55,least_upper_bound(X_55,X_18)),least_upper_bound(X_55,X_18)) )],[refute_0_1526,refute_0_1527]) ).
cnf(refute_0_1529,plain,
multiply(inverse(least_upper_bound(X_55,X_18)),least_upper_bound(X_55,X_18)) = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_55,X_18)),X_55)),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_55,X_18)),least_upper_bound(X_55,least_upper_bound(X_55,X_18))),least_upper_bound(identity,multiply(inverse(least_upper_bound(X_55,X_18)),X_55))) )],[refute_0_1525,refute_0_1528]) ).
cnf(refute_0_1530,plain,
multiply(inverse(least_upper_bound(X_55,X_18)),least_upper_bound(X_55,X_18)) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(least_upper_bound(X_55,X_18)))]]) ).
cnf(refute_0_1531,plain,
( multiply(inverse(least_upper_bound(X_55,X_18)),least_upper_bound(X_55,X_18)) != identity
| multiply(inverse(least_upper_bound(X_55,X_18)),least_upper_bound(X_55,X_18)) != least_upper_bound(identity,multiply(inverse(least_upper_bound(X_55,X_18)),X_55))
| identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_55,X_18)),X_55)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(X_55,X_18)),least_upper_bound(X_55,X_18)),least_upper_bound(identity,multiply(inverse(least_upper_bound(X_55,X_18)),X_55))) ),[0],$fot(identity)]]) ).
cnf(refute_0_1532,plain,
( multiply(inverse(least_upper_bound(X_55,X_18)),least_upper_bound(X_55,X_18)) != least_upper_bound(identity,multiply(inverse(least_upper_bound(X_55,X_18)),X_55))
| identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_55,X_18)),X_55)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_55,X_18)),least_upper_bound(X_55,X_18)),identity) )],[refute_0_1530,refute_0_1531]) ).
cnf(refute_0_1533,plain,
identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_55,X_18)),X_55)),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_55,X_18)),least_upper_bound(X_55,X_18)),least_upper_bound(identity,multiply(inverse(least_upper_bound(X_55,X_18)),X_55))) )],[refute_0_1529,refute_0_1532]) ).
cnf(refute_0_1534,plain,
identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_66,X_65)),X_66)),
inference(subst,[],[refute_0_1533:[bind(X_18,$fot(X_65)),bind(X_55,$fot(X_66))]]) ).
cnf(refute_0_1535,plain,
least_upper_bound(X_65,X_66) = least_upper_bound(X_66,X_65),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_65)),bind(Y,$fot(X_66))]]) ).
cnf(refute_0_1536,plain,
( least_upper_bound(X_65,X_66) != least_upper_bound(X_66,X_65)
| least_upper_bound(X_66,X_65) = least_upper_bound(X_65,X_66) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(least_upper_bound(X_65,X_66))),bind(Y0,$fot(least_upper_bound(X_66,X_65)))]]) ).
cnf(refute_0_1537,plain,
least_upper_bound(X_66,X_65) = least_upper_bound(X_65,X_66),
inference(resolve,[$cnf( $equal(least_upper_bound(X_65,X_66),least_upper_bound(X_66,X_65)) )],[refute_0_1535,refute_0_1536]) ).
cnf(refute_0_1538,plain,
( identity != least_upper_bound(identity,multiply(inverse(least_upper_bound(X_66,X_65)),X_66))
| least_upper_bound(X_66,X_65) != least_upper_bound(X_65,X_66)
| identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_65,X_66)),X_66)) ),
introduced(tautology,[equality,[$cnf( $equal(identity,least_upper_bound(identity,multiply(inverse(least_upper_bound(X_66,X_65)),X_66))) ),[1,1,0,0],$fot(least_upper_bound(X_65,X_66))]]) ).
cnf(refute_0_1539,plain,
( identity != least_upper_bound(identity,multiply(inverse(least_upper_bound(X_66,X_65)),X_66))
| identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_65,X_66)),X_66)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_66,X_65),least_upper_bound(X_65,X_66)) )],[refute_0_1537,refute_0_1538]) ).
cnf(refute_0_1540,plain,
identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_65,X_66)),X_66)),
inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,multiply(inverse(least_upper_bound(X_66,X_65)),X_66))) )],[refute_0_1534,refute_0_1539]) ).
cnf(refute_0_1541,plain,
( identity != least_upper_bound(identity,multiply(inverse(least_upper_bound(X_65,X_66)),X_66))
| least_upper_bound(identity,multiply(inverse(least_upper_bound(X_65,X_66)),X_66)) = identity ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(identity)),bind(Y0,$fot(least_upper_bound(identity,multiply(inverse(least_upper_bound(X_65,X_66)),X_66))))]]) ).
cnf(refute_0_1542,plain,
least_upper_bound(identity,multiply(inverse(least_upper_bound(X_65,X_66)),X_66)) = identity,
inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,multiply(inverse(least_upper_bound(X_65,X_66)),X_66))) )],[refute_0_1540,refute_0_1541]) ).
cnf(refute_0_1543,plain,
least_upper_bound(identity,multiply(inverse(least_upper_bound(Y,X_55)),X_55)) = identity,
inference(subst,[],[refute_0_1542:[bind(X_65,$fot(Y)),bind(X_66,$fot(X_55))]]) ).
cnf(refute_0_1544,plain,
( multiply(inverse(least_upper_bound(Y,X_55)),least_upper_bound(X_55,Y)) != least_upper_bound(identity,multiply(inverse(least_upper_bound(Y,X_55)),X_55))
| least_upper_bound(identity,multiply(inverse(least_upper_bound(Y,X_55)),X_55)) != identity
| multiply(inverse(least_upper_bound(Y,X_55)),least_upper_bound(X_55,Y)) = identity ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(least_upper_bound(Y,X_55)),least_upper_bound(X_55,Y)),identity) ),[0],$fot(least_upper_bound(identity,multiply(inverse(least_upper_bound(Y,X_55)),X_55)))]]) ).
cnf(refute_0_1545,plain,
( multiply(inverse(least_upper_bound(Y,X_55)),least_upper_bound(X_55,Y)) != least_upper_bound(identity,multiply(inverse(least_upper_bound(Y,X_55)),X_55))
| multiply(inverse(least_upper_bound(Y,X_55)),least_upper_bound(X_55,Y)) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(least_upper_bound(Y,X_55)),X_55)),identity) )],[refute_0_1543,refute_0_1544]) ).
cnf(refute_0_1546,plain,
multiply(inverse(least_upper_bound(Y,X_55)),least_upper_bound(X_55,Y)) = identity,
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(Y,X_55)),least_upper_bound(X_55,Y)),least_upper_bound(identity,multiply(inverse(least_upper_bound(Y,X_55)),X_55))) )],[refute_0_1524,refute_0_1545]) ).
cnf(refute_0_1547,plain,
multiply(inverse(least_upper_bound(Y,identity)),least_upper_bound(identity,Y)) = identity,
inference(subst,[],[refute_0_1546:[bind(X_55,$fot(identity))]]) ).
cnf(refute_0_1548,plain,
( multiply(inverse(least_upper_bound(Y,identity)),least_upper_bound(identity,Y)) != identity
| multiply(inverse(least_upper_bound(Y,identity)),least_upper_bound(identity,Y)) != least_upper_bound(identity,inverse(least_upper_bound(Y,identity)))
| identity = least_upper_bound(identity,inverse(least_upper_bound(Y,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(Y,identity)),least_upper_bound(identity,Y)),least_upper_bound(identity,inverse(least_upper_bound(Y,identity)))) ),[0],$fot(identity)]]) ).
cnf(refute_0_1549,plain,
( multiply(inverse(least_upper_bound(Y,identity)),least_upper_bound(identity,Y)) != least_upper_bound(identity,inverse(least_upper_bound(Y,identity)))
| identity = least_upper_bound(identity,inverse(least_upper_bound(Y,identity))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(Y,identity)),least_upper_bound(identity,Y)),identity) )],[refute_0_1547,refute_0_1548]) ).
cnf(refute_0_1550,plain,
identity = least_upper_bound(identity,inverse(least_upper_bound(Y,identity))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(Y,identity)),least_upper_bound(identity,Y)),least_upper_bound(identity,inverse(least_upper_bound(Y,identity)))) )],[refute_0_1519,refute_0_1549]) ).
cnf(refute_0_1551,plain,
identity = least_upper_bound(identity,inverse(least_upper_bound(X_293,identity))),
inference(subst,[],[refute_0_1550:[bind(Y,$fot(X_293))]]) ).
cnf(refute_0_1552,plain,
( identity != least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))
| least_upper_bound(identity,inverse(least_upper_bound(X_293,identity))) = identity ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(identity)),bind(Y0,$fot(least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))))]]) ).
cnf(refute_0_1553,plain,
least_upper_bound(identity,inverse(least_upper_bound(X_293,identity))) = identity,
inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))) )],[refute_0_1551,refute_0_1552]) ).
cnf(refute_0_1554,plain,
( multiply(greatest_lower_bound(X_120,inverse(inverse(least_upper_bound(X_293,identity)))),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))) != greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity)))),multiply(X_120,least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))))
| least_upper_bound(identity,inverse(least_upper_bound(X_293,identity))) != identity
| multiply(greatest_lower_bound(X_120,inverse(inverse(least_upper_bound(X_293,identity)))),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))) = greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity)))),multiply(X_120,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_120,inverse(inverse(least_upper_bound(X_293,identity)))),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))),greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity)))),multiply(X_120,least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))))) ),[1,1,1],$fot(identity)]]) ).
cnf(refute_0_1555,plain,
( multiply(greatest_lower_bound(X_120,inverse(inverse(least_upper_bound(X_293,identity)))),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))) != greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity)))),multiply(X_120,least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))))
| multiply(greatest_lower_bound(X_120,inverse(inverse(least_upper_bound(X_293,identity)))),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))) = greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity)))),multiply(X_120,identity)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(least_upper_bound(X_293,identity))),identity) )],[refute_0_1553,refute_0_1554]) ).
cnf(refute_0_1556,plain,
multiply(greatest_lower_bound(X_120,inverse(inverse(least_upper_bound(X_293,identity)))),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))) = greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity)))),multiply(X_120,identity)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_120,inverse(inverse(least_upper_bound(X_293,identity)))),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))),greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity)))),multiply(X_120,least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))))) )],[refute_0_1514,refute_0_1555]) ).
cnf(refute_0_1557,plain,
multiply(greatest_lower_bound(X_120,least_upper_bound(X_293,identity)),identity) = greatest_lower_bound(X_120,least_upper_bound(X_293,identity)),
inference(subst,[],[refute_0_88:[bind(X_33,$fot(greatest_lower_bound(X_120,least_upper_bound(X_293,identity))))]]) ).
cnf(refute_0_1558,plain,
multiply(greatest_lower_bound(X_120,least_upper_bound(X_293,identity)),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))) = multiply(greatest_lower_bound(X_120,least_upper_bound(X_293,identity)),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(X_120,least_upper_bound(X_293,identity)),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))))]]) ).
cnf(refute_0_1559,plain,
( multiply(greatest_lower_bound(X_120,least_upper_bound(X_293,identity)),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))) != multiply(greatest_lower_bound(X_120,least_upper_bound(X_293,identity)),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity))))
| least_upper_bound(identity,inverse(least_upper_bound(X_293,identity))) != identity
| multiply(greatest_lower_bound(X_120,least_upper_bound(X_293,identity)),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))) = multiply(greatest_lower_bound(X_120,least_upper_bound(X_293,identity)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_120,least_upper_bound(X_293,identity)),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))),multiply(greatest_lower_bound(X_120,least_upper_bound(X_293,identity)),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_1560,plain,
( least_upper_bound(identity,inverse(least_upper_bound(X_293,identity))) != identity
| multiply(greatest_lower_bound(X_120,least_upper_bound(X_293,identity)),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))) = multiply(greatest_lower_bound(X_120,least_upper_bound(X_293,identity)),identity) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_120,least_upper_bound(X_293,identity)),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))),multiply(greatest_lower_bound(X_120,least_upper_bound(X_293,identity)),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity))))) )],[refute_0_1558,refute_0_1559]) ).
cnf(refute_0_1561,plain,
multiply(greatest_lower_bound(X_120,least_upper_bound(X_293,identity)),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))) = multiply(greatest_lower_bound(X_120,least_upper_bound(X_293,identity)),identity),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(least_upper_bound(X_293,identity))),identity) )],[refute_0_1553,refute_0_1560]) ).
cnf(refute_0_1562,plain,
inverse(inverse(least_upper_bound(X_293,identity))) = least_upper_bound(X_293,identity),
inference(subst,[],[refute_0_452:[bind(X_35,$fot(least_upper_bound(X_293,identity)))]]) ).
cnf(refute_0_1563,plain,
greatest_lower_bound(X_120,inverse(inverse(least_upper_bound(X_293,identity)))) = greatest_lower_bound(X_120,inverse(inverse(least_upper_bound(X_293,identity)))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X_120,inverse(inverse(least_upper_bound(X_293,identity)))))]]) ).
cnf(refute_0_1564,plain,
( greatest_lower_bound(X_120,inverse(inverse(least_upper_bound(X_293,identity)))) != greatest_lower_bound(X_120,inverse(inverse(least_upper_bound(X_293,identity))))
| inverse(inverse(least_upper_bound(X_293,identity))) != least_upper_bound(X_293,identity)
| greatest_lower_bound(X_120,inverse(inverse(least_upper_bound(X_293,identity)))) = greatest_lower_bound(X_120,least_upper_bound(X_293,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_120,inverse(inverse(least_upper_bound(X_293,identity)))),greatest_lower_bound(X_120,inverse(inverse(least_upper_bound(X_293,identity))))) ),[1,1],$fot(least_upper_bound(X_293,identity))]]) ).
cnf(refute_0_1565,plain,
( inverse(inverse(least_upper_bound(X_293,identity))) != least_upper_bound(X_293,identity)
| greatest_lower_bound(X_120,inverse(inverse(least_upper_bound(X_293,identity)))) = greatest_lower_bound(X_120,least_upper_bound(X_293,identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_120,inverse(inverse(least_upper_bound(X_293,identity)))),greatest_lower_bound(X_120,inverse(inverse(least_upper_bound(X_293,identity))))) )],[refute_0_1563,refute_0_1564]) ).
cnf(refute_0_1566,plain,
greatest_lower_bound(X_120,inverse(inverse(least_upper_bound(X_293,identity)))) = greatest_lower_bound(X_120,least_upper_bound(X_293,identity)),
inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(X_293,identity))),least_upper_bound(X_293,identity)) )],[refute_0_1562,refute_0_1565]) ).
cnf(refute_0_1567,plain,
multiply(greatest_lower_bound(X_120,inverse(inverse(least_upper_bound(X_293,identity)))),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))) = multiply(greatest_lower_bound(X_120,inverse(inverse(least_upper_bound(X_293,identity)))),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(X_120,inverse(inverse(least_upper_bound(X_293,identity)))),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))))]]) ).
cnf(refute_0_1568,plain,
( multiply(greatest_lower_bound(X_120,inverse(inverse(least_upper_bound(X_293,identity)))),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))) != multiply(greatest_lower_bound(X_120,inverse(inverse(least_upper_bound(X_293,identity)))),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity))))
| greatest_lower_bound(X_120,inverse(inverse(least_upper_bound(X_293,identity)))) != greatest_lower_bound(X_120,least_upper_bound(X_293,identity))
| multiply(greatest_lower_bound(X_120,inverse(inverse(least_upper_bound(X_293,identity)))),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))) = multiply(greatest_lower_bound(X_120,least_upper_bound(X_293,identity)),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_120,inverse(inverse(least_upper_bound(X_293,identity)))),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))),multiply(greatest_lower_bound(X_120,inverse(inverse(least_upper_bound(X_293,identity)))),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity))))) ),[1,0],$fot(greatest_lower_bound(X_120,least_upper_bound(X_293,identity)))]]) ).
cnf(refute_0_1569,plain,
( greatest_lower_bound(X_120,inverse(inverse(least_upper_bound(X_293,identity)))) != greatest_lower_bound(X_120,least_upper_bound(X_293,identity))
| multiply(greatest_lower_bound(X_120,inverse(inverse(least_upper_bound(X_293,identity)))),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))) = multiply(greatest_lower_bound(X_120,least_upper_bound(X_293,identity)),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_120,inverse(inverse(least_upper_bound(X_293,identity)))),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))),multiply(greatest_lower_bound(X_120,inverse(inverse(least_upper_bound(X_293,identity)))),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity))))) )],[refute_0_1567,refute_0_1568]) ).
cnf(refute_0_1570,plain,
multiply(greatest_lower_bound(X_120,inverse(inverse(least_upper_bound(X_293,identity)))),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))) = multiply(greatest_lower_bound(X_120,least_upper_bound(X_293,identity)),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_120,inverse(inverse(least_upper_bound(X_293,identity)))),greatest_lower_bound(X_120,least_upper_bound(X_293,identity))) )],[refute_0_1566,refute_0_1569]) ).
cnf(refute_0_1571,plain,
( multiply(greatest_lower_bound(X_120,inverse(inverse(least_upper_bound(X_293,identity)))),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))) != multiply(greatest_lower_bound(X_120,least_upper_bound(X_293,identity)),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity))))
| multiply(greatest_lower_bound(X_120,least_upper_bound(X_293,identity)),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))) != multiply(greatest_lower_bound(X_120,least_upper_bound(X_293,identity)),identity)
| multiply(greatest_lower_bound(X_120,inverse(inverse(least_upper_bound(X_293,identity)))),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))) = multiply(greatest_lower_bound(X_120,least_upper_bound(X_293,identity)),identity) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(greatest_lower_bound(X_120,inverse(inverse(least_upper_bound(X_293,identity)))),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))))),bind(Y0,$fot(multiply(greatest_lower_bound(X_120,least_upper_bound(X_293,identity)),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))))),bind(Z0,$fot(multiply(greatest_lower_bound(X_120,least_upper_bound(X_293,identity)),identity)))]]) ).
cnf(refute_0_1572,plain,
( multiply(greatest_lower_bound(X_120,least_upper_bound(X_293,identity)),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))) != multiply(greatest_lower_bound(X_120,least_upper_bound(X_293,identity)),identity)
| multiply(greatest_lower_bound(X_120,inverse(inverse(least_upper_bound(X_293,identity)))),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))) = multiply(greatest_lower_bound(X_120,least_upper_bound(X_293,identity)),identity) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_120,inverse(inverse(least_upper_bound(X_293,identity)))),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))),multiply(greatest_lower_bound(X_120,least_upper_bound(X_293,identity)),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity))))) )],[refute_0_1570,refute_0_1571]) ).
cnf(refute_0_1573,plain,
multiply(greatest_lower_bound(X_120,inverse(inverse(least_upper_bound(X_293,identity)))),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))) = multiply(greatest_lower_bound(X_120,least_upper_bound(X_293,identity)),identity),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_120,least_upper_bound(X_293,identity)),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))),multiply(greatest_lower_bound(X_120,least_upper_bound(X_293,identity)),identity)) )],[refute_0_1561,refute_0_1572]) ).
cnf(refute_0_1574,plain,
( multiply(greatest_lower_bound(X_120,inverse(inverse(least_upper_bound(X_293,identity)))),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))) != multiply(greatest_lower_bound(X_120,least_upper_bound(X_293,identity)),identity)
| multiply(greatest_lower_bound(X_120,least_upper_bound(X_293,identity)),identity) != greatest_lower_bound(X_120,least_upper_bound(X_293,identity))
| multiply(greatest_lower_bound(X_120,inverse(inverse(least_upper_bound(X_293,identity)))),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))) = greatest_lower_bound(X_120,least_upper_bound(X_293,identity)) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(greatest_lower_bound(X_120,inverse(inverse(least_upper_bound(X_293,identity)))),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))))),bind(Y0,$fot(multiply(greatest_lower_bound(X_120,least_upper_bound(X_293,identity)),identity))),bind(Z0,$fot(greatest_lower_bound(X_120,least_upper_bound(X_293,identity))))]]) ).
cnf(refute_0_1575,plain,
( multiply(greatest_lower_bound(X_120,least_upper_bound(X_293,identity)),identity) != greatest_lower_bound(X_120,least_upper_bound(X_293,identity))
| multiply(greatest_lower_bound(X_120,inverse(inverse(least_upper_bound(X_293,identity)))),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))) = greatest_lower_bound(X_120,least_upper_bound(X_293,identity)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_120,inverse(inverse(least_upper_bound(X_293,identity)))),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))),multiply(greatest_lower_bound(X_120,least_upper_bound(X_293,identity)),identity)) )],[refute_0_1573,refute_0_1574]) ).
cnf(refute_0_1576,plain,
multiply(greatest_lower_bound(X_120,inverse(inverse(least_upper_bound(X_293,identity)))),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))) = greatest_lower_bound(X_120,least_upper_bound(X_293,identity)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_120,least_upper_bound(X_293,identity)),identity),greatest_lower_bound(X_120,least_upper_bound(X_293,identity))) )],[refute_0_1557,refute_0_1575]) ).
cnf(refute_0_1577,plain,
( multiply(greatest_lower_bound(X_120,inverse(inverse(least_upper_bound(X_293,identity)))),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))) != greatest_lower_bound(X_120,least_upper_bound(X_293,identity))
| multiply(greatest_lower_bound(X_120,inverse(inverse(least_upper_bound(X_293,identity)))),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))) != greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity)))),multiply(X_120,identity))
| greatest_lower_bound(X_120,least_upper_bound(X_293,identity)) = greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity)))),multiply(X_120,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_120,inverse(inverse(least_upper_bound(X_293,identity)))),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))),greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity)))),multiply(X_120,identity))) ),[0],$fot(greatest_lower_bound(X_120,least_upper_bound(X_293,identity)))]]) ).
cnf(refute_0_1578,plain,
( multiply(greatest_lower_bound(X_120,inverse(inverse(least_upper_bound(X_293,identity)))),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))) != greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity)))),multiply(X_120,identity))
| greatest_lower_bound(X_120,least_upper_bound(X_293,identity)) = greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity)))),multiply(X_120,identity)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_120,inverse(inverse(least_upper_bound(X_293,identity)))),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))),greatest_lower_bound(X_120,least_upper_bound(X_293,identity))) )],[refute_0_1576,refute_0_1577]) ).
cnf(refute_0_1579,plain,
multiply(X_120,identity) = X_120,
inference(subst,[],[refute_0_88:[bind(X_33,$fot(X_120))]]) ).
cnf(refute_0_1580,plain,
greatest_lower_bound(least_upper_bound(identity,X_293),multiply(X_120,identity)) = greatest_lower_bound(least_upper_bound(identity,X_293),multiply(X_120,identity)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(least_upper_bound(identity,X_293),multiply(X_120,identity)))]]) ).
cnf(refute_0_1581,plain,
( multiply(X_120,identity) != X_120
| greatest_lower_bound(least_upper_bound(identity,X_293),multiply(X_120,identity)) != greatest_lower_bound(least_upper_bound(identity,X_293),multiply(X_120,identity))
| greatest_lower_bound(least_upper_bound(identity,X_293),multiply(X_120,identity)) = greatest_lower_bound(least_upper_bound(identity,X_293),X_120) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,X_293),multiply(X_120,identity)),greatest_lower_bound(least_upper_bound(identity,X_293),multiply(X_120,identity))) ),[1,1],$fot(X_120)]]) ).
cnf(refute_0_1582,plain,
( multiply(X_120,identity) != X_120
| greatest_lower_bound(least_upper_bound(identity,X_293),multiply(X_120,identity)) = greatest_lower_bound(least_upper_bound(identity,X_293),X_120) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,X_293),multiply(X_120,identity)),greatest_lower_bound(least_upper_bound(identity,X_293),multiply(X_120,identity))) )],[refute_0_1580,refute_0_1581]) ).
cnf(refute_0_1583,plain,
greatest_lower_bound(least_upper_bound(identity,X_293),multiply(X_120,identity)) = greatest_lower_bound(least_upper_bound(identity,X_293),X_120),
inference(resolve,[$cnf( $equal(multiply(X_120,identity),X_120) )],[refute_0_1579,refute_0_1582]) ).
cnf(refute_0_1584,plain,
least_upper_bound(identity,least_upper_bound(X_293,identity)) = least_upper_bound(identity,X_293),
inference(subst,[],[refute_0_175:[bind(Y,$fot(X_293)),bind(X_15,$fot(identity))]]) ).
cnf(refute_0_1585,plain,
least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity)))) = least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity)))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity)))))]]) ).
cnf(refute_0_1586,plain,
( inverse(inverse(least_upper_bound(X_293,identity))) != least_upper_bound(X_293,identity)
| least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity)))) != least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity))))
| least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity)))) = least_upper_bound(identity,least_upper_bound(X_293,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity)))),least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity))))) ),[1,1],$fot(least_upper_bound(X_293,identity))]]) ).
cnf(refute_0_1587,plain,
( inverse(inverse(least_upper_bound(X_293,identity))) != least_upper_bound(X_293,identity)
| least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity)))) = least_upper_bound(identity,least_upper_bound(X_293,identity)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity)))),least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity))))) )],[refute_0_1585,refute_0_1586]) ).
cnf(refute_0_1588,plain,
least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity)))) = least_upper_bound(identity,least_upper_bound(X_293,identity)),
inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(X_293,identity))),least_upper_bound(X_293,identity)) )],[refute_0_1562,refute_0_1587]) ).
cnf(refute_0_1589,plain,
( least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity)))) != least_upper_bound(identity,least_upper_bound(X_293,identity))
| least_upper_bound(identity,least_upper_bound(X_293,identity)) != least_upper_bound(identity,X_293)
| least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity)))) = least_upper_bound(identity,X_293) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity)))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(X_293,identity)))),bind(Z0,$fot(least_upper_bound(identity,X_293)))]]) ).
cnf(refute_0_1590,plain,
( least_upper_bound(identity,least_upper_bound(X_293,identity)) != least_upper_bound(identity,X_293)
| least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity)))) = least_upper_bound(identity,X_293) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity)))),least_upper_bound(identity,least_upper_bound(X_293,identity))) )],[refute_0_1588,refute_0_1589]) ).
cnf(refute_0_1591,plain,
least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity)))) = least_upper_bound(identity,X_293),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_293,identity)),least_upper_bound(identity,X_293)) )],[refute_0_1584,refute_0_1590]) ).
cnf(refute_0_1592,plain,
greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity)))),multiply(X_120,identity)) = greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity)))),multiply(X_120,identity)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity)))),multiply(X_120,identity)))]]) ).
cnf(refute_0_1593,plain,
( greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity)))),multiply(X_120,identity)) != greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity)))),multiply(X_120,identity))
| least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity)))) != least_upper_bound(identity,X_293)
| greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity)))),multiply(X_120,identity)) = greatest_lower_bound(least_upper_bound(identity,X_293),multiply(X_120,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity)))),multiply(X_120,identity)),greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity)))),multiply(X_120,identity))) ),[1,0],$fot(least_upper_bound(identity,X_293))]]) ).
cnf(refute_0_1594,plain,
( least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity)))) != least_upper_bound(identity,X_293)
| greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity)))),multiply(X_120,identity)) = greatest_lower_bound(least_upper_bound(identity,X_293),multiply(X_120,identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity)))),multiply(X_120,identity)),greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity)))),multiply(X_120,identity))) )],[refute_0_1592,refute_0_1593]) ).
cnf(refute_0_1595,plain,
greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity)))),multiply(X_120,identity)) = greatest_lower_bound(least_upper_bound(identity,X_293),multiply(X_120,identity)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity)))),least_upper_bound(identity,X_293)) )],[refute_0_1591,refute_0_1594]) ).
cnf(refute_0_1596,plain,
( greatest_lower_bound(least_upper_bound(identity,X_293),multiply(X_120,identity)) != greatest_lower_bound(least_upper_bound(identity,X_293),X_120)
| greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity)))),multiply(X_120,identity)) != greatest_lower_bound(least_upper_bound(identity,X_293),multiply(X_120,identity))
| greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity)))),multiply(X_120,identity)) = greatest_lower_bound(least_upper_bound(identity,X_293),X_120) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity)))),multiply(X_120,identity)))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(identity,X_293),multiply(X_120,identity)))),bind(Z0,$fot(greatest_lower_bound(least_upper_bound(identity,X_293),X_120)))]]) ).
cnf(refute_0_1597,plain,
( greatest_lower_bound(least_upper_bound(identity,X_293),multiply(X_120,identity)) != greatest_lower_bound(least_upper_bound(identity,X_293),X_120)
| greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity)))),multiply(X_120,identity)) = greatest_lower_bound(least_upper_bound(identity,X_293),X_120) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity)))),multiply(X_120,identity)),greatest_lower_bound(least_upper_bound(identity,X_293),multiply(X_120,identity))) )],[refute_0_1595,refute_0_1596]) ).
cnf(refute_0_1598,plain,
greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity)))),multiply(X_120,identity)) = greatest_lower_bound(least_upper_bound(identity,X_293),X_120),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,X_293),multiply(X_120,identity)),greatest_lower_bound(least_upper_bound(identity,X_293),X_120)) )],[refute_0_1583,refute_0_1597]) ).
cnf(refute_0_1599,plain,
( greatest_lower_bound(X_120,least_upper_bound(X_293,identity)) != greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity)))),multiply(X_120,identity))
| greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity)))),multiply(X_120,identity)) != greatest_lower_bound(least_upper_bound(identity,X_293),X_120)
| greatest_lower_bound(X_120,least_upper_bound(X_293,identity)) = greatest_lower_bound(least_upper_bound(identity,X_293),X_120) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_120,least_upper_bound(X_293,identity)),greatest_lower_bound(least_upper_bound(identity,X_293),X_120)) ),[0],$fot(greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity)))),multiply(X_120,identity)))]]) ).
cnf(refute_0_1600,plain,
( greatest_lower_bound(X_120,least_upper_bound(X_293,identity)) != greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity)))),multiply(X_120,identity))
| greatest_lower_bound(X_120,least_upper_bound(X_293,identity)) = greatest_lower_bound(least_upper_bound(identity,X_293),X_120) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity)))),multiply(X_120,identity)),greatest_lower_bound(least_upper_bound(identity,X_293),X_120)) )],[refute_0_1598,refute_0_1599]) ).
cnf(refute_0_1601,plain,
( multiply(greatest_lower_bound(X_120,inverse(inverse(least_upper_bound(X_293,identity)))),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))) != greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity)))),multiply(X_120,identity))
| greatest_lower_bound(X_120,least_upper_bound(X_293,identity)) = greatest_lower_bound(least_upper_bound(identity,X_293),X_120) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_120,least_upper_bound(X_293,identity)),greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity)))),multiply(X_120,identity))) )],[refute_0_1578,refute_0_1600]) ).
cnf(refute_0_1602,plain,
greatest_lower_bound(X_120,least_upper_bound(X_293,identity)) = greatest_lower_bound(least_upper_bound(identity,X_293),X_120),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_120,inverse(inverse(least_upper_bound(X_293,identity)))),least_upper_bound(identity,inverse(least_upper_bound(X_293,identity)))),greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_293,identity)))),multiply(X_120,identity))) )],[refute_0_1556,refute_0_1601]) ).
cnf(refute_0_1603,plain,
( greatest_lower_bound(X_120,least_upper_bound(X_293,identity)) != greatest_lower_bound(least_upper_bound(identity,X_293),X_120)
| greatest_lower_bound(least_upper_bound(identity,X_293),X_120) = greatest_lower_bound(X_120,least_upper_bound(X_293,identity)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(greatest_lower_bound(X_120,least_upper_bound(X_293,identity)))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(identity,X_293),X_120)))]]) ).
cnf(refute_0_1604,plain,
greatest_lower_bound(least_upper_bound(identity,X_293),X_120) = greatest_lower_bound(X_120,least_upper_bound(X_293,identity)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_120,least_upper_bound(X_293,identity)),greatest_lower_bound(least_upper_bound(identity,X_293),X_120)) )],[refute_0_1602,refute_0_1603]) ).
cnf(refute_0_1605,plain,
greatest_lower_bound(least_upper_bound(identity,inverse(X_35)),least_upper_bound(identity,X_35)) = greatest_lower_bound(least_upper_bound(identity,X_35),least_upper_bound(inverse(X_35),identity)),
inference(subst,[],[refute_0_1604:[bind(X_120,$fot(least_upper_bound(identity,X_35))),bind(X_293,$fot(inverse(X_35)))]]) ).
cnf(refute_0_1606,plain,
( greatest_lower_bound(least_upper_bound(identity,X_35),least_upper_bound(inverse(X_35),identity)) != multiply(least_upper_bound(identity,X_35),greatest_lower_bound(identity,inverse(X_35)))
| greatest_lower_bound(least_upper_bound(identity,inverse(X_35)),least_upper_bound(identity,X_35)) != greatest_lower_bound(least_upper_bound(identity,X_35),least_upper_bound(inverse(X_35),identity))
| greatest_lower_bound(least_upper_bound(identity,inverse(X_35)),least_upper_bound(identity,X_35)) = multiply(least_upper_bound(identity,X_35),greatest_lower_bound(identity,inverse(X_35))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(identity,inverse(X_35)),least_upper_bound(identity,X_35)))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(identity,X_35),least_upper_bound(inverse(X_35),identity)))),bind(Z0,$fot(multiply(least_upper_bound(identity,X_35),greatest_lower_bound(identity,inverse(X_35)))))]]) ).
cnf(refute_0_1607,plain,
( greatest_lower_bound(least_upper_bound(identity,X_35),least_upper_bound(inverse(X_35),identity)) != multiply(least_upper_bound(identity,X_35),greatest_lower_bound(identity,inverse(X_35)))
| greatest_lower_bound(least_upper_bound(identity,inverse(X_35)),least_upper_bound(identity,X_35)) = multiply(least_upper_bound(identity,X_35),greatest_lower_bound(identity,inverse(X_35))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,inverse(X_35)),least_upper_bound(identity,X_35)),greatest_lower_bound(least_upper_bound(identity,X_35),least_upper_bound(inverse(X_35),identity))) )],[refute_0_1605,refute_0_1606]) ).
cnf(refute_0_1608,plain,
greatest_lower_bound(least_upper_bound(identity,inverse(X_35)),least_upper_bound(identity,X_35)) = multiply(least_upper_bound(identity,X_35),greatest_lower_bound(identity,inverse(X_35))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,X_35),least_upper_bound(inverse(X_35),identity)),multiply(least_upper_bound(identity,X_35),greatest_lower_bound(identity,inverse(X_35)))) )],[refute_0_1505,refute_0_1607]) ).
cnf(refute_0_1609,plain,
( multiply(greatest_lower_bound(identity,X_35),least_upper_bound(identity,inverse(X_35))) != greatest_lower_bound(least_upper_bound(identity,inverse(X_35)),least_upper_bound(identity,X_35))
| greatest_lower_bound(least_upper_bound(identity,inverse(X_35)),least_upper_bound(identity,X_35)) != multiply(least_upper_bound(identity,X_35),greatest_lower_bound(identity,inverse(X_35)))
| multiply(greatest_lower_bound(identity,X_35),least_upper_bound(identity,inverse(X_35))) = multiply(least_upper_bound(identity,X_35),greatest_lower_bound(identity,inverse(X_35))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(identity,X_35),least_upper_bound(identity,inverse(X_35))),multiply(least_upper_bound(identity,X_35),greatest_lower_bound(identity,inverse(X_35)))) ),[0],$fot(greatest_lower_bound(least_upper_bound(identity,inverse(X_35)),least_upper_bound(identity,X_35)))]]) ).
cnf(refute_0_1610,plain,
( multiply(greatest_lower_bound(identity,X_35),least_upper_bound(identity,inverse(X_35))) != greatest_lower_bound(least_upper_bound(identity,inverse(X_35)),least_upper_bound(identity,X_35))
| multiply(greatest_lower_bound(identity,X_35),least_upper_bound(identity,inverse(X_35))) = multiply(least_upper_bound(identity,X_35),greatest_lower_bound(identity,inverse(X_35))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,inverse(X_35)),least_upper_bound(identity,X_35)),multiply(least_upper_bound(identity,X_35),greatest_lower_bound(identity,inverse(X_35)))) )],[refute_0_1608,refute_0_1609]) ).
cnf(refute_0_1611,plain,
( multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(identity,inverse(inverse(X_35)))) != greatest_lower_bound(least_upper_bound(identity,inverse(X_35)),least_upper_bound(identity,X_35))
| multiply(greatest_lower_bound(identity,X_35),least_upper_bound(identity,inverse(X_35))) = multiply(least_upper_bound(identity,X_35),greatest_lower_bound(identity,inverse(X_35))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_35),least_upper_bound(identity,inverse(X_35))),greatest_lower_bound(least_upper_bound(identity,inverse(X_35)),least_upper_bound(identity,X_35))) )],[refute_0_1435,refute_0_1610]) ).
cnf(refute_0_1612,plain,
multiply(greatest_lower_bound(identity,X_35),least_upper_bound(identity,inverse(X_35))) = multiply(least_upper_bound(identity,X_35),greatest_lower_bound(identity,inverse(X_35))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(identity,inverse(inverse(X_35)))),greatest_lower_bound(least_upper_bound(identity,inverse(X_35)),least_upper_bound(identity,X_35))) )],[refute_0_1330,refute_0_1611]) ).
cnf(refute_0_1613,plain,
( multiply(greatest_lower_bound(identity,X_35),least_upper_bound(identity,inverse(X_35))) != multiply(least_upper_bound(identity,X_35),greatest_lower_bound(identity,inverse(X_35)))
| multiply(least_upper_bound(identity,X_35),greatest_lower_bound(identity,inverse(X_35))) = multiply(greatest_lower_bound(identity,X_35),least_upper_bound(identity,inverse(X_35))) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(greatest_lower_bound(identity,X_35),least_upper_bound(identity,inverse(X_35))))),bind(Y0,$fot(multiply(least_upper_bound(identity,X_35),greatest_lower_bound(identity,inverse(X_35)))))]]) ).
cnf(refute_0_1614,plain,
multiply(least_upper_bound(identity,X_35),greatest_lower_bound(identity,inverse(X_35))) = multiply(greatest_lower_bound(identity,X_35),least_upper_bound(identity,inverse(X_35))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_35),least_upper_bound(identity,inverse(X_35))),multiply(least_upper_bound(identity,X_35),greatest_lower_bound(identity,inverse(X_35)))) )],[refute_0_1612,refute_0_1613]) ).
cnf(refute_0_1615,plain,
multiply(least_upper_bound(identity,multiply(X_68,identity)),greatest_lower_bound(identity,inverse(multiply(X_68,identity)))) = multiply(greatest_lower_bound(identity,multiply(X_68,identity)),least_upper_bound(identity,inverse(multiply(X_68,identity)))),
inference(subst,[],[refute_0_1614:[bind(X_35,$fot(multiply(X_68,identity)))]]) ).
cnf(refute_0_1616,plain,
( multiply(greatest_lower_bound(identity,multiply(X_68,identity)),least_upper_bound(identity,inverse(multiply(X_68,identity)))) != multiply(greatest_lower_bound(X_68,identity),least_upper_bound(identity,inverse(X_68)))
| multiply(least_upper_bound(identity,multiply(X_68,identity)),greatest_lower_bound(identity,inverse(multiply(X_68,identity)))) != multiply(greatest_lower_bound(identity,multiply(X_68,identity)),least_upper_bound(identity,inverse(multiply(X_68,identity))))
| multiply(least_upper_bound(identity,multiply(X_68,identity)),greatest_lower_bound(identity,inverse(multiply(X_68,identity)))) = multiply(greatest_lower_bound(X_68,identity),least_upper_bound(identity,inverse(X_68))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(least_upper_bound(identity,multiply(X_68,identity)),greatest_lower_bound(identity,inverse(multiply(X_68,identity)))))),bind(Y0,$fot(multiply(greatest_lower_bound(identity,multiply(X_68,identity)),least_upper_bound(identity,inverse(multiply(X_68,identity)))))),bind(Z0,$fot(multiply(greatest_lower_bound(X_68,identity),least_upper_bound(identity,inverse(X_68)))))]]) ).
cnf(refute_0_1617,plain,
( multiply(greatest_lower_bound(identity,multiply(X_68,identity)),least_upper_bound(identity,inverse(multiply(X_68,identity)))) != multiply(greatest_lower_bound(X_68,identity),least_upper_bound(identity,inverse(X_68)))
| multiply(least_upper_bound(identity,multiply(X_68,identity)),greatest_lower_bound(identity,inverse(multiply(X_68,identity)))) = multiply(greatest_lower_bound(X_68,identity),least_upper_bound(identity,inverse(X_68))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(X_68,identity)),greatest_lower_bound(identity,inverse(multiply(X_68,identity)))),multiply(greatest_lower_bound(identity,multiply(X_68,identity)),least_upper_bound(identity,inverse(multiply(X_68,identity))))) )],[refute_0_1615,refute_0_1616]) ).
cnf(refute_0_1618,plain,
multiply(least_upper_bound(identity,multiply(X_68,identity)),greatest_lower_bound(identity,inverse(multiply(X_68,identity)))) = multiply(greatest_lower_bound(X_68,identity),least_upper_bound(identity,inverse(X_68))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(X_68,identity)),least_upper_bound(identity,inverse(multiply(X_68,identity)))),multiply(greatest_lower_bound(X_68,identity),least_upper_bound(identity,inverse(X_68)))) )],[refute_0_1326,refute_0_1617]) ).
cnf(refute_0_1619,plain,
( multiply(least_upper_bound(identity,multiply(X_68,identity)),greatest_lower_bound(identity,inverse(multiply(X_68,identity)))) != multiply(greatest_lower_bound(X_68,identity),least_upper_bound(identity,inverse(X_68)))
| multiply(least_upper_bound(identity,multiply(X_68,identity)),greatest_lower_bound(identity,inverse(multiply(X_68,identity)))) != greatest_lower_bound(multiply(least_upper_bound(X_68,identity),identity),least_upper_bound(identity,inverse(multiply(X_68,identity))))
| multiply(greatest_lower_bound(X_68,identity),least_upper_bound(identity,inverse(X_68))) = greatest_lower_bound(multiply(least_upper_bound(X_68,identity),identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(X_68,identity)),greatest_lower_bound(identity,inverse(multiply(X_68,identity)))),greatest_lower_bound(multiply(least_upper_bound(X_68,identity),identity),least_upper_bound(identity,inverse(multiply(X_68,identity))))) ),[0],$fot(multiply(greatest_lower_bound(X_68,identity),least_upper_bound(identity,inverse(X_68))))]]) ).
cnf(refute_0_1620,plain,
( multiply(least_upper_bound(identity,multiply(X_68,identity)),greatest_lower_bound(identity,inverse(multiply(X_68,identity)))) != greatest_lower_bound(multiply(least_upper_bound(X_68,identity),identity),least_upper_bound(identity,inverse(multiply(X_68,identity))))
| multiply(greatest_lower_bound(X_68,identity),least_upper_bound(identity,inverse(X_68))) = greatest_lower_bound(multiply(least_upper_bound(X_68,identity),identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(X_68,identity)),greatest_lower_bound(identity,inverse(multiply(X_68,identity)))),multiply(greatest_lower_bound(X_68,identity),least_upper_bound(identity,inverse(X_68)))) )],[refute_0_1618,refute_0_1619]) ).
cnf(refute_0_1621,plain,
( multiply(least_upper_bound(X_76,identity),greatest_lower_bound(identity,inverse(X_76))) != greatest_lower_bound(least_upper_bound(X_76,identity),least_upper_bound(identity,inverse(X_76)))
| greatest_lower_bound(least_upper_bound(X_76,identity),least_upper_bound(identity,inverse(X_76))) = multiply(least_upper_bound(X_76,identity),greatest_lower_bound(identity,inverse(X_76))) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(least_upper_bound(X_76,identity),greatest_lower_bound(identity,inverse(X_76))))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(X_76,identity),least_upper_bound(identity,inverse(X_76)))))]]) ).
cnf(refute_0_1622,plain,
greatest_lower_bound(least_upper_bound(X_76,identity),least_upper_bound(identity,inverse(X_76))) = multiply(least_upper_bound(X_76,identity),greatest_lower_bound(identity,inverse(X_76))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_76,identity),greatest_lower_bound(identity,inverse(X_76))),greatest_lower_bound(least_upper_bound(X_76,identity),least_upper_bound(identity,inverse(X_76)))) )],[refute_0_1275,refute_0_1621]) ).
cnf(refute_0_1623,plain,
greatest_lower_bound(least_upper_bound(X_68,identity),least_upper_bound(identity,inverse(X_68))) = multiply(least_upper_bound(X_68,identity),greatest_lower_bound(identity,inverse(X_68))),
inference(subst,[],[refute_0_1622:[bind(X_76,$fot(X_68))]]) ).
cnf(refute_0_1624,plain,
greatest_lower_bound(least_upper_bound(X_68,identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))) = greatest_lower_bound(least_upper_bound(X_68,identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(least_upper_bound(X_68,identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))))]]) ).
cnf(refute_0_1625,plain,
( greatest_lower_bound(least_upper_bound(X_68,identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))) != greatest_lower_bound(least_upper_bound(X_68,identity),least_upper_bound(identity,inverse(multiply(X_68,identity))))
| least_upper_bound(identity,inverse(multiply(X_68,identity))) != least_upper_bound(identity,inverse(X_68))
| greatest_lower_bound(least_upper_bound(X_68,identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))) = greatest_lower_bound(least_upper_bound(X_68,identity),least_upper_bound(identity,inverse(X_68))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_68,identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))),greatest_lower_bound(least_upper_bound(X_68,identity),least_upper_bound(identity,inverse(multiply(X_68,identity))))) ),[1,1],$fot(least_upper_bound(identity,inverse(X_68)))]]) ).
cnf(refute_0_1626,plain,
( least_upper_bound(identity,inverse(multiply(X_68,identity))) != least_upper_bound(identity,inverse(X_68))
| greatest_lower_bound(least_upper_bound(X_68,identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))) = greatest_lower_bound(least_upper_bound(X_68,identity),least_upper_bound(identity,inverse(X_68))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_68,identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))),greatest_lower_bound(least_upper_bound(X_68,identity),least_upper_bound(identity,inverse(multiply(X_68,identity))))) )],[refute_0_1624,refute_0_1625]) ).
cnf(refute_0_1627,plain,
greatest_lower_bound(least_upper_bound(X_68,identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))) = greatest_lower_bound(least_upper_bound(X_68,identity),least_upper_bound(identity,inverse(X_68))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(multiply(X_68,identity))),least_upper_bound(identity,inverse(X_68))) )],[refute_0_1299,refute_0_1626]) ).
cnf(refute_0_1628,plain,
multiply(least_upper_bound(X_68,identity),identity) = least_upper_bound(X_68,identity),
inference(subst,[],[refute_0_88:[bind(X_33,$fot(least_upper_bound(X_68,identity)))]]) ).
cnf(refute_0_1629,plain,
greatest_lower_bound(multiply(least_upper_bound(X_68,identity),identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))) = greatest_lower_bound(multiply(least_upper_bound(X_68,identity),identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(multiply(least_upper_bound(X_68,identity),identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))))]]) ).
cnf(refute_0_1630,plain,
( multiply(least_upper_bound(X_68,identity),identity) != least_upper_bound(X_68,identity)
| greatest_lower_bound(multiply(least_upper_bound(X_68,identity),identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))) != greatest_lower_bound(multiply(least_upper_bound(X_68,identity),identity),least_upper_bound(identity,inverse(multiply(X_68,identity))))
| greatest_lower_bound(multiply(least_upper_bound(X_68,identity),identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))) = greatest_lower_bound(least_upper_bound(X_68,identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(X_68,identity),identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))),greatest_lower_bound(multiply(least_upper_bound(X_68,identity),identity),least_upper_bound(identity,inverse(multiply(X_68,identity))))) ),[1,0],$fot(least_upper_bound(X_68,identity))]]) ).
cnf(refute_0_1631,plain,
( multiply(least_upper_bound(X_68,identity),identity) != least_upper_bound(X_68,identity)
| greatest_lower_bound(multiply(least_upper_bound(X_68,identity),identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))) = greatest_lower_bound(least_upper_bound(X_68,identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(X_68,identity),identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))),greatest_lower_bound(multiply(least_upper_bound(X_68,identity),identity),least_upper_bound(identity,inverse(multiply(X_68,identity))))) )],[refute_0_1629,refute_0_1630]) ).
cnf(refute_0_1632,plain,
greatest_lower_bound(multiply(least_upper_bound(X_68,identity),identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))) = greatest_lower_bound(least_upper_bound(X_68,identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_68,identity),identity),least_upper_bound(X_68,identity)) )],[refute_0_1628,refute_0_1631]) ).
cnf(refute_0_1633,plain,
( greatest_lower_bound(multiply(least_upper_bound(X_68,identity),identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))) != greatest_lower_bound(least_upper_bound(X_68,identity),least_upper_bound(identity,inverse(multiply(X_68,identity))))
| greatest_lower_bound(least_upper_bound(X_68,identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))) != greatest_lower_bound(least_upper_bound(X_68,identity),least_upper_bound(identity,inverse(X_68)))
| greatest_lower_bound(multiply(least_upper_bound(X_68,identity),identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))) = greatest_lower_bound(least_upper_bound(X_68,identity),least_upper_bound(identity,inverse(X_68))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(greatest_lower_bound(multiply(least_upper_bound(X_68,identity),identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(X_68,identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))))),bind(Z0,$fot(greatest_lower_bound(least_upper_bound(X_68,identity),least_upper_bound(identity,inverse(X_68)))))]]) ).
cnf(refute_0_1634,plain,
( greatest_lower_bound(least_upper_bound(X_68,identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))) != greatest_lower_bound(least_upper_bound(X_68,identity),least_upper_bound(identity,inverse(X_68)))
| greatest_lower_bound(multiply(least_upper_bound(X_68,identity),identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))) = greatest_lower_bound(least_upper_bound(X_68,identity),least_upper_bound(identity,inverse(X_68))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(X_68,identity),identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))),greatest_lower_bound(least_upper_bound(X_68,identity),least_upper_bound(identity,inverse(multiply(X_68,identity))))) )],[refute_0_1632,refute_0_1633]) ).
cnf(refute_0_1635,plain,
greatest_lower_bound(multiply(least_upper_bound(X_68,identity),identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))) = greatest_lower_bound(least_upper_bound(X_68,identity),least_upper_bound(identity,inverse(X_68))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_68,identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))),greatest_lower_bound(least_upper_bound(X_68,identity),least_upper_bound(identity,inverse(X_68)))) )],[refute_0_1627,refute_0_1634]) ).
cnf(refute_0_1636,plain,
( greatest_lower_bound(multiply(least_upper_bound(X_68,identity),identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))) != greatest_lower_bound(least_upper_bound(X_68,identity),least_upper_bound(identity,inverse(X_68)))
| greatest_lower_bound(least_upper_bound(X_68,identity),least_upper_bound(identity,inverse(X_68))) != multiply(least_upper_bound(X_68,identity),greatest_lower_bound(identity,inverse(X_68)))
| greatest_lower_bound(multiply(least_upper_bound(X_68,identity),identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))) = multiply(least_upper_bound(X_68,identity),greatest_lower_bound(identity,inverse(X_68))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(greatest_lower_bound(multiply(least_upper_bound(X_68,identity),identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(X_68,identity),least_upper_bound(identity,inverse(X_68))))),bind(Z0,$fot(multiply(least_upper_bound(X_68,identity),greatest_lower_bound(identity,inverse(X_68)))))]]) ).
cnf(refute_0_1637,plain,
( greatest_lower_bound(least_upper_bound(X_68,identity),least_upper_bound(identity,inverse(X_68))) != multiply(least_upper_bound(X_68,identity),greatest_lower_bound(identity,inverse(X_68)))
| greatest_lower_bound(multiply(least_upper_bound(X_68,identity),identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))) = multiply(least_upper_bound(X_68,identity),greatest_lower_bound(identity,inverse(X_68))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(X_68,identity),identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))),greatest_lower_bound(least_upper_bound(X_68,identity),least_upper_bound(identity,inverse(X_68)))) )],[refute_0_1635,refute_0_1636]) ).
cnf(refute_0_1638,plain,
greatest_lower_bound(multiply(least_upper_bound(X_68,identity),identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))) = multiply(least_upper_bound(X_68,identity),greatest_lower_bound(identity,inverse(X_68))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_68,identity),least_upper_bound(identity,inverse(X_68))),multiply(least_upper_bound(X_68,identity),greatest_lower_bound(identity,inverse(X_68)))) )],[refute_0_1623,refute_0_1637]) ).
cnf(refute_0_1639,plain,
( multiply(greatest_lower_bound(X_68,identity),least_upper_bound(identity,inverse(X_68))) != greatest_lower_bound(multiply(least_upper_bound(X_68,identity),identity),least_upper_bound(identity,inverse(multiply(X_68,identity))))
| greatest_lower_bound(multiply(least_upper_bound(X_68,identity),identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))) != multiply(least_upper_bound(X_68,identity),greatest_lower_bound(identity,inverse(X_68)))
| multiply(greatest_lower_bound(X_68,identity),least_upper_bound(identity,inverse(X_68))) = multiply(least_upper_bound(X_68,identity),greatest_lower_bound(identity,inverse(X_68))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_68,identity),least_upper_bound(identity,inverse(X_68))),multiply(least_upper_bound(X_68,identity),greatest_lower_bound(identity,inverse(X_68)))) ),[0],$fot(greatest_lower_bound(multiply(least_upper_bound(X_68,identity),identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))))]]) ).
cnf(refute_0_1640,plain,
( multiply(greatest_lower_bound(X_68,identity),least_upper_bound(identity,inverse(X_68))) != greatest_lower_bound(multiply(least_upper_bound(X_68,identity),identity),least_upper_bound(identity,inverse(multiply(X_68,identity))))
| multiply(greatest_lower_bound(X_68,identity),least_upper_bound(identity,inverse(X_68))) = multiply(least_upper_bound(X_68,identity),greatest_lower_bound(identity,inverse(X_68))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(X_68,identity),identity),least_upper_bound(identity,inverse(multiply(X_68,identity)))),multiply(least_upper_bound(X_68,identity),greatest_lower_bound(identity,inverse(X_68)))) )],[refute_0_1638,refute_0_1639]) ).
cnf(refute_0_1641,plain,
( multiply(least_upper_bound(identity,multiply(X_68,identity)),greatest_lower_bound(identity,inverse(multiply(X_68,identity)))) != greatest_lower_bound(multiply(least_upper_bound(X_68,identity),identity),least_upper_bound(identity,inverse(multiply(X_68,identity))))
| multiply(greatest_lower_bound(X_68,identity),least_upper_bound(identity,inverse(X_68))) = multiply(least_upper_bound(X_68,identity),greatest_lower_bound(identity,inverse(X_68))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_68,identity),least_upper_bound(identity,inverse(X_68))),greatest_lower_bound(multiply(least_upper_bound(X_68,identity),identity),least_upper_bound(identity,inverse(multiply(X_68,identity))))) )],[refute_0_1620,refute_0_1640]) ).
cnf(refute_0_1642,plain,
multiply(greatest_lower_bound(X_68,identity),least_upper_bound(identity,inverse(X_68))) = multiply(least_upper_bound(X_68,identity),greatest_lower_bound(identity,inverse(X_68))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(X_68,identity)),greatest_lower_bound(identity,inverse(multiply(X_68,identity)))),greatest_lower_bound(multiply(least_upper_bound(X_68,identity),identity),least_upper_bound(identity,inverse(multiply(X_68,identity))))) )],[refute_0_1290,refute_0_1641]) ).
cnf(refute_0_1643,plain,
( multiply(greatest_lower_bound(X_68,identity),least_upper_bound(identity,inverse(X_68))) != multiply(least_upper_bound(X_68,identity),greatest_lower_bound(identity,inverse(X_68)))
| multiply(least_upper_bound(X_68,identity),greatest_lower_bound(identity,inverse(X_68))) = multiply(greatest_lower_bound(X_68,identity),least_upper_bound(identity,inverse(X_68))) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(greatest_lower_bound(X_68,identity),least_upper_bound(identity,inverse(X_68))))),bind(Y0,$fot(multiply(least_upper_bound(X_68,identity),greatest_lower_bound(identity,inverse(X_68)))))]]) ).
cnf(refute_0_1644,plain,
multiply(least_upper_bound(X_68,identity),greatest_lower_bound(identity,inverse(X_68))) = multiply(greatest_lower_bound(X_68,identity),least_upper_bound(identity,inverse(X_68))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_68,identity),least_upper_bound(identity,inverse(X_68))),multiply(least_upper_bound(X_68,identity),greatest_lower_bound(identity,inverse(X_68)))) )],[refute_0_1642,refute_0_1643]) ).
cnf(refute_0_1645,plain,
multiply(least_upper_bound(X_76,identity),greatest_lower_bound(identity,inverse(X_76))) = multiply(greatest_lower_bound(X_76,identity),least_upper_bound(identity,inverse(X_76))),
inference(subst,[],[refute_0_1644:[bind(X_68,$fot(X_76))]]) ).
cnf(refute_0_1646,plain,
( multiply(least_upper_bound(X_76,identity),greatest_lower_bound(identity,inverse(X_76))) != multiply(greatest_lower_bound(X_76,identity),least_upper_bound(identity,inverse(X_76)))
| multiply(least_upper_bound(X_76,identity),greatest_lower_bound(identity,inverse(X_76))) != greatest_lower_bound(least_upper_bound(X_76,identity),least_upper_bound(identity,inverse(X_76)))
| multiply(greatest_lower_bound(X_76,identity),least_upper_bound(identity,inverse(X_76))) = greatest_lower_bound(least_upper_bound(X_76,identity),least_upper_bound(identity,inverse(X_76))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_76,identity),greatest_lower_bound(identity,inverse(X_76))),greatest_lower_bound(least_upper_bound(X_76,identity),least_upper_bound(identity,inverse(X_76)))) ),[0],$fot(multiply(greatest_lower_bound(X_76,identity),least_upper_bound(identity,inverse(X_76))))]]) ).
cnf(refute_0_1647,plain,
( multiply(least_upper_bound(X_76,identity),greatest_lower_bound(identity,inverse(X_76))) != greatest_lower_bound(least_upper_bound(X_76,identity),least_upper_bound(identity,inverse(X_76)))
| multiply(greatest_lower_bound(X_76,identity),least_upper_bound(identity,inverse(X_76))) = greatest_lower_bound(least_upper_bound(X_76,identity),least_upper_bound(identity,inverse(X_76))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_76,identity),greatest_lower_bound(identity,inverse(X_76))),multiply(greatest_lower_bound(X_76,identity),least_upper_bound(identity,inverse(X_76)))) )],[refute_0_1645,refute_0_1646]) ).
cnf(refute_0_1648,plain,
multiply(greatest_lower_bound(X_76,identity),least_upper_bound(identity,inverse(X_76))) = greatest_lower_bound(least_upper_bound(X_76,identity),least_upper_bound(identity,inverse(X_76))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_76,identity),greatest_lower_bound(identity,inverse(X_76))),greatest_lower_bound(least_upper_bound(X_76,identity),least_upper_bound(identity,inverse(X_76)))) )],[refute_0_1275,refute_0_1647]) ).
cnf(refute_0_1649,plain,
( multiply(greatest_lower_bound(X_76,identity),least_upper_bound(identity,inverse(X_76))) != greatest_lower_bound(least_upper_bound(X_76,identity),least_upper_bound(identity,inverse(X_76)))
| greatest_lower_bound(least_upper_bound(X_76,identity),least_upper_bound(identity,inverse(X_76))) = multiply(greatest_lower_bound(X_76,identity),least_upper_bound(identity,inverse(X_76))) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(greatest_lower_bound(X_76,identity),least_upper_bound(identity,inverse(X_76))))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(X_76,identity),least_upper_bound(identity,inverse(X_76)))))]]) ).
cnf(refute_0_1650,plain,
greatest_lower_bound(least_upper_bound(X_76,identity),least_upper_bound(identity,inverse(X_76))) = multiply(greatest_lower_bound(X_76,identity),least_upper_bound(identity,inverse(X_76))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_76,identity),least_upper_bound(identity,inverse(X_76))),greatest_lower_bound(least_upper_bound(X_76,identity),least_upper_bound(identity,inverse(X_76)))) )],[refute_0_1648,refute_0_1649]) ).
cnf(refute_0_1651,plain,
greatest_lower_bound(least_upper_bound(X_316,identity),least_upper_bound(identity,inverse(X_316))) = multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316))),
inference(subst,[],[refute_0_1650:[bind(X_76,$fot(X_316))]]) ).
cnf(refute_0_1652,plain,
greatest_lower_bound(X_128,greatest_lower_bound(X_129,greatest_lower_bound(Y,X_129))) = greatest_lower_bound(X_129,greatest_lower_bound(greatest_lower_bound(Y,X_129),X_128)),
inference(subst,[],[refute_0_1460:[bind(X,$fot(X_128)),bind(X_22,$fot(X_129)),bind(X_23,$fot(greatest_lower_bound(Y,X_129)))]]) ).
cnf(refute_0_1653,plain,
greatest_lower_bound(X_129,greatest_lower_bound(Y,X_129)) = greatest_lower_bound(X_129,Y),
inference(subst,[],[refute_0_347:[bind(X_13,$fot(X_129))]]) ).
cnf(refute_0_1654,plain,
( greatest_lower_bound(X_128,greatest_lower_bound(X_129,greatest_lower_bound(Y,X_129))) != greatest_lower_bound(X_129,greatest_lower_bound(greatest_lower_bound(Y,X_129),X_128))
| greatest_lower_bound(X_129,greatest_lower_bound(Y,X_129)) != greatest_lower_bound(X_129,Y)
| greatest_lower_bound(X_128,greatest_lower_bound(X_129,Y)) = greatest_lower_bound(X_129,greatest_lower_bound(greatest_lower_bound(Y,X_129),X_128)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_128,greatest_lower_bound(X_129,greatest_lower_bound(Y,X_129))),greatest_lower_bound(X_129,greatest_lower_bound(greatest_lower_bound(Y,X_129),X_128))) ),[0,1],$fot(greatest_lower_bound(X_129,Y))]]) ).
cnf(refute_0_1655,plain,
( greatest_lower_bound(X_128,greatest_lower_bound(X_129,greatest_lower_bound(Y,X_129))) != greatest_lower_bound(X_129,greatest_lower_bound(greatest_lower_bound(Y,X_129),X_128))
| greatest_lower_bound(X_128,greatest_lower_bound(X_129,Y)) = greatest_lower_bound(X_129,greatest_lower_bound(greatest_lower_bound(Y,X_129),X_128)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_129,greatest_lower_bound(Y,X_129)),greatest_lower_bound(X_129,Y)) )],[refute_0_1653,refute_0_1654]) ).
cnf(refute_0_1656,plain,
greatest_lower_bound(X_128,greatest_lower_bound(X_129,Y)) = greatest_lower_bound(X_129,greatest_lower_bound(greatest_lower_bound(Y,X_129),X_128)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_128,greatest_lower_bound(X_129,greatest_lower_bound(Y,X_129))),greatest_lower_bound(X_129,greatest_lower_bound(greatest_lower_bound(Y,X_129),X_128))) )],[refute_0_1652,refute_0_1655]) ).
cnf(refute_0_1657,plain,
greatest_lower_bound(X_129,greatest_lower_bound(Y,greatest_lower_bound(X_129,X_128))) = greatest_lower_bound(Y,greatest_lower_bound(X_129,X_128)),
inference(subst,[],[refute_0_1471:[bind(Y,$fot(X_128)),bind(X_22,$fot(Y)),bind(X_23,$fot(X_129))]]) ).
cnf(refute_0_1658,plain,
greatest_lower_bound(greatest_lower_bound(Y,X_129),X_128) = greatest_lower_bound(Y,greatest_lower_bound(X_129,X_128)),
inference(subst,[],[refute_0_343:[bind(X,$fot(Y)),bind(Y,$fot(X_129)),bind(Z,$fot(X_128))]]) ).
cnf(refute_0_1659,plain,
greatest_lower_bound(X_129,greatest_lower_bound(greatest_lower_bound(Y,X_129),X_128)) = greatest_lower_bound(X_129,greatest_lower_bound(greatest_lower_bound(Y,X_129),X_128)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X_129,greatest_lower_bound(greatest_lower_bound(Y,X_129),X_128)))]]) ).
cnf(refute_0_1660,plain,
( greatest_lower_bound(X_129,greatest_lower_bound(greatest_lower_bound(Y,X_129),X_128)) != greatest_lower_bound(X_129,greatest_lower_bound(greatest_lower_bound(Y,X_129),X_128))
| greatest_lower_bound(greatest_lower_bound(Y,X_129),X_128) != greatest_lower_bound(Y,greatest_lower_bound(X_129,X_128))
| greatest_lower_bound(X_129,greatest_lower_bound(greatest_lower_bound(Y,X_129),X_128)) = greatest_lower_bound(X_129,greatest_lower_bound(Y,greatest_lower_bound(X_129,X_128))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_129,greatest_lower_bound(greatest_lower_bound(Y,X_129),X_128)),greatest_lower_bound(X_129,greatest_lower_bound(greatest_lower_bound(Y,X_129),X_128))) ),[1,1],$fot(greatest_lower_bound(Y,greatest_lower_bound(X_129,X_128)))]]) ).
cnf(refute_0_1661,plain,
( greatest_lower_bound(greatest_lower_bound(Y,X_129),X_128) != greatest_lower_bound(Y,greatest_lower_bound(X_129,X_128))
| greatest_lower_bound(X_129,greatest_lower_bound(greatest_lower_bound(Y,X_129),X_128)) = greatest_lower_bound(X_129,greatest_lower_bound(Y,greatest_lower_bound(X_129,X_128))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_129,greatest_lower_bound(greatest_lower_bound(Y,X_129),X_128)),greatest_lower_bound(X_129,greatest_lower_bound(greatest_lower_bound(Y,X_129),X_128))) )],[refute_0_1659,refute_0_1660]) ).
cnf(refute_0_1662,plain,
greatest_lower_bound(X_129,greatest_lower_bound(greatest_lower_bound(Y,X_129),X_128)) = greatest_lower_bound(X_129,greatest_lower_bound(Y,greatest_lower_bound(X_129,X_128))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(Y,X_129),X_128),greatest_lower_bound(Y,greatest_lower_bound(X_129,X_128))) )],[refute_0_1658,refute_0_1661]) ).
cnf(refute_0_1663,plain,
( greatest_lower_bound(X_129,greatest_lower_bound(Y,greatest_lower_bound(X_129,X_128))) != greatest_lower_bound(Y,greatest_lower_bound(X_129,X_128))
| greatest_lower_bound(X_129,greatest_lower_bound(greatest_lower_bound(Y,X_129),X_128)) != greatest_lower_bound(X_129,greatest_lower_bound(Y,greatest_lower_bound(X_129,X_128)))
| greatest_lower_bound(X_129,greatest_lower_bound(greatest_lower_bound(Y,X_129),X_128)) = greatest_lower_bound(Y,greatest_lower_bound(X_129,X_128)) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(greatest_lower_bound(X_129,greatest_lower_bound(greatest_lower_bound(Y,X_129),X_128)))),bind(Y0,$fot(greatest_lower_bound(X_129,greatest_lower_bound(Y,greatest_lower_bound(X_129,X_128))))),bind(Z0,$fot(greatest_lower_bound(Y,greatest_lower_bound(X_129,X_128))))]]) ).
cnf(refute_0_1664,plain,
( greatest_lower_bound(X_129,greatest_lower_bound(Y,greatest_lower_bound(X_129,X_128))) != greatest_lower_bound(Y,greatest_lower_bound(X_129,X_128))
| greatest_lower_bound(X_129,greatest_lower_bound(greatest_lower_bound(Y,X_129),X_128)) = greatest_lower_bound(Y,greatest_lower_bound(X_129,X_128)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_129,greatest_lower_bound(greatest_lower_bound(Y,X_129),X_128)),greatest_lower_bound(X_129,greatest_lower_bound(Y,greatest_lower_bound(X_129,X_128)))) )],[refute_0_1662,refute_0_1663]) ).
cnf(refute_0_1665,plain,
greatest_lower_bound(X_129,greatest_lower_bound(greatest_lower_bound(Y,X_129),X_128)) = greatest_lower_bound(Y,greatest_lower_bound(X_129,X_128)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_129,greatest_lower_bound(Y,greatest_lower_bound(X_129,X_128))),greatest_lower_bound(Y,greatest_lower_bound(X_129,X_128))) )],[refute_0_1657,refute_0_1664]) ).
cnf(refute_0_1666,plain,
( greatest_lower_bound(X_128,greatest_lower_bound(X_129,Y)) != greatest_lower_bound(X_129,greatest_lower_bound(greatest_lower_bound(Y,X_129),X_128))
| greatest_lower_bound(X_129,greatest_lower_bound(greatest_lower_bound(Y,X_129),X_128)) != greatest_lower_bound(Y,greatest_lower_bound(X_129,X_128))
| greatest_lower_bound(X_128,greatest_lower_bound(X_129,Y)) = greatest_lower_bound(Y,greatest_lower_bound(X_129,X_128)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_128,greatest_lower_bound(X_129,Y)),greatest_lower_bound(Y,greatest_lower_bound(X_129,X_128))) ),[0],$fot(greatest_lower_bound(X_129,greatest_lower_bound(greatest_lower_bound(Y,X_129),X_128)))]]) ).
cnf(refute_0_1667,plain,
( greatest_lower_bound(X_128,greatest_lower_bound(X_129,Y)) != greatest_lower_bound(X_129,greatest_lower_bound(greatest_lower_bound(Y,X_129),X_128))
| greatest_lower_bound(X_128,greatest_lower_bound(X_129,Y)) = greatest_lower_bound(Y,greatest_lower_bound(X_129,X_128)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_129,greatest_lower_bound(greatest_lower_bound(Y,X_129),X_128)),greatest_lower_bound(Y,greatest_lower_bound(X_129,X_128))) )],[refute_0_1665,refute_0_1666]) ).
cnf(refute_0_1668,plain,
greatest_lower_bound(X_128,greatest_lower_bound(X_129,Y)) = greatest_lower_bound(Y,greatest_lower_bound(X_129,X_128)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_128,greatest_lower_bound(X_129,Y)),greatest_lower_bound(X_129,greatest_lower_bound(greatest_lower_bound(Y,X_129),X_128))) )],[refute_0_1656,refute_0_1667]) ).
cnf(refute_0_1669,plain,
greatest_lower_bound(X_314,greatest_lower_bound(least_upper_bound(X_18,X_7),least_upper_bound(X_7,X_18))) = greatest_lower_bound(least_upper_bound(X_7,X_18),greatest_lower_bound(least_upper_bound(X_18,X_7),X_314)),
inference(subst,[],[refute_0_1668:[bind(Y,$fot(least_upper_bound(X_7,X_18))),bind(X_128,$fot(X_314)),bind(X_129,$fot(least_upper_bound(X_18,X_7)))]]) ).
cnf(refute_0_1670,plain,
( greatest_lower_bound(X_314,greatest_lower_bound(least_upper_bound(X_18,X_7),least_upper_bound(X_7,X_18))) != greatest_lower_bound(least_upper_bound(X_7,X_18),greatest_lower_bound(least_upper_bound(X_18,X_7),X_314))
| greatest_lower_bound(least_upper_bound(X_18,X_7),least_upper_bound(X_7,X_18)) != least_upper_bound(X_18,X_7)
| greatest_lower_bound(X_314,least_upper_bound(X_18,X_7)) = greatest_lower_bound(least_upper_bound(X_7,X_18),greatest_lower_bound(least_upper_bound(X_18,X_7),X_314)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_314,greatest_lower_bound(least_upper_bound(X_18,X_7),least_upper_bound(X_7,X_18))),greatest_lower_bound(least_upper_bound(X_7,X_18),greatest_lower_bound(least_upper_bound(X_18,X_7),X_314))) ),[0,1],$fot(least_upper_bound(X_18,X_7))]]) ).
cnf(refute_0_1671,plain,
( greatest_lower_bound(X_314,greatest_lower_bound(least_upper_bound(X_18,X_7),least_upper_bound(X_7,X_18))) != greatest_lower_bound(least_upper_bound(X_7,X_18),greatest_lower_bound(least_upper_bound(X_18,X_7),X_314))
| greatest_lower_bound(X_314,least_upper_bound(X_18,X_7)) = greatest_lower_bound(least_upper_bound(X_7,X_18),greatest_lower_bound(least_upper_bound(X_18,X_7),X_314)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_18,X_7),least_upper_bound(X_7,X_18)),least_upper_bound(X_18,X_7)) )],[refute_0_544,refute_0_1670]) ).
cnf(refute_0_1672,plain,
greatest_lower_bound(X_314,least_upper_bound(X_18,X_7)) = greatest_lower_bound(least_upper_bound(X_7,X_18),greatest_lower_bound(least_upper_bound(X_18,X_7),X_314)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_314,greatest_lower_bound(least_upper_bound(X_18,X_7),least_upper_bound(X_7,X_18))),greatest_lower_bound(least_upper_bound(X_7,X_18),greatest_lower_bound(least_upper_bound(X_18,X_7),X_314))) )],[refute_0_1669,refute_0_1671]) ).
cnf(refute_0_1673,plain,
greatest_lower_bound(least_upper_bound(X_18,X_7),greatest_lower_bound(least_upper_bound(X_7,X_18),X_24)) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_18,X_7),least_upper_bound(X_7,X_18)),X_24),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(least_upper_bound(X_18,X_7))),bind(Y,$fot(least_upper_bound(X_7,X_18))),bind(Z,$fot(X_24))]]) ).
cnf(refute_0_1674,plain,
( greatest_lower_bound(least_upper_bound(X_18,X_7),greatest_lower_bound(least_upper_bound(X_7,X_18),X_24)) != greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_18,X_7),least_upper_bound(X_7,X_18)),X_24)
| greatest_lower_bound(least_upper_bound(X_18,X_7),least_upper_bound(X_7,X_18)) != least_upper_bound(X_18,X_7)
| greatest_lower_bound(least_upper_bound(X_18,X_7),greatest_lower_bound(least_upper_bound(X_7,X_18),X_24)) = greatest_lower_bound(least_upper_bound(X_18,X_7),X_24) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_18,X_7),greatest_lower_bound(least_upper_bound(X_7,X_18),X_24)),greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_18,X_7),least_upper_bound(X_7,X_18)),X_24)) ),[1,0],$fot(least_upper_bound(X_18,X_7))]]) ).
cnf(refute_0_1675,plain,
( greatest_lower_bound(least_upper_bound(X_18,X_7),greatest_lower_bound(least_upper_bound(X_7,X_18),X_24)) != greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_18,X_7),least_upper_bound(X_7,X_18)),X_24)
| greatest_lower_bound(least_upper_bound(X_18,X_7),greatest_lower_bound(least_upper_bound(X_7,X_18),X_24)) = greatest_lower_bound(least_upper_bound(X_18,X_7),X_24) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_18,X_7),least_upper_bound(X_7,X_18)),least_upper_bound(X_18,X_7)) )],[refute_0_544,refute_0_1674]) ).
cnf(refute_0_1676,plain,
greatest_lower_bound(least_upper_bound(X_18,X_7),greatest_lower_bound(least_upper_bound(X_7,X_18),X_24)) = greatest_lower_bound(least_upper_bound(X_18,X_7),X_24),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_18,X_7),greatest_lower_bound(least_upper_bound(X_7,X_18),X_24)),greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_18,X_7),least_upper_bound(X_7,X_18)),X_24)) )],[refute_0_1673,refute_0_1675]) ).
cnf(refute_0_1677,plain,
greatest_lower_bound(least_upper_bound(X_7,X_18),greatest_lower_bound(least_upper_bound(X_18,X_7),X_314)) = greatest_lower_bound(least_upper_bound(X_7,X_18),X_314),
inference(subst,[],[refute_0_1676:[bind(X_18,$fot(X_7)),bind(X_24,$fot(X_314)),bind(X_7,$fot(X_18))]]) ).
cnf(refute_0_1678,plain,
( greatest_lower_bound(X_314,least_upper_bound(X_18,X_7)) != greatest_lower_bound(least_upper_bound(X_7,X_18),greatest_lower_bound(least_upper_bound(X_18,X_7),X_314))
| greatest_lower_bound(least_upper_bound(X_7,X_18),greatest_lower_bound(least_upper_bound(X_18,X_7),X_314)) != greatest_lower_bound(least_upper_bound(X_7,X_18),X_314)
| greatest_lower_bound(X_314,least_upper_bound(X_18,X_7)) = greatest_lower_bound(least_upper_bound(X_7,X_18),X_314) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_314,least_upper_bound(X_18,X_7)),greatest_lower_bound(least_upper_bound(X_7,X_18),X_314)) ),[0],$fot(greatest_lower_bound(least_upper_bound(X_7,X_18),greatest_lower_bound(least_upper_bound(X_18,X_7),X_314)))]]) ).
cnf(refute_0_1679,plain,
( greatest_lower_bound(X_314,least_upper_bound(X_18,X_7)) != greatest_lower_bound(least_upper_bound(X_7,X_18),greatest_lower_bound(least_upper_bound(X_18,X_7),X_314))
| greatest_lower_bound(X_314,least_upper_bound(X_18,X_7)) = greatest_lower_bound(least_upper_bound(X_7,X_18),X_314) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_7,X_18),greatest_lower_bound(least_upper_bound(X_18,X_7),X_314)),greatest_lower_bound(least_upper_bound(X_7,X_18),X_314)) )],[refute_0_1677,refute_0_1678]) ).
cnf(refute_0_1680,plain,
greatest_lower_bound(X_314,least_upper_bound(X_18,X_7)) = greatest_lower_bound(least_upper_bound(X_7,X_18),X_314),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_314,least_upper_bound(X_18,X_7)),greatest_lower_bound(least_upper_bound(X_7,X_18),greatest_lower_bound(least_upper_bound(X_18,X_7),X_314))) )],[refute_0_1672,refute_0_1679]) ).
cnf(refute_0_1681,plain,
greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),least_upper_bound(identity,X_316)) = greatest_lower_bound(least_upper_bound(X_316,identity),least_upper_bound(identity,inverse(X_316))),
inference(subst,[],[refute_0_1680:[bind(X_18,$fot(identity)),bind(X_314,$fot(least_upper_bound(identity,inverse(X_316)))),bind(X_7,$fot(X_316))]]) ).
cnf(refute_0_1682,plain,
( greatest_lower_bound(least_upper_bound(X_316,identity),least_upper_bound(identity,inverse(X_316))) != multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316)))
| greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),least_upper_bound(identity,X_316)) != greatest_lower_bound(least_upper_bound(X_316,identity),least_upper_bound(identity,inverse(X_316)))
| greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),least_upper_bound(identity,X_316)) = multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),least_upper_bound(identity,X_316)))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(X_316,identity),least_upper_bound(identity,inverse(X_316))))),bind(Z0,$fot(multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316)))))]]) ).
cnf(refute_0_1683,plain,
( greatest_lower_bound(least_upper_bound(X_316,identity),least_upper_bound(identity,inverse(X_316))) != multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316)))
| greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),least_upper_bound(identity,X_316)) = multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),least_upper_bound(identity,X_316)),greatest_lower_bound(least_upper_bound(X_316,identity),least_upper_bound(identity,inverse(X_316)))) )],[refute_0_1681,refute_0_1682]) ).
cnf(refute_0_1684,plain,
greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),least_upper_bound(identity,X_316)) = multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_316,identity),least_upper_bound(identity,inverse(X_316))),multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316)))) )],[refute_0_1651,refute_0_1683]) ).
cnf(refute_0_1685,plain,
inverse(inverse(least_upper_bound(identity,X_316))) = least_upper_bound(identity,X_316),
inference(subst,[],[refute_0_452:[bind(X_35,$fot(least_upper_bound(identity,X_316)))]]) ).
cnf(refute_0_1686,plain,
greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316)))) = greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316)))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316)))))]]) ).
cnf(refute_0_1687,plain,
( greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316)))) != greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316))))
| inverse(inverse(least_upper_bound(identity,X_316))) != least_upper_bound(identity,X_316)
| greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316)))) = greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),least_upper_bound(identity,X_316)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316)))),greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316))))) ),[1,1],$fot(least_upper_bound(identity,X_316))]]) ).
cnf(refute_0_1688,plain,
( inverse(inverse(least_upper_bound(identity,X_316))) != least_upper_bound(identity,X_316)
| greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316)))) = greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),least_upper_bound(identity,X_316)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316)))),greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316))))) )],[refute_0_1686,refute_0_1687]) ).
cnf(refute_0_1689,plain,
greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316)))) = greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),least_upper_bound(identity,X_316)),
inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(identity,X_316))),least_upper_bound(identity,X_316)) )],[refute_0_1685,refute_0_1688]) ).
cnf(refute_0_1690,plain,
( greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316)))) != greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),least_upper_bound(identity,X_316))
| greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),least_upper_bound(identity,X_316)) != multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316)))
| greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316)))) = multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316)))))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),least_upper_bound(identity,X_316)))),bind(Z0,$fot(multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316)))))]]) ).
cnf(refute_0_1691,plain,
( greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),least_upper_bound(identity,X_316)) != multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316)))
| greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316)))) = multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316)))),greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),least_upper_bound(identity,X_316))) )],[refute_0_1689,refute_0_1690]) ).
cnf(refute_0_1692,plain,
greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316)))) = multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),least_upper_bound(identity,X_316)),multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316)))) )],[refute_0_1684,refute_0_1691]) ).
cnf(refute_0_1693,plain,
inverse(greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316))))) = inverse(greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316))))),
introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316))))))]]) ).
cnf(refute_0_1694,plain,
( greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316)))) != multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316)))
| inverse(greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316))))) != inverse(greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316)))))
| inverse(greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316))))) = inverse(multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316))))),inverse(greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316)))))) ),[1,0],$fot(multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316))))]]) ).
cnf(refute_0_1695,plain,
( greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316)))) != multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316)))
| inverse(greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316))))) = inverse(multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316)))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316))))),inverse(greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316)))))) )],[refute_0_1693,refute_0_1694]) ).
cnf(refute_0_1696,plain,
inverse(greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316))))) = inverse(multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316)))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316)))),multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316)))) )],[refute_0_1692,refute_0_1695]) ).
cnf(refute_0_1697,plain,
multiply(inverse(greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316))))),greatest_lower_bound(identity,inverse(X_316))) = multiply(inverse(greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316))))),greatest_lower_bound(identity,inverse(X_316))),
introduced(tautology,[refl,[$fot(multiply(inverse(greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316))))),greatest_lower_bound(identity,inverse(X_316))))]]) ).
cnf(refute_0_1698,plain,
( multiply(inverse(greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316))))),greatest_lower_bound(identity,inverse(X_316))) != multiply(inverse(greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316))))),greatest_lower_bound(identity,inverse(X_316)))
| inverse(greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316))))) != inverse(multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316))))
| multiply(inverse(greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316))))),greatest_lower_bound(identity,inverse(X_316))) = multiply(inverse(multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316)))),greatest_lower_bound(identity,inverse(X_316))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316))))),greatest_lower_bound(identity,inverse(X_316))),multiply(inverse(greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316))))),greatest_lower_bound(identity,inverse(X_316)))) ),[1,0],$fot(inverse(multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316)))))]]) ).
cnf(refute_0_1699,plain,
( inverse(greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316))))) != inverse(multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316))))
| multiply(inverse(greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316))))),greatest_lower_bound(identity,inverse(X_316))) = multiply(inverse(multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316)))),greatest_lower_bound(identity,inverse(X_316))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316))))),greatest_lower_bound(identity,inverse(X_316))),multiply(inverse(greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316))))),greatest_lower_bound(identity,inverse(X_316)))) )],[refute_0_1697,refute_0_1698]) ).
cnf(refute_0_1700,plain,
multiply(inverse(greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316))))),greatest_lower_bound(identity,inverse(X_316))) = multiply(inverse(multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316)))),greatest_lower_bound(identity,inverse(X_316))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316))))),inverse(multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316))))) )],[refute_0_1696,refute_0_1699]) ).
cnf(refute_0_1701,plain,
( multiply(inverse(greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316))))),greatest_lower_bound(identity,inverse(X_316))) != multiply(inverse(multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316)))),greatest_lower_bound(identity,inverse(X_316)))
| inverse(least_upper_bound(identity,X_316)) != multiply(inverse(greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316))))),greatest_lower_bound(identity,inverse(X_316)))
| inverse(least_upper_bound(identity,X_316)) = multiply(inverse(multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316)))),greatest_lower_bound(identity,inverse(X_316))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,X_316)),multiply(inverse(greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316))))),greatest_lower_bound(identity,inverse(X_316)))) ),[1],$fot(multiply(inverse(multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316)))),greatest_lower_bound(identity,inverse(X_316))))]]) ).
cnf(refute_0_1702,plain,
( inverse(least_upper_bound(identity,X_316)) != multiply(inverse(greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316))))),greatest_lower_bound(identity,inverse(X_316)))
| inverse(least_upper_bound(identity,X_316)) = multiply(inverse(multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316)))),greatest_lower_bound(identity,inverse(X_316))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316))))),greatest_lower_bound(identity,inverse(X_316))),multiply(inverse(multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316)))),greatest_lower_bound(identity,inverse(X_316)))) )],[refute_0_1700,refute_0_1701]) ).
cnf(refute_0_1703,plain,
inverse(least_upper_bound(identity,X_316)) = multiply(inverse(multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316)))),greatest_lower_bound(identity,inverse(X_316))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,X_316)),multiply(inverse(greatest_lower_bound(least_upper_bound(identity,inverse(X_316)),inverse(inverse(least_upper_bound(identity,X_316))))),greatest_lower_bound(identity,inverse(X_316)))) )],[refute_0_1262,refute_0_1702]) ).
cnf(refute_0_1704,plain,
multiply(identity,greatest_lower_bound(identity,inverse(X_316))) = greatest_lower_bound(identity,inverse(X_316)),
inference(subst,[],[left_identity:[bind(X,$fot(greatest_lower_bound(identity,inverse(X_316))))]]) ).
cnf(refute_0_1705,plain,
inverse(greatest_lower_bound(inverse(X_145),X_106)) = multiply(inverse(multiply(X_145,greatest_lower_bound(inverse(X_145),X_106))),X_145),
inference(subst,[],[refute_0_96:[bind(X_45,$fot(X_145)),bind(X_46,$fot(greatest_lower_bound(inverse(X_145),X_106)))]]) ).
cnf(refute_0_1706,plain,
multiply(X_104,greatest_lower_bound(inverse(X_104),X_106)) = greatest_lower_bound(multiply(X_104,inverse(X_104)),multiply(X_104,X_106)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(X_104)),bind(Y,$fot(inverse(X_104))),bind(Z,$fot(X_106))]]) ).
cnf(refute_0_1707,plain,
multiply(X_104,inverse(X_104)) = identity,
inference(subst,[],[refute_0_71:[bind(X_35,$fot(X_104))]]) ).
cnf(refute_0_1708,plain,
( multiply(X_104,greatest_lower_bound(inverse(X_104),X_106)) != greatest_lower_bound(multiply(X_104,inverse(X_104)),multiply(X_104,X_106))
| multiply(X_104,inverse(X_104)) != identity
| multiply(X_104,greatest_lower_bound(inverse(X_104),X_106)) = greatest_lower_bound(identity,multiply(X_104,X_106)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_104,greatest_lower_bound(inverse(X_104),X_106)),greatest_lower_bound(multiply(X_104,inverse(X_104)),multiply(X_104,X_106))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_1709,plain,
( multiply(X_104,greatest_lower_bound(inverse(X_104),X_106)) != greatest_lower_bound(multiply(X_104,inverse(X_104)),multiply(X_104,X_106))
| multiply(X_104,greatest_lower_bound(inverse(X_104),X_106)) = greatest_lower_bound(identity,multiply(X_104,X_106)) ),
inference(resolve,[$cnf( $equal(multiply(X_104,inverse(X_104)),identity) )],[refute_0_1707,refute_0_1708]) ).
cnf(refute_0_1710,plain,
multiply(X_104,greatest_lower_bound(inverse(X_104),X_106)) = greatest_lower_bound(identity,multiply(X_104,X_106)),
inference(resolve,[$cnf( $equal(multiply(X_104,greatest_lower_bound(inverse(X_104),X_106)),greatest_lower_bound(multiply(X_104,inverse(X_104)),multiply(X_104,X_106))) )],[refute_0_1706,refute_0_1709]) ).
cnf(refute_0_1711,plain,
multiply(X_145,greatest_lower_bound(inverse(X_145),X_106)) = greatest_lower_bound(identity,multiply(X_145,X_106)),
inference(subst,[],[refute_0_1710:[bind(X_104,$fot(X_145))]]) ).
cnf(refute_0_1712,plain,
( multiply(X_145,greatest_lower_bound(inverse(X_145),X_106)) != greatest_lower_bound(identity,multiply(X_145,X_106))
| inverse(greatest_lower_bound(inverse(X_145),X_106)) != multiply(inverse(multiply(X_145,greatest_lower_bound(inverse(X_145),X_106))),X_145)
| inverse(greatest_lower_bound(inverse(X_145),X_106)) = multiply(inverse(greatest_lower_bound(identity,multiply(X_145,X_106))),X_145) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(inverse(X_145),X_106)),multiply(inverse(multiply(X_145,greatest_lower_bound(inverse(X_145),X_106))),X_145)) ),[1,0,0],$fot(greatest_lower_bound(identity,multiply(X_145,X_106)))]]) ).
cnf(refute_0_1713,plain,
( inverse(greatest_lower_bound(inverse(X_145),X_106)) != multiply(inverse(multiply(X_145,greatest_lower_bound(inverse(X_145),X_106))),X_145)
| inverse(greatest_lower_bound(inverse(X_145),X_106)) = multiply(inverse(greatest_lower_bound(identity,multiply(X_145,X_106))),X_145) ),
inference(resolve,[$cnf( $equal(multiply(X_145,greatest_lower_bound(inverse(X_145),X_106)),greatest_lower_bound(identity,multiply(X_145,X_106))) )],[refute_0_1711,refute_0_1712]) ).
cnf(refute_0_1714,plain,
inverse(greatest_lower_bound(inverse(X_145),X_106)) = multiply(inverse(greatest_lower_bound(identity,multiply(X_145,X_106))),X_145),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(X_145),X_106)),multiply(inverse(multiply(X_145,greatest_lower_bound(inverse(X_145),X_106))),X_145)) )],[refute_0_1705,refute_0_1713]) ).
cnf(refute_0_1715,plain,
inverse(greatest_lower_bound(inverse(inverse(least_upper_bound(identity,inverse(X_75)))),least_upper_bound(identity,X_75))) = multiply(inverse(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_75))),least_upper_bound(identity,X_75)))),inverse(least_upper_bound(identity,inverse(X_75)))),
inference(subst,[],[refute_0_1714:[bind(X_106,$fot(least_upper_bound(identity,X_75))),bind(X_145,$fot(inverse(least_upper_bound(identity,inverse(X_75)))))]]) ).
cnf(refute_0_1716,plain,
inverse(inverse(X_75)) = multiply(inverse(multiply(least_upper_bound(identity,X_75),inverse(X_75))),least_upper_bound(identity,X_75)),
inference(subst,[],[refute_0_96:[bind(X_45,$fot(least_upper_bound(identity,X_75))),bind(X_46,$fot(inverse(X_75)))]]) ).
cnf(refute_0_1717,plain,
( multiply(least_upper_bound(identity,X_75),inverse(X_75)) != least_upper_bound(identity,inverse(X_75))
| inverse(inverse(X_75)) != multiply(inverse(multiply(least_upper_bound(identity,X_75),inverse(X_75))),least_upper_bound(identity,X_75))
| inverse(inverse(X_75)) = multiply(inverse(least_upper_bound(identity,inverse(X_75))),least_upper_bound(identity,X_75)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_75)),multiply(inverse(multiply(least_upper_bound(identity,X_75),inverse(X_75))),least_upper_bound(identity,X_75))) ),[1,0,0],$fot(least_upper_bound(identity,inverse(X_75)))]]) ).
cnf(refute_0_1718,plain,
( inverse(inverse(X_75)) != multiply(inverse(multiply(least_upper_bound(identity,X_75),inverse(X_75))),least_upper_bound(identity,X_75))
| inverse(inverse(X_75)) = multiply(inverse(least_upper_bound(identity,inverse(X_75))),least_upper_bound(identity,X_75)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_75),inverse(X_75)),least_upper_bound(identity,inverse(X_75))) )],[refute_0_785,refute_0_1717]) ).
cnf(refute_0_1719,plain,
inverse(inverse(X_75)) = multiply(inverse(least_upper_bound(identity,inverse(X_75))),least_upper_bound(identity,X_75)),
inference(resolve,[$cnf( $equal(inverse(inverse(X_75)),multiply(inverse(multiply(least_upper_bound(identity,X_75),inverse(X_75))),least_upper_bound(identity,X_75))) )],[refute_0_1716,refute_0_1718]) ).
cnf(refute_0_1720,plain,
inverse(inverse(X_75)) = X_75,
inference(subst,[],[refute_0_452:[bind(X_35,$fot(X_75))]]) ).
cnf(refute_0_1721,plain,
( inverse(inverse(X_75)) != X_75
| inverse(inverse(X_75)) != multiply(inverse(least_upper_bound(identity,inverse(X_75))),least_upper_bound(identity,X_75))
| X_75 = multiply(inverse(least_upper_bound(identity,inverse(X_75))),least_upper_bound(identity,X_75)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_75)),multiply(inverse(least_upper_bound(identity,inverse(X_75))),least_upper_bound(identity,X_75))) ),[0],$fot(X_75)]]) ).
cnf(refute_0_1722,plain,
( inverse(inverse(X_75)) != multiply(inverse(least_upper_bound(identity,inverse(X_75))),least_upper_bound(identity,X_75))
| X_75 = multiply(inverse(least_upper_bound(identity,inverse(X_75))),least_upper_bound(identity,X_75)) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_75)),X_75) )],[refute_0_1720,refute_0_1721]) ).
cnf(refute_0_1723,plain,
X_75 = multiply(inverse(least_upper_bound(identity,inverse(X_75))),least_upper_bound(identity,X_75)),
inference(resolve,[$cnf( $equal(inverse(inverse(X_75)),multiply(inverse(least_upper_bound(identity,inverse(X_75))),least_upper_bound(identity,X_75))) )],[refute_0_1719,refute_0_1722]) ).
cnf(refute_0_1724,plain,
( X_75 != multiply(inverse(least_upper_bound(identity,inverse(X_75))),least_upper_bound(identity,X_75))
| multiply(inverse(least_upper_bound(identity,inverse(X_75))),least_upper_bound(identity,X_75)) = X_75 ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(X_75)),bind(Y0,$fot(multiply(inverse(least_upper_bound(identity,inverse(X_75))),least_upper_bound(identity,X_75))))]]) ).
cnf(refute_0_1725,plain,
multiply(inverse(least_upper_bound(identity,inverse(X_75))),least_upper_bound(identity,X_75)) = X_75,
inference(resolve,[$cnf( $equal(X_75,multiply(inverse(least_upper_bound(identity,inverse(X_75))),least_upper_bound(identity,X_75))) )],[refute_0_1723,refute_0_1724]) ).
cnf(refute_0_1726,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_75))),least_upper_bound(identity,X_75)) != X_75
| inverse(greatest_lower_bound(inverse(inverse(least_upper_bound(identity,inverse(X_75)))),least_upper_bound(identity,X_75))) != multiply(inverse(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_75))),least_upper_bound(identity,X_75)))),inverse(least_upper_bound(identity,inverse(X_75))))
| inverse(greatest_lower_bound(inverse(inverse(least_upper_bound(identity,inverse(X_75)))),least_upper_bound(identity,X_75))) = multiply(inverse(greatest_lower_bound(identity,X_75)),inverse(least_upper_bound(identity,inverse(X_75)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(inverse(inverse(least_upper_bound(identity,inverse(X_75)))),least_upper_bound(identity,X_75))),multiply(inverse(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_75))),least_upper_bound(identity,X_75)))),inverse(least_upper_bound(identity,inverse(X_75))))) ),[1,0,0,1],$fot(X_75)]]) ).
cnf(refute_0_1727,plain,
( inverse(greatest_lower_bound(inverse(inverse(least_upper_bound(identity,inverse(X_75)))),least_upper_bound(identity,X_75))) != multiply(inverse(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_75))),least_upper_bound(identity,X_75)))),inverse(least_upper_bound(identity,inverse(X_75))))
| inverse(greatest_lower_bound(inverse(inverse(least_upper_bound(identity,inverse(X_75)))),least_upper_bound(identity,X_75))) = multiply(inverse(greatest_lower_bound(identity,X_75)),inverse(least_upper_bound(identity,inverse(X_75)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_75))),least_upper_bound(identity,X_75)),X_75) )],[refute_0_1725,refute_0_1726]) ).
