TSTP Solution File: GRP183-3 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP183-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n019.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 10:37:45 EDT 2022
% Result : Unsatisfiable 9.88s 10.06s
% Output : CNFRefutation 9.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 96
% Number of leaves : 238
% Syntax : Number of clauses : 1154 ( 606 unt; 0 nHn; 545 RR)
% Number of literals : 1934 (1933 equ; 784 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 : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 2259 ( 63 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
multiply(identity,X) = X ).
cnf(left_inverse,axiom,
multiply(inverse(X),X) = identity ).
cnf(associativity,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ).
cnf(symmetry_of_glb,axiom,
greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ).
cnf(symmetry_of_lub,axiom,
least_upper_bound(X,Y) = least_upper_bound(Y,X) ).
cnf(associativity_of_glb,axiom,
greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) ).
cnf(associativity_of_lub,axiom,
least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) ).
cnf(idempotence_of_lub,axiom,
least_upper_bound(X,X) = X ).
cnf(idempotence_of_gld,axiom,
greatest_lower_bound(X,X) = X ).
cnf(lub_absorbtion,axiom,
least_upper_bound(X,greatest_lower_bound(X,Y)) = X ).
cnf(glb_absorbtion,axiom,
greatest_lower_bound(X,least_upper_bound(X,Y)) = X ).
cnf(monotony_lub1,axiom,
multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ).
cnf(monotony_glb1,axiom,
multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)) ).
cnf(monotony_lub2,axiom,
multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) ).
cnf(monotony_glb2,axiom,
multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) ).
cnf(prove_20x,negated_conjecture,
greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(inverse(a),identity)) != identity ).
cnf(refute_0_0,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_1,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_2,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( least_upper_bound(X,Y) != least_upper_bound(Y,X)
| least_upper_bound(Y,X) = least_upper_bound(X,Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X,Y))),bind(Y0,$fot(least_upper_bound(Y,X)))]]) ).
cnf(refute_0_4,plain,
least_upper_bound(Y,X) = least_upper_bound(X,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(X,Y),least_upper_bound(Y,X)) )],[symmetry_of_lub,refute_0_3]) ).
cnf(refute_0_5,plain,
least_upper_bound(inverse(a),identity) = least_upper_bound(identity,inverse(a)),
inference(subst,[],[refute_0_4:[bind(X,$fot(identity)),bind(Y,$fot(inverse(a)))]]) ).
cnf(refute_0_6,plain,
greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(inverse(a),identity)) = greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(inverse(a),identity)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(inverse(a),identity)))]]) ).
cnf(refute_0_7,plain,
( greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(inverse(a),identity)) != greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(inverse(a),identity))
| least_upper_bound(inverse(a),identity) != least_upper_bound(identity,inverse(a))
| greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(inverse(a),identity)) = greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(identity,inverse(a))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(inverse(a),identity)),greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(inverse(a),identity))) ),[1,1],$fot(least_upper_bound(identity,inverse(a)))]]) ).
cnf(refute_0_8,plain,
( least_upper_bound(inverse(a),identity) != least_upper_bound(identity,inverse(a))
| greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(inverse(a),identity)) = greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(identity,inverse(a))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(inverse(a),identity)),greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(inverse(a),identity))) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(inverse(a),identity)) = greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(identity,inverse(a))),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(a),identity),least_upper_bound(identity,inverse(a))) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
( greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(identity,inverse(a))) != identity
| greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(inverse(a),identity)) != greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(identity,inverse(a)))
| greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(inverse(a),identity)) = identity ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(inverse(a),identity)),greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(identity,inverse(a)))) ),[1],$fot(identity)]]) ).
cnf(refute_0_11,plain,
( greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(identity,inverse(a))) != identity
| greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(inverse(a),identity)) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(inverse(a),identity)),greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(identity,inverse(a)))) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(identity,inverse(a))) != identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(inverse(a),identity)),identity) )],[refute_0_11,prove_20x]) ).
cnf(refute_0_13,plain,
multiply(greatest_lower_bound(X_29,identity),X_28) = greatest_lower_bound(multiply(X_29,X_28),multiply(identity,X_28)),
inference(subst,[],[monotony_glb2:[bind(X,$fot(X_28)),bind(Y,$fot(X_29)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_14,plain,
multiply(identity,X_28) = X_28,
inference(subst,[],[left_identity:[bind(X,$fot(X_28))]]) ).
cnf(refute_0_15,plain,
( multiply(greatest_lower_bound(X_29,identity),X_28) != greatest_lower_bound(multiply(X_29,X_28),multiply(identity,X_28))
| multiply(identity,X_28) != X_28
| multiply(greatest_lower_bound(X_29,identity),X_28) = greatest_lower_bound(multiply(X_29,X_28),X_28) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_29,identity),X_28),greatest_lower_bound(multiply(X_29,X_28),multiply(identity,X_28))) ),[1,1],$fot(X_28)]]) ).
cnf(refute_0_16,plain,
( multiply(greatest_lower_bound(X_29,identity),X_28) != greatest_lower_bound(multiply(X_29,X_28),multiply(identity,X_28))
| multiply(greatest_lower_bound(X_29,identity),X_28) = greatest_lower_bound(multiply(X_29,X_28),X_28) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_28),X_28) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
multiply(greatest_lower_bound(X_29,identity),X_28) = greatest_lower_bound(multiply(X_29,X_28),X_28),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_29,identity),X_28),greatest_lower_bound(multiply(X_29,X_28),multiply(identity,X_28))) )],[refute_0_13,refute_0_16]) ).
cnf(refute_0_18,plain,
( greatest_lower_bound(X,Y) != greatest_lower_bound(Y,X)
| greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X,Y))),bind(Y0,$fot(greatest_lower_bound(Y,X)))]]) ).
cnf(refute_0_19,plain,
greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X)) )],[symmetry_of_glb,refute_0_18]) ).
cnf(refute_0_20,plain,
greatest_lower_bound(multiply(X_29,X_28),X_28) = greatest_lower_bound(X_28,multiply(X_29,X_28)),
inference(subst,[],[refute_0_19:[bind(X,$fot(X_28)),bind(Y,$fot(multiply(X_29,X_28)))]]) ).
cnf(refute_0_21,plain,
( multiply(greatest_lower_bound(X_29,identity),X_28) != greatest_lower_bound(multiply(X_29,X_28),X_28)
| greatest_lower_bound(multiply(X_29,X_28),X_28) != greatest_lower_bound(X_28,multiply(X_29,X_28))
| multiply(greatest_lower_bound(X_29,identity),X_28) = greatest_lower_bound(X_28,multiply(X_29,X_28)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_29,identity),X_28),greatest_lower_bound(X_28,multiply(X_29,X_28))) ),[0],$fot(greatest_lower_bound(multiply(X_29,X_28),X_28))]]) ).
cnf(refute_0_22,plain,
( multiply(greatest_lower_bound(X_29,identity),X_28) != greatest_lower_bound(multiply(X_29,X_28),X_28)
| multiply(greatest_lower_bound(X_29,identity),X_28) = greatest_lower_bound(X_28,multiply(X_29,X_28)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_29,X_28),X_28),greatest_lower_bound(X_28,multiply(X_29,X_28))) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
multiply(greatest_lower_bound(X_29,identity),X_28) = greatest_lower_bound(X_28,multiply(X_29,X_28)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_29,identity),X_28),greatest_lower_bound(multiply(X_29,X_28),X_28)) )],[refute_0_17,refute_0_22]) ).
cnf(refute_0_24,plain,
multiply(greatest_lower_bound(inverse(X_128),identity),least_upper_bound(X_128,identity)) = greatest_lower_bound(least_upper_bound(X_128,identity),multiply(inverse(X_128),least_upper_bound(X_128,identity))),
inference(subst,[],[refute_0_23:[bind(X_28,$fot(least_upper_bound(X_128,identity))),bind(X_29,$fot(inverse(X_128)))]]) ).
cnf(refute_0_25,plain,
multiply(inverse(X_80),least_upper_bound(X_79,X_80)) = least_upper_bound(multiply(inverse(X_80),X_79),multiply(inverse(X_80),X_80)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(inverse(X_80))),bind(Y,$fot(X_79)),bind(Z,$fot(X_80))]]) ).
cnf(refute_0_26,plain,
multiply(inverse(X_80),X_80) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_80))]]) ).
cnf(refute_0_27,plain,
( multiply(inverse(X_80),X_80) != identity
| multiply(inverse(X_80),least_upper_bound(X_79,X_80)) != least_upper_bound(multiply(inverse(X_80),X_79),multiply(inverse(X_80),X_80))
| multiply(inverse(X_80),least_upper_bound(X_79,X_80)) = least_upper_bound(multiply(inverse(X_80),X_79),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_80),least_upper_bound(X_79,X_80)),least_upper_bound(multiply(inverse(X_80),X_79),multiply(inverse(X_80),X_80))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_28,plain,
( multiply(inverse(X_80),least_upper_bound(X_79,X_80)) != least_upper_bound(multiply(inverse(X_80),X_79),multiply(inverse(X_80),X_80))
| multiply(inverse(X_80),least_upper_bound(X_79,X_80)) = least_upper_bound(multiply(inverse(X_80),X_79),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_80),X_80),identity) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
multiply(inverse(X_80),least_upper_bound(X_79,X_80)) = least_upper_bound(multiply(inverse(X_80),X_79),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_80),least_upper_bound(X_79,X_80)),least_upper_bound(multiply(inverse(X_80),X_79),multiply(inverse(X_80),X_80))) )],[refute_0_25,refute_0_28]) ).
cnf(refute_0_30,plain,
least_upper_bound(X_33,X_32) = least_upper_bound(X_32,X_33),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_33)),bind(Y,$fot(X_32))]]) ).
cnf(refute_0_31,plain,
least_upper_bound(multiply(inverse(X_80),X_79),identity) = least_upper_bound(identity,multiply(inverse(X_80),X_79)),
inference(subst,[],[refute_0_30:[bind(X_32,$fot(identity)),bind(X_33,$fot(multiply(inverse(X_80),X_79)))]]) ).
cnf(refute_0_32,plain,
( multiply(inverse(X_80),least_upper_bound(X_79,X_80)) != least_upper_bound(multiply(inverse(X_80),X_79),identity)
| least_upper_bound(multiply(inverse(X_80),X_79),identity) != least_upper_bound(identity,multiply(inverse(X_80),X_79))
| multiply(inverse(X_80),least_upper_bound(X_79,X_80)) = least_upper_bound(identity,multiply(inverse(X_80),X_79)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_80),least_upper_bound(X_79,X_80)),least_upper_bound(identity,multiply(inverse(X_80),X_79))) ),[0],$fot(least_upper_bound(multiply(inverse(X_80),X_79),identity))]]) ).
cnf(refute_0_33,plain,
( multiply(inverse(X_80),least_upper_bound(X_79,X_80)) != least_upper_bound(multiply(inverse(X_80),X_79),identity)
| multiply(inverse(X_80),least_upper_bound(X_79,X_80)) = least_upper_bound(identity,multiply(inverse(X_80),X_79)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(X_80),X_79),identity),least_upper_bound(identity,multiply(inverse(X_80),X_79))) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
multiply(inverse(X_80),least_upper_bound(X_79,X_80)) = least_upper_bound(identity,multiply(inverse(X_80),X_79)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_80),least_upper_bound(X_79,X_80)),least_upper_bound(multiply(inverse(X_80),X_79),identity)) )],[refute_0_29,refute_0_33]) ).
cnf(refute_0_35,plain,
multiply(inverse(X_80),least_upper_bound(least_upper_bound(identity,X_80),X_80)) = least_upper_bound(identity,multiply(inverse(X_80),least_upper_bound(identity,X_80))),
inference(subst,[],[refute_0_34:[bind(X_79,$fot(least_upper_bound(identity,X_80)))]]) ).
cnf(refute_0_36,plain,
multiply(inverse(X_82),least_upper_bound(identity,X_82)) = least_upper_bound(identity,multiply(inverse(X_82),identity)),
inference(subst,[],[refute_0_34:[bind(X_79,$fot(identity)),bind(X_80,$fot(X_82))]]) ).
cnf(refute_0_37,plain,
multiply(multiply(inverse(X_71),X_71),X_72) = multiply(inverse(X_71),multiply(X_71,X_72)),
inference(subst,[],[associativity:[bind(X,$fot(inverse(X_71))),bind(Y,$fot(X_71)),bind(Z,$fot(X_72))]]) ).
cnf(refute_0_38,plain,
multiply(inverse(X_71),X_71) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_71))]]) ).
cnf(refute_0_39,plain,
( multiply(multiply(inverse(X_71),X_71),X_72) != multiply(inverse(X_71),multiply(X_71,X_72))
| multiply(inverse(X_71),X_71) != identity
| multiply(identity,X_72) = multiply(inverse(X_71),multiply(X_71,X_72)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_71),X_71),X_72),multiply(inverse(X_71),multiply(X_71,X_72))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_40,plain,
( multiply(multiply(inverse(X_71),X_71),X_72) != multiply(inverse(X_71),multiply(X_71,X_72))
| multiply(identity,X_72) = multiply(inverse(X_71),multiply(X_71,X_72)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_71),X_71),identity) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
multiply(identity,X_72) = multiply(inverse(X_71),multiply(X_71,X_72)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_71),X_71),X_72),multiply(inverse(X_71),multiply(X_71,X_72))) )],[refute_0_37,refute_0_40]) ).
cnf(refute_0_42,plain,
multiply(identity,X_72) = X_72,
inference(subst,[],[left_identity:[bind(X,$fot(X_72))]]) ).
cnf(refute_0_43,plain,
( multiply(identity,X_72) != X_72
| multiply(identity,X_72) != multiply(inverse(X_71),multiply(X_71,X_72))
| X_72 = multiply(inverse(X_71),multiply(X_71,X_72)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_72),multiply(inverse(X_71),multiply(X_71,X_72))) ),[0],$fot(X_72)]]) ).
cnf(refute_0_44,plain,
( multiply(identity,X_72) != multiply(inverse(X_71),multiply(X_71,X_72))
| X_72 = multiply(inverse(X_71),multiply(X_71,X_72)) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_72),X_72) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
X_72 = multiply(inverse(X_71),multiply(X_71,X_72)),
inference(resolve,[$cnf( $equal(multiply(identity,X_72),multiply(inverse(X_71),multiply(X_71,X_72))) )],[refute_0_41,refute_0_44]) ).
cnf(refute_0_46,plain,
X_74 = multiply(inverse(inverse(X_74)),multiply(inverse(X_74),X_74)),
inference(subst,[],[refute_0_45:[bind(X_71,$fot(inverse(X_74))),bind(X_72,$fot(X_74))]]) ).
cnf(refute_0_47,plain,
multiply(inverse(X_74),X_74) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_74))]]) ).
cnf(refute_0_48,plain,
( X_74 != multiply(inverse(inverse(X_74)),multiply(inverse(X_74),X_74))
| multiply(inverse(X_74),X_74) != identity
| X_74 = multiply(inverse(inverse(X_74)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(X_74,multiply(inverse(inverse(X_74)),multiply(inverse(X_74),X_74))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_49,plain,
( X_74 != multiply(inverse(inverse(X_74)),multiply(inverse(X_74),X_74))
| X_74 = multiply(inverse(inverse(X_74)),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_74),X_74),identity) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
X_74 = multiply(inverse(inverse(X_74)),identity),
inference(resolve,[$cnf( $equal(X_74,multiply(inverse(inverse(X_74)),multiply(inverse(X_74),X_74))) )],[refute_0_46,refute_0_49]) ).
cnf(refute_0_51,plain,
multiply(X_73,X_74) = multiply(inverse(inverse(X_73)),multiply(inverse(X_73),multiply(X_73,X_74))),
inference(subst,[],[refute_0_45:[bind(X_71,$fot(inverse(X_73))),bind(X_72,$fot(multiply(X_73,X_74)))]]) ).
cnf(refute_0_52,plain,
X_74 = multiply(inverse(X_73),multiply(X_73,X_74)),
inference(subst,[],[refute_0_45:[bind(X_71,$fot(X_73)),bind(X_72,$fot(X_74))]]) ).
cnf(refute_0_53,plain,
( X_74 != multiply(inverse(X_73),multiply(X_73,X_74))
| multiply(inverse(X_73),multiply(X_73,X_74)) = X_74 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_74)),bind(Y0,$fot(multiply(inverse(X_73),multiply(X_73,X_74))))]]) ).
cnf(refute_0_54,plain,
multiply(inverse(X_73),multiply(X_73,X_74)) = X_74,
inference(resolve,[$cnf( $equal(X_74,multiply(inverse(X_73),multiply(X_73,X_74))) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
( multiply(X_73,X_74) != multiply(inverse(inverse(X_73)),multiply(inverse(X_73),multiply(X_73,X_74)))
| multiply(inverse(X_73),multiply(X_73,X_74)) != X_74
| multiply(X_73,X_74) = multiply(inverse(inverse(X_73)),X_74) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_73,X_74),multiply(inverse(inverse(X_73)),multiply(inverse(X_73),multiply(X_73,X_74)))) ),[1,1],$fot(X_74)]]) ).
cnf(refute_0_56,plain,
( multiply(X_73,X_74) != multiply(inverse(inverse(X_73)),multiply(inverse(X_73),multiply(X_73,X_74)))
| multiply(X_73,X_74) = multiply(inverse(inverse(X_73)),X_74) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_73),multiply(X_73,X_74)),X_74) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
multiply(X_73,X_74) = multiply(inverse(inverse(X_73)),X_74),
inference(resolve,[$cnf( $equal(multiply(X_73,X_74),multiply(inverse(inverse(X_73)),multiply(inverse(X_73),multiply(X_73,X_74)))) )],[refute_0_51,refute_0_56]) ).
cnf(refute_0_58,plain,
( multiply(X_73,X_74) != multiply(inverse(inverse(X_73)),X_74)
| multiply(inverse(inverse(X_73)),X_74) = multiply(X_73,X_74) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X_73,X_74))),bind(Y0,$fot(multiply(inverse(inverse(X_73)),X_74)))]]) ).
cnf(refute_0_59,plain,
multiply(inverse(inverse(X_73)),X_74) = multiply(X_73,X_74),
inference(resolve,[$cnf( $equal(multiply(X_73,X_74),multiply(inverse(inverse(X_73)),X_74)) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
multiply(inverse(inverse(X_74)),identity) = multiply(X_74,identity),
inference(subst,[],[refute_0_59:[bind(X_73,$fot(X_74)),bind(X_74,$fot(identity))]]) ).
cnf(refute_0_61,plain,
( X_74 != multiply(inverse(inverse(X_74)),identity)
| multiply(inverse(inverse(X_74)),identity) != multiply(X_74,identity)
| X_74 = multiply(X_74,identity) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_74,multiply(X_74,identity)) ),[0],$fot(multiply(inverse(inverse(X_74)),identity))]]) ).
cnf(refute_0_62,plain,
( X_74 != multiply(inverse(inverse(X_74)),identity)
| X_74 = multiply(X_74,identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_74)),identity),multiply(X_74,identity)) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
X_74 = multiply(X_74,identity),
inference(resolve,[$cnf( $equal(X_74,multiply(inverse(inverse(X_74)),identity)) )],[refute_0_50,refute_0_62]) ).
cnf(refute_0_64,plain,
inverse(X_82) = multiply(inverse(X_82),identity),
inference(subst,[],[refute_0_63:[bind(X_74,$fot(inverse(X_82)))]]) ).
cnf(refute_0_65,plain,
( inverse(X_82) != multiply(inverse(X_82),identity)
| multiply(inverse(X_82),identity) = inverse(X_82) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(X_82))),bind(Y0,$fot(multiply(inverse(X_82),identity)))]]) ).
cnf(refute_0_66,plain,
multiply(inverse(X_82),identity) = inverse(X_82),
inference(resolve,[$cnf( $equal(inverse(X_82),multiply(inverse(X_82),identity)) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
( multiply(inverse(X_82),identity) != inverse(X_82)
| multiply(inverse(X_82),least_upper_bound(identity,X_82)) != least_upper_bound(identity,multiply(inverse(X_82),identity))
| multiply(inverse(X_82),least_upper_bound(identity,X_82)) = least_upper_bound(identity,inverse(X_82)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_82),least_upper_bound(identity,X_82)),least_upper_bound(identity,multiply(inverse(X_82),identity))) ),[1,1],$fot(inverse(X_82))]]) ).
cnf(refute_0_68,plain,
( multiply(inverse(X_82),least_upper_bound(identity,X_82)) != least_upper_bound(identity,multiply(inverse(X_82),identity))
| multiply(inverse(X_82),least_upper_bound(identity,X_82)) = least_upper_bound(identity,inverse(X_82)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_82),identity),inverse(X_82)) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
multiply(inverse(X_82),least_upper_bound(identity,X_82)) = least_upper_bound(identity,inverse(X_82)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_82),least_upper_bound(identity,X_82)),least_upper_bound(identity,multiply(inverse(X_82),identity))) )],[refute_0_36,refute_0_68]) ).
cnf(refute_0_70,plain,
multiply(inverse(X_80),least_upper_bound(identity,X_80)) = least_upper_bound(identity,inverse(X_80)),
inference(subst,[],[refute_0_69:[bind(X_82,$fot(X_80))]]) ).
cnf(refute_0_71,plain,
( multiply(inverse(X_80),least_upper_bound(identity,X_80)) != least_upper_bound(identity,inverse(X_80))
| multiply(inverse(X_80),least_upper_bound(least_upper_bound(identity,X_80),X_80)) != least_upper_bound(identity,multiply(inverse(X_80),least_upper_bound(identity,X_80)))
| multiply(inverse(X_80),least_upper_bound(least_upper_bound(identity,X_80),X_80)) = least_upper_bound(identity,least_upper_bound(identity,inverse(X_80))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_80),least_upper_bound(least_upper_bound(identity,X_80),X_80)),least_upper_bound(identity,multiply(inverse(X_80),least_upper_bound(identity,X_80)))) ),[1,1],$fot(least_upper_bound(identity,inverse(X_80)))]]) ).
cnf(refute_0_72,plain,
( multiply(inverse(X_80),least_upper_bound(least_upper_bound(identity,X_80),X_80)) != least_upper_bound(identity,multiply(inverse(X_80),least_upper_bound(identity,X_80)))
| multiply(inverse(X_80),least_upper_bound(least_upper_bound(identity,X_80),X_80)) = least_upper_bound(identity,least_upper_bound(identity,inverse(X_80))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_80),least_upper_bound(identity,X_80)),least_upper_bound(identity,inverse(X_80))) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
multiply(inverse(X_80),least_upper_bound(least_upper_bound(identity,X_80),X_80)) = least_upper_bound(identity,least_upper_bound(identity,inverse(X_80))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_80),least_upper_bound(least_upper_bound(identity,X_80),X_80)),least_upper_bound(identity,multiply(inverse(X_80),least_upper_bound(identity,X_80)))) )],[refute_0_35,refute_0_72]) ).
cnf(refute_0_74,plain,
least_upper_bound(X_12,greatest_lower_bound(X_12,X_13)) = X_12,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_12)),bind(Y,$fot(X_13))]]) ).
cnf(refute_0_75,plain,
greatest_lower_bound(X_13,X_12) = greatest_lower_bound(X_12,X_13),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_13)),bind(Y,$fot(X_12))]]) ).
cnf(refute_0_76,plain,
( greatest_lower_bound(X_13,X_12) != greatest_lower_bound(X_12,X_13)
| greatest_lower_bound(X_12,X_13) = greatest_lower_bound(X_13,X_12) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X_13,X_12))),bind(Y0,$fot(greatest_lower_bound(X_12,X_13)))]]) ).
cnf(refute_0_77,plain,
greatest_lower_bound(X_12,X_13) = greatest_lower_bound(X_13,X_12),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_13,X_12),greatest_lower_bound(X_12,X_13)) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
( greatest_lower_bound(X_12,X_13) != greatest_lower_bound(X_13,X_12)
| least_upper_bound(X_12,greatest_lower_bound(X_12,X_13)) != X_12
| least_upper_bound(X_12,greatest_lower_bound(X_13,X_12)) = X_12 ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_12,greatest_lower_bound(X_12,X_13)),X_12) ),[0,1],$fot(greatest_lower_bound(X_13,X_12))]]) ).
cnf(refute_0_79,plain,
( least_upper_bound(X_12,greatest_lower_bound(X_12,X_13)) != X_12
| least_upper_bound(X_12,greatest_lower_bound(X_13,X_12)) = X_12 ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_12,X_13),greatest_lower_bound(X_13,X_12)) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
least_upper_bound(X_12,greatest_lower_bound(X_13,X_12)) = X_12,
inference(resolve,[$cnf( $equal(least_upper_bound(X_12,greatest_lower_bound(X_12,X_13)),X_12) )],[refute_0_74,refute_0_79]) ).
cnf(refute_0_81,plain,
least_upper_bound(least_upper_bound(X_17,Y),greatest_lower_bound(X_17,least_upper_bound(X_17,Y))) = least_upper_bound(X_17,Y),
inference(subst,[],[refute_0_80:[bind(X_12,$fot(least_upper_bound(X_17,Y))),bind(X_13,$fot(X_17))]]) ).
cnf(refute_0_82,plain,
greatest_lower_bound(X_17,least_upper_bound(X_17,Y)) = X_17,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_17))]]) ).
cnf(refute_0_83,plain,
( greatest_lower_bound(X_17,least_upper_bound(X_17,Y)) != X_17
| least_upper_bound(least_upper_bound(X_17,Y),greatest_lower_bound(X_17,least_upper_bound(X_17,Y))) != least_upper_bound(X_17,Y)
| least_upper_bound(least_upper_bound(X_17,Y),X_17) = least_upper_bound(X_17,Y) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_17,Y),greatest_lower_bound(X_17,least_upper_bound(X_17,Y))),least_upper_bound(X_17,Y)) ),[0,1],$fot(X_17)]]) ).
cnf(refute_0_84,plain,
( least_upper_bound(least_upper_bound(X_17,Y),greatest_lower_bound(X_17,least_upper_bound(X_17,Y))) != least_upper_bound(X_17,Y)
| least_upper_bound(least_upper_bound(X_17,Y),X_17) = least_upper_bound(X_17,Y) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,least_upper_bound(X_17,Y)),X_17) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
least_upper_bound(least_upper_bound(X_17,Y),X_17) = least_upper_bound(X_17,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_17,Y),greatest_lower_bound(X_17,least_upper_bound(X_17,Y))),least_upper_bound(X_17,Y)) )],[refute_0_81,refute_0_84]) ).
cnf(refute_0_86,plain,
( least_upper_bound(X,least_upper_bound(Y,Z)) != least_upper_bound(least_upper_bound(X,Y),Z)
| least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(Y,Z)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X,Y),Z)))]]) ).
cnf(refute_0_87,plain,
least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,Z)),least_upper_bound(least_upper_bound(X,Y),Z)) )],[associativity_of_lub,refute_0_86]) ).
cnf(refute_0_88,plain,
least_upper_bound(least_upper_bound(X_17,Y),X_17) = least_upper_bound(X_17,least_upper_bound(Y,X_17)),
inference(subst,[],[refute_0_87:[bind(X,$fot(X_17)),bind(Z,$fot(X_17))]]) ).
cnf(refute_0_89,plain,
( least_upper_bound(least_upper_bound(X_17,Y),X_17) != least_upper_bound(X_17,Y)
| least_upper_bound(least_upper_bound(X_17,Y),X_17) != least_upper_bound(X_17,least_upper_bound(Y,X_17))
| least_upper_bound(X_17,least_upper_bound(Y,X_17)) = least_upper_bound(X_17,Y) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_17,Y),X_17),least_upper_bound(X_17,Y)) ),[0],$fot(least_upper_bound(X_17,least_upper_bound(Y,X_17)))]]) ).
cnf(refute_0_90,plain,
( least_upper_bound(least_upper_bound(X_17,Y),X_17) != least_upper_bound(X_17,Y)
| least_upper_bound(X_17,least_upper_bound(Y,X_17)) = least_upper_bound(X_17,Y) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_17,Y),X_17),least_upper_bound(X_17,least_upper_bound(Y,X_17))) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
least_upper_bound(X_17,least_upper_bound(Y,X_17)) = least_upper_bound(X_17,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_17,Y),X_17),least_upper_bound(X_17,Y)) )],[refute_0_85,refute_0_90]) ).
cnf(refute_0_92,plain,
least_upper_bound(X_80,least_upper_bound(identity,X_80)) = least_upper_bound(X_80,identity),
inference(subst,[],[refute_0_91:[bind(Y,$fot(identity)),bind(X_17,$fot(X_80))]]) ).
cnf(refute_0_93,plain,
multiply(inverse(X_80),least_upper_bound(X_80,least_upper_bound(identity,X_80))) = multiply(inverse(X_80),least_upper_bound(X_80,least_upper_bound(identity,X_80))),
introduced(tautology,[refl,[$fot(multiply(inverse(X_80),least_upper_bound(X_80,least_upper_bound(identity,X_80))))]]) ).
cnf(refute_0_94,plain,
( multiply(inverse(X_80),least_upper_bound(X_80,least_upper_bound(identity,X_80))) != multiply(inverse(X_80),least_upper_bound(X_80,least_upper_bound(identity,X_80)))
| least_upper_bound(X_80,least_upper_bound(identity,X_80)) != least_upper_bound(X_80,identity)
| multiply(inverse(X_80),least_upper_bound(X_80,least_upper_bound(identity,X_80))) = multiply(inverse(X_80),least_upper_bound(X_80,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_80),least_upper_bound(X_80,least_upper_bound(identity,X_80))),multiply(inverse(X_80),least_upper_bound(X_80,least_upper_bound(identity,X_80)))) ),[1,1],$fot(least_upper_bound(X_80,identity))]]) ).
cnf(refute_0_95,plain,
( least_upper_bound(X_80,least_upper_bound(identity,X_80)) != least_upper_bound(X_80,identity)
| multiply(inverse(X_80),least_upper_bound(X_80,least_upper_bound(identity,X_80))) = multiply(inverse(X_80),least_upper_bound(X_80,identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_80),least_upper_bound(X_80,least_upper_bound(identity,X_80))),multiply(inverse(X_80),least_upper_bound(X_80,least_upper_bound(identity,X_80)))) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
multiply(inverse(X_80),least_upper_bound(X_80,least_upper_bound(identity,X_80))) = multiply(inverse(X_80),least_upper_bound(X_80,identity)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_80,least_upper_bound(identity,X_80)),least_upper_bound(X_80,identity)) )],[refute_0_92,refute_0_95]) ).
cnf(refute_0_97,plain,
least_upper_bound(X_32,least_upper_bound(X_32,X_33)) = least_upper_bound(least_upper_bound(X_32,X_32),X_33),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_32)),bind(Y,$fot(X_32)),bind(Z,$fot(X_33))]]) ).
cnf(refute_0_98,plain,
least_upper_bound(X_32,X_32) = X_32,
inference(subst,[],[idempotence_of_lub:[bind(X,$fot(X_32))]]) ).
cnf(refute_0_99,plain,
( least_upper_bound(X_32,X_32) != X_32
| least_upper_bound(X_32,least_upper_bound(X_32,X_33)) != least_upper_bound(least_upper_bound(X_32,X_32),X_33)
| least_upper_bound(X_32,least_upper_bound(X_32,X_33)) = least_upper_bound(X_32,X_33) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_32,least_upper_bound(X_32,X_33)),least_upper_bound(least_upper_bound(X_32,X_32),X_33)) ),[1,0],$fot(X_32)]]) ).
cnf(refute_0_100,plain,
( least_upper_bound(X_32,least_upper_bound(X_32,X_33)) != least_upper_bound(least_upper_bound(X_32,X_32),X_33)
| least_upper_bound(X_32,least_upper_bound(X_32,X_33)) = least_upper_bound(X_32,X_33) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_32,X_32),X_32) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
least_upper_bound(X_32,least_upper_bound(X_32,X_33)) = least_upper_bound(X_32,X_33),
inference(resolve,[$cnf( $equal(least_upper_bound(X_32,least_upper_bound(X_32,X_33)),least_upper_bound(least_upper_bound(X_32,X_32),X_33)) )],[refute_0_97,refute_0_100]) ).
cnf(refute_0_102,plain,
least_upper_bound(multiply(X_78,X_79),least_upper_bound(multiply(X_78,X_79),multiply(X_78,X_80))) = least_upper_bound(multiply(X_78,X_79),multiply(X_78,X_80)),
inference(subst,[],[refute_0_101:[bind(X_32,$fot(multiply(X_78,X_79))),bind(X_33,$fot(multiply(X_78,X_80)))]]) ).
cnf(refute_0_103,plain,
multiply(X_78,least_upper_bound(X_79,X_80)) = least_upper_bound(multiply(X_78,X_79),multiply(X_78,X_80)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(X_78)),bind(Y,$fot(X_79)),bind(Z,$fot(X_80))]]) ).
cnf(refute_0_104,plain,
( multiply(X_78,least_upper_bound(X_79,X_80)) != least_upper_bound(multiply(X_78,X_79),multiply(X_78,X_80))
| least_upper_bound(multiply(X_78,X_79),multiply(X_78,X_80)) = multiply(X_78,least_upper_bound(X_79,X_80)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X_78,least_upper_bound(X_79,X_80)))),bind(Y0,$fot(least_upper_bound(multiply(X_78,X_79),multiply(X_78,X_80))))]]) ).
cnf(refute_0_105,plain,
least_upper_bound(multiply(X_78,X_79),multiply(X_78,X_80)) = multiply(X_78,least_upper_bound(X_79,X_80)),
inference(resolve,[$cnf( $equal(multiply(X_78,least_upper_bound(X_79,X_80)),least_upper_bound(multiply(X_78,X_79),multiply(X_78,X_80))) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
( least_upper_bound(multiply(X_78,X_79),multiply(X_78,X_80)) != multiply(X_78,least_upper_bound(X_79,X_80))
| least_upper_bound(multiply(X_78,X_79),least_upper_bound(multiply(X_78,X_79),multiply(X_78,X_80))) != least_upper_bound(multiply(X_78,X_79),multiply(X_78,X_80))
| least_upper_bound(multiply(X_78,X_79),least_upper_bound(multiply(X_78,X_79),multiply(X_78,X_80))) = multiply(X_78,least_upper_bound(X_79,X_80)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_78,X_79),least_upper_bound(multiply(X_78,X_79),multiply(X_78,X_80))),least_upper_bound(multiply(X_78,X_79),multiply(X_78,X_80))) ),[1],$fot(multiply(X_78,least_upper_bound(X_79,X_80)))]]) ).
cnf(refute_0_107,plain,
( least_upper_bound(multiply(X_78,X_79),least_upper_bound(multiply(X_78,X_79),multiply(X_78,X_80))) != least_upper_bound(multiply(X_78,X_79),multiply(X_78,X_80))
| least_upper_bound(multiply(X_78,X_79),least_upper_bound(multiply(X_78,X_79),multiply(X_78,X_80))) = multiply(X_78,least_upper_bound(X_79,X_80)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_78,X_79),multiply(X_78,X_80)),multiply(X_78,least_upper_bound(X_79,X_80))) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
least_upper_bound(multiply(X_78,X_79),least_upper_bound(multiply(X_78,X_79),multiply(X_78,X_80))) = multiply(X_78,least_upper_bound(X_79,X_80)),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_78,X_79),least_upper_bound(multiply(X_78,X_79),multiply(X_78,X_80))),least_upper_bound(multiply(X_78,X_79),multiply(X_78,X_80))) )],[refute_0_102,refute_0_107]) ).
cnf(refute_0_109,plain,
least_upper_bound(X_79,X_79) = X_79,
inference(subst,[],[idempotence_of_lub:[bind(X,$fot(X_79))]]) ).
cnf(refute_0_110,plain,
least_upper_bound(X_80,least_upper_bound(X_79,X_79)) = least_upper_bound(X_80,least_upper_bound(X_79,X_79)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_80,least_upper_bound(X_79,X_79)))]]) ).
cnf(refute_0_111,plain,
( least_upper_bound(X_79,X_79) != X_79
| least_upper_bound(X_80,least_upper_bound(X_79,X_79)) != least_upper_bound(X_80,least_upper_bound(X_79,X_79))
| least_upper_bound(X_80,least_upper_bound(X_79,X_79)) = least_upper_bound(X_80,X_79) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_80,least_upper_bound(X_79,X_79)),least_upper_bound(X_80,least_upper_bound(X_79,X_79))) ),[1,1],$fot(X_79)]]) ).
cnf(refute_0_112,plain,
( least_upper_bound(X_79,X_79) != X_79
| least_upper_bound(X_80,least_upper_bound(X_79,X_79)) = least_upper_bound(X_80,X_79) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_80,least_upper_bound(X_79,X_79)),least_upper_bound(X_80,least_upper_bound(X_79,X_79))) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
least_upper_bound(X_80,least_upper_bound(X_79,X_79)) = least_upper_bound(X_80,X_79),
inference(resolve,[$cnf( $equal(least_upper_bound(X_79,X_79),X_79) )],[refute_0_109,refute_0_112]) ).
cnf(refute_0_114,plain,
multiply(X_78,least_upper_bound(X_80,least_upper_bound(X_79,X_79))) = multiply(X_78,least_upper_bound(X_80,least_upper_bound(X_79,X_79))),
introduced(tautology,[refl,[$fot(multiply(X_78,least_upper_bound(X_80,least_upper_bound(X_79,X_79))))]]) ).
cnf(refute_0_115,plain,
( multiply(X_78,least_upper_bound(X_80,least_upper_bound(X_79,X_79))) != multiply(X_78,least_upper_bound(X_80,least_upper_bound(X_79,X_79)))
| least_upper_bound(X_80,least_upper_bound(X_79,X_79)) != least_upper_bound(X_80,X_79)
| multiply(X_78,least_upper_bound(X_80,least_upper_bound(X_79,X_79))) = multiply(X_78,least_upper_bound(X_80,X_79)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_78,least_upper_bound(X_80,least_upper_bound(X_79,X_79))),multiply(X_78,least_upper_bound(X_80,least_upper_bound(X_79,X_79)))) ),[1,1],$fot(least_upper_bound(X_80,X_79))]]) ).
cnf(refute_0_116,plain,
( least_upper_bound(X_80,least_upper_bound(X_79,X_79)) != least_upper_bound(X_80,X_79)
| multiply(X_78,least_upper_bound(X_80,least_upper_bound(X_79,X_79))) = multiply(X_78,least_upper_bound(X_80,X_79)) ),
inference(resolve,[$cnf( $equal(multiply(X_78,least_upper_bound(X_80,least_upper_bound(X_79,X_79))),multiply(X_78,least_upper_bound(X_80,least_upper_bound(X_79,X_79)))) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
multiply(X_78,least_upper_bound(X_80,least_upper_bound(X_79,X_79))) = multiply(X_78,least_upper_bound(X_80,X_79)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_80,least_upper_bound(X_79,X_79)),least_upper_bound(X_80,X_79)) )],[refute_0_113,refute_0_116]) ).
cnf(refute_0_118,plain,
( multiply(X,least_upper_bound(Y,Z)) != least_upper_bound(multiply(X,Y),multiply(X,Z))
| least_upper_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X,least_upper_bound(Y,Z)))),bind(Y0,$fot(least_upper_bound(multiply(X,Y),multiply(X,Z))))]]) ).
cnf(refute_0_119,plain,
least_upper_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Y),multiply(X,Z))) )],[monotony_lub1,refute_0_118]) ).
cnf(refute_0_120,plain,
least_upper_bound(multiply(X_78,X_80),multiply(X_78,least_upper_bound(X_79,X_79))) = multiply(X_78,least_upper_bound(X_80,least_upper_bound(X_79,X_79))),
inference(subst,[],[refute_0_119:[bind(X,$fot(X_78)),bind(Y,$fot(X_80)),bind(Z,$fot(least_upper_bound(X_79,X_79)))]]) ).
cnf(refute_0_121,plain,
least_upper_bound(X,least_upper_bound(X_31,X_32)) = least_upper_bound(least_upper_bound(X_31,X_32),X),
inference(subst,[],[symmetry_of_lub:[bind(Y,$fot(least_upper_bound(X_31,X_32)))]]) ).
cnf(refute_0_122,plain,
least_upper_bound(X_31,least_upper_bound(X_32,X)) = least_upper_bound(least_upper_bound(X_31,X_32),X),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_31)),bind(Y,$fot(X_32)),bind(Z,$fot(X))]]) ).
cnf(refute_0_123,plain,
( least_upper_bound(X_31,least_upper_bound(X_32,X)) != least_upper_bound(least_upper_bound(X_31,X_32),X)
| least_upper_bound(least_upper_bound(X_31,X_32),X) = least_upper_bound(X_31,least_upper_bound(X_32,X)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X_31,least_upper_bound(X_32,X)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X_31,X_32),X)))]]) ).
cnf(refute_0_124,plain,
least_upper_bound(least_upper_bound(X_31,X_32),X) = least_upper_bound(X_31,least_upper_bound(X_32,X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_31,least_upper_bound(X_32,X)),least_upper_bound(least_upper_bound(X_31,X_32),X)) )],[refute_0_122,refute_0_123]) ).
cnf(refute_0_125,plain,
( least_upper_bound(X,least_upper_bound(X_31,X_32)) != least_upper_bound(least_upper_bound(X_31,X_32),X)
| least_upper_bound(least_upper_bound(X_31,X_32),X) != least_upper_bound(X_31,least_upper_bound(X_32,X))
| least_upper_bound(X,least_upper_bound(X_31,X_32)) = least_upper_bound(X_31,least_upper_bound(X_32,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,least_upper_bound(X_31,X_32)),least_upper_bound(X_31,least_upper_bound(X_32,X))) ),[0],$fot(least_upper_bound(least_upper_bound(X_31,X_32),X))]]) ).
cnf(refute_0_126,plain,
( least_upper_bound(X,least_upper_bound(X_31,X_32)) != least_upper_bound(least_upper_bound(X_31,X_32),X)
| least_upper_bound(X,least_upper_bound(X_31,X_32)) = least_upper_bound(X_31,least_upper_bound(X_32,X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_31,X_32),X),least_upper_bound(X_31,least_upper_bound(X_32,X))) )],[refute_0_124,refute_0_125]) ).
cnf(refute_0_127,plain,
least_upper_bound(X,least_upper_bound(X_31,X_32)) = least_upper_bound(X_31,least_upper_bound(X_32,X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_31,X_32)),least_upper_bound(least_upper_bound(X_31,X_32),X)) )],[refute_0_121,refute_0_126]) ).
cnf(refute_0_128,plain,
least_upper_bound(X,least_upper_bound(multiply(X_78,X_79),multiply(X_78,X_80))) = least_upper_bound(multiply(X_78,X_79),least_upper_bound(multiply(X_78,X_80),X)),
inference(subst,[],[refute_0_127:[bind(X_31,$fot(multiply(X_78,X_79))),bind(X_32,$fot(multiply(X_78,X_80)))]]) ).
cnf(refute_0_129,plain,
( least_upper_bound(X,least_upper_bound(multiply(X_78,X_79),multiply(X_78,X_80))) != least_upper_bound(multiply(X_78,X_79),least_upper_bound(multiply(X_78,X_80),X))
| least_upper_bound(multiply(X_78,X_79),multiply(X_78,X_80)) != multiply(X_78,least_upper_bound(X_79,X_80))
| least_upper_bound(X,multiply(X_78,least_upper_bound(X_79,X_80))) = least_upper_bound(multiply(X_78,X_79),least_upper_bound(multiply(X_78,X_80),X)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(multiply(X_78,X_79),multiply(X_78,X_80))),least_upper_bound(multiply(X_78,X_79),least_upper_bound(multiply(X_78,X_80),X))) ),[0,1],$fot(multiply(X_78,least_upper_bound(X_79,X_80)))]]) ).
cnf(refute_0_130,plain,
( least_upper_bound(X,least_upper_bound(multiply(X_78,X_79),multiply(X_78,X_80))) != least_upper_bound(multiply(X_78,X_79),least_upper_bound(multiply(X_78,X_80),X))
| least_upper_bound(X,multiply(X_78,least_upper_bound(X_79,X_80))) = least_upper_bound(multiply(X_78,X_79),least_upper_bound(multiply(X_78,X_80),X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_78,X_79),multiply(X_78,X_80)),multiply(X_78,least_upper_bound(X_79,X_80))) )],[refute_0_105,refute_0_129]) ).
cnf(refute_0_131,plain,
least_upper_bound(X,multiply(X_78,least_upper_bound(X_79,X_80))) = least_upper_bound(multiply(X_78,X_79),least_upper_bound(multiply(X_78,X_80),X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(multiply(X_78,X_79),multiply(X_78,X_80))),least_upper_bound(multiply(X_78,X_79),least_upper_bound(multiply(X_78,X_80),X))) )],[refute_0_128,refute_0_130]) ).
cnf(refute_0_132,plain,
( least_upper_bound(X,multiply(X_78,least_upper_bound(X_79,X_80))) != least_upper_bound(multiply(X_78,X_79),least_upper_bound(multiply(X_78,X_80),X))
| least_upper_bound(multiply(X_78,X_79),least_upper_bound(multiply(X_78,X_80),X)) = least_upper_bound(X,multiply(X_78,least_upper_bound(X_79,X_80))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X,multiply(X_78,least_upper_bound(X_79,X_80))))),bind(Y0,$fot(least_upper_bound(multiply(X_78,X_79),least_upper_bound(multiply(X_78,X_80),X))))]]) ).
cnf(refute_0_133,plain,
least_upper_bound(multiply(X_78,X_79),least_upper_bound(multiply(X_78,X_80),X)) = least_upper_bound(X,multiply(X_78,least_upper_bound(X_79,X_80))),
inference(resolve,[$cnf( $equal(least_upper_bound(X,multiply(X_78,least_upper_bound(X_79,X_80))),least_upper_bound(multiply(X_78,X_79),least_upper_bound(multiply(X_78,X_80),X))) )],[refute_0_131,refute_0_132]) ).
cnf(refute_0_134,plain,
least_upper_bound(multiply(X_78,X_79),least_upper_bound(multiply(X_78,X_79),multiply(X_78,X_80))) = least_upper_bound(multiply(X_78,X_80),multiply(X_78,least_upper_bound(X_79,X_79))),
inference(subst,[],[refute_0_133:[bind(X,$fot(multiply(X_78,X_80))),bind(X_80,$fot(X_79))]]) ).
cnf(refute_0_135,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_136,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_2,refute_0_135]) ).
cnf(refute_0_137,plain,
( least_upper_bound(multiply(X_78,X_79),least_upper_bound(multiply(X_78,X_79),multiply(X_78,X_80))) != least_upper_bound(multiply(X_78,X_80),multiply(X_78,least_upper_bound(X_79,X_79)))
| least_upper_bound(multiply(X_78,X_80),multiply(X_78,least_upper_bound(X_79,X_79))) != multiply(X_78,least_upper_bound(X_80,least_upper_bound(X_79,X_79)))
| least_upper_bound(multiply(X_78,X_79),least_upper_bound(multiply(X_78,X_79),multiply(X_78,X_80))) = multiply(X_78,least_upper_bound(X_80,least_upper_bound(X_79,X_79))) ),
inference(subst,[],[refute_0_136:[bind(X0,$fot(least_upper_bound(multiply(X_78,X_79),least_upper_bound(multiply(X_78,X_79),multiply(X_78,X_80))))),bind(Y0,$fot(least_upper_bound(multiply(X_78,X_80),multiply(X_78,least_upper_bound(X_79,X_79))))),bind(Z0,$fot(multiply(X_78,least_upper_bound(X_80,least_upper_bound(X_79,X_79)))))]]) ).
cnf(refute_0_138,plain,
( least_upper_bound(multiply(X_78,X_80),multiply(X_78,least_upper_bound(X_79,X_79))) != multiply(X_78,least_upper_bound(X_80,least_upper_bound(X_79,X_79)))
| least_upper_bound(multiply(X_78,X_79),least_upper_bound(multiply(X_78,X_79),multiply(X_78,X_80))) = multiply(X_78,least_upper_bound(X_80,least_upper_bound(X_79,X_79))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_78,X_79),least_upper_bound(multiply(X_78,X_79),multiply(X_78,X_80))),least_upper_bound(multiply(X_78,X_80),multiply(X_78,least_upper_bound(X_79,X_79)))) )],[refute_0_134,refute_0_137]) ).
cnf(refute_0_139,plain,
least_upper_bound(multiply(X_78,X_79),least_upper_bound(multiply(X_78,X_79),multiply(X_78,X_80))) = multiply(X_78,least_upper_bound(X_80,least_upper_bound(X_79,X_79))),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_78,X_80),multiply(X_78,least_upper_bound(X_79,X_79))),multiply(X_78,least_upper_bound(X_80,least_upper_bound(X_79,X_79)))) )],[refute_0_120,refute_0_138]) ).
cnf(refute_0_140,plain,
( multiply(X_78,least_upper_bound(X_80,least_upper_bound(X_79,X_79))) != multiply(X_78,least_upper_bound(X_80,X_79))
| least_upper_bound(multiply(X_78,X_79),least_upper_bound(multiply(X_78,X_79),multiply(X_78,X_80))) != multiply(X_78,least_upper_bound(X_80,least_upper_bound(X_79,X_79)))
| least_upper_bound(multiply(X_78,X_79),least_upper_bound(multiply(X_78,X_79),multiply(X_78,X_80))) = multiply(X_78,least_upper_bound(X_80,X_79)) ),
inference(subst,[],[refute_0_136:[bind(X0,$fot(least_upper_bound(multiply(X_78,X_79),least_upper_bound(multiply(X_78,X_79),multiply(X_78,X_80))))),bind(Y0,$fot(multiply(X_78,least_upper_bound(X_80,least_upper_bound(X_79,X_79))))),bind(Z0,$fot(multiply(X_78,least_upper_bound(X_80,X_79))))]]) ).
cnf(refute_0_141,plain,
( multiply(X_78,least_upper_bound(X_80,least_upper_bound(X_79,X_79))) != multiply(X_78,least_upper_bound(X_80,X_79))
| least_upper_bound(multiply(X_78,X_79),least_upper_bound(multiply(X_78,X_79),multiply(X_78,X_80))) = multiply(X_78,least_upper_bound(X_80,X_79)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_78,X_79),least_upper_bound(multiply(X_78,X_79),multiply(X_78,X_80))),multiply(X_78,least_upper_bound(X_80,least_upper_bound(X_79,X_79)))) )],[refute_0_139,refute_0_140]) ).
cnf(refute_0_142,plain,
least_upper_bound(multiply(X_78,X_79),least_upper_bound(multiply(X_78,X_79),multiply(X_78,X_80))) = multiply(X_78,least_upper_bound(X_80,X_79)),
inference(resolve,[$cnf( $equal(multiply(X_78,least_upper_bound(X_80,least_upper_bound(X_79,X_79))),multiply(X_78,least_upper_bound(X_80,X_79))) )],[refute_0_117,refute_0_141]) ).
cnf(refute_0_143,plain,
( least_upper_bound(multiply(X_78,X_79),least_upper_bound(multiply(X_78,X_79),multiply(X_78,X_80))) != multiply(X_78,least_upper_bound(X_79,X_80))
| least_upper_bound(multiply(X_78,X_79),least_upper_bound(multiply(X_78,X_79),multiply(X_78,X_80))) != multiply(X_78,least_upper_bound(X_80,X_79))
| multiply(X_78,least_upper_bound(X_80,X_79)) = multiply(X_78,least_upper_bound(X_79,X_80)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_78,X_79),least_upper_bound(multiply(X_78,X_79),multiply(X_78,X_80))),multiply(X_78,least_upper_bound(X_79,X_80))) ),[0],$fot(multiply(X_78,least_upper_bound(X_80,X_79)))]]) ).
cnf(refute_0_144,plain,
( least_upper_bound(multiply(X_78,X_79),least_upper_bound(multiply(X_78,X_79),multiply(X_78,X_80))) != multiply(X_78,least_upper_bound(X_79,X_80))
| multiply(X_78,least_upper_bound(X_80,X_79)) = multiply(X_78,least_upper_bound(X_79,X_80)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_78,X_79),least_upper_bound(multiply(X_78,X_79),multiply(X_78,X_80))),multiply(X_78,least_upper_bound(X_80,X_79))) )],[refute_0_142,refute_0_143]) ).
cnf(refute_0_145,plain,
multiply(X_78,least_upper_bound(X_80,X_79)) = multiply(X_78,least_upper_bound(X_79,X_80)),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_78,X_79),least_upper_bound(multiply(X_78,X_79),multiply(X_78,X_80))),multiply(X_78,least_upper_bound(X_79,X_80))) )],[refute_0_108,refute_0_144]) ).
cnf(refute_0_146,plain,
( multiply(X_78,least_upper_bound(X_80,X_79)) != multiply(X_78,least_upper_bound(X_79,X_80))
| multiply(X_78,least_upper_bound(X_79,X_80)) = multiply(X_78,least_upper_bound(X_80,X_79)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X_78,least_upper_bound(X_80,X_79)))),bind(Y0,$fot(multiply(X_78,least_upper_bound(X_79,X_80))))]]) ).
cnf(refute_0_147,plain,
multiply(X_78,least_upper_bound(X_79,X_80)) = multiply(X_78,least_upper_bound(X_80,X_79)),
inference(resolve,[$cnf( $equal(multiply(X_78,least_upper_bound(X_80,X_79)),multiply(X_78,least_upper_bound(X_79,X_80))) )],[refute_0_145,refute_0_146]) ).
cnf(refute_0_148,plain,
multiply(inverse(X_80),least_upper_bound(least_upper_bound(identity,X_80),X_80)) = multiply(inverse(X_80),least_upper_bound(X_80,least_upper_bound(identity,X_80))),
inference(subst,[],[refute_0_147:[bind(X_78,$fot(inverse(X_80))),bind(X_79,$fot(least_upper_bound(identity,X_80)))]]) ).
cnf(refute_0_149,plain,
( multiply(inverse(X_80),least_upper_bound(X_80,least_upper_bound(identity,X_80))) != multiply(inverse(X_80),least_upper_bound(X_80,identity))
| multiply(inverse(X_80),least_upper_bound(least_upper_bound(identity,X_80),X_80)) != multiply(inverse(X_80),least_upper_bound(X_80,least_upper_bound(identity,X_80)))
| multiply(inverse(X_80),least_upper_bound(least_upper_bound(identity,X_80),X_80)) = multiply(inverse(X_80),least_upper_bound(X_80,identity)) ),
inference(subst,[],[refute_0_136:[bind(X0,$fot(multiply(inverse(X_80),least_upper_bound(least_upper_bound(identity,X_80),X_80)))),bind(Y0,$fot(multiply(inverse(X_80),least_upper_bound(X_80,least_upper_bound(identity,X_80))))),bind(Z0,$fot(multiply(inverse(X_80),least_upper_bound(X_80,identity))))]]) ).
cnf(refute_0_150,plain,
( multiply(inverse(X_80),least_upper_bound(X_80,least_upper_bound(identity,X_80))) != multiply(inverse(X_80),least_upper_bound(X_80,identity))
| multiply(inverse(X_80),least_upper_bound(least_upper_bound(identity,X_80),X_80)) = multiply(inverse(X_80),least_upper_bound(X_80,identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_80),least_upper_bound(least_upper_bound(identity,X_80),X_80)),multiply(inverse(X_80),least_upper_bound(X_80,least_upper_bound(identity,X_80)))) )],[refute_0_148,refute_0_149]) ).
cnf(refute_0_151,plain,
multiply(inverse(X_80),least_upper_bound(least_upper_bound(identity,X_80),X_80)) = multiply(inverse(X_80),least_upper_bound(X_80,identity)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_80),least_upper_bound(X_80,least_upper_bound(identity,X_80))),multiply(inverse(X_80),least_upper_bound(X_80,identity))) )],[refute_0_96,refute_0_150]) ).
cnf(refute_0_152,plain,
( multiply(inverse(X_80),least_upper_bound(least_upper_bound(identity,X_80),X_80)) != multiply(inverse(X_80),least_upper_bound(X_80,identity))
| multiply(inverse(X_80),least_upper_bound(least_upper_bound(identity,X_80),X_80)) != least_upper_bound(identity,least_upper_bound(identity,inverse(X_80)))
| multiply(inverse(X_80),least_upper_bound(X_80,identity)) = least_upper_bound(identity,least_upper_bound(identity,inverse(X_80))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_80),least_upper_bound(least_upper_bound(identity,X_80),X_80)),least_upper_bound(identity,least_upper_bound(identity,inverse(X_80)))) ),[0],$fot(multiply(inverse(X_80),least_upper_bound(X_80,identity)))]]) ).
cnf(refute_0_153,plain,
( multiply(inverse(X_80),least_upper_bound(least_upper_bound(identity,X_80),X_80)) != least_upper_bound(identity,least_upper_bound(identity,inverse(X_80)))
| multiply(inverse(X_80),least_upper_bound(X_80,identity)) = least_upper_bound(identity,least_upper_bound(identity,inverse(X_80))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_80),least_upper_bound(least_upper_bound(identity,X_80),X_80)),multiply(inverse(X_80),least_upper_bound(X_80,identity))) )],[refute_0_151,refute_0_152]) ).
cnf(refute_0_154,plain,
least_upper_bound(identity,least_upper_bound(identity,inverse(X_80))) = least_upper_bound(identity,inverse(X_80)),
inference(subst,[],[refute_0_101:[bind(X_32,$fot(identity)),bind(X_33,$fot(inverse(X_80)))]]) ).
cnf(refute_0_155,plain,
( multiply(inverse(X_80),least_upper_bound(X_80,identity)) != least_upper_bound(identity,least_upper_bound(identity,inverse(X_80)))
| least_upper_bound(identity,least_upper_bound(identity,inverse(X_80))) != least_upper_bound(identity,inverse(X_80))
| multiply(inverse(X_80),least_upper_bound(X_80,identity)) = least_upper_bound(identity,inverse(X_80)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_80),least_upper_bound(X_80,identity)),least_upper_bound(identity,inverse(X_80))) ),[0],$fot(least_upper_bound(identity,least_upper_bound(identity,inverse(X_80))))]]) ).
cnf(refute_0_156,plain,
( multiply(inverse(X_80),least_upper_bound(X_80,identity)) != least_upper_bound(identity,least_upper_bound(identity,inverse(X_80)))
| multiply(inverse(X_80),least_upper_bound(X_80,identity)) = least_upper_bound(identity,inverse(X_80)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(identity,inverse(X_80))),least_upper_bound(identity,inverse(X_80))) )],[refute_0_154,refute_0_155]) ).
cnf(refute_0_157,plain,
( multiply(inverse(X_80),least_upper_bound(least_upper_bound(identity,X_80),X_80)) != least_upper_bound(identity,least_upper_bound(identity,inverse(X_80)))
| multiply(inverse(X_80),least_upper_bound(X_80,identity)) = least_upper_bound(identity,inverse(X_80)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_80),least_upper_bound(X_80,identity)),least_upper_bound(identity,least_upper_bound(identity,inverse(X_80)))) )],[refute_0_153,refute_0_156]) ).
cnf(refute_0_158,plain,
multiply(inverse(X_80),least_upper_bound(X_80,identity)) = least_upper_bound(identity,inverse(X_80)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_80),least_upper_bound(least_upper_bound(identity,X_80),X_80)),least_upper_bound(identity,least_upper_bound(identity,inverse(X_80)))) )],[refute_0_73,refute_0_157]) ).
cnf(refute_0_159,plain,
multiply(inverse(X_128),least_upper_bound(X_128,identity)) = least_upper_bound(identity,inverse(X_128)),
inference(subst,[],[refute_0_158:[bind(X_80,$fot(X_128))]]) ).
cnf(refute_0_160,plain,
( multiply(greatest_lower_bound(inverse(X_128),identity),least_upper_bound(X_128,identity)) != greatest_lower_bound(least_upper_bound(X_128,identity),multiply(inverse(X_128),least_upper_bound(X_128,identity)))
| multiply(inverse(X_128),least_upper_bound(X_128,identity)) != least_upper_bound(identity,inverse(X_128))
| multiply(greatest_lower_bound(inverse(X_128),identity),least_upper_bound(X_128,identity)) = greatest_lower_bound(least_upper_bound(X_128,identity),least_upper_bound(identity,inverse(X_128))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_128),identity),least_upper_bound(X_128,identity)),greatest_lower_bound(least_upper_bound(X_128,identity),multiply(inverse(X_128),least_upper_bound(X_128,identity)))) ),[1,1],$fot(least_upper_bound(identity,inverse(X_128)))]]) ).
cnf(refute_0_161,plain,
( multiply(greatest_lower_bound(inverse(X_128),identity),least_upper_bound(X_128,identity)) != greatest_lower_bound(least_upper_bound(X_128,identity),multiply(inverse(X_128),least_upper_bound(X_128,identity)))
| multiply(greatest_lower_bound(inverse(X_128),identity),least_upper_bound(X_128,identity)) = greatest_lower_bound(least_upper_bound(X_128,identity),least_upper_bound(identity,inverse(X_128))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_128),least_upper_bound(X_128,identity)),least_upper_bound(identity,inverse(X_128))) )],[refute_0_159,refute_0_160]) ).
