TSTP Solution File: GRP167-4 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP167-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 10:37:12 EDT 2022
% Result : Unsatisfiable 56.85s 57.03s
% Output : CNFRefutation 57.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 97
% Number of leaves : 511
% Syntax : Number of clauses : 2382 (1204 unt; 0 nHn;1146 RR)
% Number of literals : 4075 (4074 equ;1696 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 4810 ( 47 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
multiply(identity,X) = X ).
cnf(left_inverse,axiom,
multiply(inverse(X),X) = identity ).
cnf(associativity,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ).
cnf(symmetry_of_glb,axiom,
greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ).
cnf(symmetry_of_lub,axiom,
least_upper_bound(X,Y) = least_upper_bound(Y,X) ).
cnf(associativity_of_glb,axiom,
greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) ).
cnf(associativity_of_lub,axiom,
least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) ).
cnf(idempotence_of_lub,axiom,
least_upper_bound(X,X) = X ).
cnf(idempotence_of_gld,axiom,
greatest_lower_bound(X,X) = X ).
cnf(lub_absorbtion,axiom,
least_upper_bound(X,greatest_lower_bound(X,Y)) = X ).
cnf(glb_absorbtion,axiom,
greatest_lower_bound(X,least_upper_bound(X,Y)) = X ).
cnf(monotony_lub1,axiom,
multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ).
cnf(monotony_glb1,axiom,
multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)) ).
cnf(monotony_lub2,axiom,
multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) ).
cnf(monotony_glb2,axiom,
multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) ).
cnf(p19_1,axiom,
inverse(identity) = identity ).
cnf(p19_2,axiom,
inverse(inverse(X)) = X ).
cnf(p19_3,axiom,
inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) ).
cnf(prove_p19,negated_conjecture,
a != multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)) ).
cnf(refute_0_0,plain,
multiply(X_55,least_upper_bound(X_56,identity)) = least_upper_bound(multiply(X_55,X_56),multiply(X_55,identity)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(X_55)),bind(Y,$fot(X_56)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_1,plain,
inverse(multiply(identity,X_24)) = multiply(inverse(X_24),inverse(identity)),
inference(subst,[],[p19_3:[bind(X,$fot(identity)),bind(Y,$fot(X_24))]]) ).
cnf(refute_0_2,plain,
( inverse(multiply(identity,X_24)) != multiply(inverse(X_24),inverse(identity))
| inverse(identity) != identity
| inverse(multiply(identity,X_24)) = multiply(inverse(X_24),identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(identity,X_24)),multiply(inverse(X_24),inverse(identity))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_3,plain,
( inverse(multiply(identity,X_24)) != multiply(inverse(X_24),inverse(identity))
| inverse(multiply(identity,X_24)) = multiply(inverse(X_24),identity) ),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[p19_1,refute_0_2]) ).
cnf(refute_0_4,plain,
inverse(multiply(identity,X_24)) = multiply(inverse(X_24),identity),
inference(resolve,[$cnf( $equal(inverse(multiply(identity,X_24)),multiply(inverse(X_24),inverse(identity))) )],[refute_0_1,refute_0_3]) ).
cnf(refute_0_5,plain,
multiply(identity,X_24) = X_24,
inference(subst,[],[left_identity:[bind(X,$fot(X_24))]]) ).
cnf(refute_0_6,plain,
inverse(multiply(identity,X_24)) = inverse(multiply(identity,X_24)),
introduced(tautology,[refl,[$fot(inverse(multiply(identity,X_24)))]]) ).
cnf(refute_0_7,plain,
( multiply(identity,X_24) != X_24
| inverse(multiply(identity,X_24)) != inverse(multiply(identity,X_24))
| inverse(multiply(identity,X_24)) = inverse(X_24) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(identity,X_24)),inverse(multiply(identity,X_24))) ),[1,0],$fot(X_24)]]) ).
cnf(refute_0_8,plain,
( multiply(identity,X_24) != X_24
| inverse(multiply(identity,X_24)) = inverse(X_24) ),
inference(resolve,[$cnf( $equal(inverse(multiply(identity,X_24)),inverse(multiply(identity,X_24))) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
inverse(multiply(identity,X_24)) = inverse(X_24),
inference(resolve,[$cnf( $equal(multiply(identity,X_24),X_24) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
( inverse(multiply(identity,X_24)) != multiply(inverse(X_24),identity)
| inverse(multiply(identity,X_24)) != inverse(X_24)
| inverse(X_24) = multiply(inverse(X_24),identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(identity,X_24)),multiply(inverse(X_24),identity)) ),[0],$fot(inverse(X_24))]]) ).
cnf(refute_0_11,plain,
( inverse(multiply(identity,X_24)) != multiply(inverse(X_24),identity)
| inverse(X_24) = multiply(inverse(X_24),identity) ),
inference(resolve,[$cnf( $equal(inverse(multiply(identity,X_24)),inverse(X_24)) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
inverse(X_24) = multiply(inverse(X_24),identity),
inference(resolve,[$cnf( $equal(inverse(multiply(identity,X_24)),multiply(inverse(X_24),identity)) )],[refute_0_4,refute_0_11]) ).
cnf(refute_0_13,plain,
inverse(inverse(X)) = multiply(inverse(inverse(X)),identity),
inference(subst,[],[refute_0_12:[bind(X_24,$fot(inverse(X)))]]) ).
cnf(refute_0_14,plain,
( inverse(inverse(X)) != X
| inverse(inverse(X)) != multiply(inverse(inverse(X)),identity)
| inverse(inverse(X)) = multiply(X,identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X)),multiply(inverse(inverse(X)),identity)) ),[1,0],$fot(X)]]) ).
cnf(refute_0_15,plain,
( inverse(inverse(X)) != multiply(inverse(inverse(X)),identity)
| inverse(inverse(X)) = multiply(X,identity) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p19_2,refute_0_14]) ).
cnf(refute_0_16,plain,
inverse(inverse(X)) = multiply(X,identity),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),multiply(inverse(inverse(X)),identity)) )],[refute_0_13,refute_0_15]) ).
cnf(refute_0_17,plain,
( inverse(inverse(X)) != X
| inverse(inverse(X)) != multiply(X,identity)
| X = multiply(X,identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X)),multiply(X,identity)) ),[0],$fot(X)]]) ).
cnf(refute_0_18,plain,
( inverse(inverse(X)) != multiply(X,identity)
| X = multiply(X,identity) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p19_2,refute_0_17]) ).
cnf(refute_0_19,plain,
X = multiply(X,identity),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),multiply(X,identity)) )],[refute_0_16,refute_0_18]) ).
cnf(refute_0_20,plain,
X_55 = multiply(X_55,identity),
inference(subst,[],[refute_0_19:[bind(X,$fot(X_55))]]) ).
cnf(refute_0_21,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_22,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_23,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
( X_55 != multiply(X_55,identity)
| multiply(X_55,identity) = X_55 ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(X_55)),bind(Y0,$fot(multiply(X_55,identity)))]]) ).
cnf(refute_0_25,plain,
multiply(X_55,identity) = X_55,
inference(resolve,[$cnf( $equal(X_55,multiply(X_55,identity)) )],[refute_0_20,refute_0_24]) ).
cnf(refute_0_26,plain,
( multiply(X_55,identity) != X_55
| multiply(X_55,least_upper_bound(X_56,identity)) != least_upper_bound(multiply(X_55,X_56),multiply(X_55,identity))
| multiply(X_55,least_upper_bound(X_56,identity)) = least_upper_bound(multiply(X_55,X_56),X_55) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_55,least_upper_bound(X_56,identity)),least_upper_bound(multiply(X_55,X_56),multiply(X_55,identity))) ),[1,1],$fot(X_55)]]) ).
cnf(refute_0_27,plain,
( multiply(X_55,least_upper_bound(X_56,identity)) != least_upper_bound(multiply(X_55,X_56),multiply(X_55,identity))
| multiply(X_55,least_upper_bound(X_56,identity)) = least_upper_bound(multiply(X_55,X_56),X_55) ),
inference(resolve,[$cnf( $equal(multiply(X_55,identity),X_55) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
multiply(X_55,least_upper_bound(X_56,identity)) = least_upper_bound(multiply(X_55,X_56),X_55),
inference(resolve,[$cnf( $equal(multiply(X_55,least_upper_bound(X_56,identity)),least_upper_bound(multiply(X_55,X_56),multiply(X_55,identity))) )],[refute_0_0,refute_0_27]) ).
cnf(refute_0_29,plain,
( least_upper_bound(X,Y) != least_upper_bound(Y,X)
| least_upper_bound(Y,X) = least_upper_bound(X,Y) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(least_upper_bound(X,Y))),bind(Y0,$fot(least_upper_bound(Y,X)))]]) ).
cnf(refute_0_30,plain,
least_upper_bound(Y,X) = least_upper_bound(X,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(X,Y),least_upper_bound(Y,X)) )],[symmetry_of_lub,refute_0_29]) ).
cnf(refute_0_31,plain,
least_upper_bound(multiply(X_55,X_56),X_55) = least_upper_bound(X_55,multiply(X_55,X_56)),
inference(subst,[],[refute_0_30:[bind(X,$fot(X_55)),bind(Y,$fot(multiply(X_55,X_56)))]]) ).
cnf(refute_0_32,plain,
( multiply(X_55,least_upper_bound(X_56,identity)) != least_upper_bound(multiply(X_55,X_56),X_55)
| least_upper_bound(multiply(X_55,X_56),X_55) != least_upper_bound(X_55,multiply(X_55,X_56))
| multiply(X_55,least_upper_bound(X_56,identity)) = least_upper_bound(X_55,multiply(X_55,X_56)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_55,least_upper_bound(X_56,identity)),least_upper_bound(X_55,multiply(X_55,X_56))) ),[0],$fot(least_upper_bound(multiply(X_55,X_56),X_55))]]) ).
cnf(refute_0_33,plain,
( multiply(X_55,least_upper_bound(X_56,identity)) != least_upper_bound(multiply(X_55,X_56),X_55)
| multiply(X_55,least_upper_bound(X_56,identity)) = least_upper_bound(X_55,multiply(X_55,X_56)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_55,X_56),X_55),least_upper_bound(X_55,multiply(X_55,X_56))) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
multiply(X_55,least_upper_bound(X_56,identity)) = least_upper_bound(X_55,multiply(X_55,X_56)),
inference(resolve,[$cnf( $equal(multiply(X_55,least_upper_bound(X_56,identity)),least_upper_bound(multiply(X_55,X_56),X_55)) )],[refute_0_28,refute_0_33]) ).
cnf(refute_0_35,plain,
multiply(greatest_lower_bound(X_56,identity),least_upper_bound(X_56,identity)) = least_upper_bound(greatest_lower_bound(X_56,identity),multiply(greatest_lower_bound(X_56,identity),X_56)),
inference(subst,[],[refute_0_34:[bind(X_55,$fot(greatest_lower_bound(X_56,identity)))]]) ).
cnf(refute_0_36,plain,
multiply(greatest_lower_bound(X_87,identity),X_86) = greatest_lower_bound(multiply(X_87,X_86),multiply(identity,X_86)),
inference(subst,[],[monotony_glb2:[bind(X,$fot(X_86)),bind(Y,$fot(X_87)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_37,plain,
multiply(identity,X_86) = X_86,
inference(subst,[],[left_identity:[bind(X,$fot(X_86))]]) ).
cnf(refute_0_38,plain,
( multiply(greatest_lower_bound(X_87,identity),X_86) != greatest_lower_bound(multiply(X_87,X_86),multiply(identity,X_86))
| multiply(identity,X_86) != X_86
| multiply(greatest_lower_bound(X_87,identity),X_86) = greatest_lower_bound(multiply(X_87,X_86),X_86) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_87,identity),X_86),greatest_lower_bound(multiply(X_87,X_86),multiply(identity,X_86))) ),[1,1],$fot(X_86)]]) ).
cnf(refute_0_39,plain,
( multiply(greatest_lower_bound(X_87,identity),X_86) != greatest_lower_bound(multiply(X_87,X_86),multiply(identity,X_86))
| multiply(greatest_lower_bound(X_87,identity),X_86) = greatest_lower_bound(multiply(X_87,X_86),X_86) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_86),X_86) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
multiply(greatest_lower_bound(X_87,identity),X_86) = greatest_lower_bound(multiply(X_87,X_86),X_86),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_87,identity),X_86),greatest_lower_bound(multiply(X_87,X_86),multiply(identity,X_86))) )],[refute_0_36,refute_0_39]) ).
cnf(refute_0_41,plain,
greatest_lower_bound(X_22,X_21) = greatest_lower_bound(X_21,X_22),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_22)),bind(Y,$fot(X_21))]]) ).
cnf(refute_0_42,plain,
greatest_lower_bound(multiply(X_87,X_86),X_86) = greatest_lower_bound(X_86,multiply(X_87,X_86)),
inference(subst,[],[refute_0_41:[bind(X_21,$fot(X_86)),bind(X_22,$fot(multiply(X_87,X_86)))]]) ).
cnf(refute_0_43,plain,
( multiply(greatest_lower_bound(X_87,identity),X_86) != greatest_lower_bound(multiply(X_87,X_86),X_86)
| greatest_lower_bound(multiply(X_87,X_86),X_86) != greatest_lower_bound(X_86,multiply(X_87,X_86))
| multiply(greatest_lower_bound(X_87,identity),X_86) = greatest_lower_bound(X_86,multiply(X_87,X_86)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_87,identity),X_86),greatest_lower_bound(X_86,multiply(X_87,X_86))) ),[0],$fot(greatest_lower_bound(multiply(X_87,X_86),X_86))]]) ).
cnf(refute_0_44,plain,
( multiply(greatest_lower_bound(X_87,identity),X_86) != greatest_lower_bound(multiply(X_87,X_86),X_86)
| multiply(greatest_lower_bound(X_87,identity),X_86) = greatest_lower_bound(X_86,multiply(X_87,X_86)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_87,X_86),X_86),greatest_lower_bound(X_86,multiply(X_87,X_86))) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
multiply(greatest_lower_bound(X_87,identity),X_86) = greatest_lower_bound(X_86,multiply(X_87,X_86)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_87,identity),X_86),greatest_lower_bound(multiply(X_87,X_86),X_86)) )],[refute_0_40,refute_0_44]) ).
cnf(refute_0_46,plain,
multiply(greatest_lower_bound(X_87,identity),X_87) = greatest_lower_bound(X_87,multiply(X_87,X_87)),
inference(subst,[],[refute_0_45:[bind(X_86,$fot(X_87))]]) ).
cnf(refute_0_47,plain,
multiply(X_67,greatest_lower_bound(X_68,identity)) = greatest_lower_bound(multiply(X_67,X_68),multiply(X_67,identity)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(X_67)),bind(Y,$fot(X_68)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_48,plain,
X_67 = multiply(X_67,identity),
inference(subst,[],[refute_0_19:[bind(X,$fot(X_67))]]) ).
cnf(refute_0_49,plain,
( X_67 != multiply(X_67,identity)
| multiply(X_67,identity) = X_67 ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(X_67)),bind(Y0,$fot(multiply(X_67,identity)))]]) ).
cnf(refute_0_50,plain,
multiply(X_67,identity) = X_67,
inference(resolve,[$cnf( $equal(X_67,multiply(X_67,identity)) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
( multiply(X_67,greatest_lower_bound(X_68,identity)) != greatest_lower_bound(multiply(X_67,X_68),multiply(X_67,identity))
| multiply(X_67,identity) != X_67
| multiply(X_67,greatest_lower_bound(X_68,identity)) = greatest_lower_bound(multiply(X_67,X_68),X_67) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_67,greatest_lower_bound(X_68,identity)),greatest_lower_bound(multiply(X_67,X_68),multiply(X_67,identity))) ),[1,1],$fot(X_67)]]) ).
cnf(refute_0_52,plain,
( multiply(X_67,greatest_lower_bound(X_68,identity)) != greatest_lower_bound(multiply(X_67,X_68),multiply(X_67,identity))
| multiply(X_67,greatest_lower_bound(X_68,identity)) = greatest_lower_bound(multiply(X_67,X_68),X_67) ),
inference(resolve,[$cnf( $equal(multiply(X_67,identity),X_67) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
multiply(X_67,greatest_lower_bound(X_68,identity)) = greatest_lower_bound(multiply(X_67,X_68),X_67),
inference(resolve,[$cnf( $equal(multiply(X_67,greatest_lower_bound(X_68,identity)),greatest_lower_bound(multiply(X_67,X_68),multiply(X_67,identity))) )],[refute_0_47,refute_0_52]) ).
cnf(refute_0_54,plain,
greatest_lower_bound(multiply(X_67,X_68),X_67) = greatest_lower_bound(X_67,multiply(X_67,X_68)),
inference(subst,[],[refute_0_41:[bind(X_21,$fot(X_67)),bind(X_22,$fot(multiply(X_67,X_68)))]]) ).
cnf(refute_0_55,plain,
( multiply(X_67,greatest_lower_bound(X_68,identity)) != greatest_lower_bound(multiply(X_67,X_68),X_67)
| greatest_lower_bound(multiply(X_67,X_68),X_67) != greatest_lower_bound(X_67,multiply(X_67,X_68))
| multiply(X_67,greatest_lower_bound(X_68,identity)) = greatest_lower_bound(X_67,multiply(X_67,X_68)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_67,greatest_lower_bound(X_68,identity)),greatest_lower_bound(X_67,multiply(X_67,X_68))) ),[0],$fot(greatest_lower_bound(multiply(X_67,X_68),X_67))]]) ).
cnf(refute_0_56,plain,
( multiply(X_67,greatest_lower_bound(X_68,identity)) != greatest_lower_bound(multiply(X_67,X_68),X_67)
| multiply(X_67,greatest_lower_bound(X_68,identity)) = greatest_lower_bound(X_67,multiply(X_67,X_68)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_67,X_68),X_67),greatest_lower_bound(X_67,multiply(X_67,X_68))) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
multiply(X_67,greatest_lower_bound(X_68,identity)) = greatest_lower_bound(X_67,multiply(X_67,X_68)),
inference(resolve,[$cnf( $equal(multiply(X_67,greatest_lower_bound(X_68,identity)),greatest_lower_bound(multiply(X_67,X_68),X_67)) )],[refute_0_53,refute_0_56]) ).
cnf(refute_0_58,plain,
multiply(X_87,greatest_lower_bound(X_87,identity)) = greatest_lower_bound(X_87,multiply(X_87,X_87)),
inference(subst,[],[refute_0_57:[bind(X_67,$fot(X_87)),bind(X_68,$fot(X_87))]]) ).
cnf(refute_0_59,plain,
( multiply(X_87,greatest_lower_bound(X_87,identity)) != greatest_lower_bound(X_87,multiply(X_87,X_87))
| greatest_lower_bound(X_87,multiply(X_87,X_87)) = multiply(X_87,greatest_lower_bound(X_87,identity)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(multiply(X_87,greatest_lower_bound(X_87,identity)))),bind(Y0,$fot(greatest_lower_bound(X_87,multiply(X_87,X_87))))]]) ).
cnf(refute_0_60,plain,
greatest_lower_bound(X_87,multiply(X_87,X_87)) = multiply(X_87,greatest_lower_bound(X_87,identity)),
inference(resolve,[$cnf( $equal(multiply(X_87,greatest_lower_bound(X_87,identity)),greatest_lower_bound(X_87,multiply(X_87,X_87))) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
( multiply(greatest_lower_bound(X_87,identity),X_87) != greatest_lower_bound(X_87,multiply(X_87,X_87))
| greatest_lower_bound(X_87,multiply(X_87,X_87)) != multiply(X_87,greatest_lower_bound(X_87,identity))
| multiply(greatest_lower_bound(X_87,identity),X_87) = multiply(X_87,greatest_lower_bound(X_87,identity)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_87,identity),X_87),multiply(X_87,greatest_lower_bound(X_87,identity))) ),[0],$fot(greatest_lower_bound(X_87,multiply(X_87,X_87)))]]) ).
cnf(refute_0_62,plain,
( multiply(greatest_lower_bound(X_87,identity),X_87) != greatest_lower_bound(X_87,multiply(X_87,X_87))
| multiply(greatest_lower_bound(X_87,identity),X_87) = multiply(X_87,greatest_lower_bound(X_87,identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_87,multiply(X_87,X_87)),multiply(X_87,greatest_lower_bound(X_87,identity))) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
multiply(greatest_lower_bound(X_87,identity),X_87) = multiply(X_87,greatest_lower_bound(X_87,identity)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_87,identity),X_87),greatest_lower_bound(X_87,multiply(X_87,X_87))) )],[refute_0_46,refute_0_62]) ).
cnf(refute_0_64,plain,
multiply(greatest_lower_bound(X_56,identity),X_56) = multiply(X_56,greatest_lower_bound(X_56,identity)),
inference(subst,[],[refute_0_63:[bind(X_87,$fot(X_56))]]) ).
cnf(refute_0_65,plain,
( multiply(greatest_lower_bound(X_56,identity),X_56) != multiply(X_56,greatest_lower_bound(X_56,identity))
| multiply(greatest_lower_bound(X_56,identity),least_upper_bound(X_56,identity)) != least_upper_bound(greatest_lower_bound(X_56,identity),multiply(greatest_lower_bound(X_56,identity),X_56))
| multiply(greatest_lower_bound(X_56,identity),least_upper_bound(X_56,identity)) = least_upper_bound(greatest_lower_bound(X_56,identity),multiply(X_56,greatest_lower_bound(X_56,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_56,identity),least_upper_bound(X_56,identity)),least_upper_bound(greatest_lower_bound(X_56,identity),multiply(greatest_lower_bound(X_56,identity),X_56))) ),[1,1],$fot(multiply(X_56,greatest_lower_bound(X_56,identity)))]]) ).
cnf(refute_0_66,plain,
( multiply(greatest_lower_bound(X_56,identity),least_upper_bound(X_56,identity)) != least_upper_bound(greatest_lower_bound(X_56,identity),multiply(greatest_lower_bound(X_56,identity),X_56))
| multiply(greatest_lower_bound(X_56,identity),least_upper_bound(X_56,identity)) = least_upper_bound(greatest_lower_bound(X_56,identity),multiply(X_56,greatest_lower_bound(X_56,identity))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_56,identity),X_56),multiply(X_56,greatest_lower_bound(X_56,identity))) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
multiply(greatest_lower_bound(X_56,identity),least_upper_bound(X_56,identity)) = least_upper_bound(greatest_lower_bound(X_56,identity),multiply(X_56,greatest_lower_bound(X_56,identity))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_56,identity),least_upper_bound(X_56,identity)),least_upper_bound(greatest_lower_bound(X_56,identity),multiply(greatest_lower_bound(X_56,identity),X_56))) )],[refute_0_35,refute_0_66]) ).
cnf(refute_0_68,plain,
multiply(least_upper_bound(X_77,identity),X_76) = least_upper_bound(multiply(X_77,X_76),multiply(identity,X_76)),
inference(subst,[],[monotony_lub2:[bind(X,$fot(X_76)),bind(Y,$fot(X_77)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_69,plain,
multiply(identity,X_76) = X_76,
inference(subst,[],[left_identity:[bind(X,$fot(X_76))]]) ).
cnf(refute_0_70,plain,
( multiply(identity,X_76) != X_76
| multiply(least_upper_bound(X_77,identity),X_76) != least_upper_bound(multiply(X_77,X_76),multiply(identity,X_76))
| multiply(least_upper_bound(X_77,identity),X_76) = least_upper_bound(multiply(X_77,X_76),X_76) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_77,identity),X_76),least_upper_bound(multiply(X_77,X_76),multiply(identity,X_76))) ),[1,1],$fot(X_76)]]) ).
cnf(refute_0_71,plain,
( multiply(least_upper_bound(X_77,identity),X_76) != least_upper_bound(multiply(X_77,X_76),multiply(identity,X_76))
| multiply(least_upper_bound(X_77,identity),X_76) = least_upper_bound(multiply(X_77,X_76),X_76) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_76),X_76) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
multiply(least_upper_bound(X_77,identity),X_76) = least_upper_bound(multiply(X_77,X_76),X_76),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_77,identity),X_76),least_upper_bound(multiply(X_77,X_76),multiply(identity,X_76))) )],[refute_0_68,refute_0_71]) ).
cnf(refute_0_73,plain,
least_upper_bound(multiply(X_77,X_76),X_76) = least_upper_bound(X_76,multiply(X_77,X_76)),
inference(subst,[],[refute_0_30:[bind(X,$fot(X_76)),bind(Y,$fot(multiply(X_77,X_76)))]]) ).
cnf(refute_0_74,plain,
( multiply(least_upper_bound(X_77,identity),X_76) != least_upper_bound(multiply(X_77,X_76),X_76)
| least_upper_bound(multiply(X_77,X_76),X_76) != least_upper_bound(X_76,multiply(X_77,X_76))
| multiply(least_upper_bound(X_77,identity),X_76) = least_upper_bound(X_76,multiply(X_77,X_76)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_77,identity),X_76),least_upper_bound(X_76,multiply(X_77,X_76))) ),[0],$fot(least_upper_bound(multiply(X_77,X_76),X_76))]]) ).
cnf(refute_0_75,plain,
( multiply(least_upper_bound(X_77,identity),X_76) != least_upper_bound(multiply(X_77,X_76),X_76)
| multiply(least_upper_bound(X_77,identity),X_76) = least_upper_bound(X_76,multiply(X_77,X_76)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_77,X_76),X_76),least_upper_bound(X_76,multiply(X_77,X_76))) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
multiply(least_upper_bound(X_77,identity),X_76) = least_upper_bound(X_76,multiply(X_77,X_76)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_77,identity),X_76),least_upper_bound(multiply(X_77,X_76),X_76)) )],[refute_0_72,refute_0_75]) ).
cnf(refute_0_77,plain,
( multiply(least_upper_bound(X_77,identity),X_76) != least_upper_bound(X_76,multiply(X_77,X_76))
| least_upper_bound(X_76,multiply(X_77,X_76)) = multiply(least_upper_bound(X_77,identity),X_76) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(multiply(least_upper_bound(X_77,identity),X_76))),bind(Y0,$fot(least_upper_bound(X_76,multiply(X_77,X_76))))]]) ).
cnf(refute_0_78,plain,
least_upper_bound(X_76,multiply(X_77,X_76)) = multiply(least_upper_bound(X_77,identity),X_76),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_77,identity),X_76),least_upper_bound(X_76,multiply(X_77,X_76))) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
least_upper_bound(greatest_lower_bound(X_56,identity),multiply(X_56,greatest_lower_bound(X_56,identity))) = multiply(least_upper_bound(X_56,identity),greatest_lower_bound(X_56,identity)),
inference(subst,[],[refute_0_78:[bind(X_76,$fot(greatest_lower_bound(X_56,identity))),bind(X_77,$fot(X_56))]]) ).
cnf(refute_0_80,plain,
( multiply(greatest_lower_bound(X_56,identity),least_upper_bound(X_56,identity)) != least_upper_bound(greatest_lower_bound(X_56,identity),multiply(X_56,greatest_lower_bound(X_56,identity)))
| least_upper_bound(greatest_lower_bound(X_56,identity),multiply(X_56,greatest_lower_bound(X_56,identity))) != multiply(least_upper_bound(X_56,identity),greatest_lower_bound(X_56,identity))
| multiply(greatest_lower_bound(X_56,identity),least_upper_bound(X_56,identity)) = multiply(least_upper_bound(X_56,identity),greatest_lower_bound(X_56,identity)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_56,identity),least_upper_bound(X_56,identity)),multiply(least_upper_bound(X_56,identity),greatest_lower_bound(X_56,identity))) ),[0],$fot(least_upper_bound(greatest_lower_bound(X_56,identity),multiply(X_56,greatest_lower_bound(X_56,identity))))]]) ).
cnf(refute_0_81,plain,
( multiply(greatest_lower_bound(X_56,identity),least_upper_bound(X_56,identity)) != least_upper_bound(greatest_lower_bound(X_56,identity),multiply(X_56,greatest_lower_bound(X_56,identity)))
| multiply(greatest_lower_bound(X_56,identity),least_upper_bound(X_56,identity)) = multiply(least_upper_bound(X_56,identity),greatest_lower_bound(X_56,identity)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_56,identity),multiply(X_56,greatest_lower_bound(X_56,identity))),multiply(least_upper_bound(X_56,identity),greatest_lower_bound(X_56,identity))) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
multiply(greatest_lower_bound(X_56,identity),least_upper_bound(X_56,identity)) = multiply(least_upper_bound(X_56,identity),greatest_lower_bound(X_56,identity)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_56,identity),least_upper_bound(X_56,identity)),least_upper_bound(greatest_lower_bound(X_56,identity),multiply(X_56,greatest_lower_bound(X_56,identity)))) )],[refute_0_67,refute_0_81]) ).
cnf(refute_0_83,plain,
( multiply(greatest_lower_bound(X_56,identity),least_upper_bound(X_56,identity)) != multiply(least_upper_bound(X_56,identity),greatest_lower_bound(X_56,identity))
| multiply(least_upper_bound(X_56,identity),greatest_lower_bound(X_56,identity)) = multiply(greatest_lower_bound(X_56,identity),least_upper_bound(X_56,identity)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(multiply(greatest_lower_bound(X_56,identity),least_upper_bound(X_56,identity)))),bind(Y0,$fot(multiply(least_upper_bound(X_56,identity),greatest_lower_bound(X_56,identity))))]]) ).
cnf(refute_0_84,plain,
multiply(least_upper_bound(X_56,identity),greatest_lower_bound(X_56,identity)) = multiply(greatest_lower_bound(X_56,identity),least_upper_bound(X_56,identity)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_56,identity),least_upper_bound(X_56,identity)),multiply(least_upper_bound(X_56,identity),greatest_lower_bound(X_56,identity))) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)) = multiply(greatest_lower_bound(a,identity),least_upper_bound(a,identity)),
inference(subst,[],[refute_0_84:[bind(X_56,$fot(a))]]) ).
cnf(refute_0_86,plain,
( multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)) != multiply(greatest_lower_bound(a,identity),least_upper_bound(a,identity))
| a != multiply(greatest_lower_bound(a,identity),least_upper_bound(a,identity))
| a = multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(a,multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity))) ),[1],$fot(multiply(greatest_lower_bound(a,identity),least_upper_bound(a,identity)))]]) ).
cnf(refute_0_87,plain,
( a != multiply(greatest_lower_bound(a,identity),least_upper_bound(a,identity))
| a = multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)),multiply(greatest_lower_bound(a,identity),least_upper_bound(a,identity))) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
a != multiply(greatest_lower_bound(a,identity),least_upper_bound(a,identity)),
inference(resolve,[$cnf( $equal(a,multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity))) )],[refute_0_87,prove_p19]) ).
cnf(refute_0_89,plain,
multiply(multiply(inverse(X_45),X_45),X_46) = multiply(inverse(X_45),multiply(X_45,X_46)),
inference(subst,[],[associativity:[bind(X,$fot(inverse(X_45))),bind(Y,$fot(X_45)),bind(Z,$fot(X_46))]]) ).
cnf(refute_0_90,plain,
multiply(inverse(X_45),X_45) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_45))]]) ).
cnf(refute_0_91,plain,
( multiply(multiply(inverse(X_45),X_45),X_46) != multiply(inverse(X_45),multiply(X_45,X_46))
| multiply(inverse(X_45),X_45) != identity
| multiply(identity,X_46) = multiply(inverse(X_45),multiply(X_45,X_46)) ),
introduced(tautology,[equality,[$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_92,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( $equal(multiply(inverse(X_45),X_45),identity) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
multiply(identity,X_46) = multiply(inverse(X_45),multiply(X_45,X_46)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_45),X_45),X_46),multiply(inverse(X_45),multiply(X_45,X_46))) )],[refute_0_89,refute_0_92]) ).
cnf(refute_0_94,plain,
multiply(identity,X_46) = X_46,
inference(subst,[],[left_identity:[bind(X,$fot(X_46))]]) ).
cnf(refute_0_95,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_96,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( $equal(multiply(identity,X_46),X_46) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
X_46 = multiply(inverse(X_45),multiply(X_45,X_46)),
inference(resolve,[$cnf( $equal(multiply(identity,X_46),multiply(inverse(X_45),multiply(X_45,X_46))) )],[refute_0_93,refute_0_96]) ).
cnf(refute_0_98,plain,
inverse(X) = multiply(inverse(inverse(Y)),multiply(inverse(Y),inverse(X))),
inference(subst,[],[refute_0_97:[bind(X_45,$fot(inverse(Y))),bind(X_46,$fot(inverse(X)))]]) ).
cnf(refute_0_99,plain,
( inverse(multiply(X,Y)) != multiply(inverse(Y),inverse(X))
| multiply(inverse(Y),inverse(X)) = inverse(multiply(X,Y)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(inverse(multiply(X,Y)))),bind(Y0,$fot(multiply(inverse(Y),inverse(X))))]]) ).
cnf(refute_0_100,plain,
multiply(inverse(Y),inverse(X)) = inverse(multiply(X,Y)),
inference(resolve,[$cnf( $equal(inverse(multiply(X,Y)),multiply(inverse(Y),inverse(X))) )],[p19_3,refute_0_99]) ).
cnf(refute_0_101,plain,
( multiply(inverse(Y),inverse(X)) != inverse(multiply(X,Y))
| inverse(X) != multiply(inverse(inverse(Y)),multiply(inverse(Y),inverse(X)))
| inverse(X) = multiply(inverse(inverse(Y)),inverse(multiply(X,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(X),multiply(inverse(inverse(Y)),multiply(inverse(Y),inverse(X)))) ),[1,1],$fot(inverse(multiply(X,Y)))]]) ).
cnf(refute_0_102,plain,
( inverse(X) != multiply(inverse(inverse(Y)),multiply(inverse(Y),inverse(X)))
| inverse(X) = multiply(inverse(inverse(Y)),inverse(multiply(X,Y))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(Y),inverse(X)),inverse(multiply(X,Y))) )],[refute_0_100,refute_0_101]) ).
cnf(refute_0_103,plain,
inverse(X) = multiply(inverse(inverse(Y)),inverse(multiply(X,Y))),
inference(resolve,[$cnf( $equal(inverse(X),multiply(inverse(inverse(Y)),multiply(inverse(Y),inverse(X)))) )],[refute_0_98,refute_0_102]) ).
cnf(refute_0_104,plain,
inverse(multiply(X_23,inverse(X))) = multiply(inverse(inverse(X)),inverse(X_23)),
inference(subst,[],[p19_3:[bind(X,$fot(X_23)),bind(Y,$fot(inverse(X)))]]) ).
cnf(refute_0_105,plain,
( inverse(multiply(X_23,inverse(X))) != multiply(inverse(inverse(X)),inverse(X_23))
| inverse(inverse(X)) != X
| inverse(multiply(X_23,inverse(X))) = multiply(X,inverse(X_23)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_23,inverse(X))),multiply(inverse(inverse(X)),inverse(X_23))) ),[1,0],$fot(X)]]) ).
cnf(refute_0_106,plain,
( inverse(multiply(X_23,inverse(X))) != multiply(inverse(inverse(X)),inverse(X_23))
| inverse(multiply(X_23,inverse(X))) = multiply(X,inverse(X_23)) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p19_2,refute_0_105]) ).
cnf(refute_0_107,plain,
inverse(multiply(X_23,inverse(X))) = multiply(X,inverse(X_23)),
inference(resolve,[$cnf( $equal(inverse(multiply(X_23,inverse(X))),multiply(inverse(inverse(X)),inverse(X_23))) )],[refute_0_104,refute_0_106]) ).
cnf(refute_0_108,plain,
inverse(multiply(multiply(X,Y),inverse(Y))) = multiply(Y,inverse(multiply(X,Y))),
inference(subst,[],[refute_0_107:[bind(X,$fot(Y)),bind(X_23,$fot(multiply(X,Y)))]]) ).
cnf(refute_0_109,plain,
multiply(inverse(inverse(Y)),inverse(multiply(X,Y))) = inverse(multiply(multiply(X,Y),inverse(Y))),
inference(subst,[],[refute_0_100:[bind(X,$fot(multiply(X,Y))),bind(Y,$fot(inverse(Y)))]]) ).
cnf(refute_0_110,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_111,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_23,refute_0_110]) ).
cnf(refute_0_112,plain,
( multiply(inverse(inverse(Y)),inverse(multiply(X,Y))) != inverse(multiply(multiply(X,Y),inverse(Y)))
| inverse(multiply(multiply(X,Y),inverse(Y))) != multiply(Y,inverse(multiply(X,Y)))
| multiply(inverse(inverse(Y)),inverse(multiply(X,Y))) = multiply(Y,inverse(multiply(X,Y))) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(multiply(inverse(inverse(Y)),inverse(multiply(X,Y))))),bind(Y0,$fot(inverse(multiply(multiply(X,Y),inverse(Y))))),bind(Z0,$fot(multiply(Y,inverse(multiply(X,Y)))))]]) ).
cnf(refute_0_113,plain,
( inverse(multiply(multiply(X,Y),inverse(Y))) != multiply(Y,inverse(multiply(X,Y)))
| multiply(inverse(inverse(Y)),inverse(multiply(X,Y))) = multiply(Y,inverse(multiply(X,Y))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(Y)),inverse(multiply(X,Y))),inverse(multiply(multiply(X,Y),inverse(Y)))) )],[refute_0_109,refute_0_112]) ).
cnf(refute_0_114,plain,
multiply(inverse(inverse(Y)),inverse(multiply(X,Y))) = multiply(Y,inverse(multiply(X,Y))),
inference(resolve,[$cnf( $equal(inverse(multiply(multiply(X,Y),inverse(Y))),multiply(Y,inverse(multiply(X,Y)))) )],[refute_0_108,refute_0_113]) ).
cnf(refute_0_115,plain,
( multiply(inverse(inverse(Y)),inverse(multiply(X,Y))) != multiply(Y,inverse(multiply(X,Y)))
| inverse(X) != multiply(inverse(inverse(Y)),inverse(multiply(X,Y)))
| inverse(X) = multiply(Y,inverse(multiply(X,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(X),multiply(inverse(inverse(Y)),inverse(multiply(X,Y)))) ),[1],$fot(multiply(Y,inverse(multiply(X,Y))))]]) ).
cnf(refute_0_116,plain,
( inverse(X) != multiply(inverse(inverse(Y)),inverse(multiply(X,Y)))
| inverse(X) = multiply(Y,inverse(multiply(X,Y))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(Y)),inverse(multiply(X,Y))),multiply(Y,inverse(multiply(X,Y)))) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
inverse(X) = multiply(Y,inverse(multiply(X,Y))),
inference(resolve,[$cnf( $equal(inverse(X),multiply(inverse(inverse(Y)),inverse(multiply(X,Y)))) )],[refute_0_103,refute_0_116]) ).
cnf(refute_0_118,plain,
inverse(inverse(X_64)) = multiply(least_upper_bound(identity,X_64),inverse(multiply(inverse(X_64),least_upper_bound(identity,X_64)))),
inference(subst,[],[refute_0_117:[bind(X,$fot(inverse(X_64))),bind(Y,$fot(least_upper_bound(identity,X_64)))]]) ).
cnf(refute_0_119,plain,
multiply(inverse(X_57),least_upper_bound(X_56,X_57)) = least_upper_bound(multiply(inverse(X_57),X_56),multiply(inverse(X_57),X_57)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(inverse(X_57))),bind(Y,$fot(X_56)),bind(Z,$fot(X_57))]]) ).
cnf(refute_0_120,plain,
multiply(inverse(X_57),X_57) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_57))]]) ).
cnf(refute_0_121,plain,
( multiply(inverse(X_57),X_57) != identity
| multiply(inverse(X_57),least_upper_bound(X_56,X_57)) != least_upper_bound(multiply(inverse(X_57),X_56),multiply(inverse(X_57),X_57))
| multiply(inverse(X_57),least_upper_bound(X_56,X_57)) = least_upper_bound(multiply(inverse(X_57),X_56),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_57),least_upper_bound(X_56,X_57)),least_upper_bound(multiply(inverse(X_57),X_56),multiply(inverse(X_57),X_57))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_122,plain,
( multiply(inverse(X_57),least_upper_bound(X_56,X_57)) != least_upper_bound(multiply(inverse(X_57),X_56),multiply(inverse(X_57),X_57))
| multiply(inverse(X_57),least_upper_bound(X_56,X_57)) = least_upper_bound(multiply(inverse(X_57),X_56),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_57),X_57),identity) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
multiply(inverse(X_57),least_upper_bound(X_56,X_57)) = least_upper_bound(multiply(inverse(X_57),X_56),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_57),least_upper_bound(X_56,X_57)),least_upper_bound(multiply(inverse(X_57),X_56),multiply(inverse(X_57),X_57))) )],[refute_0_119,refute_0_122]) ).
cnf(refute_0_124,plain,
least_upper_bound(multiply(inverse(X_57),X_56),identity) = least_upper_bound(identity,multiply(inverse(X_57),X_56)),
inference(subst,[],[refute_0_30:[bind(X,$fot(identity)),bind(Y,$fot(multiply(inverse(X_57),X_56)))]]) ).
cnf(refute_0_125,plain,
( multiply(inverse(X_57),least_upper_bound(X_56,X_57)) != least_upper_bound(multiply(inverse(X_57),X_56),identity)
| least_upper_bound(multiply(inverse(X_57),X_56),identity) != least_upper_bound(identity,multiply(inverse(X_57),X_56))
| multiply(inverse(X_57),least_upper_bound(X_56,X_57)) = least_upper_bound(identity,multiply(inverse(X_57),X_56)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_57),least_upper_bound(X_56,X_57)),least_upper_bound(identity,multiply(inverse(X_57),X_56))) ),[0],$fot(least_upper_bound(multiply(inverse(X_57),X_56),identity))]]) ).
cnf(refute_0_126,plain,
( multiply(inverse(X_57),least_upper_bound(X_56,X_57)) != least_upper_bound(multiply(inverse(X_57),X_56),identity)
| multiply(inverse(X_57),least_upper_bound(X_56,X_57)) = least_upper_bound(identity,multiply(inverse(X_57),X_56)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(X_57),X_56),identity),least_upper_bound(identity,multiply(inverse(X_57),X_56))) )],[refute_0_124,refute_0_125]) ).
cnf(refute_0_127,plain,
multiply(inverse(X_57),least_upper_bound(X_56,X_57)) = least_upper_bound(identity,multiply(inverse(X_57),X_56)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_57),least_upper_bound(X_56,X_57)),least_upper_bound(multiply(inverse(X_57),X_56),identity)) )],[refute_0_123,refute_0_126]) ).
cnf(refute_0_128,plain,
multiply(inverse(X_63),least_upper_bound(identity,X_63)) = least_upper_bound(identity,multiply(inverse(X_63),identity)),
inference(subst,[],[refute_0_127:[bind(X_56,$fot(identity)),bind(X_57,$fot(X_63))]]) ).
cnf(refute_0_129,plain,
inverse(X_63) = multiply(inverse(X_63),identity),
inference(subst,[],[refute_0_19:[bind(X,$fot(inverse(X_63)))]]) ).
cnf(refute_0_130,plain,
( inverse(X_63) != multiply(inverse(X_63),identity)
| multiply(inverse(X_63),identity) = inverse(X_63) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(inverse(X_63))),bind(Y0,$fot(multiply(inverse(X_63),identity)))]]) ).
cnf(refute_0_131,plain,
multiply(inverse(X_63),identity) = inverse(X_63),
inference(resolve,[$cnf( $equal(inverse(X_63),multiply(inverse(X_63),identity)) )],[refute_0_129,refute_0_130]) ).
cnf(refute_0_132,plain,
( multiply(inverse(X_63),identity) != inverse(X_63)
| multiply(inverse(X_63),least_upper_bound(identity,X_63)) != least_upper_bound(identity,multiply(inverse(X_63),identity))
| multiply(inverse(X_63),least_upper_bound(identity,X_63)) = least_upper_bound(identity,inverse(X_63)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_63),least_upper_bound(identity,X_63)),least_upper_bound(identity,multiply(inverse(X_63),identity))) ),[1,1],$fot(inverse(X_63))]]) ).
cnf(refute_0_133,plain,
( multiply(inverse(X_63),least_upper_bound(identity,X_63)) != least_upper_bound(identity,multiply(inverse(X_63),identity))
| multiply(inverse(X_63),least_upper_bound(identity,X_63)) = least_upper_bound(identity,inverse(X_63)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_63),identity),inverse(X_63)) )],[refute_0_131,refute_0_132]) ).
cnf(refute_0_134,plain,
multiply(inverse(X_63),least_upper_bound(identity,X_63)) = least_upper_bound(identity,inverse(X_63)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_63),least_upper_bound(identity,X_63)),least_upper_bound(identity,multiply(inverse(X_63),identity))) )],[refute_0_128,refute_0_133]) ).
cnf(refute_0_135,plain,
multiply(inverse(X_64),least_upper_bound(identity,X_64)) = least_upper_bound(identity,inverse(X_64)),
inference(subst,[],[refute_0_134:[bind(X_63,$fot(X_64))]]) ).
cnf(refute_0_136,plain,
( multiply(inverse(X_64),least_upper_bound(identity,X_64)) != least_upper_bound(identity,inverse(X_64))
| inverse(inverse(X_64)) != multiply(least_upper_bound(identity,X_64),inverse(multiply(inverse(X_64),least_upper_bound(identity,X_64))))
| inverse(inverse(X_64)) = multiply(least_upper_bound(identity,X_64),inverse(least_upper_bound(identity,inverse(X_64)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_64)),multiply(least_upper_bound(identity,X_64),inverse(multiply(inverse(X_64),least_upper_bound(identity,X_64))))) ),[1,1,0],$fot(least_upper_bound(identity,inverse(X_64)))]]) ).
cnf(refute_0_137,plain,
( inverse(inverse(X_64)) != multiply(least_upper_bound(identity,X_64),inverse(multiply(inverse(X_64),least_upper_bound(identity,X_64))))
| inverse(inverse(X_64)) = multiply(least_upper_bound(identity,X_64),inverse(least_upper_bound(identity,inverse(X_64)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_64),least_upper_bound(identity,X_64)),least_upper_bound(identity,inverse(X_64))) )],[refute_0_135,refute_0_136]) ).
cnf(refute_0_138,plain,
inverse(inverse(X_64)) = multiply(least_upper_bound(identity,X_64),inverse(least_upper_bound(identity,inverse(X_64)))),
inference(resolve,[$cnf( $equal(inverse(inverse(X_64)),multiply(least_upper_bound(identity,X_64),inverse(multiply(inverse(X_64),least_upper_bound(identity,X_64))))) )],[refute_0_118,refute_0_137]) ).
cnf(refute_0_139,plain,
inverse(inverse(X_64)) = X_64,
inference(subst,[],[p19_2:[bind(X,$fot(X_64))]]) ).
cnf(refute_0_140,plain,
( inverse(inverse(X_64)) != X_64
| inverse(inverse(X_64)) != multiply(least_upper_bound(identity,X_64),inverse(least_upper_bound(identity,inverse(X_64))))
| X_64 = multiply(least_upper_bound(identity,X_64),inverse(least_upper_bound(identity,inverse(X_64)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_64)),multiply(least_upper_bound(identity,X_64),inverse(least_upper_bound(identity,inverse(X_64))))) ),[0],$fot(X_64)]]) ).