cnf(refute_0_1728,plain,
inverse(greatest_lower_bound(inverse(inverse(least_upper_bound(identity,inverse(X_75)))),least_upper_bound(identity,X_75))) = multiply(inverse(greatest_lower_bound(identity,X_75)),inverse(least_upper_bound(identity,inverse(X_75)))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(inverse(least_upper_bound(identity,inverse(X_75)))),least_upper_bound(identity,X_75))),multiply(inverse(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_75))),least_upper_bound(identity,X_75)))),inverse(least_upper_bound(identity,inverse(X_75))))) )],[refute_0_1715,refute_0_1727]) ).
cnf(refute_0_1729,plain,
greatest_lower_bound(least_upper_bound(X_75,identity),least_upper_bound(identity,inverse(X_75))) = multiply(least_upper_bound(X_75,identity),greatest_lower_bound(identity,inverse(X_75))),
inference(subst,[],[refute_0_1622:[bind(X_76,$fot(X_75))]]) ).
cnf(refute_0_1730,plain,
inverse(inverse(least_upper_bound(identity,inverse(X_75)))) = least_upper_bound(identity,inverse(X_75)),
inference(subst,[],[refute_0_452:[bind(X_35,$fot(least_upper_bound(identity,inverse(X_75))))]]) ).
cnf(refute_0_1731,plain,
greatest_lower_bound(least_upper_bound(X_75,identity),inverse(inverse(least_upper_bound(identity,inverse(X_75))))) = greatest_lower_bound(least_upper_bound(X_75,identity),inverse(inverse(least_upper_bound(identity,inverse(X_75))))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(least_upper_bound(X_75,identity),inverse(inverse(least_upper_bound(identity,inverse(X_75))))))]]) ).
cnf(refute_0_1732,plain,
( greatest_lower_bound(least_upper_bound(X_75,identity),inverse(inverse(least_upper_bound(identity,inverse(X_75))))) != greatest_lower_bound(least_upper_bound(X_75,identity),inverse(inverse(least_upper_bound(identity,inverse(X_75)))))
| inverse(inverse(least_upper_bound(identity,inverse(X_75)))) != least_upper_bound(identity,inverse(X_75))
| greatest_lower_bound(least_upper_bound(X_75,identity),inverse(inverse(least_upper_bound(identity,inverse(X_75))))) = greatest_lower_bound(least_upper_bound(X_75,identity),least_upper_bound(identity,inverse(X_75))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_75,identity),inverse(inverse(least_upper_bound(identity,inverse(X_75))))),greatest_lower_bound(least_upper_bound(X_75,identity),inverse(inverse(least_upper_bound(identity,inverse(X_75)))))) ),[1,1],$fot(least_upper_bound(identity,inverse(X_75)))]]) ).
cnf(refute_0_1733,plain,
( inverse(inverse(least_upper_bound(identity,inverse(X_75)))) != least_upper_bound(identity,inverse(X_75))
| greatest_lower_bound(least_upper_bound(X_75,identity),inverse(inverse(least_upper_bound(identity,inverse(X_75))))) = greatest_lower_bound(least_upper_bound(X_75,identity),least_upper_bound(identity,inverse(X_75))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_75,identity),inverse(inverse(least_upper_bound(identity,inverse(X_75))))),greatest_lower_bound(least_upper_bound(X_75,identity),inverse(inverse(least_upper_bound(identity,inverse(X_75)))))) )],[refute_0_1731,refute_0_1732]) ).
cnf(refute_0_1734,plain,
greatest_lower_bound(least_upper_bound(X_75,identity),inverse(inverse(least_upper_bound(identity,inverse(X_75))))) = greatest_lower_bound(least_upper_bound(X_75,identity),least_upper_bound(identity,inverse(X_75))),
inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(identity,inverse(X_75)))),least_upper_bound(identity,inverse(X_75))) )],[refute_0_1730,refute_0_1733]) ).
cnf(refute_0_1735,plain,
( greatest_lower_bound(least_upper_bound(X_75,identity),inverse(inverse(least_upper_bound(identity,inverse(X_75))))) != greatest_lower_bound(least_upper_bound(X_75,identity),least_upper_bound(identity,inverse(X_75)))
| greatest_lower_bound(least_upper_bound(X_75,identity),least_upper_bound(identity,inverse(X_75))) != multiply(least_upper_bound(X_75,identity),greatest_lower_bound(identity,inverse(X_75)))
| greatest_lower_bound(least_upper_bound(X_75,identity),inverse(inverse(least_upper_bound(identity,inverse(X_75))))) = multiply(least_upper_bound(X_75,identity),greatest_lower_bound(identity,inverse(X_75))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(X_75,identity),inverse(inverse(least_upper_bound(identity,inverse(X_75))))))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(X_75,identity),least_upper_bound(identity,inverse(X_75))))),bind(Z0,$fot(multiply(least_upper_bound(X_75,identity),greatest_lower_bound(identity,inverse(X_75)))))]]) ).
cnf(refute_0_1736,plain,
( greatest_lower_bound(least_upper_bound(X_75,identity),least_upper_bound(identity,inverse(X_75))) != multiply(least_upper_bound(X_75,identity),greatest_lower_bound(identity,inverse(X_75)))
| greatest_lower_bound(least_upper_bound(X_75,identity),inverse(inverse(least_upper_bound(identity,inverse(X_75))))) = multiply(least_upper_bound(X_75,identity),greatest_lower_bound(identity,inverse(X_75))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_75,identity),inverse(inverse(least_upper_bound(identity,inverse(X_75))))),greatest_lower_bound(least_upper_bound(X_75,identity),least_upper_bound(identity,inverse(X_75)))) )],[refute_0_1734,refute_0_1735]) ).
cnf(refute_0_1737,plain,
greatest_lower_bound(least_upper_bound(X_75,identity),inverse(inverse(least_upper_bound(identity,inverse(X_75))))) = multiply(least_upper_bound(X_75,identity),greatest_lower_bound(identity,inverse(X_75))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_75,identity),least_upper_bound(identity,inverse(X_75))),multiply(least_upper_bound(X_75,identity),greatest_lower_bound(identity,inverse(X_75)))) )],[refute_0_1729,refute_0_1736]) ).
cnf(refute_0_1738,plain,
inverse(greatest_lower_bound(least_upper_bound(X_75,identity),inverse(inverse(least_upper_bound(identity,inverse(X_75)))))) = inverse(greatest_lower_bound(least_upper_bound(X_75,identity),inverse(inverse(least_upper_bound(identity,inverse(X_75)))))),
introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(least_upper_bound(X_75,identity),inverse(inverse(least_upper_bound(identity,inverse(X_75)))))))]]) ).
cnf(refute_0_1739,plain,
( greatest_lower_bound(least_upper_bound(X_75,identity),inverse(inverse(least_upper_bound(identity,inverse(X_75))))) != multiply(least_upper_bound(X_75,identity),greatest_lower_bound(identity,inverse(X_75)))
| inverse(greatest_lower_bound(least_upper_bound(X_75,identity),inverse(inverse(least_upper_bound(identity,inverse(X_75)))))) != inverse(greatest_lower_bound(least_upper_bound(X_75,identity),inverse(inverse(least_upper_bound(identity,inverse(X_75))))))
| inverse(greatest_lower_bound(least_upper_bound(X_75,identity),inverse(inverse(least_upper_bound(identity,inverse(X_75)))))) = inverse(multiply(least_upper_bound(X_75,identity),greatest_lower_bound(identity,inverse(X_75)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(least_upper_bound(X_75,identity),inverse(inverse(least_upper_bound(identity,inverse(X_75)))))),inverse(greatest_lower_bound(least_upper_bound(X_75,identity),inverse(inverse(least_upper_bound(identity,inverse(X_75))))))) ),[1,0],$fot(multiply(least_upper_bound(X_75,identity),greatest_lower_bound(identity,inverse(X_75))))]]) ).
cnf(refute_0_1740,plain,
( greatest_lower_bound(least_upper_bound(X_75,identity),inverse(inverse(least_upper_bound(identity,inverse(X_75))))) != multiply(least_upper_bound(X_75,identity),greatest_lower_bound(identity,inverse(X_75)))
| inverse(greatest_lower_bound(least_upper_bound(X_75,identity),inverse(inverse(least_upper_bound(identity,inverse(X_75)))))) = inverse(multiply(least_upper_bound(X_75,identity),greatest_lower_bound(identity,inverse(X_75)))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(least_upper_bound(X_75,identity),inverse(inverse(least_upper_bound(identity,inverse(X_75)))))),inverse(greatest_lower_bound(least_upper_bound(X_75,identity),inverse(inverse(least_upper_bound(identity,inverse(X_75))))))) )],[refute_0_1738,refute_0_1739]) ).
cnf(refute_0_1741,plain,
inverse(greatest_lower_bound(least_upper_bound(X_75,identity),inverse(inverse(least_upper_bound(identity,inverse(X_75)))))) = inverse(multiply(least_upper_bound(X_75,identity),greatest_lower_bound(identity,inverse(X_75)))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_75,identity),inverse(inverse(least_upper_bound(identity,inverse(X_75))))),multiply(least_upper_bound(X_75,identity),greatest_lower_bound(identity,inverse(X_75)))) )],[refute_0_1737,refute_0_1740]) ).
cnf(refute_0_1742,plain,
inverse(greatest_lower_bound(least_upper_bound(identity,X_163),X_250)) = inverse(greatest_lower_bound(X_250,least_upper_bound(identity,X_163))),
inference(subst,[],[refute_0_1239:[bind(X_247,$fot(least_upper_bound(identity,X_163))),bind(X_248,$fot(X_250))]]) ).
cnf(refute_0_1743,plain,
greatest_lower_bound(least_upper_bound(X_163,identity),X_162) = multiply(inverse(inverse(X_163)),multiply(inverse(X_163),greatest_lower_bound(least_upper_bound(X_163,identity),X_162))),
inference(subst,[],[refute_0_9:[bind(X_30,$fot(inverse(X_163))),bind(X_31,$fot(greatest_lower_bound(least_upper_bound(X_163,identity),X_162)))]]) ).
cnf(refute_0_1744,plain,
multiply(inverse(X_57),greatest_lower_bound(least_upper_bound(X_57,identity),X_106)) = greatest_lower_bound(multiply(inverse(X_57),least_upper_bound(X_57,identity)),multiply(inverse(X_57),X_106)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(inverse(X_57))),bind(Y,$fot(least_upper_bound(X_57,identity))),bind(Z,$fot(X_106))]]) ).
cnf(refute_0_1745,plain,
( multiply(inverse(X_57),greatest_lower_bound(least_upper_bound(X_57,identity),X_106)) != greatest_lower_bound(multiply(inverse(X_57),least_upper_bound(X_57,identity)),multiply(inverse(X_57),X_106))
| multiply(inverse(X_57),least_upper_bound(X_57,identity)) != least_upper_bound(identity,inverse(X_57))
| multiply(inverse(X_57),greatest_lower_bound(least_upper_bound(X_57,identity),X_106)) = greatest_lower_bound(least_upper_bound(identity,inverse(X_57)),multiply(inverse(X_57),X_106)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_57),greatest_lower_bound(least_upper_bound(X_57,identity),X_106)),greatest_lower_bound(multiply(inverse(X_57),least_upper_bound(X_57,identity)),multiply(inverse(X_57),X_106))) ),[1,0],$fot(least_upper_bound(identity,inverse(X_57)))]]) ).
cnf(refute_0_1746,plain,
( multiply(inverse(X_57),greatest_lower_bound(least_upper_bound(X_57,identity),X_106)) != greatest_lower_bound(multiply(inverse(X_57),least_upper_bound(X_57,identity)),multiply(inverse(X_57),X_106))
| multiply(inverse(X_57),greatest_lower_bound(least_upper_bound(X_57,identity),X_106)) = greatest_lower_bound(least_upper_bound(identity,inverse(X_57)),multiply(inverse(X_57),X_106)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_57),least_upper_bound(X_57,identity)),least_upper_bound(identity,inverse(X_57))) )],[refute_0_267,refute_0_1745]) ).
cnf(refute_0_1747,plain,
multiply(inverse(X_57),greatest_lower_bound(least_upper_bound(X_57,identity),X_106)) = greatest_lower_bound(least_upper_bound(identity,inverse(X_57)),multiply(inverse(X_57),X_106)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_57),greatest_lower_bound(least_upper_bound(X_57,identity),X_106)),greatest_lower_bound(multiply(inverse(X_57),least_upper_bound(X_57,identity)),multiply(inverse(X_57),X_106))) )],[refute_0_1744,refute_0_1746]) ).
cnf(refute_0_1748,plain,
greatest_lower_bound(least_upper_bound(identity,inverse(X_57)),multiply(inverse(X_57),X_106)) = multiply(inverse(X_57),greatest_lower_bound(least_upper_bound(identity,X_57),X_106)),
inference(subst,[],[refute_0_1088:[bind(X_56,$fot(X_57))]]) ).
cnf(refute_0_1749,plain,
( multiply(inverse(X_57),greatest_lower_bound(least_upper_bound(X_57,identity),X_106)) != greatest_lower_bound(least_upper_bound(identity,inverse(X_57)),multiply(inverse(X_57),X_106))
| greatest_lower_bound(least_upper_bound(identity,inverse(X_57)),multiply(inverse(X_57),X_106)) != multiply(inverse(X_57),greatest_lower_bound(least_upper_bound(identity,X_57),X_106))
| multiply(inverse(X_57),greatest_lower_bound(least_upper_bound(X_57,identity),X_106)) = multiply(inverse(X_57),greatest_lower_bound(least_upper_bound(identity,X_57),X_106)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_57),greatest_lower_bound(least_upper_bound(X_57,identity),X_106)),multiply(inverse(X_57),greatest_lower_bound(least_upper_bound(identity,X_57),X_106))) ),[0],$fot(greatest_lower_bound(least_upper_bound(identity,inverse(X_57)),multiply(inverse(X_57),X_106)))]]) ).
cnf(refute_0_1750,plain,
( multiply(inverse(X_57),greatest_lower_bound(least_upper_bound(X_57,identity),X_106)) != greatest_lower_bound(least_upper_bound(identity,inverse(X_57)),multiply(inverse(X_57),X_106))
| multiply(inverse(X_57),greatest_lower_bound(least_upper_bound(X_57,identity),X_106)) = multiply(inverse(X_57),greatest_lower_bound(least_upper_bound(identity,X_57),X_106)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,inverse(X_57)),multiply(inverse(X_57),X_106)),multiply(inverse(X_57),greatest_lower_bound(least_upper_bound(identity,X_57),X_106))) )],[refute_0_1748,refute_0_1749]) ).
cnf(refute_0_1751,plain,
multiply(inverse(X_57),greatest_lower_bound(least_upper_bound(X_57,identity),X_106)) = multiply(inverse(X_57),greatest_lower_bound(least_upper_bound(identity,X_57),X_106)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_57),greatest_lower_bound(least_upper_bound(X_57,identity),X_106)),greatest_lower_bound(least_upper_bound(identity,inverse(X_57)),multiply(inverse(X_57),X_106))) )],[refute_0_1747,refute_0_1750]) ).
cnf(refute_0_1752,plain,
multiply(inverse(X_163),greatest_lower_bound(least_upper_bound(X_163,identity),X_162)) = multiply(inverse(X_163),greatest_lower_bound(least_upper_bound(identity,X_163),X_162)),
inference(subst,[],[refute_0_1751:[bind(X_106,$fot(X_162)),bind(X_57,$fot(X_163))]]) ).
cnf(refute_0_1753,plain,
( multiply(inverse(X_163),greatest_lower_bound(least_upper_bound(X_163,identity),X_162)) != multiply(inverse(X_163),greatest_lower_bound(least_upper_bound(identity,X_163),X_162))
| greatest_lower_bound(least_upper_bound(X_163,identity),X_162) != multiply(inverse(inverse(X_163)),multiply(inverse(X_163),greatest_lower_bound(least_upper_bound(X_163,identity),X_162)))
| greatest_lower_bound(least_upper_bound(X_163,identity),X_162) = multiply(inverse(inverse(X_163)),multiply(inverse(X_163),greatest_lower_bound(least_upper_bound(identity,X_163),X_162))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_163,identity),X_162),multiply(inverse(inverse(X_163)),multiply(inverse(X_163),greatest_lower_bound(least_upper_bound(X_163,identity),X_162)))) ),[1,1],$fot(multiply(inverse(X_163),greatest_lower_bound(least_upper_bound(identity,X_163),X_162)))]]) ).
cnf(refute_0_1754,plain,
( greatest_lower_bound(least_upper_bound(X_163,identity),X_162) != multiply(inverse(inverse(X_163)),multiply(inverse(X_163),greatest_lower_bound(least_upper_bound(X_163,identity),X_162)))
| greatest_lower_bound(least_upper_bound(X_163,identity),X_162) = multiply(inverse(inverse(X_163)),multiply(inverse(X_163),greatest_lower_bound(least_upper_bound(identity,X_163),X_162))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_163),greatest_lower_bound(least_upper_bound(X_163,identity),X_162)),multiply(inverse(X_163),greatest_lower_bound(least_upper_bound(identity,X_163),X_162))) )],[refute_0_1752,refute_0_1753]) ).
cnf(refute_0_1755,plain,
greatest_lower_bound(least_upper_bound(X_163,identity),X_162) = multiply(inverse(inverse(X_163)),multiply(inverse(X_163),greatest_lower_bound(least_upper_bound(identity,X_163),X_162))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_163,identity),X_162),multiply(inverse(inverse(X_163)),multiply(inverse(X_163),greatest_lower_bound(least_upper_bound(X_163,identity),X_162)))) )],[refute_0_1743,refute_0_1754]) ).
cnf(refute_0_1756,plain,
multiply(identity,greatest_lower_bound(least_upper_bound(identity,X_163),X_162)) = greatest_lower_bound(least_upper_bound(identity,X_163),X_162),
inference(subst,[],[left_identity:[bind(X,$fot(greatest_lower_bound(least_upper_bound(identity,X_163),X_162)))]]) ).
cnf(refute_0_1757,plain,
multiply(inverse(identity),identity) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(identity))]]) ).
cnf(refute_0_1758,plain,
inverse(identity) = multiply(inverse(identity),identity),
inference(subst,[],[refute_0_86:[bind(X_33,$fot(inverse(identity)))]]) ).
cnf(refute_0_1759,plain,
( inverse(identity) != multiply(inverse(identity),identity)
| multiply(inverse(identity),identity) = inverse(identity) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(inverse(identity))),bind(Y0,$fot(multiply(inverse(identity),identity)))]]) ).
cnf(refute_0_1760,plain,
multiply(inverse(identity),identity) = inverse(identity),
inference(resolve,[$cnf( $equal(inverse(identity),multiply(inverse(identity),identity)) )],[refute_0_1758,refute_0_1759]) ).
cnf(refute_0_1761,plain,
( multiply(inverse(identity),identity) != identity
| multiply(inverse(identity),identity) != inverse(identity)
| inverse(identity) = identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(identity),identity),identity) ),[0],$fot(inverse(identity))]]) ).
cnf(refute_0_1762,plain,
( multiply(inverse(identity),identity) != identity
| inverse(identity) = identity ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),identity),inverse(identity)) )],[refute_0_1760,refute_0_1761]) ).
cnf(refute_0_1763,plain,
inverse(identity) = identity,
inference(resolve,[$cnf( $equal(multiply(inverse(identity),identity),identity) )],[refute_0_1757,refute_0_1762]) ).
cnf(refute_0_1764,plain,
multiply(X_163,inverse(X_163)) = identity,
inference(subst,[],[refute_0_71:[bind(X_35,$fot(X_163))]]) ).
cnf(refute_0_1765,plain,
inverse(multiply(X_163,inverse(X_163))) = inverse(multiply(X_163,inverse(X_163))),
introduced(tautology,[refl,[$fot(inverse(multiply(X_163,inverse(X_163))))]]) ).
cnf(refute_0_1766,plain,
( multiply(X_163,inverse(X_163)) != identity
| inverse(multiply(X_163,inverse(X_163))) != inverse(multiply(X_163,inverse(X_163)))
| inverse(multiply(X_163,inverse(X_163))) = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_163,inverse(X_163))),inverse(multiply(X_163,inverse(X_163)))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_1767,plain,
( multiply(X_163,inverse(X_163)) != identity
| inverse(multiply(X_163,inverse(X_163))) = inverse(identity) ),
inference(resolve,[$cnf( $equal(inverse(multiply(X_163,inverse(X_163))),inverse(multiply(X_163,inverse(X_163)))) )],[refute_0_1765,refute_0_1766]) ).
cnf(refute_0_1768,plain,
inverse(multiply(X_163,inverse(X_163))) = inverse(identity),
inference(resolve,[$cnf( $equal(multiply(X_163,inverse(X_163)),identity) )],[refute_0_1764,refute_0_1767]) ).
cnf(refute_0_1769,plain,
( inverse(multiply(X_163,inverse(X_163))) != inverse(identity)
| inverse(identity) != identity
| inverse(multiply(X_163,inverse(X_163))) = identity ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(inverse(multiply(X_163,inverse(X_163))))),bind(Y0,$fot(inverse(identity))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_1770,plain,
( inverse(identity) != identity
| inverse(multiply(X_163,inverse(X_163))) = identity ),
inference(resolve,[$cnf( $equal(inverse(multiply(X_163,inverse(X_163))),inverse(identity)) )],[refute_0_1768,refute_0_1769]) ).
cnf(refute_0_1771,plain,
inverse(multiply(X_163,inverse(X_163))) = identity,
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_1763,refute_0_1770]) ).
cnf(refute_0_1772,plain,
multiply(inverse(multiply(X_163,inverse(X_163))),greatest_lower_bound(least_upper_bound(identity,X_163),X_162)) = multiply(inverse(multiply(X_163,inverse(X_163))),greatest_lower_bound(least_upper_bound(identity,X_163),X_162)),
introduced(tautology,[refl,[$fot(multiply(inverse(multiply(X_163,inverse(X_163))),greatest_lower_bound(least_upper_bound(identity,X_163),X_162)))]]) ).
cnf(refute_0_1773,plain,
( multiply(inverse(multiply(X_163,inverse(X_163))),greatest_lower_bound(least_upper_bound(identity,X_163),X_162)) != multiply(inverse(multiply(X_163,inverse(X_163))),greatest_lower_bound(least_upper_bound(identity,X_163),X_162))
| inverse(multiply(X_163,inverse(X_163))) != identity
| multiply(inverse(multiply(X_163,inverse(X_163))),greatest_lower_bound(least_upper_bound(identity,X_163),X_162)) = multiply(identity,greatest_lower_bound(least_upper_bound(identity,X_163),X_162)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(X_163,inverse(X_163))),greatest_lower_bound(least_upper_bound(identity,X_163),X_162)),multiply(inverse(multiply(X_163,inverse(X_163))),greatest_lower_bound(least_upper_bound(identity,X_163),X_162))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_1774,plain,
( inverse(multiply(X_163,inverse(X_163))) != identity
| multiply(inverse(multiply(X_163,inverse(X_163))),greatest_lower_bound(least_upper_bound(identity,X_163),X_162)) = multiply(identity,greatest_lower_bound(least_upper_bound(identity,X_163),X_162)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_163,inverse(X_163))),greatest_lower_bound(least_upper_bound(identity,X_163),X_162)),multiply(inverse(multiply(X_163,inverse(X_163))),greatest_lower_bound(least_upper_bound(identity,X_163),X_162))) )],[refute_0_1772,refute_0_1773]) ).
cnf(refute_0_1775,plain,
multiply(inverse(multiply(X_163,inverse(X_163))),greatest_lower_bound(least_upper_bound(identity,X_163),X_162)) = multiply(identity,greatest_lower_bound(least_upper_bound(identity,X_163),X_162)),
inference(resolve,[$cnf( $equal(inverse(multiply(X_163,inverse(X_163))),identity) )],[refute_0_1771,refute_0_1774]) ).
cnf(refute_0_1776,plain,
( multiply(identity,greatest_lower_bound(least_upper_bound(identity,X_163),X_162)) != greatest_lower_bound(least_upper_bound(identity,X_163),X_162)
| multiply(inverse(multiply(X_163,inverse(X_163))),greatest_lower_bound(least_upper_bound(identity,X_163),X_162)) != multiply(identity,greatest_lower_bound(least_upper_bound(identity,X_163),X_162))
| multiply(inverse(multiply(X_163,inverse(X_163))),greatest_lower_bound(least_upper_bound(identity,X_163),X_162)) = greatest_lower_bound(least_upper_bound(identity,X_163),X_162) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(inverse(multiply(X_163,inverse(X_163))),greatest_lower_bound(least_upper_bound(identity,X_163),X_162)))),bind(Y0,$fot(multiply(identity,greatest_lower_bound(least_upper_bound(identity,X_163),X_162)))),bind(Z0,$fot(greatest_lower_bound(least_upper_bound(identity,X_163),X_162)))]]) ).
cnf(refute_0_1777,plain,
( multiply(identity,greatest_lower_bound(least_upper_bound(identity,X_163),X_162)) != greatest_lower_bound(least_upper_bound(identity,X_163),X_162)
| multiply(inverse(multiply(X_163,inverse(X_163))),greatest_lower_bound(least_upper_bound(identity,X_163),X_162)) = greatest_lower_bound(least_upper_bound(identity,X_163),X_162) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_163,inverse(X_163))),greatest_lower_bound(least_upper_bound(identity,X_163),X_162)),multiply(identity,greatest_lower_bound(least_upper_bound(identity,X_163),X_162))) )],[refute_0_1775,refute_0_1776]) ).
cnf(refute_0_1778,plain,
multiply(inverse(multiply(X_163,inverse(X_163))),greatest_lower_bound(least_upper_bound(identity,X_163),X_162)) = greatest_lower_bound(least_upper_bound(identity,X_163),X_162),
inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(least_upper_bound(identity,X_163),X_162)),greatest_lower_bound(least_upper_bound(identity,X_163),X_162)) )],[refute_0_1756,refute_0_1777]) ).
cnf(refute_0_1779,plain,
multiply(inverse(inverse(X_163)),multiply(inverse(X_163),greatest_lower_bound(least_upper_bound(identity,X_163),X_162))) = multiply(inverse(multiply(X_163,inverse(X_163))),greatest_lower_bound(least_upper_bound(identity,X_163),X_162)),
inference(subst,[],[refute_0_824:[bind(X_148,$fot(X_163)),bind(X_149,$fot(greatest_lower_bound(least_upper_bound(identity,X_163),X_162))),bind(X_31,$fot(inverse(X_163)))]]) ).
cnf(refute_0_1780,plain,
( multiply(inverse(multiply(X_163,inverse(X_163))),greatest_lower_bound(least_upper_bound(identity,X_163),X_162)) != greatest_lower_bound(least_upper_bound(identity,X_163),X_162)
| multiply(inverse(inverse(X_163)),multiply(inverse(X_163),greatest_lower_bound(least_upper_bound(identity,X_163),X_162))) != multiply(inverse(multiply(X_163,inverse(X_163))),greatest_lower_bound(least_upper_bound(identity,X_163),X_162))
| multiply(inverse(inverse(X_163)),multiply(inverse(X_163),greatest_lower_bound(least_upper_bound(identity,X_163),X_162))) = greatest_lower_bound(least_upper_bound(identity,X_163),X_162) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(inverse(inverse(X_163)),multiply(inverse(X_163),greatest_lower_bound(least_upper_bound(identity,X_163),X_162))))),bind(Y0,$fot(multiply(inverse(multiply(X_163,inverse(X_163))),greatest_lower_bound(least_upper_bound(identity,X_163),X_162)))),bind(Z0,$fot(greatest_lower_bound(least_upper_bound(identity,X_163),X_162)))]]) ).
cnf(refute_0_1781,plain,
( multiply(inverse(multiply(X_163,inverse(X_163))),greatest_lower_bound(least_upper_bound(identity,X_163),X_162)) != greatest_lower_bound(least_upper_bound(identity,X_163),X_162)
| multiply(inverse(inverse(X_163)),multiply(inverse(X_163),greatest_lower_bound(least_upper_bound(identity,X_163),X_162))) = greatest_lower_bound(least_upper_bound(identity,X_163),X_162) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_163)),multiply(inverse(X_163),greatest_lower_bound(least_upper_bound(identity,X_163),X_162))),multiply(inverse(multiply(X_163,inverse(X_163))),greatest_lower_bound(least_upper_bound(identity,X_163),X_162))) )],[refute_0_1779,refute_0_1780]) ).
cnf(refute_0_1782,plain,
multiply(inverse(inverse(X_163)),multiply(inverse(X_163),greatest_lower_bound(least_upper_bound(identity,X_163),X_162))) = greatest_lower_bound(least_upper_bound(identity,X_163),X_162),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_163,inverse(X_163))),greatest_lower_bound(least_upper_bound(identity,X_163),X_162)),greatest_lower_bound(least_upper_bound(identity,X_163),X_162)) )],[refute_0_1778,refute_0_1781]) ).
cnf(refute_0_1783,plain,
( multiply(inverse(inverse(X_163)),multiply(inverse(X_163),greatest_lower_bound(least_upper_bound(identity,X_163),X_162))) != greatest_lower_bound(least_upper_bound(identity,X_163),X_162)
| greatest_lower_bound(least_upper_bound(X_163,identity),X_162) != multiply(inverse(inverse(X_163)),multiply(inverse(X_163),greatest_lower_bound(least_upper_bound(identity,X_163),X_162)))
| greatest_lower_bound(least_upper_bound(X_163,identity),X_162) = greatest_lower_bound(least_upper_bound(identity,X_163),X_162) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_163,identity),X_162),multiply(inverse(inverse(X_163)),multiply(inverse(X_163),greatest_lower_bound(least_upper_bound(identity,X_163),X_162)))) ),[1],$fot(greatest_lower_bound(least_upper_bound(identity,X_163),X_162))]]) ).
cnf(refute_0_1784,plain,
( greatest_lower_bound(least_upper_bound(X_163,identity),X_162) != multiply(inverse(inverse(X_163)),multiply(inverse(X_163),greatest_lower_bound(least_upper_bound(identity,X_163),X_162)))
| greatest_lower_bound(least_upper_bound(X_163,identity),X_162) = greatest_lower_bound(least_upper_bound(identity,X_163),X_162) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_163)),multiply(inverse(X_163),greatest_lower_bound(least_upper_bound(identity,X_163),X_162))),greatest_lower_bound(least_upper_bound(identity,X_163),X_162)) )],[refute_0_1782,refute_0_1783]) ).
cnf(refute_0_1785,plain,
greatest_lower_bound(least_upper_bound(X_163,identity),X_162) = greatest_lower_bound(least_upper_bound(identity,X_163),X_162),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_163,identity),X_162),multiply(inverse(inverse(X_163)),multiply(inverse(X_163),greatest_lower_bound(least_upper_bound(identity,X_163),X_162)))) )],[refute_0_1755,refute_0_1784]) ).
cnf(refute_0_1786,plain,
greatest_lower_bound(least_upper_bound(X_163,identity),X_250) = greatest_lower_bound(least_upper_bound(identity,X_163),X_250),
inference(subst,[],[refute_0_1785:[bind(X_162,$fot(X_250))]]) ).
cnf(refute_0_1787,plain,
( greatest_lower_bound(least_upper_bound(X_163,identity),X_250) != greatest_lower_bound(least_upper_bound(identity,X_163),X_250)
| greatest_lower_bound(least_upper_bound(identity,X_163),X_250) = greatest_lower_bound(least_upper_bound(X_163,identity),X_250) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(X_163,identity),X_250))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(identity,X_163),X_250)))]]) ).
cnf(refute_0_1788,plain,
greatest_lower_bound(least_upper_bound(identity,X_163),X_250) = greatest_lower_bound(least_upper_bound(X_163,identity),X_250),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_163,identity),X_250),greatest_lower_bound(least_upper_bound(identity,X_163),X_250)) )],[refute_0_1786,refute_0_1787]) ).
cnf(refute_0_1789,plain,
( greatest_lower_bound(least_upper_bound(identity,X_163),X_250) != greatest_lower_bound(least_upper_bound(X_163,identity),X_250)
| inverse(greatest_lower_bound(least_upper_bound(identity,X_163),X_250)) != inverse(greatest_lower_bound(X_250,least_upper_bound(identity,X_163)))
| inverse(greatest_lower_bound(least_upper_bound(X_163,identity),X_250)) = inverse(greatest_lower_bound(X_250,least_upper_bound(identity,X_163))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(least_upper_bound(identity,X_163),X_250)),inverse(greatest_lower_bound(X_250,least_upper_bound(identity,X_163)))) ),[0,0],$fot(greatest_lower_bound(least_upper_bound(X_163,identity),X_250))]]) ).
cnf(refute_0_1790,plain,
( inverse(greatest_lower_bound(least_upper_bound(identity,X_163),X_250)) != inverse(greatest_lower_bound(X_250,least_upper_bound(identity,X_163)))
| inverse(greatest_lower_bound(least_upper_bound(X_163,identity),X_250)) = inverse(greatest_lower_bound(X_250,least_upper_bound(identity,X_163))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,X_163),X_250),greatest_lower_bound(least_upper_bound(X_163,identity),X_250)) )],[refute_0_1788,refute_0_1789]) ).
cnf(refute_0_1791,plain,
inverse(greatest_lower_bound(least_upper_bound(X_163,identity),X_250)) = inverse(greatest_lower_bound(X_250,least_upper_bound(identity,X_163))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(least_upper_bound(identity,X_163),X_250)),inverse(greatest_lower_bound(X_250,least_upper_bound(identity,X_163)))) )],[refute_0_1742,refute_0_1790]) ).
cnf(refute_0_1792,plain,
( inverse(greatest_lower_bound(least_upper_bound(X_163,identity),X_250)) != inverse(greatest_lower_bound(X_250,least_upper_bound(identity,X_163)))
| inverse(greatest_lower_bound(X_250,least_upper_bound(identity,X_163))) = inverse(greatest_lower_bound(least_upper_bound(X_163,identity),X_250)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(inverse(greatest_lower_bound(least_upper_bound(X_163,identity),X_250)))),bind(Y0,$fot(inverse(greatest_lower_bound(X_250,least_upper_bound(identity,X_163)))))]]) ).
cnf(refute_0_1793,plain,
inverse(greatest_lower_bound(X_250,least_upper_bound(identity,X_163))) = inverse(greatest_lower_bound(least_upper_bound(X_163,identity),X_250)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(least_upper_bound(X_163,identity),X_250)),inverse(greatest_lower_bound(X_250,least_upper_bound(identity,X_163)))) )],[refute_0_1791,refute_0_1792]) ).
cnf(refute_0_1794,plain,
inverse(greatest_lower_bound(inverse(inverse(least_upper_bound(identity,inverse(X_75)))),least_upper_bound(identity,X_75))) = inverse(greatest_lower_bound(least_upper_bound(X_75,identity),inverse(inverse(least_upper_bound(identity,inverse(X_75)))))),
inference(subst,[],[refute_0_1793:[bind(X_163,$fot(X_75)),bind(X_250,$fot(inverse(inverse(least_upper_bound(identity,inverse(X_75))))))]]) ).
cnf(refute_0_1795,plain,
( inverse(greatest_lower_bound(inverse(inverse(least_upper_bound(identity,inverse(X_75)))),least_upper_bound(identity,X_75))) != inverse(greatest_lower_bound(least_upper_bound(X_75,identity),inverse(inverse(least_upper_bound(identity,inverse(X_75))))))
| inverse(greatest_lower_bound(least_upper_bound(X_75,identity),inverse(inverse(least_upper_bound(identity,inverse(X_75)))))) != inverse(multiply(least_upper_bound(X_75,identity),greatest_lower_bound(identity,inverse(X_75))))
| inverse(greatest_lower_bound(inverse(inverse(least_upper_bound(identity,inverse(X_75)))),least_upper_bound(identity,X_75))) = inverse(multiply(least_upper_bound(X_75,identity),greatest_lower_bound(identity,inverse(X_75)))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(inverse(greatest_lower_bound(inverse(inverse(least_upper_bound(identity,inverse(X_75)))),least_upper_bound(identity,X_75))))),bind(Y0,$fot(inverse(greatest_lower_bound(least_upper_bound(X_75,identity),inverse(inverse(least_upper_bound(identity,inverse(X_75)))))))),bind(Z0,$fot(inverse(multiply(least_upper_bound(X_75,identity),greatest_lower_bound(identity,inverse(X_75))))))]]) ).
cnf(refute_0_1796,plain,
( inverse(greatest_lower_bound(least_upper_bound(X_75,identity),inverse(inverse(least_upper_bound(identity,inverse(X_75)))))) != inverse(multiply(least_upper_bound(X_75,identity),greatest_lower_bound(identity,inverse(X_75))))
| inverse(greatest_lower_bound(inverse(inverse(least_upper_bound(identity,inverse(X_75)))),least_upper_bound(identity,X_75))) = inverse(multiply(least_upper_bound(X_75,identity),greatest_lower_bound(identity,inverse(X_75)))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(inverse(least_upper_bound(identity,inverse(X_75)))),least_upper_bound(identity,X_75))),inverse(greatest_lower_bound(least_upper_bound(X_75,identity),inverse(inverse(least_upper_bound(identity,inverse(X_75))))))) )],[refute_0_1794,refute_0_1795]) ).
cnf(refute_0_1797,plain,
inverse(greatest_lower_bound(inverse(inverse(least_upper_bound(identity,inverse(X_75)))),least_upper_bound(identity,X_75))) = inverse(multiply(least_upper_bound(X_75,identity),greatest_lower_bound(identity,inverse(X_75)))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(least_upper_bound(X_75,identity),inverse(inverse(least_upper_bound(identity,inverse(X_75)))))),inverse(multiply(least_upper_bound(X_75,identity),greatest_lower_bound(identity,inverse(X_75))))) )],[refute_0_1741,refute_0_1796]) ).
cnf(refute_0_1798,plain,
( inverse(greatest_lower_bound(inverse(inverse(least_upper_bound(identity,inverse(X_75)))),least_upper_bound(identity,X_75))) != multiply(inverse(greatest_lower_bound(identity,X_75)),inverse(least_upper_bound(identity,inverse(X_75))))
| inverse(greatest_lower_bound(inverse(inverse(least_upper_bound(identity,inverse(X_75)))),least_upper_bound(identity,X_75))) != inverse(multiply(least_upper_bound(X_75,identity),greatest_lower_bound(identity,inverse(X_75))))
| inverse(multiply(least_upper_bound(X_75,identity),greatest_lower_bound(identity,inverse(X_75)))) = multiply(inverse(greatest_lower_bound(identity,X_75)),inverse(least_upper_bound(identity,inverse(X_75)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(inverse(inverse(least_upper_bound(identity,inverse(X_75)))),least_upper_bound(identity,X_75))),multiply(inverse(greatest_lower_bound(identity,X_75)),inverse(least_upper_bound(identity,inverse(X_75))))) ),[0],$fot(inverse(multiply(least_upper_bound(X_75,identity),greatest_lower_bound(identity,inverse(X_75)))))]]) ).
cnf(refute_0_1799,plain,
( inverse(greatest_lower_bound(inverse(inverse(least_upper_bound(identity,inverse(X_75)))),least_upper_bound(identity,X_75))) != multiply(inverse(greatest_lower_bound(identity,X_75)),inverse(least_upper_bound(identity,inverse(X_75))))
| inverse(multiply(least_upper_bound(X_75,identity),greatest_lower_bound(identity,inverse(X_75)))) = multiply(inverse(greatest_lower_bound(identity,X_75)),inverse(least_upper_bound(identity,inverse(X_75)))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(inverse(least_upper_bound(identity,inverse(X_75)))),least_upper_bound(identity,X_75))),inverse(multiply(least_upper_bound(X_75,identity),greatest_lower_bound(identity,inverse(X_75))))) )],[refute_0_1797,refute_0_1798]) ).
cnf(refute_0_1800,plain,
multiply(least_upper_bound(identity,inverse(X_75)),greatest_lower_bound(identity,X_75)) = multiply(greatest_lower_bound(identity,X_75),least_upper_bound(identity,inverse(X_75))),
inference(subst,[],[refute_0_1421:[bind(X_114,$fot(X_75))]]) ).
cnf(refute_0_1801,plain,
inverse(multiply(least_upper_bound(identity,inverse(X_75)),greatest_lower_bound(identity,X_75))) = inverse(multiply(least_upper_bound(identity,inverse(X_75)),greatest_lower_bound(identity,X_75))),
introduced(tautology,[refl,[$fot(inverse(multiply(least_upper_bound(identity,inverse(X_75)),greatest_lower_bound(identity,X_75))))]]) ).
cnf(refute_0_1802,plain,
( multiply(least_upper_bound(identity,inverse(X_75)),greatest_lower_bound(identity,X_75)) != multiply(greatest_lower_bound(identity,X_75),least_upper_bound(identity,inverse(X_75)))
| inverse(multiply(least_upper_bound(identity,inverse(X_75)),greatest_lower_bound(identity,X_75))) != inverse(multiply(least_upper_bound(identity,inverse(X_75)),greatest_lower_bound(identity,X_75)))
| inverse(multiply(least_upper_bound(identity,inverse(X_75)),greatest_lower_bound(identity,X_75))) = inverse(multiply(greatest_lower_bound(identity,X_75),least_upper_bound(identity,inverse(X_75)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(least_upper_bound(identity,inverse(X_75)),greatest_lower_bound(identity,X_75))),inverse(multiply(least_upper_bound(identity,inverse(X_75)),greatest_lower_bound(identity,X_75)))) ),[1,0],$fot(multiply(greatest_lower_bound(identity,X_75),least_upper_bound(identity,inverse(X_75))))]]) ).
cnf(refute_0_1803,plain,
( multiply(least_upper_bound(identity,inverse(X_75)),greatest_lower_bound(identity,X_75)) != multiply(greatest_lower_bound(identity,X_75),least_upper_bound(identity,inverse(X_75)))
| inverse(multiply(least_upper_bound(identity,inverse(X_75)),greatest_lower_bound(identity,X_75))) = inverse(multiply(greatest_lower_bound(identity,X_75),least_upper_bound(identity,inverse(X_75)))) ),
inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(identity,inverse(X_75)),greatest_lower_bound(identity,X_75))),inverse(multiply(least_upper_bound(identity,inverse(X_75)),greatest_lower_bound(identity,X_75)))) )],[refute_0_1801,refute_0_1802]) ).
cnf(refute_0_1804,plain,
inverse(multiply(least_upper_bound(identity,inverse(X_75)),greatest_lower_bound(identity,X_75))) = inverse(multiply(greatest_lower_bound(identity,X_75),least_upper_bound(identity,inverse(X_75)))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_75)),greatest_lower_bound(identity,X_75)),multiply(greatest_lower_bound(identity,X_75),least_upper_bound(identity,inverse(X_75)))) )],[refute_0_1800,refute_0_1803]) ).
cnf(refute_0_1805,plain,
multiply(inverse(greatest_lower_bound(identity,X_75)),inverse(least_upper_bound(identity,inverse(X_75)))) = inverse(multiply(least_upper_bound(identity,inverse(X_75)),greatest_lower_bound(identity,X_75))),
inference(subst,[],[refute_0_490:[bind(X_30,$fot(least_upper_bound(identity,inverse(X_75)))),bind(X_31,$fot(greatest_lower_bound(identity,X_75)))]]) ).
cnf(refute_0_1806,plain,
( multiply(inverse(greatest_lower_bound(identity,X_75)),inverse(least_upper_bound(identity,inverse(X_75)))) != inverse(multiply(least_upper_bound(identity,inverse(X_75)),greatest_lower_bound(identity,X_75)))
| inverse(multiply(least_upper_bound(identity,inverse(X_75)),greatest_lower_bound(identity,X_75))) != inverse(multiply(greatest_lower_bound(identity,X_75),least_upper_bound(identity,inverse(X_75))))
| multiply(inverse(greatest_lower_bound(identity,X_75)),inverse(least_upper_bound(identity,inverse(X_75)))) = inverse(multiply(greatest_lower_bound(identity,X_75),least_upper_bound(identity,inverse(X_75)))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(identity,X_75)),inverse(least_upper_bound(identity,inverse(X_75)))))),bind(Y0,$fot(inverse(multiply(least_upper_bound(identity,inverse(X_75)),greatest_lower_bound(identity,X_75))))),bind(Z0,$fot(inverse(multiply(greatest_lower_bound(identity,X_75),least_upper_bound(identity,inverse(X_75))))))]]) ).
cnf(refute_0_1807,plain,
( inverse(multiply(least_upper_bound(identity,inverse(X_75)),greatest_lower_bound(identity,X_75))) != inverse(multiply(greatest_lower_bound(identity,X_75),least_upper_bound(identity,inverse(X_75))))
| multiply(inverse(greatest_lower_bound(identity,X_75)),inverse(least_upper_bound(identity,inverse(X_75)))) = inverse(multiply(greatest_lower_bound(identity,X_75),least_upper_bound(identity,inverse(X_75)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_75)),inverse(least_upper_bound(identity,inverse(X_75)))),inverse(multiply(least_upper_bound(identity,inverse(X_75)),greatest_lower_bound(identity,X_75)))) )],[refute_0_1805,refute_0_1806]) ).
cnf(refute_0_1808,plain,
multiply(inverse(greatest_lower_bound(identity,X_75)),inverse(least_upper_bound(identity,inverse(X_75)))) = inverse(multiply(greatest_lower_bound(identity,X_75),least_upper_bound(identity,inverse(X_75)))),
inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(identity,inverse(X_75)),greatest_lower_bound(identity,X_75))),inverse(multiply(greatest_lower_bound(identity,X_75),least_upper_bound(identity,inverse(X_75))))) )],[refute_0_1804,refute_0_1807]) ).
cnf(refute_0_1809,plain,
( multiply(inverse(greatest_lower_bound(identity,X_75)),inverse(least_upper_bound(identity,inverse(X_75)))) != inverse(multiply(greatest_lower_bound(identity,X_75),least_upper_bound(identity,inverse(X_75))))
| inverse(multiply(least_upper_bound(X_75,identity),greatest_lower_bound(identity,inverse(X_75)))) != multiply(inverse(greatest_lower_bound(identity,X_75)),inverse(least_upper_bound(identity,inverse(X_75))))
| inverse(multiply(least_upper_bound(X_75,identity),greatest_lower_bound(identity,inverse(X_75)))) = inverse(multiply(greatest_lower_bound(identity,X_75),least_upper_bound(identity,inverse(X_75)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(least_upper_bound(X_75,identity),greatest_lower_bound(identity,inverse(X_75)))),multiply(inverse(greatest_lower_bound(identity,X_75)),inverse(least_upper_bound(identity,inverse(X_75))))) ),[1],$fot(inverse(multiply(greatest_lower_bound(identity,X_75),least_upper_bound(identity,inverse(X_75)))))]]) ).
cnf(refute_0_1810,plain,
( inverse(multiply(least_upper_bound(X_75,identity),greatest_lower_bound(identity,inverse(X_75)))) != multiply(inverse(greatest_lower_bound(identity,X_75)),inverse(least_upper_bound(identity,inverse(X_75))))
| inverse(multiply(least_upper_bound(X_75,identity),greatest_lower_bound(identity,inverse(X_75)))) = inverse(multiply(greatest_lower_bound(identity,X_75),least_upper_bound(identity,inverse(X_75)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_75)),inverse(least_upper_bound(identity,inverse(X_75)))),inverse(multiply(greatest_lower_bound(identity,X_75),least_upper_bound(identity,inverse(X_75))))) )],[refute_0_1808,refute_0_1809]) ).
cnf(refute_0_1811,plain,
( inverse(greatest_lower_bound(inverse(inverse(least_upper_bound(identity,inverse(X_75)))),least_upper_bound(identity,X_75))) != multiply(inverse(greatest_lower_bound(identity,X_75)),inverse(least_upper_bound(identity,inverse(X_75))))
| inverse(multiply(least_upper_bound(X_75,identity),greatest_lower_bound(identity,inverse(X_75)))) = inverse(multiply(greatest_lower_bound(identity,X_75),least_upper_bound(identity,inverse(X_75)))) ),
inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(X_75,identity),greatest_lower_bound(identity,inverse(X_75)))),multiply(inverse(greatest_lower_bound(identity,X_75)),inverse(least_upper_bound(identity,inverse(X_75))))) )],[refute_0_1799,refute_0_1810]) ).
cnf(refute_0_1812,plain,
inverse(multiply(least_upper_bound(X_75,identity),greatest_lower_bound(identity,inverse(X_75)))) = inverse(multiply(greatest_lower_bound(identity,X_75),least_upper_bound(identity,inverse(X_75)))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(inverse(least_upper_bound(identity,inverse(X_75)))),least_upper_bound(identity,X_75))),multiply(inverse(greatest_lower_bound(identity,X_75)),inverse(least_upper_bound(identity,inverse(X_75))))) )],[refute_0_1728,refute_0_1811]) ).
cnf(refute_0_1813,plain,
multiply(least_upper_bound(X_75,identity),greatest_lower_bound(identity,inverse(X_75))) = multiply(greatest_lower_bound(X_75,identity),least_upper_bound(identity,inverse(X_75))),
inference(subst,[],[refute_0_1644:[bind(X_68,$fot(X_75))]]) ).
cnf(refute_0_1814,plain,
inverse(multiply(least_upper_bound(X_75,identity),greatest_lower_bound(identity,inverse(X_75)))) = inverse(multiply(least_upper_bound(X_75,identity),greatest_lower_bound(identity,inverse(X_75)))),
introduced(tautology,[refl,[$fot(inverse(multiply(least_upper_bound(X_75,identity),greatest_lower_bound(identity,inverse(X_75)))))]]) ).
cnf(refute_0_1815,plain,
( multiply(least_upper_bound(X_75,identity),greatest_lower_bound(identity,inverse(X_75))) != multiply(greatest_lower_bound(X_75,identity),least_upper_bound(identity,inverse(X_75)))
| inverse(multiply(least_upper_bound(X_75,identity),greatest_lower_bound(identity,inverse(X_75)))) != inverse(multiply(least_upper_bound(X_75,identity),greatest_lower_bound(identity,inverse(X_75))))
| inverse(multiply(least_upper_bound(X_75,identity),greatest_lower_bound(identity,inverse(X_75)))) = inverse(multiply(greatest_lower_bound(X_75,identity),least_upper_bound(identity,inverse(X_75)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(least_upper_bound(X_75,identity),greatest_lower_bound(identity,inverse(X_75)))),inverse(multiply(least_upper_bound(X_75,identity),greatest_lower_bound(identity,inverse(X_75))))) ),[1,0],$fot(multiply(greatest_lower_bound(X_75,identity),least_upper_bound(identity,inverse(X_75))))]]) ).
cnf(refute_0_1816,plain,
( multiply(least_upper_bound(X_75,identity),greatest_lower_bound(identity,inverse(X_75))) != multiply(greatest_lower_bound(X_75,identity),least_upper_bound(identity,inverse(X_75)))
| inverse(multiply(least_upper_bound(X_75,identity),greatest_lower_bound(identity,inverse(X_75)))) = inverse(multiply(greatest_lower_bound(X_75,identity),least_upper_bound(identity,inverse(X_75)))) ),
inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(X_75,identity),greatest_lower_bound(identity,inverse(X_75)))),inverse(multiply(least_upper_bound(X_75,identity),greatest_lower_bound(identity,inverse(X_75))))) )],[refute_0_1814,refute_0_1815]) ).
cnf(refute_0_1817,plain,
inverse(multiply(least_upper_bound(X_75,identity),greatest_lower_bound(identity,inverse(X_75)))) = inverse(multiply(greatest_lower_bound(X_75,identity),least_upper_bound(identity,inverse(X_75)))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_75,identity),greatest_lower_bound(identity,inverse(X_75))),multiply(greatest_lower_bound(X_75,identity),least_upper_bound(identity,inverse(X_75)))) )],[refute_0_1813,refute_0_1816]) ).
cnf(refute_0_1818,plain,
( inverse(multiply(least_upper_bound(X_75,identity),greatest_lower_bound(identity,inverse(X_75)))) != inverse(multiply(greatest_lower_bound(X_75,identity),least_upper_bound(identity,inverse(X_75))))
| inverse(multiply(least_upper_bound(X_75,identity),greatest_lower_bound(identity,inverse(X_75)))) != inverse(multiply(greatest_lower_bound(identity,X_75),least_upper_bound(identity,inverse(X_75))))
| inverse(multiply(greatest_lower_bound(X_75,identity),least_upper_bound(identity,inverse(X_75)))) = inverse(multiply(greatest_lower_bound(identity,X_75),least_upper_bound(identity,inverse(X_75)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(least_upper_bound(X_75,identity),greatest_lower_bound(identity,inverse(X_75)))),inverse(multiply(greatest_lower_bound(identity,X_75),least_upper_bound(identity,inverse(X_75))))) ),[0],$fot(inverse(multiply(greatest_lower_bound(X_75,identity),least_upper_bound(identity,inverse(X_75)))))]]) ).
cnf(refute_0_1819,plain,
( inverse(multiply(least_upper_bound(X_75,identity),greatest_lower_bound(identity,inverse(X_75)))) != inverse(multiply(greatest_lower_bound(identity,X_75),least_upper_bound(identity,inverse(X_75))))
| inverse(multiply(greatest_lower_bound(X_75,identity),least_upper_bound(identity,inverse(X_75)))) = inverse(multiply(greatest_lower_bound(identity,X_75),least_upper_bound(identity,inverse(X_75)))) ),
inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(X_75,identity),greatest_lower_bound(identity,inverse(X_75)))),inverse(multiply(greatest_lower_bound(X_75,identity),least_upper_bound(identity,inverse(X_75))))) )],[refute_0_1817,refute_0_1818]) ).
cnf(refute_0_1820,plain,
inverse(multiply(greatest_lower_bound(X_75,identity),least_upper_bound(identity,inverse(X_75)))) = inverse(multiply(greatest_lower_bound(identity,X_75),least_upper_bound(identity,inverse(X_75)))),
inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(X_75,identity),greatest_lower_bound(identity,inverse(X_75)))),inverse(multiply(greatest_lower_bound(identity,X_75),least_upper_bound(identity,inverse(X_75))))) )],[refute_0_1812,refute_0_1819]) ).
cnf(refute_0_1821,plain,
multiply(least_upper_bound(X_74,greatest_lower_bound(X_11,X_74)),inverse(greatest_lower_bound(X_11,X_74))) = least_upper_bound(identity,multiply(X_74,inverse(greatest_lower_bound(X_11,X_74)))),
inference(subst,[],[refute_0_780:[bind(X_68,$fot(X_74)),bind(X_69,$fot(greatest_lower_bound(X_11,X_74)))]]) ).
cnf(refute_0_1822,plain,
least_upper_bound(X_74,greatest_lower_bound(X_11,X_74)) = X_74,
inference(subst,[],[refute_0_145:[bind(X_10,$fot(X_74))]]) ).
cnf(refute_0_1823,plain,
( multiply(least_upper_bound(X_74,greatest_lower_bound(X_11,X_74)),inverse(greatest_lower_bound(X_11,X_74))) != least_upper_bound(identity,multiply(X_74,inverse(greatest_lower_bound(X_11,X_74))))
| least_upper_bound(X_74,greatest_lower_bound(X_11,X_74)) != X_74
| multiply(X_74,inverse(greatest_lower_bound(X_11,X_74))) = least_upper_bound(identity,multiply(X_74,inverse(greatest_lower_bound(X_11,X_74)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_74,greatest_lower_bound(X_11,X_74)),inverse(greatest_lower_bound(X_11,X_74))),least_upper_bound(identity,multiply(X_74,inverse(greatest_lower_bound(X_11,X_74))))) ),[0,0],$fot(X_74)]]) ).
cnf(refute_0_1824,plain,
( multiply(least_upper_bound(X_74,greatest_lower_bound(X_11,X_74)),inverse(greatest_lower_bound(X_11,X_74))) != least_upper_bound(identity,multiply(X_74,inverse(greatest_lower_bound(X_11,X_74))))
| multiply(X_74,inverse(greatest_lower_bound(X_11,X_74))) = least_upper_bound(identity,multiply(X_74,inverse(greatest_lower_bound(X_11,X_74)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_74,greatest_lower_bound(X_11,X_74)),X_74) )],[refute_0_1822,refute_0_1823]) ).
cnf(refute_0_1825,plain,
multiply(X_74,inverse(greatest_lower_bound(X_11,X_74))) = least_upper_bound(identity,multiply(X_74,inverse(greatest_lower_bound(X_11,X_74)))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_74,greatest_lower_bound(X_11,X_74)),inverse(greatest_lower_bound(X_11,X_74))),least_upper_bound(identity,multiply(X_74,inverse(greatest_lower_bound(X_11,X_74))))) )],[refute_0_1821,refute_0_1824]) ).
cnf(refute_0_1826,plain,
multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))) = least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))),
inference(subst,[],[refute_0_1825:[bind(X_11,$fot(identity)),bind(X_74,$fot(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))]]) ).
cnf(refute_0_1827,plain,
greatest_lower_bound(least_upper_bound(X_322,X_324),greatest_lower_bound(least_upper_bound(X_324,X_322),inverse(greatest_lower_bound(identity,least_upper_bound(X_322,X_324))))) = greatest_lower_bound(least_upper_bound(X_322,X_324),inverse(greatest_lower_bound(identity,least_upper_bound(X_322,X_324)))),
inference(subst,[],[refute_0_1676:[bind(X_18,$fot(X_322)),bind(X_24,$fot(inverse(greatest_lower_bound(identity,least_upper_bound(X_322,X_324))))),bind(X_7,$fot(X_324))]]) ).
cnf(refute_0_1828,plain,
greatest_lower_bound(identity,X_283) = multiply(inverse(greatest_lower_bound(greatest_lower_bound(identity,inverse(X_283)),inverse(greatest_lower_bound(identity,X_283)))),greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,inverse(X_283)),greatest_lower_bound(identity,X_283)))),
inference(subst,[],[refute_0_1037:[bind(X_123,$fot(greatest_lower_bound(identity,inverse(X_283)))),bind(X_31,$fot(greatest_lower_bound(identity,X_283)))]]) ).
cnf(refute_0_1829,plain,
multiply(greatest_lower_bound(inverse(X_114),identity),greatest_lower_bound(identity,X_114)) = greatest_lower_bound(greatest_lower_bound(identity,X_114),multiply(inverse(X_114),greatest_lower_bound(identity,X_114))),
inference(subst,[],[refute_0_1313:[bind(X_119,$fot(greatest_lower_bound(identity,X_114))),bind(X_120,$fot(inverse(X_114)))]]) ).
cnf(refute_0_1830,plain,
( multiply(greatest_lower_bound(inverse(X_114),identity),greatest_lower_bound(identity,X_114)) != greatest_lower_bound(greatest_lower_bound(identity,X_114),multiply(inverse(X_114),greatest_lower_bound(identity,X_114)))
| multiply(inverse(X_114),greatest_lower_bound(identity,X_114)) != greatest_lower_bound(identity,inverse(X_114))
| multiply(greatest_lower_bound(inverse(X_114),identity),greatest_lower_bound(identity,X_114)) = greatest_lower_bound(greatest_lower_bound(identity,X_114),greatest_lower_bound(identity,inverse(X_114))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_114),identity),greatest_lower_bound(identity,X_114)),greatest_lower_bound(greatest_lower_bound(identity,X_114),multiply(inverse(X_114),greatest_lower_bound(identity,X_114)))) ),[1,1],$fot(greatest_lower_bound(identity,inverse(X_114)))]]) ).
cnf(refute_0_1831,plain,
( multiply(greatest_lower_bound(inverse(X_114),identity),greatest_lower_bound(identity,X_114)) != greatest_lower_bound(greatest_lower_bound(identity,X_114),multiply(inverse(X_114),greatest_lower_bound(identity,X_114)))
| multiply(greatest_lower_bound(inverse(X_114),identity),greatest_lower_bound(identity,X_114)) = greatest_lower_bound(greatest_lower_bound(identity,X_114),greatest_lower_bound(identity,inverse(X_114))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_114),greatest_lower_bound(identity,X_114)),greatest_lower_bound(identity,inverse(X_114))) )],[refute_0_644,refute_0_1830]) ).
cnf(refute_0_1832,plain,
multiply(greatest_lower_bound(inverse(X_114),identity),greatest_lower_bound(identity,X_114)) = greatest_lower_bound(greatest_lower_bound(identity,X_114),greatest_lower_bound(identity,inverse(X_114))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_114),identity),greatest_lower_bound(identity,X_114)),greatest_lower_bound(greatest_lower_bound(identity,X_114),multiply(inverse(X_114),greatest_lower_bound(identity,X_114)))) )],[refute_0_1829,refute_0_1831]) ).
cnf(refute_0_1833,plain,
greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_172,X_17))) = greatest_lower_bound(X_17,multiply(X_172,X_17)),
inference(subst,[],[refute_0_354:[bind(X_16,$fot(multiply(X_172,X_17)))]]) ).
cnf(refute_0_1834,plain,
multiply(greatest_lower_bound(X_172,identity),X_17) = greatest_lower_bound(X_17,multiply(X_172,X_17)),
inference(subst,[],[refute_0_1313:[bind(X_119,$fot(X_17)),bind(X_120,$fot(X_172))]]) ).
cnf(refute_0_1835,plain,
( multiply(greatest_lower_bound(X_172,identity),X_17) != greatest_lower_bound(X_17,multiply(X_172,X_17))
| greatest_lower_bound(X_17,multiply(X_172,X_17)) = multiply(greatest_lower_bound(X_172,identity),X_17) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(greatest_lower_bound(X_172,identity),X_17))),bind(Y0,$fot(greatest_lower_bound(X_17,multiply(X_172,X_17))))]]) ).
cnf(refute_0_1836,plain,
greatest_lower_bound(X_17,multiply(X_172,X_17)) = multiply(greatest_lower_bound(X_172,identity),X_17),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_172,identity),X_17),greatest_lower_bound(X_17,multiply(X_172,X_17))) )],[refute_0_1834,refute_0_1835]) ).
cnf(refute_0_1837,plain,
( greatest_lower_bound(X_17,multiply(X_172,X_17)) != multiply(greatest_lower_bound(X_172,identity),X_17)
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_172,X_17))) != greatest_lower_bound(X_17,multiply(X_172,X_17))
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_172,X_17))) = multiply(greatest_lower_bound(X_172,identity),X_17) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_172,X_17))),greatest_lower_bound(X_17,multiply(X_172,X_17))) ),[1],$fot(multiply(greatest_lower_bound(X_172,identity),X_17))]]) ).
cnf(refute_0_1838,plain,
( greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_172,X_17))) != greatest_lower_bound(X_17,multiply(X_172,X_17))
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_172,X_17))) = multiply(greatest_lower_bound(X_172,identity),X_17) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,multiply(X_172,X_17)),multiply(greatest_lower_bound(X_172,identity),X_17)) )],[refute_0_1836,refute_0_1837]) ).
cnf(refute_0_1839,plain,
greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_172,X_17))) = multiply(greatest_lower_bound(X_172,identity),X_17),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_172,X_17))),greatest_lower_bound(X_17,multiply(X_172,X_17))) )],[refute_0_1833,refute_0_1838]) ).
cnf(refute_0_1840,plain,
greatest_lower_bound(identity,greatest_lower_bound(X_172,identity)) = greatest_lower_bound(identity,X_172),
inference(subst,[],[refute_0_347:[bind(Y,$fot(X_172)),bind(X_13,$fot(identity))]]) ).
cnf(refute_0_1841,plain,
multiply(greatest_lower_bound(identity,greatest_lower_bound(X_172,identity)),X_17) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_172,identity)),X_17),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_172,identity)),X_17))]]) ).
cnf(refute_0_1842,plain,
( multiply(greatest_lower_bound(identity,greatest_lower_bound(X_172,identity)),X_17) != multiply(greatest_lower_bound(identity,greatest_lower_bound(X_172,identity)),X_17)
| greatest_lower_bound(identity,greatest_lower_bound(X_172,identity)) != greatest_lower_bound(identity,X_172)
| multiply(greatest_lower_bound(identity,greatest_lower_bound(X_172,identity)),X_17) = multiply(greatest_lower_bound(identity,X_172),X_17) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_172,identity)),X_17),multiply(greatest_lower_bound(identity,greatest_lower_bound(X_172,identity)),X_17)) ),[1,0],$fot(greatest_lower_bound(identity,X_172))]]) ).
cnf(refute_0_1843,plain,
( greatest_lower_bound(identity,greatest_lower_bound(X_172,identity)) != greatest_lower_bound(identity,X_172)
| multiply(greatest_lower_bound(identity,greatest_lower_bound(X_172,identity)),X_17) = multiply(greatest_lower_bound(identity,X_172),X_17) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_172,identity)),X_17),multiply(greatest_lower_bound(identity,greatest_lower_bound(X_172,identity)),X_17)) )],[refute_0_1841,refute_0_1842]) ).
cnf(refute_0_1844,plain,
multiply(greatest_lower_bound(identity,greatest_lower_bound(X_172,identity)),X_17) = multiply(greatest_lower_bound(identity,X_172),X_17),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_172,identity)),greatest_lower_bound(identity,X_172)) )],[refute_0_1840,refute_0_1843]) ).
cnf(refute_0_1845,plain,
least_upper_bound(greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119)),greatest_lower_bound(multiply(X_120,X_119),multiply(X_121,X_119))) = greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119)),
inference(subst,[],[refute_0_371:[bind(X_11,$fot(multiply(X_120,X_119))),bind(X_16,$fot(multiply(X_121,X_119)))]]) ).
cnf(refute_0_1846,plain,
multiply(greatest_lower_bound(X_120,X_121),X_119) = greatest_lower_bound(multiply(X_120,X_119),multiply(X_121,X_119)),
inference(subst,[],[monotony_glb2:[bind(X,$fot(X_119)),bind(Y,$fot(X_120)),bind(Z,$fot(X_121))]]) ).
cnf(refute_0_1847,plain,
( multiply(greatest_lower_bound(X_120,X_121),X_119) != greatest_lower_bound(multiply(X_120,X_119),multiply(X_121,X_119))
| greatest_lower_bound(multiply(X_120,X_119),multiply(X_121,X_119)) = multiply(greatest_lower_bound(X_120,X_121),X_119) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(greatest_lower_bound(X_120,X_121),X_119))),bind(Y0,$fot(greatest_lower_bound(multiply(X_120,X_119),multiply(X_121,X_119))))]]) ).
cnf(refute_0_1848,plain,
greatest_lower_bound(multiply(X_120,X_119),multiply(X_121,X_119)) = multiply(greatest_lower_bound(X_120,X_121),X_119),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_120,X_121),X_119),greatest_lower_bound(multiply(X_120,X_119),multiply(X_121,X_119))) )],[refute_0_1846,refute_0_1847]) ).
cnf(refute_0_1849,plain,
( greatest_lower_bound(multiply(X_120,X_119),multiply(X_121,X_119)) != multiply(greatest_lower_bound(X_120,X_121),X_119)
| least_upper_bound(greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119)),greatest_lower_bound(multiply(X_120,X_119),multiply(X_121,X_119))) != greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119))
| least_upper_bound(greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119)),multiply(greatest_lower_bound(X_120,X_121),X_119)) = greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119)),greatest_lower_bound(multiply(X_120,X_119),multiply(X_121,X_119))),greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119))) ),[0,1],$fot(multiply(greatest_lower_bound(X_120,X_121),X_119))]]) ).
cnf(refute_0_1850,plain,
( least_upper_bound(greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119)),greatest_lower_bound(multiply(X_120,X_119),multiply(X_121,X_119))) != greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119))
| least_upper_bound(greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119)),multiply(greatest_lower_bound(X_120,X_121),X_119)) = greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_120,X_119),multiply(X_121,X_119)),multiply(greatest_lower_bound(X_120,X_121),X_119)) )],[refute_0_1848,refute_0_1849]) ).
cnf(refute_0_1851,plain,
least_upper_bound(greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119)),multiply(greatest_lower_bound(X_120,X_121),X_119)) = greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119)),greatest_lower_bound(multiply(X_120,X_119),multiply(X_121,X_119))),greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119))) )],[refute_0_1845,refute_0_1850]) ).
cnf(refute_0_1852,plain,
least_upper_bound(greatest_lower_bound(X_120,X_121),greatest_lower_bound(X_121,X_120)) = greatest_lower_bound(X_120,X_121),
inference(subst,[],[refute_0_371:[bind(X_11,$fot(X_121)),bind(X_16,$fot(X_120))]]) ).
cnf(refute_0_1853,plain,
multiply(least_upper_bound(greatest_lower_bound(X_120,X_121),greatest_lower_bound(X_121,X_120)),X_119) = multiply(least_upper_bound(greatest_lower_bound(X_120,X_121),greatest_lower_bound(X_121,X_120)),X_119),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(greatest_lower_bound(X_120,X_121),greatest_lower_bound(X_121,X_120)),X_119))]]) ).
cnf(refute_0_1854,plain,
( multiply(least_upper_bound(greatest_lower_bound(X_120,X_121),greatest_lower_bound(X_121,X_120)),X_119) != multiply(least_upper_bound(greatest_lower_bound(X_120,X_121),greatest_lower_bound(X_121,X_120)),X_119)
| least_upper_bound(greatest_lower_bound(X_120,X_121),greatest_lower_bound(X_121,X_120)) != greatest_lower_bound(X_120,X_121)
| multiply(least_upper_bound(greatest_lower_bound(X_120,X_121),greatest_lower_bound(X_121,X_120)),X_119) = multiply(greatest_lower_bound(X_120,X_121),X_119) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(X_120,X_121),greatest_lower_bound(X_121,X_120)),X_119),multiply(least_upper_bound(greatest_lower_bound(X_120,X_121),greatest_lower_bound(X_121,X_120)),X_119)) ),[1,0],$fot(greatest_lower_bound(X_120,X_121))]]) ).
cnf(refute_0_1855,plain,
( least_upper_bound(greatest_lower_bound(X_120,X_121),greatest_lower_bound(X_121,X_120)) != greatest_lower_bound(X_120,X_121)
| multiply(least_upper_bound(greatest_lower_bound(X_120,X_121),greatest_lower_bound(X_121,X_120)),X_119) = multiply(greatest_lower_bound(X_120,X_121),X_119) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(X_120,X_121),greatest_lower_bound(X_121,X_120)),X_119),multiply(least_upper_bound(greatest_lower_bound(X_120,X_121),greatest_lower_bound(X_121,X_120)),X_119)) )],[refute_0_1853,refute_0_1854]) ).
cnf(refute_0_1856,plain,
multiply(least_upper_bound(greatest_lower_bound(X_120,X_121),greatest_lower_bound(X_121,X_120)),X_119) = multiply(greatest_lower_bound(X_120,X_121),X_119),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_120,X_121),greatest_lower_bound(X_121,X_120)),greatest_lower_bound(X_120,X_121)) )],[refute_0_1852,refute_0_1855]) ).
cnf(refute_0_1857,plain,
least_upper_bound(multiply(greatest_lower_bound(X_120,X_121),X_119),multiply(greatest_lower_bound(X_121,X_120),X_119)) = multiply(least_upper_bound(greatest_lower_bound(X_120,X_121),greatest_lower_bound(X_121,X_120)),X_119),
inference(subst,[],[refute_0_744:[bind(X,$fot(X_119)),bind(Y,$fot(greatest_lower_bound(X_120,X_121))),bind(Z,$fot(greatest_lower_bound(X_121,X_120)))]]) ).
cnf(refute_0_1858,plain,
( multiply(least_upper_bound(greatest_lower_bound(X_120,X_121),greatest_lower_bound(X_121,X_120)),X_119) != multiply(greatest_lower_bound(X_120,X_121),X_119)
| least_upper_bound(multiply(greatest_lower_bound(X_120,X_121),X_119),multiply(greatest_lower_bound(X_121,X_120),X_119)) != multiply(least_upper_bound(greatest_lower_bound(X_120,X_121),greatest_lower_bound(X_121,X_120)),X_119)
| least_upper_bound(multiply(greatest_lower_bound(X_120,X_121),X_119),multiply(greatest_lower_bound(X_121,X_120),X_119)) = multiply(greatest_lower_bound(X_120,X_121),X_119) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(least_upper_bound(multiply(greatest_lower_bound(X_120,X_121),X_119),multiply(greatest_lower_bound(X_121,X_120),X_119)))),bind(Y0,$fot(multiply(least_upper_bound(greatest_lower_bound(X_120,X_121),greatest_lower_bound(X_121,X_120)),X_119))),bind(Z0,$fot(multiply(greatest_lower_bound(X_120,X_121),X_119)))]]) ).
cnf(refute_0_1859,plain,
( multiply(least_upper_bound(greatest_lower_bound(X_120,X_121),greatest_lower_bound(X_121,X_120)),X_119) != multiply(greatest_lower_bound(X_120,X_121),X_119)
| least_upper_bound(multiply(greatest_lower_bound(X_120,X_121),X_119),multiply(greatest_lower_bound(X_121,X_120),X_119)) = multiply(greatest_lower_bound(X_120,X_121),X_119) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(X_120,X_121),X_119),multiply(greatest_lower_bound(X_121,X_120),X_119)),multiply(least_upper_bound(greatest_lower_bound(X_120,X_121),greatest_lower_bound(X_121,X_120)),X_119)) )],[refute_0_1857,refute_0_1858]) ).
cnf(refute_0_1860,plain,
least_upper_bound(multiply(greatest_lower_bound(X_120,X_121),X_119),multiply(greatest_lower_bound(X_121,X_120),X_119)) = multiply(greatest_lower_bound(X_120,X_121),X_119),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(X_120,X_121),greatest_lower_bound(X_121,X_120)),X_119),multiply(greatest_lower_bound(X_120,X_121),X_119)) )],[refute_0_1856,refute_0_1859]) ).
cnf(refute_0_1861,plain,
greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119)) = multiply(greatest_lower_bound(X_121,X_120),X_119),
inference(subst,[],[refute_0_1360:[bind(X,$fot(X_119)),bind(Y,$fot(X_121)),bind(Z,$fot(X_120))]]) ).
cnf(refute_0_1862,plain,
least_upper_bound(multiply(greatest_lower_bound(X_120,X_121),X_119),greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119))) = least_upper_bound(multiply(greatest_lower_bound(X_120,X_121),X_119),greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119))),
introduced(tautology,[refl,[$fot(least_upper_bound(multiply(greatest_lower_bound(X_120,X_121),X_119),greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119))))]]) ).
cnf(refute_0_1863,plain,
( greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119)) != multiply(greatest_lower_bound(X_121,X_120),X_119)
| least_upper_bound(multiply(greatest_lower_bound(X_120,X_121),X_119),greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119))) != least_upper_bound(multiply(greatest_lower_bound(X_120,X_121),X_119),greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119)))
| least_upper_bound(multiply(greatest_lower_bound(X_120,X_121),X_119),greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119))) = least_upper_bound(multiply(greatest_lower_bound(X_120,X_121),X_119),multiply(greatest_lower_bound(X_121,X_120),X_119)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(X_120,X_121),X_119),greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119))),least_upper_bound(multiply(greatest_lower_bound(X_120,X_121),X_119),greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119)))) ),[1,1],$fot(multiply(greatest_lower_bound(X_121,X_120),X_119))]]) ).
cnf(refute_0_1864,plain,
( greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119)) != multiply(greatest_lower_bound(X_121,X_120),X_119)
| least_upper_bound(multiply(greatest_lower_bound(X_120,X_121),X_119),greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119))) = least_upper_bound(multiply(greatest_lower_bound(X_120,X_121),X_119),multiply(greatest_lower_bound(X_121,X_120),X_119)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(X_120,X_121),X_119),greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119))),least_upper_bound(multiply(greatest_lower_bound(X_120,X_121),X_119),greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119)))) )],[refute_0_1862,refute_0_1863]) ).
cnf(refute_0_1865,plain,
least_upper_bound(multiply(greatest_lower_bound(X_120,X_121),X_119),greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119))) = least_upper_bound(multiply(greatest_lower_bound(X_120,X_121),X_119),multiply(greatest_lower_bound(X_121,X_120),X_119)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119)),multiply(greatest_lower_bound(X_121,X_120),X_119)) )],[refute_0_1861,refute_0_1864]) ).
cnf(refute_0_1866,plain,
( least_upper_bound(multiply(greatest_lower_bound(X_120,X_121),X_119),multiply(greatest_lower_bound(X_121,X_120),X_119)) != multiply(greatest_lower_bound(X_120,X_121),X_119)
| least_upper_bound(multiply(greatest_lower_bound(X_120,X_121),X_119),greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119))) != least_upper_bound(multiply(greatest_lower_bound(X_120,X_121),X_119),multiply(greatest_lower_bound(X_121,X_120),X_119))
| least_upper_bound(multiply(greatest_lower_bound(X_120,X_121),X_119),greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119))) = multiply(greatest_lower_bound(X_120,X_121),X_119) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(least_upper_bound(multiply(greatest_lower_bound(X_120,X_121),X_119),greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119))))),bind(Y0,$fot(least_upper_bound(multiply(greatest_lower_bound(X_120,X_121),X_119),multiply(greatest_lower_bound(X_121,X_120),X_119)))),bind(Z0,$fot(multiply(greatest_lower_bound(X_120,X_121),X_119)))]]) ).
cnf(refute_0_1867,plain,
( least_upper_bound(multiply(greatest_lower_bound(X_120,X_121),X_119),multiply(greatest_lower_bound(X_121,X_120),X_119)) != multiply(greatest_lower_bound(X_120,X_121),X_119)
| least_upper_bound(multiply(greatest_lower_bound(X_120,X_121),X_119),greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119))) = multiply(greatest_lower_bound(X_120,X_121),X_119) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(X_120,X_121),X_119),greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119))),least_upper_bound(multiply(greatest_lower_bound(X_120,X_121),X_119),multiply(greatest_lower_bound(X_121,X_120),X_119))) )],[refute_0_1865,refute_0_1866]) ).
cnf(refute_0_1868,plain,
least_upper_bound(multiply(greatest_lower_bound(X_120,X_121),X_119),greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119))) = multiply(greatest_lower_bound(X_120,X_121),X_119),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(X_120,X_121),X_119),multiply(greatest_lower_bound(X_121,X_120),X_119)),multiply(greatest_lower_bound(X_120,X_121),X_119)) )],[refute_0_1860,refute_0_1867]) ).
cnf(refute_0_1869,plain,
least_upper_bound(greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119)),multiply(greatest_lower_bound(X_120,X_121),X_119)) = least_upper_bound(multiply(greatest_lower_bound(X_120,X_121),X_119),greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119))),
inference(subst,[],[refute_0_25:[bind(X,$fot(multiply(greatest_lower_bound(X_120,X_121),X_119))),bind(Y,$fot(greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119))))]]) ).
cnf(refute_0_1870,plain,
( least_upper_bound(multiply(greatest_lower_bound(X_120,X_121),X_119),greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119))) != multiply(greatest_lower_bound(X_120,X_121),X_119)
| least_upper_bound(greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119)),multiply(greatest_lower_bound(X_120,X_121),X_119)) != least_upper_bound(multiply(greatest_lower_bound(X_120,X_121),X_119),greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119)))
| least_upper_bound(greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119)),multiply(greatest_lower_bound(X_120,X_121),X_119)) = multiply(greatest_lower_bound(X_120,X_121),X_119) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119)),multiply(greatest_lower_bound(X_120,X_121),X_119)))),bind(Y0,$fot(least_upper_bound(multiply(greatest_lower_bound(X_120,X_121),X_119),greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119))))),bind(Z0,$fot(multiply(greatest_lower_bound(X_120,X_121),X_119)))]]) ).
cnf(refute_0_1871,plain,
( least_upper_bound(multiply(greatest_lower_bound(X_120,X_121),X_119),greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119))) != multiply(greatest_lower_bound(X_120,X_121),X_119)
| least_upper_bound(greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119)),multiply(greatest_lower_bound(X_120,X_121),X_119)) = multiply(greatest_lower_bound(X_120,X_121),X_119) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119)),multiply(greatest_lower_bound(X_120,X_121),X_119)),least_upper_bound(multiply(greatest_lower_bound(X_120,X_121),X_119),greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119)))) )],[refute_0_1869,refute_0_1870]) ).
cnf(refute_0_1872,plain,
least_upper_bound(greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119)),multiply(greatest_lower_bound(X_120,X_121),X_119)) = multiply(greatest_lower_bound(X_120,X_121),X_119),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(X_120,X_121),X_119),greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119))),multiply(greatest_lower_bound(X_120,X_121),X_119)) )],[refute_0_1868,refute_0_1871]) ).
cnf(refute_0_1873,plain,
( least_upper_bound(greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119)),multiply(greatest_lower_bound(X_120,X_121),X_119)) != multiply(greatest_lower_bound(X_120,X_121),X_119)
| least_upper_bound(greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119)),multiply(greatest_lower_bound(X_120,X_121),X_119)) != greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119))
| multiply(greatest_lower_bound(X_120,X_121),X_119) = greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119)),multiply(greatest_lower_bound(X_120,X_121),X_119)),greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119))) ),[0],$fot(multiply(greatest_lower_bound(X_120,X_121),X_119))]]) ).
cnf(refute_0_1874,plain,
( least_upper_bound(greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119)),multiply(greatest_lower_bound(X_120,X_121),X_119)) != greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119))
| multiply(greatest_lower_bound(X_120,X_121),X_119) = greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119)),multiply(greatest_lower_bound(X_120,X_121),X_119)),multiply(greatest_lower_bound(X_120,X_121),X_119)) )],[refute_0_1872,refute_0_1873]) ).
cnf(refute_0_1875,plain,
( multiply(greatest_lower_bound(X_120,X_121),X_119) != greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119))
| greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119)) != multiply(greatest_lower_bound(X_121,X_120),X_119)
| multiply(greatest_lower_bound(X_120,X_121),X_119) = multiply(greatest_lower_bound(X_121,X_120),X_119) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_120,X_121),X_119),multiply(greatest_lower_bound(X_121,X_120),X_119)) ),[0],$fot(greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119)))]]) ).
cnf(refute_0_1876,plain,
( multiply(greatest_lower_bound(X_120,X_121),X_119) != greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119))
| multiply(greatest_lower_bound(X_120,X_121),X_119) = multiply(greatest_lower_bound(X_121,X_120),X_119) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119)),multiply(greatest_lower_bound(X_121,X_120),X_119)) )],[refute_0_1861,refute_0_1875]) ).
cnf(refute_0_1877,plain,
( least_upper_bound(greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119)),multiply(greatest_lower_bound(X_120,X_121),X_119)) != greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119))
| multiply(greatest_lower_bound(X_120,X_121),X_119) = multiply(greatest_lower_bound(X_121,X_120),X_119) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_120,X_121),X_119),greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119))) )],[refute_0_1874,refute_0_1876]) ).
cnf(refute_0_1878,plain,
multiply(greatest_lower_bound(X_120,X_121),X_119) = multiply(greatest_lower_bound(X_121,X_120),X_119),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119)),multiply(greatest_lower_bound(X_120,X_121),X_119)),greatest_lower_bound(multiply(X_121,X_119),multiply(X_120,X_119))) )],[refute_0_1851,refute_0_1877]) ).
cnf(refute_0_1879,plain,
( multiply(greatest_lower_bound(X_120,X_121),X_119) != multiply(greatest_lower_bound(X_121,X_120),X_119)
| multiply(greatest_lower_bound(X_121,X_120),X_119) = multiply(greatest_lower_bound(X_120,X_121),X_119) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(greatest_lower_bound(X_120,X_121),X_119))),bind(Y0,$fot(multiply(greatest_lower_bound(X_121,X_120),X_119)))]]) ).
cnf(refute_0_1880,plain,
multiply(greatest_lower_bound(X_121,X_120),X_119) = multiply(greatest_lower_bound(X_120,X_121),X_119),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_120,X_121),X_119),multiply(greatest_lower_bound(X_121,X_120),X_119)) )],[refute_0_1878,refute_0_1879]) ).
cnf(refute_0_1881,plain,
multiply(greatest_lower_bound(greatest_lower_bound(X_172,identity),identity),X_17) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_172,identity)),X_17),
inference(subst,[],[refute_0_1880:[bind(X_119,$fot(X_17)),bind(X_120,$fot(identity)),bind(X_121,$fot(greatest_lower_bound(X_172,identity)))]]) ).
cnf(refute_0_1882,plain,
greatest_lower_bound(X_17,multiply(greatest_lower_bound(X_172,identity),X_17)) = multiply(greatest_lower_bound(greatest_lower_bound(X_172,identity),identity),X_17),
inference(subst,[],[refute_0_1315:[bind(X_119,$fot(X_17)),bind(X_120,$fot(greatest_lower_bound(X_172,identity)))]]) ).
cnf(refute_0_1883,plain,
( multiply(greatest_lower_bound(greatest_lower_bound(X_172,identity),identity),X_17) != multiply(greatest_lower_bound(identity,greatest_lower_bound(X_172,identity)),X_17)
| greatest_lower_bound(X_17,multiply(greatest_lower_bound(X_172,identity),X_17)) != multiply(greatest_lower_bound(greatest_lower_bound(X_172,identity),identity),X_17)
| greatest_lower_bound(X_17,multiply(greatest_lower_bound(X_172,identity),X_17)) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_172,identity)),X_17) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(greatest_lower_bound(X_17,multiply(greatest_lower_bound(X_172,identity),X_17)))),bind(Y0,$fot(multiply(greatest_lower_bound(greatest_lower_bound(X_172,identity),identity),X_17))),bind(Z0,$fot(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_172,identity)),X_17)))]]) ).
cnf(refute_0_1884,plain,
( multiply(greatest_lower_bound(greatest_lower_bound(X_172,identity),identity),X_17) != multiply(greatest_lower_bound(identity,greatest_lower_bound(X_172,identity)),X_17)
| greatest_lower_bound(X_17,multiply(greatest_lower_bound(X_172,identity),X_17)) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_172,identity)),X_17) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,multiply(greatest_lower_bound(X_172,identity),X_17)),multiply(greatest_lower_bound(greatest_lower_bound(X_172,identity),identity),X_17)) )],[refute_0_1882,refute_0_1883]) ).
cnf(refute_0_1885,plain,
greatest_lower_bound(X_17,multiply(greatest_lower_bound(X_172,identity),X_17)) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_172,identity)),X_17),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(greatest_lower_bound(X_172,identity),identity),X_17),multiply(greatest_lower_bound(identity,greatest_lower_bound(X_172,identity)),X_17)) )],[refute_0_1881,refute_0_1884]) ).
cnf(refute_0_1886,plain,
greatest_lower_bound(multiply(X_172,X_23),greatest_lower_bound(X_22,X_23)) = greatest_lower_bound(X_22,greatest_lower_bound(X_23,multiply(X_172,X_23))),
inference(subst,[],[refute_0_1460:[bind(X,$fot(multiply(X_172,X_23)))]]) ).
cnf(refute_0_1887,plain,
multiply(greatest_lower_bound(X_172,identity),X_23) = greatest_lower_bound(X_23,multiply(X_172,X_23)),
inference(subst,[],[refute_0_1313:[bind(X_119,$fot(X_23)),bind(X_120,$fot(X_172))]]) ).
cnf(refute_0_1888,plain,
( multiply(greatest_lower_bound(X_172,identity),X_23) != greatest_lower_bound(X_23,multiply(X_172,X_23))
| greatest_lower_bound(X_23,multiply(X_172,X_23)) = multiply(greatest_lower_bound(X_172,identity),X_23) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(greatest_lower_bound(X_172,identity),X_23))),bind(Y0,$fot(greatest_lower_bound(X_23,multiply(X_172,X_23))))]]) ).
cnf(refute_0_1889,plain,
greatest_lower_bound(X_23,multiply(X_172,X_23)) = multiply(greatest_lower_bound(X_172,identity),X_23),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_172,identity),X_23),greatest_lower_bound(X_23,multiply(X_172,X_23))) )],[refute_0_1887,refute_0_1888]) ).
cnf(refute_0_1890,plain,
( greatest_lower_bound(X_23,multiply(X_172,X_23)) != multiply(greatest_lower_bound(X_172,identity),X_23)
| greatest_lower_bound(multiply(X_172,X_23),greatest_lower_bound(X_22,X_23)) != greatest_lower_bound(X_22,greatest_lower_bound(X_23,multiply(X_172,X_23)))
| greatest_lower_bound(multiply(X_172,X_23),greatest_lower_bound(X_22,X_23)) = greatest_lower_bound(X_22,multiply(greatest_lower_bound(X_172,identity),X_23)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_172,X_23),greatest_lower_bound(X_22,X_23)),greatest_lower_bound(X_22,greatest_lower_bound(X_23,multiply(X_172,X_23)))) ),[1,1],$fot(multiply(greatest_lower_bound(X_172,identity),X_23))]]) ).
cnf(refute_0_1891,plain,
( greatest_lower_bound(multiply(X_172,X_23),greatest_lower_bound(X_22,X_23)) != greatest_lower_bound(X_22,greatest_lower_bound(X_23,multiply(X_172,X_23)))
| greatest_lower_bound(multiply(X_172,X_23),greatest_lower_bound(X_22,X_23)) = greatest_lower_bound(X_22,multiply(greatest_lower_bound(X_172,identity),X_23)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_23,multiply(X_172,X_23)),multiply(greatest_lower_bound(X_172,identity),X_23)) )],[refute_0_1889,refute_0_1890]) ).
cnf(refute_0_1892,plain,
greatest_lower_bound(multiply(X_172,X_23),greatest_lower_bound(X_22,X_23)) = greatest_lower_bound(X_22,multiply(greatest_lower_bound(X_172,identity),X_23)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_172,X_23),greatest_lower_bound(X_22,X_23)),greatest_lower_bound(X_22,greatest_lower_bound(X_23,multiply(X_172,X_23)))) )],[refute_0_1886,refute_0_1891]) ).
cnf(refute_0_1893,plain,
( greatest_lower_bound(X_128,greatest_lower_bound(X_129,Y)) != greatest_lower_bound(Y,greatest_lower_bound(X_129,X_128))
| greatest_lower_bound(Y,greatest_lower_bound(X_129,X_128)) = greatest_lower_bound(X_128,greatest_lower_bound(X_129,Y)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(greatest_lower_bound(X_128,greatest_lower_bound(X_129,Y)))),bind(Y0,$fot(greatest_lower_bound(Y,greatest_lower_bound(X_129,X_128))))]]) ).
cnf(refute_0_1894,plain,
greatest_lower_bound(Y,greatest_lower_bound(X_129,X_128)) = greatest_lower_bound(X_128,greatest_lower_bound(X_129,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_128,greatest_lower_bound(X_129,Y)),greatest_lower_bound(Y,greatest_lower_bound(X_129,X_128))) )],[refute_0_1668,refute_0_1893]) ).
cnf(refute_0_1895,plain,
greatest_lower_bound(multiply(X_172,X_23),greatest_lower_bound(X_22,X_23)) = greatest_lower_bound(X_23,greatest_lower_bound(X_22,multiply(X_172,X_23))),
inference(subst,[],[refute_0_1894:[bind(Y,$fot(multiply(X_172,X_23))),bind(X_128,$fot(X_23)),bind(X_129,$fot(X_22))]]) ).
cnf(refute_0_1896,plain,
( greatest_lower_bound(multiply(X_172,X_23),greatest_lower_bound(X_22,X_23)) != greatest_lower_bound(X_22,multiply(greatest_lower_bound(X_172,identity),X_23))
| greatest_lower_bound(multiply(X_172,X_23),greatest_lower_bound(X_22,X_23)) != greatest_lower_bound(X_23,greatest_lower_bound(X_22,multiply(X_172,X_23)))
| greatest_lower_bound(X_23,greatest_lower_bound(X_22,multiply(X_172,X_23))) = greatest_lower_bound(X_22,multiply(greatest_lower_bound(X_172,identity),X_23)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_172,X_23),greatest_lower_bound(X_22,X_23)),greatest_lower_bound(X_22,multiply(greatest_lower_bound(X_172,identity),X_23))) ),[0],$fot(greatest_lower_bound(X_23,greatest_lower_bound(X_22,multiply(X_172,X_23))))]]) ).
cnf(refute_0_1897,plain,
( greatest_lower_bound(multiply(X_172,X_23),greatest_lower_bound(X_22,X_23)) != greatest_lower_bound(X_22,multiply(greatest_lower_bound(X_172,identity),X_23))
| greatest_lower_bound(X_23,greatest_lower_bound(X_22,multiply(X_172,X_23))) = greatest_lower_bound(X_22,multiply(greatest_lower_bound(X_172,identity),X_23)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_172,X_23),greatest_lower_bound(X_22,X_23)),greatest_lower_bound(X_23,greatest_lower_bound(X_22,multiply(X_172,X_23)))) )],[refute_0_1895,refute_0_1896]) ).
cnf(refute_0_1898,plain,
greatest_lower_bound(X_23,greatest_lower_bound(X_22,multiply(X_172,X_23))) = greatest_lower_bound(X_22,multiply(greatest_lower_bound(X_172,identity),X_23)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_172,X_23),greatest_lower_bound(X_22,X_23)),greatest_lower_bound(X_22,multiply(greatest_lower_bound(X_172,identity),X_23))) )],[refute_0_1892,refute_0_1897]) ).
cnf(refute_0_1899,plain,
greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_172,X_17))) = greatest_lower_bound(X_17,multiply(greatest_lower_bound(X_172,identity),X_17)),
inference(subst,[],[refute_0_1898:[bind(X_22,$fot(X_17)),bind(X_23,$fot(X_17))]]) ).
cnf(refute_0_1900,plain,
( greatest_lower_bound(X_17,multiply(greatest_lower_bound(X_172,identity),X_17)) != multiply(greatest_lower_bound(identity,greatest_lower_bound(X_172,identity)),X_17)
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_172,X_17))) != greatest_lower_bound(X_17,multiply(greatest_lower_bound(X_172,identity),X_17))
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_172,X_17))) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_172,identity)),X_17) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_172,X_17))))),bind(Y0,$fot(greatest_lower_bound(X_17,multiply(greatest_lower_bound(X_172,identity),X_17)))),bind(Z0,$fot(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_172,identity)),X_17)))]]) ).
cnf(refute_0_1901,plain,
( greatest_lower_bound(X_17,multiply(greatest_lower_bound(X_172,identity),X_17)) != multiply(greatest_lower_bound(identity,greatest_lower_bound(X_172,identity)),X_17)
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_172,X_17))) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_172,identity)),X_17) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_172,X_17))),greatest_lower_bound(X_17,multiply(greatest_lower_bound(X_172,identity),X_17))) )],[refute_0_1899,refute_0_1900]) ).
cnf(refute_0_1902,plain,
greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_172,X_17))) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_172,identity)),X_17),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,multiply(greatest_lower_bound(X_172,identity),X_17)),multiply(greatest_lower_bound(identity,greatest_lower_bound(X_172,identity)),X_17)) )],[refute_0_1885,refute_0_1901]) ).
cnf(refute_0_1903,plain,
( multiply(greatest_lower_bound(identity,greatest_lower_bound(X_172,identity)),X_17) != multiply(greatest_lower_bound(identity,X_172),X_17)
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_172,X_17))) != multiply(greatest_lower_bound(identity,greatest_lower_bound(X_172,identity)),X_17)
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_172,X_17))) = multiply(greatest_lower_bound(identity,X_172),X_17) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_172,X_17))))),bind(Y0,$fot(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_172,identity)),X_17))),bind(Z0,$fot(multiply(greatest_lower_bound(identity,X_172),X_17)))]]) ).
cnf(refute_0_1904,plain,
( multiply(greatest_lower_bound(identity,greatest_lower_bound(X_172,identity)),X_17) != multiply(greatest_lower_bound(identity,X_172),X_17)
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_172,X_17))) = multiply(greatest_lower_bound(identity,X_172),X_17) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_172,X_17))),multiply(greatest_lower_bound(identity,greatest_lower_bound(X_172,identity)),X_17)) )],[refute_0_1902,refute_0_1903]) ).
cnf(refute_0_1905,plain,
greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_172,X_17))) = multiply(greatest_lower_bound(identity,X_172),X_17),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_172,identity)),X_17),multiply(greatest_lower_bound(identity,X_172),X_17)) )],[refute_0_1844,refute_0_1904]) ).
cnf(refute_0_1906,plain,
( greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_172,X_17))) != multiply(greatest_lower_bound(X_172,identity),X_17)
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_172,X_17))) != multiply(greatest_lower_bound(identity,X_172),X_17)
| multiply(greatest_lower_bound(identity,X_172),X_17) = multiply(greatest_lower_bound(X_172,identity),X_17) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_172,X_17))),multiply(greatest_lower_bound(X_172,identity),X_17)) ),[0],$fot(multiply(greatest_lower_bound(identity,X_172),X_17))]]) ).
