TSTP Solution File: GRP190-2 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP190-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n022.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 10:37:55 EDT 2022
% Result : Unsatisfiable 2.54s 2.74s
% Output : CNFRefutation 2.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 52
% Number of leaves : 112
% Syntax : Number of clauses : 517 ( 276 unt; 0 nHn; 257 RR)
% Number of literals : 861 ( 860 equ; 345 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 982 ( 24 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
multiply(identity,X) = X ).
cnf(left_inverse,axiom,
multiply(inverse(X),X) = identity ).
cnf(associativity,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ).
cnf(symmetry_of_glb,axiom,
greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ).
cnf(symmetry_of_lub,axiom,
least_upper_bound(X,Y) = least_upper_bound(Y,X) ).
cnf(associativity_of_glb,axiom,
greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) ).
cnf(associativity_of_lub,axiom,
least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) ).
cnf(idempotence_of_lub,axiom,
least_upper_bound(X,X) = X ).
cnf(lub_absorbtion,axiom,
least_upper_bound(X,greatest_lower_bound(X,Y)) = X ).
cnf(glb_absorbtion,axiom,
greatest_lower_bound(X,least_upper_bound(X,Y)) = X ).
cnf(monotony_lub1,axiom,
multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ).
cnf(monotony_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(p39c_1,hypothesis,
least_upper_bound(a,b) = a ).
cnf(prove_p39c,negated_conjecture,
greatest_lower_bound(inverse(a),inverse(b)) != inverse(a) ).
cnf(refute_0_0,plain,
greatest_lower_bound(inverse(a),least_upper_bound(inverse(a),inverse(b))) = inverse(a),
inference(subst,[],[glb_absorbtion:[bind(X,$fot(inverse(a))),bind(Y,$fot(inverse(b)))]]) ).
cnf(refute_0_1,plain,
multiply(multiply(inverse(X_45),X_45),X_46) = multiply(inverse(X_45),multiply(X_45,X_46)),
inference(subst,[],[associativity:[bind(X,$fot(inverse(X_45))),bind(Y,$fot(X_45)),bind(Z,$fot(X_46))]]) ).
cnf(refute_0_2,plain,
multiply(inverse(X_45),X_45) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_45))]]) ).
cnf(refute_0_3,plain,
( multiply(multiply(inverse(X_45),X_45),X_46) != multiply(inverse(X_45),multiply(X_45,X_46))
| multiply(inverse(X_45),X_45) != identity
| multiply(identity,X_46) = multiply(inverse(X_45),multiply(X_45,X_46)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_45),X_45),X_46),multiply(inverse(X_45),multiply(X_45,X_46))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_4,plain,
( multiply(multiply(inverse(X_45),X_45),X_46) != multiply(inverse(X_45),multiply(X_45,X_46))
| multiply(identity,X_46) = multiply(inverse(X_45),multiply(X_45,X_46)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_45),X_45),identity) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
multiply(identity,X_46) = multiply(inverse(X_45),multiply(X_45,X_46)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_45),X_45),X_46),multiply(inverse(X_45),multiply(X_45,X_46))) )],[refute_0_1,refute_0_4]) ).
cnf(refute_0_6,plain,
multiply(identity,X_46) = X_46,
inference(subst,[],[left_identity:[bind(X,$fot(X_46))]]) ).
cnf(refute_0_7,plain,
( multiply(identity,X_46) != X_46
| multiply(identity,X_46) != multiply(inverse(X_45),multiply(X_45,X_46))
| X_46 = multiply(inverse(X_45),multiply(X_45,X_46)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_46),multiply(inverse(X_45),multiply(X_45,X_46))) ),[0],$fot(X_46)]]) ).
cnf(refute_0_8,plain,
( multiply(identity,X_46) != multiply(inverse(X_45),multiply(X_45,X_46))
| X_46 = multiply(inverse(X_45),multiply(X_45,X_46)) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_46),X_46) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
X_46 = multiply(inverse(X_45),multiply(X_45,X_46)),
inference(resolve,[$cnf( $equal(multiply(identity,X_46),multiply(inverse(X_45),multiply(X_45,X_46))) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
X_48 = multiply(inverse(inverse(X_48)),multiply(inverse(X_48),X_48)),
inference(subst,[],[refute_0_9:[bind(X_45,$fot(inverse(X_48))),bind(X_46,$fot(X_48))]]) ).
cnf(refute_0_11,plain,
multiply(inverse(X_48),X_48) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_48))]]) ).
cnf(refute_0_12,plain,
( X_48 != multiply(inverse(inverse(X_48)),multiply(inverse(X_48),X_48))
| multiply(inverse(X_48),X_48) != identity
| X_48 = multiply(inverse(inverse(X_48)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(X_48,multiply(inverse(inverse(X_48)),multiply(inverse(X_48),X_48))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_13,plain,
( X_48 != multiply(inverse(inverse(X_48)),multiply(inverse(X_48),X_48))
| X_48 = multiply(inverse(inverse(X_48)),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_48),X_48),identity) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
X_48 = multiply(inverse(inverse(X_48)),identity),
inference(resolve,[$cnf( $equal(X_48,multiply(inverse(inverse(X_48)),multiply(inverse(X_48),X_48))) )],[refute_0_10,refute_0_13]) ).
cnf(refute_0_15,plain,
multiply(X_47,X_48) = multiply(inverse(inverse(X_47)),multiply(inverse(X_47),multiply(X_47,X_48))),
inference(subst,[],[refute_0_9:[bind(X_45,$fot(inverse(X_47))),bind(X_46,$fot(multiply(X_47,X_48)))]]) ).
cnf(refute_0_16,plain,
X_48 = multiply(inverse(X_47),multiply(X_47,X_48)),
inference(subst,[],[refute_0_9:[bind(X_45,$fot(X_47)),bind(X_46,$fot(X_48))]]) ).
cnf(refute_0_17,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_18,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_19,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
( X_48 != multiply(inverse(X_47),multiply(X_47,X_48))
| multiply(inverse(X_47),multiply(X_47,X_48)) = X_48 ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(X_48)),bind(Y0,$fot(multiply(inverse(X_47),multiply(X_47,X_48))))]]) ).
cnf(refute_0_21,plain,
multiply(inverse(X_47),multiply(X_47,X_48)) = X_48,
inference(resolve,[$cnf( $equal(X_48,multiply(inverse(X_47),multiply(X_47,X_48))) )],[refute_0_16,refute_0_20]) ).
cnf(refute_0_22,plain,
( multiply(X_47,X_48) != multiply(inverse(inverse(X_47)),multiply(inverse(X_47),multiply(X_47,X_48)))
| multiply(inverse(X_47),multiply(X_47,X_48)) != X_48
| multiply(X_47,X_48) = multiply(inverse(inverse(X_47)),X_48) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_47,X_48),multiply(inverse(inverse(X_47)),multiply(inverse(X_47),multiply(X_47,X_48)))) ),[1,1],$fot(X_48)]]) ).
cnf(refute_0_23,plain,
( multiply(X_47,X_48) != multiply(inverse(inverse(X_47)),multiply(inverse(X_47),multiply(X_47,X_48)))
| multiply(X_47,X_48) = multiply(inverse(inverse(X_47)),X_48) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_47),multiply(X_47,X_48)),X_48) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
multiply(X_47,X_48) = multiply(inverse(inverse(X_47)),X_48),
inference(resolve,[$cnf( $equal(multiply(X_47,X_48),multiply(inverse(inverse(X_47)),multiply(inverse(X_47),multiply(X_47,X_48)))) )],[refute_0_15,refute_0_23]) ).
cnf(refute_0_25,plain,
( multiply(X_47,X_48) != multiply(inverse(inverse(X_47)),X_48)
| multiply(inverse(inverse(X_47)),X_48) = multiply(X_47,X_48) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(X_47,X_48))),bind(Y0,$fot(multiply(inverse(inverse(X_47)),X_48)))]]) ).
cnf(refute_0_26,plain,
multiply(inverse(inverse(X_47)),X_48) = multiply(X_47,X_48),
inference(resolve,[$cnf( $equal(multiply(X_47,X_48),multiply(inverse(inverse(X_47)),X_48)) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
multiply(inverse(inverse(X_48)),identity) = multiply(X_48,identity),
inference(subst,[],[refute_0_26:[bind(X_47,$fot(X_48)),bind(X_48,$fot(identity))]]) ).
cnf(refute_0_28,plain,
( X_48 != multiply(inverse(inverse(X_48)),identity)
| multiply(inverse(inverse(X_48)),identity) != multiply(X_48,identity)
| X_48 = multiply(X_48,identity) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_48,multiply(X_48,identity)) ),[0],$fot(multiply(inverse(inverse(X_48)),identity))]]) ).
cnf(refute_0_29,plain,
( X_48 != multiply(inverse(inverse(X_48)),identity)
| X_48 = multiply(X_48,identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_48)),identity),multiply(X_48,identity)) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
X_48 = multiply(X_48,identity),
inference(resolve,[$cnf( $equal(X_48,multiply(inverse(inverse(X_48)),identity)) )],[refute_0_14,refute_0_29]) ).
cnf(refute_0_31,plain,
inverse(inverse(X_50)) = multiply(inverse(inverse(X_50)),identity),
inference(subst,[],[refute_0_30:[bind(X_48,$fot(inverse(inverse(X_50))))]]) ).
cnf(refute_0_32,plain,
multiply(X_50,identity) = multiply(inverse(inverse(X_50)),identity),
inference(subst,[],[refute_0_24:[bind(X_47,$fot(X_50)),bind(X_48,$fot(identity))]]) ).
cnf(refute_0_33,plain,
( multiply(X_50,identity) != multiply(inverse(inverse(X_50)),identity)
| multiply(inverse(inverse(X_50)),identity) = multiply(X_50,identity) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(X_50,identity))),bind(Y0,$fot(multiply(inverse(inverse(X_50)),identity)))]]) ).
cnf(refute_0_34,plain,
multiply(inverse(inverse(X_50)),identity) = multiply(X_50,identity),
inference(resolve,[$cnf( $equal(multiply(X_50,identity),multiply(inverse(inverse(X_50)),identity)) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
( multiply(inverse(inverse(X_50)),identity) != multiply(X_50,identity)
| inverse(inverse(X_50)) != multiply(inverse(inverse(X_50)),identity)
| inverse(inverse(X_50)) = multiply(X_50,identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_50)),multiply(inverse(inverse(X_50)),identity)) ),[1],$fot(multiply(X_50,identity))]]) ).
cnf(refute_0_36,plain,
( inverse(inverse(X_50)) != multiply(inverse(inverse(X_50)),identity)
| inverse(inverse(X_50)) = multiply(X_50,identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_50)),identity),multiply(X_50,identity)) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
inverse(inverse(X_50)) = multiply(X_50,identity),
inference(resolve,[$cnf( $equal(inverse(inverse(X_50)),multiply(inverse(inverse(X_50)),identity)) )],[refute_0_31,refute_0_36]) ).
cnf(refute_0_38,plain,
( X_48 != multiply(X_48,identity)
| multiply(X_48,identity) = X_48 ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(X_48)),bind(Y0,$fot(multiply(X_48,identity)))]]) ).
cnf(refute_0_39,plain,
multiply(X_48,identity) = X_48,
inference(resolve,[$cnf( $equal(X_48,multiply(X_48,identity)) )],[refute_0_30,refute_0_38]) ).
cnf(refute_0_40,plain,
multiply(X_50,identity) = X_50,
inference(subst,[],[refute_0_39:[bind(X_48,$fot(X_50))]]) ).
cnf(refute_0_41,plain,
( multiply(X_50,identity) != X_50
| inverse(inverse(X_50)) != multiply(X_50,identity)
| inverse(inverse(X_50)) = X_50 ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_50)),multiply(X_50,identity)) ),[1],$fot(X_50)]]) ).
cnf(refute_0_42,plain,
( inverse(inverse(X_50)) != multiply(X_50,identity)
| inverse(inverse(X_50)) = X_50 ),
inference(resolve,[$cnf( $equal(multiply(X_50,identity),X_50) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
inverse(inverse(X_50)) = X_50,
inference(resolve,[$cnf( $equal(inverse(inverse(X_50)),multiply(X_50,identity)) )],[refute_0_37,refute_0_42]) ).
cnf(refute_0_44,plain,
inverse(inverse(least_upper_bound(inverse(a),inverse(b)))) = least_upper_bound(inverse(a),inverse(b)),
inference(subst,[],[refute_0_43:[bind(X_50,$fot(least_upper_bound(inverse(a),inverse(b))))]]) ).
cnf(refute_0_45,plain,
X_46 = multiply(inverse(least_upper_bound(X_194,inverse(X_46))),multiply(least_upper_bound(X_194,inverse(X_46)),X_46)),
inference(subst,[],[refute_0_9:[bind(X_45,$fot(least_upper_bound(X_194,inverse(X_46))))]]) ).
cnf(refute_0_46,plain,
multiply(least_upper_bound(X_83,inverse(X_82)),X_82) = least_upper_bound(multiply(X_83,X_82),multiply(inverse(X_82),X_82)),
inference(subst,[],[monotony_lub2:[bind(X,$fot(X_82)),bind(Y,$fot(X_83)),bind(Z,$fot(inverse(X_82)))]]) ).
cnf(refute_0_47,plain,
multiply(inverse(X_82),X_82) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_82))]]) ).
cnf(refute_0_48,plain,
( multiply(inverse(X_82),X_82) != identity
| multiply(least_upper_bound(X_83,inverse(X_82)),X_82) != least_upper_bound(multiply(X_83,X_82),multiply(inverse(X_82),X_82))
| multiply(least_upper_bound(X_83,inverse(X_82)),X_82) = least_upper_bound(multiply(X_83,X_82),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_83,inverse(X_82)),X_82),least_upper_bound(multiply(X_83,X_82),multiply(inverse(X_82),X_82))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_49,plain,
( multiply(least_upper_bound(X_83,inverse(X_82)),X_82) != least_upper_bound(multiply(X_83,X_82),multiply(inverse(X_82),X_82))
| multiply(least_upper_bound(X_83,inverse(X_82)),X_82) = least_upper_bound(multiply(X_83,X_82),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_82),X_82),identity) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
multiply(least_upper_bound(X_83,inverse(X_82)),X_82) = least_upper_bound(multiply(X_83,X_82),identity),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_83,inverse(X_82)),X_82),least_upper_bound(multiply(X_83,X_82),multiply(inverse(X_82),X_82))) )],[refute_0_46,refute_0_49]) ).
cnf(refute_0_51,plain,
( least_upper_bound(X,Y) != least_upper_bound(Y,X)
| least_upper_bound(Y,X) = least_upper_bound(X,Y) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(least_upper_bound(X,Y))),bind(Y0,$fot(least_upper_bound(Y,X)))]]) ).
cnf(refute_0_52,plain,
least_upper_bound(Y,X) = least_upper_bound(X,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(X,Y),least_upper_bound(Y,X)) )],[symmetry_of_lub,refute_0_51]) ).
cnf(refute_0_53,plain,
least_upper_bound(multiply(X_83,X_82),identity) = least_upper_bound(identity,multiply(X_83,X_82)),
inference(subst,[],[refute_0_52:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_83,X_82)))]]) ).
cnf(refute_0_54,plain,
( multiply(least_upper_bound(X_83,inverse(X_82)),X_82) != least_upper_bound(multiply(X_83,X_82),identity)
| least_upper_bound(multiply(X_83,X_82),identity) != least_upper_bound(identity,multiply(X_83,X_82))
| multiply(least_upper_bound(X_83,inverse(X_82)),X_82) = least_upper_bound(identity,multiply(X_83,X_82)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_83,inverse(X_82)),X_82),least_upper_bound(identity,multiply(X_83,X_82))) ),[0],$fot(least_upper_bound(multiply(X_83,X_82),identity))]]) ).
cnf(refute_0_55,plain,
( multiply(least_upper_bound(X_83,inverse(X_82)),X_82) != least_upper_bound(multiply(X_83,X_82),identity)
| multiply(least_upper_bound(X_83,inverse(X_82)),X_82) = least_upper_bound(identity,multiply(X_83,X_82)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_83,X_82),identity),least_upper_bound(identity,multiply(X_83,X_82))) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
multiply(least_upper_bound(X_83,inverse(X_82)),X_82) = least_upper_bound(identity,multiply(X_83,X_82)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_83,inverse(X_82)),X_82),least_upper_bound(multiply(X_83,X_82),identity)) )],[refute_0_50,refute_0_55]) ).
cnf(refute_0_57,plain,
multiply(least_upper_bound(X_194,inverse(X_46)),X_46) = least_upper_bound(identity,multiply(X_194,X_46)),
inference(subst,[],[refute_0_56:[bind(X_82,$fot(X_46)),bind(X_83,$fot(X_194))]]) ).
cnf(refute_0_58,plain,
( X_46 != multiply(inverse(least_upper_bound(X_194,inverse(X_46))),multiply(least_upper_bound(X_194,inverse(X_46)),X_46))
| multiply(least_upper_bound(X_194,inverse(X_46)),X_46) != least_upper_bound(identity,multiply(X_194,X_46))
| X_46 = multiply(inverse(least_upper_bound(X_194,inverse(X_46))),least_upper_bound(identity,multiply(X_194,X_46))) ),
introduced(tautology,[equality,[$cnf( $equal(X_46,multiply(inverse(least_upper_bound(X_194,inverse(X_46))),multiply(least_upper_bound(X_194,inverse(X_46)),X_46))) ),[1,1],$fot(least_upper_bound(identity,multiply(X_194,X_46)))]]) ).
cnf(refute_0_59,plain,
( X_46 != multiply(inverse(least_upper_bound(X_194,inverse(X_46))),multiply(least_upper_bound(X_194,inverse(X_46)),X_46))
| X_46 = multiply(inverse(least_upper_bound(X_194,inverse(X_46))),least_upper_bound(identity,multiply(X_194,X_46))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_194,inverse(X_46)),X_46),least_upper_bound(identity,multiply(X_194,X_46))) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
X_46 = multiply(inverse(least_upper_bound(X_194,inverse(X_46))),least_upper_bound(identity,multiply(X_194,X_46))),
inference(resolve,[$cnf( $equal(X_46,multiply(inverse(least_upper_bound(X_194,inverse(X_46))),multiply(least_upper_bound(X_194,inverse(X_46)),X_46))) )],[refute_0_45,refute_0_59]) ).
cnf(refute_0_61,plain,
b = multiply(inverse(least_upper_bound(inverse(least_upper_bound(a,X_142)),inverse(b))),least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_142)),b))),
inference(subst,[],[refute_0_60:[bind(X_194,$fot(inverse(least_upper_bound(a,X_142)))),bind(X_46,$fot(b))]]) ).
cnf(refute_0_62,plain,
multiply(inverse(X_64),least_upper_bound(X_64,X_65)) = least_upper_bound(multiply(inverse(X_64),X_64),multiply(inverse(X_64),X_65)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(inverse(X_64))),bind(Y,$fot(X_64)),bind(Z,$fot(X_65))]]) ).
cnf(refute_0_63,plain,
multiply(inverse(X_64),X_64) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_64))]]) ).
cnf(refute_0_64,plain,
( multiply(inverse(X_64),X_64) != identity
| multiply(inverse(X_64),least_upper_bound(X_64,X_65)) != least_upper_bound(multiply(inverse(X_64),X_64),multiply(inverse(X_64),X_65))
| multiply(inverse(X_64),least_upper_bound(X_64,X_65)) = least_upper_bound(identity,multiply(inverse(X_64),X_65)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_64),least_upper_bound(X_64,X_65)),least_upper_bound(multiply(inverse(X_64),X_64),multiply(inverse(X_64),X_65))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_65,plain,
( multiply(inverse(X_64),least_upper_bound(X_64,X_65)) != least_upper_bound(multiply(inverse(X_64),X_64),multiply(inverse(X_64),X_65))
| multiply(inverse(X_64),least_upper_bound(X_64,X_65)) = least_upper_bound(identity,multiply(inverse(X_64),X_65)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_64),X_64),identity) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
multiply(inverse(X_64),least_upper_bound(X_64,X_65)) = least_upper_bound(identity,multiply(inverse(X_64),X_65)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_64),least_upper_bound(X_64,X_65)),least_upper_bound(multiply(inverse(X_64),X_64),multiply(inverse(X_64),X_65))) )],[refute_0_62,refute_0_65]) ).
cnf(refute_0_67,plain,
multiply(inverse(X_66),least_upper_bound(X_66,greatest_lower_bound(X_11,X_66))) = least_upper_bound(identity,multiply(inverse(X_66),greatest_lower_bound(X_11,X_66))),
inference(subst,[],[refute_0_66:[bind(X_64,$fot(X_66)),bind(X_65,$fot(greatest_lower_bound(X_11,X_66)))]]) ).
cnf(refute_0_68,plain,
least_upper_bound(X_10,greatest_lower_bound(X_10,X_11)) = X_10,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_10)),bind(Y,$fot(X_11))]]) ).
cnf(refute_0_69,plain,
greatest_lower_bound(X_11,X_10) = greatest_lower_bound(X_10,X_11),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_11)),bind(Y,$fot(X_10))]]) ).
cnf(refute_0_70,plain,
( greatest_lower_bound(X_11,X_10) != greatest_lower_bound(X_10,X_11)
| greatest_lower_bound(X_10,X_11) = greatest_lower_bound(X_11,X_10) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(greatest_lower_bound(X_11,X_10))),bind(Y0,$fot(greatest_lower_bound(X_10,X_11)))]]) ).
cnf(refute_0_71,plain,
greatest_lower_bound(X_10,X_11) = greatest_lower_bound(X_11,X_10),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_11,X_10),greatest_lower_bound(X_10,X_11)) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
( greatest_lower_bound(X_10,X_11) != greatest_lower_bound(X_11,X_10)
| least_upper_bound(X_10,greatest_lower_bound(X_10,X_11)) != X_10
| least_upper_bound(X_10,greatest_lower_bound(X_11,X_10)) = X_10 ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_10,greatest_lower_bound(X_10,X_11)),X_10) ),[0,1],$fot(greatest_lower_bound(X_11,X_10))]]) ).
cnf(refute_0_73,plain,
( least_upper_bound(X_10,greatest_lower_bound(X_10,X_11)) != X_10
| least_upper_bound(X_10,greatest_lower_bound(X_11,X_10)) = X_10 ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_10,X_11),greatest_lower_bound(X_11,X_10)) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
least_upper_bound(X_10,greatest_lower_bound(X_11,X_10)) = X_10,
inference(resolve,[$cnf( $equal(least_upper_bound(X_10,greatest_lower_bound(X_10,X_11)),X_10) )],[refute_0_68,refute_0_73]) ).
cnf(refute_0_75,plain,
least_upper_bound(X_66,greatest_lower_bound(X_11,X_66)) = X_66,
inference(subst,[],[refute_0_74:[bind(X_10,$fot(X_66))]]) ).
cnf(refute_0_76,plain,
( multiply(inverse(X_66),least_upper_bound(X_66,greatest_lower_bound(X_11,X_66))) != least_upper_bound(identity,multiply(inverse(X_66),greatest_lower_bound(X_11,X_66)))
| least_upper_bound(X_66,greatest_lower_bound(X_11,X_66)) != X_66
| multiply(inverse(X_66),X_66) = least_upper_bound(identity,multiply(inverse(X_66),greatest_lower_bound(X_11,X_66))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_66),least_upper_bound(X_66,greatest_lower_bound(X_11,X_66))),least_upper_bound(identity,multiply(inverse(X_66),greatest_lower_bound(X_11,X_66)))) ),[0,1],$fot(X_66)]]) ).
cnf(refute_0_77,plain,
( multiply(inverse(X_66),least_upper_bound(X_66,greatest_lower_bound(X_11,X_66))) != least_upper_bound(identity,multiply(inverse(X_66),greatest_lower_bound(X_11,X_66)))
| multiply(inverse(X_66),X_66) = least_upper_bound(identity,multiply(inverse(X_66),greatest_lower_bound(X_11,X_66))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_66,greatest_lower_bound(X_11,X_66)),X_66) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
multiply(inverse(X_66),X_66) = least_upper_bound(identity,multiply(inverse(X_66),greatest_lower_bound(X_11,X_66))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_66),least_upper_bound(X_66,greatest_lower_bound(X_11,X_66))),least_upper_bound(identity,multiply(inverse(X_66),greatest_lower_bound(X_11,X_66)))) )],[refute_0_67,refute_0_77]) ).
cnf(refute_0_79,plain,
multiply(inverse(X_66),X_66) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_66))]]) ).
cnf(refute_0_80,plain,
( multiply(inverse(X_66),X_66) != identity
| multiply(inverse(X_66),X_66) != least_upper_bound(identity,multiply(inverse(X_66),greatest_lower_bound(X_11,X_66)))
| identity = least_upper_bound(identity,multiply(inverse(X_66),greatest_lower_bound(X_11,X_66))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_66),X_66),least_upper_bound(identity,multiply(inverse(X_66),greatest_lower_bound(X_11,X_66)))) ),[0],$fot(identity)]]) ).