cnf(refute_0_141,plain,
( inverse(inverse(X_64)) != multiply(least_upper_bound(identity,X_64),inverse(least_upper_bound(identity,inverse(X_64))))
| X_64 = multiply(least_upper_bound(identity,X_64),inverse(least_upper_bound(identity,inverse(X_64)))) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_64)),X_64) )],[refute_0_139,refute_0_140]) ).
cnf(refute_0_142,plain,
X_64 = multiply(least_upper_bound(identity,X_64),inverse(least_upper_bound(identity,inverse(X_64)))),
inference(resolve,[$cnf( $equal(inverse(inverse(X_64)),multiply(least_upper_bound(identity,X_64),inverse(least_upper_bound(identity,inverse(X_64))))) )],[refute_0_138,refute_0_141]) ).
cnf(refute_0_143,plain,
X_99 = multiply(least_upper_bound(identity,X_99),inverse(least_upper_bound(identity,inverse(X_99)))),
inference(subst,[],[refute_0_142:[bind(X_64,$fot(X_99))]]) ).
cnf(refute_0_144,plain,
least_upper_bound(X_99,identity) = least_upper_bound(identity,X_99),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_99)),bind(Y,$fot(identity))]]) ).
cnf(refute_0_145,plain,
( least_upper_bound(X_99,identity) != least_upper_bound(identity,X_99)
| least_upper_bound(identity,X_99) = least_upper_bound(X_99,identity) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(least_upper_bound(X_99,identity))),bind(Y0,$fot(least_upper_bound(identity,X_99)))]]) ).
cnf(refute_0_146,plain,
least_upper_bound(identity,X_99) = least_upper_bound(X_99,identity),
inference(resolve,[$cnf( $equal(least_upper_bound(X_99,identity),least_upper_bound(identity,X_99)) )],[refute_0_144,refute_0_145]) ).
cnf(refute_0_147,plain,
( X_99 != multiply(least_upper_bound(identity,X_99),inverse(least_upper_bound(identity,inverse(X_99))))
| least_upper_bound(identity,X_99) != least_upper_bound(X_99,identity)
| X_99 = multiply(least_upper_bound(X_99,identity),inverse(least_upper_bound(identity,inverse(X_99)))) ),
introduced(tautology,[equality,[$cnf( $equal(X_99,multiply(least_upper_bound(identity,X_99),inverse(least_upper_bound(identity,inverse(X_99))))) ),[1,0],$fot(least_upper_bound(X_99,identity))]]) ).
cnf(refute_0_148,plain,
( X_99 != multiply(least_upper_bound(identity,X_99),inverse(least_upper_bound(identity,inverse(X_99))))
| X_99 = multiply(least_upper_bound(X_99,identity),inverse(least_upper_bound(identity,inverse(X_99)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,X_99),least_upper_bound(X_99,identity)) )],[refute_0_146,refute_0_147]) ).
cnf(refute_0_149,plain,
X_99 = multiply(least_upper_bound(X_99,identity),inverse(least_upper_bound(identity,inverse(X_99)))),
inference(resolve,[$cnf( $equal(X_99,multiply(least_upper_bound(identity,X_99),inverse(least_upper_bound(identity,inverse(X_99))))) )],[refute_0_143,refute_0_148]) ).
cnf(refute_0_150,plain,
multiply(least_upper_bound(X_99,identity),greatest_lower_bound(X_99,identity)) = multiply(greatest_lower_bound(X_99,identity),least_upper_bound(X_99,identity)),
inference(subst,[],[refute_0_84:[bind(X_56,$fot(X_99))]]) ).
cnf(refute_0_151,plain,
inverse(X) = multiply(greatest_lower_bound(inverse(X),X_73),inverse(multiply(X,greatest_lower_bound(inverse(X),X_73)))),
inference(subst,[],[refute_0_117:[bind(Y,$fot(greatest_lower_bound(inverse(X),X_73)))]]) ).
cnf(refute_0_152,plain,
multiply(X_67,greatest_lower_bound(inverse(X_67),X_69)) = greatest_lower_bound(multiply(X_67,inverse(X_67)),multiply(X_67,X_69)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(X_67)),bind(Y,$fot(inverse(X_67))),bind(Z,$fot(X_69))]]) ).
cnf(refute_0_153,plain,
multiply(inverse(inverse(X)),inverse(X)) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(inverse(X)))]]) ).
cnf(refute_0_154,plain,
( multiply(inverse(inverse(X)),inverse(X)) != identity
| inverse(inverse(X)) != X
| multiply(X,inverse(X)) = identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X)),inverse(X)),identity) ),[0,0],$fot(X)]]) ).
cnf(refute_0_155,plain,
( multiply(inverse(inverse(X)),inverse(X)) != identity
| multiply(X,inverse(X)) = identity ),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p19_2,refute_0_154]) ).
cnf(refute_0_156,plain,
multiply(X,inverse(X)) = identity,
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X)),inverse(X)),identity) )],[refute_0_153,refute_0_155]) ).
cnf(refute_0_157,plain,
multiply(X_67,inverse(X_67)) = identity,
inference(subst,[],[refute_0_156:[bind(X,$fot(X_67))]]) ).
cnf(refute_0_158,plain,
( multiply(X_67,greatest_lower_bound(inverse(X_67),X_69)) != greatest_lower_bound(multiply(X_67,inverse(X_67)),multiply(X_67,X_69))
| multiply(X_67,inverse(X_67)) != identity
| multiply(X_67,greatest_lower_bound(inverse(X_67),X_69)) = greatest_lower_bound(identity,multiply(X_67,X_69)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_67,greatest_lower_bound(inverse(X_67),X_69)),greatest_lower_bound(multiply(X_67,inverse(X_67)),multiply(X_67,X_69))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_159,plain,
( multiply(X_67,greatest_lower_bound(inverse(X_67),X_69)) != greatest_lower_bound(multiply(X_67,inverse(X_67)),multiply(X_67,X_69))
| multiply(X_67,greatest_lower_bound(inverse(X_67),X_69)) = greatest_lower_bound(identity,multiply(X_67,X_69)) ),
inference(resolve,[$cnf( $equal(multiply(X_67,inverse(X_67)),identity) )],[refute_0_157,refute_0_158]) ).
cnf(refute_0_160,plain,
multiply(X_67,greatest_lower_bound(inverse(X_67),X_69)) = greatest_lower_bound(identity,multiply(X_67,X_69)),
inference(resolve,[$cnf( $equal(multiply(X_67,greatest_lower_bound(inverse(X_67),X_69)),greatest_lower_bound(multiply(X_67,inverse(X_67)),multiply(X_67,X_69))) )],[refute_0_152,refute_0_159]) ).
cnf(refute_0_161,plain,
multiply(X,greatest_lower_bound(inverse(X),X_73)) = greatest_lower_bound(identity,multiply(X,X_73)),
inference(subst,[],[refute_0_160:[bind(X_67,$fot(X)),bind(X_69,$fot(X_73))]]) ).
cnf(refute_0_162,plain,
( multiply(X,greatest_lower_bound(inverse(X),X_73)) != greatest_lower_bound(identity,multiply(X,X_73))
| inverse(X) != multiply(greatest_lower_bound(inverse(X),X_73),inverse(multiply(X,greatest_lower_bound(inverse(X),X_73))))
| inverse(X) = multiply(greatest_lower_bound(inverse(X),X_73),inverse(greatest_lower_bound(identity,multiply(X,X_73)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(X),multiply(greatest_lower_bound(inverse(X),X_73),inverse(multiply(X,greatest_lower_bound(inverse(X),X_73))))) ),[1,1,0],$fot(greatest_lower_bound(identity,multiply(X,X_73)))]]) ).
cnf(refute_0_163,plain,
( inverse(X) != multiply(greatest_lower_bound(inverse(X),X_73),inverse(multiply(X,greatest_lower_bound(inverse(X),X_73))))
| inverse(X) = multiply(greatest_lower_bound(inverse(X),X_73),inverse(greatest_lower_bound(identity,multiply(X,X_73)))) ),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(inverse(X),X_73)),greatest_lower_bound(identity,multiply(X,X_73))) )],[refute_0_161,refute_0_162]) ).
cnf(refute_0_164,plain,
inverse(X) = multiply(greatest_lower_bound(inverse(X),X_73),inverse(greatest_lower_bound(identity,multiply(X,X_73)))),
inference(resolve,[$cnf( $equal(inverse(X),multiply(greatest_lower_bound(inverse(X),X_73),inverse(multiply(X,greatest_lower_bound(inverse(X),X_73))))) )],[refute_0_151,refute_0_163]) ).
cnf(refute_0_165,plain,
inverse(least_upper_bound(identity,inverse(X_310))) = multiply(greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_310))),inverse(least_upper_bound(identity,X_310))),inverse(greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X_310)),inverse(least_upper_bound(identity,X_310)))))),
inference(subst,[],[refute_0_164:[bind(X,$fot(least_upper_bound(identity,inverse(X_310)))),bind(X_73,$fot(inverse(least_upper_bound(identity,X_310))))]]) ).
cnf(refute_0_166,plain,
inverse(multiply(least_upper_bound(identity,X_99),inverse(least_upper_bound(identity,inverse(X_99))))) = multiply(inverse(inverse(least_upper_bound(identity,inverse(X_99)))),inverse(least_upper_bound(identity,X_99))),
inference(subst,[],[p19_3:[bind(X,$fot(least_upper_bound(identity,X_99))),bind(Y,$fot(inverse(least_upper_bound(identity,inverse(X_99)))))]]) ).
cnf(refute_0_167,plain,
( X_99 != multiply(least_upper_bound(identity,X_99),inverse(least_upper_bound(identity,inverse(X_99))))
| multiply(least_upper_bound(identity,X_99),inverse(least_upper_bound(identity,inverse(X_99)))) = X_99 ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(X_99)),bind(Y0,$fot(multiply(least_upper_bound(identity,X_99),inverse(least_upper_bound(identity,inverse(X_99))))))]]) ).
cnf(refute_0_168,plain,
multiply(least_upper_bound(identity,X_99),inverse(least_upper_bound(identity,inverse(X_99)))) = X_99,
inference(resolve,[$cnf( $equal(X_99,multiply(least_upper_bound(identity,X_99),inverse(least_upper_bound(identity,inverse(X_99))))) )],[refute_0_143,refute_0_167]) ).
cnf(refute_0_169,plain,
( multiply(least_upper_bound(identity,X_99),inverse(least_upper_bound(identity,inverse(X_99)))) != X_99
| inverse(multiply(least_upper_bound(identity,X_99),inverse(least_upper_bound(identity,inverse(X_99))))) != multiply(inverse(inverse(least_upper_bound(identity,inverse(X_99)))),inverse(least_upper_bound(identity,X_99)))
| inverse(X_99) = multiply(inverse(inverse(least_upper_bound(identity,inverse(X_99)))),inverse(least_upper_bound(identity,X_99))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(least_upper_bound(identity,X_99),inverse(least_upper_bound(identity,inverse(X_99))))),multiply(inverse(inverse(least_upper_bound(identity,inverse(X_99)))),inverse(least_upper_bound(identity,X_99)))) ),[0,0],$fot(X_99)]]) ).
cnf(refute_0_170,plain,
( inverse(multiply(least_upper_bound(identity,X_99),inverse(least_upper_bound(identity,inverse(X_99))))) != multiply(inverse(inverse(least_upper_bound(identity,inverse(X_99)))),inverse(least_upper_bound(identity,X_99)))
| inverse(X_99) = multiply(inverse(inverse(least_upper_bound(identity,inverse(X_99)))),inverse(least_upper_bound(identity,X_99))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_99),inverse(least_upper_bound(identity,inverse(X_99)))),X_99) )],[refute_0_168,refute_0_169]) ).
cnf(refute_0_171,plain,
inverse(X_99) = multiply(inverse(inverse(least_upper_bound(identity,inverse(X_99)))),inverse(least_upper_bound(identity,X_99))),
inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(identity,X_99),inverse(least_upper_bound(identity,inverse(X_99))))),multiply(inverse(inverse(least_upper_bound(identity,inverse(X_99)))),inverse(least_upper_bound(identity,X_99)))) )],[refute_0_166,refute_0_170]) ).
cnf(refute_0_172,plain,
inverse(multiply(least_upper_bound(identity,X_99),inverse(least_upper_bound(identity,inverse(X_99))))) = multiply(least_upper_bound(identity,inverse(X_99)),inverse(least_upper_bound(identity,X_99))),
inference(subst,[],[refute_0_107:[bind(X,$fot(least_upper_bound(identity,inverse(X_99)))),bind(X_23,$fot(least_upper_bound(identity,X_99)))]]) ).
cnf(refute_0_173,plain,
multiply(inverse(inverse(least_upper_bound(identity,inverse(X_99)))),inverse(least_upper_bound(identity,X_99))) = inverse(multiply(least_upper_bound(identity,X_99),inverse(least_upper_bound(identity,inverse(X_99))))),
inference(subst,[],[refute_0_100:[bind(X,$fot(least_upper_bound(identity,X_99))),bind(Y,$fot(inverse(least_upper_bound(identity,inverse(X_99)))))]]) ).
cnf(refute_0_174,plain,
( multiply(inverse(inverse(least_upper_bound(identity,inverse(X_99)))),inverse(least_upper_bound(identity,X_99))) != inverse(multiply(least_upper_bound(identity,X_99),inverse(least_upper_bound(identity,inverse(X_99)))))
| inverse(multiply(least_upper_bound(identity,X_99),inverse(least_upper_bound(identity,inverse(X_99))))) != multiply(least_upper_bound(identity,inverse(X_99)),inverse(least_upper_bound(identity,X_99)))
| multiply(inverse(inverse(least_upper_bound(identity,inverse(X_99)))),inverse(least_upper_bound(identity,X_99))) = multiply(least_upper_bound(identity,inverse(X_99)),inverse(least_upper_bound(identity,X_99))) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(multiply(inverse(inverse(least_upper_bound(identity,inverse(X_99)))),inverse(least_upper_bound(identity,X_99))))),bind(Y0,$fot(inverse(multiply(least_upper_bound(identity,X_99),inverse(least_upper_bound(identity,inverse(X_99))))))),bind(Z0,$fot(multiply(least_upper_bound(identity,inverse(X_99)),inverse(least_upper_bound(identity,X_99)))))]]) ).
cnf(refute_0_175,plain,
( inverse(multiply(least_upper_bound(identity,X_99),inverse(least_upper_bound(identity,inverse(X_99))))) != multiply(least_upper_bound(identity,inverse(X_99)),inverse(least_upper_bound(identity,X_99)))
| multiply(inverse(inverse(least_upper_bound(identity,inverse(X_99)))),inverse(least_upper_bound(identity,X_99))) = multiply(least_upper_bound(identity,inverse(X_99)),inverse(least_upper_bound(identity,X_99))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(identity,inverse(X_99)))),inverse(least_upper_bound(identity,X_99))),inverse(multiply(least_upper_bound(identity,X_99),inverse(least_upper_bound(identity,inverse(X_99)))))) )],[refute_0_173,refute_0_174]) ).
cnf(refute_0_176,plain,
multiply(inverse(inverse(least_upper_bound(identity,inverse(X_99)))),inverse(least_upper_bound(identity,X_99))) = multiply(least_upper_bound(identity,inverse(X_99)),inverse(least_upper_bound(identity,X_99))),
inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(identity,X_99),inverse(least_upper_bound(identity,inverse(X_99))))),multiply(least_upper_bound(identity,inverse(X_99)),inverse(least_upper_bound(identity,X_99)))) )],[refute_0_172,refute_0_175]) ).
cnf(refute_0_177,plain,
( multiply(inverse(inverse(least_upper_bound(identity,inverse(X_99)))),inverse(least_upper_bound(identity,X_99))) != multiply(least_upper_bound(identity,inverse(X_99)),inverse(least_upper_bound(identity,X_99)))
| inverse(X_99) != multiply(inverse(inverse(least_upper_bound(identity,inverse(X_99)))),inverse(least_upper_bound(identity,X_99)))
| inverse(X_99) = multiply(least_upper_bound(identity,inverse(X_99)),inverse(least_upper_bound(identity,X_99))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(X_99),multiply(inverse(inverse(least_upper_bound(identity,inverse(X_99)))),inverse(least_upper_bound(identity,X_99)))) ),[1],$fot(multiply(least_upper_bound(identity,inverse(X_99)),inverse(least_upper_bound(identity,X_99))))]]) ).
cnf(refute_0_178,plain,
( inverse(X_99) != multiply(inverse(inverse(least_upper_bound(identity,inverse(X_99)))),inverse(least_upper_bound(identity,X_99)))
| inverse(X_99) = multiply(least_upper_bound(identity,inverse(X_99)),inverse(least_upper_bound(identity,X_99))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(identity,inverse(X_99)))),inverse(least_upper_bound(identity,X_99))),multiply(least_upper_bound(identity,inverse(X_99)),inverse(least_upper_bound(identity,X_99)))) )],[refute_0_176,refute_0_177]) ).
cnf(refute_0_179,plain,
inverse(X_99) = multiply(least_upper_bound(identity,inverse(X_99)),inverse(least_upper_bound(identity,X_99))),
inference(resolve,[$cnf( $equal(inverse(X_99),multiply(inverse(inverse(least_upper_bound(identity,inverse(X_99)))),inverse(least_upper_bound(identity,X_99)))) )],[refute_0_171,refute_0_178]) ).
cnf(refute_0_180,plain,
inverse(X_310) = multiply(least_upper_bound(identity,inverse(X_310)),inverse(least_upper_bound(identity,X_310))),
inference(subst,[],[refute_0_179:[bind(X_99,$fot(X_310))]]) ).
cnf(refute_0_181,plain,
( inverse(X_310) != multiply(least_upper_bound(identity,inverse(X_310)),inverse(least_upper_bound(identity,X_310)))
| multiply(least_upper_bound(identity,inverse(X_310)),inverse(least_upper_bound(identity,X_310))) = inverse(X_310) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(inverse(X_310))),bind(Y0,$fot(multiply(least_upper_bound(identity,inverse(X_310)),inverse(least_upper_bound(identity,X_310)))))]]) ).
cnf(refute_0_182,plain,
multiply(least_upper_bound(identity,inverse(X_310)),inverse(least_upper_bound(identity,X_310))) = inverse(X_310),
inference(resolve,[$cnf( $equal(inverse(X_310),multiply(least_upper_bound(identity,inverse(X_310)),inverse(least_upper_bound(identity,X_310)))) )],[refute_0_180,refute_0_181]) ).
cnf(refute_0_183,plain,
( multiply(least_upper_bound(identity,inverse(X_310)),inverse(least_upper_bound(identity,X_310))) != inverse(X_310)
| inverse(least_upper_bound(identity,inverse(X_310))) != multiply(greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_310))),inverse(least_upper_bound(identity,X_310))),inverse(greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X_310)),inverse(least_upper_bound(identity,X_310))))))
| inverse(least_upper_bound(identity,inverse(X_310))) = multiply(greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_310))),inverse(least_upper_bound(identity,X_310))),inverse(greatest_lower_bound(identity,inverse(X_310)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_310))),multiply(greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_310))),inverse(least_upper_bound(identity,X_310))),inverse(greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X_310)),inverse(least_upper_bound(identity,X_310))))))) ),[1,1,0,1],$fot(inverse(X_310))]]) ).
cnf(refute_0_184,plain,
( inverse(least_upper_bound(identity,inverse(X_310))) != multiply(greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_310))),inverse(least_upper_bound(identity,X_310))),inverse(greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X_310)),inverse(least_upper_bound(identity,X_310))))))
| inverse(least_upper_bound(identity,inverse(X_310))) = multiply(greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_310))),inverse(least_upper_bound(identity,X_310))),inverse(greatest_lower_bound(identity,inverse(X_310)))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_310)),inverse(least_upper_bound(identity,X_310))),inverse(X_310)) )],[refute_0_182,refute_0_183]) ).
cnf(refute_0_185,plain,
inverse(least_upper_bound(identity,inverse(X_310))) = multiply(greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_310))),inverse(least_upper_bound(identity,X_310))),inverse(greatest_lower_bound(identity,inverse(X_310)))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_310))),multiply(greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_310))),inverse(least_upper_bound(identity,X_310))),inverse(greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X_310)),inverse(least_upper_bound(identity,X_310))))))) )],[refute_0_165,refute_0_184]) ).
cnf(refute_0_186,plain,
multiply(least_upper_bound(identity,X_84),greatest_lower_bound(inverse(X_84),identity)) = greatest_lower_bound(least_upper_bound(identity,X_84),multiply(least_upper_bound(identity,X_84),inverse(X_84))),
inference(subst,[],[refute_0_57:[bind(X_67,$fot(least_upper_bound(identity,X_84))),bind(X_68,$fot(inverse(X_84)))]]) ).
cnf(refute_0_187,plain,
multiply(least_upper_bound(X_77,X_78),inverse(X_78)) = least_upper_bound(multiply(X_77,inverse(X_78)),multiply(X_78,inverse(X_78))),
inference(subst,[],[monotony_lub2:[bind(X,$fot(inverse(X_78))),bind(Y,$fot(X_77)),bind(Z,$fot(X_78))]]) ).
cnf(refute_0_188,plain,
multiply(X_78,inverse(X_78)) = identity,
inference(subst,[],[refute_0_156:[bind(X,$fot(X_78))]]) ).
cnf(refute_0_189,plain,
( multiply(X_78,inverse(X_78)) != identity
| multiply(least_upper_bound(X_77,X_78),inverse(X_78)) != least_upper_bound(multiply(X_77,inverse(X_78)),multiply(X_78,inverse(X_78)))
| multiply(least_upper_bound(X_77,X_78),inverse(X_78)) = least_upper_bound(multiply(X_77,inverse(X_78)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_77,X_78),inverse(X_78)),least_upper_bound(multiply(X_77,inverse(X_78)),multiply(X_78,inverse(X_78)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_190,plain,
( multiply(least_upper_bound(X_77,X_78),inverse(X_78)) != least_upper_bound(multiply(X_77,inverse(X_78)),multiply(X_78,inverse(X_78)))
| multiply(least_upper_bound(X_77,X_78),inverse(X_78)) = least_upper_bound(multiply(X_77,inverse(X_78)),identity) ),
inference(resolve,[$cnf( $equal(multiply(X_78,inverse(X_78)),identity) )],[refute_0_188,refute_0_189]) ).
cnf(refute_0_191,plain,
multiply(least_upper_bound(X_77,X_78),inverse(X_78)) = least_upper_bound(multiply(X_77,inverse(X_78)),identity),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_77,X_78),inverse(X_78)),least_upper_bound(multiply(X_77,inverse(X_78)),multiply(X_78,inverse(X_78)))) )],[refute_0_187,refute_0_190]) ).
cnf(refute_0_192,plain,
least_upper_bound(multiply(X_77,inverse(X_78)),identity) = least_upper_bound(identity,multiply(X_77,inverse(X_78))),
inference(subst,[],[refute_0_30:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_77,inverse(X_78))))]]) ).
cnf(refute_0_193,plain,
( multiply(least_upper_bound(X_77,X_78),inverse(X_78)) != least_upper_bound(multiply(X_77,inverse(X_78)),identity)
| least_upper_bound(multiply(X_77,inverse(X_78)),identity) != least_upper_bound(identity,multiply(X_77,inverse(X_78)))
| multiply(least_upper_bound(X_77,X_78),inverse(X_78)) = least_upper_bound(identity,multiply(X_77,inverse(X_78))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_77,X_78),inverse(X_78)),least_upper_bound(identity,multiply(X_77,inverse(X_78)))) ),[0],$fot(least_upper_bound(multiply(X_77,inverse(X_78)),identity))]]) ).
cnf(refute_0_194,plain,
( multiply(least_upper_bound(X_77,X_78),inverse(X_78)) != least_upper_bound(multiply(X_77,inverse(X_78)),identity)
| multiply(least_upper_bound(X_77,X_78),inverse(X_78)) = least_upper_bound(identity,multiply(X_77,inverse(X_78))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_77,inverse(X_78)),identity),least_upper_bound(identity,multiply(X_77,inverse(X_78)))) )],[refute_0_192,refute_0_193]) ).
cnf(refute_0_195,plain,
multiply(least_upper_bound(X_77,X_78),inverse(X_78)) = least_upper_bound(identity,multiply(X_77,inverse(X_78))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_77,X_78),inverse(X_78)),least_upper_bound(multiply(X_77,inverse(X_78)),identity)) )],[refute_0_191,refute_0_194]) ).
cnf(refute_0_196,plain,
multiply(least_upper_bound(identity,X_84),inverse(X_84)) = least_upper_bound(identity,multiply(identity,inverse(X_84))),
inference(subst,[],[refute_0_195:[bind(X_77,$fot(identity)),bind(X_78,$fot(X_84))]]) ).
cnf(refute_0_197,plain,
multiply(identity,inverse(X_84)) = inverse(X_84),
inference(subst,[],[left_identity:[bind(X,$fot(inverse(X_84)))]]) ).
cnf(refute_0_198,plain,
( multiply(identity,inverse(X_84)) != inverse(X_84)
| multiply(least_upper_bound(identity,X_84),inverse(X_84)) != least_upper_bound(identity,multiply(identity,inverse(X_84)))
| multiply(least_upper_bound(identity,X_84),inverse(X_84)) = least_upper_bound(identity,inverse(X_84)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,X_84),inverse(X_84)),least_upper_bound(identity,multiply(identity,inverse(X_84)))) ),[1,1],$fot(inverse(X_84))]]) ).
cnf(refute_0_199,plain,
( multiply(least_upper_bound(identity,X_84),inverse(X_84)) != least_upper_bound(identity,multiply(identity,inverse(X_84)))
| multiply(least_upper_bound(identity,X_84),inverse(X_84)) = least_upper_bound(identity,inverse(X_84)) ),
inference(resolve,[$cnf( $equal(multiply(identity,inverse(X_84)),inverse(X_84)) )],[refute_0_197,refute_0_198]) ).
cnf(refute_0_200,plain,
multiply(least_upper_bound(identity,X_84),inverse(X_84)) = least_upper_bound(identity,inverse(X_84)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_84),inverse(X_84)),least_upper_bound(identity,multiply(identity,inverse(X_84)))) )],[refute_0_196,refute_0_199]) ).
cnf(refute_0_201,plain,
( multiply(least_upper_bound(identity,X_84),greatest_lower_bound(inverse(X_84),identity)) != greatest_lower_bound(least_upper_bound(identity,X_84),multiply(least_upper_bound(identity,X_84),inverse(X_84)))
| multiply(least_upper_bound(identity,X_84),inverse(X_84)) != least_upper_bound(identity,inverse(X_84))
| multiply(least_upper_bound(identity,X_84),greatest_lower_bound(inverse(X_84),identity)) = greatest_lower_bound(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,X_84),greatest_lower_bound(inverse(X_84),identity)),greatest_lower_bound(least_upper_bound(identity,X_84),multiply(least_upper_bound(identity,X_84),inverse(X_84)))) ),[1,1],$fot(least_upper_bound(identity,inverse(X_84)))]]) ).
cnf(refute_0_202,plain,
( multiply(least_upper_bound(identity,X_84),greatest_lower_bound(inverse(X_84),identity)) != greatest_lower_bound(least_upper_bound(identity,X_84),multiply(least_upper_bound(identity,X_84),inverse(X_84)))
| multiply(least_upper_bound(identity,X_84),greatest_lower_bound(inverse(X_84),identity)) = greatest_lower_bound(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_84),inverse(X_84)),least_upper_bound(identity,inverse(X_84))) )],[refute_0_200,refute_0_201]) ).
cnf(refute_0_203,plain,
multiply(least_upper_bound(identity,X_84),greatest_lower_bound(inverse(X_84),identity)) = greatest_lower_bound(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_84),greatest_lower_bound(inverse(X_84),identity)),greatest_lower_bound(least_upper_bound(identity,X_84),multiply(least_upper_bound(identity,X_84),inverse(X_84)))) )],[refute_0_186,refute_0_202]) ).
cnf(refute_0_204,plain,
greatest_lower_bound(X_21,greatest_lower_bound(X_21,X_22)) = greatest_lower_bound(greatest_lower_bound(X_21,X_21),X_22),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_21)),bind(Y,$fot(X_21)),bind(Z,$fot(X_22))]]) ).
cnf(refute_0_205,plain,
greatest_lower_bound(X_21,X_21) = X_21,
inference(subst,[],[idempotence_of_gld:[bind(X,$fot(X_21))]]) ).
cnf(refute_0_206,plain,
( greatest_lower_bound(X_21,X_21) != X_21
| greatest_lower_bound(X_21,greatest_lower_bound(X_21,X_22)) != greatest_lower_bound(greatest_lower_bound(X_21,X_21),X_22)
| greatest_lower_bound(X_21,greatest_lower_bound(X_21,X_22)) = greatest_lower_bound(X_21,X_22) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_21,greatest_lower_bound(X_21,X_22)),greatest_lower_bound(greatest_lower_bound(X_21,X_21),X_22)) ),[1,0],$fot(X_21)]]) ).
cnf(refute_0_207,plain,
( greatest_lower_bound(X_21,greatest_lower_bound(X_21,X_22)) != greatest_lower_bound(greatest_lower_bound(X_21,X_21),X_22)
| greatest_lower_bound(X_21,greatest_lower_bound(X_21,X_22)) = greatest_lower_bound(X_21,X_22) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_21,X_21),X_21) )],[refute_0_205,refute_0_206]) ).
cnf(refute_0_208,plain,
greatest_lower_bound(X_21,greatest_lower_bound(X_21,X_22)) = greatest_lower_bound(X_21,X_22),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_21,greatest_lower_bound(X_21,X_22)),greatest_lower_bound(greatest_lower_bound(X_21,X_21),X_22)) )],[refute_0_204,refute_0_207]) ).
cnf(refute_0_209,plain,
greatest_lower_bound(X_21,greatest_lower_bound(X_21,multiply(X_21,X_142))) = greatest_lower_bound(X_21,multiply(X_21,X_142)),
inference(subst,[],[refute_0_208:[bind(X_22,$fot(multiply(X_21,X_142)))]]) ).
cnf(refute_0_210,plain,
multiply(X_21,greatest_lower_bound(X_142,identity)) = greatest_lower_bound(X_21,multiply(X_21,X_142)),
inference(subst,[],[refute_0_57:[bind(X_67,$fot(X_21)),bind(X_68,$fot(X_142))]]) ).
cnf(refute_0_211,plain,
( multiply(X_21,greatest_lower_bound(X_142,identity)) != greatest_lower_bound(X_21,multiply(X_21,X_142))
| greatest_lower_bound(X_21,multiply(X_21,X_142)) = multiply(X_21,greatest_lower_bound(X_142,identity)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(multiply(X_21,greatest_lower_bound(X_142,identity)))),bind(Y0,$fot(greatest_lower_bound(X_21,multiply(X_21,X_142))))]]) ).
cnf(refute_0_212,plain,
greatest_lower_bound(X_21,multiply(X_21,X_142)) = multiply(X_21,greatest_lower_bound(X_142,identity)),
inference(resolve,[$cnf( $equal(multiply(X_21,greatest_lower_bound(X_142,identity)),greatest_lower_bound(X_21,multiply(X_21,X_142))) )],[refute_0_210,refute_0_211]) ).
cnf(refute_0_213,plain,
( greatest_lower_bound(X_21,multiply(X_21,X_142)) != multiply(X_21,greatest_lower_bound(X_142,identity))
| greatest_lower_bound(X_21,greatest_lower_bound(X_21,multiply(X_21,X_142))) != greatest_lower_bound(X_21,multiply(X_21,X_142))
| greatest_lower_bound(X_21,greatest_lower_bound(X_21,multiply(X_21,X_142))) = multiply(X_21,greatest_lower_bound(X_142,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_21,greatest_lower_bound(X_21,multiply(X_21,X_142))),greatest_lower_bound(X_21,multiply(X_21,X_142))) ),[1],$fot(multiply(X_21,greatest_lower_bound(X_142,identity)))]]) ).
cnf(refute_0_214,plain,
( greatest_lower_bound(X_21,greatest_lower_bound(X_21,multiply(X_21,X_142))) != greatest_lower_bound(X_21,multiply(X_21,X_142))
| greatest_lower_bound(X_21,greatest_lower_bound(X_21,multiply(X_21,X_142))) = multiply(X_21,greatest_lower_bound(X_142,identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_21,multiply(X_21,X_142)),multiply(X_21,greatest_lower_bound(X_142,identity))) )],[refute_0_212,refute_0_213]) ).
cnf(refute_0_215,plain,
greatest_lower_bound(X_21,greatest_lower_bound(X_21,multiply(X_21,X_142))) = multiply(X_21,greatest_lower_bound(X_142,identity)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_21,greatest_lower_bound(X_21,multiply(X_21,X_142))),greatest_lower_bound(X_21,multiply(X_21,X_142))) )],[refute_0_209,refute_0_214]) ).
cnf(refute_0_216,plain,
( greatest_lower_bound(X,least_upper_bound(X,Y)) != X
| least_upper_bound(X,Y) != least_upper_bound(Y,X)
| greatest_lower_bound(X,least_upper_bound(Y,X)) = X ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X,least_upper_bound(X,Y)),X) ),[0,1],$fot(least_upper_bound(Y,X))]]) ).
cnf(refute_0_217,plain,
( greatest_lower_bound(X,least_upper_bound(X,Y)) != X
| greatest_lower_bound(X,least_upper_bound(Y,X)) = X ),
inference(resolve,[$cnf( $equal(least_upper_bound(X,Y),least_upper_bound(Y,X)) )],[symmetry_of_lub,refute_0_216]) ).
cnf(refute_0_218,plain,
greatest_lower_bound(X,least_upper_bound(Y,X)) = X,
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,least_upper_bound(X,Y)),X) )],[glb_absorbtion,refute_0_217]) ).
cnf(refute_0_219,plain,
greatest_lower_bound(greatest_lower_bound(Y,X_15),least_upper_bound(Y,greatest_lower_bound(Y,X_15))) = greatest_lower_bound(Y,X_15),
inference(subst,[],[refute_0_218:[bind(X,$fot(greatest_lower_bound(Y,X_15)))]]) ).
cnf(refute_0_220,plain,
least_upper_bound(Y,greatest_lower_bound(Y,X_15)) = Y,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(Y)),bind(Y,$fot(X_15))]]) ).
cnf(refute_0_221,plain,
( greatest_lower_bound(greatest_lower_bound(Y,X_15),least_upper_bound(Y,greatest_lower_bound(Y,X_15))) != greatest_lower_bound(Y,X_15)
| least_upper_bound(Y,greatest_lower_bound(Y,X_15)) != Y
| greatest_lower_bound(greatest_lower_bound(Y,X_15),Y) = greatest_lower_bound(Y,X_15) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(Y,X_15),least_upper_bound(Y,greatest_lower_bound(Y,X_15))),greatest_lower_bound(Y,X_15)) ),[0,1],$fot(Y)]]) ).
cnf(refute_0_222,plain,
( greatest_lower_bound(greatest_lower_bound(Y,X_15),least_upper_bound(Y,greatest_lower_bound(Y,X_15))) != greatest_lower_bound(Y,X_15)
| greatest_lower_bound(greatest_lower_bound(Y,X_15),Y) = greatest_lower_bound(Y,X_15) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,greatest_lower_bound(Y,X_15)),Y) )],[refute_0_220,refute_0_221]) ).
cnf(refute_0_223,plain,
greatest_lower_bound(greatest_lower_bound(Y,X_15),Y) = greatest_lower_bound(Y,X_15),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(Y,X_15),least_upper_bound(Y,greatest_lower_bound(Y,X_15))),greatest_lower_bound(Y,X_15)) )],[refute_0_219,refute_0_222]) ).
cnf(refute_0_224,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,Z)) != greatest_lower_bound(greatest_lower_bound(X,Y),Z)
| greatest_lower_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(Y,Z)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X,Y),Z)))]]) ).
cnf(refute_0_225,plain,
greatest_lower_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(greatest_lower_bound(X,Y),Z)) )],[associativity_of_glb,refute_0_224]) ).
cnf(refute_0_226,plain,
greatest_lower_bound(greatest_lower_bound(Y,X_15),Y) = greatest_lower_bound(Y,greatest_lower_bound(X_15,Y)),
inference(subst,[],[refute_0_225:[bind(X,$fot(Y)),bind(Y,$fot(X_15)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_227,plain,
( greatest_lower_bound(greatest_lower_bound(Y,X_15),Y) != greatest_lower_bound(Y,X_15)
| greatest_lower_bound(greatest_lower_bound(Y,X_15),Y) != greatest_lower_bound(Y,greatest_lower_bound(X_15,Y))
| greatest_lower_bound(Y,greatest_lower_bound(X_15,Y)) = greatest_lower_bound(Y,X_15) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(Y,X_15),Y),greatest_lower_bound(Y,X_15)) ),[0],$fot(greatest_lower_bound(Y,greatest_lower_bound(X_15,Y)))]]) ).
cnf(refute_0_228,plain,
( greatest_lower_bound(greatest_lower_bound(Y,X_15),Y) != greatest_lower_bound(Y,X_15)
| greatest_lower_bound(Y,greatest_lower_bound(X_15,Y)) = greatest_lower_bound(Y,X_15) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(Y,X_15),Y),greatest_lower_bound(Y,greatest_lower_bound(X_15,Y))) )],[refute_0_226,refute_0_227]) ).
cnf(refute_0_229,plain,
greatest_lower_bound(Y,greatest_lower_bound(X_15,Y)) = greatest_lower_bound(Y,X_15),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(Y,X_15),Y),greatest_lower_bound(Y,X_15)) )],[refute_0_223,refute_0_228]) ).
cnf(refute_0_230,plain,
greatest_lower_bound(identity,greatest_lower_bound(X_142,identity)) = greatest_lower_bound(identity,X_142),
inference(subst,[],[refute_0_229:[bind(Y,$fot(identity)),bind(X_15,$fot(X_142))]]) ).
cnf(refute_0_231,plain,
multiply(X_21,greatest_lower_bound(identity,greatest_lower_bound(X_142,identity))) = multiply(X_21,greatest_lower_bound(identity,greatest_lower_bound(X_142,identity))),
introduced(tautology,[refl,[$fot(multiply(X_21,greatest_lower_bound(identity,greatest_lower_bound(X_142,identity))))]]) ).
cnf(refute_0_232,plain,
( multiply(X_21,greatest_lower_bound(identity,greatest_lower_bound(X_142,identity))) != multiply(X_21,greatest_lower_bound(identity,greatest_lower_bound(X_142,identity)))
| greatest_lower_bound(identity,greatest_lower_bound(X_142,identity)) != greatest_lower_bound(identity,X_142)
| multiply(X_21,greatest_lower_bound(identity,greatest_lower_bound(X_142,identity))) = multiply(X_21,greatest_lower_bound(identity,X_142)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_21,greatest_lower_bound(identity,greatest_lower_bound(X_142,identity))),multiply(X_21,greatest_lower_bound(identity,greatest_lower_bound(X_142,identity)))) ),[1,1],$fot(greatest_lower_bound(identity,X_142))]]) ).
cnf(refute_0_233,plain,
( greatest_lower_bound(identity,greatest_lower_bound(X_142,identity)) != greatest_lower_bound(identity,X_142)
| multiply(X_21,greatest_lower_bound(identity,greatest_lower_bound(X_142,identity))) = multiply(X_21,greatest_lower_bound(identity,X_142)) ),
inference(resolve,[$cnf( $equal(multiply(X_21,greatest_lower_bound(identity,greatest_lower_bound(X_142,identity))),multiply(X_21,greatest_lower_bound(identity,greatest_lower_bound(X_142,identity)))) )],[refute_0_231,refute_0_232]) ).
cnf(refute_0_234,plain,
multiply(X_21,greatest_lower_bound(identity,greatest_lower_bound(X_142,identity))) = multiply(X_21,greatest_lower_bound(identity,X_142)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_142,identity)),greatest_lower_bound(identity,X_142)) )],[refute_0_230,refute_0_233]) ).
cnf(refute_0_235,plain,
greatest_lower_bound(multiply(X,Y),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)),
inference(subst,[],[refute_0_208:[bind(X_21,$fot(multiply(X,Y))),bind(X_22,$fot(multiply(X,Z)))]]) ).
cnf(refute_0_236,plain,
( multiply(X,greatest_lower_bound(Y,Z)) != greatest_lower_bound(multiply(X,Y),multiply(X,Z))
| greatest_lower_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,greatest_lower_bound(Y,Z)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(multiply(X,greatest_lower_bound(Y,Z)))),bind(Y0,$fot(greatest_lower_bound(multiply(X,Y),multiply(X,Z))))]]) ).
cnf(refute_0_237,plain,
greatest_lower_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) )],[monotony_glb1,refute_0_236]) ).
cnf(refute_0_238,plain,
( greatest_lower_bound(multiply(X,Y),multiply(X,Z)) != multiply(X,greatest_lower_bound(Y,Z))
| greatest_lower_bound(multiply(X,Y),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) != greatest_lower_bound(multiply(X,Y),multiply(X,Z))
| greatest_lower_bound(multiply(X,Y),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) = multiply(X,greatest_lower_bound(Y,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X,Y),greatest_lower_bound(multiply(X,Y),multiply(X,Z))),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) ),[1],$fot(multiply(X,greatest_lower_bound(Y,Z)))]]) ).
cnf(refute_0_239,plain,
( greatest_lower_bound(multiply(X,Y),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) != greatest_lower_bound(multiply(X,Y),multiply(X,Z))
| greatest_lower_bound(multiply(X,Y),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) = multiply(X,greatest_lower_bound(Y,Z)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,Y),multiply(X,Z)),multiply(X,greatest_lower_bound(Y,Z))) )],[refute_0_237,refute_0_238]) ).
cnf(refute_0_240,plain,
greatest_lower_bound(multiply(X,Y),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) = multiply(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,Y),greatest_lower_bound(multiply(X,Y),multiply(X,Z))),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) )],[refute_0_235,refute_0_239]) ).
cnf(refute_0_241,plain,
greatest_lower_bound(multiply(X,Z),multiply(X,Y)) = multiply(X,greatest_lower_bound(Z,Y)),
inference(subst,[],[refute_0_237:[bind(Y,$fot(Z)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_242,plain,
multiply(greatest_lower_bound(X,X),Y) = multiply(greatest_lower_bound(X,X),Y),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(X,X),Y))]]) ).
cnf(refute_0_243,plain,
( multiply(greatest_lower_bound(X,X),Y) != multiply(greatest_lower_bound(X,X),Y)
| greatest_lower_bound(X,X) != X
| multiply(greatest_lower_bound(X,X),Y) = multiply(X,Y) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X,X),Y),multiply(greatest_lower_bound(X,X),Y)) ),[1,0],$fot(X)]]) ).
cnf(refute_0_244,plain,
( greatest_lower_bound(X,X) != X
| multiply(greatest_lower_bound(X,X),Y) = multiply(X,Y) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X,X),Y),multiply(greatest_lower_bound(X,X),Y)) )],[refute_0_242,refute_0_243]) ).
cnf(refute_0_245,plain,
multiply(greatest_lower_bound(X,X),Y) = multiply(X,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,X),X) )],[idempotence_of_gld,refute_0_244]) ).
cnf(refute_0_246,plain,
greatest_lower_bound(multiply(X,Z),multiply(greatest_lower_bound(X,X),Y)) = greatest_lower_bound(multiply(X,Z),multiply(greatest_lower_bound(X,X),Y)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(multiply(X,Z),multiply(greatest_lower_bound(X,X),Y)))]]) ).
cnf(refute_0_247,plain,
( multiply(greatest_lower_bound(X,X),Y) != multiply(X,Y)
| greatest_lower_bound(multiply(X,Z),multiply(greatest_lower_bound(X,X),Y)) != greatest_lower_bound(multiply(X,Z),multiply(greatest_lower_bound(X,X),Y))
| greatest_lower_bound(multiply(X,Z),multiply(greatest_lower_bound(X,X),Y)) = greatest_lower_bound(multiply(X,Z),multiply(X,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X,Z),multiply(greatest_lower_bound(X,X),Y)),greatest_lower_bound(multiply(X,Z),multiply(greatest_lower_bound(X,X),Y))) ),[1,1],$fot(multiply(X,Y))]]) ).
cnf(refute_0_248,plain,
( multiply(greatest_lower_bound(X,X),Y) != multiply(X,Y)
| greatest_lower_bound(multiply(X,Z),multiply(greatest_lower_bound(X,X),Y)) = greatest_lower_bound(multiply(X,Z),multiply(X,Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,Z),multiply(greatest_lower_bound(X,X),Y)),greatest_lower_bound(multiply(X,Z),multiply(greatest_lower_bound(X,X),Y))) )],[refute_0_246,refute_0_247]) ).
cnf(refute_0_249,plain,
greatest_lower_bound(multiply(X,Z),multiply(greatest_lower_bound(X,X),Y)) = greatest_lower_bound(multiply(X,Z),multiply(X,Y)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X,X),Y),multiply(X,Y)) )],[refute_0_245,refute_0_248]) ).
cnf(refute_0_250,plain,
( greatest_lower_bound(multiply(X,Z),multiply(X,Y)) != multiply(X,greatest_lower_bound(Z,Y))
| greatest_lower_bound(multiply(X,Z),multiply(greatest_lower_bound(X,X),Y)) != greatest_lower_bound(multiply(X,Z),multiply(X,Y))
| greatest_lower_bound(multiply(X,Z),multiply(greatest_lower_bound(X,X),Y)) = multiply(X,greatest_lower_bound(Z,Y)) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(greatest_lower_bound(multiply(X,Z),multiply(greatest_lower_bound(X,X),Y)))),bind(Y0,$fot(greatest_lower_bound(multiply(X,Z),multiply(X,Y)))),bind(Z0,$fot(multiply(X,greatest_lower_bound(Z,Y))))]]) ).
cnf(refute_0_251,plain,
( greatest_lower_bound(multiply(X,Z),multiply(X,Y)) != multiply(X,greatest_lower_bound(Z,Y))
| greatest_lower_bound(multiply(X,Z),multiply(greatest_lower_bound(X,X),Y)) = multiply(X,greatest_lower_bound(Z,Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,Z),multiply(greatest_lower_bound(X,X),Y)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) )],[refute_0_249,refute_0_250]) ).
cnf(refute_0_252,plain,
greatest_lower_bound(multiply(X,Z),multiply(greatest_lower_bound(X,X),Y)) = multiply(X,greatest_lower_bound(Z,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Z,Y))) )],[refute_0_241,refute_0_251]) ).
cnf(refute_0_253,plain,
greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_35,Y))) = greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_35,Y)),
inference(subst,[],[associativity_of_glb:[bind(Z,$fot(greatest_lower_bound(X_35,Y)))]]) ).
cnf(refute_0_254,plain,
greatest_lower_bound(Y,greatest_lower_bound(X_35,Y)) = greatest_lower_bound(Y,X_35),
inference(subst,[],[refute_0_229:[bind(X_15,$fot(X_35))]]) ).
cnf(refute_0_255,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_35,Y))) != greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_35,Y))
| greatest_lower_bound(Y,greatest_lower_bound(X_35,Y)) != greatest_lower_bound(Y,X_35)
| greatest_lower_bound(X,greatest_lower_bound(Y,X_35)) = greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_35,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_35,Y))),greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_35,Y))) ),[0,1],$fot(greatest_lower_bound(Y,X_35))]]) ).