cnf(refute_0_1907,plain,
( greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_172,X_17))) != multiply(greatest_lower_bound(X_172,identity),X_17)
| multiply(greatest_lower_bound(identity,X_172),X_17) = multiply(greatest_lower_bound(X_172,identity),X_17) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_172,X_17))),multiply(greatest_lower_bound(identity,X_172),X_17)) )],[refute_0_1905,refute_0_1906]) ).
cnf(refute_0_1908,plain,
multiply(greatest_lower_bound(identity,X_172),X_17) = multiply(greatest_lower_bound(X_172,identity),X_17),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_172,X_17))),multiply(greatest_lower_bound(X_172,identity),X_17)) )],[refute_0_1839,refute_0_1907]) ).
cnf(refute_0_1909,plain,
( multiply(greatest_lower_bound(identity,X_172),X_17) != multiply(greatest_lower_bound(X_172,identity),X_17)
| multiply(greatest_lower_bound(X_172,identity),X_17) = multiply(greatest_lower_bound(identity,X_172),X_17) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(greatest_lower_bound(identity,X_172),X_17))),bind(Y0,$fot(multiply(greatest_lower_bound(X_172,identity),X_17)))]]) ).
cnf(refute_0_1910,plain,
multiply(greatest_lower_bound(X_172,identity),X_17) = multiply(greatest_lower_bound(identity,X_172),X_17),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_172),X_17),multiply(greatest_lower_bound(X_172,identity),X_17)) )],[refute_0_1908,refute_0_1909]) ).
cnf(refute_0_1911,plain,
multiply(greatest_lower_bound(inverse(X_114),identity),greatest_lower_bound(identity,X_114)) = multiply(greatest_lower_bound(identity,inverse(X_114)),greatest_lower_bound(identity,X_114)),
inference(subst,[],[refute_0_1910:[bind(X_17,$fot(greatest_lower_bound(identity,X_114))),bind(X_172,$fot(inverse(X_114)))]]) ).
cnf(refute_0_1912,plain,
( multiply(greatest_lower_bound(inverse(X_114),identity),greatest_lower_bound(identity,X_114)) != multiply(greatest_lower_bound(identity,inverse(X_114)),greatest_lower_bound(identity,X_114))
| multiply(greatest_lower_bound(inverse(X_114),identity),greatest_lower_bound(identity,X_114)) != greatest_lower_bound(greatest_lower_bound(identity,X_114),greatest_lower_bound(identity,inverse(X_114)))
| multiply(greatest_lower_bound(identity,inverse(X_114)),greatest_lower_bound(identity,X_114)) = greatest_lower_bound(greatest_lower_bound(identity,X_114),greatest_lower_bound(identity,inverse(X_114))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_114),identity),greatest_lower_bound(identity,X_114)),greatest_lower_bound(greatest_lower_bound(identity,X_114),greatest_lower_bound(identity,inverse(X_114)))) ),[0],$fot(multiply(greatest_lower_bound(identity,inverse(X_114)),greatest_lower_bound(identity,X_114)))]]) ).
cnf(refute_0_1913,plain,
( multiply(greatest_lower_bound(inverse(X_114),identity),greatest_lower_bound(identity,X_114)) != greatest_lower_bound(greatest_lower_bound(identity,X_114),greatest_lower_bound(identity,inverse(X_114)))
| multiply(greatest_lower_bound(identity,inverse(X_114)),greatest_lower_bound(identity,X_114)) = greatest_lower_bound(greatest_lower_bound(identity,X_114),greatest_lower_bound(identity,inverse(X_114))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_114),identity),greatest_lower_bound(identity,X_114)),multiply(greatest_lower_bound(identity,inverse(X_114)),greatest_lower_bound(identity,X_114))) )],[refute_0_1911,refute_0_1912]) ).
cnf(refute_0_1914,plain,
greatest_lower_bound(identity,greatest_lower_bound(X_114,greatest_lower_bound(identity,inverse(X_114)))) = greatest_lower_bound(X_114,greatest_lower_bound(identity,inverse(X_114))),
inference(subst,[],[refute_0_1471:[bind(Y,$fot(inverse(X_114))),bind(X_22,$fot(X_114)),bind(X_23,$fot(identity))]]) ).
cnf(refute_0_1915,plain,
greatest_lower_bound(greatest_lower_bound(X_130,X_128),greatest_lower_bound(X_22,X_23)) = greatest_lower_bound(X_22,greatest_lower_bound(X_23,greatest_lower_bound(X_130,X_128))),
inference(subst,[],[refute_0_1460:[bind(X,$fot(greatest_lower_bound(X_130,X_128)))]]) ).
cnf(refute_0_1916,plain,
greatest_lower_bound(X_128,greatest_lower_bound(X_23,X_130)) = greatest_lower_bound(X_23,greatest_lower_bound(X_130,X_128)),
inference(subst,[],[refute_0_1460:[bind(X,$fot(X_128)),bind(X_22,$fot(X_23)),bind(X_23,$fot(X_130))]]) ).
cnf(refute_0_1917,plain,
( greatest_lower_bound(X_128,greatest_lower_bound(X_23,X_130)) != greatest_lower_bound(X_23,greatest_lower_bound(X_130,X_128))
| greatest_lower_bound(X_23,greatest_lower_bound(X_130,X_128)) = greatest_lower_bound(X_128,greatest_lower_bound(X_23,X_130)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(greatest_lower_bound(X_128,greatest_lower_bound(X_23,X_130)))),bind(Y0,$fot(greatest_lower_bound(X_23,greatest_lower_bound(X_130,X_128))))]]) ).
cnf(refute_0_1918,plain,
greatest_lower_bound(X_23,greatest_lower_bound(X_130,X_128)) = greatest_lower_bound(X_128,greatest_lower_bound(X_23,X_130)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_128,greatest_lower_bound(X_23,X_130)),greatest_lower_bound(X_23,greatest_lower_bound(X_130,X_128))) )],[refute_0_1916,refute_0_1917]) ).
cnf(refute_0_1919,plain,
( greatest_lower_bound(X_23,greatest_lower_bound(X_130,X_128)) != greatest_lower_bound(X_128,greatest_lower_bound(X_23,X_130))
| greatest_lower_bound(greatest_lower_bound(X_130,X_128),greatest_lower_bound(X_22,X_23)) != greatest_lower_bound(X_22,greatest_lower_bound(X_23,greatest_lower_bound(X_130,X_128)))
| greatest_lower_bound(greatest_lower_bound(X_130,X_128),greatest_lower_bound(X_22,X_23)) = greatest_lower_bound(X_22,greatest_lower_bound(X_128,greatest_lower_bound(X_23,X_130))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_130,X_128),greatest_lower_bound(X_22,X_23)),greatest_lower_bound(X_22,greatest_lower_bound(X_23,greatest_lower_bound(X_130,X_128)))) ),[1,1],$fot(greatest_lower_bound(X_128,greatest_lower_bound(X_23,X_130)))]]) ).
cnf(refute_0_1920,plain,
( greatest_lower_bound(greatest_lower_bound(X_130,X_128),greatest_lower_bound(X_22,X_23)) != greatest_lower_bound(X_22,greatest_lower_bound(X_23,greatest_lower_bound(X_130,X_128)))
| greatest_lower_bound(greatest_lower_bound(X_130,X_128),greatest_lower_bound(X_22,X_23)) = greatest_lower_bound(X_22,greatest_lower_bound(X_128,greatest_lower_bound(X_23,X_130))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_23,greatest_lower_bound(X_130,X_128)),greatest_lower_bound(X_128,greatest_lower_bound(X_23,X_130))) )],[refute_0_1918,refute_0_1919]) ).
cnf(refute_0_1921,plain,
greatest_lower_bound(greatest_lower_bound(X_130,X_128),greatest_lower_bound(X_22,X_23)) = greatest_lower_bound(X_22,greatest_lower_bound(X_128,greatest_lower_bound(X_23,X_130))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_130,X_128),greatest_lower_bound(X_22,X_23)),greatest_lower_bound(X_22,greatest_lower_bound(X_23,greatest_lower_bound(X_130,X_128)))) )],[refute_0_1915,refute_0_1920]) ).
cnf(refute_0_1922,plain,
greatest_lower_bound(greatest_lower_bound(X_130,X_128),greatest_lower_bound(X_22,X_23)) = greatest_lower_bound(X_130,greatest_lower_bound(X_128,greatest_lower_bound(X_22,X_23))),
inference(subst,[],[refute_0_343:[bind(X,$fot(X_130)),bind(Y,$fot(X_128)),bind(Z,$fot(greatest_lower_bound(X_22,X_23)))]]) ).
cnf(refute_0_1923,plain,
( greatest_lower_bound(greatest_lower_bound(X_130,X_128),greatest_lower_bound(X_22,X_23)) != greatest_lower_bound(X_130,greatest_lower_bound(X_128,greatest_lower_bound(X_22,X_23)))
| greatest_lower_bound(greatest_lower_bound(X_130,X_128),greatest_lower_bound(X_22,X_23)) != greatest_lower_bound(X_22,greatest_lower_bound(X_128,greatest_lower_bound(X_23,X_130)))
| greatest_lower_bound(X_130,greatest_lower_bound(X_128,greatest_lower_bound(X_22,X_23))) = greatest_lower_bound(X_22,greatest_lower_bound(X_128,greatest_lower_bound(X_23,X_130))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_130,X_128),greatest_lower_bound(X_22,X_23)),greatest_lower_bound(X_22,greatest_lower_bound(X_128,greatest_lower_bound(X_23,X_130)))) ),[0],$fot(greatest_lower_bound(X_130,greatest_lower_bound(X_128,greatest_lower_bound(X_22,X_23))))]]) ).
cnf(refute_0_1924,plain,
( greatest_lower_bound(greatest_lower_bound(X_130,X_128),greatest_lower_bound(X_22,X_23)) != greatest_lower_bound(X_22,greatest_lower_bound(X_128,greatest_lower_bound(X_23,X_130)))
| greatest_lower_bound(X_130,greatest_lower_bound(X_128,greatest_lower_bound(X_22,X_23))) = greatest_lower_bound(X_22,greatest_lower_bound(X_128,greatest_lower_bound(X_23,X_130))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_130,X_128),greatest_lower_bound(X_22,X_23)),greatest_lower_bound(X_130,greatest_lower_bound(X_128,greatest_lower_bound(X_22,X_23)))) )],[refute_0_1922,refute_0_1923]) ).
cnf(refute_0_1925,plain,
greatest_lower_bound(X_130,greatest_lower_bound(X_128,greatest_lower_bound(X_22,X_23))) = greatest_lower_bound(X_22,greatest_lower_bound(X_128,greatest_lower_bound(X_23,X_130))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_130,X_128),greatest_lower_bound(X_22,X_23)),greatest_lower_bound(X_22,greatest_lower_bound(X_128,greatest_lower_bound(X_23,X_130)))) )],[refute_0_1921,refute_0_1924]) ).
cnf(refute_0_1926,plain,
( greatest_lower_bound(X_130,greatest_lower_bound(X_128,greatest_lower_bound(X_22,X_23))) != greatest_lower_bound(X_22,greatest_lower_bound(X_128,greatest_lower_bound(X_23,X_130)))
| greatest_lower_bound(X_22,greatest_lower_bound(X_128,greatest_lower_bound(X_23,X_130))) = greatest_lower_bound(X_130,greatest_lower_bound(X_128,greatest_lower_bound(X_22,X_23))) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(greatest_lower_bound(X_130,greatest_lower_bound(X_128,greatest_lower_bound(X_22,X_23))))),bind(Y0,$fot(greatest_lower_bound(X_22,greatest_lower_bound(X_128,greatest_lower_bound(X_23,X_130)))))]]) ).
cnf(refute_0_1927,plain,
greatest_lower_bound(X_22,greatest_lower_bound(X_128,greatest_lower_bound(X_23,X_130))) = greatest_lower_bound(X_130,greatest_lower_bound(X_128,greatest_lower_bound(X_22,X_23))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_130,greatest_lower_bound(X_128,greatest_lower_bound(X_22,X_23))),greatest_lower_bound(X_22,greatest_lower_bound(X_128,greatest_lower_bound(X_23,X_130)))) )],[refute_0_1925,refute_0_1926]) ).
cnf(refute_0_1928,plain,
greatest_lower_bound(identity,greatest_lower_bound(X_114,greatest_lower_bound(inverse(X_114),identity))) = greatest_lower_bound(identity,greatest_lower_bound(X_114,greatest_lower_bound(identity,inverse(X_114)))),
inference(subst,[],[refute_0_1927:[bind(X_128,$fot(X_114)),bind(X_130,$fot(identity)),bind(X_22,$fot(identity)),bind(X_23,$fot(inverse(X_114)))]]) ).
cnf(refute_0_1929,plain,
( greatest_lower_bound(identity,greatest_lower_bound(X_114,greatest_lower_bound(identity,inverse(X_114)))) != greatest_lower_bound(X_114,greatest_lower_bound(identity,inverse(X_114)))
| greatest_lower_bound(identity,greatest_lower_bound(X_114,greatest_lower_bound(inverse(X_114),identity))) != greatest_lower_bound(identity,greatest_lower_bound(X_114,greatest_lower_bound(identity,inverse(X_114))))
| greatest_lower_bound(identity,greatest_lower_bound(X_114,greatest_lower_bound(inverse(X_114),identity))) = greatest_lower_bound(X_114,greatest_lower_bound(identity,inverse(X_114))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(greatest_lower_bound(identity,greatest_lower_bound(X_114,greatest_lower_bound(inverse(X_114),identity))))),bind(Y0,$fot(greatest_lower_bound(identity,greatest_lower_bound(X_114,greatest_lower_bound(identity,inverse(X_114)))))),bind(Z0,$fot(greatest_lower_bound(X_114,greatest_lower_bound(identity,inverse(X_114)))))]]) ).
cnf(refute_0_1930,plain,
( greatest_lower_bound(identity,greatest_lower_bound(X_114,greatest_lower_bound(identity,inverse(X_114)))) != greatest_lower_bound(X_114,greatest_lower_bound(identity,inverse(X_114)))
| greatest_lower_bound(identity,greatest_lower_bound(X_114,greatest_lower_bound(inverse(X_114),identity))) = greatest_lower_bound(X_114,greatest_lower_bound(identity,inverse(X_114))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_114,greatest_lower_bound(inverse(X_114),identity))),greatest_lower_bound(identity,greatest_lower_bound(X_114,greatest_lower_bound(identity,inverse(X_114))))) )],[refute_0_1928,refute_0_1929]) ).
cnf(refute_0_1931,plain,
greatest_lower_bound(identity,greatest_lower_bound(X_114,greatest_lower_bound(inverse(X_114),identity))) = greatest_lower_bound(X_114,greatest_lower_bound(identity,inverse(X_114))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_114,greatest_lower_bound(identity,inverse(X_114)))),greatest_lower_bound(X_114,greatest_lower_bound(identity,inverse(X_114)))) )],[refute_0_1914,refute_0_1930]) ).
cnf(refute_0_1932,plain,
greatest_lower_bound(X,greatest_lower_bound(X_22,greatest_lower_bound(X_130,X_128))) = greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X)),
inference(subst,[],[refute_0_1460:[bind(X_23,$fot(greatest_lower_bound(X_130,X_128)))]]) ).
cnf(refute_0_1933,plain,
greatest_lower_bound(X_128,greatest_lower_bound(X_22,X_130)) = greatest_lower_bound(X_22,greatest_lower_bound(X_130,X_128)),
inference(subst,[],[refute_0_1460:[bind(X,$fot(X_128)),bind(X_23,$fot(X_130))]]) ).
cnf(refute_0_1934,plain,
( greatest_lower_bound(X_128,greatest_lower_bound(X_22,X_130)) != greatest_lower_bound(X_22,greatest_lower_bound(X_130,X_128))
| greatest_lower_bound(X_22,greatest_lower_bound(X_130,X_128)) = greatest_lower_bound(X_128,greatest_lower_bound(X_22,X_130)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(greatest_lower_bound(X_128,greatest_lower_bound(X_22,X_130)))),bind(Y0,$fot(greatest_lower_bound(X_22,greatest_lower_bound(X_130,X_128))))]]) ).
cnf(refute_0_1935,plain,
greatest_lower_bound(X_22,greatest_lower_bound(X_130,X_128)) = greatest_lower_bound(X_128,greatest_lower_bound(X_22,X_130)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_128,greatest_lower_bound(X_22,X_130)),greatest_lower_bound(X_22,greatest_lower_bound(X_130,X_128))) )],[refute_0_1933,refute_0_1934]) ).
cnf(refute_0_1936,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_22,greatest_lower_bound(X_130,X_128))) != greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X))
| greatest_lower_bound(X_22,greatest_lower_bound(X_130,X_128)) != greatest_lower_bound(X_128,greatest_lower_bound(X_22,X_130))
| greatest_lower_bound(X,greatest_lower_bound(X_128,greatest_lower_bound(X_22,X_130))) = greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_22,greatest_lower_bound(X_130,X_128))),greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X))) ),[0,1],$fot(greatest_lower_bound(X_128,greatest_lower_bound(X_22,X_130)))]]) ).
cnf(refute_0_1937,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_22,greatest_lower_bound(X_130,X_128))) != greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X))
| greatest_lower_bound(X,greatest_lower_bound(X_128,greatest_lower_bound(X_22,X_130))) = greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_22,greatest_lower_bound(X_130,X_128)),greatest_lower_bound(X_128,greatest_lower_bound(X_22,X_130))) )],[refute_0_1935,refute_0_1936]) ).
cnf(refute_0_1938,plain,
greatest_lower_bound(X,greatest_lower_bound(X_128,greatest_lower_bound(X_22,X_130))) = greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_22,greatest_lower_bound(X_130,X_128))),greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X))) )],[refute_0_1932,refute_0_1937]) ).
cnf(refute_0_1939,plain,
greatest_lower_bound(greatest_lower_bound(X_130,X_128),X) = greatest_lower_bound(X_130,greatest_lower_bound(X_128,X)),
inference(subst,[],[refute_0_343:[bind(X,$fot(X_130)),bind(Y,$fot(X_128)),bind(Z,$fot(X))]]) ).
cnf(refute_0_1940,plain,
greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X)) = greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X)))]]) ).
cnf(refute_0_1941,plain,
( greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X)) != greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X))
| greatest_lower_bound(greatest_lower_bound(X_130,X_128),X) != greatest_lower_bound(X_130,greatest_lower_bound(X_128,X))
| greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X)) = greatest_lower_bound(X_22,greatest_lower_bound(X_130,greatest_lower_bound(X_128,X))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X)),greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X))) ),[1,1],$fot(greatest_lower_bound(X_130,greatest_lower_bound(X_128,X)))]]) ).
cnf(refute_0_1942,plain,
( greatest_lower_bound(greatest_lower_bound(X_130,X_128),X) != greatest_lower_bound(X_130,greatest_lower_bound(X_128,X))
| greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X)) = greatest_lower_bound(X_22,greatest_lower_bound(X_130,greatest_lower_bound(X_128,X))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X)),greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X))) )],[refute_0_1940,refute_0_1941]) ).
cnf(refute_0_1943,plain,
greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X)) = greatest_lower_bound(X_22,greatest_lower_bound(X_130,greatest_lower_bound(X_128,X))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_130,X_128),X),greatest_lower_bound(X_130,greatest_lower_bound(X_128,X))) )],[refute_0_1939,refute_0_1942]) ).
cnf(refute_0_1944,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_128,greatest_lower_bound(X_22,X_130))) != greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X))
| greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X)) != greatest_lower_bound(X_22,greatest_lower_bound(X_130,greatest_lower_bound(X_128,X)))
| greatest_lower_bound(X,greatest_lower_bound(X_128,greatest_lower_bound(X_22,X_130))) = greatest_lower_bound(X_22,greatest_lower_bound(X_130,greatest_lower_bound(X_128,X))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X,greatest_lower_bound(X_128,greatest_lower_bound(X_22,X_130))),greatest_lower_bound(X_22,greatest_lower_bound(X_130,greatest_lower_bound(X_128,X)))) ),[0],$fot(greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X)))]]) ).
cnf(refute_0_1945,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_128,greatest_lower_bound(X_22,X_130))) != greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X))
| greatest_lower_bound(X,greatest_lower_bound(X_128,greatest_lower_bound(X_22,X_130))) = greatest_lower_bound(X_22,greatest_lower_bound(X_130,greatest_lower_bound(X_128,X))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X)),greatest_lower_bound(X_22,greatest_lower_bound(X_130,greatest_lower_bound(X_128,X)))) )],[refute_0_1943,refute_0_1944]) ).
cnf(refute_0_1946,plain,
greatest_lower_bound(X,greatest_lower_bound(X_128,greatest_lower_bound(X_22,X_130))) = greatest_lower_bound(X_22,greatest_lower_bound(X_130,greatest_lower_bound(X_128,X))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_128,greatest_lower_bound(X_22,X_130))),greatest_lower_bound(X_22,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X))) )],[refute_0_1938,refute_0_1945]) ).
cnf(refute_0_1947,plain,
greatest_lower_bound(identity,greatest_lower_bound(inverse(X_114),greatest_lower_bound(identity,X_114))) = greatest_lower_bound(identity,greatest_lower_bound(X_114,greatest_lower_bound(inverse(X_114),identity))),
inference(subst,[],[refute_0_1946:[bind(X,$fot(identity)),bind(X_128,$fot(inverse(X_114))),bind(X_130,$fot(X_114)),bind(X_22,$fot(identity))]]) ).
cnf(refute_0_1948,plain,
( greatest_lower_bound(identity,greatest_lower_bound(X_114,greatest_lower_bound(inverse(X_114),identity))) != greatest_lower_bound(X_114,greatest_lower_bound(identity,inverse(X_114)))
| greatest_lower_bound(identity,greatest_lower_bound(inverse(X_114),greatest_lower_bound(identity,X_114))) != greatest_lower_bound(identity,greatest_lower_bound(X_114,greatest_lower_bound(inverse(X_114),identity)))
| greatest_lower_bound(identity,greatest_lower_bound(inverse(X_114),greatest_lower_bound(identity,X_114))) = greatest_lower_bound(X_114,greatest_lower_bound(identity,inverse(X_114))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_114),greatest_lower_bound(identity,X_114))))),bind(Y0,$fot(greatest_lower_bound(identity,greatest_lower_bound(X_114,greatest_lower_bound(inverse(X_114),identity))))),bind(Z0,$fot(greatest_lower_bound(X_114,greatest_lower_bound(identity,inverse(X_114)))))]]) ).
cnf(refute_0_1949,plain,
( greatest_lower_bound(identity,greatest_lower_bound(X_114,greatest_lower_bound(inverse(X_114),identity))) != greatest_lower_bound(X_114,greatest_lower_bound(identity,inverse(X_114)))
| greatest_lower_bound(identity,greatest_lower_bound(inverse(X_114),greatest_lower_bound(identity,X_114))) = greatest_lower_bound(X_114,greatest_lower_bound(identity,inverse(X_114))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_114),greatest_lower_bound(identity,X_114))),greatest_lower_bound(identity,greatest_lower_bound(X_114,greatest_lower_bound(inverse(X_114),identity)))) )],[refute_0_1947,refute_0_1948]) ).
cnf(refute_0_1950,plain,
greatest_lower_bound(identity,greatest_lower_bound(inverse(X_114),greatest_lower_bound(identity,X_114))) = greatest_lower_bound(X_114,greatest_lower_bound(identity,inverse(X_114))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_114,greatest_lower_bound(inverse(X_114),identity))),greatest_lower_bound(X_114,greatest_lower_bound(identity,inverse(X_114)))) )],[refute_0_1931,refute_0_1949]) ).
cnf(refute_0_1951,plain,
greatest_lower_bound(greatest_lower_bound(X_130,X_128),greatest_lower_bound(Y,greatest_lower_bound(X_130,X_128))) = greatest_lower_bound(greatest_lower_bound(X_130,X_128),Y),
inference(subst,[],[refute_0_347:[bind(X_13,$fot(greatest_lower_bound(X_130,X_128)))]]) ).
cnf(refute_0_1952,plain,
greatest_lower_bound(X_128,greatest_lower_bound(Y,X_130)) = greatest_lower_bound(Y,greatest_lower_bound(X_130,X_128)),
inference(subst,[],[refute_0_1460:[bind(X,$fot(X_128)),bind(X_22,$fot(Y)),bind(X_23,$fot(X_130))]]) ).
cnf(refute_0_1953,plain,
( greatest_lower_bound(X_128,greatest_lower_bound(Y,X_130)) != greatest_lower_bound(Y,greatest_lower_bound(X_130,X_128))
| greatest_lower_bound(Y,greatest_lower_bound(X_130,X_128)) = greatest_lower_bound(X_128,greatest_lower_bound(Y,X_130)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(greatest_lower_bound(X_128,greatest_lower_bound(Y,X_130)))),bind(Y0,$fot(greatest_lower_bound(Y,greatest_lower_bound(X_130,X_128))))]]) ).
cnf(refute_0_1954,plain,
greatest_lower_bound(Y,greatest_lower_bound(X_130,X_128)) = greatest_lower_bound(X_128,greatest_lower_bound(Y,X_130)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_128,greatest_lower_bound(Y,X_130)),greatest_lower_bound(Y,greatest_lower_bound(X_130,X_128))) )],[refute_0_1952,refute_0_1953]) ).
cnf(refute_0_1955,plain,
( greatest_lower_bound(Y,greatest_lower_bound(X_130,X_128)) != greatest_lower_bound(X_128,greatest_lower_bound(Y,X_130))
| greatest_lower_bound(greatest_lower_bound(X_130,X_128),greatest_lower_bound(Y,greatest_lower_bound(X_130,X_128))) != greatest_lower_bound(greatest_lower_bound(X_130,X_128),Y)
| greatest_lower_bound(greatest_lower_bound(X_130,X_128),greatest_lower_bound(X_128,greatest_lower_bound(Y,X_130))) = greatest_lower_bound(greatest_lower_bound(X_130,X_128),Y) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_130,X_128),greatest_lower_bound(Y,greatest_lower_bound(X_130,X_128))),greatest_lower_bound(greatest_lower_bound(X_130,X_128),Y)) ),[0,1],$fot(greatest_lower_bound(X_128,greatest_lower_bound(Y,X_130)))]]) ).
cnf(refute_0_1956,plain,
( greatest_lower_bound(greatest_lower_bound(X_130,X_128),greatest_lower_bound(Y,greatest_lower_bound(X_130,X_128))) != greatest_lower_bound(greatest_lower_bound(X_130,X_128),Y)
| greatest_lower_bound(greatest_lower_bound(X_130,X_128),greatest_lower_bound(X_128,greatest_lower_bound(Y,X_130))) = greatest_lower_bound(greatest_lower_bound(X_130,X_128),Y) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(X_130,X_128)),greatest_lower_bound(X_128,greatest_lower_bound(Y,X_130))) )],[refute_0_1954,refute_0_1955]) ).
cnf(refute_0_1957,plain,
greatest_lower_bound(greatest_lower_bound(X_130,X_128),greatest_lower_bound(X_128,greatest_lower_bound(Y,X_130))) = greatest_lower_bound(greatest_lower_bound(X_130,X_128),Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_130,X_128),greatest_lower_bound(Y,greatest_lower_bound(X_130,X_128))),greatest_lower_bound(greatest_lower_bound(X_130,X_128),Y)) )],[refute_0_1951,refute_0_1956]) ).
cnf(refute_0_1958,plain,
greatest_lower_bound(X_13,greatest_lower_bound(greatest_lower_bound(X_22,X_23),X_13)) = greatest_lower_bound(X_13,greatest_lower_bound(X_22,X_23)),
inference(subst,[],[refute_0_347:[bind(Y,$fot(greatest_lower_bound(X_22,X_23)))]]) ).
cnf(refute_0_1959,plain,
greatest_lower_bound(X_22,greatest_lower_bound(X_23,X_13)) = greatest_lower_bound(greatest_lower_bound(X_22,X_23),X_13),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_22)),bind(Y,$fot(X_23)),bind(Z,$fot(X_13))]]) ).
cnf(refute_0_1960,plain,
( greatest_lower_bound(X_22,greatest_lower_bound(X_23,X_13)) != greatest_lower_bound(greatest_lower_bound(X_22,X_23),X_13)
| greatest_lower_bound(greatest_lower_bound(X_22,X_23),X_13) = greatest_lower_bound(X_22,greatest_lower_bound(X_23,X_13)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(greatest_lower_bound(X_22,greatest_lower_bound(X_23,X_13)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X_22,X_23),X_13)))]]) ).
cnf(refute_0_1961,plain,
greatest_lower_bound(greatest_lower_bound(X_22,X_23),X_13) = greatest_lower_bound(X_22,greatest_lower_bound(X_23,X_13)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_22,greatest_lower_bound(X_23,X_13)),greatest_lower_bound(greatest_lower_bound(X_22,X_23),X_13)) )],[refute_0_1959,refute_0_1960]) ).
cnf(refute_0_1962,plain,
( greatest_lower_bound(X_13,greatest_lower_bound(greatest_lower_bound(X_22,X_23),X_13)) != greatest_lower_bound(X_13,greatest_lower_bound(X_22,X_23))
| greatest_lower_bound(greatest_lower_bound(X_22,X_23),X_13) != greatest_lower_bound(X_22,greatest_lower_bound(X_23,X_13))
| greatest_lower_bound(X_13,greatest_lower_bound(X_22,greatest_lower_bound(X_23,X_13))) = greatest_lower_bound(X_13,greatest_lower_bound(X_22,X_23)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_13,greatest_lower_bound(greatest_lower_bound(X_22,X_23),X_13)),greatest_lower_bound(X_13,greatest_lower_bound(X_22,X_23))) ),[0,1],$fot(greatest_lower_bound(X_22,greatest_lower_bound(X_23,X_13)))]]) ).
cnf(refute_0_1963,plain,
( greatest_lower_bound(X_13,greatest_lower_bound(greatest_lower_bound(X_22,X_23),X_13)) != greatest_lower_bound(X_13,greatest_lower_bound(X_22,X_23))
| greatest_lower_bound(X_13,greatest_lower_bound(X_22,greatest_lower_bound(X_23,X_13))) = greatest_lower_bound(X_13,greatest_lower_bound(X_22,X_23)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_22,X_23),X_13),greatest_lower_bound(X_22,greatest_lower_bound(X_23,X_13))) )],[refute_0_1961,refute_0_1962]) ).
cnf(refute_0_1964,plain,
greatest_lower_bound(X_13,greatest_lower_bound(X_22,greatest_lower_bound(X_23,X_13))) = greatest_lower_bound(X_13,greatest_lower_bound(X_22,X_23)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_13,greatest_lower_bound(greatest_lower_bound(X_22,X_23),X_13)),greatest_lower_bound(X_13,greatest_lower_bound(X_22,X_23))) )],[refute_0_1958,refute_0_1963]) ).
cnf(refute_0_1965,plain,
greatest_lower_bound(X_130,greatest_lower_bound(Y,greatest_lower_bound(X_128,X_130))) = greatest_lower_bound(X_130,greatest_lower_bound(Y,X_128)),
inference(subst,[],[refute_0_1964:[bind(X_13,$fot(X_130)),bind(X_22,$fot(Y)),bind(X_23,$fot(X_128))]]) ).
cnf(refute_0_1966,plain,
greatest_lower_bound(X_128,greatest_lower_bound(X_130,X_128)) = greatest_lower_bound(X_128,X_130),
inference(subst,[],[refute_0_347:[bind(Y,$fot(X_130)),bind(X_13,$fot(X_128))]]) ).
cnf(refute_0_1967,plain,
greatest_lower_bound(Y,greatest_lower_bound(X_128,greatest_lower_bound(X_130,X_128))) = greatest_lower_bound(Y,greatest_lower_bound(X_128,greatest_lower_bound(X_130,X_128))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(Y,greatest_lower_bound(X_128,greatest_lower_bound(X_130,X_128))))]]) ).
cnf(refute_0_1968,plain,
( greatest_lower_bound(Y,greatest_lower_bound(X_128,greatest_lower_bound(X_130,X_128))) != greatest_lower_bound(Y,greatest_lower_bound(X_128,greatest_lower_bound(X_130,X_128)))
| greatest_lower_bound(X_128,greatest_lower_bound(X_130,X_128)) != greatest_lower_bound(X_128,X_130)
| greatest_lower_bound(Y,greatest_lower_bound(X_128,greatest_lower_bound(X_130,X_128))) = greatest_lower_bound(Y,greatest_lower_bound(X_128,X_130)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(X_128,greatest_lower_bound(X_130,X_128))),greatest_lower_bound(Y,greatest_lower_bound(X_128,greatest_lower_bound(X_130,X_128)))) ),[1,1],$fot(greatest_lower_bound(X_128,X_130))]]) ).
cnf(refute_0_1969,plain,
( greatest_lower_bound(X_128,greatest_lower_bound(X_130,X_128)) != greatest_lower_bound(X_128,X_130)
| greatest_lower_bound(Y,greatest_lower_bound(X_128,greatest_lower_bound(X_130,X_128))) = greatest_lower_bound(Y,greatest_lower_bound(X_128,X_130)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(X_128,greatest_lower_bound(X_130,X_128))),greatest_lower_bound(Y,greatest_lower_bound(X_128,greatest_lower_bound(X_130,X_128)))) )],[refute_0_1967,refute_0_1968]) ).
cnf(refute_0_1970,plain,
greatest_lower_bound(Y,greatest_lower_bound(X_128,greatest_lower_bound(X_130,X_128))) = greatest_lower_bound(Y,greatest_lower_bound(X_128,X_130)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_128,greatest_lower_bound(X_130,X_128)),greatest_lower_bound(X_128,X_130)) )],[refute_0_1966,refute_0_1969]) ).
cnf(refute_0_1971,plain,
greatest_lower_bound(greatest_lower_bound(X_102,greatest_lower_bound(X_103,X_7)),least_upper_bound(X_7,greatest_lower_bound(X_102,greatest_lower_bound(X_103,X_7)))) = greatest_lower_bound(X_102,greatest_lower_bound(X_103,X_7)),
inference(subst,[],[refute_0_153:[bind(X_6,$fot(greatest_lower_bound(X_102,greatest_lower_bound(X_103,X_7))))]]) ).
cnf(refute_0_1972,plain,
least_upper_bound(X_10,greatest_lower_bound(greatest_lower_bound(X_22,X_23),X_10)) = X_10,
inference(subst,[],[refute_0_145:[bind(X_11,$fot(greatest_lower_bound(X_22,X_23)))]]) ).
cnf(refute_0_1973,plain,
greatest_lower_bound(X_22,greatest_lower_bound(X_23,X_10)) = greatest_lower_bound(greatest_lower_bound(X_22,X_23),X_10),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_22)),bind(Y,$fot(X_23)),bind(Z,$fot(X_10))]]) ).
cnf(refute_0_1974,plain,
( greatest_lower_bound(X_22,greatest_lower_bound(X_23,X_10)) != greatest_lower_bound(greatest_lower_bound(X_22,X_23),X_10)
| greatest_lower_bound(greatest_lower_bound(X_22,X_23),X_10) = greatest_lower_bound(X_22,greatest_lower_bound(X_23,X_10)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(greatest_lower_bound(X_22,greatest_lower_bound(X_23,X_10)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X_22,X_23),X_10)))]]) ).
cnf(refute_0_1975,plain,
greatest_lower_bound(greatest_lower_bound(X_22,X_23),X_10) = greatest_lower_bound(X_22,greatest_lower_bound(X_23,X_10)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_22,greatest_lower_bound(X_23,X_10)),greatest_lower_bound(greatest_lower_bound(X_22,X_23),X_10)) )],[refute_0_1973,refute_0_1974]) ).
cnf(refute_0_1976,plain,
( greatest_lower_bound(greatest_lower_bound(X_22,X_23),X_10) != greatest_lower_bound(X_22,greatest_lower_bound(X_23,X_10))
| least_upper_bound(X_10,greatest_lower_bound(greatest_lower_bound(X_22,X_23),X_10)) != X_10
| least_upper_bound(X_10,greatest_lower_bound(X_22,greatest_lower_bound(X_23,X_10))) = X_10 ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_10,greatest_lower_bound(greatest_lower_bound(X_22,X_23),X_10)),X_10) ),[0,1],$fot(greatest_lower_bound(X_22,greatest_lower_bound(X_23,X_10)))]]) ).
cnf(refute_0_1977,plain,
( least_upper_bound(X_10,greatest_lower_bound(greatest_lower_bound(X_22,X_23),X_10)) != X_10
| least_upper_bound(X_10,greatest_lower_bound(X_22,greatest_lower_bound(X_23,X_10))) = X_10 ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_22,X_23),X_10),greatest_lower_bound(X_22,greatest_lower_bound(X_23,X_10))) )],[refute_0_1975,refute_0_1976]) ).
cnf(refute_0_1978,plain,
least_upper_bound(X_10,greatest_lower_bound(X_22,greatest_lower_bound(X_23,X_10))) = X_10,
inference(resolve,[$cnf( $equal(least_upper_bound(X_10,greatest_lower_bound(greatest_lower_bound(X_22,X_23),X_10)),X_10) )],[refute_0_1972,refute_0_1977]) ).
cnf(refute_0_1979,plain,
least_upper_bound(X_7,greatest_lower_bound(X_102,greatest_lower_bound(X_103,X_7))) = X_7,
inference(subst,[],[refute_0_1978:[bind(X_10,$fot(X_7)),bind(X_22,$fot(X_102)),bind(X_23,$fot(X_103))]]) ).
cnf(refute_0_1980,plain,
( greatest_lower_bound(greatest_lower_bound(X_102,greatest_lower_bound(X_103,X_7)),least_upper_bound(X_7,greatest_lower_bound(X_102,greatest_lower_bound(X_103,X_7)))) != greatest_lower_bound(X_102,greatest_lower_bound(X_103,X_7))
| least_upper_bound(X_7,greatest_lower_bound(X_102,greatest_lower_bound(X_103,X_7))) != X_7
| greatest_lower_bound(greatest_lower_bound(X_102,greatest_lower_bound(X_103,X_7)),X_7) = greatest_lower_bound(X_102,greatest_lower_bound(X_103,X_7)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_102,greatest_lower_bound(X_103,X_7)),least_upper_bound(X_7,greatest_lower_bound(X_102,greatest_lower_bound(X_103,X_7)))),greatest_lower_bound(X_102,greatest_lower_bound(X_103,X_7))) ),[0,1],$fot(X_7)]]) ).
cnf(refute_0_1981,plain,
( greatest_lower_bound(greatest_lower_bound(X_102,greatest_lower_bound(X_103,X_7)),least_upper_bound(X_7,greatest_lower_bound(X_102,greatest_lower_bound(X_103,X_7)))) != greatest_lower_bound(X_102,greatest_lower_bound(X_103,X_7))
| greatest_lower_bound(greatest_lower_bound(X_102,greatest_lower_bound(X_103,X_7)),X_7) = greatest_lower_bound(X_102,greatest_lower_bound(X_103,X_7)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_7,greatest_lower_bound(X_102,greatest_lower_bound(X_103,X_7))),X_7) )],[refute_0_1979,refute_0_1980]) ).
cnf(refute_0_1982,plain,
greatest_lower_bound(greatest_lower_bound(X_102,greatest_lower_bound(X_103,X_7)),X_7) = greatest_lower_bound(X_102,greatest_lower_bound(X_103,X_7)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_102,greatest_lower_bound(X_103,X_7)),least_upper_bound(X_7,greatest_lower_bound(X_102,greatest_lower_bound(X_103,X_7)))),greatest_lower_bound(X_102,greatest_lower_bound(X_103,X_7))) )],[refute_0_1971,refute_0_1981]) ).
cnf(refute_0_1983,plain,
greatest_lower_bound(X_7,greatest_lower_bound(X_103,X_7)) = greatest_lower_bound(X_7,X_103),
inference(subst,[],[refute_0_347:[bind(Y,$fot(X_103)),bind(X_13,$fot(X_7))]]) ).
cnf(refute_0_1984,plain,
greatest_lower_bound(X_102,greatest_lower_bound(X_7,greatest_lower_bound(X_103,X_7))) = greatest_lower_bound(X_102,greatest_lower_bound(X_7,greatest_lower_bound(X_103,X_7))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X_102,greatest_lower_bound(X_7,greatest_lower_bound(X_103,X_7))))]]) ).
cnf(refute_0_1985,plain,
( greatest_lower_bound(X_102,greatest_lower_bound(X_7,greatest_lower_bound(X_103,X_7))) != greatest_lower_bound(X_102,greatest_lower_bound(X_7,greatest_lower_bound(X_103,X_7)))
| greatest_lower_bound(X_7,greatest_lower_bound(X_103,X_7)) != greatest_lower_bound(X_7,X_103)
| greatest_lower_bound(X_102,greatest_lower_bound(X_7,greatest_lower_bound(X_103,X_7))) = greatest_lower_bound(X_102,greatest_lower_bound(X_7,X_103)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_102,greatest_lower_bound(X_7,greatest_lower_bound(X_103,X_7))),greatest_lower_bound(X_102,greatest_lower_bound(X_7,greatest_lower_bound(X_103,X_7)))) ),[1,1],$fot(greatest_lower_bound(X_7,X_103))]]) ).
cnf(refute_0_1986,plain,
( greatest_lower_bound(X_7,greatest_lower_bound(X_103,X_7)) != greatest_lower_bound(X_7,X_103)
| greatest_lower_bound(X_102,greatest_lower_bound(X_7,greatest_lower_bound(X_103,X_7))) = greatest_lower_bound(X_102,greatest_lower_bound(X_7,X_103)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_102,greatest_lower_bound(X_7,greatest_lower_bound(X_103,X_7))),greatest_lower_bound(X_102,greatest_lower_bound(X_7,greatest_lower_bound(X_103,X_7)))) )],[refute_0_1984,refute_0_1985]) ).
cnf(refute_0_1987,plain,
greatest_lower_bound(X_102,greatest_lower_bound(X_7,greatest_lower_bound(X_103,X_7))) = greatest_lower_bound(X_102,greatest_lower_bound(X_7,X_103)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_7,greatest_lower_bound(X_103,X_7)),greatest_lower_bound(X_7,X_103)) )],[refute_0_1983,refute_0_1986]) ).
cnf(refute_0_1988,plain,
greatest_lower_bound(X_22,greatest_lower_bound(X_23,X_24)) = greatest_lower_bound(greatest_lower_bound(X_22,X_23),X_24),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_22)),bind(Y,$fot(X_23)),bind(Z,$fot(X_24))]]) ).
cnf(refute_0_1989,plain,
greatest_lower_bound(X_24,X_23) = greatest_lower_bound(X_23,X_24),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_24)),bind(Y,$fot(X_23))]]) ).
cnf(refute_0_1990,plain,
( greatest_lower_bound(X_24,X_23) != greatest_lower_bound(X_23,X_24)
| greatest_lower_bound(X_23,X_24) = greatest_lower_bound(X_24,X_23) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(greatest_lower_bound(X_24,X_23))),bind(Y0,$fot(greatest_lower_bound(X_23,X_24)))]]) ).
cnf(refute_0_1991,plain,
greatest_lower_bound(X_23,X_24) = greatest_lower_bound(X_24,X_23),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_24,X_23),greatest_lower_bound(X_23,X_24)) )],[refute_0_1989,refute_0_1990]) ).
cnf(refute_0_1992,plain,
( greatest_lower_bound(X_22,greatest_lower_bound(X_23,X_24)) != greatest_lower_bound(greatest_lower_bound(X_22,X_23),X_24)
| greatest_lower_bound(X_23,X_24) != greatest_lower_bound(X_24,X_23)
| greatest_lower_bound(X_22,greatest_lower_bound(X_24,X_23)) = greatest_lower_bound(greatest_lower_bound(X_22,X_23),X_24) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_22,greatest_lower_bound(X_23,X_24)),greatest_lower_bound(greatest_lower_bound(X_22,X_23),X_24)) ),[0,1],$fot(greatest_lower_bound(X_24,X_23))]]) ).
cnf(refute_0_1993,plain,
( greatest_lower_bound(X_22,greatest_lower_bound(X_23,X_24)) != greatest_lower_bound(greatest_lower_bound(X_22,X_23),X_24)
| greatest_lower_bound(X_22,greatest_lower_bound(X_24,X_23)) = greatest_lower_bound(greatest_lower_bound(X_22,X_23),X_24) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_23,X_24),greatest_lower_bound(X_24,X_23)) )],[refute_0_1991,refute_0_1992]) ).
cnf(refute_0_1994,plain,
greatest_lower_bound(X_22,greatest_lower_bound(X_24,X_23)) = greatest_lower_bound(greatest_lower_bound(X_22,X_23),X_24),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_22,greatest_lower_bound(X_23,X_24)),greatest_lower_bound(greatest_lower_bound(X_22,X_23),X_24)) )],[refute_0_1988,refute_0_1993]) ).
cnf(refute_0_1995,plain,
greatest_lower_bound(greatest_lower_bound(X_22,X_23),X_24) = greatest_lower_bound(X_22,greatest_lower_bound(X_23,X_24)),
inference(subst,[],[refute_0_343:[bind(X,$fot(X_22)),bind(Y,$fot(X_23)),bind(Z,$fot(X_24))]]) ).
cnf(refute_0_1996,plain,
( greatest_lower_bound(X_22,greatest_lower_bound(X_24,X_23)) != greatest_lower_bound(greatest_lower_bound(X_22,X_23),X_24)
| greatest_lower_bound(greatest_lower_bound(X_22,X_23),X_24) != greatest_lower_bound(X_22,greatest_lower_bound(X_23,X_24))
| greatest_lower_bound(X_22,greatest_lower_bound(X_24,X_23)) = greatest_lower_bound(X_22,greatest_lower_bound(X_23,X_24)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_22,greatest_lower_bound(X_24,X_23)),greatest_lower_bound(X_22,greatest_lower_bound(X_23,X_24))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_22,X_23),X_24))]]) ).
cnf(refute_0_1997,plain,
( greatest_lower_bound(X_22,greatest_lower_bound(X_24,X_23)) != greatest_lower_bound(greatest_lower_bound(X_22,X_23),X_24)
| greatest_lower_bound(X_22,greatest_lower_bound(X_24,X_23)) = greatest_lower_bound(X_22,greatest_lower_bound(X_23,X_24)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_22,X_23),X_24),greatest_lower_bound(X_22,greatest_lower_bound(X_23,X_24))) )],[refute_0_1995,refute_0_1996]) ).
cnf(refute_0_1998,plain,
greatest_lower_bound(X_22,greatest_lower_bound(X_24,X_23)) = greatest_lower_bound(X_22,greatest_lower_bound(X_23,X_24)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_22,greatest_lower_bound(X_24,X_23)),greatest_lower_bound(greatest_lower_bound(X_22,X_23),X_24)) )],[refute_0_1994,refute_0_1997]) ).
cnf(refute_0_1999,plain,
( greatest_lower_bound(X_22,greatest_lower_bound(X_24,X_23)) != greatest_lower_bound(X_22,greatest_lower_bound(X_23,X_24))
| greatest_lower_bound(X_22,greatest_lower_bound(X_23,X_24)) = greatest_lower_bound(X_22,greatest_lower_bound(X_24,X_23)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(greatest_lower_bound(X_22,greatest_lower_bound(X_24,X_23)))),bind(Y0,$fot(greatest_lower_bound(X_22,greatest_lower_bound(X_23,X_24))))]]) ).
cnf(refute_0_2000,plain,
greatest_lower_bound(X_22,greatest_lower_bound(X_23,X_24)) = greatest_lower_bound(X_22,greatest_lower_bound(X_24,X_23)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_22,greatest_lower_bound(X_24,X_23)),greatest_lower_bound(X_22,greatest_lower_bound(X_23,X_24))) )],[refute_0_1998,refute_0_1999]) ).
cnf(refute_0_2001,plain,
greatest_lower_bound(X_102,greatest_lower_bound(greatest_lower_bound(X_103,X_7),X_7)) = greatest_lower_bound(X_102,greatest_lower_bound(X_7,greatest_lower_bound(X_103,X_7))),
inference(subst,[],[refute_0_2000:[bind(X_22,$fot(X_102)),bind(X_23,$fot(greatest_lower_bound(X_103,X_7))),bind(X_24,$fot(X_7))]]) ).
cnf(refute_0_2002,plain,
greatest_lower_bound(greatest_lower_bound(X_102,greatest_lower_bound(X_103,X_7)),X_7) = greatest_lower_bound(X_102,greatest_lower_bound(greatest_lower_bound(X_103,X_7),X_7)),
inference(subst,[],[refute_0_343:[bind(X,$fot(X_102)),bind(Y,$fot(greatest_lower_bound(X_103,X_7))),bind(Z,$fot(X_7))]]) ).
cnf(refute_0_2003,plain,
( greatest_lower_bound(X_102,greatest_lower_bound(greatest_lower_bound(X_103,X_7),X_7)) != greatest_lower_bound(X_102,greatest_lower_bound(X_7,greatest_lower_bound(X_103,X_7)))
| greatest_lower_bound(greatest_lower_bound(X_102,greatest_lower_bound(X_103,X_7)),X_7) != greatest_lower_bound(X_102,greatest_lower_bound(greatest_lower_bound(X_103,X_7),X_7))
| greatest_lower_bound(greatest_lower_bound(X_102,greatest_lower_bound(X_103,X_7)),X_7) = greatest_lower_bound(X_102,greatest_lower_bound(X_7,greatest_lower_bound(X_103,X_7))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(X_102,greatest_lower_bound(X_103,X_7)),X_7))),bind(Y0,$fot(greatest_lower_bound(X_102,greatest_lower_bound(greatest_lower_bound(X_103,X_7),X_7)))),bind(Z0,$fot(greatest_lower_bound(X_102,greatest_lower_bound(X_7,greatest_lower_bound(X_103,X_7)))))]]) ).
cnf(refute_0_2004,plain,
( greatest_lower_bound(X_102,greatest_lower_bound(greatest_lower_bound(X_103,X_7),X_7)) != greatest_lower_bound(X_102,greatest_lower_bound(X_7,greatest_lower_bound(X_103,X_7)))
| greatest_lower_bound(greatest_lower_bound(X_102,greatest_lower_bound(X_103,X_7)),X_7) = greatest_lower_bound(X_102,greatest_lower_bound(X_7,greatest_lower_bound(X_103,X_7))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_102,greatest_lower_bound(X_103,X_7)),X_7),greatest_lower_bound(X_102,greatest_lower_bound(greatest_lower_bound(X_103,X_7),X_7))) )],[refute_0_2002,refute_0_2003]) ).
cnf(refute_0_2005,plain,
greatest_lower_bound(greatest_lower_bound(X_102,greatest_lower_bound(X_103,X_7)),X_7) = greatest_lower_bound(X_102,greatest_lower_bound(X_7,greatest_lower_bound(X_103,X_7))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_102,greatest_lower_bound(greatest_lower_bound(X_103,X_7),X_7)),greatest_lower_bound(X_102,greatest_lower_bound(X_7,greatest_lower_bound(X_103,X_7)))) )],[refute_0_2001,refute_0_2004]) ).
cnf(refute_0_2006,plain,
( greatest_lower_bound(X_102,greatest_lower_bound(X_7,greatest_lower_bound(X_103,X_7))) != greatest_lower_bound(X_102,greatest_lower_bound(X_7,X_103))
| greatest_lower_bound(greatest_lower_bound(X_102,greatest_lower_bound(X_103,X_7)),X_7) != greatest_lower_bound(X_102,greatest_lower_bound(X_7,greatest_lower_bound(X_103,X_7)))
| greatest_lower_bound(greatest_lower_bound(X_102,greatest_lower_bound(X_103,X_7)),X_7) = greatest_lower_bound(X_102,greatest_lower_bound(X_7,X_103)) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(X_102,greatest_lower_bound(X_103,X_7)),X_7))),bind(Y0,$fot(greatest_lower_bound(X_102,greatest_lower_bound(X_7,greatest_lower_bound(X_103,X_7))))),bind(Z0,$fot(greatest_lower_bound(X_102,greatest_lower_bound(X_7,X_103))))]]) ).
cnf(refute_0_2007,plain,
( greatest_lower_bound(X_102,greatest_lower_bound(X_7,greatest_lower_bound(X_103,X_7))) != greatest_lower_bound(X_102,greatest_lower_bound(X_7,X_103))
| greatest_lower_bound(greatest_lower_bound(X_102,greatest_lower_bound(X_103,X_7)),X_7) = greatest_lower_bound(X_102,greatest_lower_bound(X_7,X_103)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_102,greatest_lower_bound(X_103,X_7)),X_7),greatest_lower_bound(X_102,greatest_lower_bound(X_7,greatest_lower_bound(X_103,X_7)))) )],[refute_0_2005,refute_0_2006]) ).
cnf(refute_0_2008,plain,
greatest_lower_bound(greatest_lower_bound(X_102,greatest_lower_bound(X_103,X_7)),X_7) = greatest_lower_bound(X_102,greatest_lower_bound(X_7,X_103)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_102,greatest_lower_bound(X_7,greatest_lower_bound(X_103,X_7))),greatest_lower_bound(X_102,greatest_lower_bound(X_7,X_103))) )],[refute_0_1987,refute_0_2007]) ).
cnf(refute_0_2009,plain,
( greatest_lower_bound(greatest_lower_bound(X_102,greatest_lower_bound(X_103,X_7)),X_7) != greatest_lower_bound(X_102,greatest_lower_bound(X_103,X_7))
| greatest_lower_bound(greatest_lower_bound(X_102,greatest_lower_bound(X_103,X_7)),X_7) != greatest_lower_bound(X_102,greatest_lower_bound(X_7,X_103))
| greatest_lower_bound(X_102,greatest_lower_bound(X_7,X_103)) = greatest_lower_bound(X_102,greatest_lower_bound(X_103,X_7)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_102,greatest_lower_bound(X_103,X_7)),X_7),greatest_lower_bound(X_102,greatest_lower_bound(X_103,X_7))) ),[0],$fot(greatest_lower_bound(X_102,greatest_lower_bound(X_7,X_103)))]]) ).
cnf(refute_0_2010,plain,
( greatest_lower_bound(greatest_lower_bound(X_102,greatest_lower_bound(X_103,X_7)),X_7) != greatest_lower_bound(X_102,greatest_lower_bound(X_103,X_7))
| greatest_lower_bound(X_102,greatest_lower_bound(X_7,X_103)) = greatest_lower_bound(X_102,greatest_lower_bound(X_103,X_7)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_102,greatest_lower_bound(X_103,X_7)),X_7),greatest_lower_bound(X_102,greatest_lower_bound(X_7,X_103))) )],[refute_0_2008,refute_0_2009]) ).
cnf(refute_0_2011,plain,
greatest_lower_bound(X_102,greatest_lower_bound(X_7,X_103)) = greatest_lower_bound(X_102,greatest_lower_bound(X_103,X_7)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_102,greatest_lower_bound(X_103,X_7)),X_7),greatest_lower_bound(X_102,greatest_lower_bound(X_103,X_7))) )],[refute_0_1982,refute_0_2010]) ).
cnf(refute_0_2012,plain,
( greatest_lower_bound(X_102,greatest_lower_bound(X_7,X_103)) != greatest_lower_bound(X_102,greatest_lower_bound(X_103,X_7))
| greatest_lower_bound(X_102,greatest_lower_bound(X_103,X_7)) = greatest_lower_bound(X_102,greatest_lower_bound(X_7,X_103)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(greatest_lower_bound(X_102,greatest_lower_bound(X_7,X_103)))),bind(Y0,$fot(greatest_lower_bound(X_102,greatest_lower_bound(X_103,X_7))))]]) ).
cnf(refute_0_2013,plain,
greatest_lower_bound(X_102,greatest_lower_bound(X_103,X_7)) = greatest_lower_bound(X_102,greatest_lower_bound(X_7,X_103)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_102,greatest_lower_bound(X_7,X_103)),greatest_lower_bound(X_102,greatest_lower_bound(X_103,X_7))) )],[refute_0_2011,refute_0_2012]) ).
cnf(refute_0_2014,plain,
greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X_128)) = greatest_lower_bound(Y,greatest_lower_bound(X_128,greatest_lower_bound(X_130,X_128))),
inference(subst,[],[refute_0_2013:[bind(X_102,$fot(Y)),bind(X_103,$fot(greatest_lower_bound(X_130,X_128))),bind(X_7,$fot(X_128))]]) ).
cnf(refute_0_2015,plain,
( greatest_lower_bound(Y,greatest_lower_bound(X_128,greatest_lower_bound(X_130,X_128))) != greatest_lower_bound(Y,greatest_lower_bound(X_128,X_130))
| greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X_128)) != greatest_lower_bound(Y,greatest_lower_bound(X_128,greatest_lower_bound(X_130,X_128)))
| greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X_128)) = greatest_lower_bound(Y,greatest_lower_bound(X_128,X_130)) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X_128)))),bind(Y0,$fot(greatest_lower_bound(Y,greatest_lower_bound(X_128,greatest_lower_bound(X_130,X_128))))),bind(Z0,$fot(greatest_lower_bound(Y,greatest_lower_bound(X_128,X_130))))]]) ).
cnf(refute_0_2016,plain,
( greatest_lower_bound(Y,greatest_lower_bound(X_128,greatest_lower_bound(X_130,X_128))) != greatest_lower_bound(Y,greatest_lower_bound(X_128,X_130))
| greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X_128)) = greatest_lower_bound(Y,greatest_lower_bound(X_128,X_130)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X_128)),greatest_lower_bound(Y,greatest_lower_bound(X_128,greatest_lower_bound(X_130,X_128)))) )],[refute_0_2014,refute_0_2015]) ).
cnf(refute_0_2017,plain,
greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X_128)) = greatest_lower_bound(Y,greatest_lower_bound(X_128,X_130)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(X_128,greatest_lower_bound(X_130,X_128))),greatest_lower_bound(Y,greatest_lower_bound(X_128,X_130))) )],[refute_0_1970,refute_0_2016]) ).
cnf(refute_0_2018,plain,
greatest_lower_bound(X_130,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X_128))) = greatest_lower_bound(X_130,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X_128))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X_130,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X_128))))]]) ).
cnf(refute_0_2019,plain,
( greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X_128)) != greatest_lower_bound(Y,greatest_lower_bound(X_128,X_130))
| greatest_lower_bound(X_130,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X_128))) != greatest_lower_bound(X_130,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X_128)))
| greatest_lower_bound(X_130,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X_128))) = greatest_lower_bound(X_130,greatest_lower_bound(Y,greatest_lower_bound(X_128,X_130))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_130,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X_128))),greatest_lower_bound(X_130,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X_128)))) ),[1,1],$fot(greatest_lower_bound(Y,greatest_lower_bound(X_128,X_130)))]]) ).
cnf(refute_0_2020,plain,
( greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X_128)) != greatest_lower_bound(Y,greatest_lower_bound(X_128,X_130))
| greatest_lower_bound(X_130,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X_128))) = greatest_lower_bound(X_130,greatest_lower_bound(Y,greatest_lower_bound(X_128,X_130))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_130,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X_128))),greatest_lower_bound(X_130,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X_128)))) )],[refute_0_2018,refute_0_2019]) ).
cnf(refute_0_2021,plain,
greatest_lower_bound(X_130,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X_128))) = greatest_lower_bound(X_130,greatest_lower_bound(Y,greatest_lower_bound(X_128,X_130))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X_128)),greatest_lower_bound(Y,greatest_lower_bound(X_128,X_130))) )],[refute_0_2017,refute_0_2020]) ).
cnf(refute_0_2022,plain,
( greatest_lower_bound(X_130,greatest_lower_bound(Y,greatest_lower_bound(X_128,X_130))) != greatest_lower_bound(X_130,greatest_lower_bound(Y,X_128))
| greatest_lower_bound(X_130,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X_128))) != greatest_lower_bound(X_130,greatest_lower_bound(Y,greatest_lower_bound(X_128,X_130)))
| greatest_lower_bound(X_130,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X_128))) = greatest_lower_bound(X_130,greatest_lower_bound(Y,X_128)) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(greatest_lower_bound(X_130,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X_128))))),bind(Y0,$fot(greatest_lower_bound(X_130,greatest_lower_bound(Y,greatest_lower_bound(X_128,X_130))))),bind(Z0,$fot(greatest_lower_bound(X_130,greatest_lower_bound(Y,X_128))))]]) ).
cnf(refute_0_2023,plain,
( greatest_lower_bound(X_130,greatest_lower_bound(Y,greatest_lower_bound(X_128,X_130))) != greatest_lower_bound(X_130,greatest_lower_bound(Y,X_128))
| greatest_lower_bound(X_130,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X_128))) = greatest_lower_bound(X_130,greatest_lower_bound(Y,X_128)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_130,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X_128))),greatest_lower_bound(X_130,greatest_lower_bound(Y,greatest_lower_bound(X_128,X_130)))) )],[refute_0_2021,refute_0_2022]) ).
cnf(refute_0_2024,plain,
greatest_lower_bound(X_130,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X_128))) = greatest_lower_bound(X_130,greatest_lower_bound(Y,X_128)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_130,greatest_lower_bound(Y,greatest_lower_bound(X_128,X_130))),greatest_lower_bound(X_130,greatest_lower_bound(Y,X_128))) )],[refute_0_1965,refute_0_2023]) ).
cnf(refute_0_2025,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_128,greatest_lower_bound(X_22,X_130))) != greatest_lower_bound(X_22,greatest_lower_bound(X_130,greatest_lower_bound(X_128,X)))
| greatest_lower_bound(X_22,greatest_lower_bound(X_130,greatest_lower_bound(X_128,X))) = greatest_lower_bound(X,greatest_lower_bound(X_128,greatest_lower_bound(X_22,X_130))) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(X_128,greatest_lower_bound(X_22,X_130))))),bind(Y0,$fot(greatest_lower_bound(X_22,greatest_lower_bound(X_130,greatest_lower_bound(X_128,X)))))]]) ).
cnf(refute_0_2026,plain,
greatest_lower_bound(X_22,greatest_lower_bound(X_130,greatest_lower_bound(X_128,X))) = greatest_lower_bound(X,greatest_lower_bound(X_128,greatest_lower_bound(X_22,X_130))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_128,greatest_lower_bound(X_22,X_130))),greatest_lower_bound(X_22,greatest_lower_bound(X_130,greatest_lower_bound(X_128,X)))) )],[refute_0_1946,refute_0_2025]) ).
cnf(refute_0_2027,plain,
greatest_lower_bound(greatest_lower_bound(X_130,X_128),greatest_lower_bound(X_128,greatest_lower_bound(Y,X_130))) = greatest_lower_bound(X_130,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X_128))),
inference(subst,[],[refute_0_2026:[bind(X,$fot(X_130)),bind(X_128,$fot(Y)),bind(X_130,$fot(X_128)),bind(X_22,$fot(greatest_lower_bound(X_130,X_128)))]]) ).
cnf(refute_0_2028,plain,
( greatest_lower_bound(X_130,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X_128))) != greatest_lower_bound(X_130,greatest_lower_bound(Y,X_128))
| greatest_lower_bound(greatest_lower_bound(X_130,X_128),greatest_lower_bound(X_128,greatest_lower_bound(Y,X_130))) != greatest_lower_bound(X_130,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X_128)))
| greatest_lower_bound(greatest_lower_bound(X_130,X_128),greatest_lower_bound(X_128,greatest_lower_bound(Y,X_130))) = greatest_lower_bound(X_130,greatest_lower_bound(Y,X_128)) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(X_130,X_128),greatest_lower_bound(X_128,greatest_lower_bound(Y,X_130))))),bind(Y0,$fot(greatest_lower_bound(X_130,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X_128))))),bind(Z0,$fot(greatest_lower_bound(X_130,greatest_lower_bound(Y,X_128))))]]) ).
cnf(refute_0_2029,plain,
( greatest_lower_bound(X_130,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X_128))) != greatest_lower_bound(X_130,greatest_lower_bound(Y,X_128))
| greatest_lower_bound(greatest_lower_bound(X_130,X_128),greatest_lower_bound(X_128,greatest_lower_bound(Y,X_130))) = greatest_lower_bound(X_130,greatest_lower_bound(Y,X_128)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_130,X_128),greatest_lower_bound(X_128,greatest_lower_bound(Y,X_130))),greatest_lower_bound(X_130,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X_128)))) )],[refute_0_2027,refute_0_2028]) ).
cnf(refute_0_2030,plain,
greatest_lower_bound(greatest_lower_bound(X_130,X_128),greatest_lower_bound(X_128,greatest_lower_bound(Y,X_130))) = greatest_lower_bound(X_130,greatest_lower_bound(Y,X_128)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_130,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_130,X_128),X_128))),greatest_lower_bound(X_130,greatest_lower_bound(Y,X_128))) )],[refute_0_2024,refute_0_2029]) ).
cnf(refute_0_2031,plain,
( greatest_lower_bound(greatest_lower_bound(X_130,X_128),greatest_lower_bound(X_128,greatest_lower_bound(Y,X_130))) != greatest_lower_bound(X_130,greatest_lower_bound(Y,X_128))
| greatest_lower_bound(greatest_lower_bound(X_130,X_128),greatest_lower_bound(X_128,greatest_lower_bound(Y,X_130))) != greatest_lower_bound(greatest_lower_bound(X_130,X_128),Y)
| greatest_lower_bound(X_130,greatest_lower_bound(Y,X_128)) = greatest_lower_bound(greatest_lower_bound(X_130,X_128),Y) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_130,X_128),greatest_lower_bound(X_128,greatest_lower_bound(Y,X_130))),greatest_lower_bound(greatest_lower_bound(X_130,X_128),Y)) ),[0],$fot(greatest_lower_bound(X_130,greatest_lower_bound(Y,X_128)))]]) ).
cnf(refute_0_2032,plain,
( greatest_lower_bound(greatest_lower_bound(X_130,X_128),greatest_lower_bound(X_128,greatest_lower_bound(Y,X_130))) != greatest_lower_bound(greatest_lower_bound(X_130,X_128),Y)
| greatest_lower_bound(X_130,greatest_lower_bound(Y,X_128)) = greatest_lower_bound(greatest_lower_bound(X_130,X_128),Y) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_130,X_128),greatest_lower_bound(X_128,greatest_lower_bound(Y,X_130))),greatest_lower_bound(X_130,greatest_lower_bound(Y,X_128))) )],[refute_0_2030,refute_0_2031]) ).
cnf(refute_0_2033,plain,
greatest_lower_bound(greatest_lower_bound(X_130,X_128),Y) = greatest_lower_bound(X_130,greatest_lower_bound(X_128,Y)),
inference(subst,[],[refute_0_343:[bind(X,$fot(X_130)),bind(Y,$fot(X_128)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_2034,plain,
( greatest_lower_bound(X_130,greatest_lower_bound(Y,X_128)) != greatest_lower_bound(greatest_lower_bound(X_130,X_128),Y)
| greatest_lower_bound(greatest_lower_bound(X_130,X_128),Y) != greatest_lower_bound(X_130,greatest_lower_bound(X_128,Y))
| greatest_lower_bound(X_130,greatest_lower_bound(Y,X_128)) = greatest_lower_bound(X_130,greatest_lower_bound(X_128,Y)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_130,greatest_lower_bound(Y,X_128)),greatest_lower_bound(X_130,greatest_lower_bound(X_128,Y))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_130,X_128),Y))]]) ).
cnf(refute_0_2035,plain,
( greatest_lower_bound(X_130,greatest_lower_bound(Y,X_128)) != greatest_lower_bound(greatest_lower_bound(X_130,X_128),Y)
| greatest_lower_bound(X_130,greatest_lower_bound(Y,X_128)) = greatest_lower_bound(X_130,greatest_lower_bound(X_128,Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_130,X_128),Y),greatest_lower_bound(X_130,greatest_lower_bound(X_128,Y))) )],[refute_0_2033,refute_0_2034]) ).
cnf(refute_0_2036,plain,
( greatest_lower_bound(greatest_lower_bound(X_130,X_128),greatest_lower_bound(X_128,greatest_lower_bound(Y,X_130))) != greatest_lower_bound(greatest_lower_bound(X_130,X_128),Y)
| greatest_lower_bound(X_130,greatest_lower_bound(Y,X_128)) = greatest_lower_bound(X_130,greatest_lower_bound(X_128,Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_130,greatest_lower_bound(Y,X_128)),greatest_lower_bound(greatest_lower_bound(X_130,X_128),Y)) )],[refute_0_2032,refute_0_2035]) ).
cnf(refute_0_2037,plain,
greatest_lower_bound(X_130,greatest_lower_bound(Y,X_128)) = greatest_lower_bound(X_130,greatest_lower_bound(X_128,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_130,X_128),greatest_lower_bound(X_128,greatest_lower_bound(Y,X_130))),greatest_lower_bound(greatest_lower_bound(X_130,X_128),Y)) )],[refute_0_1957,refute_0_2036]) ).
cnf(refute_0_2038,plain,
( greatest_lower_bound(X_130,greatest_lower_bound(Y,X_128)) != greatest_lower_bound(X_130,greatest_lower_bound(X_128,Y))
| greatest_lower_bound(X_130,greatest_lower_bound(X_128,Y)) = greatest_lower_bound(X_130,greatest_lower_bound(Y,X_128)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(greatest_lower_bound(X_130,greatest_lower_bound(Y,X_128)))),bind(Y0,$fot(greatest_lower_bound(X_130,greatest_lower_bound(X_128,Y))))]]) ).
cnf(refute_0_2039,plain,
greatest_lower_bound(X_130,greatest_lower_bound(X_128,Y)) = greatest_lower_bound(X_130,greatest_lower_bound(Y,X_128)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_130,greatest_lower_bound(Y,X_128)),greatest_lower_bound(X_130,greatest_lower_bound(X_128,Y))) )],[refute_0_2037,refute_0_2038]) ).
cnf(refute_0_2040,plain,
greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(identity,X_114),inverse(X_114))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X_114),greatest_lower_bound(identity,X_114))),
inference(subst,[],[refute_0_2039:[bind(Y,$fot(inverse(X_114))),bind(X_128,$fot(greatest_lower_bound(identity,X_114))),bind(X_130,$fot(identity))]]) ).
cnf(refute_0_2041,plain,
( greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(identity,X_114),inverse(X_114))) != greatest_lower_bound(identity,greatest_lower_bound(inverse(X_114),greatest_lower_bound(identity,X_114)))
| greatest_lower_bound(identity,greatest_lower_bound(inverse(X_114),greatest_lower_bound(identity,X_114))) != greatest_lower_bound(X_114,greatest_lower_bound(identity,inverse(X_114)))
| greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(identity,X_114),inverse(X_114))) = greatest_lower_bound(X_114,greatest_lower_bound(identity,inverse(X_114))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(identity,X_114),inverse(X_114))))),bind(Y0,$fot(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_114),greatest_lower_bound(identity,X_114))))),bind(Z0,$fot(greatest_lower_bound(X_114,greatest_lower_bound(identity,inverse(X_114)))))]]) ).
cnf(refute_0_2042,plain,
( greatest_lower_bound(identity,greatest_lower_bound(inverse(X_114),greatest_lower_bound(identity,X_114))) != greatest_lower_bound(X_114,greatest_lower_bound(identity,inverse(X_114)))
| greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(identity,X_114),inverse(X_114))) = greatest_lower_bound(X_114,greatest_lower_bound(identity,inverse(X_114))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(identity,X_114),inverse(X_114))),greatest_lower_bound(identity,greatest_lower_bound(inverse(X_114),greatest_lower_bound(identity,X_114)))) )],[refute_0_2040,refute_0_2041]) ).
cnf(refute_0_2043,plain,
greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(identity,X_114),inverse(X_114))) = greatest_lower_bound(X_114,greatest_lower_bound(identity,inverse(X_114))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_114),greatest_lower_bound(identity,X_114))),greatest_lower_bound(X_114,greatest_lower_bound(identity,inverse(X_114)))) )],[refute_0_1950,refute_0_2042]) ).
cnf(refute_0_2044,plain,
greatest_lower_bound(greatest_lower_bound(Y,X_130),greatest_lower_bound(X_129,X_130)) = greatest_lower_bound(X_129,greatest_lower_bound(X_130,greatest_lower_bound(Y,X_130))),
inference(subst,[],[refute_0_1460:[bind(X,$fot(greatest_lower_bound(Y,X_130))),bind(X_22,$fot(X_129)),bind(X_23,$fot(X_130))]]) ).
cnf(refute_0_2045,plain,
greatest_lower_bound(X_130,greatest_lower_bound(Y,X_130)) = greatest_lower_bound(X_130,Y),
inference(subst,[],[refute_0_347:[bind(X_13,$fot(X_130))]]) ).
cnf(refute_0_2046,plain,
( greatest_lower_bound(X_130,greatest_lower_bound(Y,X_130)) != greatest_lower_bound(X_130,Y)
| greatest_lower_bound(greatest_lower_bound(Y,X_130),greatest_lower_bound(X_129,X_130)) != greatest_lower_bound(X_129,greatest_lower_bound(X_130,greatest_lower_bound(Y,X_130)))
| greatest_lower_bound(greatest_lower_bound(Y,X_130),greatest_lower_bound(X_129,X_130)) = greatest_lower_bound(X_129,greatest_lower_bound(X_130,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(Y,X_130),greatest_lower_bound(X_129,X_130)),greatest_lower_bound(X_129,greatest_lower_bound(X_130,greatest_lower_bound(Y,X_130)))) ),[1,1],$fot(greatest_lower_bound(X_130,Y))]]) ).
cnf(refute_0_2047,plain,
( greatest_lower_bound(greatest_lower_bound(Y,X_130),greatest_lower_bound(X_129,X_130)) != greatest_lower_bound(X_129,greatest_lower_bound(X_130,greatest_lower_bound(Y,X_130)))
| greatest_lower_bound(greatest_lower_bound(Y,X_130),greatest_lower_bound(X_129,X_130)) = greatest_lower_bound(X_129,greatest_lower_bound(X_130,Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_130,greatest_lower_bound(Y,X_130)),greatest_lower_bound(X_130,Y)) )],[refute_0_2045,refute_0_2046]) ).
cnf(refute_0_2048,plain,
greatest_lower_bound(greatest_lower_bound(Y,X_130),greatest_lower_bound(X_129,X_130)) = greatest_lower_bound(X_129,greatest_lower_bound(X_130,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(Y,X_130),greatest_lower_bound(X_129,X_130)),greatest_lower_bound(X_129,greatest_lower_bound(X_130,greatest_lower_bound(Y,X_130)))) )],[refute_0_2044,refute_0_2047]) ).
cnf(refute_0_2049,plain,
greatest_lower_bound(X_130,greatest_lower_bound(X_129,greatest_lower_bound(Y,X_130))) = greatest_lower_bound(X_130,greatest_lower_bound(X_129,Y)),
inference(subst,[],[refute_0_1964:[bind(X_13,$fot(X_130)),bind(X_22,$fot(X_129)),bind(X_23,$fot(Y))]]) ).
cnf(refute_0_2050,plain,
greatest_lower_bound(greatest_lower_bound(Y,X_130),greatest_lower_bound(X_129,X_130)) = greatest_lower_bound(X_130,greatest_lower_bound(X_129,greatest_lower_bound(Y,X_130))),
inference(subst,[],[refute_0_1894:[bind(Y,$fot(greatest_lower_bound(Y,X_130))),bind(X_128,$fot(X_130))]]) ).
cnf(refute_0_2051,plain,
( greatest_lower_bound(X_130,greatest_lower_bound(X_129,greatest_lower_bound(Y,X_130))) != greatest_lower_bound(X_130,greatest_lower_bound(X_129,Y))
| greatest_lower_bound(greatest_lower_bound(Y,X_130),greatest_lower_bound(X_129,X_130)) != greatest_lower_bound(X_130,greatest_lower_bound(X_129,greatest_lower_bound(Y,X_130)))
| greatest_lower_bound(greatest_lower_bound(Y,X_130),greatest_lower_bound(X_129,X_130)) = greatest_lower_bound(X_130,greatest_lower_bound(X_129,Y)) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(Y,X_130),greatest_lower_bound(X_129,X_130)))),bind(Y0,$fot(greatest_lower_bound(X_130,greatest_lower_bound(X_129,greatest_lower_bound(Y,X_130))))),bind(Z0,$fot(greatest_lower_bound(X_130,greatest_lower_bound(X_129,Y))))]]) ).
cnf(refute_0_2052,plain,
( greatest_lower_bound(X_130,greatest_lower_bound(X_129,greatest_lower_bound(Y,X_130))) != greatest_lower_bound(X_130,greatest_lower_bound(X_129,Y))
| greatest_lower_bound(greatest_lower_bound(Y,X_130),greatest_lower_bound(X_129,X_130)) = greatest_lower_bound(X_130,greatest_lower_bound(X_129,Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(Y,X_130),greatest_lower_bound(X_129,X_130)),greatest_lower_bound(X_130,greatest_lower_bound(X_129,greatest_lower_bound(Y,X_130)))) )],[refute_0_2050,refute_0_2051]) ).
cnf(refute_0_2053,plain,
greatest_lower_bound(greatest_lower_bound(Y,X_130),greatest_lower_bound(X_129,X_130)) = greatest_lower_bound(X_130,greatest_lower_bound(X_129,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_130,greatest_lower_bound(X_129,greatest_lower_bound(Y,X_130))),greatest_lower_bound(X_130,greatest_lower_bound(X_129,Y))) )],[refute_0_2049,refute_0_2052]) ).
cnf(refute_0_2054,plain,
( greatest_lower_bound(greatest_lower_bound(Y,X_130),greatest_lower_bound(X_129,X_130)) != greatest_lower_bound(X_129,greatest_lower_bound(X_130,Y))
| greatest_lower_bound(greatest_lower_bound(Y,X_130),greatest_lower_bound(X_129,X_130)) != greatest_lower_bound(X_130,greatest_lower_bound(X_129,Y))
| greatest_lower_bound(X_130,greatest_lower_bound(X_129,Y)) = greatest_lower_bound(X_129,greatest_lower_bound(X_130,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(Y,X_130),greatest_lower_bound(X_129,X_130)),greatest_lower_bound(X_129,greatest_lower_bound(X_130,Y))) ),[0],$fot(greatest_lower_bound(X_130,greatest_lower_bound(X_129,Y)))]]) ).
cnf(refute_0_2055,plain,
( greatest_lower_bound(greatest_lower_bound(Y,X_130),greatest_lower_bound(X_129,X_130)) != greatest_lower_bound(X_129,greatest_lower_bound(X_130,Y))
| greatest_lower_bound(X_130,greatest_lower_bound(X_129,Y)) = greatest_lower_bound(X_129,greatest_lower_bound(X_130,Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(Y,X_130),greatest_lower_bound(X_129,X_130)),greatest_lower_bound(X_130,greatest_lower_bound(X_129,Y))) )],[refute_0_2053,refute_0_2054]) ).
cnf(refute_0_2056,plain,
greatest_lower_bound(X_130,greatest_lower_bound(X_129,Y)) = greatest_lower_bound(X_129,greatest_lower_bound(X_130,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(Y,X_130),greatest_lower_bound(X_129,X_130)),greatest_lower_bound(X_129,greatest_lower_bound(X_130,Y))) )],[refute_0_2048,refute_0_2055]) ).
cnf(refute_0_2057,plain,
( greatest_lower_bound(X_130,greatest_lower_bound(X_129,Y)) != greatest_lower_bound(X_129,greatest_lower_bound(X_130,Y))
| greatest_lower_bound(X_129,greatest_lower_bound(X_130,Y)) = greatest_lower_bound(X_130,greatest_lower_bound(X_129,Y)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(greatest_lower_bound(X_130,greatest_lower_bound(X_129,Y)))),bind(Y0,$fot(greatest_lower_bound(X_129,greatest_lower_bound(X_130,Y))))]]) ).
cnf(refute_0_2058,plain,
greatest_lower_bound(X_129,greatest_lower_bound(X_130,Y)) = greatest_lower_bound(X_130,greatest_lower_bound(X_129,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_130,greatest_lower_bound(X_129,Y)),greatest_lower_bound(X_129,greatest_lower_bound(X_130,Y))) )],[refute_0_2056,refute_0_2057]) ).
cnf(refute_0_2059,plain,
greatest_lower_bound(greatest_lower_bound(identity,X_114),greatest_lower_bound(identity,inverse(X_114))) = greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(identity,X_114),inverse(X_114))),
inference(subst,[],[refute_0_2058:[bind(Y,$fot(inverse(X_114))),bind(X_129,$fot(greatest_lower_bound(identity,X_114))),bind(X_130,$fot(identity))]]) ).
cnf(refute_0_2060,plain,
( greatest_lower_bound(greatest_lower_bound(identity,X_114),greatest_lower_bound(identity,inverse(X_114))) != greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(identity,X_114),inverse(X_114)))
| greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(identity,X_114),inverse(X_114))) != greatest_lower_bound(X_114,greatest_lower_bound(identity,inverse(X_114)))
| greatest_lower_bound(greatest_lower_bound(identity,X_114),greatest_lower_bound(identity,inverse(X_114))) = greatest_lower_bound(X_114,greatest_lower_bound(identity,inverse(X_114))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(identity,X_114),greatest_lower_bound(identity,inverse(X_114))))),bind(Y0,$fot(greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(identity,X_114),inverse(X_114))))),bind(Z0,$fot(greatest_lower_bound(X_114,greatest_lower_bound(identity,inverse(X_114)))))]]) ).
cnf(refute_0_2061,plain,
( greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(identity,X_114),inverse(X_114))) != greatest_lower_bound(X_114,greatest_lower_bound(identity,inverse(X_114)))
| greatest_lower_bound(greatest_lower_bound(identity,X_114),greatest_lower_bound(identity,inverse(X_114))) = greatest_lower_bound(X_114,greatest_lower_bound(identity,inverse(X_114))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(identity,X_114),greatest_lower_bound(identity,inverse(X_114))),greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(identity,X_114),inverse(X_114)))) )],[refute_0_2059,refute_0_2060]) ).
cnf(refute_0_2062,plain,
greatest_lower_bound(greatest_lower_bound(identity,X_114),greatest_lower_bound(identity,inverse(X_114))) = greatest_lower_bound(X_114,greatest_lower_bound(identity,inverse(X_114))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(identity,X_114),inverse(X_114))),greatest_lower_bound(X_114,greatest_lower_bound(identity,inverse(X_114)))) )],[refute_0_2043,refute_0_2061]) ).
cnf(refute_0_2063,plain,
( multiply(greatest_lower_bound(identity,inverse(X_114)),greatest_lower_bound(identity,X_114)) != greatest_lower_bound(greatest_lower_bound(identity,X_114),greatest_lower_bound(identity,inverse(X_114)))
| greatest_lower_bound(greatest_lower_bound(identity,X_114),greatest_lower_bound(identity,inverse(X_114))) != greatest_lower_bound(X_114,greatest_lower_bound(identity,inverse(X_114)))
| multiply(greatest_lower_bound(identity,inverse(X_114)),greatest_lower_bound(identity,X_114)) = greatest_lower_bound(X_114,greatest_lower_bound(identity,inverse(X_114))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(identity,inverse(X_114)),greatest_lower_bound(identity,X_114)),greatest_lower_bound(X_114,greatest_lower_bound(identity,inverse(X_114)))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(identity,X_114),greatest_lower_bound(identity,inverse(X_114))))]]) ).
cnf(refute_0_2064,plain,
( multiply(greatest_lower_bound(identity,inverse(X_114)),greatest_lower_bound(identity,X_114)) != greatest_lower_bound(greatest_lower_bound(identity,X_114),greatest_lower_bound(identity,inverse(X_114)))
| multiply(greatest_lower_bound(identity,inverse(X_114)),greatest_lower_bound(identity,X_114)) = greatest_lower_bound(X_114,greatest_lower_bound(identity,inverse(X_114))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(identity,X_114),greatest_lower_bound(identity,inverse(X_114))),greatest_lower_bound(X_114,greatest_lower_bound(identity,inverse(X_114)))) )],[refute_0_2062,refute_0_2063]) ).
cnf(refute_0_2065,plain,
( multiply(greatest_lower_bound(inverse(X_114),identity),greatest_lower_bound(identity,X_114)) != greatest_lower_bound(greatest_lower_bound(identity,X_114),greatest_lower_bound(identity,inverse(X_114)))
| multiply(greatest_lower_bound(identity,inverse(X_114)),greatest_lower_bound(identity,X_114)) = greatest_lower_bound(X_114,greatest_lower_bound(identity,inverse(X_114))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(X_114)),greatest_lower_bound(identity,X_114)),greatest_lower_bound(greatest_lower_bound(identity,X_114),greatest_lower_bound(identity,inverse(X_114)))) )],[refute_0_1913,refute_0_2064]) ).
cnf(refute_0_2066,plain,
multiply(greatest_lower_bound(identity,inverse(X_114)),greatest_lower_bound(identity,X_114)) = greatest_lower_bound(X_114,greatest_lower_bound(identity,inverse(X_114))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_114),identity),greatest_lower_bound(identity,X_114)),greatest_lower_bound(greatest_lower_bound(identity,X_114),greatest_lower_bound(identity,inverse(X_114)))) )],[refute_0_1832,refute_0_2065]) ).
cnf(refute_0_2067,plain,
multiply(greatest_lower_bound(identity,inverse(X_283)),greatest_lower_bound(identity,X_283)) = greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))),
inference(subst,[],[refute_0_2066:[bind(X_114,$fot(X_283))]]) ).
cnf(refute_0_2068,plain,
( multiply(greatest_lower_bound(identity,inverse(X_283)),greatest_lower_bound(identity,X_283)) != greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283)))
| greatest_lower_bound(identity,X_283) != multiply(inverse(greatest_lower_bound(greatest_lower_bound(identity,inverse(X_283)),inverse(greatest_lower_bound(identity,X_283)))),greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,inverse(X_283)),greatest_lower_bound(identity,X_283))))
| greatest_lower_bound(identity,X_283) = multiply(inverse(greatest_lower_bound(greatest_lower_bound(identity,inverse(X_283)),inverse(greatest_lower_bound(identity,X_283)))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,X_283),multiply(inverse(greatest_lower_bound(greatest_lower_bound(identity,inverse(X_283)),inverse(greatest_lower_bound(identity,X_283)))),greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,inverse(X_283)),greatest_lower_bound(identity,X_283))))) ),[1,1,1],$fot(greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))]]) ).
cnf(refute_0_2069,plain,
( greatest_lower_bound(identity,X_283) != multiply(inverse(greatest_lower_bound(greatest_lower_bound(identity,inverse(X_283)),inverse(greatest_lower_bound(identity,X_283)))),greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,inverse(X_283)),greatest_lower_bound(identity,X_283))))
| greatest_lower_bound(identity,X_283) = multiply(inverse(greatest_lower_bound(greatest_lower_bound(identity,inverse(X_283)),inverse(greatest_lower_bound(identity,X_283)))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(X_283)),greatest_lower_bound(identity,X_283)),greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283)))) )],[refute_0_2067,refute_0_2068]) ).
cnf(refute_0_2070,plain,
greatest_lower_bound(identity,X_283) = multiply(inverse(greatest_lower_bound(greatest_lower_bound(identity,inverse(X_283)),inverse(greatest_lower_bound(identity,X_283)))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,X_283),multiply(inverse(greatest_lower_bound(greatest_lower_bound(identity,inverse(X_283)),inverse(greatest_lower_bound(identity,X_283)))),greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,inverse(X_283)),greatest_lower_bound(identity,X_283))))) )],[refute_0_1828,refute_0_2069]) ).
cnf(refute_0_2071,plain,
inverse(inverse(X_283)) = X_283,
inference(subst,[],[refute_0_452:[bind(X_35,$fot(X_283))]]) ).
cnf(refute_0_2072,plain,
greatest_lower_bound(identity,inverse(inverse(X_283))) = greatest_lower_bound(identity,inverse(inverse(X_283))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,inverse(inverse(X_283))))]]) ).
cnf(refute_0_2073,plain,
( greatest_lower_bound(identity,inverse(inverse(X_283))) != greatest_lower_bound(identity,inverse(inverse(X_283)))
| inverse(inverse(X_283)) != X_283
| greatest_lower_bound(identity,inverse(inverse(X_283))) = greatest_lower_bound(identity,X_283) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,inverse(inverse(X_283))),greatest_lower_bound(identity,inverse(inverse(X_283)))) ),[1,1],$fot(X_283)]]) ).
cnf(refute_0_2074,plain,
( inverse(inverse(X_283)) != X_283
| greatest_lower_bound(identity,inverse(inverse(X_283))) = greatest_lower_bound(identity,X_283) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(inverse(X_283))),greatest_lower_bound(identity,inverse(inverse(X_283)))) )],[refute_0_2072,refute_0_2073]) ).
cnf(refute_0_2075,plain,
greatest_lower_bound(identity,inverse(inverse(X_283))) = greatest_lower_bound(identity,X_283),
inference(resolve,[$cnf( $equal(inverse(inverse(X_283)),X_283) )],[refute_0_2071,refute_0_2074]) ).
cnf(refute_0_2076,plain,
multiply(greatest_lower_bound(identity,inverse(inverse(X_283))),identity) = greatest_lower_bound(identity,inverse(inverse(X_283))),
inference(subst,[],[refute_0_88:[bind(X_33,$fot(greatest_lower_bound(identity,inverse(inverse(X_283)))))]]) ).
cnf(refute_0_2077,plain,
multiply(greatest_lower_bound(inverse(inverse(X_283)),identity),identity) = multiply(greatest_lower_bound(identity,inverse(inverse(X_283))),identity),
inference(subst,[],[refute_0_1910:[bind(X_17,$fot(identity)),bind(X_172,$fot(inverse(inverse(X_283))))]]) ).
cnf(refute_0_2078,plain,
( multiply(greatest_lower_bound(identity,inverse(inverse(X_283))),identity) != greatest_lower_bound(identity,inverse(inverse(X_283)))
| multiply(greatest_lower_bound(inverse(inverse(X_283)),identity),identity) != multiply(greatest_lower_bound(identity,inverse(inverse(X_283))),identity)
| multiply(greatest_lower_bound(inverse(inverse(X_283)),identity),identity) = greatest_lower_bound(identity,inverse(inverse(X_283))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(greatest_lower_bound(inverse(inverse(X_283)),identity),identity))),bind(Y0,$fot(multiply(greatest_lower_bound(identity,inverse(inverse(X_283))),identity))),bind(Z0,$fot(greatest_lower_bound(identity,inverse(inverse(X_283)))))]]) ).
cnf(refute_0_2079,plain,
( multiply(greatest_lower_bound(identity,inverse(inverse(X_283))),identity) != greatest_lower_bound(identity,inverse(inverse(X_283)))
| multiply(greatest_lower_bound(inverse(inverse(X_283)),identity),identity) = greatest_lower_bound(identity,inverse(inverse(X_283))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(inverse(X_283)),identity),identity),multiply(greatest_lower_bound(identity,inverse(inverse(X_283))),identity)) )],[refute_0_2077,refute_0_2078]) ).
cnf(refute_0_2080,plain,
multiply(greatest_lower_bound(inverse(inverse(X_283)),identity),identity) = greatest_lower_bound(identity,inverse(inverse(X_283))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(inverse(X_283))),identity),greatest_lower_bound(identity,inverse(inverse(X_283)))) )],[refute_0_2076,refute_0_2079]) ).
cnf(refute_0_2081,plain,
greatest_lower_bound(identity,multiply(inverse(inverse(X_283)),identity)) = multiply(greatest_lower_bound(inverse(inverse(X_283)),identity),identity),
inference(subst,[],[refute_0_1315:[bind(X_119,$fot(identity)),bind(X_120,$fot(inverse(inverse(X_283))))]]) ).
cnf(refute_0_2082,plain,
( multiply(greatest_lower_bound(inverse(inverse(X_283)),identity),identity) != greatest_lower_bound(identity,inverse(inverse(X_283)))
| greatest_lower_bound(identity,multiply(inverse(inverse(X_283)),identity)) != multiply(greatest_lower_bound(inverse(inverse(X_283)),identity),identity)
| greatest_lower_bound(identity,multiply(inverse(inverse(X_283)),identity)) = greatest_lower_bound(identity,inverse(inverse(X_283))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(greatest_lower_bound(identity,multiply(inverse(inverse(X_283)),identity)))),bind(Y0,$fot(multiply(greatest_lower_bound(inverse(inverse(X_283)),identity),identity))),bind(Z0,$fot(greatest_lower_bound(identity,inverse(inverse(X_283)))))]]) ).
cnf(refute_0_2083,plain,
( multiply(greatest_lower_bound(inverse(inverse(X_283)),identity),identity) != greatest_lower_bound(identity,inverse(inverse(X_283)))
| greatest_lower_bound(identity,multiply(inverse(inverse(X_283)),identity)) = greatest_lower_bound(identity,inverse(inverse(X_283))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(inverse(X_283)),identity)),multiply(greatest_lower_bound(inverse(inverse(X_283)),identity),identity)) )],[refute_0_2081,refute_0_2082]) ).
cnf(refute_0_2084,plain,
greatest_lower_bound(identity,multiply(inverse(inverse(X_283)),identity)) = greatest_lower_bound(identity,inverse(inverse(X_283))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(inverse(X_283)),identity),identity),greatest_lower_bound(identity,inverse(inverse(X_283)))) )],[refute_0_2080,refute_0_2083]) ).
cnf(refute_0_2085,plain,
( greatest_lower_bound(identity,multiply(inverse(inverse(X_283)),identity)) != greatest_lower_bound(identity,inverse(inverse(X_283)))
| greatest_lower_bound(identity,inverse(inverse(X_283))) != greatest_lower_bound(identity,X_283)
| greatest_lower_bound(identity,multiply(inverse(inverse(X_283)),identity)) = greatest_lower_bound(identity,X_283) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(greatest_lower_bound(identity,multiply(inverse(inverse(X_283)),identity)))),bind(Y0,$fot(greatest_lower_bound(identity,inverse(inverse(X_283))))),bind(Z0,$fot(greatest_lower_bound(identity,X_283)))]]) ).
cnf(refute_0_2086,plain,
( greatest_lower_bound(identity,inverse(inverse(X_283))) != greatest_lower_bound(identity,X_283)
| greatest_lower_bound(identity,multiply(inverse(inverse(X_283)),identity)) = greatest_lower_bound(identity,X_283) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(inverse(X_283)),identity)),greatest_lower_bound(identity,inverse(inverse(X_283)))) )],[refute_0_2084,refute_0_2085]) ).
cnf(refute_0_2087,plain,
greatest_lower_bound(identity,multiply(inverse(inverse(X_283)),identity)) = greatest_lower_bound(identity,X_283),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(inverse(X_283))),greatest_lower_bound(identity,X_283)) )],[refute_0_2075,refute_0_2086]) ).
cnf(refute_0_2088,plain,
inverse(greatest_lower_bound(identity,multiply(inverse(inverse(X_283)),identity))) = inverse(greatest_lower_bound(identity,multiply(inverse(inverse(X_283)),identity))),
introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(identity,multiply(inverse(inverse(X_283)),identity))))]]) ).
cnf(refute_0_2089,plain,
( greatest_lower_bound(identity,multiply(inverse(inverse(X_283)),identity)) != greatest_lower_bound(identity,X_283)
| inverse(greatest_lower_bound(identity,multiply(inverse(inverse(X_283)),identity))) != inverse(greatest_lower_bound(identity,multiply(inverse(inverse(X_283)),identity)))
| inverse(greatest_lower_bound(identity,multiply(inverse(inverse(X_283)),identity))) = inverse(greatest_lower_bound(identity,X_283)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(inverse(X_283)),identity))),inverse(greatest_lower_bound(identity,multiply(inverse(inverse(X_283)),identity)))) ),[1,0],$fot(greatest_lower_bound(identity,X_283))]]) ).
cnf(refute_0_2090,plain,
( greatest_lower_bound(identity,multiply(inverse(inverse(X_283)),identity)) != greatest_lower_bound(identity,X_283)
| inverse(greatest_lower_bound(identity,multiply(inverse(inverse(X_283)),identity))) = inverse(greatest_lower_bound(identity,X_283)) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(inverse(X_283)),identity))),inverse(greatest_lower_bound(identity,multiply(inverse(inverse(X_283)),identity)))) )],[refute_0_2088,refute_0_2089]) ).
cnf(refute_0_2091,plain,
inverse(greatest_lower_bound(identity,multiply(inverse(inverse(X_283)),identity))) = inverse(greatest_lower_bound(identity,X_283)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(inverse(X_283)),identity)),greatest_lower_bound(identity,X_283)) )],[refute_0_2087,refute_0_2090]) ).
cnf(refute_0_2092,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),inverse(X_283)) = inverse(greatest_lower_bound(identity,multiply(inverse(inverse(X_283)),identity))),
inference(subst,[],[refute_0_771:[bind(X_105,$fot(identity)),bind(X_106,$fot(inverse(X_283)))]]) ).