cnf(refute_0_162,plain,
multiply(greatest_lower_bound(inverse(X_128),identity),least_upper_bound(X_128,identity)) = greatest_lower_bound(least_upper_bound(X_128,identity),least_upper_bound(identity,inverse(X_128))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_128),identity),least_upper_bound(X_128,identity)),greatest_lower_bound(least_upper_bound(X_128,identity),multiply(inverse(X_128),least_upper_bound(X_128,identity)))) )],[refute_0_24,refute_0_161]) ).
cnf(refute_0_163,plain,
least_upper_bound(greatest_lower_bound(X_13,X_17),greatest_lower_bound(X_17,greatest_lower_bound(X_13,X_17))) = greatest_lower_bound(X_13,X_17),
inference(subst,[],[refute_0_80:[bind(X_12,$fot(greatest_lower_bound(X_13,X_17))),bind(X_13,$fot(X_17))]]) ).
cnf(refute_0_164,plain,
greatest_lower_bound(X_8,least_upper_bound(X_8,X_9)) = X_8,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_8)),bind(Y,$fot(X_9))]]) ).
cnf(refute_0_165,plain,
least_upper_bound(X_9,X_8) = least_upper_bound(X_8,X_9),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_9)),bind(Y,$fot(X_8))]]) ).
cnf(refute_0_166,plain,
( least_upper_bound(X_9,X_8) != least_upper_bound(X_8,X_9)
| least_upper_bound(X_8,X_9) = least_upper_bound(X_9,X_8) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X_9,X_8))),bind(Y0,$fot(least_upper_bound(X_8,X_9)))]]) ).
cnf(refute_0_167,plain,
least_upper_bound(X_8,X_9) = least_upper_bound(X_9,X_8),
inference(resolve,[$cnf( $equal(least_upper_bound(X_9,X_8),least_upper_bound(X_8,X_9)) )],[refute_0_165,refute_0_166]) ).
cnf(refute_0_168,plain,
( greatest_lower_bound(X_8,least_upper_bound(X_8,X_9)) != X_8
| least_upper_bound(X_8,X_9) != least_upper_bound(X_9,X_8)
| greatest_lower_bound(X_8,least_upper_bound(X_9,X_8)) = X_8 ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_8,least_upper_bound(X_8,X_9)),X_8) ),[0,1],$fot(least_upper_bound(X_9,X_8))]]) ).
cnf(refute_0_169,plain,
( greatest_lower_bound(X_8,least_upper_bound(X_8,X_9)) != X_8
| greatest_lower_bound(X_8,least_upper_bound(X_9,X_8)) = X_8 ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_8,X_9),least_upper_bound(X_9,X_8)) )],[refute_0_167,refute_0_168]) ).
cnf(refute_0_170,plain,
greatest_lower_bound(X_8,least_upper_bound(X_9,X_8)) = X_8,
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_8,least_upper_bound(X_8,X_9)),X_8) )],[refute_0_164,refute_0_169]) ).
cnf(refute_0_171,plain,
greatest_lower_bound(greatest_lower_bound(X_9,X_13),least_upper_bound(X_9,greatest_lower_bound(X_9,X_13))) = greatest_lower_bound(X_9,X_13),
inference(subst,[],[refute_0_170:[bind(X_8,$fot(greatest_lower_bound(X_9,X_13)))]]) ).
cnf(refute_0_172,plain,
least_upper_bound(X_9,greatest_lower_bound(X_9,X_13)) = X_9,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_9)),bind(Y,$fot(X_13))]]) ).
cnf(refute_0_173,plain,
( greatest_lower_bound(greatest_lower_bound(X_9,X_13),least_upper_bound(X_9,greatest_lower_bound(X_9,X_13))) != greatest_lower_bound(X_9,X_13)
| least_upper_bound(X_9,greatest_lower_bound(X_9,X_13)) != X_9
| greatest_lower_bound(greatest_lower_bound(X_9,X_13),X_9) = greatest_lower_bound(X_9,X_13) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_9,X_13),least_upper_bound(X_9,greatest_lower_bound(X_9,X_13))),greatest_lower_bound(X_9,X_13)) ),[0,1],$fot(X_9)]]) ).
cnf(refute_0_174,plain,
( greatest_lower_bound(greatest_lower_bound(X_9,X_13),least_upper_bound(X_9,greatest_lower_bound(X_9,X_13))) != greatest_lower_bound(X_9,X_13)
| greatest_lower_bound(greatest_lower_bound(X_9,X_13),X_9) = greatest_lower_bound(X_9,X_13) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_9,greatest_lower_bound(X_9,X_13)),X_9) )],[refute_0_172,refute_0_173]) ).
cnf(refute_0_175,plain,
greatest_lower_bound(greatest_lower_bound(X_9,X_13),X_9) = greatest_lower_bound(X_9,X_13),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_9,X_13),least_upper_bound(X_9,greatest_lower_bound(X_9,X_13))),greatest_lower_bound(X_9,X_13)) )],[refute_0_171,refute_0_174]) ).
cnf(refute_0_176,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,Z)) != greatest_lower_bound(greatest_lower_bound(X,Y),Z)
| greatest_lower_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(Y,Z)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X,Y),Z)))]]) ).
cnf(refute_0_177,plain,
greatest_lower_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(greatest_lower_bound(X,Y),Z)) )],[associativity_of_glb,refute_0_176]) ).
cnf(refute_0_178,plain,
greatest_lower_bound(greatest_lower_bound(X_9,X_13),X_9) = greatest_lower_bound(X_9,greatest_lower_bound(X_13,X_9)),
inference(subst,[],[refute_0_177:[bind(X,$fot(X_9)),bind(Y,$fot(X_13)),bind(Z,$fot(X_9))]]) ).
cnf(refute_0_179,plain,
( greatest_lower_bound(greatest_lower_bound(X_9,X_13),X_9) != greatest_lower_bound(X_9,X_13)
| greatest_lower_bound(greatest_lower_bound(X_9,X_13),X_9) != greatest_lower_bound(X_9,greatest_lower_bound(X_13,X_9))
| greatest_lower_bound(X_9,greatest_lower_bound(X_13,X_9)) = greatest_lower_bound(X_9,X_13) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_9,X_13),X_9),greatest_lower_bound(X_9,X_13)) ),[0],$fot(greatest_lower_bound(X_9,greatest_lower_bound(X_13,X_9)))]]) ).
cnf(refute_0_180,plain,
( greatest_lower_bound(greatest_lower_bound(X_9,X_13),X_9) != greatest_lower_bound(X_9,X_13)
| greatest_lower_bound(X_9,greatest_lower_bound(X_13,X_9)) = greatest_lower_bound(X_9,X_13) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_9,X_13),X_9),greatest_lower_bound(X_9,greatest_lower_bound(X_13,X_9))) )],[refute_0_178,refute_0_179]) ).
cnf(refute_0_181,plain,
greatest_lower_bound(X_9,greatest_lower_bound(X_13,X_9)) = greatest_lower_bound(X_9,X_13),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_9,X_13),X_9),greatest_lower_bound(X_9,X_13)) )],[refute_0_175,refute_0_180]) ).
cnf(refute_0_182,plain,
greatest_lower_bound(X_17,greatest_lower_bound(X_13,X_17)) = greatest_lower_bound(X_17,X_13),
inference(subst,[],[refute_0_181:[bind(X_9,$fot(X_17))]]) ).
cnf(refute_0_183,plain,
( greatest_lower_bound(X_17,greatest_lower_bound(X_13,X_17)) != greatest_lower_bound(X_17,X_13)
| least_upper_bound(greatest_lower_bound(X_13,X_17),greatest_lower_bound(X_17,greatest_lower_bound(X_13,X_17))) != greatest_lower_bound(X_13,X_17)
| least_upper_bound(greatest_lower_bound(X_13,X_17),greatest_lower_bound(X_17,X_13)) = greatest_lower_bound(X_13,X_17) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_13,X_17),greatest_lower_bound(X_17,greatest_lower_bound(X_13,X_17))),greatest_lower_bound(X_13,X_17)) ),[0,1],$fot(greatest_lower_bound(X_17,X_13))]]) ).
cnf(refute_0_184,plain,
( least_upper_bound(greatest_lower_bound(X_13,X_17),greatest_lower_bound(X_17,greatest_lower_bound(X_13,X_17))) != greatest_lower_bound(X_13,X_17)
| least_upper_bound(greatest_lower_bound(X_13,X_17),greatest_lower_bound(X_17,X_13)) = greatest_lower_bound(X_13,X_17) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,greatest_lower_bound(X_13,X_17)),greatest_lower_bound(X_17,X_13)) )],[refute_0_182,refute_0_183]) ).
cnf(refute_0_185,plain,
least_upper_bound(greatest_lower_bound(X_13,X_17),greatest_lower_bound(X_17,X_13)) = greatest_lower_bound(X_13,X_17),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_13,X_17),greatest_lower_bound(X_17,greatest_lower_bound(X_13,X_17))),greatest_lower_bound(X_13,X_17)) )],[refute_0_163,refute_0_184]) ).
cnf(refute_0_186,plain,
least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),greatest_lower_bound(multiply(Y,X),multiply(Z,X))) = greatest_lower_bound(multiply(Z,X),multiply(Y,X)),
inference(subst,[],[refute_0_185:[bind(X_13,$fot(multiply(Z,X))),bind(X_17,$fot(multiply(Y,X)))]]) ).
cnf(refute_0_187,plain,
( multiply(greatest_lower_bound(Y,Z),X) != greatest_lower_bound(multiply(Y,X),multiply(Z,X))
| greatest_lower_bound(multiply(Y,X),multiply(Z,X)) = multiply(greatest_lower_bound(Y,Z),X) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(greatest_lower_bound(Y,Z),X))),bind(Y0,$fot(greatest_lower_bound(multiply(Y,X),multiply(Z,X))))]]) ).
cnf(refute_0_188,plain,
greatest_lower_bound(multiply(Y,X),multiply(Z,X)) = multiply(greatest_lower_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Y,X),multiply(Z,X))) )],[monotony_glb2,refute_0_187]) ).
cnf(refute_0_189,plain,
( greatest_lower_bound(multiply(Y,X),multiply(Z,X)) != multiply(greatest_lower_bound(Y,Z),X)
| least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),greatest_lower_bound(multiply(Y,X),multiply(Z,X))) != greatest_lower_bound(multiply(Z,X),multiply(Y,X))
| least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),multiply(greatest_lower_bound(Y,Z),X)) = greatest_lower_bound(multiply(Z,X),multiply(Y,X)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),greatest_lower_bound(multiply(Y,X),multiply(Z,X))),greatest_lower_bound(multiply(Z,X),multiply(Y,X))) ),[0,1],$fot(multiply(greatest_lower_bound(Y,Z),X))]]) ).
cnf(refute_0_190,plain,
( least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),greatest_lower_bound(multiply(Y,X),multiply(Z,X))) != greatest_lower_bound(multiply(Z,X),multiply(Y,X))
| least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),multiply(greatest_lower_bound(Y,Z),X)) = greatest_lower_bound(multiply(Z,X),multiply(Y,X)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(Y,X),multiply(Z,X)),multiply(greatest_lower_bound(Y,Z),X)) )],[refute_0_188,refute_0_189]) ).
cnf(refute_0_191,plain,
least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),multiply(greatest_lower_bound(Y,Z),X)) = greatest_lower_bound(multiply(Z,X),multiply(Y,X)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),greatest_lower_bound(multiply(Y,X),multiply(Z,X))),greatest_lower_bound(multiply(Z,X),multiply(Y,X))) )],[refute_0_186,refute_0_190]) ).
cnf(refute_0_192,plain,
least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)) = greatest_lower_bound(Y,Z),
inference(subst,[],[refute_0_185:[bind(X_13,$fot(Y)),bind(X_17,$fot(Z))]]) ).
cnf(refute_0_193,plain,
multiply(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),X) = multiply(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),X),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),X))]]) ).
cnf(refute_0_194,plain,
( multiply(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),X) != multiply(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),X)
| least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)) != greatest_lower_bound(Y,Z)
| multiply(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),X) = multiply(greatest_lower_bound(Y,Z),X) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),X),multiply(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),X)) ),[1,0],$fot(greatest_lower_bound(Y,Z))]]) ).
cnf(refute_0_195,plain,
( least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)) != greatest_lower_bound(Y,Z)
| multiply(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),X) = multiply(greatest_lower_bound(Y,Z),X) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),X),multiply(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),X)) )],[refute_0_193,refute_0_194]) ).
cnf(refute_0_196,plain,
multiply(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),X) = multiply(greatest_lower_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),greatest_lower_bound(Y,Z)) )],[refute_0_192,refute_0_195]) ).
cnf(refute_0_197,plain,
( multiply(least_upper_bound(Y,Z),X) != least_upper_bound(multiply(Y,X),multiply(Z,X))
| least_upper_bound(multiply(Y,X),multiply(Z,X)) = multiply(least_upper_bound(Y,Z),X) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(Y,Z),X))),bind(Y0,$fot(least_upper_bound(multiply(Y,X),multiply(Z,X))))]]) ).
cnf(refute_0_198,plain,
least_upper_bound(multiply(Y,X),multiply(Z,X)) = multiply(least_upper_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Y,X),multiply(Z,X))) )],[monotony_lub2,refute_0_197]) ).
cnf(refute_0_199,plain,
least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),multiply(greatest_lower_bound(Z,Y),X)) = multiply(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),X),
inference(subst,[],[refute_0_198:[bind(Y,$fot(greatest_lower_bound(Y,Z))),bind(Z,$fot(greatest_lower_bound(Z,Y)))]]) ).
cnf(refute_0_200,plain,
( multiply(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),X) != multiply(greatest_lower_bound(Y,Z),X)
| least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),multiply(greatest_lower_bound(Z,Y),X)) != multiply(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),X)
| least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),multiply(greatest_lower_bound(Z,Y),X)) = multiply(greatest_lower_bound(Y,Z),X) ),
inference(subst,[],[refute_0_136:[bind(X0,$fot(least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),multiply(greatest_lower_bound(Z,Y),X)))),bind(Y0,$fot(multiply(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),X))),bind(Z0,$fot(multiply(greatest_lower_bound(Y,Z),X)))]]) ).
cnf(refute_0_201,plain,
( multiply(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),X) != multiply(greatest_lower_bound(Y,Z),X)
| least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),multiply(greatest_lower_bound(Z,Y),X)) = multiply(greatest_lower_bound(Y,Z),X) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),multiply(greatest_lower_bound(Z,Y),X)),multiply(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),X)) )],[refute_0_199,refute_0_200]) ).
cnf(refute_0_202,plain,
least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),multiply(greatest_lower_bound(Z,Y),X)) = multiply(greatest_lower_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),X),multiply(greatest_lower_bound(Y,Z),X)) )],[refute_0_196,refute_0_201]) ).
cnf(refute_0_203,plain,
greatest_lower_bound(multiply(Z,X),multiply(Y,X)) = multiply(greatest_lower_bound(Z,Y),X),
inference(subst,[],[refute_0_188:[bind(Y,$fot(Z)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_204,plain,
least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))) = least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))),
introduced(tautology,[refl,[$fot(least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))))]]) ).
cnf(refute_0_205,plain,
( greatest_lower_bound(multiply(Z,X),multiply(Y,X)) != multiply(greatest_lower_bound(Z,Y),X)
| least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))) != least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X)))
| least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))) = least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),multiply(greatest_lower_bound(Z,Y),X)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))),least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X)))) ),[1,1],$fot(multiply(greatest_lower_bound(Z,Y),X))]]) ).
cnf(refute_0_206,plain,
( greatest_lower_bound(multiply(Z,X),multiply(Y,X)) != multiply(greatest_lower_bound(Z,Y),X)
| least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))) = least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),multiply(greatest_lower_bound(Z,Y),X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))),least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X)))) )],[refute_0_204,refute_0_205]) ).
cnf(refute_0_207,plain,
least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))) = least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),multiply(greatest_lower_bound(Z,Y),X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),multiply(greatest_lower_bound(Z,Y),X)) )],[refute_0_203,refute_0_206]) ).
cnf(refute_0_208,plain,
( least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),multiply(greatest_lower_bound(Z,Y),X)) != multiply(greatest_lower_bound(Y,Z),X)
| least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))) != least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),multiply(greatest_lower_bound(Z,Y),X))
| least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))) = multiply(greatest_lower_bound(Y,Z),X) ),
inference(subst,[],[refute_0_136:[bind(X0,$fot(least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))))),bind(Y0,$fot(least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),multiply(greatest_lower_bound(Z,Y),X)))),bind(Z0,$fot(multiply(greatest_lower_bound(Y,Z),X)))]]) ).
cnf(refute_0_209,plain,
( least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),multiply(greatest_lower_bound(Z,Y),X)) != multiply(greatest_lower_bound(Y,Z),X)
| least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))) = multiply(greatest_lower_bound(Y,Z),X) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))),least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),multiply(greatest_lower_bound(Z,Y),X))) )],[refute_0_207,refute_0_208]) ).
cnf(refute_0_210,plain,
least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))) = multiply(greatest_lower_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),multiply(greatest_lower_bound(Z,Y),X)),multiply(greatest_lower_bound(Y,Z),X)) )],[refute_0_202,refute_0_209]) ).
cnf(refute_0_211,plain,
least_upper_bound(X_81,X_82) = multiply(inverse(inverse(X_82)),multiply(inverse(X_82),least_upper_bound(X_81,X_82))),
inference(subst,[],[refute_0_45:[bind(X_71,$fot(inverse(X_82))),bind(X_72,$fot(least_upper_bound(X_81,X_82)))]]) ).
cnf(refute_0_212,plain,
multiply(inverse(X_82),least_upper_bound(X_81,X_82)) = least_upper_bound(identity,multiply(inverse(X_82),X_81)),
inference(subst,[],[refute_0_34:[bind(X_79,$fot(X_81)),bind(X_80,$fot(X_82))]]) ).
cnf(refute_0_213,plain,
( multiply(inverse(X_82),least_upper_bound(X_81,X_82)) != least_upper_bound(identity,multiply(inverse(X_82),X_81))
| least_upper_bound(X_81,X_82) != multiply(inverse(inverse(X_82)),multiply(inverse(X_82),least_upper_bound(X_81,X_82)))
| least_upper_bound(X_81,X_82) = multiply(inverse(inverse(X_82)),least_upper_bound(identity,multiply(inverse(X_82),X_81))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_81,X_82),multiply(inverse(inverse(X_82)),multiply(inverse(X_82),least_upper_bound(X_81,X_82)))) ),[1,1],$fot(least_upper_bound(identity,multiply(inverse(X_82),X_81)))]]) ).
cnf(refute_0_214,plain,
( least_upper_bound(X_81,X_82) != multiply(inverse(inverse(X_82)),multiply(inverse(X_82),least_upper_bound(X_81,X_82)))
| least_upper_bound(X_81,X_82) = multiply(inverse(inverse(X_82)),least_upper_bound(identity,multiply(inverse(X_82),X_81))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_82),least_upper_bound(X_81,X_82)),least_upper_bound(identity,multiply(inverse(X_82),X_81))) )],[refute_0_212,refute_0_213]) ).
cnf(refute_0_215,plain,
least_upper_bound(X_81,X_82) = multiply(inverse(inverse(X_82)),least_upper_bound(identity,multiply(inverse(X_82),X_81))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_81,X_82),multiply(inverse(inverse(X_82)),multiply(inverse(X_82),least_upper_bound(X_81,X_82)))) )],[refute_0_211,refute_0_214]) ).
cnf(refute_0_216,plain,
( X_74 != multiply(X_74,identity)
| multiply(X_74,identity) = X_74 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_74)),bind(Y0,$fot(multiply(X_74,identity)))]]) ).
cnf(refute_0_217,plain,
multiply(X_74,identity) = X_74,
inference(resolve,[$cnf( $equal(X_74,multiply(X_74,identity)) )],[refute_0_63,refute_0_216]) ).
cnf(refute_0_218,plain,
multiply(inverse(inverse(X_82)),identity) = inverse(inverse(X_82)),
inference(subst,[],[refute_0_217:[bind(X_74,$fot(inverse(inverse(X_82))))]]) ).
cnf(refute_0_219,plain,
least_upper_bound(multiply(inverse(inverse(X_82)),identity),X_81) = least_upper_bound(multiply(inverse(inverse(X_82)),identity),X_81),
introduced(tautology,[refl,[$fot(least_upper_bound(multiply(inverse(inverse(X_82)),identity),X_81))]]) ).
cnf(refute_0_220,plain,
( multiply(inverse(inverse(X_82)),identity) != inverse(inverse(X_82))
| least_upper_bound(multiply(inverse(inverse(X_82)),identity),X_81) != least_upper_bound(multiply(inverse(inverse(X_82)),identity),X_81)
| least_upper_bound(multiply(inverse(inverse(X_82)),identity),X_81) = least_upper_bound(inverse(inverse(X_82)),X_81) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(inverse(inverse(X_82)),identity),X_81),least_upper_bound(multiply(inverse(inverse(X_82)),identity),X_81)) ),[1,0],$fot(inverse(inverse(X_82)))]]) ).
cnf(refute_0_221,plain,
( multiply(inverse(inverse(X_82)),identity) != inverse(inverse(X_82))
| least_upper_bound(multiply(inverse(inverse(X_82)),identity),X_81) = least_upper_bound(inverse(inverse(X_82)),X_81) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(inverse(X_82)),identity),X_81),least_upper_bound(multiply(inverse(inverse(X_82)),identity),X_81)) )],[refute_0_219,refute_0_220]) ).
cnf(refute_0_222,plain,
least_upper_bound(multiply(inverse(inverse(X_82)),identity),X_81) = least_upper_bound(inverse(inverse(X_82)),X_81),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_82)),identity),inverse(inverse(X_82))) )],[refute_0_218,refute_0_221]) ).
cnf(refute_0_223,plain,
multiply(inverse(X_71),least_upper_bound(X_79,multiply(X_71,X_72))) = least_upper_bound(multiply(inverse(X_71),X_79),multiply(inverse(X_71),multiply(X_71,X_72))),
inference(subst,[],[monotony_lub1:[bind(X,$fot(inverse(X_71))),bind(Y,$fot(X_79)),bind(Z,$fot(multiply(X_71,X_72)))]]) ).
cnf(refute_0_224,plain,
( X_72 != multiply(inverse(X_71),multiply(X_71,X_72))
| multiply(inverse(X_71),multiply(X_71,X_72)) = X_72 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_72)),bind(Y0,$fot(multiply(inverse(X_71),multiply(X_71,X_72))))]]) ).
cnf(refute_0_225,plain,
multiply(inverse(X_71),multiply(X_71,X_72)) = X_72,
inference(resolve,[$cnf( $equal(X_72,multiply(inverse(X_71),multiply(X_71,X_72))) )],[refute_0_45,refute_0_224]) ).
cnf(refute_0_226,plain,
( multiply(inverse(X_71),multiply(X_71,X_72)) != X_72
| multiply(inverse(X_71),least_upper_bound(X_79,multiply(X_71,X_72))) != least_upper_bound(multiply(inverse(X_71),X_79),multiply(inverse(X_71),multiply(X_71,X_72)))
| multiply(inverse(X_71),least_upper_bound(X_79,multiply(X_71,X_72))) = least_upper_bound(multiply(inverse(X_71),X_79),X_72) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_71),least_upper_bound(X_79,multiply(X_71,X_72))),least_upper_bound(multiply(inverse(X_71),X_79),multiply(inverse(X_71),multiply(X_71,X_72)))) ),[1,1],$fot(X_72)]]) ).
cnf(refute_0_227,plain,
( multiply(inverse(X_71),least_upper_bound(X_79,multiply(X_71,X_72))) != least_upper_bound(multiply(inverse(X_71),X_79),multiply(inverse(X_71),multiply(X_71,X_72)))
| multiply(inverse(X_71),least_upper_bound(X_79,multiply(X_71,X_72))) = least_upper_bound(multiply(inverse(X_71),X_79),X_72) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_71),multiply(X_71,X_72)),X_72) )],[refute_0_225,refute_0_226]) ).
cnf(refute_0_228,plain,
multiply(inverse(X_71),least_upper_bound(X_79,multiply(X_71,X_72))) = least_upper_bound(multiply(inverse(X_71),X_79),X_72),
inference(resolve,[$cnf( $equal(multiply(inverse(X_71),least_upper_bound(X_79,multiply(X_71,X_72))),least_upper_bound(multiply(inverse(X_71),X_79),multiply(inverse(X_71),multiply(X_71,X_72)))) )],[refute_0_223,refute_0_227]) ).
cnf(refute_0_229,plain,
multiply(inverse(inverse(X_82)),least_upper_bound(identity,multiply(inverse(X_82),X_81))) = least_upper_bound(multiply(inverse(inverse(X_82)),identity),X_81),
inference(subst,[],[refute_0_228:[bind(X_71,$fot(inverse(X_82))),bind(X_72,$fot(X_81)),bind(X_79,$fot(identity))]]) ).
cnf(refute_0_230,plain,
( multiply(inverse(inverse(X_82)),least_upper_bound(identity,multiply(inverse(X_82),X_81))) != least_upper_bound(multiply(inverse(inverse(X_82)),identity),X_81)
| least_upper_bound(multiply(inverse(inverse(X_82)),identity),X_81) != least_upper_bound(inverse(inverse(X_82)),X_81)
| multiply(inverse(inverse(X_82)),least_upper_bound(identity,multiply(inverse(X_82),X_81))) = least_upper_bound(inverse(inverse(X_82)),X_81) ),
inference(subst,[],[refute_0_136:[bind(X0,$fot(multiply(inverse(inverse(X_82)),least_upper_bound(identity,multiply(inverse(X_82),X_81))))),bind(Y0,$fot(least_upper_bound(multiply(inverse(inverse(X_82)),identity),X_81))),bind(Z0,$fot(least_upper_bound(inverse(inverse(X_82)),X_81)))]]) ).
cnf(refute_0_231,plain,
( least_upper_bound(multiply(inverse(inverse(X_82)),identity),X_81) != least_upper_bound(inverse(inverse(X_82)),X_81)
| multiply(inverse(inverse(X_82)),least_upper_bound(identity,multiply(inverse(X_82),X_81))) = least_upper_bound(inverse(inverse(X_82)),X_81) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_82)),least_upper_bound(identity,multiply(inverse(X_82),X_81))),least_upper_bound(multiply(inverse(inverse(X_82)),identity),X_81)) )],[refute_0_229,refute_0_230]) ).
cnf(refute_0_232,plain,
multiply(inverse(inverse(X_82)),least_upper_bound(identity,multiply(inverse(X_82),X_81))) = least_upper_bound(inverse(inverse(X_82)),X_81),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(inverse(X_82)),identity),X_81),least_upper_bound(inverse(inverse(X_82)),X_81)) )],[refute_0_222,refute_0_231]) ).
cnf(refute_0_233,plain,
( multiply(inverse(inverse(X_82)),least_upper_bound(identity,multiply(inverse(X_82),X_81))) != least_upper_bound(inverse(inverse(X_82)),X_81)
| least_upper_bound(X_81,X_82) != multiply(inverse(inverse(X_82)),least_upper_bound(identity,multiply(inverse(X_82),X_81)))
| least_upper_bound(X_81,X_82) = least_upper_bound(inverse(inverse(X_82)),X_81) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_81,X_82),multiply(inverse(inverse(X_82)),least_upper_bound(identity,multiply(inverse(X_82),X_81)))) ),[1],$fot(least_upper_bound(inverse(inverse(X_82)),X_81))]]) ).
cnf(refute_0_234,plain,
( least_upper_bound(X_81,X_82) != multiply(inverse(inverse(X_82)),least_upper_bound(identity,multiply(inverse(X_82),X_81)))
| least_upper_bound(X_81,X_82) = least_upper_bound(inverse(inverse(X_82)),X_81) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_82)),least_upper_bound(identity,multiply(inverse(X_82),X_81))),least_upper_bound(inverse(inverse(X_82)),X_81)) )],[refute_0_232,refute_0_233]) ).
cnf(refute_0_235,plain,
least_upper_bound(X_81,X_82) = least_upper_bound(inverse(inverse(X_82)),X_81),
inference(resolve,[$cnf( $equal(least_upper_bound(X_81,X_82),multiply(inverse(inverse(X_82)),least_upper_bound(identity,multiply(inverse(X_82),X_81)))) )],[refute_0_215,refute_0_234]) ).
cnf(refute_0_236,plain,
least_upper_bound(X_12,greatest_lower_bound(greatest_lower_bound(X_18,X_19),X_12)) = X_12,
inference(subst,[],[refute_0_80:[bind(X_13,$fot(greatest_lower_bound(X_18,X_19)))]]) ).
cnf(refute_0_237,plain,
greatest_lower_bound(X_18,greatest_lower_bound(X_19,X_12)) = greatest_lower_bound(greatest_lower_bound(X_18,X_19),X_12),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_18)),bind(Y,$fot(X_19)),bind(Z,$fot(X_12))]]) ).
cnf(refute_0_238,plain,
( greatest_lower_bound(X_18,greatest_lower_bound(X_19,X_12)) != greatest_lower_bound(greatest_lower_bound(X_18,X_19),X_12)
| greatest_lower_bound(greatest_lower_bound(X_18,X_19),X_12) = greatest_lower_bound(X_18,greatest_lower_bound(X_19,X_12)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X_18,greatest_lower_bound(X_19,X_12)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X_18,X_19),X_12)))]]) ).
cnf(refute_0_239,plain,
greatest_lower_bound(greatest_lower_bound(X_18,X_19),X_12) = greatest_lower_bound(X_18,greatest_lower_bound(X_19,X_12)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_18,greatest_lower_bound(X_19,X_12)),greatest_lower_bound(greatest_lower_bound(X_18,X_19),X_12)) )],[refute_0_237,refute_0_238]) ).
cnf(refute_0_240,plain,
( greatest_lower_bound(greatest_lower_bound(X_18,X_19),X_12) != greatest_lower_bound(X_18,greatest_lower_bound(X_19,X_12))
| least_upper_bound(X_12,greatest_lower_bound(greatest_lower_bound(X_18,X_19),X_12)) != X_12
| least_upper_bound(X_12,greatest_lower_bound(X_18,greatest_lower_bound(X_19,X_12))) = X_12 ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_12,greatest_lower_bound(greatest_lower_bound(X_18,X_19),X_12)),X_12) ),[0,1],$fot(greatest_lower_bound(X_18,greatest_lower_bound(X_19,X_12)))]]) ).
cnf(refute_0_241,plain,
( least_upper_bound(X_12,greatest_lower_bound(greatest_lower_bound(X_18,X_19),X_12)) != X_12
| least_upper_bound(X_12,greatest_lower_bound(X_18,greatest_lower_bound(X_19,X_12))) = X_12 ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_18,X_19),X_12),greatest_lower_bound(X_18,greatest_lower_bound(X_19,X_12))) )],[refute_0_239,refute_0_240]) ).
cnf(refute_0_242,plain,
least_upper_bound(X_12,greatest_lower_bound(X_18,greatest_lower_bound(X_19,X_12))) = X_12,
inference(resolve,[$cnf( $equal(least_upper_bound(X_12,greatest_lower_bound(greatest_lower_bound(X_18,X_19),X_12)),X_12) )],[refute_0_236,refute_0_241]) ).
cnf(refute_0_243,plain,
least_upper_bound(inverse(inverse(X_77)),greatest_lower_bound(X_18,greatest_lower_bound(identity,inverse(inverse(X_77))))) = inverse(inverse(X_77)),
inference(subst,[],[refute_0_242:[bind(X_12,$fot(inverse(inverse(X_77)))),bind(X_19,$fot(identity))]]) ).
cnf(refute_0_244,plain,
greatest_lower_bound(X_76,identity) = multiply(inverse(inverse(X_76)),multiply(inverse(X_76),greatest_lower_bound(X_76,identity))),
inference(subst,[],[refute_0_45:[bind(X_71,$fot(inverse(X_76))),bind(X_72,$fot(greatest_lower_bound(X_76,identity)))]]) ).
cnf(refute_0_245,plain,
multiply(inverse(X_22),greatest_lower_bound(X_22,X_23)) = greatest_lower_bound(multiply(inverse(X_22),X_22),multiply(inverse(X_22),X_23)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(inverse(X_22))),bind(Y,$fot(X_22)),bind(Z,$fot(X_23))]]) ).
cnf(refute_0_246,plain,
multiply(inverse(X_22),X_22) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_22))]]) ).
cnf(refute_0_247,plain,
( multiply(inverse(X_22),X_22) != identity
| multiply(inverse(X_22),greatest_lower_bound(X_22,X_23)) != greatest_lower_bound(multiply(inverse(X_22),X_22),multiply(inverse(X_22),X_23))
| multiply(inverse(X_22),greatest_lower_bound(X_22,X_23)) = greatest_lower_bound(identity,multiply(inverse(X_22),X_23)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_22),greatest_lower_bound(X_22,X_23)),greatest_lower_bound(multiply(inverse(X_22),X_22),multiply(inverse(X_22),X_23))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_248,plain,
( multiply(inverse(X_22),greatest_lower_bound(X_22,X_23)) != greatest_lower_bound(multiply(inverse(X_22),X_22),multiply(inverse(X_22),X_23))
| multiply(inverse(X_22),greatest_lower_bound(X_22,X_23)) = greatest_lower_bound(identity,multiply(inverse(X_22),X_23)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_22),X_22),identity) )],[refute_0_246,refute_0_247]) ).
cnf(refute_0_249,plain,
multiply(inverse(X_22),greatest_lower_bound(X_22,X_23)) = greatest_lower_bound(identity,multiply(inverse(X_22),X_23)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_22),greatest_lower_bound(X_22,X_23)),greatest_lower_bound(multiply(inverse(X_22),X_22),multiply(inverse(X_22),X_23))) )],[refute_0_245,refute_0_248]) ).
cnf(refute_0_250,plain,
multiply(inverse(X_22),greatest_lower_bound(X_22,identity)) = greatest_lower_bound(identity,multiply(inverse(X_22),identity)),
inference(subst,[],[refute_0_249:[bind(X_23,$fot(identity))]]) ).
cnf(refute_0_251,plain,
inverse(X_22) = multiply(inverse(X_22),identity),
inference(subst,[],[refute_0_63:[bind(X_74,$fot(inverse(X_22)))]]) ).
cnf(refute_0_252,plain,
( inverse(X_22) != multiply(inverse(X_22),identity)
| multiply(inverse(X_22),identity) = inverse(X_22) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(X_22))),bind(Y0,$fot(multiply(inverse(X_22),identity)))]]) ).
cnf(refute_0_253,plain,
multiply(inverse(X_22),identity) = inverse(X_22),
inference(resolve,[$cnf( $equal(inverse(X_22),multiply(inverse(X_22),identity)) )],[refute_0_251,refute_0_252]) ).
cnf(refute_0_254,plain,
( multiply(inverse(X_22),greatest_lower_bound(X_22,identity)) != greatest_lower_bound(identity,multiply(inverse(X_22),identity))
| multiply(inverse(X_22),identity) != inverse(X_22)
| multiply(inverse(X_22),greatest_lower_bound(X_22,identity)) = greatest_lower_bound(identity,inverse(X_22)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_22),greatest_lower_bound(X_22,identity)),greatest_lower_bound(identity,multiply(inverse(X_22),identity))) ),[1,1],$fot(inverse(X_22))]]) ).
cnf(refute_0_255,plain,
( multiply(inverse(X_22),greatest_lower_bound(X_22,identity)) != greatest_lower_bound(identity,multiply(inverse(X_22),identity))
| multiply(inverse(X_22),greatest_lower_bound(X_22,identity)) = greatest_lower_bound(identity,inverse(X_22)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_22),identity),inverse(X_22)) )],[refute_0_253,refute_0_254]) ).
cnf(refute_0_256,plain,
multiply(inverse(X_22),greatest_lower_bound(X_22,identity)) = greatest_lower_bound(identity,inverse(X_22)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_22),greatest_lower_bound(X_22,identity)),greatest_lower_bound(identity,multiply(inverse(X_22),identity))) )],[refute_0_250,refute_0_255]) ).
cnf(refute_0_257,plain,
multiply(inverse(X_76),greatest_lower_bound(X_76,identity)) = greatest_lower_bound(identity,inverse(X_76)),
inference(subst,[],[refute_0_256:[bind(X_22,$fot(X_76))]]) ).
cnf(refute_0_258,plain,
( multiply(inverse(X_76),greatest_lower_bound(X_76,identity)) != greatest_lower_bound(identity,inverse(X_76))
| greatest_lower_bound(X_76,identity) != multiply(inverse(inverse(X_76)),multiply(inverse(X_76),greatest_lower_bound(X_76,identity)))
| greatest_lower_bound(X_76,identity) = multiply(inverse(inverse(X_76)),greatest_lower_bound(identity,inverse(X_76))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_76,identity),multiply(inverse(inverse(X_76)),multiply(inverse(X_76),greatest_lower_bound(X_76,identity)))) ),[1,1],$fot(greatest_lower_bound(identity,inverse(X_76)))]]) ).
cnf(refute_0_259,plain,
( greatest_lower_bound(X_76,identity) != multiply(inverse(inverse(X_76)),multiply(inverse(X_76),greatest_lower_bound(X_76,identity)))
| greatest_lower_bound(X_76,identity) = multiply(inverse(inverse(X_76)),greatest_lower_bound(identity,inverse(X_76))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_76),greatest_lower_bound(X_76,identity)),greatest_lower_bound(identity,inverse(X_76))) )],[refute_0_257,refute_0_258]) ).
cnf(refute_0_260,plain,
greatest_lower_bound(X_76,identity) = multiply(inverse(inverse(X_76)),greatest_lower_bound(identity,inverse(X_76))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_76,identity),multiply(inverse(inverse(X_76)),multiply(inverse(X_76),greatest_lower_bound(X_76,identity)))) )],[refute_0_244,refute_0_259]) ).
cnf(refute_0_261,plain,
multiply(inverse(X_23),greatest_lower_bound(X_22,X_23)) = greatest_lower_bound(multiply(inverse(X_23),X_22),multiply(inverse(X_23),X_23)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(inverse(X_23))),bind(Y,$fot(X_22)),bind(Z,$fot(X_23))]]) ).
cnf(refute_0_262,plain,
multiply(inverse(X_23),X_23) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_23))]]) ).
cnf(refute_0_263,plain,
( multiply(inverse(X_23),X_23) != identity
| multiply(inverse(X_23),greatest_lower_bound(X_22,X_23)) != greatest_lower_bound(multiply(inverse(X_23),X_22),multiply(inverse(X_23),X_23))
| multiply(inverse(X_23),greatest_lower_bound(X_22,X_23)) = greatest_lower_bound(multiply(inverse(X_23),X_22),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_23),greatest_lower_bound(X_22,X_23)),greatest_lower_bound(multiply(inverse(X_23),X_22),multiply(inverse(X_23),X_23))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_264,plain,
( multiply(inverse(X_23),greatest_lower_bound(X_22,X_23)) != greatest_lower_bound(multiply(inverse(X_23),X_22),multiply(inverse(X_23),X_23))
| multiply(inverse(X_23),greatest_lower_bound(X_22,X_23)) = greatest_lower_bound(multiply(inverse(X_23),X_22),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_23),X_23),identity) )],[refute_0_262,refute_0_263]) ).
cnf(refute_0_265,plain,
multiply(inverse(X_23),greatest_lower_bound(X_22,X_23)) = greatest_lower_bound(multiply(inverse(X_23),X_22),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_23),greatest_lower_bound(X_22,X_23)),greatest_lower_bound(multiply(inverse(X_23),X_22),multiply(inverse(X_23),X_23))) )],[refute_0_261,refute_0_264]) ).
cnf(refute_0_266,plain,
greatest_lower_bound(multiply(inverse(X_23),X_22),identity) = greatest_lower_bound(identity,multiply(inverse(X_23),X_22)),
inference(subst,[],[refute_0_19:[bind(X,$fot(identity)),bind(Y,$fot(multiply(inverse(X_23),X_22)))]]) ).
cnf(refute_0_267,plain,
( multiply(inverse(X_23),greatest_lower_bound(X_22,X_23)) != greatest_lower_bound(multiply(inverse(X_23),X_22),identity)
| greatest_lower_bound(multiply(inverse(X_23),X_22),identity) != greatest_lower_bound(identity,multiply(inverse(X_23),X_22))
| multiply(inverse(X_23),greatest_lower_bound(X_22,X_23)) = greatest_lower_bound(identity,multiply(inverse(X_23),X_22)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_23),greatest_lower_bound(X_22,X_23)),greatest_lower_bound(identity,multiply(inverse(X_23),X_22))) ),[0],$fot(greatest_lower_bound(multiply(inverse(X_23),X_22),identity))]]) ).
cnf(refute_0_268,plain,
( multiply(inverse(X_23),greatest_lower_bound(X_22,X_23)) != greatest_lower_bound(multiply(inverse(X_23),X_22),identity)
| multiply(inverse(X_23),greatest_lower_bound(X_22,X_23)) = greatest_lower_bound(identity,multiply(inverse(X_23),X_22)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(inverse(X_23),X_22),identity),greatest_lower_bound(identity,multiply(inverse(X_23),X_22))) )],[refute_0_266,refute_0_267]) ).
cnf(refute_0_269,plain,
multiply(inverse(X_23),greatest_lower_bound(X_22,X_23)) = greatest_lower_bound(identity,multiply(inverse(X_23),X_22)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_23),greatest_lower_bound(X_22,X_23)),greatest_lower_bound(multiply(inverse(X_23),X_22),identity)) )],[refute_0_265,refute_0_268]) ).
cnf(refute_0_270,plain,
multiply(inverse(X_23),greatest_lower_bound(identity,X_23)) = greatest_lower_bound(identity,multiply(inverse(X_23),identity)),
inference(subst,[],[refute_0_269:[bind(X_22,$fot(identity))]]) ).
cnf(refute_0_271,plain,
inverse(X_23) = multiply(inverse(X_23),identity),
inference(subst,[],[refute_0_63:[bind(X_74,$fot(inverse(X_23)))]]) ).
cnf(refute_0_272,plain,
( inverse(X_23) != multiply(inverse(X_23),identity)
| multiply(inverse(X_23),identity) = inverse(X_23) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(X_23))),bind(Y0,$fot(multiply(inverse(X_23),identity)))]]) ).
cnf(refute_0_273,plain,
multiply(inverse(X_23),identity) = inverse(X_23),
inference(resolve,[$cnf( $equal(inverse(X_23),multiply(inverse(X_23),identity)) )],[refute_0_271,refute_0_272]) ).
cnf(refute_0_274,plain,
( multiply(inverse(X_23),greatest_lower_bound(identity,X_23)) != greatest_lower_bound(identity,multiply(inverse(X_23),identity))
| multiply(inverse(X_23),identity) != inverse(X_23)
| multiply(inverse(X_23),greatest_lower_bound(identity,X_23)) = greatest_lower_bound(identity,inverse(X_23)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_23),greatest_lower_bound(identity,X_23)),greatest_lower_bound(identity,multiply(inverse(X_23),identity))) ),[1,1],$fot(inverse(X_23))]]) ).
cnf(refute_0_275,plain,
( multiply(inverse(X_23),greatest_lower_bound(identity,X_23)) != greatest_lower_bound(identity,multiply(inverse(X_23),identity))
| multiply(inverse(X_23),greatest_lower_bound(identity,X_23)) = greatest_lower_bound(identity,inverse(X_23)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_23),identity),inverse(X_23)) )],[refute_0_273,refute_0_274]) ).
cnf(refute_0_276,plain,
multiply(inverse(X_23),greatest_lower_bound(identity,X_23)) = greatest_lower_bound(identity,inverse(X_23)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_23),greatest_lower_bound(identity,X_23)),greatest_lower_bound(identity,multiply(inverse(X_23),identity))) )],[refute_0_270,refute_0_275]) ).
cnf(refute_0_277,plain,
multiply(inverse(inverse(X_76)),greatest_lower_bound(identity,inverse(X_76))) = greatest_lower_bound(identity,inverse(inverse(X_76))),
inference(subst,[],[refute_0_276:[bind(X_23,$fot(inverse(X_76)))]]) ).
cnf(refute_0_278,plain,
( multiply(inverse(inverse(X_76)),greatest_lower_bound(identity,inverse(X_76))) != greatest_lower_bound(identity,inverse(inverse(X_76)))
| greatest_lower_bound(X_76,identity) != multiply(inverse(inverse(X_76)),greatest_lower_bound(identity,inverse(X_76)))
| greatest_lower_bound(X_76,identity) = greatest_lower_bound(identity,inverse(inverse(X_76))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_76,identity),multiply(inverse(inverse(X_76)),greatest_lower_bound(identity,inverse(X_76)))) ),[1],$fot(greatest_lower_bound(identity,inverse(inverse(X_76))))]]) ).
cnf(refute_0_279,plain,
( greatest_lower_bound(X_76,identity) != multiply(inverse(inverse(X_76)),greatest_lower_bound(identity,inverse(X_76)))
| greatest_lower_bound(X_76,identity) = greatest_lower_bound(identity,inverse(inverse(X_76))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_76)),greatest_lower_bound(identity,inverse(X_76))),greatest_lower_bound(identity,inverse(inverse(X_76)))) )],[refute_0_277,refute_0_278]) ).
cnf(refute_0_280,plain,
greatest_lower_bound(X_76,identity) = greatest_lower_bound(identity,inverse(inverse(X_76))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_76,identity),multiply(inverse(inverse(X_76)),greatest_lower_bound(identity,inverse(X_76)))) )],[refute_0_260,refute_0_279]) ).
cnf(refute_0_281,plain,
greatest_lower_bound(X_77,identity) = greatest_lower_bound(identity,inverse(inverse(X_77))),
inference(subst,[],[refute_0_280:[bind(X_76,$fot(X_77))]]) ).
cnf(refute_0_282,plain,
( greatest_lower_bound(X_77,identity) != greatest_lower_bound(identity,inverse(inverse(X_77)))
| greatest_lower_bound(identity,inverse(inverse(X_77))) = greatest_lower_bound(X_77,identity) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X_77,identity))),bind(Y0,$fot(greatest_lower_bound(identity,inverse(inverse(X_77)))))]]) ).
cnf(refute_0_283,plain,
greatest_lower_bound(identity,inverse(inverse(X_77))) = greatest_lower_bound(X_77,identity),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_77,identity),greatest_lower_bound(identity,inverse(inverse(X_77)))) )],[refute_0_281,refute_0_282]) ).
cnf(refute_0_284,plain,
( greatest_lower_bound(identity,inverse(inverse(X_77))) != greatest_lower_bound(X_77,identity)
| least_upper_bound(inverse(inverse(X_77)),greatest_lower_bound(X_18,greatest_lower_bound(identity,inverse(inverse(X_77))))) != inverse(inverse(X_77))
| least_upper_bound(inverse(inverse(X_77)),greatest_lower_bound(X_18,greatest_lower_bound(X_77,identity))) = inverse(inverse(X_77)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(inverse(X_77)),greatest_lower_bound(X_18,greatest_lower_bound(identity,inverse(inverse(X_77))))),inverse(inverse(X_77))) ),[0,1,1],$fot(greatest_lower_bound(X_77,identity))]]) ).
cnf(refute_0_285,plain,
( least_upper_bound(inverse(inverse(X_77)),greatest_lower_bound(X_18,greatest_lower_bound(identity,inverse(inverse(X_77))))) != inverse(inverse(X_77))
| least_upper_bound(inverse(inverse(X_77)),greatest_lower_bound(X_18,greatest_lower_bound(X_77,identity))) = inverse(inverse(X_77)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(inverse(X_77))),greatest_lower_bound(X_77,identity)) )],[refute_0_283,refute_0_284]) ).
cnf(refute_0_286,plain,
least_upper_bound(inverse(inverse(X_77)),greatest_lower_bound(X_18,greatest_lower_bound(X_77,identity))) = inverse(inverse(X_77)),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(inverse(X_77)),greatest_lower_bound(X_18,greatest_lower_bound(identity,inverse(inverse(X_77))))),inverse(inverse(X_77))) )],[refute_0_243,refute_0_285]) ).
cnf(refute_0_287,plain,
least_upper_bound(X_67,greatest_lower_bound(X_68,greatest_lower_bound(X_69,X_67))) = X_67,
inference(subst,[],[refute_0_242:[bind(X_12,$fot(X_67)),bind(X_18,$fot(X_68)),bind(X_19,$fot(X_69))]]) ).
cnf(refute_0_288,plain,
greatest_lower_bound(X_67,X_69) = greatest_lower_bound(X_69,X_67),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_67)),bind(Y,$fot(X_69))]]) ).
cnf(refute_0_289,plain,
( greatest_lower_bound(X_67,X_69) != greatest_lower_bound(X_69,X_67)
| greatest_lower_bound(X_69,X_67) = greatest_lower_bound(X_67,X_69) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X_67,X_69))),bind(Y0,$fot(greatest_lower_bound(X_69,X_67)))]]) ).
cnf(refute_0_290,plain,
greatest_lower_bound(X_69,X_67) = greatest_lower_bound(X_67,X_69),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_67,X_69),greatest_lower_bound(X_69,X_67)) )],[refute_0_288,refute_0_289]) ).
cnf(refute_0_291,plain,
( greatest_lower_bound(X_69,X_67) != greatest_lower_bound(X_67,X_69)
| least_upper_bound(X_67,greatest_lower_bound(X_68,greatest_lower_bound(X_69,X_67))) != X_67
| least_upper_bound(X_67,greatest_lower_bound(X_68,greatest_lower_bound(X_67,X_69))) = X_67 ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_67,greatest_lower_bound(X_68,greatest_lower_bound(X_69,X_67))),X_67) ),[0,1,1],$fot(greatest_lower_bound(X_67,X_69))]]) ).
cnf(refute_0_292,plain,
( least_upper_bound(X_67,greatest_lower_bound(X_68,greatest_lower_bound(X_69,X_67))) != X_67
| least_upper_bound(X_67,greatest_lower_bound(X_68,greatest_lower_bound(X_67,X_69))) = X_67 ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_69,X_67),greatest_lower_bound(X_67,X_69)) )],[refute_0_290,refute_0_291]) ).
cnf(refute_0_293,plain,
least_upper_bound(X_67,greatest_lower_bound(X_68,greatest_lower_bound(X_67,X_69))) = X_67,
inference(resolve,[$cnf( $equal(least_upper_bound(X_67,greatest_lower_bound(X_68,greatest_lower_bound(X_69,X_67))),X_67) )],[refute_0_287,refute_0_292]) ).
cnf(refute_0_294,plain,
least_upper_bound(X_77,greatest_lower_bound(X_18,greatest_lower_bound(X_77,identity))) = X_77,
inference(subst,[],[refute_0_293:[bind(X_67,$fot(X_77)),bind(X_68,$fot(X_18)),bind(X_69,$fot(identity))]]) ).
cnf(refute_0_295,plain,
least_upper_bound(greatest_lower_bound(X_18,greatest_lower_bound(X_77,identity)),X_77) = least_upper_bound(X_77,greatest_lower_bound(X_18,greatest_lower_bound(X_77,identity))),
inference(subst,[],[refute_0_30:[bind(X_32,$fot(X_77)),bind(X_33,$fot(greatest_lower_bound(X_18,greatest_lower_bound(X_77,identity))))]]) ).
cnf(refute_0_296,plain,
( least_upper_bound(X_77,greatest_lower_bound(X_18,greatest_lower_bound(X_77,identity))) != X_77
| least_upper_bound(greatest_lower_bound(X_18,greatest_lower_bound(X_77,identity)),X_77) != least_upper_bound(X_77,greatest_lower_bound(X_18,greatest_lower_bound(X_77,identity)))
| least_upper_bound(greatest_lower_bound(X_18,greatest_lower_bound(X_77,identity)),X_77) = X_77 ),
inference(subst,[],[refute_0_136:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(X_18,greatest_lower_bound(X_77,identity)),X_77))),bind(Y0,$fot(least_upper_bound(X_77,greatest_lower_bound(X_18,greatest_lower_bound(X_77,identity))))),bind(Z0,$fot(X_77))]]) ).
cnf(refute_0_297,plain,
( least_upper_bound(X_77,greatest_lower_bound(X_18,greatest_lower_bound(X_77,identity))) != X_77
| least_upper_bound(greatest_lower_bound(X_18,greatest_lower_bound(X_77,identity)),X_77) = X_77 ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_18,greatest_lower_bound(X_77,identity)),X_77),least_upper_bound(X_77,greatest_lower_bound(X_18,greatest_lower_bound(X_77,identity)))) )],[refute_0_295,refute_0_296]) ).
cnf(refute_0_298,plain,
least_upper_bound(greatest_lower_bound(X_18,greatest_lower_bound(X_77,identity)),X_77) = X_77,
inference(resolve,[$cnf( $equal(least_upper_bound(X_77,greatest_lower_bound(X_18,greatest_lower_bound(X_77,identity))),X_77) )],[refute_0_294,refute_0_297]) ).
cnf(refute_0_299,plain,
( least_upper_bound(X_81,X_82) != least_upper_bound(inverse(inverse(X_82)),X_81)
| least_upper_bound(inverse(inverse(X_82)),X_81) = least_upper_bound(X_81,X_82) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X_81,X_82))),bind(Y0,$fot(least_upper_bound(inverse(inverse(X_82)),X_81)))]]) ).
cnf(refute_0_300,plain,
least_upper_bound(inverse(inverse(X_82)),X_81) = least_upper_bound(X_81,X_82),
inference(resolve,[$cnf( $equal(least_upper_bound(X_81,X_82),least_upper_bound(inverse(inverse(X_82)),X_81)) )],[refute_0_235,refute_0_299]) ).
cnf(refute_0_301,plain,
least_upper_bound(inverse(inverse(X_77)),greatest_lower_bound(X_18,greatest_lower_bound(X_77,identity))) = least_upper_bound(greatest_lower_bound(X_18,greatest_lower_bound(X_77,identity)),X_77),
inference(subst,[],[refute_0_300:[bind(X_81,$fot(greatest_lower_bound(X_18,greatest_lower_bound(X_77,identity)))),bind(X_82,$fot(X_77))]]) ).
cnf(refute_0_302,plain,
( least_upper_bound(greatest_lower_bound(X_18,greatest_lower_bound(X_77,identity)),X_77) != X_77
| least_upper_bound(inverse(inverse(X_77)),greatest_lower_bound(X_18,greatest_lower_bound(X_77,identity))) != least_upper_bound(greatest_lower_bound(X_18,greatest_lower_bound(X_77,identity)),X_77)
| least_upper_bound(inverse(inverse(X_77)),greatest_lower_bound(X_18,greatest_lower_bound(X_77,identity))) = X_77 ),
inference(subst,[],[refute_0_136:[bind(X0,$fot(least_upper_bound(inverse(inverse(X_77)),greatest_lower_bound(X_18,greatest_lower_bound(X_77,identity))))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(X_18,greatest_lower_bound(X_77,identity)),X_77))),bind(Z0,$fot(X_77))]]) ).
cnf(refute_0_303,plain,
( least_upper_bound(greatest_lower_bound(X_18,greatest_lower_bound(X_77,identity)),X_77) != X_77
| least_upper_bound(inverse(inverse(X_77)),greatest_lower_bound(X_18,greatest_lower_bound(X_77,identity))) = X_77 ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(inverse(X_77)),greatest_lower_bound(X_18,greatest_lower_bound(X_77,identity))),least_upper_bound(greatest_lower_bound(X_18,greatest_lower_bound(X_77,identity)),X_77)) )],[refute_0_301,refute_0_302]) ).
cnf(refute_0_304,plain,
least_upper_bound(inverse(inverse(X_77)),greatest_lower_bound(X_18,greatest_lower_bound(X_77,identity))) = X_77,
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_18,greatest_lower_bound(X_77,identity)),X_77),X_77) )],[refute_0_298,refute_0_303]) ).
cnf(refute_0_305,plain,
( least_upper_bound(inverse(inverse(X_77)),greatest_lower_bound(X_18,greatest_lower_bound(X_77,identity))) != X_77
| least_upper_bound(inverse(inverse(X_77)),greatest_lower_bound(X_18,greatest_lower_bound(X_77,identity))) != inverse(inverse(X_77))
| X_77 = inverse(inverse(X_77)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(inverse(X_77)),greatest_lower_bound(X_18,greatest_lower_bound(X_77,identity))),inverse(inverse(X_77))) ),[0],$fot(X_77)]]) ).
cnf(refute_0_306,plain,
( least_upper_bound(inverse(inverse(X_77)),greatest_lower_bound(X_18,greatest_lower_bound(X_77,identity))) != inverse(inverse(X_77))
| X_77 = inverse(inverse(X_77)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(inverse(X_77)),greatest_lower_bound(X_18,greatest_lower_bound(X_77,identity))),X_77) )],[refute_0_304,refute_0_305]) ).
cnf(refute_0_307,plain,
X_77 = inverse(inverse(X_77)),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(inverse(X_77)),greatest_lower_bound(X_18,greatest_lower_bound(X_77,identity))),inverse(inverse(X_77))) )],[refute_0_286,refute_0_306]) ).
cnf(refute_0_308,plain,
( X_77 != inverse(inverse(X_77))
| inverse(inverse(X_77)) = X_77 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_77)),bind(Y0,$fot(inverse(inverse(X_77))))]]) ).
cnf(refute_0_309,plain,
inverse(inverse(X_77)) = X_77,
inference(resolve,[$cnf( $equal(X_77,inverse(inverse(X_77))) )],[refute_0_307,refute_0_308]) ).
cnf(refute_0_310,plain,
inverse(inverse(X_82)) = X_82,
inference(subst,[],[refute_0_309:[bind(X_77,$fot(X_82))]]) ).
cnf(refute_0_311,plain,
least_upper_bound(inverse(inverse(X_82)),X_81) = least_upper_bound(inverse(inverse(X_82)),X_81),
introduced(tautology,[refl,[$fot(least_upper_bound(inverse(inverse(X_82)),X_81))]]) ).
cnf(refute_0_312,plain,
( inverse(inverse(X_82)) != X_82
| least_upper_bound(inverse(inverse(X_82)),X_81) != least_upper_bound(inverse(inverse(X_82)),X_81)
| least_upper_bound(inverse(inverse(X_82)),X_81) = least_upper_bound(X_82,X_81) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(inverse(X_82)),X_81),least_upper_bound(inverse(inverse(X_82)),X_81)) ),[1,0],$fot(X_82)]]) ).
cnf(refute_0_313,plain,
( inverse(inverse(X_82)) != X_82
| least_upper_bound(inverse(inverse(X_82)),X_81) = least_upper_bound(X_82,X_81) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(inverse(X_82)),X_81),least_upper_bound(inverse(inverse(X_82)),X_81)) )],[refute_0_311,refute_0_312]) ).
cnf(refute_0_314,plain,
least_upper_bound(inverse(inverse(X_82)),X_81) = least_upper_bound(X_82,X_81),
inference(resolve,[$cnf( $equal(inverse(inverse(X_82)),X_82) )],[refute_0_310,refute_0_313]) ).
cnf(refute_0_315,plain,
( least_upper_bound(X_81,X_82) != least_upper_bound(inverse(inverse(X_82)),X_81)
| least_upper_bound(inverse(inverse(X_82)),X_81) != least_upper_bound(X_82,X_81)
| least_upper_bound(X_81,X_82) = least_upper_bound(X_82,X_81) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_81,X_82),least_upper_bound(X_82,X_81)) ),[0],$fot(least_upper_bound(inverse(inverse(X_82)),X_81))]]) ).
cnf(refute_0_316,plain,
( least_upper_bound(X_81,X_82) != least_upper_bound(inverse(inverse(X_82)),X_81)
| least_upper_bound(X_81,X_82) = least_upper_bound(X_82,X_81) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(inverse(X_82)),X_81),least_upper_bound(X_82,X_81)) )],[refute_0_314,refute_0_315]) ).
cnf(refute_0_317,plain,
least_upper_bound(X_81,X_82) = least_upper_bound(X_82,X_81),
inference(resolve,[$cnf( $equal(least_upper_bound(X_81,X_82),least_upper_bound(inverse(inverse(X_82)),X_81)) )],[refute_0_235,refute_0_316]) ).
cnf(refute_0_318,plain,
( least_upper_bound(X_81,X_82) != least_upper_bound(X_82,X_81)
| least_upper_bound(X_82,X_81) = least_upper_bound(X_81,X_82) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X_81,X_82))),bind(Y0,$fot(least_upper_bound(X_82,X_81)))]]) ).