cnf(refute_0_256,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_35,Y))) != greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_35,Y))
| greatest_lower_bound(X,greatest_lower_bound(Y,X_35)) = greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_35,Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(X_35,Y)),greatest_lower_bound(Y,X_35)) )],[refute_0_254,refute_0_255]) ).
cnf(refute_0_257,plain,
greatest_lower_bound(X,greatest_lower_bound(Y,X_35)) = greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_35,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_35,Y))),greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_35,Y))) )],[refute_0_253,refute_0_256]) ).
cnf(refute_0_258,plain,
greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_35,greatest_lower_bound(X,Y)))) = greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_35,greatest_lower_bound(X,Y))),
inference(subst,[],[associativity_of_glb:[bind(Z,$fot(greatest_lower_bound(X_35,greatest_lower_bound(X,Y))))]]) ).
cnf(refute_0_259,plain,
greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_35,greatest_lower_bound(X,Y))) = greatest_lower_bound(greatest_lower_bound(X,Y),X_35),
inference(subst,[],[refute_0_229:[bind(Y,$fot(greatest_lower_bound(X,Y))),bind(X_15,$fot(X_35))]]) ).
cnf(refute_0_260,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_35,greatest_lower_bound(X,Y)))) != greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_35,greatest_lower_bound(X,Y)))
| greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_35,greatest_lower_bound(X,Y))) != greatest_lower_bound(greatest_lower_bound(X,Y),X_35)
| greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_35,greatest_lower_bound(X,Y)))) = greatest_lower_bound(greatest_lower_bound(X,Y),X_35) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_35,greatest_lower_bound(X,Y)))),greatest_lower_bound(greatest_lower_bound(X,Y),X_35)) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_35,greatest_lower_bound(X,Y))))]]) ).
cnf(refute_0_261,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_35,greatest_lower_bound(X,Y)))) != greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_35,greatest_lower_bound(X,Y)))
| greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_35,greatest_lower_bound(X,Y)))) = greatest_lower_bound(greatest_lower_bound(X,Y),X_35) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_35,greatest_lower_bound(X,Y))),greatest_lower_bound(greatest_lower_bound(X,Y),X_35)) )],[refute_0_259,refute_0_260]) ).
cnf(refute_0_262,plain,
greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_35,greatest_lower_bound(X,Y)))) = greatest_lower_bound(greatest_lower_bound(X,Y),X_35),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_35,greatest_lower_bound(X,Y)))),greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_35,greatest_lower_bound(X,Y)))) )],[refute_0_258,refute_0_261]) ).
cnf(refute_0_263,plain,
greatest_lower_bound(greatest_lower_bound(X_30,greatest_lower_bound(X_31,Y)),least_upper_bound(Y,greatest_lower_bound(X_30,greatest_lower_bound(X_31,Y)))) = greatest_lower_bound(X_30,greatest_lower_bound(X_31,Y)),
inference(subst,[],[refute_0_218:[bind(X,$fot(greatest_lower_bound(X_30,greatest_lower_bound(X_31,Y))))]]) ).
cnf(refute_0_264,plain,
least_upper_bound(X_14,greatest_lower_bound(X_14,X_15)) = X_14,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_14)),bind(Y,$fot(X_15))]]) ).
cnf(refute_0_265,plain,
greatest_lower_bound(X_15,X_14) = greatest_lower_bound(X_14,X_15),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_15)),bind(Y,$fot(X_14))]]) ).
cnf(refute_0_266,plain,
( greatest_lower_bound(X_15,X_14) != greatest_lower_bound(X_14,X_15)
| greatest_lower_bound(X_14,X_15) = greatest_lower_bound(X_15,X_14) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(greatest_lower_bound(X_15,X_14))),bind(Y0,$fot(greatest_lower_bound(X_14,X_15)))]]) ).
cnf(refute_0_267,plain,
greatest_lower_bound(X_14,X_15) = greatest_lower_bound(X_15,X_14),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_15,X_14),greatest_lower_bound(X_14,X_15)) )],[refute_0_265,refute_0_266]) ).
cnf(refute_0_268,plain,
( greatest_lower_bound(X_14,X_15) != greatest_lower_bound(X_15,X_14)
| least_upper_bound(X_14,greatest_lower_bound(X_14,X_15)) != X_14
| least_upper_bound(X_14,greatest_lower_bound(X_15,X_14)) = X_14 ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_14,greatest_lower_bound(X_14,X_15)),X_14) ),[0,1],$fot(greatest_lower_bound(X_15,X_14))]]) ).
cnf(refute_0_269,plain,
( least_upper_bound(X_14,greatest_lower_bound(X_14,X_15)) != X_14
| least_upper_bound(X_14,greatest_lower_bound(X_15,X_14)) = X_14 ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_14,X_15),greatest_lower_bound(X_15,X_14)) )],[refute_0_267,refute_0_268]) ).
cnf(refute_0_270,plain,
least_upper_bound(X_14,greatest_lower_bound(X_15,X_14)) = X_14,
inference(resolve,[$cnf( $equal(least_upper_bound(X_14,greatest_lower_bound(X_14,X_15)),X_14) )],[refute_0_264,refute_0_269]) ).
cnf(refute_0_271,plain,
least_upper_bound(X_14,greatest_lower_bound(greatest_lower_bound(X_20,X_21),X_14)) = X_14,
inference(subst,[],[refute_0_270:[bind(X_15,$fot(greatest_lower_bound(X_20,X_21)))]]) ).
cnf(refute_0_272,plain,
greatest_lower_bound(X_20,greatest_lower_bound(X_21,X_14)) = greatest_lower_bound(greatest_lower_bound(X_20,X_21),X_14),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_20)),bind(Y,$fot(X_21)),bind(Z,$fot(X_14))]]) ).
cnf(refute_0_273,plain,
( greatest_lower_bound(X_20,greatest_lower_bound(X_21,X_14)) != greatest_lower_bound(greatest_lower_bound(X_20,X_21),X_14)
| greatest_lower_bound(greatest_lower_bound(X_20,X_21),X_14) = greatest_lower_bound(X_20,greatest_lower_bound(X_21,X_14)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(greatest_lower_bound(X_20,greatest_lower_bound(X_21,X_14)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X_20,X_21),X_14)))]]) ).
cnf(refute_0_274,plain,
greatest_lower_bound(greatest_lower_bound(X_20,X_21),X_14) = greatest_lower_bound(X_20,greatest_lower_bound(X_21,X_14)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_20,greatest_lower_bound(X_21,X_14)),greatest_lower_bound(greatest_lower_bound(X_20,X_21),X_14)) )],[refute_0_272,refute_0_273]) ).
cnf(refute_0_275,plain,
( greatest_lower_bound(greatest_lower_bound(X_20,X_21),X_14) != greatest_lower_bound(X_20,greatest_lower_bound(X_21,X_14))
| least_upper_bound(X_14,greatest_lower_bound(greatest_lower_bound(X_20,X_21),X_14)) != X_14
| least_upper_bound(X_14,greatest_lower_bound(X_20,greatest_lower_bound(X_21,X_14))) = X_14 ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_14,greatest_lower_bound(greatest_lower_bound(X_20,X_21),X_14)),X_14) ),[0,1],$fot(greatest_lower_bound(X_20,greatest_lower_bound(X_21,X_14)))]]) ).
cnf(refute_0_276,plain,
( least_upper_bound(X_14,greatest_lower_bound(greatest_lower_bound(X_20,X_21),X_14)) != X_14
| least_upper_bound(X_14,greatest_lower_bound(X_20,greatest_lower_bound(X_21,X_14))) = X_14 ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_20,X_21),X_14),greatest_lower_bound(X_20,greatest_lower_bound(X_21,X_14))) )],[refute_0_274,refute_0_275]) ).
cnf(refute_0_277,plain,
least_upper_bound(X_14,greatest_lower_bound(X_20,greatest_lower_bound(X_21,X_14))) = X_14,
inference(resolve,[$cnf( $equal(least_upper_bound(X_14,greatest_lower_bound(greatest_lower_bound(X_20,X_21),X_14)),X_14) )],[refute_0_271,refute_0_276]) ).
cnf(refute_0_278,plain,
least_upper_bound(Y,greatest_lower_bound(X_30,greatest_lower_bound(X_31,Y))) = Y,
inference(subst,[],[refute_0_277:[bind(X_14,$fot(Y)),bind(X_20,$fot(X_30)),bind(X_21,$fot(X_31))]]) ).
cnf(refute_0_279,plain,
( greatest_lower_bound(greatest_lower_bound(X_30,greatest_lower_bound(X_31,Y)),least_upper_bound(Y,greatest_lower_bound(X_30,greatest_lower_bound(X_31,Y)))) != greatest_lower_bound(X_30,greatest_lower_bound(X_31,Y))
| least_upper_bound(Y,greatest_lower_bound(X_30,greatest_lower_bound(X_31,Y))) != Y
| greatest_lower_bound(greatest_lower_bound(X_30,greatest_lower_bound(X_31,Y)),Y) = greatest_lower_bound(X_30,greatest_lower_bound(X_31,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_30,greatest_lower_bound(X_31,Y)),least_upper_bound(Y,greatest_lower_bound(X_30,greatest_lower_bound(X_31,Y)))),greatest_lower_bound(X_30,greatest_lower_bound(X_31,Y))) ),[0,1],$fot(Y)]]) ).
cnf(refute_0_280,plain,
( greatest_lower_bound(greatest_lower_bound(X_30,greatest_lower_bound(X_31,Y)),least_upper_bound(Y,greatest_lower_bound(X_30,greatest_lower_bound(X_31,Y)))) != greatest_lower_bound(X_30,greatest_lower_bound(X_31,Y))
| greatest_lower_bound(greatest_lower_bound(X_30,greatest_lower_bound(X_31,Y)),Y) = greatest_lower_bound(X_30,greatest_lower_bound(X_31,Y)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,greatest_lower_bound(X_30,greatest_lower_bound(X_31,Y))),Y) )],[refute_0_278,refute_0_279]) ).
cnf(refute_0_281,plain,
greatest_lower_bound(greatest_lower_bound(X_30,greatest_lower_bound(X_31,Y)),Y) = greatest_lower_bound(X_30,greatest_lower_bound(X_31,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_30,greatest_lower_bound(X_31,Y)),least_upper_bound(Y,greatest_lower_bound(X_30,greatest_lower_bound(X_31,Y)))),greatest_lower_bound(X_30,greatest_lower_bound(X_31,Y))) )],[refute_0_263,refute_0_280]) ).
cnf(refute_0_282,plain,
greatest_lower_bound(greatest_lower_bound(X_30,greatest_lower_bound(X_31,Y)),Y) = greatest_lower_bound(Y,greatest_lower_bound(X_30,greatest_lower_bound(X_31,Y))),
inference(subst,[],[refute_0_41:[bind(X_21,$fot(Y)),bind(X_22,$fot(greatest_lower_bound(X_30,greatest_lower_bound(X_31,Y))))]]) ).
cnf(refute_0_283,plain,
( greatest_lower_bound(greatest_lower_bound(X_30,greatest_lower_bound(X_31,Y)),Y) != greatest_lower_bound(Y,greatest_lower_bound(X_30,greatest_lower_bound(X_31,Y)))
| greatest_lower_bound(greatest_lower_bound(X_30,greatest_lower_bound(X_31,Y)),Y) != greatest_lower_bound(X_30,greatest_lower_bound(X_31,Y))
| greatest_lower_bound(Y,greatest_lower_bound(X_30,greatest_lower_bound(X_31,Y))) = greatest_lower_bound(X_30,greatest_lower_bound(X_31,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_30,greatest_lower_bound(X_31,Y)),Y),greatest_lower_bound(X_30,greatest_lower_bound(X_31,Y))) ),[0],$fot(greatest_lower_bound(Y,greatest_lower_bound(X_30,greatest_lower_bound(X_31,Y))))]]) ).
cnf(refute_0_284,plain,
( greatest_lower_bound(greatest_lower_bound(X_30,greatest_lower_bound(X_31,Y)),Y) != greatest_lower_bound(X_30,greatest_lower_bound(X_31,Y))
| greatest_lower_bound(Y,greatest_lower_bound(X_30,greatest_lower_bound(X_31,Y))) = greatest_lower_bound(X_30,greatest_lower_bound(X_31,Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_30,greatest_lower_bound(X_31,Y)),Y),greatest_lower_bound(Y,greatest_lower_bound(X_30,greatest_lower_bound(X_31,Y)))) )],[refute_0_282,refute_0_283]) ).
cnf(refute_0_285,plain,
greatest_lower_bound(Y,greatest_lower_bound(X_30,greatest_lower_bound(X_31,Y))) = greatest_lower_bound(X_30,greatest_lower_bound(X_31,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_30,greatest_lower_bound(X_31,Y)),Y),greatest_lower_bound(X_30,greatest_lower_bound(X_31,Y))) )],[refute_0_281,refute_0_284]) ).
cnf(refute_0_286,plain,
greatest_lower_bound(Y,greatest_lower_bound(X_35,greatest_lower_bound(X,Y))) = greatest_lower_bound(X_35,greatest_lower_bound(X,Y)),
inference(subst,[],[refute_0_285:[bind(X_30,$fot(X_35)),bind(X_31,$fot(X))]]) ).
cnf(refute_0_287,plain,
greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_35,greatest_lower_bound(X,Y)))) = greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_35,greatest_lower_bound(X,Y)))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_35,greatest_lower_bound(X,Y)))))]]) ).
cnf(refute_0_288,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_35,greatest_lower_bound(X,Y)))) != greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_35,greatest_lower_bound(X,Y))))
| greatest_lower_bound(Y,greatest_lower_bound(X_35,greatest_lower_bound(X,Y))) != greatest_lower_bound(X_35,greatest_lower_bound(X,Y))
| greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_35,greatest_lower_bound(X,Y)))) = greatest_lower_bound(X,greatest_lower_bound(X_35,greatest_lower_bound(X,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_35,greatest_lower_bound(X,Y)))),greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_35,greatest_lower_bound(X,Y))))) ),[1,1],$fot(greatest_lower_bound(X_35,greatest_lower_bound(X,Y)))]]) ).
cnf(refute_0_289,plain,
( greatest_lower_bound(Y,greatest_lower_bound(X_35,greatest_lower_bound(X,Y))) != greatest_lower_bound(X_35,greatest_lower_bound(X,Y))
| greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_35,greatest_lower_bound(X,Y)))) = greatest_lower_bound(X,greatest_lower_bound(X_35,greatest_lower_bound(X,Y))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_35,greatest_lower_bound(X,Y)))),greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_35,greatest_lower_bound(X,Y))))) )],[refute_0_287,refute_0_288]) ).
cnf(refute_0_290,plain,
greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_35,greatest_lower_bound(X,Y)))) = greatest_lower_bound(X,greatest_lower_bound(X_35,greatest_lower_bound(X,Y))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(X_35,greatest_lower_bound(X,Y))),greatest_lower_bound(X_35,greatest_lower_bound(X,Y))) )],[refute_0_286,refute_0_289]) ).
cnf(refute_0_291,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_35,greatest_lower_bound(X,Y)))) != greatest_lower_bound(X,greatest_lower_bound(X_35,greatest_lower_bound(X,Y)))
| greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_35,greatest_lower_bound(X,Y)))) != greatest_lower_bound(greatest_lower_bound(X,Y),X_35)
| greatest_lower_bound(X,greatest_lower_bound(X_35,greatest_lower_bound(X,Y))) = greatest_lower_bound(greatest_lower_bound(X,Y),X_35) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_35,greatest_lower_bound(X,Y)))),greatest_lower_bound(greatest_lower_bound(X,Y),X_35)) ),[0],$fot(greatest_lower_bound(X,greatest_lower_bound(X_35,greatest_lower_bound(X,Y))))]]) ).
cnf(refute_0_292,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_35,greatest_lower_bound(X,Y)))) != greatest_lower_bound(greatest_lower_bound(X,Y),X_35)
| greatest_lower_bound(X,greatest_lower_bound(X_35,greatest_lower_bound(X,Y))) = greatest_lower_bound(greatest_lower_bound(X,Y),X_35) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_35,greatest_lower_bound(X,Y)))),greatest_lower_bound(X,greatest_lower_bound(X_35,greatest_lower_bound(X,Y)))) )],[refute_0_290,refute_0_291]) ).
cnf(refute_0_293,plain,
greatest_lower_bound(greatest_lower_bound(X,Y),X_35) = greatest_lower_bound(X,greatest_lower_bound(Y,X_35)),
inference(subst,[],[refute_0_225:[bind(Z,$fot(X_35))]]) ).
cnf(refute_0_294,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_35,greatest_lower_bound(X,Y))) != greatest_lower_bound(greatest_lower_bound(X,Y),X_35)
| greatest_lower_bound(greatest_lower_bound(X,Y),X_35) != greatest_lower_bound(X,greatest_lower_bound(Y,X_35))
| greatest_lower_bound(X,greatest_lower_bound(X_35,greatest_lower_bound(X,Y))) = greatest_lower_bound(X,greatest_lower_bound(Y,X_35)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X,greatest_lower_bound(X_35,greatest_lower_bound(X,Y))),greatest_lower_bound(X,greatest_lower_bound(Y,X_35))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X,Y),X_35))]]) ).
cnf(refute_0_295,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_35,greatest_lower_bound(X,Y))) != greatest_lower_bound(greatest_lower_bound(X,Y),X_35)
| greatest_lower_bound(X,greatest_lower_bound(X_35,greatest_lower_bound(X,Y))) = greatest_lower_bound(X,greatest_lower_bound(Y,X_35)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X,Y),X_35),greatest_lower_bound(X,greatest_lower_bound(Y,X_35))) )],[refute_0_293,refute_0_294]) ).
cnf(refute_0_296,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_35,greatest_lower_bound(X,Y)))) != greatest_lower_bound(greatest_lower_bound(X,Y),X_35)
| greatest_lower_bound(X,greatest_lower_bound(X_35,greatest_lower_bound(X,Y))) = greatest_lower_bound(X,greatest_lower_bound(Y,X_35)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_35,greatest_lower_bound(X,Y))),greatest_lower_bound(greatest_lower_bound(X,Y),X_35)) )],[refute_0_292,refute_0_295]) ).
cnf(refute_0_297,plain,
greatest_lower_bound(X,greatest_lower_bound(X_35,greatest_lower_bound(X,Y))) = greatest_lower_bound(X,greatest_lower_bound(Y,X_35)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_35,greatest_lower_bound(X,Y)))),greatest_lower_bound(greatest_lower_bound(X,Y),X_35)) )],[refute_0_262,refute_0_296]) ).
cnf(refute_0_298,plain,
greatest_lower_bound(Y,greatest_lower_bound(X,greatest_lower_bound(Y,X_35))) = greatest_lower_bound(Y,greatest_lower_bound(X_35,X)),
inference(subst,[],[refute_0_297:[bind(X,$fot(Y)),bind(Y,$fot(X_35)),bind(X_35,$fot(X))]]) ).
cnf(refute_0_299,plain,
greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_35)) = greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_35)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_35)))]]) ).
cnf(refute_0_300,plain,
( greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_35)) != greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_35))
| greatest_lower_bound(greatest_lower_bound(X,Y),X_35) != greatest_lower_bound(X,greatest_lower_bound(Y,X_35))
| greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_35)) = greatest_lower_bound(Y,greatest_lower_bound(X,greatest_lower_bound(Y,X_35))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_35)),greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_35))) ),[1,1],$fot(greatest_lower_bound(X,greatest_lower_bound(Y,X_35)))]]) ).
cnf(refute_0_301,plain,
( greatest_lower_bound(greatest_lower_bound(X,Y),X_35) != greatest_lower_bound(X,greatest_lower_bound(Y,X_35))
| greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_35)) = greatest_lower_bound(Y,greatest_lower_bound(X,greatest_lower_bound(Y,X_35))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_35)),greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_35))) )],[refute_0_299,refute_0_300]) ).
cnf(refute_0_302,plain,
greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_35)) = greatest_lower_bound(Y,greatest_lower_bound(X,greatest_lower_bound(Y,X_35))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X,Y),X_35),greatest_lower_bound(X,greatest_lower_bound(Y,X_35))) )],[refute_0_293,refute_0_301]) ).
cnf(refute_0_303,plain,
( greatest_lower_bound(Y,greatest_lower_bound(X,greatest_lower_bound(Y,X_35))) != greatest_lower_bound(Y,greatest_lower_bound(X_35,X))
| greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_35)) != greatest_lower_bound(Y,greatest_lower_bound(X,greatest_lower_bound(Y,X_35)))
| greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_35)) = greatest_lower_bound(Y,greatest_lower_bound(X_35,X)) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_35)))),bind(Y0,$fot(greatest_lower_bound(Y,greatest_lower_bound(X,greatest_lower_bound(Y,X_35))))),bind(Z0,$fot(greatest_lower_bound(Y,greatest_lower_bound(X_35,X))))]]) ).
cnf(refute_0_304,plain,
( greatest_lower_bound(Y,greatest_lower_bound(X,greatest_lower_bound(Y,X_35))) != greatest_lower_bound(Y,greatest_lower_bound(X_35,X))
| greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_35)) = greatest_lower_bound(Y,greatest_lower_bound(X_35,X)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_35)),greatest_lower_bound(Y,greatest_lower_bound(X,greatest_lower_bound(Y,X_35)))) )],[refute_0_302,refute_0_303]) ).
cnf(refute_0_305,plain,
greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_35)) = greatest_lower_bound(Y,greatest_lower_bound(X_35,X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(X,greatest_lower_bound(Y,X_35))),greatest_lower_bound(Y,greatest_lower_bound(X_35,X))) )],[refute_0_298,refute_0_304]) ).
cnf(refute_0_306,plain,
greatest_lower_bound(X,greatest_lower_bound(X_20,X_21)) = greatest_lower_bound(greatest_lower_bound(X_20,X_21),X),
inference(subst,[],[symmetry_of_glb:[bind(Y,$fot(greatest_lower_bound(X_20,X_21)))]]) ).
cnf(refute_0_307,plain,
greatest_lower_bound(X_20,greatest_lower_bound(X_21,X)) = greatest_lower_bound(greatest_lower_bound(X_20,X_21),X),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_20)),bind(Y,$fot(X_21)),bind(Z,$fot(X))]]) ).
cnf(refute_0_308,plain,
( greatest_lower_bound(X_20,greatest_lower_bound(X_21,X)) != greatest_lower_bound(greatest_lower_bound(X_20,X_21),X)
| greatest_lower_bound(greatest_lower_bound(X_20,X_21),X) = greatest_lower_bound(X_20,greatest_lower_bound(X_21,X)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(greatest_lower_bound(X_20,greatest_lower_bound(X_21,X)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X_20,X_21),X)))]]) ).
cnf(refute_0_309,plain,
greatest_lower_bound(greatest_lower_bound(X_20,X_21),X) = greatest_lower_bound(X_20,greatest_lower_bound(X_21,X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_20,greatest_lower_bound(X_21,X)),greatest_lower_bound(greatest_lower_bound(X_20,X_21),X)) )],[refute_0_307,refute_0_308]) ).
cnf(refute_0_310,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_20,X_21)) != greatest_lower_bound(greatest_lower_bound(X_20,X_21),X)
| greatest_lower_bound(greatest_lower_bound(X_20,X_21),X) != greatest_lower_bound(X_20,greatest_lower_bound(X_21,X))
| greatest_lower_bound(X,greatest_lower_bound(X_20,X_21)) = greatest_lower_bound(X_20,greatest_lower_bound(X_21,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X,greatest_lower_bound(X_20,X_21)),greatest_lower_bound(X_20,greatest_lower_bound(X_21,X))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_20,X_21),X))]]) ).
cnf(refute_0_311,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_20,X_21)) != greatest_lower_bound(greatest_lower_bound(X_20,X_21),X)
| greatest_lower_bound(X,greatest_lower_bound(X_20,X_21)) = greatest_lower_bound(X_20,greatest_lower_bound(X_21,X)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_20,X_21),X),greatest_lower_bound(X_20,greatest_lower_bound(X_21,X))) )],[refute_0_309,refute_0_310]) ).
cnf(refute_0_312,plain,
greatest_lower_bound(X,greatest_lower_bound(X_20,X_21)) = greatest_lower_bound(X_20,greatest_lower_bound(X_21,X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_20,X_21)),greatest_lower_bound(greatest_lower_bound(X_20,X_21),X)) )],[refute_0_306,refute_0_311]) ).
cnf(refute_0_313,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_20,X_21)) != greatest_lower_bound(X_20,greatest_lower_bound(X_21,X))
| greatest_lower_bound(X_20,greatest_lower_bound(X_21,X)) = greatest_lower_bound(X,greatest_lower_bound(X_20,X_21)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(X_20,X_21)))),bind(Y0,$fot(greatest_lower_bound(X_20,greatest_lower_bound(X_21,X))))]]) ).
cnf(refute_0_314,plain,
greatest_lower_bound(X_20,greatest_lower_bound(X_21,X)) = greatest_lower_bound(X,greatest_lower_bound(X_20,X_21)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_20,X_21)),greatest_lower_bound(X_20,greatest_lower_bound(X_21,X))) )],[refute_0_312,refute_0_313]) ).
cnf(refute_0_315,plain,
greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_35,Y)) = greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_35)),
inference(subst,[],[refute_0_314:[bind(X,$fot(Y)),bind(X_20,$fot(greatest_lower_bound(X,Y))),bind(X_21,$fot(X_35))]]) ).
cnf(refute_0_316,plain,
( greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_35)) != greatest_lower_bound(Y,greatest_lower_bound(X_35,X))
| greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_35,Y)) != greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_35))
| greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_35,Y)) = greatest_lower_bound(Y,greatest_lower_bound(X_35,X)) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_35,Y)))),bind(Y0,$fot(greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_35)))),bind(Z0,$fot(greatest_lower_bound(Y,greatest_lower_bound(X_35,X))))]]) ).
cnf(refute_0_317,plain,
( greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_35)) != greatest_lower_bound(Y,greatest_lower_bound(X_35,X))
| greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_35,Y)) = greatest_lower_bound(Y,greatest_lower_bound(X_35,X)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_35,Y)),greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_35))) )],[refute_0_315,refute_0_316]) ).
cnf(refute_0_318,plain,
greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_35,Y)) = greatest_lower_bound(Y,greatest_lower_bound(X_35,X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_35)),greatest_lower_bound(Y,greatest_lower_bound(X_35,X))) )],[refute_0_305,refute_0_317]) ).
cnf(refute_0_319,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,X_35)) != greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_35,Y))
| greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_35,Y)) != greatest_lower_bound(Y,greatest_lower_bound(X_35,X))
| greatest_lower_bound(X,greatest_lower_bound(Y,X_35)) = greatest_lower_bound(Y,greatest_lower_bound(X_35,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X,greatest_lower_bound(Y,X_35)),greatest_lower_bound(Y,greatest_lower_bound(X_35,X))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_35,Y)))]]) ).
cnf(refute_0_320,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,X_35)) != greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_35,Y))
| greatest_lower_bound(X,greatest_lower_bound(Y,X_35)) = greatest_lower_bound(Y,greatest_lower_bound(X_35,X)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_35,Y)),greatest_lower_bound(Y,greatest_lower_bound(X_35,X))) )],[refute_0_318,refute_0_319]) ).
cnf(refute_0_321,plain,
greatest_lower_bound(X,greatest_lower_bound(Y,X_35)) = greatest_lower_bound(Y,greatest_lower_bound(X_35,X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,X_35)),greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_35,Y))) )],[refute_0_257,refute_0_320]) ).
cnf(refute_0_322,plain,
greatest_lower_bound(X,greatest_lower_bound(multiply(X_87,X_86),multiply(X_88,X_86))) = greatest_lower_bound(multiply(X_87,X_86),greatest_lower_bound(multiply(X_88,X_86),X)),
inference(subst,[],[refute_0_321:[bind(Y,$fot(multiply(X_87,X_86))),bind(X_35,$fot(multiply(X_88,X_86)))]]) ).
cnf(refute_0_323,plain,
multiply(greatest_lower_bound(X_87,X_88),X_86) = greatest_lower_bound(multiply(X_87,X_86),multiply(X_88,X_86)),
inference(subst,[],[monotony_glb2:[bind(X,$fot(X_86)),bind(Y,$fot(X_87)),bind(Z,$fot(X_88))]]) ).
cnf(refute_0_324,plain,
( multiply(greatest_lower_bound(X_87,X_88),X_86) != greatest_lower_bound(multiply(X_87,X_86),multiply(X_88,X_86))
| greatest_lower_bound(multiply(X_87,X_86),multiply(X_88,X_86)) = multiply(greatest_lower_bound(X_87,X_88),X_86) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(multiply(greatest_lower_bound(X_87,X_88),X_86))),bind(Y0,$fot(greatest_lower_bound(multiply(X_87,X_86),multiply(X_88,X_86))))]]) ).
cnf(refute_0_325,plain,
greatest_lower_bound(multiply(X_87,X_86),multiply(X_88,X_86)) = multiply(greatest_lower_bound(X_87,X_88),X_86),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_87,X_88),X_86),greatest_lower_bound(multiply(X_87,X_86),multiply(X_88,X_86))) )],[refute_0_323,refute_0_324]) ).
cnf(refute_0_326,plain,
( greatest_lower_bound(X,greatest_lower_bound(multiply(X_87,X_86),multiply(X_88,X_86))) != greatest_lower_bound(multiply(X_87,X_86),greatest_lower_bound(multiply(X_88,X_86),X))
| greatest_lower_bound(multiply(X_87,X_86),multiply(X_88,X_86)) != multiply(greatest_lower_bound(X_87,X_88),X_86)
| greatest_lower_bound(X,multiply(greatest_lower_bound(X_87,X_88),X_86)) = greatest_lower_bound(multiply(X_87,X_86),greatest_lower_bound(multiply(X_88,X_86),X)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(multiply(X_87,X_86),multiply(X_88,X_86))),greatest_lower_bound(multiply(X_87,X_86),greatest_lower_bound(multiply(X_88,X_86),X))) ),[0,1],$fot(multiply(greatest_lower_bound(X_87,X_88),X_86))]]) ).
cnf(refute_0_327,plain,
( greatest_lower_bound(X,greatest_lower_bound(multiply(X_87,X_86),multiply(X_88,X_86))) != greatest_lower_bound(multiply(X_87,X_86),greatest_lower_bound(multiply(X_88,X_86),X))
| greatest_lower_bound(X,multiply(greatest_lower_bound(X_87,X_88),X_86)) = greatest_lower_bound(multiply(X_87,X_86),greatest_lower_bound(multiply(X_88,X_86),X)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_87,X_86),multiply(X_88,X_86)),multiply(greatest_lower_bound(X_87,X_88),X_86)) )],[refute_0_325,refute_0_326]) ).
cnf(refute_0_328,plain,
greatest_lower_bound(X,multiply(greatest_lower_bound(X_87,X_88),X_86)) = greatest_lower_bound(multiply(X_87,X_86),greatest_lower_bound(multiply(X_88,X_86),X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(multiply(X_87,X_86),multiply(X_88,X_86))),greatest_lower_bound(multiply(X_87,X_86),greatest_lower_bound(multiply(X_88,X_86),X))) )],[refute_0_322,refute_0_327]) ).
cnf(refute_0_329,plain,
( greatest_lower_bound(X,multiply(greatest_lower_bound(X_87,X_88),X_86)) != greatest_lower_bound(multiply(X_87,X_86),greatest_lower_bound(multiply(X_88,X_86),X))
| greatest_lower_bound(multiply(X_87,X_86),greatest_lower_bound(multiply(X_88,X_86),X)) = greatest_lower_bound(X,multiply(greatest_lower_bound(X_87,X_88),X_86)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(greatest_lower_bound(X,multiply(greatest_lower_bound(X_87,X_88),X_86)))),bind(Y0,$fot(greatest_lower_bound(multiply(X_87,X_86),greatest_lower_bound(multiply(X_88,X_86),X))))]]) ).
cnf(refute_0_330,plain,
greatest_lower_bound(multiply(X_87,X_86),greatest_lower_bound(multiply(X_88,X_86),X)) = greatest_lower_bound(X,multiply(greatest_lower_bound(X_87,X_88),X_86)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,multiply(greatest_lower_bound(X_87,X_88),X_86)),greatest_lower_bound(multiply(X_87,X_86),greatest_lower_bound(multiply(X_88,X_86),X))) )],[refute_0_328,refute_0_329]) ).
cnf(refute_0_331,plain,
greatest_lower_bound(multiply(X,Y),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) = greatest_lower_bound(multiply(X,Z),multiply(greatest_lower_bound(X,X),Y)),
inference(subst,[],[refute_0_330:[bind(X,$fot(multiply(X,Z))),bind(X_86,$fot(Y)),bind(X_87,$fot(X)),bind(X_88,$fot(X))]]) ).
cnf(refute_0_332,plain,
( greatest_lower_bound(multiply(X,Y),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) != greatest_lower_bound(multiply(X,Z),multiply(greatest_lower_bound(X,X),Y))
| greatest_lower_bound(multiply(X,Z),multiply(greatest_lower_bound(X,X),Y)) != multiply(X,greatest_lower_bound(Z,Y))
| greatest_lower_bound(multiply(X,Y),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) = multiply(X,greatest_lower_bound(Z,Y)) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(greatest_lower_bound(multiply(X,Y),greatest_lower_bound(multiply(X,Y),multiply(X,Z))))),bind(Y0,$fot(greatest_lower_bound(multiply(X,Z),multiply(greatest_lower_bound(X,X),Y)))),bind(Z0,$fot(multiply(X,greatest_lower_bound(Z,Y))))]]) ).
cnf(refute_0_333,plain,
( greatest_lower_bound(multiply(X,Z),multiply(greatest_lower_bound(X,X),Y)) != multiply(X,greatest_lower_bound(Z,Y))
| greatest_lower_bound(multiply(X,Y),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) = multiply(X,greatest_lower_bound(Z,Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,Y),greatest_lower_bound(multiply(X,Y),multiply(X,Z))),greatest_lower_bound(multiply(X,Z),multiply(greatest_lower_bound(X,X),Y))) )],[refute_0_331,refute_0_332]) ).
cnf(refute_0_334,plain,
greatest_lower_bound(multiply(X,Y),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) = multiply(X,greatest_lower_bound(Z,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,Z),multiply(greatest_lower_bound(X,X),Y)),multiply(X,greatest_lower_bound(Z,Y))) )],[refute_0_252,refute_0_333]) ).
cnf(refute_0_335,plain,
( greatest_lower_bound(multiply(X,Y),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) != multiply(X,greatest_lower_bound(Y,Z))
| greatest_lower_bound(multiply(X,Y),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) != multiply(X,greatest_lower_bound(Z,Y))
| multiply(X,greatest_lower_bound(Z,Y)) = multiply(X,greatest_lower_bound(Y,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X,Y),greatest_lower_bound(multiply(X,Y),multiply(X,Z))),multiply(X,greatest_lower_bound(Y,Z))) ),[0],$fot(multiply(X,greatest_lower_bound(Z,Y)))]]) ).
cnf(refute_0_336,plain,
( greatest_lower_bound(multiply(X,Y),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) != multiply(X,greatest_lower_bound(Y,Z))
| multiply(X,greatest_lower_bound(Z,Y)) = multiply(X,greatest_lower_bound(Y,Z)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,Y),greatest_lower_bound(multiply(X,Y),multiply(X,Z))),multiply(X,greatest_lower_bound(Z,Y))) )],[refute_0_334,refute_0_335]) ).
cnf(refute_0_337,plain,
multiply(X,greatest_lower_bound(Z,Y)) = multiply(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,Y),greatest_lower_bound(multiply(X,Y),multiply(X,Z))),multiply(X,greatest_lower_bound(Y,Z))) )],[refute_0_240,refute_0_336]) ).
cnf(refute_0_338,plain,
( multiply(X,greatest_lower_bound(Z,Y)) != multiply(X,greatest_lower_bound(Y,Z))
| multiply(X,greatest_lower_bound(Y,Z)) = multiply(X,greatest_lower_bound(Z,Y)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(multiply(X,greatest_lower_bound(Z,Y)))),bind(Y0,$fot(multiply(X,greatest_lower_bound(Y,Z))))]]) ).
cnf(refute_0_339,plain,
multiply(X,greatest_lower_bound(Y,Z)) = multiply(X,greatest_lower_bound(Z,Y)),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(Z,Y)),multiply(X,greatest_lower_bound(Y,Z))) )],[refute_0_337,refute_0_338]) ).
cnf(refute_0_340,plain,
multiply(X_21,greatest_lower_bound(greatest_lower_bound(X_142,identity),identity)) = multiply(X_21,greatest_lower_bound(identity,greatest_lower_bound(X_142,identity))),
inference(subst,[],[refute_0_339:[bind(X,$fot(X_21)),bind(Y,$fot(greatest_lower_bound(X_142,identity))),bind(Z,$fot(identity))]]) ).
cnf(refute_0_341,plain,
( multiply(X_67,greatest_lower_bound(X_68,identity)) != greatest_lower_bound(X_67,multiply(X_67,X_68))
| greatest_lower_bound(X_67,multiply(X_67,X_68)) = multiply(X_67,greatest_lower_bound(X_68,identity)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(multiply(X_67,greatest_lower_bound(X_68,identity)))),bind(Y0,$fot(greatest_lower_bound(X_67,multiply(X_67,X_68))))]]) ).
cnf(refute_0_342,plain,
greatest_lower_bound(X_67,multiply(X_67,X_68)) = multiply(X_67,greatest_lower_bound(X_68,identity)),
inference(resolve,[$cnf( $equal(multiply(X_67,greatest_lower_bound(X_68,identity)),greatest_lower_bound(X_67,multiply(X_67,X_68))) )],[refute_0_57,refute_0_341]) ).
cnf(refute_0_343,plain,
greatest_lower_bound(X_21,multiply(X_21,greatest_lower_bound(X_142,identity))) = multiply(X_21,greatest_lower_bound(greatest_lower_bound(X_142,identity),identity)),
inference(subst,[],[refute_0_342:[bind(X_67,$fot(X_21)),bind(X_68,$fot(greatest_lower_bound(X_142,identity)))]]) ).
cnf(refute_0_344,plain,
( multiply(X_21,greatest_lower_bound(greatest_lower_bound(X_142,identity),identity)) != multiply(X_21,greatest_lower_bound(identity,greatest_lower_bound(X_142,identity)))
| greatest_lower_bound(X_21,multiply(X_21,greatest_lower_bound(X_142,identity))) != multiply(X_21,greatest_lower_bound(greatest_lower_bound(X_142,identity),identity))
| greatest_lower_bound(X_21,multiply(X_21,greatest_lower_bound(X_142,identity))) = multiply(X_21,greatest_lower_bound(identity,greatest_lower_bound(X_142,identity))) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(greatest_lower_bound(X_21,multiply(X_21,greatest_lower_bound(X_142,identity))))),bind(Y0,$fot(multiply(X_21,greatest_lower_bound(greatest_lower_bound(X_142,identity),identity)))),bind(Z0,$fot(multiply(X_21,greatest_lower_bound(identity,greatest_lower_bound(X_142,identity)))))]]) ).
cnf(refute_0_345,plain,
( multiply(X_21,greatest_lower_bound(greatest_lower_bound(X_142,identity),identity)) != multiply(X_21,greatest_lower_bound(identity,greatest_lower_bound(X_142,identity)))
| greatest_lower_bound(X_21,multiply(X_21,greatest_lower_bound(X_142,identity))) = multiply(X_21,greatest_lower_bound(identity,greatest_lower_bound(X_142,identity))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_21,multiply(X_21,greatest_lower_bound(X_142,identity))),multiply(X_21,greatest_lower_bound(greatest_lower_bound(X_142,identity),identity))) )],[refute_0_343,refute_0_344]) ).
cnf(refute_0_346,plain,
greatest_lower_bound(X_21,multiply(X_21,greatest_lower_bound(X_142,identity))) = multiply(X_21,greatest_lower_bound(identity,greatest_lower_bound(X_142,identity))),
inference(resolve,[$cnf( $equal(multiply(X_21,greatest_lower_bound(greatest_lower_bound(X_142,identity),identity)),multiply(X_21,greatest_lower_bound(identity,greatest_lower_bound(X_142,identity)))) )],[refute_0_340,refute_0_345]) ).
cnf(refute_0_347,plain,
greatest_lower_bound(X_20,greatest_lower_bound(X_21,X_22)) = greatest_lower_bound(greatest_lower_bound(X_20,X_21),X_22),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_20)),bind(Y,$fot(X_21)),bind(Z,$fot(X_22))]]) ).
cnf(refute_0_348,plain,
greatest_lower_bound(X_21,X_20) = greatest_lower_bound(X_20,X_21),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_21)),bind(Y,$fot(X_20))]]) ).
cnf(refute_0_349,plain,
( greatest_lower_bound(X_21,X_20) != greatest_lower_bound(X_20,X_21)
| greatest_lower_bound(X_20,X_21) = greatest_lower_bound(X_21,X_20) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(greatest_lower_bound(X_21,X_20))),bind(Y0,$fot(greatest_lower_bound(X_20,X_21)))]]) ).
cnf(refute_0_350,plain,
greatest_lower_bound(X_20,X_21) = greatest_lower_bound(X_21,X_20),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_21,X_20),greatest_lower_bound(X_20,X_21)) )],[refute_0_348,refute_0_349]) ).
cnf(refute_0_351,plain,
( greatest_lower_bound(X_20,X_21) != greatest_lower_bound(X_21,X_20)
| greatest_lower_bound(X_20,greatest_lower_bound(X_21,X_22)) != greatest_lower_bound(greatest_lower_bound(X_20,X_21),X_22)
| greatest_lower_bound(X_20,greatest_lower_bound(X_21,X_22)) = greatest_lower_bound(greatest_lower_bound(X_21,X_20),X_22) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_20,greatest_lower_bound(X_21,X_22)),greatest_lower_bound(greatest_lower_bound(X_20,X_21),X_22)) ),[1,0],$fot(greatest_lower_bound(X_21,X_20))]]) ).
cnf(refute_0_352,plain,
( greatest_lower_bound(X_20,greatest_lower_bound(X_21,X_22)) != greatest_lower_bound(greatest_lower_bound(X_20,X_21),X_22)
| greatest_lower_bound(X_20,greatest_lower_bound(X_21,X_22)) = greatest_lower_bound(greatest_lower_bound(X_21,X_20),X_22) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_20,X_21),greatest_lower_bound(X_21,X_20)) )],[refute_0_350,refute_0_351]) ).
cnf(refute_0_353,plain,
greatest_lower_bound(X_20,greatest_lower_bound(X_21,X_22)) = greatest_lower_bound(greatest_lower_bound(X_21,X_20),X_22),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_20,greatest_lower_bound(X_21,X_22)),greatest_lower_bound(greatest_lower_bound(X_20,X_21),X_22)) )],[refute_0_347,refute_0_352]) ).
cnf(refute_0_354,plain,
greatest_lower_bound(greatest_lower_bound(X_21,X_20),X_22) = greatest_lower_bound(X_21,greatest_lower_bound(X_20,X_22)),
inference(subst,[],[refute_0_225:[bind(X,$fot(X_21)),bind(Y,$fot(X_20)),bind(Z,$fot(X_22))]]) ).
cnf(refute_0_355,plain,
( greatest_lower_bound(X_20,greatest_lower_bound(X_21,X_22)) != greatest_lower_bound(greatest_lower_bound(X_21,X_20),X_22)
| greatest_lower_bound(greatest_lower_bound(X_21,X_20),X_22) != greatest_lower_bound(X_21,greatest_lower_bound(X_20,X_22))
| greatest_lower_bound(X_20,greatest_lower_bound(X_21,X_22)) = greatest_lower_bound(X_21,greatest_lower_bound(X_20,X_22)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_20,greatest_lower_bound(X_21,X_22)),greatest_lower_bound(X_21,greatest_lower_bound(X_20,X_22))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_21,X_20),X_22))]]) ).
cnf(refute_0_356,plain,
( greatest_lower_bound(X_20,greatest_lower_bound(X_21,X_22)) != greatest_lower_bound(greatest_lower_bound(X_21,X_20),X_22)
| greatest_lower_bound(X_20,greatest_lower_bound(X_21,X_22)) = greatest_lower_bound(X_21,greatest_lower_bound(X_20,X_22)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_21,X_20),X_22),greatest_lower_bound(X_21,greatest_lower_bound(X_20,X_22))) )],[refute_0_354,refute_0_355]) ).
cnf(refute_0_357,plain,
greatest_lower_bound(X_20,greatest_lower_bound(X_21,X_22)) = greatest_lower_bound(X_21,greatest_lower_bound(X_20,X_22)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_20,greatest_lower_bound(X_21,X_22)),greatest_lower_bound(greatest_lower_bound(X_21,X_20),X_22)) )],[refute_0_353,refute_0_356]) ).
cnf(refute_0_358,plain,
greatest_lower_bound(X_20,greatest_lower_bound(X_21,multiply(X_20,X_142))) = greatest_lower_bound(X_21,greatest_lower_bound(X_20,multiply(X_20,X_142))),
inference(subst,[],[refute_0_357:[bind(X_22,$fot(multiply(X_20,X_142)))]]) ).
cnf(refute_0_359,plain,
multiply(X_20,greatest_lower_bound(X_142,identity)) = greatest_lower_bound(X_20,multiply(X_20,X_142)),
inference(subst,[],[refute_0_57:[bind(X_67,$fot(X_20)),bind(X_68,$fot(X_142))]]) ).
cnf(refute_0_360,plain,
( multiply(X_20,greatest_lower_bound(X_142,identity)) != greatest_lower_bound(X_20,multiply(X_20,X_142))
| greatest_lower_bound(X_20,multiply(X_20,X_142)) = multiply(X_20,greatest_lower_bound(X_142,identity)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(multiply(X_20,greatest_lower_bound(X_142,identity)))),bind(Y0,$fot(greatest_lower_bound(X_20,multiply(X_20,X_142))))]]) ).
cnf(refute_0_361,plain,
greatest_lower_bound(X_20,multiply(X_20,X_142)) = multiply(X_20,greatest_lower_bound(X_142,identity)),
inference(resolve,[$cnf( $equal(multiply(X_20,greatest_lower_bound(X_142,identity)),greatest_lower_bound(X_20,multiply(X_20,X_142))) )],[refute_0_359,refute_0_360]) ).
cnf(refute_0_362,plain,
( greatest_lower_bound(X_20,multiply(X_20,X_142)) != multiply(X_20,greatest_lower_bound(X_142,identity))
| greatest_lower_bound(X_20,greatest_lower_bound(X_21,multiply(X_20,X_142))) != greatest_lower_bound(X_21,greatest_lower_bound(X_20,multiply(X_20,X_142)))
| greatest_lower_bound(X_20,greatest_lower_bound(X_21,multiply(X_20,X_142))) = greatest_lower_bound(X_21,multiply(X_20,greatest_lower_bound(X_142,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_20,greatest_lower_bound(X_21,multiply(X_20,X_142))),greatest_lower_bound(X_21,greatest_lower_bound(X_20,multiply(X_20,X_142)))) ),[1,1],$fot(multiply(X_20,greatest_lower_bound(X_142,identity)))]]) ).