cnf(refute_0_2093,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),inverse(X_283)) != inverse(greatest_lower_bound(identity,multiply(inverse(inverse(X_283)),identity)))
| inverse(greatest_lower_bound(identity,multiply(inverse(inverse(X_283)),identity))) != inverse(greatest_lower_bound(identity,X_283))
| multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),inverse(X_283)) = inverse(greatest_lower_bound(identity,X_283)) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),inverse(X_283)))),bind(Y0,$fot(inverse(greatest_lower_bound(identity,multiply(inverse(inverse(X_283)),identity))))),bind(Z0,$fot(inverse(greatest_lower_bound(identity,X_283))))]]) ).
cnf(refute_0_2094,plain,
( inverse(greatest_lower_bound(identity,multiply(inverse(inverse(X_283)),identity))) != inverse(greatest_lower_bound(identity,X_283))
| multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),inverse(X_283)) = inverse(greatest_lower_bound(identity,X_283)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),inverse(X_283)),inverse(greatest_lower_bound(identity,multiply(inverse(inverse(X_283)),identity)))) )],[refute_0_2092,refute_0_2093]) ).
cnf(refute_0_2095,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),inverse(X_283)) = inverse(greatest_lower_bound(identity,X_283)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(inverse(X_283)),identity))),inverse(greatest_lower_bound(identity,X_283))) )],[refute_0_2091,refute_0_2094]) ).
cnf(refute_0_2096,plain,
greatest_lower_bound(X_283,multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),inverse(X_283))) = greatest_lower_bound(X_283,multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),inverse(X_283))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X_283,multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),inverse(X_283))))]]) ).
cnf(refute_0_2097,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),inverse(X_283)) != inverse(greatest_lower_bound(identity,X_283))
| greatest_lower_bound(X_283,multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),inverse(X_283))) != greatest_lower_bound(X_283,multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),inverse(X_283)))
| greatest_lower_bound(X_283,multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),inverse(X_283))) = greatest_lower_bound(X_283,inverse(greatest_lower_bound(identity,X_283))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_283,multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),inverse(X_283))),greatest_lower_bound(X_283,multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),inverse(X_283)))) ),[1,1],$fot(inverse(greatest_lower_bound(identity,X_283)))]]) ).
cnf(refute_0_2098,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),inverse(X_283)) != inverse(greatest_lower_bound(identity,X_283))
| greatest_lower_bound(X_283,multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),inverse(X_283))) = greatest_lower_bound(X_283,inverse(greatest_lower_bound(identity,X_283))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_283,multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),inverse(X_283))),greatest_lower_bound(X_283,multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),inverse(X_283)))) )],[refute_0_2096,refute_0_2097]) ).
cnf(refute_0_2099,plain,
greatest_lower_bound(X_283,multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),inverse(X_283))) = greatest_lower_bound(X_283,inverse(greatest_lower_bound(identity,X_283))),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),inverse(X_283)),inverse(greatest_lower_bound(identity,X_283))) )],[refute_0_2095,refute_0_2098]) ).
cnf(refute_0_2100,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),greatest_lower_bound(greatest_lower_bound(X_259,identity),Z)) = greatest_lower_bound(multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),greatest_lower_bound(X_259,identity)),multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),Z)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(inverse(greatest_lower_bound(identity,inverse(X_259))))),bind(Y,$fot(greatest_lower_bound(X_259,identity)))]]) ).
cnf(refute_0_2101,plain,
multiply(identity,X_105) = multiply(inverse(greatest_lower_bound(identity,inverse(multiply(identity,X_105)))),greatest_lower_bound(identity,multiply(identity,X_105))),
inference(subst,[],[refute_0_456:[bind(X_125,$fot(multiply(identity,X_105)))]]) ).
cnf(refute_0_2102,plain,
multiply(identity,greatest_lower_bound(X_105,identity)) = greatest_lower_bound(identity,multiply(identity,X_105)),
inference(subst,[],[refute_0_319:[bind(X_104,$fot(identity))]]) ).
cnf(refute_0_2103,plain,
( multiply(identity,greatest_lower_bound(X_105,identity)) != greatest_lower_bound(identity,multiply(identity,X_105))
| greatest_lower_bound(identity,multiply(identity,X_105)) = multiply(identity,greatest_lower_bound(X_105,identity)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(identity,greatest_lower_bound(X_105,identity)))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(identity,X_105))))]]) ).
cnf(refute_0_2104,plain,
greatest_lower_bound(identity,multiply(identity,X_105)) = multiply(identity,greatest_lower_bound(X_105,identity)),
inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(X_105,identity)),greatest_lower_bound(identity,multiply(identity,X_105))) )],[refute_0_2102,refute_0_2103]) ).
cnf(refute_0_2105,plain,
( multiply(identity,X_105) != multiply(inverse(greatest_lower_bound(identity,inverse(multiply(identity,X_105)))),greatest_lower_bound(identity,multiply(identity,X_105)))
| greatest_lower_bound(identity,multiply(identity,X_105)) != multiply(identity,greatest_lower_bound(X_105,identity))
| multiply(identity,X_105) = multiply(inverse(greatest_lower_bound(identity,inverse(multiply(identity,X_105)))),multiply(identity,greatest_lower_bound(X_105,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_105),multiply(inverse(greatest_lower_bound(identity,inverse(multiply(identity,X_105)))),greatest_lower_bound(identity,multiply(identity,X_105)))) ),[1,1],$fot(multiply(identity,greatest_lower_bound(X_105,identity)))]]) ).
cnf(refute_0_2106,plain,
( multiply(identity,X_105) != multiply(inverse(greatest_lower_bound(identity,inverse(multiply(identity,X_105)))),greatest_lower_bound(identity,multiply(identity,X_105)))
| multiply(identity,X_105) = multiply(inverse(greatest_lower_bound(identity,inverse(multiply(identity,X_105)))),multiply(identity,greatest_lower_bound(X_105,identity))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(identity,X_105)),multiply(identity,greatest_lower_bound(X_105,identity))) )],[refute_0_2104,refute_0_2105]) ).
cnf(refute_0_2107,plain,
multiply(identity,X_105) = multiply(inverse(greatest_lower_bound(identity,inverse(multiply(identity,X_105)))),multiply(identity,greatest_lower_bound(X_105,identity))),
inference(resolve,[$cnf( $equal(multiply(identity,X_105),multiply(inverse(greatest_lower_bound(identity,inverse(multiply(identity,X_105)))),greatest_lower_bound(identity,multiply(identity,X_105)))) )],[refute_0_2101,refute_0_2106]) ).
cnf(refute_0_2108,plain,
multiply(identity,X_105) = X_105,
inference(subst,[],[left_identity:[bind(X,$fot(X_105))]]) ).
cnf(refute_0_2109,plain,
( multiply(identity,X_105) != X_105
| multiply(identity,X_105) != multiply(inverse(greatest_lower_bound(identity,inverse(multiply(identity,X_105)))),multiply(identity,greatest_lower_bound(X_105,identity)))
| X_105 = multiply(inverse(greatest_lower_bound(identity,inverse(multiply(identity,X_105)))),multiply(identity,greatest_lower_bound(X_105,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_105),multiply(inverse(greatest_lower_bound(identity,inverse(multiply(identity,X_105)))),multiply(identity,greatest_lower_bound(X_105,identity)))) ),[0],$fot(X_105)]]) ).
cnf(refute_0_2110,plain,
( multiply(identity,X_105) != multiply(inverse(greatest_lower_bound(identity,inverse(multiply(identity,X_105)))),multiply(identity,greatest_lower_bound(X_105,identity)))
| X_105 = multiply(inverse(greatest_lower_bound(identity,inverse(multiply(identity,X_105)))),multiply(identity,greatest_lower_bound(X_105,identity))) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_105),X_105) )],[refute_0_2108,refute_0_2109]) ).
cnf(refute_0_2111,plain,
multiply(identity,greatest_lower_bound(X_105,identity)) = greatest_lower_bound(X_105,identity),
inference(subst,[],[left_identity:[bind(X,$fot(greatest_lower_bound(X_105,identity)))]]) ).
cnf(refute_0_2112,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X_105))),multiply(identity,greatest_lower_bound(X_105,identity))) = multiply(inverse(greatest_lower_bound(identity,inverse(X_105))),multiply(identity,greatest_lower_bound(X_105,identity))),
introduced(tautology,[refl,[$fot(multiply(inverse(greatest_lower_bound(identity,inverse(X_105))),multiply(identity,greatest_lower_bound(X_105,identity))))]]) ).
cnf(refute_0_2113,plain,
( multiply(identity,greatest_lower_bound(X_105,identity)) != greatest_lower_bound(X_105,identity)
| multiply(inverse(greatest_lower_bound(identity,inverse(X_105))),multiply(identity,greatest_lower_bound(X_105,identity))) != multiply(inverse(greatest_lower_bound(identity,inverse(X_105))),multiply(identity,greatest_lower_bound(X_105,identity)))
| multiply(inverse(greatest_lower_bound(identity,inverse(X_105))),multiply(identity,greatest_lower_bound(X_105,identity))) = multiply(inverse(greatest_lower_bound(identity,inverse(X_105))),greatest_lower_bound(X_105,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X_105))),multiply(identity,greatest_lower_bound(X_105,identity))),multiply(inverse(greatest_lower_bound(identity,inverse(X_105))),multiply(identity,greatest_lower_bound(X_105,identity)))) ),[1,1],$fot(greatest_lower_bound(X_105,identity))]]) ).
cnf(refute_0_2114,plain,
( multiply(identity,greatest_lower_bound(X_105,identity)) != greatest_lower_bound(X_105,identity)
| multiply(inverse(greatest_lower_bound(identity,inverse(X_105))),multiply(identity,greatest_lower_bound(X_105,identity))) = multiply(inverse(greatest_lower_bound(identity,inverse(X_105))),greatest_lower_bound(X_105,identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X_105))),multiply(identity,greatest_lower_bound(X_105,identity))),multiply(inverse(greatest_lower_bound(identity,inverse(X_105))),multiply(identity,greatest_lower_bound(X_105,identity)))) )],[refute_0_2112,refute_0_2113]) ).
cnf(refute_0_2115,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X_105))),multiply(identity,greatest_lower_bound(X_105,identity))) = multiply(inverse(greatest_lower_bound(identity,inverse(X_105))),greatest_lower_bound(X_105,identity)),
inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(X_105,identity)),greatest_lower_bound(X_105,identity)) )],[refute_0_2111,refute_0_2114]) ).
cnf(refute_0_2116,plain,
inverse(multiply(identity,X_105)) = inverse(multiply(identity,X_105)),
introduced(tautology,[refl,[$fot(inverse(multiply(identity,X_105)))]]) ).
cnf(refute_0_2117,plain,
( multiply(identity,X_105) != X_105
| inverse(multiply(identity,X_105)) != inverse(multiply(identity,X_105))
| inverse(multiply(identity,X_105)) = inverse(X_105) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(identity,X_105)),inverse(multiply(identity,X_105))) ),[1,0],$fot(X_105)]]) ).
cnf(refute_0_2118,plain,
( multiply(identity,X_105) != X_105
| inverse(multiply(identity,X_105)) = inverse(X_105) ),
inference(resolve,[$cnf( $equal(inverse(multiply(identity,X_105)),inverse(multiply(identity,X_105))) )],[refute_0_2116,refute_0_2117]) ).
cnf(refute_0_2119,plain,
inverse(multiply(identity,X_105)) = inverse(X_105),
inference(resolve,[$cnf( $equal(multiply(identity,X_105),X_105) )],[refute_0_2108,refute_0_2118]) ).
cnf(refute_0_2120,plain,
greatest_lower_bound(identity,inverse(multiply(identity,X_105))) = greatest_lower_bound(identity,inverse(multiply(identity,X_105))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,inverse(multiply(identity,X_105))))]]) ).
cnf(refute_0_2121,plain,
( greatest_lower_bound(identity,inverse(multiply(identity,X_105))) != greatest_lower_bound(identity,inverse(multiply(identity,X_105)))
| inverse(multiply(identity,X_105)) != inverse(X_105)
| greatest_lower_bound(identity,inverse(multiply(identity,X_105))) = greatest_lower_bound(identity,inverse(X_105)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,inverse(multiply(identity,X_105))),greatest_lower_bound(identity,inverse(multiply(identity,X_105)))) ),[1,1],$fot(inverse(X_105))]]) ).
cnf(refute_0_2122,plain,
( inverse(multiply(identity,X_105)) != inverse(X_105)
| greatest_lower_bound(identity,inverse(multiply(identity,X_105))) = greatest_lower_bound(identity,inverse(X_105)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(multiply(identity,X_105))),greatest_lower_bound(identity,inverse(multiply(identity,X_105)))) )],[refute_0_2120,refute_0_2121]) ).
cnf(refute_0_2123,plain,
greatest_lower_bound(identity,inverse(multiply(identity,X_105))) = greatest_lower_bound(identity,inverse(X_105)),
inference(resolve,[$cnf( $equal(inverse(multiply(identity,X_105)),inverse(X_105)) )],[refute_0_2119,refute_0_2122]) ).
cnf(refute_0_2124,plain,
inverse(greatest_lower_bound(identity,inverse(multiply(identity,X_105)))) = inverse(greatest_lower_bound(identity,inverse(multiply(identity,X_105)))),
introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(identity,inverse(multiply(identity,X_105)))))]]) ).
cnf(refute_0_2125,plain,
( greatest_lower_bound(identity,inverse(multiply(identity,X_105))) != greatest_lower_bound(identity,inverse(X_105))
| inverse(greatest_lower_bound(identity,inverse(multiply(identity,X_105)))) != inverse(greatest_lower_bound(identity,inverse(multiply(identity,X_105))))
| inverse(greatest_lower_bound(identity,inverse(multiply(identity,X_105)))) = inverse(greatest_lower_bound(identity,inverse(X_105))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(multiply(identity,X_105)))),inverse(greatest_lower_bound(identity,inverse(multiply(identity,X_105))))) ),[1,0],$fot(greatest_lower_bound(identity,inverse(X_105)))]]) ).
cnf(refute_0_2126,plain,
( greatest_lower_bound(identity,inverse(multiply(identity,X_105))) != greatest_lower_bound(identity,inverse(X_105))
| inverse(greatest_lower_bound(identity,inverse(multiply(identity,X_105)))) = inverse(greatest_lower_bound(identity,inverse(X_105))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(multiply(identity,X_105)))),inverse(greatest_lower_bound(identity,inverse(multiply(identity,X_105))))) )],[refute_0_2124,refute_0_2125]) ).
cnf(refute_0_2127,plain,
inverse(greatest_lower_bound(identity,inverse(multiply(identity,X_105)))) = inverse(greatest_lower_bound(identity,inverse(X_105))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(multiply(identity,X_105))),greatest_lower_bound(identity,inverse(X_105))) )],[refute_0_2123,refute_0_2126]) ).
cnf(refute_0_2128,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(multiply(identity,X_105)))),multiply(identity,greatest_lower_bound(X_105,identity))) = multiply(inverse(greatest_lower_bound(identity,inverse(multiply(identity,X_105)))),multiply(identity,greatest_lower_bound(X_105,identity))),
introduced(tautology,[refl,[$fot(multiply(inverse(greatest_lower_bound(identity,inverse(multiply(identity,X_105)))),multiply(identity,greatest_lower_bound(X_105,identity))))]]) ).
cnf(refute_0_2129,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(multiply(identity,X_105)))),multiply(identity,greatest_lower_bound(X_105,identity))) != multiply(inverse(greatest_lower_bound(identity,inverse(multiply(identity,X_105)))),multiply(identity,greatest_lower_bound(X_105,identity)))
| inverse(greatest_lower_bound(identity,inverse(multiply(identity,X_105)))) != inverse(greatest_lower_bound(identity,inverse(X_105)))
| multiply(inverse(greatest_lower_bound(identity,inverse(multiply(identity,X_105)))),multiply(identity,greatest_lower_bound(X_105,identity))) = multiply(inverse(greatest_lower_bound(identity,inverse(X_105))),multiply(identity,greatest_lower_bound(X_105,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(multiply(identity,X_105)))),multiply(identity,greatest_lower_bound(X_105,identity))),multiply(inverse(greatest_lower_bound(identity,inverse(multiply(identity,X_105)))),multiply(identity,greatest_lower_bound(X_105,identity)))) ),[1,0],$fot(inverse(greatest_lower_bound(identity,inverse(X_105))))]]) ).
cnf(refute_0_2130,plain,
( inverse(greatest_lower_bound(identity,inverse(multiply(identity,X_105)))) != inverse(greatest_lower_bound(identity,inverse(X_105)))
| multiply(inverse(greatest_lower_bound(identity,inverse(multiply(identity,X_105)))),multiply(identity,greatest_lower_bound(X_105,identity))) = multiply(inverse(greatest_lower_bound(identity,inverse(X_105))),multiply(identity,greatest_lower_bound(X_105,identity))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(multiply(identity,X_105)))),multiply(identity,greatest_lower_bound(X_105,identity))),multiply(inverse(greatest_lower_bound(identity,inverse(multiply(identity,X_105)))),multiply(identity,greatest_lower_bound(X_105,identity)))) )],[refute_0_2128,refute_0_2129]) ).
cnf(refute_0_2131,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(multiply(identity,X_105)))),multiply(identity,greatest_lower_bound(X_105,identity))) = multiply(inverse(greatest_lower_bound(identity,inverse(X_105))),multiply(identity,greatest_lower_bound(X_105,identity))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(multiply(identity,X_105)))),inverse(greatest_lower_bound(identity,inverse(X_105)))) )],[refute_0_2127,refute_0_2130]) ).
cnf(refute_0_2132,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(X_105))),multiply(identity,greatest_lower_bound(X_105,identity))) != multiply(inverse(greatest_lower_bound(identity,inverse(X_105))),greatest_lower_bound(X_105,identity))
| multiply(inverse(greatest_lower_bound(identity,inverse(multiply(identity,X_105)))),multiply(identity,greatest_lower_bound(X_105,identity))) != multiply(inverse(greatest_lower_bound(identity,inverse(X_105))),multiply(identity,greatest_lower_bound(X_105,identity)))
| multiply(inverse(greatest_lower_bound(identity,inverse(multiply(identity,X_105)))),multiply(identity,greatest_lower_bound(X_105,identity))) = multiply(inverse(greatest_lower_bound(identity,inverse(X_105))),greatest_lower_bound(X_105,identity)) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(identity,inverse(multiply(identity,X_105)))),multiply(identity,greatest_lower_bound(X_105,identity))))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(identity,inverse(X_105))),multiply(identity,greatest_lower_bound(X_105,identity))))),bind(Z0,$fot(multiply(inverse(greatest_lower_bound(identity,inverse(X_105))),greatest_lower_bound(X_105,identity))))]]) ).
cnf(refute_0_2133,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(X_105))),multiply(identity,greatest_lower_bound(X_105,identity))) != multiply(inverse(greatest_lower_bound(identity,inverse(X_105))),greatest_lower_bound(X_105,identity))
| multiply(inverse(greatest_lower_bound(identity,inverse(multiply(identity,X_105)))),multiply(identity,greatest_lower_bound(X_105,identity))) = multiply(inverse(greatest_lower_bound(identity,inverse(X_105))),greatest_lower_bound(X_105,identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(multiply(identity,X_105)))),multiply(identity,greatest_lower_bound(X_105,identity))),multiply(inverse(greatest_lower_bound(identity,inverse(X_105))),multiply(identity,greatest_lower_bound(X_105,identity)))) )],[refute_0_2131,refute_0_2132]) ).
cnf(refute_0_2134,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(multiply(identity,X_105)))),multiply(identity,greatest_lower_bound(X_105,identity))) = multiply(inverse(greatest_lower_bound(identity,inverse(X_105))),greatest_lower_bound(X_105,identity)),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X_105))),multiply(identity,greatest_lower_bound(X_105,identity))),multiply(inverse(greatest_lower_bound(identity,inverse(X_105))),greatest_lower_bound(X_105,identity))) )],[refute_0_2115,refute_0_2133]) ).
cnf(refute_0_2135,plain,
( X_105 != multiply(inverse(greatest_lower_bound(identity,inverse(multiply(identity,X_105)))),multiply(identity,greatest_lower_bound(X_105,identity)))
| multiply(inverse(greatest_lower_bound(identity,inverse(multiply(identity,X_105)))),multiply(identity,greatest_lower_bound(X_105,identity))) != multiply(inverse(greatest_lower_bound(identity,inverse(X_105))),greatest_lower_bound(X_105,identity))
| X_105 = multiply(inverse(greatest_lower_bound(identity,inverse(X_105))),greatest_lower_bound(X_105,identity)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_105,multiply(inverse(greatest_lower_bound(identity,inverse(X_105))),greatest_lower_bound(X_105,identity))) ),[0],$fot(multiply(inverse(greatest_lower_bound(identity,inverse(multiply(identity,X_105)))),multiply(identity,greatest_lower_bound(X_105,identity))))]]) ).
cnf(refute_0_2136,plain,
( X_105 != multiply(inverse(greatest_lower_bound(identity,inverse(multiply(identity,X_105)))),multiply(identity,greatest_lower_bound(X_105,identity)))
| X_105 = multiply(inverse(greatest_lower_bound(identity,inverse(X_105))),greatest_lower_bound(X_105,identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(multiply(identity,X_105)))),multiply(identity,greatest_lower_bound(X_105,identity))),multiply(inverse(greatest_lower_bound(identity,inverse(X_105))),greatest_lower_bound(X_105,identity))) )],[refute_0_2134,refute_0_2135]) ).
cnf(refute_0_2137,plain,
( multiply(identity,X_105) != multiply(inverse(greatest_lower_bound(identity,inverse(multiply(identity,X_105)))),multiply(identity,greatest_lower_bound(X_105,identity)))
| X_105 = multiply(inverse(greatest_lower_bound(identity,inverse(X_105))),greatest_lower_bound(X_105,identity)) ),
inference(resolve,[$cnf( $equal(X_105,multiply(inverse(greatest_lower_bound(identity,inverse(multiply(identity,X_105)))),multiply(identity,greatest_lower_bound(X_105,identity)))) )],[refute_0_2110,refute_0_2136]) ).
cnf(refute_0_2138,plain,
X_105 = multiply(inverse(greatest_lower_bound(identity,inverse(X_105))),greatest_lower_bound(X_105,identity)),
inference(resolve,[$cnf( $equal(multiply(identity,X_105),multiply(inverse(greatest_lower_bound(identity,inverse(multiply(identity,X_105)))),multiply(identity,greatest_lower_bound(X_105,identity)))) )],[refute_0_2107,refute_0_2137]) ).
cnf(refute_0_2139,plain,
X_259 = multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),greatest_lower_bound(X_259,identity)),
inference(subst,[],[refute_0_2138:[bind(X_105,$fot(X_259))]]) ).
cnf(refute_0_2140,plain,
( X_259 != multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),greatest_lower_bound(X_259,identity))
| multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),greatest_lower_bound(X_259,identity)) = X_259 ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(X_259)),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),greatest_lower_bound(X_259,identity))))]]) ).
cnf(refute_0_2141,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),greatest_lower_bound(X_259,identity)) = X_259,
inference(resolve,[$cnf( $equal(X_259,multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),greatest_lower_bound(X_259,identity))) )],[refute_0_2139,refute_0_2140]) ).
cnf(refute_0_2142,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),greatest_lower_bound(X_259,identity)) != X_259
| multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),greatest_lower_bound(greatest_lower_bound(X_259,identity),Z)) != greatest_lower_bound(multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),greatest_lower_bound(X_259,identity)),multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),Z))
| multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),greatest_lower_bound(greatest_lower_bound(X_259,identity),Z)) = greatest_lower_bound(X_259,multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),Z)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),greatest_lower_bound(greatest_lower_bound(X_259,identity),Z)),greatest_lower_bound(multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),greatest_lower_bound(X_259,identity)),multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),Z))) ),[1,0],$fot(X_259)]]) ).
cnf(refute_0_2143,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),greatest_lower_bound(greatest_lower_bound(X_259,identity),Z)) != greatest_lower_bound(multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),greatest_lower_bound(X_259,identity)),multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),Z))
| multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),greatest_lower_bound(greatest_lower_bound(X_259,identity),Z)) = greatest_lower_bound(X_259,multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),Z)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),greatest_lower_bound(X_259,identity)),X_259) )],[refute_0_2141,refute_0_2142]) ).
cnf(refute_0_2144,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),greatest_lower_bound(greatest_lower_bound(X_259,identity),Z)) = greatest_lower_bound(X_259,multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),Z)),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),greatest_lower_bound(greatest_lower_bound(X_259,identity),Z)),greatest_lower_bound(multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),greatest_lower_bound(X_259,identity)),multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),Z))) )],[refute_0_2100,refute_0_2143]) ).
cnf(refute_0_2145,plain,
greatest_lower_bound(greatest_lower_bound(X_259,identity),Z) = greatest_lower_bound(X_259,greatest_lower_bound(identity,Z)),
inference(subst,[],[refute_0_343:[bind(X,$fot(X_259)),bind(Y,$fot(identity))]]) ).
cnf(refute_0_2146,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),greatest_lower_bound(greatest_lower_bound(X_259,identity),Z)) = multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),greatest_lower_bound(greatest_lower_bound(X_259,identity),Z)),
introduced(tautology,[refl,[$fot(multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),greatest_lower_bound(greatest_lower_bound(X_259,identity),Z)))]]) ).
cnf(refute_0_2147,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),greatest_lower_bound(greatest_lower_bound(X_259,identity),Z)) != multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),greatest_lower_bound(greatest_lower_bound(X_259,identity),Z))
| greatest_lower_bound(greatest_lower_bound(X_259,identity),Z) != greatest_lower_bound(X_259,greatest_lower_bound(identity,Z))
| multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),greatest_lower_bound(greatest_lower_bound(X_259,identity),Z)) = multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),greatest_lower_bound(X_259,greatest_lower_bound(identity,Z))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),greatest_lower_bound(greatest_lower_bound(X_259,identity),Z)),multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),greatest_lower_bound(greatest_lower_bound(X_259,identity),Z))) ),[1,1],$fot(greatest_lower_bound(X_259,greatest_lower_bound(identity,Z)))]]) ).
cnf(refute_0_2148,plain,
( greatest_lower_bound(greatest_lower_bound(X_259,identity),Z) != greatest_lower_bound(X_259,greatest_lower_bound(identity,Z))
| multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),greatest_lower_bound(greatest_lower_bound(X_259,identity),Z)) = multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),greatest_lower_bound(X_259,greatest_lower_bound(identity,Z))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),greatest_lower_bound(greatest_lower_bound(X_259,identity),Z)),multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),greatest_lower_bound(greatest_lower_bound(X_259,identity),Z))) )],[refute_0_2146,refute_0_2147]) ).
cnf(refute_0_2149,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),greatest_lower_bound(greatest_lower_bound(X_259,identity),Z)) = multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),greatest_lower_bound(X_259,greatest_lower_bound(identity,Z))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_259,identity),Z),greatest_lower_bound(X_259,greatest_lower_bound(identity,Z))) )],[refute_0_2145,refute_0_2148]) ).
cnf(refute_0_2150,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),greatest_lower_bound(greatest_lower_bound(X_259,identity),Z)) != multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),greatest_lower_bound(X_259,greatest_lower_bound(identity,Z)))
| multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),greatest_lower_bound(greatest_lower_bound(X_259,identity),Z)) != greatest_lower_bound(X_259,multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),Z))
| multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),greatest_lower_bound(X_259,greatest_lower_bound(identity,Z))) = greatest_lower_bound(X_259,multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),Z)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),greatest_lower_bound(greatest_lower_bound(X_259,identity),Z)),greatest_lower_bound(X_259,multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),Z))) ),[0],$fot(multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),greatest_lower_bound(X_259,greatest_lower_bound(identity,Z))))]]) ).
cnf(refute_0_2151,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),greatest_lower_bound(greatest_lower_bound(X_259,identity),Z)) != greatest_lower_bound(X_259,multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),Z))
| multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),greatest_lower_bound(X_259,greatest_lower_bound(identity,Z))) = greatest_lower_bound(X_259,multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),Z)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),greatest_lower_bound(greatest_lower_bound(X_259,identity),Z)),multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),greatest_lower_bound(X_259,greatest_lower_bound(identity,Z)))) )],[refute_0_2149,refute_0_2150]) ).
cnf(refute_0_2152,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),greatest_lower_bound(X_259,greatest_lower_bound(identity,Z))) = greatest_lower_bound(X_259,multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),Z)),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),greatest_lower_bound(greatest_lower_bound(X_259,identity),Z)),greatest_lower_bound(X_259,multiply(inverse(greatest_lower_bound(identity,inverse(X_259))),Z))) )],[refute_0_2144,refute_0_2151]) ).
cnf(refute_0_2153,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283)))) = greatest_lower_bound(X_283,multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),inverse(X_283))),
inference(subst,[],[refute_0_2152:[bind(Z,$fot(inverse(X_283))),bind(X_259,$fot(X_283))]]) ).
cnf(refute_0_2154,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283)))) != greatest_lower_bound(X_283,multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),inverse(X_283)))
| greatest_lower_bound(X_283,multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),inverse(X_283))) != greatest_lower_bound(X_283,inverse(greatest_lower_bound(identity,X_283)))
| multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283)))) = greatest_lower_bound(X_283,inverse(greatest_lower_bound(identity,X_283))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283)))))),bind(Y0,$fot(greatest_lower_bound(X_283,multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),inverse(X_283))))),bind(Z0,$fot(greatest_lower_bound(X_283,inverse(greatest_lower_bound(identity,X_283)))))]]) ).
cnf(refute_0_2155,plain,
( greatest_lower_bound(X_283,multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),inverse(X_283))) != greatest_lower_bound(X_283,inverse(greatest_lower_bound(identity,X_283)))
| multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283)))) = greatest_lower_bound(X_283,inverse(greatest_lower_bound(identity,X_283))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283)))),greatest_lower_bound(X_283,multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),inverse(X_283)))) )],[refute_0_2153,refute_0_2154]) ).
cnf(refute_0_2156,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283)))) = greatest_lower_bound(X_283,inverse(greatest_lower_bound(identity,X_283))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_283,multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),inverse(X_283))),greatest_lower_bound(X_283,inverse(greatest_lower_bound(identity,X_283)))) )],[refute_0_2099,refute_0_2155]) ).
cnf(refute_0_2157,plain,
greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283)))) = greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))),
inference(subst,[],[refute_0_1471:[bind(Y,$fot(inverse(X_283))),bind(X_22,$fot(X_283)),bind(X_23,$fot(identity))]]) ).
cnf(refute_0_2158,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))) = multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))),
introduced(tautology,[refl,[$fot(multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))))]]) ).
cnf(refute_0_2159,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))) != multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283)))))
| greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283)))) != greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283)))
| multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))) = multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))),multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283)))))) ),[1,1],$fot(greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))]]) ).
cnf(refute_0_2160,plain,
( greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283)))) != greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283)))
| multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))) = multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))),multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283)))))) )],[refute_0_2158,refute_0_2159]) ).
cnf(refute_0_2161,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))) = multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283)))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283)))),greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283)))) )],[refute_0_2157,refute_0_2160]) ).
cnf(refute_0_2162,plain,
greatest_lower_bound(inverse(X_283),identity) = greatest_lower_bound(identity,inverse(X_283)),
inference(subst,[],[refute_0_42:[bind(X,$fot(identity)),bind(Y,$fot(inverse(X_283)))]]) ).
cnf(refute_0_2163,plain,
greatest_lower_bound(inverse(greatest_lower_bound(identity,X_131)),greatest_lower_bound(X_22,identity)) = greatest_lower_bound(X_22,greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_131)))),
inference(subst,[],[refute_0_1460:[bind(X,$fot(inverse(greatest_lower_bound(identity,X_131)))),bind(X_23,$fot(identity))]]) ).
cnf(refute_0_2164,plain,
identity = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_131))),
inference(subst,[],[refute_0_653:[bind(X_16,$fot(X_131))]]) ).
cnf(refute_0_2165,plain,
( identity != greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_131)))
| greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_131))) = identity ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(identity)),bind(Y0,$fot(greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_131)))))]]) ).
cnf(refute_0_2166,plain,
greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_131))) = identity,
inference(resolve,[$cnf( $equal(identity,greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_131)))) )],[refute_0_2164,refute_0_2165]) ).
cnf(refute_0_2167,plain,
( greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_131))) != identity
| greatest_lower_bound(inverse(greatest_lower_bound(identity,X_131)),greatest_lower_bound(X_22,identity)) != greatest_lower_bound(X_22,greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_131))))
| greatest_lower_bound(inverse(greatest_lower_bound(identity,X_131)),greatest_lower_bound(X_22,identity)) = greatest_lower_bound(X_22,identity) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_131)),greatest_lower_bound(X_22,identity)),greatest_lower_bound(X_22,greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_131))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_2168,plain,
( greatest_lower_bound(inverse(greatest_lower_bound(identity,X_131)),greatest_lower_bound(X_22,identity)) != greatest_lower_bound(X_22,greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_131))))
| greatest_lower_bound(inverse(greatest_lower_bound(identity,X_131)),greatest_lower_bound(X_22,identity)) = greatest_lower_bound(X_22,identity) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_131))),identity) )],[refute_0_2166,refute_0_2167]) ).
cnf(refute_0_2169,plain,
greatest_lower_bound(inverse(greatest_lower_bound(identity,X_131)),greatest_lower_bound(X_22,identity)) = greatest_lower_bound(X_22,identity),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_131)),greatest_lower_bound(X_22,identity)),greatest_lower_bound(X_22,greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_131))))) )],[refute_0_2163,refute_0_2168]) ).
cnf(refute_0_2170,plain,
greatest_lower_bound(inverse(greatest_lower_bound(identity,X_131)),greatest_lower_bound(X_22,identity)) = greatest_lower_bound(identity,greatest_lower_bound(X_22,inverse(greatest_lower_bound(identity,X_131)))),
inference(subst,[],[refute_0_1894:[bind(Y,$fot(inverse(greatest_lower_bound(identity,X_131)))),bind(X_128,$fot(identity)),bind(X_129,$fot(X_22))]]) ).
cnf(refute_0_2171,plain,
( greatest_lower_bound(inverse(greatest_lower_bound(identity,X_131)),greatest_lower_bound(X_22,identity)) != greatest_lower_bound(X_22,identity)
| greatest_lower_bound(inverse(greatest_lower_bound(identity,X_131)),greatest_lower_bound(X_22,identity)) != greatest_lower_bound(identity,greatest_lower_bound(X_22,inverse(greatest_lower_bound(identity,X_131))))
| greatest_lower_bound(identity,greatest_lower_bound(X_22,inverse(greatest_lower_bound(identity,X_131)))) = greatest_lower_bound(X_22,identity) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_131)),greatest_lower_bound(X_22,identity)),greatest_lower_bound(X_22,identity)) ),[0],$fot(greatest_lower_bound(identity,greatest_lower_bound(X_22,inverse(greatest_lower_bound(identity,X_131)))))]]) ).
cnf(refute_0_2172,plain,
( greatest_lower_bound(inverse(greatest_lower_bound(identity,X_131)),greatest_lower_bound(X_22,identity)) != greatest_lower_bound(X_22,identity)
| greatest_lower_bound(identity,greatest_lower_bound(X_22,inverse(greatest_lower_bound(identity,X_131)))) = greatest_lower_bound(X_22,identity) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_131)),greatest_lower_bound(X_22,identity)),greatest_lower_bound(identity,greatest_lower_bound(X_22,inverse(greatest_lower_bound(identity,X_131))))) )],[refute_0_2170,refute_0_2171]) ).
cnf(refute_0_2173,plain,
greatest_lower_bound(identity,greatest_lower_bound(X_22,inverse(greatest_lower_bound(identity,X_131)))) = greatest_lower_bound(X_22,identity),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_131)),greatest_lower_bound(X_22,identity)),greatest_lower_bound(X_22,identity)) )],[refute_0_2169,refute_0_2172]) ).
cnf(refute_0_2174,plain,
greatest_lower_bound(identity,greatest_lower_bound(inverse(X_283),inverse(greatest_lower_bound(identity,X_283)))) = greatest_lower_bound(inverse(X_283),identity),
inference(subst,[],[refute_0_2173:[bind(X_131,$fot(X_283)),bind(X_22,$fot(inverse(X_283)))]]) ).
cnf(refute_0_2175,plain,
( greatest_lower_bound(identity,greatest_lower_bound(inverse(X_283),inverse(greatest_lower_bound(identity,X_283)))) != greatest_lower_bound(inverse(X_283),identity)
| greatest_lower_bound(inverse(X_283),identity) != greatest_lower_bound(identity,inverse(X_283))
| greatest_lower_bound(identity,greatest_lower_bound(inverse(X_283),inverse(greatest_lower_bound(identity,X_283)))) = greatest_lower_bound(identity,inverse(X_283)) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_283),inverse(greatest_lower_bound(identity,X_283)))))),bind(Y0,$fot(greatest_lower_bound(inverse(X_283),identity))),bind(Z0,$fot(greatest_lower_bound(identity,inverse(X_283))))]]) ).
cnf(refute_0_2176,plain,
( greatest_lower_bound(inverse(X_283),identity) != greatest_lower_bound(identity,inverse(X_283))
| greatest_lower_bound(identity,greatest_lower_bound(inverse(X_283),inverse(greatest_lower_bound(identity,X_283)))) = greatest_lower_bound(identity,inverse(X_283)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_283),inverse(greatest_lower_bound(identity,X_283)))),greatest_lower_bound(inverse(X_283),identity)) )],[refute_0_2174,refute_0_2175]) ).
cnf(refute_0_2177,plain,
greatest_lower_bound(identity,greatest_lower_bound(inverse(X_283),inverse(greatest_lower_bound(identity,X_283)))) = greatest_lower_bound(identity,inverse(X_283)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_283),identity),greatest_lower_bound(identity,inverse(X_283))) )],[refute_0_2162,refute_0_2176]) ).
cnf(refute_0_2178,plain,
inverse(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_283),inverse(greatest_lower_bound(identity,X_283))))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_283),inverse(greatest_lower_bound(identity,X_283))))),
introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_283),inverse(greatest_lower_bound(identity,X_283))))))]]) ).
cnf(refute_0_2179,plain,
( greatest_lower_bound(identity,greatest_lower_bound(inverse(X_283),inverse(greatest_lower_bound(identity,X_283)))) != greatest_lower_bound(identity,inverse(X_283))
| inverse(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_283),inverse(greatest_lower_bound(identity,X_283))))) != inverse(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_283),inverse(greatest_lower_bound(identity,X_283)))))
| inverse(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_283),inverse(greatest_lower_bound(identity,X_283))))) = inverse(greatest_lower_bound(identity,inverse(X_283))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_283),inverse(greatest_lower_bound(identity,X_283))))),inverse(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_283),inverse(greatest_lower_bound(identity,X_283)))))) ),[1,0],$fot(greatest_lower_bound(identity,inverse(X_283)))]]) ).
cnf(refute_0_2180,plain,
( greatest_lower_bound(identity,greatest_lower_bound(inverse(X_283),inverse(greatest_lower_bound(identity,X_283)))) != greatest_lower_bound(identity,inverse(X_283))
| inverse(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_283),inverse(greatest_lower_bound(identity,X_283))))) = inverse(greatest_lower_bound(identity,inverse(X_283))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_283),inverse(greatest_lower_bound(identity,X_283))))),inverse(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_283),inverse(greatest_lower_bound(identity,X_283)))))) )],[refute_0_2178,refute_0_2179]) ).
cnf(refute_0_2181,plain,
inverse(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_283),inverse(greatest_lower_bound(identity,X_283))))) = inverse(greatest_lower_bound(identity,inverse(X_283))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_283),inverse(greatest_lower_bound(identity,X_283)))),greatest_lower_bound(identity,inverse(X_283))) )],[refute_0_2177,refute_0_2180]) ).
cnf(refute_0_2182,plain,
inverse(greatest_lower_bound(identity,greatest_lower_bound(X_23,X))) = least_upper_bound(identity,inverse(greatest_lower_bound(identity,greatest_lower_bound(X_23,X)))),
inference(subst,[],[refute_0_135:[bind(Y,$fot(greatest_lower_bound(X_23,X)))]]) ).
cnf(refute_0_2183,plain,
greatest_lower_bound(X,greatest_lower_bound(identity,X_23)) = greatest_lower_bound(identity,greatest_lower_bound(X_23,X)),
inference(subst,[],[refute_0_1460:[bind(X_22,$fot(identity))]]) ).
cnf(refute_0_2184,plain,
( greatest_lower_bound(X,greatest_lower_bound(identity,X_23)) != greatest_lower_bound(identity,greatest_lower_bound(X_23,X))
| greatest_lower_bound(identity,greatest_lower_bound(X_23,X)) = greatest_lower_bound(X,greatest_lower_bound(identity,X_23)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(identity,X_23)))),bind(Y0,$fot(greatest_lower_bound(identity,greatest_lower_bound(X_23,X))))]]) ).
cnf(refute_0_2185,plain,
greatest_lower_bound(identity,greatest_lower_bound(X_23,X)) = greatest_lower_bound(X,greatest_lower_bound(identity,X_23)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(identity,X_23)),greatest_lower_bound(identity,greatest_lower_bound(X_23,X))) )],[refute_0_2183,refute_0_2184]) ).
cnf(refute_0_2186,plain,
( greatest_lower_bound(identity,greatest_lower_bound(X_23,X)) != greatest_lower_bound(X,greatest_lower_bound(identity,X_23))
| inverse(greatest_lower_bound(identity,greatest_lower_bound(X_23,X))) != least_upper_bound(identity,inverse(greatest_lower_bound(identity,greatest_lower_bound(X_23,X))))
| inverse(greatest_lower_bound(X,greatest_lower_bound(identity,X_23))) = least_upper_bound(identity,inverse(greatest_lower_bound(identity,greatest_lower_bound(X_23,X)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(X_23,X))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,greatest_lower_bound(X_23,X))))) ),[0,0],$fot(greatest_lower_bound(X,greatest_lower_bound(identity,X_23)))]]) ).
cnf(refute_0_2187,plain,
( inverse(greatest_lower_bound(identity,greatest_lower_bound(X_23,X))) != least_upper_bound(identity,inverse(greatest_lower_bound(identity,greatest_lower_bound(X_23,X))))
| inverse(greatest_lower_bound(X,greatest_lower_bound(identity,X_23))) = least_upper_bound(identity,inverse(greatest_lower_bound(identity,greatest_lower_bound(X_23,X)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_23,X)),greatest_lower_bound(X,greatest_lower_bound(identity,X_23))) )],[refute_0_2185,refute_0_2186]) ).
cnf(refute_0_2188,plain,
inverse(greatest_lower_bound(X,greatest_lower_bound(identity,X_23))) = least_upper_bound(identity,inverse(greatest_lower_bound(identity,greatest_lower_bound(X_23,X)))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(X_23,X))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,greatest_lower_bound(X_23,X))))) )],[refute_0_2182,refute_0_2187]) ).
cnf(refute_0_2189,plain,
least_upper_bound(identity,inverse(greatest_lower_bound(identity,greatest_lower_bound(X_23,X)))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(X_23,X))),
inference(subst,[],[refute_0_137:[bind(Y,$fot(greatest_lower_bound(X_23,X)))]]) ).
cnf(refute_0_2190,plain,
( inverse(greatest_lower_bound(X,greatest_lower_bound(identity,X_23))) != least_upper_bound(identity,inverse(greatest_lower_bound(identity,greatest_lower_bound(X_23,X))))
| least_upper_bound(identity,inverse(greatest_lower_bound(identity,greatest_lower_bound(X_23,X)))) != inverse(greatest_lower_bound(identity,greatest_lower_bound(X_23,X)))
| inverse(greatest_lower_bound(X,greatest_lower_bound(identity,X_23))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(X_23,X))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(inverse(greatest_lower_bound(X,greatest_lower_bound(identity,X_23))),inverse(greatest_lower_bound(identity,greatest_lower_bound(X_23,X)))) ),[0],$fot(least_upper_bound(identity,inverse(greatest_lower_bound(identity,greatest_lower_bound(X_23,X)))))]]) ).
cnf(refute_0_2191,plain,
( inverse(greatest_lower_bound(X,greatest_lower_bound(identity,X_23))) != least_upper_bound(identity,inverse(greatest_lower_bound(identity,greatest_lower_bound(X_23,X))))
| inverse(greatest_lower_bound(X,greatest_lower_bound(identity,X_23))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(X_23,X))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(greatest_lower_bound(identity,greatest_lower_bound(X_23,X)))),inverse(greatest_lower_bound(identity,greatest_lower_bound(X_23,X)))) )],[refute_0_2189,refute_0_2190]) ).
cnf(refute_0_2192,plain,
inverse(greatest_lower_bound(X,greatest_lower_bound(identity,X_23))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(X_23,X))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X,greatest_lower_bound(identity,X_23))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,greatest_lower_bound(X_23,X))))) )],[refute_0_2188,refute_0_2191]) ).
cnf(refute_0_2193,plain,
inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_283)),greatest_lower_bound(identity,inverse(X_283)))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_283),inverse(greatest_lower_bound(identity,X_283))))),
inference(subst,[],[refute_0_2192:[bind(X,$fot(inverse(greatest_lower_bound(identity,X_283)))),bind(X_23,$fot(inverse(X_283)))]]) ).
cnf(refute_0_2194,plain,
( inverse(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_283),inverse(greatest_lower_bound(identity,X_283))))) != inverse(greatest_lower_bound(identity,inverse(X_283)))
| inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_283)),greatest_lower_bound(identity,inverse(X_283)))) != inverse(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_283),inverse(greatest_lower_bound(identity,X_283)))))
| inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_283)),greatest_lower_bound(identity,inverse(X_283)))) = inverse(greatest_lower_bound(identity,inverse(X_283))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_283)),greatest_lower_bound(identity,inverse(X_283)))))),bind(Y0,$fot(inverse(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_283),inverse(greatest_lower_bound(identity,X_283))))))),bind(Z0,$fot(inverse(greatest_lower_bound(identity,inverse(X_283)))))]]) ).
cnf(refute_0_2195,plain,
( inverse(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_283),inverse(greatest_lower_bound(identity,X_283))))) != inverse(greatest_lower_bound(identity,inverse(X_283)))
| inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_283)),greatest_lower_bound(identity,inverse(X_283)))) = inverse(greatest_lower_bound(identity,inverse(X_283))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_283)),greatest_lower_bound(identity,inverse(X_283)))),inverse(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_283),inverse(greatest_lower_bound(identity,X_283)))))) )],[refute_0_2193,refute_0_2194]) ).
cnf(refute_0_2196,plain,
inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_283)),greatest_lower_bound(identity,inverse(X_283)))) = inverse(greatest_lower_bound(identity,inverse(X_283))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_283),inverse(greatest_lower_bound(identity,X_283))))),inverse(greatest_lower_bound(identity,inverse(X_283)))) )],[refute_0_2181,refute_0_2195]) ).
cnf(refute_0_2197,plain,
multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_283)),greatest_lower_bound(identity,inverse(X_283)))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))) = multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_283)),greatest_lower_bound(identity,inverse(X_283)))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))),
introduced(tautology,[refl,[$fot(multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_283)),greatest_lower_bound(identity,inverse(X_283)))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))))]]) ).
cnf(refute_0_2198,plain,
( multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_283)),greatest_lower_bound(identity,inverse(X_283)))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))) != multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_283)),greatest_lower_bound(identity,inverse(X_283)))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283)))))
| inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_283)),greatest_lower_bound(identity,inverse(X_283)))) != inverse(greatest_lower_bound(identity,inverse(X_283)))
| multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_283)),greatest_lower_bound(identity,inverse(X_283)))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))) = multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_283)),greatest_lower_bound(identity,inverse(X_283)))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))),multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_283)),greatest_lower_bound(identity,inverse(X_283)))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283)))))) ),[1,0],$fot(inverse(greatest_lower_bound(identity,inverse(X_283))))]]) ).
cnf(refute_0_2199,plain,
( inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_283)),greatest_lower_bound(identity,inverse(X_283)))) != inverse(greatest_lower_bound(identity,inverse(X_283)))
| multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_283)),greatest_lower_bound(identity,inverse(X_283)))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))) = multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_283)),greatest_lower_bound(identity,inverse(X_283)))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))),multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_283)),greatest_lower_bound(identity,inverse(X_283)))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283)))))) )],[refute_0_2197,refute_0_2198]) ).
cnf(refute_0_2200,plain,
multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_283)),greatest_lower_bound(identity,inverse(X_283)))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))) = multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_283)),greatest_lower_bound(identity,inverse(X_283)))),inverse(greatest_lower_bound(identity,inverse(X_283)))) )],[refute_0_2196,refute_0_2199]) ).
cnf(refute_0_2201,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))) != multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))
| multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_283)),greatest_lower_bound(identity,inverse(X_283)))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))) != multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283)))))
| multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_283)),greatest_lower_bound(identity,inverse(X_283)))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))) = multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283)))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_283)),greatest_lower_bound(identity,inverse(X_283)))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))))),bind(Z0,$fot(multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))))]]) ).
cnf(refute_0_2202,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))) != multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))
| multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_283)),greatest_lower_bound(identity,inverse(X_283)))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))) = multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_283)),greatest_lower_bound(identity,inverse(X_283)))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))),multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283)))))) )],[refute_0_2200,refute_0_2201]) ).
cnf(refute_0_2203,plain,
multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_283)),greatest_lower_bound(identity,inverse(X_283)))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))) = multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283)))),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))),multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))) )],[refute_0_2161,refute_0_2202]) ).
cnf(refute_0_2204,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283)))) != greatest_lower_bound(X_283,inverse(greatest_lower_bound(identity,X_283)))
| multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_283)),greatest_lower_bound(identity,inverse(X_283)))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))) != multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))
| multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_283)),greatest_lower_bound(identity,inverse(X_283)))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))) = greatest_lower_bound(X_283,inverse(greatest_lower_bound(identity,X_283))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_283)),greatest_lower_bound(identity,inverse(X_283)))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283)))))),bind(Z0,$fot(greatest_lower_bound(X_283,inverse(greatest_lower_bound(identity,X_283)))))]]) ).
cnf(refute_0_2205,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283)))) != greatest_lower_bound(X_283,inverse(greatest_lower_bound(identity,X_283)))
| multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_283)),greatest_lower_bound(identity,inverse(X_283)))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))) = greatest_lower_bound(X_283,inverse(greatest_lower_bound(identity,X_283))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_283)),greatest_lower_bound(identity,inverse(X_283)))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))),multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))) )],[refute_0_2203,refute_0_2204]) ).
cnf(refute_0_2206,plain,
multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_283)),greatest_lower_bound(identity,inverse(X_283)))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))) = greatest_lower_bound(X_283,inverse(greatest_lower_bound(identity,X_283))),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X_283))),greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283)))),greatest_lower_bound(X_283,inverse(greatest_lower_bound(identity,X_283)))) )],[refute_0_2156,refute_0_2205]) ).
cnf(refute_0_2207,plain,
inverse(multiply(inverse(X_145),greatest_lower_bound(X_249,X_250))) = multiply(inverse(greatest_lower_bound(X_249,X_250)),X_145),
inference(subst,[],[refute_0_110:[bind(X_31,$fot(greatest_lower_bound(X_249,X_250)))]]) ).
cnf(refute_0_2208,plain,
( inverse(multiply(inverse(X_145),greatest_lower_bound(X_249,X_250))) != multiply(inverse(greatest_lower_bound(X_249,X_250)),X_145)
| inverse(greatest_lower_bound(X_249,X_250)) != inverse(greatest_lower_bound(X_250,X_249))
| inverse(multiply(inverse(X_145),greatest_lower_bound(X_249,X_250))) = multiply(inverse(greatest_lower_bound(X_250,X_249)),X_145) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X_145),greatest_lower_bound(X_249,X_250))),multiply(inverse(greatest_lower_bound(X_249,X_250)),X_145)) ),[1,0],$fot(inverse(greatest_lower_bound(X_250,X_249)))]]) ).
cnf(refute_0_2209,plain,
( inverse(multiply(inverse(X_145),greatest_lower_bound(X_249,X_250))) != multiply(inverse(greatest_lower_bound(X_249,X_250)),X_145)
| inverse(multiply(inverse(X_145),greatest_lower_bound(X_249,X_250))) = multiply(inverse(greatest_lower_bound(X_250,X_249)),X_145) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_249,X_250)),inverse(greatest_lower_bound(X_250,X_249))) )],[refute_0_1240,refute_0_2208]) ).
cnf(refute_0_2210,plain,
inverse(multiply(inverse(X_145),greatest_lower_bound(X_249,X_250))) = multiply(inverse(greatest_lower_bound(X_250,X_249)),X_145),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_145),greatest_lower_bound(X_249,X_250))),multiply(inverse(greatest_lower_bound(X_249,X_250)),X_145)) )],[refute_0_2207,refute_0_2209]) ).
cnf(refute_0_2211,plain,
( inverse(multiply(inverse(X_145),greatest_lower_bound(X_249,X_250))) != multiply(inverse(greatest_lower_bound(X_249,X_250)),X_145)
| inverse(multiply(inverse(X_145),greatest_lower_bound(X_249,X_250))) != multiply(inverse(greatest_lower_bound(X_250,X_249)),X_145)
| multiply(inverse(greatest_lower_bound(X_249,X_250)),X_145) = multiply(inverse(greatest_lower_bound(X_250,X_249)),X_145) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X_145),greatest_lower_bound(X_249,X_250))),multiply(inverse(greatest_lower_bound(X_250,X_249)),X_145)) ),[0],$fot(multiply(inverse(greatest_lower_bound(X_249,X_250)),X_145))]]) ).
cnf(refute_0_2212,plain,
( inverse(multiply(inverse(X_145),greatest_lower_bound(X_249,X_250))) != multiply(inverse(greatest_lower_bound(X_250,X_249)),X_145)
| multiply(inverse(greatest_lower_bound(X_249,X_250)),X_145) = multiply(inverse(greatest_lower_bound(X_250,X_249)),X_145) ),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_145),greatest_lower_bound(X_249,X_250))),multiply(inverse(greatest_lower_bound(X_249,X_250)),X_145)) )],[refute_0_2207,refute_0_2211]) ).
cnf(refute_0_2213,plain,
multiply(inverse(greatest_lower_bound(X_249,X_250)),X_145) = multiply(inverse(greatest_lower_bound(X_250,X_249)),X_145),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_145),greatest_lower_bound(X_249,X_250))),multiply(inverse(greatest_lower_bound(X_250,X_249)),X_145)) )],[refute_0_2210,refute_0_2212]) ).
cnf(refute_0_2214,plain,
( multiply(inverse(greatest_lower_bound(X_249,X_250)),X_145) != multiply(inverse(greatest_lower_bound(X_250,X_249)),X_145)
| multiply(inverse(greatest_lower_bound(X_250,X_249)),X_145) = multiply(inverse(greatest_lower_bound(X_249,X_250)),X_145) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(X_249,X_250)),X_145))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(X_250,X_249)),X_145)))]]) ).
cnf(refute_0_2215,plain,
multiply(inverse(greatest_lower_bound(X_250,X_249)),X_145) = multiply(inverse(greatest_lower_bound(X_249,X_250)),X_145),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_249,X_250)),X_145),multiply(inverse(greatest_lower_bound(X_250,X_249)),X_145)) )],[refute_0_2213,refute_0_2214]) ).
cnf(refute_0_2216,plain,
multiply(inverse(greatest_lower_bound(greatest_lower_bound(identity,inverse(X_283)),inverse(greatest_lower_bound(identity,X_283)))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))) = multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_283)),greatest_lower_bound(identity,inverse(X_283)))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))),
inference(subst,[],[refute_0_2215:[bind(X_145,$fot(greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283)))))),bind(X_249,$fot(inverse(greatest_lower_bound(identity,X_283)))),bind(X_250,$fot(greatest_lower_bound(identity,inverse(X_283))))]]) ).
cnf(refute_0_2217,plain,
( multiply(inverse(greatest_lower_bound(greatest_lower_bound(identity,inverse(X_283)),inverse(greatest_lower_bound(identity,X_283)))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))) != multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_283)),greatest_lower_bound(identity,inverse(X_283)))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283)))))
| multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_283)),greatest_lower_bound(identity,inverse(X_283)))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))) != greatest_lower_bound(X_283,inverse(greatest_lower_bound(identity,X_283)))
| multiply(inverse(greatest_lower_bound(greatest_lower_bound(identity,inverse(X_283)),inverse(greatest_lower_bound(identity,X_283)))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))) = greatest_lower_bound(X_283,inverse(greatest_lower_bound(identity,X_283))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(greatest_lower_bound(identity,inverse(X_283)),inverse(greatest_lower_bound(identity,X_283)))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_283)),greatest_lower_bound(identity,inverse(X_283)))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))))),bind(Z0,$fot(greatest_lower_bound(X_283,inverse(greatest_lower_bound(identity,X_283)))))]]) ).
cnf(refute_0_2218,plain,
( multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_283)),greatest_lower_bound(identity,inverse(X_283)))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))) != greatest_lower_bound(X_283,inverse(greatest_lower_bound(identity,X_283)))
| multiply(inverse(greatest_lower_bound(greatest_lower_bound(identity,inverse(X_283)),inverse(greatest_lower_bound(identity,X_283)))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))) = greatest_lower_bound(X_283,inverse(greatest_lower_bound(identity,X_283))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(greatest_lower_bound(identity,inverse(X_283)),inverse(greatest_lower_bound(identity,X_283)))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))),multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_283)),greatest_lower_bound(identity,inverse(X_283)))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283)))))) )],[refute_0_2216,refute_0_2217]) ).
cnf(refute_0_2219,plain,
multiply(inverse(greatest_lower_bound(greatest_lower_bound(identity,inverse(X_283)),inverse(greatest_lower_bound(identity,X_283)))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))) = greatest_lower_bound(X_283,inverse(greatest_lower_bound(identity,X_283))),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_283)),greatest_lower_bound(identity,inverse(X_283)))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))),greatest_lower_bound(X_283,inverse(greatest_lower_bound(identity,X_283)))) )],[refute_0_2206,refute_0_2218]) ).
cnf(refute_0_2220,plain,
( multiply(inverse(greatest_lower_bound(greatest_lower_bound(identity,inverse(X_283)),inverse(greatest_lower_bound(identity,X_283)))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))) != greatest_lower_bound(X_283,inverse(greatest_lower_bound(identity,X_283)))
| greatest_lower_bound(identity,X_283) != multiply(inverse(greatest_lower_bound(greatest_lower_bound(identity,inverse(X_283)),inverse(greatest_lower_bound(identity,X_283)))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283)))))
| greatest_lower_bound(identity,X_283) = greatest_lower_bound(X_283,inverse(greatest_lower_bound(identity,X_283))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,X_283),multiply(inverse(greatest_lower_bound(greatest_lower_bound(identity,inverse(X_283)),inverse(greatest_lower_bound(identity,X_283)))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283)))))) ),[1],$fot(greatest_lower_bound(X_283,inverse(greatest_lower_bound(identity,X_283))))]]) ).
cnf(refute_0_2221,plain,
( greatest_lower_bound(identity,X_283) != multiply(inverse(greatest_lower_bound(greatest_lower_bound(identity,inverse(X_283)),inverse(greatest_lower_bound(identity,X_283)))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283)))))
| greatest_lower_bound(identity,X_283) = greatest_lower_bound(X_283,inverse(greatest_lower_bound(identity,X_283))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(greatest_lower_bound(identity,inverse(X_283)),inverse(greatest_lower_bound(identity,X_283)))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283))))),greatest_lower_bound(X_283,inverse(greatest_lower_bound(identity,X_283)))) )],[refute_0_2219,refute_0_2220]) ).
cnf(refute_0_2222,plain,
greatest_lower_bound(identity,X_283) = greatest_lower_bound(X_283,inverse(greatest_lower_bound(identity,X_283))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,X_283),multiply(inverse(greatest_lower_bound(greatest_lower_bound(identity,inverse(X_283)),inverse(greatest_lower_bound(identity,X_283)))),greatest_lower_bound(identity,greatest_lower_bound(X_283,greatest_lower_bound(identity,inverse(X_283)))))) )],[refute_0_2070,refute_0_2221]) ).
cnf(refute_0_2223,plain,
greatest_lower_bound(identity,least_upper_bound(X_322,X_324)) = greatest_lower_bound(least_upper_bound(X_322,X_324),inverse(greatest_lower_bound(identity,least_upper_bound(X_322,X_324)))),
inference(subst,[],[refute_0_2222:[bind(X_283,$fot(least_upper_bound(X_322,X_324)))]]) ).
cnf(refute_0_2224,plain,
( greatest_lower_bound(identity,least_upper_bound(X_322,X_324)) != greatest_lower_bound(least_upper_bound(X_322,X_324),inverse(greatest_lower_bound(identity,least_upper_bound(X_322,X_324))))
| greatest_lower_bound(least_upper_bound(X_322,X_324),inverse(greatest_lower_bound(identity,least_upper_bound(X_322,X_324)))) = greatest_lower_bound(identity,least_upper_bound(X_322,X_324)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(greatest_lower_bound(identity,least_upper_bound(X_322,X_324)))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(X_322,X_324),inverse(greatest_lower_bound(identity,least_upper_bound(X_322,X_324))))))]]) ).
cnf(refute_0_2225,plain,
greatest_lower_bound(least_upper_bound(X_322,X_324),inverse(greatest_lower_bound(identity,least_upper_bound(X_322,X_324)))) = greatest_lower_bound(identity,least_upper_bound(X_322,X_324)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(X_322,X_324)),greatest_lower_bound(least_upper_bound(X_322,X_324),inverse(greatest_lower_bound(identity,least_upper_bound(X_322,X_324))))) )],[refute_0_2223,refute_0_2224]) ).
cnf(refute_0_2226,plain,
( greatest_lower_bound(least_upper_bound(X_322,X_324),greatest_lower_bound(least_upper_bound(X_324,X_322),inverse(greatest_lower_bound(identity,least_upper_bound(X_322,X_324))))) != greatest_lower_bound(least_upper_bound(X_322,X_324),inverse(greatest_lower_bound(identity,least_upper_bound(X_322,X_324))))
| greatest_lower_bound(least_upper_bound(X_322,X_324),inverse(greatest_lower_bound(identity,least_upper_bound(X_322,X_324)))) != greatest_lower_bound(identity,least_upper_bound(X_322,X_324))
| greatest_lower_bound(least_upper_bound(X_322,X_324),greatest_lower_bound(least_upper_bound(X_324,X_322),inverse(greatest_lower_bound(identity,least_upper_bound(X_322,X_324))))) = greatest_lower_bound(identity,least_upper_bound(X_322,X_324)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(least_upper_bound(X_322,X_324),greatest_lower_bound(least_upper_bound(X_324,X_322),inverse(greatest_lower_bound(identity,least_upper_bound(X_322,X_324))))),greatest_lower_bound(identity,least_upper_bound(X_322,X_324))) ),[0],$fot(greatest_lower_bound(least_upper_bound(X_322,X_324),inverse(greatest_lower_bound(identity,least_upper_bound(X_322,X_324)))))]]) ).
cnf(refute_0_2227,plain,
( greatest_lower_bound(least_upper_bound(X_322,X_324),greatest_lower_bound(least_upper_bound(X_324,X_322),inverse(greatest_lower_bound(identity,least_upper_bound(X_322,X_324))))) != greatest_lower_bound(least_upper_bound(X_322,X_324),inverse(greatest_lower_bound(identity,least_upper_bound(X_322,X_324))))
| greatest_lower_bound(least_upper_bound(X_322,X_324),greatest_lower_bound(least_upper_bound(X_324,X_322),inverse(greatest_lower_bound(identity,least_upper_bound(X_322,X_324))))) = greatest_lower_bound(identity,least_upper_bound(X_322,X_324)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_322,X_324),inverse(greatest_lower_bound(identity,least_upper_bound(X_322,X_324)))),greatest_lower_bound(identity,least_upper_bound(X_322,X_324))) )],[refute_0_2225,refute_0_2226]) ).
cnf(refute_0_2228,plain,
greatest_lower_bound(least_upper_bound(X_322,X_324),greatest_lower_bound(least_upper_bound(X_324,X_322),inverse(greatest_lower_bound(identity,least_upper_bound(X_322,X_324))))) = greatest_lower_bound(identity,least_upper_bound(X_322,X_324)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_322,X_324),greatest_lower_bound(least_upper_bound(X_324,X_322),inverse(greatest_lower_bound(identity,least_upper_bound(X_322,X_324))))),greatest_lower_bound(least_upper_bound(X_322,X_324),inverse(greatest_lower_bound(identity,least_upper_bound(X_322,X_324))))) )],[refute_0_1827,refute_0_2227]) ).
cnf(refute_0_2229,plain,
greatest_lower_bound(least_upper_bound(X_324,X_322),least_upper_bound(X_322,X_324)) = least_upper_bound(X_324,X_322),
inference(subst,[],[refute_0_544:[bind(X_18,$fot(X_324)),bind(X_7,$fot(X_322))]]) ).
cnf(refute_0_2230,plain,
greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_324,X_322),least_upper_bound(X_322,X_324))) = greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_324,X_322),least_upper_bound(X_322,X_324))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_324,X_322),least_upper_bound(X_322,X_324))))]]) ).
cnf(refute_0_2231,plain,
( greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_324,X_322),least_upper_bound(X_322,X_324))) != greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_324,X_322),least_upper_bound(X_322,X_324)))
| greatest_lower_bound(least_upper_bound(X_324,X_322),least_upper_bound(X_322,X_324)) != least_upper_bound(X_324,X_322)
| greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_324,X_322),least_upper_bound(X_322,X_324))) = greatest_lower_bound(identity,least_upper_bound(X_324,X_322)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_324,X_322),least_upper_bound(X_322,X_324))),greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_324,X_322),least_upper_bound(X_322,X_324)))) ),[1,1],$fot(least_upper_bound(X_324,X_322))]]) ).
cnf(refute_0_2232,plain,
( greatest_lower_bound(least_upper_bound(X_324,X_322),least_upper_bound(X_322,X_324)) != least_upper_bound(X_324,X_322)
| greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_324,X_322),least_upper_bound(X_322,X_324))) = greatest_lower_bound(identity,least_upper_bound(X_324,X_322)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_324,X_322),least_upper_bound(X_322,X_324))),greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_324,X_322),least_upper_bound(X_322,X_324)))) )],[refute_0_2230,refute_0_2231]) ).
cnf(refute_0_2233,plain,
greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_324,X_322),least_upper_bound(X_322,X_324))) = greatest_lower_bound(identity,least_upper_bound(X_324,X_322)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_324,X_322),least_upper_bound(X_322,X_324)),least_upper_bound(X_324,X_322)) )],[refute_0_2229,refute_0_2232]) ).
cnf(refute_0_2234,plain,
greatest_lower_bound(least_upper_bound(X_324,X_322),greatest_lower_bound(identity,least_upper_bound(X_322,X_324))) = greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_324,X_322),least_upper_bound(X_322,X_324))),
inference(subst,[],[refute_0_2058:[bind(Y,$fot(least_upper_bound(X_322,X_324))),bind(X_129,$fot(least_upper_bound(X_324,X_322))),bind(X_130,$fot(identity))]]) ).
cnf(refute_0_2235,plain,
greatest_lower_bound(Y,greatest_lower_bound(X_22,inverse(greatest_lower_bound(identity,Y)))) = greatest_lower_bound(X_22,greatest_lower_bound(Y,inverse(greatest_lower_bound(identity,Y)))),
inference(subst,[],[refute_0_1487:[bind(X_24,$fot(inverse(greatest_lower_bound(identity,Y))))]]) ).
cnf(refute_0_2236,plain,
greatest_lower_bound(identity,Y) = greatest_lower_bound(Y,inverse(greatest_lower_bound(identity,Y))),
inference(subst,[],[refute_0_2222:[bind(X_283,$fot(Y))]]) ).
cnf(refute_0_2237,plain,
( greatest_lower_bound(identity,Y) != greatest_lower_bound(Y,inverse(greatest_lower_bound(identity,Y)))
| greatest_lower_bound(Y,inverse(greatest_lower_bound(identity,Y))) = greatest_lower_bound(identity,Y) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(greatest_lower_bound(identity,Y))),bind(Y0,$fot(greatest_lower_bound(Y,inverse(greatest_lower_bound(identity,Y)))))]]) ).
cnf(refute_0_2238,plain,
greatest_lower_bound(Y,inverse(greatest_lower_bound(identity,Y))) = greatest_lower_bound(identity,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,Y),greatest_lower_bound(Y,inverse(greatest_lower_bound(identity,Y)))) )],[refute_0_2236,refute_0_2237]) ).
cnf(refute_0_2239,plain,
( greatest_lower_bound(Y,greatest_lower_bound(X_22,inverse(greatest_lower_bound(identity,Y)))) != greatest_lower_bound(X_22,greatest_lower_bound(Y,inverse(greatest_lower_bound(identity,Y))))
| greatest_lower_bound(Y,inverse(greatest_lower_bound(identity,Y))) != greatest_lower_bound(identity,Y)
| greatest_lower_bound(Y,greatest_lower_bound(X_22,inverse(greatest_lower_bound(identity,Y)))) = greatest_lower_bound(X_22,greatest_lower_bound(identity,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(X_22,inverse(greatest_lower_bound(identity,Y)))),greatest_lower_bound(X_22,greatest_lower_bound(Y,inverse(greatest_lower_bound(identity,Y))))) ),[1,1],$fot(greatest_lower_bound(identity,Y))]]) ).
cnf(refute_0_2240,plain,
( greatest_lower_bound(Y,greatest_lower_bound(X_22,inverse(greatest_lower_bound(identity,Y)))) != greatest_lower_bound(X_22,greatest_lower_bound(Y,inverse(greatest_lower_bound(identity,Y))))
| greatest_lower_bound(Y,greatest_lower_bound(X_22,inverse(greatest_lower_bound(identity,Y)))) = greatest_lower_bound(X_22,greatest_lower_bound(identity,Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,inverse(greatest_lower_bound(identity,Y))),greatest_lower_bound(identity,Y)) )],[refute_0_2238,refute_0_2239]) ).
cnf(refute_0_2241,plain,
greatest_lower_bound(Y,greatest_lower_bound(X_22,inverse(greatest_lower_bound(identity,Y)))) = greatest_lower_bound(X_22,greatest_lower_bound(identity,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(X_22,inverse(greatest_lower_bound(identity,Y)))),greatest_lower_bound(X_22,greatest_lower_bound(Y,inverse(greatest_lower_bound(identity,Y))))) )],[refute_0_2235,refute_0_2240]) ).
cnf(refute_0_2242,plain,
greatest_lower_bound(least_upper_bound(X_322,X_324),greatest_lower_bound(least_upper_bound(X_324,X_322),inverse(greatest_lower_bound(identity,least_upper_bound(X_322,X_324))))) = greatest_lower_bound(least_upper_bound(X_324,X_322),greatest_lower_bound(identity,least_upper_bound(X_322,X_324))),
inference(subst,[],[refute_0_2241:[bind(Y,$fot(least_upper_bound(X_322,X_324))),bind(X_22,$fot(least_upper_bound(X_324,X_322)))]]) ).
cnf(refute_0_2243,plain,
( greatest_lower_bound(least_upper_bound(X_322,X_324),greatest_lower_bound(least_upper_bound(X_324,X_322),inverse(greatest_lower_bound(identity,least_upper_bound(X_322,X_324))))) != greatest_lower_bound(least_upper_bound(X_324,X_322),greatest_lower_bound(identity,least_upper_bound(X_322,X_324)))
| greatest_lower_bound(least_upper_bound(X_324,X_322),greatest_lower_bound(identity,least_upper_bound(X_322,X_324))) != greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_324,X_322),least_upper_bound(X_322,X_324)))
| greatest_lower_bound(least_upper_bound(X_322,X_324),greatest_lower_bound(least_upper_bound(X_324,X_322),inverse(greatest_lower_bound(identity,least_upper_bound(X_322,X_324))))) = greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_324,X_322),least_upper_bound(X_322,X_324))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(X_322,X_324),greatest_lower_bound(least_upper_bound(X_324,X_322),inverse(greatest_lower_bound(identity,least_upper_bound(X_322,X_324))))))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(X_324,X_322),greatest_lower_bound(identity,least_upper_bound(X_322,X_324))))),bind(Z0,$fot(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_324,X_322),least_upper_bound(X_322,X_324)))))]]) ).
cnf(refute_0_2244,plain,
( greatest_lower_bound(least_upper_bound(X_324,X_322),greatest_lower_bound(identity,least_upper_bound(X_322,X_324))) != greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_324,X_322),least_upper_bound(X_322,X_324)))
| greatest_lower_bound(least_upper_bound(X_322,X_324),greatest_lower_bound(least_upper_bound(X_324,X_322),inverse(greatest_lower_bound(identity,least_upper_bound(X_322,X_324))))) = greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_324,X_322),least_upper_bound(X_322,X_324))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_322,X_324),greatest_lower_bound(least_upper_bound(X_324,X_322),inverse(greatest_lower_bound(identity,least_upper_bound(X_322,X_324))))),greatest_lower_bound(least_upper_bound(X_324,X_322),greatest_lower_bound(identity,least_upper_bound(X_322,X_324)))) )],[refute_0_2242,refute_0_2243]) ).
cnf(refute_0_2245,plain,
greatest_lower_bound(least_upper_bound(X_322,X_324),greatest_lower_bound(least_upper_bound(X_324,X_322),inverse(greatest_lower_bound(identity,least_upper_bound(X_322,X_324))))) = greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_324,X_322),least_upper_bound(X_322,X_324))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_324,X_322),greatest_lower_bound(identity,least_upper_bound(X_322,X_324))),greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_324,X_322),least_upper_bound(X_322,X_324)))) )],[refute_0_2234,refute_0_2244]) ).
cnf(refute_0_2246,plain,
( greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_324,X_322),least_upper_bound(X_322,X_324))) != greatest_lower_bound(identity,least_upper_bound(X_324,X_322))
| greatest_lower_bound(least_upper_bound(X_322,X_324),greatest_lower_bound(least_upper_bound(X_324,X_322),inverse(greatest_lower_bound(identity,least_upper_bound(X_322,X_324))))) != greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_324,X_322),least_upper_bound(X_322,X_324)))
| greatest_lower_bound(least_upper_bound(X_322,X_324),greatest_lower_bound(least_upper_bound(X_324,X_322),inverse(greatest_lower_bound(identity,least_upper_bound(X_322,X_324))))) = greatest_lower_bound(identity,least_upper_bound(X_324,X_322)) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(X_322,X_324),greatest_lower_bound(least_upper_bound(X_324,X_322),inverse(greatest_lower_bound(identity,least_upper_bound(X_322,X_324))))))),bind(Y0,$fot(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_324,X_322),least_upper_bound(X_322,X_324))))),bind(Z0,$fot(greatest_lower_bound(identity,least_upper_bound(X_324,X_322))))]]) ).
cnf(refute_0_2247,plain,
( greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_324,X_322),least_upper_bound(X_322,X_324))) != greatest_lower_bound(identity,least_upper_bound(X_324,X_322))
| greatest_lower_bound(least_upper_bound(X_322,X_324),greatest_lower_bound(least_upper_bound(X_324,X_322),inverse(greatest_lower_bound(identity,least_upper_bound(X_322,X_324))))) = greatest_lower_bound(identity,least_upper_bound(X_324,X_322)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_322,X_324),greatest_lower_bound(least_upper_bound(X_324,X_322),inverse(greatest_lower_bound(identity,least_upper_bound(X_322,X_324))))),greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_324,X_322),least_upper_bound(X_322,X_324)))) )],[refute_0_2245,refute_0_2246]) ).
cnf(refute_0_2248,plain,
greatest_lower_bound(least_upper_bound(X_322,X_324),greatest_lower_bound(least_upper_bound(X_324,X_322),inverse(greatest_lower_bound(identity,least_upper_bound(X_322,X_324))))) = greatest_lower_bound(identity,least_upper_bound(X_324,X_322)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_324,X_322),least_upper_bound(X_322,X_324))),greatest_lower_bound(identity,least_upper_bound(X_324,X_322))) )],[refute_0_2233,refute_0_2247]) ).
cnf(refute_0_2249,plain,
( greatest_lower_bound(least_upper_bound(X_322,X_324),greatest_lower_bound(least_upper_bound(X_324,X_322),inverse(greatest_lower_bound(identity,least_upper_bound(X_322,X_324))))) != greatest_lower_bound(identity,least_upper_bound(X_322,X_324))
| greatest_lower_bound(least_upper_bound(X_322,X_324),greatest_lower_bound(least_upper_bound(X_324,X_322),inverse(greatest_lower_bound(identity,least_upper_bound(X_322,X_324))))) != greatest_lower_bound(identity,least_upper_bound(X_324,X_322))
| greatest_lower_bound(identity,least_upper_bound(X_324,X_322)) = greatest_lower_bound(identity,least_upper_bound(X_322,X_324)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_322,X_324),greatest_lower_bound(least_upper_bound(X_324,X_322),inverse(greatest_lower_bound(identity,least_upper_bound(X_322,X_324))))),greatest_lower_bound(identity,least_upper_bound(X_322,X_324))) ),[0],$fot(greatest_lower_bound(identity,least_upper_bound(X_324,X_322)))]]) ).
cnf(refute_0_2250,plain,
( greatest_lower_bound(least_upper_bound(X_322,X_324),greatest_lower_bound(least_upper_bound(X_324,X_322),inverse(greatest_lower_bound(identity,least_upper_bound(X_322,X_324))))) != greatest_lower_bound(identity,least_upper_bound(X_322,X_324))
| greatest_lower_bound(identity,least_upper_bound(X_324,X_322)) = greatest_lower_bound(identity,least_upper_bound(X_322,X_324)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_322,X_324),greatest_lower_bound(least_upper_bound(X_324,X_322),inverse(greatest_lower_bound(identity,least_upper_bound(X_322,X_324))))),greatest_lower_bound(identity,least_upper_bound(X_324,X_322))) )],[refute_0_2248,refute_0_2249]) ).
cnf(refute_0_2251,plain,
greatest_lower_bound(identity,least_upper_bound(X_324,X_322)) = greatest_lower_bound(identity,least_upper_bound(X_322,X_324)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_322,X_324),greatest_lower_bound(least_upper_bound(X_324,X_322),inverse(greatest_lower_bound(identity,least_upper_bound(X_322,X_324))))),greatest_lower_bound(identity,least_upper_bound(X_322,X_324))) )],[refute_0_2228,refute_0_2250]) ).
cnf(refute_0_2252,plain,
greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,inverse(X_443)),greatest_lower_bound(X_443,identity))) = greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_443,identity),greatest_lower_bound(identity,inverse(X_443)))),
inference(subst,[],[refute_0_2251:[bind(X_322,$fot(greatest_lower_bound(X_443,identity))),bind(X_324,$fot(greatest_lower_bound(identity,inverse(X_443))))]]) ).
cnf(refute_0_2253,plain,
multiply(least_upper_bound(inverse(X_108),identity),greatest_lower_bound(X_108,identity)) = least_upper_bound(greatest_lower_bound(X_108,identity),multiply(inverse(X_108),greatest_lower_bound(X_108,identity))),
inference(subst,[],[refute_0_761:[bind(X_67,$fot(greatest_lower_bound(X_108,identity))),bind(X_68,$fot(inverse(X_108)))]]) ).
cnf(refute_0_2254,plain,
multiply(inverse(X_108),greatest_lower_bound(X_108,identity)) = greatest_lower_bound(inverse(X_108),multiply(inverse(X_108),X_108)),
inference(subst,[],[refute_0_319:[bind(X_104,$fot(inverse(X_108))),bind(X_105,$fot(X_108))]]) ).
cnf(refute_0_2255,plain,
multiply(inverse(X_108),X_108) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_108))]]) ).
cnf(refute_0_2256,plain,
( multiply(inverse(X_108),X_108) != identity
| multiply(inverse(X_108),greatest_lower_bound(X_108,identity)) != greatest_lower_bound(inverse(X_108),multiply(inverse(X_108),X_108))
| multiply(inverse(X_108),greatest_lower_bound(X_108,identity)) = greatest_lower_bound(inverse(X_108),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_108),greatest_lower_bound(X_108,identity)),greatest_lower_bound(inverse(X_108),multiply(inverse(X_108),X_108))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_2257,plain,
( multiply(inverse(X_108),greatest_lower_bound(X_108,identity)) != greatest_lower_bound(inverse(X_108),multiply(inverse(X_108),X_108))
| multiply(inverse(X_108),greatest_lower_bound(X_108,identity)) = greatest_lower_bound(inverse(X_108),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_108),X_108),identity) )],[refute_0_2255,refute_0_2256]) ).
cnf(refute_0_2258,plain,
multiply(inverse(X_108),greatest_lower_bound(X_108,identity)) = greatest_lower_bound(inverse(X_108),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_108),greatest_lower_bound(X_108,identity)),greatest_lower_bound(inverse(X_108),multiply(inverse(X_108),X_108))) )],[refute_0_2254,refute_0_2257]) ).
cnf(refute_0_2259,plain,
greatest_lower_bound(inverse(X_108),identity) = greatest_lower_bound(identity,inverse(X_108)),
inference(subst,[],[refute_0_42:[bind(X,$fot(identity)),bind(Y,$fot(inverse(X_108)))]]) ).
cnf(refute_0_2260,plain,
( multiply(inverse(X_108),greatest_lower_bound(X_108,identity)) != greatest_lower_bound(inverse(X_108),identity)
| greatest_lower_bound(inverse(X_108),identity) != greatest_lower_bound(identity,inverse(X_108))
| multiply(inverse(X_108),greatest_lower_bound(X_108,identity)) = greatest_lower_bound(identity,inverse(X_108)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_108),greatest_lower_bound(X_108,identity)),greatest_lower_bound(identity,inverse(X_108))) ),[0],$fot(greatest_lower_bound(inverse(X_108),identity))]]) ).
cnf(refute_0_2261,plain,
( multiply(inverse(X_108),greatest_lower_bound(X_108,identity)) != greatest_lower_bound(inverse(X_108),identity)
| multiply(inverse(X_108),greatest_lower_bound(X_108,identity)) = greatest_lower_bound(identity,inverse(X_108)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_108),identity),greatest_lower_bound(identity,inverse(X_108))) )],[refute_0_2259,refute_0_2260]) ).
cnf(refute_0_2262,plain,
multiply(inverse(X_108),greatest_lower_bound(X_108,identity)) = greatest_lower_bound(identity,inverse(X_108)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_108),greatest_lower_bound(X_108,identity)),greatest_lower_bound(inverse(X_108),identity)) )],[refute_0_2258,refute_0_2261]) ).
cnf(refute_0_2263,plain,
( multiply(inverse(X_108),greatest_lower_bound(X_108,identity)) != greatest_lower_bound(identity,inverse(X_108))
| multiply(least_upper_bound(inverse(X_108),identity),greatest_lower_bound(X_108,identity)) != least_upper_bound(greatest_lower_bound(X_108,identity),multiply(inverse(X_108),greatest_lower_bound(X_108,identity)))
| multiply(least_upper_bound(inverse(X_108),identity),greatest_lower_bound(X_108,identity)) = least_upper_bound(greatest_lower_bound(X_108,identity),greatest_lower_bound(identity,inverse(X_108))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(X_108),identity),greatest_lower_bound(X_108,identity)),least_upper_bound(greatest_lower_bound(X_108,identity),multiply(inverse(X_108),greatest_lower_bound(X_108,identity)))) ),[1,1],$fot(greatest_lower_bound(identity,inverse(X_108)))]]) ).
cnf(refute_0_2264,plain,
( multiply(least_upper_bound(inverse(X_108),identity),greatest_lower_bound(X_108,identity)) != least_upper_bound(greatest_lower_bound(X_108,identity),multiply(inverse(X_108),greatest_lower_bound(X_108,identity)))
| multiply(least_upper_bound(inverse(X_108),identity),greatest_lower_bound(X_108,identity)) = least_upper_bound(greatest_lower_bound(X_108,identity),greatest_lower_bound(identity,inverse(X_108))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_108),greatest_lower_bound(X_108,identity)),greatest_lower_bound(identity,inverse(X_108))) )],[refute_0_2262,refute_0_2263]) ).
cnf(refute_0_2265,plain,
multiply(least_upper_bound(inverse(X_108),identity),greatest_lower_bound(X_108,identity)) = least_upper_bound(greatest_lower_bound(X_108,identity),greatest_lower_bound(identity,inverse(X_108))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_108),identity),greatest_lower_bound(X_108,identity)),least_upper_bound(greatest_lower_bound(X_108,identity),multiply(inverse(X_108),greatest_lower_bound(X_108,identity)))) )],[refute_0_2253,refute_0_2264]) ).
cnf(refute_0_2266,plain,
multiply(least_upper_bound(inverse(X_108),identity),greatest_lower_bound(X_108,identity)) = multiply(least_upper_bound(identity,inverse(X_108)),greatest_lower_bound(X_108,identity)),
inference(subst,[],[refute_0_1400:[bind(X_133,$fot(inverse(X_108))),bind(X_19,$fot(greatest_lower_bound(X_108,identity)))]]) ).
cnf(refute_0_2267,plain,
( multiply(least_upper_bound(inverse(X_108),identity),greatest_lower_bound(X_108,identity)) != multiply(least_upper_bound(identity,inverse(X_108)),greatest_lower_bound(X_108,identity))
| multiply(least_upper_bound(inverse(X_108),identity),greatest_lower_bound(X_108,identity)) != least_upper_bound(greatest_lower_bound(X_108,identity),greatest_lower_bound(identity,inverse(X_108)))
| multiply(least_upper_bound(identity,inverse(X_108)),greatest_lower_bound(X_108,identity)) = least_upper_bound(greatest_lower_bound(X_108,identity),greatest_lower_bound(identity,inverse(X_108))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(X_108),identity),greatest_lower_bound(X_108,identity)),least_upper_bound(greatest_lower_bound(X_108,identity),greatest_lower_bound(identity,inverse(X_108)))) ),[0],$fot(multiply(least_upper_bound(identity,inverse(X_108)),greatest_lower_bound(X_108,identity)))]]) ).
cnf(refute_0_2268,plain,
( multiply(least_upper_bound(inverse(X_108),identity),greatest_lower_bound(X_108,identity)) != least_upper_bound(greatest_lower_bound(X_108,identity),greatest_lower_bound(identity,inverse(X_108)))
| multiply(least_upper_bound(identity,inverse(X_108)),greatest_lower_bound(X_108,identity)) = least_upper_bound(greatest_lower_bound(X_108,identity),greatest_lower_bound(identity,inverse(X_108))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_108),identity),greatest_lower_bound(X_108,identity)),multiply(least_upper_bound(identity,inverse(X_108)),greatest_lower_bound(X_108,identity))) )],[refute_0_2266,refute_0_2267]) ).
cnf(refute_0_2269,plain,
multiply(least_upper_bound(identity,inverse(X_108)),greatest_lower_bound(X_108,identity)) = least_upper_bound(greatest_lower_bound(X_108,identity),greatest_lower_bound(identity,inverse(X_108))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_108),identity),greatest_lower_bound(X_108,identity)),least_upper_bound(greatest_lower_bound(X_108,identity),greatest_lower_bound(identity,inverse(X_108)))) )],[refute_0_2265,refute_0_2268]) ).
cnf(refute_0_2270,plain,
multiply(greatest_lower_bound(X_207,identity),least_upper_bound(inverse(X_207),identity)) = least_upper_bound(greatest_lower_bound(X_207,identity),multiply(greatest_lower_bound(X_207,identity),inverse(X_207))),
inference(subst,[],[refute_0_528:[bind(X_48,$fot(greatest_lower_bound(X_207,identity))),bind(X_49,$fot(inverse(X_207)))]]) ).
cnf(refute_0_2271,plain,
multiply(greatest_lower_bound(greatest_lower_bound(identity,X_121),X_121),inverse(X_121)) = greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_121),inverse(X_121))),
inference(subst,[],[refute_0_329:[bind(X_120,$fot(greatest_lower_bound(identity,X_121)))]]) ).
cnf(refute_0_2272,plain,
greatest_lower_bound(identity,inverse(X_121)) = multiply(greatest_lower_bound(identity,X_121),inverse(X_121)),
inference(subst,[],[refute_0_436:[bind(X_125,$fot(X_121))]]) ).
cnf(refute_0_2273,plain,
( greatest_lower_bound(identity,inverse(X_121)) != multiply(greatest_lower_bound(identity,X_121),inverse(X_121))
| multiply(greatest_lower_bound(identity,X_121),inverse(X_121)) = greatest_lower_bound(identity,inverse(X_121)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(greatest_lower_bound(identity,inverse(X_121)))),bind(Y0,$fot(multiply(greatest_lower_bound(identity,X_121),inverse(X_121))))]]) ).
cnf(refute_0_2274,plain,
multiply(greatest_lower_bound(identity,X_121),inverse(X_121)) = greatest_lower_bound(identity,inverse(X_121)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(X_121)),multiply(greatest_lower_bound(identity,X_121),inverse(X_121))) )],[refute_0_2272,refute_0_2273]) ).
cnf(refute_0_2275,plain,
( multiply(greatest_lower_bound(greatest_lower_bound(identity,X_121),X_121),inverse(X_121)) != greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_121),inverse(X_121)))
| multiply(greatest_lower_bound(identity,X_121),inverse(X_121)) != greatest_lower_bound(identity,inverse(X_121))
| multiply(greatest_lower_bound(greatest_lower_bound(identity,X_121),X_121),inverse(X_121)) = greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_121))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(greatest_lower_bound(identity,X_121),X_121),inverse(X_121)),greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_121),inverse(X_121)))) ),[1,1],$fot(greatest_lower_bound(identity,inverse(X_121)))]]) ).
cnf(refute_0_2276,plain,
( multiply(greatest_lower_bound(greatest_lower_bound(identity,X_121),X_121),inverse(X_121)) != greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_121),inverse(X_121)))
| multiply(greatest_lower_bound(greatest_lower_bound(identity,X_121),X_121),inverse(X_121)) = greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_121))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_121),inverse(X_121)),greatest_lower_bound(identity,inverse(X_121))) )],[refute_0_2274,refute_0_2275]) ).
cnf(refute_0_2277,plain,
multiply(greatest_lower_bound(greatest_lower_bound(identity,X_121),X_121),inverse(X_121)) = greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_121))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(greatest_lower_bound(identity,X_121),X_121),inverse(X_121)),greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_121),inverse(X_121)))) )],[refute_0_2271,refute_0_2276]) ).
cnf(refute_0_2278,plain,
greatest_lower_bound(X_121,greatest_lower_bound(identity,X_121)) = greatest_lower_bound(X_121,identity),
inference(subst,[],[refute_0_347:[bind(Y,$fot(identity)),bind(X_13,$fot(X_121))]]) ).
cnf(refute_0_2279,plain,
multiply(greatest_lower_bound(X_121,greatest_lower_bound(identity,X_121)),inverse(X_121)) = multiply(greatest_lower_bound(X_121,greatest_lower_bound(identity,X_121)),inverse(X_121)),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(X_121,greatest_lower_bound(identity,X_121)),inverse(X_121)))]]) ).
cnf(refute_0_2280,plain,
( multiply(greatest_lower_bound(X_121,greatest_lower_bound(identity,X_121)),inverse(X_121)) != multiply(greatest_lower_bound(X_121,greatest_lower_bound(identity,X_121)),inverse(X_121))
| greatest_lower_bound(X_121,greatest_lower_bound(identity,X_121)) != greatest_lower_bound(X_121,identity)
| multiply(greatest_lower_bound(X_121,greatest_lower_bound(identity,X_121)),inverse(X_121)) = multiply(greatest_lower_bound(X_121,identity),inverse(X_121)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_121,greatest_lower_bound(identity,X_121)),inverse(X_121)),multiply(greatest_lower_bound(X_121,greatest_lower_bound(identity,X_121)),inverse(X_121))) ),[1,0],$fot(greatest_lower_bound(X_121,identity))]]) ).
cnf(refute_0_2281,plain,
( greatest_lower_bound(X_121,greatest_lower_bound(identity,X_121)) != greatest_lower_bound(X_121,identity)
| multiply(greatest_lower_bound(X_121,greatest_lower_bound(identity,X_121)),inverse(X_121)) = multiply(greatest_lower_bound(X_121,identity),inverse(X_121)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_121,greatest_lower_bound(identity,X_121)),inverse(X_121)),multiply(greatest_lower_bound(X_121,greatest_lower_bound(identity,X_121)),inverse(X_121))) )],[refute_0_2279,refute_0_2280]) ).
cnf(refute_0_2282,plain,
multiply(greatest_lower_bound(X_121,greatest_lower_bound(identity,X_121)),inverse(X_121)) = multiply(greatest_lower_bound(X_121,identity),inverse(X_121)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_121,greatest_lower_bound(identity,X_121)),greatest_lower_bound(X_121,identity)) )],[refute_0_2278,refute_0_2281]) ).
cnf(refute_0_2283,plain,
multiply(greatest_lower_bound(greatest_lower_bound(identity,X_121),X_121),inverse(X_121)) = multiply(greatest_lower_bound(X_121,greatest_lower_bound(identity,X_121)),inverse(X_121)),
inference(subst,[],[refute_0_1880:[bind(X_119,$fot(inverse(X_121))),bind(X_120,$fot(X_121)),bind(X_121,$fot(greatest_lower_bound(identity,X_121)))]]) ).
cnf(refute_0_2284,plain,
( multiply(greatest_lower_bound(X_121,greatest_lower_bound(identity,X_121)),inverse(X_121)) != multiply(greatest_lower_bound(X_121,identity),inverse(X_121))
| multiply(greatest_lower_bound(greatest_lower_bound(identity,X_121),X_121),inverse(X_121)) != multiply(greatest_lower_bound(X_121,greatest_lower_bound(identity,X_121)),inverse(X_121))
| multiply(greatest_lower_bound(greatest_lower_bound(identity,X_121),X_121),inverse(X_121)) = multiply(greatest_lower_bound(X_121,identity),inverse(X_121)) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(greatest_lower_bound(greatest_lower_bound(identity,X_121),X_121),inverse(X_121)))),bind(Y0,$fot(multiply(greatest_lower_bound(X_121,greatest_lower_bound(identity,X_121)),inverse(X_121)))),bind(Z0,$fot(multiply(greatest_lower_bound(X_121,identity),inverse(X_121))))]]) ).
cnf(refute_0_2285,plain,
( multiply(greatest_lower_bound(X_121,greatest_lower_bound(identity,X_121)),inverse(X_121)) != multiply(greatest_lower_bound(X_121,identity),inverse(X_121))
| multiply(greatest_lower_bound(greatest_lower_bound(identity,X_121),X_121),inverse(X_121)) = multiply(greatest_lower_bound(X_121,identity),inverse(X_121)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(greatest_lower_bound(identity,X_121),X_121),inverse(X_121)),multiply(greatest_lower_bound(X_121,greatest_lower_bound(identity,X_121)),inverse(X_121))) )],[refute_0_2283,refute_0_2284]) ).
cnf(refute_0_2286,plain,
multiply(greatest_lower_bound(greatest_lower_bound(identity,X_121),X_121),inverse(X_121)) = multiply(greatest_lower_bound(X_121,identity),inverse(X_121)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_121,greatest_lower_bound(identity,X_121)),inverse(X_121)),multiply(greatest_lower_bound(X_121,identity),inverse(X_121))) )],[refute_0_2282,refute_0_2285]) ).
cnf(refute_0_2287,plain,
( multiply(greatest_lower_bound(greatest_lower_bound(identity,X_121),X_121),inverse(X_121)) != multiply(greatest_lower_bound(X_121,identity),inverse(X_121))
| multiply(greatest_lower_bound(greatest_lower_bound(identity,X_121),X_121),inverse(X_121)) != greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_121)))
| multiply(greatest_lower_bound(X_121,identity),inverse(X_121)) = greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_121))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(greatest_lower_bound(identity,X_121),X_121),inverse(X_121)),greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_121)))) ),[0],$fot(multiply(greatest_lower_bound(X_121,identity),inverse(X_121)))]]) ).
cnf(refute_0_2288,plain,
( multiply(greatest_lower_bound(greatest_lower_bound(identity,X_121),X_121),inverse(X_121)) != greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_121)))
| multiply(greatest_lower_bound(X_121,identity),inverse(X_121)) = greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_121))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(greatest_lower_bound(identity,X_121),X_121),inverse(X_121)),multiply(greatest_lower_bound(X_121,identity),inverse(X_121))) )],[refute_0_2286,refute_0_2287]) ).