cnf(refute_0_319,plain,
least_upper_bound(X_82,X_81) = least_upper_bound(X_81,X_82),
inference(resolve,[$cnf( $equal(least_upper_bound(X_81,X_82),least_upper_bound(X_82,X_81)) )],[refute_0_317,refute_0_318]) ).
cnf(refute_0_320,plain,
least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),multiply(greatest_lower_bound(Y,Z),X)) = least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))),
inference(subst,[],[refute_0_319:[bind(X_81,$fot(multiply(greatest_lower_bound(Y,Z),X))),bind(X_82,$fot(greatest_lower_bound(multiply(Z,X),multiply(Y,X))))]]) ).
cnf(refute_0_321,plain,
( least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))) != multiply(greatest_lower_bound(Y,Z),X)
| least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),multiply(greatest_lower_bound(Y,Z),X)) != least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X)))
| least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),multiply(greatest_lower_bound(Y,Z),X)) = multiply(greatest_lower_bound(Y,Z),X) ),
inference(subst,[],[refute_0_136:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),multiply(greatest_lower_bound(Y,Z),X)))),bind(Y0,$fot(least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))))),bind(Z0,$fot(multiply(greatest_lower_bound(Y,Z),X)))]]) ).
cnf(refute_0_322,plain,
( least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))) != multiply(greatest_lower_bound(Y,Z),X)
| least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),multiply(greatest_lower_bound(Y,Z),X)) = multiply(greatest_lower_bound(Y,Z),X) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),multiply(greatest_lower_bound(Y,Z),X)),least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X)))) )],[refute_0_320,refute_0_321]) ).
cnf(refute_0_323,plain,
least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),multiply(greatest_lower_bound(Y,Z),X)) = multiply(greatest_lower_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))),multiply(greatest_lower_bound(Y,Z),X)) )],[refute_0_210,refute_0_322]) ).
cnf(refute_0_324,plain,
( least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),multiply(greatest_lower_bound(Y,Z),X)) != multiply(greatest_lower_bound(Y,Z),X)
| least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),multiply(greatest_lower_bound(Y,Z),X)) != greatest_lower_bound(multiply(Z,X),multiply(Y,X))
| multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Z,X),multiply(Y,X)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),multiply(greatest_lower_bound(Y,Z),X)),greatest_lower_bound(multiply(Z,X),multiply(Y,X))) ),[0],$fot(multiply(greatest_lower_bound(Y,Z),X))]]) ).
cnf(refute_0_325,plain,
( least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),multiply(greatest_lower_bound(Y,Z),X)) != greatest_lower_bound(multiply(Z,X),multiply(Y,X))
| multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Z,X),multiply(Y,X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),multiply(greatest_lower_bound(Y,Z),X)),multiply(greatest_lower_bound(Y,Z),X)) )],[refute_0_323,refute_0_324]) ).
cnf(refute_0_326,plain,
( multiply(greatest_lower_bound(Y,Z),X) != greatest_lower_bound(multiply(Z,X),multiply(Y,X))
| greatest_lower_bound(multiply(Z,X),multiply(Y,X)) != multiply(greatest_lower_bound(Z,Y),X)
| multiply(greatest_lower_bound(Y,Z),X) = multiply(greatest_lower_bound(Z,Y),X) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(Y,Z),X),multiply(greatest_lower_bound(Z,Y),X)) ),[0],$fot(greatest_lower_bound(multiply(Z,X),multiply(Y,X)))]]) ).
cnf(refute_0_327,plain,
( multiply(greatest_lower_bound(Y,Z),X) != greatest_lower_bound(multiply(Z,X),multiply(Y,X))
| multiply(greatest_lower_bound(Y,Z),X) = multiply(greatest_lower_bound(Z,Y),X) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),multiply(greatest_lower_bound(Z,Y),X)) )],[refute_0_203,refute_0_326]) ).
cnf(refute_0_328,plain,
( least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),multiply(greatest_lower_bound(Y,Z),X)) != greatest_lower_bound(multiply(Z,X),multiply(Y,X))
| multiply(greatest_lower_bound(Y,Z),X) = multiply(greatest_lower_bound(Z,Y),X) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))) )],[refute_0_325,refute_0_327]) ).
cnf(refute_0_329,plain,
multiply(greatest_lower_bound(Y,Z),X) = multiply(greatest_lower_bound(Z,Y),X),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),multiply(greatest_lower_bound(Y,Z),X)),greatest_lower_bound(multiply(Z,X),multiply(Y,X))) )],[refute_0_191,refute_0_328]) ).
cnf(refute_0_330,plain,
( multiply(greatest_lower_bound(Y,Z),X) != multiply(greatest_lower_bound(Z,Y),X)
| multiply(greatest_lower_bound(Z,Y),X) = multiply(greatest_lower_bound(Y,Z),X) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(greatest_lower_bound(Y,Z),X))),bind(Y0,$fot(multiply(greatest_lower_bound(Z,Y),X)))]]) ).
cnf(refute_0_331,plain,
multiply(greatest_lower_bound(Z,Y),X) = multiply(greatest_lower_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(Y,Z),X),multiply(greatest_lower_bound(Z,Y),X)) )],[refute_0_329,refute_0_330]) ).
cnf(refute_0_332,plain,
multiply(greatest_lower_bound(inverse(X_128),identity),least_upper_bound(X_128,identity)) = multiply(greatest_lower_bound(identity,inverse(X_128)),least_upper_bound(X_128,identity)),
inference(subst,[],[refute_0_331:[bind(X,$fot(least_upper_bound(X_128,identity))),bind(Y,$fot(identity)),bind(Z,$fot(inverse(X_128)))]]) ).
cnf(refute_0_333,plain,
( multiply(greatest_lower_bound(inverse(X_128),identity),least_upper_bound(X_128,identity)) != multiply(greatest_lower_bound(identity,inverse(X_128)),least_upper_bound(X_128,identity))
| multiply(greatest_lower_bound(inverse(X_128),identity),least_upper_bound(X_128,identity)) != greatest_lower_bound(least_upper_bound(X_128,identity),least_upper_bound(identity,inverse(X_128)))
| multiply(greatest_lower_bound(identity,inverse(X_128)),least_upper_bound(X_128,identity)) = greatest_lower_bound(least_upper_bound(X_128,identity),least_upper_bound(identity,inverse(X_128))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_128),identity),least_upper_bound(X_128,identity)),greatest_lower_bound(least_upper_bound(X_128,identity),least_upper_bound(identity,inverse(X_128)))) ),[0],$fot(multiply(greatest_lower_bound(identity,inverse(X_128)),least_upper_bound(X_128,identity)))]]) ).
cnf(refute_0_334,plain,
( multiply(greatest_lower_bound(inverse(X_128),identity),least_upper_bound(X_128,identity)) != greatest_lower_bound(least_upper_bound(X_128,identity),least_upper_bound(identity,inverse(X_128)))
| multiply(greatest_lower_bound(identity,inverse(X_128)),least_upper_bound(X_128,identity)) = greatest_lower_bound(least_upper_bound(X_128,identity),least_upper_bound(identity,inverse(X_128))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_128),identity),least_upper_bound(X_128,identity)),multiply(greatest_lower_bound(identity,inverse(X_128)),least_upper_bound(X_128,identity))) )],[refute_0_332,refute_0_333]) ).
cnf(refute_0_335,plain,
multiply(greatest_lower_bound(identity,inverse(X_128)),least_upper_bound(X_128,identity)) = greatest_lower_bound(least_upper_bound(X_128,identity),least_upper_bound(identity,inverse(X_128))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_128),identity),least_upper_bound(X_128,identity)),greatest_lower_bound(least_upper_bound(X_128,identity),least_upper_bound(identity,inverse(X_128)))) )],[refute_0_162,refute_0_334]) ).
cnf(refute_0_336,plain,
( multiply(greatest_lower_bound(identity,inverse(X_128)),least_upper_bound(X_128,identity)) != greatest_lower_bound(least_upper_bound(X_128,identity),least_upper_bound(identity,inverse(X_128)))
| greatest_lower_bound(least_upper_bound(X_128,identity),least_upper_bound(identity,inverse(X_128))) = multiply(greatest_lower_bound(identity,inverse(X_128)),least_upper_bound(X_128,identity)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(greatest_lower_bound(identity,inverse(X_128)),least_upper_bound(X_128,identity)))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(X_128,identity),least_upper_bound(identity,inverse(X_128)))))]]) ).
cnf(refute_0_337,plain,
greatest_lower_bound(least_upper_bound(X_128,identity),least_upper_bound(identity,inverse(X_128))) = multiply(greatest_lower_bound(identity,inverse(X_128)),least_upper_bound(X_128,identity)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(X_128)),least_upper_bound(X_128,identity)),greatest_lower_bound(least_upper_bound(X_128,identity),least_upper_bound(identity,inverse(X_128)))) )],[refute_0_335,refute_0_336]) ).
cnf(refute_0_338,plain,
greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(identity,inverse(a))) = multiply(greatest_lower_bound(identity,inverse(a)),least_upper_bound(a,identity)),
inference(subst,[],[refute_0_337:[bind(X_128,$fot(a))]]) ).
cnf(refute_0_339,plain,
( multiply(greatest_lower_bound(identity,inverse(a)),least_upper_bound(a,identity)) != identity
| greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(identity,inverse(a))) != multiply(greatest_lower_bound(identity,inverse(a)),least_upper_bound(a,identity))
| greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(identity,inverse(a))) = identity ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(identity,inverse(a))),multiply(greatest_lower_bound(identity,inverse(a)),least_upper_bound(a,identity))) ),[1],$fot(identity)]]) ).
cnf(refute_0_340,plain,
( multiply(greatest_lower_bound(identity,inverse(a)),least_upper_bound(a,identity)) != identity
| greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(identity,inverse(a))) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(identity,inverse(a))),multiply(greatest_lower_bound(identity,inverse(a)),least_upper_bound(a,identity))) )],[refute_0_338,refute_0_339]) ).
cnf(refute_0_341,plain,
multiply(greatest_lower_bound(identity,inverse(a)),least_upper_bound(a,identity)) != identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(identity,inverse(a))),identity) )],[refute_0_340,refute_0_12]) ).
cnf(refute_0_342,plain,
multiply(multiply(inverse(X_23),greatest_lower_bound(X_22,X_23)),X_72) = multiply(inverse(X_23),multiply(greatest_lower_bound(X_22,X_23),X_72)),
inference(subst,[],[associativity:[bind(X,$fot(inverse(X_23))),bind(Y,$fot(greatest_lower_bound(X_22,X_23))),bind(Z,$fot(X_72))]]) ).
cnf(refute_0_343,plain,
( multiply(multiply(inverse(X_23),greatest_lower_bound(X_22,X_23)),X_72) != multiply(inverse(X_23),multiply(greatest_lower_bound(X_22,X_23),X_72))
| multiply(inverse(X_23),greatest_lower_bound(X_22,X_23)) != greatest_lower_bound(identity,multiply(inverse(X_23),X_22))
| multiply(greatest_lower_bound(identity,multiply(inverse(X_23),X_22)),X_72) = multiply(inverse(X_23),multiply(greatest_lower_bound(X_22,X_23),X_72)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_23),greatest_lower_bound(X_22,X_23)),X_72),multiply(inverse(X_23),multiply(greatest_lower_bound(X_22,X_23),X_72))) ),[0,0],$fot(greatest_lower_bound(identity,multiply(inverse(X_23),X_22)))]]) ).
cnf(refute_0_344,plain,
( multiply(multiply(inverse(X_23),greatest_lower_bound(X_22,X_23)),X_72) != multiply(inverse(X_23),multiply(greatest_lower_bound(X_22,X_23),X_72))
| multiply(greatest_lower_bound(identity,multiply(inverse(X_23),X_22)),X_72) = multiply(inverse(X_23),multiply(greatest_lower_bound(X_22,X_23),X_72)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_23),greatest_lower_bound(X_22,X_23)),greatest_lower_bound(identity,multiply(inverse(X_23),X_22))) )],[refute_0_269,refute_0_343]) ).
cnf(refute_0_345,plain,
multiply(greatest_lower_bound(identity,multiply(inverse(X_23),X_22)),X_72) = multiply(inverse(X_23),multiply(greatest_lower_bound(X_22,X_23),X_72)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_23),greatest_lower_bound(X_22,X_23)),X_72),multiply(inverse(X_23),multiply(greatest_lower_bound(X_22,X_23),X_72))) )],[refute_0_342,refute_0_344]) ).
cnf(refute_0_346,plain,
multiply(greatest_lower_bound(identity,multiply(inverse(X_23),identity)),least_upper_bound(X_23,identity)) = multiply(inverse(X_23),multiply(greatest_lower_bound(identity,X_23),least_upper_bound(X_23,identity))),
inference(subst,[],[refute_0_345:[bind(X_22,$fot(identity)),bind(X_72,$fot(least_upper_bound(X_23,identity)))]]) ).
cnf(refute_0_347,plain,
X_72 = multiply(inverse(least_upper_bound(inverse(X_72),X_89)),multiply(least_upper_bound(inverse(X_72),X_89),X_72)),
inference(subst,[],[refute_0_45:[bind(X_71,$fot(least_upper_bound(inverse(X_72),X_89)))]]) ).
cnf(refute_0_348,plain,
multiply(least_upper_bound(inverse(X_83),X_85),X_83) = least_upper_bound(multiply(inverse(X_83),X_83),multiply(X_85,X_83)),
inference(subst,[],[monotony_lub2:[bind(X,$fot(X_83)),bind(Y,$fot(inverse(X_83))),bind(Z,$fot(X_85))]]) ).
cnf(refute_0_349,plain,
multiply(inverse(X_83),X_83) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_83))]]) ).
cnf(refute_0_350,plain,
( multiply(inverse(X_83),X_83) != identity
| multiply(least_upper_bound(inverse(X_83),X_85),X_83) != least_upper_bound(multiply(inverse(X_83),X_83),multiply(X_85,X_83))
| multiply(least_upper_bound(inverse(X_83),X_85),X_83) = least_upper_bound(identity,multiply(X_85,X_83)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(X_83),X_85),X_83),least_upper_bound(multiply(inverse(X_83),X_83),multiply(X_85,X_83))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_351,plain,
( multiply(least_upper_bound(inverse(X_83),X_85),X_83) != least_upper_bound(multiply(inverse(X_83),X_83),multiply(X_85,X_83))
| multiply(least_upper_bound(inverse(X_83),X_85),X_83) = least_upper_bound(identity,multiply(X_85,X_83)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_83),X_83),identity) )],[refute_0_349,refute_0_350]) ).
cnf(refute_0_352,plain,
multiply(least_upper_bound(inverse(X_83),X_85),X_83) = least_upper_bound(identity,multiply(X_85,X_83)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_83),X_85),X_83),least_upper_bound(multiply(inverse(X_83),X_83),multiply(X_85,X_83))) )],[refute_0_348,refute_0_351]) ).
cnf(refute_0_353,plain,
multiply(least_upper_bound(inverse(X_72),X_89),X_72) = least_upper_bound(identity,multiply(X_89,X_72)),
inference(subst,[],[refute_0_352:[bind(X_83,$fot(X_72)),bind(X_85,$fot(X_89))]]) ).
cnf(refute_0_354,plain,
( X_72 != multiply(inverse(least_upper_bound(inverse(X_72),X_89)),multiply(least_upper_bound(inverse(X_72),X_89),X_72))
| multiply(least_upper_bound(inverse(X_72),X_89),X_72) != least_upper_bound(identity,multiply(X_89,X_72))
| X_72 = multiply(inverse(least_upper_bound(inverse(X_72),X_89)),least_upper_bound(identity,multiply(X_89,X_72))) ),
introduced(tautology,[equality,[$cnf( $equal(X_72,multiply(inverse(least_upper_bound(inverse(X_72),X_89)),multiply(least_upper_bound(inverse(X_72),X_89),X_72))) ),[1,1],$fot(least_upper_bound(identity,multiply(X_89,X_72)))]]) ).
cnf(refute_0_355,plain,
( X_72 != multiply(inverse(least_upper_bound(inverse(X_72),X_89)),multiply(least_upper_bound(inverse(X_72),X_89),X_72))
| X_72 = multiply(inverse(least_upper_bound(inverse(X_72),X_89)),least_upper_bound(identity,multiply(X_89,X_72))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_72),X_89),X_72),least_upper_bound(identity,multiply(X_89,X_72))) )],[refute_0_353,refute_0_354]) ).
cnf(refute_0_356,plain,
X_72 = multiply(inverse(least_upper_bound(inverse(X_72),X_89)),least_upper_bound(identity,multiply(X_89,X_72))),
inference(resolve,[$cnf( $equal(X_72,multiply(inverse(least_upper_bound(inverse(X_72),X_89)),multiply(least_upper_bound(inverse(X_72),X_89),X_72))) )],[refute_0_347,refute_0_355]) ).
cnf(refute_0_357,plain,
X_161 = multiply(inverse(least_upper_bound(inverse(X_161),identity)),least_upper_bound(identity,multiply(identity,X_161))),
inference(subst,[],[refute_0_356:[bind(X_72,$fot(X_161)),bind(X_89,$fot(identity))]]) ).
cnf(refute_0_358,plain,
multiply(X_78,least_upper_bound(X_79,identity)) = least_upper_bound(multiply(X_78,X_79),multiply(X_78,identity)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(X_78)),bind(Y,$fot(X_79)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_359,plain,
X_78 = multiply(X_78,identity),
inference(subst,[],[refute_0_63:[bind(X_74,$fot(X_78))]]) ).
cnf(refute_0_360,plain,
( X_78 != multiply(X_78,identity)
| multiply(X_78,identity) = X_78 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_78)),bind(Y0,$fot(multiply(X_78,identity)))]]) ).
cnf(refute_0_361,plain,
multiply(X_78,identity) = X_78,
inference(resolve,[$cnf( $equal(X_78,multiply(X_78,identity)) )],[refute_0_359,refute_0_360]) ).
cnf(refute_0_362,plain,
( multiply(X_78,identity) != X_78
| multiply(X_78,least_upper_bound(X_79,identity)) != least_upper_bound(multiply(X_78,X_79),multiply(X_78,identity))
| multiply(X_78,least_upper_bound(X_79,identity)) = least_upper_bound(multiply(X_78,X_79),X_78) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_78,least_upper_bound(X_79,identity)),least_upper_bound(multiply(X_78,X_79),multiply(X_78,identity))) ),[1,1],$fot(X_78)]]) ).
cnf(refute_0_363,plain,
( multiply(X_78,least_upper_bound(X_79,identity)) != least_upper_bound(multiply(X_78,X_79),multiply(X_78,identity))
| multiply(X_78,least_upper_bound(X_79,identity)) = least_upper_bound(multiply(X_78,X_79),X_78) ),
inference(resolve,[$cnf( $equal(multiply(X_78,identity),X_78) )],[refute_0_361,refute_0_362]) ).
cnf(refute_0_364,plain,
multiply(X_78,least_upper_bound(X_79,identity)) = least_upper_bound(multiply(X_78,X_79),X_78),
inference(resolve,[$cnf( $equal(multiply(X_78,least_upper_bound(X_79,identity)),least_upper_bound(multiply(X_78,X_79),multiply(X_78,identity))) )],[refute_0_358,refute_0_363]) ).
cnf(refute_0_365,plain,
least_upper_bound(multiply(X_78,X_79),X_78) = least_upper_bound(X_78,multiply(X_78,X_79)),
inference(subst,[],[refute_0_30:[bind(X_32,$fot(X_78)),bind(X_33,$fot(multiply(X_78,X_79)))]]) ).
cnf(refute_0_366,plain,
( multiply(X_78,least_upper_bound(X_79,identity)) != least_upper_bound(multiply(X_78,X_79),X_78)
| least_upper_bound(multiply(X_78,X_79),X_78) != least_upper_bound(X_78,multiply(X_78,X_79))
| multiply(X_78,least_upper_bound(X_79,identity)) = least_upper_bound(X_78,multiply(X_78,X_79)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_78,least_upper_bound(X_79,identity)),least_upper_bound(X_78,multiply(X_78,X_79))) ),[0],$fot(least_upper_bound(multiply(X_78,X_79),X_78))]]) ).
cnf(refute_0_367,plain,
( multiply(X_78,least_upper_bound(X_79,identity)) != least_upper_bound(multiply(X_78,X_79),X_78)
| multiply(X_78,least_upper_bound(X_79,identity)) = least_upper_bound(X_78,multiply(X_78,X_79)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_78,X_79),X_78),least_upper_bound(X_78,multiply(X_78,X_79))) )],[refute_0_365,refute_0_366]) ).
cnf(refute_0_368,plain,
multiply(X_78,least_upper_bound(X_79,identity)) = least_upper_bound(X_78,multiply(X_78,X_79)),
inference(resolve,[$cnf( $equal(multiply(X_78,least_upper_bound(X_79,identity)),least_upper_bound(multiply(X_78,X_79),X_78)) )],[refute_0_364,refute_0_367]) ).
cnf(refute_0_369,plain,
multiply(identity,least_upper_bound(X_161,identity)) = least_upper_bound(identity,multiply(identity,X_161)),
inference(subst,[],[refute_0_368:[bind(X_78,$fot(identity)),bind(X_79,$fot(X_161))]]) ).
cnf(refute_0_370,plain,
( multiply(identity,least_upper_bound(X_161,identity)) != least_upper_bound(identity,multiply(identity,X_161))
| least_upper_bound(identity,multiply(identity,X_161)) = multiply(identity,least_upper_bound(X_161,identity)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(identity,least_upper_bound(X_161,identity)))),bind(Y0,$fot(least_upper_bound(identity,multiply(identity,X_161))))]]) ).
cnf(refute_0_371,plain,
least_upper_bound(identity,multiply(identity,X_161)) = multiply(identity,least_upper_bound(X_161,identity)),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(X_161,identity)),least_upper_bound(identity,multiply(identity,X_161))) )],[refute_0_369,refute_0_370]) ).
cnf(refute_0_372,plain,
( X_161 != multiply(inverse(least_upper_bound(inverse(X_161),identity)),least_upper_bound(identity,multiply(identity,X_161)))
| least_upper_bound(identity,multiply(identity,X_161)) != multiply(identity,least_upper_bound(X_161,identity))
| X_161 = multiply(inverse(least_upper_bound(inverse(X_161),identity)),multiply(identity,least_upper_bound(X_161,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(X_161,multiply(inverse(least_upper_bound(inverse(X_161),identity)),least_upper_bound(identity,multiply(identity,X_161)))) ),[1,1],$fot(multiply(identity,least_upper_bound(X_161,identity)))]]) ).
cnf(refute_0_373,plain,
( X_161 != multiply(inverse(least_upper_bound(inverse(X_161),identity)),least_upper_bound(identity,multiply(identity,X_161)))
| X_161 = multiply(inverse(least_upper_bound(inverse(X_161),identity)),multiply(identity,least_upper_bound(X_161,identity))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(identity,X_161)),multiply(identity,least_upper_bound(X_161,identity))) )],[refute_0_371,refute_0_372]) ).
cnf(refute_0_374,plain,
X_161 = multiply(inverse(least_upper_bound(inverse(X_161),identity)),multiply(identity,least_upper_bound(X_161,identity))),
inference(resolve,[$cnf( $equal(X_161,multiply(inverse(least_upper_bound(inverse(X_161),identity)),least_upper_bound(identity,multiply(identity,X_161)))) )],[refute_0_357,refute_0_373]) ).
cnf(refute_0_375,plain,
multiply(identity,least_upper_bound(X_161,identity)) = least_upper_bound(X_161,identity),
inference(subst,[],[left_identity:[bind(X,$fot(least_upper_bound(X_161,identity)))]]) ).
cnf(refute_0_376,plain,
multiply(inverse(least_upper_bound(identity,inverse(X_161))),multiply(identity,least_upper_bound(X_161,identity))) = multiply(inverse(least_upper_bound(identity,inverse(X_161))),multiply(identity,least_upper_bound(X_161,identity))),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(identity,inverse(X_161))),multiply(identity,least_upper_bound(X_161,identity))))]]) ).
cnf(refute_0_377,plain,
( multiply(identity,least_upper_bound(X_161,identity)) != least_upper_bound(X_161,identity)
| multiply(inverse(least_upper_bound(identity,inverse(X_161))),multiply(identity,least_upper_bound(X_161,identity))) != multiply(inverse(least_upper_bound(identity,inverse(X_161))),multiply(identity,least_upper_bound(X_161,identity)))
| multiply(inverse(least_upper_bound(identity,inverse(X_161))),multiply(identity,least_upper_bound(X_161,identity))) = multiply(inverse(least_upper_bound(identity,inverse(X_161))),least_upper_bound(X_161,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_161))),multiply(identity,least_upper_bound(X_161,identity))),multiply(inverse(least_upper_bound(identity,inverse(X_161))),multiply(identity,least_upper_bound(X_161,identity)))) ),[1,1],$fot(least_upper_bound(X_161,identity))]]) ).
cnf(refute_0_378,plain,
( multiply(identity,least_upper_bound(X_161,identity)) != least_upper_bound(X_161,identity)
| multiply(inverse(least_upper_bound(identity,inverse(X_161))),multiply(identity,least_upper_bound(X_161,identity))) = multiply(inverse(least_upper_bound(identity,inverse(X_161))),least_upper_bound(X_161,identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_161))),multiply(identity,least_upper_bound(X_161,identity))),multiply(inverse(least_upper_bound(identity,inverse(X_161))),multiply(identity,least_upper_bound(X_161,identity)))) )],[refute_0_376,refute_0_377]) ).
cnf(refute_0_379,plain,
multiply(inverse(least_upper_bound(identity,inverse(X_161))),multiply(identity,least_upper_bound(X_161,identity))) = multiply(inverse(least_upper_bound(identity,inverse(X_161))),least_upper_bound(X_161,identity)),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(X_161,identity)),least_upper_bound(X_161,identity)) )],[refute_0_375,refute_0_378]) ).
cnf(refute_0_380,plain,
multiply(inverse(least_upper_bound(X_9,identity)),greatest_lower_bound(identity,least_upper_bound(X_9,identity))) = greatest_lower_bound(identity,inverse(least_upper_bound(X_9,identity))),
inference(subst,[],[refute_0_276:[bind(X_23,$fot(least_upper_bound(X_9,identity)))]]) ).
cnf(refute_0_381,plain,
greatest_lower_bound(identity,least_upper_bound(X_9,identity)) = identity,
inference(subst,[],[refute_0_170:[bind(X_8,$fot(identity))]]) ).
cnf(refute_0_382,plain,
( multiply(inverse(least_upper_bound(X_9,identity)),greatest_lower_bound(identity,least_upper_bound(X_9,identity))) != greatest_lower_bound(identity,inverse(least_upper_bound(X_9,identity)))
| greatest_lower_bound(identity,least_upper_bound(X_9,identity)) != identity
| multiply(inverse(least_upper_bound(X_9,identity)),identity) = greatest_lower_bound(identity,inverse(least_upper_bound(X_9,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(X_9,identity)),greatest_lower_bound(identity,least_upper_bound(X_9,identity))),greatest_lower_bound(identity,inverse(least_upper_bound(X_9,identity)))) ),[0,1],$fot(identity)]]) ).
cnf(refute_0_383,plain,
( multiply(inverse(least_upper_bound(X_9,identity)),greatest_lower_bound(identity,least_upper_bound(X_9,identity))) != greatest_lower_bound(identity,inverse(least_upper_bound(X_9,identity)))
| multiply(inverse(least_upper_bound(X_9,identity)),identity) = greatest_lower_bound(identity,inverse(least_upper_bound(X_9,identity))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(X_9,identity)),identity) )],[refute_0_381,refute_0_382]) ).
cnf(refute_0_384,plain,
multiply(inverse(least_upper_bound(X_9,identity)),identity) = greatest_lower_bound(identity,inverse(least_upper_bound(X_9,identity))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_9,identity)),greatest_lower_bound(identity,least_upper_bound(X_9,identity))),greatest_lower_bound(identity,inverse(least_upper_bound(X_9,identity)))) )],[refute_0_380,refute_0_383]) ).
cnf(refute_0_385,plain,
multiply(inverse(least_upper_bound(X_9,identity)),identity) = inverse(least_upper_bound(X_9,identity)),
inference(subst,[],[refute_0_217:[bind(X_74,$fot(inverse(least_upper_bound(X_9,identity))))]]) ).
cnf(refute_0_386,plain,
( multiply(inverse(least_upper_bound(X_9,identity)),identity) != greatest_lower_bound(identity,inverse(least_upper_bound(X_9,identity)))
| multiply(inverse(least_upper_bound(X_9,identity)),identity) != inverse(least_upper_bound(X_9,identity))
| inverse(least_upper_bound(X_9,identity)) = greatest_lower_bound(identity,inverse(least_upper_bound(X_9,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(X_9,identity)),identity),greatest_lower_bound(identity,inverse(least_upper_bound(X_9,identity)))) ),[0],$fot(inverse(least_upper_bound(X_9,identity)))]]) ).
cnf(refute_0_387,plain,
( multiply(inverse(least_upper_bound(X_9,identity)),identity) != greatest_lower_bound(identity,inverse(least_upper_bound(X_9,identity)))
| inverse(least_upper_bound(X_9,identity)) = greatest_lower_bound(identity,inverse(least_upper_bound(X_9,identity))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_9,identity)),identity),inverse(least_upper_bound(X_9,identity))) )],[refute_0_385,refute_0_386]) ).
cnf(refute_0_388,plain,
inverse(least_upper_bound(X_9,identity)) = greatest_lower_bound(identity,inverse(least_upper_bound(X_9,identity))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_9,identity)),identity),greatest_lower_bound(identity,inverse(least_upper_bound(X_9,identity)))) )],[refute_0_384,refute_0_387]) ).
cnf(refute_0_389,plain,
inverse(least_upper_bound(X_135,identity)) = greatest_lower_bound(identity,inverse(least_upper_bound(X_135,identity))),
inference(subst,[],[refute_0_388:[bind(X_9,$fot(X_135))]]) ).
cnf(refute_0_390,plain,
least_upper_bound(identity,X_135) = least_upper_bound(X_135,identity),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(identity)),bind(Y,$fot(X_135))]]) ).
cnf(refute_0_391,plain,
( least_upper_bound(identity,X_135) != least_upper_bound(X_135,identity)
| least_upper_bound(X_135,identity) = least_upper_bound(identity,X_135) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(identity,X_135))),bind(Y0,$fot(least_upper_bound(X_135,identity)))]]) ).
cnf(refute_0_392,plain,
least_upper_bound(X_135,identity) = least_upper_bound(identity,X_135),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,X_135),least_upper_bound(X_135,identity)) )],[refute_0_390,refute_0_391]) ).
cnf(refute_0_393,plain,
( inverse(least_upper_bound(X_135,identity)) != greatest_lower_bound(identity,inverse(least_upper_bound(X_135,identity)))
| least_upper_bound(X_135,identity) != least_upper_bound(identity,X_135)
| inverse(least_upper_bound(identity,X_135)) = greatest_lower_bound(identity,inverse(least_upper_bound(X_135,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_135,identity)),greatest_lower_bound(identity,inverse(least_upper_bound(X_135,identity)))) ),[0,0],$fot(least_upper_bound(identity,X_135))]]) ).
cnf(refute_0_394,plain,
( inverse(least_upper_bound(X_135,identity)) != greatest_lower_bound(identity,inverse(least_upper_bound(X_135,identity)))
| inverse(least_upper_bound(identity,X_135)) = greatest_lower_bound(identity,inverse(least_upper_bound(X_135,identity))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_135,identity),least_upper_bound(identity,X_135)) )],[refute_0_392,refute_0_393]) ).
cnf(refute_0_395,plain,
inverse(least_upper_bound(identity,X_135)) = greatest_lower_bound(identity,inverse(least_upper_bound(X_135,identity))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_135,identity)),greatest_lower_bound(identity,inverse(least_upper_bound(X_135,identity)))) )],[refute_0_389,refute_0_394]) ).
cnf(refute_0_396,plain,
( inverse(least_upper_bound(X_9,identity)) != greatest_lower_bound(identity,inverse(least_upper_bound(X_9,identity)))
| greatest_lower_bound(identity,inverse(least_upper_bound(X_9,identity))) = inverse(least_upper_bound(X_9,identity)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(least_upper_bound(X_9,identity)))),bind(Y0,$fot(greatest_lower_bound(identity,inverse(least_upper_bound(X_9,identity)))))]]) ).
cnf(refute_0_397,plain,
greatest_lower_bound(identity,inverse(least_upper_bound(X_9,identity))) = inverse(least_upper_bound(X_9,identity)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_9,identity)),greatest_lower_bound(identity,inverse(least_upper_bound(X_9,identity)))) )],[refute_0_388,refute_0_396]) ).
cnf(refute_0_398,plain,
greatest_lower_bound(identity,inverse(least_upper_bound(X_135,identity))) = inverse(least_upper_bound(X_135,identity)),
inference(subst,[],[refute_0_397:[bind(X_9,$fot(X_135))]]) ).
cnf(refute_0_399,plain,
( greatest_lower_bound(identity,inverse(least_upper_bound(X_135,identity))) != inverse(least_upper_bound(X_135,identity))
| inverse(least_upper_bound(identity,X_135)) != greatest_lower_bound(identity,inverse(least_upper_bound(X_135,identity)))
| inverse(least_upper_bound(identity,X_135)) = inverse(least_upper_bound(X_135,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,X_135)),greatest_lower_bound(identity,inverse(least_upper_bound(X_135,identity)))) ),[1],$fot(inverse(least_upper_bound(X_135,identity)))]]) ).
cnf(refute_0_400,plain,
( inverse(least_upper_bound(identity,X_135)) != greatest_lower_bound(identity,inverse(least_upper_bound(X_135,identity)))
| inverse(least_upper_bound(identity,X_135)) = inverse(least_upper_bound(X_135,identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(least_upper_bound(X_135,identity))),inverse(least_upper_bound(X_135,identity))) )],[refute_0_398,refute_0_399]) ).
cnf(refute_0_401,plain,
inverse(least_upper_bound(identity,X_135)) = inverse(least_upper_bound(X_135,identity)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,X_135)),greatest_lower_bound(identity,inverse(least_upper_bound(X_135,identity)))) )],[refute_0_395,refute_0_400]) ).
cnf(refute_0_402,plain,
( inverse(least_upper_bound(identity,X_135)) != inverse(least_upper_bound(X_135,identity))
| inverse(least_upper_bound(X_135,identity)) = inverse(least_upper_bound(identity,X_135)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(least_upper_bound(identity,X_135)))),bind(Y0,$fot(inverse(least_upper_bound(X_135,identity))))]]) ).
cnf(refute_0_403,plain,
inverse(least_upper_bound(X_135,identity)) = inverse(least_upper_bound(identity,X_135)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,X_135)),inverse(least_upper_bound(X_135,identity))) )],[refute_0_401,refute_0_402]) ).
cnf(refute_0_404,plain,
inverse(least_upper_bound(inverse(X_161),identity)) = inverse(least_upper_bound(identity,inverse(X_161))),
inference(subst,[],[refute_0_403:[bind(X_135,$fot(inverse(X_161)))]]) ).
cnf(refute_0_405,plain,
multiply(inverse(least_upper_bound(inverse(X_161),identity)),multiply(identity,least_upper_bound(X_161,identity))) = multiply(inverse(least_upper_bound(inverse(X_161),identity)),multiply(identity,least_upper_bound(X_161,identity))),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(inverse(X_161),identity)),multiply(identity,least_upper_bound(X_161,identity))))]]) ).
cnf(refute_0_406,plain,
( multiply(inverse(least_upper_bound(inverse(X_161),identity)),multiply(identity,least_upper_bound(X_161,identity))) != multiply(inverse(least_upper_bound(inverse(X_161),identity)),multiply(identity,least_upper_bound(X_161,identity)))
| inverse(least_upper_bound(inverse(X_161),identity)) != inverse(least_upper_bound(identity,inverse(X_161)))
| multiply(inverse(least_upper_bound(inverse(X_161),identity)),multiply(identity,least_upper_bound(X_161,identity))) = multiply(inverse(least_upper_bound(identity,inverse(X_161))),multiply(identity,least_upper_bound(X_161,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_161),identity)),multiply(identity,least_upper_bound(X_161,identity))),multiply(inverse(least_upper_bound(inverse(X_161),identity)),multiply(identity,least_upper_bound(X_161,identity)))) ),[1,0],$fot(inverse(least_upper_bound(identity,inverse(X_161))))]]) ).
cnf(refute_0_407,plain,
( inverse(least_upper_bound(inverse(X_161),identity)) != inverse(least_upper_bound(identity,inverse(X_161)))
| multiply(inverse(least_upper_bound(inverse(X_161),identity)),multiply(identity,least_upper_bound(X_161,identity))) = multiply(inverse(least_upper_bound(identity,inverse(X_161))),multiply(identity,least_upper_bound(X_161,identity))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_161),identity)),multiply(identity,least_upper_bound(X_161,identity))),multiply(inverse(least_upper_bound(inverse(X_161),identity)),multiply(identity,least_upper_bound(X_161,identity)))) )],[refute_0_405,refute_0_406]) ).
cnf(refute_0_408,plain,
multiply(inverse(least_upper_bound(inverse(X_161),identity)),multiply(identity,least_upper_bound(X_161,identity))) = multiply(inverse(least_upper_bound(identity,inverse(X_161))),multiply(identity,least_upper_bound(X_161,identity))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(X_161),identity)),inverse(least_upper_bound(identity,inverse(X_161)))) )],[refute_0_404,refute_0_407]) ).
cnf(refute_0_409,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_161))),multiply(identity,least_upper_bound(X_161,identity))) != multiply(inverse(least_upper_bound(identity,inverse(X_161))),least_upper_bound(X_161,identity))
| multiply(inverse(least_upper_bound(inverse(X_161),identity)),multiply(identity,least_upper_bound(X_161,identity))) != multiply(inverse(least_upper_bound(identity,inverse(X_161))),multiply(identity,least_upper_bound(X_161,identity)))
| multiply(inverse(least_upper_bound(inverse(X_161),identity)),multiply(identity,least_upper_bound(X_161,identity))) = multiply(inverse(least_upper_bound(identity,inverse(X_161))),least_upper_bound(X_161,identity)) ),
inference(subst,[],[refute_0_136:[bind(X0,$fot(multiply(inverse(least_upper_bound(inverse(X_161),identity)),multiply(identity,least_upper_bound(X_161,identity))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(identity,inverse(X_161))),multiply(identity,least_upper_bound(X_161,identity))))),bind(Z0,$fot(multiply(inverse(least_upper_bound(identity,inverse(X_161))),least_upper_bound(X_161,identity))))]]) ).
cnf(refute_0_410,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_161))),multiply(identity,least_upper_bound(X_161,identity))) != multiply(inverse(least_upper_bound(identity,inverse(X_161))),least_upper_bound(X_161,identity))
| multiply(inverse(least_upper_bound(inverse(X_161),identity)),multiply(identity,least_upper_bound(X_161,identity))) = multiply(inverse(least_upper_bound(identity,inverse(X_161))),least_upper_bound(X_161,identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_161),identity)),multiply(identity,least_upper_bound(X_161,identity))),multiply(inverse(least_upper_bound(identity,inverse(X_161))),multiply(identity,least_upper_bound(X_161,identity)))) )],[refute_0_408,refute_0_409]) ).
cnf(refute_0_411,plain,
multiply(inverse(least_upper_bound(inverse(X_161),identity)),multiply(identity,least_upper_bound(X_161,identity))) = multiply(inverse(least_upper_bound(identity,inverse(X_161))),least_upper_bound(X_161,identity)),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_161))),multiply(identity,least_upper_bound(X_161,identity))),multiply(inverse(least_upper_bound(identity,inverse(X_161))),least_upper_bound(X_161,identity))) )],[refute_0_379,refute_0_410]) ).
cnf(refute_0_412,plain,
( X_161 != multiply(inverse(least_upper_bound(inverse(X_161),identity)),multiply(identity,least_upper_bound(X_161,identity)))
| multiply(inverse(least_upper_bound(inverse(X_161),identity)),multiply(identity,least_upper_bound(X_161,identity))) != multiply(inverse(least_upper_bound(identity,inverse(X_161))),least_upper_bound(X_161,identity))
| X_161 = multiply(inverse(least_upper_bound(identity,inverse(X_161))),least_upper_bound(X_161,identity)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_161,multiply(inverse(least_upper_bound(identity,inverse(X_161))),least_upper_bound(X_161,identity))) ),[0],$fot(multiply(inverse(least_upper_bound(inverse(X_161),identity)),multiply(identity,least_upper_bound(X_161,identity))))]]) ).
cnf(refute_0_413,plain,
( X_161 != multiply(inverse(least_upper_bound(inverse(X_161),identity)),multiply(identity,least_upper_bound(X_161,identity)))
| X_161 = multiply(inverse(least_upper_bound(identity,inverse(X_161))),least_upper_bound(X_161,identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_161),identity)),multiply(identity,least_upper_bound(X_161,identity))),multiply(inverse(least_upper_bound(identity,inverse(X_161))),least_upper_bound(X_161,identity))) )],[refute_0_411,refute_0_412]) ).
cnf(refute_0_414,plain,
X_161 = multiply(inverse(least_upper_bound(identity,inverse(X_161))),least_upper_bound(X_161,identity)),
inference(resolve,[$cnf( $equal(X_161,multiply(inverse(least_upper_bound(inverse(X_161),identity)),multiply(identity,least_upper_bound(X_161,identity)))) )],[refute_0_374,refute_0_413]) ).
cnf(refute_0_415,plain,
greatest_lower_bound(identity,X_291) = multiply(inverse(least_upper_bound(identity,inverse(X_291))),multiply(least_upper_bound(identity,inverse(X_291)),greatest_lower_bound(identity,X_291))),
inference(subst,[],[refute_0_45:[bind(X_71,$fot(least_upper_bound(identity,inverse(X_291)))),bind(X_72,$fot(greatest_lower_bound(identity,X_291)))]]) ).
cnf(refute_0_416,plain,
multiply(least_upper_bound(X_84,inverse(X_22)),greatest_lower_bound(X_22,identity)) = least_upper_bound(multiply(X_84,greatest_lower_bound(X_22,identity)),multiply(inverse(X_22),greatest_lower_bound(X_22,identity))),
inference(subst,[],[monotony_lub2:[bind(X,$fot(greatest_lower_bound(X_22,identity))),bind(Y,$fot(X_84)),bind(Z,$fot(inverse(X_22)))]]) ).
cnf(refute_0_417,plain,
( multiply(inverse(X_22),greatest_lower_bound(X_22,identity)) != greatest_lower_bound(identity,inverse(X_22))
| multiply(least_upper_bound(X_84,inverse(X_22)),greatest_lower_bound(X_22,identity)) != least_upper_bound(multiply(X_84,greatest_lower_bound(X_22,identity)),multiply(inverse(X_22),greatest_lower_bound(X_22,identity)))
| multiply(least_upper_bound(X_84,inverse(X_22)),greatest_lower_bound(X_22,identity)) = least_upper_bound(multiply(X_84,greatest_lower_bound(X_22,identity)),greatest_lower_bound(identity,inverse(X_22))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_84,inverse(X_22)),greatest_lower_bound(X_22,identity)),least_upper_bound(multiply(X_84,greatest_lower_bound(X_22,identity)),multiply(inverse(X_22),greatest_lower_bound(X_22,identity)))) ),[1,1],$fot(greatest_lower_bound(identity,inverse(X_22)))]]) ).
cnf(refute_0_418,plain,
( multiply(least_upper_bound(X_84,inverse(X_22)),greatest_lower_bound(X_22,identity)) != least_upper_bound(multiply(X_84,greatest_lower_bound(X_22,identity)),multiply(inverse(X_22),greatest_lower_bound(X_22,identity)))
| multiply(least_upper_bound(X_84,inverse(X_22)),greatest_lower_bound(X_22,identity)) = least_upper_bound(multiply(X_84,greatest_lower_bound(X_22,identity)),greatest_lower_bound(identity,inverse(X_22))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_22),greatest_lower_bound(X_22,identity)),greatest_lower_bound(identity,inverse(X_22))) )],[refute_0_256,refute_0_417]) ).
cnf(refute_0_419,plain,
multiply(least_upper_bound(X_84,inverse(X_22)),greatest_lower_bound(X_22,identity)) = least_upper_bound(multiply(X_84,greatest_lower_bound(X_22,identity)),greatest_lower_bound(identity,inverse(X_22))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_84,inverse(X_22)),greatest_lower_bound(X_22,identity)),least_upper_bound(multiply(X_84,greatest_lower_bound(X_22,identity)),multiply(inverse(X_22),greatest_lower_bound(X_22,identity)))) )],[refute_0_416,refute_0_418]) ).
cnf(refute_0_420,plain,
least_upper_bound(multiply(X_84,greatest_lower_bound(X_22,identity)),greatest_lower_bound(identity,inverse(X_22))) = least_upper_bound(greatest_lower_bound(identity,inverse(X_22)),multiply(X_84,greatest_lower_bound(X_22,identity))),
inference(subst,[],[refute_0_319:[bind(X_81,$fot(greatest_lower_bound(identity,inverse(X_22)))),bind(X_82,$fot(multiply(X_84,greatest_lower_bound(X_22,identity))))]]) ).
cnf(refute_0_421,plain,
( multiply(least_upper_bound(X_84,inverse(X_22)),greatest_lower_bound(X_22,identity)) != least_upper_bound(multiply(X_84,greatest_lower_bound(X_22,identity)),greatest_lower_bound(identity,inverse(X_22)))
| least_upper_bound(multiply(X_84,greatest_lower_bound(X_22,identity)),greatest_lower_bound(identity,inverse(X_22))) != least_upper_bound(greatest_lower_bound(identity,inverse(X_22)),multiply(X_84,greatest_lower_bound(X_22,identity)))
| multiply(least_upper_bound(X_84,inverse(X_22)),greatest_lower_bound(X_22,identity)) = least_upper_bound(greatest_lower_bound(identity,inverse(X_22)),multiply(X_84,greatest_lower_bound(X_22,identity))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_84,inverse(X_22)),greatest_lower_bound(X_22,identity)),least_upper_bound(greatest_lower_bound(identity,inverse(X_22)),multiply(X_84,greatest_lower_bound(X_22,identity)))) ),[0],$fot(least_upper_bound(multiply(X_84,greatest_lower_bound(X_22,identity)),greatest_lower_bound(identity,inverse(X_22))))]]) ).
cnf(refute_0_422,plain,
( multiply(least_upper_bound(X_84,inverse(X_22)),greatest_lower_bound(X_22,identity)) != least_upper_bound(multiply(X_84,greatest_lower_bound(X_22,identity)),greatest_lower_bound(identity,inverse(X_22)))
| multiply(least_upper_bound(X_84,inverse(X_22)),greatest_lower_bound(X_22,identity)) = least_upper_bound(greatest_lower_bound(identity,inverse(X_22)),multiply(X_84,greatest_lower_bound(X_22,identity))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_84,greatest_lower_bound(X_22,identity)),greatest_lower_bound(identity,inverse(X_22))),least_upper_bound(greatest_lower_bound(identity,inverse(X_22)),multiply(X_84,greatest_lower_bound(X_22,identity)))) )],[refute_0_420,refute_0_421]) ).
cnf(refute_0_423,plain,
multiply(least_upper_bound(X_84,inverse(X_22)),greatest_lower_bound(X_22,identity)) = least_upper_bound(greatest_lower_bound(identity,inverse(X_22)),multiply(X_84,greatest_lower_bound(X_22,identity))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_84,inverse(X_22)),greatest_lower_bound(X_22,identity)),least_upper_bound(multiply(X_84,greatest_lower_bound(X_22,identity)),greatest_lower_bound(identity,inverse(X_22)))) )],[refute_0_419,refute_0_422]) ).
cnf(refute_0_424,plain,
multiply(least_upper_bound(identity,inverse(X_202)),greatest_lower_bound(X_202,identity)) = least_upper_bound(greatest_lower_bound(identity,inverse(X_202)),multiply(identity,greatest_lower_bound(X_202,identity))),
inference(subst,[],[refute_0_423:[bind(X_22,$fot(X_202)),bind(X_84,$fot(identity))]]) ).
cnf(refute_0_425,plain,
multiply(identity,greatest_lower_bound(X_202,identity)) = greatest_lower_bound(X_202,identity),
inference(subst,[],[left_identity:[bind(X,$fot(greatest_lower_bound(X_202,identity)))]]) ).
cnf(refute_0_426,plain,
( multiply(identity,greatest_lower_bound(X_202,identity)) != greatest_lower_bound(X_202,identity)
| multiply(least_upper_bound(identity,inverse(X_202)),greatest_lower_bound(X_202,identity)) != least_upper_bound(greatest_lower_bound(identity,inverse(X_202)),multiply(identity,greatest_lower_bound(X_202,identity)))
| multiply(least_upper_bound(identity,inverse(X_202)),greatest_lower_bound(X_202,identity)) = least_upper_bound(greatest_lower_bound(identity,inverse(X_202)),greatest_lower_bound(X_202,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_202)),greatest_lower_bound(X_202,identity)),least_upper_bound(greatest_lower_bound(identity,inverse(X_202)),multiply(identity,greatest_lower_bound(X_202,identity)))) ),[1,1],$fot(greatest_lower_bound(X_202,identity))]]) ).
cnf(refute_0_427,plain,
( multiply(least_upper_bound(identity,inverse(X_202)),greatest_lower_bound(X_202,identity)) != least_upper_bound(greatest_lower_bound(identity,inverse(X_202)),multiply(identity,greatest_lower_bound(X_202,identity)))
| multiply(least_upper_bound(identity,inverse(X_202)),greatest_lower_bound(X_202,identity)) = least_upper_bound(greatest_lower_bound(identity,inverse(X_202)),greatest_lower_bound(X_202,identity)) ),
inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(X_202,identity)),greatest_lower_bound(X_202,identity)) )],[refute_0_425,refute_0_426]) ).
cnf(refute_0_428,plain,
multiply(least_upper_bound(identity,inverse(X_202)),greatest_lower_bound(X_202,identity)) = least_upper_bound(greatest_lower_bound(identity,inverse(X_202)),greatest_lower_bound(X_202,identity)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_202)),greatest_lower_bound(X_202,identity)),least_upper_bound(greatest_lower_bound(identity,inverse(X_202)),multiply(identity,greatest_lower_bound(X_202,identity)))) )],[refute_0_424,refute_0_427]) ).
cnf(refute_0_429,plain,
multiply(greatest_lower_bound(X_146,identity),least_upper_bound(inverse(X_146),identity)) = least_upper_bound(greatest_lower_bound(X_146,identity),multiply(greatest_lower_bound(X_146,identity),inverse(X_146))),
inference(subst,[],[refute_0_368:[bind(X_78,$fot(greatest_lower_bound(X_146,identity))),bind(X_79,$fot(inverse(X_146)))]]) ).
cnf(refute_0_430,plain,
multiply(greatest_lower_bound(X_29,inverse(X_28)),X_28) = greatest_lower_bound(multiply(X_29,X_28),multiply(inverse(X_28),X_28)),
inference(subst,[],[monotony_glb2:[bind(X,$fot(X_28)),bind(Y,$fot(X_29)),bind(Z,$fot(inverse(X_28)))]]) ).
cnf(refute_0_431,plain,
multiply(inverse(X_28),X_28) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_28))]]) ).
cnf(refute_0_432,plain,
( multiply(greatest_lower_bound(X_29,inverse(X_28)),X_28) != greatest_lower_bound(multiply(X_29,X_28),multiply(inverse(X_28),X_28))
| multiply(inverse(X_28),X_28) != identity
| multiply(greatest_lower_bound(X_29,inverse(X_28)),X_28) = greatest_lower_bound(multiply(X_29,X_28),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_29,inverse(X_28)),X_28),greatest_lower_bound(multiply(X_29,X_28),multiply(inverse(X_28),X_28))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_433,plain,
( multiply(greatest_lower_bound(X_29,inverse(X_28)),X_28) != greatest_lower_bound(multiply(X_29,X_28),multiply(inverse(X_28),X_28))
| multiply(greatest_lower_bound(X_29,inverse(X_28)),X_28) = greatest_lower_bound(multiply(X_29,X_28),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_28),X_28),identity) )],[refute_0_431,refute_0_432]) ).
cnf(refute_0_434,plain,
multiply(greatest_lower_bound(X_29,inverse(X_28)),X_28) = greatest_lower_bound(multiply(X_29,X_28),identity),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_29,inverse(X_28)),X_28),greatest_lower_bound(multiply(X_29,X_28),multiply(inverse(X_28),X_28))) )],[refute_0_430,refute_0_433]) ).
cnf(refute_0_435,plain,
greatest_lower_bound(multiply(X_29,X_28),identity) = greatest_lower_bound(identity,multiply(X_29,X_28)),
inference(subst,[],[refute_0_19:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_29,X_28)))]]) ).
cnf(refute_0_436,plain,
( multiply(greatest_lower_bound(X_29,inverse(X_28)),X_28) != greatest_lower_bound(multiply(X_29,X_28),identity)
| greatest_lower_bound(multiply(X_29,X_28),identity) != greatest_lower_bound(identity,multiply(X_29,X_28))
| multiply(greatest_lower_bound(X_29,inverse(X_28)),X_28) = greatest_lower_bound(identity,multiply(X_29,X_28)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_29,inverse(X_28)),X_28),greatest_lower_bound(identity,multiply(X_29,X_28))) ),[0],$fot(greatest_lower_bound(multiply(X_29,X_28),identity))]]) ).
cnf(refute_0_437,plain,
( multiply(greatest_lower_bound(X_29,inverse(X_28)),X_28) != greatest_lower_bound(multiply(X_29,X_28),identity)
| multiply(greatest_lower_bound(X_29,inverse(X_28)),X_28) = greatest_lower_bound(identity,multiply(X_29,X_28)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_29,X_28),identity),greatest_lower_bound(identity,multiply(X_29,X_28))) )],[refute_0_435,refute_0_436]) ).
cnf(refute_0_438,plain,
multiply(greatest_lower_bound(X_29,inverse(X_28)),X_28) = greatest_lower_bound(identity,multiply(X_29,X_28)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_29,inverse(X_28)),X_28),greatest_lower_bound(multiply(X_29,X_28),identity)) )],[refute_0_434,refute_0_437]) ).
cnf(refute_0_439,plain,
multiply(greatest_lower_bound(identity,inverse(inverse(X_77))),inverse(X_77)) = greatest_lower_bound(identity,multiply(identity,inverse(X_77))),
inference(subst,[],[refute_0_438:[bind(X_28,$fot(inverse(X_77))),bind(X_29,$fot(identity))]]) ).
cnf(refute_0_440,plain,
( multiply(greatest_lower_bound(identity,inverse(inverse(X_77))),inverse(X_77)) != greatest_lower_bound(identity,multiply(identity,inverse(X_77)))
| greatest_lower_bound(identity,inverse(inverse(X_77))) != greatest_lower_bound(X_77,identity)
| multiply(greatest_lower_bound(X_77,identity),inverse(X_77)) = greatest_lower_bound(identity,multiply(identity,inverse(X_77))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(inverse(X_77))),inverse(X_77)),greatest_lower_bound(identity,multiply(identity,inverse(X_77)))) ),[0,0],$fot(greatest_lower_bound(X_77,identity))]]) ).
cnf(refute_0_441,plain,
( multiply(greatest_lower_bound(identity,inverse(inverse(X_77))),inverse(X_77)) != greatest_lower_bound(identity,multiply(identity,inverse(X_77)))
| multiply(greatest_lower_bound(X_77,identity),inverse(X_77)) = greatest_lower_bound(identity,multiply(identity,inverse(X_77))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(inverse(X_77))),greatest_lower_bound(X_77,identity)) )],[refute_0_283,refute_0_440]) ).
cnf(refute_0_442,plain,
multiply(greatest_lower_bound(X_77,identity),inverse(X_77)) = greatest_lower_bound(identity,multiply(identity,inverse(X_77))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(inverse(X_77))),inverse(X_77)),greatest_lower_bound(identity,multiply(identity,inverse(X_77)))) )],[refute_0_439,refute_0_441]) ).
cnf(refute_0_443,plain,
multiply(identity,greatest_lower_bound(identity,inverse(X_77))) = greatest_lower_bound(identity,inverse(X_77)),
inference(subst,[],[left_identity:[bind(X,$fot(greatest_lower_bound(identity,inverse(X_77))))]]) ).
cnf(refute_0_444,plain,
multiply(X,greatest_lower_bound(identity,Z)) = greatest_lower_bound(multiply(X,identity),multiply(X,Z)),
inference(subst,[],[monotony_glb1:[bind(Y,$fot(identity))]]) ).
cnf(refute_0_445,plain,
X = multiply(X,identity),
inference(subst,[],[refute_0_63:[bind(X_74,$fot(X))]]) ).
cnf(refute_0_446,plain,
( X != multiply(X,identity)
| multiply(X,identity) = X ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X)),bind(Y0,$fot(multiply(X,identity)))]]) ).
cnf(refute_0_447,plain,
multiply(X,identity) = X,
inference(resolve,[$cnf( $equal(X,multiply(X,identity)) )],[refute_0_445,refute_0_446]) ).
cnf(refute_0_448,plain,
( multiply(X,greatest_lower_bound(identity,Z)) != greatest_lower_bound(multiply(X,identity),multiply(X,Z))
| multiply(X,identity) != X
| multiply(X,greatest_lower_bound(identity,Z)) = greatest_lower_bound(X,multiply(X,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X,greatest_lower_bound(identity,Z)),greatest_lower_bound(multiply(X,identity),multiply(X,Z))) ),[1,0],$fot(X)]]) ).
cnf(refute_0_449,plain,
( multiply(X,greatest_lower_bound(identity,Z)) != greatest_lower_bound(multiply(X,identity),multiply(X,Z))
| multiply(X,greatest_lower_bound(identity,Z)) = greatest_lower_bound(X,multiply(X,Z)) ),
inference(resolve,[$cnf( $equal(multiply(X,identity),X) )],[refute_0_447,refute_0_448]) ).
cnf(refute_0_450,plain,
multiply(X,greatest_lower_bound(identity,Z)) = greatest_lower_bound(X,multiply(X,Z)),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(identity,Z)),greatest_lower_bound(multiply(X,identity),multiply(X,Z))) )],[refute_0_444,refute_0_449]) ).
cnf(refute_0_451,plain,
( multiply(X,greatest_lower_bound(identity,Z)) != greatest_lower_bound(X,multiply(X,Z))
| greatest_lower_bound(X,multiply(X,Z)) = multiply(X,greatest_lower_bound(identity,Z)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X,greatest_lower_bound(identity,Z)))),bind(Y0,$fot(greatest_lower_bound(X,multiply(X,Z))))]]) ).
cnf(refute_0_452,plain,
greatest_lower_bound(X,multiply(X,Z)) = multiply(X,greatest_lower_bound(identity,Z)),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(identity,Z)),greatest_lower_bound(X,multiply(X,Z))) )],[refute_0_450,refute_0_451]) ).
cnf(refute_0_453,plain,
greatest_lower_bound(identity,multiply(identity,inverse(X_77))) = multiply(identity,greatest_lower_bound(identity,inverse(X_77))),
inference(subst,[],[refute_0_452:[bind(X,$fot(identity)),bind(Z,$fot(inverse(X_77)))]]) ).
cnf(refute_0_454,plain,
( multiply(identity,greatest_lower_bound(identity,inverse(X_77))) != greatest_lower_bound(identity,inverse(X_77))
| greatest_lower_bound(identity,multiply(identity,inverse(X_77))) != multiply(identity,greatest_lower_bound(identity,inverse(X_77)))
| greatest_lower_bound(identity,multiply(identity,inverse(X_77))) = greatest_lower_bound(identity,inverse(X_77)) ),
inference(subst,[],[refute_0_136:[bind(X0,$fot(greatest_lower_bound(identity,multiply(identity,inverse(X_77))))),bind(Y0,$fot(multiply(identity,greatest_lower_bound(identity,inverse(X_77))))),bind(Z0,$fot(greatest_lower_bound(identity,inverse(X_77))))]]) ).
cnf(refute_0_455,plain,
( multiply(identity,greatest_lower_bound(identity,inverse(X_77))) != greatest_lower_bound(identity,inverse(X_77))
| greatest_lower_bound(identity,multiply(identity,inverse(X_77))) = greatest_lower_bound(identity,inverse(X_77)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(identity,inverse(X_77))),multiply(identity,greatest_lower_bound(identity,inverse(X_77)))) )],[refute_0_453,refute_0_454]) ).
cnf(refute_0_456,plain,
greatest_lower_bound(identity,multiply(identity,inverse(X_77))) = greatest_lower_bound(identity,inverse(X_77)),
inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(identity,inverse(X_77))),greatest_lower_bound(identity,inverse(X_77))) )],[refute_0_443,refute_0_455]) ).