cnf(refute_0_363,plain,
( greatest_lower_bound(X_20,greatest_lower_bound(X_21,multiply(X_20,X_142))) != greatest_lower_bound(X_21,greatest_lower_bound(X_20,multiply(X_20,X_142)))
| greatest_lower_bound(X_20,greatest_lower_bound(X_21,multiply(X_20,X_142))) = greatest_lower_bound(X_21,multiply(X_20,greatest_lower_bound(X_142,identity))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_20,multiply(X_20,X_142)),multiply(X_20,greatest_lower_bound(X_142,identity))) )],[refute_0_361,refute_0_362]) ).
cnf(refute_0_364,plain,
greatest_lower_bound(X_20,greatest_lower_bound(X_21,multiply(X_20,X_142))) = greatest_lower_bound(X_21,multiply(X_20,greatest_lower_bound(X_142,identity))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_20,greatest_lower_bound(X_21,multiply(X_20,X_142))),greatest_lower_bound(X_21,greatest_lower_bound(X_20,multiply(X_20,X_142)))) )],[refute_0_358,refute_0_363]) ).
cnf(refute_0_365,plain,
greatest_lower_bound(X_21,greatest_lower_bound(X_21,multiply(X_21,X_142))) = greatest_lower_bound(X_21,multiply(X_21,greatest_lower_bound(X_142,identity))),
inference(subst,[],[refute_0_364:[bind(X_20,$fot(X_21))]]) ).
cnf(refute_0_366,plain,
( greatest_lower_bound(X_21,multiply(X_21,greatest_lower_bound(X_142,identity))) != multiply(X_21,greatest_lower_bound(identity,greatest_lower_bound(X_142,identity)))
| greatest_lower_bound(X_21,greatest_lower_bound(X_21,multiply(X_21,X_142))) != greatest_lower_bound(X_21,multiply(X_21,greatest_lower_bound(X_142,identity)))
| greatest_lower_bound(X_21,greatest_lower_bound(X_21,multiply(X_21,X_142))) = multiply(X_21,greatest_lower_bound(identity,greatest_lower_bound(X_142,identity))) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(greatest_lower_bound(X_21,greatest_lower_bound(X_21,multiply(X_21,X_142))))),bind(Y0,$fot(greatest_lower_bound(X_21,multiply(X_21,greatest_lower_bound(X_142,identity))))),bind(Z0,$fot(multiply(X_21,greatest_lower_bound(identity,greatest_lower_bound(X_142,identity)))))]]) ).
cnf(refute_0_367,plain,
( greatest_lower_bound(X_21,multiply(X_21,greatest_lower_bound(X_142,identity))) != multiply(X_21,greatest_lower_bound(identity,greatest_lower_bound(X_142,identity)))
| greatest_lower_bound(X_21,greatest_lower_bound(X_21,multiply(X_21,X_142))) = multiply(X_21,greatest_lower_bound(identity,greatest_lower_bound(X_142,identity))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_21,greatest_lower_bound(X_21,multiply(X_21,X_142))),greatest_lower_bound(X_21,multiply(X_21,greatest_lower_bound(X_142,identity)))) )],[refute_0_365,refute_0_366]) ).
cnf(refute_0_368,plain,
greatest_lower_bound(X_21,greatest_lower_bound(X_21,multiply(X_21,X_142))) = multiply(X_21,greatest_lower_bound(identity,greatest_lower_bound(X_142,identity))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_21,multiply(X_21,greatest_lower_bound(X_142,identity))),multiply(X_21,greatest_lower_bound(identity,greatest_lower_bound(X_142,identity)))) )],[refute_0_346,refute_0_367]) ).
cnf(refute_0_369,plain,
( multiply(X_21,greatest_lower_bound(identity,greatest_lower_bound(X_142,identity))) != multiply(X_21,greatest_lower_bound(identity,X_142))
| greatest_lower_bound(X_21,greatest_lower_bound(X_21,multiply(X_21,X_142))) != multiply(X_21,greatest_lower_bound(identity,greatest_lower_bound(X_142,identity)))
| greatest_lower_bound(X_21,greatest_lower_bound(X_21,multiply(X_21,X_142))) = multiply(X_21,greatest_lower_bound(identity,X_142)) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(greatest_lower_bound(X_21,greatest_lower_bound(X_21,multiply(X_21,X_142))))),bind(Y0,$fot(multiply(X_21,greatest_lower_bound(identity,greatest_lower_bound(X_142,identity))))),bind(Z0,$fot(multiply(X_21,greatest_lower_bound(identity,X_142))))]]) ).
cnf(refute_0_370,plain,
( multiply(X_21,greatest_lower_bound(identity,greatest_lower_bound(X_142,identity))) != multiply(X_21,greatest_lower_bound(identity,X_142))
| greatest_lower_bound(X_21,greatest_lower_bound(X_21,multiply(X_21,X_142))) = multiply(X_21,greatest_lower_bound(identity,X_142)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_21,greatest_lower_bound(X_21,multiply(X_21,X_142))),multiply(X_21,greatest_lower_bound(identity,greatest_lower_bound(X_142,identity)))) )],[refute_0_368,refute_0_369]) ).
cnf(refute_0_371,plain,
greatest_lower_bound(X_21,greatest_lower_bound(X_21,multiply(X_21,X_142))) = multiply(X_21,greatest_lower_bound(identity,X_142)),
inference(resolve,[$cnf( $equal(multiply(X_21,greatest_lower_bound(identity,greatest_lower_bound(X_142,identity))),multiply(X_21,greatest_lower_bound(identity,X_142))) )],[refute_0_234,refute_0_370]) ).
cnf(refute_0_372,plain,
( greatest_lower_bound(X_21,greatest_lower_bound(X_21,multiply(X_21,X_142))) != multiply(X_21,greatest_lower_bound(X_142,identity))
| greatest_lower_bound(X_21,greatest_lower_bound(X_21,multiply(X_21,X_142))) != multiply(X_21,greatest_lower_bound(identity,X_142))
| multiply(X_21,greatest_lower_bound(identity,X_142)) = multiply(X_21,greatest_lower_bound(X_142,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_21,greatest_lower_bound(X_21,multiply(X_21,X_142))),multiply(X_21,greatest_lower_bound(X_142,identity))) ),[0],$fot(multiply(X_21,greatest_lower_bound(identity,X_142)))]]) ).
cnf(refute_0_373,plain,
( greatest_lower_bound(X_21,greatest_lower_bound(X_21,multiply(X_21,X_142))) != multiply(X_21,greatest_lower_bound(X_142,identity))
| multiply(X_21,greatest_lower_bound(identity,X_142)) = multiply(X_21,greatest_lower_bound(X_142,identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_21,greatest_lower_bound(X_21,multiply(X_21,X_142))),multiply(X_21,greatest_lower_bound(identity,X_142))) )],[refute_0_371,refute_0_372]) ).
cnf(refute_0_374,plain,
multiply(X_21,greatest_lower_bound(identity,X_142)) = multiply(X_21,greatest_lower_bound(X_142,identity)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_21,greatest_lower_bound(X_21,multiply(X_21,X_142))),multiply(X_21,greatest_lower_bound(X_142,identity))) )],[refute_0_215,refute_0_373]) ).
cnf(refute_0_375,plain,
( multiply(X_21,greatest_lower_bound(identity,X_142)) != multiply(X_21,greatest_lower_bound(X_142,identity))
| multiply(X_21,greatest_lower_bound(X_142,identity)) = multiply(X_21,greatest_lower_bound(identity,X_142)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(multiply(X_21,greatest_lower_bound(identity,X_142)))),bind(Y0,$fot(multiply(X_21,greatest_lower_bound(X_142,identity))))]]) ).
cnf(refute_0_376,plain,
multiply(X_21,greatest_lower_bound(X_142,identity)) = multiply(X_21,greatest_lower_bound(identity,X_142)),
inference(resolve,[$cnf( $equal(multiply(X_21,greatest_lower_bound(identity,X_142)),multiply(X_21,greatest_lower_bound(X_142,identity))) )],[refute_0_374,refute_0_375]) ).
cnf(refute_0_377,plain,
multiply(least_upper_bound(identity,X_84),greatest_lower_bound(inverse(X_84),identity)) = multiply(least_upper_bound(identity,X_84),greatest_lower_bound(identity,inverse(X_84))),
inference(subst,[],[refute_0_376:[bind(X_142,$fot(inverse(X_84))),bind(X_21,$fot(least_upper_bound(identity,X_84)))]]) ).
cnf(refute_0_378,plain,
( multiply(least_upper_bound(identity,X_84),greatest_lower_bound(inverse(X_84),identity)) != multiply(least_upper_bound(identity,X_84),greatest_lower_bound(identity,inverse(X_84)))
| multiply(least_upper_bound(identity,X_84),greatest_lower_bound(inverse(X_84),identity)) != greatest_lower_bound(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84)))
| multiply(least_upper_bound(identity,X_84),greatest_lower_bound(identity,inverse(X_84))) = greatest_lower_bound(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,X_84),greatest_lower_bound(inverse(X_84),identity)),greatest_lower_bound(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84)))) ),[0],$fot(multiply(least_upper_bound(identity,X_84),greatest_lower_bound(identity,inverse(X_84))))]]) ).
cnf(refute_0_379,plain,
( multiply(least_upper_bound(identity,X_84),greatest_lower_bound(inverse(X_84),identity)) != greatest_lower_bound(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84)))
| multiply(least_upper_bound(identity,X_84),greatest_lower_bound(identity,inverse(X_84))) = greatest_lower_bound(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_84),greatest_lower_bound(inverse(X_84),identity)),multiply(least_upper_bound(identity,X_84),greatest_lower_bound(identity,inverse(X_84)))) )],[refute_0_377,refute_0_378]) ).
cnf(refute_0_380,plain,
multiply(greatest_lower_bound(inverse(X_63),identity),least_upper_bound(identity,X_63)) = greatest_lower_bound(least_upper_bound(identity,X_63),multiply(inverse(X_63),least_upper_bound(identity,X_63))),
inference(subst,[],[refute_0_45:[bind(X_86,$fot(least_upper_bound(identity,X_63))),bind(X_87,$fot(inverse(X_63)))]]) ).
cnf(refute_0_381,plain,
( multiply(greatest_lower_bound(inverse(X_63),identity),least_upper_bound(identity,X_63)) != greatest_lower_bound(least_upper_bound(identity,X_63),multiply(inverse(X_63),least_upper_bound(identity,X_63)))
| multiply(inverse(X_63),least_upper_bound(identity,X_63)) != least_upper_bound(identity,inverse(X_63))
| multiply(greatest_lower_bound(inverse(X_63),identity),least_upper_bound(identity,X_63)) = greatest_lower_bound(least_upper_bound(identity,X_63),least_upper_bound(identity,inverse(X_63))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_63),identity),least_upper_bound(identity,X_63)),greatest_lower_bound(least_upper_bound(identity,X_63),multiply(inverse(X_63),least_upper_bound(identity,X_63)))) ),[1,1],$fot(least_upper_bound(identity,inverse(X_63)))]]) ).
cnf(refute_0_382,plain,
( multiply(greatest_lower_bound(inverse(X_63),identity),least_upper_bound(identity,X_63)) != greatest_lower_bound(least_upper_bound(identity,X_63),multiply(inverse(X_63),least_upper_bound(identity,X_63)))
| multiply(greatest_lower_bound(inverse(X_63),identity),least_upper_bound(identity,X_63)) = greatest_lower_bound(least_upper_bound(identity,X_63),least_upper_bound(identity,inverse(X_63))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_63),least_upper_bound(identity,X_63)),least_upper_bound(identity,inverse(X_63))) )],[refute_0_134,refute_0_381]) ).
cnf(refute_0_383,plain,
multiply(greatest_lower_bound(inverse(X_63),identity),least_upper_bound(identity,X_63)) = greatest_lower_bound(least_upper_bound(identity,X_63),least_upper_bound(identity,inverse(X_63))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_63),identity),least_upper_bound(identity,X_63)),greatest_lower_bound(least_upper_bound(identity,X_63),multiply(inverse(X_63),least_upper_bound(identity,X_63)))) )],[refute_0_380,refute_0_382]) ).
cnf(refute_0_384,plain,
greatest_lower_bound(Y,greatest_lower_bound(multiply(X_90,Y),Y)) = greatest_lower_bound(Y,multiply(X_90,Y)),
inference(subst,[],[refute_0_229:[bind(X_15,$fot(multiply(X_90,Y)))]]) ).
cnf(refute_0_385,plain,
multiply(greatest_lower_bound(X_90,identity),Y) = greatest_lower_bound(Y,multiply(X_90,Y)),
inference(subst,[],[refute_0_45:[bind(X_86,$fot(Y)),bind(X_87,$fot(X_90))]]) ).
cnf(refute_0_386,plain,
( multiply(greatest_lower_bound(X_90,identity),Y) != greatest_lower_bound(Y,multiply(X_90,Y))
| greatest_lower_bound(Y,multiply(X_90,Y)) = multiply(greatest_lower_bound(X_90,identity),Y) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(multiply(greatest_lower_bound(X_90,identity),Y))),bind(Y0,$fot(greatest_lower_bound(Y,multiply(X_90,Y))))]]) ).
cnf(refute_0_387,plain,
greatest_lower_bound(Y,multiply(X_90,Y)) = multiply(greatest_lower_bound(X_90,identity),Y),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_90,identity),Y),greatest_lower_bound(Y,multiply(X_90,Y))) )],[refute_0_385,refute_0_386]) ).
cnf(refute_0_388,plain,
( greatest_lower_bound(Y,multiply(X_90,Y)) != multiply(greatest_lower_bound(X_90,identity),Y)
| greatest_lower_bound(Y,greatest_lower_bound(multiply(X_90,Y),Y)) != greatest_lower_bound(Y,multiply(X_90,Y))
| greatest_lower_bound(Y,greatest_lower_bound(multiply(X_90,Y),Y)) = multiply(greatest_lower_bound(X_90,identity),Y) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(multiply(X_90,Y),Y)),greatest_lower_bound(Y,multiply(X_90,Y))) ),[1],$fot(multiply(greatest_lower_bound(X_90,identity),Y))]]) ).
cnf(refute_0_389,plain,
( greatest_lower_bound(Y,greatest_lower_bound(multiply(X_90,Y),Y)) != greatest_lower_bound(Y,multiply(X_90,Y))
| greatest_lower_bound(Y,greatest_lower_bound(multiply(X_90,Y),Y)) = multiply(greatest_lower_bound(X_90,identity),Y) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,multiply(X_90,Y)),multiply(greatest_lower_bound(X_90,identity),Y)) )],[refute_0_387,refute_0_388]) ).
cnf(refute_0_390,plain,
greatest_lower_bound(Y,greatest_lower_bound(multiply(X_90,Y),Y)) = multiply(greatest_lower_bound(X_90,identity),Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(multiply(X_90,Y),Y)),greatest_lower_bound(Y,multiply(X_90,Y))) )],[refute_0_384,refute_0_389]) ).
cnf(refute_0_391,plain,
greatest_lower_bound(identity,greatest_lower_bound(X_90,identity)) = greatest_lower_bound(identity,X_90),
inference(subst,[],[refute_0_229:[bind(Y,$fot(identity)),bind(X_15,$fot(X_90))]]) ).
cnf(refute_0_392,plain,
multiply(greatest_lower_bound(identity,greatest_lower_bound(X_90,identity)),Y) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_90,identity)),Y),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_90,identity)),Y))]]) ).
cnf(refute_0_393,plain,
( multiply(greatest_lower_bound(identity,greatest_lower_bound(X_90,identity)),Y) != multiply(greatest_lower_bound(identity,greatest_lower_bound(X_90,identity)),Y)
| greatest_lower_bound(identity,greatest_lower_bound(X_90,identity)) != greatest_lower_bound(identity,X_90)
| multiply(greatest_lower_bound(identity,greatest_lower_bound(X_90,identity)),Y) = multiply(greatest_lower_bound(identity,X_90),Y) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_90,identity)),Y),multiply(greatest_lower_bound(identity,greatest_lower_bound(X_90,identity)),Y)) ),[1,0],$fot(greatest_lower_bound(identity,X_90))]]) ).
cnf(refute_0_394,plain,
( greatest_lower_bound(identity,greatest_lower_bound(X_90,identity)) != greatest_lower_bound(identity,X_90)
| multiply(greatest_lower_bound(identity,greatest_lower_bound(X_90,identity)),Y) = multiply(greatest_lower_bound(identity,X_90),Y) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_90,identity)),Y),multiply(greatest_lower_bound(identity,greatest_lower_bound(X_90,identity)),Y)) )],[refute_0_392,refute_0_393]) ).
cnf(refute_0_395,plain,
multiply(greatest_lower_bound(identity,greatest_lower_bound(X_90,identity)),Y) = multiply(greatest_lower_bound(identity,X_90),Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_90,identity)),greatest_lower_bound(identity,X_90)) )],[refute_0_391,refute_0_394]) ).
cnf(refute_0_396,plain,
greatest_lower_bound(multiply(X_88,X_86),multiply(X_87,X_86)) = greatest_lower_bound(multiply(X_87,X_86),multiply(X_88,X_86)),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(multiply(X_88,X_86))),bind(Y,$fot(multiply(X_87,X_86)))]]) ).
cnf(refute_0_397,plain,
( greatest_lower_bound(multiply(X_87,X_86),multiply(X_88,X_86)) != multiply(greatest_lower_bound(X_87,X_88),X_86)
| greatest_lower_bound(multiply(X_88,X_86),multiply(X_87,X_86)) != greatest_lower_bound(multiply(X_87,X_86),multiply(X_88,X_86))
| greatest_lower_bound(multiply(X_88,X_86),multiply(X_87,X_86)) = multiply(greatest_lower_bound(X_87,X_88),X_86) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_88,X_86),multiply(X_87,X_86)),greatest_lower_bound(multiply(X_87,X_86),multiply(X_88,X_86))) ),[1],$fot(multiply(greatest_lower_bound(X_87,X_88),X_86))]]) ).
cnf(refute_0_398,plain,
( greatest_lower_bound(multiply(X_88,X_86),multiply(X_87,X_86)) != greatest_lower_bound(multiply(X_87,X_86),multiply(X_88,X_86))
| greatest_lower_bound(multiply(X_88,X_86),multiply(X_87,X_86)) = multiply(greatest_lower_bound(X_87,X_88),X_86) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_87,X_86),multiply(X_88,X_86)),multiply(greatest_lower_bound(X_87,X_88),X_86)) )],[refute_0_325,refute_0_397]) ).
cnf(refute_0_399,plain,
greatest_lower_bound(multiply(X_88,X_86),multiply(X_87,X_86)) = multiply(greatest_lower_bound(X_87,X_88),X_86),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_88,X_86),multiply(X_87,X_86)),greatest_lower_bound(multiply(X_87,X_86),multiply(X_88,X_86))) )],[refute_0_396,refute_0_398]) ).
cnf(refute_0_400,plain,
( multiply(greatest_lower_bound(Y,Z),X) != greatest_lower_bound(multiply(Y,X),multiply(Z,X))
| greatest_lower_bound(multiply(Y,X),multiply(Z,X)) = multiply(greatest_lower_bound(Y,Z),X) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(multiply(greatest_lower_bound(Y,Z),X))),bind(Y0,$fot(greatest_lower_bound(multiply(Y,X),multiply(Z,X))))]]) ).
cnf(refute_0_401,plain,
greatest_lower_bound(multiply(Y,X),multiply(Z,X)) = multiply(greatest_lower_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Y,X),multiply(Z,X))) )],[monotony_glb2,refute_0_400]) ).
cnf(refute_0_402,plain,
greatest_lower_bound(multiply(X_88,X_86),multiply(X_87,X_86)) = multiply(greatest_lower_bound(X_88,X_87),X_86),
inference(subst,[],[refute_0_401:[bind(X,$fot(X_86)),bind(Y,$fot(X_88)),bind(Z,$fot(X_87))]]) ).
cnf(refute_0_403,plain,
( greatest_lower_bound(multiply(X_88,X_86),multiply(X_87,X_86)) != multiply(greatest_lower_bound(X_87,X_88),X_86)
| greatest_lower_bound(multiply(X_88,X_86),multiply(X_87,X_86)) != multiply(greatest_lower_bound(X_88,X_87),X_86)
| multiply(greatest_lower_bound(X_88,X_87),X_86) = multiply(greatest_lower_bound(X_87,X_88),X_86) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_88,X_86),multiply(X_87,X_86)),multiply(greatest_lower_bound(X_87,X_88),X_86)) ),[0],$fot(multiply(greatest_lower_bound(X_88,X_87),X_86))]]) ).
cnf(refute_0_404,plain,
( greatest_lower_bound(multiply(X_88,X_86),multiply(X_87,X_86)) != multiply(greatest_lower_bound(X_87,X_88),X_86)
| multiply(greatest_lower_bound(X_88,X_87),X_86) = multiply(greatest_lower_bound(X_87,X_88),X_86) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_88,X_86),multiply(X_87,X_86)),multiply(greatest_lower_bound(X_88,X_87),X_86)) )],[refute_0_402,refute_0_403]) ).
cnf(refute_0_405,plain,
multiply(greatest_lower_bound(X_88,X_87),X_86) = multiply(greatest_lower_bound(X_87,X_88),X_86),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_88,X_86),multiply(X_87,X_86)),multiply(greatest_lower_bound(X_87,X_88),X_86)) )],[refute_0_399,refute_0_404]) ).
cnf(refute_0_406,plain,
( multiply(greatest_lower_bound(X_88,X_87),X_86) != multiply(greatest_lower_bound(X_87,X_88),X_86)
| multiply(greatest_lower_bound(X_87,X_88),X_86) = multiply(greatest_lower_bound(X_88,X_87),X_86) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(multiply(greatest_lower_bound(X_88,X_87),X_86))),bind(Y0,$fot(multiply(greatest_lower_bound(X_87,X_88),X_86)))]]) ).
cnf(refute_0_407,plain,
multiply(greatest_lower_bound(X_87,X_88),X_86) = multiply(greatest_lower_bound(X_88,X_87),X_86),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_88,X_87),X_86),multiply(greatest_lower_bound(X_87,X_88),X_86)) )],[refute_0_405,refute_0_406]) ).
cnf(refute_0_408,plain,
multiply(greatest_lower_bound(greatest_lower_bound(X_90,identity),identity),Y) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_90,identity)),Y),
inference(subst,[],[refute_0_407:[bind(X_86,$fot(Y)),bind(X_87,$fot(greatest_lower_bound(X_90,identity))),bind(X_88,$fot(identity))]]) ).
cnf(refute_0_409,plain,
( multiply(greatest_lower_bound(X_87,identity),X_86) != greatest_lower_bound(X_86,multiply(X_87,X_86))
| greatest_lower_bound(X_86,multiply(X_87,X_86)) = multiply(greatest_lower_bound(X_87,identity),X_86) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(multiply(greatest_lower_bound(X_87,identity),X_86))),bind(Y0,$fot(greatest_lower_bound(X_86,multiply(X_87,X_86))))]]) ).
cnf(refute_0_410,plain,
greatest_lower_bound(X_86,multiply(X_87,X_86)) = multiply(greatest_lower_bound(X_87,identity),X_86),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_87,identity),X_86),greatest_lower_bound(X_86,multiply(X_87,X_86))) )],[refute_0_45,refute_0_409]) ).
cnf(refute_0_411,plain,
greatest_lower_bound(Y,multiply(greatest_lower_bound(X_90,identity),Y)) = multiply(greatest_lower_bound(greatest_lower_bound(X_90,identity),identity),Y),
inference(subst,[],[refute_0_410:[bind(X_86,$fot(Y)),bind(X_87,$fot(greatest_lower_bound(X_90,identity)))]]) ).
cnf(refute_0_412,plain,
( multiply(greatest_lower_bound(greatest_lower_bound(X_90,identity),identity),Y) != multiply(greatest_lower_bound(identity,greatest_lower_bound(X_90,identity)),Y)
| greatest_lower_bound(Y,multiply(greatest_lower_bound(X_90,identity),Y)) != multiply(greatest_lower_bound(greatest_lower_bound(X_90,identity),identity),Y)
| greatest_lower_bound(Y,multiply(greatest_lower_bound(X_90,identity),Y)) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_90,identity)),Y) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(greatest_lower_bound(Y,multiply(greatest_lower_bound(X_90,identity),Y)))),bind(Y0,$fot(multiply(greatest_lower_bound(greatest_lower_bound(X_90,identity),identity),Y))),bind(Z0,$fot(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_90,identity)),Y)))]]) ).
cnf(refute_0_413,plain,
( multiply(greatest_lower_bound(greatest_lower_bound(X_90,identity),identity),Y) != multiply(greatest_lower_bound(identity,greatest_lower_bound(X_90,identity)),Y)
| greatest_lower_bound(Y,multiply(greatest_lower_bound(X_90,identity),Y)) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_90,identity)),Y) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,multiply(greatest_lower_bound(X_90,identity),Y)),multiply(greatest_lower_bound(greatest_lower_bound(X_90,identity),identity),Y)) )],[refute_0_411,refute_0_412]) ).
cnf(refute_0_414,plain,
greatest_lower_bound(Y,multiply(greatest_lower_bound(X_90,identity),Y)) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_90,identity)),Y),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(greatest_lower_bound(X_90,identity),identity),Y),multiply(greatest_lower_bound(identity,greatest_lower_bound(X_90,identity)),Y)) )],[refute_0_408,refute_0_413]) ).
cnf(refute_0_415,plain,
greatest_lower_bound(X,greatest_lower_bound(Y,multiply(X_90,Y))) = greatest_lower_bound(Y,greatest_lower_bound(multiply(X_90,Y),X)),
inference(subst,[],[refute_0_321:[bind(X_35,$fot(multiply(X_90,Y)))]]) ).
cnf(refute_0_416,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,multiply(X_90,Y))) != greatest_lower_bound(Y,greatest_lower_bound(multiply(X_90,Y),X))
| greatest_lower_bound(Y,multiply(X_90,Y)) != multiply(greatest_lower_bound(X_90,identity),Y)
| greatest_lower_bound(X,multiply(greatest_lower_bound(X_90,identity),Y)) = greatest_lower_bound(Y,greatest_lower_bound(multiply(X_90,Y),X)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,multiply(X_90,Y))),greatest_lower_bound(Y,greatest_lower_bound(multiply(X_90,Y),X))) ),[0,1],$fot(multiply(greatest_lower_bound(X_90,identity),Y))]]) ).
cnf(refute_0_417,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,multiply(X_90,Y))) != greatest_lower_bound(Y,greatest_lower_bound(multiply(X_90,Y),X))
| greatest_lower_bound(X,multiply(greatest_lower_bound(X_90,identity),Y)) = greatest_lower_bound(Y,greatest_lower_bound(multiply(X_90,Y),X)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,multiply(X_90,Y)),multiply(greatest_lower_bound(X_90,identity),Y)) )],[refute_0_387,refute_0_416]) ).
cnf(refute_0_418,plain,
greatest_lower_bound(X,multiply(greatest_lower_bound(X_90,identity),Y)) = greatest_lower_bound(Y,greatest_lower_bound(multiply(X_90,Y),X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,multiply(X_90,Y))),greatest_lower_bound(Y,greatest_lower_bound(multiply(X_90,Y),X))) )],[refute_0_415,refute_0_417]) ).
cnf(refute_0_419,plain,
( greatest_lower_bound(X,multiply(greatest_lower_bound(X_90,identity),Y)) != greatest_lower_bound(Y,greatest_lower_bound(multiply(X_90,Y),X))
| greatest_lower_bound(Y,greatest_lower_bound(multiply(X_90,Y),X)) = greatest_lower_bound(X,multiply(greatest_lower_bound(X_90,identity),Y)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(greatest_lower_bound(X,multiply(greatest_lower_bound(X_90,identity),Y)))),bind(Y0,$fot(greatest_lower_bound(Y,greatest_lower_bound(multiply(X_90,Y),X))))]]) ).
cnf(refute_0_420,plain,
greatest_lower_bound(Y,greatest_lower_bound(multiply(X_90,Y),X)) = greatest_lower_bound(X,multiply(greatest_lower_bound(X_90,identity),Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,multiply(greatest_lower_bound(X_90,identity),Y)),greatest_lower_bound(Y,greatest_lower_bound(multiply(X_90,Y),X))) )],[refute_0_418,refute_0_419]) ).
cnf(refute_0_421,plain,
greatest_lower_bound(Y,greatest_lower_bound(multiply(X_90,Y),Y)) = greatest_lower_bound(Y,multiply(greatest_lower_bound(X_90,identity),Y)),
inference(subst,[],[refute_0_420:[bind(X,$fot(Y))]]) ).
cnf(refute_0_422,plain,
( greatest_lower_bound(Y,multiply(greatest_lower_bound(X_90,identity),Y)) != multiply(greatest_lower_bound(identity,greatest_lower_bound(X_90,identity)),Y)
| greatest_lower_bound(Y,greatest_lower_bound(multiply(X_90,Y),Y)) != greatest_lower_bound(Y,multiply(greatest_lower_bound(X_90,identity),Y))
| greatest_lower_bound(Y,greatest_lower_bound(multiply(X_90,Y),Y)) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_90,identity)),Y) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(greatest_lower_bound(Y,greatest_lower_bound(multiply(X_90,Y),Y)))),bind(Y0,$fot(greatest_lower_bound(Y,multiply(greatest_lower_bound(X_90,identity),Y)))),bind(Z0,$fot(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_90,identity)),Y)))]]) ).
cnf(refute_0_423,plain,
( greatest_lower_bound(Y,multiply(greatest_lower_bound(X_90,identity),Y)) != multiply(greatest_lower_bound(identity,greatest_lower_bound(X_90,identity)),Y)
| greatest_lower_bound(Y,greatest_lower_bound(multiply(X_90,Y),Y)) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_90,identity)),Y) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(multiply(X_90,Y),Y)),greatest_lower_bound(Y,multiply(greatest_lower_bound(X_90,identity),Y))) )],[refute_0_421,refute_0_422]) ).
cnf(refute_0_424,plain,
greatest_lower_bound(Y,greatest_lower_bound(multiply(X_90,Y),Y)) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_90,identity)),Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,multiply(greatest_lower_bound(X_90,identity),Y)),multiply(greatest_lower_bound(identity,greatest_lower_bound(X_90,identity)),Y)) )],[refute_0_414,refute_0_423]) ).
cnf(refute_0_425,plain,
( multiply(greatest_lower_bound(identity,greatest_lower_bound(X_90,identity)),Y) != multiply(greatest_lower_bound(identity,X_90),Y)
| greatest_lower_bound(Y,greatest_lower_bound(multiply(X_90,Y),Y)) != multiply(greatest_lower_bound(identity,greatest_lower_bound(X_90,identity)),Y)
| greatest_lower_bound(Y,greatest_lower_bound(multiply(X_90,Y),Y)) = multiply(greatest_lower_bound(identity,X_90),Y) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(greatest_lower_bound(Y,greatest_lower_bound(multiply(X_90,Y),Y)))),bind(Y0,$fot(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_90,identity)),Y))),bind(Z0,$fot(multiply(greatest_lower_bound(identity,X_90),Y)))]]) ).
cnf(refute_0_426,plain,
( multiply(greatest_lower_bound(identity,greatest_lower_bound(X_90,identity)),Y) != multiply(greatest_lower_bound(identity,X_90),Y)
| greatest_lower_bound(Y,greatest_lower_bound(multiply(X_90,Y),Y)) = multiply(greatest_lower_bound(identity,X_90),Y) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(multiply(X_90,Y),Y)),multiply(greatest_lower_bound(identity,greatest_lower_bound(X_90,identity)),Y)) )],[refute_0_424,refute_0_425]) ).
cnf(refute_0_427,plain,
greatest_lower_bound(Y,greatest_lower_bound(multiply(X_90,Y),Y)) = multiply(greatest_lower_bound(identity,X_90),Y),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_90,identity)),Y),multiply(greatest_lower_bound(identity,X_90),Y)) )],[refute_0_395,refute_0_426]) ).
cnf(refute_0_428,plain,
( greatest_lower_bound(Y,greatest_lower_bound(multiply(X_90,Y),Y)) != multiply(greatest_lower_bound(X_90,identity),Y)
| greatest_lower_bound(Y,greatest_lower_bound(multiply(X_90,Y),Y)) != multiply(greatest_lower_bound(identity,X_90),Y)
| multiply(greatest_lower_bound(identity,X_90),Y) = multiply(greatest_lower_bound(X_90,identity),Y) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(multiply(X_90,Y),Y)),multiply(greatest_lower_bound(X_90,identity),Y)) ),[0],$fot(multiply(greatest_lower_bound(identity,X_90),Y))]]) ).
cnf(refute_0_429,plain,
( greatest_lower_bound(Y,greatest_lower_bound(multiply(X_90,Y),Y)) != multiply(greatest_lower_bound(X_90,identity),Y)
| multiply(greatest_lower_bound(identity,X_90),Y) = multiply(greatest_lower_bound(X_90,identity),Y) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(multiply(X_90,Y),Y)),multiply(greatest_lower_bound(identity,X_90),Y)) )],[refute_0_427,refute_0_428]) ).
cnf(refute_0_430,plain,
multiply(greatest_lower_bound(identity,X_90),Y) = multiply(greatest_lower_bound(X_90,identity),Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(multiply(X_90,Y),Y)),multiply(greatest_lower_bound(X_90,identity),Y)) )],[refute_0_390,refute_0_429]) ).
cnf(refute_0_431,plain,
( multiply(greatest_lower_bound(identity,X_90),Y) != multiply(greatest_lower_bound(X_90,identity),Y)
| multiply(greatest_lower_bound(X_90,identity),Y) = multiply(greatest_lower_bound(identity,X_90),Y) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(multiply(greatest_lower_bound(identity,X_90),Y))),bind(Y0,$fot(multiply(greatest_lower_bound(X_90,identity),Y)))]]) ).
cnf(refute_0_432,plain,
multiply(greatest_lower_bound(X_90,identity),Y) = multiply(greatest_lower_bound(identity,X_90),Y),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_90),Y),multiply(greatest_lower_bound(X_90,identity),Y)) )],[refute_0_430,refute_0_431]) ).
cnf(refute_0_433,plain,
multiply(greatest_lower_bound(inverse(X_63),identity),least_upper_bound(identity,X_63)) = multiply(greatest_lower_bound(identity,inverse(X_63)),least_upper_bound(identity,X_63)),
inference(subst,[],[refute_0_432:[bind(Y,$fot(least_upper_bound(identity,X_63))),bind(X_90,$fot(inverse(X_63)))]]) ).
cnf(refute_0_434,plain,
( multiply(greatest_lower_bound(inverse(X_63),identity),least_upper_bound(identity,X_63)) != multiply(greatest_lower_bound(identity,inverse(X_63)),least_upper_bound(identity,X_63))
| multiply(greatest_lower_bound(inverse(X_63),identity),least_upper_bound(identity,X_63)) != greatest_lower_bound(least_upper_bound(identity,X_63),least_upper_bound(identity,inverse(X_63)))
| multiply(greatest_lower_bound(identity,inverse(X_63)),least_upper_bound(identity,X_63)) = greatest_lower_bound(least_upper_bound(identity,X_63),least_upper_bound(identity,inverse(X_63))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_63),identity),least_upper_bound(identity,X_63)),greatest_lower_bound(least_upper_bound(identity,X_63),least_upper_bound(identity,inverse(X_63)))) ),[0],$fot(multiply(greatest_lower_bound(identity,inverse(X_63)),least_upper_bound(identity,X_63)))]]) ).
cnf(refute_0_435,plain,
( multiply(greatest_lower_bound(inverse(X_63),identity),least_upper_bound(identity,X_63)) != greatest_lower_bound(least_upper_bound(identity,X_63),least_upper_bound(identity,inverse(X_63)))
| multiply(greatest_lower_bound(identity,inverse(X_63)),least_upper_bound(identity,X_63)) = greatest_lower_bound(least_upper_bound(identity,X_63),least_upper_bound(identity,inverse(X_63))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_63),identity),least_upper_bound(identity,X_63)),multiply(greatest_lower_bound(identity,inverse(X_63)),least_upper_bound(identity,X_63))) )],[refute_0_433,refute_0_434]) ).
cnf(refute_0_436,plain,
multiply(greatest_lower_bound(identity,inverse(X_63)),least_upper_bound(identity,X_63)) = greatest_lower_bound(least_upper_bound(identity,X_63),least_upper_bound(identity,inverse(X_63))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_63),identity),least_upper_bound(identity,X_63)),greatest_lower_bound(least_upper_bound(identity,X_63),least_upper_bound(identity,inverse(X_63)))) )],[refute_0_383,refute_0_435]) ).
cnf(refute_0_437,plain,
( multiply(greatest_lower_bound(identity,inverse(X_63)),least_upper_bound(identity,X_63)) != greatest_lower_bound(least_upper_bound(identity,X_63),least_upper_bound(identity,inverse(X_63)))
| greatest_lower_bound(least_upper_bound(identity,X_63),least_upper_bound(identity,inverse(X_63))) = multiply(greatest_lower_bound(identity,inverse(X_63)),least_upper_bound(identity,X_63)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(multiply(greatest_lower_bound(identity,inverse(X_63)),least_upper_bound(identity,X_63)))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(identity,X_63),least_upper_bound(identity,inverse(X_63)))))]]) ).
cnf(refute_0_438,plain,
greatest_lower_bound(least_upper_bound(identity,X_63),least_upper_bound(identity,inverse(X_63))) = multiply(greatest_lower_bound(identity,inverse(X_63)),least_upper_bound(identity,X_63)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(X_63)),least_upper_bound(identity,X_63)),greatest_lower_bound(least_upper_bound(identity,X_63),least_upper_bound(identity,inverse(X_63)))) )],[refute_0_436,refute_0_437]) ).
cnf(refute_0_439,plain,
greatest_lower_bound(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))) = multiply(greatest_lower_bound(identity,inverse(X_84)),least_upper_bound(identity,X_84)),
inference(subst,[],[refute_0_438:[bind(X_63,$fot(X_84))]]) ).
cnf(refute_0_440,plain,
( multiply(least_upper_bound(identity,X_84),greatest_lower_bound(identity,inverse(X_84))) != greatest_lower_bound(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84)))
| greatest_lower_bound(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))) != multiply(greatest_lower_bound(identity,inverse(X_84)),least_upper_bound(identity,X_84))
| multiply(least_upper_bound(identity,X_84),greatest_lower_bound(identity,inverse(X_84))) = multiply(greatest_lower_bound(identity,inverse(X_84)),least_upper_bound(identity,X_84)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(identity,X_84),greatest_lower_bound(identity,inverse(X_84))),multiply(greatest_lower_bound(identity,inverse(X_84)),least_upper_bound(identity,X_84))) ),[0],$fot(greatest_lower_bound(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))))]]) ).
cnf(refute_0_441,plain,
( multiply(least_upper_bound(identity,X_84),greatest_lower_bound(identity,inverse(X_84))) != greatest_lower_bound(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84)))
| multiply(least_upper_bound(identity,X_84),greatest_lower_bound(identity,inverse(X_84))) = multiply(greatest_lower_bound(identity,inverse(X_84)),least_upper_bound(identity,X_84)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))),multiply(greatest_lower_bound(identity,inverse(X_84)),least_upper_bound(identity,X_84))) )],[refute_0_439,refute_0_440]) ).
cnf(refute_0_442,plain,
( multiply(least_upper_bound(identity,X_84),greatest_lower_bound(inverse(X_84),identity)) != greatest_lower_bound(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84)))
| multiply(least_upper_bound(identity,X_84),greatest_lower_bound(identity,inverse(X_84))) = multiply(greatest_lower_bound(identity,inverse(X_84)),least_upper_bound(identity,X_84)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_84),greatest_lower_bound(identity,inverse(X_84))),greatest_lower_bound(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84)))) )],[refute_0_379,refute_0_441]) ).
cnf(refute_0_443,plain,
multiply(least_upper_bound(identity,X_84),greatest_lower_bound(identity,inverse(X_84))) = multiply(greatest_lower_bound(identity,inverse(X_84)),least_upper_bound(identity,X_84)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_84),greatest_lower_bound(inverse(X_84),identity)),greatest_lower_bound(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84)))) )],[refute_0_203,refute_0_442]) ).
cnf(refute_0_444,plain,
multiply(greatest_lower_bound(identity,X_309),least_upper_bound(inverse(X_309),identity)) = least_upper_bound(greatest_lower_bound(identity,X_309),multiply(greatest_lower_bound(identity,X_309),inverse(X_309))),
inference(subst,[],[refute_0_34:[bind(X_55,$fot(greatest_lower_bound(identity,X_309))),bind(X_56,$fot(inverse(X_309)))]]) ).
cnf(refute_0_445,plain,
multiply(greatest_lower_bound(greatest_lower_bound(X_95,identity),identity),inverse(X_95)) = greatest_lower_bound(inverse(X_95),multiply(greatest_lower_bound(X_95,identity),inverse(X_95))),
inference(subst,[],[refute_0_45:[bind(X_86,$fot(inverse(X_95))),bind(X_87,$fot(greatest_lower_bound(X_95,identity)))]]) ).
cnf(refute_0_446,plain,
multiply(greatest_lower_bound(X_90,identity),inverse(X_90)) = greatest_lower_bound(inverse(X_90),multiply(X_90,inverse(X_90))),
inference(subst,[],[refute_0_45:[bind(X_86,$fot(inverse(X_90))),bind(X_87,$fot(X_90))]]) ).
cnf(refute_0_447,plain,
multiply(X_90,inverse(X_90)) = identity,
inference(subst,[],[refute_0_156:[bind(X,$fot(X_90))]]) ).
cnf(refute_0_448,plain,
( multiply(X_90,inverse(X_90)) != identity
| multiply(greatest_lower_bound(X_90,identity),inverse(X_90)) != greatest_lower_bound(inverse(X_90),multiply(X_90,inverse(X_90)))
| multiply(greatest_lower_bound(X_90,identity),inverse(X_90)) = greatest_lower_bound(inverse(X_90),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_90,identity),inverse(X_90)),greatest_lower_bound(inverse(X_90),multiply(X_90,inverse(X_90)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_449,plain,
( multiply(greatest_lower_bound(X_90,identity),inverse(X_90)) != greatest_lower_bound(inverse(X_90),multiply(X_90,inverse(X_90)))
| multiply(greatest_lower_bound(X_90,identity),inverse(X_90)) = greatest_lower_bound(inverse(X_90),identity) ),
inference(resolve,[$cnf( $equal(multiply(X_90,inverse(X_90)),identity) )],[refute_0_447,refute_0_448]) ).
cnf(refute_0_450,plain,
multiply(greatest_lower_bound(X_90,identity),inverse(X_90)) = greatest_lower_bound(inverse(X_90),identity),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_90,identity),inverse(X_90)),greatest_lower_bound(inverse(X_90),multiply(X_90,inverse(X_90)))) )],[refute_0_446,refute_0_449]) ).
cnf(refute_0_451,plain,
greatest_lower_bound(inverse(X_90),identity) = greatest_lower_bound(identity,inverse(X_90)),
inference(subst,[],[refute_0_41:[bind(X_21,$fot(identity)),bind(X_22,$fot(inverse(X_90)))]]) ).
cnf(refute_0_452,plain,
( multiply(greatest_lower_bound(X_90,identity),inverse(X_90)) != greatest_lower_bound(inverse(X_90),identity)
| greatest_lower_bound(inverse(X_90),identity) != greatest_lower_bound(identity,inverse(X_90))
| multiply(greatest_lower_bound(X_90,identity),inverse(X_90)) = greatest_lower_bound(identity,inverse(X_90)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_90,identity),inverse(X_90)),greatest_lower_bound(identity,inverse(X_90))) ),[0],$fot(greatest_lower_bound(inverse(X_90),identity))]]) ).
cnf(refute_0_453,plain,
( multiply(greatest_lower_bound(X_90,identity),inverse(X_90)) != greatest_lower_bound(inverse(X_90),identity)
| multiply(greatest_lower_bound(X_90,identity),inverse(X_90)) = greatest_lower_bound(identity,inverse(X_90)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_90),identity),greatest_lower_bound(identity,inverse(X_90))) )],[refute_0_451,refute_0_452]) ).
cnf(refute_0_454,plain,
multiply(greatest_lower_bound(X_90,identity),inverse(X_90)) = greatest_lower_bound(identity,inverse(X_90)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_90,identity),inverse(X_90)),greatest_lower_bound(inverse(X_90),identity)) )],[refute_0_450,refute_0_453]) ).
cnf(refute_0_455,plain,
multiply(greatest_lower_bound(X_95,identity),inverse(X_95)) = greatest_lower_bound(identity,inverse(X_95)),
inference(subst,[],[refute_0_454:[bind(X_90,$fot(X_95))]]) ).
cnf(refute_0_456,plain,
( multiply(greatest_lower_bound(X_95,identity),inverse(X_95)) != greatest_lower_bound(identity,inverse(X_95))
| multiply(greatest_lower_bound(greatest_lower_bound(X_95,identity),identity),inverse(X_95)) != greatest_lower_bound(inverse(X_95),multiply(greatest_lower_bound(X_95,identity),inverse(X_95)))
| multiply(greatest_lower_bound(greatest_lower_bound(X_95,identity),identity),inverse(X_95)) = greatest_lower_bound(inverse(X_95),greatest_lower_bound(identity,inverse(X_95))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(greatest_lower_bound(X_95,identity),identity),inverse(X_95)),greatest_lower_bound(inverse(X_95),multiply(greatest_lower_bound(X_95,identity),inverse(X_95)))) ),[1,1],$fot(greatest_lower_bound(identity,inverse(X_95)))]]) ).
cnf(refute_0_457,plain,
( multiply(greatest_lower_bound(greatest_lower_bound(X_95,identity),identity),inverse(X_95)) != greatest_lower_bound(inverse(X_95),multiply(greatest_lower_bound(X_95,identity),inverse(X_95)))
| multiply(greatest_lower_bound(greatest_lower_bound(X_95,identity),identity),inverse(X_95)) = greatest_lower_bound(inverse(X_95),greatest_lower_bound(identity,inverse(X_95))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_95,identity),inverse(X_95)),greatest_lower_bound(identity,inverse(X_95))) )],[refute_0_455,refute_0_456]) ).
cnf(refute_0_458,plain,
multiply(greatest_lower_bound(greatest_lower_bound(X_95,identity),identity),inverse(X_95)) = greatest_lower_bound(inverse(X_95),greatest_lower_bound(identity,inverse(X_95))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(greatest_lower_bound(X_95,identity),identity),inverse(X_95)),greatest_lower_bound(inverse(X_95),multiply(greatest_lower_bound(X_95,identity),inverse(X_95)))) )],[refute_0_445,refute_0_457]) ).
cnf(refute_0_459,plain,
greatest_lower_bound(identity,greatest_lower_bound(X_95,identity)) = greatest_lower_bound(identity,X_95),
inference(subst,[],[refute_0_229:[bind(Y,$fot(identity)),bind(X_15,$fot(X_95))]]) ).
cnf(refute_0_460,plain,
multiply(greatest_lower_bound(identity,greatest_lower_bound(X_95,identity)),inverse(X_95)) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_95,identity)),inverse(X_95)),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_95,identity)),inverse(X_95)))]]) ).