cnf(refute_0_81,plain,
( multiply(inverse(X_66),X_66) != least_upper_bound(identity,multiply(inverse(X_66),greatest_lower_bound(X_11,X_66)))
| identity = least_upper_bound(identity,multiply(inverse(X_66),greatest_lower_bound(X_11,X_66))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_66),X_66),identity) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
identity = least_upper_bound(identity,multiply(inverse(X_66),greatest_lower_bound(X_11,X_66))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_66),X_66),least_upper_bound(identity,multiply(inverse(X_66),greatest_lower_bound(X_11,X_66)))) )],[refute_0_78,refute_0_81]) ).
cnf(refute_0_83,plain,
identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_142)),greatest_lower_bound(b,least_upper_bound(a,X_142)))),
inference(subst,[],[refute_0_82:[bind(X_11,$fot(b)),bind(X_66,$fot(least_upper_bound(a,X_142)))]]) ).
cnf(refute_0_84,plain,
greatest_lower_bound(X,greatest_lower_bound(X_31,X_32)) = greatest_lower_bound(greatest_lower_bound(X_31,X_32),X),
inference(subst,[],[symmetry_of_glb:[bind(Y,$fot(greatest_lower_bound(X_31,X_32)))]]) ).
cnf(refute_0_85,plain,
greatest_lower_bound(X_31,greatest_lower_bound(X_32,X)) = greatest_lower_bound(greatest_lower_bound(X_31,X_32),X),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_31)),bind(Y,$fot(X_32)),bind(Z,$fot(X))]]) ).
cnf(refute_0_86,plain,
( greatest_lower_bound(X_31,greatest_lower_bound(X_32,X)) != greatest_lower_bound(greatest_lower_bound(X_31,X_32),X)
| greatest_lower_bound(greatest_lower_bound(X_31,X_32),X) = greatest_lower_bound(X_31,greatest_lower_bound(X_32,X)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(greatest_lower_bound(X_31,greatest_lower_bound(X_32,X)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X_31,X_32),X)))]]) ).
cnf(refute_0_87,plain,
greatest_lower_bound(greatest_lower_bound(X_31,X_32),X) = greatest_lower_bound(X_31,greatest_lower_bound(X_32,X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_31,greatest_lower_bound(X_32,X)),greatest_lower_bound(greatest_lower_bound(X_31,X_32),X)) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_31,X_32)) != greatest_lower_bound(greatest_lower_bound(X_31,X_32),X)
| greatest_lower_bound(greatest_lower_bound(X_31,X_32),X) != greatest_lower_bound(X_31,greatest_lower_bound(X_32,X))
| greatest_lower_bound(X,greatest_lower_bound(X_31,X_32)) = greatest_lower_bound(X_31,greatest_lower_bound(X_32,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X,greatest_lower_bound(X_31,X_32)),greatest_lower_bound(X_31,greatest_lower_bound(X_32,X))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_31,X_32),X))]]) ).
cnf(refute_0_89,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_31,X_32)) != greatest_lower_bound(greatest_lower_bound(X_31,X_32),X)
| greatest_lower_bound(X,greatest_lower_bound(X_31,X_32)) = greatest_lower_bound(X_31,greatest_lower_bound(X_32,X)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_31,X_32),X),greatest_lower_bound(X_31,greatest_lower_bound(X_32,X))) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
greatest_lower_bound(X,greatest_lower_bound(X_31,X_32)) = greatest_lower_bound(X_31,greatest_lower_bound(X_32,X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_31,X_32)),greatest_lower_bound(greatest_lower_bound(X_31,X_32),X)) )],[refute_0_84,refute_0_89]) ).
cnf(refute_0_91,plain,
greatest_lower_bound(greatest_lower_bound(b,X_33),greatest_lower_bound(X_42,a)) = greatest_lower_bound(X_42,greatest_lower_bound(a,greatest_lower_bound(b,X_33))),
inference(subst,[],[refute_0_90:[bind(X,$fot(greatest_lower_bound(b,X_33))),bind(X_31,$fot(X_42)),bind(X_32,$fot(a))]]) ).
cnf(refute_0_92,plain,
greatest_lower_bound(a,greatest_lower_bound(b,X_33)) = greatest_lower_bound(greatest_lower_bound(a,b),X_33),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(a)),bind(Y,$fot(b)),bind(Z,$fot(X_33))]]) ).
cnf(refute_0_93,plain,
greatest_lower_bound(X_6,least_upper_bound(X_6,X_7)) = X_6,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_6)),bind(Y,$fot(X_7))]]) ).
cnf(refute_0_94,plain,
least_upper_bound(X_7,X_6) = least_upper_bound(X_6,X_7),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_7)),bind(Y,$fot(X_6))]]) ).
cnf(refute_0_95,plain,
( least_upper_bound(X_7,X_6) != least_upper_bound(X_6,X_7)
| least_upper_bound(X_6,X_7) = least_upper_bound(X_7,X_6) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(least_upper_bound(X_7,X_6))),bind(Y0,$fot(least_upper_bound(X_6,X_7)))]]) ).
cnf(refute_0_96,plain,
least_upper_bound(X_6,X_7) = least_upper_bound(X_7,X_6),
inference(resolve,[$cnf( $equal(least_upper_bound(X_7,X_6),least_upper_bound(X_6,X_7)) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
( greatest_lower_bound(X_6,least_upper_bound(X_6,X_7)) != X_6
| least_upper_bound(X_6,X_7) != least_upper_bound(X_7,X_6)
| greatest_lower_bound(X_6,least_upper_bound(X_7,X_6)) = X_6 ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_6,least_upper_bound(X_6,X_7)),X_6) ),[0,1],$fot(least_upper_bound(X_7,X_6))]]) ).
cnf(refute_0_98,plain,
( greatest_lower_bound(X_6,least_upper_bound(X_6,X_7)) != X_6
| greatest_lower_bound(X_6,least_upper_bound(X_7,X_6)) = X_6 ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_6,X_7),least_upper_bound(X_7,X_6)) )],[refute_0_96,refute_0_97]) ).
cnf(refute_0_99,plain,
greatest_lower_bound(X_6,least_upper_bound(X_7,X_6)) = X_6,
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_6,least_upper_bound(X_6,X_7)),X_6) )],[refute_0_93,refute_0_98]) ).
cnf(refute_0_100,plain,
greatest_lower_bound(b,least_upper_bound(a,b)) = b,
inference(subst,[],[refute_0_99:[bind(X_6,$fot(b)),bind(X_7,$fot(a))]]) ).
cnf(refute_0_101,plain,
( greatest_lower_bound(b,least_upper_bound(a,b)) != b
| least_upper_bound(a,b) != a
| greatest_lower_bound(b,a) = b ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(a,b)),b) ),[0,1],$fot(a)]]) ).
cnf(refute_0_102,plain,
( greatest_lower_bound(b,least_upper_bound(a,b)) != b
| greatest_lower_bound(b,a) = b ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,b),a) )],[p39c_1,refute_0_101]) ).
cnf(refute_0_103,plain,
greatest_lower_bound(b,a) = b,
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(a,b)),b) )],[refute_0_100,refute_0_102]) ).
cnf(refute_0_104,plain,
( greatest_lower_bound(X,Y) != greatest_lower_bound(Y,X)
| greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(greatest_lower_bound(X,Y))),bind(Y0,$fot(greatest_lower_bound(Y,X)))]]) ).
cnf(refute_0_105,plain,
greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X)) )],[symmetry_of_glb,refute_0_104]) ).
cnf(refute_0_106,plain,
greatest_lower_bound(b,a) = greatest_lower_bound(a,b),
inference(subst,[],[refute_0_105:[bind(X,$fot(a)),bind(Y,$fot(b))]]) ).
cnf(refute_0_107,plain,
( greatest_lower_bound(b,a) != b
| greatest_lower_bound(b,a) != greatest_lower_bound(a,b)
| greatest_lower_bound(a,b) = b ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,a),b) ),[0],$fot(greatest_lower_bound(a,b))]]) ).
cnf(refute_0_108,plain,
( greatest_lower_bound(b,a) != b
| greatest_lower_bound(a,b) = b ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,a),greatest_lower_bound(a,b)) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
greatest_lower_bound(a,b) = b,
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,a),b) )],[refute_0_103,refute_0_108]) ).
cnf(refute_0_110,plain,
( greatest_lower_bound(a,b) != b
| greatest_lower_bound(a,greatest_lower_bound(b,X_33)) != greatest_lower_bound(greatest_lower_bound(a,b),X_33)
| greatest_lower_bound(a,greatest_lower_bound(b,X_33)) = greatest_lower_bound(b,X_33) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(b,X_33)),greatest_lower_bound(greatest_lower_bound(a,b),X_33)) ),[1,0],$fot(b)]]) ).
cnf(refute_0_111,plain,
( greatest_lower_bound(a,greatest_lower_bound(b,X_33)) != greatest_lower_bound(greatest_lower_bound(a,b),X_33)
| greatest_lower_bound(a,greatest_lower_bound(b,X_33)) = greatest_lower_bound(b,X_33) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,b),b) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
greatest_lower_bound(a,greatest_lower_bound(b,X_33)) = greatest_lower_bound(b,X_33),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(b,X_33)),greatest_lower_bound(greatest_lower_bound(a,b),X_33)) )],[refute_0_92,refute_0_111]) ).
cnf(refute_0_113,plain,
( greatest_lower_bound(a,greatest_lower_bound(b,X_33)) != greatest_lower_bound(b,X_33)
| greatest_lower_bound(greatest_lower_bound(b,X_33),greatest_lower_bound(X_42,a)) != greatest_lower_bound(X_42,greatest_lower_bound(a,greatest_lower_bound(b,X_33)))
| greatest_lower_bound(greatest_lower_bound(b,X_33),greatest_lower_bound(X_42,a)) = greatest_lower_bound(X_42,greatest_lower_bound(b,X_33)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(b,X_33),greatest_lower_bound(X_42,a)),greatest_lower_bound(X_42,greatest_lower_bound(a,greatest_lower_bound(b,X_33)))) ),[1,1],$fot(greatest_lower_bound(b,X_33))]]) ).
cnf(refute_0_114,plain,
( greatest_lower_bound(greatest_lower_bound(b,X_33),greatest_lower_bound(X_42,a)) != greatest_lower_bound(X_42,greatest_lower_bound(a,greatest_lower_bound(b,X_33)))
| greatest_lower_bound(greatest_lower_bound(b,X_33),greatest_lower_bound(X_42,a)) = greatest_lower_bound(X_42,greatest_lower_bound(b,X_33)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(b,X_33)),greatest_lower_bound(b,X_33)) )],[refute_0_112,refute_0_113]) ).
cnf(refute_0_115,plain,
greatest_lower_bound(greatest_lower_bound(b,X_33),greatest_lower_bound(X_42,a)) = greatest_lower_bound(X_42,greatest_lower_bound(b,X_33)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(b,X_33),greatest_lower_bound(X_42,a)),greatest_lower_bound(X_42,greatest_lower_bound(a,greatest_lower_bound(b,X_33)))) )],[refute_0_91,refute_0_114]) ).
cnf(refute_0_116,plain,
greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(X_35,b),Z)) = greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(X_35,b)),Z),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(a)),bind(Y,$fot(greatest_lower_bound(X_35,b)))]]) ).
cnf(refute_0_117,plain,
greatest_lower_bound(a,greatest_lower_bound(b,X_34)) = greatest_lower_bound(b,X_34),
inference(subst,[],[refute_0_112:[bind(X_33,$fot(X_34))]]) ).
cnf(refute_0_118,plain,
greatest_lower_bound(X_34,b) = greatest_lower_bound(b,X_34),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_34)),bind(Y,$fot(b))]]) ).
cnf(refute_0_119,plain,
( greatest_lower_bound(X_34,b) != greatest_lower_bound(b,X_34)
| greatest_lower_bound(b,X_34) = greatest_lower_bound(X_34,b) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(greatest_lower_bound(X_34,b))),bind(Y0,$fot(greatest_lower_bound(b,X_34)))]]) ).
cnf(refute_0_120,plain,
greatest_lower_bound(b,X_34) = greatest_lower_bound(X_34,b),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_34,b),greatest_lower_bound(b,X_34)) )],[refute_0_118,refute_0_119]) ).
cnf(refute_0_121,plain,
( greatest_lower_bound(a,greatest_lower_bound(b,X_34)) != greatest_lower_bound(b,X_34)
| greatest_lower_bound(b,X_34) != greatest_lower_bound(X_34,b)
| greatest_lower_bound(a,greatest_lower_bound(X_34,b)) = greatest_lower_bound(b,X_34) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(b,X_34)),greatest_lower_bound(b,X_34)) ),[0,1],$fot(greatest_lower_bound(X_34,b))]]) ).
cnf(refute_0_122,plain,
( greatest_lower_bound(a,greatest_lower_bound(b,X_34)) != greatest_lower_bound(b,X_34)
| greatest_lower_bound(a,greatest_lower_bound(X_34,b)) = greatest_lower_bound(b,X_34) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,X_34),greatest_lower_bound(X_34,b)) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
greatest_lower_bound(a,greatest_lower_bound(X_34,b)) = greatest_lower_bound(b,X_34),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(b,X_34)),greatest_lower_bound(b,X_34)) )],[refute_0_117,refute_0_122]) ).
cnf(refute_0_124,plain,
greatest_lower_bound(a,greatest_lower_bound(X_35,b)) = greatest_lower_bound(b,X_35),
inference(subst,[],[refute_0_123:[bind(X_34,$fot(X_35))]]) ).
cnf(refute_0_125,plain,
( greatest_lower_bound(a,greatest_lower_bound(X_35,b)) != greatest_lower_bound(b,X_35)
| greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(X_35,b),Z)) != greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(X_35,b)),Z)
| greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(X_35,b),Z)) = greatest_lower_bound(greatest_lower_bound(b,X_35),Z) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(X_35,b),Z)),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(X_35,b)),Z)) ),[1,0],$fot(greatest_lower_bound(b,X_35))]]) ).
cnf(refute_0_126,plain,
( greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(X_35,b),Z)) != greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(X_35,b)),Z)
| greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(X_35,b),Z)) = greatest_lower_bound(greatest_lower_bound(b,X_35),Z) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(X_35,b)),greatest_lower_bound(b,X_35)) )],[refute_0_124,refute_0_125]) ).
cnf(refute_0_127,plain,
greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(X_35,b),Z)) = greatest_lower_bound(greatest_lower_bound(b,X_35),Z),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(X_35,b),Z)),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(X_35,b)),Z)) )],[refute_0_116,refute_0_126]) ).
cnf(refute_0_128,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,Z)) != greatest_lower_bound(greatest_lower_bound(X,Y),Z)
| greatest_lower_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(Y,Z)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X,Y),Z)))]]) ).
cnf(refute_0_129,plain,
greatest_lower_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(greatest_lower_bound(X,Y),Z)) )],[associativity_of_glb,refute_0_128]) ).
cnf(refute_0_130,plain,
greatest_lower_bound(greatest_lower_bound(X_35,b),Z) = greatest_lower_bound(X_35,greatest_lower_bound(b,Z)),
inference(subst,[],[refute_0_129:[bind(X,$fot(X_35)),bind(Y,$fot(b))]]) ).
cnf(refute_0_131,plain,
greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(X_35,b),Z)) = greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(X_35,b),Z)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(X_35,b),Z)))]]) ).
cnf(refute_0_132,plain,
( greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(X_35,b),Z)) != greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(X_35,b),Z))
| greatest_lower_bound(greatest_lower_bound(X_35,b),Z) != greatest_lower_bound(X_35,greatest_lower_bound(b,Z))
| greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(X_35,b),Z)) = greatest_lower_bound(a,greatest_lower_bound(X_35,greatest_lower_bound(b,Z))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(X_35,b),Z)),greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(X_35,b),Z))) ),[1,1],$fot(greatest_lower_bound(X_35,greatest_lower_bound(b,Z)))]]) ).
cnf(refute_0_133,plain,
( greatest_lower_bound(greatest_lower_bound(X_35,b),Z) != greatest_lower_bound(X_35,greatest_lower_bound(b,Z))
| greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(X_35,b),Z)) = greatest_lower_bound(a,greatest_lower_bound(X_35,greatest_lower_bound(b,Z))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(X_35,b),Z)),greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(X_35,b),Z))) )],[refute_0_131,refute_0_132]) ).
cnf(refute_0_134,plain,
greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(X_35,b),Z)) = greatest_lower_bound(a,greatest_lower_bound(X_35,greatest_lower_bound(b,Z))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_35,b),Z),greatest_lower_bound(X_35,greatest_lower_bound(b,Z))) )],[refute_0_130,refute_0_133]) ).
cnf(refute_0_135,plain,
( greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(X_35,b),Z)) != greatest_lower_bound(a,greatest_lower_bound(X_35,greatest_lower_bound(b,Z)))
| greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(X_35,b),Z)) != greatest_lower_bound(greatest_lower_bound(b,X_35),Z)
| greatest_lower_bound(a,greatest_lower_bound(X_35,greatest_lower_bound(b,Z))) = greatest_lower_bound(greatest_lower_bound(b,X_35),Z) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(X_35,b),Z)),greatest_lower_bound(greatest_lower_bound(b,X_35),Z)) ),[0],$fot(greatest_lower_bound(a,greatest_lower_bound(X_35,greatest_lower_bound(b,Z))))]]) ).
cnf(refute_0_136,plain,
( greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(X_35,b),Z)) != greatest_lower_bound(greatest_lower_bound(b,X_35),Z)
| greatest_lower_bound(a,greatest_lower_bound(X_35,greatest_lower_bound(b,Z))) = greatest_lower_bound(greatest_lower_bound(b,X_35),Z) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(X_35,b),Z)),greatest_lower_bound(a,greatest_lower_bound(X_35,greatest_lower_bound(b,Z)))) )],[refute_0_134,refute_0_135]) ).
cnf(refute_0_137,plain,
greatest_lower_bound(greatest_lower_bound(b,X_35),Z) = greatest_lower_bound(b,greatest_lower_bound(X_35,Z)),
inference(subst,[],[refute_0_129:[bind(X,$fot(b)),bind(Y,$fot(X_35))]]) ).
cnf(refute_0_138,plain,
( greatest_lower_bound(a,greatest_lower_bound(X_35,greatest_lower_bound(b,Z))) != greatest_lower_bound(greatest_lower_bound(b,X_35),Z)
| greatest_lower_bound(greatest_lower_bound(b,X_35),Z) != greatest_lower_bound(b,greatest_lower_bound(X_35,Z))
| greatest_lower_bound(a,greatest_lower_bound(X_35,greatest_lower_bound(b,Z))) = greatest_lower_bound(b,greatest_lower_bound(X_35,Z)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(a,greatest_lower_bound(X_35,greatest_lower_bound(b,Z))),greatest_lower_bound(b,greatest_lower_bound(X_35,Z))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(b,X_35),Z))]]) ).
cnf(refute_0_139,plain,
( greatest_lower_bound(a,greatest_lower_bound(X_35,greatest_lower_bound(b,Z))) != greatest_lower_bound(greatest_lower_bound(b,X_35),Z)
| greatest_lower_bound(a,greatest_lower_bound(X_35,greatest_lower_bound(b,Z))) = greatest_lower_bound(b,greatest_lower_bound(X_35,Z)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(b,X_35),Z),greatest_lower_bound(b,greatest_lower_bound(X_35,Z))) )],[refute_0_137,refute_0_138]) ).
cnf(refute_0_140,plain,
( greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(X_35,b),Z)) != greatest_lower_bound(greatest_lower_bound(b,X_35),Z)
| greatest_lower_bound(a,greatest_lower_bound(X_35,greatest_lower_bound(b,Z))) = greatest_lower_bound(b,greatest_lower_bound(X_35,Z)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(X_35,greatest_lower_bound(b,Z))),greatest_lower_bound(greatest_lower_bound(b,X_35),Z)) )],[refute_0_136,refute_0_139]) ).
cnf(refute_0_141,plain,
greatest_lower_bound(a,greatest_lower_bound(X_35,greatest_lower_bound(b,Z))) = greatest_lower_bound(b,greatest_lower_bound(X_35,Z)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(X_35,b),Z)),greatest_lower_bound(greatest_lower_bound(b,X_35),Z)) )],[refute_0_127,refute_0_140]) ).
cnf(refute_0_142,plain,
greatest_lower_bound(a,greatest_lower_bound(X_42,greatest_lower_bound(b,X_33))) = greatest_lower_bound(b,greatest_lower_bound(X_42,X_33)),
inference(subst,[],[refute_0_141:[bind(Z,$fot(X_33)),bind(X_35,$fot(X_42))]]) ).
cnf(refute_0_143,plain,
greatest_lower_bound(X_41,greatest_lower_bound(X_42,greatest_lower_bound(Y,X_42))) = greatest_lower_bound(X_42,greatest_lower_bound(greatest_lower_bound(Y,X_42),X_41)),
inference(subst,[],[refute_0_90:[bind(X,$fot(X_41)),bind(X_31,$fot(X_42)),bind(X_32,$fot(greatest_lower_bound(Y,X_42)))]]) ).
cnf(refute_0_144,plain,
greatest_lower_bound(greatest_lower_bound(X_13,Y),least_upper_bound(X_13,greatest_lower_bound(X_13,Y))) = greatest_lower_bound(X_13,Y),
inference(subst,[],[refute_0_99:[bind(X_6,$fot(greatest_lower_bound(X_13,Y))),bind(X_7,$fot(X_13))]]) ).
cnf(refute_0_145,plain,
least_upper_bound(X_13,greatest_lower_bound(X_13,Y)) = X_13,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_13))]]) ).
cnf(refute_0_146,plain,
( greatest_lower_bound(greatest_lower_bound(X_13,Y),least_upper_bound(X_13,greatest_lower_bound(X_13,Y))) != greatest_lower_bound(X_13,Y)
| least_upper_bound(X_13,greatest_lower_bound(X_13,Y)) != X_13
| greatest_lower_bound(greatest_lower_bound(X_13,Y),X_13) = greatest_lower_bound(X_13,Y) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_13,Y),least_upper_bound(X_13,greatest_lower_bound(X_13,Y))),greatest_lower_bound(X_13,Y)) ),[0,1],$fot(X_13)]]) ).
cnf(refute_0_147,plain,
( greatest_lower_bound(greatest_lower_bound(X_13,Y),least_upper_bound(X_13,greatest_lower_bound(X_13,Y))) != greatest_lower_bound(X_13,Y)
| greatest_lower_bound(greatest_lower_bound(X_13,Y),X_13) = greatest_lower_bound(X_13,Y) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_13,greatest_lower_bound(X_13,Y)),X_13) )],[refute_0_145,refute_0_146]) ).
cnf(refute_0_148,plain,
greatest_lower_bound(greatest_lower_bound(X_13,Y),X_13) = greatest_lower_bound(X_13,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_13,Y),least_upper_bound(X_13,greatest_lower_bound(X_13,Y))),greatest_lower_bound(X_13,Y)) )],[refute_0_144,refute_0_147]) ).
cnf(refute_0_149,plain,
greatest_lower_bound(greatest_lower_bound(X_13,Y),X_13) = greatest_lower_bound(X_13,greatest_lower_bound(Y,X_13)),
inference(subst,[],[refute_0_129:[bind(X,$fot(X_13)),bind(Z,$fot(X_13))]]) ).
cnf(refute_0_150,plain,
( greatest_lower_bound(greatest_lower_bound(X_13,Y),X_13) != greatest_lower_bound(X_13,Y)
| greatest_lower_bound(greatest_lower_bound(X_13,Y),X_13) != greatest_lower_bound(X_13,greatest_lower_bound(Y,X_13))
| greatest_lower_bound(X_13,greatest_lower_bound(Y,X_13)) = greatest_lower_bound(X_13,Y) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_13,Y),X_13),greatest_lower_bound(X_13,Y)) ),[0],$fot(greatest_lower_bound(X_13,greatest_lower_bound(Y,X_13)))]]) ).
cnf(refute_0_151,plain,
( greatest_lower_bound(greatest_lower_bound(X_13,Y),X_13) != greatest_lower_bound(X_13,Y)
| greatest_lower_bound(X_13,greatest_lower_bound(Y,X_13)) = greatest_lower_bound(X_13,Y) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_13,Y),X_13),greatest_lower_bound(X_13,greatest_lower_bound(Y,X_13))) )],[refute_0_149,refute_0_150]) ).
cnf(refute_0_152,plain,
greatest_lower_bound(X_13,greatest_lower_bound(Y,X_13)) = greatest_lower_bound(X_13,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_13,Y),X_13),greatest_lower_bound(X_13,Y)) )],[refute_0_148,refute_0_151]) ).
cnf(refute_0_153,plain,
greatest_lower_bound(X_42,greatest_lower_bound(Y,X_42)) = greatest_lower_bound(X_42,Y),
inference(subst,[],[refute_0_152:[bind(X_13,$fot(X_42))]]) ).