cnf(refute_0_457,plain,
( multiply(greatest_lower_bound(X_77,identity),inverse(X_77)) != greatest_lower_bound(identity,multiply(identity,inverse(X_77)))
| greatest_lower_bound(identity,multiply(identity,inverse(X_77))) != greatest_lower_bound(identity,inverse(X_77))
| multiply(greatest_lower_bound(X_77,identity),inverse(X_77)) = greatest_lower_bound(identity,inverse(X_77)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_77,identity),inverse(X_77)),greatest_lower_bound(identity,inverse(X_77))) ),[0],$fot(greatest_lower_bound(identity,multiply(identity,inverse(X_77))))]]) ).
cnf(refute_0_458,plain,
( multiply(greatest_lower_bound(X_77,identity),inverse(X_77)) != greatest_lower_bound(identity,multiply(identity,inverse(X_77)))
| multiply(greatest_lower_bound(X_77,identity),inverse(X_77)) = greatest_lower_bound(identity,inverse(X_77)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(identity,inverse(X_77))),greatest_lower_bound(identity,inverse(X_77))) )],[refute_0_456,refute_0_457]) ).
cnf(refute_0_459,plain,
multiply(greatest_lower_bound(X_77,identity),inverse(X_77)) = greatest_lower_bound(identity,inverse(X_77)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_77,identity),inverse(X_77)),greatest_lower_bound(identity,multiply(identity,inverse(X_77)))) )],[refute_0_442,refute_0_458]) ).
cnf(refute_0_460,plain,
multiply(greatest_lower_bound(X_146,identity),inverse(X_146)) = greatest_lower_bound(identity,inverse(X_146)),
inference(subst,[],[refute_0_459:[bind(X_77,$fot(X_146))]]) ).
cnf(refute_0_461,plain,
( multiply(greatest_lower_bound(X_146,identity),inverse(X_146)) != greatest_lower_bound(identity,inverse(X_146))
| multiply(greatest_lower_bound(X_146,identity),least_upper_bound(inverse(X_146),identity)) != least_upper_bound(greatest_lower_bound(X_146,identity),multiply(greatest_lower_bound(X_146,identity),inverse(X_146)))
| multiply(greatest_lower_bound(X_146,identity),least_upper_bound(inverse(X_146),identity)) = least_upper_bound(greatest_lower_bound(X_146,identity),greatest_lower_bound(identity,inverse(X_146))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_146,identity),least_upper_bound(inverse(X_146),identity)),least_upper_bound(greatest_lower_bound(X_146,identity),multiply(greatest_lower_bound(X_146,identity),inverse(X_146)))) ),[1,1],$fot(greatest_lower_bound(identity,inverse(X_146)))]]) ).
cnf(refute_0_462,plain,
( multiply(greatest_lower_bound(X_146,identity),least_upper_bound(inverse(X_146),identity)) != least_upper_bound(greatest_lower_bound(X_146,identity),multiply(greatest_lower_bound(X_146,identity),inverse(X_146)))
| multiply(greatest_lower_bound(X_146,identity),least_upper_bound(inverse(X_146),identity)) = least_upper_bound(greatest_lower_bound(X_146,identity),greatest_lower_bound(identity,inverse(X_146))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_146,identity),inverse(X_146)),greatest_lower_bound(identity,inverse(X_146))) )],[refute_0_460,refute_0_461]) ).
cnf(refute_0_463,plain,
multiply(greatest_lower_bound(X_146,identity),least_upper_bound(inverse(X_146),identity)) = least_upper_bound(greatest_lower_bound(X_146,identity),greatest_lower_bound(identity,inverse(X_146))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_146,identity),least_upper_bound(inverse(X_146),identity)),least_upper_bound(greatest_lower_bound(X_146,identity),multiply(greatest_lower_bound(X_146,identity),inverse(X_146)))) )],[refute_0_429,refute_0_462]) ).
cnf(refute_0_464,plain,
least_upper_bound(X_17,least_upper_bound(multiply(X_17,X_121),X_17)) = least_upper_bound(X_17,multiply(X_17,X_121)),
inference(subst,[],[refute_0_91:[bind(Y,$fot(multiply(X_17,X_121)))]]) ).
cnf(refute_0_465,plain,
multiply(X_17,least_upper_bound(X_121,identity)) = least_upper_bound(X_17,multiply(X_17,X_121)),
inference(subst,[],[refute_0_368:[bind(X_78,$fot(X_17)),bind(X_79,$fot(X_121))]]) ).
cnf(refute_0_466,plain,
( multiply(X_17,least_upper_bound(X_121,identity)) != least_upper_bound(X_17,multiply(X_17,X_121))
| least_upper_bound(X_17,multiply(X_17,X_121)) = multiply(X_17,least_upper_bound(X_121,identity)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X_17,least_upper_bound(X_121,identity)))),bind(Y0,$fot(least_upper_bound(X_17,multiply(X_17,X_121))))]]) ).
cnf(refute_0_467,plain,
least_upper_bound(X_17,multiply(X_17,X_121)) = multiply(X_17,least_upper_bound(X_121,identity)),
inference(resolve,[$cnf( $equal(multiply(X_17,least_upper_bound(X_121,identity)),least_upper_bound(X_17,multiply(X_17,X_121))) )],[refute_0_465,refute_0_466]) ).
cnf(refute_0_468,plain,
( least_upper_bound(X_17,multiply(X_17,X_121)) != multiply(X_17,least_upper_bound(X_121,identity))
| least_upper_bound(X_17,least_upper_bound(multiply(X_17,X_121),X_17)) != least_upper_bound(X_17,multiply(X_17,X_121))
| least_upper_bound(X_17,least_upper_bound(multiply(X_17,X_121),X_17)) = multiply(X_17,least_upper_bound(X_121,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_17,least_upper_bound(multiply(X_17,X_121),X_17)),least_upper_bound(X_17,multiply(X_17,X_121))) ),[1],$fot(multiply(X_17,least_upper_bound(X_121,identity)))]]) ).
cnf(refute_0_469,plain,
( least_upper_bound(X_17,least_upper_bound(multiply(X_17,X_121),X_17)) != least_upper_bound(X_17,multiply(X_17,X_121))
| least_upper_bound(X_17,least_upper_bound(multiply(X_17,X_121),X_17)) = multiply(X_17,least_upper_bound(X_121,identity)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,multiply(X_17,X_121)),multiply(X_17,least_upper_bound(X_121,identity))) )],[refute_0_467,refute_0_468]) ).
cnf(refute_0_470,plain,
least_upper_bound(X_17,least_upper_bound(multiply(X_17,X_121),X_17)) = multiply(X_17,least_upper_bound(X_121,identity)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,least_upper_bound(multiply(X_17,X_121),X_17)),least_upper_bound(X_17,multiply(X_17,X_121))) )],[refute_0_464,refute_0_469]) ).
cnf(refute_0_471,plain,
least_upper_bound(identity,least_upper_bound(X_121,identity)) = least_upper_bound(identity,X_121),
inference(subst,[],[refute_0_91:[bind(Y,$fot(X_121)),bind(X_17,$fot(identity))]]) ).
cnf(refute_0_472,plain,
multiply(X_17,least_upper_bound(identity,least_upper_bound(X_121,identity))) = multiply(X_17,least_upper_bound(identity,least_upper_bound(X_121,identity))),
introduced(tautology,[refl,[$fot(multiply(X_17,least_upper_bound(identity,least_upper_bound(X_121,identity))))]]) ).
cnf(refute_0_473,plain,
( multiply(X_17,least_upper_bound(identity,least_upper_bound(X_121,identity))) != multiply(X_17,least_upper_bound(identity,least_upper_bound(X_121,identity)))
| least_upper_bound(identity,least_upper_bound(X_121,identity)) != least_upper_bound(identity,X_121)
| multiply(X_17,least_upper_bound(identity,least_upper_bound(X_121,identity))) = multiply(X_17,least_upper_bound(identity,X_121)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_17,least_upper_bound(identity,least_upper_bound(X_121,identity))),multiply(X_17,least_upper_bound(identity,least_upper_bound(X_121,identity)))) ),[1,1],$fot(least_upper_bound(identity,X_121))]]) ).
cnf(refute_0_474,plain,
( least_upper_bound(identity,least_upper_bound(X_121,identity)) != least_upper_bound(identity,X_121)
| multiply(X_17,least_upper_bound(identity,least_upper_bound(X_121,identity))) = multiply(X_17,least_upper_bound(identity,X_121)) ),
inference(resolve,[$cnf( $equal(multiply(X_17,least_upper_bound(identity,least_upper_bound(X_121,identity))),multiply(X_17,least_upper_bound(identity,least_upper_bound(X_121,identity)))) )],[refute_0_472,refute_0_473]) ).
cnf(refute_0_475,plain,
multiply(X_17,least_upper_bound(identity,least_upper_bound(X_121,identity))) = multiply(X_17,least_upper_bound(identity,X_121)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_121,identity)),least_upper_bound(identity,X_121)) )],[refute_0_471,refute_0_474]) ).
cnf(refute_0_476,plain,
multiply(X_17,least_upper_bound(least_upper_bound(X_121,identity),identity)) = multiply(X_17,least_upper_bound(identity,least_upper_bound(X_121,identity))),
inference(subst,[],[refute_0_147:[bind(X_78,$fot(X_17)),bind(X_79,$fot(least_upper_bound(X_121,identity))),bind(X_80,$fot(identity))]]) ).
cnf(refute_0_477,plain,
( multiply(X_78,least_upper_bound(X_79,identity)) != least_upper_bound(X_78,multiply(X_78,X_79))
| least_upper_bound(X_78,multiply(X_78,X_79)) = multiply(X_78,least_upper_bound(X_79,identity)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X_78,least_upper_bound(X_79,identity)))),bind(Y0,$fot(least_upper_bound(X_78,multiply(X_78,X_79))))]]) ).
cnf(refute_0_478,plain,
least_upper_bound(X_78,multiply(X_78,X_79)) = multiply(X_78,least_upper_bound(X_79,identity)),
inference(resolve,[$cnf( $equal(multiply(X_78,least_upper_bound(X_79,identity)),least_upper_bound(X_78,multiply(X_78,X_79))) )],[refute_0_368,refute_0_477]) ).
cnf(refute_0_479,plain,
least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_121,identity))) = multiply(X_17,least_upper_bound(least_upper_bound(X_121,identity),identity)),
inference(subst,[],[refute_0_478:[bind(X_78,$fot(X_17)),bind(X_79,$fot(least_upper_bound(X_121,identity)))]]) ).
cnf(refute_0_480,plain,
( multiply(X_17,least_upper_bound(least_upper_bound(X_121,identity),identity)) != multiply(X_17,least_upper_bound(identity,least_upper_bound(X_121,identity)))
| least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_121,identity))) != multiply(X_17,least_upper_bound(least_upper_bound(X_121,identity),identity))
| least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_121,identity))) = multiply(X_17,least_upper_bound(identity,least_upper_bound(X_121,identity))) ),
inference(subst,[],[refute_0_136:[bind(X0,$fot(least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_121,identity))))),bind(Y0,$fot(multiply(X_17,least_upper_bound(least_upper_bound(X_121,identity),identity)))),bind(Z0,$fot(multiply(X_17,least_upper_bound(identity,least_upper_bound(X_121,identity)))))]]) ).
cnf(refute_0_481,plain,
( multiply(X_17,least_upper_bound(least_upper_bound(X_121,identity),identity)) != multiply(X_17,least_upper_bound(identity,least_upper_bound(X_121,identity)))
| least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_121,identity))) = multiply(X_17,least_upper_bound(identity,least_upper_bound(X_121,identity))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_121,identity))),multiply(X_17,least_upper_bound(least_upper_bound(X_121,identity),identity))) )],[refute_0_479,refute_0_480]) ).
cnf(refute_0_482,plain,
least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_121,identity))) = multiply(X_17,least_upper_bound(identity,least_upper_bound(X_121,identity))),
inference(resolve,[$cnf( $equal(multiply(X_17,least_upper_bound(least_upper_bound(X_121,identity),identity)),multiply(X_17,least_upper_bound(identity,least_upper_bound(X_121,identity)))) )],[refute_0_476,refute_0_481]) ).
cnf(refute_0_483,plain,
least_upper_bound(X,least_upper_bound(X_31,multiply(X_31,X_121))) = least_upper_bound(X_31,least_upper_bound(multiply(X_31,X_121),X)),
inference(subst,[],[refute_0_127:[bind(X_32,$fot(multiply(X_31,X_121)))]]) ).
cnf(refute_0_484,plain,
multiply(X_31,least_upper_bound(X_121,identity)) = least_upper_bound(X_31,multiply(X_31,X_121)),
inference(subst,[],[refute_0_368:[bind(X_78,$fot(X_31)),bind(X_79,$fot(X_121))]]) ).
cnf(refute_0_485,plain,
( multiply(X_31,least_upper_bound(X_121,identity)) != least_upper_bound(X_31,multiply(X_31,X_121))
| least_upper_bound(X_31,multiply(X_31,X_121)) = multiply(X_31,least_upper_bound(X_121,identity)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X_31,least_upper_bound(X_121,identity)))),bind(Y0,$fot(least_upper_bound(X_31,multiply(X_31,X_121))))]]) ).
cnf(refute_0_486,plain,
least_upper_bound(X_31,multiply(X_31,X_121)) = multiply(X_31,least_upper_bound(X_121,identity)),
inference(resolve,[$cnf( $equal(multiply(X_31,least_upper_bound(X_121,identity)),least_upper_bound(X_31,multiply(X_31,X_121))) )],[refute_0_484,refute_0_485]) ).
cnf(refute_0_487,plain,
( least_upper_bound(X,least_upper_bound(X_31,multiply(X_31,X_121))) != least_upper_bound(X_31,least_upper_bound(multiply(X_31,X_121),X))
| least_upper_bound(X_31,multiply(X_31,X_121)) != multiply(X_31,least_upper_bound(X_121,identity))
| least_upper_bound(X,multiply(X_31,least_upper_bound(X_121,identity))) = least_upper_bound(X_31,least_upper_bound(multiply(X_31,X_121),X)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_31,multiply(X_31,X_121))),least_upper_bound(X_31,least_upper_bound(multiply(X_31,X_121),X))) ),[0,1],$fot(multiply(X_31,least_upper_bound(X_121,identity)))]]) ).
cnf(refute_0_488,plain,
( least_upper_bound(X,least_upper_bound(X_31,multiply(X_31,X_121))) != least_upper_bound(X_31,least_upper_bound(multiply(X_31,X_121),X))
| least_upper_bound(X,multiply(X_31,least_upper_bound(X_121,identity))) = least_upper_bound(X_31,least_upper_bound(multiply(X_31,X_121),X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_31,multiply(X_31,X_121)),multiply(X_31,least_upper_bound(X_121,identity))) )],[refute_0_486,refute_0_487]) ).
cnf(refute_0_489,plain,
least_upper_bound(X,multiply(X_31,least_upper_bound(X_121,identity))) = least_upper_bound(X_31,least_upper_bound(multiply(X_31,X_121),X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_31,multiply(X_31,X_121))),least_upper_bound(X_31,least_upper_bound(multiply(X_31,X_121),X))) )],[refute_0_483,refute_0_488]) ).
cnf(refute_0_490,plain,
( least_upper_bound(X,multiply(X_31,least_upper_bound(X_121,identity))) != least_upper_bound(X_31,least_upper_bound(multiply(X_31,X_121),X))
| least_upper_bound(X_31,least_upper_bound(multiply(X_31,X_121),X)) = least_upper_bound(X,multiply(X_31,least_upper_bound(X_121,identity))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X,multiply(X_31,least_upper_bound(X_121,identity))))),bind(Y0,$fot(least_upper_bound(X_31,least_upper_bound(multiply(X_31,X_121),X))))]]) ).
cnf(refute_0_491,plain,
least_upper_bound(X_31,least_upper_bound(multiply(X_31,X_121),X)) = least_upper_bound(X,multiply(X_31,least_upper_bound(X_121,identity))),
inference(resolve,[$cnf( $equal(least_upper_bound(X,multiply(X_31,least_upper_bound(X_121,identity))),least_upper_bound(X_31,least_upper_bound(multiply(X_31,X_121),X))) )],[refute_0_489,refute_0_490]) ).
cnf(refute_0_492,plain,
least_upper_bound(X_17,least_upper_bound(multiply(X_17,X_121),X_17)) = least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_121,identity))),
inference(subst,[],[refute_0_491:[bind(X,$fot(X_17)),bind(X_31,$fot(X_17))]]) ).
cnf(refute_0_493,plain,
( least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_121,identity))) != multiply(X_17,least_upper_bound(identity,least_upper_bound(X_121,identity)))
| least_upper_bound(X_17,least_upper_bound(multiply(X_17,X_121),X_17)) != least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_121,identity)))
| least_upper_bound(X_17,least_upper_bound(multiply(X_17,X_121),X_17)) = multiply(X_17,least_upper_bound(identity,least_upper_bound(X_121,identity))) ),
inference(subst,[],[refute_0_136:[bind(X0,$fot(least_upper_bound(X_17,least_upper_bound(multiply(X_17,X_121),X_17)))),bind(Y0,$fot(least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_121,identity))))),bind(Z0,$fot(multiply(X_17,least_upper_bound(identity,least_upper_bound(X_121,identity)))))]]) ).
cnf(refute_0_494,plain,
( least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_121,identity))) != multiply(X_17,least_upper_bound(identity,least_upper_bound(X_121,identity)))
| least_upper_bound(X_17,least_upper_bound(multiply(X_17,X_121),X_17)) = multiply(X_17,least_upper_bound(identity,least_upper_bound(X_121,identity))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,least_upper_bound(multiply(X_17,X_121),X_17)),least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_121,identity)))) )],[refute_0_492,refute_0_493]) ).
cnf(refute_0_495,plain,
least_upper_bound(X_17,least_upper_bound(multiply(X_17,X_121),X_17)) = multiply(X_17,least_upper_bound(identity,least_upper_bound(X_121,identity))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_121,identity))),multiply(X_17,least_upper_bound(identity,least_upper_bound(X_121,identity)))) )],[refute_0_482,refute_0_494]) ).
cnf(refute_0_496,plain,
( multiply(X_17,least_upper_bound(identity,least_upper_bound(X_121,identity))) != multiply(X_17,least_upper_bound(identity,X_121))
| least_upper_bound(X_17,least_upper_bound(multiply(X_17,X_121),X_17)) != multiply(X_17,least_upper_bound(identity,least_upper_bound(X_121,identity)))
| least_upper_bound(X_17,least_upper_bound(multiply(X_17,X_121),X_17)) = multiply(X_17,least_upper_bound(identity,X_121)) ),
inference(subst,[],[refute_0_136:[bind(X0,$fot(least_upper_bound(X_17,least_upper_bound(multiply(X_17,X_121),X_17)))),bind(Y0,$fot(multiply(X_17,least_upper_bound(identity,least_upper_bound(X_121,identity))))),bind(Z0,$fot(multiply(X_17,least_upper_bound(identity,X_121))))]]) ).
cnf(refute_0_497,plain,
( multiply(X_17,least_upper_bound(identity,least_upper_bound(X_121,identity))) != multiply(X_17,least_upper_bound(identity,X_121))
| least_upper_bound(X_17,least_upper_bound(multiply(X_17,X_121),X_17)) = multiply(X_17,least_upper_bound(identity,X_121)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,least_upper_bound(multiply(X_17,X_121),X_17)),multiply(X_17,least_upper_bound(identity,least_upper_bound(X_121,identity)))) )],[refute_0_495,refute_0_496]) ).
cnf(refute_0_498,plain,
least_upper_bound(X_17,least_upper_bound(multiply(X_17,X_121),X_17)) = multiply(X_17,least_upper_bound(identity,X_121)),
inference(resolve,[$cnf( $equal(multiply(X_17,least_upper_bound(identity,least_upper_bound(X_121,identity))),multiply(X_17,least_upper_bound(identity,X_121))) )],[refute_0_475,refute_0_497]) ).
cnf(refute_0_499,plain,
( least_upper_bound(X_17,least_upper_bound(multiply(X_17,X_121),X_17)) != multiply(X_17,least_upper_bound(X_121,identity))
| least_upper_bound(X_17,least_upper_bound(multiply(X_17,X_121),X_17)) != multiply(X_17,least_upper_bound(identity,X_121))
| multiply(X_17,least_upper_bound(identity,X_121)) = multiply(X_17,least_upper_bound(X_121,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_17,least_upper_bound(multiply(X_17,X_121),X_17)),multiply(X_17,least_upper_bound(X_121,identity))) ),[0],$fot(multiply(X_17,least_upper_bound(identity,X_121)))]]) ).
cnf(refute_0_500,plain,
( least_upper_bound(X_17,least_upper_bound(multiply(X_17,X_121),X_17)) != multiply(X_17,least_upper_bound(X_121,identity))
| multiply(X_17,least_upper_bound(identity,X_121)) = multiply(X_17,least_upper_bound(X_121,identity)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,least_upper_bound(multiply(X_17,X_121),X_17)),multiply(X_17,least_upper_bound(identity,X_121))) )],[refute_0_498,refute_0_499]) ).
cnf(refute_0_501,plain,
multiply(X_17,least_upper_bound(identity,X_121)) = multiply(X_17,least_upper_bound(X_121,identity)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,least_upper_bound(multiply(X_17,X_121),X_17)),multiply(X_17,least_upper_bound(X_121,identity))) )],[refute_0_470,refute_0_500]) ).
cnf(refute_0_502,plain,
( multiply(X_17,least_upper_bound(identity,X_121)) != multiply(X_17,least_upper_bound(X_121,identity))
| multiply(X_17,least_upper_bound(X_121,identity)) = multiply(X_17,least_upper_bound(identity,X_121)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X_17,least_upper_bound(identity,X_121)))),bind(Y0,$fot(multiply(X_17,least_upper_bound(X_121,identity))))]]) ).
cnf(refute_0_503,plain,
multiply(X_17,least_upper_bound(X_121,identity)) = multiply(X_17,least_upper_bound(identity,X_121)),
inference(resolve,[$cnf( $equal(multiply(X_17,least_upper_bound(identity,X_121)),multiply(X_17,least_upper_bound(X_121,identity))) )],[refute_0_501,refute_0_502]) ).
cnf(refute_0_504,plain,
multiply(greatest_lower_bound(X_146,identity),least_upper_bound(inverse(X_146),identity)) = multiply(greatest_lower_bound(X_146,identity),least_upper_bound(identity,inverse(X_146))),
inference(subst,[],[refute_0_503:[bind(X_121,$fot(inverse(X_146))),bind(X_17,$fot(greatest_lower_bound(X_146,identity)))]]) ).
cnf(refute_0_505,plain,
( multiply(greatest_lower_bound(X_146,identity),least_upper_bound(inverse(X_146),identity)) != multiply(greatest_lower_bound(X_146,identity),least_upper_bound(identity,inverse(X_146)))
| multiply(greatest_lower_bound(X_146,identity),least_upper_bound(inverse(X_146),identity)) != least_upper_bound(greatest_lower_bound(X_146,identity),greatest_lower_bound(identity,inverse(X_146)))
| multiply(greatest_lower_bound(X_146,identity),least_upper_bound(identity,inverse(X_146))) = least_upper_bound(greatest_lower_bound(X_146,identity),greatest_lower_bound(identity,inverse(X_146))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_146,identity),least_upper_bound(inverse(X_146),identity)),least_upper_bound(greatest_lower_bound(X_146,identity),greatest_lower_bound(identity,inverse(X_146)))) ),[0],$fot(multiply(greatest_lower_bound(X_146,identity),least_upper_bound(identity,inverse(X_146))))]]) ).
cnf(refute_0_506,plain,
( multiply(greatest_lower_bound(X_146,identity),least_upper_bound(inverse(X_146),identity)) != least_upper_bound(greatest_lower_bound(X_146,identity),greatest_lower_bound(identity,inverse(X_146)))
| multiply(greatest_lower_bound(X_146,identity),least_upper_bound(identity,inverse(X_146))) = least_upper_bound(greatest_lower_bound(X_146,identity),greatest_lower_bound(identity,inverse(X_146))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_146,identity),least_upper_bound(inverse(X_146),identity)),multiply(greatest_lower_bound(X_146,identity),least_upper_bound(identity,inverse(X_146)))) )],[refute_0_504,refute_0_505]) ).
cnf(refute_0_507,plain,
multiply(least_upper_bound(X_84,identity),X_83) = least_upper_bound(multiply(X_84,X_83),multiply(identity,X_83)),
inference(subst,[],[monotony_lub2:[bind(X,$fot(X_83)),bind(Y,$fot(X_84)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_508,plain,
multiply(identity,X_83) = X_83,
inference(subst,[],[left_identity:[bind(X,$fot(X_83))]]) ).
cnf(refute_0_509,plain,
( multiply(identity,X_83) != X_83
| multiply(least_upper_bound(X_84,identity),X_83) != least_upper_bound(multiply(X_84,X_83),multiply(identity,X_83))
| multiply(least_upper_bound(X_84,identity),X_83) = least_upper_bound(multiply(X_84,X_83),X_83) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_84,identity),X_83),least_upper_bound(multiply(X_84,X_83),multiply(identity,X_83))) ),[1,1],$fot(X_83)]]) ).
cnf(refute_0_510,plain,
( multiply(least_upper_bound(X_84,identity),X_83) != least_upper_bound(multiply(X_84,X_83),multiply(identity,X_83))
| multiply(least_upper_bound(X_84,identity),X_83) = least_upper_bound(multiply(X_84,X_83),X_83) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_83),X_83) )],[refute_0_508,refute_0_509]) ).
cnf(refute_0_511,plain,
multiply(least_upper_bound(X_84,identity),X_83) = least_upper_bound(multiply(X_84,X_83),X_83),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_84,identity),X_83),least_upper_bound(multiply(X_84,X_83),multiply(identity,X_83))) )],[refute_0_507,refute_0_510]) ).
cnf(refute_0_512,plain,
least_upper_bound(multiply(X_84,X_83),X_83) = least_upper_bound(X_83,multiply(X_84,X_83)),
inference(subst,[],[refute_0_319:[bind(X_81,$fot(X_83)),bind(X_82,$fot(multiply(X_84,X_83)))]]) ).
cnf(refute_0_513,plain,
( multiply(least_upper_bound(X_84,identity),X_83) != least_upper_bound(multiply(X_84,X_83),X_83)
| least_upper_bound(multiply(X_84,X_83),X_83) != least_upper_bound(X_83,multiply(X_84,X_83))
| multiply(least_upper_bound(X_84,identity),X_83) = least_upper_bound(X_83,multiply(X_84,X_83)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_84,identity),X_83),least_upper_bound(X_83,multiply(X_84,X_83))) ),[0],$fot(least_upper_bound(multiply(X_84,X_83),X_83))]]) ).
cnf(refute_0_514,plain,
( multiply(least_upper_bound(X_84,identity),X_83) != least_upper_bound(multiply(X_84,X_83),X_83)
| multiply(least_upper_bound(X_84,identity),X_83) = least_upper_bound(X_83,multiply(X_84,X_83)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_84,X_83),X_83),least_upper_bound(X_83,multiply(X_84,X_83))) )],[refute_0_512,refute_0_513]) ).
cnf(refute_0_515,plain,
multiply(least_upper_bound(X_84,identity),X_83) = least_upper_bound(X_83,multiply(X_84,X_83)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_84,identity),X_83),least_upper_bound(multiply(X_84,X_83),X_83)) )],[refute_0_511,refute_0_514]) ).
cnf(refute_0_516,plain,
multiply(least_upper_bound(inverse(X_22),identity),greatest_lower_bound(X_22,identity)) = least_upper_bound(greatest_lower_bound(X_22,identity),multiply(inverse(X_22),greatest_lower_bound(X_22,identity))),
inference(subst,[],[refute_0_515:[bind(X_83,$fot(greatest_lower_bound(X_22,identity))),bind(X_84,$fot(inverse(X_22)))]]) ).
cnf(refute_0_517,plain,
( multiply(inverse(X_22),greatest_lower_bound(X_22,identity)) != greatest_lower_bound(identity,inverse(X_22))
| multiply(least_upper_bound(inverse(X_22),identity),greatest_lower_bound(X_22,identity)) != least_upper_bound(greatest_lower_bound(X_22,identity),multiply(inverse(X_22),greatest_lower_bound(X_22,identity)))
| multiply(least_upper_bound(inverse(X_22),identity),greatest_lower_bound(X_22,identity)) = least_upper_bound(greatest_lower_bound(X_22,identity),greatest_lower_bound(identity,inverse(X_22))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(X_22),identity),greatest_lower_bound(X_22,identity)),least_upper_bound(greatest_lower_bound(X_22,identity),multiply(inverse(X_22),greatest_lower_bound(X_22,identity)))) ),[1,1],$fot(greatest_lower_bound(identity,inverse(X_22)))]]) ).
cnf(refute_0_518,plain,
( multiply(least_upper_bound(inverse(X_22),identity),greatest_lower_bound(X_22,identity)) != least_upper_bound(greatest_lower_bound(X_22,identity),multiply(inverse(X_22),greatest_lower_bound(X_22,identity)))
| multiply(least_upper_bound(inverse(X_22),identity),greatest_lower_bound(X_22,identity)) = least_upper_bound(greatest_lower_bound(X_22,identity),greatest_lower_bound(identity,inverse(X_22))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_22),greatest_lower_bound(X_22,identity)),greatest_lower_bound(identity,inverse(X_22))) )],[refute_0_256,refute_0_517]) ).
cnf(refute_0_519,plain,
multiply(least_upper_bound(inverse(X_22),identity),greatest_lower_bound(X_22,identity)) = least_upper_bound(greatest_lower_bound(X_22,identity),greatest_lower_bound(identity,inverse(X_22))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_22),identity),greatest_lower_bound(X_22,identity)),least_upper_bound(greatest_lower_bound(X_22,identity),multiply(inverse(X_22),greatest_lower_bound(X_22,identity)))) )],[refute_0_516,refute_0_518]) ).
cnf(refute_0_520,plain,
least_upper_bound(X_17,least_upper_bound(multiply(X_138,X_17),X_17)) = least_upper_bound(X_17,multiply(X_138,X_17)),
inference(subst,[],[refute_0_91:[bind(Y,$fot(multiply(X_138,X_17)))]]) ).
cnf(refute_0_521,plain,
multiply(least_upper_bound(X_138,identity),X_17) = least_upper_bound(X_17,multiply(X_138,X_17)),
inference(subst,[],[refute_0_515:[bind(X_83,$fot(X_17)),bind(X_84,$fot(X_138))]]) ).
cnf(refute_0_522,plain,
( multiply(least_upper_bound(X_138,identity),X_17) != least_upper_bound(X_17,multiply(X_138,X_17))
| least_upper_bound(X_17,multiply(X_138,X_17)) = multiply(least_upper_bound(X_138,identity),X_17) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(X_138,identity),X_17))),bind(Y0,$fot(least_upper_bound(X_17,multiply(X_138,X_17))))]]) ).
cnf(refute_0_523,plain,
least_upper_bound(X_17,multiply(X_138,X_17)) = multiply(least_upper_bound(X_138,identity),X_17),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_138,identity),X_17),least_upper_bound(X_17,multiply(X_138,X_17))) )],[refute_0_521,refute_0_522]) ).
cnf(refute_0_524,plain,
( least_upper_bound(X_17,multiply(X_138,X_17)) != multiply(least_upper_bound(X_138,identity),X_17)
| least_upper_bound(X_17,least_upper_bound(multiply(X_138,X_17),X_17)) != least_upper_bound(X_17,multiply(X_138,X_17))
| least_upper_bound(X_17,least_upper_bound(multiply(X_138,X_17),X_17)) = multiply(least_upper_bound(X_138,identity),X_17) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_17,least_upper_bound(multiply(X_138,X_17),X_17)),least_upper_bound(X_17,multiply(X_138,X_17))) ),[1],$fot(multiply(least_upper_bound(X_138,identity),X_17))]]) ).
cnf(refute_0_525,plain,
( least_upper_bound(X_17,least_upper_bound(multiply(X_138,X_17),X_17)) != least_upper_bound(X_17,multiply(X_138,X_17))
| least_upper_bound(X_17,least_upper_bound(multiply(X_138,X_17),X_17)) = multiply(least_upper_bound(X_138,identity),X_17) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,multiply(X_138,X_17)),multiply(least_upper_bound(X_138,identity),X_17)) )],[refute_0_523,refute_0_524]) ).
cnf(refute_0_526,plain,
least_upper_bound(X_17,least_upper_bound(multiply(X_138,X_17),X_17)) = multiply(least_upper_bound(X_138,identity),X_17),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,least_upper_bound(multiply(X_138,X_17),X_17)),least_upper_bound(X_17,multiply(X_138,X_17))) )],[refute_0_520,refute_0_525]) ).
cnf(refute_0_527,plain,
least_upper_bound(identity,least_upper_bound(X_138,identity)) = least_upper_bound(identity,X_138),
inference(subst,[],[refute_0_91:[bind(Y,$fot(X_138)),bind(X_17,$fot(identity))]]) ).
cnf(refute_0_528,plain,
multiply(least_upper_bound(identity,least_upper_bound(X_138,identity)),X_17) = multiply(least_upper_bound(identity,least_upper_bound(X_138,identity)),X_17),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(identity,least_upper_bound(X_138,identity)),X_17))]]) ).
cnf(refute_0_529,plain,
( multiply(least_upper_bound(identity,least_upper_bound(X_138,identity)),X_17) != multiply(least_upper_bound(identity,least_upper_bound(X_138,identity)),X_17)
| least_upper_bound(identity,least_upper_bound(X_138,identity)) != least_upper_bound(identity,X_138)
| multiply(least_upper_bound(identity,least_upper_bound(X_138,identity)),X_17) = multiply(least_upper_bound(identity,X_138),X_17) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(X_138,identity)),X_17),multiply(least_upper_bound(identity,least_upper_bound(X_138,identity)),X_17)) ),[1,0],$fot(least_upper_bound(identity,X_138))]]) ).
cnf(refute_0_530,plain,
( least_upper_bound(identity,least_upper_bound(X_138,identity)) != least_upper_bound(identity,X_138)
| multiply(least_upper_bound(identity,least_upper_bound(X_138,identity)),X_17) = multiply(least_upper_bound(identity,X_138),X_17) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(X_138,identity)),X_17),multiply(least_upper_bound(identity,least_upper_bound(X_138,identity)),X_17)) )],[refute_0_528,refute_0_529]) ).
cnf(refute_0_531,plain,
multiply(least_upper_bound(identity,least_upper_bound(X_138,identity)),X_17) = multiply(least_upper_bound(identity,X_138),X_17),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_138,identity)),least_upper_bound(identity,X_138)) )],[refute_0_527,refute_0_530]) ).
cnf(refute_0_532,plain,
least_upper_bound(multiply(X_84,X_83),least_upper_bound(multiply(X_84,X_83),multiply(X_85,X_83))) = least_upper_bound(multiply(X_84,X_83),multiply(X_85,X_83)),
inference(subst,[],[refute_0_101:[bind(X_32,$fot(multiply(X_84,X_83))),bind(X_33,$fot(multiply(X_85,X_83)))]]) ).
cnf(refute_0_533,plain,
multiply(least_upper_bound(X_84,X_85),X_83) = least_upper_bound(multiply(X_84,X_83),multiply(X_85,X_83)),
inference(subst,[],[monotony_lub2:[bind(X,$fot(X_83)),bind(Y,$fot(X_84)),bind(Z,$fot(X_85))]]) ).
cnf(refute_0_534,plain,
( multiply(least_upper_bound(X_84,X_85),X_83) != least_upper_bound(multiply(X_84,X_83),multiply(X_85,X_83))
| least_upper_bound(multiply(X_84,X_83),multiply(X_85,X_83)) = multiply(least_upper_bound(X_84,X_85),X_83) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(X_84,X_85),X_83))),bind(Y0,$fot(least_upper_bound(multiply(X_84,X_83),multiply(X_85,X_83))))]]) ).
cnf(refute_0_535,plain,
least_upper_bound(multiply(X_84,X_83),multiply(X_85,X_83)) = multiply(least_upper_bound(X_84,X_85),X_83),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_84,X_85),X_83),least_upper_bound(multiply(X_84,X_83),multiply(X_85,X_83))) )],[refute_0_533,refute_0_534]) ).
cnf(refute_0_536,plain,
( least_upper_bound(multiply(X_84,X_83),multiply(X_85,X_83)) != multiply(least_upper_bound(X_84,X_85),X_83)
| least_upper_bound(multiply(X_84,X_83),least_upper_bound(multiply(X_84,X_83),multiply(X_85,X_83))) != least_upper_bound(multiply(X_84,X_83),multiply(X_85,X_83))
| least_upper_bound(multiply(X_84,X_83),least_upper_bound(multiply(X_84,X_83),multiply(X_85,X_83))) = multiply(least_upper_bound(X_84,X_85),X_83) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_84,X_83),least_upper_bound(multiply(X_84,X_83),multiply(X_85,X_83))),least_upper_bound(multiply(X_84,X_83),multiply(X_85,X_83))) ),[1],$fot(multiply(least_upper_bound(X_84,X_85),X_83))]]) ).
cnf(refute_0_537,plain,
( least_upper_bound(multiply(X_84,X_83),least_upper_bound(multiply(X_84,X_83),multiply(X_85,X_83))) != least_upper_bound(multiply(X_84,X_83),multiply(X_85,X_83))
| least_upper_bound(multiply(X_84,X_83),least_upper_bound(multiply(X_84,X_83),multiply(X_85,X_83))) = multiply(least_upper_bound(X_84,X_85),X_83) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_84,X_83),multiply(X_85,X_83)),multiply(least_upper_bound(X_84,X_85),X_83)) )],[refute_0_535,refute_0_536]) ).
cnf(refute_0_538,plain,
least_upper_bound(multiply(X_84,X_83),least_upper_bound(multiply(X_84,X_83),multiply(X_85,X_83))) = multiply(least_upper_bound(X_84,X_85),X_83),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_84,X_83),least_upper_bound(multiply(X_84,X_83),multiply(X_85,X_83))),least_upper_bound(multiply(X_84,X_83),multiply(X_85,X_83))) )],[refute_0_532,refute_0_537]) ).
cnf(refute_0_539,plain,
least_upper_bound(X_84,X_84) = X_84,
inference(subst,[],[idempotence_of_lub:[bind(X,$fot(X_84))]]) ).
cnf(refute_0_540,plain,
least_upper_bound(X_85,least_upper_bound(X_84,X_84)) = least_upper_bound(X_85,least_upper_bound(X_84,X_84)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_85,least_upper_bound(X_84,X_84)))]]) ).
cnf(refute_0_541,plain,
( least_upper_bound(X_84,X_84) != X_84
| least_upper_bound(X_85,least_upper_bound(X_84,X_84)) != least_upper_bound(X_85,least_upper_bound(X_84,X_84))
| least_upper_bound(X_85,least_upper_bound(X_84,X_84)) = least_upper_bound(X_85,X_84) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_85,least_upper_bound(X_84,X_84)),least_upper_bound(X_85,least_upper_bound(X_84,X_84))) ),[1,1],$fot(X_84)]]) ).
cnf(refute_0_542,plain,
( least_upper_bound(X_84,X_84) != X_84
| least_upper_bound(X_85,least_upper_bound(X_84,X_84)) = least_upper_bound(X_85,X_84) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_85,least_upper_bound(X_84,X_84)),least_upper_bound(X_85,least_upper_bound(X_84,X_84))) )],[refute_0_540,refute_0_541]) ).
cnf(refute_0_543,plain,
least_upper_bound(X_85,least_upper_bound(X_84,X_84)) = least_upper_bound(X_85,X_84),
inference(resolve,[$cnf( $equal(least_upper_bound(X_84,X_84),X_84) )],[refute_0_539,refute_0_542]) ).
cnf(refute_0_544,plain,
multiply(least_upper_bound(X_85,least_upper_bound(X_84,X_84)),X_83) = multiply(least_upper_bound(X_85,least_upper_bound(X_84,X_84)),X_83),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(X_85,least_upper_bound(X_84,X_84)),X_83))]]) ).
cnf(refute_0_545,plain,
( multiply(least_upper_bound(X_85,least_upper_bound(X_84,X_84)),X_83) != multiply(least_upper_bound(X_85,least_upper_bound(X_84,X_84)),X_83)
| least_upper_bound(X_85,least_upper_bound(X_84,X_84)) != least_upper_bound(X_85,X_84)
| multiply(least_upper_bound(X_85,least_upper_bound(X_84,X_84)),X_83) = multiply(least_upper_bound(X_85,X_84),X_83) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_85,least_upper_bound(X_84,X_84)),X_83),multiply(least_upper_bound(X_85,least_upper_bound(X_84,X_84)),X_83)) ),[1,0],$fot(least_upper_bound(X_85,X_84))]]) ).
cnf(refute_0_546,plain,
( least_upper_bound(X_85,least_upper_bound(X_84,X_84)) != least_upper_bound(X_85,X_84)
| multiply(least_upper_bound(X_85,least_upper_bound(X_84,X_84)),X_83) = multiply(least_upper_bound(X_85,X_84),X_83) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_85,least_upper_bound(X_84,X_84)),X_83),multiply(least_upper_bound(X_85,least_upper_bound(X_84,X_84)),X_83)) )],[refute_0_544,refute_0_545]) ).
cnf(refute_0_547,plain,
multiply(least_upper_bound(X_85,least_upper_bound(X_84,X_84)),X_83) = multiply(least_upper_bound(X_85,X_84),X_83),
inference(resolve,[$cnf( $equal(least_upper_bound(X_85,least_upper_bound(X_84,X_84)),least_upper_bound(X_85,X_84)) )],[refute_0_543,refute_0_546]) ).
cnf(refute_0_548,plain,
least_upper_bound(multiply(X_85,X_83),multiply(least_upper_bound(X_84,X_84),X_83)) = multiply(least_upper_bound(X_85,least_upper_bound(X_84,X_84)),X_83),
inference(subst,[],[refute_0_198:[bind(X,$fot(X_83)),bind(Y,$fot(X_85)),bind(Z,$fot(least_upper_bound(X_84,X_84)))]]) ).
cnf(refute_0_549,plain,
least_upper_bound(X,least_upper_bound(multiply(X_84,X_83),multiply(X_85,X_83))) = least_upper_bound(multiply(X_84,X_83),least_upper_bound(multiply(X_85,X_83),X)),
inference(subst,[],[refute_0_127:[bind(X_31,$fot(multiply(X_84,X_83))),bind(X_32,$fot(multiply(X_85,X_83)))]]) ).
cnf(refute_0_550,plain,
( least_upper_bound(X,least_upper_bound(multiply(X_84,X_83),multiply(X_85,X_83))) != least_upper_bound(multiply(X_84,X_83),least_upper_bound(multiply(X_85,X_83),X))
| least_upper_bound(multiply(X_84,X_83),multiply(X_85,X_83)) != multiply(least_upper_bound(X_84,X_85),X_83)
| least_upper_bound(X,multiply(least_upper_bound(X_84,X_85),X_83)) = least_upper_bound(multiply(X_84,X_83),least_upper_bound(multiply(X_85,X_83),X)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(multiply(X_84,X_83),multiply(X_85,X_83))),least_upper_bound(multiply(X_84,X_83),least_upper_bound(multiply(X_85,X_83),X))) ),[0,1],$fot(multiply(least_upper_bound(X_84,X_85),X_83))]]) ).
cnf(refute_0_551,plain,
( least_upper_bound(X,least_upper_bound(multiply(X_84,X_83),multiply(X_85,X_83))) != least_upper_bound(multiply(X_84,X_83),least_upper_bound(multiply(X_85,X_83),X))
| least_upper_bound(X,multiply(least_upper_bound(X_84,X_85),X_83)) = least_upper_bound(multiply(X_84,X_83),least_upper_bound(multiply(X_85,X_83),X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_84,X_83),multiply(X_85,X_83)),multiply(least_upper_bound(X_84,X_85),X_83)) )],[refute_0_535,refute_0_550]) ).
cnf(refute_0_552,plain,
least_upper_bound(X,multiply(least_upper_bound(X_84,X_85),X_83)) = least_upper_bound(multiply(X_84,X_83),least_upper_bound(multiply(X_85,X_83),X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(multiply(X_84,X_83),multiply(X_85,X_83))),least_upper_bound(multiply(X_84,X_83),least_upper_bound(multiply(X_85,X_83),X))) )],[refute_0_549,refute_0_551]) ).
cnf(refute_0_553,plain,
( least_upper_bound(X,multiply(least_upper_bound(X_84,X_85),X_83)) != least_upper_bound(multiply(X_84,X_83),least_upper_bound(multiply(X_85,X_83),X))
| least_upper_bound(multiply(X_84,X_83),least_upper_bound(multiply(X_85,X_83),X)) = least_upper_bound(X,multiply(least_upper_bound(X_84,X_85),X_83)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X,multiply(least_upper_bound(X_84,X_85),X_83)))),bind(Y0,$fot(least_upper_bound(multiply(X_84,X_83),least_upper_bound(multiply(X_85,X_83),X))))]]) ).
cnf(refute_0_554,plain,
least_upper_bound(multiply(X_84,X_83),least_upper_bound(multiply(X_85,X_83),X)) = least_upper_bound(X,multiply(least_upper_bound(X_84,X_85),X_83)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,multiply(least_upper_bound(X_84,X_85),X_83)),least_upper_bound(multiply(X_84,X_83),least_upper_bound(multiply(X_85,X_83),X))) )],[refute_0_552,refute_0_553]) ).
cnf(refute_0_555,plain,
least_upper_bound(multiply(X_84,X_83),least_upper_bound(multiply(X_84,X_83),multiply(X_85,X_83))) = least_upper_bound(multiply(X_85,X_83),multiply(least_upper_bound(X_84,X_84),X_83)),
inference(subst,[],[refute_0_554:[bind(X,$fot(multiply(X_85,X_83))),bind(X_85,$fot(X_84))]]) ).
cnf(refute_0_556,plain,
( least_upper_bound(multiply(X_84,X_83),least_upper_bound(multiply(X_84,X_83),multiply(X_85,X_83))) != least_upper_bound(multiply(X_85,X_83),multiply(least_upper_bound(X_84,X_84),X_83))
| least_upper_bound(multiply(X_85,X_83),multiply(least_upper_bound(X_84,X_84),X_83)) != multiply(least_upper_bound(X_85,least_upper_bound(X_84,X_84)),X_83)
| least_upper_bound(multiply(X_84,X_83),least_upper_bound(multiply(X_84,X_83),multiply(X_85,X_83))) = multiply(least_upper_bound(X_85,least_upper_bound(X_84,X_84)),X_83) ),
inference(subst,[],[refute_0_136:[bind(X0,$fot(least_upper_bound(multiply(X_84,X_83),least_upper_bound(multiply(X_84,X_83),multiply(X_85,X_83))))),bind(Y0,$fot(least_upper_bound(multiply(X_85,X_83),multiply(least_upper_bound(X_84,X_84),X_83)))),bind(Z0,$fot(multiply(least_upper_bound(X_85,least_upper_bound(X_84,X_84)),X_83)))]]) ).
cnf(refute_0_557,plain,
( least_upper_bound(multiply(X_85,X_83),multiply(least_upper_bound(X_84,X_84),X_83)) != multiply(least_upper_bound(X_85,least_upper_bound(X_84,X_84)),X_83)
| least_upper_bound(multiply(X_84,X_83),least_upper_bound(multiply(X_84,X_83),multiply(X_85,X_83))) = multiply(least_upper_bound(X_85,least_upper_bound(X_84,X_84)),X_83) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_84,X_83),least_upper_bound(multiply(X_84,X_83),multiply(X_85,X_83))),least_upper_bound(multiply(X_85,X_83),multiply(least_upper_bound(X_84,X_84),X_83))) )],[refute_0_555,refute_0_556]) ).
cnf(refute_0_558,plain,
least_upper_bound(multiply(X_84,X_83),least_upper_bound(multiply(X_84,X_83),multiply(X_85,X_83))) = multiply(least_upper_bound(X_85,least_upper_bound(X_84,X_84)),X_83),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_85,X_83),multiply(least_upper_bound(X_84,X_84),X_83)),multiply(least_upper_bound(X_85,least_upper_bound(X_84,X_84)),X_83)) )],[refute_0_548,refute_0_557]) ).
cnf(refute_0_559,plain,
( multiply(least_upper_bound(X_85,least_upper_bound(X_84,X_84)),X_83) != multiply(least_upper_bound(X_85,X_84),X_83)
| least_upper_bound(multiply(X_84,X_83),least_upper_bound(multiply(X_84,X_83),multiply(X_85,X_83))) != multiply(least_upper_bound(X_85,least_upper_bound(X_84,X_84)),X_83)
| least_upper_bound(multiply(X_84,X_83),least_upper_bound(multiply(X_84,X_83),multiply(X_85,X_83))) = multiply(least_upper_bound(X_85,X_84),X_83) ),
inference(subst,[],[refute_0_136:[bind(X0,$fot(least_upper_bound(multiply(X_84,X_83),least_upper_bound(multiply(X_84,X_83),multiply(X_85,X_83))))),bind(Y0,$fot(multiply(least_upper_bound(X_85,least_upper_bound(X_84,X_84)),X_83))),bind(Z0,$fot(multiply(least_upper_bound(X_85,X_84),X_83)))]]) ).
cnf(refute_0_560,plain,
( multiply(least_upper_bound(X_85,least_upper_bound(X_84,X_84)),X_83) != multiply(least_upper_bound(X_85,X_84),X_83)
| least_upper_bound(multiply(X_84,X_83),least_upper_bound(multiply(X_84,X_83),multiply(X_85,X_83))) = multiply(least_upper_bound(X_85,X_84),X_83) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_84,X_83),least_upper_bound(multiply(X_84,X_83),multiply(X_85,X_83))),multiply(least_upper_bound(X_85,least_upper_bound(X_84,X_84)),X_83)) )],[refute_0_558,refute_0_559]) ).
cnf(refute_0_561,plain,
least_upper_bound(multiply(X_84,X_83),least_upper_bound(multiply(X_84,X_83),multiply(X_85,X_83))) = multiply(least_upper_bound(X_85,X_84),X_83),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_85,least_upper_bound(X_84,X_84)),X_83),multiply(least_upper_bound(X_85,X_84),X_83)) )],[refute_0_547,refute_0_560]) ).
cnf(refute_0_562,plain,
( least_upper_bound(multiply(X_84,X_83),least_upper_bound(multiply(X_84,X_83),multiply(X_85,X_83))) != multiply(least_upper_bound(X_84,X_85),X_83)
| least_upper_bound(multiply(X_84,X_83),least_upper_bound(multiply(X_84,X_83),multiply(X_85,X_83))) != multiply(least_upper_bound(X_85,X_84),X_83)
| multiply(least_upper_bound(X_85,X_84),X_83) = multiply(least_upper_bound(X_84,X_85),X_83) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_84,X_83),least_upper_bound(multiply(X_84,X_83),multiply(X_85,X_83))),multiply(least_upper_bound(X_84,X_85),X_83)) ),[0],$fot(multiply(least_upper_bound(X_85,X_84),X_83))]]) ).
cnf(refute_0_563,plain,
( least_upper_bound(multiply(X_84,X_83),least_upper_bound(multiply(X_84,X_83),multiply(X_85,X_83))) != multiply(least_upper_bound(X_84,X_85),X_83)
| multiply(least_upper_bound(X_85,X_84),X_83) = multiply(least_upper_bound(X_84,X_85),X_83) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_84,X_83),least_upper_bound(multiply(X_84,X_83),multiply(X_85,X_83))),multiply(least_upper_bound(X_85,X_84),X_83)) )],[refute_0_561,refute_0_562]) ).
cnf(refute_0_564,plain,
multiply(least_upper_bound(X_85,X_84),X_83) = multiply(least_upper_bound(X_84,X_85),X_83),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_84,X_83),least_upper_bound(multiply(X_84,X_83),multiply(X_85,X_83))),multiply(least_upper_bound(X_84,X_85),X_83)) )],[refute_0_538,refute_0_563]) ).
cnf(refute_0_565,plain,
( multiply(least_upper_bound(X_85,X_84),X_83) != multiply(least_upper_bound(X_84,X_85),X_83)
| multiply(least_upper_bound(X_84,X_85),X_83) = multiply(least_upper_bound(X_85,X_84),X_83) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(X_85,X_84),X_83))),bind(Y0,$fot(multiply(least_upper_bound(X_84,X_85),X_83)))]]) ).
cnf(refute_0_566,plain,
multiply(least_upper_bound(X_84,X_85),X_83) = multiply(least_upper_bound(X_85,X_84),X_83),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_85,X_84),X_83),multiply(least_upper_bound(X_84,X_85),X_83)) )],[refute_0_564,refute_0_565]) ).
cnf(refute_0_567,plain,
multiply(least_upper_bound(least_upper_bound(X_138,identity),identity),X_17) = multiply(least_upper_bound(identity,least_upper_bound(X_138,identity)),X_17),
inference(subst,[],[refute_0_566:[bind(X_83,$fot(X_17)),bind(X_84,$fot(least_upper_bound(X_138,identity))),bind(X_85,$fot(identity))]]) ).
cnf(refute_0_568,plain,
( multiply(least_upper_bound(X_84,identity),X_83) != least_upper_bound(X_83,multiply(X_84,X_83))
| least_upper_bound(X_83,multiply(X_84,X_83)) = multiply(least_upper_bound(X_84,identity),X_83) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(X_84,identity),X_83))),bind(Y0,$fot(least_upper_bound(X_83,multiply(X_84,X_83))))]]) ).
cnf(refute_0_569,plain,
least_upper_bound(X_83,multiply(X_84,X_83)) = multiply(least_upper_bound(X_84,identity),X_83),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_84,identity),X_83),least_upper_bound(X_83,multiply(X_84,X_83))) )],[refute_0_515,refute_0_568]) ).
cnf(refute_0_570,plain,
least_upper_bound(X_17,multiply(least_upper_bound(X_138,identity),X_17)) = multiply(least_upper_bound(least_upper_bound(X_138,identity),identity),X_17),
inference(subst,[],[refute_0_569:[bind(X_83,$fot(X_17)),bind(X_84,$fot(least_upper_bound(X_138,identity)))]]) ).
cnf(refute_0_571,plain,
( multiply(least_upper_bound(least_upper_bound(X_138,identity),identity),X_17) != multiply(least_upper_bound(identity,least_upper_bound(X_138,identity)),X_17)
| least_upper_bound(X_17,multiply(least_upper_bound(X_138,identity),X_17)) != multiply(least_upper_bound(least_upper_bound(X_138,identity),identity),X_17)
| least_upper_bound(X_17,multiply(least_upper_bound(X_138,identity),X_17)) = multiply(least_upper_bound(identity,least_upper_bound(X_138,identity)),X_17) ),
inference(subst,[],[refute_0_136:[bind(X0,$fot(least_upper_bound(X_17,multiply(least_upper_bound(X_138,identity),X_17)))),bind(Y0,$fot(multiply(least_upper_bound(least_upper_bound(X_138,identity),identity),X_17))),bind(Z0,$fot(multiply(least_upper_bound(identity,least_upper_bound(X_138,identity)),X_17)))]]) ).
cnf(refute_0_572,plain,
( multiply(least_upper_bound(least_upper_bound(X_138,identity),identity),X_17) != multiply(least_upper_bound(identity,least_upper_bound(X_138,identity)),X_17)
| least_upper_bound(X_17,multiply(least_upper_bound(X_138,identity),X_17)) = multiply(least_upper_bound(identity,least_upper_bound(X_138,identity)),X_17) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,multiply(least_upper_bound(X_138,identity),X_17)),multiply(least_upper_bound(least_upper_bound(X_138,identity),identity),X_17)) )],[refute_0_570,refute_0_571]) ).
cnf(refute_0_573,plain,
least_upper_bound(X_17,multiply(least_upper_bound(X_138,identity),X_17)) = multiply(least_upper_bound(identity,least_upper_bound(X_138,identity)),X_17),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_138,identity),identity),X_17),multiply(least_upper_bound(identity,least_upper_bound(X_138,identity)),X_17)) )],[refute_0_567,refute_0_572]) ).
cnf(refute_0_574,plain,
least_upper_bound(X,least_upper_bound(X_31,multiply(X_138,X_31))) = least_upper_bound(X_31,least_upper_bound(multiply(X_138,X_31),X)),
inference(subst,[],[refute_0_127:[bind(X_32,$fot(multiply(X_138,X_31)))]]) ).
cnf(refute_0_575,plain,
multiply(least_upper_bound(X_138,identity),X_31) = least_upper_bound(X_31,multiply(X_138,X_31)),
inference(subst,[],[refute_0_515:[bind(X_83,$fot(X_31)),bind(X_84,$fot(X_138))]]) ).
cnf(refute_0_576,plain,
( multiply(least_upper_bound(X_138,identity),X_31) != least_upper_bound(X_31,multiply(X_138,X_31))
| least_upper_bound(X_31,multiply(X_138,X_31)) = multiply(least_upper_bound(X_138,identity),X_31) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(X_138,identity),X_31))),bind(Y0,$fot(least_upper_bound(X_31,multiply(X_138,X_31))))]]) ).
cnf(refute_0_577,plain,
least_upper_bound(X_31,multiply(X_138,X_31)) = multiply(least_upper_bound(X_138,identity),X_31),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_138,identity),X_31),least_upper_bound(X_31,multiply(X_138,X_31))) )],[refute_0_575,refute_0_576]) ).
cnf(refute_0_578,plain,
( least_upper_bound(X,least_upper_bound(X_31,multiply(X_138,X_31))) != least_upper_bound(X_31,least_upper_bound(multiply(X_138,X_31),X))
| least_upper_bound(X_31,multiply(X_138,X_31)) != multiply(least_upper_bound(X_138,identity),X_31)
| least_upper_bound(X,multiply(least_upper_bound(X_138,identity),X_31)) = least_upper_bound(X_31,least_upper_bound(multiply(X_138,X_31),X)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_31,multiply(X_138,X_31))),least_upper_bound(X_31,least_upper_bound(multiply(X_138,X_31),X))) ),[0,1],$fot(multiply(least_upper_bound(X_138,identity),X_31))]]) ).
cnf(refute_0_579,plain,
( least_upper_bound(X,least_upper_bound(X_31,multiply(X_138,X_31))) != least_upper_bound(X_31,least_upper_bound(multiply(X_138,X_31),X))
| least_upper_bound(X,multiply(least_upper_bound(X_138,identity),X_31)) = least_upper_bound(X_31,least_upper_bound(multiply(X_138,X_31),X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_31,multiply(X_138,X_31)),multiply(least_upper_bound(X_138,identity),X_31)) )],[refute_0_577,refute_0_578]) ).
cnf(refute_0_580,plain,
least_upper_bound(X,multiply(least_upper_bound(X_138,identity),X_31)) = least_upper_bound(X_31,least_upper_bound(multiply(X_138,X_31),X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_31,multiply(X_138,X_31))),least_upper_bound(X_31,least_upper_bound(multiply(X_138,X_31),X))) )],[refute_0_574,refute_0_579]) ).
cnf(refute_0_581,plain,
( least_upper_bound(X,multiply(least_upper_bound(X_138,identity),X_31)) != least_upper_bound(X_31,least_upper_bound(multiply(X_138,X_31),X))
| least_upper_bound(X_31,least_upper_bound(multiply(X_138,X_31),X)) = least_upper_bound(X,multiply(least_upper_bound(X_138,identity),X_31)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X,multiply(least_upper_bound(X_138,identity),X_31)))),bind(Y0,$fot(least_upper_bound(X_31,least_upper_bound(multiply(X_138,X_31),X))))]]) ).
cnf(refute_0_582,plain,
least_upper_bound(X_31,least_upper_bound(multiply(X_138,X_31),X)) = least_upper_bound(X,multiply(least_upper_bound(X_138,identity),X_31)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,multiply(least_upper_bound(X_138,identity),X_31)),least_upper_bound(X_31,least_upper_bound(multiply(X_138,X_31),X))) )],[refute_0_580,refute_0_581]) ).
cnf(refute_0_583,plain,
least_upper_bound(X_17,least_upper_bound(multiply(X_138,X_17),X_17)) = least_upper_bound(X_17,multiply(least_upper_bound(X_138,identity),X_17)),
inference(subst,[],[refute_0_582:[bind(X,$fot(X_17)),bind(X_31,$fot(X_17))]]) ).
cnf(refute_0_584,plain,
( least_upper_bound(X_17,multiply(least_upper_bound(X_138,identity),X_17)) != multiply(least_upper_bound(identity,least_upper_bound(X_138,identity)),X_17)
| least_upper_bound(X_17,least_upper_bound(multiply(X_138,X_17),X_17)) != least_upper_bound(X_17,multiply(least_upper_bound(X_138,identity),X_17))
| least_upper_bound(X_17,least_upper_bound(multiply(X_138,X_17),X_17)) = multiply(least_upper_bound(identity,least_upper_bound(X_138,identity)),X_17) ),
inference(subst,[],[refute_0_136:[bind(X0,$fot(least_upper_bound(X_17,least_upper_bound(multiply(X_138,X_17),X_17)))),bind(Y0,$fot(least_upper_bound(X_17,multiply(least_upper_bound(X_138,identity),X_17)))),bind(Z0,$fot(multiply(least_upper_bound(identity,least_upper_bound(X_138,identity)),X_17)))]]) ).