cnf(refute_0_461,plain,
( multiply(greatest_lower_bound(identity,greatest_lower_bound(X_95,identity)),inverse(X_95)) != multiply(greatest_lower_bound(identity,greatest_lower_bound(X_95,identity)),inverse(X_95))
| greatest_lower_bound(identity,greatest_lower_bound(X_95,identity)) != greatest_lower_bound(identity,X_95)
| multiply(greatest_lower_bound(identity,greatest_lower_bound(X_95,identity)),inverse(X_95)) = multiply(greatest_lower_bound(identity,X_95),inverse(X_95)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_95,identity)),inverse(X_95)),multiply(greatest_lower_bound(identity,greatest_lower_bound(X_95,identity)),inverse(X_95))) ),[1,0],$fot(greatest_lower_bound(identity,X_95))]]) ).
cnf(refute_0_462,plain,
( greatest_lower_bound(identity,greatest_lower_bound(X_95,identity)) != greatest_lower_bound(identity,X_95)
| multiply(greatest_lower_bound(identity,greatest_lower_bound(X_95,identity)),inverse(X_95)) = multiply(greatest_lower_bound(identity,X_95),inverse(X_95)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_95,identity)),inverse(X_95)),multiply(greatest_lower_bound(identity,greatest_lower_bound(X_95,identity)),inverse(X_95))) )],[refute_0_460,refute_0_461]) ).
cnf(refute_0_463,plain,
multiply(greatest_lower_bound(identity,greatest_lower_bound(X_95,identity)),inverse(X_95)) = multiply(greatest_lower_bound(identity,X_95),inverse(X_95)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_95,identity)),greatest_lower_bound(identity,X_95)) )],[refute_0_459,refute_0_462]) ).
cnf(refute_0_464,plain,
multiply(greatest_lower_bound(greatest_lower_bound(X_95,identity),identity),inverse(X_95)) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_95,identity)),inverse(X_95)),
inference(subst,[],[refute_0_432:[bind(Y,$fot(inverse(X_95))),bind(X_90,$fot(greatest_lower_bound(X_95,identity)))]]) ).
cnf(refute_0_465,plain,
( multiply(greatest_lower_bound(greatest_lower_bound(X_95,identity),identity),inverse(X_95)) != multiply(greatest_lower_bound(identity,greatest_lower_bound(X_95,identity)),inverse(X_95))
| multiply(greatest_lower_bound(identity,greatest_lower_bound(X_95,identity)),inverse(X_95)) != multiply(greatest_lower_bound(identity,X_95),inverse(X_95))
| multiply(greatest_lower_bound(greatest_lower_bound(X_95,identity),identity),inverse(X_95)) = multiply(greatest_lower_bound(identity,X_95),inverse(X_95)) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(multiply(greatest_lower_bound(greatest_lower_bound(X_95,identity),identity),inverse(X_95)))),bind(Y0,$fot(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_95,identity)),inverse(X_95)))),bind(Z0,$fot(multiply(greatest_lower_bound(identity,X_95),inverse(X_95))))]]) ).
cnf(refute_0_466,plain,
( multiply(greatest_lower_bound(identity,greatest_lower_bound(X_95,identity)),inverse(X_95)) != multiply(greatest_lower_bound(identity,X_95),inverse(X_95))
| multiply(greatest_lower_bound(greatest_lower_bound(X_95,identity),identity),inverse(X_95)) = multiply(greatest_lower_bound(identity,X_95),inverse(X_95)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(greatest_lower_bound(X_95,identity),identity),inverse(X_95)),multiply(greatest_lower_bound(identity,greatest_lower_bound(X_95,identity)),inverse(X_95))) )],[refute_0_464,refute_0_465]) ).
cnf(refute_0_467,plain,
multiply(greatest_lower_bound(greatest_lower_bound(X_95,identity),identity),inverse(X_95)) = multiply(greatest_lower_bound(identity,X_95),inverse(X_95)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_95,identity)),inverse(X_95)),multiply(greatest_lower_bound(identity,X_95),inverse(X_95))) )],[refute_0_463,refute_0_466]) ).
cnf(refute_0_468,plain,
( multiply(greatest_lower_bound(greatest_lower_bound(X_95,identity),identity),inverse(X_95)) != multiply(greatest_lower_bound(identity,X_95),inverse(X_95))
| multiply(greatest_lower_bound(greatest_lower_bound(X_95,identity),identity),inverse(X_95)) != greatest_lower_bound(inverse(X_95),greatest_lower_bound(identity,inverse(X_95)))
| multiply(greatest_lower_bound(identity,X_95),inverse(X_95)) = greatest_lower_bound(inverse(X_95),greatest_lower_bound(identity,inverse(X_95))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(greatest_lower_bound(X_95,identity),identity),inverse(X_95)),greatest_lower_bound(inverse(X_95),greatest_lower_bound(identity,inverse(X_95)))) ),[0],$fot(multiply(greatest_lower_bound(identity,X_95),inverse(X_95)))]]) ).
cnf(refute_0_469,plain,
( multiply(greatest_lower_bound(greatest_lower_bound(X_95,identity),identity),inverse(X_95)) != greatest_lower_bound(inverse(X_95),greatest_lower_bound(identity,inverse(X_95)))
| multiply(greatest_lower_bound(identity,X_95),inverse(X_95)) = greatest_lower_bound(inverse(X_95),greatest_lower_bound(identity,inverse(X_95))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(greatest_lower_bound(X_95,identity),identity),inverse(X_95)),multiply(greatest_lower_bound(identity,X_95),inverse(X_95))) )],[refute_0_467,refute_0_468]) ).
cnf(refute_0_470,plain,
greatest_lower_bound(inverse(X_95),inverse(X_95)) = inverse(X_95),
inference(subst,[],[idempotence_of_gld:[bind(X,$fot(inverse(X_95)))]]) ).
cnf(refute_0_471,plain,
greatest_lower_bound(identity,greatest_lower_bound(inverse(X_95),inverse(X_95))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X_95),inverse(X_95))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_95),inverse(X_95))))]]) ).
cnf(refute_0_472,plain,
( greatest_lower_bound(identity,greatest_lower_bound(inverse(X_95),inverse(X_95))) != greatest_lower_bound(identity,greatest_lower_bound(inverse(X_95),inverse(X_95)))
| greatest_lower_bound(inverse(X_95),inverse(X_95)) != inverse(X_95)
| greatest_lower_bound(identity,greatest_lower_bound(inverse(X_95),inverse(X_95))) = greatest_lower_bound(identity,inverse(X_95)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_95),inverse(X_95))),greatest_lower_bound(identity,greatest_lower_bound(inverse(X_95),inverse(X_95)))) ),[1,1],$fot(inverse(X_95))]]) ).
cnf(refute_0_473,plain,
( greatest_lower_bound(inverse(X_95),inverse(X_95)) != inverse(X_95)
| greatest_lower_bound(identity,greatest_lower_bound(inverse(X_95),inverse(X_95))) = greatest_lower_bound(identity,inverse(X_95)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_95),inverse(X_95))),greatest_lower_bound(identity,greatest_lower_bound(inverse(X_95),inverse(X_95)))) )],[refute_0_471,refute_0_472]) ).
cnf(refute_0_474,plain,
greatest_lower_bound(identity,greatest_lower_bound(inverse(X_95),inverse(X_95))) = greatest_lower_bound(identity,inverse(X_95)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_95),inverse(X_95)),inverse(X_95)) )],[refute_0_470,refute_0_473]) ).
cnf(refute_0_475,plain,
greatest_lower_bound(X_39,greatest_lower_bound(X_40,greatest_lower_bound(X_15,X_40))) = greatest_lower_bound(X_40,greatest_lower_bound(greatest_lower_bound(X_15,X_40),X_39)),
inference(subst,[],[refute_0_321:[bind(X,$fot(X_39)),bind(Y,$fot(X_40)),bind(X_35,$fot(greatest_lower_bound(X_15,X_40)))]]) ).
cnf(refute_0_476,plain,
greatest_lower_bound(X_40,greatest_lower_bound(X_15,X_40)) = greatest_lower_bound(X_40,X_15),
inference(subst,[],[refute_0_229:[bind(Y,$fot(X_40))]]) ).
cnf(refute_0_477,plain,
( greatest_lower_bound(X_39,greatest_lower_bound(X_40,greatest_lower_bound(X_15,X_40))) != greatest_lower_bound(X_40,greatest_lower_bound(greatest_lower_bound(X_15,X_40),X_39))
| greatest_lower_bound(X_40,greatest_lower_bound(X_15,X_40)) != greatest_lower_bound(X_40,X_15)
| greatest_lower_bound(X_39,greatest_lower_bound(X_40,X_15)) = greatest_lower_bound(X_40,greatest_lower_bound(greatest_lower_bound(X_15,X_40),X_39)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_39,greatest_lower_bound(X_40,greatest_lower_bound(X_15,X_40))),greatest_lower_bound(X_40,greatest_lower_bound(greatest_lower_bound(X_15,X_40),X_39))) ),[0,1],$fot(greatest_lower_bound(X_40,X_15))]]) ).
cnf(refute_0_478,plain,
( greatest_lower_bound(X_39,greatest_lower_bound(X_40,greatest_lower_bound(X_15,X_40))) != greatest_lower_bound(X_40,greatest_lower_bound(greatest_lower_bound(X_15,X_40),X_39))
| greatest_lower_bound(X_39,greatest_lower_bound(X_40,X_15)) = greatest_lower_bound(X_40,greatest_lower_bound(greatest_lower_bound(X_15,X_40),X_39)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_40,greatest_lower_bound(X_15,X_40)),greatest_lower_bound(X_40,X_15)) )],[refute_0_476,refute_0_477]) ).
cnf(refute_0_479,plain,
greatest_lower_bound(X_39,greatest_lower_bound(X_40,X_15)) = greatest_lower_bound(X_40,greatest_lower_bound(greatest_lower_bound(X_15,X_40),X_39)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_39,greatest_lower_bound(X_40,greatest_lower_bound(X_15,X_40))),greatest_lower_bound(X_40,greatest_lower_bound(greatest_lower_bound(X_15,X_40),X_39))) )],[refute_0_475,refute_0_478]) ).
cnf(refute_0_480,plain,
greatest_lower_bound(X_40,greatest_lower_bound(X_15,greatest_lower_bound(X_40,X_39))) = greatest_lower_bound(X_40,greatest_lower_bound(X_39,X_15)),
inference(subst,[],[refute_0_297:[bind(X,$fot(X_40)),bind(Y,$fot(X_39)),bind(X_35,$fot(X_15))]]) ).
cnf(refute_0_481,plain,
greatest_lower_bound(greatest_lower_bound(X_15,X_40),X_39) = greatest_lower_bound(X_15,greatest_lower_bound(X_40,X_39)),
inference(subst,[],[refute_0_225:[bind(X,$fot(X_15)),bind(Y,$fot(X_40)),bind(Z,$fot(X_39))]]) ).
cnf(refute_0_482,plain,
greatest_lower_bound(X_40,greatest_lower_bound(greatest_lower_bound(X_15,X_40),X_39)) = greatest_lower_bound(X_40,greatest_lower_bound(greatest_lower_bound(X_15,X_40),X_39)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X_40,greatest_lower_bound(greatest_lower_bound(X_15,X_40),X_39)))]]) ).
cnf(refute_0_483,plain,
( greatest_lower_bound(X_40,greatest_lower_bound(greatest_lower_bound(X_15,X_40),X_39)) != greatest_lower_bound(X_40,greatest_lower_bound(greatest_lower_bound(X_15,X_40),X_39))
| greatest_lower_bound(greatest_lower_bound(X_15,X_40),X_39) != greatest_lower_bound(X_15,greatest_lower_bound(X_40,X_39))
| greatest_lower_bound(X_40,greatest_lower_bound(greatest_lower_bound(X_15,X_40),X_39)) = greatest_lower_bound(X_40,greatest_lower_bound(X_15,greatest_lower_bound(X_40,X_39))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_40,greatest_lower_bound(greatest_lower_bound(X_15,X_40),X_39)),greatest_lower_bound(X_40,greatest_lower_bound(greatest_lower_bound(X_15,X_40),X_39))) ),[1,1],$fot(greatest_lower_bound(X_15,greatest_lower_bound(X_40,X_39)))]]) ).
cnf(refute_0_484,plain,
( greatest_lower_bound(greatest_lower_bound(X_15,X_40),X_39) != greatest_lower_bound(X_15,greatest_lower_bound(X_40,X_39))
| greatest_lower_bound(X_40,greatest_lower_bound(greatest_lower_bound(X_15,X_40),X_39)) = greatest_lower_bound(X_40,greatest_lower_bound(X_15,greatest_lower_bound(X_40,X_39))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_40,greatest_lower_bound(greatest_lower_bound(X_15,X_40),X_39)),greatest_lower_bound(X_40,greatest_lower_bound(greatest_lower_bound(X_15,X_40),X_39))) )],[refute_0_482,refute_0_483]) ).
cnf(refute_0_485,plain,
greatest_lower_bound(X_40,greatest_lower_bound(greatest_lower_bound(X_15,X_40),X_39)) = greatest_lower_bound(X_40,greatest_lower_bound(X_15,greatest_lower_bound(X_40,X_39))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_15,X_40),X_39),greatest_lower_bound(X_15,greatest_lower_bound(X_40,X_39))) )],[refute_0_481,refute_0_484]) ).
cnf(refute_0_486,plain,
( greatest_lower_bound(X_40,greatest_lower_bound(X_15,greatest_lower_bound(X_40,X_39))) != greatest_lower_bound(X_40,greatest_lower_bound(X_39,X_15))
| greatest_lower_bound(X_40,greatest_lower_bound(greatest_lower_bound(X_15,X_40),X_39)) != greatest_lower_bound(X_40,greatest_lower_bound(X_15,greatest_lower_bound(X_40,X_39)))
| greatest_lower_bound(X_40,greatest_lower_bound(greatest_lower_bound(X_15,X_40),X_39)) = greatest_lower_bound(X_40,greatest_lower_bound(X_39,X_15)) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(greatest_lower_bound(X_40,greatest_lower_bound(greatest_lower_bound(X_15,X_40),X_39)))),bind(Y0,$fot(greatest_lower_bound(X_40,greatest_lower_bound(X_15,greatest_lower_bound(X_40,X_39))))),bind(Z0,$fot(greatest_lower_bound(X_40,greatest_lower_bound(X_39,X_15))))]]) ).
cnf(refute_0_487,plain,
( greatest_lower_bound(X_40,greatest_lower_bound(X_15,greatest_lower_bound(X_40,X_39))) != greatest_lower_bound(X_40,greatest_lower_bound(X_39,X_15))
| greatest_lower_bound(X_40,greatest_lower_bound(greatest_lower_bound(X_15,X_40),X_39)) = greatest_lower_bound(X_40,greatest_lower_bound(X_39,X_15)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_40,greatest_lower_bound(greatest_lower_bound(X_15,X_40),X_39)),greatest_lower_bound(X_40,greatest_lower_bound(X_15,greatest_lower_bound(X_40,X_39)))) )],[refute_0_485,refute_0_486]) ).
cnf(refute_0_488,plain,
greatest_lower_bound(X_40,greatest_lower_bound(greatest_lower_bound(X_15,X_40),X_39)) = greatest_lower_bound(X_40,greatest_lower_bound(X_39,X_15)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_40,greatest_lower_bound(X_15,greatest_lower_bound(X_40,X_39))),greatest_lower_bound(X_40,greatest_lower_bound(X_39,X_15))) )],[refute_0_480,refute_0_487]) ).
cnf(refute_0_489,plain,
( greatest_lower_bound(X_39,greatest_lower_bound(X_40,X_15)) != greatest_lower_bound(X_40,greatest_lower_bound(greatest_lower_bound(X_15,X_40),X_39))
| greatest_lower_bound(X_40,greatest_lower_bound(greatest_lower_bound(X_15,X_40),X_39)) != greatest_lower_bound(X_40,greatest_lower_bound(X_39,X_15))
| greatest_lower_bound(X_39,greatest_lower_bound(X_40,X_15)) = greatest_lower_bound(X_40,greatest_lower_bound(X_39,X_15)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_39,greatest_lower_bound(X_40,X_15)),greatest_lower_bound(X_40,greatest_lower_bound(X_39,X_15))) ),[0],$fot(greatest_lower_bound(X_40,greatest_lower_bound(greatest_lower_bound(X_15,X_40),X_39)))]]) ).
cnf(refute_0_490,plain,
( greatest_lower_bound(X_39,greatest_lower_bound(X_40,X_15)) != greatest_lower_bound(X_40,greatest_lower_bound(greatest_lower_bound(X_15,X_40),X_39))
| greatest_lower_bound(X_39,greatest_lower_bound(X_40,X_15)) = greatest_lower_bound(X_40,greatest_lower_bound(X_39,X_15)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_40,greatest_lower_bound(greatest_lower_bound(X_15,X_40),X_39)),greatest_lower_bound(X_40,greatest_lower_bound(X_39,X_15))) )],[refute_0_488,refute_0_489]) ).
cnf(refute_0_491,plain,
greatest_lower_bound(X_39,greatest_lower_bound(X_40,X_15)) = greatest_lower_bound(X_40,greatest_lower_bound(X_39,X_15)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_39,greatest_lower_bound(X_40,X_15)),greatest_lower_bound(X_40,greatest_lower_bound(greatest_lower_bound(X_15,X_40),X_39))) )],[refute_0_479,refute_0_490]) ).
cnf(refute_0_492,plain,
( greatest_lower_bound(X_39,greatest_lower_bound(X_40,X_15)) != greatest_lower_bound(X_40,greatest_lower_bound(X_39,X_15))
| greatest_lower_bound(X_40,greatest_lower_bound(X_39,X_15)) = greatest_lower_bound(X_39,greatest_lower_bound(X_40,X_15)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(greatest_lower_bound(X_39,greatest_lower_bound(X_40,X_15)))),bind(Y0,$fot(greatest_lower_bound(X_40,greatest_lower_bound(X_39,X_15))))]]) ).
cnf(refute_0_493,plain,
greatest_lower_bound(X_40,greatest_lower_bound(X_39,X_15)) = greatest_lower_bound(X_39,greatest_lower_bound(X_40,X_15)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_39,greatest_lower_bound(X_40,X_15)),greatest_lower_bound(X_40,greatest_lower_bound(X_39,X_15))) )],[refute_0_491,refute_0_492]) ).
cnf(refute_0_494,plain,
greatest_lower_bound(inverse(X_95),greatest_lower_bound(identity,inverse(X_95))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X_95),inverse(X_95))),
inference(subst,[],[refute_0_493:[bind(X_15,$fot(inverse(X_95))),bind(X_39,$fot(identity)),bind(X_40,$fot(inverse(X_95)))]]) ).
cnf(refute_0_495,plain,
( greatest_lower_bound(identity,greatest_lower_bound(inverse(X_95),inverse(X_95))) != greatest_lower_bound(identity,inverse(X_95))
| greatest_lower_bound(inverse(X_95),greatest_lower_bound(identity,inverse(X_95))) != greatest_lower_bound(identity,greatest_lower_bound(inverse(X_95),inverse(X_95)))
| greatest_lower_bound(inverse(X_95),greatest_lower_bound(identity,inverse(X_95))) = greatest_lower_bound(identity,inverse(X_95)) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(greatest_lower_bound(inverse(X_95),greatest_lower_bound(identity,inverse(X_95))))),bind(Y0,$fot(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_95),inverse(X_95))))),bind(Z0,$fot(greatest_lower_bound(identity,inverse(X_95))))]]) ).
cnf(refute_0_496,plain,
( greatest_lower_bound(identity,greatest_lower_bound(inverse(X_95),inverse(X_95))) != greatest_lower_bound(identity,inverse(X_95))
| greatest_lower_bound(inverse(X_95),greatest_lower_bound(identity,inverse(X_95))) = greatest_lower_bound(identity,inverse(X_95)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_95),greatest_lower_bound(identity,inverse(X_95))),greatest_lower_bound(identity,greatest_lower_bound(inverse(X_95),inverse(X_95)))) )],[refute_0_494,refute_0_495]) ).
cnf(refute_0_497,plain,
greatest_lower_bound(inverse(X_95),greatest_lower_bound(identity,inverse(X_95))) = greatest_lower_bound(identity,inverse(X_95)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_95),inverse(X_95))),greatest_lower_bound(identity,inverse(X_95))) )],[refute_0_474,refute_0_496]) ).
cnf(refute_0_498,plain,
( multiply(greatest_lower_bound(identity,X_95),inverse(X_95)) != greatest_lower_bound(inverse(X_95),greatest_lower_bound(identity,inverse(X_95)))
| greatest_lower_bound(inverse(X_95),greatest_lower_bound(identity,inverse(X_95))) != greatest_lower_bound(identity,inverse(X_95))
| multiply(greatest_lower_bound(identity,X_95),inverse(X_95)) = greatest_lower_bound(identity,inverse(X_95)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(identity,X_95),inverse(X_95)),greatest_lower_bound(identity,inverse(X_95))) ),[0],$fot(greatest_lower_bound(inverse(X_95),greatest_lower_bound(identity,inverse(X_95))))]]) ).
cnf(refute_0_499,plain,
( multiply(greatest_lower_bound(identity,X_95),inverse(X_95)) != greatest_lower_bound(inverse(X_95),greatest_lower_bound(identity,inverse(X_95)))
| multiply(greatest_lower_bound(identity,X_95),inverse(X_95)) = greatest_lower_bound(identity,inverse(X_95)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_95),greatest_lower_bound(identity,inverse(X_95))),greatest_lower_bound(identity,inverse(X_95))) )],[refute_0_497,refute_0_498]) ).
cnf(refute_0_500,plain,
( multiply(greatest_lower_bound(greatest_lower_bound(X_95,identity),identity),inverse(X_95)) != greatest_lower_bound(inverse(X_95),greatest_lower_bound(identity,inverse(X_95)))
| multiply(greatest_lower_bound(identity,X_95),inverse(X_95)) = greatest_lower_bound(identity,inverse(X_95)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_95),inverse(X_95)),greatest_lower_bound(inverse(X_95),greatest_lower_bound(identity,inverse(X_95)))) )],[refute_0_469,refute_0_499]) ).
cnf(refute_0_501,plain,
multiply(greatest_lower_bound(identity,X_95),inverse(X_95)) = greatest_lower_bound(identity,inverse(X_95)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(greatest_lower_bound(X_95,identity),identity),inverse(X_95)),greatest_lower_bound(inverse(X_95),greatest_lower_bound(identity,inverse(X_95)))) )],[refute_0_458,refute_0_500]) ).
cnf(refute_0_502,plain,
multiply(greatest_lower_bound(identity,X_309),inverse(X_309)) = greatest_lower_bound(identity,inverse(X_309)),
inference(subst,[],[refute_0_501:[bind(X_95,$fot(X_309))]]) ).
cnf(refute_0_503,plain,
( multiply(greatest_lower_bound(identity,X_309),inverse(X_309)) != greatest_lower_bound(identity,inverse(X_309))
| multiply(greatest_lower_bound(identity,X_309),least_upper_bound(inverse(X_309),identity)) != least_upper_bound(greatest_lower_bound(identity,X_309),multiply(greatest_lower_bound(identity,X_309),inverse(X_309)))
| multiply(greatest_lower_bound(identity,X_309),least_upper_bound(inverse(X_309),identity)) = least_upper_bound(greatest_lower_bound(identity,X_309),greatest_lower_bound(identity,inverse(X_309))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_309),least_upper_bound(inverse(X_309),identity)),least_upper_bound(greatest_lower_bound(identity,X_309),multiply(greatest_lower_bound(identity,X_309),inverse(X_309)))) ),[1,1],$fot(greatest_lower_bound(identity,inverse(X_309)))]]) ).
cnf(refute_0_504,plain,
( multiply(greatest_lower_bound(identity,X_309),least_upper_bound(inverse(X_309),identity)) != least_upper_bound(greatest_lower_bound(identity,X_309),multiply(greatest_lower_bound(identity,X_309),inverse(X_309)))
| multiply(greatest_lower_bound(identity,X_309),least_upper_bound(inverse(X_309),identity)) = least_upper_bound(greatest_lower_bound(identity,X_309),greatest_lower_bound(identity,inverse(X_309))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_309),inverse(X_309)),greatest_lower_bound(identity,inverse(X_309))) )],[refute_0_502,refute_0_503]) ).
cnf(refute_0_505,plain,
multiply(greatest_lower_bound(identity,X_309),least_upper_bound(inverse(X_309),identity)) = least_upper_bound(greatest_lower_bound(identity,X_309),greatest_lower_bound(identity,inverse(X_309))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_309),least_upper_bound(inverse(X_309),identity)),least_upper_bound(greatest_lower_bound(identity,X_309),multiply(greatest_lower_bound(identity,X_309),inverse(X_309)))) )],[refute_0_444,refute_0_504]) ).
cnf(refute_0_506,plain,
inverse(multiply(X_23,inverse(multiply(X_33,inverse(X_32))))) = multiply(multiply(X_33,inverse(X_32)),inverse(X_23)),
inference(subst,[],[refute_0_107:[bind(X,$fot(multiply(X_33,inverse(X_32))))]]) ).
cnf(refute_0_507,plain,
inverse(multiply(X_33,inverse(X_32))) = multiply(X_32,inverse(X_33)),
inference(subst,[],[refute_0_107:[bind(X,$fot(X_32)),bind(X_23,$fot(X_33))]]) ).
cnf(refute_0_508,plain,
( inverse(multiply(X_23,inverse(multiply(X_33,inverse(X_32))))) != multiply(multiply(X_33,inverse(X_32)),inverse(X_23))
| inverse(multiply(X_33,inverse(X_32))) != multiply(X_32,inverse(X_33))
| inverse(multiply(X_23,multiply(X_32,inverse(X_33)))) = multiply(multiply(X_33,inverse(X_32)),inverse(X_23)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_23,inverse(multiply(X_33,inverse(X_32))))),multiply(multiply(X_33,inverse(X_32)),inverse(X_23))) ),[0,0,1],$fot(multiply(X_32,inverse(X_33)))]]) ).
cnf(refute_0_509,plain,
( inverse(multiply(X_23,inverse(multiply(X_33,inverse(X_32))))) != multiply(multiply(X_33,inverse(X_32)),inverse(X_23))
| inverse(multiply(X_23,multiply(X_32,inverse(X_33)))) = multiply(multiply(X_33,inverse(X_32)),inverse(X_23)) ),
inference(resolve,[$cnf( $equal(inverse(multiply(X_33,inverse(X_32))),multiply(X_32,inverse(X_33))) )],[refute_0_507,refute_0_508]) ).
cnf(refute_0_510,plain,
inverse(multiply(X_23,multiply(X_32,inverse(X_33)))) = multiply(multiply(X_33,inverse(X_32)),inverse(X_23)),
inference(resolve,[$cnf( $equal(inverse(multiply(X_23,inverse(multiply(X_33,inverse(X_32))))),multiply(multiply(X_33,inverse(X_32)),inverse(X_23))) )],[refute_0_506,refute_0_509]) ).
cnf(refute_0_511,plain,
multiply(inverse(X_32),inverse(X_23)) = inverse(multiply(X_23,X_32)),
inference(subst,[],[refute_0_100:[bind(X,$fot(X_23)),bind(Y,$fot(X_32))]]) ).
cnf(refute_0_512,plain,
multiply(X_33,multiply(inverse(X_32),inverse(X_23))) = multiply(X_33,multiply(inverse(X_32),inverse(X_23))),
introduced(tautology,[refl,[$fot(multiply(X_33,multiply(inverse(X_32),inverse(X_23))))]]) ).
cnf(refute_0_513,plain,
( multiply(X_33,multiply(inverse(X_32),inverse(X_23))) != multiply(X_33,multiply(inverse(X_32),inverse(X_23)))
| multiply(inverse(X_32),inverse(X_23)) != inverse(multiply(X_23,X_32))
| multiply(X_33,multiply(inverse(X_32),inverse(X_23))) = multiply(X_33,inverse(multiply(X_23,X_32))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_33,multiply(inverse(X_32),inverse(X_23))),multiply(X_33,multiply(inverse(X_32),inverse(X_23)))) ),[1,1],$fot(inverse(multiply(X_23,X_32)))]]) ).
cnf(refute_0_514,plain,
( multiply(inverse(X_32),inverse(X_23)) != inverse(multiply(X_23,X_32))
| multiply(X_33,multiply(inverse(X_32),inverse(X_23))) = multiply(X_33,inverse(multiply(X_23,X_32))) ),
inference(resolve,[$cnf( $equal(multiply(X_33,multiply(inverse(X_32),inverse(X_23))),multiply(X_33,multiply(inverse(X_32),inverse(X_23)))) )],[refute_0_512,refute_0_513]) ).
cnf(refute_0_515,plain,
multiply(X_33,multiply(inverse(X_32),inverse(X_23))) = multiply(X_33,inverse(multiply(X_23,X_32))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_32),inverse(X_23)),inverse(multiply(X_23,X_32))) )],[refute_0_511,refute_0_514]) ).
cnf(refute_0_516,plain,
multiply(multiply(X_33,inverse(X_32)),inverse(X_23)) = multiply(X_33,multiply(inverse(X_32),inverse(X_23))),
inference(subst,[],[associativity:[bind(X,$fot(X_33)),bind(Y,$fot(inverse(X_32))),bind(Z,$fot(inverse(X_23)))]]) ).
cnf(refute_0_517,plain,
( multiply(X_33,multiply(inverse(X_32),inverse(X_23))) != multiply(X_33,inverse(multiply(X_23,X_32)))
| multiply(multiply(X_33,inverse(X_32)),inverse(X_23)) != multiply(X_33,multiply(inverse(X_32),inverse(X_23)))
| multiply(multiply(X_33,inverse(X_32)),inverse(X_23)) = multiply(X_33,inverse(multiply(X_23,X_32))) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(multiply(multiply(X_33,inverse(X_32)),inverse(X_23)))),bind(Y0,$fot(multiply(X_33,multiply(inverse(X_32),inverse(X_23))))),bind(Z0,$fot(multiply(X_33,inverse(multiply(X_23,X_32)))))]]) ).
cnf(refute_0_518,plain,
( multiply(X_33,multiply(inverse(X_32),inverse(X_23))) != multiply(X_33,inverse(multiply(X_23,X_32)))
| multiply(multiply(X_33,inverse(X_32)),inverse(X_23)) = multiply(X_33,inverse(multiply(X_23,X_32))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_33,inverse(X_32)),inverse(X_23)),multiply(X_33,multiply(inverse(X_32),inverse(X_23)))) )],[refute_0_516,refute_0_517]) ).
cnf(refute_0_519,plain,
multiply(multiply(X_33,inverse(X_32)),inverse(X_23)) = multiply(X_33,inverse(multiply(X_23,X_32))),
inference(resolve,[$cnf( $equal(multiply(X_33,multiply(inverse(X_32),inverse(X_23))),multiply(X_33,inverse(multiply(X_23,X_32)))) )],[refute_0_515,refute_0_518]) ).
cnf(refute_0_520,plain,
( multiply(multiply(X_33,inverse(X_32)),inverse(X_23)) != multiply(X_33,inverse(multiply(X_23,X_32)))
| inverse(multiply(X_23,multiply(X_32,inverse(X_33)))) != multiply(multiply(X_33,inverse(X_32)),inverse(X_23))
| inverse(multiply(X_23,multiply(X_32,inverse(X_33)))) = multiply(X_33,inverse(multiply(X_23,X_32))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_23,multiply(X_32,inverse(X_33)))),multiply(multiply(X_33,inverse(X_32)),inverse(X_23))) ),[1],$fot(multiply(X_33,inverse(multiply(X_23,X_32))))]]) ).
cnf(refute_0_521,plain,
( inverse(multiply(X_23,multiply(X_32,inverse(X_33)))) != multiply(multiply(X_33,inverse(X_32)),inverse(X_23))
| inverse(multiply(X_23,multiply(X_32,inverse(X_33)))) = multiply(X_33,inverse(multiply(X_23,X_32))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_33,inverse(X_32)),inverse(X_23)),multiply(X_33,inverse(multiply(X_23,X_32)))) )],[refute_0_519,refute_0_520]) ).
cnf(refute_0_522,plain,
inverse(multiply(X_23,multiply(X_32,inverse(X_33)))) = multiply(X_33,inverse(multiply(X_23,X_32))),
inference(resolve,[$cnf( $equal(inverse(multiply(X_23,multiply(X_32,inverse(X_33)))),multiply(multiply(X_33,inverse(X_32)),inverse(X_23))) )],[refute_0_510,refute_0_521]) ).
cnf(refute_0_523,plain,
inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),multiply(X_228,inverse(X_229)))) = multiply(X_229,inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),X_228))),
inference(subst,[],[refute_0_522:[bind(X_23,$fot(inverse(least_upper_bound(identity,multiply(X_228,X_59))))),bind(X_32,$fot(X_228)),bind(X_33,$fot(X_229))]]) ).
cnf(refute_0_524,plain,
inverse(multiply(inverse(X_47),multiply(X_47,X_48))) = multiply(inverse(multiply(X_47,X_48)),inverse(inverse(X_47))),
inference(subst,[],[p19_3:[bind(X,$fot(inverse(X_47))),bind(Y,$fot(multiply(X_47,X_48)))]]) ).
cnf(refute_0_525,plain,
X_48 = multiply(inverse(X_47),multiply(X_47,X_48)),
inference(subst,[],[refute_0_97:[bind(X_45,$fot(X_47)),bind(X_46,$fot(X_48))]]) ).
cnf(refute_0_526,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_23:[bind(X0,$fot(X_48)),bind(Y0,$fot(multiply(inverse(X_47),multiply(X_47,X_48))))]]) ).
cnf(refute_0_527,plain,
multiply(inverse(X_47),multiply(X_47,X_48)) = X_48,
inference(resolve,[$cnf( $equal(X_48,multiply(inverse(X_47),multiply(X_47,X_48))) )],[refute_0_525,refute_0_526]) ).
cnf(refute_0_528,plain,
( multiply(inverse(X_47),multiply(X_47,X_48)) != X_48
| inverse(multiply(inverse(X_47),multiply(X_47,X_48))) != multiply(inverse(multiply(X_47,X_48)),inverse(inverse(X_47)))
| inverse(X_48) = multiply(inverse(multiply(X_47,X_48)),inverse(inverse(X_47))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X_47),multiply(X_47,X_48))),multiply(inverse(multiply(X_47,X_48)),inverse(inverse(X_47)))) ),[0,0],$fot(X_48)]]) ).
cnf(refute_0_529,plain,
( inverse(multiply(inverse(X_47),multiply(X_47,X_48))) != multiply(inverse(multiply(X_47,X_48)),inverse(inverse(X_47)))
| inverse(X_48) = multiply(inverse(multiply(X_47,X_48)),inverse(inverse(X_47))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_47),multiply(X_47,X_48)),X_48) )],[refute_0_527,refute_0_528]) ).
cnf(refute_0_530,plain,
inverse(X_48) = multiply(inverse(multiply(X_47,X_48)),inverse(inverse(X_47))),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_47),multiply(X_47,X_48))),multiply(inverse(multiply(X_47,X_48)),inverse(inverse(X_47)))) )],[refute_0_524,refute_0_529]) ).
cnf(refute_0_531,plain,
inverse(multiply(inverse(X),X_24)) = multiply(inverse(X_24),inverse(inverse(X))),
inference(subst,[],[p19_3:[bind(X,$fot(inverse(X))),bind(Y,$fot(X_24))]]) ).
cnf(refute_0_532,plain,
( inverse(multiply(inverse(X),X_24)) != multiply(inverse(X_24),inverse(inverse(X)))
| inverse(inverse(X)) != X
| inverse(multiply(inverse(X),X_24)) = multiply(inverse(X_24),X) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X),X_24)),multiply(inverse(X_24),inverse(inverse(X)))) ),[1,1],$fot(X)]]) ).
cnf(refute_0_533,plain,
( inverse(multiply(inverse(X),X_24)) != multiply(inverse(X_24),inverse(inverse(X)))
| inverse(multiply(inverse(X),X_24)) = multiply(inverse(X_24),X) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p19_2,refute_0_532]) ).
cnf(refute_0_534,plain,
inverse(multiply(inverse(X),X_24)) = multiply(inverse(X_24),X),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X),X_24)),multiply(inverse(X_24),inverse(inverse(X)))) )],[refute_0_531,refute_0_533]) ).
cnf(refute_0_535,plain,
inverse(multiply(inverse(X_47),multiply(X_47,X_48))) = multiply(inverse(multiply(X_47,X_48)),X_47),
inference(subst,[],[refute_0_534:[bind(X,$fot(X_47)),bind(X_24,$fot(multiply(X_47,X_48)))]]) ).
cnf(refute_0_536,plain,
multiply(inverse(multiply(X_47,X_48)),inverse(inverse(X_47))) = inverse(multiply(inverse(X_47),multiply(X_47,X_48))),
inference(subst,[],[refute_0_100:[bind(X,$fot(inverse(X_47))),bind(Y,$fot(multiply(X_47,X_48)))]]) ).
cnf(refute_0_537,plain,
( multiply(inverse(multiply(X_47,X_48)),inverse(inverse(X_47))) != inverse(multiply(inverse(X_47),multiply(X_47,X_48)))
| inverse(multiply(inverse(X_47),multiply(X_47,X_48))) != multiply(inverse(multiply(X_47,X_48)),X_47)
| multiply(inverse(multiply(X_47,X_48)),inverse(inverse(X_47))) = multiply(inverse(multiply(X_47,X_48)),X_47) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(multiply(inverse(multiply(X_47,X_48)),inverse(inverse(X_47))))),bind(Y0,$fot(inverse(multiply(inverse(X_47),multiply(X_47,X_48))))),bind(Z0,$fot(multiply(inverse(multiply(X_47,X_48)),X_47)))]]) ).
cnf(refute_0_538,plain,
( inverse(multiply(inverse(X_47),multiply(X_47,X_48))) != multiply(inverse(multiply(X_47,X_48)),X_47)
| multiply(inverse(multiply(X_47,X_48)),inverse(inverse(X_47))) = multiply(inverse(multiply(X_47,X_48)),X_47) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_47,X_48)),inverse(inverse(X_47))),inverse(multiply(inverse(X_47),multiply(X_47,X_48)))) )],[refute_0_536,refute_0_537]) ).
cnf(refute_0_539,plain,
multiply(inverse(multiply(X_47,X_48)),inverse(inverse(X_47))) = multiply(inverse(multiply(X_47,X_48)),X_47),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_47),multiply(X_47,X_48))),multiply(inverse(multiply(X_47,X_48)),X_47)) )],[refute_0_535,refute_0_538]) ).
cnf(refute_0_540,plain,
( multiply(inverse(multiply(X_47,X_48)),inverse(inverse(X_47))) != multiply(inverse(multiply(X_47,X_48)),X_47)
| inverse(X_48) != multiply(inverse(multiply(X_47,X_48)),inverse(inverse(X_47)))
| inverse(X_48) = multiply(inverse(multiply(X_47,X_48)),X_47) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(X_48),multiply(inverse(multiply(X_47,X_48)),inverse(inverse(X_47)))) ),[1],$fot(multiply(inverse(multiply(X_47,X_48)),X_47))]]) ).
cnf(refute_0_541,plain,
( inverse(X_48) != multiply(inverse(multiply(X_47,X_48)),inverse(inverse(X_47)))
| inverse(X_48) = multiply(inverse(multiply(X_47,X_48)),X_47) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_47,X_48)),inverse(inverse(X_47))),multiply(inverse(multiply(X_47,X_48)),X_47)) )],[refute_0_539,refute_0_540]) ).
cnf(refute_0_542,plain,
inverse(X_48) = multiply(inverse(multiply(X_47,X_48)),X_47),
inference(resolve,[$cnf( $equal(inverse(X_48),multiply(inverse(multiply(X_47,X_48)),inverse(inverse(X_47)))) )],[refute_0_530,refute_0_541]) ).
cnf(refute_0_543,plain,
inverse(least_upper_bound(X_59,inverse(X_47))) = multiply(inverse(multiply(X_47,least_upper_bound(X_59,inverse(X_47)))),X_47),
inference(subst,[],[refute_0_542:[bind(X_48,$fot(least_upper_bound(X_59,inverse(X_47))))]]) ).
cnf(refute_0_544,plain,
multiply(X_55,least_upper_bound(X_56,inverse(X_55))) = least_upper_bound(multiply(X_55,X_56),multiply(X_55,inverse(X_55))),
inference(subst,[],[monotony_lub1:[bind(X,$fot(X_55)),bind(Y,$fot(X_56)),bind(Z,$fot(inverse(X_55)))]]) ).
cnf(refute_0_545,plain,
multiply(X_55,inverse(X_55)) = identity,
inference(subst,[],[refute_0_156:[bind(X,$fot(X_55))]]) ).
cnf(refute_0_546,plain,
( multiply(X_55,inverse(X_55)) != identity
| multiply(X_55,least_upper_bound(X_56,inverse(X_55))) != least_upper_bound(multiply(X_55,X_56),multiply(X_55,inverse(X_55)))
| multiply(X_55,least_upper_bound(X_56,inverse(X_55))) = least_upper_bound(multiply(X_55,X_56),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_55,least_upper_bound(X_56,inverse(X_55))),least_upper_bound(multiply(X_55,X_56),multiply(X_55,inverse(X_55)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_547,plain,
( multiply(X_55,least_upper_bound(X_56,inverse(X_55))) != least_upper_bound(multiply(X_55,X_56),multiply(X_55,inverse(X_55)))
| multiply(X_55,least_upper_bound(X_56,inverse(X_55))) = least_upper_bound(multiply(X_55,X_56),identity) ),
inference(resolve,[$cnf( $equal(multiply(X_55,inverse(X_55)),identity) )],[refute_0_545,refute_0_546]) ).
cnf(refute_0_548,plain,
multiply(X_55,least_upper_bound(X_56,inverse(X_55))) = least_upper_bound(multiply(X_55,X_56),identity),
inference(resolve,[$cnf( $equal(multiply(X_55,least_upper_bound(X_56,inverse(X_55))),least_upper_bound(multiply(X_55,X_56),multiply(X_55,inverse(X_55)))) )],[refute_0_544,refute_0_547]) ).
cnf(refute_0_549,plain,
least_upper_bound(multiply(X_55,X_56),identity) = least_upper_bound(identity,multiply(X_55,X_56)),
inference(subst,[],[refute_0_30:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_55,X_56)))]]) ).
cnf(refute_0_550,plain,
( multiply(X_55,least_upper_bound(X_56,inverse(X_55))) != least_upper_bound(multiply(X_55,X_56),identity)
| least_upper_bound(multiply(X_55,X_56),identity) != least_upper_bound(identity,multiply(X_55,X_56))
| multiply(X_55,least_upper_bound(X_56,inverse(X_55))) = least_upper_bound(identity,multiply(X_55,X_56)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_55,least_upper_bound(X_56,inverse(X_55))),least_upper_bound(identity,multiply(X_55,X_56))) ),[0],$fot(least_upper_bound(multiply(X_55,X_56),identity))]]) ).
cnf(refute_0_551,plain,
( multiply(X_55,least_upper_bound(X_56,inverse(X_55))) != least_upper_bound(multiply(X_55,X_56),identity)
| multiply(X_55,least_upper_bound(X_56,inverse(X_55))) = least_upper_bound(identity,multiply(X_55,X_56)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_55,X_56),identity),least_upper_bound(identity,multiply(X_55,X_56))) )],[refute_0_549,refute_0_550]) ).
cnf(refute_0_552,plain,
multiply(X_55,least_upper_bound(X_56,inverse(X_55))) = least_upper_bound(identity,multiply(X_55,X_56)),
inference(resolve,[$cnf( $equal(multiply(X_55,least_upper_bound(X_56,inverse(X_55))),least_upper_bound(multiply(X_55,X_56),identity)) )],[refute_0_548,refute_0_551]) ).
cnf(refute_0_553,plain,
multiply(X_47,least_upper_bound(X_59,inverse(X_47))) = least_upper_bound(identity,multiply(X_47,X_59)),
inference(subst,[],[refute_0_552:[bind(X_55,$fot(X_47)),bind(X_56,$fot(X_59))]]) ).
cnf(refute_0_554,plain,
( multiply(X_47,least_upper_bound(X_59,inverse(X_47))) != least_upper_bound(identity,multiply(X_47,X_59))
| inverse(least_upper_bound(X_59,inverse(X_47))) != multiply(inverse(multiply(X_47,least_upper_bound(X_59,inverse(X_47)))),X_47)
| inverse(least_upper_bound(X_59,inverse(X_47))) = multiply(inverse(least_upper_bound(identity,multiply(X_47,X_59))),X_47) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_59,inverse(X_47))),multiply(inverse(multiply(X_47,least_upper_bound(X_59,inverse(X_47)))),X_47)) ),[1,0,0],$fot(least_upper_bound(identity,multiply(X_47,X_59)))]]) ).
cnf(refute_0_555,plain,
( inverse(least_upper_bound(X_59,inverse(X_47))) != multiply(inverse(multiply(X_47,least_upper_bound(X_59,inverse(X_47)))),X_47)
| inverse(least_upper_bound(X_59,inverse(X_47))) = multiply(inverse(least_upper_bound(identity,multiply(X_47,X_59))),X_47) ),
inference(resolve,[$cnf( $equal(multiply(X_47,least_upper_bound(X_59,inverse(X_47))),least_upper_bound(identity,multiply(X_47,X_59))) )],[refute_0_553,refute_0_554]) ).
cnf(refute_0_556,plain,
inverse(least_upper_bound(X_59,inverse(X_47))) = multiply(inverse(least_upper_bound(identity,multiply(X_47,X_59))),X_47),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_59,inverse(X_47))),multiply(inverse(multiply(X_47,least_upper_bound(X_59,inverse(X_47)))),X_47)) )],[refute_0_543,refute_0_555]) ).
cnf(refute_0_557,plain,
inverse(least_upper_bound(X_59,inverse(X_228))) = multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),X_228),
inference(subst,[],[refute_0_556:[bind(X_47,$fot(X_228))]]) ).
cnf(refute_0_558,plain,
( inverse(least_upper_bound(X_59,inverse(X_228))) != multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),X_228)
| multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),X_228) = inverse(least_upper_bound(X_59,inverse(X_228))) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(inverse(least_upper_bound(X_59,inverse(X_228))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),X_228)))]]) ).
cnf(refute_0_559,plain,
multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),X_228) = inverse(least_upper_bound(X_59,inverse(X_228))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_59,inverse(X_228))),multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),X_228)) )],[refute_0_557,refute_0_558]) ).
cnf(refute_0_560,plain,
( multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),X_228) != inverse(least_upper_bound(X_59,inverse(X_228)))
| inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),multiply(X_228,inverse(X_229)))) != multiply(X_229,inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),X_228)))
| inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),multiply(X_228,inverse(X_229)))) = multiply(X_229,inverse(inverse(least_upper_bound(X_59,inverse(X_228))))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),multiply(X_228,inverse(X_229)))),multiply(X_229,inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),X_228)))) ),[1,1,0],$fot(inverse(least_upper_bound(X_59,inverse(X_228))))]]) ).