cnf(refute_0_154,plain,
( greatest_lower_bound(X_41,greatest_lower_bound(X_42,greatest_lower_bound(Y,X_42))) != greatest_lower_bound(X_42,greatest_lower_bound(greatest_lower_bound(Y,X_42),X_41))
| greatest_lower_bound(X_42,greatest_lower_bound(Y,X_42)) != greatest_lower_bound(X_42,Y)
| greatest_lower_bound(X_41,greatest_lower_bound(X_42,Y)) = greatest_lower_bound(X_42,greatest_lower_bound(greatest_lower_bound(Y,X_42),X_41)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_41,greatest_lower_bound(X_42,greatest_lower_bound(Y,X_42))),greatest_lower_bound(X_42,greatest_lower_bound(greatest_lower_bound(Y,X_42),X_41))) ),[0,1],$fot(greatest_lower_bound(X_42,Y))]]) ).
cnf(refute_0_155,plain,
( greatest_lower_bound(X_41,greatest_lower_bound(X_42,greatest_lower_bound(Y,X_42))) != greatest_lower_bound(X_42,greatest_lower_bound(greatest_lower_bound(Y,X_42),X_41))
| greatest_lower_bound(X_41,greatest_lower_bound(X_42,Y)) = greatest_lower_bound(X_42,greatest_lower_bound(greatest_lower_bound(Y,X_42),X_41)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_42,greatest_lower_bound(Y,X_42)),greatest_lower_bound(X_42,Y)) )],[refute_0_153,refute_0_154]) ).
cnf(refute_0_156,plain,
greatest_lower_bound(X_41,greatest_lower_bound(X_42,Y)) = greatest_lower_bound(X_42,greatest_lower_bound(greatest_lower_bound(Y,X_42),X_41)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_41,greatest_lower_bound(X_42,greatest_lower_bound(Y,X_42))),greatest_lower_bound(X_42,greatest_lower_bound(greatest_lower_bound(Y,X_42),X_41))) )],[refute_0_143,refute_0_155]) ).
cnf(refute_0_157,plain,
greatest_lower_bound(X_31,greatest_lower_bound(X_32,greatest_lower_bound(Y,X_32))) = greatest_lower_bound(greatest_lower_bound(X_31,X_32),greatest_lower_bound(Y,X_32)),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_31)),bind(Y,$fot(X_32)),bind(Z,$fot(greatest_lower_bound(Y,X_32)))]]) ).
cnf(refute_0_158,plain,
greatest_lower_bound(X_32,greatest_lower_bound(Y,X_32)) = greatest_lower_bound(X_32,Y),
inference(subst,[],[refute_0_152:[bind(X_13,$fot(X_32))]]) ).
cnf(refute_0_159,plain,
( greatest_lower_bound(X_31,greatest_lower_bound(X_32,greatest_lower_bound(Y,X_32))) != greatest_lower_bound(greatest_lower_bound(X_31,X_32),greatest_lower_bound(Y,X_32))
| greatest_lower_bound(X_32,greatest_lower_bound(Y,X_32)) != greatest_lower_bound(X_32,Y)
| greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y)) = greatest_lower_bound(greatest_lower_bound(X_31,X_32),greatest_lower_bound(Y,X_32)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_31,greatest_lower_bound(X_32,greatest_lower_bound(Y,X_32))),greatest_lower_bound(greatest_lower_bound(X_31,X_32),greatest_lower_bound(Y,X_32))) ),[0,1],$fot(greatest_lower_bound(X_32,Y))]]) ).
cnf(refute_0_160,plain,
( greatest_lower_bound(X_31,greatest_lower_bound(X_32,greatest_lower_bound(Y,X_32))) != greatest_lower_bound(greatest_lower_bound(X_31,X_32),greatest_lower_bound(Y,X_32))
| greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y)) = greatest_lower_bound(greatest_lower_bound(X_31,X_32),greatest_lower_bound(Y,X_32)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_32,greatest_lower_bound(Y,X_32)),greatest_lower_bound(X_32,Y)) )],[refute_0_158,refute_0_159]) ).
cnf(refute_0_161,plain,
greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y)) = greatest_lower_bound(greatest_lower_bound(X_31,X_32),greatest_lower_bound(Y,X_32)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_31,greatest_lower_bound(X_32,greatest_lower_bound(Y,X_32))),greatest_lower_bound(greatest_lower_bound(X_31,X_32),greatest_lower_bound(Y,X_32))) )],[refute_0_157,refute_0_160]) ).
cnf(refute_0_162,plain,
greatest_lower_bound(greatest_lower_bound(X_31,X_32),Y) = greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y)),
inference(subst,[],[refute_0_129:[bind(X,$fot(X_31)),bind(Y,$fot(X_32)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_163,plain,
greatest_lower_bound(X_32,greatest_lower_bound(greatest_lower_bound(X_31,X_32),Y)) = greatest_lower_bound(X_32,greatest_lower_bound(greatest_lower_bound(X_31,X_32),Y)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X_32,greatest_lower_bound(greatest_lower_bound(X_31,X_32),Y)))]]) ).
cnf(refute_0_164,plain,
( greatest_lower_bound(X_32,greatest_lower_bound(greatest_lower_bound(X_31,X_32),Y)) != greatest_lower_bound(X_32,greatest_lower_bound(greatest_lower_bound(X_31,X_32),Y))
| greatest_lower_bound(greatest_lower_bound(X_31,X_32),Y) != greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y))
| greatest_lower_bound(X_32,greatest_lower_bound(greatest_lower_bound(X_31,X_32),Y)) = greatest_lower_bound(X_32,greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_32,greatest_lower_bound(greatest_lower_bound(X_31,X_32),Y)),greatest_lower_bound(X_32,greatest_lower_bound(greatest_lower_bound(X_31,X_32),Y))) ),[1,1],$fot(greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y)))]]) ).
cnf(refute_0_165,plain,
( greatest_lower_bound(greatest_lower_bound(X_31,X_32),Y) != greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y))
| greatest_lower_bound(X_32,greatest_lower_bound(greatest_lower_bound(X_31,X_32),Y)) = greatest_lower_bound(X_32,greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_32,greatest_lower_bound(greatest_lower_bound(X_31,X_32),Y)),greatest_lower_bound(X_32,greatest_lower_bound(greatest_lower_bound(X_31,X_32),Y))) )],[refute_0_163,refute_0_164]) ).
cnf(refute_0_166,plain,
greatest_lower_bound(X_32,greatest_lower_bound(greatest_lower_bound(X_31,X_32),Y)) = greatest_lower_bound(X_32,greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_31,X_32),Y),greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y))) )],[refute_0_162,refute_0_165]) ).
cnf(refute_0_167,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_31,X_32)) != greatest_lower_bound(X_31,greatest_lower_bound(X_32,X))
| greatest_lower_bound(X_31,greatest_lower_bound(X_32,X)) = greatest_lower_bound(X,greatest_lower_bound(X_31,X_32)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(X_31,X_32)))),bind(Y0,$fot(greatest_lower_bound(X_31,greatest_lower_bound(X_32,X))))]]) ).
cnf(refute_0_168,plain,
greatest_lower_bound(X_31,greatest_lower_bound(X_32,X)) = greatest_lower_bound(X,greatest_lower_bound(X_31,X_32)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_31,X_32)),greatest_lower_bound(X_31,greatest_lower_bound(X_32,X))) )],[refute_0_90,refute_0_167]) ).
cnf(refute_0_169,plain,
greatest_lower_bound(greatest_lower_bound(X_31,X_32),greatest_lower_bound(Y,X_32)) = greatest_lower_bound(X_32,greatest_lower_bound(greatest_lower_bound(X_31,X_32),Y)),
inference(subst,[],[refute_0_168:[bind(X,$fot(X_32)),bind(X_31,$fot(greatest_lower_bound(X_31,X_32))),bind(X_32,$fot(Y))]]) ).
cnf(refute_0_170,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_171,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_19,refute_0_170]) ).
cnf(refute_0_172,plain,
( greatest_lower_bound(X_32,greatest_lower_bound(greatest_lower_bound(X_31,X_32),Y)) != greatest_lower_bound(X_32,greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y)))
| greatest_lower_bound(greatest_lower_bound(X_31,X_32),greatest_lower_bound(Y,X_32)) != greatest_lower_bound(X_32,greatest_lower_bound(greatest_lower_bound(X_31,X_32),Y))
| greatest_lower_bound(greatest_lower_bound(X_31,X_32),greatest_lower_bound(Y,X_32)) = greatest_lower_bound(X_32,greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y))) ),
inference(subst,[],[refute_0_171:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(X_31,X_32),greatest_lower_bound(Y,X_32)))),bind(Y0,$fot(greatest_lower_bound(X_32,greatest_lower_bound(greatest_lower_bound(X_31,X_32),Y)))),bind(Z0,$fot(greatest_lower_bound(X_32,greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y)))))]]) ).
cnf(refute_0_173,plain,
( greatest_lower_bound(X_32,greatest_lower_bound(greatest_lower_bound(X_31,X_32),Y)) != greatest_lower_bound(X_32,greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y)))
| greatest_lower_bound(greatest_lower_bound(X_31,X_32),greatest_lower_bound(Y,X_32)) = greatest_lower_bound(X_32,greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_31,X_32),greatest_lower_bound(Y,X_32)),greatest_lower_bound(X_32,greatest_lower_bound(greatest_lower_bound(X_31,X_32),Y))) )],[refute_0_169,refute_0_172]) ).
cnf(refute_0_174,plain,
greatest_lower_bound(greatest_lower_bound(X_31,X_32),greatest_lower_bound(Y,X_32)) = greatest_lower_bound(X_32,greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_32,greatest_lower_bound(greatest_lower_bound(X_31,X_32),Y)),greatest_lower_bound(X_32,greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y)))) )],[refute_0_166,refute_0_173]) ).
cnf(refute_0_175,plain,
( greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y)) != greatest_lower_bound(greatest_lower_bound(X_31,X_32),greatest_lower_bound(Y,X_32))
| greatest_lower_bound(greatest_lower_bound(X_31,X_32),greatest_lower_bound(Y,X_32)) != greatest_lower_bound(X_32,greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y)))
| greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y)) = greatest_lower_bound(X_32,greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y)),greatest_lower_bound(X_32,greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y)))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_31,X_32),greatest_lower_bound(Y,X_32)))]]) ).
cnf(refute_0_176,plain,
( greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y)) != greatest_lower_bound(greatest_lower_bound(X_31,X_32),greatest_lower_bound(Y,X_32))
| greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y)) = greatest_lower_bound(X_32,greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_31,X_32),greatest_lower_bound(Y,X_32)),greatest_lower_bound(X_32,greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y)))) )],[refute_0_174,refute_0_175]) ).
cnf(refute_0_177,plain,
greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y)) = greatest_lower_bound(X_32,greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y)),greatest_lower_bound(greatest_lower_bound(X_31,X_32),greatest_lower_bound(Y,X_32))) )],[refute_0_161,refute_0_176]) ).
cnf(refute_0_178,plain,
( greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y)) != greatest_lower_bound(X_32,greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y)))
| greatest_lower_bound(X_32,greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y))) = greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y)))),bind(Y0,$fot(greatest_lower_bound(X_32,greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y)))))]]) ).
cnf(refute_0_179,plain,
greatest_lower_bound(X_32,greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y))) = greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y)),greatest_lower_bound(X_32,greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y)))) )],[refute_0_177,refute_0_178]) ).
cnf(refute_0_180,plain,
greatest_lower_bound(X_42,greatest_lower_bound(Y,greatest_lower_bound(X_42,X_41))) = greatest_lower_bound(Y,greatest_lower_bound(X_42,X_41)),
inference(subst,[],[refute_0_179:[bind(Y,$fot(X_41)),bind(X_31,$fot(Y)),bind(X_32,$fot(X_42))]]) ).
cnf(refute_0_181,plain,
greatest_lower_bound(greatest_lower_bound(Y,X_42),X_41) = greatest_lower_bound(Y,greatest_lower_bound(X_42,X_41)),
inference(subst,[],[refute_0_129:[bind(X,$fot(Y)),bind(Y,$fot(X_42)),bind(Z,$fot(X_41))]]) ).
cnf(refute_0_182,plain,
greatest_lower_bound(X_42,greatest_lower_bound(greatest_lower_bound(Y,X_42),X_41)) = greatest_lower_bound(X_42,greatest_lower_bound(greatest_lower_bound(Y,X_42),X_41)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X_42,greatest_lower_bound(greatest_lower_bound(Y,X_42),X_41)))]]) ).
cnf(refute_0_183,plain,
( greatest_lower_bound(X_42,greatest_lower_bound(greatest_lower_bound(Y,X_42),X_41)) != greatest_lower_bound(X_42,greatest_lower_bound(greatest_lower_bound(Y,X_42),X_41))
| greatest_lower_bound(greatest_lower_bound(Y,X_42),X_41) != greatest_lower_bound(Y,greatest_lower_bound(X_42,X_41))
| greatest_lower_bound(X_42,greatest_lower_bound(greatest_lower_bound(Y,X_42),X_41)) = greatest_lower_bound(X_42,greatest_lower_bound(Y,greatest_lower_bound(X_42,X_41))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_42,greatest_lower_bound(greatest_lower_bound(Y,X_42),X_41)),greatest_lower_bound(X_42,greatest_lower_bound(greatest_lower_bound(Y,X_42),X_41))) ),[1,1],$fot(greatest_lower_bound(Y,greatest_lower_bound(X_42,X_41)))]]) ).
cnf(refute_0_184,plain,
( greatest_lower_bound(greatest_lower_bound(Y,X_42),X_41) != greatest_lower_bound(Y,greatest_lower_bound(X_42,X_41))
| greatest_lower_bound(X_42,greatest_lower_bound(greatest_lower_bound(Y,X_42),X_41)) = greatest_lower_bound(X_42,greatest_lower_bound(Y,greatest_lower_bound(X_42,X_41))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_42,greatest_lower_bound(greatest_lower_bound(Y,X_42),X_41)),greatest_lower_bound(X_42,greatest_lower_bound(greatest_lower_bound(Y,X_42),X_41))) )],[refute_0_182,refute_0_183]) ).
cnf(refute_0_185,plain,
greatest_lower_bound(X_42,greatest_lower_bound(greatest_lower_bound(Y,X_42),X_41)) = greatest_lower_bound(X_42,greatest_lower_bound(Y,greatest_lower_bound(X_42,X_41))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(Y,X_42),X_41),greatest_lower_bound(Y,greatest_lower_bound(X_42,X_41))) )],[refute_0_181,refute_0_184]) ).
cnf(refute_0_186,plain,
( greatest_lower_bound(X_42,greatest_lower_bound(Y,greatest_lower_bound(X_42,X_41))) != greatest_lower_bound(Y,greatest_lower_bound(X_42,X_41))
| greatest_lower_bound(X_42,greatest_lower_bound(greatest_lower_bound(Y,X_42),X_41)) != greatest_lower_bound(X_42,greatest_lower_bound(Y,greatest_lower_bound(X_42,X_41)))
| greatest_lower_bound(X_42,greatest_lower_bound(greatest_lower_bound(Y,X_42),X_41)) = greatest_lower_bound(Y,greatest_lower_bound(X_42,X_41)) ),
inference(subst,[],[refute_0_171:[bind(X0,$fot(greatest_lower_bound(X_42,greatest_lower_bound(greatest_lower_bound(Y,X_42),X_41)))),bind(Y0,$fot(greatest_lower_bound(X_42,greatest_lower_bound(Y,greatest_lower_bound(X_42,X_41))))),bind(Z0,$fot(greatest_lower_bound(Y,greatest_lower_bound(X_42,X_41))))]]) ).
cnf(refute_0_187,plain,
( greatest_lower_bound(X_42,greatest_lower_bound(Y,greatest_lower_bound(X_42,X_41))) != greatest_lower_bound(Y,greatest_lower_bound(X_42,X_41))
| greatest_lower_bound(X_42,greatest_lower_bound(greatest_lower_bound(Y,X_42),X_41)) = greatest_lower_bound(Y,greatest_lower_bound(X_42,X_41)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_42,greatest_lower_bound(greatest_lower_bound(Y,X_42),X_41)),greatest_lower_bound(X_42,greatest_lower_bound(Y,greatest_lower_bound(X_42,X_41)))) )],[refute_0_185,refute_0_186]) ).
cnf(refute_0_188,plain,
greatest_lower_bound(X_42,greatest_lower_bound(greatest_lower_bound(Y,X_42),X_41)) = greatest_lower_bound(Y,greatest_lower_bound(X_42,X_41)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_42,greatest_lower_bound(Y,greatest_lower_bound(X_42,X_41))),greatest_lower_bound(Y,greatest_lower_bound(X_42,X_41))) )],[refute_0_180,refute_0_187]) ).
cnf(refute_0_189,plain,
( greatest_lower_bound(X_41,greatest_lower_bound(X_42,Y)) != greatest_lower_bound(X_42,greatest_lower_bound(greatest_lower_bound(Y,X_42),X_41))
| greatest_lower_bound(X_42,greatest_lower_bound(greatest_lower_bound(Y,X_42),X_41)) != greatest_lower_bound(Y,greatest_lower_bound(X_42,X_41))
| greatest_lower_bound(X_41,greatest_lower_bound(X_42,Y)) = greatest_lower_bound(Y,greatest_lower_bound(X_42,X_41)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_41,greatest_lower_bound(X_42,Y)),greatest_lower_bound(Y,greatest_lower_bound(X_42,X_41))) ),[0],$fot(greatest_lower_bound(X_42,greatest_lower_bound(greatest_lower_bound(Y,X_42),X_41)))]]) ).
cnf(refute_0_190,plain,
( greatest_lower_bound(X_41,greatest_lower_bound(X_42,Y)) != greatest_lower_bound(X_42,greatest_lower_bound(greatest_lower_bound(Y,X_42),X_41))
| greatest_lower_bound(X_41,greatest_lower_bound(X_42,Y)) = greatest_lower_bound(Y,greatest_lower_bound(X_42,X_41)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_42,greatest_lower_bound(greatest_lower_bound(Y,X_42),X_41)),greatest_lower_bound(Y,greatest_lower_bound(X_42,X_41))) )],[refute_0_188,refute_0_189]) ).
cnf(refute_0_191,plain,
greatest_lower_bound(X_41,greatest_lower_bound(X_42,Y)) = greatest_lower_bound(Y,greatest_lower_bound(X_42,X_41)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_41,greatest_lower_bound(X_42,Y)),greatest_lower_bound(X_42,greatest_lower_bound(greatest_lower_bound(Y,X_42),X_41))) )],[refute_0_156,refute_0_190]) ).
cnf(refute_0_192,plain,
( greatest_lower_bound(X_41,greatest_lower_bound(X_42,Y)) != greatest_lower_bound(Y,greatest_lower_bound(X_42,X_41))
| greatest_lower_bound(Y,greatest_lower_bound(X_42,X_41)) = greatest_lower_bound(X_41,greatest_lower_bound(X_42,Y)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(greatest_lower_bound(X_41,greatest_lower_bound(X_42,Y)))),bind(Y0,$fot(greatest_lower_bound(Y,greatest_lower_bound(X_42,X_41))))]]) ).
cnf(refute_0_193,plain,
greatest_lower_bound(Y,greatest_lower_bound(X_42,X_41)) = greatest_lower_bound(X_41,greatest_lower_bound(X_42,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_41,greatest_lower_bound(X_42,Y)),greatest_lower_bound(Y,greatest_lower_bound(X_42,X_41))) )],[refute_0_191,refute_0_192]) ).
cnf(refute_0_194,plain,
greatest_lower_bound(greatest_lower_bound(b,X_33),greatest_lower_bound(X_42,a)) = greatest_lower_bound(a,greatest_lower_bound(X_42,greatest_lower_bound(b,X_33))),
inference(subst,[],[refute_0_193:[bind(Y,$fot(greatest_lower_bound(b,X_33))),bind(X_41,$fot(a))]]) ).
cnf(refute_0_195,plain,
( greatest_lower_bound(a,greatest_lower_bound(X_42,greatest_lower_bound(b,X_33))) != greatest_lower_bound(b,greatest_lower_bound(X_42,X_33))
| greatest_lower_bound(greatest_lower_bound(b,X_33),greatest_lower_bound(X_42,a)) != greatest_lower_bound(a,greatest_lower_bound(X_42,greatest_lower_bound(b,X_33)))
| greatest_lower_bound(greatest_lower_bound(b,X_33),greatest_lower_bound(X_42,a)) = greatest_lower_bound(b,greatest_lower_bound(X_42,X_33)) ),
inference(subst,[],[refute_0_171:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(b,X_33),greatest_lower_bound(X_42,a)))),bind(Y0,$fot(greatest_lower_bound(a,greatest_lower_bound(X_42,greatest_lower_bound(b,X_33))))),bind(Z0,$fot(greatest_lower_bound(b,greatest_lower_bound(X_42,X_33))))]]) ).
cnf(refute_0_196,plain,
( greatest_lower_bound(a,greatest_lower_bound(X_42,greatest_lower_bound(b,X_33))) != greatest_lower_bound(b,greatest_lower_bound(X_42,X_33))
| greatest_lower_bound(greatest_lower_bound(b,X_33),greatest_lower_bound(X_42,a)) = greatest_lower_bound(b,greatest_lower_bound(X_42,X_33)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(b,X_33),greatest_lower_bound(X_42,a)),greatest_lower_bound(a,greatest_lower_bound(X_42,greatest_lower_bound(b,X_33)))) )],[refute_0_194,refute_0_195]) ).
cnf(refute_0_197,plain,
greatest_lower_bound(greatest_lower_bound(b,X_33),greatest_lower_bound(X_42,a)) = greatest_lower_bound(b,greatest_lower_bound(X_42,X_33)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(X_42,greatest_lower_bound(b,X_33))),greatest_lower_bound(b,greatest_lower_bound(X_42,X_33))) )],[refute_0_142,refute_0_196]) ).
cnf(refute_0_198,plain,
( greatest_lower_bound(greatest_lower_bound(b,X_33),greatest_lower_bound(X_42,a)) != greatest_lower_bound(X_42,greatest_lower_bound(b,X_33))
| greatest_lower_bound(greatest_lower_bound(b,X_33),greatest_lower_bound(X_42,a)) != greatest_lower_bound(b,greatest_lower_bound(X_42,X_33))
| greatest_lower_bound(b,greatest_lower_bound(X_42,X_33)) = greatest_lower_bound(X_42,greatest_lower_bound(b,X_33)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(b,X_33),greatest_lower_bound(X_42,a)),greatest_lower_bound(X_42,greatest_lower_bound(b,X_33))) ),[0],$fot(greatest_lower_bound(b,greatest_lower_bound(X_42,X_33)))]]) ).
cnf(refute_0_199,plain,
( greatest_lower_bound(greatest_lower_bound(b,X_33),greatest_lower_bound(X_42,a)) != greatest_lower_bound(X_42,greatest_lower_bound(b,X_33))
| greatest_lower_bound(b,greatest_lower_bound(X_42,X_33)) = greatest_lower_bound(X_42,greatest_lower_bound(b,X_33)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(b,X_33),greatest_lower_bound(X_42,a)),greatest_lower_bound(b,greatest_lower_bound(X_42,X_33))) )],[refute_0_197,refute_0_198]) ).
cnf(refute_0_200,plain,
greatest_lower_bound(b,greatest_lower_bound(X_42,X_33)) = greatest_lower_bound(X_42,greatest_lower_bound(b,X_33)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(b,X_33),greatest_lower_bound(X_42,a)),greatest_lower_bound(X_42,greatest_lower_bound(b,X_33))) )],[refute_0_115,refute_0_199]) ).
cnf(refute_0_201,plain,
greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(X_141,b),least_upper_bound(a,X_141))) = greatest_lower_bound(least_upper_bound(X_141,b),greatest_lower_bound(b,least_upper_bound(a,X_141))),
inference(subst,[],[refute_0_200:[bind(X_33,$fot(least_upper_bound(a,X_141))),bind(X_42,$fot(least_upper_bound(X_141,b)))]]) ).
cnf(refute_0_202,plain,
greatest_lower_bound(least_upper_bound(X_28,b),least_upper_bound(a,least_upper_bound(X_28,b))) = least_upper_bound(X_28,b),
inference(subst,[],[refute_0_99:[bind(X_6,$fot(least_upper_bound(X_28,b))),bind(X_7,$fot(a))]]) ).
cnf(refute_0_203,plain,
least_upper_bound(least_upper_bound(X_15,Y),greatest_lower_bound(X_15,least_upper_bound(X_15,Y))) = least_upper_bound(X_15,Y),
inference(subst,[],[refute_0_74:[bind(X_10,$fot(least_upper_bound(X_15,Y))),bind(X_11,$fot(X_15))]]) ).
cnf(refute_0_204,plain,
greatest_lower_bound(X_15,least_upper_bound(X_15,Y)) = X_15,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_15))]]) ).