cnf(refute_0_585,plain,
( least_upper_bound(X_17,multiply(least_upper_bound(X_138,identity),X_17)) != multiply(least_upper_bound(identity,least_upper_bound(X_138,identity)),X_17)
| least_upper_bound(X_17,least_upper_bound(multiply(X_138,X_17),X_17)) = multiply(least_upper_bound(identity,least_upper_bound(X_138,identity)),X_17) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,least_upper_bound(multiply(X_138,X_17),X_17)),least_upper_bound(X_17,multiply(least_upper_bound(X_138,identity),X_17))) )],[refute_0_583,refute_0_584]) ).
cnf(refute_0_586,plain,
least_upper_bound(X_17,least_upper_bound(multiply(X_138,X_17),X_17)) = multiply(least_upper_bound(identity,least_upper_bound(X_138,identity)),X_17),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,multiply(least_upper_bound(X_138,identity),X_17)),multiply(least_upper_bound(identity,least_upper_bound(X_138,identity)),X_17)) )],[refute_0_573,refute_0_585]) ).
cnf(refute_0_587,plain,
( multiply(least_upper_bound(identity,least_upper_bound(X_138,identity)),X_17) != multiply(least_upper_bound(identity,X_138),X_17)
| least_upper_bound(X_17,least_upper_bound(multiply(X_138,X_17),X_17)) != multiply(least_upper_bound(identity,least_upper_bound(X_138,identity)),X_17)
| least_upper_bound(X_17,least_upper_bound(multiply(X_138,X_17),X_17)) = multiply(least_upper_bound(identity,X_138),X_17) ),
inference(subst,[],[refute_0_136:[bind(X0,$fot(least_upper_bound(X_17,least_upper_bound(multiply(X_138,X_17),X_17)))),bind(Y0,$fot(multiply(least_upper_bound(identity,least_upper_bound(X_138,identity)),X_17))),bind(Z0,$fot(multiply(least_upper_bound(identity,X_138),X_17)))]]) ).
cnf(refute_0_588,plain,
( multiply(least_upper_bound(identity,least_upper_bound(X_138,identity)),X_17) != multiply(least_upper_bound(identity,X_138),X_17)
| least_upper_bound(X_17,least_upper_bound(multiply(X_138,X_17),X_17)) = multiply(least_upper_bound(identity,X_138),X_17) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,least_upper_bound(multiply(X_138,X_17),X_17)),multiply(least_upper_bound(identity,least_upper_bound(X_138,identity)),X_17)) )],[refute_0_586,refute_0_587]) ).
cnf(refute_0_589,plain,
least_upper_bound(X_17,least_upper_bound(multiply(X_138,X_17),X_17)) = multiply(least_upper_bound(identity,X_138),X_17),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(X_138,identity)),X_17),multiply(least_upper_bound(identity,X_138),X_17)) )],[refute_0_531,refute_0_588]) ).
cnf(refute_0_590,plain,
( least_upper_bound(X_17,least_upper_bound(multiply(X_138,X_17),X_17)) != multiply(least_upper_bound(X_138,identity),X_17)
| least_upper_bound(X_17,least_upper_bound(multiply(X_138,X_17),X_17)) != multiply(least_upper_bound(identity,X_138),X_17)
| multiply(least_upper_bound(identity,X_138),X_17) = multiply(least_upper_bound(X_138,identity),X_17) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_17,least_upper_bound(multiply(X_138,X_17),X_17)),multiply(least_upper_bound(X_138,identity),X_17)) ),[0],$fot(multiply(least_upper_bound(identity,X_138),X_17))]]) ).
cnf(refute_0_591,plain,
( least_upper_bound(X_17,least_upper_bound(multiply(X_138,X_17),X_17)) != multiply(least_upper_bound(X_138,identity),X_17)
| multiply(least_upper_bound(identity,X_138),X_17) = multiply(least_upper_bound(X_138,identity),X_17) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,least_upper_bound(multiply(X_138,X_17),X_17)),multiply(least_upper_bound(identity,X_138),X_17)) )],[refute_0_589,refute_0_590]) ).
cnf(refute_0_592,plain,
multiply(least_upper_bound(identity,X_138),X_17) = multiply(least_upper_bound(X_138,identity),X_17),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,least_upper_bound(multiply(X_138,X_17),X_17)),multiply(least_upper_bound(X_138,identity),X_17)) )],[refute_0_526,refute_0_591]) ).
cnf(refute_0_593,plain,
( multiply(least_upper_bound(identity,X_138),X_17) != multiply(least_upper_bound(X_138,identity),X_17)
| multiply(least_upper_bound(X_138,identity),X_17) = multiply(least_upper_bound(identity,X_138),X_17) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(identity,X_138),X_17))),bind(Y0,$fot(multiply(least_upper_bound(X_138,identity),X_17)))]]) ).
cnf(refute_0_594,plain,
multiply(least_upper_bound(X_138,identity),X_17) = multiply(least_upper_bound(identity,X_138),X_17),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_138),X_17),multiply(least_upper_bound(X_138,identity),X_17)) )],[refute_0_592,refute_0_593]) ).
cnf(refute_0_595,plain,
multiply(least_upper_bound(inverse(X_22),identity),greatest_lower_bound(X_22,identity)) = multiply(least_upper_bound(identity,inverse(X_22)),greatest_lower_bound(X_22,identity)),
inference(subst,[],[refute_0_594:[bind(X_138,$fot(inverse(X_22))),bind(X_17,$fot(greatest_lower_bound(X_22,identity)))]]) ).
cnf(refute_0_596,plain,
( multiply(least_upper_bound(inverse(X_22),identity),greatest_lower_bound(X_22,identity)) != multiply(least_upper_bound(identity,inverse(X_22)),greatest_lower_bound(X_22,identity))
| multiply(least_upper_bound(inverse(X_22),identity),greatest_lower_bound(X_22,identity)) != least_upper_bound(greatest_lower_bound(X_22,identity),greatest_lower_bound(identity,inverse(X_22)))
| multiply(least_upper_bound(identity,inverse(X_22)),greatest_lower_bound(X_22,identity)) = least_upper_bound(greatest_lower_bound(X_22,identity),greatest_lower_bound(identity,inverse(X_22))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(X_22),identity),greatest_lower_bound(X_22,identity)),least_upper_bound(greatest_lower_bound(X_22,identity),greatest_lower_bound(identity,inverse(X_22)))) ),[0],$fot(multiply(least_upper_bound(identity,inverse(X_22)),greatest_lower_bound(X_22,identity)))]]) ).
cnf(refute_0_597,plain,
( multiply(least_upper_bound(inverse(X_22),identity),greatest_lower_bound(X_22,identity)) != least_upper_bound(greatest_lower_bound(X_22,identity),greatest_lower_bound(identity,inverse(X_22)))
| multiply(least_upper_bound(identity,inverse(X_22)),greatest_lower_bound(X_22,identity)) = least_upper_bound(greatest_lower_bound(X_22,identity),greatest_lower_bound(identity,inverse(X_22))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_22),identity),greatest_lower_bound(X_22,identity)),multiply(least_upper_bound(identity,inverse(X_22)),greatest_lower_bound(X_22,identity))) )],[refute_0_595,refute_0_596]) ).
cnf(refute_0_598,plain,
multiply(least_upper_bound(identity,inverse(X_22)),greatest_lower_bound(X_22,identity)) = least_upper_bound(greatest_lower_bound(X_22,identity),greatest_lower_bound(identity,inverse(X_22))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_22),identity),greatest_lower_bound(X_22,identity)),least_upper_bound(greatest_lower_bound(X_22,identity),greatest_lower_bound(identity,inverse(X_22)))) )],[refute_0_519,refute_0_597]) ).
cnf(refute_0_599,plain,
( multiply(least_upper_bound(identity,inverse(X_22)),greatest_lower_bound(X_22,identity)) != least_upper_bound(greatest_lower_bound(X_22,identity),greatest_lower_bound(identity,inverse(X_22)))
| least_upper_bound(greatest_lower_bound(X_22,identity),greatest_lower_bound(identity,inverse(X_22))) = multiply(least_upper_bound(identity,inverse(X_22)),greatest_lower_bound(X_22,identity)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(identity,inverse(X_22)),greatest_lower_bound(X_22,identity)))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(X_22,identity),greatest_lower_bound(identity,inverse(X_22)))))]]) ).
cnf(refute_0_600,plain,
least_upper_bound(greatest_lower_bound(X_22,identity),greatest_lower_bound(identity,inverse(X_22))) = multiply(least_upper_bound(identity,inverse(X_22)),greatest_lower_bound(X_22,identity)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_22)),greatest_lower_bound(X_22,identity)),least_upper_bound(greatest_lower_bound(X_22,identity),greatest_lower_bound(identity,inverse(X_22)))) )],[refute_0_598,refute_0_599]) ).
cnf(refute_0_601,plain,
least_upper_bound(greatest_lower_bound(X_146,identity),greatest_lower_bound(identity,inverse(X_146))) = multiply(least_upper_bound(identity,inverse(X_146)),greatest_lower_bound(X_146,identity)),
inference(subst,[],[refute_0_600:[bind(X_22,$fot(X_146))]]) ).
cnf(refute_0_602,plain,
( multiply(greatest_lower_bound(X_146,identity),least_upper_bound(identity,inverse(X_146))) != least_upper_bound(greatest_lower_bound(X_146,identity),greatest_lower_bound(identity,inverse(X_146)))
| least_upper_bound(greatest_lower_bound(X_146,identity),greatest_lower_bound(identity,inverse(X_146))) != multiply(least_upper_bound(identity,inverse(X_146)),greatest_lower_bound(X_146,identity))
| multiply(greatest_lower_bound(X_146,identity),least_upper_bound(identity,inverse(X_146))) = multiply(least_upper_bound(identity,inverse(X_146)),greatest_lower_bound(X_146,identity)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_146,identity),least_upper_bound(identity,inverse(X_146))),multiply(least_upper_bound(identity,inverse(X_146)),greatest_lower_bound(X_146,identity))) ),[0],$fot(least_upper_bound(greatest_lower_bound(X_146,identity),greatest_lower_bound(identity,inverse(X_146))))]]) ).
cnf(refute_0_603,plain,
( multiply(greatest_lower_bound(X_146,identity),least_upper_bound(identity,inverse(X_146))) != least_upper_bound(greatest_lower_bound(X_146,identity),greatest_lower_bound(identity,inverse(X_146)))
| multiply(greatest_lower_bound(X_146,identity),least_upper_bound(identity,inverse(X_146))) = multiply(least_upper_bound(identity,inverse(X_146)),greatest_lower_bound(X_146,identity)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_146,identity),greatest_lower_bound(identity,inverse(X_146))),multiply(least_upper_bound(identity,inverse(X_146)),greatest_lower_bound(X_146,identity))) )],[refute_0_601,refute_0_602]) ).
cnf(refute_0_604,plain,
( multiply(greatest_lower_bound(X_146,identity),least_upper_bound(inverse(X_146),identity)) != least_upper_bound(greatest_lower_bound(X_146,identity),greatest_lower_bound(identity,inverse(X_146)))
| multiply(greatest_lower_bound(X_146,identity),least_upper_bound(identity,inverse(X_146))) = multiply(least_upper_bound(identity,inverse(X_146)),greatest_lower_bound(X_146,identity)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_146,identity),least_upper_bound(identity,inverse(X_146))),least_upper_bound(greatest_lower_bound(X_146,identity),greatest_lower_bound(identity,inverse(X_146)))) )],[refute_0_506,refute_0_603]) ).
cnf(refute_0_605,plain,
multiply(greatest_lower_bound(X_146,identity),least_upper_bound(identity,inverse(X_146))) = multiply(least_upper_bound(identity,inverse(X_146)),greatest_lower_bound(X_146,identity)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_146,identity),least_upper_bound(inverse(X_146),identity)),least_upper_bound(greatest_lower_bound(X_146,identity),greatest_lower_bound(identity,inverse(X_146)))) )],[refute_0_463,refute_0_604]) ).
cnf(refute_0_606,plain,
( multiply(greatest_lower_bound(X_146,identity),least_upper_bound(identity,inverse(X_146))) != multiply(least_upper_bound(identity,inverse(X_146)),greatest_lower_bound(X_146,identity))
| multiply(least_upper_bound(identity,inverse(X_146)),greatest_lower_bound(X_146,identity)) = multiply(greatest_lower_bound(X_146,identity),least_upper_bound(identity,inverse(X_146))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(greatest_lower_bound(X_146,identity),least_upper_bound(identity,inverse(X_146))))),bind(Y0,$fot(multiply(least_upper_bound(identity,inverse(X_146)),greatest_lower_bound(X_146,identity))))]]) ).
cnf(refute_0_607,plain,
multiply(least_upper_bound(identity,inverse(X_146)),greatest_lower_bound(X_146,identity)) = multiply(greatest_lower_bound(X_146,identity),least_upper_bound(identity,inverse(X_146))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_146,identity),least_upper_bound(identity,inverse(X_146))),multiply(least_upper_bound(identity,inverse(X_146)),greatest_lower_bound(X_146,identity))) )],[refute_0_605,refute_0_606]) ).
cnf(refute_0_608,plain,
multiply(least_upper_bound(identity,inverse(X_202)),greatest_lower_bound(X_202,identity)) = multiply(greatest_lower_bound(X_202,identity),least_upper_bound(identity,inverse(X_202))),
inference(subst,[],[refute_0_607:[bind(X_146,$fot(X_202))]]) ).
cnf(refute_0_609,plain,
( multiply(least_upper_bound(identity,inverse(X_202)),greatest_lower_bound(X_202,identity)) != multiply(greatest_lower_bound(X_202,identity),least_upper_bound(identity,inverse(X_202)))
| multiply(least_upper_bound(identity,inverse(X_202)),greatest_lower_bound(X_202,identity)) != least_upper_bound(greatest_lower_bound(identity,inverse(X_202)),greatest_lower_bound(X_202,identity))
| multiply(greatest_lower_bound(X_202,identity),least_upper_bound(identity,inverse(X_202))) = least_upper_bound(greatest_lower_bound(identity,inverse(X_202)),greatest_lower_bound(X_202,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_202)),greatest_lower_bound(X_202,identity)),least_upper_bound(greatest_lower_bound(identity,inverse(X_202)),greatest_lower_bound(X_202,identity))) ),[0],$fot(multiply(greatest_lower_bound(X_202,identity),least_upper_bound(identity,inverse(X_202))))]]) ).
cnf(refute_0_610,plain,
( multiply(least_upper_bound(identity,inverse(X_202)),greatest_lower_bound(X_202,identity)) != least_upper_bound(greatest_lower_bound(identity,inverse(X_202)),greatest_lower_bound(X_202,identity))
| multiply(greatest_lower_bound(X_202,identity),least_upper_bound(identity,inverse(X_202))) = least_upper_bound(greatest_lower_bound(identity,inverse(X_202)),greatest_lower_bound(X_202,identity)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_202)),greatest_lower_bound(X_202,identity)),multiply(greatest_lower_bound(X_202,identity),least_upper_bound(identity,inverse(X_202)))) )],[refute_0_608,refute_0_609]) ).
cnf(refute_0_611,plain,
multiply(least_upper_bound(inverse(X_23),identity),greatest_lower_bound(identity,X_23)) = least_upper_bound(greatest_lower_bound(identity,X_23),multiply(inverse(X_23),greatest_lower_bound(identity,X_23))),
inference(subst,[],[refute_0_515:[bind(X_83,$fot(greatest_lower_bound(identity,X_23))),bind(X_84,$fot(inverse(X_23)))]]) ).
cnf(refute_0_612,plain,
( multiply(inverse(X_23),greatest_lower_bound(identity,X_23)) != greatest_lower_bound(identity,inverse(X_23))
| multiply(least_upper_bound(inverse(X_23),identity),greatest_lower_bound(identity,X_23)) != least_upper_bound(greatest_lower_bound(identity,X_23),multiply(inverse(X_23),greatest_lower_bound(identity,X_23)))
| multiply(least_upper_bound(inverse(X_23),identity),greatest_lower_bound(identity,X_23)) = least_upper_bound(greatest_lower_bound(identity,X_23),greatest_lower_bound(identity,inverse(X_23))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(X_23),identity),greatest_lower_bound(identity,X_23)),least_upper_bound(greatest_lower_bound(identity,X_23),multiply(inverse(X_23),greatest_lower_bound(identity,X_23)))) ),[1,1],$fot(greatest_lower_bound(identity,inverse(X_23)))]]) ).
cnf(refute_0_613,plain,
( multiply(least_upper_bound(inverse(X_23),identity),greatest_lower_bound(identity,X_23)) != least_upper_bound(greatest_lower_bound(identity,X_23),multiply(inverse(X_23),greatest_lower_bound(identity,X_23)))
| multiply(least_upper_bound(inverse(X_23),identity),greatest_lower_bound(identity,X_23)) = least_upper_bound(greatest_lower_bound(identity,X_23),greatest_lower_bound(identity,inverse(X_23))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_23),greatest_lower_bound(identity,X_23)),greatest_lower_bound(identity,inverse(X_23))) )],[refute_0_276,refute_0_612]) ).
cnf(refute_0_614,plain,
multiply(least_upper_bound(inverse(X_23),identity),greatest_lower_bound(identity,X_23)) = least_upper_bound(greatest_lower_bound(identity,X_23),greatest_lower_bound(identity,inverse(X_23))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_23),identity),greatest_lower_bound(identity,X_23)),least_upper_bound(greatest_lower_bound(identity,X_23),multiply(inverse(X_23),greatest_lower_bound(identity,X_23)))) )],[refute_0_611,refute_0_613]) ).
cnf(refute_0_615,plain,
multiply(least_upper_bound(inverse(X_23),identity),greatest_lower_bound(identity,X_23)) = multiply(least_upper_bound(identity,inverse(X_23)),greatest_lower_bound(identity,X_23)),
inference(subst,[],[refute_0_594:[bind(X_138,$fot(inverse(X_23))),bind(X_17,$fot(greatest_lower_bound(identity,X_23)))]]) ).
cnf(refute_0_616,plain,
( multiply(least_upper_bound(inverse(X_23),identity),greatest_lower_bound(identity,X_23)) != multiply(least_upper_bound(identity,inverse(X_23)),greatest_lower_bound(identity,X_23))
| multiply(least_upper_bound(inverse(X_23),identity),greatest_lower_bound(identity,X_23)) != least_upper_bound(greatest_lower_bound(identity,X_23),greatest_lower_bound(identity,inverse(X_23)))
| multiply(least_upper_bound(identity,inverse(X_23)),greatest_lower_bound(identity,X_23)) = least_upper_bound(greatest_lower_bound(identity,X_23),greatest_lower_bound(identity,inverse(X_23))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(X_23),identity),greatest_lower_bound(identity,X_23)),least_upper_bound(greatest_lower_bound(identity,X_23),greatest_lower_bound(identity,inverse(X_23)))) ),[0],$fot(multiply(least_upper_bound(identity,inverse(X_23)),greatest_lower_bound(identity,X_23)))]]) ).
cnf(refute_0_617,plain,
( multiply(least_upper_bound(inverse(X_23),identity),greatest_lower_bound(identity,X_23)) != least_upper_bound(greatest_lower_bound(identity,X_23),greatest_lower_bound(identity,inverse(X_23)))
| multiply(least_upper_bound(identity,inverse(X_23)),greatest_lower_bound(identity,X_23)) = least_upper_bound(greatest_lower_bound(identity,X_23),greatest_lower_bound(identity,inverse(X_23))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_23),identity),greatest_lower_bound(identity,X_23)),multiply(least_upper_bound(identity,inverse(X_23)),greatest_lower_bound(identity,X_23))) )],[refute_0_615,refute_0_616]) ).
cnf(refute_0_618,plain,
multiply(least_upper_bound(identity,inverse(X_23)),greatest_lower_bound(identity,X_23)) = least_upper_bound(greatest_lower_bound(identity,X_23),greatest_lower_bound(identity,inverse(X_23))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_23),identity),greatest_lower_bound(identity,X_23)),least_upper_bound(greatest_lower_bound(identity,X_23),greatest_lower_bound(identity,inverse(X_23)))) )],[refute_0_614,refute_0_617]) ).
cnf(refute_0_619,plain,
( multiply(least_upper_bound(identity,inverse(X_23)),greatest_lower_bound(identity,X_23)) != least_upper_bound(greatest_lower_bound(identity,X_23),greatest_lower_bound(identity,inverse(X_23)))
| least_upper_bound(greatest_lower_bound(identity,X_23),greatest_lower_bound(identity,inverse(X_23))) = multiply(least_upper_bound(identity,inverse(X_23)),greatest_lower_bound(identity,X_23)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(identity,inverse(X_23)),greatest_lower_bound(identity,X_23)))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(identity,X_23),greatest_lower_bound(identity,inverse(X_23)))))]]) ).
cnf(refute_0_620,plain,
least_upper_bound(greatest_lower_bound(identity,X_23),greatest_lower_bound(identity,inverse(X_23))) = multiply(least_upper_bound(identity,inverse(X_23)),greatest_lower_bound(identity,X_23)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_23)),greatest_lower_bound(identity,X_23)),least_upper_bound(greatest_lower_bound(identity,X_23),greatest_lower_bound(identity,inverse(X_23)))) )],[refute_0_618,refute_0_619]) ).
cnf(refute_0_621,plain,
least_upper_bound(greatest_lower_bound(identity,X_202),greatest_lower_bound(identity,inverse(X_202))) = multiply(least_upper_bound(identity,inverse(X_202)),greatest_lower_bound(identity,X_202)),
inference(subst,[],[refute_0_620:[bind(X_23,$fot(X_202))]]) ).
cnf(refute_0_622,plain,
least_upper_bound(greatest_lower_bound(X_174,X_176),Y) = least_upper_bound(Y,greatest_lower_bound(X_174,X_176)),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(greatest_lower_bound(X_174,X_176)))]]) ).
cnf(refute_0_623,plain,
least_upper_bound(greatest_lower_bound(X_100,X_99),least_upper_bound(X_31,greatest_lower_bound(X_99,X_100))) = least_upper_bound(X_31,least_upper_bound(greatest_lower_bound(X_99,X_100),greatest_lower_bound(X_100,X_99))),
inference(subst,[],[refute_0_127:[bind(X,$fot(greatest_lower_bound(X_100,X_99))),bind(X_32,$fot(greatest_lower_bound(X_99,X_100)))]]) ).
cnf(refute_0_624,plain,
least_upper_bound(greatest_lower_bound(X_99,X_100),greatest_lower_bound(X_100,X_99)) = greatest_lower_bound(X_99,X_100),
inference(subst,[],[refute_0_185:[bind(X_13,$fot(X_99)),bind(X_17,$fot(X_100))]]) ).
cnf(refute_0_625,plain,
( least_upper_bound(greatest_lower_bound(X_100,X_99),least_upper_bound(X_31,greatest_lower_bound(X_99,X_100))) != least_upper_bound(X_31,least_upper_bound(greatest_lower_bound(X_99,X_100),greatest_lower_bound(X_100,X_99)))
| least_upper_bound(greatest_lower_bound(X_99,X_100),greatest_lower_bound(X_100,X_99)) != greatest_lower_bound(X_99,X_100)
| least_upper_bound(greatest_lower_bound(X_100,X_99),least_upper_bound(X_31,greatest_lower_bound(X_99,X_100))) = least_upper_bound(X_31,greatest_lower_bound(X_99,X_100)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_100,X_99),least_upper_bound(X_31,greatest_lower_bound(X_99,X_100))),least_upper_bound(X_31,least_upper_bound(greatest_lower_bound(X_99,X_100),greatest_lower_bound(X_100,X_99)))) ),[1,1],$fot(greatest_lower_bound(X_99,X_100))]]) ).
cnf(refute_0_626,plain,
( least_upper_bound(greatest_lower_bound(X_100,X_99),least_upper_bound(X_31,greatest_lower_bound(X_99,X_100))) != least_upper_bound(X_31,least_upper_bound(greatest_lower_bound(X_99,X_100),greatest_lower_bound(X_100,X_99)))
| least_upper_bound(greatest_lower_bound(X_100,X_99),least_upper_bound(X_31,greatest_lower_bound(X_99,X_100))) = least_upper_bound(X_31,greatest_lower_bound(X_99,X_100)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_99,X_100),greatest_lower_bound(X_100,X_99)),greatest_lower_bound(X_99,X_100)) )],[refute_0_624,refute_0_625]) ).
cnf(refute_0_627,plain,
least_upper_bound(greatest_lower_bound(X_100,X_99),least_upper_bound(X_31,greatest_lower_bound(X_99,X_100))) = least_upper_bound(X_31,greatest_lower_bound(X_99,X_100)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_100,X_99),least_upper_bound(X_31,greatest_lower_bound(X_99,X_100))),least_upper_bound(X_31,least_upper_bound(greatest_lower_bound(X_99,X_100),greatest_lower_bound(X_100,X_99)))) )],[refute_0_623,refute_0_626]) ).
cnf(refute_0_628,plain,
least_upper_bound(X_31,least_upper_bound(X_32,X_33)) = least_upper_bound(least_upper_bound(X_31,X_32),X_33),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_31)),bind(Y,$fot(X_32)),bind(Z,$fot(X_33))]]) ).
cnf(refute_0_629,plain,
least_upper_bound(X_32,X_31) = least_upper_bound(X_31,X_32),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_32)),bind(Y,$fot(X_31))]]) ).
cnf(refute_0_630,plain,
( least_upper_bound(X_32,X_31) != least_upper_bound(X_31,X_32)
| least_upper_bound(X_31,X_32) = least_upper_bound(X_32,X_31) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X_32,X_31))),bind(Y0,$fot(least_upper_bound(X_31,X_32)))]]) ).
cnf(refute_0_631,plain,
least_upper_bound(X_31,X_32) = least_upper_bound(X_32,X_31),
inference(resolve,[$cnf( $equal(least_upper_bound(X_32,X_31),least_upper_bound(X_31,X_32)) )],[refute_0_629,refute_0_630]) ).
cnf(refute_0_632,plain,
( least_upper_bound(X_31,X_32) != least_upper_bound(X_32,X_31)
| least_upper_bound(X_31,least_upper_bound(X_32,X_33)) != least_upper_bound(least_upper_bound(X_31,X_32),X_33)
| least_upper_bound(X_31,least_upper_bound(X_32,X_33)) = least_upper_bound(least_upper_bound(X_32,X_31),X_33) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_31,least_upper_bound(X_32,X_33)),least_upper_bound(least_upper_bound(X_31,X_32),X_33)) ),[1,0],$fot(least_upper_bound(X_32,X_31))]]) ).
cnf(refute_0_633,plain,
( least_upper_bound(X_31,least_upper_bound(X_32,X_33)) != least_upper_bound(least_upper_bound(X_31,X_32),X_33)
| least_upper_bound(X_31,least_upper_bound(X_32,X_33)) = least_upper_bound(least_upper_bound(X_32,X_31),X_33) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_31,X_32),least_upper_bound(X_32,X_31)) )],[refute_0_631,refute_0_632]) ).
cnf(refute_0_634,plain,
least_upper_bound(X_31,least_upper_bound(X_32,X_33)) = least_upper_bound(least_upper_bound(X_32,X_31),X_33),
inference(resolve,[$cnf( $equal(least_upper_bound(X_31,least_upper_bound(X_32,X_33)),least_upper_bound(least_upper_bound(X_31,X_32),X_33)) )],[refute_0_628,refute_0_633]) ).
cnf(refute_0_635,plain,
least_upper_bound(least_upper_bound(X_32,X_31),X_33) = least_upper_bound(X_32,least_upper_bound(X_31,X_33)),
inference(subst,[],[refute_0_87:[bind(X,$fot(X_32)),bind(Y,$fot(X_31)),bind(Z,$fot(X_33))]]) ).
cnf(refute_0_636,plain,
( least_upper_bound(X_31,least_upper_bound(X_32,X_33)) != least_upper_bound(least_upper_bound(X_32,X_31),X_33)
| least_upper_bound(least_upper_bound(X_32,X_31),X_33) != least_upper_bound(X_32,least_upper_bound(X_31,X_33))
| least_upper_bound(X_31,least_upper_bound(X_32,X_33)) = least_upper_bound(X_32,least_upper_bound(X_31,X_33)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_31,least_upper_bound(X_32,X_33)),least_upper_bound(X_32,least_upper_bound(X_31,X_33))) ),[0],$fot(least_upper_bound(least_upper_bound(X_32,X_31),X_33))]]) ).
cnf(refute_0_637,plain,
( least_upper_bound(X_31,least_upper_bound(X_32,X_33)) != least_upper_bound(least_upper_bound(X_32,X_31),X_33)
| least_upper_bound(X_31,least_upper_bound(X_32,X_33)) = least_upper_bound(X_32,least_upper_bound(X_31,X_33)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_32,X_31),X_33),least_upper_bound(X_32,least_upper_bound(X_31,X_33))) )],[refute_0_635,refute_0_636]) ).
cnf(refute_0_638,plain,
least_upper_bound(X_31,least_upper_bound(X_32,X_33)) = least_upper_bound(X_32,least_upper_bound(X_31,X_33)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_31,least_upper_bound(X_32,X_33)),least_upper_bound(least_upper_bound(X_32,X_31),X_33)) )],[refute_0_634,refute_0_637]) ).
cnf(refute_0_639,plain,
least_upper_bound(greatest_lower_bound(X_99,X_100),least_upper_bound(X_32,greatest_lower_bound(X_100,X_99))) = least_upper_bound(X_32,least_upper_bound(greatest_lower_bound(X_99,X_100),greatest_lower_bound(X_100,X_99))),
inference(subst,[],[refute_0_638:[bind(X_31,$fot(greatest_lower_bound(X_99,X_100))),bind(X_33,$fot(greatest_lower_bound(X_100,X_99)))]]) ).
cnf(refute_0_640,plain,
( least_upper_bound(greatest_lower_bound(X_99,X_100),greatest_lower_bound(X_100,X_99)) != greatest_lower_bound(X_99,X_100)
| least_upper_bound(greatest_lower_bound(X_99,X_100),least_upper_bound(X_32,greatest_lower_bound(X_100,X_99))) != least_upper_bound(X_32,least_upper_bound(greatest_lower_bound(X_99,X_100),greatest_lower_bound(X_100,X_99)))
| least_upper_bound(greatest_lower_bound(X_99,X_100),least_upper_bound(X_32,greatest_lower_bound(X_100,X_99))) = least_upper_bound(X_32,greatest_lower_bound(X_99,X_100)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_99,X_100),least_upper_bound(X_32,greatest_lower_bound(X_100,X_99))),least_upper_bound(X_32,least_upper_bound(greatest_lower_bound(X_99,X_100),greatest_lower_bound(X_100,X_99)))) ),[1,1],$fot(greatest_lower_bound(X_99,X_100))]]) ).
cnf(refute_0_641,plain,
( least_upper_bound(greatest_lower_bound(X_99,X_100),least_upper_bound(X_32,greatest_lower_bound(X_100,X_99))) != least_upper_bound(X_32,least_upper_bound(greatest_lower_bound(X_99,X_100),greatest_lower_bound(X_100,X_99)))
| least_upper_bound(greatest_lower_bound(X_99,X_100),least_upper_bound(X_32,greatest_lower_bound(X_100,X_99))) = least_upper_bound(X_32,greatest_lower_bound(X_99,X_100)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_99,X_100),greatest_lower_bound(X_100,X_99)),greatest_lower_bound(X_99,X_100)) )],[refute_0_624,refute_0_640]) ).
cnf(refute_0_642,plain,
least_upper_bound(greatest_lower_bound(X_99,X_100),least_upper_bound(X_32,greatest_lower_bound(X_100,X_99))) = least_upper_bound(X_32,greatest_lower_bound(X_99,X_100)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_99,X_100),least_upper_bound(X_32,greatest_lower_bound(X_100,X_99))),least_upper_bound(X_32,least_upper_bound(greatest_lower_bound(X_99,X_100),greatest_lower_bound(X_100,X_99)))) )],[refute_0_639,refute_0_641]) ).
cnf(refute_0_643,plain,
least_upper_bound(greatest_lower_bound(X_100,X_99),least_upper_bound(X_31,greatest_lower_bound(X_99,X_100))) = least_upper_bound(X_31,greatest_lower_bound(X_100,X_99)),
inference(subst,[],[refute_0_642:[bind(X_100,$fot(X_99)),bind(X_32,$fot(X_31)),bind(X_99,$fot(X_100))]]) ).
cnf(refute_0_644,plain,
( least_upper_bound(greatest_lower_bound(X_100,X_99),least_upper_bound(X_31,greatest_lower_bound(X_99,X_100))) != least_upper_bound(X_31,greatest_lower_bound(X_100,X_99))
| least_upper_bound(greatest_lower_bound(X_100,X_99),least_upper_bound(X_31,greatest_lower_bound(X_99,X_100))) != least_upper_bound(X_31,greatest_lower_bound(X_99,X_100))
| least_upper_bound(X_31,greatest_lower_bound(X_100,X_99)) = least_upper_bound(X_31,greatest_lower_bound(X_99,X_100)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_100,X_99),least_upper_bound(X_31,greatest_lower_bound(X_99,X_100))),least_upper_bound(X_31,greatest_lower_bound(X_99,X_100))) ),[0],$fot(least_upper_bound(X_31,greatest_lower_bound(X_100,X_99)))]]) ).
cnf(refute_0_645,plain,
( least_upper_bound(greatest_lower_bound(X_100,X_99),least_upper_bound(X_31,greatest_lower_bound(X_99,X_100))) != least_upper_bound(X_31,greatest_lower_bound(X_99,X_100))
| least_upper_bound(X_31,greatest_lower_bound(X_100,X_99)) = least_upper_bound(X_31,greatest_lower_bound(X_99,X_100)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_100,X_99),least_upper_bound(X_31,greatest_lower_bound(X_99,X_100))),least_upper_bound(X_31,greatest_lower_bound(X_100,X_99))) )],[refute_0_643,refute_0_644]) ).
cnf(refute_0_646,plain,
least_upper_bound(X_31,greatest_lower_bound(X_100,X_99)) = least_upper_bound(X_31,greatest_lower_bound(X_99,X_100)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_100,X_99),least_upper_bound(X_31,greatest_lower_bound(X_99,X_100))),least_upper_bound(X_31,greatest_lower_bound(X_99,X_100))) )],[refute_0_627,refute_0_645]) ).
cnf(refute_0_647,plain,
least_upper_bound(Y,greatest_lower_bound(X_174,X_176)) = least_upper_bound(Y,greatest_lower_bound(X_176,X_174)),
inference(subst,[],[refute_0_646:[bind(X_100,$fot(X_174)),bind(X_31,$fot(Y)),bind(X_99,$fot(X_176))]]) ).
cnf(refute_0_648,plain,
( least_upper_bound(Y,greatest_lower_bound(X_174,X_176)) != least_upper_bound(Y,greatest_lower_bound(X_176,X_174))
| least_upper_bound(greatest_lower_bound(X_174,X_176),Y) != least_upper_bound(Y,greatest_lower_bound(X_174,X_176))
| least_upper_bound(greatest_lower_bound(X_174,X_176),Y) = least_upper_bound(Y,greatest_lower_bound(X_176,X_174)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_174,X_176),Y),least_upper_bound(Y,greatest_lower_bound(X_174,X_176))) ),[1],$fot(least_upper_bound(Y,greatest_lower_bound(X_176,X_174)))]]) ).
cnf(refute_0_649,plain,
( least_upper_bound(greatest_lower_bound(X_174,X_176),Y) != least_upper_bound(Y,greatest_lower_bound(X_174,X_176))
| least_upper_bound(greatest_lower_bound(X_174,X_176),Y) = least_upper_bound(Y,greatest_lower_bound(X_176,X_174)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,greatest_lower_bound(X_174,X_176)),least_upper_bound(Y,greatest_lower_bound(X_176,X_174))) )],[refute_0_647,refute_0_648]) ).
cnf(refute_0_650,plain,
least_upper_bound(greatest_lower_bound(X_174,X_176),Y) = least_upper_bound(Y,greatest_lower_bound(X_176,X_174)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_174,X_176),Y),least_upper_bound(Y,greatest_lower_bound(X_174,X_176))) )],[refute_0_622,refute_0_649]) ).
cnf(refute_0_651,plain,
( least_upper_bound(greatest_lower_bound(X_174,X_176),Y) != least_upper_bound(Y,greatest_lower_bound(X_176,X_174))
| least_upper_bound(Y,greatest_lower_bound(X_176,X_174)) = least_upper_bound(greatest_lower_bound(X_174,X_176),Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(X_174,X_176),Y))),bind(Y0,$fot(least_upper_bound(Y,greatest_lower_bound(X_176,X_174))))]]) ).
cnf(refute_0_652,plain,
least_upper_bound(Y,greatest_lower_bound(X_176,X_174)) = least_upper_bound(greatest_lower_bound(X_174,X_176),Y),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_174,X_176),Y),least_upper_bound(Y,greatest_lower_bound(X_176,X_174))) )],[refute_0_650,refute_0_651]) ).
cnf(refute_0_653,plain,
least_upper_bound(greatest_lower_bound(identity,inverse(X_202)),greatest_lower_bound(X_202,identity)) = least_upper_bound(greatest_lower_bound(identity,X_202),greatest_lower_bound(identity,inverse(X_202))),
inference(subst,[],[refute_0_652:[bind(Y,$fot(greatest_lower_bound(identity,inverse(X_202)))),bind(X_174,$fot(identity)),bind(X_176,$fot(X_202))]]) ).
cnf(refute_0_654,plain,
( least_upper_bound(greatest_lower_bound(identity,X_202),greatest_lower_bound(identity,inverse(X_202))) != multiply(least_upper_bound(identity,inverse(X_202)),greatest_lower_bound(identity,X_202))
| least_upper_bound(greatest_lower_bound(identity,inverse(X_202)),greatest_lower_bound(X_202,identity)) != least_upper_bound(greatest_lower_bound(identity,X_202),greatest_lower_bound(identity,inverse(X_202)))
| least_upper_bound(greatest_lower_bound(identity,inverse(X_202)),greatest_lower_bound(X_202,identity)) = multiply(least_upper_bound(identity,inverse(X_202)),greatest_lower_bound(identity,X_202)) ),
inference(subst,[],[refute_0_136:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(identity,inverse(X_202)),greatest_lower_bound(X_202,identity)))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(identity,X_202),greatest_lower_bound(identity,inverse(X_202))))),bind(Z0,$fot(multiply(least_upper_bound(identity,inverse(X_202)),greatest_lower_bound(identity,X_202))))]]) ).
cnf(refute_0_655,plain,
( least_upper_bound(greatest_lower_bound(identity,X_202),greatest_lower_bound(identity,inverse(X_202))) != multiply(least_upper_bound(identity,inverse(X_202)),greatest_lower_bound(identity,X_202))
| least_upper_bound(greatest_lower_bound(identity,inverse(X_202)),greatest_lower_bound(X_202,identity)) = multiply(least_upper_bound(identity,inverse(X_202)),greatest_lower_bound(identity,X_202)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,inverse(X_202)),greatest_lower_bound(X_202,identity)),least_upper_bound(greatest_lower_bound(identity,X_202),greatest_lower_bound(identity,inverse(X_202)))) )],[refute_0_653,refute_0_654]) ).
cnf(refute_0_656,plain,
least_upper_bound(greatest_lower_bound(identity,inverse(X_202)),greatest_lower_bound(X_202,identity)) = multiply(least_upper_bound(identity,inverse(X_202)),greatest_lower_bound(identity,X_202)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,X_202),greatest_lower_bound(identity,inverse(X_202))),multiply(least_upper_bound(identity,inverse(X_202)),greatest_lower_bound(identity,X_202))) )],[refute_0_621,refute_0_655]) ).
cnf(refute_0_657,plain,
( multiply(greatest_lower_bound(X_202,identity),least_upper_bound(identity,inverse(X_202))) != least_upper_bound(greatest_lower_bound(identity,inverse(X_202)),greatest_lower_bound(X_202,identity))
| least_upper_bound(greatest_lower_bound(identity,inverse(X_202)),greatest_lower_bound(X_202,identity)) != multiply(least_upper_bound(identity,inverse(X_202)),greatest_lower_bound(identity,X_202))
| multiply(greatest_lower_bound(X_202,identity),least_upper_bound(identity,inverse(X_202))) = multiply(least_upper_bound(identity,inverse(X_202)),greatest_lower_bound(identity,X_202)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_202,identity),least_upper_bound(identity,inverse(X_202))),multiply(least_upper_bound(identity,inverse(X_202)),greatest_lower_bound(identity,X_202))) ),[0],$fot(least_upper_bound(greatest_lower_bound(identity,inverse(X_202)),greatest_lower_bound(X_202,identity)))]]) ).
cnf(refute_0_658,plain,
( multiply(greatest_lower_bound(X_202,identity),least_upper_bound(identity,inverse(X_202))) != least_upper_bound(greatest_lower_bound(identity,inverse(X_202)),greatest_lower_bound(X_202,identity))
| multiply(greatest_lower_bound(X_202,identity),least_upper_bound(identity,inverse(X_202))) = multiply(least_upper_bound(identity,inverse(X_202)),greatest_lower_bound(identity,X_202)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,inverse(X_202)),greatest_lower_bound(X_202,identity)),multiply(least_upper_bound(identity,inverse(X_202)),greatest_lower_bound(identity,X_202))) )],[refute_0_656,refute_0_657]) ).
cnf(refute_0_659,plain,
( multiply(least_upper_bound(identity,inverse(X_202)),greatest_lower_bound(X_202,identity)) != least_upper_bound(greatest_lower_bound(identity,inverse(X_202)),greatest_lower_bound(X_202,identity))
| multiply(greatest_lower_bound(X_202,identity),least_upper_bound(identity,inverse(X_202))) = multiply(least_upper_bound(identity,inverse(X_202)),greatest_lower_bound(identity,X_202)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_202,identity),least_upper_bound(identity,inverse(X_202))),least_upper_bound(greatest_lower_bound(identity,inverse(X_202)),greatest_lower_bound(X_202,identity))) )],[refute_0_610,refute_0_658]) ).
cnf(refute_0_660,plain,
multiply(greatest_lower_bound(X_202,identity),least_upper_bound(identity,inverse(X_202))) = multiply(least_upper_bound(identity,inverse(X_202)),greatest_lower_bound(identity,X_202)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_202)),greatest_lower_bound(X_202,identity)),least_upper_bound(greatest_lower_bound(identity,inverse(X_202)),greatest_lower_bound(X_202,identity))) )],[refute_0_428,refute_0_659]) ).
cnf(refute_0_661,plain,
multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291))) = multiply(least_upper_bound(identity,inverse(X_291)),greatest_lower_bound(identity,X_291)),
inference(subst,[],[refute_0_660:[bind(X_202,$fot(X_291))]]) ).
cnf(refute_0_662,plain,
( multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291))) != multiply(least_upper_bound(identity,inverse(X_291)),greatest_lower_bound(identity,X_291))
| multiply(least_upper_bound(identity,inverse(X_291)),greatest_lower_bound(identity,X_291)) = multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291))))),bind(Y0,$fot(multiply(least_upper_bound(identity,inverse(X_291)),greatest_lower_bound(identity,X_291))))]]) ).
cnf(refute_0_663,plain,
multiply(least_upper_bound(identity,inverse(X_291)),greatest_lower_bound(identity,X_291)) = multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291))),multiply(least_upper_bound(identity,inverse(X_291)),greatest_lower_bound(identity,X_291))) )],[refute_0_661,refute_0_662]) ).
cnf(refute_0_664,plain,
( multiply(least_upper_bound(identity,inverse(X_291)),greatest_lower_bound(identity,X_291)) != multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))
| greatest_lower_bound(identity,X_291) != multiply(inverse(least_upper_bound(identity,inverse(X_291))),multiply(least_upper_bound(identity,inverse(X_291)),greatest_lower_bound(identity,X_291)))
| greatest_lower_bound(identity,X_291) = multiply(inverse(least_upper_bound(identity,inverse(X_291))),multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,X_291),multiply(inverse(least_upper_bound(identity,inverse(X_291))),multiply(least_upper_bound(identity,inverse(X_291)),greatest_lower_bound(identity,X_291)))) ),[1,1],$fot(multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291))))]]) ).
cnf(refute_0_665,plain,
( greatest_lower_bound(identity,X_291) != multiply(inverse(least_upper_bound(identity,inverse(X_291))),multiply(least_upper_bound(identity,inverse(X_291)),greatest_lower_bound(identity,X_291)))
| greatest_lower_bound(identity,X_291) = multiply(inverse(least_upper_bound(identity,inverse(X_291))),multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_291)),greatest_lower_bound(identity,X_291)),multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))) )],[refute_0_663,refute_0_664]) ).
cnf(refute_0_666,plain,
greatest_lower_bound(identity,X_291) = multiply(inverse(least_upper_bound(identity,inverse(X_291))),multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,X_291),multiply(inverse(least_upper_bound(identity,inverse(X_291))),multiply(least_upper_bound(identity,inverse(X_291)),greatest_lower_bound(identity,X_291)))) )],[refute_0_415,refute_0_665]) ).
cnf(refute_0_667,plain,
multiply(inverse(least_upper_bound(identity,inverse(X_291))),identity) = inverse(least_upper_bound(identity,inverse(X_291))),
inference(subst,[],[refute_0_217:[bind(X_74,$fot(inverse(least_upper_bound(identity,inverse(X_291)))))]]) ).
cnf(refute_0_668,plain,
multiply(inverse(least_upper_bound(X_9,X_24)),greatest_lower_bound(X_24,least_upper_bound(X_9,X_24))) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_9,X_24)),X_24)),
inference(subst,[],[refute_0_269:[bind(X_22,$fot(X_24)),bind(X_23,$fot(least_upper_bound(X_9,X_24)))]]) ).
cnf(refute_0_669,plain,
greatest_lower_bound(X_24,least_upper_bound(X_9,X_24)) = X_24,
inference(subst,[],[refute_0_170:[bind(X_8,$fot(X_24))]]) ).
cnf(refute_0_670,plain,
( multiply(inverse(least_upper_bound(X_9,X_24)),greatest_lower_bound(X_24,least_upper_bound(X_9,X_24))) != greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_9,X_24)),X_24))
| greatest_lower_bound(X_24,least_upper_bound(X_9,X_24)) != X_24
| multiply(inverse(least_upper_bound(X_9,X_24)),X_24) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_9,X_24)),X_24)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(X_9,X_24)),greatest_lower_bound(X_24,least_upper_bound(X_9,X_24))),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_9,X_24)),X_24))) ),[0,1],$fot(X_24)]]) ).
cnf(refute_0_671,plain,
( multiply(inverse(least_upper_bound(X_9,X_24)),greatest_lower_bound(X_24,least_upper_bound(X_9,X_24))) != greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_9,X_24)),X_24))
| multiply(inverse(least_upper_bound(X_9,X_24)),X_24) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_9,X_24)),X_24)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_24,least_upper_bound(X_9,X_24)),X_24) )],[refute_0_669,refute_0_670]) ).
cnf(refute_0_672,plain,
multiply(inverse(least_upper_bound(X_9,X_24)),X_24) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_9,X_24)),X_24)),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_9,X_24)),greatest_lower_bound(X_24,least_upper_bound(X_9,X_24))),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_9,X_24)),X_24))) )],[refute_0_668,refute_0_671]) ).
cnf(refute_0_673,plain,
multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),
inference(subst,[],[refute_0_672:[bind(X_24,$fot(multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),bind(X_9,$fot(identity))]]) ).
cnf(refute_0_674,plain,
multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X_291)),least_upper_bound(identity,inverse(X_291))),greatest_lower_bound(identity,X_291)) = least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_291)),greatest_lower_bound(identity,X_291))),
inference(subst,[],[refute_0_352:[bind(X_83,$fot(greatest_lower_bound(identity,X_291))),bind(X_85,$fot(least_upper_bound(identity,inverse(X_291))))]]) ).
cnf(refute_0_675,plain,
( multiply(least_upper_bound(identity,inverse(X_291)),greatest_lower_bound(identity,X_291)) != multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))
| multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X_291)),least_upper_bound(identity,inverse(X_291))),greatest_lower_bound(identity,X_291)) != least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_291)),greatest_lower_bound(identity,X_291)))
| multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X_291)),least_upper_bound(identity,inverse(X_291))),greatest_lower_bound(identity,X_291)) = least_upper_bound(identity,multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X_291)),least_upper_bound(identity,inverse(X_291))),greatest_lower_bound(identity,X_291)),least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_291)),greatest_lower_bound(identity,X_291)))) ),[1,1],$fot(multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291))))]]) ).
cnf(refute_0_676,plain,
( multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X_291)),least_upper_bound(identity,inverse(X_291))),greatest_lower_bound(identity,X_291)) != least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_291)),greatest_lower_bound(identity,X_291)))
| multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X_291)),least_upper_bound(identity,inverse(X_291))),greatest_lower_bound(identity,X_291)) = least_upper_bound(identity,multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_291)),greatest_lower_bound(identity,X_291)),multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))) )],[refute_0_663,refute_0_675]) ).
cnf(refute_0_677,plain,
multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X_291)),least_upper_bound(identity,inverse(X_291))),greatest_lower_bound(identity,X_291)) = least_upper_bound(identity,multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X_291)),least_upper_bound(identity,inverse(X_291))),greatest_lower_bound(identity,X_291)),least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_291)),greatest_lower_bound(identity,X_291)))) )],[refute_0_674,refute_0_676]) ).
cnf(refute_0_678,plain,
least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_25),X_24))) = identity,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(identity)),bind(Y,$fot(multiply(inverse(X_25),X_24)))]]) ).
cnf(refute_0_679,plain,
multiply(inverse(X_25),greatest_lower_bound(X_24,X_25)) = greatest_lower_bound(identity,multiply(inverse(X_25),X_24)),
inference(subst,[],[refute_0_269:[bind(X_22,$fot(X_24)),bind(X_23,$fot(X_25))]]) ).
cnf(refute_0_680,plain,
( multiply(inverse(X_25),greatest_lower_bound(X_24,X_25)) != greatest_lower_bound(identity,multiply(inverse(X_25),X_24))
| greatest_lower_bound(identity,multiply(inverse(X_25),X_24)) = multiply(inverse(X_25),greatest_lower_bound(X_24,X_25)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(inverse(X_25),greatest_lower_bound(X_24,X_25)))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(inverse(X_25),X_24))))]]) ).
cnf(refute_0_681,plain,
greatest_lower_bound(identity,multiply(inverse(X_25),X_24)) = multiply(inverse(X_25),greatest_lower_bound(X_24,X_25)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_25),greatest_lower_bound(X_24,X_25)),greatest_lower_bound(identity,multiply(inverse(X_25),X_24))) )],[refute_0_679,refute_0_680]) ).
cnf(refute_0_682,plain,
( greatest_lower_bound(identity,multiply(inverse(X_25),X_24)) != multiply(inverse(X_25),greatest_lower_bound(X_24,X_25))
| least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_25),X_24))) != identity
| least_upper_bound(identity,multiply(inverse(X_25),greatest_lower_bound(X_24,X_25))) = identity ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_25),X_24))),identity) ),[0,1],$fot(multiply(inverse(X_25),greatest_lower_bound(X_24,X_25)))]]) ).
cnf(refute_0_683,plain,
( least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_25),X_24))) != identity
| least_upper_bound(identity,multiply(inverse(X_25),greatest_lower_bound(X_24,X_25))) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(X_25),X_24)),multiply(inverse(X_25),greatest_lower_bound(X_24,X_25))) )],[refute_0_681,refute_0_682]) ).
cnf(refute_0_684,plain,
least_upper_bound(identity,multiply(inverse(X_25),greatest_lower_bound(X_24,X_25))) = identity,
inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_25),X_24))),identity) )],[refute_0_678,refute_0_683]) ).
cnf(refute_0_685,plain,
least_upper_bound(identity,multiply(inverse(X_291),greatest_lower_bound(identity,X_291))) = identity,
inference(subst,[],[refute_0_684:[bind(X_24,$fot(identity)),bind(X_25,$fot(X_291))]]) ).
cnf(refute_0_686,plain,
least_upper_bound(X_31,least_upper_bound(greatest_lower_bound(X_31,Y),X_33)) = least_upper_bound(least_upper_bound(X_31,greatest_lower_bound(X_31,Y)),X_33),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_31)),bind(Y,$fot(greatest_lower_bound(X_31,Y))),bind(Z,$fot(X_33))]]) ).
cnf(refute_0_687,plain,
least_upper_bound(X_31,greatest_lower_bound(X_31,Y)) = X_31,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_31))]]) ).
cnf(refute_0_688,plain,
( least_upper_bound(X_31,greatest_lower_bound(X_31,Y)) != X_31
| least_upper_bound(X_31,least_upper_bound(greatest_lower_bound(X_31,Y),X_33)) != least_upper_bound(least_upper_bound(X_31,greatest_lower_bound(X_31,Y)),X_33)
| least_upper_bound(X_31,least_upper_bound(greatest_lower_bound(X_31,Y),X_33)) = least_upper_bound(X_31,X_33) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_31,least_upper_bound(greatest_lower_bound(X_31,Y),X_33)),least_upper_bound(least_upper_bound(X_31,greatest_lower_bound(X_31,Y)),X_33)) ),[1,0],$fot(X_31)]]) ).
cnf(refute_0_689,plain,
( least_upper_bound(X_31,least_upper_bound(greatest_lower_bound(X_31,Y),X_33)) != least_upper_bound(least_upper_bound(X_31,greatest_lower_bound(X_31,Y)),X_33)
| least_upper_bound(X_31,least_upper_bound(greatest_lower_bound(X_31,Y),X_33)) = least_upper_bound(X_31,X_33) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_31,greatest_lower_bound(X_31,Y)),X_31) )],[refute_0_687,refute_0_688]) ).
cnf(refute_0_690,plain,
least_upper_bound(X_31,least_upper_bound(greatest_lower_bound(X_31,Y),X_33)) = least_upper_bound(X_31,X_33),
inference(resolve,[$cnf( $equal(least_upper_bound(X_31,least_upper_bound(greatest_lower_bound(X_31,Y),X_33)),least_upper_bound(least_upper_bound(X_31,greatest_lower_bound(X_31,Y)),X_33)) )],[refute_0_686,refute_0_689]) ).
cnf(refute_0_691,plain,
least_upper_bound(X_200,least_upper_bound(greatest_lower_bound(X_200,X_199),multiply(X_84,greatest_lower_bound(X_200,X_199)))) = least_upper_bound(X_200,multiply(X_84,greatest_lower_bound(X_200,X_199))),
inference(subst,[],[refute_0_690:[bind(Y,$fot(X_199)),bind(X_31,$fot(X_200)),bind(X_33,$fot(multiply(X_84,greatest_lower_bound(X_200,X_199))))]]) ).
cnf(refute_0_692,plain,
multiply(least_upper_bound(X_84,identity),greatest_lower_bound(X_200,X_199)) = least_upper_bound(greatest_lower_bound(X_200,X_199),multiply(X_84,greatest_lower_bound(X_200,X_199))),
inference(subst,[],[refute_0_515:[bind(X_83,$fot(greatest_lower_bound(X_200,X_199)))]]) ).
cnf(refute_0_693,plain,
( multiply(least_upper_bound(X_84,identity),greatest_lower_bound(X_200,X_199)) != least_upper_bound(greatest_lower_bound(X_200,X_199),multiply(X_84,greatest_lower_bound(X_200,X_199)))
| least_upper_bound(greatest_lower_bound(X_200,X_199),multiply(X_84,greatest_lower_bound(X_200,X_199))) = multiply(least_upper_bound(X_84,identity),greatest_lower_bound(X_200,X_199)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(X_84,identity),greatest_lower_bound(X_200,X_199)))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(X_200,X_199),multiply(X_84,greatest_lower_bound(X_200,X_199)))))]]) ).
cnf(refute_0_694,plain,
least_upper_bound(greatest_lower_bound(X_200,X_199),multiply(X_84,greatest_lower_bound(X_200,X_199))) = multiply(least_upper_bound(X_84,identity),greatest_lower_bound(X_200,X_199)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_84,identity),greatest_lower_bound(X_200,X_199)),least_upper_bound(greatest_lower_bound(X_200,X_199),multiply(X_84,greatest_lower_bound(X_200,X_199)))) )],[refute_0_692,refute_0_693]) ).
cnf(refute_0_695,plain,
( least_upper_bound(X_200,least_upper_bound(greatest_lower_bound(X_200,X_199),multiply(X_84,greatest_lower_bound(X_200,X_199)))) != least_upper_bound(X_200,multiply(X_84,greatest_lower_bound(X_200,X_199)))
| least_upper_bound(greatest_lower_bound(X_200,X_199),multiply(X_84,greatest_lower_bound(X_200,X_199))) != multiply(least_upper_bound(X_84,identity),greatest_lower_bound(X_200,X_199))
| least_upper_bound(X_200,multiply(least_upper_bound(X_84,identity),greatest_lower_bound(X_200,X_199))) = least_upper_bound(X_200,multiply(X_84,greatest_lower_bound(X_200,X_199))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_200,least_upper_bound(greatest_lower_bound(X_200,X_199),multiply(X_84,greatest_lower_bound(X_200,X_199)))),least_upper_bound(X_200,multiply(X_84,greatest_lower_bound(X_200,X_199)))) ),[0,1],$fot(multiply(least_upper_bound(X_84,identity),greatest_lower_bound(X_200,X_199)))]]) ).
cnf(refute_0_696,plain,
( least_upper_bound(X_200,least_upper_bound(greatest_lower_bound(X_200,X_199),multiply(X_84,greatest_lower_bound(X_200,X_199)))) != least_upper_bound(X_200,multiply(X_84,greatest_lower_bound(X_200,X_199)))
| least_upper_bound(X_200,multiply(least_upper_bound(X_84,identity),greatest_lower_bound(X_200,X_199))) = least_upper_bound(X_200,multiply(X_84,greatest_lower_bound(X_200,X_199))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_200,X_199),multiply(X_84,greatest_lower_bound(X_200,X_199))),multiply(least_upper_bound(X_84,identity),greatest_lower_bound(X_200,X_199))) )],[refute_0_694,refute_0_695]) ).
cnf(refute_0_697,plain,
least_upper_bound(X_200,multiply(least_upper_bound(X_84,identity),greatest_lower_bound(X_200,X_199))) = least_upper_bound(X_200,multiply(X_84,greatest_lower_bound(X_200,X_199))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_200,least_upper_bound(greatest_lower_bound(X_200,X_199),multiply(X_84,greatest_lower_bound(X_200,X_199)))),least_upper_bound(X_200,multiply(X_84,greatest_lower_bound(X_200,X_199)))) )],[refute_0_691,refute_0_696]) ).
cnf(refute_0_698,plain,
least_upper_bound(identity,multiply(least_upper_bound(inverse(X_291),identity),greatest_lower_bound(identity,X_291))) = least_upper_bound(identity,multiply(inverse(X_291),greatest_lower_bound(identity,X_291))),
inference(subst,[],[refute_0_697:[bind(X_199,$fot(X_291)),bind(X_200,$fot(identity)),bind(X_84,$fot(inverse(X_291)))]]) ).
cnf(refute_0_699,plain,
( least_upper_bound(identity,multiply(inverse(X_291),greatest_lower_bound(identity,X_291))) != identity
| least_upper_bound(identity,multiply(least_upper_bound(inverse(X_291),identity),greatest_lower_bound(identity,X_291))) != least_upper_bound(identity,multiply(inverse(X_291),greatest_lower_bound(identity,X_291)))
| least_upper_bound(identity,multiply(least_upper_bound(inverse(X_291),identity),greatest_lower_bound(identity,X_291))) = identity ),
inference(subst,[],[refute_0_136:[bind(X0,$fot(least_upper_bound(identity,multiply(least_upper_bound(inverse(X_291),identity),greatest_lower_bound(identity,X_291))))),bind(Y0,$fot(least_upper_bound(identity,multiply(inverse(X_291),greatest_lower_bound(identity,X_291))))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_700,plain,
( least_upper_bound(identity,multiply(inverse(X_291),greatest_lower_bound(identity,X_291))) != identity
| least_upper_bound(identity,multiply(least_upper_bound(inverse(X_291),identity),greatest_lower_bound(identity,X_291))) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(least_upper_bound(inverse(X_291),identity),greatest_lower_bound(identity,X_291))),least_upper_bound(identity,multiply(inverse(X_291),greatest_lower_bound(identity,X_291)))) )],[refute_0_698,refute_0_699]) ).