cnf(refute_0_2289,plain,
greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_121))) = greatest_lower_bound(identity,inverse(X_121)),
inference(subst,[],[refute_0_354:[bind(X_16,$fot(inverse(X_121))),bind(X_17,$fot(identity))]]) ).
cnf(refute_0_2290,plain,
( multiply(greatest_lower_bound(X_121,identity),inverse(X_121)) != greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_121)))
| greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_121))) != greatest_lower_bound(identity,inverse(X_121))
| multiply(greatest_lower_bound(X_121,identity),inverse(X_121)) = greatest_lower_bound(identity,inverse(X_121)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_121,identity),inverse(X_121)),greatest_lower_bound(identity,inverse(X_121))) ),[0],$fot(greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_121))))]]) ).
cnf(refute_0_2291,plain,
( multiply(greatest_lower_bound(X_121,identity),inverse(X_121)) != greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_121)))
| multiply(greatest_lower_bound(X_121,identity),inverse(X_121)) = greatest_lower_bound(identity,inverse(X_121)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_121))),greatest_lower_bound(identity,inverse(X_121))) )],[refute_0_2289,refute_0_2290]) ).
cnf(refute_0_2292,plain,
( multiply(greatest_lower_bound(greatest_lower_bound(identity,X_121),X_121),inverse(X_121)) != greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_121)))
| multiply(greatest_lower_bound(X_121,identity),inverse(X_121)) = greatest_lower_bound(identity,inverse(X_121)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_121,identity),inverse(X_121)),greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_121)))) )],[refute_0_2288,refute_0_2291]) ).
cnf(refute_0_2293,plain,
multiply(greatest_lower_bound(X_121,identity),inverse(X_121)) = greatest_lower_bound(identity,inverse(X_121)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(greatest_lower_bound(identity,X_121),X_121),inverse(X_121)),greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_121)))) )],[refute_0_2277,refute_0_2292]) ).
cnf(refute_0_2294,plain,
multiply(greatest_lower_bound(X_207,identity),inverse(X_207)) = greatest_lower_bound(identity,inverse(X_207)),
inference(subst,[],[refute_0_2293:[bind(X_121,$fot(X_207))]]) ).
cnf(refute_0_2295,plain,
( multiply(greatest_lower_bound(X_207,identity),inverse(X_207)) != greatest_lower_bound(identity,inverse(X_207))
| multiply(greatest_lower_bound(X_207,identity),least_upper_bound(inverse(X_207),identity)) != least_upper_bound(greatest_lower_bound(X_207,identity),multiply(greatest_lower_bound(X_207,identity),inverse(X_207)))
| multiply(greatest_lower_bound(X_207,identity),least_upper_bound(inverse(X_207),identity)) = least_upper_bound(greatest_lower_bound(X_207,identity),greatest_lower_bound(identity,inverse(X_207))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_207,identity),least_upper_bound(inverse(X_207),identity)),least_upper_bound(greatest_lower_bound(X_207,identity),multiply(greatest_lower_bound(X_207,identity),inverse(X_207)))) ),[1,1],$fot(greatest_lower_bound(identity,inverse(X_207)))]]) ).
cnf(refute_0_2296,plain,
( multiply(greatest_lower_bound(X_207,identity),least_upper_bound(inverse(X_207),identity)) != least_upper_bound(greatest_lower_bound(X_207,identity),multiply(greatest_lower_bound(X_207,identity),inverse(X_207)))
| multiply(greatest_lower_bound(X_207,identity),least_upper_bound(inverse(X_207),identity)) = least_upper_bound(greatest_lower_bound(X_207,identity),greatest_lower_bound(identity,inverse(X_207))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_207,identity),inverse(X_207)),greatest_lower_bound(identity,inverse(X_207))) )],[refute_0_2294,refute_0_2295]) ).
cnf(refute_0_2297,plain,
multiply(greatest_lower_bound(X_207,identity),least_upper_bound(inverse(X_207),identity)) = least_upper_bound(greatest_lower_bound(X_207,identity),greatest_lower_bound(identity,inverse(X_207))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_207,identity),least_upper_bound(inverse(X_207),identity)),least_upper_bound(greatest_lower_bound(X_207,identity),multiply(greatest_lower_bound(X_207,identity),inverse(X_207)))) )],[refute_0_2270,refute_0_2296]) ).
cnf(refute_0_2298,plain,
multiply(greatest_lower_bound(X_207,identity),least_upper_bound(inverse(X_207),identity)) = multiply(greatest_lower_bound(X_207,identity),least_upper_bound(identity,inverse(X_207))),
inference(subst,[],[refute_0_598:[bind(X_19,$fot(greatest_lower_bound(X_207,identity))),bind(X_88,$fot(inverse(X_207)))]]) ).
cnf(refute_0_2299,plain,
( multiply(greatest_lower_bound(X_207,identity),least_upper_bound(inverse(X_207),identity)) != multiply(greatest_lower_bound(X_207,identity),least_upper_bound(identity,inverse(X_207)))
| multiply(greatest_lower_bound(X_207,identity),least_upper_bound(inverse(X_207),identity)) != least_upper_bound(greatest_lower_bound(X_207,identity),greatest_lower_bound(identity,inverse(X_207)))
| multiply(greatest_lower_bound(X_207,identity),least_upper_bound(identity,inverse(X_207))) = least_upper_bound(greatest_lower_bound(X_207,identity),greatest_lower_bound(identity,inverse(X_207))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_207,identity),least_upper_bound(inverse(X_207),identity)),least_upper_bound(greatest_lower_bound(X_207,identity),greatest_lower_bound(identity,inverse(X_207)))) ),[0],$fot(multiply(greatest_lower_bound(X_207,identity),least_upper_bound(identity,inverse(X_207))))]]) ).
cnf(refute_0_2300,plain,
( multiply(greatest_lower_bound(X_207,identity),least_upper_bound(inverse(X_207),identity)) != least_upper_bound(greatest_lower_bound(X_207,identity),greatest_lower_bound(identity,inverse(X_207)))
| multiply(greatest_lower_bound(X_207,identity),least_upper_bound(identity,inverse(X_207))) = least_upper_bound(greatest_lower_bound(X_207,identity),greatest_lower_bound(identity,inverse(X_207))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_207,identity),least_upper_bound(inverse(X_207),identity)),multiply(greatest_lower_bound(X_207,identity),least_upper_bound(identity,inverse(X_207)))) )],[refute_0_2298,refute_0_2299]) ).
cnf(refute_0_2301,plain,
( multiply(least_upper_bound(identity,inverse(X_108)),greatest_lower_bound(X_108,identity)) != least_upper_bound(greatest_lower_bound(X_108,identity),greatest_lower_bound(identity,inverse(X_108)))
| least_upper_bound(greatest_lower_bound(X_108,identity),greatest_lower_bound(identity,inverse(X_108))) = multiply(least_upper_bound(identity,inverse(X_108)),greatest_lower_bound(X_108,identity)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(least_upper_bound(identity,inverse(X_108)),greatest_lower_bound(X_108,identity)))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(X_108,identity),greatest_lower_bound(identity,inverse(X_108)))))]]) ).
cnf(refute_0_2302,plain,
least_upper_bound(greatest_lower_bound(X_108,identity),greatest_lower_bound(identity,inverse(X_108))) = multiply(least_upper_bound(identity,inverse(X_108)),greatest_lower_bound(X_108,identity)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_108)),greatest_lower_bound(X_108,identity)),least_upper_bound(greatest_lower_bound(X_108,identity),greatest_lower_bound(identity,inverse(X_108)))) )],[refute_0_2269,refute_0_2301]) ).
cnf(refute_0_2303,plain,
least_upper_bound(greatest_lower_bound(X_207,identity),greatest_lower_bound(identity,inverse(X_207))) = multiply(least_upper_bound(identity,inverse(X_207)),greatest_lower_bound(X_207,identity)),
inference(subst,[],[refute_0_2302:[bind(X_108,$fot(X_207))]]) ).
cnf(refute_0_2304,plain,
( multiply(greatest_lower_bound(X_207,identity),least_upper_bound(identity,inverse(X_207))) != least_upper_bound(greatest_lower_bound(X_207,identity),greatest_lower_bound(identity,inverse(X_207)))
| least_upper_bound(greatest_lower_bound(X_207,identity),greatest_lower_bound(identity,inverse(X_207))) != multiply(least_upper_bound(identity,inverse(X_207)),greatest_lower_bound(X_207,identity))
| multiply(greatest_lower_bound(X_207,identity),least_upper_bound(identity,inverse(X_207))) = multiply(least_upper_bound(identity,inverse(X_207)),greatest_lower_bound(X_207,identity)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_207,identity),least_upper_bound(identity,inverse(X_207))),multiply(least_upper_bound(identity,inverse(X_207)),greatest_lower_bound(X_207,identity))) ),[0],$fot(least_upper_bound(greatest_lower_bound(X_207,identity),greatest_lower_bound(identity,inverse(X_207))))]]) ).
cnf(refute_0_2305,plain,
( multiply(greatest_lower_bound(X_207,identity),least_upper_bound(identity,inverse(X_207))) != least_upper_bound(greatest_lower_bound(X_207,identity),greatest_lower_bound(identity,inverse(X_207)))
| multiply(greatest_lower_bound(X_207,identity),least_upper_bound(identity,inverse(X_207))) = multiply(least_upper_bound(identity,inverse(X_207)),greatest_lower_bound(X_207,identity)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_207,identity),greatest_lower_bound(identity,inverse(X_207))),multiply(least_upper_bound(identity,inverse(X_207)),greatest_lower_bound(X_207,identity))) )],[refute_0_2303,refute_0_2304]) ).
cnf(refute_0_2306,plain,
( multiply(greatest_lower_bound(X_207,identity),least_upper_bound(inverse(X_207),identity)) != least_upper_bound(greatest_lower_bound(X_207,identity),greatest_lower_bound(identity,inverse(X_207)))
| multiply(greatest_lower_bound(X_207,identity),least_upper_bound(identity,inverse(X_207))) = multiply(least_upper_bound(identity,inverse(X_207)),greatest_lower_bound(X_207,identity)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_207,identity),least_upper_bound(identity,inverse(X_207))),least_upper_bound(greatest_lower_bound(X_207,identity),greatest_lower_bound(identity,inverse(X_207)))) )],[refute_0_2300,refute_0_2305]) ).
cnf(refute_0_2307,plain,
multiply(greatest_lower_bound(X_207,identity),least_upper_bound(identity,inverse(X_207))) = multiply(least_upper_bound(identity,inverse(X_207)),greatest_lower_bound(X_207,identity)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_207,identity),least_upper_bound(inverse(X_207),identity)),least_upper_bound(greatest_lower_bound(X_207,identity),greatest_lower_bound(identity,inverse(X_207)))) )],[refute_0_2297,refute_0_2306]) ).
cnf(refute_0_2308,plain,
( multiply(greatest_lower_bound(X_207,identity),least_upper_bound(identity,inverse(X_207))) != multiply(least_upper_bound(identity,inverse(X_207)),greatest_lower_bound(X_207,identity))
| multiply(least_upper_bound(identity,inverse(X_207)),greatest_lower_bound(X_207,identity)) = multiply(greatest_lower_bound(X_207,identity),least_upper_bound(identity,inverse(X_207))) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(greatest_lower_bound(X_207,identity),least_upper_bound(identity,inverse(X_207))))),bind(Y0,$fot(multiply(least_upper_bound(identity,inverse(X_207)),greatest_lower_bound(X_207,identity))))]]) ).
cnf(refute_0_2309,plain,
multiply(least_upper_bound(identity,inverse(X_207)),greatest_lower_bound(X_207,identity)) = multiply(greatest_lower_bound(X_207,identity),least_upper_bound(identity,inverse(X_207))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_207,identity),least_upper_bound(identity,inverse(X_207))),multiply(least_upper_bound(identity,inverse(X_207)),greatest_lower_bound(X_207,identity))) )],[refute_0_2307,refute_0_2308]) ).
cnf(refute_0_2310,plain,
multiply(least_upper_bound(identity,inverse(X_108)),greatest_lower_bound(X_108,identity)) = multiply(greatest_lower_bound(X_108,identity),least_upper_bound(identity,inverse(X_108))),
inference(subst,[],[refute_0_2309:[bind(X_207,$fot(X_108))]]) ).
cnf(refute_0_2311,plain,
( multiply(least_upper_bound(identity,inverse(X_108)),greatest_lower_bound(X_108,identity)) != multiply(greatest_lower_bound(X_108,identity),least_upper_bound(identity,inverse(X_108)))
| multiply(least_upper_bound(identity,inverse(X_108)),greatest_lower_bound(X_108,identity)) != least_upper_bound(greatest_lower_bound(X_108,identity),greatest_lower_bound(identity,inverse(X_108)))
| multiply(greatest_lower_bound(X_108,identity),least_upper_bound(identity,inverse(X_108))) = least_upper_bound(greatest_lower_bound(X_108,identity),greatest_lower_bound(identity,inverse(X_108))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_108)),greatest_lower_bound(X_108,identity)),least_upper_bound(greatest_lower_bound(X_108,identity),greatest_lower_bound(identity,inverse(X_108)))) ),[0],$fot(multiply(greatest_lower_bound(X_108,identity),least_upper_bound(identity,inverse(X_108))))]]) ).
cnf(refute_0_2312,plain,
( multiply(least_upper_bound(identity,inverse(X_108)),greatest_lower_bound(X_108,identity)) != least_upper_bound(greatest_lower_bound(X_108,identity),greatest_lower_bound(identity,inverse(X_108)))
| multiply(greatest_lower_bound(X_108,identity),least_upper_bound(identity,inverse(X_108))) = least_upper_bound(greatest_lower_bound(X_108,identity),greatest_lower_bound(identity,inverse(X_108))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_108)),greatest_lower_bound(X_108,identity)),multiply(greatest_lower_bound(X_108,identity),least_upper_bound(identity,inverse(X_108)))) )],[refute_0_2310,refute_0_2311]) ).
cnf(refute_0_2313,plain,
multiply(greatest_lower_bound(X_108,identity),least_upper_bound(identity,inverse(X_108))) = least_upper_bound(greatest_lower_bound(X_108,identity),greatest_lower_bound(identity,inverse(X_108))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_108)),greatest_lower_bound(X_108,identity)),least_upper_bound(greatest_lower_bound(X_108,identity),greatest_lower_bound(identity,inverse(X_108)))) )],[refute_0_2269,refute_0_2312]) ).
cnf(refute_0_2314,plain,
multiply(greatest_lower_bound(X_443,identity),least_upper_bound(identity,inverse(X_443))) = least_upper_bound(greatest_lower_bound(X_443,identity),greatest_lower_bound(identity,inverse(X_443))),
inference(subst,[],[refute_0_2313:[bind(X_108,$fot(X_443))]]) ).
cnf(refute_0_2315,plain,
( multiply(greatest_lower_bound(X_443,identity),least_upper_bound(identity,inverse(X_443))) != least_upper_bound(greatest_lower_bound(X_443,identity),greatest_lower_bound(identity,inverse(X_443)))
| least_upper_bound(greatest_lower_bound(X_443,identity),greatest_lower_bound(identity,inverse(X_443))) = multiply(greatest_lower_bound(X_443,identity),least_upper_bound(identity,inverse(X_443))) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(greatest_lower_bound(X_443,identity),least_upper_bound(identity,inverse(X_443))))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(X_443,identity),greatest_lower_bound(identity,inverse(X_443)))))]]) ).
cnf(refute_0_2316,plain,
least_upper_bound(greatest_lower_bound(X_443,identity),greatest_lower_bound(identity,inverse(X_443))) = multiply(greatest_lower_bound(X_443,identity),least_upper_bound(identity,inverse(X_443))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_443,identity),least_upper_bound(identity,inverse(X_443))),least_upper_bound(greatest_lower_bound(X_443,identity),greatest_lower_bound(identity,inverse(X_443)))) )],[refute_0_2314,refute_0_2315]) ).
cnf(refute_0_2317,plain,
( greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,inverse(X_443)),greatest_lower_bound(X_443,identity))) != greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_443,identity),greatest_lower_bound(identity,inverse(X_443))))
| least_upper_bound(greatest_lower_bound(X_443,identity),greatest_lower_bound(identity,inverse(X_443))) != multiply(greatest_lower_bound(X_443,identity),least_upper_bound(identity,inverse(X_443)))
| greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,inverse(X_443)),greatest_lower_bound(X_443,identity))) = greatest_lower_bound(identity,multiply(greatest_lower_bound(X_443,identity),least_upper_bound(identity,inverse(X_443)))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,inverse(X_443)),greatest_lower_bound(X_443,identity))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_443,identity),greatest_lower_bound(identity,inverse(X_443))))) ),[1,1],$fot(multiply(greatest_lower_bound(X_443,identity),least_upper_bound(identity,inverse(X_443))))]]) ).
cnf(refute_0_2318,plain,
( greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,inverse(X_443)),greatest_lower_bound(X_443,identity))) != greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_443,identity),greatest_lower_bound(identity,inverse(X_443))))
| greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,inverse(X_443)),greatest_lower_bound(X_443,identity))) = greatest_lower_bound(identity,multiply(greatest_lower_bound(X_443,identity),least_upper_bound(identity,inverse(X_443)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_443,identity),greatest_lower_bound(identity,inverse(X_443))),multiply(greatest_lower_bound(X_443,identity),least_upper_bound(identity,inverse(X_443)))) )],[refute_0_2316,refute_0_2317]) ).
cnf(refute_0_2319,plain,
greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,inverse(X_443)),greatest_lower_bound(X_443,identity))) = greatest_lower_bound(identity,multiply(greatest_lower_bound(X_443,identity),least_upper_bound(identity,inverse(X_443)))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,inverse(X_443)),greatest_lower_bound(X_443,identity))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_443,identity),greatest_lower_bound(identity,inverse(X_443))))) )],[refute_0_2252,refute_0_2318]) ).
cnf(refute_0_2320,plain,
least_upper_bound(greatest_lower_bound(identity,X_443),greatest_lower_bound(identity,inverse(X_443))) = multiply(greatest_lower_bound(identity,X_443),least_upper_bound(identity,inverse(X_443))),
inference(subst,[],[refute_0_1416:[bind(X_126,$fot(X_443))]]) ).
cnf(refute_0_2321,plain,
greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_443),greatest_lower_bound(identity,inverse(X_443)))) = greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_443),greatest_lower_bound(identity,inverse(X_443)))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_443),greatest_lower_bound(identity,inverse(X_443)))))]]) ).
cnf(refute_0_2322,plain,
( greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_443),greatest_lower_bound(identity,inverse(X_443)))) != greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_443),greatest_lower_bound(identity,inverse(X_443))))
| least_upper_bound(greatest_lower_bound(identity,X_443),greatest_lower_bound(identity,inverse(X_443))) != multiply(greatest_lower_bound(identity,X_443),least_upper_bound(identity,inverse(X_443)))
| greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_443),greatest_lower_bound(identity,inverse(X_443)))) = greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_443),least_upper_bound(identity,inverse(X_443)))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_443),greatest_lower_bound(identity,inverse(X_443)))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_443),greatest_lower_bound(identity,inverse(X_443))))) ),[1,1],$fot(multiply(greatest_lower_bound(identity,X_443),least_upper_bound(identity,inverse(X_443))))]]) ).
cnf(refute_0_2323,plain,
( least_upper_bound(greatest_lower_bound(identity,X_443),greatest_lower_bound(identity,inverse(X_443))) != multiply(greatest_lower_bound(identity,X_443),least_upper_bound(identity,inverse(X_443)))
| greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_443),greatest_lower_bound(identity,inverse(X_443)))) = greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_443),least_upper_bound(identity,inverse(X_443)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_443),greatest_lower_bound(identity,inverse(X_443)))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_443),greatest_lower_bound(identity,inverse(X_443))))) )],[refute_0_2321,refute_0_2322]) ).
cnf(refute_0_2324,plain,
greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_443),greatest_lower_bound(identity,inverse(X_443)))) = greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_443),least_upper_bound(identity,inverse(X_443)))),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,X_443),greatest_lower_bound(identity,inverse(X_443))),multiply(greatest_lower_bound(identity,X_443),least_upper_bound(identity,inverse(X_443)))) )],[refute_0_2320,refute_0_2323]) ).
cnf(refute_0_2325,plain,
greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_410),X_322)) = greatest_lower_bound(identity,least_upper_bound(X_322,greatest_lower_bound(identity,X_410))),
inference(subst,[],[refute_0_2251:[bind(X_324,$fot(greatest_lower_bound(identity,X_410)))]]) ).
cnf(refute_0_2326,plain,
multiply(X_48,least_upper_bound(greatest_lower_bound(inverse(X_48),X_112),identity)) = least_upper_bound(X_48,multiply(X_48,greatest_lower_bound(inverse(X_48),X_112))),
inference(subst,[],[refute_0_528:[bind(X_49,$fot(greatest_lower_bound(inverse(X_48),X_112)))]]) ).
cnf(refute_0_2327,plain,
multiply(X_48,greatest_lower_bound(inverse(X_48),X_112)) = greatest_lower_bound(identity,multiply(X_48,X_112)),
inference(subst,[],[refute_0_1710:[bind(X_104,$fot(X_48)),bind(X_106,$fot(X_112))]]) ).
cnf(refute_0_2328,plain,
( multiply(X_48,greatest_lower_bound(inverse(X_48),X_112)) != greatest_lower_bound(identity,multiply(X_48,X_112))
| multiply(X_48,least_upper_bound(greatest_lower_bound(inverse(X_48),X_112),identity)) != least_upper_bound(X_48,multiply(X_48,greatest_lower_bound(inverse(X_48),X_112)))
| multiply(X_48,least_upper_bound(greatest_lower_bound(inverse(X_48),X_112),identity)) = least_upper_bound(X_48,greatest_lower_bound(identity,multiply(X_48,X_112))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_48,least_upper_bound(greatest_lower_bound(inverse(X_48),X_112),identity)),least_upper_bound(X_48,multiply(X_48,greatest_lower_bound(inverse(X_48),X_112)))) ),[1,1],$fot(greatest_lower_bound(identity,multiply(X_48,X_112)))]]) ).
cnf(refute_0_2329,plain,
( multiply(X_48,least_upper_bound(greatest_lower_bound(inverse(X_48),X_112),identity)) != least_upper_bound(X_48,multiply(X_48,greatest_lower_bound(inverse(X_48),X_112)))
| multiply(X_48,least_upper_bound(greatest_lower_bound(inverse(X_48),X_112),identity)) = least_upper_bound(X_48,greatest_lower_bound(identity,multiply(X_48,X_112))) ),
inference(resolve,[$cnf( $equal(multiply(X_48,greatest_lower_bound(inverse(X_48),X_112)),greatest_lower_bound(identity,multiply(X_48,X_112))) )],[refute_0_2327,refute_0_2328]) ).
cnf(refute_0_2330,plain,
multiply(X_48,least_upper_bound(greatest_lower_bound(inverse(X_48),X_112),identity)) = least_upper_bound(X_48,greatest_lower_bound(identity,multiply(X_48,X_112))),
inference(resolve,[$cnf( $equal(multiply(X_48,least_upper_bound(greatest_lower_bound(inverse(X_48),X_112),identity)),least_upper_bound(X_48,multiply(X_48,greatest_lower_bound(inverse(X_48),X_112)))) )],[refute_0_2326,refute_0_2329]) ).
cnf(refute_0_2331,plain,
multiply(X_48,least_upper_bound(greatest_lower_bound(inverse(X_48),X_112),identity)) = multiply(X_48,least_upper_bound(identity,greatest_lower_bound(inverse(X_48),X_112))),
inference(subst,[],[refute_0_598:[bind(X_19,$fot(X_48)),bind(X_88,$fot(greatest_lower_bound(inverse(X_48),X_112)))]]) ).
cnf(refute_0_2332,plain,
( multiply(X_48,least_upper_bound(greatest_lower_bound(inverse(X_48),X_112),identity)) != multiply(X_48,least_upper_bound(identity,greatest_lower_bound(inverse(X_48),X_112)))
| multiply(X_48,least_upper_bound(greatest_lower_bound(inverse(X_48),X_112),identity)) != least_upper_bound(X_48,greatest_lower_bound(identity,multiply(X_48,X_112)))
| multiply(X_48,least_upper_bound(identity,greatest_lower_bound(inverse(X_48),X_112))) = least_upper_bound(X_48,greatest_lower_bound(identity,multiply(X_48,X_112))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_48,least_upper_bound(greatest_lower_bound(inverse(X_48),X_112),identity)),least_upper_bound(X_48,greatest_lower_bound(identity,multiply(X_48,X_112)))) ),[0],$fot(multiply(X_48,least_upper_bound(identity,greatest_lower_bound(inverse(X_48),X_112))))]]) ).
cnf(refute_0_2333,plain,
( multiply(X_48,least_upper_bound(greatest_lower_bound(inverse(X_48),X_112),identity)) != least_upper_bound(X_48,greatest_lower_bound(identity,multiply(X_48,X_112)))
| multiply(X_48,least_upper_bound(identity,greatest_lower_bound(inverse(X_48),X_112))) = least_upper_bound(X_48,greatest_lower_bound(identity,multiply(X_48,X_112))) ),
inference(resolve,[$cnf( $equal(multiply(X_48,least_upper_bound(greatest_lower_bound(inverse(X_48),X_112),identity)),multiply(X_48,least_upper_bound(identity,greatest_lower_bound(inverse(X_48),X_112)))) )],[refute_0_2331,refute_0_2332]) ).
cnf(refute_0_2334,plain,
multiply(X_48,least_upper_bound(identity,greatest_lower_bound(inverse(X_48),X_112))) = least_upper_bound(X_48,greatest_lower_bound(identity,multiply(X_48,X_112))),
inference(resolve,[$cnf( $equal(multiply(X_48,least_upper_bound(greatest_lower_bound(inverse(X_48),X_112),identity)),least_upper_bound(X_48,greatest_lower_bound(identity,multiply(X_48,X_112)))) )],[refute_0_2330,refute_0_2333]) ).
cnf(refute_0_2335,plain,
multiply(X_399,least_upper_bound(identity,greatest_lower_bound(inverse(X_399),multiply(inverse(X_399),X_105)))) = least_upper_bound(X_399,greatest_lower_bound(identity,multiply(X_399,multiply(inverse(X_399),X_105)))),
inference(subst,[],[refute_0_2334:[bind(X_112,$fot(multiply(inverse(X_399),X_105))),bind(X_48,$fot(X_399))]]) ).
cnf(refute_0_2336,plain,
multiply(inverse(X_399),greatest_lower_bound(X_105,identity)) = greatest_lower_bound(inverse(X_399),multiply(inverse(X_399),X_105)),
inference(subst,[],[refute_0_319:[bind(X_104,$fot(inverse(X_399)))]]) ).
cnf(refute_0_2337,plain,
( multiply(inverse(X_399),greatest_lower_bound(X_105,identity)) != greatest_lower_bound(inverse(X_399),multiply(inverse(X_399),X_105))
| greatest_lower_bound(inverse(X_399),multiply(inverse(X_399),X_105)) = multiply(inverse(X_399),greatest_lower_bound(X_105,identity)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(inverse(X_399),greatest_lower_bound(X_105,identity)))),bind(Y0,$fot(greatest_lower_bound(inverse(X_399),multiply(inverse(X_399),X_105))))]]) ).
cnf(refute_0_2338,plain,
greatest_lower_bound(inverse(X_399),multiply(inverse(X_399),X_105)) = multiply(inverse(X_399),greatest_lower_bound(X_105,identity)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_399),greatest_lower_bound(X_105,identity)),greatest_lower_bound(inverse(X_399),multiply(inverse(X_399),X_105))) )],[refute_0_2336,refute_0_2337]) ).
cnf(refute_0_2339,plain,
( multiply(X_399,least_upper_bound(identity,greatest_lower_bound(inverse(X_399),multiply(inverse(X_399),X_105)))) != least_upper_bound(X_399,greatest_lower_bound(identity,multiply(X_399,multiply(inverse(X_399),X_105))))
| greatest_lower_bound(inverse(X_399),multiply(inverse(X_399),X_105)) != multiply(inverse(X_399),greatest_lower_bound(X_105,identity))
| multiply(X_399,least_upper_bound(identity,multiply(inverse(X_399),greatest_lower_bound(X_105,identity)))) = least_upper_bound(X_399,greatest_lower_bound(identity,multiply(X_399,multiply(inverse(X_399),X_105)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_399,least_upper_bound(identity,greatest_lower_bound(inverse(X_399),multiply(inverse(X_399),X_105)))),least_upper_bound(X_399,greatest_lower_bound(identity,multiply(X_399,multiply(inverse(X_399),X_105))))) ),[0,1,1],$fot(multiply(inverse(X_399),greatest_lower_bound(X_105,identity)))]]) ).
cnf(refute_0_2340,plain,
( multiply(X_399,least_upper_bound(identity,greatest_lower_bound(inverse(X_399),multiply(inverse(X_399),X_105)))) != least_upper_bound(X_399,greatest_lower_bound(identity,multiply(X_399,multiply(inverse(X_399),X_105))))
| multiply(X_399,least_upper_bound(identity,multiply(inverse(X_399),greatest_lower_bound(X_105,identity)))) = least_upper_bound(X_399,greatest_lower_bound(identity,multiply(X_399,multiply(inverse(X_399),X_105)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_399),multiply(inverse(X_399),X_105)),multiply(inverse(X_399),greatest_lower_bound(X_105,identity))) )],[refute_0_2338,refute_0_2339]) ).
cnf(refute_0_2341,plain,
multiply(X_399,least_upper_bound(identity,multiply(inverse(X_399),greatest_lower_bound(X_105,identity)))) = least_upper_bound(X_399,greatest_lower_bound(identity,multiply(X_399,multiply(inverse(X_399),X_105)))),
inference(resolve,[$cnf( $equal(multiply(X_399,least_upper_bound(identity,greatest_lower_bound(inverse(X_399),multiply(inverse(X_399),X_105)))),least_upper_bound(X_399,greatest_lower_bound(identity,multiply(X_399,multiply(inverse(X_399),X_105))))) )],[refute_0_2335,refute_0_2340]) ).
cnf(refute_0_2342,plain,
multiply(X_399,identity) = X_399,
inference(subst,[],[refute_0_88:[bind(X_33,$fot(X_399))]]) ).
cnf(refute_0_2343,plain,
least_upper_bound(multiply(X_399,identity),greatest_lower_bound(X_105,identity)) = least_upper_bound(multiply(X_399,identity),greatest_lower_bound(X_105,identity)),
introduced(tautology,[refl,[$fot(least_upper_bound(multiply(X_399,identity),greatest_lower_bound(X_105,identity)))]]) ).
cnf(refute_0_2344,plain,
( multiply(X_399,identity) != X_399
| least_upper_bound(multiply(X_399,identity),greatest_lower_bound(X_105,identity)) != least_upper_bound(multiply(X_399,identity),greatest_lower_bound(X_105,identity))
| least_upper_bound(multiply(X_399,identity),greatest_lower_bound(X_105,identity)) = least_upper_bound(X_399,greatest_lower_bound(X_105,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_399,identity),greatest_lower_bound(X_105,identity)),least_upper_bound(multiply(X_399,identity),greatest_lower_bound(X_105,identity))) ),[1,0],$fot(X_399)]]) ).
cnf(refute_0_2345,plain,
( multiply(X_399,identity) != X_399
| least_upper_bound(multiply(X_399,identity),greatest_lower_bound(X_105,identity)) = least_upper_bound(X_399,greatest_lower_bound(X_105,identity)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_399,identity),greatest_lower_bound(X_105,identity)),least_upper_bound(multiply(X_399,identity),greatest_lower_bound(X_105,identity))) )],[refute_0_2343,refute_0_2344]) ).
cnf(refute_0_2346,plain,
least_upper_bound(multiply(X_399,identity),greatest_lower_bound(X_105,identity)) = least_upper_bound(X_399,greatest_lower_bound(X_105,identity)),
inference(resolve,[$cnf( $equal(multiply(X_399,identity),X_399) )],[refute_0_2342,refute_0_2345]) ).
cnf(refute_0_2347,plain,
multiply(X_399,least_upper_bound(identity,multiply(inverse(X_399),greatest_lower_bound(X_105,identity)))) = least_upper_bound(multiply(X_399,identity),greatest_lower_bound(X_105,identity)),
inference(subst,[],[refute_0_987:[bind(X,$fot(X_399)),bind(Y,$fot(identity)),bind(X_81,$fot(greatest_lower_bound(X_105,identity)))]]) ).
cnf(refute_0_2348,plain,
( multiply(X_399,least_upper_bound(identity,multiply(inverse(X_399),greatest_lower_bound(X_105,identity)))) != least_upper_bound(multiply(X_399,identity),greatest_lower_bound(X_105,identity))
| least_upper_bound(multiply(X_399,identity),greatest_lower_bound(X_105,identity)) != least_upper_bound(X_399,greatest_lower_bound(X_105,identity))
| multiply(X_399,least_upper_bound(identity,multiply(inverse(X_399),greatest_lower_bound(X_105,identity)))) = least_upper_bound(X_399,greatest_lower_bound(X_105,identity)) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(X_399,least_upper_bound(identity,multiply(inverse(X_399),greatest_lower_bound(X_105,identity)))))),bind(Y0,$fot(least_upper_bound(multiply(X_399,identity),greatest_lower_bound(X_105,identity)))),bind(Z0,$fot(least_upper_bound(X_399,greatest_lower_bound(X_105,identity))))]]) ).
cnf(refute_0_2349,plain,
( least_upper_bound(multiply(X_399,identity),greatest_lower_bound(X_105,identity)) != least_upper_bound(X_399,greatest_lower_bound(X_105,identity))
| multiply(X_399,least_upper_bound(identity,multiply(inverse(X_399),greatest_lower_bound(X_105,identity)))) = least_upper_bound(X_399,greatest_lower_bound(X_105,identity)) ),
inference(resolve,[$cnf( $equal(multiply(X_399,least_upper_bound(identity,multiply(inverse(X_399),greatest_lower_bound(X_105,identity)))),least_upper_bound(multiply(X_399,identity),greatest_lower_bound(X_105,identity))) )],[refute_0_2347,refute_0_2348]) ).
cnf(refute_0_2350,plain,
multiply(X_399,least_upper_bound(identity,multiply(inverse(X_399),greatest_lower_bound(X_105,identity)))) = least_upper_bound(X_399,greatest_lower_bound(X_105,identity)),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_399,identity),greatest_lower_bound(X_105,identity)),least_upper_bound(X_399,greatest_lower_bound(X_105,identity))) )],[refute_0_2346,refute_0_2349]) ).
cnf(refute_0_2351,plain,
( multiply(X_399,least_upper_bound(identity,multiply(inverse(X_399),greatest_lower_bound(X_105,identity)))) != least_upper_bound(X_399,greatest_lower_bound(X_105,identity))
| multiply(X_399,least_upper_bound(identity,multiply(inverse(X_399),greatest_lower_bound(X_105,identity)))) != least_upper_bound(X_399,greatest_lower_bound(identity,multiply(X_399,multiply(inverse(X_399),X_105))))
| least_upper_bound(X_399,greatest_lower_bound(X_105,identity)) = least_upper_bound(X_399,greatest_lower_bound(identity,multiply(X_399,multiply(inverse(X_399),X_105)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_399,least_upper_bound(identity,multiply(inverse(X_399),greatest_lower_bound(X_105,identity)))),least_upper_bound(X_399,greatest_lower_bound(identity,multiply(X_399,multiply(inverse(X_399),X_105))))) ),[0],$fot(least_upper_bound(X_399,greatest_lower_bound(X_105,identity)))]]) ).
cnf(refute_0_2352,plain,
( multiply(X_399,least_upper_bound(identity,multiply(inverse(X_399),greatest_lower_bound(X_105,identity)))) != least_upper_bound(X_399,greatest_lower_bound(identity,multiply(X_399,multiply(inverse(X_399),X_105))))
| least_upper_bound(X_399,greatest_lower_bound(X_105,identity)) = least_upper_bound(X_399,greatest_lower_bound(identity,multiply(X_399,multiply(inverse(X_399),X_105)))) ),
inference(resolve,[$cnf( $equal(multiply(X_399,least_upper_bound(identity,multiply(inverse(X_399),greatest_lower_bound(X_105,identity)))),least_upper_bound(X_399,greatest_lower_bound(X_105,identity))) )],[refute_0_2350,refute_0_2351]) ).
cnf(refute_0_2353,plain,
( X_31 != multiply(X_35,multiply(inverse(X_35),X_31))
| multiply(X_35,multiply(inverse(X_35),X_31)) = X_31 ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(X_31)),bind(Y0,$fot(multiply(X_35,multiply(inverse(X_35),X_31))))]]) ).
cnf(refute_0_2354,plain,
multiply(X_35,multiply(inverse(X_35),X_31)) = X_31,
inference(resolve,[$cnf( $equal(X_31,multiply(X_35,multiply(inverse(X_35),X_31))) )],[refute_0_104,refute_0_2353]) ).
cnf(refute_0_2355,plain,
multiply(X_399,multiply(inverse(X_399),X_105)) = X_105,
inference(subst,[],[refute_0_2354:[bind(X_31,$fot(X_105)),bind(X_35,$fot(X_399))]]) ).
cnf(refute_0_2356,plain,
greatest_lower_bound(identity,multiply(X_399,multiply(inverse(X_399),X_105))) = greatest_lower_bound(identity,multiply(X_399,multiply(inverse(X_399),X_105))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,multiply(X_399,multiply(inverse(X_399),X_105))))]]) ).
cnf(refute_0_2357,plain,
( multiply(X_399,multiply(inverse(X_399),X_105)) != X_105
| greatest_lower_bound(identity,multiply(X_399,multiply(inverse(X_399),X_105))) != greatest_lower_bound(identity,multiply(X_399,multiply(inverse(X_399),X_105)))
| greatest_lower_bound(identity,multiply(X_399,multiply(inverse(X_399),X_105))) = greatest_lower_bound(identity,X_105) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_399,multiply(inverse(X_399),X_105))),greatest_lower_bound(identity,multiply(X_399,multiply(inverse(X_399),X_105)))) ),[1,1],$fot(X_105)]]) ).
cnf(refute_0_2358,plain,
( multiply(X_399,multiply(inverse(X_399),X_105)) != X_105
| greatest_lower_bound(identity,multiply(X_399,multiply(inverse(X_399),X_105))) = greatest_lower_bound(identity,X_105) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_399,multiply(inverse(X_399),X_105))),greatest_lower_bound(identity,multiply(X_399,multiply(inverse(X_399),X_105)))) )],[refute_0_2356,refute_0_2357]) ).
cnf(refute_0_2359,plain,
greatest_lower_bound(identity,multiply(X_399,multiply(inverse(X_399),X_105))) = greatest_lower_bound(identity,X_105),
inference(resolve,[$cnf( $equal(multiply(X_399,multiply(inverse(X_399),X_105)),X_105) )],[refute_0_2355,refute_0_2358]) ).
cnf(refute_0_2360,plain,
least_upper_bound(X_399,greatest_lower_bound(identity,multiply(X_399,multiply(inverse(X_399),X_105)))) = least_upper_bound(X_399,greatest_lower_bound(identity,multiply(X_399,multiply(inverse(X_399),X_105)))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_399,greatest_lower_bound(identity,multiply(X_399,multiply(inverse(X_399),X_105)))))]]) ).
cnf(refute_0_2361,plain,
( greatest_lower_bound(identity,multiply(X_399,multiply(inverse(X_399),X_105))) != greatest_lower_bound(identity,X_105)
| least_upper_bound(X_399,greatest_lower_bound(identity,multiply(X_399,multiply(inverse(X_399),X_105)))) != least_upper_bound(X_399,greatest_lower_bound(identity,multiply(X_399,multiply(inverse(X_399),X_105))))
| least_upper_bound(X_399,greatest_lower_bound(identity,multiply(X_399,multiply(inverse(X_399),X_105)))) = least_upper_bound(X_399,greatest_lower_bound(identity,X_105)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_399,greatest_lower_bound(identity,multiply(X_399,multiply(inverse(X_399),X_105)))),least_upper_bound(X_399,greatest_lower_bound(identity,multiply(X_399,multiply(inverse(X_399),X_105))))) ),[1,1],$fot(greatest_lower_bound(identity,X_105))]]) ).
cnf(refute_0_2362,plain,
( greatest_lower_bound(identity,multiply(X_399,multiply(inverse(X_399),X_105))) != greatest_lower_bound(identity,X_105)
| least_upper_bound(X_399,greatest_lower_bound(identity,multiply(X_399,multiply(inverse(X_399),X_105)))) = least_upper_bound(X_399,greatest_lower_bound(identity,X_105)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_399,greatest_lower_bound(identity,multiply(X_399,multiply(inverse(X_399),X_105)))),least_upper_bound(X_399,greatest_lower_bound(identity,multiply(X_399,multiply(inverse(X_399),X_105))))) )],[refute_0_2360,refute_0_2361]) ).
cnf(refute_0_2363,plain,
least_upper_bound(X_399,greatest_lower_bound(identity,multiply(X_399,multiply(inverse(X_399),X_105)))) = least_upper_bound(X_399,greatest_lower_bound(identity,X_105)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_399,multiply(inverse(X_399),X_105))),greatest_lower_bound(identity,X_105)) )],[refute_0_2359,refute_0_2362]) ).
cnf(refute_0_2364,plain,
( least_upper_bound(X_399,greatest_lower_bound(X_105,identity)) != least_upper_bound(X_399,greatest_lower_bound(identity,multiply(X_399,multiply(inverse(X_399),X_105))))
| least_upper_bound(X_399,greatest_lower_bound(identity,multiply(X_399,multiply(inverse(X_399),X_105)))) != least_upper_bound(X_399,greatest_lower_bound(identity,X_105))
| least_upper_bound(X_399,greatest_lower_bound(X_105,identity)) = least_upper_bound(X_399,greatest_lower_bound(identity,X_105)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_399,greatest_lower_bound(X_105,identity)),least_upper_bound(X_399,greatest_lower_bound(identity,X_105))) ),[0],$fot(least_upper_bound(X_399,greatest_lower_bound(identity,multiply(X_399,multiply(inverse(X_399),X_105)))))]]) ).
cnf(refute_0_2365,plain,
( least_upper_bound(X_399,greatest_lower_bound(X_105,identity)) != least_upper_bound(X_399,greatest_lower_bound(identity,multiply(X_399,multiply(inverse(X_399),X_105))))
| least_upper_bound(X_399,greatest_lower_bound(X_105,identity)) = least_upper_bound(X_399,greatest_lower_bound(identity,X_105)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_399,greatest_lower_bound(identity,multiply(X_399,multiply(inverse(X_399),X_105)))),least_upper_bound(X_399,greatest_lower_bound(identity,X_105))) )],[refute_0_2363,refute_0_2364]) ).
cnf(refute_0_2366,plain,
( multiply(X_399,least_upper_bound(identity,multiply(inverse(X_399),greatest_lower_bound(X_105,identity)))) != least_upper_bound(X_399,greatest_lower_bound(identity,multiply(X_399,multiply(inverse(X_399),X_105))))
| least_upper_bound(X_399,greatest_lower_bound(X_105,identity)) = least_upper_bound(X_399,greatest_lower_bound(identity,X_105)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_399,greatest_lower_bound(X_105,identity)),least_upper_bound(X_399,greatest_lower_bound(identity,multiply(X_399,multiply(inverse(X_399),X_105))))) )],[refute_0_2352,refute_0_2365]) ).
cnf(refute_0_2367,plain,
least_upper_bound(X_399,greatest_lower_bound(X_105,identity)) = least_upper_bound(X_399,greatest_lower_bound(identity,X_105)),
inference(resolve,[$cnf( $equal(multiply(X_399,least_upper_bound(identity,multiply(inverse(X_399),greatest_lower_bound(X_105,identity)))),least_upper_bound(X_399,greatest_lower_bound(identity,multiply(X_399,multiply(inverse(X_399),X_105))))) )],[refute_0_2341,refute_0_2366]) ).
cnf(refute_0_2368,plain,
least_upper_bound(X_322,greatest_lower_bound(X_410,identity)) = least_upper_bound(X_322,greatest_lower_bound(identity,X_410)),
inference(subst,[],[refute_0_2367:[bind(X_105,$fot(X_410)),bind(X_399,$fot(X_322))]]) ).
cnf(refute_0_2369,plain,
( least_upper_bound(X_322,greatest_lower_bound(X_410,identity)) != least_upper_bound(X_322,greatest_lower_bound(identity,X_410))
| least_upper_bound(X_322,greatest_lower_bound(identity,X_410)) = least_upper_bound(X_322,greatest_lower_bound(X_410,identity)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(least_upper_bound(X_322,greatest_lower_bound(X_410,identity)))),bind(Y0,$fot(least_upper_bound(X_322,greatest_lower_bound(identity,X_410))))]]) ).
cnf(refute_0_2370,plain,
least_upper_bound(X_322,greatest_lower_bound(identity,X_410)) = least_upper_bound(X_322,greatest_lower_bound(X_410,identity)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_322,greatest_lower_bound(X_410,identity)),least_upper_bound(X_322,greatest_lower_bound(identity,X_410))) )],[refute_0_2368,refute_0_2369]) ).
cnf(refute_0_2371,plain,
( greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_410),X_322)) != greatest_lower_bound(identity,least_upper_bound(X_322,greatest_lower_bound(identity,X_410)))
| least_upper_bound(X_322,greatest_lower_bound(identity,X_410)) != least_upper_bound(X_322,greatest_lower_bound(X_410,identity))
| greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_410),X_322)) = greatest_lower_bound(identity,least_upper_bound(X_322,greatest_lower_bound(X_410,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_410),X_322)),greatest_lower_bound(identity,least_upper_bound(X_322,greatest_lower_bound(identity,X_410)))) ),[1,1],$fot(least_upper_bound(X_322,greatest_lower_bound(X_410,identity)))]]) ).
cnf(refute_0_2372,plain,
( greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_410),X_322)) != greatest_lower_bound(identity,least_upper_bound(X_322,greatest_lower_bound(identity,X_410)))
| greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_410),X_322)) = greatest_lower_bound(identity,least_upper_bound(X_322,greatest_lower_bound(X_410,identity))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_322,greatest_lower_bound(identity,X_410)),least_upper_bound(X_322,greatest_lower_bound(X_410,identity))) )],[refute_0_2370,refute_0_2371]) ).
cnf(refute_0_2373,plain,
greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_410),X_322)) = greatest_lower_bound(identity,least_upper_bound(X_322,greatest_lower_bound(X_410,identity))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_410),X_322)),greatest_lower_bound(identity,least_upper_bound(X_322,greatest_lower_bound(identity,X_410)))) )],[refute_0_2325,refute_0_2372]) ).
cnf(refute_0_2374,plain,
( greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_410),X_322)) != greatest_lower_bound(identity,least_upper_bound(X_322,greatest_lower_bound(X_410,identity)))
| greatest_lower_bound(identity,least_upper_bound(X_322,greatest_lower_bound(X_410,identity))) = greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_410),X_322)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_410),X_322)))),bind(Y0,$fot(greatest_lower_bound(identity,least_upper_bound(X_322,greatest_lower_bound(X_410,identity)))))]]) ).
cnf(refute_0_2375,plain,
greatest_lower_bound(identity,least_upper_bound(X_322,greatest_lower_bound(X_410,identity))) = greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_410),X_322)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_410),X_322)),greatest_lower_bound(identity,least_upper_bound(X_322,greatest_lower_bound(X_410,identity)))) )],[refute_0_2373,refute_0_2374]) ).
cnf(refute_0_2376,plain,
greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,inverse(X_443)),greatest_lower_bound(X_443,identity))) = greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_443),greatest_lower_bound(identity,inverse(X_443)))),
inference(subst,[],[refute_0_2375:[bind(X_322,$fot(greatest_lower_bound(identity,inverse(X_443)))),bind(X_410,$fot(X_443))]]) ).
cnf(refute_0_2377,plain,
( greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_443),greatest_lower_bound(identity,inverse(X_443)))) != greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_443),least_upper_bound(identity,inverse(X_443))))
| greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,inverse(X_443)),greatest_lower_bound(X_443,identity))) != greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_443),greatest_lower_bound(identity,inverse(X_443))))
| greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,inverse(X_443)),greatest_lower_bound(X_443,identity))) = greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_443),least_upper_bound(identity,inverse(X_443)))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,inverse(X_443)),greatest_lower_bound(X_443,identity))))),bind(Y0,$fot(greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_443),greatest_lower_bound(identity,inverse(X_443)))))),bind(Z0,$fot(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_443),least_upper_bound(identity,inverse(X_443))))))]]) ).
cnf(refute_0_2378,plain,
( greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_443),greatest_lower_bound(identity,inverse(X_443)))) != greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_443),least_upper_bound(identity,inverse(X_443))))
| greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,inverse(X_443)),greatest_lower_bound(X_443,identity))) = greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_443),least_upper_bound(identity,inverse(X_443)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,inverse(X_443)),greatest_lower_bound(X_443,identity))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_443),greatest_lower_bound(identity,inverse(X_443))))) )],[refute_0_2376,refute_0_2377]) ).
cnf(refute_0_2379,plain,
greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,inverse(X_443)),greatest_lower_bound(X_443,identity))) = greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_443),least_upper_bound(identity,inverse(X_443)))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_443),greatest_lower_bound(identity,inverse(X_443)))),greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_443),least_upper_bound(identity,inverse(X_443))))) )],[refute_0_2324,refute_0_2378]) ).
cnf(refute_0_2380,plain,
( greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,inverse(X_443)),greatest_lower_bound(X_443,identity))) != greatest_lower_bound(identity,multiply(greatest_lower_bound(X_443,identity),least_upper_bound(identity,inverse(X_443))))
| greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,inverse(X_443)),greatest_lower_bound(X_443,identity))) != greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_443),least_upper_bound(identity,inverse(X_443))))
| greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_443),least_upper_bound(identity,inverse(X_443)))) = greatest_lower_bound(identity,multiply(greatest_lower_bound(X_443,identity),least_upper_bound(identity,inverse(X_443)))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,inverse(X_443)),greatest_lower_bound(X_443,identity))),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_443,identity),least_upper_bound(identity,inverse(X_443))))) ),[0],$fot(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_443),least_upper_bound(identity,inverse(X_443)))))]]) ).
cnf(refute_0_2381,plain,
( greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,inverse(X_443)),greatest_lower_bound(X_443,identity))) != greatest_lower_bound(identity,multiply(greatest_lower_bound(X_443,identity),least_upper_bound(identity,inverse(X_443))))
| greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_443),least_upper_bound(identity,inverse(X_443)))) = greatest_lower_bound(identity,multiply(greatest_lower_bound(X_443,identity),least_upper_bound(identity,inverse(X_443)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,inverse(X_443)),greatest_lower_bound(X_443,identity))),greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_443),least_upper_bound(identity,inverse(X_443))))) )],[refute_0_2379,refute_0_2380]) ).
cnf(refute_0_2382,plain,
greatest_lower_bound(identity,least_upper_bound(X_443,identity)) = identity,
inference(subst,[],[refute_0_153:[bind(X_6,$fot(identity)),bind(X_7,$fot(X_443))]]) ).
cnf(refute_0_2383,plain,
multiply(least_upper_bound(X_443,identity),identity) = least_upper_bound(X_443,identity),
inference(subst,[],[refute_0_88:[bind(X_33,$fot(least_upper_bound(X_443,identity)))]]) ).
cnf(refute_0_2384,plain,
least_upper_bound(identity,multiply(X_443,identity)) = multiply(least_upper_bound(X_443,identity),identity),
inference(subst,[],[refute_0_763:[bind(X_67,$fot(identity)),bind(X_68,$fot(X_443))]]) ).
cnf(refute_0_2385,plain,
( multiply(least_upper_bound(X_443,identity),identity) != least_upper_bound(X_443,identity)
| least_upper_bound(identity,multiply(X_443,identity)) != multiply(least_upper_bound(X_443,identity),identity)
| least_upper_bound(identity,multiply(X_443,identity)) = least_upper_bound(X_443,identity) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(least_upper_bound(identity,multiply(X_443,identity)))),bind(Y0,$fot(multiply(least_upper_bound(X_443,identity),identity))),bind(Z0,$fot(least_upper_bound(X_443,identity)))]]) ).
cnf(refute_0_2386,plain,
( multiply(least_upper_bound(X_443,identity),identity) != least_upper_bound(X_443,identity)
| least_upper_bound(identity,multiply(X_443,identity)) = least_upper_bound(X_443,identity) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_443,identity)),multiply(least_upper_bound(X_443,identity),identity)) )],[refute_0_2384,refute_0_2385]) ).
cnf(refute_0_2387,plain,
least_upper_bound(identity,multiply(X_443,identity)) = least_upper_bound(X_443,identity),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_443,identity),identity),least_upper_bound(X_443,identity)) )],[refute_0_2383,refute_0_2386]) ).
cnf(refute_0_2388,plain,
multiply(X_48,least_upper_bound(X_49,inverse(X_48))) = least_upper_bound(multiply(X_48,X_49),multiply(X_48,inverse(X_48))),
inference(subst,[],[monotony_lub1:[bind(X,$fot(X_48)),bind(Y,$fot(X_49)),bind(Z,$fot(inverse(X_48)))]]) ).
cnf(refute_0_2389,plain,
multiply(X_48,inverse(X_48)) = identity,
inference(subst,[],[refute_0_71:[bind(X_35,$fot(X_48))]]) ).
cnf(refute_0_2390,plain,
( multiply(X_48,inverse(X_48)) != identity
| multiply(X_48,least_upper_bound(X_49,inverse(X_48))) != least_upper_bound(multiply(X_48,X_49),multiply(X_48,inverse(X_48)))
| multiply(X_48,least_upper_bound(X_49,inverse(X_48))) = least_upper_bound(multiply(X_48,X_49),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_48,least_upper_bound(X_49,inverse(X_48))),least_upper_bound(multiply(X_48,X_49),multiply(X_48,inverse(X_48)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_2391,plain,
( multiply(X_48,least_upper_bound(X_49,inverse(X_48))) != least_upper_bound(multiply(X_48,X_49),multiply(X_48,inverse(X_48)))
| multiply(X_48,least_upper_bound(X_49,inverse(X_48))) = least_upper_bound(multiply(X_48,X_49),identity) ),
inference(resolve,[$cnf( $equal(multiply(X_48,inverse(X_48)),identity) )],[refute_0_2389,refute_0_2390]) ).
cnf(refute_0_2392,plain,
multiply(X_48,least_upper_bound(X_49,inverse(X_48))) = least_upper_bound(multiply(X_48,X_49),identity),
inference(resolve,[$cnf( $equal(multiply(X_48,least_upper_bound(X_49,inverse(X_48))),least_upper_bound(multiply(X_48,X_49),multiply(X_48,inverse(X_48)))) )],[refute_0_2388,refute_0_2391]) ).
cnf(refute_0_2393,plain,
least_upper_bound(multiply(X_48,X_49),identity) = least_upper_bound(identity,multiply(X_48,X_49)),
inference(subst,[],[refute_0_25:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_48,X_49)))]]) ).
cnf(refute_0_2394,plain,
( multiply(X_48,least_upper_bound(X_49,inverse(X_48))) != least_upper_bound(multiply(X_48,X_49),identity)
| least_upper_bound(multiply(X_48,X_49),identity) != least_upper_bound(identity,multiply(X_48,X_49))
| multiply(X_48,least_upper_bound(X_49,inverse(X_48))) = least_upper_bound(identity,multiply(X_48,X_49)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_48,least_upper_bound(X_49,inverse(X_48))),least_upper_bound(identity,multiply(X_48,X_49))) ),[0],$fot(least_upper_bound(multiply(X_48,X_49),identity))]]) ).
cnf(refute_0_2395,plain,
( multiply(X_48,least_upper_bound(X_49,inverse(X_48))) != least_upper_bound(multiply(X_48,X_49),identity)
| multiply(X_48,least_upper_bound(X_49,inverse(X_48))) = least_upper_bound(identity,multiply(X_48,X_49)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_48,X_49),identity),least_upper_bound(identity,multiply(X_48,X_49))) )],[refute_0_2393,refute_0_2394]) ).
cnf(refute_0_2396,plain,
multiply(X_48,least_upper_bound(X_49,inverse(X_48))) = least_upper_bound(identity,multiply(X_48,X_49)),
inference(resolve,[$cnf( $equal(multiply(X_48,least_upper_bound(X_49,inverse(X_48))),least_upper_bound(multiply(X_48,X_49),identity)) )],[refute_0_2392,refute_0_2395]) ).
cnf(refute_0_2397,plain,
multiply(X_443,least_upper_bound(identity,inverse(X_443))) = least_upper_bound(identity,multiply(X_443,identity)),
inference(subst,[],[refute_0_2396:[bind(X_48,$fot(X_443)),bind(X_49,$fot(identity))]]) ).
cnf(refute_0_2398,plain,
( multiply(X_443,least_upper_bound(identity,inverse(X_443))) != least_upper_bound(identity,multiply(X_443,identity))
| least_upper_bound(identity,multiply(X_443,identity)) != least_upper_bound(X_443,identity)
| multiply(X_443,least_upper_bound(identity,inverse(X_443))) = least_upper_bound(X_443,identity) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(X_443,least_upper_bound(identity,inverse(X_443))))),bind(Y0,$fot(least_upper_bound(identity,multiply(X_443,identity)))),bind(Z0,$fot(least_upper_bound(X_443,identity)))]]) ).
cnf(refute_0_2399,plain,
( least_upper_bound(identity,multiply(X_443,identity)) != least_upper_bound(X_443,identity)
| multiply(X_443,least_upper_bound(identity,inverse(X_443))) = least_upper_bound(X_443,identity) ),
inference(resolve,[$cnf( $equal(multiply(X_443,least_upper_bound(identity,inverse(X_443))),least_upper_bound(identity,multiply(X_443,identity))) )],[refute_0_2397,refute_0_2398]) ).
cnf(refute_0_2400,plain,
multiply(X_443,least_upper_bound(identity,inverse(X_443))) = least_upper_bound(X_443,identity),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_443,identity)),least_upper_bound(X_443,identity)) )],[refute_0_2387,refute_0_2399]) ).
cnf(refute_0_2401,plain,
greatest_lower_bound(identity,multiply(X_443,least_upper_bound(identity,inverse(X_443)))) = greatest_lower_bound(identity,multiply(X_443,least_upper_bound(identity,inverse(X_443)))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,multiply(X_443,least_upper_bound(identity,inverse(X_443)))))]]) ).
cnf(refute_0_2402,plain,
( multiply(X_443,least_upper_bound(identity,inverse(X_443))) != least_upper_bound(X_443,identity)
| greatest_lower_bound(identity,multiply(X_443,least_upper_bound(identity,inverse(X_443)))) != greatest_lower_bound(identity,multiply(X_443,least_upper_bound(identity,inverse(X_443))))
| greatest_lower_bound(identity,multiply(X_443,least_upper_bound(identity,inverse(X_443)))) = greatest_lower_bound(identity,least_upper_bound(X_443,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_443,least_upper_bound(identity,inverse(X_443)))),greatest_lower_bound(identity,multiply(X_443,least_upper_bound(identity,inverse(X_443))))) ),[1,1],$fot(least_upper_bound(X_443,identity))]]) ).
cnf(refute_0_2403,plain,
( multiply(X_443,least_upper_bound(identity,inverse(X_443))) != least_upper_bound(X_443,identity)
| greatest_lower_bound(identity,multiply(X_443,least_upper_bound(identity,inverse(X_443)))) = greatest_lower_bound(identity,least_upper_bound(X_443,identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_443,least_upper_bound(identity,inverse(X_443)))),greatest_lower_bound(identity,multiply(X_443,least_upper_bound(identity,inverse(X_443))))) )],[refute_0_2401,refute_0_2402]) ).
cnf(refute_0_2404,plain,
greatest_lower_bound(identity,multiply(X_443,least_upper_bound(identity,inverse(X_443)))) = greatest_lower_bound(identity,least_upper_bound(X_443,identity)),
inference(resolve,[$cnf( $equal(multiply(X_443,least_upper_bound(identity,inverse(X_443))),least_upper_bound(X_443,identity)) )],[refute_0_2400,refute_0_2403]) ).
cnf(refute_0_2405,plain,
( greatest_lower_bound(identity,multiply(X_443,least_upper_bound(identity,inverse(X_443)))) != greatest_lower_bound(identity,least_upper_bound(X_443,identity))
| greatest_lower_bound(identity,least_upper_bound(X_443,identity)) != identity
| greatest_lower_bound(identity,multiply(X_443,least_upper_bound(identity,inverse(X_443)))) = identity ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(greatest_lower_bound(identity,multiply(X_443,least_upper_bound(identity,inverse(X_443)))))),bind(Y0,$fot(greatest_lower_bound(identity,least_upper_bound(X_443,identity)))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_2406,plain,
( greatest_lower_bound(identity,least_upper_bound(X_443,identity)) != identity
| greatest_lower_bound(identity,multiply(X_443,least_upper_bound(identity,inverse(X_443)))) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_443,least_upper_bound(identity,inverse(X_443)))),greatest_lower_bound(identity,least_upper_bound(X_443,identity))) )],[refute_0_2404,refute_0_2405]) ).
cnf(refute_0_2407,plain,
greatest_lower_bound(identity,multiply(X_443,least_upper_bound(identity,inverse(X_443)))) = identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(X_443,identity)),identity) )],[refute_0_2382,refute_0_2406]) ).
cnf(refute_0_2408,plain,
greatest_lower_bound(X_205,greatest_lower_bound(least_upper_bound(X_205,X_204),multiply(X_120,least_upper_bound(X_205,X_204)))) = greatest_lower_bound(X_205,multiply(X_120,least_upper_bound(X_205,X_204))),
inference(subst,[],[refute_0_1096:[bind(Y,$fot(X_204)),bind(X_22,$fot(X_205)),bind(X_24,$fot(multiply(X_120,least_upper_bound(X_205,X_204))))]]) ).
cnf(refute_0_2409,plain,
multiply(greatest_lower_bound(X_120,identity),least_upper_bound(X_205,X_204)) = greatest_lower_bound(least_upper_bound(X_205,X_204),multiply(X_120,least_upper_bound(X_205,X_204))),
inference(subst,[],[refute_0_1313:[bind(X_119,$fot(least_upper_bound(X_205,X_204)))]]) ).
cnf(refute_0_2410,plain,
( multiply(greatest_lower_bound(X_120,identity),least_upper_bound(X_205,X_204)) != greatest_lower_bound(least_upper_bound(X_205,X_204),multiply(X_120,least_upper_bound(X_205,X_204)))
| greatest_lower_bound(least_upper_bound(X_205,X_204),multiply(X_120,least_upper_bound(X_205,X_204))) = multiply(greatest_lower_bound(X_120,identity),least_upper_bound(X_205,X_204)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(greatest_lower_bound(X_120,identity),least_upper_bound(X_205,X_204)))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(X_205,X_204),multiply(X_120,least_upper_bound(X_205,X_204)))))]]) ).
cnf(refute_0_2411,plain,
greatest_lower_bound(least_upper_bound(X_205,X_204),multiply(X_120,least_upper_bound(X_205,X_204))) = multiply(greatest_lower_bound(X_120,identity),least_upper_bound(X_205,X_204)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_120,identity),least_upper_bound(X_205,X_204)),greatest_lower_bound(least_upper_bound(X_205,X_204),multiply(X_120,least_upper_bound(X_205,X_204)))) )],[refute_0_2409,refute_0_2410]) ).
cnf(refute_0_2412,plain,
( greatest_lower_bound(X_205,greatest_lower_bound(least_upper_bound(X_205,X_204),multiply(X_120,least_upper_bound(X_205,X_204)))) != greatest_lower_bound(X_205,multiply(X_120,least_upper_bound(X_205,X_204)))
| greatest_lower_bound(least_upper_bound(X_205,X_204),multiply(X_120,least_upper_bound(X_205,X_204))) != multiply(greatest_lower_bound(X_120,identity),least_upper_bound(X_205,X_204))
| greatest_lower_bound(X_205,multiply(greatest_lower_bound(X_120,identity),least_upper_bound(X_205,X_204))) = greatest_lower_bound(X_205,multiply(X_120,least_upper_bound(X_205,X_204))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_205,greatest_lower_bound(least_upper_bound(X_205,X_204),multiply(X_120,least_upper_bound(X_205,X_204)))),greatest_lower_bound(X_205,multiply(X_120,least_upper_bound(X_205,X_204)))) ),[0,1],$fot(multiply(greatest_lower_bound(X_120,identity),least_upper_bound(X_205,X_204)))]]) ).
cnf(refute_0_2413,plain,
( greatest_lower_bound(X_205,greatest_lower_bound(least_upper_bound(X_205,X_204),multiply(X_120,least_upper_bound(X_205,X_204)))) != greatest_lower_bound(X_205,multiply(X_120,least_upper_bound(X_205,X_204)))
| greatest_lower_bound(X_205,multiply(greatest_lower_bound(X_120,identity),least_upper_bound(X_205,X_204))) = greatest_lower_bound(X_205,multiply(X_120,least_upper_bound(X_205,X_204))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_205,X_204),multiply(X_120,least_upper_bound(X_205,X_204))),multiply(greatest_lower_bound(X_120,identity),least_upper_bound(X_205,X_204))) )],[refute_0_2411,refute_0_2412]) ).
cnf(refute_0_2414,plain,
greatest_lower_bound(X_205,multiply(greatest_lower_bound(X_120,identity),least_upper_bound(X_205,X_204))) = greatest_lower_bound(X_205,multiply(X_120,least_upper_bound(X_205,X_204))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_205,greatest_lower_bound(least_upper_bound(X_205,X_204),multiply(X_120,least_upper_bound(X_205,X_204)))),greatest_lower_bound(X_205,multiply(X_120,least_upper_bound(X_205,X_204)))) )],[refute_0_2408,refute_0_2413]) ).
cnf(refute_0_2415,plain,
greatest_lower_bound(identity,multiply(greatest_lower_bound(X_443,identity),least_upper_bound(identity,inverse(X_443)))) = greatest_lower_bound(identity,multiply(X_443,least_upper_bound(identity,inverse(X_443)))),
inference(subst,[],[refute_0_2414:[bind(X_120,$fot(X_443)),bind(X_204,$fot(inverse(X_443))),bind(X_205,$fot(identity))]]) ).
cnf(refute_0_2416,plain,
( greatest_lower_bound(identity,multiply(X_443,least_upper_bound(identity,inverse(X_443)))) != identity
| greatest_lower_bound(identity,multiply(greatest_lower_bound(X_443,identity),least_upper_bound(identity,inverse(X_443)))) != greatest_lower_bound(identity,multiply(X_443,least_upper_bound(identity,inverse(X_443))))
| greatest_lower_bound(identity,multiply(greatest_lower_bound(X_443,identity),least_upper_bound(identity,inverse(X_443)))) = identity ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(greatest_lower_bound(identity,multiply(greatest_lower_bound(X_443,identity),least_upper_bound(identity,inverse(X_443)))))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(X_443,least_upper_bound(identity,inverse(X_443)))))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_2417,plain,
( greatest_lower_bound(identity,multiply(X_443,least_upper_bound(identity,inverse(X_443)))) != identity
| greatest_lower_bound(identity,multiply(greatest_lower_bound(X_443,identity),least_upper_bound(identity,inverse(X_443)))) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(greatest_lower_bound(X_443,identity),least_upper_bound(identity,inverse(X_443)))),greatest_lower_bound(identity,multiply(X_443,least_upper_bound(identity,inverse(X_443))))) )],[refute_0_2415,refute_0_2416]) ).
cnf(refute_0_2418,plain,
greatest_lower_bound(identity,multiply(greatest_lower_bound(X_443,identity),least_upper_bound(identity,inverse(X_443)))) = identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_443,least_upper_bound(identity,inverse(X_443)))),identity) )],[refute_0_2407,refute_0_2417]) ).
cnf(refute_0_2419,plain,
( greatest_lower_bound(identity,multiply(greatest_lower_bound(X_443,identity),least_upper_bound(identity,inverse(X_443)))) != identity
| greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_443),least_upper_bound(identity,inverse(X_443)))) != greatest_lower_bound(identity,multiply(greatest_lower_bound(X_443,identity),least_upper_bound(identity,inverse(X_443))))
| greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_443),least_upper_bound(identity,inverse(X_443)))) = identity ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_443),least_upper_bound(identity,inverse(X_443)))),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_443,identity),least_upper_bound(identity,inverse(X_443))))) ),[1],$fot(identity)]]) ).
cnf(refute_0_2420,plain,
( greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_443),least_upper_bound(identity,inverse(X_443)))) != greatest_lower_bound(identity,multiply(greatest_lower_bound(X_443,identity),least_upper_bound(identity,inverse(X_443))))
| greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_443),least_upper_bound(identity,inverse(X_443)))) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(greatest_lower_bound(X_443,identity),least_upper_bound(identity,inverse(X_443)))),identity) )],[refute_0_2418,refute_0_2419]) ).
cnf(refute_0_2421,plain,
( greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,inverse(X_443)),greatest_lower_bound(X_443,identity))) != greatest_lower_bound(identity,multiply(greatest_lower_bound(X_443,identity),least_upper_bound(identity,inverse(X_443))))
| greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_443),least_upper_bound(identity,inverse(X_443)))) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_443),least_upper_bound(identity,inverse(X_443)))),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_443,identity),least_upper_bound(identity,inverse(X_443))))) )],[refute_0_2381,refute_0_2420]) ).
cnf(refute_0_2422,plain,
greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_443),least_upper_bound(identity,inverse(X_443)))) = identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,inverse(X_443)),greatest_lower_bound(X_443,identity))),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_443,identity),least_upper_bound(identity,inverse(X_443))))) )],[refute_0_2319,refute_0_2421]) ).
cnf(refute_0_2423,plain,
greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))) = identity,
inference(subst,[],[refute_0_2422:[bind(X_443,$fot(X_444))]]) ).
cnf(refute_0_2424,plain,
( multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))) != least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))))
| greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))) != identity
| multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(identity)) = least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))),least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))))) ),[0,1,0],$fot(identity)]]) ).
cnf(refute_0_2425,plain,
( multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))) != least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))))
| multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(identity)) = least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))),identity) )],[refute_0_2423,refute_0_2424]) ).
cnf(refute_0_2426,plain,
multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(identity)) = least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))),
inference(resolve,[$cnf( $equal(multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))),least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))))) )],[refute_0_1826,refute_0_2425]) ).
cnf(refute_0_2427,plain,
multiply(identity,X_444) = X_444,
inference(subst,[],[left_identity:[bind(X,$fot(X_444))]]) ).
cnf(refute_0_2428,plain,
inverse(multiply(identity,X_444)) = inverse(multiply(identity,X_444)),
introduced(tautology,[refl,[$fot(inverse(multiply(identity,X_444)))]]) ).
cnf(refute_0_2429,plain,
( multiply(identity,X_444) != X_444
| inverse(multiply(identity,X_444)) != inverse(multiply(identity,X_444))
| inverse(multiply(identity,X_444)) = inverse(X_444) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(identity,X_444)),inverse(multiply(identity,X_444))) ),[1,0],$fot(X_444)]]) ).
cnf(refute_0_2430,plain,
( multiply(identity,X_444) != X_444
| inverse(multiply(identity,X_444)) = inverse(X_444) ),
inference(resolve,[$cnf( $equal(inverse(multiply(identity,X_444)),inverse(multiply(identity,X_444))) )],[refute_0_2428,refute_0_2429]) ).
cnf(refute_0_2431,plain,
inverse(multiply(identity,X_444)) = inverse(X_444),
inference(resolve,[$cnf( $equal(multiply(identity,X_444),X_444) )],[refute_0_2427,refute_0_2430]) ).
cnf(refute_0_2432,plain,
least_upper_bound(identity,inverse(multiply(identity,X_444))) = least_upper_bound(identity,inverse(multiply(identity,X_444))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,inverse(multiply(identity,X_444))))]]) ).
cnf(refute_0_2433,plain,
( inverse(multiply(identity,X_444)) != inverse(X_444)
| least_upper_bound(identity,inverse(multiply(identity,X_444))) != least_upper_bound(identity,inverse(multiply(identity,X_444)))
| least_upper_bound(identity,inverse(multiply(identity,X_444))) = least_upper_bound(identity,inverse(X_444)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,inverse(multiply(identity,X_444))),least_upper_bound(identity,inverse(multiply(identity,X_444)))) ),[1,1],$fot(inverse(X_444))]]) ).
cnf(refute_0_2434,plain,
( inverse(multiply(identity,X_444)) != inverse(X_444)
| least_upper_bound(identity,inverse(multiply(identity,X_444))) = least_upper_bound(identity,inverse(X_444)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(multiply(identity,X_444))),least_upper_bound(identity,inverse(multiply(identity,X_444)))) )],[refute_0_2432,refute_0_2433]) ).
cnf(refute_0_2435,plain,
least_upper_bound(identity,inverse(multiply(identity,X_444))) = least_upper_bound(identity,inverse(X_444)),
inference(resolve,[$cnf( $equal(inverse(multiply(identity,X_444)),inverse(X_444)) )],[refute_0_2431,refute_0_2434]) ).
cnf(refute_0_2436,plain,
multiply(inverse(X_56),least_upper_bound(least_upper_bound(inverse(inverse(X_56)),X_50),X_56)) = least_upper_bound(identity,multiply(inverse(X_56),least_upper_bound(inverse(inverse(X_56)),X_50))),
inference(subst,[],[refute_0_29:[bind(X_49,$fot(least_upper_bound(inverse(inverse(X_56)),X_50))),bind(X_50,$fot(X_56))]]) ).
cnf(refute_0_2437,plain,
multiply(X_48,least_upper_bound(inverse(X_48),X_50)) = least_upper_bound(multiply(X_48,inverse(X_48)),multiply(X_48,X_50)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(X_48)),bind(Y,$fot(inverse(X_48))),bind(Z,$fot(X_50))]]) ).
cnf(refute_0_2438,plain,
( multiply(X_48,inverse(X_48)) != identity
| multiply(X_48,least_upper_bound(inverse(X_48),X_50)) != least_upper_bound(multiply(X_48,inverse(X_48)),multiply(X_48,X_50))
| multiply(X_48,least_upper_bound(inverse(X_48),X_50)) = least_upper_bound(identity,multiply(X_48,X_50)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_48,least_upper_bound(inverse(X_48),X_50)),least_upper_bound(multiply(X_48,inverse(X_48)),multiply(X_48,X_50))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_2439,plain,
( multiply(X_48,least_upper_bound(inverse(X_48),X_50)) != least_upper_bound(multiply(X_48,inverse(X_48)),multiply(X_48,X_50))
| multiply(X_48,least_upper_bound(inverse(X_48),X_50)) = least_upper_bound(identity,multiply(X_48,X_50)) ),
inference(resolve,[$cnf( $equal(multiply(X_48,inverse(X_48)),identity) )],[refute_0_2389,refute_0_2438]) ).
cnf(refute_0_2440,plain,
multiply(X_48,least_upper_bound(inverse(X_48),X_50)) = least_upper_bound(identity,multiply(X_48,X_50)),
inference(resolve,[$cnf( $equal(multiply(X_48,least_upper_bound(inverse(X_48),X_50)),least_upper_bound(multiply(X_48,inverse(X_48)),multiply(X_48,X_50))) )],[refute_0_2437,refute_0_2439]) ).
cnf(refute_0_2441,plain,
multiply(inverse(X_56),least_upper_bound(inverse(inverse(X_56)),X_50)) = least_upper_bound(identity,multiply(inverse(X_56),X_50)),
inference(subst,[],[refute_0_2440:[bind(X_48,$fot(inverse(X_56)))]]) ).
cnf(refute_0_2442,plain,
( multiply(inverse(X_56),least_upper_bound(inverse(inverse(X_56)),X_50)) != least_upper_bound(identity,multiply(inverse(X_56),X_50))
| multiply(inverse(X_56),least_upper_bound(least_upper_bound(inverse(inverse(X_56)),X_50),X_56)) != least_upper_bound(identity,multiply(inverse(X_56),least_upper_bound(inverse(inverse(X_56)),X_50)))
| multiply(inverse(X_56),least_upper_bound(least_upper_bound(inverse(inverse(X_56)),X_50),X_56)) = least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_56),X_50))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_56),least_upper_bound(least_upper_bound(inverse(inverse(X_56)),X_50),X_56)),least_upper_bound(identity,multiply(inverse(X_56),least_upper_bound(inverse(inverse(X_56)),X_50)))) ),[1,1],$fot(least_upper_bound(identity,multiply(inverse(X_56),X_50)))]]) ).
cnf(refute_0_2443,plain,
( multiply(inverse(X_56),least_upper_bound(least_upper_bound(inverse(inverse(X_56)),X_50),X_56)) != least_upper_bound(identity,multiply(inverse(X_56),least_upper_bound(inverse(inverse(X_56)),X_50)))
| multiply(inverse(X_56),least_upper_bound(least_upper_bound(inverse(inverse(X_56)),X_50),X_56)) = least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_56),X_50))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_56),least_upper_bound(inverse(inverse(X_56)),X_50)),least_upper_bound(identity,multiply(inverse(X_56),X_50))) )],[refute_0_2441,refute_0_2442]) ).
cnf(refute_0_2444,plain,
multiply(inverse(X_56),least_upper_bound(least_upper_bound(inverse(inverse(X_56)),X_50),X_56)) = least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_56),X_50))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_56),least_upper_bound(least_upper_bound(inverse(inverse(X_56)),X_50),X_56)),least_upper_bound(identity,multiply(inverse(X_56),least_upper_bound(inverse(inverse(X_56)),X_50)))) )],[refute_0_2436,refute_0_2443]) ).
cnf(refute_0_2445,plain,
multiply(X,least_upper_bound(least_upper_bound(X_52,inverse(X)),Z)) = least_upper_bound(multiply(X,least_upper_bound(X_52,inverse(X))),multiply(X,Z)),
inference(subst,[],[monotony_lub1:[bind(Y,$fot(least_upper_bound(X_52,inverse(X))))]]) ).
cnf(refute_0_2446,plain,
multiply(X,least_upper_bound(X_52,inverse(X))) = least_upper_bound(identity,multiply(X,X_52)),
inference(subst,[],[refute_0_2396:[bind(X_48,$fot(X)),bind(X_49,$fot(X_52))]]) ).
cnf(refute_0_2447,plain,
( multiply(X,least_upper_bound(X_52,inverse(X))) != least_upper_bound(identity,multiply(X,X_52))
| multiply(X,least_upper_bound(least_upper_bound(X_52,inverse(X)),Z)) != least_upper_bound(multiply(X,least_upper_bound(X_52,inverse(X))),multiply(X,Z))
| multiply(X,least_upper_bound(least_upper_bound(X_52,inverse(X)),Z)) = least_upper_bound(least_upper_bound(identity,multiply(X,X_52)),multiply(X,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X,least_upper_bound(least_upper_bound(X_52,inverse(X)),Z)),least_upper_bound(multiply(X,least_upper_bound(X_52,inverse(X))),multiply(X,Z))) ),[1,0],$fot(least_upper_bound(identity,multiply(X,X_52)))]]) ).
cnf(refute_0_2448,plain,
( multiply(X,least_upper_bound(least_upper_bound(X_52,inverse(X)),Z)) != least_upper_bound(multiply(X,least_upper_bound(X_52,inverse(X))),multiply(X,Z))
| multiply(X,least_upper_bound(least_upper_bound(X_52,inverse(X)),Z)) = least_upper_bound(least_upper_bound(identity,multiply(X,X_52)),multiply(X,Z)) ),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(X_52,inverse(X))),least_upper_bound(identity,multiply(X,X_52))) )],[refute_0_2446,refute_0_2447]) ).
cnf(refute_0_2449,plain,
multiply(X,least_upper_bound(least_upper_bound(X_52,inverse(X)),Z)) = least_upper_bound(least_upper_bound(identity,multiply(X,X_52)),multiply(X,Z)),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(least_upper_bound(X_52,inverse(X)),Z)),least_upper_bound(multiply(X,least_upper_bound(X_52,inverse(X))),multiply(X,Z))) )],[refute_0_2445,refute_0_2448]) ).
cnf(refute_0_2450,plain,
least_upper_bound(least_upper_bound(X_52,inverse(X)),Z) = least_upper_bound(X_52,least_upper_bound(inverse(X),Z)),
inference(subst,[],[refute_0_171:[bind(X,$fot(X_52)),bind(Y,$fot(inverse(X)))]]) ).
cnf(refute_0_2451,plain,
multiply(X,least_upper_bound(least_upper_bound(X_52,inverse(X)),Z)) = multiply(X,least_upper_bound(least_upper_bound(X_52,inverse(X)),Z)),
introduced(tautology,[refl,[$fot(multiply(X,least_upper_bound(least_upper_bound(X_52,inverse(X)),Z)))]]) ).
cnf(refute_0_2452,plain,
( multiply(X,least_upper_bound(least_upper_bound(X_52,inverse(X)),Z)) != multiply(X,least_upper_bound(least_upper_bound(X_52,inverse(X)),Z))
| least_upper_bound(least_upper_bound(X_52,inverse(X)),Z) != least_upper_bound(X_52,least_upper_bound(inverse(X),Z))
| multiply(X,least_upper_bound(least_upper_bound(X_52,inverse(X)),Z)) = multiply(X,least_upper_bound(X_52,least_upper_bound(inverse(X),Z))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X,least_upper_bound(least_upper_bound(X_52,inverse(X)),Z)),multiply(X,least_upper_bound(least_upper_bound(X_52,inverse(X)),Z))) ),[1,1],$fot(least_upper_bound(X_52,least_upper_bound(inverse(X),Z)))]]) ).
cnf(refute_0_2453,plain,
( least_upper_bound(least_upper_bound(X_52,inverse(X)),Z) != least_upper_bound(X_52,least_upper_bound(inverse(X),Z))
| multiply(X,least_upper_bound(least_upper_bound(X_52,inverse(X)),Z)) = multiply(X,least_upper_bound(X_52,least_upper_bound(inverse(X),Z))) ),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(least_upper_bound(X_52,inverse(X)),Z)),multiply(X,least_upper_bound(least_upper_bound(X_52,inverse(X)),Z))) )],[refute_0_2451,refute_0_2452]) ).
cnf(refute_0_2454,plain,
multiply(X,least_upper_bound(least_upper_bound(X_52,inverse(X)),Z)) = multiply(X,least_upper_bound(X_52,least_upper_bound(inverse(X),Z))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_52,inverse(X)),Z),least_upper_bound(X_52,least_upper_bound(inverse(X),Z))) )],[refute_0_2450,refute_0_2453]) ).
cnf(refute_0_2455,plain,
( multiply(X,least_upper_bound(least_upper_bound(X_52,inverse(X)),Z)) != multiply(X,least_upper_bound(X_52,least_upper_bound(inverse(X),Z)))
| multiply(X,least_upper_bound(least_upper_bound(X_52,inverse(X)),Z)) != least_upper_bound(least_upper_bound(identity,multiply(X,X_52)),multiply(X,Z))
| multiply(X,least_upper_bound(X_52,least_upper_bound(inverse(X),Z))) = least_upper_bound(least_upper_bound(identity,multiply(X,X_52)),multiply(X,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X,least_upper_bound(least_upper_bound(X_52,inverse(X)),Z)),least_upper_bound(least_upper_bound(identity,multiply(X,X_52)),multiply(X,Z))) ),[0],$fot(multiply(X,least_upper_bound(X_52,least_upper_bound(inverse(X),Z))))]]) ).
cnf(refute_0_2456,plain,
( multiply(X,least_upper_bound(least_upper_bound(X_52,inverse(X)),Z)) != least_upper_bound(least_upper_bound(identity,multiply(X,X_52)),multiply(X,Z))
| multiply(X,least_upper_bound(X_52,least_upper_bound(inverse(X),Z))) = least_upper_bound(least_upper_bound(identity,multiply(X,X_52)),multiply(X,Z)) ),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(least_upper_bound(X_52,inverse(X)),Z)),multiply(X,least_upper_bound(X_52,least_upper_bound(inverse(X),Z)))) )],[refute_0_2454,refute_0_2455]) ).
cnf(refute_0_2457,plain,
least_upper_bound(multiply(X,X_52),multiply(X,Z)) = multiply(X,least_upper_bound(X_52,Z)),
inference(subst,[],[refute_0_385:[bind(Y,$fot(X_52))]]) ).
cnf(refute_0_2458,plain,
least_upper_bound(identity,least_upper_bound(multiply(X,X_52),multiply(X,Z))) = least_upper_bound(identity,least_upper_bound(multiply(X,X_52),multiply(X,Z))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,least_upper_bound(multiply(X,X_52),multiply(X,Z))))]]) ).
cnf(refute_0_2459,plain,
( least_upper_bound(multiply(X,X_52),multiply(X,Z)) != multiply(X,least_upper_bound(X_52,Z))
| least_upper_bound(identity,least_upper_bound(multiply(X,X_52),multiply(X,Z))) != least_upper_bound(identity,least_upper_bound(multiply(X,X_52),multiply(X,Z)))
| least_upper_bound(identity,least_upper_bound(multiply(X,X_52),multiply(X,Z))) = least_upper_bound(identity,multiply(X,least_upper_bound(X_52,Z))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(X,X_52),multiply(X,Z))),least_upper_bound(identity,least_upper_bound(multiply(X,X_52),multiply(X,Z)))) ),[1,1],$fot(multiply(X,least_upper_bound(X_52,Z)))]]) ).
cnf(refute_0_2460,plain,
( least_upper_bound(multiply(X,X_52),multiply(X,Z)) != multiply(X,least_upper_bound(X_52,Z))
| least_upper_bound(identity,least_upper_bound(multiply(X,X_52),multiply(X,Z))) = least_upper_bound(identity,multiply(X,least_upper_bound(X_52,Z))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(X,X_52),multiply(X,Z))),least_upper_bound(identity,least_upper_bound(multiply(X,X_52),multiply(X,Z)))) )],[refute_0_2458,refute_0_2459]) ).
cnf(refute_0_2461,plain,
least_upper_bound(identity,least_upper_bound(multiply(X,X_52),multiply(X,Z))) = least_upper_bound(identity,multiply(X,least_upper_bound(X_52,Z))),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,X_52),multiply(X,Z)),multiply(X,least_upper_bound(X_52,Z))) )],[refute_0_2457,refute_0_2460]) ).
cnf(refute_0_2462,plain,
least_upper_bound(least_upper_bound(identity,multiply(X,X_52)),multiply(X,Z)) = least_upper_bound(identity,least_upper_bound(multiply(X,X_52),multiply(X,Z))),
inference(subst,[],[refute_0_171:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X,X_52))),bind(Z,$fot(multiply(X,Z)))]]) ).
cnf(refute_0_2463,plain,
( least_upper_bound(identity,least_upper_bound(multiply(X,X_52),multiply(X,Z))) != least_upper_bound(identity,multiply(X,least_upper_bound(X_52,Z)))
| least_upper_bound(least_upper_bound(identity,multiply(X,X_52)),multiply(X,Z)) != least_upper_bound(identity,least_upper_bound(multiply(X,X_52),multiply(X,Z)))
| least_upper_bound(least_upper_bound(identity,multiply(X,X_52)),multiply(X,Z)) = least_upper_bound(identity,multiply(X,least_upper_bound(X_52,Z))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(least_upper_bound(least_upper_bound(identity,multiply(X,X_52)),multiply(X,Z)))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(multiply(X,X_52),multiply(X,Z))))),bind(Z0,$fot(least_upper_bound(identity,multiply(X,least_upper_bound(X_52,Z)))))]]) ).
cnf(refute_0_2464,plain,
( least_upper_bound(identity,least_upper_bound(multiply(X,X_52),multiply(X,Z))) != least_upper_bound(identity,multiply(X,least_upper_bound(X_52,Z)))
| least_upper_bound(least_upper_bound(identity,multiply(X,X_52)),multiply(X,Z)) = least_upper_bound(identity,multiply(X,least_upper_bound(X_52,Z))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(identity,multiply(X,X_52)),multiply(X,Z)),least_upper_bound(identity,least_upper_bound(multiply(X,X_52),multiply(X,Z)))) )],[refute_0_2462,refute_0_2463]) ).
cnf(refute_0_2465,plain,
least_upper_bound(least_upper_bound(identity,multiply(X,X_52)),multiply(X,Z)) = least_upper_bound(identity,multiply(X,least_upper_bound(X_52,Z))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(X,X_52),multiply(X,Z))),least_upper_bound(identity,multiply(X,least_upper_bound(X_52,Z)))) )],[refute_0_2461,refute_0_2464]) ).
cnf(refute_0_2466,plain,
( multiply(X,least_upper_bound(X_52,least_upper_bound(inverse(X),Z))) != least_upper_bound(least_upper_bound(identity,multiply(X,X_52)),multiply(X,Z))
| least_upper_bound(least_upper_bound(identity,multiply(X,X_52)),multiply(X,Z)) != least_upper_bound(identity,multiply(X,least_upper_bound(X_52,Z)))
| multiply(X,least_upper_bound(X_52,least_upper_bound(inverse(X),Z))) = least_upper_bound(identity,multiply(X,least_upper_bound(X_52,Z))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X,least_upper_bound(X_52,least_upper_bound(inverse(X),Z))),least_upper_bound(identity,multiply(X,least_upper_bound(X_52,Z)))) ),[0],$fot(least_upper_bound(least_upper_bound(identity,multiply(X,X_52)),multiply(X,Z)))]]) ).
cnf(refute_0_2467,plain,
( multiply(X,least_upper_bound(X_52,least_upper_bound(inverse(X),Z))) != least_upper_bound(least_upper_bound(identity,multiply(X,X_52)),multiply(X,Z))
| multiply(X,least_upper_bound(X_52,least_upper_bound(inverse(X),Z))) = least_upper_bound(identity,multiply(X,least_upper_bound(X_52,Z))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(identity,multiply(X,X_52)),multiply(X,Z)),least_upper_bound(identity,multiply(X,least_upper_bound(X_52,Z)))) )],[refute_0_2465,refute_0_2466]) ).
cnf(refute_0_2468,plain,
( multiply(X,least_upper_bound(least_upper_bound(X_52,inverse(X)),Z)) != least_upper_bound(least_upper_bound(identity,multiply(X,X_52)),multiply(X,Z))
| multiply(X,least_upper_bound(X_52,least_upper_bound(inverse(X),Z))) = least_upper_bound(identity,multiply(X,least_upper_bound(X_52,Z))) ),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(X_52,least_upper_bound(inverse(X),Z))),least_upper_bound(least_upper_bound(identity,multiply(X,X_52)),multiply(X,Z))) )],[refute_0_2456,refute_0_2467]) ).
cnf(refute_0_2469,plain,
multiply(X,least_upper_bound(X_52,least_upper_bound(inverse(X),Z))) = least_upper_bound(identity,multiply(X,least_upper_bound(X_52,Z))),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(least_upper_bound(X_52,inverse(X)),Z)),least_upper_bound(least_upper_bound(identity,multiply(X,X_52)),multiply(X,Z))) )],[refute_0_2449,refute_0_2468]) ).
cnf(refute_0_2470,plain,
multiply(inverse(X_56),least_upper_bound(X_56,least_upper_bound(inverse(inverse(X_56)),X_50))) = least_upper_bound(identity,multiply(inverse(X_56),least_upper_bound(X_56,X_50))),
inference(subst,[],[refute_0_2469:[bind(X,$fot(inverse(X_56))),bind(Z,$fot(X_50)),bind(X_52,$fot(X_56))]]) ).
cnf(refute_0_2471,plain,
multiply(inverse(X_56),least_upper_bound(least_upper_bound(inverse(inverse(X_56)),X_50),X_56)) = multiply(inverse(X_56),least_upper_bound(X_56,least_upper_bound(inverse(inverse(X_56)),X_50))),
inference(subst,[],[refute_0_580:[bind(X_48,$fot(inverse(X_56))),bind(X_49,$fot(X_56)),bind(X_50,$fot(least_upper_bound(inverse(inverse(X_56)),X_50)))]]) ).
cnf(refute_0_2472,plain,
( multiply(inverse(X_56),least_upper_bound(X_56,least_upper_bound(inverse(inverse(X_56)),X_50))) != least_upper_bound(identity,multiply(inverse(X_56),least_upper_bound(X_56,X_50)))
| multiply(inverse(X_56),least_upper_bound(least_upper_bound(inverse(inverse(X_56)),X_50),X_56)) != multiply(inverse(X_56),least_upper_bound(X_56,least_upper_bound(inverse(inverse(X_56)),X_50)))
| multiply(inverse(X_56),least_upper_bound(least_upper_bound(inverse(inverse(X_56)),X_50),X_56)) = least_upper_bound(identity,multiply(inverse(X_56),least_upper_bound(X_56,X_50))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(inverse(X_56),least_upper_bound(least_upper_bound(inverse(inverse(X_56)),X_50),X_56)))),bind(Y0,$fot(multiply(inverse(X_56),least_upper_bound(X_56,least_upper_bound(inverse(inverse(X_56)),X_50))))),bind(Z0,$fot(least_upper_bound(identity,multiply(inverse(X_56),least_upper_bound(X_56,X_50)))))]]) ).
cnf(refute_0_2473,plain,
( multiply(inverse(X_56),least_upper_bound(X_56,least_upper_bound(inverse(inverse(X_56)),X_50))) != least_upper_bound(identity,multiply(inverse(X_56),least_upper_bound(X_56,X_50)))
| multiply(inverse(X_56),least_upper_bound(least_upper_bound(inverse(inverse(X_56)),X_50),X_56)) = least_upper_bound(identity,multiply(inverse(X_56),least_upper_bound(X_56,X_50))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_56),least_upper_bound(least_upper_bound(inverse(inverse(X_56)),X_50),X_56)),multiply(inverse(X_56),least_upper_bound(X_56,least_upper_bound(inverse(inverse(X_56)),X_50)))) )],[refute_0_2471,refute_0_2472]) ).
cnf(refute_0_2474,plain,
multiply(inverse(X_56),least_upper_bound(least_upper_bound(inverse(inverse(X_56)),X_50),X_56)) = least_upper_bound(identity,multiply(inverse(X_56),least_upper_bound(X_56,X_50))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_56),least_upper_bound(X_56,least_upper_bound(inverse(inverse(X_56)),X_50))),least_upper_bound(identity,multiply(inverse(X_56),least_upper_bound(X_56,X_50)))) )],[refute_0_2470,refute_0_2473]) ).
cnf(refute_0_2475,plain,
( multiply(inverse(X_56),least_upper_bound(least_upper_bound(inverse(inverse(X_56)),X_50),X_56)) != least_upper_bound(identity,multiply(inverse(X_56),least_upper_bound(X_56,X_50)))
| multiply(inverse(X_56),least_upper_bound(least_upper_bound(inverse(inverse(X_56)),X_50),X_56)) != least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_56),X_50)))
| least_upper_bound(identity,multiply(inverse(X_56),least_upper_bound(X_56,X_50))) = least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_56),X_50))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_56),least_upper_bound(least_upper_bound(inverse(inverse(X_56)),X_50),X_56)),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_56),X_50)))) ),[0],$fot(least_upper_bound(identity,multiply(inverse(X_56),least_upper_bound(X_56,X_50))))]]) ).
cnf(refute_0_2476,plain,
( multiply(inverse(X_56),least_upper_bound(least_upper_bound(inverse(inverse(X_56)),X_50),X_56)) != least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_56),X_50)))
| least_upper_bound(identity,multiply(inverse(X_56),least_upper_bound(X_56,X_50))) = least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_56),X_50))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_56),least_upper_bound(least_upper_bound(inverse(inverse(X_56)),X_50),X_56)),least_upper_bound(identity,multiply(inverse(X_56),least_upper_bound(X_56,X_50)))) )],[refute_0_2474,refute_0_2475]) ).
cnf(refute_0_2477,plain,
least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_56),X_50))) = least_upper_bound(identity,multiply(inverse(X_56),X_50)),
inference(subst,[],[refute_0_516:[bind(X_18,$fot(multiply(inverse(X_56),X_50))),bind(X_19,$fot(identity))]]) ).
cnf(refute_0_2478,plain,
( least_upper_bound(identity,multiply(inverse(X_56),least_upper_bound(X_56,X_50))) != least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_56),X_50)))
| least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_56),X_50))) != least_upper_bound(identity,multiply(inverse(X_56),X_50))
| least_upper_bound(identity,multiply(inverse(X_56),least_upper_bound(X_56,X_50))) = least_upper_bound(identity,multiply(inverse(X_56),X_50)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(identity,multiply(inverse(X_56),least_upper_bound(X_56,X_50))),least_upper_bound(identity,multiply(inverse(X_56),X_50))) ),[0],$fot(least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_56),X_50))))]]) ).