cnf(refute_0_561,plain,
( inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),multiply(X_228,inverse(X_229)))) != multiply(X_229,inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),X_228)))
| inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),multiply(X_228,inverse(X_229)))) = multiply(X_229,inverse(inverse(least_upper_bound(X_59,inverse(X_228))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),X_228),inverse(least_upper_bound(X_59,inverse(X_228)))) )],[refute_0_559,refute_0_560]) ).
cnf(refute_0_562,plain,
inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),multiply(X_228,inverse(X_229)))) = multiply(X_229,inverse(inverse(least_upper_bound(X_59,inverse(X_228))))),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),multiply(X_228,inverse(X_229)))),multiply(X_229,inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),X_228)))) )],[refute_0_523,refute_0_561]) ).
cnf(refute_0_563,plain,
( X != multiply(X,identity)
| multiply(X,identity) = X ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(X)),bind(Y0,$fot(multiply(X,identity)))]]) ).
cnf(refute_0_564,plain,
multiply(X,identity) = X,
inference(resolve,[$cnf( $equal(X,multiply(X,identity)) )],[refute_0_19,refute_0_563]) ).
cnf(refute_0_565,plain,
multiply(inverse(X_228),identity) = inverse(X_228),
inference(subst,[],[refute_0_564:[bind(X,$fot(inverse(X_228)))]]) ).
cnf(refute_0_566,plain,
least_upper_bound(multiply(inverse(X_228),identity),X_59) = least_upper_bound(multiply(inverse(X_228),identity),X_59),
introduced(tautology,[refl,[$fot(least_upper_bound(multiply(inverse(X_228),identity),X_59))]]) ).
cnf(refute_0_567,plain,
( multiply(inverse(X_228),identity) != inverse(X_228)
| least_upper_bound(multiply(inverse(X_228),identity),X_59) != least_upper_bound(multiply(inverse(X_228),identity),X_59)
| least_upper_bound(multiply(inverse(X_228),identity),X_59) = least_upper_bound(inverse(X_228),X_59) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(inverse(X_228),identity),X_59),least_upper_bound(multiply(inverse(X_228),identity),X_59)) ),[1,0],$fot(inverse(X_228))]]) ).
cnf(refute_0_568,plain,
( multiply(inverse(X_228),identity) != inverse(X_228)
| least_upper_bound(multiply(inverse(X_228),identity),X_59) = least_upper_bound(inverse(X_228),X_59) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(X_228),identity),X_59),least_upper_bound(multiply(inverse(X_228),identity),X_59)) )],[refute_0_566,refute_0_567]) ).
cnf(refute_0_569,plain,
least_upper_bound(multiply(inverse(X_228),identity),X_59) = least_upper_bound(inverse(X_228),X_59),
inference(resolve,[$cnf( $equal(multiply(inverse(X_228),identity),inverse(X_228)) )],[refute_0_565,refute_0_568]) ).
cnf(refute_0_570,plain,
multiply(inverse(X_45),least_upper_bound(X_56,multiply(X_45,X_46))) = least_upper_bound(multiply(inverse(X_45),X_56),multiply(inverse(X_45),multiply(X_45,X_46))),
inference(subst,[],[monotony_lub1:[bind(X,$fot(inverse(X_45))),bind(Y,$fot(X_56)),bind(Z,$fot(multiply(X_45,X_46)))]]) ).
cnf(refute_0_571,plain,
( X_46 != multiply(inverse(X_45),multiply(X_45,X_46))
| multiply(inverse(X_45),multiply(X_45,X_46)) = X_46 ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(X_46)),bind(Y0,$fot(multiply(inverse(X_45),multiply(X_45,X_46))))]]) ).
cnf(refute_0_572,plain,
multiply(inverse(X_45),multiply(X_45,X_46)) = X_46,
inference(resolve,[$cnf( $equal(X_46,multiply(inverse(X_45),multiply(X_45,X_46))) )],[refute_0_97,refute_0_571]) ).
cnf(refute_0_573,plain,
( multiply(inverse(X_45),multiply(X_45,X_46)) != X_46
| multiply(inverse(X_45),least_upper_bound(X_56,multiply(X_45,X_46))) != least_upper_bound(multiply(inverse(X_45),X_56),multiply(inverse(X_45),multiply(X_45,X_46)))
| multiply(inverse(X_45),least_upper_bound(X_56,multiply(X_45,X_46))) = least_upper_bound(multiply(inverse(X_45),X_56),X_46) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_45),least_upper_bound(X_56,multiply(X_45,X_46))),least_upper_bound(multiply(inverse(X_45),X_56),multiply(inverse(X_45),multiply(X_45,X_46)))) ),[1,1],$fot(X_46)]]) ).
cnf(refute_0_574,plain,
( multiply(inverse(X_45),least_upper_bound(X_56,multiply(X_45,X_46))) != least_upper_bound(multiply(inverse(X_45),X_56),multiply(inverse(X_45),multiply(X_45,X_46)))
| multiply(inverse(X_45),least_upper_bound(X_56,multiply(X_45,X_46))) = least_upper_bound(multiply(inverse(X_45),X_56),X_46) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_45),multiply(X_45,X_46)),X_46) )],[refute_0_572,refute_0_573]) ).
cnf(refute_0_575,plain,
multiply(inverse(X_45),least_upper_bound(X_56,multiply(X_45,X_46))) = least_upper_bound(multiply(inverse(X_45),X_56),X_46),
inference(resolve,[$cnf( $equal(multiply(inverse(X_45),least_upper_bound(X_56,multiply(X_45,X_46))),least_upper_bound(multiply(inverse(X_45),X_56),multiply(inverse(X_45),multiply(X_45,X_46)))) )],[refute_0_570,refute_0_574]) ).
cnf(refute_0_576,plain,
multiply(inverse(X_228),least_upper_bound(identity,multiply(X_228,X_59))) = least_upper_bound(multiply(inverse(X_228),identity),X_59),
inference(subst,[],[refute_0_575:[bind(X_45,$fot(X_228)),bind(X_46,$fot(X_59)),bind(X_56,$fot(identity))]]) ).
cnf(refute_0_577,plain,
inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),X_228)) = multiply(inverse(X_228),least_upper_bound(identity,multiply(X_228,X_59))),
inference(subst,[],[refute_0_534:[bind(X,$fot(least_upper_bound(identity,multiply(X_228,X_59)))),bind(X_24,$fot(X_228))]]) ).
cnf(refute_0_578,plain,
( multiply(inverse(X_228),least_upper_bound(identity,multiply(X_228,X_59))) != least_upper_bound(multiply(inverse(X_228),identity),X_59)
| inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),X_228)) != multiply(inverse(X_228),least_upper_bound(identity,multiply(X_228,X_59)))
| inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),X_228)) = least_upper_bound(multiply(inverse(X_228),identity),X_59) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),X_228)))),bind(Y0,$fot(multiply(inverse(X_228),least_upper_bound(identity,multiply(X_228,X_59))))),bind(Z0,$fot(least_upper_bound(multiply(inverse(X_228),identity),X_59)))]]) ).
cnf(refute_0_579,plain,
( multiply(inverse(X_228),least_upper_bound(identity,multiply(X_228,X_59))) != least_upper_bound(multiply(inverse(X_228),identity),X_59)
| inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),X_228)) = least_upper_bound(multiply(inverse(X_228),identity),X_59) ),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),X_228)),multiply(inverse(X_228),least_upper_bound(identity,multiply(X_228,X_59)))) )],[refute_0_577,refute_0_578]) ).
cnf(refute_0_580,plain,
inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),X_228)) = least_upper_bound(multiply(inverse(X_228),identity),X_59),
inference(resolve,[$cnf( $equal(multiply(inverse(X_228),least_upper_bound(identity,multiply(X_228,X_59))),least_upper_bound(multiply(inverse(X_228),identity),X_59)) )],[refute_0_576,refute_0_579]) ).
cnf(refute_0_581,plain,
( inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),X_228)) != least_upper_bound(multiply(inverse(X_228),identity),X_59)
| least_upper_bound(multiply(inverse(X_228),identity),X_59) != least_upper_bound(inverse(X_228),X_59)
| inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),X_228)) = least_upper_bound(inverse(X_228),X_59) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),X_228)))),bind(Y0,$fot(least_upper_bound(multiply(inverse(X_228),identity),X_59))),bind(Z0,$fot(least_upper_bound(inverse(X_228),X_59)))]]) ).
cnf(refute_0_582,plain,
( least_upper_bound(multiply(inverse(X_228),identity),X_59) != least_upper_bound(inverse(X_228),X_59)
| inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),X_228)) = least_upper_bound(inverse(X_228),X_59) ),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),X_228)),least_upper_bound(multiply(inverse(X_228),identity),X_59)) )],[refute_0_580,refute_0_581]) ).
cnf(refute_0_583,plain,
inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),X_228)) = least_upper_bound(inverse(X_228),X_59),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(X_228),identity),X_59),least_upper_bound(inverse(X_228),X_59)) )],[refute_0_569,refute_0_582]) ).
cnf(refute_0_584,plain,
multiply(X_229,inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),X_228))) = multiply(X_229,inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),X_228))),
introduced(tautology,[refl,[$fot(multiply(X_229,inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),X_228))))]]) ).
cnf(refute_0_585,plain,
( multiply(X_229,inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),X_228))) != multiply(X_229,inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),X_228)))
| inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),X_228)) != least_upper_bound(inverse(X_228),X_59)
| multiply(X_229,inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),X_228))) = multiply(X_229,least_upper_bound(inverse(X_228),X_59)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_229,inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),X_228))),multiply(X_229,inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),X_228)))) ),[1,1],$fot(least_upper_bound(inverse(X_228),X_59))]]) ).
cnf(refute_0_586,plain,
( inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),X_228)) != least_upper_bound(inverse(X_228),X_59)
| multiply(X_229,inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),X_228))) = multiply(X_229,least_upper_bound(inverse(X_228),X_59)) ),
inference(resolve,[$cnf( $equal(multiply(X_229,inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),X_228))),multiply(X_229,inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),X_228)))) )],[refute_0_584,refute_0_585]) ).
cnf(refute_0_587,plain,
multiply(X_229,inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),X_228))) = multiply(X_229,least_upper_bound(inverse(X_228),X_59)),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),X_228)),least_upper_bound(inverse(X_228),X_59)) )],[refute_0_583,refute_0_586]) ).
cnf(refute_0_588,plain,
( multiply(X_229,inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),X_228))) != multiply(X_229,least_upper_bound(inverse(X_228),X_59))
| inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),multiply(X_228,inverse(X_229)))) != multiply(X_229,inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),X_228)))
| inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),multiply(X_228,inverse(X_229)))) = multiply(X_229,least_upper_bound(inverse(X_228),X_59)) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),multiply(X_228,inverse(X_229)))))),bind(Y0,$fot(multiply(X_229,inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),X_228))))),bind(Z0,$fot(multiply(X_229,least_upper_bound(inverse(X_228),X_59))))]]) ).
cnf(refute_0_589,plain,
( multiply(X_229,inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),X_228))) != multiply(X_229,least_upper_bound(inverse(X_228),X_59))
| inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),multiply(X_228,inverse(X_229)))) = multiply(X_229,least_upper_bound(inverse(X_228),X_59)) ),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),multiply(X_228,inverse(X_229)))),multiply(X_229,inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),X_228)))) )],[refute_0_523,refute_0_588]) ).
cnf(refute_0_590,plain,
inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),multiply(X_228,inverse(X_229)))) = multiply(X_229,least_upper_bound(inverse(X_228),X_59)),
inference(resolve,[$cnf( $equal(multiply(X_229,inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),X_228))),multiply(X_229,least_upper_bound(inverse(X_228),X_59))) )],[refute_0_587,refute_0_589]) ).
cnf(refute_0_591,plain,
( inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),multiply(X_228,inverse(X_229)))) != multiply(X_229,inverse(inverse(least_upper_bound(X_59,inverse(X_228)))))
| inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),multiply(X_228,inverse(X_229)))) != multiply(X_229,least_upper_bound(inverse(X_228),X_59))
| multiply(X_229,least_upper_bound(inverse(X_228),X_59)) = multiply(X_229,inverse(inverse(least_upper_bound(X_59,inverse(X_228))))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),multiply(X_228,inverse(X_229)))),multiply(X_229,inverse(inverse(least_upper_bound(X_59,inverse(X_228)))))) ),[0],$fot(multiply(X_229,least_upper_bound(inverse(X_228),X_59)))]]) ).
cnf(refute_0_592,plain,
( inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),multiply(X_228,inverse(X_229)))) != multiply(X_229,inverse(inverse(least_upper_bound(X_59,inverse(X_228)))))
| multiply(X_229,least_upper_bound(inverse(X_228),X_59)) = multiply(X_229,inverse(inverse(least_upper_bound(X_59,inverse(X_228))))) ),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),multiply(X_228,inverse(X_229)))),multiply(X_229,least_upper_bound(inverse(X_228),X_59))) )],[refute_0_590,refute_0_591]) ).
cnf(refute_0_593,plain,
inverse(inverse(least_upper_bound(X_59,inverse(X_228)))) = least_upper_bound(X_59,inverse(X_228)),
inference(subst,[],[p19_2:[bind(X,$fot(least_upper_bound(X_59,inverse(X_228))))]]) ).
cnf(refute_0_594,plain,
multiply(X_229,inverse(inverse(least_upper_bound(X_59,inverse(X_228))))) = multiply(X_229,inverse(inverse(least_upper_bound(X_59,inverse(X_228))))),
introduced(tautology,[refl,[$fot(multiply(X_229,inverse(inverse(least_upper_bound(X_59,inverse(X_228))))))]]) ).
cnf(refute_0_595,plain,
( multiply(X_229,inverse(inverse(least_upper_bound(X_59,inverse(X_228))))) != multiply(X_229,inverse(inverse(least_upper_bound(X_59,inverse(X_228)))))
| inverse(inverse(least_upper_bound(X_59,inverse(X_228)))) != least_upper_bound(X_59,inverse(X_228))
| multiply(X_229,inverse(inverse(least_upper_bound(X_59,inverse(X_228))))) = multiply(X_229,least_upper_bound(X_59,inverse(X_228))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_229,inverse(inverse(least_upper_bound(X_59,inverse(X_228))))),multiply(X_229,inverse(inverse(least_upper_bound(X_59,inverse(X_228)))))) ),[1,1],$fot(least_upper_bound(X_59,inverse(X_228)))]]) ).
cnf(refute_0_596,plain,
( inverse(inverse(least_upper_bound(X_59,inverse(X_228)))) != least_upper_bound(X_59,inverse(X_228))
| multiply(X_229,inverse(inverse(least_upper_bound(X_59,inverse(X_228))))) = multiply(X_229,least_upper_bound(X_59,inverse(X_228))) ),
inference(resolve,[$cnf( $equal(multiply(X_229,inverse(inverse(least_upper_bound(X_59,inverse(X_228))))),multiply(X_229,inverse(inverse(least_upper_bound(X_59,inverse(X_228)))))) )],[refute_0_594,refute_0_595]) ).
cnf(refute_0_597,plain,
multiply(X_229,inverse(inverse(least_upper_bound(X_59,inverse(X_228))))) = multiply(X_229,least_upper_bound(X_59,inverse(X_228))),
inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(X_59,inverse(X_228)))),least_upper_bound(X_59,inverse(X_228))) )],[refute_0_593,refute_0_596]) ).
cnf(refute_0_598,plain,
( multiply(X_229,inverse(inverse(least_upper_bound(X_59,inverse(X_228))))) != multiply(X_229,least_upper_bound(X_59,inverse(X_228)))
| multiply(X_229,least_upper_bound(inverse(X_228),X_59)) != multiply(X_229,inverse(inverse(least_upper_bound(X_59,inverse(X_228)))))
| multiply(X_229,least_upper_bound(inverse(X_228),X_59)) = multiply(X_229,least_upper_bound(X_59,inverse(X_228))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_229,least_upper_bound(inverse(X_228),X_59)),multiply(X_229,inverse(inverse(least_upper_bound(X_59,inverse(X_228)))))) ),[1],$fot(multiply(X_229,least_upper_bound(X_59,inverse(X_228))))]]) ).
cnf(refute_0_599,plain,
( multiply(X_229,least_upper_bound(inverse(X_228),X_59)) != multiply(X_229,inverse(inverse(least_upper_bound(X_59,inverse(X_228)))))
| multiply(X_229,least_upper_bound(inverse(X_228),X_59)) = multiply(X_229,least_upper_bound(X_59,inverse(X_228))) ),
inference(resolve,[$cnf( $equal(multiply(X_229,inverse(inverse(least_upper_bound(X_59,inverse(X_228))))),multiply(X_229,least_upper_bound(X_59,inverse(X_228)))) )],[refute_0_597,refute_0_598]) ).
cnf(refute_0_600,plain,
( inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),multiply(X_228,inverse(X_229)))) != multiply(X_229,inverse(inverse(least_upper_bound(X_59,inverse(X_228)))))
| multiply(X_229,least_upper_bound(inverse(X_228),X_59)) = multiply(X_229,least_upper_bound(X_59,inverse(X_228))) ),
inference(resolve,[$cnf( $equal(multiply(X_229,least_upper_bound(inverse(X_228),X_59)),multiply(X_229,inverse(inverse(least_upper_bound(X_59,inverse(X_228)))))) )],[refute_0_592,refute_0_599]) ).
cnf(refute_0_601,plain,
multiply(X_229,least_upper_bound(inverse(X_228),X_59)) = multiply(X_229,least_upper_bound(X_59,inverse(X_228))),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(least_upper_bound(identity,multiply(X_228,X_59))),multiply(X_228,inverse(X_229)))),multiply(X_229,inverse(inverse(least_upper_bound(X_59,inverse(X_228)))))) )],[refute_0_562,refute_0_600]) ).
cnf(refute_0_602,plain,
multiply(greatest_lower_bound(identity,X_309),least_upper_bound(inverse(X_309),identity)) = multiply(greatest_lower_bound(identity,X_309),least_upper_bound(identity,inverse(X_309))),
inference(subst,[],[refute_0_601:[bind(X_228,$fot(X_309)),bind(X_229,$fot(greatest_lower_bound(identity,X_309))),bind(X_59,$fot(identity))]]) ).
cnf(refute_0_603,plain,
( multiply(greatest_lower_bound(identity,X_309),least_upper_bound(inverse(X_309),identity)) != multiply(greatest_lower_bound(identity,X_309),least_upper_bound(identity,inverse(X_309)))
| multiply(greatest_lower_bound(identity,X_309),least_upper_bound(inverse(X_309),identity)) != least_upper_bound(greatest_lower_bound(identity,X_309),greatest_lower_bound(identity,inverse(X_309)))
| multiply(greatest_lower_bound(identity,X_309),least_upper_bound(identity,inverse(X_309))) = least_upper_bound(greatest_lower_bound(identity,X_309),greatest_lower_bound(identity,inverse(X_309))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_309),least_upper_bound(inverse(X_309),identity)),least_upper_bound(greatest_lower_bound(identity,X_309),greatest_lower_bound(identity,inverse(X_309)))) ),[0],$fot(multiply(greatest_lower_bound(identity,X_309),least_upper_bound(identity,inverse(X_309))))]]) ).
cnf(refute_0_604,plain,
( multiply(greatest_lower_bound(identity,X_309),least_upper_bound(inverse(X_309),identity)) != least_upper_bound(greatest_lower_bound(identity,X_309),greatest_lower_bound(identity,inverse(X_309)))
| multiply(greatest_lower_bound(identity,X_309),least_upper_bound(identity,inverse(X_309))) = least_upper_bound(greatest_lower_bound(identity,X_309),greatest_lower_bound(identity,inverse(X_309))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_309),least_upper_bound(inverse(X_309),identity)),multiply(greatest_lower_bound(identity,X_309),least_upper_bound(identity,inverse(X_309)))) )],[refute_0_602,refute_0_603]) ).
cnf(refute_0_605,plain,
multiply(least_upper_bound(inverse(X_75),identity),greatest_lower_bound(identity,X_75)) = least_upper_bound(greatest_lower_bound(identity,X_75),multiply(inverse(X_75),greatest_lower_bound(identity,X_75))),
inference(subst,[],[refute_0_76:[bind(X_76,$fot(greatest_lower_bound(identity,X_75))),bind(X_77,$fot(inverse(X_75)))]]) ).
cnf(refute_0_606,plain,
multiply(inverse(X_69),greatest_lower_bound(X_68,X_69)) = greatest_lower_bound(multiply(inverse(X_69),X_68),multiply(inverse(X_69),X_69)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(inverse(X_69))),bind(Y,$fot(X_68)),bind(Z,$fot(X_69))]]) ).
cnf(refute_0_607,plain,
multiply(inverse(X_69),X_69) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_69))]]) ).
cnf(refute_0_608,plain,
( multiply(inverse(X_69),X_69) != identity
| multiply(inverse(X_69),greatest_lower_bound(X_68,X_69)) != greatest_lower_bound(multiply(inverse(X_69),X_68),multiply(inverse(X_69),X_69))
| multiply(inverse(X_69),greatest_lower_bound(X_68,X_69)) = greatest_lower_bound(multiply(inverse(X_69),X_68),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_69),greatest_lower_bound(X_68,X_69)),greatest_lower_bound(multiply(inverse(X_69),X_68),multiply(inverse(X_69),X_69))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_609,plain,
( multiply(inverse(X_69),greatest_lower_bound(X_68,X_69)) != greatest_lower_bound(multiply(inverse(X_69),X_68),multiply(inverse(X_69),X_69))
| multiply(inverse(X_69),greatest_lower_bound(X_68,X_69)) = greatest_lower_bound(multiply(inverse(X_69),X_68),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_69),X_69),identity) )],[refute_0_607,refute_0_608]) ).
cnf(refute_0_610,plain,
multiply(inverse(X_69),greatest_lower_bound(X_68,X_69)) = greatest_lower_bound(multiply(inverse(X_69),X_68),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_69),greatest_lower_bound(X_68,X_69)),greatest_lower_bound(multiply(inverse(X_69),X_68),multiply(inverse(X_69),X_69))) )],[refute_0_606,refute_0_609]) ).
cnf(refute_0_611,plain,
greatest_lower_bound(multiply(inverse(X_69),X_68),identity) = greatest_lower_bound(identity,multiply(inverse(X_69),X_68)),
inference(subst,[],[refute_0_41:[bind(X_21,$fot(identity)),bind(X_22,$fot(multiply(inverse(X_69),X_68)))]]) ).
cnf(refute_0_612,plain,
( multiply(inverse(X_69),greatest_lower_bound(X_68,X_69)) != greatest_lower_bound(multiply(inverse(X_69),X_68),identity)
| greatest_lower_bound(multiply(inverse(X_69),X_68),identity) != greatest_lower_bound(identity,multiply(inverse(X_69),X_68))
| multiply(inverse(X_69),greatest_lower_bound(X_68,X_69)) = greatest_lower_bound(identity,multiply(inverse(X_69),X_68)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_69),greatest_lower_bound(X_68,X_69)),greatest_lower_bound(identity,multiply(inverse(X_69),X_68))) ),[0],$fot(greatest_lower_bound(multiply(inverse(X_69),X_68),identity))]]) ).
cnf(refute_0_613,plain,
( multiply(inverse(X_69),greatest_lower_bound(X_68,X_69)) != greatest_lower_bound(multiply(inverse(X_69),X_68),identity)
| multiply(inverse(X_69),greatest_lower_bound(X_68,X_69)) = greatest_lower_bound(identity,multiply(inverse(X_69),X_68)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(inverse(X_69),X_68),identity),greatest_lower_bound(identity,multiply(inverse(X_69),X_68))) )],[refute_0_611,refute_0_612]) ).
cnf(refute_0_614,plain,
multiply(inverse(X_69),greatest_lower_bound(X_68,X_69)) = greatest_lower_bound(identity,multiply(inverse(X_69),X_68)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_69),greatest_lower_bound(X_68,X_69)),greatest_lower_bound(multiply(inverse(X_69),X_68),identity)) )],[refute_0_610,refute_0_613]) ).
cnf(refute_0_615,plain,
multiply(inverse(X_75),greatest_lower_bound(identity,X_75)) = greatest_lower_bound(identity,multiply(inverse(X_75),identity)),
inference(subst,[],[refute_0_614:[bind(X_68,$fot(identity)),bind(X_69,$fot(X_75))]]) ).
cnf(refute_0_616,plain,
inverse(X_75) = multiply(inverse(X_75),identity),
inference(subst,[],[refute_0_19:[bind(X,$fot(inverse(X_75)))]]) ).
cnf(refute_0_617,plain,
( inverse(X_75) != multiply(inverse(X_75),identity)
| multiply(inverse(X_75),identity) = inverse(X_75) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(inverse(X_75))),bind(Y0,$fot(multiply(inverse(X_75),identity)))]]) ).
cnf(refute_0_618,plain,
multiply(inverse(X_75),identity) = inverse(X_75),
inference(resolve,[$cnf( $equal(inverse(X_75),multiply(inverse(X_75),identity)) )],[refute_0_616,refute_0_617]) ).
cnf(refute_0_619,plain,
( multiply(inverse(X_75),greatest_lower_bound(identity,X_75)) != greatest_lower_bound(identity,multiply(inverse(X_75),identity))
| multiply(inverse(X_75),identity) != inverse(X_75)
| multiply(inverse(X_75),greatest_lower_bound(identity,X_75)) = greatest_lower_bound(identity,inverse(X_75)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_75),greatest_lower_bound(identity,X_75)),greatest_lower_bound(identity,multiply(inverse(X_75),identity))) ),[1,1],$fot(inverse(X_75))]]) ).
cnf(refute_0_620,plain,
( multiply(inverse(X_75),greatest_lower_bound(identity,X_75)) != greatest_lower_bound(identity,multiply(inverse(X_75),identity))
| multiply(inverse(X_75),greatest_lower_bound(identity,X_75)) = greatest_lower_bound(identity,inverse(X_75)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_75),identity),inverse(X_75)) )],[refute_0_618,refute_0_619]) ).
cnf(refute_0_621,plain,
multiply(inverse(X_75),greatest_lower_bound(identity,X_75)) = greatest_lower_bound(identity,inverse(X_75)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_75),greatest_lower_bound(identity,X_75)),greatest_lower_bound(identity,multiply(inverse(X_75),identity))) )],[refute_0_615,refute_0_620]) ).
cnf(refute_0_622,plain,
( multiply(inverse(X_75),greatest_lower_bound(identity,X_75)) != greatest_lower_bound(identity,inverse(X_75))
| multiply(least_upper_bound(inverse(X_75),identity),greatest_lower_bound(identity,X_75)) != least_upper_bound(greatest_lower_bound(identity,X_75),multiply(inverse(X_75),greatest_lower_bound(identity,X_75)))
| multiply(least_upper_bound(inverse(X_75),identity),greatest_lower_bound(identity,X_75)) = least_upper_bound(greatest_lower_bound(identity,X_75),greatest_lower_bound(identity,inverse(X_75))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(X_75),identity),greatest_lower_bound(identity,X_75)),least_upper_bound(greatest_lower_bound(identity,X_75),multiply(inverse(X_75),greatest_lower_bound(identity,X_75)))) ),[1,1],$fot(greatest_lower_bound(identity,inverse(X_75)))]]) ).
cnf(refute_0_623,plain,
( multiply(least_upper_bound(inverse(X_75),identity),greatest_lower_bound(identity,X_75)) != least_upper_bound(greatest_lower_bound(identity,X_75),multiply(inverse(X_75),greatest_lower_bound(identity,X_75)))
| multiply(least_upper_bound(inverse(X_75),identity),greatest_lower_bound(identity,X_75)) = least_upper_bound(greatest_lower_bound(identity,X_75),greatest_lower_bound(identity,inverse(X_75))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_75),greatest_lower_bound(identity,X_75)),greatest_lower_bound(identity,inverse(X_75))) )],[refute_0_621,refute_0_622]) ).
cnf(refute_0_624,plain,
multiply(least_upper_bound(inverse(X_75),identity),greatest_lower_bound(identity,X_75)) = least_upper_bound(greatest_lower_bound(identity,X_75),greatest_lower_bound(identity,inverse(X_75))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_75),identity),greatest_lower_bound(identity,X_75)),least_upper_bound(greatest_lower_bound(identity,X_75),multiply(inverse(X_75),greatest_lower_bound(identity,X_75)))) )],[refute_0_605,refute_0_623]) ).
cnf(refute_0_625,plain,
least_upper_bound(least_upper_bound(X_17,Y),greatest_lower_bound(X_17,least_upper_bound(X_17,Y))) = least_upper_bound(X_17,Y),
inference(subst,[],[refute_0_270:[bind(X_14,$fot(least_upper_bound(X_17,Y))),bind(X_15,$fot(X_17))]]) ).
cnf(refute_0_626,plain,
greatest_lower_bound(X_17,least_upper_bound(X_17,Y)) = X_17,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_17))]]) ).
cnf(refute_0_627,plain,
( greatest_lower_bound(X_17,least_upper_bound(X_17,Y)) != X_17
| least_upper_bound(least_upper_bound(X_17,Y),greatest_lower_bound(X_17,least_upper_bound(X_17,Y))) != least_upper_bound(X_17,Y)
| least_upper_bound(least_upper_bound(X_17,Y),X_17) = least_upper_bound(X_17,Y) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_17,Y),greatest_lower_bound(X_17,least_upper_bound(X_17,Y))),least_upper_bound(X_17,Y)) ),[0,1],$fot(X_17)]]) ).
cnf(refute_0_628,plain,
( least_upper_bound(least_upper_bound(X_17,Y),greatest_lower_bound(X_17,least_upper_bound(X_17,Y))) != least_upper_bound(X_17,Y)
| least_upper_bound(least_upper_bound(X_17,Y),X_17) = least_upper_bound(X_17,Y) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,least_upper_bound(X_17,Y)),X_17) )],[refute_0_626,refute_0_627]) ).
cnf(refute_0_629,plain,
least_upper_bound(least_upper_bound(X_17,Y),X_17) = least_upper_bound(X_17,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_17,Y),greatest_lower_bound(X_17,least_upper_bound(X_17,Y))),least_upper_bound(X_17,Y)) )],[refute_0_625,refute_0_628]) ).
cnf(refute_0_630,plain,
( least_upper_bound(X,least_upper_bound(Y,Z)) != least_upper_bound(least_upper_bound(X,Y),Z)
| least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(Y,Z)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X,Y),Z)))]]) ).
cnf(refute_0_631,plain,
least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,Z)),least_upper_bound(least_upper_bound(X,Y),Z)) )],[associativity_of_lub,refute_0_630]) ).
cnf(refute_0_632,plain,
least_upper_bound(least_upper_bound(X_17,Y),X_17) = least_upper_bound(X_17,least_upper_bound(Y,X_17)),
inference(subst,[],[refute_0_631:[bind(X,$fot(X_17)),bind(Z,$fot(X_17))]]) ).
cnf(refute_0_633,plain,
( least_upper_bound(least_upper_bound(X_17,Y),X_17) != least_upper_bound(X_17,Y)
| least_upper_bound(least_upper_bound(X_17,Y),X_17) != least_upper_bound(X_17,least_upper_bound(Y,X_17))
| least_upper_bound(X_17,least_upper_bound(Y,X_17)) = least_upper_bound(X_17,Y) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_17,Y),X_17),least_upper_bound(X_17,Y)) ),[0],$fot(least_upper_bound(X_17,least_upper_bound(Y,X_17)))]]) ).
cnf(refute_0_634,plain,
( least_upper_bound(least_upper_bound(X_17,Y),X_17) != least_upper_bound(X_17,Y)
| least_upper_bound(X_17,least_upper_bound(Y,X_17)) = least_upper_bound(X_17,Y) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_17,Y),X_17),least_upper_bound(X_17,least_upper_bound(Y,X_17))) )],[refute_0_632,refute_0_633]) ).
cnf(refute_0_635,plain,
least_upper_bound(X_17,least_upper_bound(Y,X_17)) = least_upper_bound(X_17,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_17,Y),X_17),least_upper_bound(X_17,Y)) )],[refute_0_629,refute_0_634]) ).
cnf(refute_0_636,plain,
least_upper_bound(X_19,least_upper_bound(X_18,X_19)) = least_upper_bound(X_19,X_18),
inference(subst,[],[refute_0_635:[bind(Y,$fot(X_18)),bind(X_17,$fot(X_19))]]) ).
cnf(refute_0_637,plain,
least_upper_bound(X_19,X_18) = least_upper_bound(X_18,X_19),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_19)),bind(Y,$fot(X_18))]]) ).
cnf(refute_0_638,plain,
( least_upper_bound(X_19,X_18) != least_upper_bound(X_18,X_19)
| least_upper_bound(X_18,X_19) = least_upper_bound(X_19,X_18) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(least_upper_bound(X_19,X_18))),bind(Y0,$fot(least_upper_bound(X_18,X_19)))]]) ).
cnf(refute_0_639,plain,
least_upper_bound(X_18,X_19) = least_upper_bound(X_19,X_18),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,X_18),least_upper_bound(X_18,X_19)) )],[refute_0_637,refute_0_638]) ).
cnf(refute_0_640,plain,
( least_upper_bound(X_18,X_19) != least_upper_bound(X_19,X_18)
| least_upper_bound(X_19,least_upper_bound(X_18,X_19)) != least_upper_bound(X_19,X_18)
| least_upper_bound(X_19,least_upper_bound(X_19,X_18)) = least_upper_bound(X_19,X_18) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_19,least_upper_bound(X_18,X_19)),least_upper_bound(X_19,X_18)) ),[0,1],$fot(least_upper_bound(X_19,X_18))]]) ).
cnf(refute_0_641,plain,
( least_upper_bound(X_19,least_upper_bound(X_18,X_19)) != least_upper_bound(X_19,X_18)
| least_upper_bound(X_19,least_upper_bound(X_19,X_18)) = least_upper_bound(X_19,X_18) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,X_19),least_upper_bound(X_19,X_18)) )],[refute_0_639,refute_0_640]) ).
cnf(refute_0_642,plain,
least_upper_bound(X_19,least_upper_bound(X_19,X_18)) = least_upper_bound(X_19,X_18),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,least_upper_bound(X_18,X_19)),least_upper_bound(X_19,X_18)) )],[refute_0_636,refute_0_641]) ).
cnf(refute_0_643,plain,
least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_146,X_19))) = least_upper_bound(X_19,multiply(X_146,X_19)),
inference(subst,[],[refute_0_642:[bind(X_18,$fot(multiply(X_146,X_19)))]]) ).
cnf(refute_0_644,plain,
multiply(least_upper_bound(X_146,identity),X_19) = least_upper_bound(X_19,multiply(X_146,X_19)),
inference(subst,[],[refute_0_76:[bind(X_76,$fot(X_19)),bind(X_77,$fot(X_146))]]) ).
cnf(refute_0_645,plain,
( multiply(least_upper_bound(X_146,identity),X_19) != least_upper_bound(X_19,multiply(X_146,X_19))
| least_upper_bound(X_19,multiply(X_146,X_19)) = multiply(least_upper_bound(X_146,identity),X_19) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(multiply(least_upper_bound(X_146,identity),X_19))),bind(Y0,$fot(least_upper_bound(X_19,multiply(X_146,X_19))))]]) ).
cnf(refute_0_646,plain,
least_upper_bound(X_19,multiply(X_146,X_19)) = multiply(least_upper_bound(X_146,identity),X_19),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_146,identity),X_19),least_upper_bound(X_19,multiply(X_146,X_19))) )],[refute_0_644,refute_0_645]) ).
cnf(refute_0_647,plain,
( least_upper_bound(X_19,multiply(X_146,X_19)) != multiply(least_upper_bound(X_146,identity),X_19)
| least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_146,X_19))) != least_upper_bound(X_19,multiply(X_146,X_19))
| least_upper_bound(X_19,multiply(least_upper_bound(X_146,identity),X_19)) = least_upper_bound(X_19,multiply(X_146,X_19)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_146,X_19))),least_upper_bound(X_19,multiply(X_146,X_19))) ),[0,1],$fot(multiply(least_upper_bound(X_146,identity),X_19))]]) ).
cnf(refute_0_648,plain,
( least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_146,X_19))) != least_upper_bound(X_19,multiply(X_146,X_19))
| least_upper_bound(X_19,multiply(least_upper_bound(X_146,identity),X_19)) = least_upper_bound(X_19,multiply(X_146,X_19)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,multiply(X_146,X_19)),multiply(least_upper_bound(X_146,identity),X_19)) )],[refute_0_646,refute_0_647]) ).
cnf(refute_0_649,plain,
least_upper_bound(X_19,multiply(least_upper_bound(X_146,identity),X_19)) = least_upper_bound(X_19,multiply(X_146,X_19)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_146,X_19))),least_upper_bound(X_19,multiply(X_146,X_19))) )],[refute_0_643,refute_0_648]) ).
cnf(refute_0_650,plain,
least_upper_bound(identity,least_upper_bound(X_146,identity)) = least_upper_bound(identity,X_146),
inference(subst,[],[refute_0_635:[bind(Y,$fot(X_146)),bind(X_17,$fot(identity))]]) ).
cnf(refute_0_651,plain,
multiply(least_upper_bound(identity,least_upper_bound(X_146,identity)),X_19) = multiply(least_upper_bound(identity,least_upper_bound(X_146,identity)),X_19),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(identity,least_upper_bound(X_146,identity)),X_19))]]) ).
cnf(refute_0_652,plain,
( multiply(least_upper_bound(identity,least_upper_bound(X_146,identity)),X_19) != multiply(least_upper_bound(identity,least_upper_bound(X_146,identity)),X_19)
| least_upper_bound(identity,least_upper_bound(X_146,identity)) != least_upper_bound(identity,X_146)
| multiply(least_upper_bound(identity,least_upper_bound(X_146,identity)),X_19) = multiply(least_upper_bound(identity,X_146),X_19) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(X_146,identity)),X_19),multiply(least_upper_bound(identity,least_upper_bound(X_146,identity)),X_19)) ),[1,0],$fot(least_upper_bound(identity,X_146))]]) ).
cnf(refute_0_653,plain,
( least_upper_bound(identity,least_upper_bound(X_146,identity)) != least_upper_bound(identity,X_146)
| multiply(least_upper_bound(identity,least_upper_bound(X_146,identity)),X_19) = multiply(least_upper_bound(identity,X_146),X_19) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(X_146,identity)),X_19),multiply(least_upper_bound(identity,least_upper_bound(X_146,identity)),X_19)) )],[refute_0_651,refute_0_652]) ).
cnf(refute_0_654,plain,
multiply(least_upper_bound(identity,least_upper_bound(X_146,identity)),X_19) = multiply(least_upper_bound(identity,X_146),X_19),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_146,identity)),least_upper_bound(identity,X_146)) )],[refute_0_650,refute_0_653]) ).
cnf(refute_0_655,plain,
greatest_lower_bound(least_upper_bound(X_18,Y),least_upper_bound(Y,least_upper_bound(X_18,Y))) = least_upper_bound(X_18,Y),
inference(subst,[],[refute_0_218:[bind(X,$fot(least_upper_bound(X_18,Y)))]]) ).
cnf(refute_0_656,plain,
least_upper_bound(Y,least_upper_bound(X_18,Y)) = least_upper_bound(Y,X_18),
inference(subst,[],[refute_0_635:[bind(Y,$fot(X_18)),bind(X_17,$fot(Y))]]) ).
cnf(refute_0_657,plain,
( greatest_lower_bound(least_upper_bound(X_18,Y),least_upper_bound(Y,least_upper_bound(X_18,Y))) != least_upper_bound(X_18,Y)
| least_upper_bound(Y,least_upper_bound(X_18,Y)) != least_upper_bound(Y,X_18)
| greatest_lower_bound(least_upper_bound(X_18,Y),least_upper_bound(Y,X_18)) = least_upper_bound(X_18,Y) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_18,Y),least_upper_bound(Y,least_upper_bound(X_18,Y))),least_upper_bound(X_18,Y)) ),[0,1],$fot(least_upper_bound(Y,X_18))]]) ).
cnf(refute_0_658,plain,
( greatest_lower_bound(least_upper_bound(X_18,Y),least_upper_bound(Y,least_upper_bound(X_18,Y))) != least_upper_bound(X_18,Y)
| greatest_lower_bound(least_upper_bound(X_18,Y),least_upper_bound(Y,X_18)) = least_upper_bound(X_18,Y) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_18,Y)),least_upper_bound(Y,X_18)) )],[refute_0_656,refute_0_657]) ).
cnf(refute_0_659,plain,
greatest_lower_bound(least_upper_bound(X_18,Y),least_upper_bound(Y,X_18)) = least_upper_bound(X_18,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_18,Y),least_upper_bound(Y,least_upper_bound(X_18,Y))),least_upper_bound(X_18,Y)) )],[refute_0_655,refute_0_658]) ).
cnf(refute_0_660,plain,
greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),least_upper_bound(multiply(Y,X),multiply(Z,X))) = least_upper_bound(multiply(Z,X),multiply(Y,X)),
inference(subst,[],[refute_0_659:[bind(Y,$fot(multiply(Y,X))),bind(X_18,$fot(multiply(Z,X)))]]) ).
cnf(refute_0_661,plain,
( multiply(least_upper_bound(Y,Z),X) != least_upper_bound(multiply(Y,X),multiply(Z,X))
| least_upper_bound(multiply(Y,X),multiply(Z,X)) = multiply(least_upper_bound(Y,Z),X) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(multiply(least_upper_bound(Y,Z),X))),bind(Y0,$fot(least_upper_bound(multiply(Y,X),multiply(Z,X))))]]) ).
cnf(refute_0_662,plain,
least_upper_bound(multiply(Y,X),multiply(Z,X)) = multiply(least_upper_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Y,X),multiply(Z,X))) )],[monotony_lub2,refute_0_661]) ).
cnf(refute_0_663,plain,
( greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),least_upper_bound(multiply(Y,X),multiply(Z,X))) != least_upper_bound(multiply(Z,X),multiply(Y,X))
| least_upper_bound(multiply(Y,X),multiply(Z,X)) != multiply(least_upper_bound(Y,Z),X)
| greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) = least_upper_bound(multiply(Z,X),multiply(Y,X)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),least_upper_bound(multiply(Y,X),multiply(Z,X))),least_upper_bound(multiply(Z,X),multiply(Y,X))) ),[0,1],$fot(multiply(least_upper_bound(Y,Z),X))]]) ).
cnf(refute_0_664,plain,
( greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),least_upper_bound(multiply(Y,X),multiply(Z,X))) != least_upper_bound(multiply(Z,X),multiply(Y,X))
| greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) = least_upper_bound(multiply(Z,X),multiply(Y,X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(Y,X),multiply(Z,X)),multiply(least_upper_bound(Y,Z),X)) )],[refute_0_662,refute_0_663]) ).
cnf(refute_0_665,plain,
greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) = least_upper_bound(multiply(Z,X),multiply(Y,X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),least_upper_bound(multiply(Y,X),multiply(Z,X))),least_upper_bound(multiply(Z,X),multiply(Y,X))) )],[refute_0_660,refute_0_664]) ).
cnf(refute_0_666,plain,
greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)) = least_upper_bound(Y,Z),
inference(subst,[],[refute_0_659:[bind(Y,$fot(Z)),bind(X_18,$fot(Y))]]) ).
cnf(refute_0_667,plain,
multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X) = multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X))]]) ).
cnf(refute_0_668,plain,
( multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X) != multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X)
| greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)) != least_upper_bound(Y,Z)
| multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X) = multiply(least_upper_bound(Y,Z),X) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X),multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X)) ),[1,0],$fot(least_upper_bound(Y,Z))]]) ).
cnf(refute_0_669,plain,
( greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)) != least_upper_bound(Y,Z)
| multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X) = multiply(least_upper_bound(Y,Z),X) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X),multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X)) )],[refute_0_667,refute_0_668]) ).
cnf(refute_0_670,plain,
multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X) = multiply(least_upper_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),least_upper_bound(Y,Z)) )],[refute_0_666,refute_0_669]) ).
cnf(refute_0_671,plain,
greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) = multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X),
inference(subst,[],[refute_0_401:[bind(Y,$fot(least_upper_bound(Y,Z))),bind(Z,$fot(least_upper_bound(Z,Y)))]]) ).
cnf(refute_0_672,plain,
( multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X) != multiply(least_upper_bound(Y,Z),X)
| greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) != multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X)
| greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) = multiply(least_upper_bound(Y,Z),X) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)))),bind(Y0,$fot(multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X))),bind(Z0,$fot(multiply(least_upper_bound(Y,Z),X)))]]) ).
cnf(refute_0_673,plain,
( multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X) != multiply(least_upper_bound(Y,Z),X)
| greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) = multiply(least_upper_bound(Y,Z),X) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)),multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X)) )],[refute_0_671,refute_0_672]) ).
cnf(refute_0_674,plain,
greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) = multiply(least_upper_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X),multiply(least_upper_bound(Y,Z),X)) )],[refute_0_670,refute_0_673]) ).
cnf(refute_0_675,plain,
least_upper_bound(multiply(Z,X),multiply(Y,X)) = multiply(least_upper_bound(Z,Y),X),
inference(subst,[],[refute_0_662:[bind(Y,$fot(Z)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_676,plain,
greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) = greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))))]]) ).
cnf(refute_0_677,plain,
( greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) != greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X)))
| least_upper_bound(multiply(Z,X),multiply(Y,X)) != multiply(least_upper_bound(Z,Y),X)
| greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) = greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))),greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X)))) ),[1,1],$fot(multiply(least_upper_bound(Z,Y),X))]]) ).
cnf(refute_0_678,plain,
( least_upper_bound(multiply(Z,X),multiply(Y,X)) != multiply(least_upper_bound(Z,Y),X)
| greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) = greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))),greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X)))) )],[refute_0_676,refute_0_677]) ).
cnf(refute_0_679,plain,
greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) = greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Z,Y),X)) )],[refute_0_675,refute_0_678]) ).
cnf(refute_0_680,plain,
( greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) != multiply(least_upper_bound(Y,Z),X)
| greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) != greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X))
| greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) = multiply(least_upper_bound(Y,Z),X) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))))),bind(Y0,$fot(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)))),bind(Z0,$fot(multiply(least_upper_bound(Y,Z),X)))]]) ).
cnf(refute_0_681,plain,
( greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) != multiply(least_upper_bound(Y,Z),X)
| greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) = multiply(least_upper_bound(Y,Z),X) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))),greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X))) )],[refute_0_679,refute_0_680]) ).
cnf(refute_0_682,plain,
greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) = multiply(least_upper_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)),multiply(least_upper_bound(Y,Z),X)) )],[refute_0_674,refute_0_681]) ).
cnf(refute_0_683,plain,
greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) = greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))),
inference(subst,[],[refute_0_41:[bind(X_21,$fot(multiply(least_upper_bound(Y,Z),X))),bind(X_22,$fot(least_upper_bound(multiply(Z,X),multiply(Y,X))))]]) ).
cnf(refute_0_684,plain,
( greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) != multiply(least_upper_bound(Y,Z),X)
| greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) != greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X)))
| greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) = multiply(least_upper_bound(Y,Z),X) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)))),bind(Y0,$fot(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))))),bind(Z0,$fot(multiply(least_upper_bound(Y,Z),X)))]]) ).