cnf(refute_0_701,plain,
least_upper_bound(identity,multiply(least_upper_bound(inverse(X_291),identity),greatest_lower_bound(identity,X_291))) = identity,
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(X_291),greatest_lower_bound(identity,X_291))),identity) )],[refute_0_685,refute_0_700]) ).
cnf(refute_0_702,plain,
multiply(least_upper_bound(Y,least_upper_bound(X_87,inverse(X))),X) = least_upper_bound(multiply(Y,X),multiply(least_upper_bound(X_87,inverse(X)),X)),
inference(subst,[],[monotony_lub2:[bind(Z,$fot(least_upper_bound(X_87,inverse(X))))]]) ).
cnf(refute_0_703,plain,
multiply(least_upper_bound(X_84,inverse(X_83)),X_83) = least_upper_bound(multiply(X_84,X_83),multiply(inverse(X_83),X_83)),
inference(subst,[],[monotony_lub2:[bind(X,$fot(X_83)),bind(Y,$fot(X_84)),bind(Z,$fot(inverse(X_83)))]]) ).
cnf(refute_0_704,plain,
( multiply(inverse(X_83),X_83) != identity
| multiply(least_upper_bound(X_84,inverse(X_83)),X_83) != least_upper_bound(multiply(X_84,X_83),multiply(inverse(X_83),X_83))
| multiply(least_upper_bound(X_84,inverse(X_83)),X_83) = least_upper_bound(multiply(X_84,X_83),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_84,inverse(X_83)),X_83),least_upper_bound(multiply(X_84,X_83),multiply(inverse(X_83),X_83))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_705,plain,
( multiply(least_upper_bound(X_84,inverse(X_83)),X_83) != least_upper_bound(multiply(X_84,X_83),multiply(inverse(X_83),X_83))
| multiply(least_upper_bound(X_84,inverse(X_83)),X_83) = least_upper_bound(multiply(X_84,X_83),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_83),X_83),identity) )],[refute_0_349,refute_0_704]) ).
cnf(refute_0_706,plain,
multiply(least_upper_bound(X_84,inverse(X_83)),X_83) = least_upper_bound(multiply(X_84,X_83),identity),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_84,inverse(X_83)),X_83),least_upper_bound(multiply(X_84,X_83),multiply(inverse(X_83),X_83))) )],[refute_0_703,refute_0_705]) ).
cnf(refute_0_707,plain,
least_upper_bound(multiply(X_84,X_83),identity) = least_upper_bound(identity,multiply(X_84,X_83)),
inference(subst,[],[refute_0_319:[bind(X_81,$fot(identity)),bind(X_82,$fot(multiply(X_84,X_83)))]]) ).
cnf(refute_0_708,plain,
( multiply(least_upper_bound(X_84,inverse(X_83)),X_83) != least_upper_bound(multiply(X_84,X_83),identity)
| least_upper_bound(multiply(X_84,X_83),identity) != least_upper_bound(identity,multiply(X_84,X_83))
| multiply(least_upper_bound(X_84,inverse(X_83)),X_83) = least_upper_bound(identity,multiply(X_84,X_83)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_84,inverse(X_83)),X_83),least_upper_bound(identity,multiply(X_84,X_83))) ),[0],$fot(least_upper_bound(multiply(X_84,X_83),identity))]]) ).
cnf(refute_0_709,plain,
( multiply(least_upper_bound(X_84,inverse(X_83)),X_83) != least_upper_bound(multiply(X_84,X_83),identity)
| multiply(least_upper_bound(X_84,inverse(X_83)),X_83) = least_upper_bound(identity,multiply(X_84,X_83)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_84,X_83),identity),least_upper_bound(identity,multiply(X_84,X_83))) )],[refute_0_707,refute_0_708]) ).
cnf(refute_0_710,plain,
multiply(least_upper_bound(X_84,inverse(X_83)),X_83) = least_upper_bound(identity,multiply(X_84,X_83)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_84,inverse(X_83)),X_83),least_upper_bound(multiply(X_84,X_83),identity)) )],[refute_0_706,refute_0_709]) ).
cnf(refute_0_711,plain,
multiply(least_upper_bound(X_87,inverse(X)),X) = least_upper_bound(identity,multiply(X_87,X)),
inference(subst,[],[refute_0_710:[bind(X_83,$fot(X)),bind(X_84,$fot(X_87))]]) ).
cnf(refute_0_712,plain,
( multiply(least_upper_bound(Y,least_upper_bound(X_87,inverse(X))),X) != least_upper_bound(multiply(Y,X),multiply(least_upper_bound(X_87,inverse(X)),X))
| multiply(least_upper_bound(X_87,inverse(X)),X) != least_upper_bound(identity,multiply(X_87,X))
| multiply(least_upper_bound(Y,least_upper_bound(X_87,inverse(X))),X) = least_upper_bound(multiply(Y,X),least_upper_bound(identity,multiply(X_87,X))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(Y,least_upper_bound(X_87,inverse(X))),X),least_upper_bound(multiply(Y,X),multiply(least_upper_bound(X_87,inverse(X)),X))) ),[1,1],$fot(least_upper_bound(identity,multiply(X_87,X)))]]) ).
cnf(refute_0_713,plain,
( multiply(least_upper_bound(Y,least_upper_bound(X_87,inverse(X))),X) != least_upper_bound(multiply(Y,X),multiply(least_upper_bound(X_87,inverse(X)),X))
| multiply(least_upper_bound(Y,least_upper_bound(X_87,inverse(X))),X) = least_upper_bound(multiply(Y,X),least_upper_bound(identity,multiply(X_87,X))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_87,inverse(X)),X),least_upper_bound(identity,multiply(X_87,X))) )],[refute_0_711,refute_0_712]) ).
cnf(refute_0_714,plain,
multiply(least_upper_bound(Y,least_upper_bound(X_87,inverse(X))),X) = least_upper_bound(multiply(Y,X),least_upper_bound(identity,multiply(X_87,X))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,least_upper_bound(X_87,inverse(X))),X),least_upper_bound(multiply(Y,X),multiply(least_upper_bound(X_87,inverse(X)),X))) )],[refute_0_702,refute_0_713]) ).
cnf(refute_0_715,plain,
least_upper_bound(multiply(X_84,X_83),least_upper_bound(X_32,multiply(X_85,X_83))) = least_upper_bound(X_32,least_upper_bound(multiply(X_84,X_83),multiply(X_85,X_83))),
inference(subst,[],[refute_0_638:[bind(X_31,$fot(multiply(X_84,X_83))),bind(X_33,$fot(multiply(X_85,X_83)))]]) ).
cnf(refute_0_716,plain,
( least_upper_bound(multiply(X_84,X_83),multiply(X_85,X_83)) != multiply(least_upper_bound(X_84,X_85),X_83)
| least_upper_bound(multiply(X_84,X_83),least_upper_bound(X_32,multiply(X_85,X_83))) != least_upper_bound(X_32,least_upper_bound(multiply(X_84,X_83),multiply(X_85,X_83)))
| least_upper_bound(multiply(X_84,X_83),least_upper_bound(X_32,multiply(X_85,X_83))) = least_upper_bound(X_32,multiply(least_upper_bound(X_84,X_85),X_83)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_84,X_83),least_upper_bound(X_32,multiply(X_85,X_83))),least_upper_bound(X_32,least_upper_bound(multiply(X_84,X_83),multiply(X_85,X_83)))) ),[1,1],$fot(multiply(least_upper_bound(X_84,X_85),X_83))]]) ).
cnf(refute_0_717,plain,
( least_upper_bound(multiply(X_84,X_83),least_upper_bound(X_32,multiply(X_85,X_83))) != least_upper_bound(X_32,least_upper_bound(multiply(X_84,X_83),multiply(X_85,X_83)))
| least_upper_bound(multiply(X_84,X_83),least_upper_bound(X_32,multiply(X_85,X_83))) = least_upper_bound(X_32,multiply(least_upper_bound(X_84,X_85),X_83)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_84,X_83),multiply(X_85,X_83)),multiply(least_upper_bound(X_84,X_85),X_83)) )],[refute_0_535,refute_0_716]) ).
cnf(refute_0_718,plain,
least_upper_bound(multiply(X_84,X_83),least_upper_bound(X_32,multiply(X_85,X_83))) = least_upper_bound(X_32,multiply(least_upper_bound(X_84,X_85),X_83)),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_84,X_83),least_upper_bound(X_32,multiply(X_85,X_83))),least_upper_bound(X_32,least_upper_bound(multiply(X_84,X_83),multiply(X_85,X_83)))) )],[refute_0_715,refute_0_717]) ).
cnf(refute_0_719,plain,
least_upper_bound(multiply(Y,X),least_upper_bound(identity,multiply(X_87,X))) = least_upper_bound(identity,multiply(least_upper_bound(Y,X_87),X)),
inference(subst,[],[refute_0_718:[bind(X_32,$fot(identity)),bind(X_83,$fot(X)),bind(X_84,$fot(Y)),bind(X_85,$fot(X_87))]]) ).
cnf(refute_0_720,plain,
( multiply(least_upper_bound(Y,least_upper_bound(X_87,inverse(X))),X) != least_upper_bound(multiply(Y,X),least_upper_bound(identity,multiply(X_87,X)))
| least_upper_bound(multiply(Y,X),least_upper_bound(identity,multiply(X_87,X))) != least_upper_bound(identity,multiply(least_upper_bound(Y,X_87),X))
| multiply(least_upper_bound(Y,least_upper_bound(X_87,inverse(X))),X) = least_upper_bound(identity,multiply(least_upper_bound(Y,X_87),X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(Y,least_upper_bound(X_87,inverse(X))),X),least_upper_bound(identity,multiply(least_upper_bound(Y,X_87),X))) ),[0],$fot(least_upper_bound(multiply(Y,X),least_upper_bound(identity,multiply(X_87,X))))]]) ).
cnf(refute_0_721,plain,
( multiply(least_upper_bound(Y,least_upper_bound(X_87,inverse(X))),X) != least_upper_bound(multiply(Y,X),least_upper_bound(identity,multiply(X_87,X)))
| multiply(least_upper_bound(Y,least_upper_bound(X_87,inverse(X))),X) = least_upper_bound(identity,multiply(least_upper_bound(Y,X_87),X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(Y,X),least_upper_bound(identity,multiply(X_87,X))),least_upper_bound(identity,multiply(least_upper_bound(Y,X_87),X))) )],[refute_0_719,refute_0_720]) ).
cnf(refute_0_722,plain,
multiply(least_upper_bound(Y,least_upper_bound(X_87,inverse(X))),X) = least_upper_bound(identity,multiply(least_upper_bound(Y,X_87),X)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,least_upper_bound(X_87,inverse(X))),X),least_upper_bound(multiply(Y,X),least_upper_bound(identity,multiply(X_87,X)))) )],[refute_0_714,refute_0_721]) ).
cnf(refute_0_723,plain,
multiply(least_upper_bound(inverse(X_291),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_291)))),greatest_lower_bound(identity,X_291)) = least_upper_bound(identity,multiply(least_upper_bound(inverse(X_291),identity),greatest_lower_bound(identity,X_291))),
inference(subst,[],[refute_0_722:[bind(X,$fot(greatest_lower_bound(identity,X_291))),bind(Y,$fot(inverse(X_291))),bind(X_87,$fot(identity))]]) ).
cnf(refute_0_724,plain,
( multiply(least_upper_bound(inverse(X_291),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_291)))),greatest_lower_bound(identity,X_291)) != least_upper_bound(identity,multiply(least_upper_bound(inverse(X_291),identity),greatest_lower_bound(identity,X_291)))
| least_upper_bound(identity,multiply(least_upper_bound(inverse(X_291),identity),greatest_lower_bound(identity,X_291))) != identity
| multiply(least_upper_bound(inverse(X_291),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_291)))),greatest_lower_bound(identity,X_291)) = identity ),
inference(subst,[],[refute_0_136:[bind(X0,$fot(multiply(least_upper_bound(inverse(X_291),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_291)))),greatest_lower_bound(identity,X_291)))),bind(Y0,$fot(least_upper_bound(identity,multiply(least_upper_bound(inverse(X_291),identity),greatest_lower_bound(identity,X_291))))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_725,plain,
( least_upper_bound(identity,multiply(least_upper_bound(inverse(X_291),identity),greatest_lower_bound(identity,X_291))) != identity
| multiply(least_upper_bound(inverse(X_291),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_291)))),greatest_lower_bound(identity,X_291)) = identity ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_291),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_291)))),greatest_lower_bound(identity,X_291)),least_upper_bound(identity,multiply(least_upper_bound(inverse(X_291),identity),greatest_lower_bound(identity,X_291)))) )],[refute_0_723,refute_0_724]) ).
cnf(refute_0_726,plain,
multiply(least_upper_bound(inverse(X_291),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_291)))),greatest_lower_bound(identity,X_291)) = identity,
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(least_upper_bound(inverse(X_291),identity),greatest_lower_bound(identity,X_291))),identity) )],[refute_0_701,refute_0_725]) ).
cnf(refute_0_727,plain,
multiply(least_upper_bound(Y,least_upper_bound(X_181,X_182)),X) = least_upper_bound(multiply(Y,X),multiply(least_upper_bound(X_181,X_182),X)),
inference(subst,[],[monotony_lub2:[bind(Z,$fot(least_upper_bound(X_181,X_182)))]]) ).
cnf(refute_0_728,plain,
least_upper_bound(X_31,least_upper_bound(X_32,X)) = least_upper_bound(X_32,least_upper_bound(X_31,X)),
inference(subst,[],[refute_0_638:[bind(X_33,$fot(X))]]) ).
cnf(refute_0_729,plain,
( least_upper_bound(X,least_upper_bound(X_31,X_32)) != least_upper_bound(X_31,least_upper_bound(X_32,X))
| least_upper_bound(X_31,least_upper_bound(X_32,X)) != least_upper_bound(X_32,least_upper_bound(X_31,X))
| least_upper_bound(X,least_upper_bound(X_31,X_32)) = least_upper_bound(X_32,least_upper_bound(X_31,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,least_upper_bound(X_31,X_32)),least_upper_bound(X_32,least_upper_bound(X_31,X))) ),[0],$fot(least_upper_bound(X_31,least_upper_bound(X_32,X)))]]) ).
cnf(refute_0_730,plain,
( least_upper_bound(X,least_upper_bound(X_31,X_32)) != least_upper_bound(X_31,least_upper_bound(X_32,X))
| least_upper_bound(X,least_upper_bound(X_31,X_32)) = least_upper_bound(X_32,least_upper_bound(X_31,X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_31,least_upper_bound(X_32,X)),least_upper_bound(X_32,least_upper_bound(X_31,X))) )],[refute_0_728,refute_0_729]) ).
cnf(refute_0_731,plain,
least_upper_bound(X,least_upper_bound(X_31,X_32)) = least_upper_bound(X_32,least_upper_bound(X_31,X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_31,X_32)),least_upper_bound(X_31,least_upper_bound(X_32,X))) )],[refute_0_127,refute_0_730]) ).
cnf(refute_0_732,plain,
least_upper_bound(Y,least_upper_bound(X_181,X_182)) = least_upper_bound(X_182,least_upper_bound(X_181,Y)),
inference(subst,[],[refute_0_731:[bind(X,$fot(Y)),bind(X_31,$fot(X_181)),bind(X_32,$fot(X_182))]]) ).
cnf(refute_0_733,plain,
( multiply(least_upper_bound(Y,least_upper_bound(X_181,X_182)),X) != least_upper_bound(multiply(Y,X),multiply(least_upper_bound(X_181,X_182),X))
| least_upper_bound(Y,least_upper_bound(X_181,X_182)) != least_upper_bound(X_182,least_upper_bound(X_181,Y))
| multiply(least_upper_bound(X_182,least_upper_bound(X_181,Y)),X) = least_upper_bound(multiply(Y,X),multiply(least_upper_bound(X_181,X_182),X)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(Y,least_upper_bound(X_181,X_182)),X),least_upper_bound(multiply(Y,X),multiply(least_upper_bound(X_181,X_182),X))) ),[0,0],$fot(least_upper_bound(X_182,least_upper_bound(X_181,Y)))]]) ).
cnf(refute_0_734,plain,
( multiply(least_upper_bound(Y,least_upper_bound(X_181,X_182)),X) != least_upper_bound(multiply(Y,X),multiply(least_upper_bound(X_181,X_182),X))
| multiply(least_upper_bound(X_182,least_upper_bound(X_181,Y)),X) = least_upper_bound(multiply(Y,X),multiply(least_upper_bound(X_181,X_182),X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_181,X_182)),least_upper_bound(X_182,least_upper_bound(X_181,Y))) )],[refute_0_732,refute_0_733]) ).
cnf(refute_0_735,plain,
multiply(least_upper_bound(X_182,least_upper_bound(X_181,Y)),X) = least_upper_bound(multiply(Y,X),multiply(least_upper_bound(X_181,X_182),X)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,least_upper_bound(X_181,X_182)),X),least_upper_bound(multiply(Y,X),multiply(least_upper_bound(X_181,X_182),X))) )],[refute_0_727,refute_0_734]) ).
cnf(refute_0_736,plain,
least_upper_bound(multiply(Y,X),multiply(least_upper_bound(X_181,X_182),X)) = multiply(least_upper_bound(Y,least_upper_bound(X_181,X_182)),X),
inference(subst,[],[refute_0_198:[bind(Z,$fot(least_upper_bound(X_181,X_182)))]]) ).
cnf(refute_0_737,plain,
( multiply(least_upper_bound(X_182,least_upper_bound(X_181,Y)),X) != least_upper_bound(multiply(Y,X),multiply(least_upper_bound(X_181,X_182),X))
| least_upper_bound(multiply(Y,X),multiply(least_upper_bound(X_181,X_182),X)) != multiply(least_upper_bound(Y,least_upper_bound(X_181,X_182)),X)
| multiply(least_upper_bound(X_182,least_upper_bound(X_181,Y)),X) = multiply(least_upper_bound(Y,least_upper_bound(X_181,X_182)),X) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_182,least_upper_bound(X_181,Y)),X),multiply(least_upper_bound(Y,least_upper_bound(X_181,X_182)),X)) ),[0],$fot(least_upper_bound(multiply(Y,X),multiply(least_upper_bound(X_181,X_182),X)))]]) ).
cnf(refute_0_738,plain,
( multiply(least_upper_bound(X_182,least_upper_bound(X_181,Y)),X) != least_upper_bound(multiply(Y,X),multiply(least_upper_bound(X_181,X_182),X))
| multiply(least_upper_bound(X_182,least_upper_bound(X_181,Y)),X) = multiply(least_upper_bound(Y,least_upper_bound(X_181,X_182)),X) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(Y,X),multiply(least_upper_bound(X_181,X_182),X)),multiply(least_upper_bound(Y,least_upper_bound(X_181,X_182)),X)) )],[refute_0_736,refute_0_737]) ).
cnf(refute_0_739,plain,
multiply(least_upper_bound(X_182,least_upper_bound(X_181,Y)),X) = multiply(least_upper_bound(Y,least_upper_bound(X_181,X_182)),X),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_182,least_upper_bound(X_181,Y)),X),least_upper_bound(multiply(Y,X),multiply(least_upper_bound(X_181,X_182),X))) )],[refute_0_735,refute_0_738]) ).
cnf(refute_0_740,plain,
( multiply(least_upper_bound(X_182,least_upper_bound(X_181,Y)),X) != multiply(least_upper_bound(Y,least_upper_bound(X_181,X_182)),X)
| multiply(least_upper_bound(Y,least_upper_bound(X_181,X_182)),X) = multiply(least_upper_bound(X_182,least_upper_bound(X_181,Y)),X) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(X_182,least_upper_bound(X_181,Y)),X))),bind(Y0,$fot(multiply(least_upper_bound(Y,least_upper_bound(X_181,X_182)),X)))]]) ).
cnf(refute_0_741,plain,
multiply(least_upper_bound(Y,least_upper_bound(X_181,X_182)),X) = multiply(least_upper_bound(X_182,least_upper_bound(X_181,Y)),X),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_182,least_upper_bound(X_181,Y)),X),multiply(least_upper_bound(Y,least_upper_bound(X_181,X_182)),X)) )],[refute_0_739,refute_0_740]) ).
cnf(refute_0_742,plain,
multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X_291)),least_upper_bound(identity,inverse(X_291))),greatest_lower_bound(identity,X_291)) = multiply(least_upper_bound(inverse(X_291),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_291)))),greatest_lower_bound(identity,X_291)),
inference(subst,[],[refute_0_741:[bind(X,$fot(greatest_lower_bound(identity,X_291))),bind(Y,$fot(inverse(greatest_lower_bound(identity,X_291)))),bind(X_181,$fot(identity)),bind(X_182,$fot(inverse(X_291)))]]) ).
cnf(refute_0_743,plain,
( multiply(least_upper_bound(inverse(X_291),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_291)))),greatest_lower_bound(identity,X_291)) != identity
| multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X_291)),least_upper_bound(identity,inverse(X_291))),greatest_lower_bound(identity,X_291)) != multiply(least_upper_bound(inverse(X_291),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_291)))),greatest_lower_bound(identity,X_291))
| multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X_291)),least_upper_bound(identity,inverse(X_291))),greatest_lower_bound(identity,X_291)) = identity ),
inference(subst,[],[refute_0_136:[bind(X0,$fot(multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X_291)),least_upper_bound(identity,inverse(X_291))),greatest_lower_bound(identity,X_291)))),bind(Y0,$fot(multiply(least_upper_bound(inverse(X_291),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_291)))),greatest_lower_bound(identity,X_291)))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_744,plain,
( multiply(least_upper_bound(inverse(X_291),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_291)))),greatest_lower_bound(identity,X_291)) != identity
| multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X_291)),least_upper_bound(identity,inverse(X_291))),greatest_lower_bound(identity,X_291)) = identity ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X_291)),least_upper_bound(identity,inverse(X_291))),greatest_lower_bound(identity,X_291)),multiply(least_upper_bound(inverse(X_291),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_291)))),greatest_lower_bound(identity,X_291))) )],[refute_0_742,refute_0_743]) ).
cnf(refute_0_745,plain,
multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X_291)),least_upper_bound(identity,inverse(X_291))),greatest_lower_bound(identity,X_291)) = identity,
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_291),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_291)))),greatest_lower_bound(identity,X_291)),identity) )],[refute_0_726,refute_0_744]) ).
cnf(refute_0_746,plain,
( multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X_291)),least_upper_bound(identity,inverse(X_291))),greatest_lower_bound(identity,X_291)) != identity
| multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X_291)),least_upper_bound(identity,inverse(X_291))),greatest_lower_bound(identity,X_291)) != least_upper_bound(identity,multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291))))
| identity = least_upper_bound(identity,multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X_291)),least_upper_bound(identity,inverse(X_291))),greatest_lower_bound(identity,X_291)),least_upper_bound(identity,multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291))))) ),[0],$fot(identity)]]) ).
cnf(refute_0_747,plain,
( multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X_291)),least_upper_bound(identity,inverse(X_291))),greatest_lower_bound(identity,X_291)) != least_upper_bound(identity,multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291))))
| identity = least_upper_bound(identity,multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X_291)),least_upper_bound(identity,inverse(X_291))),greatest_lower_bound(identity,X_291)),identity) )],[refute_0_745,refute_0_746]) ).
cnf(refute_0_748,plain,
identity = least_upper_bound(identity,multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X_291)),least_upper_bound(identity,inverse(X_291))),greatest_lower_bound(identity,X_291)),least_upper_bound(identity,multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291))))) )],[refute_0_677,refute_0_747]) ).
cnf(refute_0_749,plain,
identity = least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))),
inference(subst,[],[refute_0_748:[bind(X_291,$fot(X_292))]]) ).
cnf(refute_0_750,plain,
( identity != least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))
| least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))) = identity ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(identity)),bind(Y0,$fot(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))))]]) ).
cnf(refute_0_751,plain,
least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))) = identity,
inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))) )],[refute_0_749,refute_0_750]) ).
cnf(refute_0_752,plain,
( multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))) != greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))))
| least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))) != identity
| multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))) = greatest_lower_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))))) ),[1,1,0,0],$fot(identity)]]) ).
cnf(refute_0_753,plain,
( multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))) != greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))))
| multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))) = greatest_lower_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))),identity) )],[refute_0_751,refute_0_752]) ).
cnf(refute_0_754,plain,
multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))) = greatest_lower_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))))) )],[refute_0_673,refute_0_753]) ).
cnf(refute_0_755,plain,
multiply(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))) = multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))),
inference(subst,[],[left_identity:[bind(X,$fot(multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))))]]) ).
cnf(refute_0_756,plain,
multiply(inverse(identity),identity) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(identity))]]) ).
cnf(refute_0_757,plain,
inverse(identity) = multiply(inverse(identity),identity),
inference(subst,[],[refute_0_63:[bind(X_74,$fot(inverse(identity)))]]) ).
cnf(refute_0_758,plain,
( inverse(identity) != multiply(inverse(identity),identity)
| multiply(inverse(identity),identity) = inverse(identity) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(identity))),bind(Y0,$fot(multiply(inverse(identity),identity)))]]) ).
cnf(refute_0_759,plain,
multiply(inverse(identity),identity) = inverse(identity),
inference(resolve,[$cnf( $equal(inverse(identity),multiply(inverse(identity),identity)) )],[refute_0_757,refute_0_758]) ).
cnf(refute_0_760,plain,
( multiply(inverse(identity),identity) != identity
| multiply(inverse(identity),identity) != inverse(identity)
| inverse(identity) = identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(identity),identity),identity) ),[0],$fot(inverse(identity))]]) ).
cnf(refute_0_761,plain,
( multiply(inverse(identity),identity) != identity
| inverse(identity) = identity ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),identity),inverse(identity)) )],[refute_0_759,refute_0_760]) ).
cnf(refute_0_762,plain,
inverse(identity) = identity,
inference(resolve,[$cnf( $equal(multiply(inverse(identity),identity),identity) )],[refute_0_756,refute_0_761]) ).
cnf(refute_0_763,plain,
inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))) = inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))))]]) ).
cnf(refute_0_764,plain,
( inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))) != inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))))
| least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))) != identity
| inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))) = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_765,plain,
( least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))) != identity
| inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))) = inverse(identity) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))))) )],[refute_0_763,refute_0_764]) ).
cnf(refute_0_766,plain,
inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))) = inverse(identity),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))),identity) )],[refute_0_751,refute_0_765]) ).
cnf(refute_0_767,plain,
( inverse(identity) != identity
| inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))) != inverse(identity)
| inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))) = identity ),
inference(subst,[],[refute_0_136:[bind(X0,$fot(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))))),bind(Y0,$fot(inverse(identity))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_768,plain,
( inverse(identity) != identity
| inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))) = identity ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),inverse(identity)) )],[refute_0_766,refute_0_767]) ).
cnf(refute_0_769,plain,
inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))) = identity,
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_762,refute_0_768]) ).
cnf(refute_0_770,plain,
multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))) = multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))))]]) ).
cnf(refute_0_771,plain,
( multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))) != multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))
| inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))) != identity
| multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))) = multiply(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))),multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_772,plain,
( inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))) != identity
| multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))) = multiply(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))),multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))) )],[refute_0_770,refute_0_771]) ).
cnf(refute_0_773,plain,
multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))) = multiply(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),identity) )],[refute_0_769,refute_0_772]) ).
cnf(refute_0_774,plain,
( multiply(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))) != multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))
| multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))) != multiply(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))
| multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))) = multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))) ),
inference(subst,[],[refute_0_136:[bind(X0,$fot(multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))))),bind(Y0,$fot(multiply(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))))),bind(Z0,$fot(multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))))]]) ).
cnf(refute_0_775,plain,
( multiply(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))) != multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))
| multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))) = multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))),multiply(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))) )],[refute_0_773,refute_0_774]) ).
cnf(refute_0_776,plain,
multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))) = multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))),
inference(resolve,[$cnf( $equal(multiply(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))) )],[refute_0_755,refute_0_775]) ).
cnf(refute_0_777,plain,
( multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))) != multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))
| multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))) != greatest_lower_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))))
| multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))) = greatest_lower_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))),greatest_lower_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))))) ),[0],$fot(multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))]]) ).
cnf(refute_0_778,plain,
( multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))) != greatest_lower_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))))
| multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))) = greatest_lower_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))) )],[refute_0_776,refute_0_777]) ).
cnf(refute_0_779,plain,
multiply(identity,identity) = identity,
inference(subst,[],[refute_0_217:[bind(X_74,$fot(identity))]]) ).
cnf(refute_0_780,plain,
greatest_lower_bound(identity,least_upper_bound(X_292,identity)) = identity,
inference(subst,[],[refute_0_170:[bind(X_8,$fot(identity)),bind(X_9,$fot(X_292))]]) ).
cnf(refute_0_781,plain,
multiply(least_upper_bound(X_292,identity),identity) = least_upper_bound(X_292,identity),
inference(subst,[],[refute_0_217:[bind(X_74,$fot(least_upper_bound(X_292,identity)))]]) ).
cnf(refute_0_782,plain,
least_upper_bound(identity,multiply(X_292,identity)) = multiply(least_upper_bound(X_292,identity),identity),
inference(subst,[],[refute_0_569:[bind(X_83,$fot(identity)),bind(X_84,$fot(X_292))]]) ).
cnf(refute_0_783,plain,
( multiply(least_upper_bound(X_292,identity),identity) != least_upper_bound(X_292,identity)
| least_upper_bound(identity,multiply(X_292,identity)) != multiply(least_upper_bound(X_292,identity),identity)
| least_upper_bound(identity,multiply(X_292,identity)) = least_upper_bound(X_292,identity) ),
inference(subst,[],[refute_0_136:[bind(X0,$fot(least_upper_bound(identity,multiply(X_292,identity)))),bind(Y0,$fot(multiply(least_upper_bound(X_292,identity),identity))),bind(Z0,$fot(least_upper_bound(X_292,identity)))]]) ).
cnf(refute_0_784,plain,
( multiply(least_upper_bound(X_292,identity),identity) != least_upper_bound(X_292,identity)
| least_upper_bound(identity,multiply(X_292,identity)) = least_upper_bound(X_292,identity) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_292,identity)),multiply(least_upper_bound(X_292,identity),identity)) )],[refute_0_782,refute_0_783]) ).
cnf(refute_0_785,plain,
least_upper_bound(identity,multiply(X_292,identity)) = least_upper_bound(X_292,identity),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_292,identity),identity),least_upper_bound(X_292,identity)) )],[refute_0_781,refute_0_784]) ).
cnf(refute_0_786,plain,
multiply(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),least_upper_bound(X_79,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))))) = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),X_79)),
inference(subst,[],[refute_0_34:[bind(X_80,$fot(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))))]]) ).
cnf(refute_0_787,plain,
X_74 = multiply(inverse(greatest_lower_bound(inverse(X_74),X_30)),multiply(greatest_lower_bound(inverse(X_74),X_30),X_74)),
inference(subst,[],[refute_0_45:[bind(X_71,$fot(greatest_lower_bound(inverse(X_74),X_30))),bind(X_72,$fot(X_74))]]) ).
cnf(refute_0_788,plain,
multiply(greatest_lower_bound(inverse(X_28),X_30),X_28) = greatest_lower_bound(multiply(inverse(X_28),X_28),multiply(X_30,X_28)),
inference(subst,[],[monotony_glb2:[bind(X,$fot(X_28)),bind(Y,$fot(inverse(X_28))),bind(Z,$fot(X_30))]]) ).
cnf(refute_0_789,plain,
( multiply(greatest_lower_bound(inverse(X_28),X_30),X_28) != greatest_lower_bound(multiply(inverse(X_28),X_28),multiply(X_30,X_28))
| multiply(inverse(X_28),X_28) != identity
| multiply(greatest_lower_bound(inverse(X_28),X_30),X_28) = greatest_lower_bound(identity,multiply(X_30,X_28)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_28),X_30),X_28),greatest_lower_bound(multiply(inverse(X_28),X_28),multiply(X_30,X_28))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_790,plain,
( multiply(greatest_lower_bound(inverse(X_28),X_30),X_28) != greatest_lower_bound(multiply(inverse(X_28),X_28),multiply(X_30,X_28))
| multiply(greatest_lower_bound(inverse(X_28),X_30),X_28) = greatest_lower_bound(identity,multiply(X_30,X_28)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_28),X_28),identity) )],[refute_0_431,refute_0_789]) ).
cnf(refute_0_791,plain,
multiply(greatest_lower_bound(inverse(X_28),X_30),X_28) = greatest_lower_bound(identity,multiply(X_30,X_28)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_28),X_30),X_28),greatest_lower_bound(multiply(inverse(X_28),X_28),multiply(X_30,X_28))) )],[refute_0_788,refute_0_790]) ).
cnf(refute_0_792,plain,
multiply(greatest_lower_bound(inverse(X_74),X_30),X_74) = greatest_lower_bound(identity,multiply(X_30,X_74)),
inference(subst,[],[refute_0_791:[bind(X_28,$fot(X_74))]]) ).
cnf(refute_0_793,plain,
( X_74 != multiply(inverse(greatest_lower_bound(inverse(X_74),X_30)),multiply(greatest_lower_bound(inverse(X_74),X_30),X_74))
| multiply(greatest_lower_bound(inverse(X_74),X_30),X_74) != greatest_lower_bound(identity,multiply(X_30,X_74))
| X_74 = multiply(inverse(greatest_lower_bound(inverse(X_74),X_30)),greatest_lower_bound(identity,multiply(X_30,X_74))) ),
introduced(tautology,[equality,[$cnf( $equal(X_74,multiply(inverse(greatest_lower_bound(inverse(X_74),X_30)),multiply(greatest_lower_bound(inverse(X_74),X_30),X_74))) ),[1,1],$fot(greatest_lower_bound(identity,multiply(X_30,X_74)))]]) ).
cnf(refute_0_794,plain,
( X_74 != multiply(inverse(greatest_lower_bound(inverse(X_74),X_30)),multiply(greatest_lower_bound(inverse(X_74),X_30),X_74))
| X_74 = multiply(inverse(greatest_lower_bound(inverse(X_74),X_30)),greatest_lower_bound(identity,multiply(X_30,X_74))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_74),X_30),X_74),greatest_lower_bound(identity,multiply(X_30,X_74))) )],[refute_0_792,refute_0_793]) ).
cnf(refute_0_795,plain,
X_74 = multiply(inverse(greatest_lower_bound(inverse(X_74),X_30)),greatest_lower_bound(identity,multiply(X_30,X_74))),
inference(resolve,[$cnf( $equal(X_74,multiply(inverse(greatest_lower_bound(inverse(X_74),X_30)),multiply(greatest_lower_bound(inverse(X_74),X_30),X_74))) )],[refute_0_787,refute_0_794]) ).
cnf(refute_0_796,plain,
X_123 = multiply(inverse(greatest_lower_bound(inverse(X_123),inverse(greatest_lower_bound(X_13,X_123)))),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_13,X_123)),X_123))),
inference(subst,[],[refute_0_795:[bind(X_30,$fot(inverse(greatest_lower_bound(X_13,X_123)))),bind(X_74,$fot(X_123))]]) ).
cnf(refute_0_797,plain,
multiply(inverse(X_26),greatest_lower_bound(X_26,least_upper_bound(X_9,X_26))) = greatest_lower_bound(identity,multiply(inverse(X_26),least_upper_bound(X_9,X_26))),
inference(subst,[],[refute_0_249:[bind(X_22,$fot(X_26)),bind(X_23,$fot(least_upper_bound(X_9,X_26)))]]) ).
cnf(refute_0_798,plain,
greatest_lower_bound(X_26,least_upper_bound(X_9,X_26)) = X_26,
inference(subst,[],[refute_0_170:[bind(X_8,$fot(X_26))]]) ).
cnf(refute_0_799,plain,
( multiply(inverse(X_26),greatest_lower_bound(X_26,least_upper_bound(X_9,X_26))) != greatest_lower_bound(identity,multiply(inverse(X_26),least_upper_bound(X_9,X_26)))
| greatest_lower_bound(X_26,least_upper_bound(X_9,X_26)) != X_26
| multiply(inverse(X_26),X_26) = greatest_lower_bound(identity,multiply(inverse(X_26),least_upper_bound(X_9,X_26))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_26),greatest_lower_bound(X_26,least_upper_bound(X_9,X_26))),greatest_lower_bound(identity,multiply(inverse(X_26),least_upper_bound(X_9,X_26)))) ),[0,1],$fot(X_26)]]) ).
cnf(refute_0_800,plain,
( multiply(inverse(X_26),greatest_lower_bound(X_26,least_upper_bound(X_9,X_26))) != greatest_lower_bound(identity,multiply(inverse(X_26),least_upper_bound(X_9,X_26)))
| multiply(inverse(X_26),X_26) = greatest_lower_bound(identity,multiply(inverse(X_26),least_upper_bound(X_9,X_26))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_26,least_upper_bound(X_9,X_26)),X_26) )],[refute_0_798,refute_0_799]) ).
cnf(refute_0_801,plain,
multiply(inverse(X_26),X_26) = greatest_lower_bound(identity,multiply(inverse(X_26),least_upper_bound(X_9,X_26))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_26),greatest_lower_bound(X_26,least_upper_bound(X_9,X_26))),greatest_lower_bound(identity,multiply(inverse(X_26),least_upper_bound(X_9,X_26)))) )],[refute_0_797,refute_0_800]) ).
cnf(refute_0_802,plain,
multiply(inverse(X_26),X_26) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_26))]]) ).
cnf(refute_0_803,plain,
( multiply(inverse(X_26),X_26) != greatest_lower_bound(identity,multiply(inverse(X_26),least_upper_bound(X_9,X_26)))
| multiply(inverse(X_26),X_26) != identity
| identity = greatest_lower_bound(identity,multiply(inverse(X_26),least_upper_bound(X_9,X_26))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_26),X_26),greatest_lower_bound(identity,multiply(inverse(X_26),least_upper_bound(X_9,X_26)))) ),[0],$fot(identity)]]) ).
cnf(refute_0_804,plain,
( multiply(inverse(X_26),X_26) != greatest_lower_bound(identity,multiply(inverse(X_26),least_upper_bound(X_9,X_26)))
| identity = greatest_lower_bound(identity,multiply(inverse(X_26),least_upper_bound(X_9,X_26))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_26),X_26),identity) )],[refute_0_802,refute_0_803]) ).
cnf(refute_0_805,plain,
identity = greatest_lower_bound(identity,multiply(inverse(X_26),least_upper_bound(X_9,X_26))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_26),X_26),greatest_lower_bound(identity,multiply(inverse(X_26),least_upper_bound(X_9,X_26)))) )],[refute_0_801,refute_0_804]) ).
cnf(refute_0_806,plain,
identity = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_13,X_47)),least_upper_bound(X_47,greatest_lower_bound(X_13,X_47)))),
inference(subst,[],[refute_0_805:[bind(X_26,$fot(greatest_lower_bound(X_13,X_47))),bind(X_9,$fot(X_47))]]) ).
cnf(refute_0_807,plain,
least_upper_bound(X_47,greatest_lower_bound(X_13,X_47)) = X_47,
inference(subst,[],[refute_0_80:[bind(X_12,$fot(X_47))]]) ).
cnf(refute_0_808,plain,
( identity != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_13,X_47)),least_upper_bound(X_47,greatest_lower_bound(X_13,X_47))))
| least_upper_bound(X_47,greatest_lower_bound(X_13,X_47)) != X_47
| identity = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_13,X_47)),X_47)) ),
introduced(tautology,[equality,[$cnf( $equal(identity,greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_13,X_47)),least_upper_bound(X_47,greatest_lower_bound(X_13,X_47))))) ),[1,1,1],$fot(X_47)]]) ).
cnf(refute_0_809,plain,
( identity != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_13,X_47)),least_upper_bound(X_47,greatest_lower_bound(X_13,X_47))))
| identity = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_13,X_47)),X_47)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_47,greatest_lower_bound(X_13,X_47)),X_47) )],[refute_0_807,refute_0_808]) ).
cnf(refute_0_810,plain,
identity = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_13,X_47)),X_47)),
inference(resolve,[$cnf( $equal(identity,greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_13,X_47)),least_upper_bound(X_47,greatest_lower_bound(X_13,X_47))))) )],[refute_0_806,refute_0_809]) ).
cnf(refute_0_811,plain,
identity = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_13,X_123)),X_123)),
inference(subst,[],[refute_0_810:[bind(X_47,$fot(X_123))]]) ).
cnf(refute_0_812,plain,
( identity != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_13,X_123)),X_123))
| greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_13,X_123)),X_123)) = identity ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(identity)),bind(Y0,$fot(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_13,X_123)),X_123))))]]) ).
cnf(refute_0_813,plain,
greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_13,X_123)),X_123)) = identity,
inference(resolve,[$cnf( $equal(identity,greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_13,X_123)),X_123))) )],[refute_0_811,refute_0_812]) ).
cnf(refute_0_814,plain,
( X_123 != multiply(inverse(greatest_lower_bound(inverse(X_123),inverse(greatest_lower_bound(X_13,X_123)))),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_13,X_123)),X_123)))
| greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_13,X_123)),X_123)) != identity
| X_123 = multiply(inverse(greatest_lower_bound(inverse(X_123),inverse(greatest_lower_bound(X_13,X_123)))),identity) ),
introduced(tautology,[equality,[$cnf( $equal(X_123,multiply(inverse(greatest_lower_bound(inverse(X_123),inverse(greatest_lower_bound(X_13,X_123)))),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_13,X_123)),X_123)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_815,plain,
( X_123 != multiply(inverse(greatest_lower_bound(inverse(X_123),inverse(greatest_lower_bound(X_13,X_123)))),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_13,X_123)),X_123)))
| X_123 = multiply(inverse(greatest_lower_bound(inverse(X_123),inverse(greatest_lower_bound(X_13,X_123)))),identity) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_13,X_123)),X_123)),identity) )],[refute_0_813,refute_0_814]) ).
cnf(refute_0_816,plain,
X_123 = multiply(inverse(greatest_lower_bound(inverse(X_123),inverse(greatest_lower_bound(X_13,X_123)))),identity),
inference(resolve,[$cnf( $equal(X_123,multiply(inverse(greatest_lower_bound(inverse(X_123),inverse(greatest_lower_bound(X_13,X_123)))),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_13,X_123)),X_123)))) )],[refute_0_796,refute_0_815]) ).
cnf(refute_0_817,plain,
multiply(inverse(greatest_lower_bound(inverse(X_123),inverse(greatest_lower_bound(X_13,X_123)))),identity) = inverse(greatest_lower_bound(inverse(X_123),inverse(greatest_lower_bound(X_13,X_123)))),
inference(subst,[],[refute_0_217:[bind(X_74,$fot(inverse(greatest_lower_bound(inverse(X_123),inverse(greatest_lower_bound(X_13,X_123))))))]]) ).
cnf(refute_0_818,plain,
( X_123 != multiply(inverse(greatest_lower_bound(inverse(X_123),inverse(greatest_lower_bound(X_13,X_123)))),identity)
| multiply(inverse(greatest_lower_bound(inverse(X_123),inverse(greatest_lower_bound(X_13,X_123)))),identity) != inverse(greatest_lower_bound(inverse(X_123),inverse(greatest_lower_bound(X_13,X_123))))
| X_123 = inverse(greatest_lower_bound(inverse(X_123),inverse(greatest_lower_bound(X_13,X_123)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_123,inverse(greatest_lower_bound(inverse(X_123),inverse(greatest_lower_bound(X_13,X_123))))) ),[0],$fot(multiply(inverse(greatest_lower_bound(inverse(X_123),inverse(greatest_lower_bound(X_13,X_123)))),identity))]]) ).
cnf(refute_0_819,plain,
( X_123 != multiply(inverse(greatest_lower_bound(inverse(X_123),inverse(greatest_lower_bound(X_13,X_123)))),identity)
| X_123 = inverse(greatest_lower_bound(inverse(X_123),inverse(greatest_lower_bound(X_13,X_123)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(X_123),inverse(greatest_lower_bound(X_13,X_123)))),identity),inverse(greatest_lower_bound(inverse(X_123),inverse(greatest_lower_bound(X_13,X_123))))) )],[refute_0_817,refute_0_818]) ).
cnf(refute_0_820,plain,
X_123 = inverse(greatest_lower_bound(inverse(X_123),inverse(greatest_lower_bound(X_13,X_123)))),
inference(resolve,[$cnf( $equal(X_123,multiply(inverse(greatest_lower_bound(inverse(X_123),inverse(greatest_lower_bound(X_13,X_123)))),identity)) )],[refute_0_816,refute_0_819]) ).
cnf(refute_0_821,plain,
X_167 = inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),
inference(subst,[],[refute_0_820:[bind(X_123,$fot(X_167)),bind(X_13,$fot(X_168))]]) ).
cnf(refute_0_822,plain,
( X_167 != inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))))
| inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))) = X_167 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_167)),bind(Y0,$fot(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))))))]]) ).
cnf(refute_0_823,plain,
inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))) = X_167,
inference(resolve,[$cnf( $equal(X_167,inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))))) )],[refute_0_821,refute_0_822]) ).
cnf(refute_0_824,plain,
( multiply(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),least_upper_bound(X_79,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))))) != least_upper_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),X_79))
| inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))) != X_167
| multiply(X_167,least_upper_bound(X_79,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))))) = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),X_79)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),least_upper_bound(X_79,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),X_79))) ),[0,0],$fot(X_167)]]) ).
cnf(refute_0_825,plain,
( multiply(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),least_upper_bound(X_79,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))))) != least_upper_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),X_79))
| multiply(X_167,least_upper_bound(X_79,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))))) = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),X_79)) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),X_167) )],[refute_0_823,refute_0_824]) ).
cnf(refute_0_826,plain,
multiply(X_167,least_upper_bound(X_79,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))))) = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),X_79)),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),least_upper_bound(X_79,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),X_79))) )],[refute_0_786,refute_0_825]) ).
cnf(refute_0_827,plain,
greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))) = inverse(greatest_lower_bound(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),inverse(greatest_lower_bound(X_13,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))))))),
inference(subst,[],[refute_0_820:[bind(X_123,$fot(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))))]]) ).
cnf(refute_0_828,plain,
( greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))) != inverse(greatest_lower_bound(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),inverse(greatest_lower_bound(X_13,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))))))
| inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))) != X_167
| greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))) = inverse(greatest_lower_bound(X_167,inverse(greatest_lower_bound(X_13,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))))))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))),inverse(greatest_lower_bound(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),inverse(greatest_lower_bound(X_13,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))))))) ),[1,0,0],$fot(X_167)]]) ).
cnf(refute_0_829,plain,
( greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))) != inverse(greatest_lower_bound(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),inverse(greatest_lower_bound(X_13,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))))))
| greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))) = inverse(greatest_lower_bound(X_167,inverse(greatest_lower_bound(X_13,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))))))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),X_167) )],[refute_0_823,refute_0_828]) ).
cnf(refute_0_830,plain,
greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))) = inverse(greatest_lower_bound(X_167,inverse(greatest_lower_bound(X_13,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))))))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))),inverse(greatest_lower_bound(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),inverse(greatest_lower_bound(X_13,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))))))) )],[refute_0_827,refute_0_829]) ).
cnf(refute_0_831,plain,
X_123 = multiply(inverse(greatest_lower_bound(inverse(X_123),greatest_lower_bound(inverse(X_123),X_14))),greatest_lower_bound(identity,multiply(greatest_lower_bound(inverse(X_123),X_14),X_123))),
inference(subst,[],[refute_0_795:[bind(X_30,$fot(greatest_lower_bound(inverse(X_123),X_14))),bind(X_74,$fot(X_123))]]) ).
cnf(refute_0_832,plain,
greatest_lower_bound(X_15,greatest_lower_bound(X_14,X_15)) = greatest_lower_bound(X_15,X_14),
inference(subst,[],[refute_0_181:[bind(X_13,$fot(X_14)),bind(X_9,$fot(X_15))]]) ).
cnf(refute_0_833,plain,
greatest_lower_bound(X_15,X_14) = greatest_lower_bound(X_14,X_15),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_15)),bind(Y,$fot(X_14))]]) ).
cnf(refute_0_834,plain,
( greatest_lower_bound(X_15,X_14) != greatest_lower_bound(X_14,X_15)
| greatest_lower_bound(X_14,X_15) = greatest_lower_bound(X_15,X_14) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X_15,X_14))),bind(Y0,$fot(greatest_lower_bound(X_14,X_15)))]]) ).
cnf(refute_0_835,plain,
greatest_lower_bound(X_14,X_15) = greatest_lower_bound(X_15,X_14),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_15,X_14),greatest_lower_bound(X_14,X_15)) )],[refute_0_833,refute_0_834]) ).
cnf(refute_0_836,plain,
( greatest_lower_bound(X_14,X_15) != greatest_lower_bound(X_15,X_14)
| greatest_lower_bound(X_15,greatest_lower_bound(X_14,X_15)) != greatest_lower_bound(X_15,X_14)
| greatest_lower_bound(X_15,greatest_lower_bound(X_15,X_14)) = greatest_lower_bound(X_15,X_14) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_15,greatest_lower_bound(X_14,X_15)),greatest_lower_bound(X_15,X_14)) ),[0,1],$fot(greatest_lower_bound(X_15,X_14))]]) ).
cnf(refute_0_837,plain,
( greatest_lower_bound(X_15,greatest_lower_bound(X_14,X_15)) != greatest_lower_bound(X_15,X_14)
| greatest_lower_bound(X_15,greatest_lower_bound(X_15,X_14)) = greatest_lower_bound(X_15,X_14) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_14,X_15),greatest_lower_bound(X_15,X_14)) )],[refute_0_835,refute_0_836]) ).
cnf(refute_0_838,plain,
greatest_lower_bound(X_15,greatest_lower_bound(X_15,X_14)) = greatest_lower_bound(X_15,X_14),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_15,greatest_lower_bound(X_14,X_15)),greatest_lower_bound(X_15,X_14)) )],[refute_0_832,refute_0_837]) ).
cnf(refute_0_839,plain,
greatest_lower_bound(inverse(X_123),greatest_lower_bound(inverse(X_123),X_14)) = greatest_lower_bound(inverse(X_123),X_14),
inference(subst,[],[refute_0_838:[bind(X_15,$fot(inverse(X_123)))]]) ).
cnf(refute_0_840,plain,
( X_123 != multiply(inverse(greatest_lower_bound(inverse(X_123),greatest_lower_bound(inverse(X_123),X_14))),greatest_lower_bound(identity,multiply(greatest_lower_bound(inverse(X_123),X_14),X_123)))
| greatest_lower_bound(inverse(X_123),greatest_lower_bound(inverse(X_123),X_14)) != greatest_lower_bound(inverse(X_123),X_14)
| X_123 = multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),greatest_lower_bound(identity,multiply(greatest_lower_bound(inverse(X_123),X_14),X_123))) ),
introduced(tautology,[equality,[$cnf( $equal(X_123,multiply(inverse(greatest_lower_bound(inverse(X_123),greatest_lower_bound(inverse(X_123),X_14))),greatest_lower_bound(identity,multiply(greatest_lower_bound(inverse(X_123),X_14),X_123)))) ),[1,0,0],$fot(greatest_lower_bound(inverse(X_123),X_14))]]) ).
cnf(refute_0_841,plain,
( X_123 != multiply(inverse(greatest_lower_bound(inverse(X_123),greatest_lower_bound(inverse(X_123),X_14))),greatest_lower_bound(identity,multiply(greatest_lower_bound(inverse(X_123),X_14),X_123)))
| X_123 = multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),greatest_lower_bound(identity,multiply(greatest_lower_bound(inverse(X_123),X_14),X_123))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_123),greatest_lower_bound(inverse(X_123),X_14)),greatest_lower_bound(inverse(X_123),X_14)) )],[refute_0_839,refute_0_840]) ).
cnf(refute_0_842,plain,
X_123 = multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),greatest_lower_bound(identity,multiply(greatest_lower_bound(inverse(X_123),X_14),X_123))),
inference(resolve,[$cnf( $equal(X_123,multiply(inverse(greatest_lower_bound(inverse(X_123),greatest_lower_bound(inverse(X_123),X_14))),greatest_lower_bound(identity,multiply(greatest_lower_bound(inverse(X_123),X_14),X_123)))) )],[refute_0_831,refute_0_841]) ).
cnf(refute_0_843,plain,
multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),identity) = inverse(greatest_lower_bound(inverse(X_123),X_14)),
inference(subst,[],[refute_0_217:[bind(X_74,$fot(inverse(greatest_lower_bound(inverse(X_123),X_14))))]]) ).
cnf(refute_0_844,plain,
greatest_lower_bound(X_123,multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),identity)) = greatest_lower_bound(X_123,multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),identity)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X_123,multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),identity)))]]) ).
cnf(refute_0_845,plain,
( multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),identity) != inverse(greatest_lower_bound(inverse(X_123),X_14))
| greatest_lower_bound(X_123,multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),identity)) != greatest_lower_bound(X_123,multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),identity))
| greatest_lower_bound(X_123,multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),identity)) = greatest_lower_bound(X_123,inverse(greatest_lower_bound(inverse(X_123),X_14))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_123,multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),identity)),greatest_lower_bound(X_123,multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),identity))) ),[1,1],$fot(inverse(greatest_lower_bound(inverse(X_123),X_14)))]]) ).
cnf(refute_0_846,plain,
( multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),identity) != inverse(greatest_lower_bound(inverse(X_123),X_14))
| greatest_lower_bound(X_123,multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),identity)) = greatest_lower_bound(X_123,inverse(greatest_lower_bound(inverse(X_123),X_14))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_123,multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),identity)),greatest_lower_bound(X_123,multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),identity))) )],[refute_0_844,refute_0_845]) ).
cnf(refute_0_847,plain,
greatest_lower_bound(X_123,multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),identity)) = greatest_lower_bound(X_123,inverse(greatest_lower_bound(inverse(X_123),X_14))),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),identity),inverse(greatest_lower_bound(inverse(X_123),X_14))) )],[refute_0_843,refute_0_846]) ).
cnf(refute_0_848,plain,
greatest_lower_bound(X_22,X_23) = multiply(inverse(inverse(X_23)),multiply(inverse(X_23),greatest_lower_bound(X_22,X_23))),
inference(subst,[],[refute_0_45:[bind(X_71,$fot(inverse(X_23))),bind(X_72,$fot(greatest_lower_bound(X_22,X_23)))]]) ).
cnf(refute_0_849,plain,
( multiply(inverse(X_23),greatest_lower_bound(X_22,X_23)) != greatest_lower_bound(identity,multiply(inverse(X_23),X_22))
| greatest_lower_bound(X_22,X_23) != multiply(inverse(inverse(X_23)),multiply(inverse(X_23),greatest_lower_bound(X_22,X_23)))
| greatest_lower_bound(X_22,X_23) = multiply(inverse(inverse(X_23)),greatest_lower_bound(identity,multiply(inverse(X_23),X_22))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_22,X_23),multiply(inverse(inverse(X_23)),multiply(inverse(X_23),greatest_lower_bound(X_22,X_23)))) ),[1,1],$fot(greatest_lower_bound(identity,multiply(inverse(X_23),X_22)))]]) ).
cnf(refute_0_850,plain,
( greatest_lower_bound(X_22,X_23) != multiply(inverse(inverse(X_23)),multiply(inverse(X_23),greatest_lower_bound(X_22,X_23)))
| greatest_lower_bound(X_22,X_23) = multiply(inverse(inverse(X_23)),greatest_lower_bound(identity,multiply(inverse(X_23),X_22))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_23),greatest_lower_bound(X_22,X_23)),greatest_lower_bound(identity,multiply(inverse(X_23),X_22))) )],[refute_0_269,refute_0_849]) ).
cnf(refute_0_851,plain,
greatest_lower_bound(X_22,X_23) = multiply(inverse(inverse(X_23)),greatest_lower_bound(identity,multiply(inverse(X_23),X_22))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_22,X_23),multiply(inverse(inverse(X_23)),multiply(inverse(X_23),greatest_lower_bound(X_22,X_23)))) )],[refute_0_848,refute_0_850]) ).
cnf(refute_0_852,plain,
greatest_lower_bound(X_22,X_23) = multiply(inverse(inverse(X_22)),multiply(inverse(X_22),greatest_lower_bound(X_22,X_23))),
inference(subst,[],[refute_0_45:[bind(X_71,$fot(inverse(X_22))),bind(X_72,$fot(greatest_lower_bound(X_22,X_23)))]]) ).
cnf(refute_0_853,plain,
( multiply(inverse(X_22),greatest_lower_bound(X_22,X_23)) != greatest_lower_bound(identity,multiply(inverse(X_22),X_23))
| greatest_lower_bound(X_22,X_23) != multiply(inverse(inverse(X_22)),multiply(inverse(X_22),greatest_lower_bound(X_22,X_23)))
| greatest_lower_bound(X_22,X_23) = multiply(inverse(inverse(X_22)),greatest_lower_bound(identity,multiply(inverse(X_22),X_23))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_22,X_23),multiply(inverse(inverse(X_22)),multiply(inverse(X_22),greatest_lower_bound(X_22,X_23)))) ),[1,1],$fot(greatest_lower_bound(identity,multiply(inverse(X_22),X_23)))]]) ).
cnf(refute_0_854,plain,
( greatest_lower_bound(X_22,X_23) != multiply(inverse(inverse(X_22)),multiply(inverse(X_22),greatest_lower_bound(X_22,X_23)))
| greatest_lower_bound(X_22,X_23) = multiply(inverse(inverse(X_22)),greatest_lower_bound(identity,multiply(inverse(X_22),X_23))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_22),greatest_lower_bound(X_22,X_23)),greatest_lower_bound(identity,multiply(inverse(X_22),X_23))) )],[refute_0_249,refute_0_853]) ).
cnf(refute_0_855,plain,
greatest_lower_bound(X_22,X_23) = multiply(inverse(inverse(X_22)),greatest_lower_bound(identity,multiply(inverse(X_22),X_23))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_22,X_23),multiply(inverse(inverse(X_22)),multiply(inverse(X_22),greatest_lower_bound(X_22,X_23)))) )],[refute_0_852,refute_0_854]) ).
cnf(refute_0_856,plain,
multiply(inverse(inverse(X_22)),identity) = multiply(X_22,identity),
inference(subst,[],[refute_0_59:[bind(X_73,$fot(X_22)),bind(X_74,$fot(identity))]]) ).
cnf(refute_0_857,plain,
greatest_lower_bound(multiply(inverse(inverse(X_22)),identity),X_23) = greatest_lower_bound(multiply(inverse(inverse(X_22)),identity),X_23),
introduced(tautology,[refl,[$fot(greatest_lower_bound(multiply(inverse(inverse(X_22)),identity),X_23))]]) ).
cnf(refute_0_858,plain,
( multiply(inverse(inverse(X_22)),identity) != multiply(X_22,identity)
| greatest_lower_bound(multiply(inverse(inverse(X_22)),identity),X_23) != greatest_lower_bound(multiply(inverse(inverse(X_22)),identity),X_23)
| greatest_lower_bound(multiply(inverse(inverse(X_22)),identity),X_23) = greatest_lower_bound(multiply(X_22,identity),X_23) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(inverse(inverse(X_22)),identity),X_23),greatest_lower_bound(multiply(inverse(inverse(X_22)),identity),X_23)) ),[1,0],$fot(multiply(X_22,identity))]]) ).
cnf(refute_0_859,plain,
( multiply(inverse(inverse(X_22)),identity) != multiply(X_22,identity)
| greatest_lower_bound(multiply(inverse(inverse(X_22)),identity),X_23) = greatest_lower_bound(multiply(X_22,identity),X_23) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(inverse(inverse(X_22)),identity),X_23),greatest_lower_bound(multiply(inverse(inverse(X_22)),identity),X_23)) )],[refute_0_857,refute_0_858]) ).
cnf(refute_0_860,plain,
greatest_lower_bound(multiply(inverse(inverse(X_22)),identity),X_23) = greatest_lower_bound(multiply(X_22,identity),X_23),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_22)),identity),multiply(X_22,identity)) )],[refute_0_856,refute_0_859]) ).
cnf(refute_0_861,plain,
multiply(inverse(X_73),greatest_lower_bound(Y,multiply(X_73,X_74))) = greatest_lower_bound(multiply(inverse(X_73),Y),multiply(inverse(X_73),multiply(X_73,X_74))),
inference(subst,[],[monotony_glb1:[bind(X,$fot(inverse(X_73))),bind(Z,$fot(multiply(X_73,X_74)))]]) ).