cnf(refute_0_205,plain,
( greatest_lower_bound(X_15,least_upper_bound(X_15,Y)) != X_15
| least_upper_bound(least_upper_bound(X_15,Y),greatest_lower_bound(X_15,least_upper_bound(X_15,Y))) != least_upper_bound(X_15,Y)
| least_upper_bound(least_upper_bound(X_15,Y),X_15) = least_upper_bound(X_15,Y) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_15,Y),greatest_lower_bound(X_15,least_upper_bound(X_15,Y))),least_upper_bound(X_15,Y)) ),[0,1],$fot(X_15)]]) ).
cnf(refute_0_206,plain,
( least_upper_bound(least_upper_bound(X_15,Y),greatest_lower_bound(X_15,least_upper_bound(X_15,Y))) != least_upper_bound(X_15,Y)
| least_upper_bound(least_upper_bound(X_15,Y),X_15) = least_upper_bound(X_15,Y) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_15,least_upper_bound(X_15,Y)),X_15) )],[refute_0_204,refute_0_205]) ).
cnf(refute_0_207,plain,
least_upper_bound(least_upper_bound(X_15,Y),X_15) = least_upper_bound(X_15,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_15,Y),greatest_lower_bound(X_15,least_upper_bound(X_15,Y))),least_upper_bound(X_15,Y)) )],[refute_0_203,refute_0_206]) ).
cnf(refute_0_208,plain,
( least_upper_bound(X,least_upper_bound(Y,Z)) != least_upper_bound(least_upper_bound(X,Y),Z)
| least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(Y,Z)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X,Y),Z)))]]) ).
cnf(refute_0_209,plain,
least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,Z)),least_upper_bound(least_upper_bound(X,Y),Z)) )],[associativity_of_lub,refute_0_208]) ).
cnf(refute_0_210,plain,
least_upper_bound(least_upper_bound(X_15,Y),X_15) = least_upper_bound(X_15,least_upper_bound(Y,X_15)),
inference(subst,[],[refute_0_209:[bind(X,$fot(X_15)),bind(Z,$fot(X_15))]]) ).
cnf(refute_0_211,plain,
( least_upper_bound(least_upper_bound(X_15,Y),X_15) != least_upper_bound(X_15,Y)
| least_upper_bound(least_upper_bound(X_15,Y),X_15) != least_upper_bound(X_15,least_upper_bound(Y,X_15))
| least_upper_bound(X_15,least_upper_bound(Y,X_15)) = least_upper_bound(X_15,Y) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_15,Y),X_15),least_upper_bound(X_15,Y)) ),[0],$fot(least_upper_bound(X_15,least_upper_bound(Y,X_15)))]]) ).
cnf(refute_0_212,plain,
( least_upper_bound(least_upper_bound(X_15,Y),X_15) != least_upper_bound(X_15,Y)
| least_upper_bound(X_15,least_upper_bound(Y,X_15)) = least_upper_bound(X_15,Y) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_15,Y),X_15),least_upper_bound(X_15,least_upper_bound(Y,X_15))) )],[refute_0_210,refute_0_211]) ).
cnf(refute_0_213,plain,
least_upper_bound(X_15,least_upper_bound(Y,X_15)) = least_upper_bound(X_15,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_15,Y),X_15),least_upper_bound(X_15,Y)) )],[refute_0_207,refute_0_212]) ).
cnf(refute_0_214,plain,
least_upper_bound(least_upper_bound(b,X_21),least_upper_bound(a,least_upper_bound(b,X_21))) = least_upper_bound(least_upper_bound(b,X_21),a),
inference(subst,[],[refute_0_213:[bind(Y,$fot(a)),bind(X_15,$fot(least_upper_bound(b,X_21)))]]) ).
cnf(refute_0_215,plain,
least_upper_bound(a,least_upper_bound(b,X_20)) = least_upper_bound(least_upper_bound(a,b),X_20),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(a)),bind(Y,$fot(b)),bind(Z,$fot(X_20))]]) ).
cnf(refute_0_216,plain,
( least_upper_bound(a,b) != a
| least_upper_bound(a,least_upper_bound(b,X_20)) != least_upper_bound(least_upper_bound(a,b),X_20)
| least_upper_bound(a,least_upper_bound(b,X_20)) = least_upper_bound(a,X_20) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(a,least_upper_bound(b,X_20)),least_upper_bound(least_upper_bound(a,b),X_20)) ),[1,0],$fot(a)]]) ).
cnf(refute_0_217,plain,
( least_upper_bound(a,least_upper_bound(b,X_20)) != least_upper_bound(least_upper_bound(a,b),X_20)
| least_upper_bound(a,least_upper_bound(b,X_20)) = least_upper_bound(a,X_20) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,b),a) )],[p39c_1,refute_0_216]) ).
cnf(refute_0_218,plain,
least_upper_bound(a,least_upper_bound(b,X_20)) = least_upper_bound(a,X_20),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(b,X_20)),least_upper_bound(least_upper_bound(a,b),X_20)) )],[refute_0_215,refute_0_217]) ).
cnf(refute_0_219,plain,
least_upper_bound(a,least_upper_bound(b,X_21)) = least_upper_bound(a,X_21),
inference(subst,[],[refute_0_218:[bind(X_20,$fot(X_21))]]) ).
cnf(refute_0_220,plain,
( least_upper_bound(a,least_upper_bound(b,X_21)) != least_upper_bound(a,X_21)
| least_upper_bound(least_upper_bound(b,X_21),least_upper_bound(a,least_upper_bound(b,X_21))) != least_upper_bound(least_upper_bound(b,X_21),a)
| least_upper_bound(least_upper_bound(b,X_21),least_upper_bound(a,X_21)) = least_upper_bound(least_upper_bound(b,X_21),a) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(b,X_21),least_upper_bound(a,least_upper_bound(b,X_21))),least_upper_bound(least_upper_bound(b,X_21),a)) ),[0,1],$fot(least_upper_bound(a,X_21))]]) ).
cnf(refute_0_221,plain,
( least_upper_bound(least_upper_bound(b,X_21),least_upper_bound(a,least_upper_bound(b,X_21))) != least_upper_bound(least_upper_bound(b,X_21),a)
| least_upper_bound(least_upper_bound(b,X_21),least_upper_bound(a,X_21)) = least_upper_bound(least_upper_bound(b,X_21),a) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(b,X_21)),least_upper_bound(a,X_21)) )],[refute_0_219,refute_0_220]) ).
cnf(refute_0_222,plain,
least_upper_bound(least_upper_bound(b,X_21),least_upper_bound(a,X_21)) = least_upper_bound(least_upper_bound(b,X_21),a),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(b,X_21),least_upper_bound(a,least_upper_bound(b,X_21))),least_upper_bound(least_upper_bound(b,X_21),a)) )],[refute_0_214,refute_0_221]) ).
cnf(refute_0_223,plain,
least_upper_bound(X_21,least_upper_bound(b,X_21)) = least_upper_bound(X_21,b),
inference(subst,[],[refute_0_213:[bind(Y,$fot(b)),bind(X_15,$fot(X_21))]]) ).
cnf(refute_0_224,plain,
least_upper_bound(a,least_upper_bound(X_21,least_upper_bound(b,X_21))) = least_upper_bound(a,least_upper_bound(X_21,least_upper_bound(b,X_21))),
introduced(tautology,[refl,[$fot(least_upper_bound(a,least_upper_bound(X_21,least_upper_bound(b,X_21))))]]) ).
cnf(refute_0_225,plain,
( least_upper_bound(X_21,least_upper_bound(b,X_21)) != least_upper_bound(X_21,b)
| least_upper_bound(a,least_upper_bound(X_21,least_upper_bound(b,X_21))) != least_upper_bound(a,least_upper_bound(X_21,least_upper_bound(b,X_21)))
| least_upper_bound(a,least_upper_bound(X_21,least_upper_bound(b,X_21))) = least_upper_bound(a,least_upper_bound(X_21,b)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(a,least_upper_bound(X_21,least_upper_bound(b,X_21))),least_upper_bound(a,least_upper_bound(X_21,least_upper_bound(b,X_21)))) ),[1,1],$fot(least_upper_bound(X_21,b))]]) ).
cnf(refute_0_226,plain,
( least_upper_bound(X_21,least_upper_bound(b,X_21)) != least_upper_bound(X_21,b)
| least_upper_bound(a,least_upper_bound(X_21,least_upper_bound(b,X_21))) = least_upper_bound(a,least_upper_bound(X_21,b)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(X_21,least_upper_bound(b,X_21))),least_upper_bound(a,least_upper_bound(X_21,least_upper_bound(b,X_21)))) )],[refute_0_224,refute_0_225]) ).
cnf(refute_0_227,plain,
least_upper_bound(a,least_upper_bound(X_21,least_upper_bound(b,X_21))) = least_upper_bound(a,least_upper_bound(X_21,b)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_21,least_upper_bound(b,X_21)),least_upper_bound(X_21,b)) )],[refute_0_223,refute_0_226]) ).
cnf(refute_0_228,plain,
least_upper_bound(X_18,least_upper_bound(X_19,X_20)) = least_upper_bound(least_upper_bound(X_18,X_19),X_20),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_18)),bind(Y,$fot(X_19)),bind(Z,$fot(X_20))]]) ).
cnf(refute_0_229,plain,
least_upper_bound(X_20,X_19) = least_upper_bound(X_19,X_20),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_20)),bind(Y,$fot(X_19))]]) ).
cnf(refute_0_230,plain,
( least_upper_bound(X_20,X_19) != least_upper_bound(X_19,X_20)
| least_upper_bound(X_19,X_20) = least_upper_bound(X_20,X_19) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(least_upper_bound(X_20,X_19))),bind(Y0,$fot(least_upper_bound(X_19,X_20)))]]) ).
cnf(refute_0_231,plain,
least_upper_bound(X_19,X_20) = least_upper_bound(X_20,X_19),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,X_19),least_upper_bound(X_19,X_20)) )],[refute_0_229,refute_0_230]) ).
cnf(refute_0_232,plain,
( least_upper_bound(X_18,least_upper_bound(X_19,X_20)) != least_upper_bound(least_upper_bound(X_18,X_19),X_20)
| least_upper_bound(X_19,X_20) != least_upper_bound(X_20,X_19)
| least_upper_bound(X_18,least_upper_bound(X_20,X_19)) = least_upper_bound(least_upper_bound(X_18,X_19),X_20) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(X_19,X_20)),least_upper_bound(least_upper_bound(X_18,X_19),X_20)) ),[0,1],$fot(least_upper_bound(X_20,X_19))]]) ).
cnf(refute_0_233,plain,
( least_upper_bound(X_18,least_upper_bound(X_19,X_20)) != least_upper_bound(least_upper_bound(X_18,X_19),X_20)
| least_upper_bound(X_18,least_upper_bound(X_20,X_19)) = least_upper_bound(least_upper_bound(X_18,X_19),X_20) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,X_20),least_upper_bound(X_20,X_19)) )],[refute_0_231,refute_0_232]) ).
cnf(refute_0_234,plain,
least_upper_bound(X_18,least_upper_bound(X_20,X_19)) = least_upper_bound(least_upper_bound(X_18,X_19),X_20),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(X_19,X_20)),least_upper_bound(least_upper_bound(X_18,X_19),X_20)) )],[refute_0_228,refute_0_233]) ).
cnf(refute_0_235,plain,
least_upper_bound(least_upper_bound(X_18,X_19),X_20) = least_upper_bound(X_18,least_upper_bound(X_19,X_20)),
inference(subst,[],[refute_0_209:[bind(X,$fot(X_18)),bind(Y,$fot(X_19)),bind(Z,$fot(X_20))]]) ).
cnf(refute_0_236,plain,
( least_upper_bound(X_18,least_upper_bound(X_20,X_19)) != least_upper_bound(least_upper_bound(X_18,X_19),X_20)
| least_upper_bound(least_upper_bound(X_18,X_19),X_20) != least_upper_bound(X_18,least_upper_bound(X_19,X_20))
| least_upper_bound(X_18,least_upper_bound(X_20,X_19)) = least_upper_bound(X_18,least_upper_bound(X_19,X_20)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_18,least_upper_bound(X_20,X_19)),least_upper_bound(X_18,least_upper_bound(X_19,X_20))) ),[0],$fot(least_upper_bound(least_upper_bound(X_18,X_19),X_20))]]) ).
cnf(refute_0_237,plain,
( least_upper_bound(X_18,least_upper_bound(X_20,X_19)) != least_upper_bound(least_upper_bound(X_18,X_19),X_20)
| least_upper_bound(X_18,least_upper_bound(X_20,X_19)) = least_upper_bound(X_18,least_upper_bound(X_19,X_20)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_18,X_19),X_20),least_upper_bound(X_18,least_upper_bound(X_19,X_20))) )],[refute_0_235,refute_0_236]) ).
cnf(refute_0_238,plain,
least_upper_bound(X_18,least_upper_bound(X_20,X_19)) = least_upper_bound(X_18,least_upper_bound(X_19,X_20)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(X_20,X_19)),least_upper_bound(least_upper_bound(X_18,X_19),X_20)) )],[refute_0_234,refute_0_237]) ).
cnf(refute_0_239,plain,
( least_upper_bound(X_18,least_upper_bound(X_20,X_19)) != least_upper_bound(X_18,least_upper_bound(X_19,X_20))
| least_upper_bound(X_18,least_upper_bound(X_19,X_20)) = least_upper_bound(X_18,least_upper_bound(X_20,X_19)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(least_upper_bound(X_18,least_upper_bound(X_20,X_19)))),bind(Y0,$fot(least_upper_bound(X_18,least_upper_bound(X_19,X_20))))]]) ).
cnf(refute_0_240,plain,
least_upper_bound(X_18,least_upper_bound(X_19,X_20)) = least_upper_bound(X_18,least_upper_bound(X_20,X_19)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(X_20,X_19)),least_upper_bound(X_18,least_upper_bound(X_19,X_20))) )],[refute_0_238,refute_0_239]) ).
cnf(refute_0_241,plain,
least_upper_bound(a,least_upper_bound(least_upper_bound(b,X_21),X_21)) = least_upper_bound(a,least_upper_bound(X_21,least_upper_bound(b,X_21))),
inference(subst,[],[refute_0_240:[bind(X_18,$fot(a)),bind(X_19,$fot(least_upper_bound(b,X_21))),bind(X_20,$fot(X_21))]]) ).
cnf(refute_0_242,plain,
least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) = least_upper_bound(least_upper_bound(X_18,least_upper_bound(Y,X_18)),X_20),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_18)),bind(Y,$fot(least_upper_bound(Y,X_18))),bind(Z,$fot(X_20))]]) ).
cnf(refute_0_243,plain,
least_upper_bound(X_18,least_upper_bound(Y,X_18)) = least_upper_bound(X_18,Y),
inference(subst,[],[refute_0_213:[bind(X_15,$fot(X_18))]]) ).
cnf(refute_0_244,plain,
( least_upper_bound(X_18,least_upper_bound(Y,X_18)) != least_upper_bound(X_18,Y)
| least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) != least_upper_bound(least_upper_bound(X_18,least_upper_bound(Y,X_18)),X_20)
| least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) = least_upper_bound(least_upper_bound(X_18,Y),X_20) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)),least_upper_bound(least_upper_bound(X_18,least_upper_bound(Y,X_18)),X_20)) ),[1,0],$fot(least_upper_bound(X_18,Y))]]) ).
cnf(refute_0_245,plain,
( least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) != least_upper_bound(least_upper_bound(X_18,least_upper_bound(Y,X_18)),X_20)
| least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) = least_upper_bound(least_upper_bound(X_18,Y),X_20) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(Y,X_18)),least_upper_bound(X_18,Y)) )],[refute_0_243,refute_0_244]) ).
cnf(refute_0_246,plain,
least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) = least_upper_bound(least_upper_bound(X_18,Y),X_20),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)),least_upper_bound(least_upper_bound(X_18,least_upper_bound(Y,X_18)),X_20)) )],[refute_0_242,refute_0_245]) ).
cnf(refute_0_247,plain,
least_upper_bound(X_18,least_upper_bound(X_19,least_upper_bound(Y,X_19))) = least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_18)),bind(Y,$fot(X_19)),bind(Z,$fot(least_upper_bound(Y,X_19)))]]) ).
cnf(refute_0_248,plain,
least_upper_bound(X_19,least_upper_bound(Y,X_19)) = least_upper_bound(X_19,Y),
inference(subst,[],[refute_0_213:[bind(X_15,$fot(X_19))]]) ).
cnf(refute_0_249,plain,
( least_upper_bound(X_18,least_upper_bound(X_19,least_upper_bound(Y,X_19))) != least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19))
| least_upper_bound(X_19,least_upper_bound(Y,X_19)) != least_upper_bound(X_19,Y)
| least_upper_bound(X_18,least_upper_bound(X_19,Y)) = least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(X_19,least_upper_bound(Y,X_19))),least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19))) ),[0,1],$fot(least_upper_bound(X_19,Y))]]) ).
cnf(refute_0_250,plain,
( least_upper_bound(X_18,least_upper_bound(X_19,least_upper_bound(Y,X_19))) != least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19))
| least_upper_bound(X_18,least_upper_bound(X_19,Y)) = least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,least_upper_bound(Y,X_19)),least_upper_bound(X_19,Y)) )],[refute_0_248,refute_0_249]) ).
cnf(refute_0_251,plain,
least_upper_bound(X_18,least_upper_bound(X_19,Y)) = least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(X_19,least_upper_bound(Y,X_19))),least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19))) )],[refute_0_247,refute_0_250]) ).
cnf(refute_0_252,plain,
least_upper_bound(least_upper_bound(X_18,X_19),Y) = least_upper_bound(X_18,least_upper_bound(X_19,Y)),
inference(subst,[],[refute_0_209:[bind(X,$fot(X_18)),bind(Y,$fot(X_19)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_253,plain,
least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)) = least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)))]]) ).
cnf(refute_0_254,plain,
( least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)) != least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y))
| least_upper_bound(least_upper_bound(X_18,X_19),Y) != least_upper_bound(X_18,least_upper_bound(X_19,Y))
| least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)) = least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)),least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y))) ),[1,1],$fot(least_upper_bound(X_18,least_upper_bound(X_19,Y)))]]) ).
cnf(refute_0_255,plain,
( least_upper_bound(least_upper_bound(X_18,X_19),Y) != least_upper_bound(X_18,least_upper_bound(X_19,Y))
| least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)) = least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)),least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y))) )],[refute_0_253,refute_0_254]) ).
cnf(refute_0_256,plain,
least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)) = least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_18,X_19),Y),least_upper_bound(X_18,least_upper_bound(X_19,Y))) )],[refute_0_252,refute_0_255]) ).
cnf(refute_0_257,plain,
least_upper_bound(X,least_upper_bound(X_18,X_19)) = least_upper_bound(least_upper_bound(X_18,X_19),X),
inference(subst,[],[symmetry_of_lub:[bind(Y,$fot(least_upper_bound(X_18,X_19)))]]) ).
cnf(refute_0_258,plain,
least_upper_bound(X_18,least_upper_bound(X_19,X)) = least_upper_bound(least_upper_bound(X_18,X_19),X),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_18)),bind(Y,$fot(X_19)),bind(Z,$fot(X))]]) ).
cnf(refute_0_259,plain,
( least_upper_bound(X_18,least_upper_bound(X_19,X)) != least_upper_bound(least_upper_bound(X_18,X_19),X)
| least_upper_bound(least_upper_bound(X_18,X_19),X) = least_upper_bound(X_18,least_upper_bound(X_19,X)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(least_upper_bound(X_18,least_upper_bound(X_19,X)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X_18,X_19),X)))]]) ).
cnf(refute_0_260,plain,
least_upper_bound(least_upper_bound(X_18,X_19),X) = least_upper_bound(X_18,least_upper_bound(X_19,X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(X_19,X)),least_upper_bound(least_upper_bound(X_18,X_19),X)) )],[refute_0_258,refute_0_259]) ).
cnf(refute_0_261,plain,
( least_upper_bound(X,least_upper_bound(X_18,X_19)) != least_upper_bound(least_upper_bound(X_18,X_19),X)
| least_upper_bound(least_upper_bound(X_18,X_19),X) != least_upper_bound(X_18,least_upper_bound(X_19,X))
| least_upper_bound(X,least_upper_bound(X_18,X_19)) = least_upper_bound(X_18,least_upper_bound(X_19,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,least_upper_bound(X_18,X_19)),least_upper_bound(X_18,least_upper_bound(X_19,X))) ),[0],$fot(least_upper_bound(least_upper_bound(X_18,X_19),X))]]) ).
cnf(refute_0_262,plain,
( least_upper_bound(X,least_upper_bound(X_18,X_19)) != least_upper_bound(least_upper_bound(X_18,X_19),X)
| least_upper_bound(X,least_upper_bound(X_18,X_19)) = least_upper_bound(X_18,least_upper_bound(X_19,X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_18,X_19),X),least_upper_bound(X_18,least_upper_bound(X_19,X))) )],[refute_0_260,refute_0_261]) ).
cnf(refute_0_263,plain,
least_upper_bound(X,least_upper_bound(X_18,X_19)) = least_upper_bound(X_18,least_upper_bound(X_19,X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_18,X_19)),least_upper_bound(least_upper_bound(X_18,X_19),X)) )],[refute_0_257,refute_0_262]) ).
cnf(refute_0_264,plain,
( least_upper_bound(X,least_upper_bound(X_18,X_19)) != least_upper_bound(X_18,least_upper_bound(X_19,X))
| least_upper_bound(X_18,least_upper_bound(X_19,X)) = least_upper_bound(X,least_upper_bound(X_18,X_19)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(X_18,X_19)))),bind(Y0,$fot(least_upper_bound(X_18,least_upper_bound(X_19,X))))]]) ).
cnf(refute_0_265,plain,
least_upper_bound(X_18,least_upper_bound(X_19,X)) = least_upper_bound(X,least_upper_bound(X_18,X_19)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_18,X_19)),least_upper_bound(X_18,least_upper_bound(X_19,X))) )],[refute_0_263,refute_0_264]) ).
cnf(refute_0_266,plain,
least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)) = least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)),
inference(subst,[],[refute_0_265:[bind(X,$fot(X_19)),bind(X_18,$fot(least_upper_bound(X_18,X_19))),bind(X_19,$fot(Y))]]) ).
cnf(refute_0_267,plain,
( least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)) != least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y)))
| least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)) != least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y))
| least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)) = least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y))) ),
inference(subst,[],[refute_0_171:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)))),bind(Y0,$fot(least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)))),bind(Z0,$fot(least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y)))))]]) ).
cnf(refute_0_268,plain,
( least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)) != least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y)))
| least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)) = least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)),least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y))) )],[refute_0_266,refute_0_267]) ).
cnf(refute_0_269,plain,
least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)) = least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)),least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y)))) )],[refute_0_256,refute_0_268]) ).
cnf(refute_0_270,plain,
( least_upper_bound(X_18,least_upper_bound(X_19,Y)) != least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19))
| least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)) != least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y)))
| least_upper_bound(X_18,least_upper_bound(X_19,Y)) = least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_18,least_upper_bound(X_19,Y)),least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y)))) ),[0],$fot(least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)))]]) ).
cnf(refute_0_271,plain,
( least_upper_bound(X_18,least_upper_bound(X_19,Y)) != least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19))
| least_upper_bound(X_18,least_upper_bound(X_19,Y)) = least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)),least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y)))) )],[refute_0_269,refute_0_270]) ).
cnf(refute_0_272,plain,
least_upper_bound(X_18,least_upper_bound(X_19,Y)) = least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(X_19,Y)),least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19))) )],[refute_0_251,refute_0_271]) ).
cnf(refute_0_273,plain,
( least_upper_bound(X_18,least_upper_bound(X_19,Y)) != least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y)))
| least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y))) = least_upper_bound(X_18,least_upper_bound(X_19,Y)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(least_upper_bound(X_18,least_upper_bound(X_19,Y)))),bind(Y0,$fot(least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y)))))]]) ).
cnf(refute_0_274,plain,
least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y))) = least_upper_bound(X_18,least_upper_bound(X_19,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(X_19,Y)),least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y)))) )],[refute_0_272,refute_0_273]) ).
cnf(refute_0_275,plain,
least_upper_bound(X_18,least_upper_bound(Y,least_upper_bound(X_18,X_20))) = least_upper_bound(Y,least_upper_bound(X_18,X_20)),
inference(subst,[],[refute_0_274:[bind(Y,$fot(X_20)),bind(X_18,$fot(Y)),bind(X_19,$fot(X_18))]]) ).
cnf(refute_0_276,plain,
least_upper_bound(least_upper_bound(Y,X_18),X_20) = least_upper_bound(Y,least_upper_bound(X_18,X_20)),
inference(subst,[],[refute_0_209:[bind(X,$fot(Y)),bind(Y,$fot(X_18)),bind(Z,$fot(X_20))]]) ).
cnf(refute_0_277,plain,
least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) = least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)))]]) ).