cnf(refute_0_685,plain,
( greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) != multiply(least_upper_bound(Y,Z),X)
| greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) = multiply(least_upper_bound(Y,Z),X) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)),greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X)))) )],[refute_0_683,refute_0_684]) ).
cnf(refute_0_686,plain,
greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) = multiply(least_upper_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))),multiply(least_upper_bound(Y,Z),X)) )],[refute_0_682,refute_0_685]) ).
cnf(refute_0_687,plain,
( greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) != multiply(least_upper_bound(Y,Z),X)
| greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) != least_upper_bound(multiply(Z,X),multiply(Y,X))
| multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Z,X),multiply(Y,X)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)),least_upper_bound(multiply(Z,X),multiply(Y,X))) ),[0],$fot(multiply(least_upper_bound(Y,Z),X))]]) ).
cnf(refute_0_688,plain,
( greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) != least_upper_bound(multiply(Z,X),multiply(Y,X))
| multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Z,X),multiply(Y,X)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)),multiply(least_upper_bound(Y,Z),X)) )],[refute_0_686,refute_0_687]) ).
cnf(refute_0_689,plain,
( multiply(least_upper_bound(Y,Z),X) != least_upper_bound(multiply(Z,X),multiply(Y,X))
| least_upper_bound(multiply(Z,X),multiply(Y,X)) != multiply(least_upper_bound(Z,Y),X)
| multiply(least_upper_bound(Y,Z),X) = multiply(least_upper_bound(Z,Y),X) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) ),[0],$fot(least_upper_bound(multiply(Z,X),multiply(Y,X)))]]) ).
cnf(refute_0_690,plain,
( multiply(least_upper_bound(Y,Z),X) != least_upper_bound(multiply(Z,X),multiply(Y,X))
| multiply(least_upper_bound(Y,Z),X) = multiply(least_upper_bound(Z,Y),X) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Z,Y),X)) )],[refute_0_675,refute_0_689]) ).
cnf(refute_0_691,plain,
( greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) != least_upper_bound(multiply(Z,X),multiply(Y,X))
| multiply(least_upper_bound(Y,Z),X) = multiply(least_upper_bound(Z,Y),X) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) )],[refute_0_688,refute_0_690]) ).
cnf(refute_0_692,plain,
multiply(least_upper_bound(Y,Z),X) = multiply(least_upper_bound(Z,Y),X),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)),least_upper_bound(multiply(Z,X),multiply(Y,X))) )],[refute_0_665,refute_0_691]) ).
cnf(refute_0_693,plain,
( multiply(least_upper_bound(Y,Z),X) != multiply(least_upper_bound(Z,Y),X)
| multiply(least_upper_bound(Z,Y),X) = multiply(least_upper_bound(Y,Z),X) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(multiply(least_upper_bound(Y,Z),X))),bind(Y0,$fot(multiply(least_upper_bound(Z,Y),X)))]]) ).
cnf(refute_0_694,plain,
multiply(least_upper_bound(Z,Y),X) = multiply(least_upper_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) )],[refute_0_692,refute_0_693]) ).
cnf(refute_0_695,plain,
multiply(least_upper_bound(least_upper_bound(X_146,identity),identity),X_19) = multiply(least_upper_bound(identity,least_upper_bound(X_146,identity)),X_19),
inference(subst,[],[refute_0_694:[bind(X,$fot(X_19)),bind(Y,$fot(identity)),bind(Z,$fot(least_upper_bound(X_146,identity)))]]) ).
cnf(refute_0_696,plain,
least_upper_bound(X_19,multiply(least_upper_bound(X_146,identity),X_19)) = multiply(least_upper_bound(least_upper_bound(X_146,identity),identity),X_19),
inference(subst,[],[refute_0_78:[bind(X_76,$fot(X_19)),bind(X_77,$fot(least_upper_bound(X_146,identity)))]]) ).
cnf(refute_0_697,plain,
( multiply(least_upper_bound(least_upper_bound(X_146,identity),identity),X_19) != multiply(least_upper_bound(identity,least_upper_bound(X_146,identity)),X_19)
| least_upper_bound(X_19,multiply(least_upper_bound(X_146,identity),X_19)) != multiply(least_upper_bound(least_upper_bound(X_146,identity),identity),X_19)
| least_upper_bound(X_19,multiply(least_upper_bound(X_146,identity),X_19)) = multiply(least_upper_bound(identity,least_upper_bound(X_146,identity)),X_19) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(least_upper_bound(X_19,multiply(least_upper_bound(X_146,identity),X_19)))),bind(Y0,$fot(multiply(least_upper_bound(least_upper_bound(X_146,identity),identity),X_19))),bind(Z0,$fot(multiply(least_upper_bound(identity,least_upper_bound(X_146,identity)),X_19)))]]) ).
cnf(refute_0_698,plain,
( multiply(least_upper_bound(least_upper_bound(X_146,identity),identity),X_19) != multiply(least_upper_bound(identity,least_upper_bound(X_146,identity)),X_19)
| least_upper_bound(X_19,multiply(least_upper_bound(X_146,identity),X_19)) = multiply(least_upper_bound(identity,least_upper_bound(X_146,identity)),X_19) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,multiply(least_upper_bound(X_146,identity),X_19)),multiply(least_upper_bound(least_upper_bound(X_146,identity),identity),X_19)) )],[refute_0_696,refute_0_697]) ).
cnf(refute_0_699,plain,
least_upper_bound(X_19,multiply(least_upper_bound(X_146,identity),X_19)) = multiply(least_upper_bound(identity,least_upper_bound(X_146,identity)),X_19),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_146,identity),identity),X_19),multiply(least_upper_bound(identity,least_upper_bound(X_146,identity)),X_19)) )],[refute_0_695,refute_0_698]) ).
cnf(refute_0_700,plain,
( multiply(least_upper_bound(identity,least_upper_bound(X_146,identity)),X_19) != multiply(least_upper_bound(identity,X_146),X_19)
| least_upper_bound(X_19,multiply(least_upper_bound(X_146,identity),X_19)) != multiply(least_upper_bound(identity,least_upper_bound(X_146,identity)),X_19)
| least_upper_bound(X_19,multiply(least_upper_bound(X_146,identity),X_19)) = multiply(least_upper_bound(identity,X_146),X_19) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(least_upper_bound(X_19,multiply(least_upper_bound(X_146,identity),X_19)))),bind(Y0,$fot(multiply(least_upper_bound(identity,least_upper_bound(X_146,identity)),X_19))),bind(Z0,$fot(multiply(least_upper_bound(identity,X_146),X_19)))]]) ).
cnf(refute_0_701,plain,
( multiply(least_upper_bound(identity,least_upper_bound(X_146,identity)),X_19) != multiply(least_upper_bound(identity,X_146),X_19)
| least_upper_bound(X_19,multiply(least_upper_bound(X_146,identity),X_19)) = multiply(least_upper_bound(identity,X_146),X_19) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,multiply(least_upper_bound(X_146,identity),X_19)),multiply(least_upper_bound(identity,least_upper_bound(X_146,identity)),X_19)) )],[refute_0_699,refute_0_700]) ).
cnf(refute_0_702,plain,
least_upper_bound(X_19,multiply(least_upper_bound(X_146,identity),X_19)) = multiply(least_upper_bound(identity,X_146),X_19),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(X_146,identity)),X_19),multiply(least_upper_bound(identity,X_146),X_19)) )],[refute_0_654,refute_0_701]) ).
cnf(refute_0_703,plain,
( least_upper_bound(X_19,multiply(least_upper_bound(X_146,identity),X_19)) != multiply(least_upper_bound(identity,X_146),X_19)
| least_upper_bound(X_19,multiply(least_upper_bound(X_146,identity),X_19)) != least_upper_bound(X_19,multiply(X_146,X_19))
| multiply(least_upper_bound(identity,X_146),X_19) = least_upper_bound(X_19,multiply(X_146,X_19)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_19,multiply(least_upper_bound(X_146,identity),X_19)),least_upper_bound(X_19,multiply(X_146,X_19))) ),[0],$fot(multiply(least_upper_bound(identity,X_146),X_19))]]) ).
cnf(refute_0_704,plain,
( least_upper_bound(X_19,multiply(least_upper_bound(X_146,identity),X_19)) != least_upper_bound(X_19,multiply(X_146,X_19))
| multiply(least_upper_bound(identity,X_146),X_19) = least_upper_bound(X_19,multiply(X_146,X_19)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,multiply(least_upper_bound(X_146,identity),X_19)),multiply(least_upper_bound(identity,X_146),X_19)) )],[refute_0_702,refute_0_703]) ).
cnf(refute_0_705,plain,
( multiply(least_upper_bound(identity,X_146),X_19) != least_upper_bound(X_19,multiply(X_146,X_19))
| least_upper_bound(X_19,multiply(X_146,X_19)) != multiply(least_upper_bound(X_146,identity),X_19)
| multiply(least_upper_bound(identity,X_146),X_19) = multiply(least_upper_bound(X_146,identity),X_19) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(identity,X_146),X_19),multiply(least_upper_bound(X_146,identity),X_19)) ),[0],$fot(least_upper_bound(X_19,multiply(X_146,X_19)))]]) ).
cnf(refute_0_706,plain,
( multiply(least_upper_bound(identity,X_146),X_19) != least_upper_bound(X_19,multiply(X_146,X_19))
| multiply(least_upper_bound(identity,X_146),X_19) = multiply(least_upper_bound(X_146,identity),X_19) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,multiply(X_146,X_19)),multiply(least_upper_bound(X_146,identity),X_19)) )],[refute_0_646,refute_0_705]) ).
cnf(refute_0_707,plain,
( least_upper_bound(X_19,multiply(least_upper_bound(X_146,identity),X_19)) != least_upper_bound(X_19,multiply(X_146,X_19))
| multiply(least_upper_bound(identity,X_146),X_19) = multiply(least_upper_bound(X_146,identity),X_19) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_146),X_19),least_upper_bound(X_19,multiply(X_146,X_19))) )],[refute_0_704,refute_0_706]) ).
cnf(refute_0_708,plain,
multiply(least_upper_bound(identity,X_146),X_19) = multiply(least_upper_bound(X_146,identity),X_19),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,multiply(least_upper_bound(X_146,identity),X_19)),least_upper_bound(X_19,multiply(X_146,X_19))) )],[refute_0_649,refute_0_707]) ).
cnf(refute_0_709,plain,
( multiply(least_upper_bound(identity,X_146),X_19) != multiply(least_upper_bound(X_146,identity),X_19)
| multiply(least_upper_bound(X_146,identity),X_19) = multiply(least_upper_bound(identity,X_146),X_19) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(multiply(least_upper_bound(identity,X_146),X_19))),bind(Y0,$fot(multiply(least_upper_bound(X_146,identity),X_19)))]]) ).
cnf(refute_0_710,plain,
multiply(least_upper_bound(X_146,identity),X_19) = multiply(least_upper_bound(identity,X_146),X_19),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_146),X_19),multiply(least_upper_bound(X_146,identity),X_19)) )],[refute_0_708,refute_0_709]) ).
cnf(refute_0_711,plain,
multiply(least_upper_bound(inverse(X_75),identity),greatest_lower_bound(identity,X_75)) = multiply(least_upper_bound(identity,inverse(X_75)),greatest_lower_bound(identity,X_75)),
inference(subst,[],[refute_0_710:[bind(X_146,$fot(inverse(X_75))),bind(X_19,$fot(greatest_lower_bound(identity,X_75)))]]) ).
cnf(refute_0_712,plain,
( multiply(least_upper_bound(inverse(X_75),identity),greatest_lower_bound(identity,X_75)) != multiply(least_upper_bound(identity,inverse(X_75)),greatest_lower_bound(identity,X_75))
| multiply(least_upper_bound(inverse(X_75),identity),greatest_lower_bound(identity,X_75)) != least_upper_bound(greatest_lower_bound(identity,X_75),greatest_lower_bound(identity,inverse(X_75)))
| multiply(least_upper_bound(identity,inverse(X_75)),greatest_lower_bound(identity,X_75)) = least_upper_bound(greatest_lower_bound(identity,X_75),greatest_lower_bound(identity,inverse(X_75))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(X_75),identity),greatest_lower_bound(identity,X_75)),least_upper_bound(greatest_lower_bound(identity,X_75),greatest_lower_bound(identity,inverse(X_75)))) ),[0],$fot(multiply(least_upper_bound(identity,inverse(X_75)),greatest_lower_bound(identity,X_75)))]]) ).
cnf(refute_0_713,plain,
( multiply(least_upper_bound(inverse(X_75),identity),greatest_lower_bound(identity,X_75)) != least_upper_bound(greatest_lower_bound(identity,X_75),greatest_lower_bound(identity,inverse(X_75)))
| multiply(least_upper_bound(identity,inverse(X_75)),greatest_lower_bound(identity,X_75)) = least_upper_bound(greatest_lower_bound(identity,X_75),greatest_lower_bound(identity,inverse(X_75))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_75),identity),greatest_lower_bound(identity,X_75)),multiply(least_upper_bound(identity,inverse(X_75)),greatest_lower_bound(identity,X_75))) )],[refute_0_711,refute_0_712]) ).
cnf(refute_0_714,plain,
multiply(least_upper_bound(identity,inverse(X_75)),greatest_lower_bound(identity,X_75)) = least_upper_bound(greatest_lower_bound(identity,X_75),greatest_lower_bound(identity,inverse(X_75))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_75),identity),greatest_lower_bound(identity,X_75)),least_upper_bound(greatest_lower_bound(identity,X_75),greatest_lower_bound(identity,inverse(X_75)))) )],[refute_0_624,refute_0_713]) ).
cnf(refute_0_715,plain,
( multiply(least_upper_bound(identity,X_84),greatest_lower_bound(identity,inverse(X_84))) != multiply(greatest_lower_bound(identity,inverse(X_84)),least_upper_bound(identity,X_84))
| multiply(greatest_lower_bound(identity,inverse(X_84)),least_upper_bound(identity,X_84)) = multiply(least_upper_bound(identity,X_84),greatest_lower_bound(identity,inverse(X_84))) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(multiply(least_upper_bound(identity,X_84),greatest_lower_bound(identity,inverse(X_84))))),bind(Y0,$fot(multiply(greatest_lower_bound(identity,inverse(X_84)),least_upper_bound(identity,X_84))))]]) ).
cnf(refute_0_716,plain,
multiply(greatest_lower_bound(identity,inverse(X_84)),least_upper_bound(identity,X_84)) = multiply(least_upper_bound(identity,X_84),greatest_lower_bound(identity,inverse(X_84))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_84),greatest_lower_bound(identity,inverse(X_84))),multiply(greatest_lower_bound(identity,inverse(X_84)),least_upper_bound(identity,X_84))) )],[refute_0_443,refute_0_715]) ).
cnf(refute_0_717,plain,
multiply(greatest_lower_bound(identity,inverse(X_63)),least_upper_bound(identity,X_63)) = multiply(least_upper_bound(identity,X_63),greatest_lower_bound(identity,inverse(X_63))),
inference(subst,[],[refute_0_716:[bind(X_84,$fot(X_63))]]) ).
cnf(refute_0_718,plain,
( multiply(greatest_lower_bound(identity,inverse(X_63)),least_upper_bound(identity,X_63)) != multiply(least_upper_bound(identity,X_63),greatest_lower_bound(identity,inverse(X_63)))
| multiply(greatest_lower_bound(identity,inverse(X_63)),least_upper_bound(identity,X_63)) != greatest_lower_bound(least_upper_bound(identity,X_63),least_upper_bound(identity,inverse(X_63)))
| multiply(least_upper_bound(identity,X_63),greatest_lower_bound(identity,inverse(X_63))) = greatest_lower_bound(least_upper_bound(identity,X_63),least_upper_bound(identity,inverse(X_63))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(X_63)),least_upper_bound(identity,X_63)),greatest_lower_bound(least_upper_bound(identity,X_63),least_upper_bound(identity,inverse(X_63)))) ),[0],$fot(multiply(least_upper_bound(identity,X_63),greatest_lower_bound(identity,inverse(X_63))))]]) ).
cnf(refute_0_719,plain,
( multiply(greatest_lower_bound(identity,inverse(X_63)),least_upper_bound(identity,X_63)) != greatest_lower_bound(least_upper_bound(identity,X_63),least_upper_bound(identity,inverse(X_63)))
| multiply(least_upper_bound(identity,X_63),greatest_lower_bound(identity,inverse(X_63))) = greatest_lower_bound(least_upper_bound(identity,X_63),least_upper_bound(identity,inverse(X_63))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(X_63)),least_upper_bound(identity,X_63)),multiply(least_upper_bound(identity,X_63),greatest_lower_bound(identity,inverse(X_63)))) )],[refute_0_717,refute_0_718]) ).
cnf(refute_0_720,plain,
multiply(least_upper_bound(identity,X_63),greatest_lower_bound(identity,inverse(X_63))) = greatest_lower_bound(least_upper_bound(identity,X_63),least_upper_bound(identity,inverse(X_63))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(X_63)),least_upper_bound(identity,X_63)),greatest_lower_bound(least_upper_bound(identity,X_63),least_upper_bound(identity,inverse(X_63)))) )],[refute_0_436,refute_0_719]) ).
cnf(refute_0_721,plain,
multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,inverse(inverse(X)))) = greatest_lower_bound(least_upper_bound(identity,inverse(X)),least_upper_bound(identity,inverse(inverse(X)))),
inference(subst,[],[refute_0_720:[bind(X_63,$fot(inverse(X)))]]) ).
cnf(refute_0_722,plain,
( multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,inverse(inverse(X)))) != greatest_lower_bound(least_upper_bound(identity,inverse(X)),least_upper_bound(identity,inverse(inverse(X))))
| inverse(inverse(X)) != X
| multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,inverse(inverse(X)))) = greatest_lower_bound(least_upper_bound(identity,inverse(X)),least_upper_bound(identity,X)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,inverse(inverse(X)))),greatest_lower_bound(least_upper_bound(identity,inverse(X)),least_upper_bound(identity,inverse(inverse(X))))) ),[1,1,1],$fot(X)]]) ).
cnf(refute_0_723,plain,
( multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,inverse(inverse(X)))) != greatest_lower_bound(least_upper_bound(identity,inverse(X)),least_upper_bound(identity,inverse(inverse(X))))
| multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,inverse(inverse(X)))) = greatest_lower_bound(least_upper_bound(identity,inverse(X)),least_upper_bound(identity,X)) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p19_2,refute_0_722]) ).
cnf(refute_0_724,plain,
multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,inverse(inverse(X)))) = greatest_lower_bound(least_upper_bound(identity,inverse(X)),least_upper_bound(identity,X)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,inverse(inverse(X)))),greatest_lower_bound(least_upper_bound(identity,inverse(X)),least_upper_bound(identity,inverse(inverse(X))))) )],[refute_0_721,refute_0_723]) ).
cnf(refute_0_725,plain,
greatest_lower_bound(identity,inverse(inverse(X))) = greatest_lower_bound(identity,inverse(inverse(X))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,inverse(inverse(X))))]]) ).
cnf(refute_0_726,plain,
( greatest_lower_bound(identity,inverse(inverse(X))) != greatest_lower_bound(identity,inverse(inverse(X)))
| inverse(inverse(X)) != X
| greatest_lower_bound(identity,inverse(inverse(X))) = greatest_lower_bound(identity,X) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,inverse(inverse(X))),greatest_lower_bound(identity,inverse(inverse(X)))) ),[1,1],$fot(X)]]) ).
cnf(refute_0_727,plain,
( inverse(inverse(X)) != X
| greatest_lower_bound(identity,inverse(inverse(X))) = greatest_lower_bound(identity,X) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(inverse(X))),greatest_lower_bound(identity,inverse(inverse(X)))) )],[refute_0_725,refute_0_726]) ).
cnf(refute_0_728,plain,
greatest_lower_bound(identity,inverse(inverse(X))) = greatest_lower_bound(identity,X),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p19_2,refute_0_727]) ).
cnf(refute_0_729,plain,
multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,inverse(inverse(X)))) = multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,inverse(inverse(X)))),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,inverse(inverse(X)))))]]) ).
cnf(refute_0_730,plain,
( multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,inverse(inverse(X)))) != multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,inverse(inverse(X))))
| greatest_lower_bound(identity,inverse(inverse(X))) != greatest_lower_bound(identity,X)
| multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,inverse(inverse(X)))) = multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,X)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,inverse(inverse(X)))),multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,inverse(inverse(X))))) ),[1,1],$fot(greatest_lower_bound(identity,X))]]) ).
cnf(refute_0_731,plain,
( greatest_lower_bound(identity,inverse(inverse(X))) != greatest_lower_bound(identity,X)
| multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,inverse(inverse(X)))) = multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,X)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,inverse(inverse(X)))),multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,inverse(inverse(X))))) )],[refute_0_729,refute_0_730]) ).
cnf(refute_0_732,plain,
multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,inverse(inverse(X)))) = multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(inverse(X))),greatest_lower_bound(identity,X)) )],[refute_0_728,refute_0_731]) ).
cnf(refute_0_733,plain,
( multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,inverse(inverse(X)))) != multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,X))
| multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,inverse(inverse(X)))) != greatest_lower_bound(least_upper_bound(identity,inverse(X)),least_upper_bound(identity,X))
| multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,X)) = greatest_lower_bound(least_upper_bound(identity,inverse(X)),least_upper_bound(identity,X)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,inverse(inverse(X)))),greatest_lower_bound(least_upper_bound(identity,inverse(X)),least_upper_bound(identity,X))) ),[0],$fot(multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,X)))]]) ).
cnf(refute_0_734,plain,
( multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,inverse(inverse(X)))) != greatest_lower_bound(least_upper_bound(identity,inverse(X)),least_upper_bound(identity,X))
| multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,X)) = greatest_lower_bound(least_upper_bound(identity,inverse(X)),least_upper_bound(identity,X)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,inverse(inverse(X)))),multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,X))) )],[refute_0_732,refute_0_733]) ).
cnf(refute_0_735,plain,
multiply(greatest_lower_bound(inverse(X_273),identity),least_upper_bound(X_273,identity)) = greatest_lower_bound(least_upper_bound(X_273,identity),multiply(inverse(X_273),least_upper_bound(X_273,identity))),
inference(subst,[],[refute_0_45:[bind(X_86,$fot(least_upper_bound(X_273,identity))),bind(X_87,$fot(inverse(X_273)))]]) ).
cnf(refute_0_736,plain,
multiply(inverse(X_57),least_upper_bound(least_upper_bound(identity,X_57),X_57)) = least_upper_bound(identity,multiply(inverse(X_57),least_upper_bound(identity,X_57))),
inference(subst,[],[refute_0_127:[bind(X_56,$fot(least_upper_bound(identity,X_57)))]]) ).
cnf(refute_0_737,plain,
multiply(inverse(X_57),least_upper_bound(identity,X_57)) = least_upper_bound(identity,inverse(X_57)),
inference(subst,[],[refute_0_134:[bind(X_63,$fot(X_57))]]) ).
cnf(refute_0_738,plain,
( multiply(inverse(X_57),least_upper_bound(identity,X_57)) != least_upper_bound(identity,inverse(X_57))
| multiply(inverse(X_57),least_upper_bound(least_upper_bound(identity,X_57),X_57)) != least_upper_bound(identity,multiply(inverse(X_57),least_upper_bound(identity,X_57)))
| multiply(inverse(X_57),least_upper_bound(least_upper_bound(identity,X_57),X_57)) = least_upper_bound(identity,least_upper_bound(identity,inverse(X_57))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_57),least_upper_bound(least_upper_bound(identity,X_57),X_57)),least_upper_bound(identity,multiply(inverse(X_57),least_upper_bound(identity,X_57)))) ),[1,1],$fot(least_upper_bound(identity,inverse(X_57)))]]) ).
cnf(refute_0_739,plain,
( multiply(inverse(X_57),least_upper_bound(least_upper_bound(identity,X_57),X_57)) != least_upper_bound(identity,multiply(inverse(X_57),least_upper_bound(identity,X_57)))
| multiply(inverse(X_57),least_upper_bound(least_upper_bound(identity,X_57),X_57)) = least_upper_bound(identity,least_upper_bound(identity,inverse(X_57))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_57),least_upper_bound(identity,X_57)),least_upper_bound(identity,inverse(X_57))) )],[refute_0_737,refute_0_738]) ).
cnf(refute_0_740,plain,
multiply(inverse(X_57),least_upper_bound(least_upper_bound(identity,X_57),X_57)) = least_upper_bound(identity,least_upper_bound(identity,inverse(X_57))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_57),least_upper_bound(least_upper_bound(identity,X_57),X_57)),least_upper_bound(identity,multiply(inverse(X_57),least_upper_bound(identity,X_57)))) )],[refute_0_736,refute_0_739]) ).
cnf(refute_0_741,plain,
least_upper_bound(X_57,least_upper_bound(identity,X_57)) = least_upper_bound(X_57,identity),
inference(subst,[],[refute_0_635:[bind(Y,$fot(identity)),bind(X_17,$fot(X_57))]]) ).
cnf(refute_0_742,plain,
multiply(inverse(X_57),least_upper_bound(X_57,least_upper_bound(identity,X_57))) = multiply(inverse(X_57),least_upper_bound(X_57,least_upper_bound(identity,X_57))),
introduced(tautology,[refl,[$fot(multiply(inverse(X_57),least_upper_bound(X_57,least_upper_bound(identity,X_57))))]]) ).
cnf(refute_0_743,plain,
( multiply(inverse(X_57),least_upper_bound(X_57,least_upper_bound(identity,X_57))) != multiply(inverse(X_57),least_upper_bound(X_57,least_upper_bound(identity,X_57)))
| least_upper_bound(X_57,least_upper_bound(identity,X_57)) != least_upper_bound(X_57,identity)
| multiply(inverse(X_57),least_upper_bound(X_57,least_upper_bound(identity,X_57))) = multiply(inverse(X_57),least_upper_bound(X_57,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_57),least_upper_bound(X_57,least_upper_bound(identity,X_57))),multiply(inverse(X_57),least_upper_bound(X_57,least_upper_bound(identity,X_57)))) ),[1,1],$fot(least_upper_bound(X_57,identity))]]) ).
cnf(refute_0_744,plain,
( least_upper_bound(X_57,least_upper_bound(identity,X_57)) != least_upper_bound(X_57,identity)
| multiply(inverse(X_57),least_upper_bound(X_57,least_upper_bound(identity,X_57))) = multiply(inverse(X_57),least_upper_bound(X_57,identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_57),least_upper_bound(X_57,least_upper_bound(identity,X_57))),multiply(inverse(X_57),least_upper_bound(X_57,least_upper_bound(identity,X_57)))) )],[refute_0_742,refute_0_743]) ).
cnf(refute_0_745,plain,
multiply(inverse(X_57),least_upper_bound(X_57,least_upper_bound(identity,X_57))) = multiply(inverse(X_57),least_upper_bound(X_57,identity)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_57,least_upper_bound(identity,X_57)),least_upper_bound(X_57,identity)) )],[refute_0_741,refute_0_744]) ).
cnf(refute_0_746,plain,
least_upper_bound(multiply(X_55,X_57),multiply(X_55,X_56)) = least_upper_bound(multiply(X_55,X_56),multiply(X_55,X_57)),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(multiply(X_55,X_57))),bind(Y,$fot(multiply(X_55,X_56)))]]) ).
cnf(refute_0_747,plain,
multiply(X_55,least_upper_bound(X_56,X_57)) = least_upper_bound(multiply(X_55,X_56),multiply(X_55,X_57)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(X_55)),bind(Y,$fot(X_56)),bind(Z,$fot(X_57))]]) ).
cnf(refute_0_748,plain,
( multiply(X_55,least_upper_bound(X_56,X_57)) != least_upper_bound(multiply(X_55,X_56),multiply(X_55,X_57))
| least_upper_bound(multiply(X_55,X_56),multiply(X_55,X_57)) = multiply(X_55,least_upper_bound(X_56,X_57)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(multiply(X_55,least_upper_bound(X_56,X_57)))),bind(Y0,$fot(least_upper_bound(multiply(X_55,X_56),multiply(X_55,X_57))))]]) ).
cnf(refute_0_749,plain,
least_upper_bound(multiply(X_55,X_56),multiply(X_55,X_57)) = multiply(X_55,least_upper_bound(X_56,X_57)),
inference(resolve,[$cnf( $equal(multiply(X_55,least_upper_bound(X_56,X_57)),least_upper_bound(multiply(X_55,X_56),multiply(X_55,X_57))) )],[refute_0_747,refute_0_748]) ).
cnf(refute_0_750,plain,
( least_upper_bound(multiply(X_55,X_56),multiply(X_55,X_57)) != multiply(X_55,least_upper_bound(X_56,X_57))
| least_upper_bound(multiply(X_55,X_57),multiply(X_55,X_56)) != least_upper_bound(multiply(X_55,X_56),multiply(X_55,X_57))
| least_upper_bound(multiply(X_55,X_57),multiply(X_55,X_56)) = multiply(X_55,least_upper_bound(X_56,X_57)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_55,X_57),multiply(X_55,X_56)),least_upper_bound(multiply(X_55,X_56),multiply(X_55,X_57))) ),[1],$fot(multiply(X_55,least_upper_bound(X_56,X_57)))]]) ).
cnf(refute_0_751,plain,
( least_upper_bound(multiply(X_55,X_57),multiply(X_55,X_56)) != least_upper_bound(multiply(X_55,X_56),multiply(X_55,X_57))
| least_upper_bound(multiply(X_55,X_57),multiply(X_55,X_56)) = multiply(X_55,least_upper_bound(X_56,X_57)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_55,X_56),multiply(X_55,X_57)),multiply(X_55,least_upper_bound(X_56,X_57))) )],[refute_0_749,refute_0_750]) ).
cnf(refute_0_752,plain,
least_upper_bound(multiply(X_55,X_57),multiply(X_55,X_56)) = multiply(X_55,least_upper_bound(X_56,X_57)),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_55,X_57),multiply(X_55,X_56)),least_upper_bound(multiply(X_55,X_56),multiply(X_55,X_57))) )],[refute_0_746,refute_0_751]) ).
cnf(refute_0_753,plain,
( multiply(X,least_upper_bound(Y,Z)) != least_upper_bound(multiply(X,Y),multiply(X,Z))
| least_upper_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(multiply(X,least_upper_bound(Y,Z)))),bind(Y0,$fot(least_upper_bound(multiply(X,Y),multiply(X,Z))))]]) ).
cnf(refute_0_754,plain,
least_upper_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Y),multiply(X,Z))) )],[monotony_lub1,refute_0_753]) ).
cnf(refute_0_755,plain,
least_upper_bound(multiply(X_55,X_57),multiply(X_55,X_56)) = multiply(X_55,least_upper_bound(X_57,X_56)),
inference(subst,[],[refute_0_754:[bind(X,$fot(X_55)),bind(Y,$fot(X_57)),bind(Z,$fot(X_56))]]) ).
cnf(refute_0_756,plain,
( least_upper_bound(multiply(X_55,X_57),multiply(X_55,X_56)) != multiply(X_55,least_upper_bound(X_56,X_57))
| least_upper_bound(multiply(X_55,X_57),multiply(X_55,X_56)) != multiply(X_55,least_upper_bound(X_57,X_56))
| multiply(X_55,least_upper_bound(X_57,X_56)) = multiply(X_55,least_upper_bound(X_56,X_57)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_55,X_57),multiply(X_55,X_56)),multiply(X_55,least_upper_bound(X_56,X_57))) ),[0],$fot(multiply(X_55,least_upper_bound(X_57,X_56)))]]) ).
cnf(refute_0_757,plain,
( least_upper_bound(multiply(X_55,X_57),multiply(X_55,X_56)) != multiply(X_55,least_upper_bound(X_56,X_57))
| multiply(X_55,least_upper_bound(X_57,X_56)) = multiply(X_55,least_upper_bound(X_56,X_57)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_55,X_57),multiply(X_55,X_56)),multiply(X_55,least_upper_bound(X_57,X_56))) )],[refute_0_755,refute_0_756]) ).
cnf(refute_0_758,plain,
multiply(X_55,least_upper_bound(X_57,X_56)) = multiply(X_55,least_upper_bound(X_56,X_57)),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_55,X_57),multiply(X_55,X_56)),multiply(X_55,least_upper_bound(X_56,X_57))) )],[refute_0_752,refute_0_757]) ).
cnf(refute_0_759,plain,
( multiply(X_55,least_upper_bound(X_57,X_56)) != multiply(X_55,least_upper_bound(X_56,X_57))
| multiply(X_55,least_upper_bound(X_56,X_57)) = multiply(X_55,least_upper_bound(X_57,X_56)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(multiply(X_55,least_upper_bound(X_57,X_56)))),bind(Y0,$fot(multiply(X_55,least_upper_bound(X_56,X_57))))]]) ).
cnf(refute_0_760,plain,
multiply(X_55,least_upper_bound(X_56,X_57)) = multiply(X_55,least_upper_bound(X_57,X_56)),
inference(resolve,[$cnf( $equal(multiply(X_55,least_upper_bound(X_57,X_56)),multiply(X_55,least_upper_bound(X_56,X_57))) )],[refute_0_758,refute_0_759]) ).
cnf(refute_0_761,plain,
multiply(inverse(X_57),least_upper_bound(least_upper_bound(identity,X_57),X_57)) = multiply(inverse(X_57),least_upper_bound(X_57,least_upper_bound(identity,X_57))),
inference(subst,[],[refute_0_760:[bind(X_55,$fot(inverse(X_57))),bind(X_56,$fot(least_upper_bound(identity,X_57)))]]) ).
cnf(refute_0_762,plain,
( multiply(inverse(X_57),least_upper_bound(X_57,least_upper_bound(identity,X_57))) != multiply(inverse(X_57),least_upper_bound(X_57,identity))
| multiply(inverse(X_57),least_upper_bound(least_upper_bound(identity,X_57),X_57)) != multiply(inverse(X_57),least_upper_bound(X_57,least_upper_bound(identity,X_57)))
| multiply(inverse(X_57),least_upper_bound(least_upper_bound(identity,X_57),X_57)) = multiply(inverse(X_57),least_upper_bound(X_57,identity)) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(multiply(inverse(X_57),least_upper_bound(least_upper_bound(identity,X_57),X_57)))),bind(Y0,$fot(multiply(inverse(X_57),least_upper_bound(X_57,least_upper_bound(identity,X_57))))),bind(Z0,$fot(multiply(inverse(X_57),least_upper_bound(X_57,identity))))]]) ).
cnf(refute_0_763,plain,
( multiply(inverse(X_57),least_upper_bound(X_57,least_upper_bound(identity,X_57))) != multiply(inverse(X_57),least_upper_bound(X_57,identity))
| multiply(inverse(X_57),least_upper_bound(least_upper_bound(identity,X_57),X_57)) = multiply(inverse(X_57),least_upper_bound(X_57,identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_57),least_upper_bound(least_upper_bound(identity,X_57),X_57)),multiply(inverse(X_57),least_upper_bound(X_57,least_upper_bound(identity,X_57)))) )],[refute_0_761,refute_0_762]) ).
cnf(refute_0_764,plain,
multiply(inverse(X_57),least_upper_bound(least_upper_bound(identity,X_57),X_57)) = multiply(inverse(X_57),least_upper_bound(X_57,identity)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_57),least_upper_bound(X_57,least_upper_bound(identity,X_57))),multiply(inverse(X_57),least_upper_bound(X_57,identity))) )],[refute_0_745,refute_0_763]) ).
cnf(refute_0_765,plain,
( multiply(inverse(X_57),least_upper_bound(least_upper_bound(identity,X_57),X_57)) != multiply(inverse(X_57),least_upper_bound(X_57,identity))
| multiply(inverse(X_57),least_upper_bound(least_upper_bound(identity,X_57),X_57)) != least_upper_bound(identity,least_upper_bound(identity,inverse(X_57)))
| multiply(inverse(X_57),least_upper_bound(X_57,identity)) = least_upper_bound(identity,least_upper_bound(identity,inverse(X_57))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_57),least_upper_bound(least_upper_bound(identity,X_57),X_57)),least_upper_bound(identity,least_upper_bound(identity,inverse(X_57)))) ),[0],$fot(multiply(inverse(X_57),least_upper_bound(X_57,identity)))]]) ).
cnf(refute_0_766,plain,
( multiply(inverse(X_57),least_upper_bound(least_upper_bound(identity,X_57),X_57)) != least_upper_bound(identity,least_upper_bound(identity,inverse(X_57)))
| multiply(inverse(X_57),least_upper_bound(X_57,identity)) = least_upper_bound(identity,least_upper_bound(identity,inverse(X_57))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_57),least_upper_bound(least_upper_bound(identity,X_57),X_57)),multiply(inverse(X_57),least_upper_bound(X_57,identity))) )],[refute_0_764,refute_0_765]) ).
cnf(refute_0_767,plain,
least_upper_bound(identity,least_upper_bound(identity,inverse(X_57))) = least_upper_bound(identity,inverse(X_57)),
inference(subst,[],[refute_0_642:[bind(X_18,$fot(inverse(X_57))),bind(X_19,$fot(identity))]]) ).
cnf(refute_0_768,plain,
( multiply(inverse(X_57),least_upper_bound(X_57,identity)) != least_upper_bound(identity,least_upper_bound(identity,inverse(X_57)))
| least_upper_bound(identity,least_upper_bound(identity,inverse(X_57))) != least_upper_bound(identity,inverse(X_57))
| multiply(inverse(X_57),least_upper_bound(X_57,identity)) = least_upper_bound(identity,inverse(X_57)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_57),least_upper_bound(X_57,identity)),least_upper_bound(identity,inverse(X_57))) ),[0],$fot(least_upper_bound(identity,least_upper_bound(identity,inverse(X_57))))]]) ).
cnf(refute_0_769,plain,
( multiply(inverse(X_57),least_upper_bound(X_57,identity)) != least_upper_bound(identity,least_upper_bound(identity,inverse(X_57)))
| multiply(inverse(X_57),least_upper_bound(X_57,identity)) = least_upper_bound(identity,inverse(X_57)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(identity,inverse(X_57))),least_upper_bound(identity,inverse(X_57))) )],[refute_0_767,refute_0_768]) ).
cnf(refute_0_770,plain,
( multiply(inverse(X_57),least_upper_bound(least_upper_bound(identity,X_57),X_57)) != least_upper_bound(identity,least_upper_bound(identity,inverse(X_57)))
| multiply(inverse(X_57),least_upper_bound(X_57,identity)) = least_upper_bound(identity,inverse(X_57)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_57),least_upper_bound(X_57,identity)),least_upper_bound(identity,least_upper_bound(identity,inverse(X_57)))) )],[refute_0_766,refute_0_769]) ).
cnf(refute_0_771,plain,
multiply(inverse(X_57),least_upper_bound(X_57,identity)) = least_upper_bound(identity,inverse(X_57)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_57),least_upper_bound(least_upper_bound(identity,X_57),X_57)),least_upper_bound(identity,least_upper_bound(identity,inverse(X_57)))) )],[refute_0_740,refute_0_770]) ).
cnf(refute_0_772,plain,
multiply(inverse(X_273),least_upper_bound(X_273,identity)) = least_upper_bound(identity,inverse(X_273)),
inference(subst,[],[refute_0_771:[bind(X_57,$fot(X_273))]]) ).
cnf(refute_0_773,plain,
( multiply(greatest_lower_bound(inverse(X_273),identity),least_upper_bound(X_273,identity)) != greatest_lower_bound(least_upper_bound(X_273,identity),multiply(inverse(X_273),least_upper_bound(X_273,identity)))
| multiply(inverse(X_273),least_upper_bound(X_273,identity)) != least_upper_bound(identity,inverse(X_273))
| multiply(greatest_lower_bound(inverse(X_273),identity),least_upper_bound(X_273,identity)) = greatest_lower_bound(least_upper_bound(X_273,identity),least_upper_bound(identity,inverse(X_273))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_273),identity),least_upper_bound(X_273,identity)),greatest_lower_bound(least_upper_bound(X_273,identity),multiply(inverse(X_273),least_upper_bound(X_273,identity)))) ),[1,1],$fot(least_upper_bound(identity,inverse(X_273)))]]) ).
cnf(refute_0_774,plain,
( multiply(greatest_lower_bound(inverse(X_273),identity),least_upper_bound(X_273,identity)) != greatest_lower_bound(least_upper_bound(X_273,identity),multiply(inverse(X_273),least_upper_bound(X_273,identity)))
| multiply(greatest_lower_bound(inverse(X_273),identity),least_upper_bound(X_273,identity)) = greatest_lower_bound(least_upper_bound(X_273,identity),least_upper_bound(identity,inverse(X_273))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_273),least_upper_bound(X_273,identity)),least_upper_bound(identity,inverse(X_273))) )],[refute_0_772,refute_0_773]) ).
cnf(refute_0_775,plain,
multiply(greatest_lower_bound(inverse(X_273),identity),least_upper_bound(X_273,identity)) = greatest_lower_bound(least_upper_bound(X_273,identity),least_upper_bound(identity,inverse(X_273))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_273),identity),least_upper_bound(X_273,identity)),greatest_lower_bound(least_upper_bound(X_273,identity),multiply(inverse(X_273),least_upper_bound(X_273,identity)))) )],[refute_0_735,refute_0_774]) ).
cnf(refute_0_776,plain,
multiply(greatest_lower_bound(identity,inverse(X_273)),least_upper_bound(identity,X_273)) = multiply(least_upper_bound(identity,X_273),greatest_lower_bound(identity,inverse(X_273))),
inference(subst,[],[refute_0_716:[bind(X_84,$fot(X_273))]]) ).
cnf(refute_0_777,plain,
multiply(greatest_lower_bound(identity,X_90),least_upper_bound(X_252,X_253)) = multiply(greatest_lower_bound(X_90,identity),least_upper_bound(X_252,X_253)),
inference(subst,[],[refute_0_430:[bind(Y,$fot(least_upper_bound(X_252,X_253)))]]) ).
cnf(refute_0_778,plain,
greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),least_upper_bound(multiply(X,Y),multiply(X,Z))) = least_upper_bound(multiply(X,Z),multiply(X,Y)),
inference(subst,[],[refute_0_659:[bind(Y,$fot(multiply(X,Y))),bind(X_18,$fot(multiply(X,Z)))]]) ).
cnf(refute_0_779,plain,
( greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),least_upper_bound(multiply(X,Y),multiply(X,Z))) != least_upper_bound(multiply(X,Z),multiply(X,Y))
| least_upper_bound(multiply(X,Y),multiply(X,Z)) != multiply(X,least_upper_bound(Y,Z))
| greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = least_upper_bound(multiply(X,Z),multiply(X,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),least_upper_bound(multiply(X,Y),multiply(X,Z))),least_upper_bound(multiply(X,Z),multiply(X,Y))) ),[0,1],$fot(multiply(X,least_upper_bound(Y,Z)))]]) ).
cnf(refute_0_780,plain,
( greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),least_upper_bound(multiply(X,Y),multiply(X,Z))) != least_upper_bound(multiply(X,Z),multiply(X,Y))
| greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = least_upper_bound(multiply(X,Z),multiply(X,Y)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,Y),multiply(X,Z)),multiply(X,least_upper_bound(Y,Z))) )],[refute_0_754,refute_0_779]) ).
cnf(refute_0_781,plain,
greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = least_upper_bound(multiply(X,Z),multiply(X,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),least_upper_bound(multiply(X,Y),multiply(X,Z))),least_upper_bound(multiply(X,Z),multiply(X,Y))) )],[refute_0_778,refute_0_780]) ).
cnf(refute_0_782,plain,
multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) = multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))),
introduced(tautology,[refl,[$fot(multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))))]]) ).
cnf(refute_0_783,plain,
( multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) != multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)))
| greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)) != least_upper_bound(Y,Z)
| multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) = multiply(X,least_upper_bound(Y,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))),multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)))) ),[1,1],$fot(least_upper_bound(Y,Z))]]) ).
cnf(refute_0_784,plain,
( greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)) != least_upper_bound(Y,Z)
| multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) = multiply(X,least_upper_bound(Y,Z)) ),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))),multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)))) )],[refute_0_782,refute_0_783]) ).
cnf(refute_0_785,plain,
multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) = multiply(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),least_upper_bound(Y,Z)) )],[refute_0_666,refute_0_784]) ).
cnf(refute_0_786,plain,
greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) = multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))),
inference(subst,[],[refute_0_237:[bind(Y,$fot(least_upper_bound(Y,Z))),bind(Z,$fot(least_upper_bound(Z,Y)))]]) ).
cnf(refute_0_787,plain,
( multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) != multiply(X,least_upper_bound(Y,Z))
| greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) != multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)))
| greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) = multiply(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))))),bind(Y0,$fot(multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))))),bind(Z0,$fot(multiply(X,least_upper_bound(Y,Z))))]]) ).
cnf(refute_0_788,plain,
( multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) != multiply(X,least_upper_bound(Y,Z))
| greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) = multiply(X,least_upper_bound(Y,Z)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))),multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)))) )],[refute_0_786,refute_0_787]) ).
cnf(refute_0_789,plain,
greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) = multiply(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))),multiply(X,least_upper_bound(Y,Z))) )],[refute_0_785,refute_0_788]) ).
cnf(refute_0_790,plain,
least_upper_bound(multiply(X,Z),multiply(X,Y)) = multiply(X,least_upper_bound(Z,Y)),
inference(subst,[],[refute_0_754:[bind(Y,$fot(Z)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_791,plain,
greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))))]]) ).
cnf(refute_0_792,plain,
( greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) != greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y)))
| least_upper_bound(multiply(X,Z),multiply(X,Y)) != multiply(X,least_upper_bound(Z,Y))
| greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))),greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y)))) ),[1,1],$fot(multiply(X,least_upper_bound(Z,Y)))]]) ).
cnf(refute_0_793,plain,
( least_upper_bound(multiply(X,Z),multiply(X,Y)) != multiply(X,least_upper_bound(Z,Y))
| greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))),greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y)))) )],[refute_0_791,refute_0_792]) ).
cnf(refute_0_794,plain,
greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Z,Y))) )],[refute_0_790,refute_0_793]) ).
cnf(refute_0_795,plain,
( greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) != multiply(X,least_upper_bound(Y,Z))
| greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) != greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y)))
| greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = multiply(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))))),bind(Y0,$fot(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))))),bind(Z0,$fot(multiply(X,least_upper_bound(Y,Z))))]]) ).
cnf(refute_0_796,plain,
( greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) != multiply(X,least_upper_bound(Y,Z))
| greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = multiply(X,least_upper_bound(Y,Z)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))),greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y)))) )],[refute_0_794,refute_0_795]) ).
cnf(refute_0_797,plain,
greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = multiply(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))),multiply(X,least_upper_bound(Y,Z))) )],[refute_0_789,refute_0_796]) ).
cnf(refute_0_798,plain,
greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))),
inference(subst,[],[refute_0_41:[bind(X_21,$fot(multiply(X,least_upper_bound(Y,Z)))),bind(X_22,$fot(least_upper_bound(multiply(X,Z),multiply(X,Y))))]]) ).