cnf(refute_0_862,plain,
( multiply(inverse(X_73),multiply(X_73,X_74)) != X_74
| multiply(inverse(X_73),greatest_lower_bound(Y,multiply(X_73,X_74))) != greatest_lower_bound(multiply(inverse(X_73),Y),multiply(inverse(X_73),multiply(X_73,X_74)))
| multiply(inverse(X_73),greatest_lower_bound(Y,multiply(X_73,X_74))) = greatest_lower_bound(multiply(inverse(X_73),Y),X_74) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_73),greatest_lower_bound(Y,multiply(X_73,X_74))),greatest_lower_bound(multiply(inverse(X_73),Y),multiply(inverse(X_73),multiply(X_73,X_74)))) ),[1,1],$fot(X_74)]]) ).
cnf(refute_0_863,plain,
( multiply(inverse(X_73),greatest_lower_bound(Y,multiply(X_73,X_74))) != greatest_lower_bound(multiply(inverse(X_73),Y),multiply(inverse(X_73),multiply(X_73,X_74)))
| multiply(inverse(X_73),greatest_lower_bound(Y,multiply(X_73,X_74))) = greatest_lower_bound(multiply(inverse(X_73),Y),X_74) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_73),multiply(X_73,X_74)),X_74) )],[refute_0_54,refute_0_862]) ).
cnf(refute_0_864,plain,
multiply(inverse(X_73),greatest_lower_bound(Y,multiply(X_73,X_74))) = greatest_lower_bound(multiply(inverse(X_73),Y),X_74),
inference(resolve,[$cnf( $equal(multiply(inverse(X_73),greatest_lower_bound(Y,multiply(X_73,X_74))),greatest_lower_bound(multiply(inverse(X_73),Y),multiply(inverse(X_73),multiply(X_73,X_74)))) )],[refute_0_861,refute_0_863]) ).
cnf(refute_0_865,plain,
multiply(inverse(inverse(X_22)),greatest_lower_bound(identity,multiply(inverse(X_22),X_23))) = greatest_lower_bound(multiply(inverse(inverse(X_22)),identity),X_23),
inference(subst,[],[refute_0_864:[bind(Y,$fot(identity)),bind(X_73,$fot(inverse(X_22))),bind(X_74,$fot(X_23))]]) ).
cnf(refute_0_866,plain,
( multiply(inverse(inverse(X_22)),greatest_lower_bound(identity,multiply(inverse(X_22),X_23))) != greatest_lower_bound(multiply(inverse(inverse(X_22)),identity),X_23)
| greatest_lower_bound(multiply(inverse(inverse(X_22)),identity),X_23) != greatest_lower_bound(multiply(X_22,identity),X_23)
| multiply(inverse(inverse(X_22)),greatest_lower_bound(identity,multiply(inverse(X_22),X_23))) = greatest_lower_bound(multiply(X_22,identity),X_23) ),
inference(subst,[],[refute_0_136:[bind(X0,$fot(multiply(inverse(inverse(X_22)),greatest_lower_bound(identity,multiply(inverse(X_22),X_23))))),bind(Y0,$fot(greatest_lower_bound(multiply(inverse(inverse(X_22)),identity),X_23))),bind(Z0,$fot(greatest_lower_bound(multiply(X_22,identity),X_23)))]]) ).
cnf(refute_0_867,plain,
( greatest_lower_bound(multiply(inverse(inverse(X_22)),identity),X_23) != greatest_lower_bound(multiply(X_22,identity),X_23)
| multiply(inverse(inverse(X_22)),greatest_lower_bound(identity,multiply(inverse(X_22),X_23))) = greatest_lower_bound(multiply(X_22,identity),X_23) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_22)),greatest_lower_bound(identity,multiply(inverse(X_22),X_23))),greatest_lower_bound(multiply(inverse(inverse(X_22)),identity),X_23)) )],[refute_0_865,refute_0_866]) ).
cnf(refute_0_868,plain,
multiply(inverse(inverse(X_22)),greatest_lower_bound(identity,multiply(inverse(X_22),X_23))) = greatest_lower_bound(multiply(X_22,identity),X_23),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(inverse(inverse(X_22)),identity),X_23),greatest_lower_bound(multiply(X_22,identity),X_23)) )],[refute_0_860,refute_0_867]) ).
cnf(refute_0_869,plain,
( multiply(inverse(inverse(X_22)),greatest_lower_bound(identity,multiply(inverse(X_22),X_23))) != greatest_lower_bound(multiply(X_22,identity),X_23)
| greatest_lower_bound(X_22,X_23) != multiply(inverse(inverse(X_22)),greatest_lower_bound(identity,multiply(inverse(X_22),X_23)))
| greatest_lower_bound(X_22,X_23) = greatest_lower_bound(multiply(X_22,identity),X_23) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_22,X_23),multiply(inverse(inverse(X_22)),greatest_lower_bound(identity,multiply(inverse(X_22),X_23)))) ),[1],$fot(greatest_lower_bound(multiply(X_22,identity),X_23))]]) ).
cnf(refute_0_870,plain,
( greatest_lower_bound(X_22,X_23) != multiply(inverse(inverse(X_22)),greatest_lower_bound(identity,multiply(inverse(X_22),X_23)))
| greatest_lower_bound(X_22,X_23) = greatest_lower_bound(multiply(X_22,identity),X_23) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_22)),greatest_lower_bound(identity,multiply(inverse(X_22),X_23))),greatest_lower_bound(multiply(X_22,identity),X_23)) )],[refute_0_868,refute_0_869]) ).
cnf(refute_0_871,plain,
greatest_lower_bound(X_22,X_23) = greatest_lower_bound(multiply(X_22,identity),X_23),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_22,X_23),multiply(inverse(inverse(X_22)),greatest_lower_bound(identity,multiply(inverse(X_22),X_23)))) )],[refute_0_855,refute_0_870]) ).
cnf(refute_0_872,plain,
( greatest_lower_bound(X_22,X_23) != greatest_lower_bound(multiply(X_22,identity),X_23)
| greatest_lower_bound(multiply(X_22,identity),X_23) = greatest_lower_bound(X_22,X_23) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X_22,X_23))),bind(Y0,$fot(greatest_lower_bound(multiply(X_22,identity),X_23)))]]) ).
cnf(refute_0_873,plain,
greatest_lower_bound(multiply(X_22,identity),X_23) = greatest_lower_bound(X_22,X_23),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_22,X_23),greatest_lower_bound(multiply(X_22,identity),X_23)) )],[refute_0_871,refute_0_872]) ).
cnf(refute_0_874,plain,
greatest_lower_bound(multiply(inverse(inverse(X_23)),identity),X_22) = greatest_lower_bound(inverse(inverse(X_23)),X_22),
inference(subst,[],[refute_0_873:[bind(X_22,$fot(inverse(inverse(X_23)))),bind(X_23,$fot(X_22))]]) ).
cnf(refute_0_875,plain,
multiply(inverse(inverse(X_23)),greatest_lower_bound(identity,multiply(inverse(X_23),X_22))) = greatest_lower_bound(multiply(inverse(inverse(X_23)),identity),X_22),
inference(subst,[],[refute_0_864:[bind(Y,$fot(identity)),bind(X_73,$fot(inverse(X_23))),bind(X_74,$fot(X_22))]]) ).
cnf(refute_0_876,plain,
( multiply(inverse(inverse(X_23)),greatest_lower_bound(identity,multiply(inverse(X_23),X_22))) != greatest_lower_bound(multiply(inverse(inverse(X_23)),identity),X_22)
| greatest_lower_bound(multiply(inverse(inverse(X_23)),identity),X_22) != greatest_lower_bound(inverse(inverse(X_23)),X_22)
| multiply(inverse(inverse(X_23)),greatest_lower_bound(identity,multiply(inverse(X_23),X_22))) = greatest_lower_bound(inverse(inverse(X_23)),X_22) ),
inference(subst,[],[refute_0_136:[bind(X0,$fot(multiply(inverse(inverse(X_23)),greatest_lower_bound(identity,multiply(inverse(X_23),X_22))))),bind(Y0,$fot(greatest_lower_bound(multiply(inverse(inverse(X_23)),identity),X_22))),bind(Z0,$fot(greatest_lower_bound(inverse(inverse(X_23)),X_22)))]]) ).
cnf(refute_0_877,plain,
( greatest_lower_bound(multiply(inverse(inverse(X_23)),identity),X_22) != greatest_lower_bound(inverse(inverse(X_23)),X_22)
| multiply(inverse(inverse(X_23)),greatest_lower_bound(identity,multiply(inverse(X_23),X_22))) = greatest_lower_bound(inverse(inverse(X_23)),X_22) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_23)),greatest_lower_bound(identity,multiply(inverse(X_23),X_22))),greatest_lower_bound(multiply(inverse(inverse(X_23)),identity),X_22)) )],[refute_0_875,refute_0_876]) ).
cnf(refute_0_878,plain,
multiply(inverse(inverse(X_23)),greatest_lower_bound(identity,multiply(inverse(X_23),X_22))) = greatest_lower_bound(inverse(inverse(X_23)),X_22),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(inverse(inverse(X_23)),identity),X_22),greatest_lower_bound(inverse(inverse(X_23)),X_22)) )],[refute_0_874,refute_0_877]) ).
cnf(refute_0_879,plain,
( multiply(inverse(inverse(X_23)),greatest_lower_bound(identity,multiply(inverse(X_23),X_22))) != greatest_lower_bound(inverse(inverse(X_23)),X_22)
| greatest_lower_bound(X_22,X_23) != multiply(inverse(inverse(X_23)),greatest_lower_bound(identity,multiply(inverse(X_23),X_22)))
| greatest_lower_bound(X_22,X_23) = greatest_lower_bound(inverse(inverse(X_23)),X_22) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_22,X_23),multiply(inverse(inverse(X_23)),greatest_lower_bound(identity,multiply(inverse(X_23),X_22)))) ),[1],$fot(greatest_lower_bound(inverse(inverse(X_23)),X_22))]]) ).
cnf(refute_0_880,plain,
( greatest_lower_bound(X_22,X_23) != multiply(inverse(inverse(X_23)),greatest_lower_bound(identity,multiply(inverse(X_23),X_22)))
| greatest_lower_bound(X_22,X_23) = greatest_lower_bound(inverse(inverse(X_23)),X_22) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_23)),greatest_lower_bound(identity,multiply(inverse(X_23),X_22))),greatest_lower_bound(inverse(inverse(X_23)),X_22)) )],[refute_0_878,refute_0_879]) ).
cnf(refute_0_881,plain,
greatest_lower_bound(X_22,X_23) = greatest_lower_bound(inverse(inverse(X_23)),X_22),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_22,X_23),multiply(inverse(inverse(X_23)),greatest_lower_bound(identity,multiply(inverse(X_23),X_22)))) )],[refute_0_851,refute_0_880]) ).
cnf(refute_0_882,plain,
inverse(inverse(X_23)) = X_23,
inference(subst,[],[refute_0_309:[bind(X_77,$fot(X_23))]]) ).
cnf(refute_0_883,plain,
greatest_lower_bound(inverse(inverse(X_23)),X_22) = greatest_lower_bound(inverse(inverse(X_23)),X_22),
introduced(tautology,[refl,[$fot(greatest_lower_bound(inverse(inverse(X_23)),X_22))]]) ).
cnf(refute_0_884,plain,
( greatest_lower_bound(inverse(inverse(X_23)),X_22) != greatest_lower_bound(inverse(inverse(X_23)),X_22)
| inverse(inverse(X_23)) != X_23
| greatest_lower_bound(inverse(inverse(X_23)),X_22) = greatest_lower_bound(X_23,X_22) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(inverse(inverse(X_23)),X_22),greatest_lower_bound(inverse(inverse(X_23)),X_22)) ),[1,0],$fot(X_23)]]) ).
cnf(refute_0_885,plain,
( inverse(inverse(X_23)) != X_23
| greatest_lower_bound(inverse(inverse(X_23)),X_22) = greatest_lower_bound(X_23,X_22) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(inverse(X_23)),X_22),greatest_lower_bound(inverse(inverse(X_23)),X_22)) )],[refute_0_883,refute_0_884]) ).
cnf(refute_0_886,plain,
greatest_lower_bound(inverse(inverse(X_23)),X_22) = greatest_lower_bound(X_23,X_22),
inference(resolve,[$cnf( $equal(inverse(inverse(X_23)),X_23) )],[refute_0_882,refute_0_885]) ).
cnf(refute_0_887,plain,
( greatest_lower_bound(X_22,X_23) != greatest_lower_bound(inverse(inverse(X_23)),X_22)
| greatest_lower_bound(inverse(inverse(X_23)),X_22) != greatest_lower_bound(X_23,X_22)
| greatest_lower_bound(X_22,X_23) = greatest_lower_bound(X_23,X_22) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_22,X_23),greatest_lower_bound(X_23,X_22)) ),[0],$fot(greatest_lower_bound(inverse(inverse(X_23)),X_22))]]) ).
cnf(refute_0_888,plain,
( greatest_lower_bound(X_22,X_23) != greatest_lower_bound(inverse(inverse(X_23)),X_22)
| greatest_lower_bound(X_22,X_23) = greatest_lower_bound(X_23,X_22) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(inverse(X_23)),X_22),greatest_lower_bound(X_23,X_22)) )],[refute_0_886,refute_0_887]) ).
cnf(refute_0_889,plain,
greatest_lower_bound(X_22,X_23) = greatest_lower_bound(X_23,X_22),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_22,X_23),greatest_lower_bound(inverse(inverse(X_23)),X_22)) )],[refute_0_881,refute_0_888]) ).
cnf(refute_0_890,plain,
( greatest_lower_bound(X_22,X_23) != greatest_lower_bound(X_23,X_22)
| greatest_lower_bound(X_23,X_22) = greatest_lower_bound(X_22,X_23) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X_22,X_23))),bind(Y0,$fot(greatest_lower_bound(X_23,X_22)))]]) ).
cnf(refute_0_891,plain,
greatest_lower_bound(X_23,X_22) = greatest_lower_bound(X_22,X_23),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_22,X_23),greatest_lower_bound(X_23,X_22)) )],[refute_0_889,refute_0_890]) ).
cnf(refute_0_892,plain,
greatest_lower_bound(multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),identity),X_123) = greatest_lower_bound(X_123,multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),identity)),
inference(subst,[],[refute_0_891:[bind(X_22,$fot(X_123)),bind(X_23,$fot(multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),identity)))]]) ).
cnf(refute_0_893,plain,
multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),greatest_lower_bound(identity,multiply(greatest_lower_bound(inverse(X_123),X_14),X_123))) = greatest_lower_bound(multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),identity),X_123),
inference(subst,[],[refute_0_864:[bind(Y,$fot(identity)),bind(X_73,$fot(greatest_lower_bound(inverse(X_123),X_14))),bind(X_74,$fot(X_123))]]) ).
cnf(refute_0_894,plain,
( multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),greatest_lower_bound(identity,multiply(greatest_lower_bound(inverse(X_123),X_14),X_123))) != greatest_lower_bound(multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),identity),X_123)
| greatest_lower_bound(multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),identity),X_123) != greatest_lower_bound(X_123,multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),identity))
| multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),greatest_lower_bound(identity,multiply(greatest_lower_bound(inverse(X_123),X_14),X_123))) = greatest_lower_bound(X_123,multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),identity)) ),
inference(subst,[],[refute_0_136:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),greatest_lower_bound(identity,multiply(greatest_lower_bound(inverse(X_123),X_14),X_123))))),bind(Y0,$fot(greatest_lower_bound(multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),identity),X_123))),bind(Z0,$fot(greatest_lower_bound(X_123,multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),identity))))]]) ).
cnf(refute_0_895,plain,
( greatest_lower_bound(multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),identity),X_123) != greatest_lower_bound(X_123,multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),identity))
| multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),greatest_lower_bound(identity,multiply(greatest_lower_bound(inverse(X_123),X_14),X_123))) = greatest_lower_bound(X_123,multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),greatest_lower_bound(identity,multiply(greatest_lower_bound(inverse(X_123),X_14),X_123))),greatest_lower_bound(multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),identity),X_123)) )],[refute_0_893,refute_0_894]) ).
cnf(refute_0_896,plain,
multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),greatest_lower_bound(identity,multiply(greatest_lower_bound(inverse(X_123),X_14),X_123))) = greatest_lower_bound(X_123,multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),identity)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),identity),X_123),greatest_lower_bound(X_123,multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),identity))) )],[refute_0_892,refute_0_895]) ).
cnf(refute_0_897,plain,
( multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),greatest_lower_bound(identity,multiply(greatest_lower_bound(inverse(X_123),X_14),X_123))) != greatest_lower_bound(X_123,multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),identity))
| greatest_lower_bound(X_123,multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),identity)) != greatest_lower_bound(X_123,inverse(greatest_lower_bound(inverse(X_123),X_14)))
| multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),greatest_lower_bound(identity,multiply(greatest_lower_bound(inverse(X_123),X_14),X_123))) = greatest_lower_bound(X_123,inverse(greatest_lower_bound(inverse(X_123),X_14))) ),
inference(subst,[],[refute_0_136:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),greatest_lower_bound(identity,multiply(greatest_lower_bound(inverse(X_123),X_14),X_123))))),bind(Y0,$fot(greatest_lower_bound(X_123,multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),identity)))),bind(Z0,$fot(greatest_lower_bound(X_123,inverse(greatest_lower_bound(inverse(X_123),X_14)))))]]) ).
cnf(refute_0_898,plain,
( greatest_lower_bound(X_123,multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),identity)) != greatest_lower_bound(X_123,inverse(greatest_lower_bound(inverse(X_123),X_14)))
| multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),greatest_lower_bound(identity,multiply(greatest_lower_bound(inverse(X_123),X_14),X_123))) = greatest_lower_bound(X_123,inverse(greatest_lower_bound(inverse(X_123),X_14))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),greatest_lower_bound(identity,multiply(greatest_lower_bound(inverse(X_123),X_14),X_123))),greatest_lower_bound(X_123,multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),identity))) )],[refute_0_896,refute_0_897]) ).
cnf(refute_0_899,plain,
multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),greatest_lower_bound(identity,multiply(greatest_lower_bound(inverse(X_123),X_14),X_123))) = greatest_lower_bound(X_123,inverse(greatest_lower_bound(inverse(X_123),X_14))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_123,multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),identity)),greatest_lower_bound(X_123,inverse(greatest_lower_bound(inverse(X_123),X_14)))) )],[refute_0_847,refute_0_898]) ).
cnf(refute_0_900,plain,
( X_123 != multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),greatest_lower_bound(identity,multiply(greatest_lower_bound(inverse(X_123),X_14),X_123)))
| multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),greatest_lower_bound(identity,multiply(greatest_lower_bound(inverse(X_123),X_14),X_123))) != greatest_lower_bound(X_123,inverse(greatest_lower_bound(inverse(X_123),X_14)))
| X_123 = greatest_lower_bound(X_123,inverse(greatest_lower_bound(inverse(X_123),X_14))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_123,greatest_lower_bound(X_123,inverse(greatest_lower_bound(inverse(X_123),X_14)))) ),[0],$fot(multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),greatest_lower_bound(identity,multiply(greatest_lower_bound(inverse(X_123),X_14),X_123))))]]) ).
cnf(refute_0_901,plain,
( X_123 != multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),greatest_lower_bound(identity,multiply(greatest_lower_bound(inverse(X_123),X_14),X_123)))
| X_123 = greatest_lower_bound(X_123,inverse(greatest_lower_bound(inverse(X_123),X_14))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),greatest_lower_bound(identity,multiply(greatest_lower_bound(inverse(X_123),X_14),X_123))),greatest_lower_bound(X_123,inverse(greatest_lower_bound(inverse(X_123),X_14)))) )],[refute_0_899,refute_0_900]) ).
cnf(refute_0_902,plain,
X_123 = greatest_lower_bound(X_123,inverse(greatest_lower_bound(inverse(X_123),X_14))),
inference(resolve,[$cnf( $equal(X_123,multiply(inverse(greatest_lower_bound(inverse(X_123),X_14)),greatest_lower_bound(identity,multiply(greatest_lower_bound(inverse(X_123),X_14),X_123)))) )],[refute_0_842,refute_0_901]) ).
cnf(refute_0_903,plain,
X_126 = greatest_lower_bound(X_126,inverse(greatest_lower_bound(inverse(X_126),greatest_lower_bound(X_19,X)))),
inference(subst,[],[refute_0_902:[bind(X_123,$fot(X_126)),bind(X_14,$fot(greatest_lower_bound(X_19,X)))]]) ).
cnf(refute_0_904,plain,
greatest_lower_bound(X,greatest_lower_bound(X_18,X_19)) = greatest_lower_bound(greatest_lower_bound(X_18,X_19),X),
inference(subst,[],[symmetry_of_glb:[bind(Y,$fot(greatest_lower_bound(X_18,X_19)))]]) ).
cnf(refute_0_905,plain,
greatest_lower_bound(X_18,greatest_lower_bound(X_19,X)) = greatest_lower_bound(greatest_lower_bound(X_18,X_19),X),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_18)),bind(Y,$fot(X_19)),bind(Z,$fot(X))]]) ).
cnf(refute_0_906,plain,
( greatest_lower_bound(X_18,greatest_lower_bound(X_19,X)) != greatest_lower_bound(greatest_lower_bound(X_18,X_19),X)
| greatest_lower_bound(greatest_lower_bound(X_18,X_19),X) = greatest_lower_bound(X_18,greatest_lower_bound(X_19,X)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X_18,greatest_lower_bound(X_19,X)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X_18,X_19),X)))]]) ).
cnf(refute_0_907,plain,
greatest_lower_bound(greatest_lower_bound(X_18,X_19),X) = greatest_lower_bound(X_18,greatest_lower_bound(X_19,X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_18,greatest_lower_bound(X_19,X)),greatest_lower_bound(greatest_lower_bound(X_18,X_19),X)) )],[refute_0_905,refute_0_906]) ).
cnf(refute_0_908,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_18,X_19)) != greatest_lower_bound(greatest_lower_bound(X_18,X_19),X)
| greatest_lower_bound(greatest_lower_bound(X_18,X_19),X) != greatest_lower_bound(X_18,greatest_lower_bound(X_19,X))
| greatest_lower_bound(X,greatest_lower_bound(X_18,X_19)) = greatest_lower_bound(X_18,greatest_lower_bound(X_19,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X,greatest_lower_bound(X_18,X_19)),greatest_lower_bound(X_18,greatest_lower_bound(X_19,X))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_18,X_19),X))]]) ).
cnf(refute_0_909,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_18,X_19)) != greatest_lower_bound(greatest_lower_bound(X_18,X_19),X)
| greatest_lower_bound(X,greatest_lower_bound(X_18,X_19)) = greatest_lower_bound(X_18,greatest_lower_bound(X_19,X)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_18,X_19),X),greatest_lower_bound(X_18,greatest_lower_bound(X_19,X))) )],[refute_0_907,refute_0_908]) ).
cnf(refute_0_910,plain,
greatest_lower_bound(X,greatest_lower_bound(X_18,X_19)) = greatest_lower_bound(X_18,greatest_lower_bound(X_19,X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_18,X_19)),greatest_lower_bound(greatest_lower_bound(X_18,X_19),X)) )],[refute_0_904,refute_0_909]) ).
cnf(refute_0_911,plain,
greatest_lower_bound(X,greatest_lower_bound(inverse(X_126),X_19)) = greatest_lower_bound(inverse(X_126),greatest_lower_bound(X_19,X)),
inference(subst,[],[refute_0_910:[bind(X_18,$fot(inverse(X_126)))]]) ).
cnf(refute_0_912,plain,
( greatest_lower_bound(X,greatest_lower_bound(inverse(X_126),X_19)) != greatest_lower_bound(inverse(X_126),greatest_lower_bound(X_19,X))
| greatest_lower_bound(inverse(X_126),greatest_lower_bound(X_19,X)) = greatest_lower_bound(X,greatest_lower_bound(inverse(X_126),X_19)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(inverse(X_126),X_19)))),bind(Y0,$fot(greatest_lower_bound(inverse(X_126),greatest_lower_bound(X_19,X))))]]) ).
cnf(refute_0_913,plain,
greatest_lower_bound(inverse(X_126),greatest_lower_bound(X_19,X)) = greatest_lower_bound(X,greatest_lower_bound(inverse(X_126),X_19)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(inverse(X_126),X_19)),greatest_lower_bound(inverse(X_126),greatest_lower_bound(X_19,X))) )],[refute_0_911,refute_0_912]) ).
cnf(refute_0_914,plain,
( X_126 != greatest_lower_bound(X_126,inverse(greatest_lower_bound(inverse(X_126),greatest_lower_bound(X_19,X))))
| greatest_lower_bound(inverse(X_126),greatest_lower_bound(X_19,X)) != greatest_lower_bound(X,greatest_lower_bound(inverse(X_126),X_19))
| X_126 = greatest_lower_bound(X_126,inverse(greatest_lower_bound(X,greatest_lower_bound(inverse(X_126),X_19)))) ),
introduced(tautology,[equality,[$cnf( $equal(X_126,greatest_lower_bound(X_126,inverse(greatest_lower_bound(inverse(X_126),greatest_lower_bound(X_19,X))))) ),[1,1,0],$fot(greatest_lower_bound(X,greatest_lower_bound(inverse(X_126),X_19)))]]) ).
cnf(refute_0_915,plain,
( X_126 != greatest_lower_bound(X_126,inverse(greatest_lower_bound(inverse(X_126),greatest_lower_bound(X_19,X))))
| X_126 = greatest_lower_bound(X_126,inverse(greatest_lower_bound(X,greatest_lower_bound(inverse(X_126),X_19)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_126),greatest_lower_bound(X_19,X)),greatest_lower_bound(X,greatest_lower_bound(inverse(X_126),X_19))) )],[refute_0_913,refute_0_914]) ).
cnf(refute_0_916,plain,
X_126 = greatest_lower_bound(X_126,inverse(greatest_lower_bound(X,greatest_lower_bound(inverse(X_126),X_19)))),
inference(resolve,[$cnf( $equal(X_126,greatest_lower_bound(X_126,inverse(greatest_lower_bound(inverse(X_126),greatest_lower_bound(X_19,X))))) )],[refute_0_903,refute_0_915]) ).
cnf(refute_0_917,plain,
( X_126 != greatest_lower_bound(X_126,inverse(greatest_lower_bound(X,greatest_lower_bound(inverse(X_126),X_19))))
| greatest_lower_bound(X_126,inverse(greatest_lower_bound(X,greatest_lower_bound(inverse(X_126),X_19)))) = X_126 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_126)),bind(Y0,$fot(greatest_lower_bound(X_126,inverse(greatest_lower_bound(X,greatest_lower_bound(inverse(X_126),X_19))))))]]) ).
cnf(refute_0_918,plain,
greatest_lower_bound(X_126,inverse(greatest_lower_bound(X,greatest_lower_bound(inverse(X_126),X_19)))) = X_126,
inference(resolve,[$cnf( $equal(X_126,greatest_lower_bound(X_126,inverse(greatest_lower_bound(X,greatest_lower_bound(inverse(X_126),X_19))))) )],[refute_0_916,refute_0_917]) ).
cnf(refute_0_919,plain,
greatest_lower_bound(X_167,inverse(greatest_lower_bound(X_13,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))))) = X_167,
inference(subst,[],[refute_0_918:[bind(X,$fot(X_13)),bind(X_126,$fot(X_167)),bind(X_19,$fot(inverse(greatest_lower_bound(X_168,X_167))))]]) ).
cnf(refute_0_920,plain,
inverse(greatest_lower_bound(X_167,inverse(greatest_lower_bound(X_13,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))))))) = inverse(greatest_lower_bound(X_167,inverse(greatest_lower_bound(X_13,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))))))),
introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(X_167,inverse(greatest_lower_bound(X_13,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))))))))]]) ).
cnf(refute_0_921,plain,
( greatest_lower_bound(X_167,inverse(greatest_lower_bound(X_13,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))))) != X_167
| inverse(greatest_lower_bound(X_167,inverse(greatest_lower_bound(X_13,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))))))) != inverse(greatest_lower_bound(X_167,inverse(greatest_lower_bound(X_13,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))))))
| inverse(greatest_lower_bound(X_167,inverse(greatest_lower_bound(X_13,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))))))) = inverse(X_167) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X_167,inverse(greatest_lower_bound(X_13,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))))))),inverse(greatest_lower_bound(X_167,inverse(greatest_lower_bound(X_13,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))))))) ),[1,0],$fot(X_167)]]) ).
cnf(refute_0_922,plain,
( greatest_lower_bound(X_167,inverse(greatest_lower_bound(X_13,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))))) != X_167
| inverse(greatest_lower_bound(X_167,inverse(greatest_lower_bound(X_13,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))))))) = inverse(X_167) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_167,inverse(greatest_lower_bound(X_13,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))))))),inverse(greatest_lower_bound(X_167,inverse(greatest_lower_bound(X_13,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))))))) )],[refute_0_920,refute_0_921]) ).
cnf(refute_0_923,plain,
inverse(greatest_lower_bound(X_167,inverse(greatest_lower_bound(X_13,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))))))) = inverse(X_167),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_167,inverse(greatest_lower_bound(X_13,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))))),X_167) )],[refute_0_919,refute_0_922]) ).
cnf(refute_0_924,plain,
( greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))) != inverse(greatest_lower_bound(X_167,inverse(greatest_lower_bound(X_13,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))))))
| inverse(greatest_lower_bound(X_167,inverse(greatest_lower_bound(X_13,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))))))) != inverse(X_167)
| greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))) = inverse(X_167) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))),inverse(X_167)) ),[0],$fot(inverse(greatest_lower_bound(X_167,inverse(greatest_lower_bound(X_13,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))))))))]]) ).
cnf(refute_0_925,plain,
( greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))) != inverse(greatest_lower_bound(X_167,inverse(greatest_lower_bound(X_13,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))))))
| greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))) = inverse(X_167) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_167,inverse(greatest_lower_bound(X_13,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))))))),inverse(X_167)) )],[refute_0_923,refute_0_924]) ).
cnf(refute_0_926,plain,
greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))) = inverse(X_167),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))),inverse(greatest_lower_bound(X_167,inverse(greatest_lower_bound(X_13,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))))))) )],[refute_0_830,refute_0_925]) ).
cnf(refute_0_927,plain,
least_upper_bound(X_79,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))) = least_upper_bound(X_79,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_79,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))))]]) ).
cnf(refute_0_928,plain,
( greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))) != inverse(X_167)
| least_upper_bound(X_79,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))) != least_upper_bound(X_79,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))))
| least_upper_bound(X_79,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))) = least_upper_bound(X_79,inverse(X_167)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_79,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),least_upper_bound(X_79,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))))) ),[1,1],$fot(inverse(X_167))]]) ).
cnf(refute_0_929,plain,
( greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))) != inverse(X_167)
| least_upper_bound(X_79,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))) = least_upper_bound(X_79,inverse(X_167)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_79,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),least_upper_bound(X_79,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))))) )],[refute_0_927,refute_0_928]) ).
cnf(refute_0_930,plain,
least_upper_bound(X_79,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))) = least_upper_bound(X_79,inverse(X_167)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))),inverse(X_167)) )],[refute_0_926,refute_0_929]) ).
cnf(refute_0_931,plain,
multiply(X_167,least_upper_bound(X_79,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))))) = multiply(X_167,least_upper_bound(X_79,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))))),
introduced(tautology,[refl,[$fot(multiply(X_167,least_upper_bound(X_79,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))))))]]) ).
cnf(refute_0_932,plain,
( multiply(X_167,least_upper_bound(X_79,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))))) != multiply(X_167,least_upper_bound(X_79,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))))
| least_upper_bound(X_79,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))) != least_upper_bound(X_79,inverse(X_167))
| multiply(X_167,least_upper_bound(X_79,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))))) = multiply(X_167,least_upper_bound(X_79,inverse(X_167))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_167,least_upper_bound(X_79,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))))),multiply(X_167,least_upper_bound(X_79,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))))) ),[1,1],$fot(least_upper_bound(X_79,inverse(X_167)))]]) ).
cnf(refute_0_933,plain,
( least_upper_bound(X_79,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))) != least_upper_bound(X_79,inverse(X_167))
| multiply(X_167,least_upper_bound(X_79,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))))) = multiply(X_167,least_upper_bound(X_79,inverse(X_167))) ),
inference(resolve,[$cnf( $equal(multiply(X_167,least_upper_bound(X_79,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))))),multiply(X_167,least_upper_bound(X_79,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))))) )],[refute_0_931,refute_0_932]) ).
cnf(refute_0_934,plain,
multiply(X_167,least_upper_bound(X_79,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))))) = multiply(X_167,least_upper_bound(X_79,inverse(X_167))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_79,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),least_upper_bound(X_79,inverse(X_167))) )],[refute_0_930,refute_0_933]) ).
cnf(refute_0_935,plain,
( multiply(X_167,least_upper_bound(X_79,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))))) != multiply(X_167,least_upper_bound(X_79,inverse(X_167)))
| multiply(X_167,least_upper_bound(X_79,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))))) != least_upper_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),X_79))
| multiply(X_167,least_upper_bound(X_79,inverse(X_167))) = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),X_79)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_167,least_upper_bound(X_79,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),X_79))) ),[0],$fot(multiply(X_167,least_upper_bound(X_79,inverse(X_167))))]]) ).
cnf(refute_0_936,plain,
( multiply(X_167,least_upper_bound(X_79,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))))) != least_upper_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),X_79))
| multiply(X_167,least_upper_bound(X_79,inverse(X_167))) = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),X_79)) ),
inference(resolve,[$cnf( $equal(multiply(X_167,least_upper_bound(X_79,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))))),multiply(X_167,least_upper_bound(X_79,inverse(X_167)))) )],[refute_0_934,refute_0_935]) ).
cnf(refute_0_937,plain,
multiply(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),X_79) = multiply(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),X_79),
introduced(tautology,[refl,[$fot(multiply(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),X_79))]]) ).
cnf(refute_0_938,plain,
( multiply(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),X_79) != multiply(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),X_79)
| inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))) != X_167
| multiply(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),X_79) = multiply(X_167,X_79) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),X_79),multiply(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),X_79)) ),[1,0],$fot(X_167)]]) ).
cnf(refute_0_939,plain,
( inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))) != X_167
| multiply(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),X_79) = multiply(X_167,X_79) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),X_79),multiply(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),X_79)) )],[refute_0_937,refute_0_938]) ).
cnf(refute_0_940,plain,
multiply(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),X_79) = multiply(X_167,X_79),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),X_167) )],[refute_0_823,refute_0_939]) ).
cnf(refute_0_941,plain,
least_upper_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),X_79)) = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),X_79)),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),X_79)))]]) ).
cnf(refute_0_942,plain,
( multiply(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),X_79) != multiply(X_167,X_79)
| least_upper_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),X_79)) != least_upper_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),X_79))
| least_upper_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),X_79)) = least_upper_bound(identity,multiply(X_167,X_79)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),X_79)),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),X_79))) ),[1,1],$fot(multiply(X_167,X_79))]]) ).
cnf(refute_0_943,plain,
( multiply(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),X_79) != multiply(X_167,X_79)
| least_upper_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),X_79)) = least_upper_bound(identity,multiply(X_167,X_79)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),X_79)),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),X_79))) )],[refute_0_941,refute_0_942]) ).
cnf(refute_0_944,plain,
least_upper_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),X_79)) = least_upper_bound(identity,multiply(X_167,X_79)),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),X_79),multiply(X_167,X_79)) )],[refute_0_940,refute_0_943]) ).
cnf(refute_0_945,plain,
( multiply(X_167,least_upper_bound(X_79,inverse(X_167))) != least_upper_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),X_79))
| least_upper_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),X_79)) != least_upper_bound(identity,multiply(X_167,X_79))
| multiply(X_167,least_upper_bound(X_79,inverse(X_167))) = least_upper_bound(identity,multiply(X_167,X_79)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_167,least_upper_bound(X_79,inverse(X_167))),least_upper_bound(identity,multiply(X_167,X_79))) ),[0],$fot(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),X_79)))]]) ).
cnf(refute_0_946,plain,
( multiply(X_167,least_upper_bound(X_79,inverse(X_167))) != least_upper_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),X_79))
| multiply(X_167,least_upper_bound(X_79,inverse(X_167))) = least_upper_bound(identity,multiply(X_167,X_79)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),X_79)),least_upper_bound(identity,multiply(X_167,X_79))) )],[refute_0_944,refute_0_945]) ).
cnf(refute_0_947,plain,
( multiply(X_167,least_upper_bound(X_79,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))))) != least_upper_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),X_79))
| multiply(X_167,least_upper_bound(X_79,inverse(X_167))) = least_upper_bound(identity,multiply(X_167,X_79)) ),
inference(resolve,[$cnf( $equal(multiply(X_167,least_upper_bound(X_79,inverse(X_167))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),X_79))) )],[refute_0_936,refute_0_946]) ).
cnf(refute_0_948,plain,
multiply(X_167,least_upper_bound(X_79,inverse(X_167))) = least_upper_bound(identity,multiply(X_167,X_79)),
inference(resolve,[$cnf( $equal(multiply(X_167,least_upper_bound(X_79,greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167))))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_167),inverse(greatest_lower_bound(X_168,X_167)))),X_79))) )],[refute_0_826,refute_0_947]) ).
cnf(refute_0_949,plain,
multiply(X_292,least_upper_bound(identity,inverse(X_292))) = least_upper_bound(identity,multiply(X_292,identity)),
inference(subst,[],[refute_0_948:[bind(X_167,$fot(X_292)),bind(X_79,$fot(identity))]]) ).
cnf(refute_0_950,plain,
( multiply(X_292,least_upper_bound(identity,inverse(X_292))) != least_upper_bound(identity,multiply(X_292,identity))
| least_upper_bound(identity,multiply(X_292,identity)) != least_upper_bound(X_292,identity)
| multiply(X_292,least_upper_bound(identity,inverse(X_292))) = least_upper_bound(X_292,identity) ),
inference(subst,[],[refute_0_136:[bind(X0,$fot(multiply(X_292,least_upper_bound(identity,inverse(X_292))))),bind(Y0,$fot(least_upper_bound(identity,multiply(X_292,identity)))),bind(Z0,$fot(least_upper_bound(X_292,identity)))]]) ).
cnf(refute_0_951,plain,
( least_upper_bound(identity,multiply(X_292,identity)) != least_upper_bound(X_292,identity)
| multiply(X_292,least_upper_bound(identity,inverse(X_292))) = least_upper_bound(X_292,identity) ),
inference(resolve,[$cnf( $equal(multiply(X_292,least_upper_bound(identity,inverse(X_292))),least_upper_bound(identity,multiply(X_292,identity))) )],[refute_0_949,refute_0_950]) ).
cnf(refute_0_952,plain,
multiply(X_292,least_upper_bound(identity,inverse(X_292))) = least_upper_bound(X_292,identity),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_292,identity)),least_upper_bound(X_292,identity)) )],[refute_0_785,refute_0_951]) ).
cnf(refute_0_953,plain,
greatest_lower_bound(identity,multiply(X_292,least_upper_bound(identity,inverse(X_292)))) = greatest_lower_bound(identity,multiply(X_292,least_upper_bound(identity,inverse(X_292)))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,multiply(X_292,least_upper_bound(identity,inverse(X_292)))))]]) ).
cnf(refute_0_954,plain,
( multiply(X_292,least_upper_bound(identity,inverse(X_292))) != least_upper_bound(X_292,identity)
| greatest_lower_bound(identity,multiply(X_292,least_upper_bound(identity,inverse(X_292)))) != greatest_lower_bound(identity,multiply(X_292,least_upper_bound(identity,inverse(X_292))))
| greatest_lower_bound(identity,multiply(X_292,least_upper_bound(identity,inverse(X_292)))) = greatest_lower_bound(identity,least_upper_bound(X_292,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_292,least_upper_bound(identity,inverse(X_292)))),greatest_lower_bound(identity,multiply(X_292,least_upper_bound(identity,inverse(X_292))))) ),[1,1],$fot(least_upper_bound(X_292,identity))]]) ).
cnf(refute_0_955,plain,
( multiply(X_292,least_upper_bound(identity,inverse(X_292))) != least_upper_bound(X_292,identity)
| greatest_lower_bound(identity,multiply(X_292,least_upper_bound(identity,inverse(X_292)))) = greatest_lower_bound(identity,least_upper_bound(X_292,identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_292,least_upper_bound(identity,inverse(X_292)))),greatest_lower_bound(identity,multiply(X_292,least_upper_bound(identity,inverse(X_292))))) )],[refute_0_953,refute_0_954]) ).
cnf(refute_0_956,plain,
greatest_lower_bound(identity,multiply(X_292,least_upper_bound(identity,inverse(X_292)))) = greatest_lower_bound(identity,least_upper_bound(X_292,identity)),
inference(resolve,[$cnf( $equal(multiply(X_292,least_upper_bound(identity,inverse(X_292))),least_upper_bound(X_292,identity)) )],[refute_0_952,refute_0_955]) ).
cnf(refute_0_957,plain,
( greatest_lower_bound(identity,multiply(X_292,least_upper_bound(identity,inverse(X_292)))) != greatest_lower_bound(identity,least_upper_bound(X_292,identity))
| greatest_lower_bound(identity,least_upper_bound(X_292,identity)) != identity
| greatest_lower_bound(identity,multiply(X_292,least_upper_bound(identity,inverse(X_292)))) = identity ),
inference(subst,[],[refute_0_136:[bind(X0,$fot(greatest_lower_bound(identity,multiply(X_292,least_upper_bound(identity,inverse(X_292)))))),bind(Y0,$fot(greatest_lower_bound(identity,least_upper_bound(X_292,identity)))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_958,plain,
( greatest_lower_bound(identity,least_upper_bound(X_292,identity)) != identity
| greatest_lower_bound(identity,multiply(X_292,least_upper_bound(identity,inverse(X_292)))) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_292,least_upper_bound(identity,inverse(X_292)))),greatest_lower_bound(identity,least_upper_bound(X_292,identity))) )],[refute_0_956,refute_0_957]) ).
cnf(refute_0_959,plain,
greatest_lower_bound(identity,multiply(X_292,least_upper_bound(identity,inverse(X_292)))) = identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(X_292,identity)),identity) )],[refute_0_780,refute_0_958]) ).
cnf(refute_0_960,plain,
greatest_lower_bound(X_18,greatest_lower_bound(least_upper_bound(X_18,Y),X_20)) = greatest_lower_bound(greatest_lower_bound(X_18,least_upper_bound(X_18,Y)),X_20),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_18)),bind(Y,$fot(least_upper_bound(X_18,Y))),bind(Z,$fot(X_20))]]) ).
cnf(refute_0_961,plain,
greatest_lower_bound(X_18,least_upper_bound(X_18,Y)) = X_18,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_18))]]) ).
cnf(refute_0_962,plain,
( greatest_lower_bound(X_18,greatest_lower_bound(least_upper_bound(X_18,Y),X_20)) != greatest_lower_bound(greatest_lower_bound(X_18,least_upper_bound(X_18,Y)),X_20)
| greatest_lower_bound(X_18,least_upper_bound(X_18,Y)) != X_18
| greatest_lower_bound(X_18,greatest_lower_bound(least_upper_bound(X_18,Y),X_20)) = greatest_lower_bound(X_18,X_20) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_18,greatest_lower_bound(least_upper_bound(X_18,Y),X_20)),greatest_lower_bound(greatest_lower_bound(X_18,least_upper_bound(X_18,Y)),X_20)) ),[1,0],$fot(X_18)]]) ).
cnf(refute_0_963,plain,
( greatest_lower_bound(X_18,greatest_lower_bound(least_upper_bound(X_18,Y),X_20)) != greatest_lower_bound(greatest_lower_bound(X_18,least_upper_bound(X_18,Y)),X_20)
| greatest_lower_bound(X_18,greatest_lower_bound(least_upper_bound(X_18,Y),X_20)) = greatest_lower_bound(X_18,X_20) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_18,least_upper_bound(X_18,Y)),X_18) )],[refute_0_961,refute_0_962]) ).
cnf(refute_0_964,plain,
greatest_lower_bound(X_18,greatest_lower_bound(least_upper_bound(X_18,Y),X_20)) = greatest_lower_bound(X_18,X_20),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_18,greatest_lower_bound(least_upper_bound(X_18,Y),X_20)),greatest_lower_bound(greatest_lower_bound(X_18,least_upper_bound(X_18,Y)),X_20)) )],[refute_0_960,refute_0_963]) ).
cnf(refute_0_965,plain,
greatest_lower_bound(X_18,greatest_lower_bound(least_upper_bound(X_18,Y),multiply(X_91,least_upper_bound(X_18,Y)))) = greatest_lower_bound(X_18,multiply(X_91,least_upper_bound(X_18,Y))),
inference(subst,[],[refute_0_964:[bind(X_20,$fot(multiply(X_91,least_upper_bound(X_18,Y))))]]) ).
cnf(refute_0_966,plain,
multiply(greatest_lower_bound(X_91,identity),least_upper_bound(X_18,Y)) = greatest_lower_bound(least_upper_bound(X_18,Y),multiply(X_91,least_upper_bound(X_18,Y))),
inference(subst,[],[refute_0_23:[bind(X_28,$fot(least_upper_bound(X_18,Y))),bind(X_29,$fot(X_91))]]) ).
cnf(refute_0_967,plain,
( multiply(greatest_lower_bound(X_91,identity),least_upper_bound(X_18,Y)) != greatest_lower_bound(least_upper_bound(X_18,Y),multiply(X_91,least_upper_bound(X_18,Y)))
| greatest_lower_bound(least_upper_bound(X_18,Y),multiply(X_91,least_upper_bound(X_18,Y))) = multiply(greatest_lower_bound(X_91,identity),least_upper_bound(X_18,Y)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(greatest_lower_bound(X_91,identity),least_upper_bound(X_18,Y)))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(X_18,Y),multiply(X_91,least_upper_bound(X_18,Y)))))]]) ).
cnf(refute_0_968,plain,
greatest_lower_bound(least_upper_bound(X_18,Y),multiply(X_91,least_upper_bound(X_18,Y))) = multiply(greatest_lower_bound(X_91,identity),least_upper_bound(X_18,Y)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_91,identity),least_upper_bound(X_18,Y)),greatest_lower_bound(least_upper_bound(X_18,Y),multiply(X_91,least_upper_bound(X_18,Y)))) )],[refute_0_966,refute_0_967]) ).
cnf(refute_0_969,plain,
( greatest_lower_bound(X_18,greatest_lower_bound(least_upper_bound(X_18,Y),multiply(X_91,least_upper_bound(X_18,Y)))) != greatest_lower_bound(X_18,multiply(X_91,least_upper_bound(X_18,Y)))
| greatest_lower_bound(least_upper_bound(X_18,Y),multiply(X_91,least_upper_bound(X_18,Y))) != multiply(greatest_lower_bound(X_91,identity),least_upper_bound(X_18,Y))
| greatest_lower_bound(X_18,multiply(greatest_lower_bound(X_91,identity),least_upper_bound(X_18,Y))) = greatest_lower_bound(X_18,multiply(X_91,least_upper_bound(X_18,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_18,greatest_lower_bound(least_upper_bound(X_18,Y),multiply(X_91,least_upper_bound(X_18,Y)))),greatest_lower_bound(X_18,multiply(X_91,least_upper_bound(X_18,Y)))) ),[0,1],$fot(multiply(greatest_lower_bound(X_91,identity),least_upper_bound(X_18,Y)))]]) ).
cnf(refute_0_970,plain,
( greatest_lower_bound(X_18,greatest_lower_bound(least_upper_bound(X_18,Y),multiply(X_91,least_upper_bound(X_18,Y)))) != greatest_lower_bound(X_18,multiply(X_91,least_upper_bound(X_18,Y)))
| greatest_lower_bound(X_18,multiply(greatest_lower_bound(X_91,identity),least_upper_bound(X_18,Y))) = greatest_lower_bound(X_18,multiply(X_91,least_upper_bound(X_18,Y))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_18,Y),multiply(X_91,least_upper_bound(X_18,Y))),multiply(greatest_lower_bound(X_91,identity),least_upper_bound(X_18,Y))) )],[refute_0_968,refute_0_969]) ).
cnf(refute_0_971,plain,
greatest_lower_bound(X_18,multiply(greatest_lower_bound(X_91,identity),least_upper_bound(X_18,Y))) = greatest_lower_bound(X_18,multiply(X_91,least_upper_bound(X_18,Y))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_18,greatest_lower_bound(least_upper_bound(X_18,Y),multiply(X_91,least_upper_bound(X_18,Y)))),greatest_lower_bound(X_18,multiply(X_91,least_upper_bound(X_18,Y)))) )],[refute_0_965,refute_0_970]) ).
cnf(refute_0_972,plain,
greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))) = greatest_lower_bound(identity,multiply(X_292,least_upper_bound(identity,inverse(X_292)))),
inference(subst,[],[refute_0_971:[bind(Y,$fot(inverse(X_292))),bind(X_18,$fot(identity)),bind(X_91,$fot(X_292))]]) ).
cnf(refute_0_973,plain,
( greatest_lower_bound(identity,multiply(X_292,least_upper_bound(identity,inverse(X_292)))) != identity
| greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))) != greatest_lower_bound(identity,multiply(X_292,least_upper_bound(identity,inverse(X_292))))
| greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))) = identity ),
inference(subst,[],[refute_0_136:[bind(X0,$fot(greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(X_292,least_upper_bound(identity,inverse(X_292)))))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_974,plain,
( greatest_lower_bound(identity,multiply(X_292,least_upper_bound(identity,inverse(X_292)))) != identity
| greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))),greatest_lower_bound(identity,multiply(X_292,least_upper_bound(identity,inverse(X_292))))) )],[refute_0_972,refute_0_973]) ).
cnf(refute_0_975,plain,
greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))) = identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_292,least_upper_bound(identity,inverse(X_292)))),identity) )],[refute_0_959,refute_0_974]) ).
cnf(refute_0_976,plain,
multiply(identity,greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))) = multiply(identity,greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),
introduced(tautology,[refl,[$fot(multiply(identity,greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))))]]) ).
cnf(refute_0_977,plain,
( multiply(identity,greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))) != multiply(identity,greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))))
| greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))) != identity
| multiply(identity,greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))) = multiply(identity,identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),multiply(identity,greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_978,plain,
( greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))) != identity
| multiply(identity,greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))) = multiply(identity,identity) ),
inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),multiply(identity,greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))))) )],[refute_0_976,refute_0_977]) ).
cnf(refute_0_979,plain,
multiply(identity,greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))) = multiply(identity,identity),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))),identity) )],[refute_0_975,refute_0_978]) ).
cnf(refute_0_980,plain,
multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))) = multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),
introduced(tautology,[refl,[$fot(multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))))]]) ).
cnf(refute_0_981,plain,
( multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))) != multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))))
| inverse(identity) != identity
| multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))) = multiply(identity,greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_982,plain,
( inverse(identity) != identity
| multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))) = multiply(identity,greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))))) )],[refute_0_980,refute_0_981]) ).
cnf(refute_0_983,plain,
multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))) = multiply(identity,greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_762,refute_0_982]) ).
cnf(refute_0_984,plain,
( multiply(identity,greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))) != multiply(identity,identity)
| multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))) != multiply(identity,greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))))
| multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))) = multiply(identity,identity) ),
inference(subst,[],[refute_0_136:[bind(X0,$fot(multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))))),bind(Y0,$fot(multiply(identity,greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))))),bind(Z0,$fot(multiply(identity,identity)))]]) ).
cnf(refute_0_985,plain,
( multiply(identity,greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))) != multiply(identity,identity)
| multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))) = multiply(identity,identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),multiply(identity,greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))))) )],[refute_0_983,refute_0_984]) ).
cnf(refute_0_986,plain,
multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))) = multiply(identity,identity),
inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),multiply(identity,identity)) )],[refute_0_979,refute_0_985]) ).
cnf(refute_0_987,plain,
( multiply(identity,identity) != identity
| multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))) != multiply(identity,identity)
| multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))) = identity ),
inference(subst,[],[refute_0_136:[bind(X0,$fot(multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))))),bind(Y0,$fot(multiply(identity,identity))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_988,plain,
( multiply(identity,identity) != identity
| multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))) = identity ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),multiply(identity,identity)) )],[refute_0_986,refute_0_987]) ).
cnf(refute_0_989,plain,
multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))) = identity,
inference(resolve,[$cnf( $equal(multiply(identity,identity),identity) )],[refute_0_779,refute_0_988]) ).
cnf(refute_0_990,plain,
greatest_lower_bound(multiply(X_21,X_22),greatest_lower_bound(multiply(X_21,X_23),Z)) = greatest_lower_bound(greatest_lower_bound(multiply(X_21,X_22),multiply(X_21,X_23)),Z),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(multiply(X_21,X_22))),bind(Y,$fot(multiply(X_21,X_23)))]]) ).
cnf(refute_0_991,plain,
multiply(X_21,greatest_lower_bound(X_22,X_23)) = greatest_lower_bound(multiply(X_21,X_22),multiply(X_21,X_23)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(X_21)),bind(Y,$fot(X_22)),bind(Z,$fot(X_23))]]) ).
cnf(refute_0_992,plain,
( multiply(X_21,greatest_lower_bound(X_22,X_23)) != greatest_lower_bound(multiply(X_21,X_22),multiply(X_21,X_23))
| greatest_lower_bound(multiply(X_21,X_22),multiply(X_21,X_23)) = multiply(X_21,greatest_lower_bound(X_22,X_23)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X_21,greatest_lower_bound(X_22,X_23)))),bind(Y0,$fot(greatest_lower_bound(multiply(X_21,X_22),multiply(X_21,X_23))))]]) ).
cnf(refute_0_993,plain,
greatest_lower_bound(multiply(X_21,X_22),multiply(X_21,X_23)) = multiply(X_21,greatest_lower_bound(X_22,X_23)),
inference(resolve,[$cnf( $equal(multiply(X_21,greatest_lower_bound(X_22,X_23)),greatest_lower_bound(multiply(X_21,X_22),multiply(X_21,X_23))) )],[refute_0_991,refute_0_992]) ).
cnf(refute_0_994,plain,
( greatest_lower_bound(multiply(X_21,X_22),multiply(X_21,X_23)) != multiply(X_21,greatest_lower_bound(X_22,X_23))
| greatest_lower_bound(multiply(X_21,X_22),greatest_lower_bound(multiply(X_21,X_23),Z)) != greatest_lower_bound(greatest_lower_bound(multiply(X_21,X_22),multiply(X_21,X_23)),Z)
| greatest_lower_bound(multiply(X_21,X_22),greatest_lower_bound(multiply(X_21,X_23),Z)) = greatest_lower_bound(multiply(X_21,greatest_lower_bound(X_22,X_23)),Z) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_21,X_22),greatest_lower_bound(multiply(X_21,X_23),Z)),greatest_lower_bound(greatest_lower_bound(multiply(X_21,X_22),multiply(X_21,X_23)),Z)) ),[1,0],$fot(multiply(X_21,greatest_lower_bound(X_22,X_23)))]]) ).
cnf(refute_0_995,plain,
( greatest_lower_bound(multiply(X_21,X_22),greatest_lower_bound(multiply(X_21,X_23),Z)) != greatest_lower_bound(greatest_lower_bound(multiply(X_21,X_22),multiply(X_21,X_23)),Z)
| greatest_lower_bound(multiply(X_21,X_22),greatest_lower_bound(multiply(X_21,X_23),Z)) = greatest_lower_bound(multiply(X_21,greatest_lower_bound(X_22,X_23)),Z) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_21,X_22),multiply(X_21,X_23)),multiply(X_21,greatest_lower_bound(X_22,X_23))) )],[refute_0_993,refute_0_994]) ).
cnf(refute_0_996,plain,
greatest_lower_bound(multiply(X_21,X_22),greatest_lower_bound(multiply(X_21,X_23),Z)) = greatest_lower_bound(multiply(X_21,greatest_lower_bound(X_22,X_23)),Z),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_21,X_22),greatest_lower_bound(multiply(X_21,X_23),Z)),greatest_lower_bound(greatest_lower_bound(multiply(X_21,X_22),multiply(X_21,X_23)),Z)) )],[refute_0_990,refute_0_995]) ).
cnf(refute_0_997,plain,
greatest_lower_bound(multiply(X_212,X_213),greatest_lower_bound(multiply(X_212,X_214),multiply(X_212,X_214))) = greatest_lower_bound(multiply(X_212,greatest_lower_bound(X_213,X_214)),multiply(X_212,X_214)),
inference(subst,[],[refute_0_996:[bind(Z,$fot(multiply(X_212,X_214))),bind(X_21,$fot(X_212)),bind(X_22,$fot(X_213)),bind(X_23,$fot(X_214))]]) ).
cnf(refute_0_998,plain,
greatest_lower_bound(multiply(X_212,X_214),multiply(X_212,X_214)) = multiply(X_212,X_214),
inference(subst,[],[idempotence_of_gld:[bind(X,$fot(multiply(X_212,X_214)))]]) ).
cnf(refute_0_999,plain,
( greatest_lower_bound(multiply(X_212,X_213),greatest_lower_bound(multiply(X_212,X_214),multiply(X_212,X_214))) != greatest_lower_bound(multiply(X_212,greatest_lower_bound(X_213,X_214)),multiply(X_212,X_214))
| greatest_lower_bound(multiply(X_212,X_214),multiply(X_212,X_214)) != multiply(X_212,X_214)
| greatest_lower_bound(multiply(X_212,X_213),multiply(X_212,X_214)) = greatest_lower_bound(multiply(X_212,greatest_lower_bound(X_213,X_214)),multiply(X_212,X_214)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_212,X_213),greatest_lower_bound(multiply(X_212,X_214),multiply(X_212,X_214))),greatest_lower_bound(multiply(X_212,greatest_lower_bound(X_213,X_214)),multiply(X_212,X_214))) ),[0,1],$fot(multiply(X_212,X_214))]]) ).
cnf(refute_0_1000,plain,
( greatest_lower_bound(multiply(X_212,X_213),greatest_lower_bound(multiply(X_212,X_214),multiply(X_212,X_214))) != greatest_lower_bound(multiply(X_212,greatest_lower_bound(X_213,X_214)),multiply(X_212,X_214))
| greatest_lower_bound(multiply(X_212,X_213),multiply(X_212,X_214)) = greatest_lower_bound(multiply(X_212,greatest_lower_bound(X_213,X_214)),multiply(X_212,X_214)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_212,X_214),multiply(X_212,X_214)),multiply(X_212,X_214)) )],[refute_0_998,refute_0_999]) ).
cnf(refute_0_1001,plain,
greatest_lower_bound(multiply(X_212,X_213),multiply(X_212,X_214)) = greatest_lower_bound(multiply(X_212,greatest_lower_bound(X_213,X_214)),multiply(X_212,X_214)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_212,X_213),greatest_lower_bound(multiply(X_212,X_214),multiply(X_212,X_214))),greatest_lower_bound(multiply(X_212,greatest_lower_bound(X_213,X_214)),multiply(X_212,X_214))) )],[refute_0_997,refute_0_1000]) ).
cnf(refute_0_1002,plain,
( multiply(X,greatest_lower_bound(Y,Z)) != greatest_lower_bound(multiply(X,Y),multiply(X,Z))
| greatest_lower_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,greatest_lower_bound(Y,Z)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X,greatest_lower_bound(Y,Z)))),bind(Y0,$fot(greatest_lower_bound(multiply(X,Y),multiply(X,Z))))]]) ).
cnf(refute_0_1003,plain,
greatest_lower_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) )],[monotony_glb1,refute_0_1002]) ).
cnf(refute_0_1004,plain,
greatest_lower_bound(multiply(X_212,X_213),multiply(X_212,X_214)) = multiply(X_212,greatest_lower_bound(X_213,X_214)),
inference(subst,[],[refute_0_1003:[bind(X,$fot(X_212)),bind(Y,$fot(X_213)),bind(Z,$fot(X_214))]]) ).
cnf(refute_0_1005,plain,
( greatest_lower_bound(multiply(X_212,X_213),multiply(X_212,X_214)) != multiply(X_212,greatest_lower_bound(X_213,X_214))
| greatest_lower_bound(multiply(X_212,X_213),multiply(X_212,X_214)) != greatest_lower_bound(multiply(X_212,greatest_lower_bound(X_213,X_214)),multiply(X_212,X_214))
| multiply(X_212,greatest_lower_bound(X_213,X_214)) = greatest_lower_bound(multiply(X_212,greatest_lower_bound(X_213,X_214)),multiply(X_212,X_214)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_212,X_213),multiply(X_212,X_214)),greatest_lower_bound(multiply(X_212,greatest_lower_bound(X_213,X_214)),multiply(X_212,X_214))) ),[0],$fot(multiply(X_212,greatest_lower_bound(X_213,X_214)))]]) ).