cnf(refute_0_278,plain,
( least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) != least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20))
| least_upper_bound(least_upper_bound(Y,X_18),X_20) != least_upper_bound(Y,least_upper_bound(X_18,X_20))
| least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) = least_upper_bound(X_18,least_upper_bound(Y,least_upper_bound(X_18,X_20))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)),least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20))) ),[1,1],$fot(least_upper_bound(Y,least_upper_bound(X_18,X_20)))]]) ).
cnf(refute_0_279,plain,
( least_upper_bound(least_upper_bound(Y,X_18),X_20) != least_upper_bound(Y,least_upper_bound(X_18,X_20))
| least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) = least_upper_bound(X_18,least_upper_bound(Y,least_upper_bound(X_18,X_20))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)),least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20))) )],[refute_0_277,refute_0_278]) ).
cnf(refute_0_280,plain,
least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) = least_upper_bound(X_18,least_upper_bound(Y,least_upper_bound(X_18,X_20))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_18),X_20),least_upper_bound(Y,least_upper_bound(X_18,X_20))) )],[refute_0_276,refute_0_279]) ).
cnf(refute_0_281,plain,
( least_upper_bound(X_18,least_upper_bound(Y,least_upper_bound(X_18,X_20))) != least_upper_bound(Y,least_upper_bound(X_18,X_20))
| least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) != least_upper_bound(X_18,least_upper_bound(Y,least_upper_bound(X_18,X_20)))
| least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) = least_upper_bound(Y,least_upper_bound(X_18,X_20)) ),
inference(subst,[],[refute_0_171:[bind(X0,$fot(least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)))),bind(Y0,$fot(least_upper_bound(X_18,least_upper_bound(Y,least_upper_bound(X_18,X_20))))),bind(Z0,$fot(least_upper_bound(Y,least_upper_bound(X_18,X_20))))]]) ).
cnf(refute_0_282,plain,
( least_upper_bound(X_18,least_upper_bound(Y,least_upper_bound(X_18,X_20))) != least_upper_bound(Y,least_upper_bound(X_18,X_20))
| least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) = least_upper_bound(Y,least_upper_bound(X_18,X_20)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)),least_upper_bound(X_18,least_upper_bound(Y,least_upper_bound(X_18,X_20)))) )],[refute_0_280,refute_0_281]) ).
cnf(refute_0_283,plain,
least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) = least_upper_bound(Y,least_upper_bound(X_18,X_20)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(Y,least_upper_bound(X_18,X_20))),least_upper_bound(Y,least_upper_bound(X_18,X_20))) )],[refute_0_275,refute_0_282]) ).
cnf(refute_0_284,plain,
( least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) != least_upper_bound(Y,least_upper_bound(X_18,X_20))
| least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) != least_upper_bound(least_upper_bound(X_18,Y),X_20)
| least_upper_bound(Y,least_upper_bound(X_18,X_20)) = least_upper_bound(least_upper_bound(X_18,Y),X_20) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)),least_upper_bound(least_upper_bound(X_18,Y),X_20)) ),[0],$fot(least_upper_bound(Y,least_upper_bound(X_18,X_20)))]]) ).
cnf(refute_0_285,plain,
( least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) != least_upper_bound(least_upper_bound(X_18,Y),X_20)
| least_upper_bound(Y,least_upper_bound(X_18,X_20)) = least_upper_bound(least_upper_bound(X_18,Y),X_20) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)),least_upper_bound(Y,least_upper_bound(X_18,X_20))) )],[refute_0_283,refute_0_284]) ).
cnf(refute_0_286,plain,
least_upper_bound(least_upper_bound(X_18,Y),X_20) = least_upper_bound(X_18,least_upper_bound(Y,X_20)),
inference(subst,[],[refute_0_209:[bind(X,$fot(X_18)),bind(Z,$fot(X_20))]]) ).
cnf(refute_0_287,plain,
( least_upper_bound(Y,least_upper_bound(X_18,X_20)) != least_upper_bound(least_upper_bound(X_18,Y),X_20)
| least_upper_bound(least_upper_bound(X_18,Y),X_20) != least_upper_bound(X_18,least_upper_bound(Y,X_20))
| least_upper_bound(Y,least_upper_bound(X_18,X_20)) = least_upper_bound(X_18,least_upper_bound(Y,X_20)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(Y,least_upper_bound(X_18,X_20)),least_upper_bound(X_18,least_upper_bound(Y,X_20))) ),[0],$fot(least_upper_bound(least_upper_bound(X_18,Y),X_20))]]) ).
cnf(refute_0_288,plain,
( least_upper_bound(Y,least_upper_bound(X_18,X_20)) != least_upper_bound(least_upper_bound(X_18,Y),X_20)
| least_upper_bound(Y,least_upper_bound(X_18,X_20)) = least_upper_bound(X_18,least_upper_bound(Y,X_20)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_18,Y),X_20),least_upper_bound(X_18,least_upper_bound(Y,X_20))) )],[refute_0_286,refute_0_287]) ).
cnf(refute_0_289,plain,
( least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) != least_upper_bound(least_upper_bound(X_18,Y),X_20)
| least_upper_bound(Y,least_upper_bound(X_18,X_20)) = least_upper_bound(X_18,least_upper_bound(Y,X_20)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_18,X_20)),least_upper_bound(least_upper_bound(X_18,Y),X_20)) )],[refute_0_285,refute_0_288]) ).
cnf(refute_0_290,plain,
least_upper_bound(Y,least_upper_bound(X_18,X_20)) = least_upper_bound(X_18,least_upper_bound(Y,X_20)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)),least_upper_bound(least_upper_bound(X_18,Y),X_20)) )],[refute_0_246,refute_0_289]) ).
cnf(refute_0_291,plain,
( least_upper_bound(Y,least_upper_bound(X_18,X_20)) != least_upper_bound(X_18,least_upper_bound(Y,X_20))
| least_upper_bound(X_18,least_upper_bound(Y,X_20)) = least_upper_bound(Y,least_upper_bound(X_18,X_20)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(least_upper_bound(Y,least_upper_bound(X_18,X_20)))),bind(Y0,$fot(least_upper_bound(X_18,least_upper_bound(Y,X_20))))]]) ).
cnf(refute_0_292,plain,
least_upper_bound(X_18,least_upper_bound(Y,X_20)) = least_upper_bound(Y,least_upper_bound(X_18,X_20)),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_18,X_20)),least_upper_bound(X_18,least_upper_bound(Y,X_20))) )],[refute_0_290,refute_0_291]) ).
cnf(refute_0_293,plain,
least_upper_bound(least_upper_bound(b,X_21),least_upper_bound(a,X_21)) = least_upper_bound(a,least_upper_bound(least_upper_bound(b,X_21),X_21)),
inference(subst,[],[refute_0_292:[bind(Y,$fot(a)),bind(X_18,$fot(least_upper_bound(b,X_21))),bind(X_20,$fot(X_21))]]) ).
cnf(refute_0_294,plain,
( least_upper_bound(a,least_upper_bound(least_upper_bound(b,X_21),X_21)) != least_upper_bound(a,least_upper_bound(X_21,least_upper_bound(b,X_21)))
| least_upper_bound(least_upper_bound(b,X_21),least_upper_bound(a,X_21)) != least_upper_bound(a,least_upper_bound(least_upper_bound(b,X_21),X_21))
| least_upper_bound(least_upper_bound(b,X_21),least_upper_bound(a,X_21)) = least_upper_bound(a,least_upper_bound(X_21,least_upper_bound(b,X_21))) ),
inference(subst,[],[refute_0_171:[bind(X0,$fot(least_upper_bound(least_upper_bound(b,X_21),least_upper_bound(a,X_21)))),bind(Y0,$fot(least_upper_bound(a,least_upper_bound(least_upper_bound(b,X_21),X_21)))),bind(Z0,$fot(least_upper_bound(a,least_upper_bound(X_21,least_upper_bound(b,X_21)))))]]) ).
cnf(refute_0_295,plain,
( least_upper_bound(a,least_upper_bound(least_upper_bound(b,X_21),X_21)) != least_upper_bound(a,least_upper_bound(X_21,least_upper_bound(b,X_21)))
| least_upper_bound(least_upper_bound(b,X_21),least_upper_bound(a,X_21)) = least_upper_bound(a,least_upper_bound(X_21,least_upper_bound(b,X_21))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(b,X_21),least_upper_bound(a,X_21)),least_upper_bound(a,least_upper_bound(least_upper_bound(b,X_21),X_21))) )],[refute_0_293,refute_0_294]) ).
cnf(refute_0_296,plain,
least_upper_bound(least_upper_bound(b,X_21),least_upper_bound(a,X_21)) = least_upper_bound(a,least_upper_bound(X_21,least_upper_bound(b,X_21))),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(least_upper_bound(b,X_21),X_21)),least_upper_bound(a,least_upper_bound(X_21,least_upper_bound(b,X_21)))) )],[refute_0_241,refute_0_295]) ).
cnf(refute_0_297,plain,
( least_upper_bound(a,least_upper_bound(X_21,least_upper_bound(b,X_21))) != least_upper_bound(a,least_upper_bound(X_21,b))
| least_upper_bound(least_upper_bound(b,X_21),least_upper_bound(a,X_21)) != least_upper_bound(a,least_upper_bound(X_21,least_upper_bound(b,X_21)))
| least_upper_bound(least_upper_bound(b,X_21),least_upper_bound(a,X_21)) = least_upper_bound(a,least_upper_bound(X_21,b)) ),
inference(subst,[],[refute_0_171:[bind(X0,$fot(least_upper_bound(least_upper_bound(b,X_21),least_upper_bound(a,X_21)))),bind(Y0,$fot(least_upper_bound(a,least_upper_bound(X_21,least_upper_bound(b,X_21))))),bind(Z0,$fot(least_upper_bound(a,least_upper_bound(X_21,b))))]]) ).
cnf(refute_0_298,plain,
( least_upper_bound(a,least_upper_bound(X_21,least_upper_bound(b,X_21))) != least_upper_bound(a,least_upper_bound(X_21,b))
| least_upper_bound(least_upper_bound(b,X_21),least_upper_bound(a,X_21)) = least_upper_bound(a,least_upper_bound(X_21,b)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(b,X_21),least_upper_bound(a,X_21)),least_upper_bound(a,least_upper_bound(X_21,least_upper_bound(b,X_21)))) )],[refute_0_296,refute_0_297]) ).
cnf(refute_0_299,plain,
least_upper_bound(least_upper_bound(b,X_21),least_upper_bound(a,X_21)) = least_upper_bound(a,least_upper_bound(X_21,b)),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(X_21,least_upper_bound(b,X_21))),least_upper_bound(a,least_upper_bound(X_21,b))) )],[refute_0_227,refute_0_298]) ).
cnf(refute_0_300,plain,
( least_upper_bound(least_upper_bound(b,X_21),least_upper_bound(a,X_21)) != least_upper_bound(a,least_upper_bound(X_21,b))
| least_upper_bound(least_upper_bound(b,X_21),least_upper_bound(a,X_21)) != least_upper_bound(least_upper_bound(b,X_21),a)
| least_upper_bound(a,least_upper_bound(X_21,b)) = least_upper_bound(least_upper_bound(b,X_21),a) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(b,X_21),least_upper_bound(a,X_21)),least_upper_bound(least_upper_bound(b,X_21),a)) ),[0],$fot(least_upper_bound(a,least_upper_bound(X_21,b)))]]) ).
cnf(refute_0_301,plain,
( least_upper_bound(least_upper_bound(b,X_21),least_upper_bound(a,X_21)) != least_upper_bound(least_upper_bound(b,X_21),a)
| least_upper_bound(a,least_upper_bound(X_21,b)) = least_upper_bound(least_upper_bound(b,X_21),a) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(b,X_21),least_upper_bound(a,X_21)),least_upper_bound(a,least_upper_bound(X_21,b))) )],[refute_0_299,refute_0_300]) ).
cnf(refute_0_302,plain,
least_upper_bound(b,least_upper_bound(X_21,a)) = least_upper_bound(a,least_upper_bound(b,X_21)),
inference(subst,[],[refute_0_265:[bind(X,$fot(a)),bind(X_18,$fot(b)),bind(X_19,$fot(X_21))]]) ).
cnf(refute_0_303,plain,
( least_upper_bound(a,least_upper_bound(b,X_21)) != least_upper_bound(a,X_21)
| least_upper_bound(b,least_upper_bound(X_21,a)) != least_upper_bound(a,least_upper_bound(b,X_21))
| least_upper_bound(b,least_upper_bound(X_21,a)) = least_upper_bound(a,X_21) ),
inference(subst,[],[refute_0_171:[bind(X0,$fot(least_upper_bound(b,least_upper_bound(X_21,a)))),bind(Y0,$fot(least_upper_bound(a,least_upper_bound(b,X_21)))),bind(Z0,$fot(least_upper_bound(a,X_21)))]]) ).
cnf(refute_0_304,plain,
( least_upper_bound(a,least_upper_bound(b,X_21)) != least_upper_bound(a,X_21)
| least_upper_bound(b,least_upper_bound(X_21,a)) = least_upper_bound(a,X_21) ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(X_21,a)),least_upper_bound(a,least_upper_bound(b,X_21))) )],[refute_0_302,refute_0_303]) ).
cnf(refute_0_305,plain,
least_upper_bound(b,least_upper_bound(X_21,a)) = least_upper_bound(a,X_21),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(b,X_21)),least_upper_bound(a,X_21)) )],[refute_0_219,refute_0_304]) ).
cnf(refute_0_306,plain,
least_upper_bound(least_upper_bound(b,X_21),a) = least_upper_bound(b,least_upper_bound(X_21,a)),
inference(subst,[],[refute_0_209:[bind(X,$fot(b)),bind(Y,$fot(X_21)),bind(Z,$fot(a))]]) ).
cnf(refute_0_307,plain,
( least_upper_bound(b,least_upper_bound(X_21,a)) != least_upper_bound(a,X_21)
| least_upper_bound(least_upper_bound(b,X_21),a) != least_upper_bound(b,least_upper_bound(X_21,a))
| least_upper_bound(least_upper_bound(b,X_21),a) = least_upper_bound(a,X_21) ),
inference(subst,[],[refute_0_171:[bind(X0,$fot(least_upper_bound(least_upper_bound(b,X_21),a))),bind(Y0,$fot(least_upper_bound(b,least_upper_bound(X_21,a)))),bind(Z0,$fot(least_upper_bound(a,X_21)))]]) ).
cnf(refute_0_308,plain,
( least_upper_bound(b,least_upper_bound(X_21,a)) != least_upper_bound(a,X_21)
| least_upper_bound(least_upper_bound(b,X_21),a) = least_upper_bound(a,X_21) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(b,X_21),a),least_upper_bound(b,least_upper_bound(X_21,a))) )],[refute_0_306,refute_0_307]) ).
cnf(refute_0_309,plain,
least_upper_bound(least_upper_bound(b,X_21),a) = least_upper_bound(a,X_21),
inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(X_21,a)),least_upper_bound(a,X_21)) )],[refute_0_305,refute_0_308]) ).
cnf(refute_0_310,plain,
( least_upper_bound(a,least_upper_bound(X_21,b)) != least_upper_bound(least_upper_bound(b,X_21),a)
| least_upper_bound(least_upper_bound(b,X_21),a) != least_upper_bound(a,X_21)
| least_upper_bound(a,least_upper_bound(X_21,b)) = least_upper_bound(a,X_21) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(a,least_upper_bound(X_21,b)),least_upper_bound(a,X_21)) ),[0],$fot(least_upper_bound(least_upper_bound(b,X_21),a))]]) ).
cnf(refute_0_311,plain,
( least_upper_bound(a,least_upper_bound(X_21,b)) != least_upper_bound(least_upper_bound(b,X_21),a)
| least_upper_bound(a,least_upper_bound(X_21,b)) = least_upper_bound(a,X_21) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(b,X_21),a),least_upper_bound(a,X_21)) )],[refute_0_309,refute_0_310]) ).
cnf(refute_0_312,plain,
( least_upper_bound(least_upper_bound(b,X_21),least_upper_bound(a,X_21)) != least_upper_bound(least_upper_bound(b,X_21),a)
| least_upper_bound(a,least_upper_bound(X_21,b)) = least_upper_bound(a,X_21) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(X_21,b)),least_upper_bound(least_upper_bound(b,X_21),a)) )],[refute_0_301,refute_0_311]) ).
cnf(refute_0_313,plain,
least_upper_bound(a,least_upper_bound(X_21,b)) = least_upper_bound(a,X_21),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(b,X_21),least_upper_bound(a,X_21)),least_upper_bound(least_upper_bound(b,X_21),a)) )],[refute_0_222,refute_0_312]) ).
cnf(refute_0_314,plain,
least_upper_bound(a,least_upper_bound(X_28,b)) = least_upper_bound(a,X_28),
inference(subst,[],[refute_0_313:[bind(X_21,$fot(X_28))]]) ).
cnf(refute_0_315,plain,
( greatest_lower_bound(least_upper_bound(X_28,b),least_upper_bound(a,least_upper_bound(X_28,b))) != least_upper_bound(X_28,b)
| least_upper_bound(a,least_upper_bound(X_28,b)) != least_upper_bound(a,X_28)
| greatest_lower_bound(least_upper_bound(X_28,b),least_upper_bound(a,X_28)) = least_upper_bound(X_28,b) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_28,b),least_upper_bound(a,least_upper_bound(X_28,b))),least_upper_bound(X_28,b)) ),[0,1],$fot(least_upper_bound(a,X_28))]]) ).
cnf(refute_0_316,plain,
( greatest_lower_bound(least_upper_bound(X_28,b),least_upper_bound(a,least_upper_bound(X_28,b))) != least_upper_bound(X_28,b)
| greatest_lower_bound(least_upper_bound(X_28,b),least_upper_bound(a,X_28)) = least_upper_bound(X_28,b) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(X_28,b)),least_upper_bound(a,X_28)) )],[refute_0_314,refute_0_315]) ).
cnf(refute_0_317,plain,
greatest_lower_bound(least_upper_bound(X_28,b),least_upper_bound(a,X_28)) = least_upper_bound(X_28,b),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_28,b),least_upper_bound(a,least_upper_bound(X_28,b))),least_upper_bound(X_28,b)) )],[refute_0_202,refute_0_316]) ).
cnf(refute_0_318,plain,
greatest_lower_bound(least_upper_bound(X_141,b),least_upper_bound(a,X_141)) = least_upper_bound(X_141,b),
inference(subst,[],[refute_0_317:[bind(X_28,$fot(X_141))]]) ).
cnf(refute_0_319,plain,
( greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(X_141,b),least_upper_bound(a,X_141))) != greatest_lower_bound(least_upper_bound(X_141,b),greatest_lower_bound(b,least_upper_bound(a,X_141)))
| greatest_lower_bound(least_upper_bound(X_141,b),least_upper_bound(a,X_141)) != least_upper_bound(X_141,b)
| greatest_lower_bound(b,least_upper_bound(X_141,b)) = greatest_lower_bound(least_upper_bound(X_141,b),greatest_lower_bound(b,least_upper_bound(a,X_141))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(X_141,b),least_upper_bound(a,X_141))),greatest_lower_bound(least_upper_bound(X_141,b),greatest_lower_bound(b,least_upper_bound(a,X_141)))) ),[0,1],$fot(least_upper_bound(X_141,b))]]) ).
cnf(refute_0_320,plain,
( greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(X_141,b),least_upper_bound(a,X_141))) != greatest_lower_bound(least_upper_bound(X_141,b),greatest_lower_bound(b,least_upper_bound(a,X_141)))
| greatest_lower_bound(b,least_upper_bound(X_141,b)) = greatest_lower_bound(least_upper_bound(X_141,b),greatest_lower_bound(b,least_upper_bound(a,X_141))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_141,b),least_upper_bound(a,X_141)),least_upper_bound(X_141,b)) )],[refute_0_318,refute_0_319]) ).
cnf(refute_0_321,plain,
greatest_lower_bound(b,least_upper_bound(X_141,b)) = greatest_lower_bound(least_upper_bound(X_141,b),greatest_lower_bound(b,least_upper_bound(a,X_141))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(X_141,b),least_upper_bound(a,X_141))),greatest_lower_bound(least_upper_bound(X_141,b),greatest_lower_bound(b,least_upper_bound(a,X_141)))) )],[refute_0_201,refute_0_320]) ).
cnf(refute_0_322,plain,
greatest_lower_bound(b,least_upper_bound(X_141,b)) = b,
inference(subst,[],[refute_0_99:[bind(X_6,$fot(b)),bind(X_7,$fot(X_141))]]) ).
cnf(refute_0_323,plain,
( greatest_lower_bound(b,least_upper_bound(X_141,b)) != b
| greatest_lower_bound(b,least_upper_bound(X_141,b)) != greatest_lower_bound(least_upper_bound(X_141,b),greatest_lower_bound(b,least_upper_bound(a,X_141)))
| b = greatest_lower_bound(least_upper_bound(X_141,b),greatest_lower_bound(b,least_upper_bound(a,X_141))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(X_141,b)),greatest_lower_bound(least_upper_bound(X_141,b),greatest_lower_bound(b,least_upper_bound(a,X_141)))) ),[0],$fot(b)]]) ).
cnf(refute_0_324,plain,
( greatest_lower_bound(b,least_upper_bound(X_141,b)) != greatest_lower_bound(least_upper_bound(X_141,b),greatest_lower_bound(b,least_upper_bound(a,X_141)))
| b = greatest_lower_bound(least_upper_bound(X_141,b),greatest_lower_bound(b,least_upper_bound(a,X_141))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(X_141,b)),b) )],[refute_0_322,refute_0_323]) ).
cnf(refute_0_325,plain,
greatest_lower_bound(X_31,greatest_lower_bound(least_upper_bound(X_7,X_31),X_33)) = greatest_lower_bound(greatest_lower_bound(X_31,least_upper_bound(X_7,X_31)),X_33),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_31)),bind(Y,$fot(least_upper_bound(X_7,X_31))),bind(Z,$fot(X_33))]]) ).
cnf(refute_0_326,plain,
greatest_lower_bound(X_31,least_upper_bound(X_7,X_31)) = X_31,
inference(subst,[],[refute_0_99:[bind(X_6,$fot(X_31))]]) ).
cnf(refute_0_327,plain,
( greatest_lower_bound(X_31,greatest_lower_bound(least_upper_bound(X_7,X_31),X_33)) != greatest_lower_bound(greatest_lower_bound(X_31,least_upper_bound(X_7,X_31)),X_33)
| greatest_lower_bound(X_31,least_upper_bound(X_7,X_31)) != X_31
| greatest_lower_bound(X_31,greatest_lower_bound(least_upper_bound(X_7,X_31),X_33)) = greatest_lower_bound(X_31,X_33) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_31,greatest_lower_bound(least_upper_bound(X_7,X_31),X_33)),greatest_lower_bound(greatest_lower_bound(X_31,least_upper_bound(X_7,X_31)),X_33)) ),[1,0],$fot(X_31)]]) ).
cnf(refute_0_328,plain,
( greatest_lower_bound(X_31,greatest_lower_bound(least_upper_bound(X_7,X_31),X_33)) != greatest_lower_bound(greatest_lower_bound(X_31,least_upper_bound(X_7,X_31)),X_33)
| greatest_lower_bound(X_31,greatest_lower_bound(least_upper_bound(X_7,X_31),X_33)) = greatest_lower_bound(X_31,X_33) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_31,least_upper_bound(X_7,X_31)),X_31) )],[refute_0_326,refute_0_327]) ).
cnf(refute_0_329,plain,
greatest_lower_bound(X_31,greatest_lower_bound(least_upper_bound(X_7,X_31),X_33)) = greatest_lower_bound(X_31,X_33),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_31,greatest_lower_bound(least_upper_bound(X_7,X_31),X_33)),greatest_lower_bound(greatest_lower_bound(X_31,least_upper_bound(X_7,X_31)),X_33)) )],[refute_0_325,refute_0_328]) ).
cnf(refute_0_330,plain,
greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(X_141,b),least_upper_bound(a,X_141))) = greatest_lower_bound(b,least_upper_bound(a,X_141)),
inference(subst,[],[refute_0_329:[bind(X_31,$fot(b)),bind(X_33,$fot(least_upper_bound(a,X_141))),bind(X_7,$fot(X_141))]]) ).
cnf(refute_0_331,plain,
greatest_lower_bound(greatest_lower_bound(Y,X_43),greatest_lower_bound(X_42,X_43)) = greatest_lower_bound(X_42,greatest_lower_bound(X_43,greatest_lower_bound(Y,X_43))),
inference(subst,[],[refute_0_90:[bind(X,$fot(greatest_lower_bound(Y,X_43))),bind(X_31,$fot(X_42)),bind(X_32,$fot(X_43))]]) ).
cnf(refute_0_332,plain,
greatest_lower_bound(X_43,greatest_lower_bound(Y,X_43)) = greatest_lower_bound(X_43,Y),
inference(subst,[],[refute_0_152:[bind(X_13,$fot(X_43))]]) ).