cnf(refute_0_2479,plain,
( least_upper_bound(identity,multiply(inverse(X_56),least_upper_bound(X_56,X_50))) != least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_56),X_50)))
| least_upper_bound(identity,multiply(inverse(X_56),least_upper_bound(X_56,X_50))) = least_upper_bound(identity,multiply(inverse(X_56),X_50)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_56),X_50))),least_upper_bound(identity,multiply(inverse(X_56),X_50))) )],[refute_0_2477,refute_0_2478]) ).
cnf(refute_0_2480,plain,
( multiply(inverse(X_56),least_upper_bound(least_upper_bound(inverse(inverse(X_56)),X_50),X_56)) != least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_56),X_50)))
| least_upper_bound(identity,multiply(inverse(X_56),least_upper_bound(X_56,X_50))) = least_upper_bound(identity,multiply(inverse(X_56),X_50)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(X_56),least_upper_bound(X_56,X_50))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_56),X_50)))) )],[refute_0_2476,refute_0_2479]) ).
cnf(refute_0_2481,plain,
least_upper_bound(identity,multiply(inverse(X_56),least_upper_bound(X_56,X_50))) = least_upper_bound(identity,multiply(inverse(X_56),X_50)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_56),least_upper_bound(least_upper_bound(inverse(inverse(X_56)),X_50),X_56)),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_56),X_50)))) )],[refute_0_2444,refute_0_2480]) ).
cnf(refute_0_2482,plain,
least_upper_bound(identity,multiply(inverse(X_269),least_upper_bound(X_269,inverse(X_68)))) = least_upper_bound(identity,multiply(inverse(X_269),inverse(X_68))),
inference(subst,[],[refute_0_2481:[bind(X_50,$fot(inverse(X_68))),bind(X_56,$fot(X_269))]]) ).
cnf(refute_0_2483,plain,
multiply(least_upper_bound(X_68,inverse(X_269)),inverse(X_68)) = least_upper_bound(identity,multiply(inverse(X_269),inverse(X_68))),
inference(subst,[],[refute_0_1189:[bind(X_69,$fot(inverse(X_269)))]]) ).
cnf(refute_0_2484,plain,
( multiply(least_upper_bound(X_68,inverse(X_269)),inverse(X_68)) != least_upper_bound(identity,multiply(inverse(X_269),inverse(X_68)))
| least_upper_bound(identity,multiply(inverse(X_269),inverse(X_68))) = multiply(least_upper_bound(X_68,inverse(X_269)),inverse(X_68)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(least_upper_bound(X_68,inverse(X_269)),inverse(X_68)))),bind(Y0,$fot(least_upper_bound(identity,multiply(inverse(X_269),inverse(X_68)))))]]) ).
cnf(refute_0_2485,plain,
least_upper_bound(identity,multiply(inverse(X_269),inverse(X_68))) = multiply(least_upper_bound(X_68,inverse(X_269)),inverse(X_68)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_68,inverse(X_269)),inverse(X_68)),least_upper_bound(identity,multiply(inverse(X_269),inverse(X_68)))) )],[refute_0_2483,refute_0_2484]) ).
cnf(refute_0_2486,plain,
( least_upper_bound(identity,multiply(inverse(X_269),inverse(X_68))) != multiply(least_upper_bound(X_68,inverse(X_269)),inverse(X_68))
| least_upper_bound(identity,multiply(inverse(X_269),least_upper_bound(X_269,inverse(X_68)))) != least_upper_bound(identity,multiply(inverse(X_269),inverse(X_68)))
| least_upper_bound(identity,multiply(inverse(X_269),least_upper_bound(X_269,inverse(X_68)))) = multiply(least_upper_bound(X_68,inverse(X_269)),inverse(X_68)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(X_269),least_upper_bound(X_269,inverse(X_68)))),least_upper_bound(identity,multiply(inverse(X_269),inverse(X_68)))) ),[1],$fot(multiply(least_upper_bound(X_68,inverse(X_269)),inverse(X_68)))]]) ).
cnf(refute_0_2487,plain,
( least_upper_bound(identity,multiply(inverse(X_269),least_upper_bound(X_269,inverse(X_68)))) != least_upper_bound(identity,multiply(inverse(X_269),inverse(X_68)))
| least_upper_bound(identity,multiply(inverse(X_269),least_upper_bound(X_269,inverse(X_68)))) = multiply(least_upper_bound(X_68,inverse(X_269)),inverse(X_68)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(X_269),inverse(X_68))),multiply(least_upper_bound(X_68,inverse(X_269)),inverse(X_68))) )],[refute_0_2485,refute_0_2486]) ).
cnf(refute_0_2488,plain,
least_upper_bound(identity,multiply(inverse(X_269),least_upper_bound(X_269,inverse(X_68)))) = multiply(least_upper_bound(X_68,inverse(X_269)),inverse(X_68)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(X_269),least_upper_bound(X_269,inverse(X_68)))),least_upper_bound(identity,multiply(inverse(X_269),inverse(X_68)))) )],[refute_0_2482,refute_0_2487]) ).
cnf(refute_0_2489,plain,
multiply(inverse(X_269),inverse(X_68)) = inverse(multiply(X_68,X_269)),
inference(subst,[],[refute_0_490:[bind(X_30,$fot(X_68)),bind(X_31,$fot(X_269))]]) ).
cnf(refute_0_2490,plain,
least_upper_bound(identity,multiply(inverse(X_269),inverse(X_68))) = least_upper_bound(identity,multiply(inverse(X_269),inverse(X_68))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,multiply(inverse(X_269),inverse(X_68))))]]) ).
cnf(refute_0_2491,plain,
( multiply(inverse(X_269),inverse(X_68)) != inverse(multiply(X_68,X_269))
| least_upper_bound(identity,multiply(inverse(X_269),inverse(X_68))) != least_upper_bound(identity,multiply(inverse(X_269),inverse(X_68)))
| least_upper_bound(identity,multiply(inverse(X_269),inverse(X_68))) = least_upper_bound(identity,inverse(multiply(X_68,X_269))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(X_269),inverse(X_68))),least_upper_bound(identity,multiply(inverse(X_269),inverse(X_68)))) ),[1,1],$fot(inverse(multiply(X_68,X_269)))]]) ).
cnf(refute_0_2492,plain,
( multiply(inverse(X_269),inverse(X_68)) != inverse(multiply(X_68,X_269))
| least_upper_bound(identity,multiply(inverse(X_269),inverse(X_68))) = least_upper_bound(identity,inverse(multiply(X_68,X_269))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(X_269),inverse(X_68))),least_upper_bound(identity,multiply(inverse(X_269),inverse(X_68)))) )],[refute_0_2490,refute_0_2491]) ).
cnf(refute_0_2493,plain,
least_upper_bound(identity,multiply(inverse(X_269),inverse(X_68))) = least_upper_bound(identity,inverse(multiply(X_68,X_269))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_269),inverse(X_68)),inverse(multiply(X_68,X_269))) )],[refute_0_2489,refute_0_2492]) ).
cnf(refute_0_2494,plain,
( least_upper_bound(identity,multiply(inverse(X_269),inverse(X_68))) != least_upper_bound(identity,inverse(multiply(X_68,X_269)))
| least_upper_bound(identity,multiply(inverse(X_269),least_upper_bound(X_269,inverse(X_68)))) != least_upper_bound(identity,multiply(inverse(X_269),inverse(X_68)))
| least_upper_bound(identity,multiply(inverse(X_269),least_upper_bound(X_269,inverse(X_68)))) = least_upper_bound(identity,inverse(multiply(X_68,X_269))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(least_upper_bound(identity,multiply(inverse(X_269),least_upper_bound(X_269,inverse(X_68)))))),bind(Y0,$fot(least_upper_bound(identity,multiply(inverse(X_269),inverse(X_68))))),bind(Z0,$fot(least_upper_bound(identity,inverse(multiply(X_68,X_269)))))]]) ).
cnf(refute_0_2495,plain,
( least_upper_bound(identity,multiply(inverse(X_269),inverse(X_68))) != least_upper_bound(identity,inverse(multiply(X_68,X_269)))
| least_upper_bound(identity,multiply(inverse(X_269),least_upper_bound(X_269,inverse(X_68)))) = least_upper_bound(identity,inverse(multiply(X_68,X_269))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(X_269),least_upper_bound(X_269,inverse(X_68)))),least_upper_bound(identity,multiply(inverse(X_269),inverse(X_68)))) )],[refute_0_2482,refute_0_2494]) ).
cnf(refute_0_2496,plain,
least_upper_bound(identity,multiply(inverse(X_269),least_upper_bound(X_269,inverse(X_68)))) = least_upper_bound(identity,inverse(multiply(X_68,X_269))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(X_269),inverse(X_68))),least_upper_bound(identity,inverse(multiply(X_68,X_269)))) )],[refute_0_2493,refute_0_2495]) ).
cnf(refute_0_2497,plain,
( least_upper_bound(identity,multiply(inverse(X_269),least_upper_bound(X_269,inverse(X_68)))) != multiply(least_upper_bound(X_68,inverse(X_269)),inverse(X_68))
| least_upper_bound(identity,multiply(inverse(X_269),least_upper_bound(X_269,inverse(X_68)))) != least_upper_bound(identity,inverse(multiply(X_68,X_269)))
| least_upper_bound(identity,inverse(multiply(X_68,X_269))) = multiply(least_upper_bound(X_68,inverse(X_269)),inverse(X_68)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(X_269),least_upper_bound(X_269,inverse(X_68)))),multiply(least_upper_bound(X_68,inverse(X_269)),inverse(X_68))) ),[0],$fot(least_upper_bound(identity,inverse(multiply(X_68,X_269))))]]) ).
cnf(refute_0_2498,plain,
( least_upper_bound(identity,multiply(inverse(X_269),least_upper_bound(X_269,inverse(X_68)))) != multiply(least_upper_bound(X_68,inverse(X_269)),inverse(X_68))
| least_upper_bound(identity,inverse(multiply(X_68,X_269))) = multiply(least_upper_bound(X_68,inverse(X_269)),inverse(X_68)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(X_269),least_upper_bound(X_269,inverse(X_68)))),least_upper_bound(identity,inverse(multiply(X_68,X_269)))) )],[refute_0_2496,refute_0_2497]) ).
cnf(refute_0_2499,plain,
least_upper_bound(identity,inverse(multiply(X_68,X_269))) = multiply(least_upper_bound(X_68,inverse(X_269)),inverse(X_68)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(X_269),least_upper_bound(X_269,inverse(X_68)))),multiply(least_upper_bound(X_68,inverse(X_269)),inverse(X_68))) )],[refute_0_2488,refute_0_2498]) ).
cnf(refute_0_2500,plain,
( least_upper_bound(identity,inverse(multiply(X_68,X_269))) != multiply(least_upper_bound(X_68,inverse(X_269)),inverse(X_68))
| multiply(least_upper_bound(X_68,inverse(X_269)),inverse(X_68)) = least_upper_bound(identity,inverse(multiply(X_68,X_269))) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(least_upper_bound(identity,inverse(multiply(X_68,X_269))))),bind(Y0,$fot(multiply(least_upper_bound(X_68,inverse(X_269)),inverse(X_68))))]]) ).
cnf(refute_0_2501,plain,
multiply(least_upper_bound(X_68,inverse(X_269)),inverse(X_68)) = least_upper_bound(identity,inverse(multiply(X_68,X_269))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(multiply(X_68,X_269))),multiply(least_upper_bound(X_68,inverse(X_269)),inverse(X_68))) )],[refute_0_2499,refute_0_2500]) ).
cnf(refute_0_2502,plain,
multiply(least_upper_bound(identity,inverse(X_444)),inverse(identity)) = least_upper_bound(identity,inverse(multiply(identity,X_444))),
inference(subst,[],[refute_0_2501:[bind(X_269,$fot(X_444)),bind(X_68,$fot(identity))]]) ).
cnf(refute_0_2503,plain,
( multiply(least_upper_bound(identity,inverse(X_444)),inverse(identity)) != least_upper_bound(identity,inverse(multiply(identity,X_444)))
| least_upper_bound(identity,inverse(multiply(identity,X_444))) != least_upper_bound(identity,inverse(X_444))
| multiply(least_upper_bound(identity,inverse(X_444)),inverse(identity)) = least_upper_bound(identity,inverse(X_444)) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(least_upper_bound(identity,inverse(X_444)),inverse(identity)))),bind(Y0,$fot(least_upper_bound(identity,inverse(multiply(identity,X_444))))),bind(Z0,$fot(least_upper_bound(identity,inverse(X_444))))]]) ).
cnf(refute_0_2504,plain,
( least_upper_bound(identity,inverse(multiply(identity,X_444))) != least_upper_bound(identity,inverse(X_444))
| multiply(least_upper_bound(identity,inverse(X_444)),inverse(identity)) = least_upper_bound(identity,inverse(X_444)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_444)),inverse(identity)),least_upper_bound(identity,inverse(multiply(identity,X_444)))) )],[refute_0_2502,refute_0_2503]) ).
cnf(refute_0_2505,plain,
multiply(least_upper_bound(identity,inverse(X_444)),inverse(identity)) = least_upper_bound(identity,inverse(X_444)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(multiply(identity,X_444))),least_upper_bound(identity,inverse(X_444))) )],[refute_0_2435,refute_0_2504]) ).
cnf(refute_0_2506,plain,
multiply(greatest_lower_bound(identity,X_444),multiply(least_upper_bound(identity,inverse(X_444)),inverse(identity))) = multiply(greatest_lower_bound(identity,X_444),multiply(least_upper_bound(identity,inverse(X_444)),inverse(identity))),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(identity,X_444),multiply(least_upper_bound(identity,inverse(X_444)),inverse(identity))))]]) ).
cnf(refute_0_2507,plain,
( multiply(greatest_lower_bound(identity,X_444),multiply(least_upper_bound(identity,inverse(X_444)),inverse(identity))) != multiply(greatest_lower_bound(identity,X_444),multiply(least_upper_bound(identity,inverse(X_444)),inverse(identity)))
| multiply(least_upper_bound(identity,inverse(X_444)),inverse(identity)) != least_upper_bound(identity,inverse(X_444))
| multiply(greatest_lower_bound(identity,X_444),multiply(least_upper_bound(identity,inverse(X_444)),inverse(identity))) = multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_444),multiply(least_upper_bound(identity,inverse(X_444)),inverse(identity))),multiply(greatest_lower_bound(identity,X_444),multiply(least_upper_bound(identity,inverse(X_444)),inverse(identity)))) ),[1,1],$fot(least_upper_bound(identity,inverse(X_444)))]]) ).
cnf(refute_0_2508,plain,
( multiply(least_upper_bound(identity,inverse(X_444)),inverse(identity)) != least_upper_bound(identity,inverse(X_444))
| multiply(greatest_lower_bound(identity,X_444),multiply(least_upper_bound(identity,inverse(X_444)),inverse(identity))) = multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_444),multiply(least_upper_bound(identity,inverse(X_444)),inverse(identity))),multiply(greatest_lower_bound(identity,X_444),multiply(least_upper_bound(identity,inverse(X_444)),inverse(identity)))) )],[refute_0_2506,refute_0_2507]) ).
cnf(refute_0_2509,plain,
multiply(greatest_lower_bound(identity,X_444),multiply(least_upper_bound(identity,inverse(X_444)),inverse(identity))) = multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_444)),inverse(identity)),least_upper_bound(identity,inverse(X_444))) )],[refute_0_2505,refute_0_2508]) ).
cnf(refute_0_2510,plain,
multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(identity)) = multiply(greatest_lower_bound(identity,X_444),multiply(least_upper_bound(identity,inverse(X_444)),inverse(identity))),
inference(subst,[],[associativity:[bind(X,$fot(greatest_lower_bound(identity,X_444))),bind(Y,$fot(least_upper_bound(identity,inverse(X_444)))),bind(Z,$fot(inverse(identity)))]]) ).
cnf(refute_0_2511,plain,
( multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(identity)) != multiply(greatest_lower_bound(identity,X_444),multiply(least_upper_bound(identity,inverse(X_444)),inverse(identity)))
| multiply(greatest_lower_bound(identity,X_444),multiply(least_upper_bound(identity,inverse(X_444)),inverse(identity))) != multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))
| multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(identity)) = multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(identity)))),bind(Y0,$fot(multiply(greatest_lower_bound(identity,X_444),multiply(least_upper_bound(identity,inverse(X_444)),inverse(identity))))),bind(Z0,$fot(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))]]) ).
cnf(refute_0_2512,plain,
( multiply(greatest_lower_bound(identity,X_444),multiply(least_upper_bound(identity,inverse(X_444)),inverse(identity))) != multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))
| multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(identity)) = multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(identity)),multiply(greatest_lower_bound(identity,X_444),multiply(least_upper_bound(identity,inverse(X_444)),inverse(identity)))) )],[refute_0_2510,refute_0_2511]) ).
cnf(refute_0_2513,plain,
multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(identity)) = multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_444),multiply(least_upper_bound(identity,inverse(X_444)),inverse(identity))),multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))) )],[refute_0_2509,refute_0_2512]) ).
cnf(refute_0_2514,plain,
( multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(identity)) != multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))
| multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(identity)) != least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))))
| multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))) = least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(identity)),least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))))) ),[0],$fot(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))]]) ).
cnf(refute_0_2515,plain,
( multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(identity)) != least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))))
| multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))) = least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(identity)),multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))) )],[refute_0_2513,refute_0_2514]) ).
cnf(refute_0_2516,plain,
( multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))) != least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))))
| greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))) != identity
| multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))) = least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(identity))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))),least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))))) ),[1,1,1,0],$fot(identity)]]) ).
cnf(refute_0_2517,plain,
( multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))) != least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))))
| multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))) = least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(identity))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))),identity) )],[refute_0_2423,refute_0_2516]) ).
cnf(refute_0_2518,plain,
multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))) = least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(identity))),
inference(resolve,[$cnf( $equal(multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))),least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))))) )],[refute_0_1826,refute_0_2517]) ).
cnf(refute_0_2519,plain,
multiply(identity,greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))) = greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))),
inference(subst,[],[left_identity:[bind(X,$fot(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))))]]) ).
cnf(refute_0_2520,plain,
multiply(inverse(multiply(X_105,X_146)),greatest_lower_bound(X_105,identity)) = greatest_lower_bound(inverse(multiply(X_105,X_146)),multiply(inverse(multiply(X_105,X_146)),X_105)),
inference(subst,[],[refute_0_319:[bind(X_104,$fot(inverse(multiply(X_105,X_146))))]]) ).
cnf(refute_0_2521,plain,
inverse(X_146) = multiply(inverse(multiply(X_105,X_146)),X_105),
inference(subst,[],[refute_0_96:[bind(X_45,$fot(X_105)),bind(X_46,$fot(X_146))]]) ).
cnf(refute_0_2522,plain,
( inverse(X_146) != multiply(inverse(multiply(X_105,X_146)),X_105)
| multiply(inverse(multiply(X_105,X_146)),X_105) = inverse(X_146) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(inverse(X_146))),bind(Y0,$fot(multiply(inverse(multiply(X_105,X_146)),X_105)))]]) ).
cnf(refute_0_2523,plain,
multiply(inverse(multiply(X_105,X_146)),X_105) = inverse(X_146),
inference(resolve,[$cnf( $equal(inverse(X_146),multiply(inverse(multiply(X_105,X_146)),X_105)) )],[refute_0_2521,refute_0_2522]) ).
cnf(refute_0_2524,plain,
( multiply(inverse(multiply(X_105,X_146)),X_105) != inverse(X_146)
| multiply(inverse(multiply(X_105,X_146)),greatest_lower_bound(X_105,identity)) != greatest_lower_bound(inverse(multiply(X_105,X_146)),multiply(inverse(multiply(X_105,X_146)),X_105))
| multiply(inverse(multiply(X_105,X_146)),greatest_lower_bound(X_105,identity)) = greatest_lower_bound(inverse(multiply(X_105,X_146)),inverse(X_146)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(X_105,X_146)),greatest_lower_bound(X_105,identity)),greatest_lower_bound(inverse(multiply(X_105,X_146)),multiply(inverse(multiply(X_105,X_146)),X_105))) ),[1,1],$fot(inverse(X_146))]]) ).
cnf(refute_0_2525,plain,
( multiply(inverse(multiply(X_105,X_146)),greatest_lower_bound(X_105,identity)) != greatest_lower_bound(inverse(multiply(X_105,X_146)),multiply(inverse(multiply(X_105,X_146)),X_105))
| multiply(inverse(multiply(X_105,X_146)),greatest_lower_bound(X_105,identity)) = greatest_lower_bound(inverse(multiply(X_105,X_146)),inverse(X_146)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_105,X_146)),X_105),inverse(X_146)) )],[refute_0_2523,refute_0_2524]) ).
cnf(refute_0_2526,plain,
multiply(inverse(multiply(X_105,X_146)),greatest_lower_bound(X_105,identity)) = greatest_lower_bound(inverse(multiply(X_105,X_146)),inverse(X_146)),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_105,X_146)),greatest_lower_bound(X_105,identity)),greatest_lower_bound(inverse(multiply(X_105,X_146)),multiply(inverse(multiply(X_105,X_146)),X_105))) )],[refute_0_2520,refute_0_2525]) ).
cnf(refute_0_2527,plain,
greatest_lower_bound(inverse(multiply(X_105,X_146)),inverse(X_146)) = greatest_lower_bound(inverse(X_146),inverse(multiply(X_105,X_146))),
inference(subst,[],[refute_0_42:[bind(X,$fot(inverse(X_146))),bind(Y,$fot(inverse(multiply(X_105,X_146))))]]) ).
cnf(refute_0_2528,plain,
( multiply(inverse(multiply(X_105,X_146)),greatest_lower_bound(X_105,identity)) != greatest_lower_bound(inverse(multiply(X_105,X_146)),inverse(X_146))
| greatest_lower_bound(inverse(multiply(X_105,X_146)),inverse(X_146)) != greatest_lower_bound(inverse(X_146),inverse(multiply(X_105,X_146)))
| multiply(inverse(multiply(X_105,X_146)),greatest_lower_bound(X_105,identity)) = greatest_lower_bound(inverse(X_146),inverse(multiply(X_105,X_146))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(multiply(X_105,X_146)),greatest_lower_bound(X_105,identity)),greatest_lower_bound(inverse(X_146),inverse(multiply(X_105,X_146)))) ),[0],$fot(greatest_lower_bound(inverse(multiply(X_105,X_146)),inverse(X_146)))]]) ).
cnf(refute_0_2529,plain,
( multiply(inverse(multiply(X_105,X_146)),greatest_lower_bound(X_105,identity)) != greatest_lower_bound(inverse(multiply(X_105,X_146)),inverse(X_146))
| multiply(inverse(multiply(X_105,X_146)),greatest_lower_bound(X_105,identity)) = greatest_lower_bound(inverse(X_146),inverse(multiply(X_105,X_146))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(multiply(X_105,X_146)),inverse(X_146)),greatest_lower_bound(inverse(X_146),inverse(multiply(X_105,X_146)))) )],[refute_0_2527,refute_0_2528]) ).
cnf(refute_0_2530,plain,
multiply(inverse(multiply(X_105,X_146)),greatest_lower_bound(X_105,identity)) = greatest_lower_bound(inverse(X_146),inverse(multiply(X_105,X_146))),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_105,X_146)),greatest_lower_bound(X_105,identity)),greatest_lower_bound(inverse(multiply(X_105,X_146)),inverse(X_146))) )],[refute_0_2526,refute_0_2529]) ).
cnf(refute_0_2531,plain,
multiply(inverse(X_353),greatest_lower_bound(inverse(X_352),identity)) = greatest_lower_bound(inverse(X_353),multiply(inverse(X_353),inverse(X_352))),
inference(subst,[],[refute_0_319:[bind(X_104,$fot(inverse(X_353))),bind(X_105,$fot(inverse(X_352)))]]) ).
cnf(refute_0_2532,plain,
inverse(multiply(X_352,X_353)) = multiply(inverse(X_353),inverse(X_352)),
inference(subst,[],[refute_0_488:[bind(X_30,$fot(X_352)),bind(X_31,$fot(X_353))]]) ).
cnf(refute_0_2533,plain,
( inverse(multiply(X_352,X_353)) != multiply(inverse(X_353),inverse(X_352))
| multiply(inverse(X_353),inverse(X_352)) = inverse(multiply(X_352,X_353)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(inverse(multiply(X_352,X_353)))),bind(Y0,$fot(multiply(inverse(X_353),inverse(X_352))))]]) ).
cnf(refute_0_2534,plain,
multiply(inverse(X_353),inverse(X_352)) = inverse(multiply(X_352,X_353)),
inference(resolve,[$cnf( $equal(inverse(multiply(X_352,X_353)),multiply(inverse(X_353),inverse(X_352))) )],[refute_0_2532,refute_0_2533]) ).
cnf(refute_0_2535,plain,
( multiply(inverse(X_353),greatest_lower_bound(inverse(X_352),identity)) != greatest_lower_bound(inverse(X_353),multiply(inverse(X_353),inverse(X_352)))
| multiply(inverse(X_353),inverse(X_352)) != inverse(multiply(X_352,X_353))
| multiply(inverse(X_353),greatest_lower_bound(inverse(X_352),identity)) = greatest_lower_bound(inverse(X_353),inverse(multiply(X_352,X_353))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_353),greatest_lower_bound(inverse(X_352),identity)),greatest_lower_bound(inverse(X_353),multiply(inverse(X_353),inverse(X_352)))) ),[1,1],$fot(inverse(multiply(X_352,X_353)))]]) ).
cnf(refute_0_2536,plain,
( multiply(inverse(X_353),greatest_lower_bound(inverse(X_352),identity)) != greatest_lower_bound(inverse(X_353),multiply(inverse(X_353),inverse(X_352)))
| multiply(inverse(X_353),greatest_lower_bound(inverse(X_352),identity)) = greatest_lower_bound(inverse(X_353),inverse(multiply(X_352,X_353))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_353),inverse(X_352)),inverse(multiply(X_352,X_353))) )],[refute_0_2534,refute_0_2535]) ).
cnf(refute_0_2537,plain,
multiply(inverse(X_353),greatest_lower_bound(inverse(X_352),identity)) = greatest_lower_bound(inverse(X_353),inverse(multiply(X_352,X_353))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_353),greatest_lower_bound(inverse(X_352),identity)),greatest_lower_bound(inverse(X_353),multiply(inverse(X_353),inverse(X_352)))) )],[refute_0_2531,refute_0_2536]) ).
cnf(refute_0_2538,plain,
multiply(inverse(X_353),greatest_lower_bound(inverse(X_352),identity)) = multiply(inverse(X_353),greatest_lower_bound(identity,inverse(X_352))),
inference(subst,[],[refute_0_1249:[bind(X_249,$fot(inverse(X_352))),bind(X_250,$fot(identity)),bind(X_31,$fot(X_353))]]) ).
cnf(refute_0_2539,plain,
( multiply(inverse(X_353),greatest_lower_bound(inverse(X_352),identity)) != multiply(inverse(X_353),greatest_lower_bound(identity,inverse(X_352)))
| multiply(inverse(X_353),greatest_lower_bound(inverse(X_352),identity)) != greatest_lower_bound(inverse(X_353),inverse(multiply(X_352,X_353)))
| multiply(inverse(X_353),greatest_lower_bound(identity,inverse(X_352))) = greatest_lower_bound(inverse(X_353),inverse(multiply(X_352,X_353))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_353),greatest_lower_bound(inverse(X_352),identity)),greatest_lower_bound(inverse(X_353),inverse(multiply(X_352,X_353)))) ),[0],$fot(multiply(inverse(X_353),greatest_lower_bound(identity,inverse(X_352))))]]) ).
cnf(refute_0_2540,plain,
( multiply(inverse(X_353),greatest_lower_bound(inverse(X_352),identity)) != greatest_lower_bound(inverse(X_353),inverse(multiply(X_352,X_353)))
| multiply(inverse(X_353),greatest_lower_bound(identity,inverse(X_352))) = greatest_lower_bound(inverse(X_353),inverse(multiply(X_352,X_353))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_353),greatest_lower_bound(inverse(X_352),identity)),multiply(inverse(X_353),greatest_lower_bound(identity,inverse(X_352)))) )],[refute_0_2538,refute_0_2539]) ).
cnf(refute_0_2541,plain,
multiply(inverse(X_353),greatest_lower_bound(identity,inverse(X_352))) = greatest_lower_bound(inverse(X_353),inverse(multiply(X_352,X_353))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_353),greatest_lower_bound(inverse(X_352),identity)),greatest_lower_bound(inverse(X_353),inverse(multiply(X_352,X_353)))) )],[refute_0_2537,refute_0_2540]) ).
cnf(refute_0_2542,plain,
( multiply(inverse(X_353),greatest_lower_bound(identity,inverse(X_352))) != greatest_lower_bound(inverse(X_353),inverse(multiply(X_352,X_353)))
| greatest_lower_bound(inverse(X_353),inverse(multiply(X_352,X_353))) = multiply(inverse(X_353),greatest_lower_bound(identity,inverse(X_352))) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(inverse(X_353),greatest_lower_bound(identity,inverse(X_352))))),bind(Y0,$fot(greatest_lower_bound(inverse(X_353),inverse(multiply(X_352,X_353)))))]]) ).
cnf(refute_0_2543,plain,
greatest_lower_bound(inverse(X_353),inverse(multiply(X_352,X_353))) = multiply(inverse(X_353),greatest_lower_bound(identity,inverse(X_352))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_353),greatest_lower_bound(identity,inverse(X_352))),greatest_lower_bound(inverse(X_353),inverse(multiply(X_352,X_353)))) )],[refute_0_2541,refute_0_2542]) ).
cnf(refute_0_2544,plain,
greatest_lower_bound(inverse(X_146),inverse(multiply(X_105,X_146))) = multiply(inverse(X_146),greatest_lower_bound(identity,inverse(X_105))),
inference(subst,[],[refute_0_2543:[bind(X_352,$fot(X_105)),bind(X_353,$fot(X_146))]]) ).
cnf(refute_0_2545,plain,
( multiply(inverse(multiply(X_105,X_146)),greatest_lower_bound(X_105,identity)) != greatest_lower_bound(inverse(X_146),inverse(multiply(X_105,X_146)))
| greatest_lower_bound(inverse(X_146),inverse(multiply(X_105,X_146))) != multiply(inverse(X_146),greatest_lower_bound(identity,inverse(X_105)))
| multiply(inverse(multiply(X_105,X_146)),greatest_lower_bound(X_105,identity)) = multiply(inverse(X_146),greatest_lower_bound(identity,inverse(X_105))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(multiply(X_105,X_146)),greatest_lower_bound(X_105,identity)),multiply(inverse(X_146),greatest_lower_bound(identity,inverse(X_105)))) ),[0],$fot(greatest_lower_bound(inverse(X_146),inverse(multiply(X_105,X_146))))]]) ).
cnf(refute_0_2546,plain,
( multiply(inverse(multiply(X_105,X_146)),greatest_lower_bound(X_105,identity)) != greatest_lower_bound(inverse(X_146),inverse(multiply(X_105,X_146)))
| multiply(inverse(multiply(X_105,X_146)),greatest_lower_bound(X_105,identity)) = multiply(inverse(X_146),greatest_lower_bound(identity,inverse(X_105))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_146),inverse(multiply(X_105,X_146))),multiply(inverse(X_146),greatest_lower_bound(identity,inverse(X_105)))) )],[refute_0_2544,refute_0_2545]) ).
cnf(refute_0_2547,plain,
multiply(inverse(multiply(X_105,X_146)),greatest_lower_bound(X_105,identity)) = multiply(inverse(X_146),greatest_lower_bound(identity,inverse(X_105))),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_105,X_146)),greatest_lower_bound(X_105,identity)),greatest_lower_bound(inverse(X_146),inverse(multiply(X_105,X_146)))) )],[refute_0_2530,refute_0_2546]) ).
cnf(refute_0_2548,plain,
multiply(inverse(multiply(inverse(X_31),inverse(X_30))),greatest_lower_bound(inverse(X_31),identity)) = multiply(inverse(inverse(X_30)),greatest_lower_bound(identity,inverse(inverse(X_31)))),
inference(subst,[],[refute_0_2547:[bind(X_105,$fot(inverse(X_31))),bind(X_146,$fot(inverse(X_30)))]]) ).
cnf(refute_0_2549,plain,
( multiply(inverse(X_31),inverse(X_30)) != inverse(multiply(X_30,X_31))
| multiply(inverse(multiply(inverse(X_31),inverse(X_30))),greatest_lower_bound(inverse(X_31),identity)) != multiply(inverse(inverse(X_30)),greatest_lower_bound(identity,inverse(inverse(X_31))))
| multiply(inverse(inverse(multiply(X_30,X_31))),greatest_lower_bound(inverse(X_31),identity)) = multiply(inverse(inverse(X_30)),greatest_lower_bound(identity,inverse(inverse(X_31)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(inverse(X_31),inverse(X_30))),greatest_lower_bound(inverse(X_31),identity)),multiply(inverse(inverse(X_30)),greatest_lower_bound(identity,inverse(inverse(X_31))))) ),[0,0,0],$fot(inverse(multiply(X_30,X_31)))]]) ).
cnf(refute_0_2550,plain,
( multiply(inverse(multiply(inverse(X_31),inverse(X_30))),greatest_lower_bound(inverse(X_31),identity)) != multiply(inverse(inverse(X_30)),greatest_lower_bound(identity,inverse(inverse(X_31))))
| multiply(inverse(inverse(multiply(X_30,X_31))),greatest_lower_bound(inverse(X_31),identity)) = multiply(inverse(inverse(X_30)),greatest_lower_bound(identity,inverse(inverse(X_31)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_31),inverse(X_30)),inverse(multiply(X_30,X_31))) )],[refute_0_490,refute_0_2549]) ).
cnf(refute_0_2551,plain,
multiply(inverse(inverse(multiply(X_30,X_31))),greatest_lower_bound(inverse(X_31),identity)) = multiply(inverse(inverse(X_30)),greatest_lower_bound(identity,inverse(inverse(X_31)))),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(X_31),inverse(X_30))),greatest_lower_bound(inverse(X_31),identity)),multiply(inverse(inverse(X_30)),greatest_lower_bound(identity,inverse(inverse(X_31))))) )],[refute_0_2548,refute_0_2550]) ).
cnf(refute_0_2552,plain,
multiply(greatest_lower_bound(X_31,identity),identity) = greatest_lower_bound(X_31,identity),
inference(subst,[],[refute_0_88:[bind(X_33,$fot(greatest_lower_bound(X_31,identity)))]]) ).
cnf(refute_0_2553,plain,
greatest_lower_bound(identity,multiply(X_31,identity)) = multiply(greatest_lower_bound(X_31,identity),identity),
inference(subst,[],[refute_0_1315:[bind(X_119,$fot(identity)),bind(X_120,$fot(X_31))]]) ).
cnf(refute_0_2554,plain,
( multiply(greatest_lower_bound(X_31,identity),identity) != greatest_lower_bound(X_31,identity)
| greatest_lower_bound(identity,multiply(X_31,identity)) != multiply(greatest_lower_bound(X_31,identity),identity)
| greatest_lower_bound(identity,multiply(X_31,identity)) = greatest_lower_bound(X_31,identity) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(greatest_lower_bound(identity,multiply(X_31,identity)))),bind(Y0,$fot(multiply(greatest_lower_bound(X_31,identity),identity))),bind(Z0,$fot(greatest_lower_bound(X_31,identity)))]]) ).
cnf(refute_0_2555,plain,
( multiply(greatest_lower_bound(X_31,identity),identity) != greatest_lower_bound(X_31,identity)
| greatest_lower_bound(identity,multiply(X_31,identity)) = greatest_lower_bound(X_31,identity) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_31,identity)),multiply(greatest_lower_bound(X_31,identity),identity)) )],[refute_0_2553,refute_0_2554]) ).
cnf(refute_0_2556,plain,
greatest_lower_bound(identity,multiply(X_31,identity)) = greatest_lower_bound(X_31,identity),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_31,identity),identity),greatest_lower_bound(X_31,identity)) )],[refute_0_2552,refute_0_2555]) ).
cnf(refute_0_2557,plain,
multiply(X_104,greatest_lower_bound(X_105,inverse(X_104))) = greatest_lower_bound(multiply(X_104,X_105),multiply(X_104,inverse(X_104))),
inference(subst,[],[monotony_glb1:[bind(X,$fot(X_104)),bind(Y,$fot(X_105)),bind(Z,$fot(inverse(X_104)))]]) ).
cnf(refute_0_2558,plain,
( multiply(X_104,greatest_lower_bound(X_105,inverse(X_104))) != greatest_lower_bound(multiply(X_104,X_105),multiply(X_104,inverse(X_104)))
| multiply(X_104,inverse(X_104)) != identity
| multiply(X_104,greatest_lower_bound(X_105,inverse(X_104))) = greatest_lower_bound(multiply(X_104,X_105),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_104,greatest_lower_bound(X_105,inverse(X_104))),greatest_lower_bound(multiply(X_104,X_105),multiply(X_104,inverse(X_104)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_2559,plain,
( multiply(X_104,greatest_lower_bound(X_105,inverse(X_104))) != greatest_lower_bound(multiply(X_104,X_105),multiply(X_104,inverse(X_104)))
| multiply(X_104,greatest_lower_bound(X_105,inverse(X_104))) = greatest_lower_bound(multiply(X_104,X_105),identity) ),
inference(resolve,[$cnf( $equal(multiply(X_104,inverse(X_104)),identity) )],[refute_0_1707,refute_0_2558]) ).
cnf(refute_0_2560,plain,
multiply(X_104,greatest_lower_bound(X_105,inverse(X_104))) = greatest_lower_bound(multiply(X_104,X_105),identity),
inference(resolve,[$cnf( $equal(multiply(X_104,greatest_lower_bound(X_105,inverse(X_104))),greatest_lower_bound(multiply(X_104,X_105),multiply(X_104,inverse(X_104)))) )],[refute_0_2557,refute_0_2559]) ).
cnf(refute_0_2561,plain,
greatest_lower_bound(multiply(X_104,X_105),identity) = greatest_lower_bound(identity,multiply(X_104,X_105)),
inference(subst,[],[refute_0_42:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_104,X_105)))]]) ).
cnf(refute_0_2562,plain,
( multiply(X_104,greatest_lower_bound(X_105,inverse(X_104))) != greatest_lower_bound(multiply(X_104,X_105),identity)
| greatest_lower_bound(multiply(X_104,X_105),identity) != greatest_lower_bound(identity,multiply(X_104,X_105))
| multiply(X_104,greatest_lower_bound(X_105,inverse(X_104))) = greatest_lower_bound(identity,multiply(X_104,X_105)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_104,greatest_lower_bound(X_105,inverse(X_104))),greatest_lower_bound(identity,multiply(X_104,X_105))) ),[0],$fot(greatest_lower_bound(multiply(X_104,X_105),identity))]]) ).
cnf(refute_0_2563,plain,
( multiply(X_104,greatest_lower_bound(X_105,inverse(X_104))) != greatest_lower_bound(multiply(X_104,X_105),identity)
| multiply(X_104,greatest_lower_bound(X_105,inverse(X_104))) = greatest_lower_bound(identity,multiply(X_104,X_105)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_104,X_105),identity),greatest_lower_bound(identity,multiply(X_104,X_105))) )],[refute_0_2561,refute_0_2562]) ).
cnf(refute_0_2564,plain,
multiply(X_104,greatest_lower_bound(X_105,inverse(X_104))) = greatest_lower_bound(identity,multiply(X_104,X_105)),
inference(resolve,[$cnf( $equal(multiply(X_104,greatest_lower_bound(X_105,inverse(X_104))),greatest_lower_bound(multiply(X_104,X_105),identity)) )],[refute_0_2560,refute_0_2563]) ).
cnf(refute_0_2565,plain,
multiply(X_31,greatest_lower_bound(identity,inverse(X_31))) = greatest_lower_bound(identity,multiply(X_31,identity)),
inference(subst,[],[refute_0_2564:[bind(X_104,$fot(X_31)),bind(X_105,$fot(identity))]]) ).
cnf(refute_0_2566,plain,
( multiply(X_31,greatest_lower_bound(identity,inverse(X_31))) != greatest_lower_bound(identity,multiply(X_31,identity))
| greatest_lower_bound(identity,multiply(X_31,identity)) != greatest_lower_bound(X_31,identity)
| multiply(X_31,greatest_lower_bound(identity,inverse(X_31))) = greatest_lower_bound(X_31,identity) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(X_31,greatest_lower_bound(identity,inverse(X_31))))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(X_31,identity)))),bind(Z0,$fot(greatest_lower_bound(X_31,identity)))]]) ).
cnf(refute_0_2567,plain,
( greatest_lower_bound(identity,multiply(X_31,identity)) != greatest_lower_bound(X_31,identity)
| multiply(X_31,greatest_lower_bound(identity,inverse(X_31))) = greatest_lower_bound(X_31,identity) ),
inference(resolve,[$cnf( $equal(multiply(X_31,greatest_lower_bound(identity,inverse(X_31))),greatest_lower_bound(identity,multiply(X_31,identity))) )],[refute_0_2565,refute_0_2566]) ).
cnf(refute_0_2568,plain,
multiply(X_31,greatest_lower_bound(identity,inverse(X_31))) = greatest_lower_bound(X_31,identity),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_31,identity)),greatest_lower_bound(X_31,identity)) )],[refute_0_2556,refute_0_2567]) ).
cnf(refute_0_2569,plain,
multiply(X_30,multiply(X_31,greatest_lower_bound(identity,inverse(X_31)))) = multiply(X_30,multiply(X_31,greatest_lower_bound(identity,inverse(X_31)))),
introduced(tautology,[refl,[$fot(multiply(X_30,multiply(X_31,greatest_lower_bound(identity,inverse(X_31)))))]]) ).
cnf(refute_0_2570,plain,
( multiply(X_30,multiply(X_31,greatest_lower_bound(identity,inverse(X_31)))) != multiply(X_30,multiply(X_31,greatest_lower_bound(identity,inverse(X_31))))
| multiply(X_31,greatest_lower_bound(identity,inverse(X_31))) != greatest_lower_bound(X_31,identity)
| multiply(X_30,multiply(X_31,greatest_lower_bound(identity,inverse(X_31)))) = multiply(X_30,greatest_lower_bound(X_31,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_30,multiply(X_31,greatest_lower_bound(identity,inverse(X_31)))),multiply(X_30,multiply(X_31,greatest_lower_bound(identity,inverse(X_31))))) ),[1,1],$fot(greatest_lower_bound(X_31,identity))]]) ).
cnf(refute_0_2571,plain,
( multiply(X_31,greatest_lower_bound(identity,inverse(X_31))) != greatest_lower_bound(X_31,identity)
| multiply(X_30,multiply(X_31,greatest_lower_bound(identity,inverse(X_31)))) = multiply(X_30,greatest_lower_bound(X_31,identity)) ),
inference(resolve,[$cnf( $equal(multiply(X_30,multiply(X_31,greatest_lower_bound(identity,inverse(X_31)))),multiply(X_30,multiply(X_31,greatest_lower_bound(identity,inverse(X_31))))) )],[refute_0_2569,refute_0_2570]) ).
cnf(refute_0_2572,plain,
multiply(X_30,multiply(X_31,greatest_lower_bound(identity,inverse(X_31)))) = multiply(X_30,greatest_lower_bound(X_31,identity)),
inference(resolve,[$cnf( $equal(multiply(X_31,greatest_lower_bound(identity,inverse(X_31))),greatest_lower_bound(X_31,identity)) )],[refute_0_2568,refute_0_2571]) ).
cnf(refute_0_2573,plain,
multiply(multiply(X_30,X_31),greatest_lower_bound(identity,inverse(X_31))) = multiply(X_30,multiply(X_31,greatest_lower_bound(identity,inverse(X_31)))),
inference(subst,[],[associativity:[bind(X,$fot(X_30)),bind(Y,$fot(X_31)),bind(Z,$fot(greatest_lower_bound(identity,inverse(X_31))))]]) ).
cnf(refute_0_2574,plain,
( multiply(X_30,multiply(X_31,greatest_lower_bound(identity,inverse(X_31)))) != multiply(X_30,greatest_lower_bound(X_31,identity))
| multiply(multiply(X_30,X_31),greatest_lower_bound(identity,inverse(X_31))) != multiply(X_30,multiply(X_31,greatest_lower_bound(identity,inverse(X_31))))
| multiply(multiply(X_30,X_31),greatest_lower_bound(identity,inverse(X_31))) = multiply(X_30,greatest_lower_bound(X_31,identity)) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(multiply(X_30,X_31),greatest_lower_bound(identity,inverse(X_31))))),bind(Y0,$fot(multiply(X_30,multiply(X_31,greatest_lower_bound(identity,inverse(X_31)))))),bind(Z0,$fot(multiply(X_30,greatest_lower_bound(X_31,identity))))]]) ).
cnf(refute_0_2575,plain,
( multiply(X_30,multiply(X_31,greatest_lower_bound(identity,inverse(X_31)))) != multiply(X_30,greatest_lower_bound(X_31,identity))
| multiply(multiply(X_30,X_31),greatest_lower_bound(identity,inverse(X_31))) = multiply(X_30,greatest_lower_bound(X_31,identity)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_30,X_31),greatest_lower_bound(identity,inverse(X_31))),multiply(X_30,multiply(X_31,greatest_lower_bound(identity,inverse(X_31))))) )],[refute_0_2573,refute_0_2574]) ).
cnf(refute_0_2576,plain,
multiply(multiply(X_30,X_31),greatest_lower_bound(identity,inverse(X_31))) = multiply(X_30,greatest_lower_bound(X_31,identity)),
inference(resolve,[$cnf( $equal(multiply(X_30,multiply(X_31,greatest_lower_bound(identity,inverse(X_31)))),multiply(X_30,greatest_lower_bound(X_31,identity))) )],[refute_0_2572,refute_0_2575]) ).
cnf(refute_0_2577,plain,
inverse(inverse(multiply(X_30,X_31))) = multiply(X_30,X_31),
inference(subst,[],[refute_0_452:[bind(X_35,$fot(multiply(X_30,X_31)))]]) ).
cnf(refute_0_2578,plain,
multiply(inverse(inverse(multiply(X_30,X_31))),greatest_lower_bound(identity,inverse(X_31))) = multiply(inverse(inverse(multiply(X_30,X_31))),greatest_lower_bound(identity,inverse(X_31))),
introduced(tautology,[refl,[$fot(multiply(inverse(inverse(multiply(X_30,X_31))),greatest_lower_bound(identity,inverse(X_31))))]]) ).
cnf(refute_0_2579,plain,
( multiply(inverse(inverse(multiply(X_30,X_31))),greatest_lower_bound(identity,inverse(X_31))) != multiply(inverse(inverse(multiply(X_30,X_31))),greatest_lower_bound(identity,inverse(X_31)))
| inverse(inverse(multiply(X_30,X_31))) != multiply(X_30,X_31)
| multiply(inverse(inverse(multiply(X_30,X_31))),greatest_lower_bound(identity,inverse(X_31))) = multiply(multiply(X_30,X_31),greatest_lower_bound(identity,inverse(X_31))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(multiply(X_30,X_31))),greatest_lower_bound(identity,inverse(X_31))),multiply(inverse(inverse(multiply(X_30,X_31))),greatest_lower_bound(identity,inverse(X_31)))) ),[1,0],$fot(multiply(X_30,X_31))]]) ).
cnf(refute_0_2580,plain,
( inverse(inverse(multiply(X_30,X_31))) != multiply(X_30,X_31)
| multiply(inverse(inverse(multiply(X_30,X_31))),greatest_lower_bound(identity,inverse(X_31))) = multiply(multiply(X_30,X_31),greatest_lower_bound(identity,inverse(X_31))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(multiply(X_30,X_31))),greatest_lower_bound(identity,inverse(X_31))),multiply(inverse(inverse(multiply(X_30,X_31))),greatest_lower_bound(identity,inverse(X_31)))) )],[refute_0_2578,refute_0_2579]) ).
cnf(refute_0_2581,plain,
multiply(inverse(inverse(multiply(X_30,X_31))),greatest_lower_bound(identity,inverse(X_31))) = multiply(multiply(X_30,X_31),greatest_lower_bound(identity,inverse(X_31))),
inference(resolve,[$cnf( $equal(inverse(inverse(multiply(X_30,X_31))),multiply(X_30,X_31)) )],[refute_0_2577,refute_0_2580]) ).
cnf(refute_0_2582,plain,
( multiply(multiply(X_30,X_31),greatest_lower_bound(identity,inverse(X_31))) != multiply(X_30,greatest_lower_bound(X_31,identity))
| multiply(inverse(inverse(multiply(X_30,X_31))),greatest_lower_bound(identity,inverse(X_31))) != multiply(multiply(X_30,X_31),greatest_lower_bound(identity,inverse(X_31)))
| multiply(inverse(inverse(multiply(X_30,X_31))),greatest_lower_bound(identity,inverse(X_31))) = multiply(X_30,greatest_lower_bound(X_31,identity)) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(inverse(inverse(multiply(X_30,X_31))),greatest_lower_bound(identity,inverse(X_31))))),bind(Y0,$fot(multiply(multiply(X_30,X_31),greatest_lower_bound(identity,inverse(X_31))))),bind(Z0,$fot(multiply(X_30,greatest_lower_bound(X_31,identity))))]]) ).
cnf(refute_0_2583,plain,
( multiply(multiply(X_30,X_31),greatest_lower_bound(identity,inverse(X_31))) != multiply(X_30,greatest_lower_bound(X_31,identity))
| multiply(inverse(inverse(multiply(X_30,X_31))),greatest_lower_bound(identity,inverse(X_31))) = multiply(X_30,greatest_lower_bound(X_31,identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(multiply(X_30,X_31))),greatest_lower_bound(identity,inverse(X_31))),multiply(multiply(X_30,X_31),greatest_lower_bound(identity,inverse(X_31)))) )],[refute_0_2581,refute_0_2582]) ).
cnf(refute_0_2584,plain,
multiply(inverse(inverse(multiply(X_30,X_31))),greatest_lower_bound(identity,inverse(X_31))) = multiply(X_30,greatest_lower_bound(X_31,identity)),
inference(resolve,[$cnf( $equal(multiply(multiply(X_30,X_31),greatest_lower_bound(identity,inverse(X_31))),multiply(X_30,greatest_lower_bound(X_31,identity))) )],[refute_0_2576,refute_0_2583]) ).
cnf(refute_0_2585,plain,
multiply(inverse(multiply(inverse(greatest_lower_bound(X_150,identity)),X_442)),greatest_lower_bound(inverse(greatest_lower_bound(X_150,identity)),identity)) = multiply(inverse(X_442),greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_150,identity))))),
inference(subst,[],[refute_0_2547:[bind(X_105,$fot(inverse(greatest_lower_bound(X_150,identity)))),bind(X_146,$fot(X_442))]]) ).
cnf(refute_0_2586,plain,
multiply(least_upper_bound(identity,X_75),greatest_lower_bound(X_105,inverse(X_75))) = greatest_lower_bound(multiply(least_upper_bound(identity,X_75),X_105),multiply(least_upper_bound(identity,X_75),inverse(X_75))),
inference(subst,[],[monotony_glb1:[bind(X,$fot(least_upper_bound(identity,X_75))),bind(Y,$fot(X_105)),bind(Z,$fot(inverse(X_75)))]]) ).
cnf(refute_0_2587,plain,
( multiply(least_upper_bound(identity,X_75),greatest_lower_bound(X_105,inverse(X_75))) != greatest_lower_bound(multiply(least_upper_bound(identity,X_75),X_105),multiply(least_upper_bound(identity,X_75),inverse(X_75)))
| multiply(least_upper_bound(identity,X_75),inverse(X_75)) != least_upper_bound(identity,inverse(X_75))
| multiply(least_upper_bound(identity,X_75),greatest_lower_bound(X_105,inverse(X_75))) = greatest_lower_bound(multiply(least_upper_bound(identity,X_75),X_105),least_upper_bound(identity,inverse(X_75))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,X_75),greatest_lower_bound(X_105,inverse(X_75))),greatest_lower_bound(multiply(least_upper_bound(identity,X_75),X_105),multiply(least_upper_bound(identity,X_75),inverse(X_75)))) ),[1,1],$fot(least_upper_bound(identity,inverse(X_75)))]]) ).
cnf(refute_0_2588,plain,
( multiply(least_upper_bound(identity,X_75),greatest_lower_bound(X_105,inverse(X_75))) != greatest_lower_bound(multiply(least_upper_bound(identity,X_75),X_105),multiply(least_upper_bound(identity,X_75),inverse(X_75)))
| multiply(least_upper_bound(identity,X_75),greatest_lower_bound(X_105,inverse(X_75))) = greatest_lower_bound(multiply(least_upper_bound(identity,X_75),X_105),least_upper_bound(identity,inverse(X_75))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_75),inverse(X_75)),least_upper_bound(identity,inverse(X_75))) )],[refute_0_785,refute_0_2587]) ).
cnf(refute_0_2589,plain,
multiply(least_upper_bound(identity,X_75),greatest_lower_bound(X_105,inverse(X_75))) = greatest_lower_bound(multiply(least_upper_bound(identity,X_75),X_105),least_upper_bound(identity,inverse(X_75))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_75),greatest_lower_bound(X_105,inverse(X_75))),greatest_lower_bound(multiply(least_upper_bound(identity,X_75),X_105),multiply(least_upper_bound(identity,X_75),inverse(X_75)))) )],[refute_0_2586,refute_0_2588]) ).
cnf(refute_0_2590,plain,
greatest_lower_bound(multiply(least_upper_bound(identity,X_75),X_105),least_upper_bound(identity,inverse(X_75))) = greatest_lower_bound(least_upper_bound(identity,inverse(X_75)),multiply(least_upper_bound(identity,X_75),X_105)),
inference(subst,[],[refute_0_42:[bind(X,$fot(least_upper_bound(identity,inverse(X_75)))),bind(Y,$fot(multiply(least_upper_bound(identity,X_75),X_105)))]]) ).
cnf(refute_0_2591,plain,
( multiply(least_upper_bound(identity,X_75),greatest_lower_bound(X_105,inverse(X_75))) != greatest_lower_bound(multiply(least_upper_bound(identity,X_75),X_105),least_upper_bound(identity,inverse(X_75)))
| greatest_lower_bound(multiply(least_upper_bound(identity,X_75),X_105),least_upper_bound(identity,inverse(X_75))) != greatest_lower_bound(least_upper_bound(identity,inverse(X_75)),multiply(least_upper_bound(identity,X_75),X_105))
| multiply(least_upper_bound(identity,X_75),greatest_lower_bound(X_105,inverse(X_75))) = greatest_lower_bound(least_upper_bound(identity,inverse(X_75)),multiply(least_upper_bound(identity,X_75),X_105)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(identity,X_75),greatest_lower_bound(X_105,inverse(X_75))),greatest_lower_bound(least_upper_bound(identity,inverse(X_75)),multiply(least_upper_bound(identity,X_75),X_105))) ),[0],$fot(greatest_lower_bound(multiply(least_upper_bound(identity,X_75),X_105),least_upper_bound(identity,inverse(X_75))))]]) ).
cnf(refute_0_2592,plain,
( multiply(least_upper_bound(identity,X_75),greatest_lower_bound(X_105,inverse(X_75))) != greatest_lower_bound(multiply(least_upper_bound(identity,X_75),X_105),least_upper_bound(identity,inverse(X_75)))
| multiply(least_upper_bound(identity,X_75),greatest_lower_bound(X_105,inverse(X_75))) = greatest_lower_bound(least_upper_bound(identity,inverse(X_75)),multiply(least_upper_bound(identity,X_75),X_105)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(identity,X_75),X_105),least_upper_bound(identity,inverse(X_75))),greatest_lower_bound(least_upper_bound(identity,inverse(X_75)),multiply(least_upper_bound(identity,X_75),X_105))) )],[refute_0_2590,refute_0_2591]) ).
cnf(refute_0_2593,plain,
multiply(least_upper_bound(identity,X_75),greatest_lower_bound(X_105,inverse(X_75))) = greatest_lower_bound(least_upper_bound(identity,inverse(X_75)),multiply(least_upper_bound(identity,X_75),X_105)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_75),greatest_lower_bound(X_105,inverse(X_75))),greatest_lower_bound(multiply(least_upper_bound(identity,X_75),X_105),least_upper_bound(identity,inverse(X_75)))) )],[refute_0_2589,refute_0_2592]) ).
cnf(refute_0_2594,plain,
multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150)))) = greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_150))),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245)),
inference(subst,[],[refute_0_2593:[bind(X_105,$fot(X_245)),bind(X_75,$fot(greatest_lower_bound(identity,X_150)))]]) ).
cnf(refute_0_2595,plain,
( multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150)))) != greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_150))),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245))
| inverse(greatest_lower_bound(identity,X_150)) != inverse(greatest_lower_bound(X_150,identity))
| multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150)))) = greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(X_150,identity))),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150)))),greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_150))),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245))) ),[1,0,1],$fot(inverse(greatest_lower_bound(X_150,identity)))]]) ).
cnf(refute_0_2596,plain,
( multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150)))) != greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_150))),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245))
| multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150)))) = greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(X_150,identity))),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245)) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,X_150)),inverse(greatest_lower_bound(X_150,identity))) )],[refute_0_497,refute_0_2595]) ).
cnf(refute_0_2597,plain,
multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150)))) = greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(X_150,identity))),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150)))),greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_150))),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245))) )],[refute_0_2594,refute_0_2596]) ).
cnf(refute_0_2598,plain,
multiply(identity,greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150)))) = greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150))),
inference(subst,[],[left_identity:[bind(X,$fot(greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150)))))]]) ).
cnf(refute_0_2599,plain,
multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150)))) = multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150)))),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150)))))]]) ).
cnf(refute_0_2600,plain,
( multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150)))) != multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150))))
| least_upper_bound(identity,greatest_lower_bound(identity,X_150)) != identity
| multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150)))) = multiply(identity,greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150)))),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150))))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_2601,plain,
( least_upper_bound(identity,greatest_lower_bound(identity,X_150)) != identity
| multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150)))) = multiply(identity,greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150)))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150)))),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150))))) )],[refute_0_2599,refute_0_2600]) ).
cnf(refute_0_2602,plain,
multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150)))) = multiply(identity,greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150)))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),identity) )],[refute_0_502,refute_0_2601]) ).
cnf(refute_0_2603,plain,
( multiply(identity,greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150)))) != greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150)))
| multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150)))) != multiply(identity,greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150))))
| multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150)))) = greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150)))))),bind(Y0,$fot(multiply(identity,greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150)))))),bind(Z0,$fot(greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150)))))]]) ).
cnf(refute_0_2604,plain,
( multiply(identity,greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150)))) != greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150)))
| multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150)))) = greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150)))),multiply(identity,greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150))))) )],[refute_0_2602,refute_0_2603]) ).
cnf(refute_0_2605,plain,
multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150)))) = greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150))),
inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150)))),greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150)))) )],[refute_0_2598,refute_0_2604]) ).
cnf(refute_0_2606,plain,
( multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150)))) != greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150)))
| multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150)))) != greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(X_150,identity))),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245))
| greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150))) = greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(X_150,identity))),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150)))),greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(X_150,identity))),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245))) ),[0],$fot(greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150))))]]) ).
cnf(refute_0_2607,plain,
( multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150)))) != greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(X_150,identity))),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245))
| greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150))) = greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(X_150,identity))),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150)))),greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150)))) )],[refute_0_2605,refute_0_2606]) ).
cnf(refute_0_2608,plain,
multiply(identity,X_245) = X_245,
inference(subst,[],[left_identity:[bind(X,$fot(X_245))]]) ).
cnf(refute_0_2609,plain,
multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245) = multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245))]]) ).
cnf(refute_0_2610,plain,
( multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245) != multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245)
| least_upper_bound(identity,greatest_lower_bound(identity,X_150)) != identity
| multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245) = multiply(identity,X_245) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245)) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_2611,plain,
( least_upper_bound(identity,greatest_lower_bound(identity,X_150)) != identity
| multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245) = multiply(identity,X_245) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245)) )],[refute_0_2609,refute_0_2610]) ).
cnf(refute_0_2612,plain,
multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245) = multiply(identity,X_245),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),identity) )],[refute_0_502,refute_0_2611]) ).
cnf(refute_0_2613,plain,
( multiply(identity,X_245) != X_245
| multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245) != multiply(identity,X_245)
| multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245) = X_245 ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245))),bind(Y0,$fot(multiply(identity,X_245))),bind(Z0,$fot(X_245))]]) ).
cnf(refute_0_2614,plain,
( multiply(identity,X_245) != X_245
| multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245) = X_245 ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245),multiply(identity,X_245)) )],[refute_0_2612,refute_0_2613]) ).
cnf(refute_0_2615,plain,
multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245) = X_245,
inference(resolve,[$cnf( $equal(multiply(identity,X_245),X_245) )],[refute_0_2608,refute_0_2614]) ).
cnf(refute_0_2616,plain,
greatest_lower_bound(inverse(greatest_lower_bound(X_150,identity)),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245)) = greatest_lower_bound(inverse(greatest_lower_bound(X_150,identity)),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(inverse(greatest_lower_bound(X_150,identity)),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245)))]]) ).
cnf(refute_0_2617,plain,
( multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245) != X_245
| greatest_lower_bound(inverse(greatest_lower_bound(X_150,identity)),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245)) != greatest_lower_bound(inverse(greatest_lower_bound(X_150,identity)),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245))
| greatest_lower_bound(inverse(greatest_lower_bound(X_150,identity)),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245)) = greatest_lower_bound(inverse(greatest_lower_bound(X_150,identity)),X_245) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(inverse(greatest_lower_bound(X_150,identity)),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245)),greatest_lower_bound(inverse(greatest_lower_bound(X_150,identity)),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245))) ),[1,1],$fot(X_245)]]) ).
cnf(refute_0_2618,plain,
( multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245) != X_245
| greatest_lower_bound(inverse(greatest_lower_bound(X_150,identity)),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245)) = greatest_lower_bound(inverse(greatest_lower_bound(X_150,identity)),X_245) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(greatest_lower_bound(X_150,identity)),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245)),greatest_lower_bound(inverse(greatest_lower_bound(X_150,identity)),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245))) )],[refute_0_2616,refute_0_2617]) ).
cnf(refute_0_2619,plain,
greatest_lower_bound(inverse(greatest_lower_bound(X_150,identity)),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245)) = greatest_lower_bound(inverse(greatest_lower_bound(X_150,identity)),X_245),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245),X_245) )],[refute_0_2615,refute_0_2618]) ).
cnf(refute_0_2620,plain,
least_upper_bound(identity,inverse(greatest_lower_bound(X_150,identity))) = inverse(greatest_lower_bound(X_150,identity)),
inference(subst,[],[refute_0_222:[bind(X_11,$fot(X_150))]]) ).
cnf(refute_0_2621,plain,
greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(X_150,identity))),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245)) = greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(X_150,identity))),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(X_150,identity))),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245)))]]) ).
cnf(refute_0_2622,plain,
( greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(X_150,identity))),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245)) != greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(X_150,identity))),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245))
| least_upper_bound(identity,inverse(greatest_lower_bound(X_150,identity))) != inverse(greatest_lower_bound(X_150,identity))
| greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(X_150,identity))),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245)) = greatest_lower_bound(inverse(greatest_lower_bound(X_150,identity)),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(X_150,identity))),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245)),greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(X_150,identity))),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245))) ),[1,0],$fot(inverse(greatest_lower_bound(X_150,identity)))]]) ).
cnf(refute_0_2623,plain,
( least_upper_bound(identity,inverse(greatest_lower_bound(X_150,identity))) != inverse(greatest_lower_bound(X_150,identity))
| greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(X_150,identity))),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245)) = greatest_lower_bound(inverse(greatest_lower_bound(X_150,identity)),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(X_150,identity))),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245)),greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(X_150,identity))),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245))) )],[refute_0_2621,refute_0_2622]) ).
cnf(refute_0_2624,plain,
greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(X_150,identity))),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245)) = greatest_lower_bound(inverse(greatest_lower_bound(X_150,identity)),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(greatest_lower_bound(X_150,identity))),inverse(greatest_lower_bound(X_150,identity))) )],[refute_0_2620,refute_0_2623]) ).
cnf(refute_0_2625,plain,
( greatest_lower_bound(inverse(greatest_lower_bound(X_150,identity)),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245)) != greatest_lower_bound(inverse(greatest_lower_bound(X_150,identity)),X_245)
| greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(X_150,identity))),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245)) != greatest_lower_bound(inverse(greatest_lower_bound(X_150,identity)),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245))
| greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(X_150,identity))),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245)) = greatest_lower_bound(inverse(greatest_lower_bound(X_150,identity)),X_245) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(X_150,identity))),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245)))),bind(Y0,$fot(greatest_lower_bound(inverse(greatest_lower_bound(X_150,identity)),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245)))),bind(Z0,$fot(greatest_lower_bound(inverse(greatest_lower_bound(X_150,identity)),X_245)))]]) ).
cnf(refute_0_2626,plain,
( greatest_lower_bound(inverse(greatest_lower_bound(X_150,identity)),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245)) != greatest_lower_bound(inverse(greatest_lower_bound(X_150,identity)),X_245)
| greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(X_150,identity))),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245)) = greatest_lower_bound(inverse(greatest_lower_bound(X_150,identity)),X_245) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(X_150,identity))),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245)),greatest_lower_bound(inverse(greatest_lower_bound(X_150,identity)),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245))) )],[refute_0_2624,refute_0_2625]) ).
cnf(refute_0_2627,plain,
greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(X_150,identity))),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245)) = greatest_lower_bound(inverse(greatest_lower_bound(X_150,identity)),X_245),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(greatest_lower_bound(X_150,identity)),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245)),greatest_lower_bound(inverse(greatest_lower_bound(X_150,identity)),X_245)) )],[refute_0_2619,refute_0_2626]) ).
cnf(refute_0_2628,plain,
( greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150))) != greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(X_150,identity))),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245))
| greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(X_150,identity))),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245)) != greatest_lower_bound(inverse(greatest_lower_bound(X_150,identity)),X_245)
| greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150))) = greatest_lower_bound(inverse(greatest_lower_bound(X_150,identity)),X_245) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150))),greatest_lower_bound(inverse(greatest_lower_bound(X_150,identity)),X_245)) ),[0],$fot(greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(X_150,identity))),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245)))]]) ).
cnf(refute_0_2629,plain,
( greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150))) != greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(X_150,identity))),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245))
| greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150))) = greatest_lower_bound(inverse(greatest_lower_bound(X_150,identity)),X_245) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(X_150,identity))),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245)),greatest_lower_bound(inverse(greatest_lower_bound(X_150,identity)),X_245)) )],[refute_0_2627,refute_0_2628]) ).
cnf(refute_0_2630,plain,
( multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150)))) != greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(X_150,identity))),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245))
| greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150))) = greatest_lower_bound(inverse(greatest_lower_bound(X_150,identity)),X_245) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150))),greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(X_150,identity))),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245))) )],[refute_0_2607,refute_0_2629]) ).
cnf(refute_0_2631,plain,
greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150))) = greatest_lower_bound(inverse(greatest_lower_bound(X_150,identity)),X_245),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),greatest_lower_bound(X_245,inverse(greatest_lower_bound(identity,X_150)))),greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(X_150,identity))),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X_150)),X_245))) )],[refute_0_2597,refute_0_2630]) ).
cnf(refute_0_2632,plain,
greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150))) = greatest_lower_bound(inverse(greatest_lower_bound(X_150,identity)),identity),
inference(subst,[],[refute_0_2631:[bind(X_245,$fot(identity))]]) ).
cnf(refute_0_2633,plain,
( greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150))) != greatest_lower_bound(inverse(greatest_lower_bound(X_150,identity)),identity)
| greatest_lower_bound(inverse(greatest_lower_bound(X_150,identity)),identity) = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150))) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150))))),bind(Y0,$fot(greatest_lower_bound(inverse(greatest_lower_bound(X_150,identity)),identity)))]]) ).
cnf(refute_0_2634,plain,
greatest_lower_bound(inverse(greatest_lower_bound(X_150,identity)),identity) = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150))),greatest_lower_bound(inverse(greatest_lower_bound(X_150,identity)),identity)) )],[refute_0_2632,refute_0_2633]) ).
cnf(refute_0_2635,plain,
( multiply(inverse(multiply(inverse(greatest_lower_bound(X_150,identity)),X_442)),greatest_lower_bound(inverse(greatest_lower_bound(X_150,identity)),identity)) != multiply(inverse(X_442),greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_150,identity)))))
| greatest_lower_bound(inverse(greatest_lower_bound(X_150,identity)),identity) != greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150)))
| multiply(inverse(multiply(inverse(greatest_lower_bound(X_150,identity)),X_442)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150)))) = multiply(inverse(X_442),greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_150,identity))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(inverse(greatest_lower_bound(X_150,identity)),X_442)),greatest_lower_bound(inverse(greatest_lower_bound(X_150,identity)),identity)),multiply(inverse(X_442),greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_150,identity)))))) ),[0,1],$fot(greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150))))]]) ).
cnf(refute_0_2636,plain,
( multiply(inverse(multiply(inverse(greatest_lower_bound(X_150,identity)),X_442)),greatest_lower_bound(inverse(greatest_lower_bound(X_150,identity)),identity)) != multiply(inverse(X_442),greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_150,identity)))))
| multiply(inverse(multiply(inverse(greatest_lower_bound(X_150,identity)),X_442)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150)))) = multiply(inverse(X_442),greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_150,identity))))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(greatest_lower_bound(X_150,identity)),identity),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150)))) )],[refute_0_2634,refute_0_2635]) ).
cnf(refute_0_2637,plain,
multiply(inverse(multiply(inverse(greatest_lower_bound(X_150,identity)),X_442)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150)))) = multiply(inverse(X_442),greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_150,identity))))),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(greatest_lower_bound(X_150,identity)),X_442)),greatest_lower_bound(inverse(greatest_lower_bound(X_150,identity)),identity)),multiply(inverse(X_442),greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_150,identity)))))) )],[refute_0_2585,refute_0_2636]) ).
cnf(refute_0_2638,plain,
multiply(multiply(inverse(X_442),greatest_lower_bound(X_150,identity)),identity) = multiply(inverse(X_442),greatest_lower_bound(X_150,identity)),
inference(subst,[],[refute_0_88:[bind(X_33,$fot(multiply(inverse(X_442),greatest_lower_bound(X_150,identity))))]]) ).
cnf(refute_0_2639,plain,
greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150))) = identity,
inference(subst,[],[refute_0_655:[bind(X_16,$fot(X_150))]]) ).
cnf(refute_0_2640,plain,
multiply(multiply(inverse(X_442),greatest_lower_bound(X_150,identity)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150)))) = multiply(multiply(inverse(X_442),greatest_lower_bound(X_150,identity)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150)))),
introduced(tautology,[refl,[$fot(multiply(multiply(inverse(X_442),greatest_lower_bound(X_150,identity)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150)))))]]) ).
cnf(refute_0_2641,plain,
( multiply(multiply(inverse(X_442),greatest_lower_bound(X_150,identity)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150)))) != multiply(multiply(inverse(X_442),greatest_lower_bound(X_150,identity)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150))))
| greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150))) != identity
| multiply(multiply(inverse(X_442),greatest_lower_bound(X_150,identity)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150)))) = multiply(multiply(inverse(X_442),greatest_lower_bound(X_150,identity)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_442),greatest_lower_bound(X_150,identity)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150)))),multiply(multiply(inverse(X_442),greatest_lower_bound(X_150,identity)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_2642,plain,
( greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150))) != identity
| multiply(multiply(inverse(X_442),greatest_lower_bound(X_150,identity)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150)))) = multiply(multiply(inverse(X_442),greatest_lower_bound(X_150,identity)),identity) ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_442),greatest_lower_bound(X_150,identity)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150)))),multiply(multiply(inverse(X_442),greatest_lower_bound(X_150,identity)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150))))) )],[refute_0_2640,refute_0_2641]) ).
cnf(refute_0_2643,plain,
multiply(multiply(inverse(X_442),greatest_lower_bound(X_150,identity)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150)))) = multiply(multiply(inverse(X_442),greatest_lower_bound(X_150,identity)),identity),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150))),identity) )],[refute_0_2639,refute_0_2642]) ).
cnf(refute_0_2644,plain,
inverse(multiply(inverse(greatest_lower_bound(X_150,identity)),X_442)) = multiply(inverse(X_442),greatest_lower_bound(X_150,identity)),
inference(subst,[],[refute_0_110:[bind(X_145,$fot(greatest_lower_bound(X_150,identity))),bind(X_31,$fot(X_442))]]) ).
cnf(refute_0_2645,plain,
multiply(inverse(multiply(inverse(greatest_lower_bound(X_150,identity)),X_442)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150)))) = multiply(inverse(multiply(inverse(greatest_lower_bound(X_150,identity)),X_442)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150)))),
introduced(tautology,[refl,[$fot(multiply(inverse(multiply(inverse(greatest_lower_bound(X_150,identity)),X_442)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150)))))]]) ).
cnf(refute_0_2646,plain,
( multiply(inverse(multiply(inverse(greatest_lower_bound(X_150,identity)),X_442)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150)))) != multiply(inverse(multiply(inverse(greatest_lower_bound(X_150,identity)),X_442)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150))))
| inverse(multiply(inverse(greatest_lower_bound(X_150,identity)),X_442)) != multiply(inverse(X_442),greatest_lower_bound(X_150,identity))
| multiply(inverse(multiply(inverse(greatest_lower_bound(X_150,identity)),X_442)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150)))) = multiply(multiply(inverse(X_442),greatest_lower_bound(X_150,identity)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(inverse(greatest_lower_bound(X_150,identity)),X_442)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150)))),multiply(inverse(multiply(inverse(greatest_lower_bound(X_150,identity)),X_442)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150))))) ),[1,0],$fot(multiply(inverse(X_442),greatest_lower_bound(X_150,identity)))]]) ).
cnf(refute_0_2647,plain,
( inverse(multiply(inverse(greatest_lower_bound(X_150,identity)),X_442)) != multiply(inverse(X_442),greatest_lower_bound(X_150,identity))
| multiply(inverse(multiply(inverse(greatest_lower_bound(X_150,identity)),X_442)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150)))) = multiply(multiply(inverse(X_442),greatest_lower_bound(X_150,identity)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(greatest_lower_bound(X_150,identity)),X_442)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150)))),multiply(inverse(multiply(inverse(greatest_lower_bound(X_150,identity)),X_442)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150))))) )],[refute_0_2645,refute_0_2646]) ).
cnf(refute_0_2648,plain,
multiply(inverse(multiply(inverse(greatest_lower_bound(X_150,identity)),X_442)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150)))) = multiply(multiply(inverse(X_442),greatest_lower_bound(X_150,identity)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150)))),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(greatest_lower_bound(X_150,identity)),X_442)),multiply(inverse(X_442),greatest_lower_bound(X_150,identity))) )],[refute_0_2644,refute_0_2647]) ).
cnf(refute_0_2649,plain,
( multiply(multiply(inverse(X_442),greatest_lower_bound(X_150,identity)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150)))) != multiply(multiply(inverse(X_442),greatest_lower_bound(X_150,identity)),identity)
| multiply(inverse(multiply(inverse(greatest_lower_bound(X_150,identity)),X_442)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150)))) != multiply(multiply(inverse(X_442),greatest_lower_bound(X_150,identity)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150))))
| multiply(inverse(multiply(inverse(greatest_lower_bound(X_150,identity)),X_442)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150)))) = multiply(multiply(inverse(X_442),greatest_lower_bound(X_150,identity)),identity) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(inverse(multiply(inverse(greatest_lower_bound(X_150,identity)),X_442)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150)))))),bind(Y0,$fot(multiply(multiply(inverse(X_442),greatest_lower_bound(X_150,identity)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150)))))),bind(Z0,$fot(multiply(multiply(inverse(X_442),greatest_lower_bound(X_150,identity)),identity)))]]) ).
cnf(refute_0_2650,plain,
( multiply(multiply(inverse(X_442),greatest_lower_bound(X_150,identity)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150)))) != multiply(multiply(inverse(X_442),greatest_lower_bound(X_150,identity)),identity)
| multiply(inverse(multiply(inverse(greatest_lower_bound(X_150,identity)),X_442)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150)))) = multiply(multiply(inverse(X_442),greatest_lower_bound(X_150,identity)),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(greatest_lower_bound(X_150,identity)),X_442)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150)))),multiply(multiply(inverse(X_442),greatest_lower_bound(X_150,identity)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150))))) )],[refute_0_2648,refute_0_2649]) ).
cnf(refute_0_2651,plain,
multiply(inverse(multiply(inverse(greatest_lower_bound(X_150,identity)),X_442)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150)))) = multiply(multiply(inverse(X_442),greatest_lower_bound(X_150,identity)),identity),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_442),greatest_lower_bound(X_150,identity)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150)))),multiply(multiply(inverse(X_442),greatest_lower_bound(X_150,identity)),identity)) )],[refute_0_2643,refute_0_2650]) ).
cnf(refute_0_2652,plain,
( multiply(multiply(inverse(X_442),greatest_lower_bound(X_150,identity)),identity) != multiply(inverse(X_442),greatest_lower_bound(X_150,identity))
| multiply(inverse(multiply(inverse(greatest_lower_bound(X_150,identity)),X_442)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150)))) != multiply(multiply(inverse(X_442),greatest_lower_bound(X_150,identity)),identity)
| multiply(inverse(multiply(inverse(greatest_lower_bound(X_150,identity)),X_442)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150)))) = multiply(inverse(X_442),greatest_lower_bound(X_150,identity)) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(inverse(multiply(inverse(greatest_lower_bound(X_150,identity)),X_442)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150)))))),bind(Y0,$fot(multiply(multiply(inverse(X_442),greatest_lower_bound(X_150,identity)),identity))),bind(Z0,$fot(multiply(inverse(X_442),greatest_lower_bound(X_150,identity))))]]) ).
cnf(refute_0_2653,plain,
( multiply(multiply(inverse(X_442),greatest_lower_bound(X_150,identity)),identity) != multiply(inverse(X_442),greatest_lower_bound(X_150,identity))
| multiply(inverse(multiply(inverse(greatest_lower_bound(X_150,identity)),X_442)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150)))) = multiply(inverse(X_442),greatest_lower_bound(X_150,identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(greatest_lower_bound(X_150,identity)),X_442)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150)))),multiply(multiply(inverse(X_442),greatest_lower_bound(X_150,identity)),identity)) )],[refute_0_2651,refute_0_2652]) ).
cnf(refute_0_2654,plain,
multiply(inverse(multiply(inverse(greatest_lower_bound(X_150,identity)),X_442)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150)))) = multiply(inverse(X_442),greatest_lower_bound(X_150,identity)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_442),greatest_lower_bound(X_150,identity)),identity),multiply(inverse(X_442),greatest_lower_bound(X_150,identity))) )],[refute_0_2638,refute_0_2653]) ).
cnf(refute_0_2655,plain,
( multiply(inverse(multiply(inverse(greatest_lower_bound(X_150,identity)),X_442)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150)))) != multiply(inverse(X_442),greatest_lower_bound(X_150,identity))
| multiply(inverse(multiply(inverse(greatest_lower_bound(X_150,identity)),X_442)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150)))) != multiply(inverse(X_442),greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_150,identity)))))
| multiply(inverse(X_442),greatest_lower_bound(X_150,identity)) = multiply(inverse(X_442),greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_150,identity))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(inverse(greatest_lower_bound(X_150,identity)),X_442)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150)))),multiply(inverse(X_442),greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_150,identity)))))) ),[0],$fot(multiply(inverse(X_442),greatest_lower_bound(X_150,identity)))]]) ).
cnf(refute_0_2656,plain,
( multiply(inverse(multiply(inverse(greatest_lower_bound(X_150,identity)),X_442)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150)))) != multiply(inverse(X_442),greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_150,identity)))))
| multiply(inverse(X_442),greatest_lower_bound(X_150,identity)) = multiply(inverse(X_442),greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_150,identity))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(greatest_lower_bound(X_150,identity)),X_442)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150)))),multiply(inverse(X_442),greatest_lower_bound(X_150,identity))) )],[refute_0_2654,refute_0_2655]) ).
cnf(refute_0_2657,plain,
greatest_lower_bound(identity,greatest_lower_bound(X_150,identity)) = greatest_lower_bound(identity,X_150),
inference(subst,[],[refute_0_347:[bind(Y,$fot(X_150)),bind(X_13,$fot(identity))]]) ).
cnf(refute_0_2658,plain,
inverse(inverse(greatest_lower_bound(X_150,identity))) = greatest_lower_bound(X_150,identity),
inference(subst,[],[refute_0_452:[bind(X_35,$fot(greatest_lower_bound(X_150,identity)))]]) ).
cnf(refute_0_2659,plain,
greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_150,identity)))) = greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_150,identity)))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_150,identity)))))]]) ).
cnf(refute_0_2660,plain,
( greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_150,identity)))) != greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_150,identity))))
| inverse(inverse(greatest_lower_bound(X_150,identity))) != greatest_lower_bound(X_150,identity)
| greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_150,identity)))) = greatest_lower_bound(identity,greatest_lower_bound(X_150,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_150,identity)))),greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_150,identity))))) ),[1,1],$fot(greatest_lower_bound(X_150,identity))]]) ).
cnf(refute_0_2661,plain,
( inverse(inverse(greatest_lower_bound(X_150,identity))) != greatest_lower_bound(X_150,identity)
| greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_150,identity)))) = greatest_lower_bound(identity,greatest_lower_bound(X_150,identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_150,identity)))),greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_150,identity))))) )],[refute_0_2659,refute_0_2660]) ).
cnf(refute_0_2662,plain,
greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_150,identity)))) = greatest_lower_bound(identity,greatest_lower_bound(X_150,identity)),
inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(X_150,identity))),greatest_lower_bound(X_150,identity)) )],[refute_0_2658,refute_0_2661]) ).
cnf(refute_0_2663,plain,
( greatest_lower_bound(identity,greatest_lower_bound(X_150,identity)) != greatest_lower_bound(identity,X_150)
| greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_150,identity)))) != greatest_lower_bound(identity,greatest_lower_bound(X_150,identity))
| greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_150,identity)))) = greatest_lower_bound(identity,X_150) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_150,identity)))))),bind(Y0,$fot(greatest_lower_bound(identity,greatest_lower_bound(X_150,identity)))),bind(Z0,$fot(greatest_lower_bound(identity,X_150)))]]) ).
cnf(refute_0_2664,plain,
( greatest_lower_bound(identity,greatest_lower_bound(X_150,identity)) != greatest_lower_bound(identity,X_150)
| greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_150,identity)))) = greatest_lower_bound(identity,X_150) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_150,identity)))),greatest_lower_bound(identity,greatest_lower_bound(X_150,identity))) )],[refute_0_2662,refute_0_2663]) ).
cnf(refute_0_2665,plain,
greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_150,identity)))) = greatest_lower_bound(identity,X_150),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_150,identity)),greatest_lower_bound(identity,X_150)) )],[refute_0_2657,refute_0_2664]) ).
cnf(refute_0_2666,plain,
multiply(inverse(X_442),greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_150,identity))))) = multiply(inverse(X_442),greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_150,identity))))),
introduced(tautology,[refl,[$fot(multiply(inverse(X_442),greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_150,identity))))))]]) ).
cnf(refute_0_2667,plain,
( multiply(inverse(X_442),greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_150,identity))))) != multiply(inverse(X_442),greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_150,identity)))))
| greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_150,identity)))) != greatest_lower_bound(identity,X_150)
| multiply(inverse(X_442),greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_150,identity))))) = multiply(inverse(X_442),greatest_lower_bound(identity,X_150)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_442),greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_150,identity))))),multiply(inverse(X_442),greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_150,identity)))))) ),[1,1],$fot(greatest_lower_bound(identity,X_150))]]) ).
cnf(refute_0_2668,plain,
( greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_150,identity)))) != greatest_lower_bound(identity,X_150)
| multiply(inverse(X_442),greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_150,identity))))) = multiply(inverse(X_442),greatest_lower_bound(identity,X_150)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_442),greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_150,identity))))),multiply(inverse(X_442),greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_150,identity)))))) )],[refute_0_2666,refute_0_2667]) ).
cnf(refute_0_2669,plain,
multiply(inverse(X_442),greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_150,identity))))) = multiply(inverse(X_442),greatest_lower_bound(identity,X_150)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_150,identity)))),greatest_lower_bound(identity,X_150)) )],[refute_0_2665,refute_0_2668]) ).
cnf(refute_0_2670,plain,
( multiply(inverse(X_442),greatest_lower_bound(X_150,identity)) != multiply(inverse(X_442),greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_150,identity)))))
| multiply(inverse(X_442),greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_150,identity))))) != multiply(inverse(X_442),greatest_lower_bound(identity,X_150))
| multiply(inverse(X_442),greatest_lower_bound(X_150,identity)) = multiply(inverse(X_442),greatest_lower_bound(identity,X_150)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_442),greatest_lower_bound(X_150,identity)),multiply(inverse(X_442),greatest_lower_bound(identity,X_150))) ),[0],$fot(multiply(inverse(X_442),greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_150,identity))))))]]) ).
cnf(refute_0_2671,plain,
( multiply(inverse(X_442),greatest_lower_bound(X_150,identity)) != multiply(inverse(X_442),greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_150,identity)))))
| multiply(inverse(X_442),greatest_lower_bound(X_150,identity)) = multiply(inverse(X_442),greatest_lower_bound(identity,X_150)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_442),greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_150,identity))))),multiply(inverse(X_442),greatest_lower_bound(identity,X_150))) )],[refute_0_2669,refute_0_2670]) ).
cnf(refute_0_2672,plain,
( multiply(inverse(multiply(inverse(greatest_lower_bound(X_150,identity)),X_442)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150)))) != multiply(inverse(X_442),greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_150,identity)))))
| multiply(inverse(X_442),greatest_lower_bound(X_150,identity)) = multiply(inverse(X_442),greatest_lower_bound(identity,X_150)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_442),greatest_lower_bound(X_150,identity)),multiply(inverse(X_442),greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_150,identity)))))) )],[refute_0_2656,refute_0_2671]) ).
cnf(refute_0_2673,plain,
multiply(inverse(X_442),greatest_lower_bound(X_150,identity)) = multiply(inverse(X_442),greatest_lower_bound(identity,X_150)),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(greatest_lower_bound(X_150,identity)),X_442)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_150)))),multiply(inverse(X_442),greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(X_150,identity)))))) )],[refute_0_2637,refute_0_2672]) ).
cnf(refute_0_2674,plain,
multiply(inverse(inverse(multiply(X_30,X_31))),greatest_lower_bound(inverse(X_31),identity)) = multiply(inverse(inverse(multiply(X_30,X_31))),greatest_lower_bound(identity,inverse(X_31))),
inference(subst,[],[refute_0_2673:[bind(X_150,$fot(inverse(X_31))),bind(X_442,$fot(inverse(multiply(X_30,X_31))))]]) ).
cnf(refute_0_2675,plain,
( multiply(inverse(inverse(multiply(X_30,X_31))),greatest_lower_bound(identity,inverse(X_31))) != multiply(X_30,greatest_lower_bound(X_31,identity))
| multiply(inverse(inverse(multiply(X_30,X_31))),greatest_lower_bound(inverse(X_31),identity)) != multiply(inverse(inverse(multiply(X_30,X_31))),greatest_lower_bound(identity,inverse(X_31)))
| multiply(inverse(inverse(multiply(X_30,X_31))),greatest_lower_bound(inverse(X_31),identity)) = multiply(X_30,greatest_lower_bound(X_31,identity)) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(inverse(inverse(multiply(X_30,X_31))),greatest_lower_bound(inverse(X_31),identity)))),bind(Y0,$fot(multiply(inverse(inverse(multiply(X_30,X_31))),greatest_lower_bound(identity,inverse(X_31))))),bind(Z0,$fot(multiply(X_30,greatest_lower_bound(X_31,identity))))]]) ).
cnf(refute_0_2676,plain,
( multiply(inverse(inverse(multiply(X_30,X_31))),greatest_lower_bound(identity,inverse(X_31))) != multiply(X_30,greatest_lower_bound(X_31,identity))
| multiply(inverse(inverse(multiply(X_30,X_31))),greatest_lower_bound(inverse(X_31),identity)) = multiply(X_30,greatest_lower_bound(X_31,identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(multiply(X_30,X_31))),greatest_lower_bound(inverse(X_31),identity)),multiply(inverse(inverse(multiply(X_30,X_31))),greatest_lower_bound(identity,inverse(X_31)))) )],[refute_0_2674,refute_0_2675]) ).
cnf(refute_0_2677,plain,
multiply(inverse(inverse(multiply(X_30,X_31))),greatest_lower_bound(inverse(X_31),identity)) = multiply(X_30,greatest_lower_bound(X_31,identity)),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(multiply(X_30,X_31))),greatest_lower_bound(identity,inverse(X_31))),multiply(X_30,greatest_lower_bound(X_31,identity))) )],[refute_0_2584,refute_0_2676]) ).
cnf(refute_0_2678,plain,
( multiply(inverse(inverse(multiply(X_30,X_31))),greatest_lower_bound(inverse(X_31),identity)) != multiply(X_30,greatest_lower_bound(X_31,identity))
| multiply(inverse(inverse(multiply(X_30,X_31))),greatest_lower_bound(inverse(X_31),identity)) != multiply(inverse(inverse(X_30)),greatest_lower_bound(identity,inverse(inverse(X_31))))
| multiply(X_30,greatest_lower_bound(X_31,identity)) = multiply(inverse(inverse(X_30)),greatest_lower_bound(identity,inverse(inverse(X_31)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(multiply(X_30,X_31))),greatest_lower_bound(inverse(X_31),identity)),multiply(inverse(inverse(X_30)),greatest_lower_bound(identity,inverse(inverse(X_31))))) ),[0],$fot(multiply(X_30,greatest_lower_bound(X_31,identity)))]]) ).
cnf(refute_0_2679,plain,
( multiply(inverse(inverse(multiply(X_30,X_31))),greatest_lower_bound(inverse(X_31),identity)) != multiply(inverse(inverse(X_30)),greatest_lower_bound(identity,inverse(inverse(X_31))))
| multiply(X_30,greatest_lower_bound(X_31,identity)) = multiply(inverse(inverse(X_30)),greatest_lower_bound(identity,inverse(inverse(X_31)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(multiply(X_30,X_31))),greatest_lower_bound(inverse(X_31),identity)),multiply(X_30,greatest_lower_bound(X_31,identity))) )],[refute_0_2677,refute_0_2678]) ).
cnf(refute_0_2680,plain,
inverse(inverse(X_31)) = X_31,
inference(subst,[],[refute_0_452:[bind(X_35,$fot(X_31))]]) ).
cnf(refute_0_2681,plain,
greatest_lower_bound(identity,inverse(inverse(X_31))) = greatest_lower_bound(identity,inverse(inverse(X_31))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,inverse(inverse(X_31))))]]) ).
cnf(refute_0_2682,plain,
( greatest_lower_bound(identity,inverse(inverse(X_31))) != greatest_lower_bound(identity,inverse(inverse(X_31)))
| inverse(inverse(X_31)) != X_31
| greatest_lower_bound(identity,inverse(inverse(X_31))) = greatest_lower_bound(identity,X_31) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,inverse(inverse(X_31))),greatest_lower_bound(identity,inverse(inverse(X_31)))) ),[1,1],$fot(X_31)]]) ).
cnf(refute_0_2683,plain,
( inverse(inverse(X_31)) != X_31
| greatest_lower_bound(identity,inverse(inverse(X_31))) = greatest_lower_bound(identity,X_31) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(inverse(X_31))),greatest_lower_bound(identity,inverse(inverse(X_31)))) )],[refute_0_2681,refute_0_2682]) ).
cnf(refute_0_2684,plain,
greatest_lower_bound(identity,inverse(inverse(X_31))) = greatest_lower_bound(identity,X_31),
inference(resolve,[$cnf( $equal(inverse(inverse(X_31)),X_31) )],[refute_0_2680,refute_0_2683]) ).
cnf(refute_0_2685,plain,
multiply(X_30,greatest_lower_bound(identity,inverse(inverse(X_31)))) = multiply(X_30,greatest_lower_bound(identity,inverse(inverse(X_31)))),
introduced(tautology,[refl,[$fot(multiply(X_30,greatest_lower_bound(identity,inverse(inverse(X_31)))))]]) ).
cnf(refute_0_2686,plain,
( multiply(X_30,greatest_lower_bound(identity,inverse(inverse(X_31)))) != multiply(X_30,greatest_lower_bound(identity,inverse(inverse(X_31))))
| greatest_lower_bound(identity,inverse(inverse(X_31))) != greatest_lower_bound(identity,X_31)
| multiply(X_30,greatest_lower_bound(identity,inverse(inverse(X_31)))) = multiply(X_30,greatest_lower_bound(identity,X_31)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_30,greatest_lower_bound(identity,inverse(inverse(X_31)))),multiply(X_30,greatest_lower_bound(identity,inverse(inverse(X_31))))) ),[1,1],$fot(greatest_lower_bound(identity,X_31))]]) ).
cnf(refute_0_2687,plain,
( greatest_lower_bound(identity,inverse(inverse(X_31))) != greatest_lower_bound(identity,X_31)
| multiply(X_30,greatest_lower_bound(identity,inverse(inverse(X_31)))) = multiply(X_30,greatest_lower_bound(identity,X_31)) ),
inference(resolve,[$cnf( $equal(multiply(X_30,greatest_lower_bound(identity,inverse(inverse(X_31)))),multiply(X_30,greatest_lower_bound(identity,inverse(inverse(X_31))))) )],[refute_0_2685,refute_0_2686]) ).
cnf(refute_0_2688,plain,
multiply(X_30,greatest_lower_bound(identity,inverse(inverse(X_31)))) = multiply(X_30,greatest_lower_bound(identity,X_31)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(inverse(X_31))),greatest_lower_bound(identity,X_31)) )],[refute_0_2684,refute_0_2687]) ).
cnf(refute_0_2689,plain,
inverse(inverse(X_30)) = X_30,
inference(subst,[],[refute_0_452:[bind(X_35,$fot(X_30))]]) ).
cnf(refute_0_2690,plain,
multiply(inverse(inverse(X_30)),greatest_lower_bound(identity,inverse(inverse(X_31)))) = multiply(inverse(inverse(X_30)),greatest_lower_bound(identity,inverse(inverse(X_31)))),
introduced(tautology,[refl,[$fot(multiply(inverse(inverse(X_30)),greatest_lower_bound(identity,inverse(inverse(X_31)))))]]) ).
cnf(refute_0_2691,plain,
( multiply(inverse(inverse(X_30)),greatest_lower_bound(identity,inverse(inverse(X_31)))) != multiply(inverse(inverse(X_30)),greatest_lower_bound(identity,inverse(inverse(X_31))))
| inverse(inverse(X_30)) != X_30
| multiply(inverse(inverse(X_30)),greatest_lower_bound(identity,inverse(inverse(X_31)))) = multiply(X_30,greatest_lower_bound(identity,inverse(inverse(X_31)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X_30)),greatest_lower_bound(identity,inverse(inverse(X_31)))),multiply(inverse(inverse(X_30)),greatest_lower_bound(identity,inverse(inverse(X_31))))) ),[1,0],$fot(X_30)]]) ).
cnf(refute_0_2692,plain,
( inverse(inverse(X_30)) != X_30
| multiply(inverse(inverse(X_30)),greatest_lower_bound(identity,inverse(inverse(X_31)))) = multiply(X_30,greatest_lower_bound(identity,inverse(inverse(X_31)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_30)),greatest_lower_bound(identity,inverse(inverse(X_31)))),multiply(inverse(inverse(X_30)),greatest_lower_bound(identity,inverse(inverse(X_31))))) )],[refute_0_2690,refute_0_2691]) ).
cnf(refute_0_2693,plain,
multiply(inverse(inverse(X_30)),greatest_lower_bound(identity,inverse(inverse(X_31)))) = multiply(X_30,greatest_lower_bound(identity,inverse(inverse(X_31)))),
inference(resolve,[$cnf( $equal(inverse(inverse(X_30)),X_30) )],[refute_0_2689,refute_0_2692]) ).
cnf(refute_0_2694,plain,
( multiply(X_30,greatest_lower_bound(identity,inverse(inverse(X_31)))) != multiply(X_30,greatest_lower_bound(identity,X_31))
| multiply(inverse(inverse(X_30)),greatest_lower_bound(identity,inverse(inverse(X_31)))) != multiply(X_30,greatest_lower_bound(identity,inverse(inverse(X_31))))
| multiply(inverse(inverse(X_30)),greatest_lower_bound(identity,inverse(inverse(X_31)))) = multiply(X_30,greatest_lower_bound(identity,X_31)) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(inverse(inverse(X_30)),greatest_lower_bound(identity,inverse(inverse(X_31)))))),bind(Y0,$fot(multiply(X_30,greatest_lower_bound(identity,inverse(inverse(X_31)))))),bind(Z0,$fot(multiply(X_30,greatest_lower_bound(identity,X_31))))]]) ).