cnf(refute_0_1006,plain,
( greatest_lower_bound(multiply(X_212,X_213),multiply(X_212,X_214)) != greatest_lower_bound(multiply(X_212,greatest_lower_bound(X_213,X_214)),multiply(X_212,X_214))
| multiply(X_212,greatest_lower_bound(X_213,X_214)) = greatest_lower_bound(multiply(X_212,greatest_lower_bound(X_213,X_214)),multiply(X_212,X_214)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_212,X_213),multiply(X_212,X_214)),multiply(X_212,greatest_lower_bound(X_213,X_214))) )],[refute_0_1004,refute_0_1005]) ).
cnf(refute_0_1007,plain,
greatest_lower_bound(X_214,greatest_lower_bound(X_214,X_213)) = greatest_lower_bound(X_214,X_213),
inference(subst,[],[refute_0_838:[bind(X_14,$fot(X_213)),bind(X_15,$fot(X_214))]]) ).
cnf(refute_0_1008,plain,
multiply(X_212,greatest_lower_bound(X_214,greatest_lower_bound(X_214,X_213))) = multiply(X_212,greatest_lower_bound(X_214,greatest_lower_bound(X_214,X_213))),
introduced(tautology,[refl,[$fot(multiply(X_212,greatest_lower_bound(X_214,greatest_lower_bound(X_214,X_213))))]]) ).
cnf(refute_0_1009,plain,
( multiply(X_212,greatest_lower_bound(X_214,greatest_lower_bound(X_214,X_213))) != multiply(X_212,greatest_lower_bound(X_214,greatest_lower_bound(X_214,X_213)))
| greatest_lower_bound(X_214,greatest_lower_bound(X_214,X_213)) != greatest_lower_bound(X_214,X_213)
| multiply(X_212,greatest_lower_bound(X_214,greatest_lower_bound(X_214,X_213))) = multiply(X_212,greatest_lower_bound(X_214,X_213)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_212,greatest_lower_bound(X_214,greatest_lower_bound(X_214,X_213))),multiply(X_212,greatest_lower_bound(X_214,greatest_lower_bound(X_214,X_213)))) ),[1,1],$fot(greatest_lower_bound(X_214,X_213))]]) ).
cnf(refute_0_1010,plain,
( greatest_lower_bound(X_214,greatest_lower_bound(X_214,X_213)) != greatest_lower_bound(X_214,X_213)
| multiply(X_212,greatest_lower_bound(X_214,greatest_lower_bound(X_214,X_213))) = multiply(X_212,greatest_lower_bound(X_214,X_213)) ),
inference(resolve,[$cnf( $equal(multiply(X_212,greatest_lower_bound(X_214,greatest_lower_bound(X_214,X_213))),multiply(X_212,greatest_lower_bound(X_214,greatest_lower_bound(X_214,X_213)))) )],[refute_0_1008,refute_0_1009]) ).
cnf(refute_0_1011,plain,
multiply(X_212,greatest_lower_bound(X_214,greatest_lower_bound(X_214,X_213))) = multiply(X_212,greatest_lower_bound(X_214,X_213)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_214,greatest_lower_bound(X_214,X_213)),greatest_lower_bound(X_214,X_213)) )],[refute_0_1007,refute_0_1010]) ).
cnf(refute_0_1012,plain,
greatest_lower_bound(multiply(X_212,X_214),multiply(X_212,greatest_lower_bound(X_214,X_213))) = multiply(X_212,greatest_lower_bound(X_214,greatest_lower_bound(X_214,X_213))),
inference(subst,[],[refute_0_1003:[bind(X,$fot(X_212)),bind(Y,$fot(X_214)),bind(Z,$fot(greatest_lower_bound(X_214,X_213)))]]) ).
cnf(refute_0_1013,plain,
greatest_lower_bound(multiply(X_212,X_213),greatest_lower_bound(multiply(X_212,X_214),X_211)) = greatest_lower_bound(multiply(X_212,greatest_lower_bound(X_213,X_214)),X_211),
inference(subst,[],[refute_0_996:[bind(Z,$fot(X_211)),bind(X_21,$fot(X_212)),bind(X_22,$fot(X_213)),bind(X_23,$fot(X_214))]]) ).
cnf(refute_0_1014,plain,
greatest_lower_bound(X_211,multiply(X_212,X_214)) = greatest_lower_bound(multiply(X_212,X_214),X_211),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_211)),bind(Y,$fot(multiply(X_212,X_214)))]]) ).
cnf(refute_0_1015,plain,
( greatest_lower_bound(X_211,multiply(X_212,X_214)) != greatest_lower_bound(multiply(X_212,X_214),X_211)
| greatest_lower_bound(multiply(X_212,X_214),X_211) = greatest_lower_bound(X_211,multiply(X_212,X_214)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X_211,multiply(X_212,X_214)))),bind(Y0,$fot(greatest_lower_bound(multiply(X_212,X_214),X_211)))]]) ).
cnf(refute_0_1016,plain,
greatest_lower_bound(multiply(X_212,X_214),X_211) = greatest_lower_bound(X_211,multiply(X_212,X_214)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_211,multiply(X_212,X_214)),greatest_lower_bound(multiply(X_212,X_214),X_211)) )],[refute_0_1014,refute_0_1015]) ).
cnf(refute_0_1017,plain,
( greatest_lower_bound(multiply(X_212,X_213),greatest_lower_bound(multiply(X_212,X_214),X_211)) != greatest_lower_bound(multiply(X_212,greatest_lower_bound(X_213,X_214)),X_211)
| greatest_lower_bound(multiply(X_212,X_214),X_211) != greatest_lower_bound(X_211,multiply(X_212,X_214))
| greatest_lower_bound(multiply(X_212,X_213),greatest_lower_bound(X_211,multiply(X_212,X_214))) = greatest_lower_bound(multiply(X_212,greatest_lower_bound(X_213,X_214)),X_211) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_212,X_213),greatest_lower_bound(multiply(X_212,X_214),X_211)),greatest_lower_bound(multiply(X_212,greatest_lower_bound(X_213,X_214)),X_211)) ),[0,1],$fot(greatest_lower_bound(X_211,multiply(X_212,X_214)))]]) ).
cnf(refute_0_1018,plain,
( greatest_lower_bound(multiply(X_212,X_213),greatest_lower_bound(multiply(X_212,X_214),X_211)) != greatest_lower_bound(multiply(X_212,greatest_lower_bound(X_213,X_214)),X_211)
| greatest_lower_bound(multiply(X_212,X_213),greatest_lower_bound(X_211,multiply(X_212,X_214))) = greatest_lower_bound(multiply(X_212,greatest_lower_bound(X_213,X_214)),X_211) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_212,X_214),X_211),greatest_lower_bound(X_211,multiply(X_212,X_214))) )],[refute_0_1016,refute_0_1017]) ).
cnf(refute_0_1019,plain,
greatest_lower_bound(multiply(X_212,X_213),greatest_lower_bound(X_211,multiply(X_212,X_214))) = greatest_lower_bound(multiply(X_212,greatest_lower_bound(X_213,X_214)),X_211),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_212,X_213),greatest_lower_bound(multiply(X_212,X_214),X_211)),greatest_lower_bound(multiply(X_212,greatest_lower_bound(X_213,X_214)),X_211)) )],[refute_0_1013,refute_0_1018]) ).
cnf(refute_0_1020,plain,
greatest_lower_bound(multiply(X,Z),greatest_lower_bound(X_113,multiply(X,Y))) = greatest_lower_bound(X_113,greatest_lower_bound(multiply(X,Y),multiply(X,Z))),
inference(subst,[],[refute_0_910:[bind(X,$fot(multiply(X,Z))),bind(X_18,$fot(X_113)),bind(X_19,$fot(multiply(X,Y)))]]) ).
cnf(refute_0_1021,plain,
( greatest_lower_bound(multiply(X,Y),multiply(X,Z)) != multiply(X,greatest_lower_bound(Y,Z))
| greatest_lower_bound(multiply(X,Z),greatest_lower_bound(X_113,multiply(X,Y))) != greatest_lower_bound(X_113,greatest_lower_bound(multiply(X,Y),multiply(X,Z)))
| greatest_lower_bound(multiply(X,Z),greatest_lower_bound(X_113,multiply(X,Y))) = greatest_lower_bound(X_113,multiply(X,greatest_lower_bound(Y,Z))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X,Z),greatest_lower_bound(X_113,multiply(X,Y))),greatest_lower_bound(X_113,greatest_lower_bound(multiply(X,Y),multiply(X,Z)))) ),[1,1],$fot(multiply(X,greatest_lower_bound(Y,Z)))]]) ).
cnf(refute_0_1022,plain,
( greatest_lower_bound(multiply(X,Z),greatest_lower_bound(X_113,multiply(X,Y))) != greatest_lower_bound(X_113,greatest_lower_bound(multiply(X,Y),multiply(X,Z)))
| greatest_lower_bound(multiply(X,Z),greatest_lower_bound(X_113,multiply(X,Y))) = greatest_lower_bound(X_113,multiply(X,greatest_lower_bound(Y,Z))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,Y),multiply(X,Z)),multiply(X,greatest_lower_bound(Y,Z))) )],[refute_0_1003,refute_0_1021]) ).
cnf(refute_0_1023,plain,
greatest_lower_bound(multiply(X,Z),greatest_lower_bound(X_113,multiply(X,Y))) = greatest_lower_bound(X_113,multiply(X,greatest_lower_bound(Y,Z))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,Z),greatest_lower_bound(X_113,multiply(X,Y))),greatest_lower_bound(X_113,greatest_lower_bound(multiply(X,Y),multiply(X,Z)))) )],[refute_0_1020,refute_0_1022]) ).
cnf(refute_0_1024,plain,
greatest_lower_bound(multiply(X_212,X_213),greatest_lower_bound(X_211,multiply(X_212,X_214))) = greatest_lower_bound(X_211,multiply(X_212,greatest_lower_bound(X_214,X_213))),
inference(subst,[],[refute_0_1023:[bind(X,$fot(X_212)),bind(Y,$fot(X_214)),bind(Z,$fot(X_213)),bind(X_113,$fot(X_211))]]) ).
cnf(refute_0_1025,plain,
( greatest_lower_bound(multiply(X_212,X_213),greatest_lower_bound(X_211,multiply(X_212,X_214))) != greatest_lower_bound(X_211,multiply(X_212,greatest_lower_bound(X_214,X_213)))
| greatest_lower_bound(multiply(X_212,X_213),greatest_lower_bound(X_211,multiply(X_212,X_214))) != greatest_lower_bound(multiply(X_212,greatest_lower_bound(X_213,X_214)),X_211)
| greatest_lower_bound(X_211,multiply(X_212,greatest_lower_bound(X_214,X_213))) = greatest_lower_bound(multiply(X_212,greatest_lower_bound(X_213,X_214)),X_211) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_212,X_213),greatest_lower_bound(X_211,multiply(X_212,X_214))),greatest_lower_bound(multiply(X_212,greatest_lower_bound(X_213,X_214)),X_211)) ),[0],$fot(greatest_lower_bound(X_211,multiply(X_212,greatest_lower_bound(X_214,X_213))))]]) ).
cnf(refute_0_1026,plain,
( greatest_lower_bound(multiply(X_212,X_213),greatest_lower_bound(X_211,multiply(X_212,X_214))) != greatest_lower_bound(multiply(X_212,greatest_lower_bound(X_213,X_214)),X_211)
| greatest_lower_bound(X_211,multiply(X_212,greatest_lower_bound(X_214,X_213))) = greatest_lower_bound(multiply(X_212,greatest_lower_bound(X_213,X_214)),X_211) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_212,X_213),greatest_lower_bound(X_211,multiply(X_212,X_214))),greatest_lower_bound(X_211,multiply(X_212,greatest_lower_bound(X_214,X_213)))) )],[refute_0_1024,refute_0_1025]) ).
cnf(refute_0_1027,plain,
greatest_lower_bound(X_211,multiply(X_212,greatest_lower_bound(X_214,X_213))) = greatest_lower_bound(multiply(X_212,greatest_lower_bound(X_213,X_214)),X_211),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_212,X_213),greatest_lower_bound(X_211,multiply(X_212,X_214))),greatest_lower_bound(multiply(X_212,greatest_lower_bound(X_213,X_214)),X_211)) )],[refute_0_1019,refute_0_1026]) ).
cnf(refute_0_1028,plain,
( greatest_lower_bound(X_211,multiply(X_212,greatest_lower_bound(X_214,X_213))) != greatest_lower_bound(multiply(X_212,greatest_lower_bound(X_213,X_214)),X_211)
| greatest_lower_bound(multiply(X_212,greatest_lower_bound(X_213,X_214)),X_211) = greatest_lower_bound(X_211,multiply(X_212,greatest_lower_bound(X_214,X_213))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X_211,multiply(X_212,greatest_lower_bound(X_214,X_213))))),bind(Y0,$fot(greatest_lower_bound(multiply(X_212,greatest_lower_bound(X_213,X_214)),X_211)))]]) ).
cnf(refute_0_1029,plain,
greatest_lower_bound(multiply(X_212,greatest_lower_bound(X_213,X_214)),X_211) = greatest_lower_bound(X_211,multiply(X_212,greatest_lower_bound(X_214,X_213))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_211,multiply(X_212,greatest_lower_bound(X_214,X_213))),greatest_lower_bound(multiply(X_212,greatest_lower_bound(X_213,X_214)),X_211)) )],[refute_0_1027,refute_0_1028]) ).
cnf(refute_0_1030,plain,
greatest_lower_bound(multiply(X_212,greatest_lower_bound(X_213,X_214)),multiply(X_212,X_214)) = greatest_lower_bound(multiply(X_212,X_214),multiply(X_212,greatest_lower_bound(X_214,X_213))),
inference(subst,[],[refute_0_1029:[bind(X_211,$fot(multiply(X_212,X_214)))]]) ).
cnf(refute_0_1031,plain,
( greatest_lower_bound(multiply(X_212,X_214),multiply(X_212,greatest_lower_bound(X_214,X_213))) != multiply(X_212,greatest_lower_bound(X_214,greatest_lower_bound(X_214,X_213)))
| greatest_lower_bound(multiply(X_212,greatest_lower_bound(X_213,X_214)),multiply(X_212,X_214)) != greatest_lower_bound(multiply(X_212,X_214),multiply(X_212,greatest_lower_bound(X_214,X_213)))
| greatest_lower_bound(multiply(X_212,greatest_lower_bound(X_213,X_214)),multiply(X_212,X_214)) = multiply(X_212,greatest_lower_bound(X_214,greatest_lower_bound(X_214,X_213))) ),
inference(subst,[],[refute_0_136:[bind(X0,$fot(greatest_lower_bound(multiply(X_212,greatest_lower_bound(X_213,X_214)),multiply(X_212,X_214)))),bind(Y0,$fot(greatest_lower_bound(multiply(X_212,X_214),multiply(X_212,greatest_lower_bound(X_214,X_213))))),bind(Z0,$fot(multiply(X_212,greatest_lower_bound(X_214,greatest_lower_bound(X_214,X_213)))))]]) ).
cnf(refute_0_1032,plain,
( greatest_lower_bound(multiply(X_212,X_214),multiply(X_212,greatest_lower_bound(X_214,X_213))) != multiply(X_212,greatest_lower_bound(X_214,greatest_lower_bound(X_214,X_213)))
| greatest_lower_bound(multiply(X_212,greatest_lower_bound(X_213,X_214)),multiply(X_212,X_214)) = multiply(X_212,greatest_lower_bound(X_214,greatest_lower_bound(X_214,X_213))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_212,greatest_lower_bound(X_213,X_214)),multiply(X_212,X_214)),greatest_lower_bound(multiply(X_212,X_214),multiply(X_212,greatest_lower_bound(X_214,X_213)))) )],[refute_0_1030,refute_0_1031]) ).
cnf(refute_0_1033,plain,
greatest_lower_bound(multiply(X_212,greatest_lower_bound(X_213,X_214)),multiply(X_212,X_214)) = multiply(X_212,greatest_lower_bound(X_214,greatest_lower_bound(X_214,X_213))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_212,X_214),multiply(X_212,greatest_lower_bound(X_214,X_213))),multiply(X_212,greatest_lower_bound(X_214,greatest_lower_bound(X_214,X_213)))) )],[refute_0_1012,refute_0_1032]) ).
cnf(refute_0_1034,plain,
( multiply(X_212,greatest_lower_bound(X_214,greatest_lower_bound(X_214,X_213))) != multiply(X_212,greatest_lower_bound(X_214,X_213))
| greatest_lower_bound(multiply(X_212,greatest_lower_bound(X_213,X_214)),multiply(X_212,X_214)) != multiply(X_212,greatest_lower_bound(X_214,greatest_lower_bound(X_214,X_213)))
| greatest_lower_bound(multiply(X_212,greatest_lower_bound(X_213,X_214)),multiply(X_212,X_214)) = multiply(X_212,greatest_lower_bound(X_214,X_213)) ),
inference(subst,[],[refute_0_136:[bind(X0,$fot(greatest_lower_bound(multiply(X_212,greatest_lower_bound(X_213,X_214)),multiply(X_212,X_214)))),bind(Y0,$fot(multiply(X_212,greatest_lower_bound(X_214,greatest_lower_bound(X_214,X_213))))),bind(Z0,$fot(multiply(X_212,greatest_lower_bound(X_214,X_213))))]]) ).
cnf(refute_0_1035,plain,
( multiply(X_212,greatest_lower_bound(X_214,greatest_lower_bound(X_214,X_213))) != multiply(X_212,greatest_lower_bound(X_214,X_213))
| greatest_lower_bound(multiply(X_212,greatest_lower_bound(X_213,X_214)),multiply(X_212,X_214)) = multiply(X_212,greatest_lower_bound(X_214,X_213)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_212,greatest_lower_bound(X_213,X_214)),multiply(X_212,X_214)),multiply(X_212,greatest_lower_bound(X_214,greatest_lower_bound(X_214,X_213)))) )],[refute_0_1033,refute_0_1034]) ).
cnf(refute_0_1036,plain,
greatest_lower_bound(multiply(X_212,greatest_lower_bound(X_213,X_214)),multiply(X_212,X_214)) = multiply(X_212,greatest_lower_bound(X_214,X_213)),
inference(resolve,[$cnf( $equal(multiply(X_212,greatest_lower_bound(X_214,greatest_lower_bound(X_214,X_213))),multiply(X_212,greatest_lower_bound(X_214,X_213))) )],[refute_0_1011,refute_0_1035]) ).
cnf(refute_0_1037,plain,
( multiply(X_212,greatest_lower_bound(X_213,X_214)) != greatest_lower_bound(multiply(X_212,greatest_lower_bound(X_213,X_214)),multiply(X_212,X_214))
| greatest_lower_bound(multiply(X_212,greatest_lower_bound(X_213,X_214)),multiply(X_212,X_214)) != multiply(X_212,greatest_lower_bound(X_214,X_213))
| multiply(X_212,greatest_lower_bound(X_213,X_214)) = multiply(X_212,greatest_lower_bound(X_214,X_213)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_212,greatest_lower_bound(X_213,X_214)),multiply(X_212,greatest_lower_bound(X_214,X_213))) ),[0],$fot(greatest_lower_bound(multiply(X_212,greatest_lower_bound(X_213,X_214)),multiply(X_212,X_214)))]]) ).
cnf(refute_0_1038,plain,
( multiply(X_212,greatest_lower_bound(X_213,X_214)) != greatest_lower_bound(multiply(X_212,greatest_lower_bound(X_213,X_214)),multiply(X_212,X_214))
| multiply(X_212,greatest_lower_bound(X_213,X_214)) = multiply(X_212,greatest_lower_bound(X_214,X_213)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_212,greatest_lower_bound(X_213,X_214)),multiply(X_212,X_214)),multiply(X_212,greatest_lower_bound(X_214,X_213))) )],[refute_0_1036,refute_0_1037]) ).
cnf(refute_0_1039,plain,
( greatest_lower_bound(multiply(X_212,X_213),multiply(X_212,X_214)) != greatest_lower_bound(multiply(X_212,greatest_lower_bound(X_213,X_214)),multiply(X_212,X_214))
| multiply(X_212,greatest_lower_bound(X_213,X_214)) = multiply(X_212,greatest_lower_bound(X_214,X_213)) ),
inference(resolve,[$cnf( $equal(multiply(X_212,greatest_lower_bound(X_213,X_214)),greatest_lower_bound(multiply(X_212,greatest_lower_bound(X_213,X_214)),multiply(X_212,X_214))) )],[refute_0_1006,refute_0_1038]) ).
cnf(refute_0_1040,plain,
multiply(X_212,greatest_lower_bound(X_213,X_214)) = multiply(X_212,greatest_lower_bound(X_214,X_213)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_212,X_213),multiply(X_212,X_214)),greatest_lower_bound(multiply(X_212,greatest_lower_bound(X_213,X_214)),multiply(X_212,X_214))) )],[refute_0_1001,refute_0_1039]) ).
cnf(refute_0_1041,plain,
( multiply(X_212,greatest_lower_bound(X_213,X_214)) != multiply(X_212,greatest_lower_bound(X_214,X_213))
| multiply(X_212,greatest_lower_bound(X_214,X_213)) = multiply(X_212,greatest_lower_bound(X_213,X_214)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X_212,greatest_lower_bound(X_213,X_214)))),bind(Y0,$fot(multiply(X_212,greatest_lower_bound(X_214,X_213))))]]) ).
cnf(refute_0_1042,plain,
multiply(X_212,greatest_lower_bound(X_214,X_213)) = multiply(X_212,greatest_lower_bound(X_213,X_214)),
inference(resolve,[$cnf( $equal(multiply(X_212,greatest_lower_bound(X_213,X_214)),multiply(X_212,greatest_lower_bound(X_214,X_213))) )],[refute_0_1040,refute_0_1041]) ).
cnf(refute_0_1043,plain,
multiply(inverse(identity),greatest_lower_bound(multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))),identity)) = multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),
inference(subst,[],[refute_0_1042:[bind(X_212,$fot(inverse(identity))),bind(X_213,$fot(identity)),bind(X_214,$fot(multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))))]]) ).
cnf(refute_0_1044,plain,
greatest_lower_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))) = multiply(inverse(identity),greatest_lower_bound(multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))),identity)),
inference(subst,[],[refute_0_681:[bind(X_24,$fot(multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),bind(X_25,$fot(identity))]]) ).
cnf(refute_0_1045,plain,
( multiply(inverse(identity),greatest_lower_bound(multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))),identity)) != multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))))
| greatest_lower_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))) != multiply(inverse(identity),greatest_lower_bound(multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))),identity))
| greatest_lower_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))) = multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))) ),
inference(subst,[],[refute_0_136:[bind(X0,$fot(greatest_lower_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))))),bind(Y0,$fot(multiply(inverse(identity),greatest_lower_bound(multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))),identity)))),bind(Z0,$fot(multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))))))]]) ).
cnf(refute_0_1046,plain,
( multiply(inverse(identity),greatest_lower_bound(multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))),identity)) != multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))))
| greatest_lower_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))) = multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),multiply(inverse(identity),greatest_lower_bound(multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))),identity))) )],[refute_0_1044,refute_0_1045]) ).
cnf(refute_0_1047,plain,
greatest_lower_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))) = multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),greatest_lower_bound(multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))),identity)),multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))))) )],[refute_0_1043,refute_0_1046]) ).
cnf(refute_0_1048,plain,
( multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))) != identity
| greatest_lower_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))) != multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))))
| greatest_lower_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))) = identity ),
inference(subst,[],[refute_0_136:[bind(X0,$fot(greatest_lower_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))))),bind(Y0,$fot(multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_1049,plain,
( multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))) != identity
| greatest_lower_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))))) )],[refute_0_1047,refute_0_1048]) ).
cnf(refute_0_1050,plain,
greatest_lower_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))) = identity,
inference(resolve,[$cnf( $equal(multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),identity) )],[refute_0_989,refute_0_1049]) ).
cnf(refute_0_1051,plain,
( multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))) != greatest_lower_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))))
| greatest_lower_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))) != identity
| multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))) = identity ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))),identity) ),[0],$fot(greatest_lower_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))))]]) ).
cnf(refute_0_1052,plain,
( multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))) != greatest_lower_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))))
| multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),identity) )],[refute_0_1050,refute_0_1051]) ).
cnf(refute_0_1053,plain,
( multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))) != greatest_lower_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))))
| multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))) = identity ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))),greatest_lower_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))))) )],[refute_0_778,refute_0_1052]) ).
cnf(refute_0_1054,plain,
multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))) = identity,
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292))))),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))),greatest_lower_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(X_292,identity),least_upper_bound(identity,inverse(X_292)))))) )],[refute_0_754,refute_0_1053]) ).
cnf(refute_0_1055,plain,
multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291))) = identity,
inference(subst,[],[refute_0_1054:[bind(X_292,$fot(X_291))]]) ).
cnf(refute_0_1056,plain,
multiply(inverse(least_upper_bound(identity,inverse(X_291))),multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))) = multiply(inverse(least_upper_bound(identity,inverse(X_291))),multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(identity,inverse(X_291))),multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))))]]) ).
cnf(refute_0_1057,plain,
( multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291))) != identity
| multiply(inverse(least_upper_bound(identity,inverse(X_291))),multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))) != multiply(inverse(least_upper_bound(identity,inverse(X_291))),multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291))))
| multiply(inverse(least_upper_bound(identity,inverse(X_291))),multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))) = multiply(inverse(least_upper_bound(identity,inverse(X_291))),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_291))),multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))),multiply(inverse(least_upper_bound(identity,inverse(X_291))),multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_1058,plain,
( multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291))) != identity
| multiply(inverse(least_upper_bound(identity,inverse(X_291))),multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))) = multiply(inverse(least_upper_bound(identity,inverse(X_291))),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_291))),multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))),multiply(inverse(least_upper_bound(identity,inverse(X_291))),multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291))))) )],[refute_0_1056,refute_0_1057]) ).
cnf(refute_0_1059,plain,
multiply(inverse(least_upper_bound(identity,inverse(X_291))),multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))) = multiply(inverse(least_upper_bound(identity,inverse(X_291))),identity),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291))),identity) )],[refute_0_1055,refute_0_1058]) ).
cnf(refute_0_1060,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_291))),multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))) != multiply(inverse(least_upper_bound(identity,inverse(X_291))),identity)
| multiply(inverse(least_upper_bound(identity,inverse(X_291))),identity) != inverse(least_upper_bound(identity,inverse(X_291)))
| multiply(inverse(least_upper_bound(identity,inverse(X_291))),multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))) = inverse(least_upper_bound(identity,inverse(X_291))) ),
inference(subst,[],[refute_0_136:[bind(X0,$fot(multiply(inverse(least_upper_bound(identity,inverse(X_291))),multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(identity,inverse(X_291))),identity))),bind(Z0,$fot(inverse(least_upper_bound(identity,inverse(X_291)))))]]) ).
cnf(refute_0_1061,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_291))),identity) != inverse(least_upper_bound(identity,inverse(X_291)))
| multiply(inverse(least_upper_bound(identity,inverse(X_291))),multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))) = inverse(least_upper_bound(identity,inverse(X_291))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_291))),multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))),multiply(inverse(least_upper_bound(identity,inverse(X_291))),identity)) )],[refute_0_1059,refute_0_1060]) ).
cnf(refute_0_1062,plain,
multiply(inverse(least_upper_bound(identity,inverse(X_291))),multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))) = inverse(least_upper_bound(identity,inverse(X_291))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_291))),identity),inverse(least_upper_bound(identity,inverse(X_291)))) )],[refute_0_667,refute_0_1061]) ).
cnf(refute_0_1063,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_291))),multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))) != inverse(least_upper_bound(identity,inverse(X_291)))
| greatest_lower_bound(identity,X_291) != multiply(inverse(least_upper_bound(identity,inverse(X_291))),multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291))))
| greatest_lower_bound(identity,X_291) = inverse(least_upper_bound(identity,inverse(X_291))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,X_291),multiply(inverse(least_upper_bound(identity,inverse(X_291))),multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291))))) ),[1],$fot(inverse(least_upper_bound(identity,inverse(X_291))))]]) ).
cnf(refute_0_1064,plain,
( greatest_lower_bound(identity,X_291) != multiply(inverse(least_upper_bound(identity,inverse(X_291))),multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291))))
| greatest_lower_bound(identity,X_291) = inverse(least_upper_bound(identity,inverse(X_291))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_291))),multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))),inverse(least_upper_bound(identity,inverse(X_291)))) )],[refute_0_1062,refute_0_1063]) ).
cnf(refute_0_1065,plain,
greatest_lower_bound(identity,X_291) = inverse(least_upper_bound(identity,inverse(X_291))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,X_291),multiply(inverse(least_upper_bound(identity,inverse(X_291))),multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291))))) )],[refute_0_666,refute_0_1064]) ).
cnf(refute_0_1066,plain,
( greatest_lower_bound(identity,X_291) != inverse(least_upper_bound(identity,inverse(X_291)))
| inverse(least_upper_bound(identity,inverse(X_291))) = greatest_lower_bound(identity,X_291) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(identity,X_291))),bind(Y0,$fot(inverse(least_upper_bound(identity,inverse(X_291)))))]]) ).
cnf(refute_0_1067,plain,
inverse(least_upper_bound(identity,inverse(X_291))) = greatest_lower_bound(identity,X_291),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,X_291),inverse(least_upper_bound(identity,inverse(X_291)))) )],[refute_0_1065,refute_0_1066]) ).
cnf(refute_0_1068,plain,
inverse(least_upper_bound(identity,inverse(X_161))) = greatest_lower_bound(identity,X_161),
inference(subst,[],[refute_0_1067:[bind(X_291,$fot(X_161))]]) ).
cnf(refute_0_1069,plain,
multiply(inverse(least_upper_bound(identity,inverse(X_161))),least_upper_bound(X_161,identity)) = multiply(inverse(least_upper_bound(identity,inverse(X_161))),least_upper_bound(X_161,identity)),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(identity,inverse(X_161))),least_upper_bound(X_161,identity)))]]) ).
cnf(refute_0_1070,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_161))),least_upper_bound(X_161,identity)) != multiply(inverse(least_upper_bound(identity,inverse(X_161))),least_upper_bound(X_161,identity))
| inverse(least_upper_bound(identity,inverse(X_161))) != greatest_lower_bound(identity,X_161)
| multiply(inverse(least_upper_bound(identity,inverse(X_161))),least_upper_bound(X_161,identity)) = multiply(greatest_lower_bound(identity,X_161),least_upper_bound(X_161,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_161))),least_upper_bound(X_161,identity)),multiply(inverse(least_upper_bound(identity,inverse(X_161))),least_upper_bound(X_161,identity))) ),[1,0],$fot(greatest_lower_bound(identity,X_161))]]) ).
cnf(refute_0_1071,plain,
( inverse(least_upper_bound(identity,inverse(X_161))) != greatest_lower_bound(identity,X_161)
| multiply(inverse(least_upper_bound(identity,inverse(X_161))),least_upper_bound(X_161,identity)) = multiply(greatest_lower_bound(identity,X_161),least_upper_bound(X_161,identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_161))),least_upper_bound(X_161,identity)),multiply(inverse(least_upper_bound(identity,inverse(X_161))),least_upper_bound(X_161,identity))) )],[refute_0_1069,refute_0_1070]) ).
cnf(refute_0_1072,plain,
multiply(inverse(least_upper_bound(identity,inverse(X_161))),least_upper_bound(X_161,identity)) = multiply(greatest_lower_bound(identity,X_161),least_upper_bound(X_161,identity)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_161))),greatest_lower_bound(identity,X_161)) )],[refute_0_1068,refute_0_1071]) ).
cnf(refute_0_1073,plain,
( X_161 != multiply(inverse(least_upper_bound(identity,inverse(X_161))),least_upper_bound(X_161,identity))
| multiply(inverse(least_upper_bound(identity,inverse(X_161))),least_upper_bound(X_161,identity)) != multiply(greatest_lower_bound(identity,X_161),least_upper_bound(X_161,identity))
| X_161 = multiply(greatest_lower_bound(identity,X_161),least_upper_bound(X_161,identity)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_161,multiply(greatest_lower_bound(identity,X_161),least_upper_bound(X_161,identity))) ),[0],$fot(multiply(inverse(least_upper_bound(identity,inverse(X_161))),least_upper_bound(X_161,identity)))]]) ).
cnf(refute_0_1074,plain,
( X_161 != multiply(inverse(least_upper_bound(identity,inverse(X_161))),least_upper_bound(X_161,identity))
| X_161 = multiply(greatest_lower_bound(identity,X_161),least_upper_bound(X_161,identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_161))),least_upper_bound(X_161,identity)),multiply(greatest_lower_bound(identity,X_161),least_upper_bound(X_161,identity))) )],[refute_0_1072,refute_0_1073]) ).
cnf(refute_0_1075,plain,
X_161 = multiply(greatest_lower_bound(identity,X_161),least_upper_bound(X_161,identity)),
inference(resolve,[$cnf( $equal(X_161,multiply(inverse(least_upper_bound(identity,inverse(X_161))),least_upper_bound(X_161,identity))) )],[refute_0_414,refute_0_1074]) ).
cnf(refute_0_1076,plain,
X_23 = multiply(greatest_lower_bound(identity,X_23),least_upper_bound(X_23,identity)),
inference(subst,[],[refute_0_1075:[bind(X_161,$fot(X_23))]]) ).
cnf(refute_0_1077,plain,
( X_23 != multiply(greatest_lower_bound(identity,X_23),least_upper_bound(X_23,identity))
| multiply(greatest_lower_bound(identity,X_23),least_upper_bound(X_23,identity)) = X_23 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_23)),bind(Y0,$fot(multiply(greatest_lower_bound(identity,X_23),least_upper_bound(X_23,identity))))]]) ).
cnf(refute_0_1078,plain,
multiply(greatest_lower_bound(identity,X_23),least_upper_bound(X_23,identity)) = X_23,
inference(resolve,[$cnf( $equal(X_23,multiply(greatest_lower_bound(identity,X_23),least_upper_bound(X_23,identity))) )],[refute_0_1076,refute_0_1077]) ).
cnf(refute_0_1079,plain,
( multiply(greatest_lower_bound(identity,X_23),least_upper_bound(X_23,identity)) != X_23
| multiply(greatest_lower_bound(identity,multiply(inverse(X_23),identity)),least_upper_bound(X_23,identity)) != multiply(inverse(X_23),multiply(greatest_lower_bound(identity,X_23),least_upper_bound(X_23,identity)))
| multiply(greatest_lower_bound(identity,multiply(inverse(X_23),identity)),least_upper_bound(X_23,identity)) = multiply(inverse(X_23),X_23) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(inverse(X_23),identity)),least_upper_bound(X_23,identity)),multiply(inverse(X_23),multiply(greatest_lower_bound(identity,X_23),least_upper_bound(X_23,identity)))) ),[1,1],$fot(X_23)]]) ).
cnf(refute_0_1080,plain,
( multiply(greatest_lower_bound(identity,multiply(inverse(X_23),identity)),least_upper_bound(X_23,identity)) != multiply(inverse(X_23),multiply(greatest_lower_bound(identity,X_23),least_upper_bound(X_23,identity)))
| multiply(greatest_lower_bound(identity,multiply(inverse(X_23),identity)),least_upper_bound(X_23,identity)) = multiply(inverse(X_23),X_23) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_23),least_upper_bound(X_23,identity)),X_23) )],[refute_0_1078,refute_0_1079]) ).
cnf(refute_0_1081,plain,
multiply(greatest_lower_bound(identity,multiply(inverse(X_23),identity)),least_upper_bound(X_23,identity)) = multiply(inverse(X_23),X_23),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(inverse(X_23),identity)),least_upper_bound(X_23,identity)),multiply(inverse(X_23),multiply(greatest_lower_bound(identity,X_23),least_upper_bound(X_23,identity)))) )],[refute_0_346,refute_0_1080]) ).
cnf(refute_0_1082,plain,
multiply(greatest_lower_bound(identity,inverse(X_23)),identity) = greatest_lower_bound(identity,inverse(X_23)),
inference(subst,[],[refute_0_217:[bind(X_74,$fot(greatest_lower_bound(identity,inverse(X_23))))]]) ).
cnf(refute_0_1083,plain,
multiply(greatest_lower_bound(identity,multiply(inverse(identity),X_183)),X_185) = multiply(inverse(identity),multiply(greatest_lower_bound(X_183,identity),X_185)),
inference(subst,[],[refute_0_345:[bind(X_22,$fot(X_183)),bind(X_23,$fot(identity)),bind(X_72,$fot(X_185))]]) ).
cnf(refute_0_1084,plain,
( multiply(greatest_lower_bound(identity,multiply(inverse(identity),X_183)),X_185) != multiply(inverse(identity),multiply(greatest_lower_bound(X_183,identity),X_185))
| inverse(identity) != identity
| multiply(greatest_lower_bound(identity,multiply(identity,X_183)),X_185) = multiply(inverse(identity),multiply(greatest_lower_bound(X_183,identity),X_185)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(inverse(identity),X_183)),X_185),multiply(inverse(identity),multiply(greatest_lower_bound(X_183,identity),X_185))) ),[0,0,1,0],$fot(identity)]]) ).
cnf(refute_0_1085,plain,
( multiply(greatest_lower_bound(identity,multiply(inverse(identity),X_183)),X_185) != multiply(inverse(identity),multiply(greatest_lower_bound(X_183,identity),X_185))
| multiply(greatest_lower_bound(identity,multiply(identity,X_183)),X_185) = multiply(inverse(identity),multiply(greatest_lower_bound(X_183,identity),X_185)) ),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_762,refute_0_1084]) ).
cnf(refute_0_1086,plain,
multiply(greatest_lower_bound(identity,multiply(identity,X_183)),X_185) = multiply(inverse(identity),multiply(greatest_lower_bound(X_183,identity),X_185)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(inverse(identity),X_183)),X_185),multiply(inverse(identity),multiply(greatest_lower_bound(X_183,identity),X_185))) )],[refute_0_1083,refute_0_1085]) ).
cnf(refute_0_1087,plain,
multiply(identity,greatest_lower_bound(identity,X_183)) = greatest_lower_bound(identity,X_183),
inference(subst,[],[left_identity:[bind(X,$fot(greatest_lower_bound(identity,X_183)))]]) ).
cnf(refute_0_1088,plain,
greatest_lower_bound(identity,multiply(identity,X_183)) = multiply(identity,greatest_lower_bound(identity,X_183)),
inference(subst,[],[refute_0_452:[bind(X,$fot(identity)),bind(Z,$fot(X_183))]]) ).
cnf(refute_0_1089,plain,
( multiply(identity,greatest_lower_bound(identity,X_183)) != greatest_lower_bound(identity,X_183)
| greatest_lower_bound(identity,multiply(identity,X_183)) != multiply(identity,greatest_lower_bound(identity,X_183))
| greatest_lower_bound(identity,multiply(identity,X_183)) = greatest_lower_bound(identity,X_183) ),
inference(subst,[],[refute_0_136:[bind(X0,$fot(greatest_lower_bound(identity,multiply(identity,X_183)))),bind(Y0,$fot(multiply(identity,greatest_lower_bound(identity,X_183)))),bind(Z0,$fot(greatest_lower_bound(identity,X_183)))]]) ).
cnf(refute_0_1090,plain,
( multiply(identity,greatest_lower_bound(identity,X_183)) != greatest_lower_bound(identity,X_183)
| greatest_lower_bound(identity,multiply(identity,X_183)) = greatest_lower_bound(identity,X_183) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(identity,X_183)),multiply(identity,greatest_lower_bound(identity,X_183))) )],[refute_0_1088,refute_0_1089]) ).
cnf(refute_0_1091,plain,
greatest_lower_bound(identity,multiply(identity,X_183)) = greatest_lower_bound(identity,X_183),
inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(identity,X_183)),greatest_lower_bound(identity,X_183)) )],[refute_0_1087,refute_0_1090]) ).
cnf(refute_0_1092,plain,
multiply(greatest_lower_bound(identity,multiply(identity,X_183)),X_185) = multiply(greatest_lower_bound(identity,multiply(identity,X_183)),X_185),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(identity,multiply(identity,X_183)),X_185))]]) ).
cnf(refute_0_1093,plain,
( multiply(greatest_lower_bound(identity,multiply(identity,X_183)),X_185) != multiply(greatest_lower_bound(identity,multiply(identity,X_183)),X_185)
| greatest_lower_bound(identity,multiply(identity,X_183)) != greatest_lower_bound(identity,X_183)
| multiply(greatest_lower_bound(identity,multiply(identity,X_183)),X_185) = multiply(greatest_lower_bound(identity,X_183),X_185) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(identity,X_183)),X_185),multiply(greatest_lower_bound(identity,multiply(identity,X_183)),X_185)) ),[1,0],$fot(greatest_lower_bound(identity,X_183))]]) ).
cnf(refute_0_1094,plain,
( greatest_lower_bound(identity,multiply(identity,X_183)) != greatest_lower_bound(identity,X_183)
| multiply(greatest_lower_bound(identity,multiply(identity,X_183)),X_185) = multiply(greatest_lower_bound(identity,X_183),X_185) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(identity,X_183)),X_185),multiply(greatest_lower_bound(identity,multiply(identity,X_183)),X_185)) )],[refute_0_1092,refute_0_1093]) ).
cnf(refute_0_1095,plain,
multiply(greatest_lower_bound(identity,multiply(identity,X_183)),X_185) = multiply(greatest_lower_bound(identity,X_183),X_185),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(identity,X_183)),greatest_lower_bound(identity,X_183)) )],[refute_0_1091,refute_0_1094]) ).
cnf(refute_0_1096,plain,
( multiply(greatest_lower_bound(identity,multiply(identity,X_183)),X_185) != multiply(greatest_lower_bound(identity,X_183),X_185)
| multiply(greatest_lower_bound(identity,multiply(identity,X_183)),X_185) != multiply(inverse(identity),multiply(greatest_lower_bound(X_183,identity),X_185))
| multiply(greatest_lower_bound(identity,X_183),X_185) = multiply(inverse(identity),multiply(greatest_lower_bound(X_183,identity),X_185)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(identity,X_183)),X_185),multiply(inverse(identity),multiply(greatest_lower_bound(X_183,identity),X_185))) ),[0],$fot(multiply(greatest_lower_bound(identity,X_183),X_185))]]) ).
cnf(refute_0_1097,plain,
( multiply(greatest_lower_bound(identity,multiply(identity,X_183)),X_185) != multiply(inverse(identity),multiply(greatest_lower_bound(X_183,identity),X_185))
| multiply(greatest_lower_bound(identity,X_183),X_185) = multiply(inverse(identity),multiply(greatest_lower_bound(X_183,identity),X_185)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(identity,X_183)),X_185),multiply(greatest_lower_bound(identity,X_183),X_185)) )],[refute_0_1095,refute_0_1096]) ).
cnf(refute_0_1098,plain,
multiply(identity,multiply(greatest_lower_bound(X_183,identity),X_185)) = multiply(greatest_lower_bound(X_183,identity),X_185),
inference(subst,[],[left_identity:[bind(X,$fot(multiply(greatest_lower_bound(X_183,identity),X_185)))]]) ).
cnf(refute_0_1099,plain,
multiply(inverse(identity),multiply(greatest_lower_bound(X_183,identity),X_185)) = multiply(inverse(identity),multiply(greatest_lower_bound(X_183,identity),X_185)),
introduced(tautology,[refl,[$fot(multiply(inverse(identity),multiply(greatest_lower_bound(X_183,identity),X_185)))]]) ).
cnf(refute_0_1100,plain,
( multiply(inverse(identity),multiply(greatest_lower_bound(X_183,identity),X_185)) != multiply(inverse(identity),multiply(greatest_lower_bound(X_183,identity),X_185))
| inverse(identity) != identity
| multiply(inverse(identity),multiply(greatest_lower_bound(X_183,identity),X_185)) = multiply(identity,multiply(greatest_lower_bound(X_183,identity),X_185)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(identity),multiply(greatest_lower_bound(X_183,identity),X_185)),multiply(inverse(identity),multiply(greatest_lower_bound(X_183,identity),X_185))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_1101,plain,
( inverse(identity) != identity
| multiply(inverse(identity),multiply(greatest_lower_bound(X_183,identity),X_185)) = multiply(identity,multiply(greatest_lower_bound(X_183,identity),X_185)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),multiply(greatest_lower_bound(X_183,identity),X_185)),multiply(inverse(identity),multiply(greatest_lower_bound(X_183,identity),X_185))) )],[refute_0_1099,refute_0_1100]) ).
cnf(refute_0_1102,plain,
multiply(inverse(identity),multiply(greatest_lower_bound(X_183,identity),X_185)) = multiply(identity,multiply(greatest_lower_bound(X_183,identity),X_185)),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_762,refute_0_1101]) ).
cnf(refute_0_1103,plain,
( multiply(identity,multiply(greatest_lower_bound(X_183,identity),X_185)) != multiply(greatest_lower_bound(X_183,identity),X_185)
| multiply(inverse(identity),multiply(greatest_lower_bound(X_183,identity),X_185)) != multiply(identity,multiply(greatest_lower_bound(X_183,identity),X_185))
| multiply(inverse(identity),multiply(greatest_lower_bound(X_183,identity),X_185)) = multiply(greatest_lower_bound(X_183,identity),X_185) ),
inference(subst,[],[refute_0_136:[bind(X0,$fot(multiply(inverse(identity),multiply(greatest_lower_bound(X_183,identity),X_185)))),bind(Y0,$fot(multiply(identity,multiply(greatest_lower_bound(X_183,identity),X_185)))),bind(Z0,$fot(multiply(greatest_lower_bound(X_183,identity),X_185)))]]) ).
cnf(refute_0_1104,plain,
( multiply(identity,multiply(greatest_lower_bound(X_183,identity),X_185)) != multiply(greatest_lower_bound(X_183,identity),X_185)
| multiply(inverse(identity),multiply(greatest_lower_bound(X_183,identity),X_185)) = multiply(greatest_lower_bound(X_183,identity),X_185) ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),multiply(greatest_lower_bound(X_183,identity),X_185)),multiply(identity,multiply(greatest_lower_bound(X_183,identity),X_185))) )],[refute_0_1102,refute_0_1103]) ).
cnf(refute_0_1105,plain,
multiply(inverse(identity),multiply(greatest_lower_bound(X_183,identity),X_185)) = multiply(greatest_lower_bound(X_183,identity),X_185),
inference(resolve,[$cnf( $equal(multiply(identity,multiply(greatest_lower_bound(X_183,identity),X_185)),multiply(greatest_lower_bound(X_183,identity),X_185)) )],[refute_0_1098,refute_0_1104]) ).
cnf(refute_0_1106,plain,
( multiply(greatest_lower_bound(identity,X_183),X_185) != multiply(inverse(identity),multiply(greatest_lower_bound(X_183,identity),X_185))
| multiply(inverse(identity),multiply(greatest_lower_bound(X_183,identity),X_185)) != multiply(greatest_lower_bound(X_183,identity),X_185)
| multiply(greatest_lower_bound(identity,X_183),X_185) = multiply(greatest_lower_bound(X_183,identity),X_185) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(identity,X_183),X_185),multiply(greatest_lower_bound(X_183,identity),X_185)) ),[0],$fot(multiply(inverse(identity),multiply(greatest_lower_bound(X_183,identity),X_185)))]]) ).
cnf(refute_0_1107,plain,
( multiply(greatest_lower_bound(identity,X_183),X_185) != multiply(inverse(identity),multiply(greatest_lower_bound(X_183,identity),X_185))
| multiply(greatest_lower_bound(identity,X_183),X_185) = multiply(greatest_lower_bound(X_183,identity),X_185) ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),multiply(greatest_lower_bound(X_183,identity),X_185)),multiply(greatest_lower_bound(X_183,identity),X_185)) )],[refute_0_1105,refute_0_1106]) ).
cnf(refute_0_1108,plain,
( multiply(greatest_lower_bound(identity,multiply(identity,X_183)),X_185) != multiply(inverse(identity),multiply(greatest_lower_bound(X_183,identity),X_185))
| multiply(greatest_lower_bound(identity,X_183),X_185) = multiply(greatest_lower_bound(X_183,identity),X_185) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_183),X_185),multiply(inverse(identity),multiply(greatest_lower_bound(X_183,identity),X_185))) )],[refute_0_1097,refute_0_1107]) ).
cnf(refute_0_1109,plain,
multiply(greatest_lower_bound(identity,X_183),X_185) = multiply(greatest_lower_bound(X_183,identity),X_185),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(identity,X_183)),X_185),multiply(inverse(identity),multiply(greatest_lower_bound(X_183,identity),X_185))) )],[refute_0_1086,refute_0_1108]) ).
cnf(refute_0_1110,plain,
( multiply(greatest_lower_bound(identity,X_183),X_185) != multiply(greatest_lower_bound(X_183,identity),X_185)
| multiply(greatest_lower_bound(X_183,identity),X_185) = multiply(greatest_lower_bound(identity,X_183),X_185) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(greatest_lower_bound(identity,X_183),X_185))),bind(Y0,$fot(multiply(greatest_lower_bound(X_183,identity),X_185)))]]) ).
cnf(refute_0_1111,plain,
multiply(greatest_lower_bound(X_183,identity),X_185) = multiply(greatest_lower_bound(identity,X_183),X_185),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_183),X_185),multiply(greatest_lower_bound(X_183,identity),X_185)) )],[refute_0_1109,refute_0_1110]) ).
cnf(refute_0_1112,plain,
multiply(greatest_lower_bound(inverse(X_23),identity),identity) = multiply(greatest_lower_bound(identity,inverse(X_23)),identity),
inference(subst,[],[refute_0_1111:[bind(X_183,$fot(inverse(X_23))),bind(X_185,$fot(identity))]]) ).
cnf(refute_0_1113,plain,
( multiply(greatest_lower_bound(identity,inverse(X_23)),identity) != greatest_lower_bound(identity,inverse(X_23))
| multiply(greatest_lower_bound(inverse(X_23),identity),identity) != multiply(greatest_lower_bound(identity,inverse(X_23)),identity)
| multiply(greatest_lower_bound(inverse(X_23),identity),identity) = greatest_lower_bound(identity,inverse(X_23)) ),
inference(subst,[],[refute_0_136:[bind(X0,$fot(multiply(greatest_lower_bound(inverse(X_23),identity),identity))),bind(Y0,$fot(multiply(greatest_lower_bound(identity,inverse(X_23)),identity))),bind(Z0,$fot(greatest_lower_bound(identity,inverse(X_23))))]]) ).
cnf(refute_0_1114,plain,
( multiply(greatest_lower_bound(identity,inverse(X_23)),identity) != greatest_lower_bound(identity,inverse(X_23))
| multiply(greatest_lower_bound(inverse(X_23),identity),identity) = greatest_lower_bound(identity,inverse(X_23)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_23),identity),identity),multiply(greatest_lower_bound(identity,inverse(X_23)),identity)) )],[refute_0_1112,refute_0_1113]) ).
cnf(refute_0_1115,plain,
multiply(greatest_lower_bound(inverse(X_23),identity),identity) = greatest_lower_bound(identity,inverse(X_23)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(X_23)),identity),greatest_lower_bound(identity,inverse(X_23))) )],[refute_0_1082,refute_0_1114]) ).
cnf(refute_0_1116,plain,
( multiply(greatest_lower_bound(X_29,identity),X_28) != greatest_lower_bound(X_28,multiply(X_29,X_28))
| greatest_lower_bound(X_28,multiply(X_29,X_28)) = multiply(greatest_lower_bound(X_29,identity),X_28) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(greatest_lower_bound(X_29,identity),X_28))),bind(Y0,$fot(greatest_lower_bound(X_28,multiply(X_29,X_28))))]]) ).
cnf(refute_0_1117,plain,
greatest_lower_bound(X_28,multiply(X_29,X_28)) = multiply(greatest_lower_bound(X_29,identity),X_28),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_29,identity),X_28),greatest_lower_bound(X_28,multiply(X_29,X_28))) )],[refute_0_23,refute_0_1116]) ).
cnf(refute_0_1118,plain,
greatest_lower_bound(identity,multiply(inverse(X_23),identity)) = multiply(greatest_lower_bound(inverse(X_23),identity),identity),
inference(subst,[],[refute_0_1117:[bind(X_28,$fot(identity)),bind(X_29,$fot(inverse(X_23)))]]) ).
cnf(refute_0_1119,plain,
( multiply(greatest_lower_bound(inverse(X_23),identity),identity) != greatest_lower_bound(identity,inverse(X_23))
| greatest_lower_bound(identity,multiply(inverse(X_23),identity)) != multiply(greatest_lower_bound(inverse(X_23),identity),identity)
| greatest_lower_bound(identity,multiply(inverse(X_23),identity)) = greatest_lower_bound(identity,inverse(X_23)) ),
inference(subst,[],[refute_0_136:[bind(X0,$fot(greatest_lower_bound(identity,multiply(inverse(X_23),identity)))),bind(Y0,$fot(multiply(greatest_lower_bound(inverse(X_23),identity),identity))),bind(Z0,$fot(greatest_lower_bound(identity,inverse(X_23))))]]) ).
cnf(refute_0_1120,plain,
( multiply(greatest_lower_bound(inverse(X_23),identity),identity) != greatest_lower_bound(identity,inverse(X_23))
| greatest_lower_bound(identity,multiply(inverse(X_23),identity)) = greatest_lower_bound(identity,inverse(X_23)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(X_23),identity)),multiply(greatest_lower_bound(inverse(X_23),identity),identity)) )],[refute_0_1118,refute_0_1119]) ).
cnf(refute_0_1121,plain,
greatest_lower_bound(identity,multiply(inverse(X_23),identity)) = greatest_lower_bound(identity,inverse(X_23)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_23),identity),identity),greatest_lower_bound(identity,inverse(X_23))) )],[refute_0_1115,refute_0_1120]) ).
cnf(refute_0_1122,plain,
multiply(greatest_lower_bound(identity,multiply(inverse(X_23),identity)),least_upper_bound(X_23,identity)) = multiply(greatest_lower_bound(identity,multiply(inverse(X_23),identity)),least_upper_bound(X_23,identity)),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(identity,multiply(inverse(X_23),identity)),least_upper_bound(X_23,identity)))]]) ).
cnf(refute_0_1123,plain,
( multiply(greatest_lower_bound(identity,multiply(inverse(X_23),identity)),least_upper_bound(X_23,identity)) != multiply(greatest_lower_bound(identity,multiply(inverse(X_23),identity)),least_upper_bound(X_23,identity))
| greatest_lower_bound(identity,multiply(inverse(X_23),identity)) != greatest_lower_bound(identity,inverse(X_23))
| multiply(greatest_lower_bound(identity,multiply(inverse(X_23),identity)),least_upper_bound(X_23,identity)) = multiply(greatest_lower_bound(identity,inverse(X_23)),least_upper_bound(X_23,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(inverse(X_23),identity)),least_upper_bound(X_23,identity)),multiply(greatest_lower_bound(identity,multiply(inverse(X_23),identity)),least_upper_bound(X_23,identity))) ),[1,0],$fot(greatest_lower_bound(identity,inverse(X_23)))]]) ).
cnf(refute_0_1124,plain,
( greatest_lower_bound(identity,multiply(inverse(X_23),identity)) != greatest_lower_bound(identity,inverse(X_23))
| multiply(greatest_lower_bound(identity,multiply(inverse(X_23),identity)),least_upper_bound(X_23,identity)) = multiply(greatest_lower_bound(identity,inverse(X_23)),least_upper_bound(X_23,identity)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(inverse(X_23),identity)),least_upper_bound(X_23,identity)),multiply(greatest_lower_bound(identity,multiply(inverse(X_23),identity)),least_upper_bound(X_23,identity))) )],[refute_0_1122,refute_0_1123]) ).
cnf(refute_0_1125,plain,
multiply(greatest_lower_bound(identity,multiply(inverse(X_23),identity)),least_upper_bound(X_23,identity)) = multiply(greatest_lower_bound(identity,inverse(X_23)),least_upper_bound(X_23,identity)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(X_23),identity)),greatest_lower_bound(identity,inverse(X_23))) )],[refute_0_1121,refute_0_1124]) ).
cnf(refute_0_1126,plain,
( multiply(greatest_lower_bound(identity,multiply(inverse(X_23),identity)),least_upper_bound(X_23,identity)) != multiply(greatest_lower_bound(identity,inverse(X_23)),least_upper_bound(X_23,identity))
| multiply(greatest_lower_bound(identity,multiply(inverse(X_23),identity)),least_upper_bound(X_23,identity)) != multiply(inverse(X_23),X_23)
| multiply(greatest_lower_bound(identity,inverse(X_23)),least_upper_bound(X_23,identity)) = multiply(inverse(X_23),X_23) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(inverse(X_23),identity)),least_upper_bound(X_23,identity)),multiply(inverse(X_23),X_23)) ),[0],$fot(multiply(greatest_lower_bound(identity,inverse(X_23)),least_upper_bound(X_23,identity)))]]) ).
cnf(refute_0_1127,plain,
( multiply(greatest_lower_bound(identity,multiply(inverse(X_23),identity)),least_upper_bound(X_23,identity)) != multiply(inverse(X_23),X_23)
| multiply(greatest_lower_bound(identity,inverse(X_23)),least_upper_bound(X_23,identity)) = multiply(inverse(X_23),X_23) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(inverse(X_23),identity)),least_upper_bound(X_23,identity)),multiply(greatest_lower_bound(identity,inverse(X_23)),least_upper_bound(X_23,identity))) )],[refute_0_1125,refute_0_1126]) ).
cnf(refute_0_1128,plain,
( multiply(greatest_lower_bound(identity,inverse(X_23)),least_upper_bound(X_23,identity)) != multiply(inverse(X_23),X_23)
| multiply(inverse(X_23),X_23) != identity
| multiply(greatest_lower_bound(identity,inverse(X_23)),least_upper_bound(X_23,identity)) = identity ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(identity,inverse(X_23)),least_upper_bound(X_23,identity)),identity) ),[0],$fot(multiply(inverse(X_23),X_23))]]) ).
cnf(refute_0_1129,plain,
( multiply(greatest_lower_bound(identity,inverse(X_23)),least_upper_bound(X_23,identity)) != multiply(inverse(X_23),X_23)
| multiply(greatest_lower_bound(identity,inverse(X_23)),least_upper_bound(X_23,identity)) = identity ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_23),X_23),identity) )],[refute_0_262,refute_0_1128]) ).
cnf(refute_0_1130,plain,
( multiply(greatest_lower_bound(identity,multiply(inverse(X_23),identity)),least_upper_bound(X_23,identity)) != multiply(inverse(X_23),X_23)
| multiply(greatest_lower_bound(identity,inverse(X_23)),least_upper_bound(X_23,identity)) = identity ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(X_23)),least_upper_bound(X_23,identity)),multiply(inverse(X_23),X_23)) )],[refute_0_1127,refute_0_1129]) ).
cnf(refute_0_1131,plain,
multiply(greatest_lower_bound(identity,inverse(X_23)),least_upper_bound(X_23,identity)) = identity,
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(inverse(X_23),identity)),least_upper_bound(X_23,identity)),multiply(inverse(X_23),X_23)) )],[refute_0_1081,refute_0_1130]) ).
cnf(refute_0_1132,plain,
multiply(greatest_lower_bound(identity,inverse(a)),least_upper_bound(a,identity)) = identity,
inference(subst,[],[refute_0_1131:[bind(X_23,$fot(a))]]) ).
cnf(refute_0_1133,plain,
( multiply(greatest_lower_bound(identity,inverse(a)),least_upper_bound(a,identity)) != identity
| identity != identity
| multiply(greatest_lower_bound(identity,inverse(a)),least_upper_bound(a,identity)) = identity ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(identity,inverse(a)),least_upper_bound(a,identity)),identity) ),[0],$fot(identity)]]) ).
cnf(refute_0_1134,plain,
( identity != identity
| multiply(greatest_lower_bound(identity,inverse(a)),least_upper_bound(a,identity)) = identity ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(a)),least_upper_bound(a,identity)),identity) )],[refute_0_1132,refute_0_1133]) ).
cnf(refute_0_1135,plain,
identity != identity,
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(a)),least_upper_bound(a,identity)),identity) )],[refute_0_1134,refute_0_341]) ).
cnf(refute_0_1136,plain,
identity = identity,
introduced(tautology,[refl,[$fot(identity)]]) ).
cnf(refute_0_1137,plain,
$false,
inference(resolve,[$cnf( $equal(identity,identity) )],[refute_0_1136,refute_0_1135]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GRP183-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.04/0.14 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n019.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jun 13 05:04:55 EDT 2022
% 0.13/0.36 % CPUTime :
% 0.13/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 9.88/10.06 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.88/10.06
% 9.88/10.06 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.97/10.19
%------------------------------------------------------------------------------