cnf(refute_0_333,plain,
( greatest_lower_bound(X_43,greatest_lower_bound(Y,X_43)) != greatest_lower_bound(X_43,Y)
| greatest_lower_bound(greatest_lower_bound(Y,X_43),greatest_lower_bound(X_42,X_43)) != greatest_lower_bound(X_42,greatest_lower_bound(X_43,greatest_lower_bound(Y,X_43)))
| greatest_lower_bound(greatest_lower_bound(Y,X_43),greatest_lower_bound(X_42,X_43)) = greatest_lower_bound(X_42,greatest_lower_bound(X_43,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(Y,X_43),greatest_lower_bound(X_42,X_43)),greatest_lower_bound(X_42,greatest_lower_bound(X_43,greatest_lower_bound(Y,X_43)))) ),[1,1],$fot(greatest_lower_bound(X_43,Y))]]) ).
cnf(refute_0_334,plain,
( greatest_lower_bound(greatest_lower_bound(Y,X_43),greatest_lower_bound(X_42,X_43)) != greatest_lower_bound(X_42,greatest_lower_bound(X_43,greatest_lower_bound(Y,X_43)))
| greatest_lower_bound(greatest_lower_bound(Y,X_43),greatest_lower_bound(X_42,X_43)) = greatest_lower_bound(X_42,greatest_lower_bound(X_43,Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_43,greatest_lower_bound(Y,X_43)),greatest_lower_bound(X_43,Y)) )],[refute_0_332,refute_0_333]) ).
cnf(refute_0_335,plain,
greatest_lower_bound(greatest_lower_bound(Y,X_43),greatest_lower_bound(X_42,X_43)) = greatest_lower_bound(X_42,greatest_lower_bound(X_43,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(Y,X_43),greatest_lower_bound(X_42,X_43)),greatest_lower_bound(X_42,greatest_lower_bound(X_43,greatest_lower_bound(Y,X_43)))) )],[refute_0_331,refute_0_334]) ).
cnf(refute_0_336,plain,
greatest_lower_bound(X_13,greatest_lower_bound(greatest_lower_bound(X_31,X_32),X_13)) = greatest_lower_bound(X_13,greatest_lower_bound(X_31,X_32)),
inference(subst,[],[refute_0_152:[bind(Y,$fot(greatest_lower_bound(X_31,X_32)))]]) ).
cnf(refute_0_337,plain,
greatest_lower_bound(X_31,greatest_lower_bound(X_32,X_13)) = greatest_lower_bound(greatest_lower_bound(X_31,X_32),X_13),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_31)),bind(Y,$fot(X_32)),bind(Z,$fot(X_13))]]) ).
cnf(refute_0_338,plain,
( greatest_lower_bound(X_31,greatest_lower_bound(X_32,X_13)) != greatest_lower_bound(greatest_lower_bound(X_31,X_32),X_13)
| greatest_lower_bound(greatest_lower_bound(X_31,X_32),X_13) = greatest_lower_bound(X_31,greatest_lower_bound(X_32,X_13)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(greatest_lower_bound(X_31,greatest_lower_bound(X_32,X_13)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X_31,X_32),X_13)))]]) ).
cnf(refute_0_339,plain,
greatest_lower_bound(greatest_lower_bound(X_31,X_32),X_13) = greatest_lower_bound(X_31,greatest_lower_bound(X_32,X_13)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_31,greatest_lower_bound(X_32,X_13)),greatest_lower_bound(greatest_lower_bound(X_31,X_32),X_13)) )],[refute_0_337,refute_0_338]) ).
cnf(refute_0_340,plain,
( greatest_lower_bound(X_13,greatest_lower_bound(greatest_lower_bound(X_31,X_32),X_13)) != greatest_lower_bound(X_13,greatest_lower_bound(X_31,X_32))
| greatest_lower_bound(greatest_lower_bound(X_31,X_32),X_13) != greatest_lower_bound(X_31,greatest_lower_bound(X_32,X_13))
| greatest_lower_bound(X_13,greatest_lower_bound(X_31,greatest_lower_bound(X_32,X_13))) = greatest_lower_bound(X_13,greatest_lower_bound(X_31,X_32)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_13,greatest_lower_bound(greatest_lower_bound(X_31,X_32),X_13)),greatest_lower_bound(X_13,greatest_lower_bound(X_31,X_32))) ),[0,1],$fot(greatest_lower_bound(X_31,greatest_lower_bound(X_32,X_13)))]]) ).
cnf(refute_0_341,plain,
( greatest_lower_bound(X_13,greatest_lower_bound(greatest_lower_bound(X_31,X_32),X_13)) != greatest_lower_bound(X_13,greatest_lower_bound(X_31,X_32))
| greatest_lower_bound(X_13,greatest_lower_bound(X_31,greatest_lower_bound(X_32,X_13))) = greatest_lower_bound(X_13,greatest_lower_bound(X_31,X_32)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_31,X_32),X_13),greatest_lower_bound(X_31,greatest_lower_bound(X_32,X_13))) )],[refute_0_339,refute_0_340]) ).
cnf(refute_0_342,plain,
greatest_lower_bound(X_13,greatest_lower_bound(X_31,greatest_lower_bound(X_32,X_13))) = greatest_lower_bound(X_13,greatest_lower_bound(X_31,X_32)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_13,greatest_lower_bound(greatest_lower_bound(X_31,X_32),X_13)),greatest_lower_bound(X_13,greatest_lower_bound(X_31,X_32))) )],[refute_0_336,refute_0_341]) ).
cnf(refute_0_343,plain,
greatest_lower_bound(X_43,greatest_lower_bound(X_42,greatest_lower_bound(Y,X_43))) = greatest_lower_bound(X_43,greatest_lower_bound(X_42,Y)),
inference(subst,[],[refute_0_342:[bind(X_13,$fot(X_43)),bind(X_31,$fot(X_42)),bind(X_32,$fot(Y))]]) ).
cnf(refute_0_344,plain,
greatest_lower_bound(greatest_lower_bound(Y,X_43),greatest_lower_bound(X_42,X_43)) = greatest_lower_bound(X_43,greatest_lower_bound(X_42,greatest_lower_bound(Y,X_43))),
inference(subst,[],[refute_0_193:[bind(Y,$fot(greatest_lower_bound(Y,X_43))),bind(X_41,$fot(X_43))]]) ).
cnf(refute_0_345,plain,
( greatest_lower_bound(X_43,greatest_lower_bound(X_42,greatest_lower_bound(Y,X_43))) != greatest_lower_bound(X_43,greatest_lower_bound(X_42,Y))
| greatest_lower_bound(greatest_lower_bound(Y,X_43),greatest_lower_bound(X_42,X_43)) != greatest_lower_bound(X_43,greatest_lower_bound(X_42,greatest_lower_bound(Y,X_43)))
| greatest_lower_bound(greatest_lower_bound(Y,X_43),greatest_lower_bound(X_42,X_43)) = greatest_lower_bound(X_43,greatest_lower_bound(X_42,Y)) ),
inference(subst,[],[refute_0_171:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(Y,X_43),greatest_lower_bound(X_42,X_43)))),bind(Y0,$fot(greatest_lower_bound(X_43,greatest_lower_bound(X_42,greatest_lower_bound(Y,X_43))))),bind(Z0,$fot(greatest_lower_bound(X_43,greatest_lower_bound(X_42,Y))))]]) ).
cnf(refute_0_346,plain,
( greatest_lower_bound(X_43,greatest_lower_bound(X_42,greatest_lower_bound(Y,X_43))) != greatest_lower_bound(X_43,greatest_lower_bound(X_42,Y))
| greatest_lower_bound(greatest_lower_bound(Y,X_43),greatest_lower_bound(X_42,X_43)) = greatest_lower_bound(X_43,greatest_lower_bound(X_42,Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(Y,X_43),greatest_lower_bound(X_42,X_43)),greatest_lower_bound(X_43,greatest_lower_bound(X_42,greatest_lower_bound(Y,X_43)))) )],[refute_0_344,refute_0_345]) ).
cnf(refute_0_347,plain,
greatest_lower_bound(greatest_lower_bound(Y,X_43),greatest_lower_bound(X_42,X_43)) = greatest_lower_bound(X_43,greatest_lower_bound(X_42,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_43,greatest_lower_bound(X_42,greatest_lower_bound(Y,X_43))),greatest_lower_bound(X_43,greatest_lower_bound(X_42,Y))) )],[refute_0_343,refute_0_346]) ).
cnf(refute_0_348,plain,
( greatest_lower_bound(greatest_lower_bound(Y,X_43),greatest_lower_bound(X_42,X_43)) != greatest_lower_bound(X_42,greatest_lower_bound(X_43,Y))
| greatest_lower_bound(greatest_lower_bound(Y,X_43),greatest_lower_bound(X_42,X_43)) != greatest_lower_bound(X_43,greatest_lower_bound(X_42,Y))
| greatest_lower_bound(X_43,greatest_lower_bound(X_42,Y)) = greatest_lower_bound(X_42,greatest_lower_bound(X_43,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(Y,X_43),greatest_lower_bound(X_42,X_43)),greatest_lower_bound(X_42,greatest_lower_bound(X_43,Y))) ),[0],$fot(greatest_lower_bound(X_43,greatest_lower_bound(X_42,Y)))]]) ).
cnf(refute_0_349,plain,
( greatest_lower_bound(greatest_lower_bound(Y,X_43),greatest_lower_bound(X_42,X_43)) != greatest_lower_bound(X_42,greatest_lower_bound(X_43,Y))
| greatest_lower_bound(X_43,greatest_lower_bound(X_42,Y)) = greatest_lower_bound(X_42,greatest_lower_bound(X_43,Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(Y,X_43),greatest_lower_bound(X_42,X_43)),greatest_lower_bound(X_43,greatest_lower_bound(X_42,Y))) )],[refute_0_347,refute_0_348]) ).
cnf(refute_0_350,plain,
greatest_lower_bound(X_43,greatest_lower_bound(X_42,Y)) = greatest_lower_bound(X_42,greatest_lower_bound(X_43,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(Y,X_43),greatest_lower_bound(X_42,X_43)),greatest_lower_bound(X_42,greatest_lower_bound(X_43,Y))) )],[refute_0_335,refute_0_349]) ).
cnf(refute_0_351,plain,
( greatest_lower_bound(X_43,greatest_lower_bound(X_42,Y)) != greatest_lower_bound(X_42,greatest_lower_bound(X_43,Y))
| greatest_lower_bound(X_42,greatest_lower_bound(X_43,Y)) = greatest_lower_bound(X_43,greatest_lower_bound(X_42,Y)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(greatest_lower_bound(X_43,greatest_lower_bound(X_42,Y)))),bind(Y0,$fot(greatest_lower_bound(X_42,greatest_lower_bound(X_43,Y))))]]) ).
cnf(refute_0_352,plain,
greatest_lower_bound(X_42,greatest_lower_bound(X_43,Y)) = greatest_lower_bound(X_43,greatest_lower_bound(X_42,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_43,greatest_lower_bound(X_42,Y)),greatest_lower_bound(X_42,greatest_lower_bound(X_43,Y))) )],[refute_0_350,refute_0_351]) ).
cnf(refute_0_353,plain,
greatest_lower_bound(least_upper_bound(X_141,b),greatest_lower_bound(b,least_upper_bound(a,X_141))) = greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(X_141,b),least_upper_bound(a,X_141))),
inference(subst,[],[refute_0_352:[bind(Y,$fot(least_upper_bound(a,X_141))),bind(X_42,$fot(least_upper_bound(X_141,b))),bind(X_43,$fot(b))]]) ).
cnf(refute_0_354,plain,
( greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(X_141,b),least_upper_bound(a,X_141))) != greatest_lower_bound(b,least_upper_bound(a,X_141))
| greatest_lower_bound(least_upper_bound(X_141,b),greatest_lower_bound(b,least_upper_bound(a,X_141))) != greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(X_141,b),least_upper_bound(a,X_141)))
| greatest_lower_bound(least_upper_bound(X_141,b),greatest_lower_bound(b,least_upper_bound(a,X_141))) = greatest_lower_bound(b,least_upper_bound(a,X_141)) ),
inference(subst,[],[refute_0_171:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(X_141,b),greatest_lower_bound(b,least_upper_bound(a,X_141))))),bind(Y0,$fot(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(X_141,b),least_upper_bound(a,X_141))))),bind(Z0,$fot(greatest_lower_bound(b,least_upper_bound(a,X_141))))]]) ).
cnf(refute_0_355,plain,
( greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(X_141,b),least_upper_bound(a,X_141))) != greatest_lower_bound(b,least_upper_bound(a,X_141))
| greatest_lower_bound(least_upper_bound(X_141,b),greatest_lower_bound(b,least_upper_bound(a,X_141))) = greatest_lower_bound(b,least_upper_bound(a,X_141)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_141,b),greatest_lower_bound(b,least_upper_bound(a,X_141))),greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(X_141,b),least_upper_bound(a,X_141)))) )],[refute_0_353,refute_0_354]) ).
cnf(refute_0_356,plain,
greatest_lower_bound(least_upper_bound(X_141,b),greatest_lower_bound(b,least_upper_bound(a,X_141))) = greatest_lower_bound(b,least_upper_bound(a,X_141)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(X_141,b),least_upper_bound(a,X_141))),greatest_lower_bound(b,least_upper_bound(a,X_141))) )],[refute_0_330,refute_0_355]) ).
cnf(refute_0_357,plain,
( b != greatest_lower_bound(least_upper_bound(X_141,b),greatest_lower_bound(b,least_upper_bound(a,X_141)))
| greatest_lower_bound(least_upper_bound(X_141,b),greatest_lower_bound(b,least_upper_bound(a,X_141))) != greatest_lower_bound(b,least_upper_bound(a,X_141))
| b = greatest_lower_bound(b,least_upper_bound(a,X_141)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(b,greatest_lower_bound(b,least_upper_bound(a,X_141))) ),[0],$fot(greatest_lower_bound(least_upper_bound(X_141,b),greatest_lower_bound(b,least_upper_bound(a,X_141))))]]) ).
cnf(refute_0_358,plain,
( b != greatest_lower_bound(least_upper_bound(X_141,b),greatest_lower_bound(b,least_upper_bound(a,X_141)))
| b = greatest_lower_bound(b,least_upper_bound(a,X_141)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_141,b),greatest_lower_bound(b,least_upper_bound(a,X_141))),greatest_lower_bound(b,least_upper_bound(a,X_141))) )],[refute_0_356,refute_0_357]) ).
cnf(refute_0_359,plain,
( greatest_lower_bound(b,least_upper_bound(X_141,b)) != greatest_lower_bound(least_upper_bound(X_141,b),greatest_lower_bound(b,least_upper_bound(a,X_141)))
| b = greatest_lower_bound(b,least_upper_bound(a,X_141)) ),
inference(resolve,[$cnf( $equal(b,greatest_lower_bound(least_upper_bound(X_141,b),greatest_lower_bound(b,least_upper_bound(a,X_141)))) )],[refute_0_324,refute_0_358]) ).
cnf(refute_0_360,plain,
b = greatest_lower_bound(b,least_upper_bound(a,X_141)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(X_141,b)),greatest_lower_bound(least_upper_bound(X_141,b),greatest_lower_bound(b,least_upper_bound(a,X_141)))) )],[refute_0_321,refute_0_359]) ).
cnf(refute_0_361,plain,
b = greatest_lower_bound(b,least_upper_bound(a,X_142)),
inference(subst,[],[refute_0_360:[bind(X_141,$fot(X_142))]]) ).
cnf(refute_0_362,plain,
( b != greatest_lower_bound(b,least_upper_bound(a,X_142))
| greatest_lower_bound(b,least_upper_bound(a,X_142)) = b ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(b)),bind(Y0,$fot(greatest_lower_bound(b,least_upper_bound(a,X_142))))]]) ).
cnf(refute_0_363,plain,
greatest_lower_bound(b,least_upper_bound(a,X_142)) = b,
inference(resolve,[$cnf( $equal(b,greatest_lower_bound(b,least_upper_bound(a,X_142))) )],[refute_0_361,refute_0_362]) ).
cnf(refute_0_364,plain,
( greatest_lower_bound(b,least_upper_bound(a,X_142)) != b
| identity != least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_142)),greatest_lower_bound(b,least_upper_bound(a,X_142))))
| identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_142)),b)) ),
introduced(tautology,[equality,[$cnf( $equal(identity,least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_142)),greatest_lower_bound(b,least_upper_bound(a,X_142))))) ),[1,1,1],$fot(b)]]) ).
cnf(refute_0_365,plain,
( identity != least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_142)),greatest_lower_bound(b,least_upper_bound(a,X_142))))
| identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_142)),b)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(a,X_142)),b) )],[refute_0_363,refute_0_364]) ).
cnf(refute_0_366,plain,
identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_142)),b)),
inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_142)),greatest_lower_bound(b,least_upper_bound(a,X_142))))) )],[refute_0_83,refute_0_365]) ).
cnf(refute_0_367,plain,
( identity != least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_142)),b))
| least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_142)),b)) = identity ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(identity)),bind(Y0,$fot(least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_142)),b))))]]) ).
cnf(refute_0_368,plain,
least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_142)),b)) = identity,
inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_142)),b))) )],[refute_0_366,refute_0_367]) ).
cnf(refute_0_369,plain,
( b != multiply(inverse(least_upper_bound(inverse(least_upper_bound(a,X_142)),inverse(b))),least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_142)),b)))
| least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_142)),b)) != identity
| b = multiply(inverse(least_upper_bound(inverse(least_upper_bound(a,X_142)),inverse(b))),identity) ),
introduced(tautology,[equality,[$cnf( $equal(b,multiply(inverse(least_upper_bound(inverse(least_upper_bound(a,X_142)),inverse(b))),least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_142)),b)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_370,plain,
( b != multiply(inverse(least_upper_bound(inverse(least_upper_bound(a,X_142)),inverse(b))),least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_142)),b)))
| b = multiply(inverse(least_upper_bound(inverse(least_upper_bound(a,X_142)),inverse(b))),identity) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_142)),b)),identity) )],[refute_0_368,refute_0_369]) ).
cnf(refute_0_371,plain,
b = multiply(inverse(least_upper_bound(inverse(least_upper_bound(a,X_142)),inverse(b))),identity),
inference(resolve,[$cnf( $equal(b,multiply(inverse(least_upper_bound(inverse(least_upper_bound(a,X_142)),inverse(b))),least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_142)),b)))) )],[refute_0_61,refute_0_370]) ).
cnf(refute_0_372,plain,
inverse(least_upper_bound(X_16,X_7)) = multiply(inverse(least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7))))),least_upper_bound(identity,multiply(least_upper_bound(X_7,X_16),inverse(least_upper_bound(X_16,X_7))))),
inference(subst,[],[refute_0_60:[bind(X_194,$fot(least_upper_bound(X_7,X_16))),bind(X_46,$fot(inverse(least_upper_bound(X_16,X_7))))]]) ).
cnf(refute_0_373,plain,
multiply(greatest_lower_bound(X_90,X_91),inverse(X_90)) = greatest_lower_bound(multiply(X_90,inverse(X_90)),multiply(X_91,inverse(X_90))),
inference(subst,[],[monotony_glb2:[bind(X,$fot(inverse(X_90))),bind(Y,$fot(X_90)),bind(Z,$fot(X_91))]]) ).
cnf(refute_0_374,plain,
multiply(inverse(inverse(X_50)),inverse(X_50)) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(inverse(X_50)))]]) ).
cnf(refute_0_375,plain,
multiply(X_50,inverse(X_50)) = multiply(inverse(inverse(X_50)),inverse(X_50)),
inference(subst,[],[refute_0_24:[bind(X_47,$fot(X_50)),bind(X_48,$fot(inverse(X_50)))]]) ).
cnf(refute_0_376,plain,
( multiply(X_50,inverse(X_50)) != multiply(inverse(inverse(X_50)),inverse(X_50))
| multiply(inverse(inverse(X_50)),inverse(X_50)) = multiply(X_50,inverse(X_50)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(X_50,inverse(X_50)))),bind(Y0,$fot(multiply(inverse(inverse(X_50)),inverse(X_50))))]]) ).
cnf(refute_0_377,plain,
multiply(inverse(inverse(X_50)),inverse(X_50)) = multiply(X_50,inverse(X_50)),
inference(resolve,[$cnf( $equal(multiply(X_50,inverse(X_50)),multiply(inverse(inverse(X_50)),inverse(X_50))) )],[refute_0_375,refute_0_376]) ).
cnf(refute_0_378,plain,
( multiply(inverse(inverse(X_50)),inverse(X_50)) != multiply(X_50,inverse(X_50))
| multiply(inverse(inverse(X_50)),inverse(X_50)) != identity
| multiply(X_50,inverse(X_50)) = identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X_50)),inverse(X_50)),identity) ),[0],$fot(multiply(X_50,inverse(X_50)))]]) ).
cnf(refute_0_379,plain,
( multiply(inverse(inverse(X_50)),inverse(X_50)) != identity
| multiply(X_50,inverse(X_50)) = identity ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_50)),inverse(X_50)),multiply(X_50,inverse(X_50))) )],[refute_0_377,refute_0_378]) ).
cnf(refute_0_380,plain,
multiply(X_50,inverse(X_50)) = identity,
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_50)),inverse(X_50)),identity) )],[refute_0_374,refute_0_379]) ).
cnf(refute_0_381,plain,
multiply(X_90,inverse(X_90)) = identity,
inference(subst,[],[refute_0_380:[bind(X_50,$fot(X_90))]]) ).
cnf(refute_0_382,plain,
( multiply(X_90,inverse(X_90)) != identity
| multiply(greatest_lower_bound(X_90,X_91),inverse(X_90)) != greatest_lower_bound(multiply(X_90,inverse(X_90)),multiply(X_91,inverse(X_90)))
| multiply(greatest_lower_bound(X_90,X_91),inverse(X_90)) = greatest_lower_bound(identity,multiply(X_91,inverse(X_90))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_90,X_91),inverse(X_90)),greatest_lower_bound(multiply(X_90,inverse(X_90)),multiply(X_91,inverse(X_90)))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_383,plain,
( multiply(greatest_lower_bound(X_90,X_91),inverse(X_90)) != greatest_lower_bound(multiply(X_90,inverse(X_90)),multiply(X_91,inverse(X_90)))
| multiply(greatest_lower_bound(X_90,X_91),inverse(X_90)) = greatest_lower_bound(identity,multiply(X_91,inverse(X_90))) ),
inference(resolve,[$cnf( $equal(multiply(X_90,inverse(X_90)),identity) )],[refute_0_381,refute_0_382]) ).
cnf(refute_0_384,plain,
multiply(greatest_lower_bound(X_90,X_91),inverse(X_90)) = greatest_lower_bound(identity,multiply(X_91,inverse(X_90))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_90,X_91),inverse(X_90)),greatest_lower_bound(multiply(X_90,inverse(X_90)),multiply(X_91,inverse(X_90)))) )],[refute_0_373,refute_0_383]) ).
cnf(refute_0_385,plain,
multiply(greatest_lower_bound(least_upper_bound(X_16,X_7),least_upper_bound(X_7,X_16)),inverse(least_upper_bound(X_16,X_7))) = greatest_lower_bound(identity,multiply(least_upper_bound(X_7,X_16),inverse(least_upper_bound(X_16,X_7)))),
inference(subst,[],[refute_0_384:[bind(X_90,$fot(least_upper_bound(X_16,X_7))),bind(X_91,$fot(least_upper_bound(X_7,X_16)))]]) ).
cnf(refute_0_386,plain,
greatest_lower_bound(least_upper_bound(X_16,X_7),least_upper_bound(X_7,least_upper_bound(X_16,X_7))) = least_upper_bound(X_16,X_7),
inference(subst,[],[refute_0_99:[bind(X_6,$fot(least_upper_bound(X_16,X_7)))]]) ).
cnf(refute_0_387,plain,
least_upper_bound(X_7,least_upper_bound(X_16,X_7)) = least_upper_bound(X_7,X_16),
inference(subst,[],[refute_0_213:[bind(Y,$fot(X_16)),bind(X_15,$fot(X_7))]]) ).
cnf(refute_0_388,plain,
( greatest_lower_bound(least_upper_bound(X_16,X_7),least_upper_bound(X_7,least_upper_bound(X_16,X_7))) != least_upper_bound(X_16,X_7)
| least_upper_bound(X_7,least_upper_bound(X_16,X_7)) != least_upper_bound(X_7,X_16)
| greatest_lower_bound(least_upper_bound(X_16,X_7),least_upper_bound(X_7,X_16)) = least_upper_bound(X_16,X_7) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_16,X_7),least_upper_bound(X_7,least_upper_bound(X_16,X_7))),least_upper_bound(X_16,X_7)) ),[0,1],$fot(least_upper_bound(X_7,X_16))]]) ).
cnf(refute_0_389,plain,
( greatest_lower_bound(least_upper_bound(X_16,X_7),least_upper_bound(X_7,least_upper_bound(X_16,X_7))) != least_upper_bound(X_16,X_7)
| greatest_lower_bound(least_upper_bound(X_16,X_7),least_upper_bound(X_7,X_16)) = least_upper_bound(X_16,X_7) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_7,least_upper_bound(X_16,X_7)),least_upper_bound(X_7,X_16)) )],[refute_0_387,refute_0_388]) ).