cnf(refute_0_2695,plain,
( multiply(X_30,greatest_lower_bound(identity,inverse(inverse(X_31)))) != multiply(X_30,greatest_lower_bound(identity,X_31))
| multiply(inverse(inverse(X_30)),greatest_lower_bound(identity,inverse(inverse(X_31)))) = multiply(X_30,greatest_lower_bound(identity,X_31)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_30)),greatest_lower_bound(identity,inverse(inverse(X_31)))),multiply(X_30,greatest_lower_bound(identity,inverse(inverse(X_31))))) )],[refute_0_2693,refute_0_2694]) ).
cnf(refute_0_2696,plain,
multiply(inverse(inverse(X_30)),greatest_lower_bound(identity,inverse(inverse(X_31)))) = multiply(X_30,greatest_lower_bound(identity,X_31)),
inference(resolve,[$cnf( $equal(multiply(X_30,greatest_lower_bound(identity,inverse(inverse(X_31)))),multiply(X_30,greatest_lower_bound(identity,X_31))) )],[refute_0_2688,refute_0_2695]) ).
cnf(refute_0_2697,plain,
( multiply(X_30,greatest_lower_bound(X_31,identity)) != multiply(inverse(inverse(X_30)),greatest_lower_bound(identity,inverse(inverse(X_31))))
| multiply(inverse(inverse(X_30)),greatest_lower_bound(identity,inverse(inverse(X_31)))) != multiply(X_30,greatest_lower_bound(identity,X_31))
| multiply(X_30,greatest_lower_bound(X_31,identity)) = multiply(X_30,greatest_lower_bound(identity,X_31)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_30,greatest_lower_bound(X_31,identity)),multiply(X_30,greatest_lower_bound(identity,X_31))) ),[0],$fot(multiply(inverse(inverse(X_30)),greatest_lower_bound(identity,inverse(inverse(X_31)))))]]) ).
cnf(refute_0_2698,plain,
( multiply(X_30,greatest_lower_bound(X_31,identity)) != multiply(inverse(inverse(X_30)),greatest_lower_bound(identity,inverse(inverse(X_31))))
| multiply(X_30,greatest_lower_bound(X_31,identity)) = multiply(X_30,greatest_lower_bound(identity,X_31)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_30)),greatest_lower_bound(identity,inverse(inverse(X_31)))),multiply(X_30,greatest_lower_bound(identity,X_31))) )],[refute_0_2696,refute_0_2697]) ).
cnf(refute_0_2699,plain,
( multiply(inverse(inverse(multiply(X_30,X_31))),greatest_lower_bound(inverse(X_31),identity)) != multiply(inverse(inverse(X_30)),greatest_lower_bound(identity,inverse(inverse(X_31))))
| multiply(X_30,greatest_lower_bound(X_31,identity)) = multiply(X_30,greatest_lower_bound(identity,X_31)) ),
inference(resolve,[$cnf( $equal(multiply(X_30,greatest_lower_bound(X_31,identity)),multiply(inverse(inverse(X_30)),greatest_lower_bound(identity,inverse(inverse(X_31))))) )],[refute_0_2679,refute_0_2698]) ).
cnf(refute_0_2700,plain,
multiply(X_30,greatest_lower_bound(X_31,identity)) = multiply(X_30,greatest_lower_bound(identity,X_31)),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(multiply(X_30,X_31))),greatest_lower_bound(inverse(X_31),identity)),multiply(inverse(inverse(X_30)),greatest_lower_bound(identity,inverse(inverse(X_31))))) )],[refute_0_2551,refute_0_2699]) ).
cnf(refute_0_2701,plain,
multiply(identity,greatest_lower_bound(inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))),identity)) = multiply(identity,greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))),
inference(subst,[],[refute_0_2700:[bind(X_30,$fot(identity)),bind(X_31,$fot(inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))]]) ).
cnf(refute_0_2702,plain,
( multiply(identity,greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))) != greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))
| multiply(identity,greatest_lower_bound(inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))),identity)) != multiply(identity,greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))
| multiply(identity,greatest_lower_bound(inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))),identity)) = greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(identity,greatest_lower_bound(inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))),identity)))),bind(Y0,$fot(multiply(identity,greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))))),bind(Z0,$fot(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))))]]) ).
cnf(refute_0_2703,plain,
( multiply(identity,greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))) != greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))
| multiply(identity,greatest_lower_bound(inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))),identity)) = greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))) ),
inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))),identity)),multiply(identity,greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))) )],[refute_0_2701,refute_0_2702]) ).
cnf(refute_0_2704,plain,
multiply(identity,greatest_lower_bound(inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))),identity)) = greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))),
inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))),greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))) )],[refute_0_2519,refute_0_2703]) ).
cnf(refute_0_2705,plain,
greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))) = multiply(identity,greatest_lower_bound(inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))),identity)),
inference(subst,[],[refute_0_414:[bind(X_104,$fot(identity)),bind(X_105,$fot(inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))]]) ).
cnf(refute_0_2706,plain,
( multiply(identity,greatest_lower_bound(inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))),identity)) != greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))
| greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))) != multiply(identity,greatest_lower_bound(inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))),identity))
| greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))) = greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))))),bind(Y0,$fot(multiply(identity,greatest_lower_bound(inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))),identity)))),bind(Z0,$fot(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))))]]) ).
cnf(refute_0_2707,plain,
( multiply(identity,greatest_lower_bound(inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))),identity)) != greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))
| greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))) = greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))),multiply(identity,greatest_lower_bound(inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))),identity))) )],[refute_0_2705,refute_0_2706]) ).
cnf(refute_0_2708,plain,
greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))) = greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))),
inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))),identity)),greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))) )],[refute_0_2704,refute_0_2707]) ).
cnf(refute_0_2709,plain,
inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))) = inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))),
introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))))]]) ).
cnf(refute_0_2710,plain,
( greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))) != greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))
| inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))) != inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))))
| inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))) = inverse(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))),inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))))) ),[1,0],$fot(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))]]) ).
cnf(refute_0_2711,plain,
( greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))) != greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))
| inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))) = inverse(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))),inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))))) )],[refute_0_2709,refute_0_2710]) ).
cnf(refute_0_2712,plain,
inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))) = inverse(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))),greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))) )],[refute_0_2708,refute_0_2711]) ).
cnf(refute_0_2713,plain,
multiply(least_upper_bound(X_74,greatest_lower_bound(X_74,Y)),inverse(greatest_lower_bound(X_74,Y))) = least_upper_bound(identity,multiply(X_74,inverse(greatest_lower_bound(X_74,Y)))),
inference(subst,[],[refute_0_780:[bind(X_68,$fot(X_74)),bind(X_69,$fot(greatest_lower_bound(X_74,Y)))]]) ).
cnf(refute_0_2714,plain,
least_upper_bound(X_74,greatest_lower_bound(X_74,Y)) = X_74,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_74))]]) ).
cnf(refute_0_2715,plain,
( multiply(least_upper_bound(X_74,greatest_lower_bound(X_74,Y)),inverse(greatest_lower_bound(X_74,Y))) != least_upper_bound(identity,multiply(X_74,inverse(greatest_lower_bound(X_74,Y))))
| least_upper_bound(X_74,greatest_lower_bound(X_74,Y)) != X_74
| multiply(X_74,inverse(greatest_lower_bound(X_74,Y))) = least_upper_bound(identity,multiply(X_74,inverse(greatest_lower_bound(X_74,Y)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_74,greatest_lower_bound(X_74,Y)),inverse(greatest_lower_bound(X_74,Y))),least_upper_bound(identity,multiply(X_74,inverse(greatest_lower_bound(X_74,Y))))) ),[0,0],$fot(X_74)]]) ).
cnf(refute_0_2716,plain,
( multiply(least_upper_bound(X_74,greatest_lower_bound(X_74,Y)),inverse(greatest_lower_bound(X_74,Y))) != least_upper_bound(identity,multiply(X_74,inverse(greatest_lower_bound(X_74,Y))))
| multiply(X_74,inverse(greatest_lower_bound(X_74,Y))) = least_upper_bound(identity,multiply(X_74,inverse(greatest_lower_bound(X_74,Y)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_74,greatest_lower_bound(X_74,Y)),X_74) )],[refute_0_2714,refute_0_2715]) ).
cnf(refute_0_2717,plain,
multiply(X_74,inverse(greatest_lower_bound(X_74,Y))) = least_upper_bound(identity,multiply(X_74,inverse(greatest_lower_bound(X_74,Y)))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_74,greatest_lower_bound(X_74,Y)),inverse(greatest_lower_bound(X_74,Y))),least_upper_bound(identity,multiply(X_74,inverse(greatest_lower_bound(X_74,Y))))) )],[refute_0_2713,refute_0_2716]) ).
cnf(refute_0_2718,plain,
multiply(identity,inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))) = least_upper_bound(identity,multiply(identity,inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121)))))),
inference(subst,[],[refute_0_2717:[bind(Y,$fot(multiply(X_120,inverse(X_121)))),bind(X_74,$fot(identity))]]) ).
cnf(refute_0_2719,plain,
( multiply(greatest_lower_bound(X_120,X_121),inverse(X_121)) != greatest_lower_bound(identity,multiply(X_120,inverse(X_121)))
| greatest_lower_bound(identity,multiply(X_120,inverse(X_121))) = multiply(greatest_lower_bound(X_120,X_121),inverse(X_121)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(greatest_lower_bound(X_120,X_121),inverse(X_121)))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(X_120,inverse(X_121)))))]]) ).
cnf(refute_0_2720,plain,
greatest_lower_bound(identity,multiply(X_120,inverse(X_121))) = multiply(greatest_lower_bound(X_120,X_121),inverse(X_121)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_120,X_121),inverse(X_121)),greatest_lower_bound(identity,multiply(X_120,inverse(X_121)))) )],[refute_0_329,refute_0_2719]) ).
cnf(refute_0_2721,plain,
( multiply(identity,inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))) != least_upper_bound(identity,multiply(identity,inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))))
| greatest_lower_bound(identity,multiply(X_120,inverse(X_121))) != multiply(greatest_lower_bound(X_120,X_121),inverse(X_121))
| multiply(identity,inverse(multiply(greatest_lower_bound(X_120,X_121),inverse(X_121)))) = least_upper_bound(identity,multiply(identity,inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121)))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))),least_upper_bound(identity,multiply(identity,inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))))) ),[0,1,0],$fot(multiply(greatest_lower_bound(X_120,X_121),inverse(X_121)))]]) ).
cnf(refute_0_2722,plain,
( multiply(identity,inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))) != least_upper_bound(identity,multiply(identity,inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))))
| multiply(identity,inverse(multiply(greatest_lower_bound(X_120,X_121),inverse(X_121)))) = least_upper_bound(identity,multiply(identity,inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121)))))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_120,inverse(X_121))),multiply(greatest_lower_bound(X_120,X_121),inverse(X_121))) )],[refute_0_2720,refute_0_2721]) ).
cnf(refute_0_2723,plain,
multiply(identity,inverse(multiply(greatest_lower_bound(X_120,X_121),inverse(X_121)))) = least_upper_bound(identity,multiply(identity,inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121)))))),
inference(resolve,[$cnf( $equal(multiply(identity,inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))),least_upper_bound(identity,multiply(identity,inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))))) )],[refute_0_2718,refute_0_2722]) ).
cnf(refute_0_2724,plain,
inverse(multiply(X_352,inverse(X_35))) = multiply(inverse(inverse(X_35)),inverse(X_352)),
inference(subst,[],[refute_0_488:[bind(X_30,$fot(X_352)),bind(X_31,$fot(inverse(X_35)))]]) ).
cnf(refute_0_2725,plain,
( inverse(multiply(X_352,inverse(X_35))) != multiply(inverse(inverse(X_35)),inverse(X_352))
| inverse(inverse(X_35)) != X_35
| inverse(multiply(X_352,inverse(X_35))) = multiply(X_35,inverse(X_352)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_352,inverse(X_35))),multiply(inverse(inverse(X_35)),inverse(X_352))) ),[1,0],$fot(X_35)]]) ).
cnf(refute_0_2726,plain,
( inverse(multiply(X_352,inverse(X_35))) != multiply(inverse(inverse(X_35)),inverse(X_352))
| inverse(multiply(X_352,inverse(X_35))) = multiply(X_35,inverse(X_352)) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_35)),X_35) )],[refute_0_452,refute_0_2725]) ).
cnf(refute_0_2727,plain,
inverse(multiply(X_352,inverse(X_35))) = multiply(X_35,inverse(X_352)),
inference(resolve,[$cnf( $equal(inverse(multiply(X_352,inverse(X_35))),multiply(inverse(inverse(X_35)),inverse(X_352))) )],[refute_0_2724,refute_0_2726]) ).
cnf(refute_0_2728,plain,
inverse(multiply(greatest_lower_bound(X_120,X_121),inverse(X_121))) = multiply(X_121,inverse(greatest_lower_bound(X_120,X_121))),
inference(subst,[],[refute_0_2727:[bind(X_35,$fot(X_121)),bind(X_352,$fot(greatest_lower_bound(X_120,X_121)))]]) ).
cnf(refute_0_2729,plain,
multiply(identity,inverse(multiply(greatest_lower_bound(X_120,X_121),inverse(X_121)))) = inverse(multiply(greatest_lower_bound(X_120,X_121),inverse(X_121))),
inference(subst,[],[left_identity:[bind(X,$fot(inverse(multiply(greatest_lower_bound(X_120,X_121),inverse(X_121)))))]]) ).
cnf(refute_0_2730,plain,
( multiply(identity,inverse(multiply(greatest_lower_bound(X_120,X_121),inverse(X_121)))) != inverse(multiply(greatest_lower_bound(X_120,X_121),inverse(X_121)))
| inverse(multiply(greatest_lower_bound(X_120,X_121),inverse(X_121))) != multiply(X_121,inverse(greatest_lower_bound(X_120,X_121)))
| multiply(identity,inverse(multiply(greatest_lower_bound(X_120,X_121),inverse(X_121)))) = multiply(X_121,inverse(greatest_lower_bound(X_120,X_121))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(identity,inverse(multiply(greatest_lower_bound(X_120,X_121),inverse(X_121)))))),bind(Y0,$fot(inverse(multiply(greatest_lower_bound(X_120,X_121),inverse(X_121))))),bind(Z0,$fot(multiply(X_121,inverse(greatest_lower_bound(X_120,X_121)))))]]) ).
cnf(refute_0_2731,plain,
( inverse(multiply(greatest_lower_bound(X_120,X_121),inverse(X_121))) != multiply(X_121,inverse(greatest_lower_bound(X_120,X_121)))
| multiply(identity,inverse(multiply(greatest_lower_bound(X_120,X_121),inverse(X_121)))) = multiply(X_121,inverse(greatest_lower_bound(X_120,X_121))) ),
inference(resolve,[$cnf( $equal(multiply(identity,inverse(multiply(greatest_lower_bound(X_120,X_121),inverse(X_121)))),inverse(multiply(greatest_lower_bound(X_120,X_121),inverse(X_121)))) )],[refute_0_2729,refute_0_2730]) ).
cnf(refute_0_2732,plain,
multiply(identity,inverse(multiply(greatest_lower_bound(X_120,X_121),inverse(X_121)))) = multiply(X_121,inverse(greatest_lower_bound(X_120,X_121))),
inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(X_120,X_121),inverse(X_121))),multiply(X_121,inverse(greatest_lower_bound(X_120,X_121)))) )],[refute_0_2728,refute_0_2731]) ).
cnf(refute_0_2733,plain,
( multiply(identity,inverse(multiply(greatest_lower_bound(X_120,X_121),inverse(X_121)))) != multiply(X_121,inverse(greatest_lower_bound(X_120,X_121)))
| multiply(identity,inverse(multiply(greatest_lower_bound(X_120,X_121),inverse(X_121)))) != least_upper_bound(identity,multiply(identity,inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))))
| multiply(X_121,inverse(greatest_lower_bound(X_120,X_121))) = least_upper_bound(identity,multiply(identity,inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121)))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,inverse(multiply(greatest_lower_bound(X_120,X_121),inverse(X_121)))),least_upper_bound(identity,multiply(identity,inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))))) ),[0],$fot(multiply(X_121,inverse(greatest_lower_bound(X_120,X_121))))]]) ).
cnf(refute_0_2734,plain,
( multiply(identity,inverse(multiply(greatest_lower_bound(X_120,X_121),inverse(X_121)))) != least_upper_bound(identity,multiply(identity,inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))))
| multiply(X_121,inverse(greatest_lower_bound(X_120,X_121))) = least_upper_bound(identity,multiply(identity,inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121)))))) ),
inference(resolve,[$cnf( $equal(multiply(identity,inverse(multiply(greatest_lower_bound(X_120,X_121),inverse(X_121)))),multiply(X_121,inverse(greatest_lower_bound(X_120,X_121)))) )],[refute_0_2732,refute_0_2733]) ).
cnf(refute_0_2735,plain,
multiply(identity,inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))) = inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121)))),
inference(subst,[],[left_identity:[bind(X,$fot(inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))))]]) ).
cnf(refute_0_2736,plain,
( multiply(X_74,inverse(greatest_lower_bound(X_74,Y))) != least_upper_bound(identity,multiply(X_74,inverse(greatest_lower_bound(X_74,Y))))
| least_upper_bound(identity,multiply(X_74,inverse(greatest_lower_bound(X_74,Y)))) = multiply(X_74,inverse(greatest_lower_bound(X_74,Y))) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(X_74,inverse(greatest_lower_bound(X_74,Y))))),bind(Y0,$fot(least_upper_bound(identity,multiply(X_74,inverse(greatest_lower_bound(X_74,Y))))))]]) ).
cnf(refute_0_2737,plain,
least_upper_bound(identity,multiply(X_74,inverse(greatest_lower_bound(X_74,Y)))) = multiply(X_74,inverse(greatest_lower_bound(X_74,Y))),
inference(resolve,[$cnf( $equal(multiply(X_74,inverse(greatest_lower_bound(X_74,Y))),least_upper_bound(identity,multiply(X_74,inverse(greatest_lower_bound(X_74,Y))))) )],[refute_0_2717,refute_0_2736]) ).
cnf(refute_0_2738,plain,
least_upper_bound(identity,multiply(identity,inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121)))))) = multiply(identity,inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))),
inference(subst,[],[refute_0_2737:[bind(Y,$fot(multiply(X_120,inverse(X_121)))),bind(X_74,$fot(identity))]]) ).
cnf(refute_0_2739,plain,
( multiply(identity,inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))) != inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))
| least_upper_bound(identity,multiply(identity,inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121)))))) != multiply(identity,inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121)))))
| least_upper_bound(identity,multiply(identity,inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121)))))) = inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121)))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(least_upper_bound(identity,multiply(identity,inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121)))))))),bind(Y0,$fot(multiply(identity,inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))))),bind(Z0,$fot(inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))))]]) ).
cnf(refute_0_2740,plain,
( multiply(identity,inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))) != inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))
| least_upper_bound(identity,multiply(identity,inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121)))))) = inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(identity,inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121)))))),multiply(identity,inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121)))))) )],[refute_0_2738,refute_0_2739]) ).
cnf(refute_0_2741,plain,
least_upper_bound(identity,multiply(identity,inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121)))))) = inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121)))),
inference(resolve,[$cnf( $equal(multiply(identity,inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))),inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))) )],[refute_0_2735,refute_0_2740]) ).
cnf(refute_0_2742,plain,
( multiply(X_121,inverse(greatest_lower_bound(X_120,X_121))) != least_upper_bound(identity,multiply(identity,inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))))
| least_upper_bound(identity,multiply(identity,inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121)))))) != inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))
| multiply(X_121,inverse(greatest_lower_bound(X_120,X_121))) = inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_121,inverse(greatest_lower_bound(X_120,X_121))),inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))) ),[0],$fot(least_upper_bound(identity,multiply(identity,inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121)))))))]]) ).
cnf(refute_0_2743,plain,
( multiply(X_121,inverse(greatest_lower_bound(X_120,X_121))) != least_upper_bound(identity,multiply(identity,inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))))
| multiply(X_121,inverse(greatest_lower_bound(X_120,X_121))) = inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(identity,inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121)))))),inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))) )],[refute_0_2741,refute_0_2742]) ).
cnf(refute_0_2744,plain,
( multiply(identity,inverse(multiply(greatest_lower_bound(X_120,X_121),inverse(X_121)))) != least_upper_bound(identity,multiply(identity,inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))))
| multiply(X_121,inverse(greatest_lower_bound(X_120,X_121))) = inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121)))) ),
inference(resolve,[$cnf( $equal(multiply(X_121,inverse(greatest_lower_bound(X_120,X_121))),least_upper_bound(identity,multiply(identity,inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))))) )],[refute_0_2734,refute_0_2743]) ).
cnf(refute_0_2745,plain,
multiply(X_121,inverse(greatest_lower_bound(X_120,X_121))) = inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121)))),
inference(resolve,[$cnf( $equal(multiply(identity,inverse(multiply(greatest_lower_bound(X_120,X_121),inverse(X_121)))),least_upper_bound(identity,multiply(identity,inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))))) )],[refute_0_2723,refute_0_2744]) ).
cnf(refute_0_2746,plain,
multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))) = inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))),
inference(subst,[],[refute_0_2745:[bind(X_120,$fot(identity)),bind(X_121,$fot(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))]]) ).
cnf(refute_0_2747,plain,
( multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))) != inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))))
| inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))) != inverse(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))
| multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))) = inverse(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))))),bind(Y0,$fot(inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))))),bind(Z0,$fot(inverse(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))))]]) ).
cnf(refute_0_2748,plain,
( inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))) != inverse(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))
| multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))) = inverse(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))),inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))))) )],[refute_0_2746,refute_0_2747]) ).
cnf(refute_0_2749,plain,
multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))) = inverse(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))),inverse(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))) )],[refute_0_2712,refute_0_2748]) ).
cnf(refute_0_2750,plain,
( multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))) != inverse(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))
| multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))) != least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(identity)))
| inverse(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))) = least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(identity))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))),least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(identity)))) ),[0],$fot(inverse(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))))]]) ).
cnf(refute_0_2751,plain,
( multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))) != least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(identity)))
| inverse(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))) = least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(identity))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))),inverse(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))) )],[refute_0_2749,refute_0_2750]) ).
cnf(refute_0_2752,plain,
multiply(identity,identity) = identity,
inference(subst,[],[refute_0_88:[bind(X_33,$fot(identity))]]) ).
cnf(refute_0_2753,plain,
multiply(identity,inverse(identity)) = multiply(identity,inverse(identity)),
introduced(tautology,[refl,[$fot(multiply(identity,inverse(identity)))]]) ).
cnf(refute_0_2754,plain,
( multiply(identity,inverse(identity)) != multiply(identity,inverse(identity))
| inverse(identity) != identity
| multiply(identity,inverse(identity)) = multiply(identity,identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,inverse(identity)),multiply(identity,inverse(identity))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_2755,plain,
( inverse(identity) != identity
| multiply(identity,inverse(identity)) = multiply(identity,identity) ),
inference(resolve,[$cnf( $equal(multiply(identity,inverse(identity)),multiply(identity,inverse(identity))) )],[refute_0_2753,refute_0_2754]) ).
cnf(refute_0_2756,plain,
multiply(identity,inverse(identity)) = multiply(identity,identity),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_1763,refute_0_2755]) ).
cnf(refute_0_2757,plain,
least_upper_bound(identity,greatest_lower_bound(identity,X_444)) = identity,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(identity)),bind(Y,$fot(X_444))]]) ).
cnf(refute_0_2758,plain,
multiply(X_87,least_upper_bound(least_upper_bound(inverse(X_87),X_50),identity)) = least_upper_bound(X_87,multiply(X_87,least_upper_bound(inverse(X_87),X_50))),
inference(subst,[],[refute_0_528:[bind(X_48,$fot(X_87)),bind(X_49,$fot(least_upper_bound(inverse(X_87),X_50)))]]) ).
cnf(refute_0_2759,plain,
multiply(X_87,least_upper_bound(inverse(X_87),X_50)) = least_upper_bound(identity,multiply(X_87,X_50)),
inference(subst,[],[refute_0_2440:[bind(X_48,$fot(X_87))]]) ).
cnf(refute_0_2760,plain,
( multiply(X_87,least_upper_bound(inverse(X_87),X_50)) != least_upper_bound(identity,multiply(X_87,X_50))
| multiply(X_87,least_upper_bound(least_upper_bound(inverse(X_87),X_50),identity)) != least_upper_bound(X_87,multiply(X_87,least_upper_bound(inverse(X_87),X_50)))
| multiply(X_87,least_upper_bound(least_upper_bound(inverse(X_87),X_50),identity)) = least_upper_bound(X_87,least_upper_bound(identity,multiply(X_87,X_50))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_87,least_upper_bound(least_upper_bound(inverse(X_87),X_50),identity)),least_upper_bound(X_87,multiply(X_87,least_upper_bound(inverse(X_87),X_50)))) ),[1,1],$fot(least_upper_bound(identity,multiply(X_87,X_50)))]]) ).
cnf(refute_0_2761,plain,
( multiply(X_87,least_upper_bound(least_upper_bound(inverse(X_87),X_50),identity)) != least_upper_bound(X_87,multiply(X_87,least_upper_bound(inverse(X_87),X_50)))
| multiply(X_87,least_upper_bound(least_upper_bound(inverse(X_87),X_50),identity)) = least_upper_bound(X_87,least_upper_bound(identity,multiply(X_87,X_50))) ),
inference(resolve,[$cnf( $equal(multiply(X_87,least_upper_bound(inverse(X_87),X_50)),least_upper_bound(identity,multiply(X_87,X_50))) )],[refute_0_2759,refute_0_2760]) ).
cnf(refute_0_2762,plain,
multiply(X_87,least_upper_bound(least_upper_bound(inverse(X_87),X_50),identity)) = least_upper_bound(X_87,least_upper_bound(identity,multiply(X_87,X_50))),
inference(resolve,[$cnf( $equal(multiply(X_87,least_upper_bound(least_upper_bound(inverse(X_87),X_50),identity)),least_upper_bound(X_87,multiply(X_87,least_upper_bound(inverse(X_87),X_50)))) )],[refute_0_2758,refute_0_2761]) ).
cnf(refute_0_2763,plain,
multiply(X_87,least_upper_bound(identity,least_upper_bound(inverse(X_87),X_50))) = least_upper_bound(identity,multiply(X_87,least_upper_bound(identity,X_50))),
inference(subst,[],[refute_0_2469:[bind(X,$fot(X_87)),bind(Z,$fot(X_50)),bind(X_52,$fot(identity))]]) ).
cnf(refute_0_2764,plain,
multiply(X_87,least_upper_bound(least_upper_bound(inverse(X_87),X_50),identity)) = multiply(X_87,least_upper_bound(identity,least_upper_bound(inverse(X_87),X_50))),
inference(subst,[],[refute_0_598:[bind(X_19,$fot(X_87)),bind(X_88,$fot(least_upper_bound(inverse(X_87),X_50)))]]) ).
cnf(refute_0_2765,plain,
( multiply(X_87,least_upper_bound(identity,least_upper_bound(inverse(X_87),X_50))) != least_upper_bound(identity,multiply(X_87,least_upper_bound(identity,X_50)))
| multiply(X_87,least_upper_bound(least_upper_bound(inverse(X_87),X_50),identity)) != multiply(X_87,least_upper_bound(identity,least_upper_bound(inverse(X_87),X_50)))
| multiply(X_87,least_upper_bound(least_upper_bound(inverse(X_87),X_50),identity)) = least_upper_bound(identity,multiply(X_87,least_upper_bound(identity,X_50))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(X_87,least_upper_bound(least_upper_bound(inverse(X_87),X_50),identity)))),bind(Y0,$fot(multiply(X_87,least_upper_bound(identity,least_upper_bound(inverse(X_87),X_50))))),bind(Z0,$fot(least_upper_bound(identity,multiply(X_87,least_upper_bound(identity,X_50)))))]]) ).
cnf(refute_0_2766,plain,
( multiply(X_87,least_upper_bound(identity,least_upper_bound(inverse(X_87),X_50))) != least_upper_bound(identity,multiply(X_87,least_upper_bound(identity,X_50)))
| multiply(X_87,least_upper_bound(least_upper_bound(inverse(X_87),X_50),identity)) = least_upper_bound(identity,multiply(X_87,least_upper_bound(identity,X_50))) ),
inference(resolve,[$cnf( $equal(multiply(X_87,least_upper_bound(least_upper_bound(inverse(X_87),X_50),identity)),multiply(X_87,least_upper_bound(identity,least_upper_bound(inverse(X_87),X_50)))) )],[refute_0_2764,refute_0_2765]) ).
cnf(refute_0_2767,plain,
multiply(X_87,least_upper_bound(least_upper_bound(inverse(X_87),X_50),identity)) = least_upper_bound(identity,multiply(X_87,least_upper_bound(identity,X_50))),
inference(resolve,[$cnf( $equal(multiply(X_87,least_upper_bound(identity,least_upper_bound(inverse(X_87),X_50))),least_upper_bound(identity,multiply(X_87,least_upper_bound(identity,X_50)))) )],[refute_0_2763,refute_0_2766]) ).
cnf(refute_0_2768,plain,
( multiply(X_87,least_upper_bound(least_upper_bound(inverse(X_87),X_50),identity)) != least_upper_bound(X_87,least_upper_bound(identity,multiply(X_87,X_50)))
| multiply(X_87,least_upper_bound(least_upper_bound(inverse(X_87),X_50),identity)) != least_upper_bound(identity,multiply(X_87,least_upper_bound(identity,X_50)))
| least_upper_bound(identity,multiply(X_87,least_upper_bound(identity,X_50))) = least_upper_bound(X_87,least_upper_bound(identity,multiply(X_87,X_50))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_87,least_upper_bound(least_upper_bound(inverse(X_87),X_50),identity)),least_upper_bound(X_87,least_upper_bound(identity,multiply(X_87,X_50)))) ),[0],$fot(least_upper_bound(identity,multiply(X_87,least_upper_bound(identity,X_50))))]]) ).
cnf(refute_0_2769,plain,
( multiply(X_87,least_upper_bound(least_upper_bound(inverse(X_87),X_50),identity)) != least_upper_bound(X_87,least_upper_bound(identity,multiply(X_87,X_50)))
| least_upper_bound(identity,multiply(X_87,least_upper_bound(identity,X_50))) = least_upper_bound(X_87,least_upper_bound(identity,multiply(X_87,X_50))) ),
inference(resolve,[$cnf( $equal(multiply(X_87,least_upper_bound(least_upper_bound(inverse(X_87),X_50),identity)),least_upper_bound(identity,multiply(X_87,least_upper_bound(identity,X_50)))) )],[refute_0_2767,refute_0_2768]) ).
cnf(refute_0_2770,plain,
least_upper_bound(identity,multiply(X_87,least_upper_bound(identity,X_50))) = least_upper_bound(X_87,least_upper_bound(identity,multiply(X_87,X_50))),
inference(resolve,[$cnf( $equal(multiply(X_87,least_upper_bound(least_upper_bound(inverse(X_87),X_50),identity)),least_upper_bound(X_87,least_upper_bound(identity,multiply(X_87,X_50)))) )],[refute_0_2762,refute_0_2769]) ).
cnf(refute_0_2771,plain,
least_upper_bound(identity,multiply(greatest_lower_bound(X_120,X_121),least_upper_bound(identity,inverse(X_121)))) = least_upper_bound(greatest_lower_bound(X_120,X_121),least_upper_bound(identity,multiply(greatest_lower_bound(X_120,X_121),inverse(X_121)))),
inference(subst,[],[refute_0_2770:[bind(X_50,$fot(inverse(X_121))),bind(X_87,$fot(greatest_lower_bound(X_120,X_121)))]]) ).
cnf(refute_0_2772,plain,
( multiply(greatest_lower_bound(X_120,X_121),inverse(X_121)) != greatest_lower_bound(identity,multiply(X_120,inverse(X_121)))
| least_upper_bound(identity,multiply(greatest_lower_bound(X_120,X_121),least_upper_bound(identity,inverse(X_121)))) != least_upper_bound(greatest_lower_bound(X_120,X_121),least_upper_bound(identity,multiply(greatest_lower_bound(X_120,X_121),inverse(X_121))))
| least_upper_bound(identity,multiply(greatest_lower_bound(X_120,X_121),least_upper_bound(identity,inverse(X_121)))) = least_upper_bound(greatest_lower_bound(X_120,X_121),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(greatest_lower_bound(X_120,X_121),least_upper_bound(identity,inverse(X_121)))),least_upper_bound(greatest_lower_bound(X_120,X_121),least_upper_bound(identity,multiply(greatest_lower_bound(X_120,X_121),inverse(X_121))))) ),[1,1,1],$fot(greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))]]) ).
cnf(refute_0_2773,plain,
( least_upper_bound(identity,multiply(greatest_lower_bound(X_120,X_121),least_upper_bound(identity,inverse(X_121)))) != least_upper_bound(greatest_lower_bound(X_120,X_121),least_upper_bound(identity,multiply(greatest_lower_bound(X_120,X_121),inverse(X_121))))
| least_upper_bound(identity,multiply(greatest_lower_bound(X_120,X_121),least_upper_bound(identity,inverse(X_121)))) = least_upper_bound(greatest_lower_bound(X_120,X_121),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_120,X_121),inverse(X_121)),greatest_lower_bound(identity,multiply(X_120,inverse(X_121)))) )],[refute_0_329,refute_0_2772]) ).
cnf(refute_0_2774,plain,
least_upper_bound(identity,multiply(greatest_lower_bound(X_120,X_121),least_upper_bound(identity,inverse(X_121)))) = least_upper_bound(greatest_lower_bound(X_120,X_121),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(greatest_lower_bound(X_120,X_121),least_upper_bound(identity,inverse(X_121)))),least_upper_bound(greatest_lower_bound(X_120,X_121),least_upper_bound(identity,multiply(greatest_lower_bound(X_120,X_121),inverse(X_121))))) )],[refute_0_2771,refute_0_2773]) ).
cnf(refute_0_2775,plain,
greatest_lower_bound(least_upper_bound(X_163,identity),inverse(greatest_lower_bound(X_222,inverse(least_upper_bound(X_163,identity))))) = greatest_lower_bound(least_upper_bound(identity,X_163),inverse(greatest_lower_bound(X_222,inverse(least_upper_bound(X_163,identity))))),
inference(subst,[],[refute_0_1785:[bind(X_162,$fot(inverse(greatest_lower_bound(X_222,inverse(least_upper_bound(X_163,identity))))))]]) ).
cnf(refute_0_2776,plain,
inverse(inverse(X_121)) = multiply(inverse(multiply(greatest_lower_bound(X_120,X_121),inverse(X_121))),greatest_lower_bound(X_120,X_121)),
inference(subst,[],[refute_0_96:[bind(X_45,$fot(greatest_lower_bound(X_120,X_121))),bind(X_46,$fot(inverse(X_121)))]]) ).
cnf(refute_0_2777,plain,
( multiply(greatest_lower_bound(X_120,X_121),inverse(X_121)) != greatest_lower_bound(identity,multiply(X_120,inverse(X_121)))
| inverse(inverse(X_121)) != multiply(inverse(multiply(greatest_lower_bound(X_120,X_121),inverse(X_121))),greatest_lower_bound(X_120,X_121))
| inverse(inverse(X_121)) = multiply(inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121)))),greatest_lower_bound(X_120,X_121)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_121)),multiply(inverse(multiply(greatest_lower_bound(X_120,X_121),inverse(X_121))),greatest_lower_bound(X_120,X_121))) ),[1,0,0],$fot(greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))]]) ).
cnf(refute_0_2778,plain,
( inverse(inverse(X_121)) != multiply(inverse(multiply(greatest_lower_bound(X_120,X_121),inverse(X_121))),greatest_lower_bound(X_120,X_121))
| inverse(inverse(X_121)) = multiply(inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121)))),greatest_lower_bound(X_120,X_121)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_120,X_121),inverse(X_121)),greatest_lower_bound(identity,multiply(X_120,inverse(X_121)))) )],[refute_0_329,refute_0_2777]) ).
cnf(refute_0_2779,plain,
inverse(inverse(X_121)) = multiply(inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121)))),greatest_lower_bound(X_120,X_121)),
inference(resolve,[$cnf( $equal(inverse(inverse(X_121)),multiply(inverse(multiply(greatest_lower_bound(X_120,X_121),inverse(X_121))),greatest_lower_bound(X_120,X_121))) )],[refute_0_2776,refute_0_2778]) ).
cnf(refute_0_2780,plain,
inverse(inverse(X_121)) = X_121,
inference(subst,[],[refute_0_452:[bind(X_35,$fot(X_121))]]) ).
cnf(refute_0_2781,plain,
( inverse(inverse(X_121)) != X_121
| inverse(inverse(X_121)) != multiply(inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121)))),greatest_lower_bound(X_120,X_121))
| X_121 = multiply(inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121)))),greatest_lower_bound(X_120,X_121)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_121)),multiply(inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121)))),greatest_lower_bound(X_120,X_121))) ),[0],$fot(X_121)]]) ).
cnf(refute_0_2782,plain,
( inverse(inverse(X_121)) != multiply(inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121)))),greatest_lower_bound(X_120,X_121))
| X_121 = multiply(inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121)))),greatest_lower_bound(X_120,X_121)) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_121)),X_121) )],[refute_0_2780,refute_0_2781]) ).
cnf(refute_0_2783,plain,
X_121 = multiply(inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121)))),greatest_lower_bound(X_120,X_121)),
inference(resolve,[$cnf( $equal(inverse(inverse(X_121)),multiply(inverse(greatest_lower_bound(identity,multiply(X_120,inverse(X_121)))),greatest_lower_bound(X_120,X_121))) )],[refute_0_2779,refute_0_2782]) ).
cnf(refute_0_2784,plain,
X_221 = multiply(inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_11,inverse(X_221))),inverse(X_221)))),greatest_lower_bound(inverse(greatest_lower_bound(X_11,inverse(X_221))),X_221)),
inference(subst,[],[refute_0_2783:[bind(X_120,$fot(inverse(greatest_lower_bound(X_11,inverse(X_221))))),bind(X_121,$fot(X_221))]]) ).
cnf(refute_0_2785,plain,
greatest_lower_bound(identity,least_upper_bound(identity,multiply(inverse(X_56),X_55))) = identity,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(identity)),bind(Y,$fot(multiply(inverse(X_56),X_55)))]]) ).
cnf(refute_0_2786,plain,
multiply(inverse(X_56),least_upper_bound(X_55,X_56)) = least_upper_bound(identity,multiply(inverse(X_56),X_55)),
inference(subst,[],[refute_0_29:[bind(X_49,$fot(X_55)),bind(X_50,$fot(X_56))]]) ).
cnf(refute_0_2787,plain,
( multiply(inverse(X_56),least_upper_bound(X_55,X_56)) != least_upper_bound(identity,multiply(inverse(X_56),X_55))
| least_upper_bound(identity,multiply(inverse(X_56),X_55)) = multiply(inverse(X_56),least_upper_bound(X_55,X_56)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(inverse(X_56),least_upper_bound(X_55,X_56)))),bind(Y0,$fot(least_upper_bound(identity,multiply(inverse(X_56),X_55))))]]) ).
cnf(refute_0_2788,plain,
least_upper_bound(identity,multiply(inverse(X_56),X_55)) = multiply(inverse(X_56),least_upper_bound(X_55,X_56)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_56),least_upper_bound(X_55,X_56)),least_upper_bound(identity,multiply(inverse(X_56),X_55))) )],[refute_0_2786,refute_0_2787]) ).
cnf(refute_0_2789,plain,
( greatest_lower_bound(identity,least_upper_bound(identity,multiply(inverse(X_56),X_55))) != identity
| least_upper_bound(identity,multiply(inverse(X_56),X_55)) != multiply(inverse(X_56),least_upper_bound(X_55,X_56))
| greatest_lower_bound(identity,multiply(inverse(X_56),least_upper_bound(X_55,X_56))) = identity ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(identity,multiply(inverse(X_56),X_55))),identity) ),[0,1],$fot(multiply(inverse(X_56),least_upper_bound(X_55,X_56)))]]) ).
cnf(refute_0_2790,plain,
( greatest_lower_bound(identity,least_upper_bound(identity,multiply(inverse(X_56),X_55))) != identity
| greatest_lower_bound(identity,multiply(inverse(X_56),least_upper_bound(X_55,X_56))) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(X_56),X_55)),multiply(inverse(X_56),least_upper_bound(X_55,X_56))) )],[refute_0_2788,refute_0_2789]) ).
cnf(refute_0_2791,plain,
greatest_lower_bound(identity,multiply(inverse(X_56),least_upper_bound(X_55,X_56))) = identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(identity,multiply(inverse(X_56),X_55))),identity) )],[refute_0_2785,refute_0_2790]) ).
cnf(refute_0_2792,plain,
greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_11,X_63)),least_upper_bound(X_63,greatest_lower_bound(X_11,X_63)))) = identity,
inference(subst,[],[refute_0_2791:[bind(X_55,$fot(X_63)),bind(X_56,$fot(greatest_lower_bound(X_11,X_63)))]]) ).
cnf(refute_0_2793,plain,
least_upper_bound(X_63,greatest_lower_bound(X_11,X_63)) = X_63,
inference(subst,[],[refute_0_145:[bind(X_10,$fot(X_63))]]) ).
cnf(refute_0_2794,plain,
( greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_11,X_63)),least_upper_bound(X_63,greatest_lower_bound(X_11,X_63)))) != identity
| least_upper_bound(X_63,greatest_lower_bound(X_11,X_63)) != X_63
| greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_11,X_63)),X_63)) = identity ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_11,X_63)),least_upper_bound(X_63,greatest_lower_bound(X_11,X_63)))),identity) ),[0,1,1],$fot(X_63)]]) ).
cnf(refute_0_2795,plain,
( greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_11,X_63)),least_upper_bound(X_63,greatest_lower_bound(X_11,X_63)))) != identity
| greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_11,X_63)),X_63)) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_63,greatest_lower_bound(X_11,X_63)),X_63) )],[refute_0_2793,refute_0_2794]) ).
cnf(refute_0_2796,plain,
greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_11,X_63)),X_63)) = identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_11,X_63)),least_upper_bound(X_63,greatest_lower_bound(X_11,X_63)))),identity) )],[refute_0_2792,refute_0_2795]) ).
cnf(refute_0_2797,plain,
greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_11,inverse(X_221))),inverse(X_221))) = identity,
inference(subst,[],[refute_0_2796:[bind(X_63,$fot(inverse(X_221)))]]) ).
cnf(refute_0_2798,plain,
( X_221 != multiply(inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_11,inverse(X_221))),inverse(X_221)))),greatest_lower_bound(inverse(greatest_lower_bound(X_11,inverse(X_221))),X_221))
| greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_11,inverse(X_221))),inverse(X_221))) != identity
| X_221 = multiply(inverse(identity),greatest_lower_bound(inverse(greatest_lower_bound(X_11,inverse(X_221))),X_221)) ),
introduced(tautology,[equality,[$cnf( $equal(X_221,multiply(inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_11,inverse(X_221))),inverse(X_221)))),greatest_lower_bound(inverse(greatest_lower_bound(X_11,inverse(X_221))),X_221))) ),[1,0,0],$fot(identity)]]) ).
cnf(refute_0_2799,plain,
( X_221 != multiply(inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_11,inverse(X_221))),inverse(X_221)))),greatest_lower_bound(inverse(greatest_lower_bound(X_11,inverse(X_221))),X_221))
| X_221 = multiply(inverse(identity),greatest_lower_bound(inverse(greatest_lower_bound(X_11,inverse(X_221))),X_221)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_11,inverse(X_221))),inverse(X_221))),identity) )],[refute_0_2797,refute_0_2798]) ).
cnf(refute_0_2800,plain,
X_221 = multiply(inverse(identity),greatest_lower_bound(inverse(greatest_lower_bound(X_11,inverse(X_221))),X_221)),
inference(resolve,[$cnf( $equal(X_221,multiply(inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_11,inverse(X_221))),inverse(X_221)))),greatest_lower_bound(inverse(greatest_lower_bound(X_11,inverse(X_221))),X_221))) )],[refute_0_2784,refute_0_2799]) ).
cnf(refute_0_2801,plain,
multiply(identity,greatest_lower_bound(X_221,inverse(greatest_lower_bound(X_11,inverse(X_221))))) = greatest_lower_bound(X_221,inverse(greatest_lower_bound(X_11,inverse(X_221)))),
inference(subst,[],[left_identity:[bind(X,$fot(greatest_lower_bound(X_221,inverse(greatest_lower_bound(X_11,inverse(X_221))))))]]) ).
cnf(refute_0_2802,plain,
multiply(inverse(identity),greatest_lower_bound(X_221,inverse(greatest_lower_bound(X_11,inverse(X_221))))) = multiply(inverse(identity),greatest_lower_bound(X_221,inverse(greatest_lower_bound(X_11,inverse(X_221))))),
introduced(tautology,[refl,[$fot(multiply(inverse(identity),greatest_lower_bound(X_221,inverse(greatest_lower_bound(X_11,inverse(X_221))))))]]) ).
cnf(refute_0_2803,plain,
( multiply(inverse(identity),greatest_lower_bound(X_221,inverse(greatest_lower_bound(X_11,inverse(X_221))))) != multiply(inverse(identity),greatest_lower_bound(X_221,inverse(greatest_lower_bound(X_11,inverse(X_221)))))
| inverse(identity) != identity
| multiply(inverse(identity),greatest_lower_bound(X_221,inverse(greatest_lower_bound(X_11,inverse(X_221))))) = multiply(identity,greatest_lower_bound(X_221,inverse(greatest_lower_bound(X_11,inverse(X_221))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(identity),greatest_lower_bound(X_221,inverse(greatest_lower_bound(X_11,inverse(X_221))))),multiply(inverse(identity),greatest_lower_bound(X_221,inverse(greatest_lower_bound(X_11,inverse(X_221)))))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_2804,plain,
( inverse(identity) != identity
| multiply(inverse(identity),greatest_lower_bound(X_221,inverse(greatest_lower_bound(X_11,inverse(X_221))))) = multiply(identity,greatest_lower_bound(X_221,inverse(greatest_lower_bound(X_11,inverse(X_221))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),greatest_lower_bound(X_221,inverse(greatest_lower_bound(X_11,inverse(X_221))))),multiply(inverse(identity),greatest_lower_bound(X_221,inverse(greatest_lower_bound(X_11,inverse(X_221)))))) )],[refute_0_2802,refute_0_2803]) ).
cnf(refute_0_2805,plain,
multiply(inverse(identity),greatest_lower_bound(X_221,inverse(greatest_lower_bound(X_11,inverse(X_221))))) = multiply(identity,greatest_lower_bound(X_221,inverse(greatest_lower_bound(X_11,inverse(X_221))))),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_1763,refute_0_2804]) ).
cnf(refute_0_2806,plain,
( multiply(identity,greatest_lower_bound(X_221,inverse(greatest_lower_bound(X_11,inverse(X_221))))) != greatest_lower_bound(X_221,inverse(greatest_lower_bound(X_11,inverse(X_221))))
| multiply(inverse(identity),greatest_lower_bound(X_221,inverse(greatest_lower_bound(X_11,inverse(X_221))))) != multiply(identity,greatest_lower_bound(X_221,inverse(greatest_lower_bound(X_11,inverse(X_221)))))
| multiply(inverse(identity),greatest_lower_bound(X_221,inverse(greatest_lower_bound(X_11,inverse(X_221))))) = greatest_lower_bound(X_221,inverse(greatest_lower_bound(X_11,inverse(X_221)))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(inverse(identity),greatest_lower_bound(X_221,inverse(greatest_lower_bound(X_11,inverse(X_221))))))),bind(Y0,$fot(multiply(identity,greatest_lower_bound(X_221,inverse(greatest_lower_bound(X_11,inverse(X_221))))))),bind(Z0,$fot(greatest_lower_bound(X_221,inverse(greatest_lower_bound(X_11,inverse(X_221))))))]]) ).
cnf(refute_0_2807,plain,
( multiply(identity,greatest_lower_bound(X_221,inverse(greatest_lower_bound(X_11,inverse(X_221))))) != greatest_lower_bound(X_221,inverse(greatest_lower_bound(X_11,inverse(X_221))))
| multiply(inverse(identity),greatest_lower_bound(X_221,inverse(greatest_lower_bound(X_11,inverse(X_221))))) = greatest_lower_bound(X_221,inverse(greatest_lower_bound(X_11,inverse(X_221)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),greatest_lower_bound(X_221,inverse(greatest_lower_bound(X_11,inverse(X_221))))),multiply(identity,greatest_lower_bound(X_221,inverse(greatest_lower_bound(X_11,inverse(X_221)))))) )],[refute_0_2805,refute_0_2806]) ).
cnf(refute_0_2808,plain,
multiply(inverse(identity),greatest_lower_bound(X_221,inverse(greatest_lower_bound(X_11,inverse(X_221))))) = greatest_lower_bound(X_221,inverse(greatest_lower_bound(X_11,inverse(X_221)))),
inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(X_221,inverse(greatest_lower_bound(X_11,inverse(X_221))))),greatest_lower_bound(X_221,inverse(greatest_lower_bound(X_11,inverse(X_221))))) )],[refute_0_2801,refute_0_2807]) ).
cnf(refute_0_2809,plain,
multiply(inverse(identity),greatest_lower_bound(inverse(greatest_lower_bound(X_11,inverse(X_221))),X_221)) = multiply(inverse(identity),greatest_lower_bound(X_221,inverse(greatest_lower_bound(X_11,inverse(X_221))))),
inference(subst,[],[refute_0_411:[bind(X_104,$fot(inverse(identity))),bind(X_105,$fot(X_221)),bind(X_106,$fot(inverse(greatest_lower_bound(X_11,inverse(X_221)))))]]) ).
cnf(refute_0_2810,plain,
( multiply(inverse(identity),greatest_lower_bound(X_221,inverse(greatest_lower_bound(X_11,inverse(X_221))))) != greatest_lower_bound(X_221,inverse(greatest_lower_bound(X_11,inverse(X_221))))
| multiply(inverse(identity),greatest_lower_bound(inverse(greatest_lower_bound(X_11,inverse(X_221))),X_221)) != multiply(inverse(identity),greatest_lower_bound(X_221,inverse(greatest_lower_bound(X_11,inverse(X_221)))))
| multiply(inverse(identity),greatest_lower_bound(inverse(greatest_lower_bound(X_11,inverse(X_221))),X_221)) = greatest_lower_bound(X_221,inverse(greatest_lower_bound(X_11,inverse(X_221)))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(inverse(identity),greatest_lower_bound(inverse(greatest_lower_bound(X_11,inverse(X_221))),X_221)))),bind(Y0,$fot(multiply(inverse(identity),greatest_lower_bound(X_221,inverse(greatest_lower_bound(X_11,inverse(X_221))))))),bind(Z0,$fot(greatest_lower_bound(X_221,inverse(greatest_lower_bound(X_11,inverse(X_221))))))]]) ).
cnf(refute_0_2811,plain,
( multiply(inverse(identity),greatest_lower_bound(X_221,inverse(greatest_lower_bound(X_11,inverse(X_221))))) != greatest_lower_bound(X_221,inverse(greatest_lower_bound(X_11,inverse(X_221))))
| multiply(inverse(identity),greatest_lower_bound(inverse(greatest_lower_bound(X_11,inverse(X_221))),X_221)) = greatest_lower_bound(X_221,inverse(greatest_lower_bound(X_11,inverse(X_221)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),greatest_lower_bound(inverse(greatest_lower_bound(X_11,inverse(X_221))),X_221)),multiply(inverse(identity),greatest_lower_bound(X_221,inverse(greatest_lower_bound(X_11,inverse(X_221)))))) )],[refute_0_2809,refute_0_2810]) ).
cnf(refute_0_2812,plain,
multiply(inverse(identity),greatest_lower_bound(inverse(greatest_lower_bound(X_11,inverse(X_221))),X_221)) = greatest_lower_bound(X_221,inverse(greatest_lower_bound(X_11,inverse(X_221)))),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),greatest_lower_bound(X_221,inverse(greatest_lower_bound(X_11,inverse(X_221))))),greatest_lower_bound(X_221,inverse(greatest_lower_bound(X_11,inverse(X_221))))) )],[refute_0_2808,refute_0_2811]) ).
cnf(refute_0_2813,plain,
( X_221 != multiply(inverse(identity),greatest_lower_bound(inverse(greatest_lower_bound(X_11,inverse(X_221))),X_221))
| multiply(inverse(identity),greatest_lower_bound(inverse(greatest_lower_bound(X_11,inverse(X_221))),X_221)) != greatest_lower_bound(X_221,inverse(greatest_lower_bound(X_11,inverse(X_221))))
| X_221 = greatest_lower_bound(X_221,inverse(greatest_lower_bound(X_11,inverse(X_221)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_221,greatest_lower_bound(X_221,inverse(greatest_lower_bound(X_11,inverse(X_221))))) ),[0],$fot(multiply(inverse(identity),greatest_lower_bound(inverse(greatest_lower_bound(X_11,inverse(X_221))),X_221)))]]) ).
cnf(refute_0_2814,plain,
( X_221 != multiply(inverse(identity),greatest_lower_bound(inverse(greatest_lower_bound(X_11,inverse(X_221))),X_221))
| X_221 = greatest_lower_bound(X_221,inverse(greatest_lower_bound(X_11,inverse(X_221)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),greatest_lower_bound(inverse(greatest_lower_bound(X_11,inverse(X_221))),X_221)),greatest_lower_bound(X_221,inverse(greatest_lower_bound(X_11,inverse(X_221))))) )],[refute_0_2812,refute_0_2813]) ).
cnf(refute_0_2815,plain,
X_221 = greatest_lower_bound(X_221,inverse(greatest_lower_bound(X_11,inverse(X_221)))),
inference(resolve,[$cnf( $equal(X_221,multiply(inverse(identity),greatest_lower_bound(inverse(greatest_lower_bound(X_11,inverse(X_221))),X_221))) )],[refute_0_2800,refute_0_2814]) ).
cnf(refute_0_2816,plain,
least_upper_bound(X_163,identity) = greatest_lower_bound(least_upper_bound(X_163,identity),inverse(greatest_lower_bound(X_222,inverse(least_upper_bound(X_163,identity))))),
inference(subst,[],[refute_0_2815:[bind(X_11,$fot(X_222)),bind(X_221,$fot(least_upper_bound(X_163,identity)))]]) ).
cnf(refute_0_2817,plain,
( least_upper_bound(X_163,identity) != greatest_lower_bound(least_upper_bound(X_163,identity),inverse(greatest_lower_bound(X_222,inverse(least_upper_bound(X_163,identity)))))
| greatest_lower_bound(least_upper_bound(X_163,identity),inverse(greatest_lower_bound(X_222,inverse(least_upper_bound(X_163,identity))))) = least_upper_bound(X_163,identity) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(least_upper_bound(X_163,identity))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(X_163,identity),inverse(greatest_lower_bound(X_222,inverse(least_upper_bound(X_163,identity)))))))]]) ).
cnf(refute_0_2818,plain,
greatest_lower_bound(least_upper_bound(X_163,identity),inverse(greatest_lower_bound(X_222,inverse(least_upper_bound(X_163,identity))))) = least_upper_bound(X_163,identity),
inference(resolve,[$cnf( $equal(least_upper_bound(X_163,identity),greatest_lower_bound(least_upper_bound(X_163,identity),inverse(greatest_lower_bound(X_222,inverse(least_upper_bound(X_163,identity)))))) )],[refute_0_2816,refute_0_2817]) ).
cnf(refute_0_2819,plain,
( greatest_lower_bound(least_upper_bound(X_163,identity),inverse(greatest_lower_bound(X_222,inverse(least_upper_bound(X_163,identity))))) != greatest_lower_bound(least_upper_bound(identity,X_163),inverse(greatest_lower_bound(X_222,inverse(least_upper_bound(X_163,identity)))))
| greatest_lower_bound(least_upper_bound(X_163,identity),inverse(greatest_lower_bound(X_222,inverse(least_upper_bound(X_163,identity))))) != least_upper_bound(X_163,identity)
| least_upper_bound(X_163,identity) = greatest_lower_bound(least_upper_bound(identity,X_163),inverse(greatest_lower_bound(X_222,inverse(least_upper_bound(X_163,identity))))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_163,identity),inverse(greatest_lower_bound(X_222,inverse(least_upper_bound(X_163,identity))))),greatest_lower_bound(least_upper_bound(identity,X_163),inverse(greatest_lower_bound(X_222,inverse(least_upper_bound(X_163,identity)))))) ),[0],$fot(least_upper_bound(X_163,identity))]]) ).
cnf(refute_0_2820,plain,
( greatest_lower_bound(least_upper_bound(X_163,identity),inverse(greatest_lower_bound(X_222,inverse(least_upper_bound(X_163,identity))))) != greatest_lower_bound(least_upper_bound(identity,X_163),inverse(greatest_lower_bound(X_222,inverse(least_upper_bound(X_163,identity)))))
| least_upper_bound(X_163,identity) = greatest_lower_bound(least_upper_bound(identity,X_163),inverse(greatest_lower_bound(X_222,inverse(least_upper_bound(X_163,identity))))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_163,identity),inverse(greatest_lower_bound(X_222,inverse(least_upper_bound(X_163,identity))))),least_upper_bound(X_163,identity)) )],[refute_0_2818,refute_0_2819]) ).
cnf(refute_0_2821,plain,
least_upper_bound(X_163,identity) = greatest_lower_bound(least_upper_bound(identity,X_163),inverse(greatest_lower_bound(X_222,inverse(least_upper_bound(X_163,identity))))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_163,identity),inverse(greatest_lower_bound(X_222,inverse(least_upper_bound(X_163,identity))))),greatest_lower_bound(least_upper_bound(identity,X_163),inverse(greatest_lower_bound(X_222,inverse(least_upper_bound(X_163,identity)))))) )],[refute_0_2775,refute_0_2820]) ).
cnf(refute_0_2822,plain,
least_upper_bound(X_228,X_229) = greatest_lower_bound(least_upper_bound(X_228,X_229),inverse(greatest_lower_bound(X_11,inverse(least_upper_bound(X_228,X_229))))),
inference(subst,[],[refute_0_2815:[bind(X_221,$fot(least_upper_bound(X_228,X_229)))]]) ).
cnf(refute_0_2823,plain,
inverse(least_upper_bound(X_226,X_227)) = multiply(inverse(multiply(inverse(least_upper_bound(identity,multiply(X_226,inverse(X_227)))),least_upper_bound(X_226,X_227))),inverse(least_upper_bound(identity,multiply(X_226,inverse(X_227))))),
inference(subst,[],[refute_0_96:[bind(X_45,$fot(inverse(least_upper_bound(identity,multiply(X_226,inverse(X_227)))))),bind(X_46,$fot(least_upper_bound(X_226,X_227)))]]) ).
cnf(refute_0_2824,plain,
inverse(inverse(X_69)) = multiply(inverse(multiply(least_upper_bound(X_68,X_69),inverse(X_69))),least_upper_bound(X_68,X_69)),
inference(subst,[],[refute_0_96:[bind(X_45,$fot(least_upper_bound(X_68,X_69))),bind(X_46,$fot(inverse(X_69)))]]) ).
cnf(refute_0_2825,plain,
( multiply(least_upper_bound(X_68,X_69),inverse(X_69)) != least_upper_bound(identity,multiply(X_68,inverse(X_69)))
| inverse(inverse(X_69)) != multiply(inverse(multiply(least_upper_bound(X_68,X_69),inverse(X_69))),least_upper_bound(X_68,X_69))
| inverse(inverse(X_69)) = multiply(inverse(least_upper_bound(identity,multiply(X_68,inverse(X_69)))),least_upper_bound(X_68,X_69)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_69)),multiply(inverse(multiply(least_upper_bound(X_68,X_69),inverse(X_69))),least_upper_bound(X_68,X_69))) ),[1,0,0],$fot(least_upper_bound(identity,multiply(X_68,inverse(X_69))))]]) ).
cnf(refute_0_2826,plain,
( inverse(inverse(X_69)) != multiply(inverse(multiply(least_upper_bound(X_68,X_69),inverse(X_69))),least_upper_bound(X_68,X_69))
| inverse(inverse(X_69)) = multiply(inverse(least_upper_bound(identity,multiply(X_68,inverse(X_69)))),least_upper_bound(X_68,X_69)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_68,X_69),inverse(X_69)),least_upper_bound(identity,multiply(X_68,inverse(X_69)))) )],[refute_0_780,refute_0_2825]) ).
cnf(refute_0_2827,plain,
inverse(inverse(X_69)) = multiply(inverse(least_upper_bound(identity,multiply(X_68,inverse(X_69)))),least_upper_bound(X_68,X_69)),
inference(resolve,[$cnf( $equal(inverse(inverse(X_69)),multiply(inverse(multiply(least_upper_bound(X_68,X_69),inverse(X_69))),least_upper_bound(X_68,X_69))) )],[refute_0_2824,refute_0_2826]) ).
cnf(refute_0_2828,plain,
inverse(inverse(X_69)) = X_69,
inference(subst,[],[refute_0_452:[bind(X_35,$fot(X_69))]]) ).
cnf(refute_0_2829,plain,
( inverse(inverse(X_69)) != X_69
| inverse(inverse(X_69)) != multiply(inverse(least_upper_bound(identity,multiply(X_68,inverse(X_69)))),least_upper_bound(X_68,X_69))
| X_69 = multiply(inverse(least_upper_bound(identity,multiply(X_68,inverse(X_69)))),least_upper_bound(X_68,X_69)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_69)),multiply(inverse(least_upper_bound(identity,multiply(X_68,inverse(X_69)))),least_upper_bound(X_68,X_69))) ),[0],$fot(X_69)]]) ).
cnf(refute_0_2830,plain,
( inverse(inverse(X_69)) != multiply(inverse(least_upper_bound(identity,multiply(X_68,inverse(X_69)))),least_upper_bound(X_68,X_69))
| X_69 = multiply(inverse(least_upper_bound(identity,multiply(X_68,inverse(X_69)))),least_upper_bound(X_68,X_69)) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_69)),X_69) )],[refute_0_2828,refute_0_2829]) ).
cnf(refute_0_2831,plain,
X_69 = multiply(inverse(least_upper_bound(identity,multiply(X_68,inverse(X_69)))),least_upper_bound(X_68,X_69)),
inference(resolve,[$cnf( $equal(inverse(inverse(X_69)),multiply(inverse(least_upper_bound(identity,multiply(X_68,inverse(X_69)))),least_upper_bound(X_68,X_69))) )],[refute_0_2827,refute_0_2830]) ).
cnf(refute_0_2832,plain,
X_227 = multiply(inverse(least_upper_bound(identity,multiply(X_226,inverse(X_227)))),least_upper_bound(X_226,X_227)),
inference(subst,[],[refute_0_2831:[bind(X_68,$fot(X_226)),bind(X_69,$fot(X_227))]]) ).
cnf(refute_0_2833,plain,
( X_227 != multiply(inverse(least_upper_bound(identity,multiply(X_226,inverse(X_227)))),least_upper_bound(X_226,X_227))
| multiply(inverse(least_upper_bound(identity,multiply(X_226,inverse(X_227)))),least_upper_bound(X_226,X_227)) = X_227 ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(X_227)),bind(Y0,$fot(multiply(inverse(least_upper_bound(identity,multiply(X_226,inverse(X_227)))),least_upper_bound(X_226,X_227))))]]) ).
cnf(refute_0_2834,plain,
multiply(inverse(least_upper_bound(identity,multiply(X_226,inverse(X_227)))),least_upper_bound(X_226,X_227)) = X_227,
inference(resolve,[$cnf( $equal(X_227,multiply(inverse(least_upper_bound(identity,multiply(X_226,inverse(X_227)))),least_upper_bound(X_226,X_227))) )],[refute_0_2832,refute_0_2833]) ).
cnf(refute_0_2835,plain,
( multiply(inverse(least_upper_bound(identity,multiply(X_226,inverse(X_227)))),least_upper_bound(X_226,X_227)) != X_227
| inverse(least_upper_bound(X_226,X_227)) != multiply(inverse(multiply(inverse(least_upper_bound(identity,multiply(X_226,inverse(X_227)))),least_upper_bound(X_226,X_227))),inverse(least_upper_bound(identity,multiply(X_226,inverse(X_227)))))
| inverse(least_upper_bound(X_226,X_227)) = multiply(inverse(X_227),inverse(least_upper_bound(identity,multiply(X_226,inverse(X_227))))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_226,X_227)),multiply(inverse(multiply(inverse(least_upper_bound(identity,multiply(X_226,inverse(X_227)))),least_upper_bound(X_226,X_227))),inverse(least_upper_bound(identity,multiply(X_226,inverse(X_227)))))) ),[1,0,0],$fot(X_227)]]) ).
cnf(refute_0_2836,plain,
( inverse(least_upper_bound(X_226,X_227)) != multiply(inverse(multiply(inverse(least_upper_bound(identity,multiply(X_226,inverse(X_227)))),least_upper_bound(X_226,X_227))),inverse(least_upper_bound(identity,multiply(X_226,inverse(X_227)))))
| inverse(least_upper_bound(X_226,X_227)) = multiply(inverse(X_227),inverse(least_upper_bound(identity,multiply(X_226,inverse(X_227))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,multiply(X_226,inverse(X_227)))),least_upper_bound(X_226,X_227)),X_227) )],[refute_0_2834,refute_0_2835]) ).
cnf(refute_0_2837,plain,
inverse(least_upper_bound(X_226,X_227)) = multiply(inverse(X_227),inverse(least_upper_bound(identity,multiply(X_226,inverse(X_227))))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_226,X_227)),multiply(inverse(multiply(inverse(least_upper_bound(identity,multiply(X_226,inverse(X_227)))),least_upper_bound(X_226,X_227))),inverse(least_upper_bound(identity,multiply(X_226,inverse(X_227)))))) )],[refute_0_2823,refute_0_2836]) ).
cnf(refute_0_2838,plain,
least_upper_bound(X_224,X_225) = multiply(inverse(inverse(least_upper_bound(identity,multiply(X_225,inverse(X_224))))),multiply(inverse(least_upper_bound(identity,multiply(X_225,inverse(X_224)))),least_upper_bound(X_224,X_225))),
inference(subst,[],[refute_0_9:[bind(X_30,$fot(inverse(least_upper_bound(identity,multiply(X_225,inverse(X_224)))))),bind(X_31,$fot(least_upper_bound(X_224,X_225)))]]) ).
cnf(refute_0_2839,plain,
inverse(inverse(X_68)) = multiply(inverse(multiply(least_upper_bound(X_68,X_69),inverse(X_68))),least_upper_bound(X_68,X_69)),
inference(subst,[],[refute_0_96:[bind(X_45,$fot(least_upper_bound(X_68,X_69))),bind(X_46,$fot(inverse(X_68)))]]) ).
cnf(refute_0_2840,plain,
( multiply(least_upper_bound(X_68,X_69),inverse(X_68)) != least_upper_bound(identity,multiply(X_69,inverse(X_68)))
| inverse(inverse(X_68)) != multiply(inverse(multiply(least_upper_bound(X_68,X_69),inverse(X_68))),least_upper_bound(X_68,X_69))
| inverse(inverse(X_68)) = multiply(inverse(least_upper_bound(identity,multiply(X_69,inverse(X_68)))),least_upper_bound(X_68,X_69)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_68)),multiply(inverse(multiply(least_upper_bound(X_68,X_69),inverse(X_68))),least_upper_bound(X_68,X_69))) ),[1,0,0],$fot(least_upper_bound(identity,multiply(X_69,inverse(X_68))))]]) ).
cnf(refute_0_2841,plain,
( inverse(inverse(X_68)) != multiply(inverse(multiply(least_upper_bound(X_68,X_69),inverse(X_68))),least_upper_bound(X_68,X_69))
| inverse(inverse(X_68)) = multiply(inverse(least_upper_bound(identity,multiply(X_69,inverse(X_68)))),least_upper_bound(X_68,X_69)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_68,X_69),inverse(X_68)),least_upper_bound(identity,multiply(X_69,inverse(X_68)))) )],[refute_0_1189,refute_0_2840]) ).
cnf(refute_0_2842,plain,
inverse(inverse(X_68)) = multiply(inverse(least_upper_bound(identity,multiply(X_69,inverse(X_68)))),least_upper_bound(X_68,X_69)),
inference(resolve,[$cnf( $equal(inverse(inverse(X_68)),multiply(inverse(multiply(least_upper_bound(X_68,X_69),inverse(X_68))),least_upper_bound(X_68,X_69))) )],[refute_0_2839,refute_0_2841]) ).
cnf(refute_0_2843,plain,
inverse(inverse(X_68)) = X_68,
inference(subst,[],[refute_0_452:[bind(X_35,$fot(X_68))]]) ).
cnf(refute_0_2844,plain,
( inverse(inverse(X_68)) != X_68
| inverse(inverse(X_68)) != multiply(inverse(least_upper_bound(identity,multiply(X_69,inverse(X_68)))),least_upper_bound(X_68,X_69))
| X_68 = multiply(inverse(least_upper_bound(identity,multiply(X_69,inverse(X_68)))),least_upper_bound(X_68,X_69)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_68)),multiply(inverse(least_upper_bound(identity,multiply(X_69,inverse(X_68)))),least_upper_bound(X_68,X_69))) ),[0],$fot(X_68)]]) ).
cnf(refute_0_2845,plain,
( inverse(inverse(X_68)) != multiply(inverse(least_upper_bound(identity,multiply(X_69,inverse(X_68)))),least_upper_bound(X_68,X_69))
| X_68 = multiply(inverse(least_upper_bound(identity,multiply(X_69,inverse(X_68)))),least_upper_bound(X_68,X_69)) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_68)),X_68) )],[refute_0_2843,refute_0_2844]) ).
cnf(refute_0_2846,plain,
X_68 = multiply(inverse(least_upper_bound(identity,multiply(X_69,inverse(X_68)))),least_upper_bound(X_68,X_69)),
inference(resolve,[$cnf( $equal(inverse(inverse(X_68)),multiply(inverse(least_upper_bound(identity,multiply(X_69,inverse(X_68)))),least_upper_bound(X_68,X_69))) )],[refute_0_2842,refute_0_2845]) ).
cnf(refute_0_2847,plain,
X_224 = multiply(inverse(least_upper_bound(identity,multiply(X_225,inverse(X_224)))),least_upper_bound(X_224,X_225)),
inference(subst,[],[refute_0_2846:[bind(X_68,$fot(X_224)),bind(X_69,$fot(X_225))]]) ).
cnf(refute_0_2848,plain,
( X_224 != multiply(inverse(least_upper_bound(identity,multiply(X_225,inverse(X_224)))),least_upper_bound(X_224,X_225))
| multiply(inverse(least_upper_bound(identity,multiply(X_225,inverse(X_224)))),least_upper_bound(X_224,X_225)) = X_224 ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(X_224)),bind(Y0,$fot(multiply(inverse(least_upper_bound(identity,multiply(X_225,inverse(X_224)))),least_upper_bound(X_224,X_225))))]]) ).
cnf(refute_0_2849,plain,
multiply(inverse(least_upper_bound(identity,multiply(X_225,inverse(X_224)))),least_upper_bound(X_224,X_225)) = X_224,
inference(resolve,[$cnf( $equal(X_224,multiply(inverse(least_upper_bound(identity,multiply(X_225,inverse(X_224)))),least_upper_bound(X_224,X_225))) )],[refute_0_2847,refute_0_2848]) ).
cnf(refute_0_2850,plain,
( multiply(inverse(least_upper_bound(identity,multiply(X_225,inverse(X_224)))),least_upper_bound(X_224,X_225)) != X_224
| least_upper_bound(X_224,X_225) != multiply(inverse(inverse(least_upper_bound(identity,multiply(X_225,inverse(X_224))))),multiply(inverse(least_upper_bound(identity,multiply(X_225,inverse(X_224)))),least_upper_bound(X_224,X_225)))
| least_upper_bound(X_224,X_225) = multiply(inverse(inverse(least_upper_bound(identity,multiply(X_225,inverse(X_224))))),X_224) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_224,X_225),multiply(inverse(inverse(least_upper_bound(identity,multiply(X_225,inverse(X_224))))),multiply(inverse(least_upper_bound(identity,multiply(X_225,inverse(X_224)))),least_upper_bound(X_224,X_225)))) ),[1,1],$fot(X_224)]]) ).
cnf(refute_0_2851,plain,
( least_upper_bound(X_224,X_225) != multiply(inverse(inverse(least_upper_bound(identity,multiply(X_225,inverse(X_224))))),multiply(inverse(least_upper_bound(identity,multiply(X_225,inverse(X_224)))),least_upper_bound(X_224,X_225)))
| least_upper_bound(X_224,X_225) = multiply(inverse(inverse(least_upper_bound(identity,multiply(X_225,inverse(X_224))))),X_224) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,multiply(X_225,inverse(X_224)))),least_upper_bound(X_224,X_225)),X_224) )],[refute_0_2849,refute_0_2850]) ).
cnf(refute_0_2852,plain,
least_upper_bound(X_224,X_225) = multiply(inverse(inverse(least_upper_bound(identity,multiply(X_225,inverse(X_224))))),X_224),
inference(resolve,[$cnf( $equal(least_upper_bound(X_224,X_225),multiply(inverse(inverse(least_upper_bound(identity,multiply(X_225,inverse(X_224))))),multiply(inverse(least_upper_bound(identity,multiply(X_225,inverse(X_224)))),least_upper_bound(X_224,X_225)))) )],[refute_0_2838,refute_0_2851]) ).
cnf(refute_0_2853,plain,
inverse(inverse(least_upper_bound(identity,multiply(X_225,inverse(X_224))))) = least_upper_bound(identity,multiply(X_225,inverse(X_224))),
inference(subst,[],[refute_0_452:[bind(X_35,$fot(least_upper_bound(identity,multiply(X_225,inverse(X_224)))))]]) ).
cnf(refute_0_2854,plain,
multiply(inverse(inverse(least_upper_bound(identity,multiply(X_225,inverse(X_224))))),X_224) = multiply(inverse(inverse(least_upper_bound(identity,multiply(X_225,inverse(X_224))))),X_224),
introduced(tautology,[refl,[$fot(multiply(inverse(inverse(least_upper_bound(identity,multiply(X_225,inverse(X_224))))),X_224))]]) ).
cnf(refute_0_2855,plain,
( multiply(inverse(inverse(least_upper_bound(identity,multiply(X_225,inverse(X_224))))),X_224) != multiply(inverse(inverse(least_upper_bound(identity,multiply(X_225,inverse(X_224))))),X_224)
| inverse(inverse(least_upper_bound(identity,multiply(X_225,inverse(X_224))))) != least_upper_bound(identity,multiply(X_225,inverse(X_224)))
| multiply(inverse(inverse(least_upper_bound(identity,multiply(X_225,inverse(X_224))))),X_224) = multiply(least_upper_bound(identity,multiply(X_225,inverse(X_224))),X_224) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(identity,multiply(X_225,inverse(X_224))))),X_224),multiply(inverse(inverse(least_upper_bound(identity,multiply(X_225,inverse(X_224))))),X_224)) ),[1,0],$fot(least_upper_bound(identity,multiply(X_225,inverse(X_224))))]]) ).
cnf(refute_0_2856,plain,
( inverse(inverse(least_upper_bound(identity,multiply(X_225,inverse(X_224))))) != least_upper_bound(identity,multiply(X_225,inverse(X_224)))
| multiply(inverse(inverse(least_upper_bound(identity,multiply(X_225,inverse(X_224))))),X_224) = multiply(least_upper_bound(identity,multiply(X_225,inverse(X_224))),X_224) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(identity,multiply(X_225,inverse(X_224))))),X_224),multiply(inverse(inverse(least_upper_bound(identity,multiply(X_225,inverse(X_224))))),X_224)) )],[refute_0_2854,refute_0_2855]) ).
cnf(refute_0_2857,plain,
multiply(inverse(inverse(least_upper_bound(identity,multiply(X_225,inverse(X_224))))),X_224) = multiply(least_upper_bound(identity,multiply(X_225,inverse(X_224))),X_224),
inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(identity,multiply(X_225,inverse(X_224))))),least_upper_bound(identity,multiply(X_225,inverse(X_224)))) )],[refute_0_2853,refute_0_2856]) ).
cnf(refute_0_2858,plain,
( multiply(inverse(inverse(least_upper_bound(identity,multiply(X_225,inverse(X_224))))),X_224) != multiply(least_upper_bound(identity,multiply(X_225,inverse(X_224))),X_224)
| least_upper_bound(X_224,X_225) != multiply(inverse(inverse(least_upper_bound(identity,multiply(X_225,inverse(X_224))))),X_224)
| least_upper_bound(X_224,X_225) = multiply(least_upper_bound(identity,multiply(X_225,inverse(X_224))),X_224) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_224,X_225),multiply(inverse(inverse(least_upper_bound(identity,multiply(X_225,inverse(X_224))))),X_224)) ),[1],$fot(multiply(least_upper_bound(identity,multiply(X_225,inverse(X_224))),X_224))]]) ).
cnf(refute_0_2859,plain,
( least_upper_bound(X_224,X_225) != multiply(inverse(inverse(least_upper_bound(identity,multiply(X_225,inverse(X_224))))),X_224)
| least_upper_bound(X_224,X_225) = multiply(least_upper_bound(identity,multiply(X_225,inverse(X_224))),X_224) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(identity,multiply(X_225,inverse(X_224))))),X_224),multiply(least_upper_bound(identity,multiply(X_225,inverse(X_224))),X_224)) )],[refute_0_2857,refute_0_2858]) ).
cnf(refute_0_2860,plain,
least_upper_bound(X_224,X_225) = multiply(least_upper_bound(identity,multiply(X_225,inverse(X_224))),X_224),
inference(resolve,[$cnf( $equal(least_upper_bound(X_224,X_225),multiply(inverse(inverse(least_upper_bound(identity,multiply(X_225,inverse(X_224))))),X_224)) )],[refute_0_2852,refute_0_2859]) ).
cnf(refute_0_2861,plain,
( least_upper_bound(X_224,X_225) != multiply(least_upper_bound(identity,multiply(X_225,inverse(X_224))),X_224)
| multiply(least_upper_bound(identity,multiply(X_225,inverse(X_224))),X_224) = least_upper_bound(X_224,X_225) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(least_upper_bound(X_224,X_225))),bind(Y0,$fot(multiply(least_upper_bound(identity,multiply(X_225,inverse(X_224))),X_224)))]]) ).
cnf(refute_0_2862,plain,
multiply(least_upper_bound(identity,multiply(X_225,inverse(X_224))),X_224) = least_upper_bound(X_224,X_225),
inference(resolve,[$cnf( $equal(least_upper_bound(X_224,X_225),multiply(least_upper_bound(identity,multiply(X_225,inverse(X_224))),X_224)) )],[refute_0_2860,refute_0_2861]) ).
cnf(refute_0_2863,plain,
multiply(least_upper_bound(identity,multiply(X_226,inverse(X_227))),X_227) = least_upper_bound(X_227,X_226),
inference(subst,[],[refute_0_2862:[bind(X_224,$fot(X_227)),bind(X_225,$fot(X_226))]]) ).
cnf(refute_0_2864,plain,
inverse(multiply(least_upper_bound(identity,multiply(X_226,inverse(X_227))),X_227)) = inverse(multiply(least_upper_bound(identity,multiply(X_226,inverse(X_227))),X_227)),
introduced(tautology,[refl,[$fot(inverse(multiply(least_upper_bound(identity,multiply(X_226,inverse(X_227))),X_227)))]]) ).
cnf(refute_0_2865,plain,
( multiply(least_upper_bound(identity,multiply(X_226,inverse(X_227))),X_227) != least_upper_bound(X_227,X_226)
| inverse(multiply(least_upper_bound(identity,multiply(X_226,inverse(X_227))),X_227)) != inverse(multiply(least_upper_bound(identity,multiply(X_226,inverse(X_227))),X_227))
| inverse(multiply(least_upper_bound(identity,multiply(X_226,inverse(X_227))),X_227)) = inverse(least_upper_bound(X_227,X_226)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(least_upper_bound(identity,multiply(X_226,inverse(X_227))),X_227)),inverse(multiply(least_upper_bound(identity,multiply(X_226,inverse(X_227))),X_227))) ),[1,0],$fot(least_upper_bound(X_227,X_226))]]) ).
cnf(refute_0_2866,plain,
( multiply(least_upper_bound(identity,multiply(X_226,inverse(X_227))),X_227) != least_upper_bound(X_227,X_226)
| inverse(multiply(least_upper_bound(identity,multiply(X_226,inverse(X_227))),X_227)) = inverse(least_upper_bound(X_227,X_226)) ),
inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(identity,multiply(X_226,inverse(X_227))),X_227)),inverse(multiply(least_upper_bound(identity,multiply(X_226,inverse(X_227))),X_227))) )],[refute_0_2864,refute_0_2865]) ).
cnf(refute_0_2867,plain,
inverse(multiply(least_upper_bound(identity,multiply(X_226,inverse(X_227))),X_227)) = inverse(least_upper_bound(X_227,X_226)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(X_226,inverse(X_227))),X_227),least_upper_bound(X_227,X_226)) )],[refute_0_2863,refute_0_2866]) ).
cnf(refute_0_2868,plain,
multiply(inverse(X_227),inverse(least_upper_bound(identity,multiply(X_226,inverse(X_227))))) = inverse(multiply(least_upper_bound(identity,multiply(X_226,inverse(X_227))),X_227)),
inference(subst,[],[refute_0_490:[bind(X_30,$fot(least_upper_bound(identity,multiply(X_226,inverse(X_227))))),bind(X_31,$fot(X_227))]]) ).
cnf(refute_0_2869,plain,
( multiply(inverse(X_227),inverse(least_upper_bound(identity,multiply(X_226,inverse(X_227))))) != inverse(multiply(least_upper_bound(identity,multiply(X_226,inverse(X_227))),X_227))
| inverse(multiply(least_upper_bound(identity,multiply(X_226,inverse(X_227))),X_227)) != inverse(least_upper_bound(X_227,X_226))
| multiply(inverse(X_227),inverse(least_upper_bound(identity,multiply(X_226,inverse(X_227))))) = inverse(least_upper_bound(X_227,X_226)) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(inverse(X_227),inverse(least_upper_bound(identity,multiply(X_226,inverse(X_227))))))),bind(Y0,$fot(inverse(multiply(least_upper_bound(identity,multiply(X_226,inverse(X_227))),X_227)))),bind(Z0,$fot(inverse(least_upper_bound(X_227,X_226))))]]) ).
cnf(refute_0_2870,plain,
( inverse(multiply(least_upper_bound(identity,multiply(X_226,inverse(X_227))),X_227)) != inverse(least_upper_bound(X_227,X_226))
| multiply(inverse(X_227),inverse(least_upper_bound(identity,multiply(X_226,inverse(X_227))))) = inverse(least_upper_bound(X_227,X_226)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_227),inverse(least_upper_bound(identity,multiply(X_226,inverse(X_227))))),inverse(multiply(least_upper_bound(identity,multiply(X_226,inverse(X_227))),X_227))) )],[refute_0_2868,refute_0_2869]) ).
cnf(refute_0_2871,plain,
multiply(inverse(X_227),inverse(least_upper_bound(identity,multiply(X_226,inverse(X_227))))) = inverse(least_upper_bound(X_227,X_226)),
inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(identity,multiply(X_226,inverse(X_227))),X_227)),inverse(least_upper_bound(X_227,X_226))) )],[refute_0_2867,refute_0_2870]) ).
cnf(refute_0_2872,plain,
( multiply(inverse(X_227),inverse(least_upper_bound(identity,multiply(X_226,inverse(X_227))))) != inverse(least_upper_bound(X_227,X_226))
| inverse(least_upper_bound(X_226,X_227)) != multiply(inverse(X_227),inverse(least_upper_bound(identity,multiply(X_226,inverse(X_227)))))
| inverse(least_upper_bound(X_226,X_227)) = inverse(least_upper_bound(X_227,X_226)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_226,X_227)),multiply(inverse(X_227),inverse(least_upper_bound(identity,multiply(X_226,inverse(X_227)))))) ),[1],$fot(inverse(least_upper_bound(X_227,X_226)))]]) ).
cnf(refute_0_2873,plain,
( inverse(least_upper_bound(X_226,X_227)) != multiply(inverse(X_227),inverse(least_upper_bound(identity,multiply(X_226,inverse(X_227)))))
| inverse(least_upper_bound(X_226,X_227)) = inverse(least_upper_bound(X_227,X_226)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_227),inverse(least_upper_bound(identity,multiply(X_226,inverse(X_227))))),inverse(least_upper_bound(X_227,X_226))) )],[refute_0_2871,refute_0_2872]) ).
cnf(refute_0_2874,plain,
inverse(least_upper_bound(X_226,X_227)) = inverse(least_upper_bound(X_227,X_226)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_226,X_227)),multiply(inverse(X_227),inverse(least_upper_bound(identity,multiply(X_226,inverse(X_227)))))) )],[refute_0_2837,refute_0_2873]) ).
cnf(refute_0_2875,plain,
inverse(least_upper_bound(X_228,X_229)) = inverse(least_upper_bound(X_229,X_228)),
inference(subst,[],[refute_0_2874:[bind(X_226,$fot(X_228)),bind(X_227,$fot(X_229))]]) ).
cnf(refute_0_2876,plain,
( inverse(least_upper_bound(X_228,X_229)) != inverse(least_upper_bound(X_229,X_228))
| least_upper_bound(X_228,X_229) != greatest_lower_bound(least_upper_bound(X_228,X_229),inverse(greatest_lower_bound(X_11,inverse(least_upper_bound(X_228,X_229)))))
| least_upper_bound(X_228,X_229) = greatest_lower_bound(least_upper_bound(X_228,X_229),inverse(greatest_lower_bound(X_11,inverse(least_upper_bound(X_229,X_228))))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_228,X_229),greatest_lower_bound(least_upper_bound(X_228,X_229),inverse(greatest_lower_bound(X_11,inverse(least_upper_bound(X_228,X_229)))))) ),[1,1,0,1],$fot(inverse(least_upper_bound(X_229,X_228)))]]) ).
cnf(refute_0_2877,plain,
( least_upper_bound(X_228,X_229) != greatest_lower_bound(least_upper_bound(X_228,X_229),inverse(greatest_lower_bound(X_11,inverse(least_upper_bound(X_228,X_229)))))
| least_upper_bound(X_228,X_229) = greatest_lower_bound(least_upper_bound(X_228,X_229),inverse(greatest_lower_bound(X_11,inverse(least_upper_bound(X_229,X_228))))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_228,X_229)),inverse(least_upper_bound(X_229,X_228))) )],[refute_0_2875,refute_0_2876]) ).
cnf(refute_0_2878,plain,
least_upper_bound(X_228,X_229) = greatest_lower_bound(least_upper_bound(X_228,X_229),inverse(greatest_lower_bound(X_11,inverse(least_upper_bound(X_229,X_228))))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_228,X_229),greatest_lower_bound(least_upper_bound(X_228,X_229),inverse(greatest_lower_bound(X_11,inverse(least_upper_bound(X_228,X_229)))))) )],[refute_0_2822,refute_0_2877]) ).
cnf(refute_0_2879,plain,
( least_upper_bound(X_228,X_229) != greatest_lower_bound(least_upper_bound(X_228,X_229),inverse(greatest_lower_bound(X_11,inverse(least_upper_bound(X_229,X_228)))))
| greatest_lower_bound(least_upper_bound(X_228,X_229),inverse(greatest_lower_bound(X_11,inverse(least_upper_bound(X_229,X_228))))) = least_upper_bound(X_228,X_229) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(least_upper_bound(X_228,X_229))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(X_228,X_229),inverse(greatest_lower_bound(X_11,inverse(least_upper_bound(X_229,X_228)))))))]]) ).
cnf(refute_0_2880,plain,
greatest_lower_bound(least_upper_bound(X_228,X_229),inverse(greatest_lower_bound(X_11,inverse(least_upper_bound(X_229,X_228))))) = least_upper_bound(X_228,X_229),
inference(resolve,[$cnf( $equal(least_upper_bound(X_228,X_229),greatest_lower_bound(least_upper_bound(X_228,X_229),inverse(greatest_lower_bound(X_11,inverse(least_upper_bound(X_229,X_228)))))) )],[refute_0_2878,refute_0_2879]) ).
cnf(refute_0_2881,plain,
greatest_lower_bound(least_upper_bound(identity,X_163),inverse(greatest_lower_bound(X_222,inverse(least_upper_bound(X_163,identity))))) = least_upper_bound(identity,X_163),
inference(subst,[],[refute_0_2880:[bind(X_11,$fot(X_222)),bind(X_228,$fot(identity)),bind(X_229,$fot(X_163))]]) ).
cnf(refute_0_2882,plain,
( greatest_lower_bound(least_upper_bound(identity,X_163),inverse(greatest_lower_bound(X_222,inverse(least_upper_bound(X_163,identity))))) != least_upper_bound(identity,X_163)
| least_upper_bound(X_163,identity) != greatest_lower_bound(least_upper_bound(identity,X_163),inverse(greatest_lower_bound(X_222,inverse(least_upper_bound(X_163,identity)))))
| least_upper_bound(X_163,identity) = least_upper_bound(identity,X_163) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_163,identity),greatest_lower_bound(least_upper_bound(identity,X_163),inverse(greatest_lower_bound(X_222,inverse(least_upper_bound(X_163,identity)))))) ),[1],$fot(least_upper_bound(identity,X_163))]]) ).
cnf(refute_0_2883,plain,
( least_upper_bound(X_163,identity) != greatest_lower_bound(least_upper_bound(identity,X_163),inverse(greatest_lower_bound(X_222,inverse(least_upper_bound(X_163,identity)))))
| least_upper_bound(X_163,identity) = least_upper_bound(identity,X_163) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,X_163),inverse(greatest_lower_bound(X_222,inverse(least_upper_bound(X_163,identity))))),least_upper_bound(identity,X_163)) )],[refute_0_2881,refute_0_2882]) ).
cnf(refute_0_2884,plain,
least_upper_bound(X_163,identity) = least_upper_bound(identity,X_163),
inference(resolve,[$cnf( $equal(least_upper_bound(X_163,identity),greatest_lower_bound(least_upper_bound(identity,X_163),inverse(greatest_lower_bound(X_222,inverse(least_upper_bound(X_163,identity)))))) )],[refute_0_2821,refute_0_2883]) ).
cnf(refute_0_2885,plain,
least_upper_bound(greatest_lower_bound(X_120,X_121),identity) = least_upper_bound(identity,greatest_lower_bound(X_120,X_121)),
inference(subst,[],[refute_0_2884:[bind(X_163,$fot(greatest_lower_bound(X_120,X_121)))]]) ).
cnf(refute_0_2886,plain,
least_upper_bound(greatest_lower_bound(X_136,Y),least_upper_bound(X_135,X_136)) = least_upper_bound(X_135,least_upper_bound(X_136,greatest_lower_bound(X_136,Y))),
inference(subst,[],[refute_0_244:[bind(X,$fot(greatest_lower_bound(X_136,Y))),bind(X_39,$fot(X_135)),bind(X_40,$fot(X_136))]]) ).
cnf(refute_0_2887,plain,
least_upper_bound(X_136,greatest_lower_bound(X_136,Y)) = X_136,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_136))]]) ).
cnf(refute_0_2888,plain,
( least_upper_bound(X_136,greatest_lower_bound(X_136,Y)) != X_136
| least_upper_bound(greatest_lower_bound(X_136,Y),least_upper_bound(X_135,X_136)) != least_upper_bound(X_135,least_upper_bound(X_136,greatest_lower_bound(X_136,Y)))
| least_upper_bound(greatest_lower_bound(X_136,Y),least_upper_bound(X_135,X_136)) = least_upper_bound(X_135,X_136) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_136,Y),least_upper_bound(X_135,X_136)),least_upper_bound(X_135,least_upper_bound(X_136,greatest_lower_bound(X_136,Y)))) ),[1,1],$fot(X_136)]]) ).
cnf(refute_0_2889,plain,
( least_upper_bound(greatest_lower_bound(X_136,Y),least_upper_bound(X_135,X_136)) != least_upper_bound(X_135,least_upper_bound(X_136,greatest_lower_bound(X_136,Y)))
| least_upper_bound(greatest_lower_bound(X_136,Y),least_upper_bound(X_135,X_136)) = least_upper_bound(X_135,X_136) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_136,greatest_lower_bound(X_136,Y)),X_136) )],[refute_0_2887,refute_0_2888]) ).
cnf(refute_0_2890,plain,
least_upper_bound(greatest_lower_bound(X_136,Y),least_upper_bound(X_135,X_136)) = least_upper_bound(X_135,X_136),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_136,Y),least_upper_bound(X_135,X_136)),least_upper_bound(X_135,least_upper_bound(X_136,greatest_lower_bound(X_136,Y)))) )],[refute_0_2886,refute_0_2889]) ).
cnf(refute_0_2891,plain,
least_upper_bound(greatest_lower_bound(X_136,Y),least_upper_bound(X_135,X_136)) = least_upper_bound(X_136,least_upper_bound(X_135,greatest_lower_bound(X_136,Y))),
inference(subst,[],[refute_0_690:[bind(Y,$fot(greatest_lower_bound(X_136,Y))),bind(X_134,$fot(X_136))]]) ).
cnf(refute_0_2892,plain,
( least_upper_bound(greatest_lower_bound(X_136,Y),least_upper_bound(X_135,X_136)) != least_upper_bound(X_135,X_136)
| least_upper_bound(greatest_lower_bound(X_136,Y),least_upper_bound(X_135,X_136)) != least_upper_bound(X_136,least_upper_bound(X_135,greatest_lower_bound(X_136,Y)))
| least_upper_bound(X_136,least_upper_bound(X_135,greatest_lower_bound(X_136,Y))) = least_upper_bound(X_135,X_136) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_136,Y),least_upper_bound(X_135,X_136)),least_upper_bound(X_135,X_136)) ),[0],$fot(least_upper_bound(X_136,least_upper_bound(X_135,greatest_lower_bound(X_136,Y))))]]) ).
cnf(refute_0_2893,plain,
( least_upper_bound(greatest_lower_bound(X_136,Y),least_upper_bound(X_135,X_136)) != least_upper_bound(X_135,X_136)
| least_upper_bound(X_136,least_upper_bound(X_135,greatest_lower_bound(X_136,Y))) = least_upper_bound(X_135,X_136) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_136,Y),least_upper_bound(X_135,X_136)),least_upper_bound(X_136,least_upper_bound(X_135,greatest_lower_bound(X_136,Y)))) )],[refute_0_2891,refute_0_2892]) ).
cnf(refute_0_2894,plain,
least_upper_bound(X_136,least_upper_bound(X_135,greatest_lower_bound(X_136,Y))) = least_upper_bound(X_135,X_136),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_136,Y),least_upper_bound(X_135,X_136)),least_upper_bound(X_135,X_136)) )],[refute_0_2890,refute_0_2893]) ).
cnf(refute_0_2895,plain,
least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_120,X_121),greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))) = least_upper_bound(greatest_lower_bound(X_120,X_121),identity),
inference(subst,[],[refute_0_2894:[bind(Y,$fot(multiply(X_120,inverse(X_121)))),bind(X_135,$fot(greatest_lower_bound(X_120,X_121))),bind(X_136,$fot(identity))]]) ).
cnf(refute_0_2896,plain,
( least_upper_bound(greatest_lower_bound(X_120,X_121),identity) != least_upper_bound(identity,greatest_lower_bound(X_120,X_121))
| least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_120,X_121),greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))) != least_upper_bound(greatest_lower_bound(X_120,X_121),identity)
| least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_120,X_121),greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))) = least_upper_bound(identity,greatest_lower_bound(X_120,X_121)) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_120,X_121),greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(X_120,X_121),identity))),bind(Z0,$fot(least_upper_bound(identity,greatest_lower_bound(X_120,X_121))))]]) ).
cnf(refute_0_2897,plain,
( least_upper_bound(greatest_lower_bound(X_120,X_121),identity) != least_upper_bound(identity,greatest_lower_bound(X_120,X_121))
| least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_120,X_121),greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))) = least_upper_bound(identity,greatest_lower_bound(X_120,X_121)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_120,X_121),greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))),least_upper_bound(greatest_lower_bound(X_120,X_121),identity)) )],[refute_0_2895,refute_0_2896]) ).
cnf(refute_0_2898,plain,
least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_120,X_121),greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))) = least_upper_bound(identity,greatest_lower_bound(X_120,X_121)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_120,X_121),identity),least_upper_bound(identity,greatest_lower_bound(X_120,X_121))) )],[refute_0_2885,refute_0_2897]) ).