cnf(refute_0_390,plain,
greatest_lower_bound(least_upper_bound(X_16,X_7),least_upper_bound(X_7,X_16)) = least_upper_bound(X_16,X_7),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_16,X_7),least_upper_bound(X_7,least_upper_bound(X_16,X_7))),least_upper_bound(X_16,X_7)) )],[refute_0_386,refute_0_389]) ).
cnf(refute_0_391,plain,
( multiply(greatest_lower_bound(least_upper_bound(X_16,X_7),least_upper_bound(X_7,X_16)),inverse(least_upper_bound(X_16,X_7))) != greatest_lower_bound(identity,multiply(least_upper_bound(X_7,X_16),inverse(least_upper_bound(X_16,X_7))))
| greatest_lower_bound(least_upper_bound(X_16,X_7),least_upper_bound(X_7,X_16)) != least_upper_bound(X_16,X_7)
| multiply(least_upper_bound(X_16,X_7),inverse(least_upper_bound(X_16,X_7))) = greatest_lower_bound(identity,multiply(least_upper_bound(X_7,X_16),inverse(least_upper_bound(X_16,X_7)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(X_16,X_7),least_upper_bound(X_7,X_16)),inverse(least_upper_bound(X_16,X_7))),greatest_lower_bound(identity,multiply(least_upper_bound(X_7,X_16),inverse(least_upper_bound(X_16,X_7))))) ),[0,0],$fot(least_upper_bound(X_16,X_7))]]) ).
cnf(refute_0_392,plain,
( multiply(greatest_lower_bound(least_upper_bound(X_16,X_7),least_upper_bound(X_7,X_16)),inverse(least_upper_bound(X_16,X_7))) != greatest_lower_bound(identity,multiply(least_upper_bound(X_7,X_16),inverse(least_upper_bound(X_16,X_7))))
| multiply(least_upper_bound(X_16,X_7),inverse(least_upper_bound(X_16,X_7))) = greatest_lower_bound(identity,multiply(least_upper_bound(X_7,X_16),inverse(least_upper_bound(X_16,X_7)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_16,X_7),least_upper_bound(X_7,X_16)),least_upper_bound(X_16,X_7)) )],[refute_0_390,refute_0_391]) ).
cnf(refute_0_393,plain,
multiply(least_upper_bound(X_16,X_7),inverse(least_upper_bound(X_16,X_7))) = greatest_lower_bound(identity,multiply(least_upper_bound(X_7,X_16),inverse(least_upper_bound(X_16,X_7)))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(X_16,X_7),least_upper_bound(X_7,X_16)),inverse(least_upper_bound(X_16,X_7))),greatest_lower_bound(identity,multiply(least_upper_bound(X_7,X_16),inverse(least_upper_bound(X_16,X_7))))) )],[refute_0_385,refute_0_392]) ).
cnf(refute_0_394,plain,
multiply(least_upper_bound(X_16,X_7),inverse(least_upper_bound(X_16,X_7))) = identity,
inference(subst,[],[refute_0_380:[bind(X_50,$fot(least_upper_bound(X_16,X_7)))]]) ).
cnf(refute_0_395,plain,
( multiply(least_upper_bound(X_16,X_7),inverse(least_upper_bound(X_16,X_7))) != greatest_lower_bound(identity,multiply(least_upper_bound(X_7,X_16),inverse(least_upper_bound(X_16,X_7))))
| multiply(least_upper_bound(X_16,X_7),inverse(least_upper_bound(X_16,X_7))) != identity
| identity = greatest_lower_bound(identity,multiply(least_upper_bound(X_7,X_16),inverse(least_upper_bound(X_16,X_7)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_16,X_7),inverse(least_upper_bound(X_16,X_7))),greatest_lower_bound(identity,multiply(least_upper_bound(X_7,X_16),inverse(least_upper_bound(X_16,X_7))))) ),[0],$fot(identity)]]) ).
cnf(refute_0_396,plain,
( multiply(least_upper_bound(X_16,X_7),inverse(least_upper_bound(X_16,X_7))) != greatest_lower_bound(identity,multiply(least_upper_bound(X_7,X_16),inverse(least_upper_bound(X_16,X_7))))
| identity = greatest_lower_bound(identity,multiply(least_upper_bound(X_7,X_16),inverse(least_upper_bound(X_16,X_7)))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_16,X_7),inverse(least_upper_bound(X_16,X_7))),identity) )],[refute_0_394,refute_0_395]) ).
cnf(refute_0_397,plain,
multiply(greatest_lower_bound(X_90,X_91),inverse(X_91)) = greatest_lower_bound(multiply(X_90,inverse(X_91)),multiply(X_91,inverse(X_91))),
inference(subst,[],[monotony_glb2:[bind(X,$fot(inverse(X_91))),bind(Y,$fot(X_90)),bind(Z,$fot(X_91))]]) ).
cnf(refute_0_398,plain,
multiply(X_91,inverse(X_91)) = identity,
inference(subst,[],[refute_0_380:[bind(X_50,$fot(X_91))]]) ).
cnf(refute_0_399,plain,
( multiply(X_91,inverse(X_91)) != identity
| multiply(greatest_lower_bound(X_90,X_91),inverse(X_91)) != greatest_lower_bound(multiply(X_90,inverse(X_91)),multiply(X_91,inverse(X_91)))
| multiply(greatest_lower_bound(X_90,X_91),inverse(X_91)) = greatest_lower_bound(multiply(X_90,inverse(X_91)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_90,X_91),inverse(X_91)),greatest_lower_bound(multiply(X_90,inverse(X_91)),multiply(X_91,inverse(X_91)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_400,plain,
( multiply(greatest_lower_bound(X_90,X_91),inverse(X_91)) != greatest_lower_bound(multiply(X_90,inverse(X_91)),multiply(X_91,inverse(X_91)))
| multiply(greatest_lower_bound(X_90,X_91),inverse(X_91)) = greatest_lower_bound(multiply(X_90,inverse(X_91)),identity) ),
inference(resolve,[$cnf( $equal(multiply(X_91,inverse(X_91)),identity) )],[refute_0_398,refute_0_399]) ).
cnf(refute_0_401,plain,
multiply(greatest_lower_bound(X_90,X_91),inverse(X_91)) = greatest_lower_bound(multiply(X_90,inverse(X_91)),identity),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_90,X_91),inverse(X_91)),greatest_lower_bound(multiply(X_90,inverse(X_91)),multiply(X_91,inverse(X_91)))) )],[refute_0_397,refute_0_400]) ).
cnf(refute_0_402,plain,
greatest_lower_bound(multiply(X_90,inverse(X_91)),identity) = greatest_lower_bound(identity,multiply(X_90,inverse(X_91))),
inference(subst,[],[refute_0_105:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_90,inverse(X_91))))]]) ).
cnf(refute_0_403,plain,
( multiply(greatest_lower_bound(X_90,X_91),inverse(X_91)) != greatest_lower_bound(multiply(X_90,inverse(X_91)),identity)
| greatest_lower_bound(multiply(X_90,inverse(X_91)),identity) != greatest_lower_bound(identity,multiply(X_90,inverse(X_91)))
| multiply(greatest_lower_bound(X_90,X_91),inverse(X_91)) = greatest_lower_bound(identity,multiply(X_90,inverse(X_91))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_90,X_91),inverse(X_91)),greatest_lower_bound(identity,multiply(X_90,inverse(X_91)))) ),[0],$fot(greatest_lower_bound(multiply(X_90,inverse(X_91)),identity))]]) ).
cnf(refute_0_404,plain,
( multiply(greatest_lower_bound(X_90,X_91),inverse(X_91)) != greatest_lower_bound(multiply(X_90,inverse(X_91)),identity)
| multiply(greatest_lower_bound(X_90,X_91),inverse(X_91)) = greatest_lower_bound(identity,multiply(X_90,inverse(X_91))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_90,inverse(X_91)),identity),greatest_lower_bound(identity,multiply(X_90,inverse(X_91)))) )],[refute_0_402,refute_0_403]) ).
cnf(refute_0_405,plain,
multiply(greatest_lower_bound(X_90,X_91),inverse(X_91)) = greatest_lower_bound(identity,multiply(X_90,inverse(X_91))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_90,X_91),inverse(X_91)),greatest_lower_bound(multiply(X_90,inverse(X_91)),identity)) )],[refute_0_401,refute_0_404]) ).
cnf(refute_0_406,plain,
multiply(greatest_lower_bound(least_upper_bound(X_16,X_7),least_upper_bound(X_7,X_16)),inverse(least_upper_bound(X_7,X_16))) = greatest_lower_bound(identity,multiply(least_upper_bound(X_16,X_7),inverse(least_upper_bound(X_7,X_16)))),
inference(subst,[],[refute_0_405:[bind(X_90,$fot(least_upper_bound(X_16,X_7))),bind(X_91,$fot(least_upper_bound(X_7,X_16)))]]) ).
cnf(refute_0_407,plain,
( multiply(greatest_lower_bound(least_upper_bound(X_16,X_7),least_upper_bound(X_7,X_16)),inverse(least_upper_bound(X_7,X_16))) != greatest_lower_bound(identity,multiply(least_upper_bound(X_16,X_7),inverse(least_upper_bound(X_7,X_16))))
| greatest_lower_bound(least_upper_bound(X_16,X_7),least_upper_bound(X_7,X_16)) != least_upper_bound(X_16,X_7)
| multiply(least_upper_bound(X_16,X_7),inverse(least_upper_bound(X_7,X_16))) = greatest_lower_bound(identity,multiply(least_upper_bound(X_16,X_7),inverse(least_upper_bound(X_7,X_16)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(X_16,X_7),least_upper_bound(X_7,X_16)),inverse(least_upper_bound(X_7,X_16))),greatest_lower_bound(identity,multiply(least_upper_bound(X_16,X_7),inverse(least_upper_bound(X_7,X_16))))) ),[0,0],$fot(least_upper_bound(X_16,X_7))]]) ).
cnf(refute_0_408,plain,
( multiply(greatest_lower_bound(least_upper_bound(X_16,X_7),least_upper_bound(X_7,X_16)),inverse(least_upper_bound(X_7,X_16))) != greatest_lower_bound(identity,multiply(least_upper_bound(X_16,X_7),inverse(least_upper_bound(X_7,X_16))))
| multiply(least_upper_bound(X_16,X_7),inverse(least_upper_bound(X_7,X_16))) = greatest_lower_bound(identity,multiply(least_upper_bound(X_16,X_7),inverse(least_upper_bound(X_7,X_16)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_16,X_7),least_upper_bound(X_7,X_16)),least_upper_bound(X_16,X_7)) )],[refute_0_390,refute_0_407]) ).
cnf(refute_0_409,plain,
multiply(least_upper_bound(X_16,X_7),inverse(least_upper_bound(X_7,X_16))) = greatest_lower_bound(identity,multiply(least_upper_bound(X_16,X_7),inverse(least_upper_bound(X_7,X_16)))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(X_16,X_7),least_upper_bound(X_7,X_16)),inverse(least_upper_bound(X_7,X_16))),greatest_lower_bound(identity,multiply(least_upper_bound(X_16,X_7),inverse(least_upper_bound(X_7,X_16))))) )],[refute_0_406,refute_0_408]) ).
cnf(refute_0_410,plain,
( multiply(least_upper_bound(X_16,X_7),inverse(least_upper_bound(X_7,X_16))) != greatest_lower_bound(identity,multiply(least_upper_bound(X_16,X_7),inverse(least_upper_bound(X_7,X_16))))
| greatest_lower_bound(identity,multiply(least_upper_bound(X_16,X_7),inverse(least_upper_bound(X_7,X_16)))) = multiply(least_upper_bound(X_16,X_7),inverse(least_upper_bound(X_7,X_16))) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(least_upper_bound(X_16,X_7),inverse(least_upper_bound(X_7,X_16))))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(least_upper_bound(X_16,X_7),inverse(least_upper_bound(X_7,X_16))))))]]) ).
cnf(refute_0_411,plain,
greatest_lower_bound(identity,multiply(least_upper_bound(X_16,X_7),inverse(least_upper_bound(X_7,X_16)))) = multiply(least_upper_bound(X_16,X_7),inverse(least_upper_bound(X_7,X_16))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_16,X_7),inverse(least_upper_bound(X_7,X_16))),greatest_lower_bound(identity,multiply(least_upper_bound(X_16,X_7),inverse(least_upper_bound(X_7,X_16))))) )],[refute_0_409,refute_0_410]) ).
cnf(refute_0_412,plain,
greatest_lower_bound(identity,multiply(least_upper_bound(X_7,X_16),inverse(least_upper_bound(X_16,X_7)))) = multiply(least_upper_bound(X_7,X_16),inverse(least_upper_bound(X_16,X_7))),
inference(subst,[],[refute_0_411:[bind(X_16,$fot(X_7)),bind(X_7,$fot(X_16))]]) ).
cnf(refute_0_413,plain,
( greatest_lower_bound(identity,multiply(least_upper_bound(X_7,X_16),inverse(least_upper_bound(X_16,X_7)))) != multiply(least_upper_bound(X_7,X_16),inverse(least_upper_bound(X_16,X_7)))
| identity != greatest_lower_bound(identity,multiply(least_upper_bound(X_7,X_16),inverse(least_upper_bound(X_16,X_7))))
| identity = multiply(least_upper_bound(X_7,X_16),inverse(least_upper_bound(X_16,X_7))) ),
introduced(tautology,[equality,[$cnf( $equal(identity,greatest_lower_bound(identity,multiply(least_upper_bound(X_7,X_16),inverse(least_upper_bound(X_16,X_7))))) ),[1],$fot(multiply(least_upper_bound(X_7,X_16),inverse(least_upper_bound(X_16,X_7))))]]) ).
cnf(refute_0_414,plain,
( identity != greatest_lower_bound(identity,multiply(least_upper_bound(X_7,X_16),inverse(least_upper_bound(X_16,X_7))))
| identity = multiply(least_upper_bound(X_7,X_16),inverse(least_upper_bound(X_16,X_7))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(least_upper_bound(X_7,X_16),inverse(least_upper_bound(X_16,X_7)))),multiply(least_upper_bound(X_7,X_16),inverse(least_upper_bound(X_16,X_7)))) )],[refute_0_412,refute_0_413]) ).
cnf(refute_0_415,plain,
( multiply(least_upper_bound(X_16,X_7),inverse(least_upper_bound(X_16,X_7))) != greatest_lower_bound(identity,multiply(least_upper_bound(X_7,X_16),inverse(least_upper_bound(X_16,X_7))))
| identity = multiply(least_upper_bound(X_7,X_16),inverse(least_upper_bound(X_16,X_7))) ),
inference(resolve,[$cnf( $equal(identity,greatest_lower_bound(identity,multiply(least_upper_bound(X_7,X_16),inverse(least_upper_bound(X_16,X_7))))) )],[refute_0_396,refute_0_414]) ).
cnf(refute_0_416,plain,
identity = multiply(least_upper_bound(X_7,X_16),inverse(least_upper_bound(X_16,X_7))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_16,X_7),inverse(least_upper_bound(X_16,X_7))),greatest_lower_bound(identity,multiply(least_upper_bound(X_7,X_16),inverse(least_upper_bound(X_16,X_7))))) )],[refute_0_393,refute_0_415]) ).
cnf(refute_0_417,plain,
( identity != multiply(least_upper_bound(X_7,X_16),inverse(least_upper_bound(X_16,X_7)))
| multiply(least_upper_bound(X_7,X_16),inverse(least_upper_bound(X_16,X_7))) = identity ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(identity)),bind(Y0,$fot(multiply(least_upper_bound(X_7,X_16),inverse(least_upper_bound(X_16,X_7)))))]]) ).
cnf(refute_0_418,plain,
multiply(least_upper_bound(X_7,X_16),inverse(least_upper_bound(X_16,X_7))) = identity,
inference(resolve,[$cnf( $equal(identity,multiply(least_upper_bound(X_7,X_16),inverse(least_upper_bound(X_16,X_7)))) )],[refute_0_416,refute_0_417]) ).
cnf(refute_0_419,plain,
( multiply(least_upper_bound(X_7,X_16),inverse(least_upper_bound(X_16,X_7))) != identity
| inverse(least_upper_bound(X_16,X_7)) != multiply(inverse(least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7))))),least_upper_bound(identity,multiply(least_upper_bound(X_7,X_16),inverse(least_upper_bound(X_16,X_7)))))
| inverse(least_upper_bound(X_16,X_7)) = multiply(inverse(least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7))))),least_upper_bound(identity,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_16,X_7)),multiply(inverse(least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7))))),least_upper_bound(identity,multiply(least_upper_bound(X_7,X_16),inverse(least_upper_bound(X_16,X_7)))))) ),[1,1,1],$fot(identity)]]) ).
cnf(refute_0_420,plain,
( inverse(least_upper_bound(X_16,X_7)) != multiply(inverse(least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7))))),least_upper_bound(identity,multiply(least_upper_bound(X_7,X_16),inverse(least_upper_bound(X_16,X_7)))))
| inverse(least_upper_bound(X_16,X_7)) = multiply(inverse(least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7))))),least_upper_bound(identity,identity)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_7,X_16),inverse(least_upper_bound(X_16,X_7))),identity) )],[refute_0_418,refute_0_419]) ).
cnf(refute_0_421,plain,
inverse(least_upper_bound(X_16,X_7)) = multiply(inverse(least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7))))),least_upper_bound(identity,identity)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_16,X_7)),multiply(inverse(least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7))))),least_upper_bound(identity,multiply(least_upper_bound(X_7,X_16),inverse(least_upper_bound(X_16,X_7)))))) )],[refute_0_372,refute_0_420]) ).
cnf(refute_0_422,plain,
multiply(inverse(least_upper_bound(X_7,X_16)),identity) = inverse(least_upper_bound(X_7,X_16)),
inference(subst,[],[refute_0_39:[bind(X_48,$fot(inverse(least_upper_bound(X_7,X_16))))]]) ).
cnf(refute_0_423,plain,
least_upper_bound(identity,identity) = identity,
inference(subst,[],[idempotence_of_lub:[bind(X,$fot(identity))]]) ).
cnf(refute_0_424,plain,
multiply(inverse(least_upper_bound(X_7,X_16)),least_upper_bound(identity,identity)) = multiply(inverse(least_upper_bound(X_7,X_16)),least_upper_bound(identity,identity)),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(X_7,X_16)),least_upper_bound(identity,identity)))]]) ).
cnf(refute_0_425,plain,
( multiply(inverse(least_upper_bound(X_7,X_16)),least_upper_bound(identity,identity)) != multiply(inverse(least_upper_bound(X_7,X_16)),least_upper_bound(identity,identity))
| least_upper_bound(identity,identity) != identity
| multiply(inverse(least_upper_bound(X_7,X_16)),least_upper_bound(identity,identity)) = multiply(inverse(least_upper_bound(X_7,X_16)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(X_7,X_16)),least_upper_bound(identity,identity)),multiply(inverse(least_upper_bound(X_7,X_16)),least_upper_bound(identity,identity))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_426,plain,
( least_upper_bound(identity,identity) != identity
| multiply(inverse(least_upper_bound(X_7,X_16)),least_upper_bound(identity,identity)) = multiply(inverse(least_upper_bound(X_7,X_16)),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_7,X_16)),least_upper_bound(identity,identity)),multiply(inverse(least_upper_bound(X_7,X_16)),least_upper_bound(identity,identity))) )],[refute_0_424,refute_0_425]) ).
cnf(refute_0_427,plain,
multiply(inverse(least_upper_bound(X_7,X_16)),least_upper_bound(identity,identity)) = multiply(inverse(least_upper_bound(X_7,X_16)),identity),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,identity),identity) )],[refute_0_423,refute_0_426]) ).
cnf(refute_0_428,plain,
least_upper_bound(X_17,least_upper_bound(X_16,X_17)) = least_upper_bound(X_17,X_16),
inference(subst,[],[refute_0_213:[bind(Y,$fot(X_16)),bind(X_15,$fot(X_17))]]) ).
cnf(refute_0_429,plain,
least_upper_bound(X_17,X_16) = least_upper_bound(X_16,X_17),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_17)),bind(Y,$fot(X_16))]]) ).
cnf(refute_0_430,plain,
( least_upper_bound(X_17,X_16) != least_upper_bound(X_16,X_17)
| least_upper_bound(X_16,X_17) = least_upper_bound(X_17,X_16) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(least_upper_bound(X_17,X_16))),bind(Y0,$fot(least_upper_bound(X_16,X_17)))]]) ).
cnf(refute_0_431,plain,
least_upper_bound(X_16,X_17) = least_upper_bound(X_17,X_16),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,X_16),least_upper_bound(X_16,X_17)) )],[refute_0_429,refute_0_430]) ).
cnf(refute_0_432,plain,
( least_upper_bound(X_16,X_17) != least_upper_bound(X_17,X_16)
| least_upper_bound(X_17,least_upper_bound(X_16,X_17)) != least_upper_bound(X_17,X_16)
| least_upper_bound(X_17,least_upper_bound(X_17,X_16)) = least_upper_bound(X_17,X_16) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_17,least_upper_bound(X_16,X_17)),least_upper_bound(X_17,X_16)) ),[0,1],$fot(least_upper_bound(X_17,X_16))]]) ).
cnf(refute_0_433,plain,
( least_upper_bound(X_17,least_upper_bound(X_16,X_17)) != least_upper_bound(X_17,X_16)
| least_upper_bound(X_17,least_upper_bound(X_17,X_16)) = least_upper_bound(X_17,X_16) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_16,X_17),least_upper_bound(X_17,X_16)) )],[refute_0_431,refute_0_432]) ).
cnf(refute_0_434,plain,
least_upper_bound(X_17,least_upper_bound(X_17,X_16)) = least_upper_bound(X_17,X_16),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,least_upper_bound(X_16,X_17)),least_upper_bound(X_17,X_16)) )],[refute_0_428,refute_0_433]) ).
cnf(refute_0_435,plain,
least_upper_bound(X_16,least_upper_bound(X_16,X_7)) = least_upper_bound(X_16,X_7),
inference(subst,[],[refute_0_434:[bind(X_16,$fot(X_7)),bind(X_17,$fot(X_16))]]) ).
cnf(refute_0_436,plain,
inverse(inverse(least_upper_bound(X_16,X_7))) = least_upper_bound(X_16,X_7),
inference(subst,[],[refute_0_43:[bind(X_50,$fot(least_upper_bound(X_16,X_7)))]]) ).
cnf(refute_0_437,plain,
least_upper_bound(X_16,inverse(inverse(least_upper_bound(X_16,X_7)))) = least_upper_bound(X_16,inverse(inverse(least_upper_bound(X_16,X_7)))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_16,inverse(inverse(least_upper_bound(X_16,X_7)))))]]) ).
cnf(refute_0_438,plain,
( inverse(inverse(least_upper_bound(X_16,X_7))) != least_upper_bound(X_16,X_7)
| least_upper_bound(X_16,inverse(inverse(least_upper_bound(X_16,X_7)))) != least_upper_bound(X_16,inverse(inverse(least_upper_bound(X_16,X_7))))
| least_upper_bound(X_16,inverse(inverse(least_upper_bound(X_16,X_7)))) = least_upper_bound(X_16,least_upper_bound(X_16,X_7)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_16,inverse(inverse(least_upper_bound(X_16,X_7)))),least_upper_bound(X_16,inverse(inverse(least_upper_bound(X_16,X_7))))) ),[1,1],$fot(least_upper_bound(X_16,X_7))]]) ).
cnf(refute_0_439,plain,
( inverse(inverse(least_upper_bound(X_16,X_7))) != least_upper_bound(X_16,X_7)
| least_upper_bound(X_16,inverse(inverse(least_upper_bound(X_16,X_7)))) = least_upper_bound(X_16,least_upper_bound(X_16,X_7)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_16,inverse(inverse(least_upper_bound(X_16,X_7)))),least_upper_bound(X_16,inverse(inverse(least_upper_bound(X_16,X_7))))) )],[refute_0_437,refute_0_438]) ).
cnf(refute_0_440,plain,
least_upper_bound(X_16,inverse(inverse(least_upper_bound(X_16,X_7)))) = least_upper_bound(X_16,least_upper_bound(X_16,X_7)),
inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(X_16,X_7))),least_upper_bound(X_16,X_7)) )],[refute_0_436,refute_0_439]) ).
cnf(refute_0_441,plain,
( least_upper_bound(X_16,inverse(inverse(least_upper_bound(X_16,X_7)))) != least_upper_bound(X_16,least_upper_bound(X_16,X_7))
| least_upper_bound(X_16,least_upper_bound(X_16,X_7)) != least_upper_bound(X_16,X_7)
| least_upper_bound(X_16,inverse(inverse(least_upper_bound(X_16,X_7)))) = least_upper_bound(X_16,X_7) ),
inference(subst,[],[refute_0_171:[bind(X0,$fot(least_upper_bound(X_16,inverse(inverse(least_upper_bound(X_16,X_7)))))),bind(Y0,$fot(least_upper_bound(X_16,least_upper_bound(X_16,X_7)))),bind(Z0,$fot(least_upper_bound(X_16,X_7)))]]) ).
cnf(refute_0_442,plain,
( least_upper_bound(X_16,least_upper_bound(X_16,X_7)) != least_upper_bound(X_16,X_7)
| least_upper_bound(X_16,inverse(inverse(least_upper_bound(X_16,X_7)))) = least_upper_bound(X_16,X_7) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_16,inverse(inverse(least_upper_bound(X_16,X_7)))),least_upper_bound(X_16,least_upper_bound(X_16,X_7))) )],[refute_0_440,refute_0_441]) ).
cnf(refute_0_443,plain,
least_upper_bound(X_16,inverse(inverse(least_upper_bound(X_16,X_7)))) = least_upper_bound(X_16,X_7),
inference(resolve,[$cnf( $equal(least_upper_bound(X_16,least_upper_bound(X_16,X_7)),least_upper_bound(X_16,X_7)) )],[refute_0_435,refute_0_442]) ).
cnf(refute_0_444,plain,
least_upper_bound(X_7,least_upper_bound(X_16,inverse(inverse(least_upper_bound(X_16,X_7))))) = least_upper_bound(X_7,least_upper_bound(X_16,inverse(inverse(least_upper_bound(X_16,X_7))))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_7,least_upper_bound(X_16,inverse(inverse(least_upper_bound(X_16,X_7))))))]]) ).
cnf(refute_0_445,plain,
( least_upper_bound(X_16,inverse(inverse(least_upper_bound(X_16,X_7)))) != least_upper_bound(X_16,X_7)
| least_upper_bound(X_7,least_upper_bound(X_16,inverse(inverse(least_upper_bound(X_16,X_7))))) != least_upper_bound(X_7,least_upper_bound(X_16,inverse(inverse(least_upper_bound(X_16,X_7)))))
| least_upper_bound(X_7,least_upper_bound(X_16,inverse(inverse(least_upper_bound(X_16,X_7))))) = least_upper_bound(X_7,least_upper_bound(X_16,X_7)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_7,least_upper_bound(X_16,inverse(inverse(least_upper_bound(X_16,X_7))))),least_upper_bound(X_7,least_upper_bound(X_16,inverse(inverse(least_upper_bound(X_16,X_7)))))) ),[1,1],$fot(least_upper_bound(X_16,X_7))]]) ).
cnf(refute_0_446,plain,
( least_upper_bound(X_16,inverse(inverse(least_upper_bound(X_16,X_7)))) != least_upper_bound(X_16,X_7)
| least_upper_bound(X_7,least_upper_bound(X_16,inverse(inverse(least_upper_bound(X_16,X_7))))) = least_upper_bound(X_7,least_upper_bound(X_16,X_7)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_7,least_upper_bound(X_16,inverse(inverse(least_upper_bound(X_16,X_7))))),least_upper_bound(X_7,least_upper_bound(X_16,inverse(inverse(least_upper_bound(X_16,X_7)))))) )],[refute_0_444,refute_0_445]) ).
cnf(refute_0_447,plain,
least_upper_bound(X_7,least_upper_bound(X_16,inverse(inverse(least_upper_bound(X_16,X_7))))) = least_upper_bound(X_7,least_upper_bound(X_16,X_7)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_16,inverse(inverse(least_upper_bound(X_16,X_7)))),least_upper_bound(X_16,X_7)) )],[refute_0_443,refute_0_446]) ).
cnf(refute_0_448,plain,
( least_upper_bound(X_7,least_upper_bound(X_16,X_7)) != least_upper_bound(X_7,X_16)
| least_upper_bound(X_7,least_upper_bound(X_16,inverse(inverse(least_upper_bound(X_16,X_7))))) != least_upper_bound(X_7,least_upper_bound(X_16,X_7))
| least_upper_bound(X_7,least_upper_bound(X_16,inverse(inverse(least_upper_bound(X_16,X_7))))) = least_upper_bound(X_7,X_16) ),
inference(subst,[],[refute_0_171:[bind(X0,$fot(least_upper_bound(X_7,least_upper_bound(X_16,inverse(inverse(least_upper_bound(X_16,X_7))))))),bind(Y0,$fot(least_upper_bound(X_7,least_upper_bound(X_16,X_7)))),bind(Z0,$fot(least_upper_bound(X_7,X_16)))]]) ).
cnf(refute_0_449,plain,
( least_upper_bound(X_7,least_upper_bound(X_16,X_7)) != least_upper_bound(X_7,X_16)
| least_upper_bound(X_7,least_upper_bound(X_16,inverse(inverse(least_upper_bound(X_16,X_7))))) = least_upper_bound(X_7,X_16) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_7,least_upper_bound(X_16,inverse(inverse(least_upper_bound(X_16,X_7))))),least_upper_bound(X_7,least_upper_bound(X_16,X_7))) )],[refute_0_447,refute_0_448]) ).
cnf(refute_0_450,plain,
least_upper_bound(X_7,least_upper_bound(X_16,inverse(inverse(least_upper_bound(X_16,X_7))))) = least_upper_bound(X_7,X_16),
inference(resolve,[$cnf( $equal(least_upper_bound(X_7,least_upper_bound(X_16,X_7)),least_upper_bound(X_7,X_16)) )],[refute_0_387,refute_0_449]) ).
cnf(refute_0_451,plain,
least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7)))) = least_upper_bound(X_7,least_upper_bound(X_16,inverse(inverse(least_upper_bound(X_16,X_7))))),
inference(subst,[],[refute_0_209:[bind(X,$fot(X_7)),bind(Y,$fot(X_16)),bind(Z,$fot(inverse(inverse(least_upper_bound(X_16,X_7)))))]]) ).
cnf(refute_0_452,plain,
( least_upper_bound(X_7,least_upper_bound(X_16,inverse(inverse(least_upper_bound(X_16,X_7))))) != least_upper_bound(X_7,X_16)
| least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7)))) != least_upper_bound(X_7,least_upper_bound(X_16,inverse(inverse(least_upper_bound(X_16,X_7)))))
| least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7)))) = least_upper_bound(X_7,X_16) ),
inference(subst,[],[refute_0_171:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7)))))),bind(Y0,$fot(least_upper_bound(X_7,least_upper_bound(X_16,inverse(inverse(least_upper_bound(X_16,X_7))))))),bind(Z0,$fot(least_upper_bound(X_7,X_16)))]]) ).
cnf(refute_0_453,plain,
( least_upper_bound(X_7,least_upper_bound(X_16,inverse(inverse(least_upper_bound(X_16,X_7))))) != least_upper_bound(X_7,X_16)
| least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7)))) = least_upper_bound(X_7,X_16) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7)))),least_upper_bound(X_7,least_upper_bound(X_16,inverse(inverse(least_upper_bound(X_16,X_7)))))) )],[refute_0_451,refute_0_452]) ).
cnf(refute_0_454,plain,
least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7)))) = least_upper_bound(X_7,X_16),
inference(resolve,[$cnf( $equal(least_upper_bound(X_7,least_upper_bound(X_16,inverse(inverse(least_upper_bound(X_16,X_7))))),least_upper_bound(X_7,X_16)) )],[refute_0_450,refute_0_453]) ).
cnf(refute_0_455,plain,
inverse(least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7))))) = inverse(least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7))))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7))))))]]) ).
cnf(refute_0_456,plain,
( inverse(least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7))))) != inverse(least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7)))))
| least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7)))) != least_upper_bound(X_7,X_16)
| inverse(least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7))))) = inverse(least_upper_bound(X_7,X_16)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7))))),inverse(least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7)))))) ),[1,0],$fot(least_upper_bound(X_7,X_16))]]) ).
cnf(refute_0_457,plain,
( least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7)))) != least_upper_bound(X_7,X_16)
| inverse(least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7))))) = inverse(least_upper_bound(X_7,X_16)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7))))),inverse(least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7)))))) )],[refute_0_455,refute_0_456]) ).
cnf(refute_0_458,plain,
inverse(least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7))))) = inverse(least_upper_bound(X_7,X_16)),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7)))),least_upper_bound(X_7,X_16)) )],[refute_0_454,refute_0_457]) ).
cnf(refute_0_459,plain,
multiply(inverse(least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7))))),least_upper_bound(identity,identity)) = multiply(inverse(least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7))))),least_upper_bound(identity,identity)),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7))))),least_upper_bound(identity,identity)))]]) ).
cnf(refute_0_460,plain,
( multiply(inverse(least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7))))),least_upper_bound(identity,identity)) != multiply(inverse(least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7))))),least_upper_bound(identity,identity))
| inverse(least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7))))) != inverse(least_upper_bound(X_7,X_16))
| multiply(inverse(least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7))))),least_upper_bound(identity,identity)) = multiply(inverse(least_upper_bound(X_7,X_16)),least_upper_bound(identity,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7))))),least_upper_bound(identity,identity)),multiply(inverse(least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7))))),least_upper_bound(identity,identity))) ),[1,0],$fot(inverse(least_upper_bound(X_7,X_16)))]]) ).
cnf(refute_0_461,plain,
( inverse(least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7))))) != inverse(least_upper_bound(X_7,X_16))
| multiply(inverse(least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7))))),least_upper_bound(identity,identity)) = multiply(inverse(least_upper_bound(X_7,X_16)),least_upper_bound(identity,identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7))))),least_upper_bound(identity,identity)),multiply(inverse(least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7))))),least_upper_bound(identity,identity))) )],[refute_0_459,refute_0_460]) ).
cnf(refute_0_462,plain,
multiply(inverse(least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7))))),least_upper_bound(identity,identity)) = multiply(inverse(least_upper_bound(X_7,X_16)),least_upper_bound(identity,identity)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7))))),inverse(least_upper_bound(X_7,X_16))) )],[refute_0_458,refute_0_461]) ).
cnf(refute_0_463,plain,
( multiply(inverse(least_upper_bound(X_7,X_16)),least_upper_bound(identity,identity)) != multiply(inverse(least_upper_bound(X_7,X_16)),identity)
| multiply(inverse(least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7))))),least_upper_bound(identity,identity)) != multiply(inverse(least_upper_bound(X_7,X_16)),least_upper_bound(identity,identity))
| multiply(inverse(least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7))))),least_upper_bound(identity,identity)) = multiply(inverse(least_upper_bound(X_7,X_16)),identity) ),
inference(subst,[],[refute_0_171:[bind(X0,$fot(multiply(inverse(least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7))))),least_upper_bound(identity,identity)))),bind(Y0,$fot(multiply(inverse(least_upper_bound(X_7,X_16)),least_upper_bound(identity,identity)))),bind(Z0,$fot(multiply(inverse(least_upper_bound(X_7,X_16)),identity)))]]) ).
cnf(refute_0_464,plain,
( multiply(inverse(least_upper_bound(X_7,X_16)),least_upper_bound(identity,identity)) != multiply(inverse(least_upper_bound(X_7,X_16)),identity)
| multiply(inverse(least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7))))),least_upper_bound(identity,identity)) = multiply(inverse(least_upper_bound(X_7,X_16)),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7))))),least_upper_bound(identity,identity)),multiply(inverse(least_upper_bound(X_7,X_16)),least_upper_bound(identity,identity))) )],[refute_0_462,refute_0_463]) ).
cnf(refute_0_465,plain,
multiply(inverse(least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7))))),least_upper_bound(identity,identity)) = multiply(inverse(least_upper_bound(X_7,X_16)),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_7,X_16)),least_upper_bound(identity,identity)),multiply(inverse(least_upper_bound(X_7,X_16)),identity)) )],[refute_0_427,refute_0_464]) ).
cnf(refute_0_466,plain,
( multiply(inverse(least_upper_bound(X_7,X_16)),identity) != inverse(least_upper_bound(X_7,X_16))
| multiply(inverse(least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7))))),least_upper_bound(identity,identity)) != multiply(inverse(least_upper_bound(X_7,X_16)),identity)
| multiply(inverse(least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7))))),least_upper_bound(identity,identity)) = inverse(least_upper_bound(X_7,X_16)) ),
inference(subst,[],[refute_0_171:[bind(X0,$fot(multiply(inverse(least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7))))),least_upper_bound(identity,identity)))),bind(Y0,$fot(multiply(inverse(least_upper_bound(X_7,X_16)),identity))),bind(Z0,$fot(inverse(least_upper_bound(X_7,X_16))))]]) ).
cnf(refute_0_467,plain,
( multiply(inverse(least_upper_bound(X_7,X_16)),identity) != inverse(least_upper_bound(X_7,X_16))
| multiply(inverse(least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7))))),least_upper_bound(identity,identity)) = inverse(least_upper_bound(X_7,X_16)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7))))),least_upper_bound(identity,identity)),multiply(inverse(least_upper_bound(X_7,X_16)),identity)) )],[refute_0_465,refute_0_466]) ).
cnf(refute_0_468,plain,
multiply(inverse(least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7))))),least_upper_bound(identity,identity)) = inverse(least_upper_bound(X_7,X_16)),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_7,X_16)),identity),inverse(least_upper_bound(X_7,X_16))) )],[refute_0_422,refute_0_467]) ).
cnf(refute_0_469,plain,
( multiply(inverse(least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7))))),least_upper_bound(identity,identity)) != inverse(least_upper_bound(X_7,X_16))
| inverse(least_upper_bound(X_16,X_7)) != multiply(inverse(least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7))))),least_upper_bound(identity,identity))
| inverse(least_upper_bound(X_16,X_7)) = inverse(least_upper_bound(X_7,X_16)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_16,X_7)),multiply(inverse(least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7))))),least_upper_bound(identity,identity))) ),[1],$fot(inverse(least_upper_bound(X_7,X_16)))]]) ).
cnf(refute_0_470,plain,
( inverse(least_upper_bound(X_16,X_7)) != multiply(inverse(least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7))))),least_upper_bound(identity,identity))
| inverse(least_upper_bound(X_16,X_7)) = inverse(least_upper_bound(X_7,X_16)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7))))),least_upper_bound(identity,identity)),inverse(least_upper_bound(X_7,X_16))) )],[refute_0_468,refute_0_469]) ).
cnf(refute_0_471,plain,
inverse(least_upper_bound(X_16,X_7)) = inverse(least_upper_bound(X_7,X_16)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_16,X_7)),multiply(inverse(least_upper_bound(least_upper_bound(X_7,X_16),inverse(inverse(least_upper_bound(X_16,X_7))))),least_upper_bound(identity,identity))) )],[refute_0_421,refute_0_470]) ).
cnf(refute_0_472,plain,
( inverse(least_upper_bound(X_16,X_7)) != inverse(least_upper_bound(X_7,X_16))
| inverse(least_upper_bound(X_7,X_16)) = inverse(least_upper_bound(X_16,X_7)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(inverse(least_upper_bound(X_16,X_7)))),bind(Y0,$fot(inverse(least_upper_bound(X_7,X_16))))]]) ).
cnf(refute_0_473,plain,
inverse(least_upper_bound(X_7,X_16)) = inverse(least_upper_bound(X_16,X_7)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_16,X_7)),inverse(least_upper_bound(X_7,X_16))) )],[refute_0_471,refute_0_472]) ).
cnf(refute_0_474,plain,
inverse(least_upper_bound(inverse(least_upper_bound(a,X_142)),inverse(b))) = inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(a,X_142)))),
inference(subst,[],[refute_0_473:[bind(X_16,$fot(inverse(b))),bind(X_7,$fot(inverse(least_upper_bound(a,X_142))))]]) ).
cnf(refute_0_475,plain,
multiply(inverse(least_upper_bound(inverse(least_upper_bound(a,X_142)),inverse(b))),identity) = inverse(least_upper_bound(inverse(least_upper_bound(a,X_142)),inverse(b))),
inference(subst,[],[refute_0_39:[bind(X_48,$fot(inverse(least_upper_bound(inverse(least_upper_bound(a,X_142)),inverse(b)))))]]) ).
cnf(refute_0_476,plain,
( multiply(inverse(least_upper_bound(inverse(least_upper_bound(a,X_142)),inverse(b))),identity) != inverse(least_upper_bound(inverse(least_upper_bound(a,X_142)),inverse(b)))
| inverse(least_upper_bound(inverse(least_upper_bound(a,X_142)),inverse(b))) != inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(a,X_142))))
| multiply(inverse(least_upper_bound(inverse(least_upper_bound(a,X_142)),inverse(b))),identity) = inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(a,X_142)))) ),
inference(subst,[],[refute_0_171:[bind(X0,$fot(multiply(inverse(least_upper_bound(inverse(least_upper_bound(a,X_142)),inverse(b))),identity))),bind(Y0,$fot(inverse(least_upper_bound(inverse(least_upper_bound(a,X_142)),inverse(b))))),bind(Z0,$fot(inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(a,X_142))))))]]) ).
cnf(refute_0_477,plain,
( inverse(least_upper_bound(inverse(least_upper_bound(a,X_142)),inverse(b))) != inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(a,X_142))))
| multiply(inverse(least_upper_bound(inverse(least_upper_bound(a,X_142)),inverse(b))),identity) = inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(a,X_142)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(least_upper_bound(a,X_142)),inverse(b))),identity),inverse(least_upper_bound(inverse(least_upper_bound(a,X_142)),inverse(b)))) )],[refute_0_475,refute_0_476]) ).
cnf(refute_0_478,plain,
multiply(inverse(least_upper_bound(inverse(least_upper_bound(a,X_142)),inverse(b))),identity) = inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(a,X_142)))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(least_upper_bound(a,X_142)),inverse(b))),inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(a,X_142))))) )],[refute_0_474,refute_0_477]) ).
cnf(refute_0_479,plain,
( multiply(inverse(least_upper_bound(inverse(least_upper_bound(a,X_142)),inverse(b))),identity) != inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(a,X_142))))
| b != multiply(inverse(least_upper_bound(inverse(least_upper_bound(a,X_142)),inverse(b))),identity)
| b = inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(a,X_142)))) ),
introduced(tautology,[equality,[$cnf( $equal(b,multiply(inverse(least_upper_bound(inverse(least_upper_bound(a,X_142)),inverse(b))),identity)) ),[1],$fot(inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(a,X_142)))))]]) ).
cnf(refute_0_480,plain,
( b != multiply(inverse(least_upper_bound(inverse(least_upper_bound(a,X_142)),inverse(b))),identity)
| b = inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(a,X_142)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(least_upper_bound(a,X_142)),inverse(b))),identity),inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(a,X_142))))) )],[refute_0_478,refute_0_479]) ).
cnf(refute_0_481,plain,
b = inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(a,X_142)))),
inference(resolve,[$cnf( $equal(b,multiply(inverse(least_upper_bound(inverse(least_upper_bound(a,X_142)),inverse(b))),identity)) )],[refute_0_371,refute_0_480]) ).
cnf(refute_0_482,plain,
b = inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(a,greatest_lower_bound(X_11,a))))),
inference(subst,[],[refute_0_481:[bind(X_142,$fot(greatest_lower_bound(X_11,a)))]]) ).
cnf(refute_0_483,plain,
least_upper_bound(a,greatest_lower_bound(X_11,a)) = a,
inference(subst,[],[refute_0_74:[bind(X_10,$fot(a))]]) ).
cnf(refute_0_484,plain,
( b != inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(a,greatest_lower_bound(X_11,a)))))
| least_upper_bound(a,greatest_lower_bound(X_11,a)) != a
| b = inverse(least_upper_bound(inverse(b),inverse(a))) ),
introduced(tautology,[equality,[$cnf( $equal(b,inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(a,greatest_lower_bound(X_11,a)))))) ),[1,0,1,0],$fot(a)]]) ).
cnf(refute_0_485,plain,
( b != inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(a,greatest_lower_bound(X_11,a)))))
| b = inverse(least_upper_bound(inverse(b),inverse(a))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,greatest_lower_bound(X_11,a)),a) )],[refute_0_483,refute_0_484]) ).
cnf(refute_0_486,plain,
b = inverse(least_upper_bound(inverse(b),inverse(a))),
inference(resolve,[$cnf( $equal(b,inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(a,greatest_lower_bound(X_11,a)))))) )],[refute_0_482,refute_0_485]) ).
cnf(refute_0_487,plain,
inverse(least_upper_bound(inverse(b),inverse(a))) = inverse(least_upper_bound(inverse(a),inverse(b))),
inference(subst,[],[refute_0_473:[bind(X_16,$fot(inverse(a))),bind(X_7,$fot(inverse(b)))]]) ).
cnf(refute_0_488,plain,
( b != inverse(least_upper_bound(inverse(b),inverse(a)))
| inverse(least_upper_bound(inverse(b),inverse(a))) != inverse(least_upper_bound(inverse(a),inverse(b)))
| b = inverse(least_upper_bound(inverse(a),inverse(b))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(b,inverse(least_upper_bound(inverse(a),inverse(b)))) ),[0],$fot(inverse(least_upper_bound(inverse(b),inverse(a))))]]) ).
cnf(refute_0_489,plain,
( b != inverse(least_upper_bound(inverse(b),inverse(a)))
| b = inverse(least_upper_bound(inverse(a),inverse(b))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(b),inverse(a))),inverse(least_upper_bound(inverse(a),inverse(b)))) )],[refute_0_487,refute_0_488]) ).
cnf(refute_0_490,plain,
b = inverse(least_upper_bound(inverse(a),inverse(b))),
inference(resolve,[$cnf( $equal(b,inverse(least_upper_bound(inverse(b),inverse(a)))) )],[refute_0_486,refute_0_489]) ).
cnf(refute_0_491,plain,
( b != inverse(least_upper_bound(inverse(a),inverse(b)))
| inverse(least_upper_bound(inverse(a),inverse(b))) = b ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(b)),bind(Y0,$fot(inverse(least_upper_bound(inverse(a),inverse(b)))))]]) ).
cnf(refute_0_492,plain,
inverse(least_upper_bound(inverse(a),inverse(b))) = b,
inference(resolve,[$cnf( $equal(b,inverse(least_upper_bound(inverse(a),inverse(b)))) )],[refute_0_490,refute_0_491]) ).
cnf(refute_0_493,plain,
( inverse(inverse(least_upper_bound(inverse(a),inverse(b)))) != least_upper_bound(inverse(a),inverse(b))
| inverse(least_upper_bound(inverse(a),inverse(b))) != b
| inverse(b) = least_upper_bound(inverse(a),inverse(b)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(least_upper_bound(inverse(a),inverse(b)))),least_upper_bound(inverse(a),inverse(b))) ),[0,0],$fot(b)]]) ).
cnf(refute_0_494,plain,
( inverse(inverse(least_upper_bound(inverse(a),inverse(b)))) != least_upper_bound(inverse(a),inverse(b))
| inverse(b) = least_upper_bound(inverse(a),inverse(b)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(a),inverse(b))),b) )],[refute_0_492,refute_0_493]) ).
cnf(refute_0_495,plain,
inverse(b) = least_upper_bound(inverse(a),inverse(b)),
inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(inverse(a),inverse(b)))),least_upper_bound(inverse(a),inverse(b))) )],[refute_0_44,refute_0_494]) ).
cnf(refute_0_496,plain,
( inverse(b) != least_upper_bound(inverse(a),inverse(b))
| least_upper_bound(inverse(a),inverse(b)) = inverse(b) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(inverse(b))),bind(Y0,$fot(least_upper_bound(inverse(a),inverse(b))))]]) ).
cnf(refute_0_497,plain,
least_upper_bound(inverse(a),inverse(b)) = inverse(b),
inference(resolve,[$cnf( $equal(inverse(b),least_upper_bound(inverse(a),inverse(b))) )],[refute_0_495,refute_0_496]) ).
cnf(refute_0_498,plain,
( greatest_lower_bound(inverse(a),least_upper_bound(inverse(a),inverse(b))) != inverse(a)
| least_upper_bound(inverse(a),inverse(b)) != inverse(b)
| greatest_lower_bound(inverse(a),inverse(b)) = inverse(a) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(inverse(a),least_upper_bound(inverse(a),inverse(b))),inverse(a)) ),[0,1],$fot(inverse(b))]]) ).
cnf(refute_0_499,plain,
( greatest_lower_bound(inverse(a),least_upper_bound(inverse(a),inverse(b))) != inverse(a)
| greatest_lower_bound(inverse(a),inverse(b)) = inverse(a) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(a),inverse(b)),inverse(b)) )],[refute_0_497,refute_0_498]) ).
cnf(refute_0_500,plain,
greatest_lower_bound(inverse(a),inverse(b)) = inverse(a),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(a),least_upper_bound(inverse(a),inverse(b))),inverse(a)) )],[refute_0_0,refute_0_499]) ).
cnf(refute_0_501,plain,
$false,
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(a),inverse(b)),inverse(a)) )],[refute_0_500,prove_p39c]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : GRP190-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.11/0.14 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n022.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 15:46:03 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 2.54/2.74 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.54/2.74
% 2.54/2.74 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.54/2.78
%------------------------------------------------------------------------------