cnf(refute_0_2899,plain,
least_upper_bound(least_upper_bound(X_7,X_18),least_upper_bound(greatest_lower_bound(least_upper_bound(X_18,X_7),least_upper_bound(X_7,X_18)),X_139)) = least_upper_bound(least_upper_bound(X_7,X_18),X_139),
inference(subst,[],[refute_0_636:[bind(X_11,$fot(least_upper_bound(X_18,X_7))),bind(X_39,$fot(least_upper_bound(X_7,X_18))),bind(X_41,$fot(X_139))]]) ).
cnf(refute_0_2900,plain,
( greatest_lower_bound(least_upper_bound(X_18,X_7),least_upper_bound(X_7,X_18)) != least_upper_bound(X_18,X_7)
| least_upper_bound(least_upper_bound(X_7,X_18),least_upper_bound(greatest_lower_bound(least_upper_bound(X_18,X_7),least_upper_bound(X_7,X_18)),X_139)) != least_upper_bound(least_upper_bound(X_7,X_18),X_139)
| least_upper_bound(least_upper_bound(X_7,X_18),least_upper_bound(least_upper_bound(X_18,X_7),X_139)) = least_upper_bound(least_upper_bound(X_7,X_18),X_139) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_7,X_18),least_upper_bound(greatest_lower_bound(least_upper_bound(X_18,X_7),least_upper_bound(X_7,X_18)),X_139)),least_upper_bound(least_upper_bound(X_7,X_18),X_139)) ),[0,1,0],$fot(least_upper_bound(X_18,X_7))]]) ).
cnf(refute_0_2901,plain,
( least_upper_bound(least_upper_bound(X_7,X_18),least_upper_bound(greatest_lower_bound(least_upper_bound(X_18,X_7),least_upper_bound(X_7,X_18)),X_139)) != least_upper_bound(least_upper_bound(X_7,X_18),X_139)
| least_upper_bound(least_upper_bound(X_7,X_18),least_upper_bound(least_upper_bound(X_18,X_7),X_139)) = least_upper_bound(least_upper_bound(X_7,X_18),X_139) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_18,X_7),least_upper_bound(X_7,X_18)),least_upper_bound(X_18,X_7)) )],[refute_0_544,refute_0_2900]) ).
cnf(refute_0_2902,plain,
least_upper_bound(least_upper_bound(X_7,X_18),least_upper_bound(least_upper_bound(X_18,X_7),X_139)) = least_upper_bound(least_upper_bound(X_7,X_18),X_139),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_7,X_18),least_upper_bound(greatest_lower_bound(least_upper_bound(X_18,X_7),least_upper_bound(X_7,X_18)),X_139)),least_upper_bound(least_upper_bound(X_7,X_18),X_139)) )],[refute_0_2899,refute_0_2901]) ).
cnf(refute_0_2903,plain,
least_upper_bound(X_7,least_upper_bound(X_18,least_upper_bound(X_7,X_139))) = least_upper_bound(X_18,least_upper_bound(X_7,X_139)),
inference(subst,[],[refute_0_280:[bind(Y,$fot(X_139)),bind(X_39,$fot(X_18)),bind(X_40,$fot(X_7))]]) ).
cnf(refute_0_2904,plain,
least_upper_bound(X_18,least_upper_bound(X_18,least_upper_bound(X_7,X_139))) = least_upper_bound(X_18,least_upper_bound(X_7,X_139)),
inference(subst,[],[refute_0_516:[bind(X_18,$fot(least_upper_bound(X_7,X_139))),bind(X_19,$fot(X_18))]]) ).
cnf(refute_0_2905,plain,
least_upper_bound(least_upper_bound(X_18,X_7),X_139) = least_upper_bound(X_18,least_upper_bound(X_7,X_139)),
inference(subst,[],[refute_0_171:[bind(X,$fot(X_18)),bind(Y,$fot(X_7)),bind(Z,$fot(X_139))]]) ).
cnf(refute_0_2906,plain,
least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,X_7),X_139)) = least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,X_7),X_139)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,X_7),X_139)))]]) ).
cnf(refute_0_2907,plain,
( least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,X_7),X_139)) != least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,X_7),X_139))
| least_upper_bound(least_upper_bound(X_18,X_7),X_139) != least_upper_bound(X_18,least_upper_bound(X_7,X_139))
| least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,X_7),X_139)) = least_upper_bound(X_18,least_upper_bound(X_18,least_upper_bound(X_7,X_139))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,X_7),X_139)),least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,X_7),X_139))) ),[1,1],$fot(least_upper_bound(X_18,least_upper_bound(X_7,X_139)))]]) ).
cnf(refute_0_2908,plain,
( least_upper_bound(least_upper_bound(X_18,X_7),X_139) != least_upper_bound(X_18,least_upper_bound(X_7,X_139))
| least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,X_7),X_139)) = least_upper_bound(X_18,least_upper_bound(X_18,least_upper_bound(X_7,X_139))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,X_7),X_139)),least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,X_7),X_139))) )],[refute_0_2906,refute_0_2907]) ).
cnf(refute_0_2909,plain,
least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,X_7),X_139)) = least_upper_bound(X_18,least_upper_bound(X_18,least_upper_bound(X_7,X_139))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_18,X_7),X_139),least_upper_bound(X_18,least_upper_bound(X_7,X_139))) )],[refute_0_2905,refute_0_2908]) ).
cnf(refute_0_2910,plain,
( least_upper_bound(X_18,least_upper_bound(X_18,least_upper_bound(X_7,X_139))) != least_upper_bound(X_18,least_upper_bound(X_7,X_139))
| least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,X_7),X_139)) != least_upper_bound(X_18,least_upper_bound(X_18,least_upper_bound(X_7,X_139)))
| least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,X_7),X_139)) = least_upper_bound(X_18,least_upper_bound(X_7,X_139)) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,X_7),X_139)))),bind(Y0,$fot(least_upper_bound(X_18,least_upper_bound(X_18,least_upper_bound(X_7,X_139))))),bind(Z0,$fot(least_upper_bound(X_18,least_upper_bound(X_7,X_139))))]]) ).
cnf(refute_0_2911,plain,
( least_upper_bound(X_18,least_upper_bound(X_18,least_upper_bound(X_7,X_139))) != least_upper_bound(X_18,least_upper_bound(X_7,X_139))
| least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,X_7),X_139)) = least_upper_bound(X_18,least_upper_bound(X_7,X_139)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,X_7),X_139)),least_upper_bound(X_18,least_upper_bound(X_18,least_upper_bound(X_7,X_139)))) )],[refute_0_2909,refute_0_2910]) ).
cnf(refute_0_2912,plain,
least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,X_7),X_139)) = least_upper_bound(X_18,least_upper_bound(X_7,X_139)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(X_18,least_upper_bound(X_7,X_139))),least_upper_bound(X_18,least_upper_bound(X_7,X_139))) )],[refute_0_2904,refute_0_2911]) ).
cnf(refute_0_2913,plain,
least_upper_bound(X_7,least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,X_7),X_139))) = least_upper_bound(X_7,least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,X_7),X_139))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_7,least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,X_7),X_139))))]]) ).
cnf(refute_0_2914,plain,
( least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,X_7),X_139)) != least_upper_bound(X_18,least_upper_bound(X_7,X_139))
| least_upper_bound(X_7,least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,X_7),X_139))) != least_upper_bound(X_7,least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,X_7),X_139)))
| least_upper_bound(X_7,least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,X_7),X_139))) = least_upper_bound(X_7,least_upper_bound(X_18,least_upper_bound(X_7,X_139))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_7,least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,X_7),X_139))),least_upper_bound(X_7,least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,X_7),X_139)))) ),[1,1],$fot(least_upper_bound(X_18,least_upper_bound(X_7,X_139)))]]) ).
cnf(refute_0_2915,plain,
( least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,X_7),X_139)) != least_upper_bound(X_18,least_upper_bound(X_7,X_139))
| least_upper_bound(X_7,least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,X_7),X_139))) = least_upper_bound(X_7,least_upper_bound(X_18,least_upper_bound(X_7,X_139))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_7,least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,X_7),X_139))),least_upper_bound(X_7,least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,X_7),X_139)))) )],[refute_0_2913,refute_0_2914]) ).
cnf(refute_0_2916,plain,
least_upper_bound(X_7,least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,X_7),X_139))) = least_upper_bound(X_7,least_upper_bound(X_18,least_upper_bound(X_7,X_139))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,X_7),X_139)),least_upper_bound(X_18,least_upper_bound(X_7,X_139))) )],[refute_0_2912,refute_0_2915]) ).
cnf(refute_0_2917,plain,
( least_upper_bound(X_7,least_upper_bound(X_18,least_upper_bound(X_7,X_139))) != least_upper_bound(X_18,least_upper_bound(X_7,X_139))
| least_upper_bound(X_7,least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,X_7),X_139))) != least_upper_bound(X_7,least_upper_bound(X_18,least_upper_bound(X_7,X_139)))
| least_upper_bound(X_7,least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,X_7),X_139))) = least_upper_bound(X_18,least_upper_bound(X_7,X_139)) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(least_upper_bound(X_7,least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,X_7),X_139))))),bind(Y0,$fot(least_upper_bound(X_7,least_upper_bound(X_18,least_upper_bound(X_7,X_139))))),bind(Z0,$fot(least_upper_bound(X_18,least_upper_bound(X_7,X_139))))]]) ).
cnf(refute_0_2918,plain,
( least_upper_bound(X_7,least_upper_bound(X_18,least_upper_bound(X_7,X_139))) != least_upper_bound(X_18,least_upper_bound(X_7,X_139))
| least_upper_bound(X_7,least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,X_7),X_139))) = least_upper_bound(X_18,least_upper_bound(X_7,X_139)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_7,least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,X_7),X_139))),least_upper_bound(X_7,least_upper_bound(X_18,least_upper_bound(X_7,X_139)))) )],[refute_0_2916,refute_0_2917]) ).
cnf(refute_0_2919,plain,
least_upper_bound(X_7,least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,X_7),X_139))) = least_upper_bound(X_18,least_upper_bound(X_7,X_139)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_7,least_upper_bound(X_18,least_upper_bound(X_7,X_139))),least_upper_bound(X_18,least_upper_bound(X_7,X_139))) )],[refute_0_2903,refute_0_2918]) ).
cnf(refute_0_2920,plain,
least_upper_bound(least_upper_bound(X_7,X_18),least_upper_bound(least_upper_bound(X_18,X_7),X_139)) = least_upper_bound(X_7,least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,X_7),X_139))),
inference(subst,[],[refute_0_171:[bind(X,$fot(X_7)),bind(Y,$fot(X_18)),bind(Z,$fot(least_upper_bound(least_upper_bound(X_18,X_7),X_139)))]]) ).
cnf(refute_0_2921,plain,
( least_upper_bound(X_7,least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,X_7),X_139))) != least_upper_bound(X_18,least_upper_bound(X_7,X_139))
| least_upper_bound(least_upper_bound(X_7,X_18),least_upper_bound(least_upper_bound(X_18,X_7),X_139)) != least_upper_bound(X_7,least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,X_7),X_139)))
| least_upper_bound(least_upper_bound(X_7,X_18),least_upper_bound(least_upper_bound(X_18,X_7),X_139)) = least_upper_bound(X_18,least_upper_bound(X_7,X_139)) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_7,X_18),least_upper_bound(least_upper_bound(X_18,X_7),X_139)))),bind(Y0,$fot(least_upper_bound(X_7,least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,X_7),X_139))))),bind(Z0,$fot(least_upper_bound(X_18,least_upper_bound(X_7,X_139))))]]) ).
cnf(refute_0_2922,plain,
( least_upper_bound(X_7,least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,X_7),X_139))) != least_upper_bound(X_18,least_upper_bound(X_7,X_139))
| least_upper_bound(least_upper_bound(X_7,X_18),least_upper_bound(least_upper_bound(X_18,X_7),X_139)) = least_upper_bound(X_18,least_upper_bound(X_7,X_139)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_7,X_18),least_upper_bound(least_upper_bound(X_18,X_7),X_139)),least_upper_bound(X_7,least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,X_7),X_139)))) )],[refute_0_2920,refute_0_2921]) ).
cnf(refute_0_2923,plain,
least_upper_bound(least_upper_bound(X_7,X_18),least_upper_bound(least_upper_bound(X_18,X_7),X_139)) = least_upper_bound(X_18,least_upper_bound(X_7,X_139)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_7,least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,X_7),X_139))),least_upper_bound(X_18,least_upper_bound(X_7,X_139))) )],[refute_0_2919,refute_0_2922]) ).
cnf(refute_0_2924,plain,
( least_upper_bound(least_upper_bound(X_7,X_18),least_upper_bound(least_upper_bound(X_18,X_7),X_139)) != least_upper_bound(X_18,least_upper_bound(X_7,X_139))
| least_upper_bound(least_upper_bound(X_7,X_18),least_upper_bound(least_upper_bound(X_18,X_7),X_139)) != least_upper_bound(least_upper_bound(X_7,X_18),X_139)
| least_upper_bound(X_18,least_upper_bound(X_7,X_139)) = least_upper_bound(least_upper_bound(X_7,X_18),X_139) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_7,X_18),least_upper_bound(least_upper_bound(X_18,X_7),X_139)),least_upper_bound(least_upper_bound(X_7,X_18),X_139)) ),[0],$fot(least_upper_bound(X_18,least_upper_bound(X_7,X_139)))]]) ).
cnf(refute_0_2925,plain,
( least_upper_bound(least_upper_bound(X_7,X_18),least_upper_bound(least_upper_bound(X_18,X_7),X_139)) != least_upper_bound(least_upper_bound(X_7,X_18),X_139)
| least_upper_bound(X_18,least_upper_bound(X_7,X_139)) = least_upper_bound(least_upper_bound(X_7,X_18),X_139) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_7,X_18),least_upper_bound(least_upper_bound(X_18,X_7),X_139)),least_upper_bound(X_18,least_upper_bound(X_7,X_139))) )],[refute_0_2923,refute_0_2924]) ).
cnf(refute_0_2926,plain,
least_upper_bound(least_upper_bound(X_7,X_18),X_139) = least_upper_bound(X_7,least_upper_bound(X_18,X_139)),
inference(subst,[],[refute_0_171:[bind(X,$fot(X_7)),bind(Y,$fot(X_18)),bind(Z,$fot(X_139))]]) ).
cnf(refute_0_2927,plain,
( least_upper_bound(X_18,least_upper_bound(X_7,X_139)) != least_upper_bound(least_upper_bound(X_7,X_18),X_139)
| least_upper_bound(least_upper_bound(X_7,X_18),X_139) != least_upper_bound(X_7,least_upper_bound(X_18,X_139))
| least_upper_bound(X_18,least_upper_bound(X_7,X_139)) = least_upper_bound(X_7,least_upper_bound(X_18,X_139)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_18,least_upper_bound(X_7,X_139)),least_upper_bound(X_7,least_upper_bound(X_18,X_139))) ),[0],$fot(least_upper_bound(least_upper_bound(X_7,X_18),X_139))]]) ).
cnf(refute_0_2928,plain,
( least_upper_bound(X_18,least_upper_bound(X_7,X_139)) != least_upper_bound(least_upper_bound(X_7,X_18),X_139)
| least_upper_bound(X_18,least_upper_bound(X_7,X_139)) = least_upper_bound(X_7,least_upper_bound(X_18,X_139)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_7,X_18),X_139),least_upper_bound(X_7,least_upper_bound(X_18,X_139))) )],[refute_0_2926,refute_0_2927]) ).
cnf(refute_0_2929,plain,
( least_upper_bound(least_upper_bound(X_7,X_18),least_upper_bound(least_upper_bound(X_18,X_7),X_139)) != least_upper_bound(least_upper_bound(X_7,X_18),X_139)
| least_upper_bound(X_18,least_upper_bound(X_7,X_139)) = least_upper_bound(X_7,least_upper_bound(X_18,X_139)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(X_7,X_139)),least_upper_bound(least_upper_bound(X_7,X_18),X_139)) )],[refute_0_2925,refute_0_2928]) ).
cnf(refute_0_2930,plain,
least_upper_bound(X_18,least_upper_bound(X_7,X_139)) = least_upper_bound(X_7,least_upper_bound(X_18,X_139)),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_7,X_18),least_upper_bound(least_upper_bound(X_18,X_7),X_139)),least_upper_bound(least_upper_bound(X_7,X_18),X_139)) )],[refute_0_2902,refute_0_2929]) ).
cnf(refute_0_2931,plain,
( least_upper_bound(X_18,least_upper_bound(X_7,X_139)) != least_upper_bound(X_7,least_upper_bound(X_18,X_139))
| least_upper_bound(X_7,least_upper_bound(X_18,X_139)) = least_upper_bound(X_18,least_upper_bound(X_7,X_139)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(least_upper_bound(X_18,least_upper_bound(X_7,X_139)))),bind(Y0,$fot(least_upper_bound(X_7,least_upper_bound(X_18,X_139))))]]) ).
cnf(refute_0_2932,plain,
least_upper_bound(X_7,least_upper_bound(X_18,X_139)) = least_upper_bound(X_18,least_upper_bound(X_7,X_139)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(X_7,X_139)),least_upper_bound(X_7,least_upper_bound(X_18,X_139))) )],[refute_0_2930,refute_0_2931]) ).
cnf(refute_0_2933,plain,
least_upper_bound(greatest_lower_bound(X_120,X_121),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))) = least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_120,X_121),greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))),
inference(subst,[],[refute_0_2932:[bind(X_139,$fot(greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))),bind(X_18,$fot(identity)),bind(X_7,$fot(greatest_lower_bound(X_120,X_121)))]]) ).
cnf(refute_0_2934,plain,
( least_upper_bound(greatest_lower_bound(X_120,X_121),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))) != least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_120,X_121),greatest_lower_bound(identity,multiply(X_120,inverse(X_121)))))
| least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_120,X_121),greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))) != least_upper_bound(identity,greatest_lower_bound(X_120,X_121))
| least_upper_bound(greatest_lower_bound(X_120,X_121),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))) = least_upper_bound(identity,greatest_lower_bound(X_120,X_121)) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(X_120,X_121),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_120,X_121),greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))))),bind(Z0,$fot(least_upper_bound(identity,greatest_lower_bound(X_120,X_121))))]]) ).
cnf(refute_0_2935,plain,
( least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_120,X_121),greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))) != least_upper_bound(identity,greatest_lower_bound(X_120,X_121))
| least_upper_bound(greatest_lower_bound(X_120,X_121),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))) = least_upper_bound(identity,greatest_lower_bound(X_120,X_121)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_120,X_121),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))),least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_120,X_121),greatest_lower_bound(identity,multiply(X_120,inverse(X_121)))))) )],[refute_0_2933,refute_0_2934]) ).
cnf(refute_0_2936,plain,
least_upper_bound(greatest_lower_bound(X_120,X_121),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))) = least_upper_bound(identity,greatest_lower_bound(X_120,X_121)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_120,X_121),greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))),least_upper_bound(identity,greatest_lower_bound(X_120,X_121))) )],[refute_0_2898,refute_0_2935]) ).
cnf(refute_0_2937,plain,
( least_upper_bound(greatest_lower_bound(X_120,X_121),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))) != least_upper_bound(identity,greatest_lower_bound(X_120,X_121))
| least_upper_bound(identity,multiply(greatest_lower_bound(X_120,X_121),least_upper_bound(identity,inverse(X_121)))) != least_upper_bound(greatest_lower_bound(X_120,X_121),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_120,inverse(X_121)))))
| least_upper_bound(identity,multiply(greatest_lower_bound(X_120,X_121),least_upper_bound(identity,inverse(X_121)))) = least_upper_bound(identity,greatest_lower_bound(X_120,X_121)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(greatest_lower_bound(X_120,X_121),least_upper_bound(identity,inverse(X_121)))),least_upper_bound(greatest_lower_bound(X_120,X_121),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_120,inverse(X_121)))))) ),[1],$fot(least_upper_bound(identity,greatest_lower_bound(X_120,X_121)))]]) ).
cnf(refute_0_2938,plain,
( least_upper_bound(identity,multiply(greatest_lower_bound(X_120,X_121),least_upper_bound(identity,inverse(X_121)))) != least_upper_bound(greatest_lower_bound(X_120,X_121),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_120,inverse(X_121)))))
| least_upper_bound(identity,multiply(greatest_lower_bound(X_120,X_121),least_upper_bound(identity,inverse(X_121)))) = least_upper_bound(identity,greatest_lower_bound(X_120,X_121)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_120,X_121),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_120,inverse(X_121))))),least_upper_bound(identity,greatest_lower_bound(X_120,X_121))) )],[refute_0_2936,refute_0_2937]) ).
cnf(refute_0_2939,plain,
least_upper_bound(identity,multiply(greatest_lower_bound(X_120,X_121),least_upper_bound(identity,inverse(X_121)))) = least_upper_bound(identity,greatest_lower_bound(X_120,X_121)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(greatest_lower_bound(X_120,X_121),least_upper_bound(identity,inverse(X_121)))),least_upper_bound(greatest_lower_bound(X_120,X_121),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_120,inverse(X_121)))))) )],[refute_0_2774,refute_0_2938]) ).
cnf(refute_0_2940,plain,
least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))) = least_upper_bound(identity,greatest_lower_bound(identity,X_444)),
inference(subst,[],[refute_0_2939:[bind(X_120,$fot(identity)),bind(X_121,$fot(X_444))]]) ).
cnf(refute_0_2941,plain,
( least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))) != least_upper_bound(identity,greatest_lower_bound(identity,X_444))
| least_upper_bound(identity,greatest_lower_bound(identity,X_444)) != identity
| least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))) = identity ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))),bind(Y0,$fot(least_upper_bound(identity,greatest_lower_bound(identity,X_444)))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_2942,plain,
( least_upper_bound(identity,greatest_lower_bound(identity,X_444)) != identity
| least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))),least_upper_bound(identity,greatest_lower_bound(identity,X_444))) )],[refute_0_2940,refute_0_2941]) ).
cnf(refute_0_2943,plain,
least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))) = identity,
inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(identity,X_444)),identity) )],[refute_0_2757,refute_0_2942]) ).
cnf(refute_0_2944,plain,
multiply(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))),inverse(identity)) = multiply(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))),inverse(identity)),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))),inverse(identity)))]]) ).
cnf(refute_0_2945,plain,
( multiply(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))),inverse(identity)) != multiply(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))),inverse(identity))
| least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))) != identity
| multiply(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))),inverse(identity)) = multiply(identity,inverse(identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))),inverse(identity)),multiply(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))),inverse(identity))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_2946,plain,
( least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))) != identity
| multiply(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))),inverse(identity)) = multiply(identity,inverse(identity)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))),inverse(identity)),multiply(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))),inverse(identity))) )],[refute_0_2944,refute_0_2945]) ).
cnf(refute_0_2947,plain,
multiply(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))),inverse(identity)) = multiply(identity,inverse(identity)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))),identity) )],[refute_0_2943,refute_0_2946]) ).
cnf(refute_0_2948,plain,
( multiply(identity,inverse(identity)) != multiply(identity,identity)
| multiply(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))),inverse(identity)) != multiply(identity,inverse(identity))
| multiply(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))),inverse(identity)) = multiply(identity,identity) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))),inverse(identity)))),bind(Y0,$fot(multiply(identity,inverse(identity)))),bind(Z0,$fot(multiply(identity,identity)))]]) ).
cnf(refute_0_2949,plain,
( multiply(identity,inverse(identity)) != multiply(identity,identity)
| multiply(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))),inverse(identity)) = multiply(identity,identity) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))),inverse(identity)),multiply(identity,inverse(identity))) )],[refute_0_2947,refute_0_2948]) ).
cnf(refute_0_2950,plain,
multiply(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))),inverse(identity)) = multiply(identity,identity),
inference(resolve,[$cnf( $equal(multiply(identity,inverse(identity)),multiply(identity,identity)) )],[refute_0_2756,refute_0_2949]) ).
cnf(refute_0_2951,plain,
( multiply(identity,identity) != identity
| multiply(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))),inverse(identity)) != multiply(identity,identity)
| multiply(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))),inverse(identity)) = identity ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))),inverse(identity)))),bind(Y0,$fot(multiply(identity,identity))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_2952,plain,
( multiply(identity,identity) != identity
| multiply(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))),inverse(identity)) = identity ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))),inverse(identity)),multiply(identity,identity)) )],[refute_0_2950,refute_0_2951]) ).
cnf(refute_0_2953,plain,
multiply(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))),inverse(identity)) = identity,
inference(resolve,[$cnf( $equal(multiply(identity,identity),identity) )],[refute_0_2752,refute_0_2952]) ).
cnf(refute_0_2954,plain,
( multiply(least_upper_bound(X_68,X_69),inverse(X_68)) != least_upper_bound(identity,multiply(X_69,inverse(X_68)))
| least_upper_bound(identity,multiply(X_69,inverse(X_68))) = multiply(least_upper_bound(X_68,X_69),inverse(X_68)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(least_upper_bound(X_68,X_69),inverse(X_68)))),bind(Y0,$fot(least_upper_bound(identity,multiply(X_69,inverse(X_68)))))]]) ).
cnf(refute_0_2955,plain,
least_upper_bound(identity,multiply(X_69,inverse(X_68))) = multiply(least_upper_bound(X_68,X_69),inverse(X_68)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_68,X_69),inverse(X_68)),least_upper_bound(identity,multiply(X_69,inverse(X_68)))) )],[refute_0_1189,refute_0_2954]) ).
cnf(refute_0_2956,plain,
least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(identity))) = multiply(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))),inverse(identity)),
inference(subst,[],[refute_0_2955:[bind(X_68,$fot(identity)),bind(X_69,$fot(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))]]) ).
cnf(refute_0_2957,plain,
( multiply(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))),inverse(identity)) != identity
| least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(identity))) != multiply(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))),inverse(identity))
| least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(identity))) = identity ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(identity))))),bind(Y0,$fot(multiply(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))),inverse(identity)))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_2958,plain,
( multiply(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))),inverse(identity)) != identity
| least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(identity))) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(identity))),multiply(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))),inverse(identity))) )],[refute_0_2956,refute_0_2957]) ).
cnf(refute_0_2959,plain,
least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(identity))) = identity,
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))),inverse(identity)),identity) )],[refute_0_2953,refute_0_2958]) ).
cnf(refute_0_2960,plain,
( inverse(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))) != least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(identity)))
| least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(identity))) != identity
| inverse(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))) = identity ),
introduced(tautology,[equality,[$cnf( ~ $equal(inverse(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))),identity) ),[0],$fot(least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(identity))))]]) ).
cnf(refute_0_2961,plain,
( inverse(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))) != least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(identity)))
| inverse(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(identity))),identity) )],[refute_0_2959,refute_0_2960]) ).
cnf(refute_0_2962,plain,
( multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))) != least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(identity)))
| inverse(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))) = identity ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))),least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(identity)))) )],[refute_0_2751,refute_0_2961]) ).
cnf(refute_0_2963,plain,
inverse(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))) = identity,
inference(resolve,[$cnf( $equal(multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))),least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(identity)))) )],[refute_0_2518,refute_0_2962]) ).
cnf(refute_0_2964,plain,
( inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))) != inverse(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))
| inverse(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))) != identity
| inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))) = identity ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))))),bind(Y0,$fot(inverse(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_2965,plain,
( inverse(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))) != identity
| inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))) = identity ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))),inverse(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))) )],[refute_0_2712,refute_0_2964]) ).
cnf(refute_0_2966,plain,
inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))) = identity,
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))),identity) )],[refute_0_2963,refute_0_2965]) ).
cnf(refute_0_2967,plain,
( multiply(X_74,inverse(greatest_lower_bound(X_11,X_74))) != least_upper_bound(identity,multiply(X_74,inverse(greatest_lower_bound(X_11,X_74))))
| least_upper_bound(identity,multiply(X_74,inverse(greatest_lower_bound(X_11,X_74)))) = multiply(X_74,inverse(greatest_lower_bound(X_11,X_74))) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(X_74,inverse(greatest_lower_bound(X_11,X_74))))),bind(Y0,$fot(least_upper_bound(identity,multiply(X_74,inverse(greatest_lower_bound(X_11,X_74))))))]]) ).
cnf(refute_0_2968,plain,
least_upper_bound(identity,multiply(X_74,inverse(greatest_lower_bound(X_11,X_74)))) = multiply(X_74,inverse(greatest_lower_bound(X_11,X_74))),
inference(resolve,[$cnf( $equal(multiply(X_74,inverse(greatest_lower_bound(X_11,X_74))),least_upper_bound(identity,multiply(X_74,inverse(greatest_lower_bound(X_11,X_74))))) )],[refute_0_1825,refute_0_2967]) ).
cnf(refute_0_2969,plain,
least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))) = multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))),
inference(subst,[],[refute_0_2968:[bind(X_11,$fot(identity)),bind(X_74,$fot(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))]]) ).
cnf(refute_0_2970,plain,
( multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))) != inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))))
| least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))) != multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))
| least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))) = inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))))),bind(Y0,$fot(multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))))),bind(Z0,$fot(inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))))))]]) ).
cnf(refute_0_2971,plain,
( multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))) != inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))))
| least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))) = inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))),multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))) )],[refute_0_2969,refute_0_2970]) ).
cnf(refute_0_2972,plain,
least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))) = inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))),
inference(resolve,[$cnf( $equal(multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))),inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))))) )],[refute_0_2746,refute_0_2971]) ).
cnf(refute_0_2973,plain,
( inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))) != identity
| least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))) != inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))))
| least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))) = identity ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))))),bind(Y0,$fot(inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_2974,plain,
( inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))) != identity
| least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))),inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))))) )],[refute_0_2972,refute_0_2973]) ).
cnf(refute_0_2975,plain,
least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))) = identity,
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))),identity) )],[refute_0_2966,refute_0_2974]) ).
cnf(refute_0_2976,plain,
( multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))) != least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))))
| least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))) != identity
| multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))) = identity ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),identity) ),[0],$fot(least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))))]]) ).
cnf(refute_0_2977,plain,
( multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))) != least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))))
| multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))))))),identity) )],[refute_0_2975,refute_0_2976]) ).
cnf(refute_0_2978,plain,
( multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(identity)) != least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))))
| multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))) = identity ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))))) )],[refute_0_2515,refute_0_2977]) ).
cnf(refute_0_2979,plain,
multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))) = identity,
inference(resolve,[$cnf( $equal(multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(identity)),least_upper_bound(identity,multiply(multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_444),least_upper_bound(identity,inverse(X_444)))))))) )],[refute_0_2426,refute_0_2978]) ).
cnf(refute_0_2980,plain,
multiply(greatest_lower_bound(identity,X_75),least_upper_bound(identity,inverse(X_75))) = identity,
inference(subst,[],[refute_0_2979:[bind(X_444,$fot(X_75))]]) ).
cnf(refute_0_2981,plain,
inverse(multiply(greatest_lower_bound(identity,X_75),least_upper_bound(identity,inverse(X_75)))) = inverse(multiply(greatest_lower_bound(identity,X_75),least_upper_bound(identity,inverse(X_75)))),
introduced(tautology,[refl,[$fot(inverse(multiply(greatest_lower_bound(identity,X_75),least_upper_bound(identity,inverse(X_75)))))]]) ).
cnf(refute_0_2982,plain,
( multiply(greatest_lower_bound(identity,X_75),least_upper_bound(identity,inverse(X_75))) != identity
| inverse(multiply(greatest_lower_bound(identity,X_75),least_upper_bound(identity,inverse(X_75)))) != inverse(multiply(greatest_lower_bound(identity,X_75),least_upper_bound(identity,inverse(X_75))))
| inverse(multiply(greatest_lower_bound(identity,X_75),least_upper_bound(identity,inverse(X_75)))) = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(greatest_lower_bound(identity,X_75),least_upper_bound(identity,inverse(X_75)))),inverse(multiply(greatest_lower_bound(identity,X_75),least_upper_bound(identity,inverse(X_75))))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_2983,plain,
( multiply(greatest_lower_bound(identity,X_75),least_upper_bound(identity,inverse(X_75))) != identity
| inverse(multiply(greatest_lower_bound(identity,X_75),least_upper_bound(identity,inverse(X_75)))) = inverse(identity) ),
inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(identity,X_75),least_upper_bound(identity,inverse(X_75)))),inverse(multiply(greatest_lower_bound(identity,X_75),least_upper_bound(identity,inverse(X_75))))) )],[refute_0_2981,refute_0_2982]) ).
cnf(refute_0_2984,plain,
inverse(multiply(greatest_lower_bound(identity,X_75),least_upper_bound(identity,inverse(X_75)))) = inverse(identity),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_75),least_upper_bound(identity,inverse(X_75))),identity) )],[refute_0_2980,refute_0_2983]) ).
cnf(refute_0_2985,plain,
( inverse(multiply(greatest_lower_bound(identity,X_75),least_upper_bound(identity,inverse(X_75)))) != inverse(identity)
| inverse(identity) != identity
| inverse(multiply(greatest_lower_bound(identity,X_75),least_upper_bound(identity,inverse(X_75)))) = identity ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(inverse(multiply(greatest_lower_bound(identity,X_75),least_upper_bound(identity,inverse(X_75)))))),bind(Y0,$fot(inverse(identity))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_2986,plain,
( inverse(identity) != identity
| inverse(multiply(greatest_lower_bound(identity,X_75),least_upper_bound(identity,inverse(X_75)))) = identity ),
inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(identity,X_75),least_upper_bound(identity,inverse(X_75)))),inverse(identity)) )],[refute_0_2984,refute_0_2985]) ).
cnf(refute_0_2987,plain,
inverse(multiply(greatest_lower_bound(identity,X_75),least_upper_bound(identity,inverse(X_75)))) = identity,
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_1763,refute_0_2986]) ).
cnf(refute_0_2988,plain,
( inverse(multiply(greatest_lower_bound(X_75,identity),least_upper_bound(identity,inverse(X_75)))) != inverse(multiply(greatest_lower_bound(identity,X_75),least_upper_bound(identity,inverse(X_75))))
| inverse(multiply(greatest_lower_bound(identity,X_75),least_upper_bound(identity,inverse(X_75)))) != identity
| inverse(multiply(greatest_lower_bound(X_75,identity),least_upper_bound(identity,inverse(X_75)))) = identity ),
introduced(tautology,[equality,[$cnf( ~ $equal(inverse(multiply(greatest_lower_bound(X_75,identity),least_upper_bound(identity,inverse(X_75)))),identity) ),[0],$fot(inverse(multiply(greatest_lower_bound(identity,X_75),least_upper_bound(identity,inverse(X_75)))))]]) ).
cnf(refute_0_2989,plain,
( inverse(multiply(greatest_lower_bound(X_75,identity),least_upper_bound(identity,inverse(X_75)))) != inverse(multiply(greatest_lower_bound(identity,X_75),least_upper_bound(identity,inverse(X_75))))
| inverse(multiply(greatest_lower_bound(X_75,identity),least_upper_bound(identity,inverse(X_75)))) = identity ),
inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(identity,X_75),least_upper_bound(identity,inverse(X_75)))),identity) )],[refute_0_2987,refute_0_2988]) ).
cnf(refute_0_2990,plain,
inverse(multiply(greatest_lower_bound(X_75,identity),least_upper_bound(identity,inverse(X_75)))) = identity,
inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(X_75,identity),least_upper_bound(identity,inverse(X_75)))),inverse(multiply(greatest_lower_bound(identity,X_75),least_upper_bound(identity,inverse(X_75))))) )],[refute_0_1820,refute_0_2989]) ).
cnf(refute_0_2991,plain,
inverse(multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316)))) = identity,
inference(subst,[],[refute_0_2990:[bind(X_75,$fot(X_316))]]) ).
cnf(refute_0_2992,plain,
multiply(inverse(multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316)))),greatest_lower_bound(identity,inverse(X_316))) = multiply(inverse(multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316)))),greatest_lower_bound(identity,inverse(X_316))),
introduced(tautology,[refl,[$fot(multiply(inverse(multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316)))),greatest_lower_bound(identity,inverse(X_316))))]]) ).
cnf(refute_0_2993,plain,
( multiply(inverse(multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316)))),greatest_lower_bound(identity,inverse(X_316))) != multiply(inverse(multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316)))),greatest_lower_bound(identity,inverse(X_316)))
| inverse(multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316)))) != identity
| multiply(inverse(multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316)))),greatest_lower_bound(identity,inverse(X_316))) = multiply(identity,greatest_lower_bound(identity,inverse(X_316))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316)))),greatest_lower_bound(identity,inverse(X_316))),multiply(inverse(multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316)))),greatest_lower_bound(identity,inverse(X_316)))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_2994,plain,
( inverse(multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316)))) != identity
| multiply(inverse(multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316)))),greatest_lower_bound(identity,inverse(X_316))) = multiply(identity,greatest_lower_bound(identity,inverse(X_316))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316)))),greatest_lower_bound(identity,inverse(X_316))),multiply(inverse(multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316)))),greatest_lower_bound(identity,inverse(X_316)))) )],[refute_0_2992,refute_0_2993]) ).
cnf(refute_0_2995,plain,
multiply(inverse(multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316)))),greatest_lower_bound(identity,inverse(X_316))) = multiply(identity,greatest_lower_bound(identity,inverse(X_316))),
inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316)))),identity) )],[refute_0_2991,refute_0_2994]) ).
cnf(refute_0_2996,plain,
( multiply(identity,greatest_lower_bound(identity,inverse(X_316))) != greatest_lower_bound(identity,inverse(X_316))
| multiply(inverse(multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316)))),greatest_lower_bound(identity,inverse(X_316))) != multiply(identity,greatest_lower_bound(identity,inverse(X_316)))
| multiply(inverse(multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316)))),greatest_lower_bound(identity,inverse(X_316))) = greatest_lower_bound(identity,inverse(X_316)) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(inverse(multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316)))),greatest_lower_bound(identity,inverse(X_316))))),bind(Y0,$fot(multiply(identity,greatest_lower_bound(identity,inverse(X_316))))),bind(Z0,$fot(greatest_lower_bound(identity,inverse(X_316))))]]) ).
cnf(refute_0_2997,plain,
( multiply(identity,greatest_lower_bound(identity,inverse(X_316))) != greatest_lower_bound(identity,inverse(X_316))
| multiply(inverse(multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316)))),greatest_lower_bound(identity,inverse(X_316))) = greatest_lower_bound(identity,inverse(X_316)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316)))),greatest_lower_bound(identity,inverse(X_316))),multiply(identity,greatest_lower_bound(identity,inverse(X_316)))) )],[refute_0_2995,refute_0_2996]) ).
cnf(refute_0_2998,plain,
multiply(inverse(multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316)))),greatest_lower_bound(identity,inverse(X_316))) = greatest_lower_bound(identity,inverse(X_316)),
inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(identity,inverse(X_316))),greatest_lower_bound(identity,inverse(X_316))) )],[refute_0_1704,refute_0_2997]) ).
cnf(refute_0_2999,plain,
( multiply(inverse(multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316)))),greatest_lower_bound(identity,inverse(X_316))) != greatest_lower_bound(identity,inverse(X_316))
| inverse(least_upper_bound(identity,X_316)) != multiply(inverse(multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316)))),greatest_lower_bound(identity,inverse(X_316)))
| inverse(least_upper_bound(identity,X_316)) = greatest_lower_bound(identity,inverse(X_316)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,X_316)),multiply(inverse(multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316)))),greatest_lower_bound(identity,inverse(X_316)))) ),[1],$fot(greatest_lower_bound(identity,inverse(X_316)))]]) ).
cnf(refute_0_3000,plain,
( inverse(least_upper_bound(identity,X_316)) != multiply(inverse(multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316)))),greatest_lower_bound(identity,inverse(X_316)))
| inverse(least_upper_bound(identity,X_316)) = greatest_lower_bound(identity,inverse(X_316)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316)))),greatest_lower_bound(identity,inverse(X_316))),greatest_lower_bound(identity,inverse(X_316))) )],[refute_0_2998,refute_0_2999]) ).
cnf(refute_0_3001,plain,
inverse(least_upper_bound(identity,X_316)) = greatest_lower_bound(identity,inverse(X_316)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,X_316)),multiply(inverse(multiply(greatest_lower_bound(X_316,identity),least_upper_bound(identity,inverse(X_316)))),greatest_lower_bound(identity,inverse(X_316)))) )],[refute_0_1703,refute_0_3000]) ).
cnf(refute_0_3002,plain,
( inverse(least_upper_bound(identity,X_316)) != greatest_lower_bound(identity,inverse(X_316))
| greatest_lower_bound(identity,inverse(X_316)) = inverse(least_upper_bound(identity,X_316)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(inverse(least_upper_bound(identity,X_316)))),bind(Y0,$fot(greatest_lower_bound(identity,inverse(X_316))))]]) ).
cnf(refute_0_3003,plain,
greatest_lower_bound(identity,inverse(X_316)) = inverse(least_upper_bound(identity,X_316)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,X_316)),greatest_lower_bound(identity,inverse(X_316))) )],[refute_0_3001,refute_0_3002]) ).
cnf(refute_0_3004,plain,
greatest_lower_bound(identity,inverse(X_31)) = inverse(least_upper_bound(identity,X_31)),
inference(subst,[],[refute_0_3003:[bind(X_316,$fot(X_31))]]) ).
cnf(refute_0_3005,plain,
inverse(greatest_lower_bound(identity,inverse(X_31))) = inverse(greatest_lower_bound(identity,inverse(X_31))),
introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(identity,inverse(X_31))))]]) ).
cnf(refute_0_3006,plain,
( greatest_lower_bound(identity,inverse(X_31)) != inverse(least_upper_bound(identity,X_31))
| inverse(greatest_lower_bound(identity,inverse(X_31))) != inverse(greatest_lower_bound(identity,inverse(X_31)))
| inverse(greatest_lower_bound(identity,inverse(X_31))) = inverse(inverse(least_upper_bound(identity,X_31))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_31))),inverse(greatest_lower_bound(identity,inverse(X_31)))) ),[1,0],$fot(inverse(least_upper_bound(identity,X_31)))]]) ).
cnf(refute_0_3007,plain,
( greatest_lower_bound(identity,inverse(X_31)) != inverse(least_upper_bound(identity,X_31))
| inverse(greatest_lower_bound(identity,inverse(X_31))) = inverse(inverse(least_upper_bound(identity,X_31))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_31))),inverse(greatest_lower_bound(identity,inverse(X_31)))) )],[refute_0_3005,refute_0_3006]) ).
cnf(refute_0_3008,plain,
inverse(greatest_lower_bound(identity,inverse(X_31))) = inverse(inverse(least_upper_bound(identity,X_31))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(X_31)),inverse(least_upper_bound(identity,X_31))) )],[refute_0_3004,refute_0_3007]) ).
cnf(refute_0_3009,plain,
( inverse(greatest_lower_bound(identity,inverse(X_31))) != inverse(inverse(least_upper_bound(identity,X_31)))
| inverse(inverse(least_upper_bound(identity,X_31))) != least_upper_bound(identity,X_31)
| inverse(greatest_lower_bound(identity,inverse(X_31))) = least_upper_bound(identity,X_31) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(inverse(greatest_lower_bound(identity,inverse(X_31))))),bind(Y0,$fot(inverse(inverse(least_upper_bound(identity,X_31))))),bind(Z0,$fot(least_upper_bound(identity,X_31)))]]) ).
cnf(refute_0_3010,plain,
( inverse(inverse(least_upper_bound(identity,X_31))) != least_upper_bound(identity,X_31)
| inverse(greatest_lower_bound(identity,inverse(X_31))) = least_upper_bound(identity,X_31) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_31))),inverse(inverse(least_upper_bound(identity,X_31)))) )],[refute_0_3008,refute_0_3009]) ).
cnf(refute_0_3011,plain,
inverse(greatest_lower_bound(identity,inverse(X_31))) = least_upper_bound(identity,X_31),
inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(identity,X_31))),least_upper_bound(identity,X_31)) )],[refute_0_1032,refute_0_3010]) ).
cnf(refute_0_3012,plain,
multiply(greatest_lower_bound(identity,X_31),inverse(greatest_lower_bound(identity,inverse(X_31)))) = multiply(greatest_lower_bound(identity,X_31),inverse(greatest_lower_bound(identity,inverse(X_31)))),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(identity,X_31),inverse(greatest_lower_bound(identity,inverse(X_31)))))]]) ).
cnf(refute_0_3013,plain,
( multiply(greatest_lower_bound(identity,X_31),inverse(greatest_lower_bound(identity,inverse(X_31)))) != multiply(greatest_lower_bound(identity,X_31),inverse(greatest_lower_bound(identity,inverse(X_31))))
| inverse(greatest_lower_bound(identity,inverse(X_31))) != least_upper_bound(identity,X_31)
| multiply(greatest_lower_bound(identity,X_31),inverse(greatest_lower_bound(identity,inverse(X_31)))) = multiply(greatest_lower_bound(identity,X_31),least_upper_bound(identity,X_31)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_31),inverse(greatest_lower_bound(identity,inverse(X_31)))),multiply(greatest_lower_bound(identity,X_31),inverse(greatest_lower_bound(identity,inverse(X_31))))) ),[1,1],$fot(least_upper_bound(identity,X_31))]]) ).
cnf(refute_0_3014,plain,
( inverse(greatest_lower_bound(identity,inverse(X_31))) != least_upper_bound(identity,X_31)
| multiply(greatest_lower_bound(identity,X_31),inverse(greatest_lower_bound(identity,inverse(X_31)))) = multiply(greatest_lower_bound(identity,X_31),least_upper_bound(identity,X_31)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_31),inverse(greatest_lower_bound(identity,inverse(X_31)))),multiply(greatest_lower_bound(identity,X_31),inverse(greatest_lower_bound(identity,inverse(X_31))))) )],[refute_0_3012,refute_0_3013]) ).
cnf(refute_0_3015,plain,
multiply(greatest_lower_bound(identity,X_31),inverse(greatest_lower_bound(identity,inverse(X_31)))) = multiply(greatest_lower_bound(identity,X_31),least_upper_bound(identity,X_31)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_31))),least_upper_bound(identity,X_31)) )],[refute_0_3011,refute_0_3014]) ).
cnf(refute_0_3016,plain,
( X_31 != multiply(greatest_lower_bound(identity,X_31),inverse(greatest_lower_bound(identity,inverse(X_31))))
| multiply(greatest_lower_bound(identity,X_31),inverse(greatest_lower_bound(identity,inverse(X_31)))) != multiply(greatest_lower_bound(identity,X_31),least_upper_bound(identity,X_31))
| X_31 = multiply(greatest_lower_bound(identity,X_31),least_upper_bound(identity,X_31)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_31,multiply(greatest_lower_bound(identity,X_31),least_upper_bound(identity,X_31))) ),[0],$fot(multiply(greatest_lower_bound(identity,X_31),inverse(greatest_lower_bound(identity,inverse(X_31)))))]]) ).
cnf(refute_0_3017,plain,
( X_31 != multiply(greatest_lower_bound(identity,X_31),inverse(greatest_lower_bound(identity,inverse(X_31))))
| X_31 = multiply(greatest_lower_bound(identity,X_31),least_upper_bound(identity,X_31)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_31),inverse(greatest_lower_bound(identity,inverse(X_31)))),multiply(greatest_lower_bound(identity,X_31),least_upper_bound(identity,X_31))) )],[refute_0_3015,refute_0_3016]) ).
cnf(refute_0_3018,plain,
X_31 = multiply(greatest_lower_bound(identity,X_31),least_upper_bound(identity,X_31)),
inference(resolve,[$cnf( $equal(X_31,multiply(greatest_lower_bound(identity,X_31),inverse(greatest_lower_bound(identity,inverse(X_31))))) )],[refute_0_1031,refute_0_3017]) ).
cnf(refute_0_3019,plain,
( X_31 != multiply(greatest_lower_bound(identity,X_31),least_upper_bound(identity,X_31))
| multiply(greatest_lower_bound(identity,X_31),least_upper_bound(identity,X_31)) = X_31 ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(X_31)),bind(Y0,$fot(multiply(greatest_lower_bound(identity,X_31),least_upper_bound(identity,X_31))))]]) ).
cnf(refute_0_3020,plain,
multiply(greatest_lower_bound(identity,X_31),least_upper_bound(identity,X_31)) = X_31,
inference(resolve,[$cnf( $equal(X_31,multiply(greatest_lower_bound(identity,X_31),least_upper_bound(identity,X_31))) )],[refute_0_3018,refute_0_3019]) ).
cnf(refute_0_3021,plain,
multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125)) = X_125,
inference(subst,[],[refute_0_3020:[bind(X_31,$fot(X_125))]]) ).
cnf(refute_0_3022,plain,
inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125))) = inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125))),
introduced(tautology,[refl,[$fot(inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125))))]]) ).
cnf(refute_0_3023,plain,
( multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125)) != X_125
| inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125))) != inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125)))
| inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125))) = inverse(X_125) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125))),inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125)))) ),[1,0],$fot(X_125)]]) ).
cnf(refute_0_3024,plain,
( multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125)) != X_125
| inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125))) = inverse(X_125) ),
inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125))),inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125)))) )],[refute_0_3022,refute_0_3023]) ).
cnf(refute_0_3025,plain,
inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125))) = inverse(X_125),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125)),X_125) )],[refute_0_3021,refute_0_3024]) ).
cnf(refute_0_3026,plain,
multiply(inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125))),least_upper_bound(X_125,identity)) = multiply(inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125))),least_upper_bound(X_125,identity)),
introduced(tautology,[refl,[$fot(multiply(inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125))),least_upper_bound(X_125,identity)))]]) ).
cnf(refute_0_3027,plain,
( multiply(inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125))),least_upper_bound(X_125,identity)) != multiply(inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125))),least_upper_bound(X_125,identity))
| inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125))) != inverse(X_125)
| multiply(inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125))),least_upper_bound(X_125,identity)) = multiply(inverse(X_125),least_upper_bound(X_125,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125))),least_upper_bound(X_125,identity)),multiply(inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125))),least_upper_bound(X_125,identity))) ),[1,0],$fot(inverse(X_125))]]) ).
cnf(refute_0_3028,plain,
( inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125))) != inverse(X_125)
| multiply(inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125))),least_upper_bound(X_125,identity)) = multiply(inverse(X_125),least_upper_bound(X_125,identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125))),least_upper_bound(X_125,identity)),multiply(inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125))),least_upper_bound(X_125,identity))) )],[refute_0_3026,refute_0_3027]) ).
cnf(refute_0_3029,plain,
multiply(inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125))),least_upper_bound(X_125,identity)) = multiply(inverse(X_125),least_upper_bound(X_125,identity)),
inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125))),inverse(X_125)) )],[refute_0_3025,refute_0_3028]) ).
cnf(refute_0_3030,plain,
( multiply(inverse(X_125),least_upper_bound(X_125,identity)) != least_upper_bound(identity,inverse(X_125))
| multiply(inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125))),least_upper_bound(X_125,identity)) != multiply(inverse(X_125),least_upper_bound(X_125,identity))
| multiply(inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125))),least_upper_bound(X_125,identity)) = least_upper_bound(identity,inverse(X_125)) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125))),least_upper_bound(X_125,identity)))),bind(Y0,$fot(multiply(inverse(X_125),least_upper_bound(X_125,identity)))),bind(Z0,$fot(least_upper_bound(identity,inverse(X_125))))]]) ).
cnf(refute_0_3031,plain,
( multiply(inverse(X_125),least_upper_bound(X_125,identity)) != least_upper_bound(identity,inverse(X_125))
| multiply(inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125))),least_upper_bound(X_125,identity)) = least_upper_bound(identity,inverse(X_125)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125))),least_upper_bound(X_125,identity)),multiply(inverse(X_125),least_upper_bound(X_125,identity))) )],[refute_0_3029,refute_0_3030]) ).
cnf(refute_0_3032,plain,
multiply(inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125))),least_upper_bound(X_125,identity)) = least_upper_bound(identity,inverse(X_125)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_125),least_upper_bound(X_125,identity)),least_upper_bound(identity,inverse(X_125))) )],[refute_0_940,refute_0_3031]) ).
cnf(refute_0_3033,plain,
( multiply(inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125))),least_upper_bound(X_125,identity)) != least_upper_bound(identity,inverse(X_125))
| inverse(greatest_lower_bound(identity,X_125)) != multiply(inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125))),least_upper_bound(X_125,identity))
| inverse(greatest_lower_bound(identity,X_125)) = least_upper_bound(identity,inverse(X_125)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,X_125)),multiply(inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125))),least_upper_bound(X_125,identity))) ),[1],$fot(least_upper_bound(identity,inverse(X_125)))]]) ).
cnf(refute_0_3034,plain,
( inverse(greatest_lower_bound(identity,X_125)) != multiply(inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125))),least_upper_bound(X_125,identity))
| inverse(greatest_lower_bound(identity,X_125)) = least_upper_bound(identity,inverse(X_125)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125))),least_upper_bound(X_125,identity)),least_upper_bound(identity,inverse(X_125))) )],[refute_0_3032,refute_0_3033]) ).
cnf(refute_0_3035,plain,
inverse(greatest_lower_bound(identity,X_125)) = least_upper_bound(identity,inverse(X_125)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,X_125)),multiply(inverse(multiply(greatest_lower_bound(identity,X_125),least_upper_bound(identity,X_125))),least_upper_bound(X_125,identity))) )],[refute_0_939,refute_0_3034]) ).
cnf(refute_0_3036,plain,
( inverse(greatest_lower_bound(identity,X_125)) != least_upper_bound(identity,inverse(X_125))
| least_upper_bound(identity,inverse(X_125)) = inverse(greatest_lower_bound(identity,X_125)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(inverse(greatest_lower_bound(identity,X_125)))),bind(Y0,$fot(least_upper_bound(identity,inverse(X_125))))]]) ).
cnf(refute_0_3037,plain,
least_upper_bound(identity,inverse(X_125)) = inverse(greatest_lower_bound(identity,X_125)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,X_125)),least_upper_bound(identity,inverse(X_125))) )],[refute_0_3035,refute_0_3036]) ).
cnf(refute_0_3038,plain,
least_upper_bound(identity,inverse(X_75)) = inverse(greatest_lower_bound(identity,X_75)),
inference(subst,[],[refute_0_3037:[bind(X_125,$fot(X_75))]]) ).
cnf(refute_0_3039,plain,
( multiply(least_upper_bound(identity,X_75),inverse(X_75)) != least_upper_bound(identity,inverse(X_75))
| least_upper_bound(identity,inverse(X_75)) != inverse(greatest_lower_bound(identity,X_75))
| multiply(least_upper_bound(identity,X_75),inverse(X_75)) = inverse(greatest_lower_bound(identity,X_75)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(identity,X_75),inverse(X_75)),inverse(greatest_lower_bound(identity,X_75))) ),[0],$fot(least_upper_bound(identity,inverse(X_75)))]]) ).
cnf(refute_0_3040,plain,
( multiply(least_upper_bound(identity,X_75),inverse(X_75)) != least_upper_bound(identity,inverse(X_75))
| multiply(least_upper_bound(identity,X_75),inverse(X_75)) = inverse(greatest_lower_bound(identity,X_75)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(X_75)),inverse(greatest_lower_bound(identity,X_75))) )],[refute_0_3038,refute_0_3039]) ).
cnf(refute_0_3041,plain,
multiply(least_upper_bound(identity,X_75),inverse(X_75)) = inverse(greatest_lower_bound(identity,X_75)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_75),inverse(X_75)),least_upper_bound(identity,inverse(X_75))) )],[refute_0_785,refute_0_3040]) ).
cnf(refute_0_3042,plain,
multiply(least_upper_bound(identity,multiply(inverse(X_145),X_31)),inverse(multiply(inverse(X_145),X_31))) = inverse(greatest_lower_bound(identity,multiply(inverse(X_145),X_31))),
inference(subst,[],[refute_0_3041:[bind(X_75,$fot(multiply(inverse(X_145),X_31)))]]) ).
cnf(refute_0_3043,plain,
( multiply(least_upper_bound(identity,multiply(inverse(X_145),X_31)),inverse(multiply(inverse(X_145),X_31))) != inverse(greatest_lower_bound(identity,multiply(inverse(X_145),X_31)))
| inverse(multiply(inverse(X_145),X_31)) != multiply(inverse(X_31),X_145)
| multiply(least_upper_bound(identity,multiply(inverse(X_145),X_31)),multiply(inverse(X_31),X_145)) = inverse(greatest_lower_bound(identity,multiply(inverse(X_145),X_31))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(inverse(X_145),X_31)),inverse(multiply(inverse(X_145),X_31))),inverse(greatest_lower_bound(identity,multiply(inverse(X_145),X_31)))) ),[0,1],$fot(multiply(inverse(X_31),X_145))]]) ).
cnf(refute_0_3044,plain,
( multiply(least_upper_bound(identity,multiply(inverse(X_145),X_31)),inverse(multiply(inverse(X_145),X_31))) != inverse(greatest_lower_bound(identity,multiply(inverse(X_145),X_31)))
| multiply(least_upper_bound(identity,multiply(inverse(X_145),X_31)),multiply(inverse(X_31),X_145)) = inverse(greatest_lower_bound(identity,multiply(inverse(X_145),X_31))) ),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_145),X_31)),multiply(inverse(X_31),X_145)) )],[refute_0_110,refute_0_3043]) ).
cnf(refute_0_3045,plain,
multiply(least_upper_bound(identity,multiply(inverse(X_145),X_31)),multiply(inverse(X_31),X_145)) = inverse(greatest_lower_bound(identity,multiply(inverse(X_145),X_31))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(inverse(X_145),X_31)),inverse(multiply(inverse(X_145),X_31))),inverse(greatest_lower_bound(identity,multiply(inverse(X_145),X_31)))) )],[refute_0_3042,refute_0_3044]) ).
cnf(refute_0_3046,plain,
multiply(identity,least_upper_bound(identity,multiply(inverse(X_31),X_145))) = least_upper_bound(identity,multiply(inverse(X_31),X_145)),
inference(subst,[],[left_identity:[bind(X,$fot(least_upper_bound(identity,multiply(inverse(X_31),X_145))))]]) ).
cnf(refute_0_3047,plain,
multiply(identity,least_upper_bound(multiply(inverse(X_31),X_145),identity)) = multiply(identity,least_upper_bound(identity,multiply(inverse(X_31),X_145))),
inference(subst,[],[refute_0_598:[bind(X_19,$fot(identity)),bind(X_88,$fot(multiply(inverse(X_31),X_145)))]]) ).
cnf(refute_0_3048,plain,
( multiply(identity,least_upper_bound(multiply(inverse(X_31),X_145),identity)) != multiply(identity,least_upper_bound(identity,multiply(inverse(X_31),X_145)))
| multiply(identity,least_upper_bound(identity,multiply(inverse(X_31),X_145))) != least_upper_bound(identity,multiply(inverse(X_31),X_145))
| multiply(identity,least_upper_bound(multiply(inverse(X_31),X_145),identity)) = least_upper_bound(identity,multiply(inverse(X_31),X_145)) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(identity,least_upper_bound(multiply(inverse(X_31),X_145),identity)))),bind(Y0,$fot(multiply(identity,least_upper_bound(identity,multiply(inverse(X_31),X_145))))),bind(Z0,$fot(least_upper_bound(identity,multiply(inverse(X_31),X_145))))]]) ).
cnf(refute_0_3049,plain,
( multiply(identity,least_upper_bound(identity,multiply(inverse(X_31),X_145))) != least_upper_bound(identity,multiply(inverse(X_31),X_145))
| multiply(identity,least_upper_bound(multiply(inverse(X_31),X_145),identity)) = least_upper_bound(identity,multiply(inverse(X_31),X_145)) ),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(multiply(inverse(X_31),X_145),identity)),multiply(identity,least_upper_bound(identity,multiply(inverse(X_31),X_145)))) )],[refute_0_3047,refute_0_3048]) ).
cnf(refute_0_3050,plain,
multiply(identity,least_upper_bound(multiply(inverse(X_31),X_145),identity)) = least_upper_bound(identity,multiply(inverse(X_31),X_145)),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(identity,multiply(inverse(X_31),X_145))),least_upper_bound(identity,multiply(inverse(X_31),X_145))) )],[refute_0_3046,refute_0_3049]) ).
cnf(refute_0_3051,plain,
least_upper_bound(identity,multiply(identity,multiply(inverse(X_31),X_145))) = multiply(identity,least_upper_bound(multiply(inverse(X_31),X_145),identity)),
inference(subst,[],[refute_0_583:[bind(X_48,$fot(identity)),bind(X_49,$fot(multiply(inverse(X_31),X_145)))]]) ).
cnf(refute_0_3052,plain,
( multiply(identity,least_upper_bound(multiply(inverse(X_31),X_145),identity)) != least_upper_bound(identity,multiply(inverse(X_31),X_145))
| least_upper_bound(identity,multiply(identity,multiply(inverse(X_31),X_145))) != multiply(identity,least_upper_bound(multiply(inverse(X_31),X_145),identity))
| least_upper_bound(identity,multiply(identity,multiply(inverse(X_31),X_145))) = least_upper_bound(identity,multiply(inverse(X_31),X_145)) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(least_upper_bound(identity,multiply(identity,multiply(inverse(X_31),X_145))))),bind(Y0,$fot(multiply(identity,least_upper_bound(multiply(inverse(X_31),X_145),identity)))),bind(Z0,$fot(least_upper_bound(identity,multiply(inverse(X_31),X_145))))]]) ).
cnf(refute_0_3053,plain,
( multiply(identity,least_upper_bound(multiply(inverse(X_31),X_145),identity)) != least_upper_bound(identity,multiply(inverse(X_31),X_145))
| least_upper_bound(identity,multiply(identity,multiply(inverse(X_31),X_145))) = least_upper_bound(identity,multiply(inverse(X_31),X_145)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(identity,multiply(inverse(X_31),X_145))),multiply(identity,least_upper_bound(multiply(inverse(X_31),X_145),identity))) )],[refute_0_3051,refute_0_3052]) ).
cnf(refute_0_3054,plain,
least_upper_bound(identity,multiply(identity,multiply(inverse(X_31),X_145))) = least_upper_bound(identity,multiply(inverse(X_31),X_145)),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(multiply(inverse(X_31),X_145),identity)),least_upper_bound(identity,multiply(inverse(X_31),X_145))) )],[refute_0_3050,refute_0_3053]) ).
cnf(refute_0_3055,plain,
multiply(least_upper_bound(X_68,multiply(inverse(X_148),X_149)),inverse(multiply(inverse(X_148),X_149))) = least_upper_bound(identity,multiply(X_68,inverse(multiply(inverse(X_148),X_149)))),
inference(subst,[],[refute_0_780:[bind(X_69,$fot(multiply(inverse(X_148),X_149)))]]) ).
cnf(refute_0_3056,plain,
( multiply(least_upper_bound(X_68,multiply(inverse(X_148),X_149)),inverse(multiply(inverse(X_148),X_149))) != least_upper_bound(identity,multiply(X_68,inverse(multiply(inverse(X_148),X_149))))
| inverse(multiply(inverse(X_148),X_149)) != multiply(inverse(X_149),X_148)
| multiply(least_upper_bound(X_68,multiply(inverse(X_148),X_149)),multiply(inverse(X_149),X_148)) = least_upper_bound(identity,multiply(X_68,inverse(multiply(inverse(X_148),X_149)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_68,multiply(inverse(X_148),X_149)),inverse(multiply(inverse(X_148),X_149))),least_upper_bound(identity,multiply(X_68,inverse(multiply(inverse(X_148),X_149))))) ),[0,1],$fot(multiply(inverse(X_149),X_148))]]) ).
cnf(refute_0_3057,plain,
( multiply(least_upper_bound(X_68,multiply(inverse(X_148),X_149)),inverse(multiply(inverse(X_148),X_149))) != least_upper_bound(identity,multiply(X_68,inverse(multiply(inverse(X_148),X_149))))
| multiply(least_upper_bound(X_68,multiply(inverse(X_148),X_149)),multiply(inverse(X_149),X_148)) = least_upper_bound(identity,multiply(X_68,inverse(multiply(inverse(X_148),X_149)))) ),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_148),X_149)),multiply(inverse(X_149),X_148)) )],[refute_0_807,refute_0_3056]) ).
cnf(refute_0_3058,plain,
multiply(least_upper_bound(X_68,multiply(inverse(X_148),X_149)),multiply(inverse(X_149),X_148)) = least_upper_bound(identity,multiply(X_68,inverse(multiply(inverse(X_148),X_149)))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_68,multiply(inverse(X_148),X_149)),inverse(multiply(inverse(X_148),X_149))),least_upper_bound(identity,multiply(X_68,inverse(multiply(inverse(X_148),X_149))))) )],[refute_0_3055,refute_0_3057]) ).
cnf(refute_0_3059,plain,
multiply(X_68,inverse(multiply(inverse(X_148),X_149))) = multiply(X_68,inverse(multiply(inverse(X_148),X_149))),
introduced(tautology,[refl,[$fot(multiply(X_68,inverse(multiply(inverse(X_148),X_149))))]]) ).
cnf(refute_0_3060,plain,
( multiply(X_68,inverse(multiply(inverse(X_148),X_149))) != multiply(X_68,inverse(multiply(inverse(X_148),X_149)))
| inverse(multiply(inverse(X_148),X_149)) != multiply(inverse(X_149),X_148)
| multiply(X_68,inverse(multiply(inverse(X_148),X_149))) = multiply(X_68,multiply(inverse(X_149),X_148)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_68,inverse(multiply(inverse(X_148),X_149))),multiply(X_68,inverse(multiply(inverse(X_148),X_149)))) ),[1,1],$fot(multiply(inverse(X_149),X_148))]]) ).
cnf(refute_0_3061,plain,
( inverse(multiply(inverse(X_148),X_149)) != multiply(inverse(X_149),X_148)
| multiply(X_68,inverse(multiply(inverse(X_148),X_149))) = multiply(X_68,multiply(inverse(X_149),X_148)) ),
inference(resolve,[$cnf( $equal(multiply(X_68,inverse(multiply(inverse(X_148),X_149))),multiply(X_68,inverse(multiply(inverse(X_148),X_149)))) )],[refute_0_3059,refute_0_3060]) ).
cnf(refute_0_3062,plain,
multiply(X_68,inverse(multiply(inverse(X_148),X_149))) = multiply(X_68,multiply(inverse(X_149),X_148)),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_148),X_149)),multiply(inverse(X_149),X_148)) )],[refute_0_807,refute_0_3061]) ).
cnf(refute_0_3063,plain,
least_upper_bound(identity,multiply(X_68,inverse(multiply(inverse(X_148),X_149)))) = least_upper_bound(identity,multiply(X_68,inverse(multiply(inverse(X_148),X_149)))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,multiply(X_68,inverse(multiply(inverse(X_148),X_149)))))]]) ).
cnf(refute_0_3064,plain,
( multiply(X_68,inverse(multiply(inverse(X_148),X_149))) != multiply(X_68,multiply(inverse(X_149),X_148))
| least_upper_bound(identity,multiply(X_68,inverse(multiply(inverse(X_148),X_149)))) != least_upper_bound(identity,multiply(X_68,inverse(multiply(inverse(X_148),X_149))))
| least_upper_bound(identity,multiply(X_68,inverse(multiply(inverse(X_148),X_149)))) = least_upper_bound(identity,multiply(X_68,multiply(inverse(X_149),X_148))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(X_68,inverse(multiply(inverse(X_148),X_149)))),least_upper_bound(identity,multiply(X_68,inverse(multiply(inverse(X_148),X_149))))) ),[1,1],$fot(multiply(X_68,multiply(inverse(X_149),X_148)))]]) ).
cnf(refute_0_3065,plain,
( multiply(X_68,inverse(multiply(inverse(X_148),X_149))) != multiply(X_68,multiply(inverse(X_149),X_148))
| least_upper_bound(identity,multiply(X_68,inverse(multiply(inverse(X_148),X_149)))) = least_upper_bound(identity,multiply(X_68,multiply(inverse(X_149),X_148))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_68,inverse(multiply(inverse(X_148),X_149)))),least_upper_bound(identity,multiply(X_68,inverse(multiply(inverse(X_148),X_149))))) )],[refute_0_3063,refute_0_3064]) ).
cnf(refute_0_3066,plain,
least_upper_bound(identity,multiply(X_68,inverse(multiply(inverse(X_148),X_149)))) = least_upper_bound(identity,multiply(X_68,multiply(inverse(X_149),X_148))),
inference(resolve,[$cnf( $equal(multiply(X_68,inverse(multiply(inverse(X_148),X_149))),multiply(X_68,multiply(inverse(X_149),X_148))) )],[refute_0_3062,refute_0_3065]) ).
cnf(refute_0_3067,plain,
( multiply(least_upper_bound(X_68,multiply(inverse(X_148),X_149)),multiply(inverse(X_149),X_148)) != least_upper_bound(identity,multiply(X_68,inverse(multiply(inverse(X_148),X_149))))
| least_upper_bound(identity,multiply(X_68,inverse(multiply(inverse(X_148),X_149)))) != least_upper_bound(identity,multiply(X_68,multiply(inverse(X_149),X_148)))
| multiply(least_upper_bound(X_68,multiply(inverse(X_148),X_149)),multiply(inverse(X_149),X_148)) = least_upper_bound(identity,multiply(X_68,multiply(inverse(X_149),X_148))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_68,multiply(inverse(X_148),X_149)),multiply(inverse(X_149),X_148)),least_upper_bound(identity,multiply(X_68,multiply(inverse(X_149),X_148)))) ),[0],$fot(least_upper_bound(identity,multiply(X_68,inverse(multiply(inverse(X_148),X_149)))))]]) ).
cnf(refute_0_3068,plain,
( multiply(least_upper_bound(X_68,multiply(inverse(X_148),X_149)),multiply(inverse(X_149),X_148)) != least_upper_bound(identity,multiply(X_68,inverse(multiply(inverse(X_148),X_149))))
| multiply(least_upper_bound(X_68,multiply(inverse(X_148),X_149)),multiply(inverse(X_149),X_148)) = least_upper_bound(identity,multiply(X_68,multiply(inverse(X_149),X_148))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_68,inverse(multiply(inverse(X_148),X_149)))),least_upper_bound(identity,multiply(X_68,multiply(inverse(X_149),X_148)))) )],[refute_0_3066,refute_0_3067]) ).
cnf(refute_0_3069,plain,
multiply(least_upper_bound(X_68,multiply(inverse(X_148),X_149)),multiply(inverse(X_149),X_148)) = least_upper_bound(identity,multiply(X_68,multiply(inverse(X_149),X_148))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_68,multiply(inverse(X_148),X_149)),multiply(inverse(X_149),X_148)),least_upper_bound(identity,multiply(X_68,inverse(multiply(inverse(X_148),X_149))))) )],[refute_0_3058,refute_0_3068]) ).
cnf(refute_0_3070,plain,
multiply(least_upper_bound(identity,multiply(inverse(X_145),X_31)),multiply(inverse(X_31),X_145)) = least_upper_bound(identity,multiply(identity,multiply(inverse(X_31),X_145))),
inference(subst,[],[refute_0_3069:[bind(X_148,$fot(X_145)),bind(X_149,$fot(X_31)),bind(X_68,$fot(identity))]]) ).
cnf(refute_0_3071,plain,
( multiply(least_upper_bound(identity,multiply(inverse(X_145),X_31)),multiply(inverse(X_31),X_145)) != least_upper_bound(identity,multiply(identity,multiply(inverse(X_31),X_145)))
| least_upper_bound(identity,multiply(identity,multiply(inverse(X_31),X_145))) != least_upper_bound(identity,multiply(inverse(X_31),X_145))
| multiply(least_upper_bound(identity,multiply(inverse(X_145),X_31)),multiply(inverse(X_31),X_145)) = least_upper_bound(identity,multiply(inverse(X_31),X_145)) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(least_upper_bound(identity,multiply(inverse(X_145),X_31)),multiply(inverse(X_31),X_145)))),bind(Y0,$fot(least_upper_bound(identity,multiply(identity,multiply(inverse(X_31),X_145))))),bind(Z0,$fot(least_upper_bound(identity,multiply(inverse(X_31),X_145))))]]) ).
cnf(refute_0_3072,plain,
( least_upper_bound(identity,multiply(identity,multiply(inverse(X_31),X_145))) != least_upper_bound(identity,multiply(inverse(X_31),X_145))
| multiply(least_upper_bound(identity,multiply(inverse(X_145),X_31)),multiply(inverse(X_31),X_145)) = least_upper_bound(identity,multiply(inverse(X_31),X_145)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(inverse(X_145),X_31)),multiply(inverse(X_31),X_145)),least_upper_bound(identity,multiply(identity,multiply(inverse(X_31),X_145)))) )],[refute_0_3070,refute_0_3071]) ).
cnf(refute_0_3073,plain,
multiply(least_upper_bound(identity,multiply(inverse(X_145),X_31)),multiply(inverse(X_31),X_145)) = least_upper_bound(identity,multiply(inverse(X_31),X_145)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(identity,multiply(inverse(X_31),X_145))),least_upper_bound(identity,multiply(inverse(X_31),X_145))) )],[refute_0_3054,refute_0_3072]) ).
cnf(refute_0_3074,plain,
( multiply(least_upper_bound(identity,multiply(inverse(X_145),X_31)),multiply(inverse(X_31),X_145)) != inverse(greatest_lower_bound(identity,multiply(inverse(X_145),X_31)))
| multiply(least_upper_bound(identity,multiply(inverse(X_145),X_31)),multiply(inverse(X_31),X_145)) != least_upper_bound(identity,multiply(inverse(X_31),X_145))
| least_upper_bound(identity,multiply(inverse(X_31),X_145)) = inverse(greatest_lower_bound(identity,multiply(inverse(X_145),X_31))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(inverse(X_145),X_31)),multiply(inverse(X_31),X_145)),inverse(greatest_lower_bound(identity,multiply(inverse(X_145),X_31)))) ),[0],$fot(least_upper_bound(identity,multiply(inverse(X_31),X_145)))]]) ).
cnf(refute_0_3075,plain,
( multiply(least_upper_bound(identity,multiply(inverse(X_145),X_31)),multiply(inverse(X_31),X_145)) != inverse(greatest_lower_bound(identity,multiply(inverse(X_145),X_31)))
| least_upper_bound(identity,multiply(inverse(X_31),X_145)) = inverse(greatest_lower_bound(identity,multiply(inverse(X_145),X_31))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(inverse(X_145),X_31)),multiply(inverse(X_31),X_145)),least_upper_bound(identity,multiply(inverse(X_31),X_145))) )],[refute_0_3073,refute_0_3074]) ).
cnf(refute_0_3076,plain,
least_upper_bound(identity,multiply(inverse(X_31),X_145)) = inverse(greatest_lower_bound(identity,multiply(inverse(X_145),X_31))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(inverse(X_145),X_31)),multiply(inverse(X_31),X_145)),inverse(greatest_lower_bound(identity,multiply(inverse(X_145),X_31)))) )],[refute_0_3045,refute_0_3075]) ).
cnf(refute_0_3077,plain,
( least_upper_bound(identity,multiply(inverse(X_31),X_145)) != inverse(greatest_lower_bound(identity,multiply(inverse(X_145),X_31)))
| inverse(greatest_lower_bound(identity,multiply(inverse(X_145),X_31))) = least_upper_bound(identity,multiply(inverse(X_31),X_145)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(least_upper_bound(identity,multiply(inverse(X_31),X_145)))),bind(Y0,$fot(inverse(greatest_lower_bound(identity,multiply(inverse(X_145),X_31)))))]]) ).
cnf(refute_0_3078,plain,
inverse(greatest_lower_bound(identity,multiply(inverse(X_145),X_31))) = least_upper_bound(identity,multiply(inverse(X_31),X_145)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(X_31),X_145)),inverse(greatest_lower_bound(identity,multiply(inverse(X_145),X_31)))) )],[refute_0_3076,refute_0_3077]) ).
cnf(refute_0_3079,plain,
inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))) = least_upper_bound(identity,multiply(inverse(X_105),X_106)),
inference(subst,[],[refute_0_3078:[bind(X_145,$fot(X_106)),bind(X_31,$fot(X_105))]]) ).
cnf(refute_0_3080,plain,
( multiply(inverse(greatest_lower_bound(X_105,X_106)),X_106) != inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))
| inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))) != least_upper_bound(identity,multiply(inverse(X_105),X_106))
| multiply(inverse(greatest_lower_bound(X_105,X_106)),X_106) = least_upper_bound(identity,multiply(inverse(X_105),X_106)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(greatest_lower_bound(X_105,X_106)),X_106),least_upper_bound(identity,multiply(inverse(X_105),X_106))) ),[0],$fot(inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))))]]) ).
cnf(refute_0_3081,plain,
( multiply(inverse(greatest_lower_bound(X_105,X_106)),X_106) != inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))
| multiply(inverse(greatest_lower_bound(X_105,X_106)),X_106) = least_upper_bound(identity,multiply(inverse(X_105),X_106)) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105))),least_upper_bound(identity,multiply(inverse(X_105),X_106))) )],[refute_0_3079,refute_0_3080]) ).
cnf(refute_0_3082,plain,
multiply(inverse(greatest_lower_bound(X_105,X_106)),X_106) = least_upper_bound(identity,multiply(inverse(X_105),X_106)),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_105,X_106)),X_106),inverse(greatest_lower_bound(identity,multiply(inverse(X_106),X_105)))) )],[refute_0_771,refute_0_3081]) ).
cnf(refute_0_3083,plain,
multiply(inverse(greatest_lower_bound(X_657,X_31)),X_31) = least_upper_bound(identity,multiply(inverse(X_657),X_31)),
inference(subst,[],[refute_0_3082:[bind(X_105,$fot(X_657)),bind(X_106,$fot(X_31))]]) ).
cnf(refute_0_3084,plain,
( multiply(inverse(greatest_lower_bound(X_657,X_31)),X_31) != least_upper_bound(identity,multiply(inverse(X_657),X_31))
| least_upper_bound(identity,multiply(inverse(X_657),X_31)) = multiply(inverse(greatest_lower_bound(X_657,X_31)),X_31) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(X_657,X_31)),X_31))),bind(Y0,$fot(least_upper_bound(identity,multiply(inverse(X_657),X_31))))]]) ).
cnf(refute_0_3085,plain,
least_upper_bound(identity,multiply(inverse(X_657),X_31)) = multiply(inverse(greatest_lower_bound(X_657,X_31)),X_31),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_657,X_31)),X_31),least_upper_bound(identity,multiply(inverse(X_657),X_31))) )],[refute_0_3083,refute_0_3084]) ).
cnf(refute_0_3086,plain,
( multiply(inverse(inverse(X_657)),least_upper_bound(identity,multiply(inverse(X_657),X_31))) != least_upper_bound(multiply(inverse(inverse(X_657)),identity),X_31)
| least_upper_bound(identity,multiply(inverse(X_657),X_31)) != multiply(inverse(greatest_lower_bound(X_657,X_31)),X_31)
| multiply(inverse(inverse(X_657)),multiply(inverse(greatest_lower_bound(X_657,X_31)),X_31)) = least_upper_bound(multiply(inverse(inverse(X_657)),identity),X_31) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X_657)),least_upper_bound(identity,multiply(inverse(X_657),X_31))),least_upper_bound(multiply(inverse(inverse(X_657)),identity),X_31)) ),[0,1],$fot(multiply(inverse(greatest_lower_bound(X_657,X_31)),X_31))]]) ).
cnf(refute_0_3087,plain,
( multiply(inverse(inverse(X_657)),least_upper_bound(identity,multiply(inverse(X_657),X_31))) != least_upper_bound(multiply(inverse(inverse(X_657)),identity),X_31)
| multiply(inverse(inverse(X_657)),multiply(inverse(greatest_lower_bound(X_657,X_31)),X_31)) = least_upper_bound(multiply(inverse(inverse(X_657)),identity),X_31) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(X_657),X_31)),multiply(inverse(greatest_lower_bound(X_657,X_31)),X_31)) )],[refute_0_3085,refute_0_3086]) ).
cnf(refute_0_3088,plain,
multiply(inverse(inverse(X_657)),multiply(inverse(greatest_lower_bound(X_657,X_31)),X_31)) = least_upper_bound(multiply(inverse(inverse(X_657)),identity),X_31),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_657)),least_upper_bound(identity,multiply(inverse(X_657),X_31))),least_upper_bound(multiply(inverse(inverse(X_657)),identity),X_31)) )],[refute_0_18,refute_0_3087]) ).
cnf(refute_0_3089,plain,
multiply(multiply(X_657,inverse(greatest_lower_bound(X_657,X_31))),X_31) = multiply(X_657,multiply(inverse(greatest_lower_bound(X_657,X_31)),X_31)),
inference(subst,[],[associativity:[bind(X,$fot(X_657)),bind(Y,$fot(inverse(greatest_lower_bound(X_657,X_31)))),bind(Z,$fot(X_31))]]) ).
cnf(refute_0_3090,plain,
inverse(multiply(greatest_lower_bound(X_657,X_31),inverse(X_657))) = multiply(X_657,inverse(greatest_lower_bound(X_657,X_31))),
inference(subst,[],[refute_0_2727:[bind(X_35,$fot(X_657)),bind(X_352,$fot(greatest_lower_bound(X_657,X_31)))]]) ).
cnf(refute_0_3091,plain,
multiply(inverse(multiply(greatest_lower_bound(X_657,X_31),inverse(X_657))),X_31) = multiply(inverse(multiply(greatest_lower_bound(X_657,X_31),inverse(X_657))),X_31),
introduced(tautology,[refl,[$fot(multiply(inverse(multiply(greatest_lower_bound(X_657,X_31),inverse(X_657))),X_31))]]) ).
cnf(refute_0_3092,plain,
( multiply(inverse(multiply(greatest_lower_bound(X_657,X_31),inverse(X_657))),X_31) != multiply(inverse(multiply(greatest_lower_bound(X_657,X_31),inverse(X_657))),X_31)
| inverse(multiply(greatest_lower_bound(X_657,X_31),inverse(X_657))) != multiply(X_657,inverse(greatest_lower_bound(X_657,X_31)))
| multiply(inverse(multiply(greatest_lower_bound(X_657,X_31),inverse(X_657))),X_31) = multiply(multiply(X_657,inverse(greatest_lower_bound(X_657,X_31))),X_31) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(greatest_lower_bound(X_657,X_31),inverse(X_657))),X_31),multiply(inverse(multiply(greatest_lower_bound(X_657,X_31),inverse(X_657))),X_31)) ),[1,0],$fot(multiply(X_657,inverse(greatest_lower_bound(X_657,X_31))))]]) ).
cnf(refute_0_3093,plain,
( inverse(multiply(greatest_lower_bound(X_657,X_31),inverse(X_657))) != multiply(X_657,inverse(greatest_lower_bound(X_657,X_31)))
| multiply(inverse(multiply(greatest_lower_bound(X_657,X_31),inverse(X_657))),X_31) = multiply(multiply(X_657,inverse(greatest_lower_bound(X_657,X_31))),X_31) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(greatest_lower_bound(X_657,X_31),inverse(X_657))),X_31),multiply(inverse(multiply(greatest_lower_bound(X_657,X_31),inverse(X_657))),X_31)) )],[refute_0_3091,refute_0_3092]) ).
cnf(refute_0_3094,plain,
multiply(inverse(multiply(greatest_lower_bound(X_657,X_31),inverse(X_657))),X_31) = multiply(multiply(X_657,inverse(greatest_lower_bound(X_657,X_31))),X_31),
inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(X_657,X_31),inverse(X_657))),multiply(X_657,inverse(greatest_lower_bound(X_657,X_31)))) )],[refute_0_3090,refute_0_3093]) ).
cnf(refute_0_3095,plain,
( multiply(multiply(X_657,inverse(greatest_lower_bound(X_657,X_31))),X_31) != multiply(X_657,multiply(inverse(greatest_lower_bound(X_657,X_31)),X_31))
| multiply(inverse(multiply(greatest_lower_bound(X_657,X_31),inverse(X_657))),X_31) != multiply(multiply(X_657,inverse(greatest_lower_bound(X_657,X_31))),X_31)
| multiply(inverse(multiply(greatest_lower_bound(X_657,X_31),inverse(X_657))),X_31) = multiply(X_657,multiply(inverse(greatest_lower_bound(X_657,X_31)),X_31)) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(inverse(multiply(greatest_lower_bound(X_657,X_31),inverse(X_657))),X_31))),bind(Y0,$fot(multiply(multiply(X_657,inverse(greatest_lower_bound(X_657,X_31))),X_31))),bind(Z0,$fot(multiply(X_657,multiply(inverse(greatest_lower_bound(X_657,X_31)),X_31))))]]) ).
cnf(refute_0_3096,plain,
( multiply(multiply(X_657,inverse(greatest_lower_bound(X_657,X_31))),X_31) != multiply(X_657,multiply(inverse(greatest_lower_bound(X_657,X_31)),X_31))
| multiply(inverse(multiply(greatest_lower_bound(X_657,X_31),inverse(X_657))),X_31) = multiply(X_657,multiply(inverse(greatest_lower_bound(X_657,X_31)),X_31)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(greatest_lower_bound(X_657,X_31),inverse(X_657))),X_31),multiply(multiply(X_657,inverse(greatest_lower_bound(X_657,X_31))),X_31)) )],[refute_0_3094,refute_0_3095]) ).
cnf(refute_0_3097,plain,
multiply(inverse(multiply(greatest_lower_bound(X_657,X_31),inverse(X_657))),X_31) = multiply(X_657,multiply(inverse(greatest_lower_bound(X_657,X_31)),X_31)),
inference(resolve,[$cnf( $equal(multiply(multiply(X_657,inverse(greatest_lower_bound(X_657,X_31))),X_31),multiply(X_657,multiply(inverse(greatest_lower_bound(X_657,X_31)),X_31))) )],[refute_0_3089,refute_0_3096]) ).
cnf(refute_0_3098,plain,
multiply(inverse(inverse(X_657)),multiply(inverse(greatest_lower_bound(X_657,X_31)),X_31)) = multiply(inverse(multiply(greatest_lower_bound(X_657,X_31),inverse(X_657))),X_31),
inference(subst,[],[refute_0_824:[bind(X_148,$fot(greatest_lower_bound(X_657,X_31))),bind(X_149,$fot(X_31)),bind(X_31,$fot(inverse(X_657)))]]) ).
cnf(refute_0_3099,plain,
( multiply(inverse(multiply(greatest_lower_bound(X_657,X_31),inverse(X_657))),X_31) != multiply(X_657,multiply(inverse(greatest_lower_bound(X_657,X_31)),X_31))
| multiply(inverse(inverse(X_657)),multiply(inverse(greatest_lower_bound(X_657,X_31)),X_31)) != multiply(inverse(multiply(greatest_lower_bound(X_657,X_31),inverse(X_657))),X_31)
| multiply(inverse(inverse(X_657)),multiply(inverse(greatest_lower_bound(X_657,X_31)),X_31)) = multiply(X_657,multiply(inverse(greatest_lower_bound(X_657,X_31)),X_31)) ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(inverse(inverse(X_657)),multiply(inverse(greatest_lower_bound(X_657,X_31)),X_31)))),bind(Y0,$fot(multiply(inverse(multiply(greatest_lower_bound(X_657,X_31),inverse(X_657))),X_31))),bind(Z0,$fot(multiply(X_657,multiply(inverse(greatest_lower_bound(X_657,X_31)),X_31))))]]) ).
cnf(refute_0_3100,plain,
( multiply(inverse(multiply(greatest_lower_bound(X_657,X_31),inverse(X_657))),X_31) != multiply(X_657,multiply(inverse(greatest_lower_bound(X_657,X_31)),X_31))
| multiply(inverse(inverse(X_657)),multiply(inverse(greatest_lower_bound(X_657,X_31)),X_31)) = multiply(X_657,multiply(inverse(greatest_lower_bound(X_657,X_31)),X_31)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_657)),multiply(inverse(greatest_lower_bound(X_657,X_31)),X_31)),multiply(inverse(multiply(greatest_lower_bound(X_657,X_31),inverse(X_657))),X_31)) )],[refute_0_3098,refute_0_3099]) ).
cnf(refute_0_3101,plain,
multiply(inverse(inverse(X_657)),multiply(inverse(greatest_lower_bound(X_657,X_31)),X_31)) = multiply(X_657,multiply(inverse(greatest_lower_bound(X_657,X_31)),X_31)),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(greatest_lower_bound(X_657,X_31),inverse(X_657))),X_31),multiply(X_657,multiply(inverse(greatest_lower_bound(X_657,X_31)),X_31))) )],[refute_0_3097,refute_0_3100]) ).
cnf(refute_0_3102,plain,
( multiply(inverse(inverse(X_657)),multiply(inverse(greatest_lower_bound(X_657,X_31)),X_31)) != multiply(X_657,multiply(inverse(greatest_lower_bound(X_657,X_31)),X_31))
| multiply(inverse(inverse(X_657)),multiply(inverse(greatest_lower_bound(X_657,X_31)),X_31)) != least_upper_bound(multiply(inverse(inverse(X_657)),identity),X_31)
| multiply(X_657,multiply(inverse(greatest_lower_bound(X_657,X_31)),X_31)) = least_upper_bound(multiply(inverse(inverse(X_657)),identity),X_31) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X_657)),multiply(inverse(greatest_lower_bound(X_657,X_31)),X_31)),least_upper_bound(multiply(inverse(inverse(X_657)),identity),X_31)) ),[0],$fot(multiply(X_657,multiply(inverse(greatest_lower_bound(X_657,X_31)),X_31)))]]) ).
cnf(refute_0_3103,plain,
( multiply(inverse(inverse(X_657)),multiply(inverse(greatest_lower_bound(X_657,X_31)),X_31)) != least_upper_bound(multiply(inverse(inverse(X_657)),identity),X_31)
| multiply(X_657,multiply(inverse(greatest_lower_bound(X_657,X_31)),X_31)) = least_upper_bound(multiply(inverse(inverse(X_657)),identity),X_31) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_657)),multiply(inverse(greatest_lower_bound(X_657,X_31)),X_31)),multiply(X_657,multiply(inverse(greatest_lower_bound(X_657,X_31)),X_31))) )],[refute_0_3101,refute_0_3102]) ).
cnf(refute_0_3104,plain,
inverse(inverse(X_657)) = X_657,
inference(subst,[],[refute_0_452:[bind(X_35,$fot(X_657))]]) ).
cnf(refute_0_3105,plain,
multiply(inverse(inverse(X_657)),identity) = inverse(inverse(X_657)),
inference(subst,[],[refute_0_88:[bind(X_33,$fot(inverse(inverse(X_657))))]]) ).
cnf(refute_0_3106,plain,
( multiply(inverse(inverse(X_657)),identity) != inverse(inverse(X_657))
| inverse(inverse(X_657)) != X_657
| multiply(inverse(inverse(X_657)),identity) = X_657 ),
inference(subst,[],[refute_0_114:[bind(X0,$fot(multiply(inverse(inverse(X_657)),identity))),bind(Y0,$fot(inverse(inverse(X_657)))),bind(Z0,$fot(X_657))]]) ).
cnf(refute_0_3107,plain,
( inverse(inverse(X_657)) != X_657
| multiply(inverse(inverse(X_657)),identity) = X_657 ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_657)),identity),inverse(inverse(X_657))) )],[refute_0_3105,refute_0_3106]) ).
cnf(refute_0_3108,plain,
multiply(inverse(inverse(X_657)),identity) = X_657,
inference(resolve,[$cnf( $equal(inverse(inverse(X_657)),X_657) )],[refute_0_3104,refute_0_3107]) ).
cnf(refute_0_3109,plain,
least_upper_bound(multiply(inverse(inverse(X_657)),identity),X_31) = least_upper_bound(multiply(inverse(inverse(X_657)),identity),X_31),
introduced(tautology,[refl,[$fot(least_upper_bound(multiply(inverse(inverse(X_657)),identity),X_31))]]) ).
cnf(refute_0_3110,plain,
( multiply(inverse(inverse(X_657)),identity) != X_657
| least_upper_bound(multiply(inverse(inverse(X_657)),identity),X_31) != least_upper_bound(multiply(inverse(inverse(X_657)),identity),X_31)
| least_upper_bound(multiply(inverse(inverse(X_657)),identity),X_31) = least_upper_bound(X_657,X_31) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(inverse(inverse(X_657)),identity),X_31),least_upper_bound(multiply(inverse(inverse(X_657)),identity),X_31)) ),[1,0],$fot(X_657)]]) ).
cnf(refute_0_3111,plain,
( multiply(inverse(inverse(X_657)),identity) != X_657
| least_upper_bound(multiply(inverse(inverse(X_657)),identity),X_31) = least_upper_bound(X_657,X_31) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(inverse(X_657)),identity),X_31),least_upper_bound(multiply(inverse(inverse(X_657)),identity),X_31)) )],[refute_0_3109,refute_0_3110]) ).
cnf(refute_0_3112,plain,
least_upper_bound(multiply(inverse(inverse(X_657)),identity),X_31) = least_upper_bound(X_657,X_31),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_657)),identity),X_657) )],[refute_0_3108,refute_0_3111]) ).
cnf(refute_0_3113,plain,
( multiply(X_657,multiply(inverse(greatest_lower_bound(X_657,X_31)),X_31)) != least_upper_bound(multiply(inverse(inverse(X_657)),identity),X_31)
| least_upper_bound(multiply(inverse(inverse(X_657)),identity),X_31) != least_upper_bound(X_657,X_31)
| multiply(X_657,multiply(inverse(greatest_lower_bound(X_657,X_31)),X_31)) = least_upper_bound(X_657,X_31) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_657,multiply(inverse(greatest_lower_bound(X_657,X_31)),X_31)),least_upper_bound(X_657,X_31)) ),[0],$fot(least_upper_bound(multiply(inverse(inverse(X_657)),identity),X_31))]]) ).
cnf(refute_0_3114,plain,
( multiply(X_657,multiply(inverse(greatest_lower_bound(X_657,X_31)),X_31)) != least_upper_bound(multiply(inverse(inverse(X_657)),identity),X_31)
| multiply(X_657,multiply(inverse(greatest_lower_bound(X_657,X_31)),X_31)) = least_upper_bound(X_657,X_31) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(inverse(X_657)),identity),X_31),least_upper_bound(X_657,X_31)) )],[refute_0_3112,refute_0_3113]) ).
cnf(refute_0_3115,plain,
( multiply(inverse(inverse(X_657)),multiply(inverse(greatest_lower_bound(X_657,X_31)),X_31)) != least_upper_bound(multiply(inverse(inverse(X_657)),identity),X_31)
| multiply(X_657,multiply(inverse(greatest_lower_bound(X_657,X_31)),X_31)) = least_upper_bound(X_657,X_31) ),
inference(resolve,[$cnf( $equal(multiply(X_657,multiply(inverse(greatest_lower_bound(X_657,X_31)),X_31)),least_upper_bound(multiply(inverse(inverse(X_657)),identity),X_31)) )],[refute_0_3103,refute_0_3114]) ).
cnf(refute_0_3116,plain,
multiply(X_657,multiply(inverse(greatest_lower_bound(X_657,X_31)),X_31)) = least_upper_bound(X_657,X_31),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_657)),multiply(inverse(greatest_lower_bound(X_657,X_31)),X_31)),least_upper_bound(multiply(inverse(inverse(X_657)),identity),X_31)) )],[refute_0_3088,refute_0_3115]) ).
cnf(refute_0_3117,plain,
multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)) = least_upper_bound(a,b),
inference(subst,[],[refute_0_3116:[bind(X_31,$fot(b)),bind(X_657,$fot(a))]]) ).
cnf(refute_0_3118,plain,
( multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)) != least_upper_bound(a,b)
| least_upper_bound(a,b) != least_upper_bound(a,b)
| multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)) = least_upper_bound(a,b) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)),least_upper_bound(a,b)) ),[0],$fot(least_upper_bound(a,b))]]) ).
cnf(refute_0_3119,plain,
( least_upper_bound(a,b) != least_upper_bound(a,b)
| multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)) = least_upper_bound(a,b) ),
inference(resolve,[$cnf( $equal(multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)),least_upper_bound(a,b)) )],[refute_0_3117,refute_0_3118]) ).
cnf(refute_0_3120,plain,
least_upper_bound(a,b) != least_upper_bound(a,b),
inference(resolve,[$cnf( $equal(multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)),least_upper_bound(a,b)) )],[refute_0_3119,prove_p11]) ).
cnf(refute_0_3121,plain,
least_upper_bound(a,b) = least_upper_bound(a,b),
introduced(tautology,[refl,[$fot(least_upper_bound(a,b))]]) ).
cnf(refute_0_3122,plain,
$false,
inference(resolve,[$cnf( $equal(least_upper_bound(a,b),least_upper_bound(a,b)) )],[refute_0_3121,refute_0_3120]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP180-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n006.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Tue Jun 14 14:01:11 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 129.24/129.38 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 129.24/129.38
% 129.24/129.38 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 129.60/129.81
%------------------------------------------------------------------------------