cnf(refute_0_799,plain,
( greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) != multiply(X,least_upper_bound(Y,Z))
| greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) != greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y)))
| greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = multiply(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))))),bind(Y0,$fot(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))))),bind(Z0,$fot(multiply(X,least_upper_bound(Y,Z))))]]) ).
cnf(refute_0_800,plain,
( greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) != multiply(X,least_upper_bound(Y,Z))
| greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = multiply(X,least_upper_bound(Y,Z)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))),greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y)))) )],[refute_0_798,refute_0_799]) ).
cnf(refute_0_801,plain,
greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = multiply(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))),multiply(X,least_upper_bound(Y,Z))) )],[refute_0_797,refute_0_800]) ).
cnf(refute_0_802,plain,
( greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) != multiply(X,least_upper_bound(Y,Z))
| greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) != least_upper_bound(multiply(X,Z),multiply(X,Y))
| multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Z),multiply(X,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))),least_upper_bound(multiply(X,Z),multiply(X,Y))) ),[0],$fot(multiply(X,least_upper_bound(Y,Z)))]]) ).
cnf(refute_0_803,plain,
( greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) != least_upper_bound(multiply(X,Z),multiply(X,Y))
| multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Z),multiply(X,Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))),multiply(X,least_upper_bound(Y,Z))) )],[refute_0_801,refute_0_802]) ).
cnf(refute_0_804,plain,
( multiply(X,least_upper_bound(Y,Z)) != least_upper_bound(multiply(X,Z),multiply(X,Y))
| least_upper_bound(multiply(X,Z),multiply(X,Y)) != multiply(X,least_upper_bound(Z,Y))
| multiply(X,least_upper_bound(Y,Z)) = multiply(X,least_upper_bound(Z,Y)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) ),[0],$fot(least_upper_bound(multiply(X,Z),multiply(X,Y)))]]) ).
cnf(refute_0_805,plain,
( multiply(X,least_upper_bound(Y,Z)) != least_upper_bound(multiply(X,Z),multiply(X,Y))
| multiply(X,least_upper_bound(Y,Z)) = multiply(X,least_upper_bound(Z,Y)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Z,Y))) )],[refute_0_790,refute_0_804]) ).
cnf(refute_0_806,plain,
( greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) != least_upper_bound(multiply(X,Z),multiply(X,Y))
| multiply(X,least_upper_bound(Y,Z)) = multiply(X,least_upper_bound(Z,Y)) ),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) )],[refute_0_803,refute_0_805]) ).
cnf(refute_0_807,plain,
multiply(X,least_upper_bound(Y,Z)) = multiply(X,least_upper_bound(Z,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))),least_upper_bound(multiply(X,Z),multiply(X,Y))) )],[refute_0_781,refute_0_806]) ).
cnf(refute_0_808,plain,
multiply(greatest_lower_bound(identity,X_90),least_upper_bound(X_252,X_253)) = multiply(greatest_lower_bound(identity,X_90),least_upper_bound(X_253,X_252)),
inference(subst,[],[refute_0_807:[bind(X,$fot(greatest_lower_bound(identity,X_90))),bind(Y,$fot(X_252)),bind(Z,$fot(X_253))]]) ).
cnf(refute_0_809,plain,
( multiply(greatest_lower_bound(identity,X_90),least_upper_bound(X_252,X_253)) != multiply(greatest_lower_bound(X_90,identity),least_upper_bound(X_252,X_253))
| multiply(greatest_lower_bound(identity,X_90),least_upper_bound(X_252,X_253)) != multiply(greatest_lower_bound(identity,X_90),least_upper_bound(X_253,X_252))
| multiply(greatest_lower_bound(identity,X_90),least_upper_bound(X_253,X_252)) = multiply(greatest_lower_bound(X_90,identity),least_upper_bound(X_252,X_253)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_90),least_upper_bound(X_252,X_253)),multiply(greatest_lower_bound(X_90,identity),least_upper_bound(X_252,X_253))) ),[0],$fot(multiply(greatest_lower_bound(identity,X_90),least_upper_bound(X_253,X_252)))]]) ).
cnf(refute_0_810,plain,
( multiply(greatest_lower_bound(identity,X_90),least_upper_bound(X_252,X_253)) != multiply(greatest_lower_bound(X_90,identity),least_upper_bound(X_252,X_253))
| multiply(greatest_lower_bound(identity,X_90),least_upper_bound(X_253,X_252)) = multiply(greatest_lower_bound(X_90,identity),least_upper_bound(X_252,X_253)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_90),least_upper_bound(X_252,X_253)),multiply(greatest_lower_bound(identity,X_90),least_upper_bound(X_253,X_252))) )],[refute_0_808,refute_0_809]) ).
cnf(refute_0_811,plain,
multiply(greatest_lower_bound(identity,X_90),least_upper_bound(X_253,X_252)) = multiply(greatest_lower_bound(X_90,identity),least_upper_bound(X_252,X_253)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_90),least_upper_bound(X_252,X_253)),multiply(greatest_lower_bound(X_90,identity),least_upper_bound(X_252,X_253))) )],[refute_0_777,refute_0_810]) ).
cnf(refute_0_812,plain,
( multiply(greatest_lower_bound(identity,X_90),least_upper_bound(X_253,X_252)) != multiply(greatest_lower_bound(X_90,identity),least_upper_bound(X_252,X_253))
| multiply(greatest_lower_bound(X_90,identity),least_upper_bound(X_252,X_253)) = multiply(greatest_lower_bound(identity,X_90),least_upper_bound(X_253,X_252)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(multiply(greatest_lower_bound(identity,X_90),least_upper_bound(X_253,X_252)))),bind(Y0,$fot(multiply(greatest_lower_bound(X_90,identity),least_upper_bound(X_252,X_253))))]]) ).
cnf(refute_0_813,plain,
multiply(greatest_lower_bound(X_90,identity),least_upper_bound(X_252,X_253)) = multiply(greatest_lower_bound(identity,X_90),least_upper_bound(X_253,X_252)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_90),least_upper_bound(X_253,X_252)),multiply(greatest_lower_bound(X_90,identity),least_upper_bound(X_252,X_253))) )],[refute_0_811,refute_0_812]) ).
cnf(refute_0_814,plain,
multiply(greatest_lower_bound(inverse(X_273),identity),least_upper_bound(X_273,identity)) = multiply(greatest_lower_bound(identity,inverse(X_273)),least_upper_bound(identity,X_273)),
inference(subst,[],[refute_0_813:[bind(X_252,$fot(X_273)),bind(X_253,$fot(identity)),bind(X_90,$fot(inverse(X_273)))]]) ).
cnf(refute_0_815,plain,
( multiply(greatest_lower_bound(identity,inverse(X_273)),least_upper_bound(identity,X_273)) != multiply(least_upper_bound(identity,X_273),greatest_lower_bound(identity,inverse(X_273)))
| multiply(greatest_lower_bound(inverse(X_273),identity),least_upper_bound(X_273,identity)) != multiply(greatest_lower_bound(identity,inverse(X_273)),least_upper_bound(identity,X_273))
| multiply(greatest_lower_bound(inverse(X_273),identity),least_upper_bound(X_273,identity)) = multiply(least_upper_bound(identity,X_273),greatest_lower_bound(identity,inverse(X_273))) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(multiply(greatest_lower_bound(inverse(X_273),identity),least_upper_bound(X_273,identity)))),bind(Y0,$fot(multiply(greatest_lower_bound(identity,inverse(X_273)),least_upper_bound(identity,X_273)))),bind(Z0,$fot(multiply(least_upper_bound(identity,X_273),greatest_lower_bound(identity,inverse(X_273)))))]]) ).
cnf(refute_0_816,plain,
( multiply(greatest_lower_bound(identity,inverse(X_273)),least_upper_bound(identity,X_273)) != multiply(least_upper_bound(identity,X_273),greatest_lower_bound(identity,inverse(X_273)))
| multiply(greatest_lower_bound(inverse(X_273),identity),least_upper_bound(X_273,identity)) = multiply(least_upper_bound(identity,X_273),greatest_lower_bound(identity,inverse(X_273))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_273),identity),least_upper_bound(X_273,identity)),multiply(greatest_lower_bound(identity,inverse(X_273)),least_upper_bound(identity,X_273))) )],[refute_0_814,refute_0_815]) ).
cnf(refute_0_817,plain,
multiply(greatest_lower_bound(inverse(X_273),identity),least_upper_bound(X_273,identity)) = multiply(least_upper_bound(identity,X_273),greatest_lower_bound(identity,inverse(X_273))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(X_273)),least_upper_bound(identity,X_273)),multiply(least_upper_bound(identity,X_273),greatest_lower_bound(identity,inverse(X_273)))) )],[refute_0_776,refute_0_816]) ).
cnf(refute_0_818,plain,
( multiply(greatest_lower_bound(inverse(X_273),identity),least_upper_bound(X_273,identity)) != multiply(least_upper_bound(identity,X_273),greatest_lower_bound(identity,inverse(X_273)))
| multiply(greatest_lower_bound(inverse(X_273),identity),least_upper_bound(X_273,identity)) != greatest_lower_bound(least_upper_bound(X_273,identity),least_upper_bound(identity,inverse(X_273)))
| multiply(least_upper_bound(identity,X_273),greatest_lower_bound(identity,inverse(X_273))) = greatest_lower_bound(least_upper_bound(X_273,identity),least_upper_bound(identity,inverse(X_273))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_273),identity),least_upper_bound(X_273,identity)),greatest_lower_bound(least_upper_bound(X_273,identity),least_upper_bound(identity,inverse(X_273)))) ),[0],$fot(multiply(least_upper_bound(identity,X_273),greatest_lower_bound(identity,inverse(X_273))))]]) ).
cnf(refute_0_819,plain,
( multiply(greatest_lower_bound(inverse(X_273),identity),least_upper_bound(X_273,identity)) != greatest_lower_bound(least_upper_bound(X_273,identity),least_upper_bound(identity,inverse(X_273)))
| multiply(least_upper_bound(identity,X_273),greatest_lower_bound(identity,inverse(X_273))) = greatest_lower_bound(least_upper_bound(X_273,identity),least_upper_bound(identity,inverse(X_273))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_273),identity),least_upper_bound(X_273,identity)),multiply(least_upper_bound(identity,X_273),greatest_lower_bound(identity,inverse(X_273)))) )],[refute_0_817,refute_0_818]) ).
cnf(refute_0_820,plain,
multiply(least_upper_bound(identity,X_273),greatest_lower_bound(identity,inverse(X_273))) = greatest_lower_bound(least_upper_bound(X_273,identity),least_upper_bound(identity,inverse(X_273))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_273),identity),least_upper_bound(X_273,identity)),greatest_lower_bound(least_upper_bound(X_273,identity),least_upper_bound(identity,inverse(X_273)))) )],[refute_0_775,refute_0_819]) ).
cnf(refute_0_821,plain,
( multiply(least_upper_bound(identity,X_273),greatest_lower_bound(identity,inverse(X_273))) != greatest_lower_bound(least_upper_bound(X_273,identity),least_upper_bound(identity,inverse(X_273)))
| greatest_lower_bound(least_upper_bound(X_273,identity),least_upper_bound(identity,inverse(X_273))) = multiply(least_upper_bound(identity,X_273),greatest_lower_bound(identity,inverse(X_273))) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(multiply(least_upper_bound(identity,X_273),greatest_lower_bound(identity,inverse(X_273))))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(X_273,identity),least_upper_bound(identity,inverse(X_273)))))]]) ).
cnf(refute_0_822,plain,
greatest_lower_bound(least_upper_bound(X_273,identity),least_upper_bound(identity,inverse(X_273))) = multiply(least_upper_bound(identity,X_273),greatest_lower_bound(identity,inverse(X_273))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_273),greatest_lower_bound(identity,inverse(X_273))),greatest_lower_bound(least_upper_bound(X_273,identity),least_upper_bound(identity,inverse(X_273)))) )],[refute_0_820,refute_0_821]) ).
cnf(refute_0_823,plain,
greatest_lower_bound(least_upper_bound(X,identity),least_upper_bound(identity,inverse(X))) = multiply(least_upper_bound(identity,X),greatest_lower_bound(identity,inverse(X))),
inference(subst,[],[refute_0_822:[bind(X_273,$fot(X))]]) ).
cnf(refute_0_824,plain,
multiply(greatest_lower_bound(X_87,inverse(X_63)),least_upper_bound(identity,X_63)) = greatest_lower_bound(multiply(X_87,least_upper_bound(identity,X_63)),multiply(inverse(X_63),least_upper_bound(identity,X_63))),
inference(subst,[],[monotony_glb2:[bind(X,$fot(least_upper_bound(identity,X_63))),bind(Y,$fot(X_87)),bind(Z,$fot(inverse(X_63)))]]) ).
cnf(refute_0_825,plain,
( multiply(greatest_lower_bound(X_87,inverse(X_63)),least_upper_bound(identity,X_63)) != greatest_lower_bound(multiply(X_87,least_upper_bound(identity,X_63)),multiply(inverse(X_63),least_upper_bound(identity,X_63)))
| multiply(inverse(X_63),least_upper_bound(identity,X_63)) != least_upper_bound(identity,inverse(X_63))
| multiply(greatest_lower_bound(X_87,inverse(X_63)),least_upper_bound(identity,X_63)) = greatest_lower_bound(multiply(X_87,least_upper_bound(identity,X_63)),least_upper_bound(identity,inverse(X_63))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_87,inverse(X_63)),least_upper_bound(identity,X_63)),greatest_lower_bound(multiply(X_87,least_upper_bound(identity,X_63)),multiply(inverse(X_63),least_upper_bound(identity,X_63)))) ),[1,1],$fot(least_upper_bound(identity,inverse(X_63)))]]) ).
cnf(refute_0_826,plain,
( multiply(greatest_lower_bound(X_87,inverse(X_63)),least_upper_bound(identity,X_63)) != greatest_lower_bound(multiply(X_87,least_upper_bound(identity,X_63)),multiply(inverse(X_63),least_upper_bound(identity,X_63)))
| multiply(greatest_lower_bound(X_87,inverse(X_63)),least_upper_bound(identity,X_63)) = greatest_lower_bound(multiply(X_87,least_upper_bound(identity,X_63)),least_upper_bound(identity,inverse(X_63))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_63),least_upper_bound(identity,X_63)),least_upper_bound(identity,inverse(X_63))) )],[refute_0_134,refute_0_825]) ).
cnf(refute_0_827,plain,
multiply(greatest_lower_bound(X_87,inverse(X_63)),least_upper_bound(identity,X_63)) = greatest_lower_bound(multiply(X_87,least_upper_bound(identity,X_63)),least_upper_bound(identity,inverse(X_63))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_87,inverse(X_63)),least_upper_bound(identity,X_63)),greatest_lower_bound(multiply(X_87,least_upper_bound(identity,X_63)),multiply(inverse(X_63),least_upper_bound(identity,X_63)))) )],[refute_0_824,refute_0_826]) ).
cnf(refute_0_828,plain,
greatest_lower_bound(multiply(X_87,least_upper_bound(identity,X_63)),least_upper_bound(identity,inverse(X_63))) = greatest_lower_bound(least_upper_bound(identity,inverse(X_63)),multiply(X_87,least_upper_bound(identity,X_63))),
inference(subst,[],[refute_0_41:[bind(X_21,$fot(least_upper_bound(identity,inverse(X_63)))),bind(X_22,$fot(multiply(X_87,least_upper_bound(identity,X_63))))]]) ).
cnf(refute_0_829,plain,
( multiply(greatest_lower_bound(X_87,inverse(X_63)),least_upper_bound(identity,X_63)) != greatest_lower_bound(multiply(X_87,least_upper_bound(identity,X_63)),least_upper_bound(identity,inverse(X_63)))
| greatest_lower_bound(multiply(X_87,least_upper_bound(identity,X_63)),least_upper_bound(identity,inverse(X_63))) != greatest_lower_bound(least_upper_bound(identity,inverse(X_63)),multiply(X_87,least_upper_bound(identity,X_63)))
| multiply(greatest_lower_bound(X_87,inverse(X_63)),least_upper_bound(identity,X_63)) = greatest_lower_bound(least_upper_bound(identity,inverse(X_63)),multiply(X_87,least_upper_bound(identity,X_63))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_87,inverse(X_63)),least_upper_bound(identity,X_63)),greatest_lower_bound(least_upper_bound(identity,inverse(X_63)),multiply(X_87,least_upper_bound(identity,X_63)))) ),[0],$fot(greatest_lower_bound(multiply(X_87,least_upper_bound(identity,X_63)),least_upper_bound(identity,inverse(X_63))))]]) ).
cnf(refute_0_830,plain,
( multiply(greatest_lower_bound(X_87,inverse(X_63)),least_upper_bound(identity,X_63)) != greatest_lower_bound(multiply(X_87,least_upper_bound(identity,X_63)),least_upper_bound(identity,inverse(X_63)))
| multiply(greatest_lower_bound(X_87,inverse(X_63)),least_upper_bound(identity,X_63)) = greatest_lower_bound(least_upper_bound(identity,inverse(X_63)),multiply(X_87,least_upper_bound(identity,X_63))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_87,least_upper_bound(identity,X_63)),least_upper_bound(identity,inverse(X_63))),greatest_lower_bound(least_upper_bound(identity,inverse(X_63)),multiply(X_87,least_upper_bound(identity,X_63)))) )],[refute_0_828,refute_0_829]) ).
cnf(refute_0_831,plain,
multiply(greatest_lower_bound(X_87,inverse(X_63)),least_upper_bound(identity,X_63)) = greatest_lower_bound(least_upper_bound(identity,inverse(X_63)),multiply(X_87,least_upper_bound(identity,X_63))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_87,inverse(X_63)),least_upper_bound(identity,X_63)),greatest_lower_bound(multiply(X_87,least_upper_bound(identity,X_63)),least_upper_bound(identity,inverse(X_63)))) )],[refute_0_827,refute_0_830]) ).
cnf(refute_0_832,plain,
multiply(greatest_lower_bound(X_303,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))) = greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),multiply(X_303,least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity)))))),
inference(subst,[],[refute_0_831:[bind(X_63,$fot(inverse(least_upper_bound(X_162,inverse(identity))))),bind(X_87,$fot(X_303))]]) ).
cnf(refute_0_833,plain,
multiply(least_upper_bound(inverse(least_upper_bound(identity,multiply(X_76,X_162))),identity),X_76) = least_upper_bound(X_76,multiply(inverse(least_upper_bound(identity,multiply(X_76,X_162))),X_76)),
inference(subst,[],[refute_0_76:[bind(X_77,$fot(inverse(least_upper_bound(identity,multiply(X_76,X_162)))))]]) ).
cnf(refute_0_834,plain,
inverse(least_upper_bound(X_162,inverse(X_76))) = multiply(inverse(least_upper_bound(identity,multiply(X_76,X_162))),X_76),
inference(subst,[],[refute_0_556:[bind(X_47,$fot(X_76)),bind(X_59,$fot(X_162))]]) ).
cnf(refute_0_835,plain,
( inverse(least_upper_bound(X_162,inverse(X_76))) != multiply(inverse(least_upper_bound(identity,multiply(X_76,X_162))),X_76)
| multiply(inverse(least_upper_bound(identity,multiply(X_76,X_162))),X_76) = inverse(least_upper_bound(X_162,inverse(X_76))) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(inverse(least_upper_bound(X_162,inverse(X_76))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(identity,multiply(X_76,X_162))),X_76)))]]) ).
cnf(refute_0_836,plain,
multiply(inverse(least_upper_bound(identity,multiply(X_76,X_162))),X_76) = inverse(least_upper_bound(X_162,inverse(X_76))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_162,inverse(X_76))),multiply(inverse(least_upper_bound(identity,multiply(X_76,X_162))),X_76)) )],[refute_0_834,refute_0_835]) ).
cnf(refute_0_837,plain,
( multiply(inverse(least_upper_bound(identity,multiply(X_76,X_162))),X_76) != inverse(least_upper_bound(X_162,inverse(X_76)))
| multiply(least_upper_bound(inverse(least_upper_bound(identity,multiply(X_76,X_162))),identity),X_76) != least_upper_bound(X_76,multiply(inverse(least_upper_bound(identity,multiply(X_76,X_162))),X_76))
| multiply(least_upper_bound(inverse(least_upper_bound(identity,multiply(X_76,X_162))),identity),X_76) = least_upper_bound(X_76,inverse(least_upper_bound(X_162,inverse(X_76)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(least_upper_bound(identity,multiply(X_76,X_162))),identity),X_76),least_upper_bound(X_76,multiply(inverse(least_upper_bound(identity,multiply(X_76,X_162))),X_76))) ),[1,1],$fot(inverse(least_upper_bound(X_162,inverse(X_76))))]]) ).
cnf(refute_0_838,plain,
( multiply(least_upper_bound(inverse(least_upper_bound(identity,multiply(X_76,X_162))),identity),X_76) != least_upper_bound(X_76,multiply(inverse(least_upper_bound(identity,multiply(X_76,X_162))),X_76))
| multiply(least_upper_bound(inverse(least_upper_bound(identity,multiply(X_76,X_162))),identity),X_76) = least_upper_bound(X_76,inverse(least_upper_bound(X_162,inverse(X_76)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,multiply(X_76,X_162))),X_76),inverse(least_upper_bound(X_162,inverse(X_76)))) )],[refute_0_836,refute_0_837]) ).
cnf(refute_0_839,plain,
multiply(least_upper_bound(inverse(least_upper_bound(identity,multiply(X_76,X_162))),identity),X_76) = least_upper_bound(X_76,inverse(least_upper_bound(X_162,inverse(X_76)))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(least_upper_bound(identity,multiply(X_76,X_162))),identity),X_76),least_upper_bound(X_76,multiply(inverse(least_upper_bound(identity,multiply(X_76,X_162))),X_76))) )],[refute_0_833,refute_0_838]) ).
cnf(refute_0_840,plain,
multiply(inverse(least_upper_bound(identity,X_18)),least_upper_bound(identity,least_upper_bound(identity,X_18))) = least_upper_bound(identity,inverse(least_upper_bound(identity,X_18))),
inference(subst,[],[refute_0_134:[bind(X_63,$fot(least_upper_bound(identity,X_18)))]]) ).
cnf(refute_0_841,plain,
least_upper_bound(identity,least_upper_bound(identity,X_18)) = least_upper_bound(identity,X_18),
inference(subst,[],[refute_0_642:[bind(X_19,$fot(identity))]]) ).
cnf(refute_0_842,plain,
( multiply(inverse(least_upper_bound(identity,X_18)),least_upper_bound(identity,least_upper_bound(identity,X_18))) != least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))
| least_upper_bound(identity,least_upper_bound(identity,X_18)) != least_upper_bound(identity,X_18)
| multiply(inverse(least_upper_bound(identity,X_18)),least_upper_bound(identity,X_18)) = least_upper_bound(identity,inverse(least_upper_bound(identity,X_18))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_18)),least_upper_bound(identity,least_upper_bound(identity,X_18))),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))) ),[0,1],$fot(least_upper_bound(identity,X_18))]]) ).
cnf(refute_0_843,plain,
( multiply(inverse(least_upper_bound(identity,X_18)),least_upper_bound(identity,least_upper_bound(identity,X_18))) != least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))
| multiply(inverse(least_upper_bound(identity,X_18)),least_upper_bound(identity,X_18)) = least_upper_bound(identity,inverse(least_upper_bound(identity,X_18))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(identity,X_18)),least_upper_bound(identity,X_18)) )],[refute_0_841,refute_0_842]) ).
cnf(refute_0_844,plain,
multiply(inverse(least_upper_bound(identity,X_18)),least_upper_bound(identity,X_18)) = least_upper_bound(identity,inverse(least_upper_bound(identity,X_18))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_18)),least_upper_bound(identity,least_upper_bound(identity,X_18))),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))) )],[refute_0_840,refute_0_843]) ).
cnf(refute_0_845,plain,
multiply(inverse(least_upper_bound(identity,X_18)),least_upper_bound(identity,X_18)) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(least_upper_bound(identity,X_18)))]]) ).
cnf(refute_0_846,plain,
( multiply(inverse(least_upper_bound(identity,X_18)),least_upper_bound(identity,X_18)) != identity
| multiply(inverse(least_upper_bound(identity,X_18)),least_upper_bound(identity,X_18)) != least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))
| identity = least_upper_bound(identity,inverse(least_upper_bound(identity,X_18))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_18)),least_upper_bound(identity,X_18)),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))) ),[0],$fot(identity)]]) ).
cnf(refute_0_847,plain,
( multiply(inverse(least_upper_bound(identity,X_18)),least_upper_bound(identity,X_18)) != least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))
| identity = least_upper_bound(identity,inverse(least_upper_bound(identity,X_18))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_18)),least_upper_bound(identity,X_18)),identity) )],[refute_0_845,refute_0_846]) ).
cnf(refute_0_848,plain,
identity = least_upper_bound(identity,inverse(least_upper_bound(identity,X_18))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_18)),least_upper_bound(identity,X_18)),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))) )],[refute_0_844,refute_0_847]) ).
cnf(refute_0_849,plain,
( identity != least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))
| least_upper_bound(identity,inverse(least_upper_bound(identity,X_18))) = identity ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(identity)),bind(Y0,$fot(least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))))]]) ).
cnf(refute_0_850,plain,
least_upper_bound(identity,inverse(least_upper_bound(identity,X_18))) = identity,
inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))) )],[refute_0_848,refute_0_849]) ).
cnf(refute_0_851,plain,
least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(X_76,X_162)))) = identity,
inference(subst,[],[refute_0_850:[bind(X_18,$fot(multiply(X_76,X_162)))]]) ).
cnf(refute_0_852,plain,
multiply(least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(X_76,X_162)))),X_76) = multiply(least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(X_76,X_162)))),X_76),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(X_76,X_162)))),X_76))]]) ).
cnf(refute_0_853,plain,
( multiply(least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(X_76,X_162)))),X_76) != multiply(least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(X_76,X_162)))),X_76)
| least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(X_76,X_162)))) != identity
| multiply(least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(X_76,X_162)))),X_76) = multiply(identity,X_76) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(X_76,X_162)))),X_76),multiply(least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(X_76,X_162)))),X_76)) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_854,plain,
( least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(X_76,X_162)))) != identity
| multiply(least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(X_76,X_162)))),X_76) = multiply(identity,X_76) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(X_76,X_162)))),X_76),multiply(least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(X_76,X_162)))),X_76)) )],[refute_0_852,refute_0_853]) ).
cnf(refute_0_855,plain,
multiply(least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(X_76,X_162)))),X_76) = multiply(identity,X_76),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(X_76,X_162)))),identity) )],[refute_0_851,refute_0_854]) ).
cnf(refute_0_856,plain,
( multiply(identity,X_76) != X_76
| multiply(least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(X_76,X_162)))),X_76) != multiply(identity,X_76)
| multiply(least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(X_76,X_162)))),X_76) = X_76 ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(multiply(least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(X_76,X_162)))),X_76))),bind(Y0,$fot(multiply(identity,X_76))),bind(Z0,$fot(X_76))]]) ).
cnf(refute_0_857,plain,
( multiply(identity,X_76) != X_76
| multiply(least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(X_76,X_162)))),X_76) = X_76 ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(X_76,X_162)))),X_76),multiply(identity,X_76)) )],[refute_0_855,refute_0_856]) ).
cnf(refute_0_858,plain,
multiply(least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(X_76,X_162)))),X_76) = X_76,
inference(resolve,[$cnf( $equal(multiply(identity,X_76),X_76) )],[refute_0_69,refute_0_857]) ).
cnf(refute_0_859,plain,
multiply(least_upper_bound(inverse(least_upper_bound(identity,multiply(X_76,X_162))),identity),X_76) = multiply(least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(X_76,X_162)))),X_76),
inference(subst,[],[refute_0_710:[bind(X_146,$fot(inverse(least_upper_bound(identity,multiply(X_76,X_162))))),bind(X_19,$fot(X_76))]]) ).
cnf(refute_0_860,plain,
( multiply(least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(X_76,X_162)))),X_76) != X_76
| multiply(least_upper_bound(inverse(least_upper_bound(identity,multiply(X_76,X_162))),identity),X_76) != multiply(least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(X_76,X_162)))),X_76)
| multiply(least_upper_bound(inverse(least_upper_bound(identity,multiply(X_76,X_162))),identity),X_76) = X_76 ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(multiply(least_upper_bound(inverse(least_upper_bound(identity,multiply(X_76,X_162))),identity),X_76))),bind(Y0,$fot(multiply(least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(X_76,X_162)))),X_76))),bind(Z0,$fot(X_76))]]) ).
cnf(refute_0_861,plain,
( multiply(least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(X_76,X_162)))),X_76) != X_76
| multiply(least_upper_bound(inverse(least_upper_bound(identity,multiply(X_76,X_162))),identity),X_76) = X_76 ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(least_upper_bound(identity,multiply(X_76,X_162))),identity),X_76),multiply(least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(X_76,X_162)))),X_76)) )],[refute_0_859,refute_0_860]) ).
cnf(refute_0_862,plain,
multiply(least_upper_bound(inverse(least_upper_bound(identity,multiply(X_76,X_162))),identity),X_76) = X_76,
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(X_76,X_162)))),X_76),X_76) )],[refute_0_858,refute_0_861]) ).
cnf(refute_0_863,plain,
( multiply(least_upper_bound(inverse(least_upper_bound(identity,multiply(X_76,X_162))),identity),X_76) != X_76
| multiply(least_upper_bound(inverse(least_upper_bound(identity,multiply(X_76,X_162))),identity),X_76) != least_upper_bound(X_76,inverse(least_upper_bound(X_162,inverse(X_76))))
| X_76 = least_upper_bound(X_76,inverse(least_upper_bound(X_162,inverse(X_76)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(least_upper_bound(identity,multiply(X_76,X_162))),identity),X_76),least_upper_bound(X_76,inverse(least_upper_bound(X_162,inverse(X_76))))) ),[0],$fot(X_76)]]) ).
cnf(refute_0_864,plain,
( multiply(least_upper_bound(inverse(least_upper_bound(identity,multiply(X_76,X_162))),identity),X_76) != least_upper_bound(X_76,inverse(least_upper_bound(X_162,inverse(X_76))))
| X_76 = least_upper_bound(X_76,inverse(least_upper_bound(X_162,inverse(X_76)))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(least_upper_bound(identity,multiply(X_76,X_162))),identity),X_76),X_76) )],[refute_0_862,refute_0_863]) ).
cnf(refute_0_865,plain,
X_76 = least_upper_bound(X_76,inverse(least_upper_bound(X_162,inverse(X_76)))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(least_upper_bound(identity,multiply(X_76,X_162))),identity),X_76),least_upper_bound(X_76,inverse(least_upper_bound(X_162,inverse(X_76))))) )],[refute_0_839,refute_0_864]) ).
cnf(refute_0_866,plain,
identity = least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity)))),
inference(subst,[],[refute_0_865:[bind(X_76,$fot(identity))]]) ).
cnf(refute_0_867,plain,
( identity != least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))
| least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity)))) = identity ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(identity)),bind(Y0,$fot(least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))))]]) ).
cnf(refute_0_868,plain,
least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity)))) = identity,
inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))) )],[refute_0_866,refute_0_867]) ).
cnf(refute_0_869,plain,
( multiply(greatest_lower_bound(X_303,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))) != greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),multiply(X_303,least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))))
| least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity)))) != identity
| multiply(greatest_lower_bound(X_303,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))) = greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),multiply(X_303,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_303,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))),greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),multiply(X_303,least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))))) ),[1,1,1],$fot(identity)]]) ).
cnf(refute_0_870,plain,
( multiply(greatest_lower_bound(X_303,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))) != greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),multiply(X_303,least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))))
| multiply(greatest_lower_bound(X_303,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))) = greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),multiply(X_303,identity)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity)))),identity) )],[refute_0_868,refute_0_869]) ).
cnf(refute_0_871,plain,
multiply(greatest_lower_bound(X_303,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))) = greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),multiply(X_303,identity)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_303,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))),greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),multiply(X_303,least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))))) )],[refute_0_832,refute_0_870]) ).
cnf(refute_0_872,plain,
multiply(greatest_lower_bound(X_303,least_upper_bound(X_162,identity)),identity) = greatest_lower_bound(X_303,least_upper_bound(X_162,identity)),
inference(subst,[],[refute_0_564:[bind(X,$fot(greatest_lower_bound(X_303,least_upper_bound(X_162,identity))))]]) ).
cnf(refute_0_873,plain,
multiply(greatest_lower_bound(X_303,least_upper_bound(X_162,identity)),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))) = multiply(greatest_lower_bound(X_303,least_upper_bound(X_162,identity)),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(X_303,least_upper_bound(X_162,identity)),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))))]]) ).
cnf(refute_0_874,plain,
( multiply(greatest_lower_bound(X_303,least_upper_bound(X_162,identity)),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))) != multiply(greatest_lower_bound(X_303,least_upper_bound(X_162,identity)),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity)))))
| least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity)))) != identity
| multiply(greatest_lower_bound(X_303,least_upper_bound(X_162,identity)),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))) = multiply(greatest_lower_bound(X_303,least_upper_bound(X_162,identity)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_303,least_upper_bound(X_162,identity)),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))),multiply(greatest_lower_bound(X_303,least_upper_bound(X_162,identity)),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity)))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_875,plain,
( least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity)))) != identity
| multiply(greatest_lower_bound(X_303,least_upper_bound(X_162,identity)),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))) = multiply(greatest_lower_bound(X_303,least_upper_bound(X_162,identity)),identity) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_303,least_upper_bound(X_162,identity)),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))),multiply(greatest_lower_bound(X_303,least_upper_bound(X_162,identity)),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity)))))) )],[refute_0_873,refute_0_874]) ).
cnf(refute_0_876,plain,
multiply(greatest_lower_bound(X_303,least_upper_bound(X_162,identity)),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))) = multiply(greatest_lower_bound(X_303,least_upper_bound(X_162,identity)),identity),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity)))),identity) )],[refute_0_868,refute_0_875]) ).
cnf(refute_0_877,plain,
least_upper_bound(X_162,inverse(identity)) = least_upper_bound(X_162,inverse(identity)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_162,inverse(identity)))]]) ).
cnf(refute_0_878,plain,
( inverse(identity) != identity
| least_upper_bound(X_162,inverse(identity)) != least_upper_bound(X_162,inverse(identity))
| least_upper_bound(X_162,inverse(identity)) = least_upper_bound(X_162,identity) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_162,inverse(identity)),least_upper_bound(X_162,inverse(identity))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_879,plain,
( inverse(identity) != identity
| least_upper_bound(X_162,inverse(identity)) = least_upper_bound(X_162,identity) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_162,inverse(identity)),least_upper_bound(X_162,inverse(identity))) )],[refute_0_877,refute_0_878]) ).
cnf(refute_0_880,plain,
least_upper_bound(X_162,inverse(identity)) = least_upper_bound(X_162,identity),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[p19_1,refute_0_879]) ).
cnf(refute_0_881,plain,
inverse(inverse(least_upper_bound(X_162,inverse(identity)))) = least_upper_bound(X_162,inverse(identity)),
inference(subst,[],[p19_2:[bind(X,$fot(least_upper_bound(X_162,inverse(identity))))]]) ).
cnf(refute_0_882,plain,
( inverse(inverse(least_upper_bound(X_162,inverse(identity)))) != least_upper_bound(X_162,inverse(identity))
| least_upper_bound(X_162,inverse(identity)) != least_upper_bound(X_162,identity)
| inverse(inverse(least_upper_bound(X_162,inverse(identity)))) = least_upper_bound(X_162,identity) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(inverse(inverse(least_upper_bound(X_162,inverse(identity)))))),bind(Y0,$fot(least_upper_bound(X_162,inverse(identity)))),bind(Z0,$fot(least_upper_bound(X_162,identity)))]]) ).
cnf(refute_0_883,plain,
( least_upper_bound(X_162,inverse(identity)) != least_upper_bound(X_162,identity)
| inverse(inverse(least_upper_bound(X_162,inverse(identity)))) = least_upper_bound(X_162,identity) ),
inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(X_162,inverse(identity)))),least_upper_bound(X_162,inverse(identity))) )],[refute_0_881,refute_0_882]) ).
cnf(refute_0_884,plain,
inverse(inverse(least_upper_bound(X_162,inverse(identity)))) = least_upper_bound(X_162,identity),
inference(resolve,[$cnf( $equal(least_upper_bound(X_162,inverse(identity)),least_upper_bound(X_162,identity)) )],[refute_0_880,refute_0_883]) ).
cnf(refute_0_885,plain,
greatest_lower_bound(X_303,inverse(inverse(least_upper_bound(X_162,inverse(identity))))) = greatest_lower_bound(X_303,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X_303,inverse(inverse(least_upper_bound(X_162,inverse(identity))))))]]) ).
cnf(refute_0_886,plain,
( greatest_lower_bound(X_303,inverse(inverse(least_upper_bound(X_162,inverse(identity))))) != greatest_lower_bound(X_303,inverse(inverse(least_upper_bound(X_162,inverse(identity)))))
| inverse(inverse(least_upper_bound(X_162,inverse(identity)))) != least_upper_bound(X_162,identity)
| greatest_lower_bound(X_303,inverse(inverse(least_upper_bound(X_162,inverse(identity))))) = greatest_lower_bound(X_303,least_upper_bound(X_162,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_303,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),greatest_lower_bound(X_303,inverse(inverse(least_upper_bound(X_162,inverse(identity)))))) ),[1,1],$fot(least_upper_bound(X_162,identity))]]) ).
cnf(refute_0_887,plain,
( inverse(inverse(least_upper_bound(X_162,inverse(identity)))) != least_upper_bound(X_162,identity)
| greatest_lower_bound(X_303,inverse(inverse(least_upper_bound(X_162,inverse(identity))))) = greatest_lower_bound(X_303,least_upper_bound(X_162,identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_303,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),greatest_lower_bound(X_303,inverse(inverse(least_upper_bound(X_162,inverse(identity)))))) )],[refute_0_885,refute_0_886]) ).
cnf(refute_0_888,plain,
greatest_lower_bound(X_303,inverse(inverse(least_upper_bound(X_162,inverse(identity))))) = greatest_lower_bound(X_303,least_upper_bound(X_162,identity)),
inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(X_162,inverse(identity)))),least_upper_bound(X_162,identity)) )],[refute_0_884,refute_0_887]) ).
cnf(refute_0_889,plain,
multiply(greatest_lower_bound(X_303,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))) = multiply(greatest_lower_bound(X_303,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(X_303,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))))]]) ).
cnf(refute_0_890,plain,
( multiply(greatest_lower_bound(X_303,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))) != multiply(greatest_lower_bound(X_303,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity)))))
| greatest_lower_bound(X_303,inverse(inverse(least_upper_bound(X_162,inverse(identity))))) != greatest_lower_bound(X_303,least_upper_bound(X_162,identity))
| multiply(greatest_lower_bound(X_303,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))) = multiply(greatest_lower_bound(X_303,least_upper_bound(X_162,identity)),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_303,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))),multiply(greatest_lower_bound(X_303,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity)))))) ),[1,0],$fot(greatest_lower_bound(X_303,least_upper_bound(X_162,identity)))]]) ).
cnf(refute_0_891,plain,
( greatest_lower_bound(X_303,inverse(inverse(least_upper_bound(X_162,inverse(identity))))) != greatest_lower_bound(X_303,least_upper_bound(X_162,identity))
| multiply(greatest_lower_bound(X_303,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))) = multiply(greatest_lower_bound(X_303,least_upper_bound(X_162,identity)),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_303,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))),multiply(greatest_lower_bound(X_303,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity)))))) )],[refute_0_889,refute_0_890]) ).
cnf(refute_0_892,plain,
multiply(greatest_lower_bound(X_303,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))) = multiply(greatest_lower_bound(X_303,least_upper_bound(X_162,identity)),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_303,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),greatest_lower_bound(X_303,least_upper_bound(X_162,identity))) )],[refute_0_888,refute_0_891]) ).
cnf(refute_0_893,plain,
( multiply(greatest_lower_bound(X_303,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))) != multiply(greatest_lower_bound(X_303,least_upper_bound(X_162,identity)),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity)))))
| multiply(greatest_lower_bound(X_303,least_upper_bound(X_162,identity)),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))) != multiply(greatest_lower_bound(X_303,least_upper_bound(X_162,identity)),identity)
| multiply(greatest_lower_bound(X_303,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))) = multiply(greatest_lower_bound(X_303,least_upper_bound(X_162,identity)),identity) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(multiply(greatest_lower_bound(X_303,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))))),bind(Y0,$fot(multiply(greatest_lower_bound(X_303,least_upper_bound(X_162,identity)),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))))),bind(Z0,$fot(multiply(greatest_lower_bound(X_303,least_upper_bound(X_162,identity)),identity)))]]) ).
cnf(refute_0_894,plain,
( multiply(greatest_lower_bound(X_303,least_upper_bound(X_162,identity)),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))) != multiply(greatest_lower_bound(X_303,least_upper_bound(X_162,identity)),identity)
| multiply(greatest_lower_bound(X_303,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))) = multiply(greatest_lower_bound(X_303,least_upper_bound(X_162,identity)),identity) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_303,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))),multiply(greatest_lower_bound(X_303,least_upper_bound(X_162,identity)),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity)))))) )],[refute_0_892,refute_0_893]) ).
cnf(refute_0_895,plain,
multiply(greatest_lower_bound(X_303,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))) = multiply(greatest_lower_bound(X_303,least_upper_bound(X_162,identity)),identity),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_303,least_upper_bound(X_162,identity)),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))),multiply(greatest_lower_bound(X_303,least_upper_bound(X_162,identity)),identity)) )],[refute_0_876,refute_0_894]) ).
cnf(refute_0_896,plain,
( multiply(greatest_lower_bound(X_303,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))) != multiply(greatest_lower_bound(X_303,least_upper_bound(X_162,identity)),identity)
| multiply(greatest_lower_bound(X_303,least_upper_bound(X_162,identity)),identity) != greatest_lower_bound(X_303,least_upper_bound(X_162,identity))
| multiply(greatest_lower_bound(X_303,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))) = greatest_lower_bound(X_303,least_upper_bound(X_162,identity)) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(multiply(greatest_lower_bound(X_303,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))))),bind(Y0,$fot(multiply(greatest_lower_bound(X_303,least_upper_bound(X_162,identity)),identity))),bind(Z0,$fot(greatest_lower_bound(X_303,least_upper_bound(X_162,identity))))]]) ).
cnf(refute_0_897,plain,
( multiply(greatest_lower_bound(X_303,least_upper_bound(X_162,identity)),identity) != greatest_lower_bound(X_303,least_upper_bound(X_162,identity))
| multiply(greatest_lower_bound(X_303,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))) = greatest_lower_bound(X_303,least_upper_bound(X_162,identity)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_303,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))),multiply(greatest_lower_bound(X_303,least_upper_bound(X_162,identity)),identity)) )],[refute_0_895,refute_0_896]) ).
cnf(refute_0_898,plain,
multiply(greatest_lower_bound(X_303,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))) = greatest_lower_bound(X_303,least_upper_bound(X_162,identity)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_303,least_upper_bound(X_162,identity)),identity),greatest_lower_bound(X_303,least_upper_bound(X_162,identity))) )],[refute_0_872,refute_0_897]) ).
cnf(refute_0_899,plain,
( multiply(greatest_lower_bound(X_303,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))) != greatest_lower_bound(X_303,least_upper_bound(X_162,identity))
| multiply(greatest_lower_bound(X_303,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))) != greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),multiply(X_303,identity))
| greatest_lower_bound(X_303,least_upper_bound(X_162,identity)) = greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),multiply(X_303,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_303,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))),greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),multiply(X_303,identity))) ),[0],$fot(greatest_lower_bound(X_303,least_upper_bound(X_162,identity)))]]) ).
cnf(refute_0_900,plain,
( multiply(greatest_lower_bound(X_303,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))) != greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),multiply(X_303,identity))
| greatest_lower_bound(X_303,least_upper_bound(X_162,identity)) = greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),multiply(X_303,identity)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_303,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))),greatest_lower_bound(X_303,least_upper_bound(X_162,identity))) )],[refute_0_898,refute_0_899]) ).
cnf(refute_0_901,plain,
multiply(X_303,identity) = X_303,
inference(subst,[],[refute_0_564:[bind(X,$fot(X_303))]]) ).
cnf(refute_0_902,plain,
greatest_lower_bound(least_upper_bound(identity,X_162),multiply(X_303,identity)) = greatest_lower_bound(least_upper_bound(identity,X_162),multiply(X_303,identity)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(least_upper_bound(identity,X_162),multiply(X_303,identity)))]]) ).
cnf(refute_0_903,plain,
( multiply(X_303,identity) != X_303
| greatest_lower_bound(least_upper_bound(identity,X_162),multiply(X_303,identity)) != greatest_lower_bound(least_upper_bound(identity,X_162),multiply(X_303,identity))
| greatest_lower_bound(least_upper_bound(identity,X_162),multiply(X_303,identity)) = greatest_lower_bound(least_upper_bound(identity,X_162),X_303) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,X_162),multiply(X_303,identity)),greatest_lower_bound(least_upper_bound(identity,X_162),multiply(X_303,identity))) ),[1,1],$fot(X_303)]]) ).
cnf(refute_0_904,plain,
( multiply(X_303,identity) != X_303
| greatest_lower_bound(least_upper_bound(identity,X_162),multiply(X_303,identity)) = greatest_lower_bound(least_upper_bound(identity,X_162),X_303) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,X_162),multiply(X_303,identity)),greatest_lower_bound(least_upper_bound(identity,X_162),multiply(X_303,identity))) )],[refute_0_902,refute_0_903]) ).
cnf(refute_0_905,plain,
greatest_lower_bound(least_upper_bound(identity,X_162),multiply(X_303,identity)) = greatest_lower_bound(least_upper_bound(identity,X_162),X_303),
inference(resolve,[$cnf( $equal(multiply(X_303,identity),X_303) )],[refute_0_901,refute_0_904]) ).
cnf(refute_0_906,plain,
least_upper_bound(identity,least_upper_bound(X_162,identity)) = least_upper_bound(identity,X_162),
inference(subst,[],[refute_0_635:[bind(Y,$fot(X_162)),bind(X_17,$fot(identity))]]) ).
cnf(refute_0_907,plain,
least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity))))) = least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity))))))]]) ).
cnf(refute_0_908,plain,
( inverse(inverse(least_upper_bound(X_162,inverse(identity)))) != least_upper_bound(X_162,identity)
| least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity))))) != least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity)))))
| least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity))))) = least_upper_bound(identity,least_upper_bound(X_162,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity)))))) ),[1,1],$fot(least_upper_bound(X_162,identity))]]) ).
cnf(refute_0_909,plain,
( inverse(inverse(least_upper_bound(X_162,inverse(identity)))) != least_upper_bound(X_162,identity)
| least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity))))) = least_upper_bound(identity,least_upper_bound(X_162,identity)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity)))))) )],[refute_0_907,refute_0_908]) ).
cnf(refute_0_910,plain,
least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity))))) = least_upper_bound(identity,least_upper_bound(X_162,identity)),
inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(X_162,inverse(identity)))),least_upper_bound(X_162,identity)) )],[refute_0_884,refute_0_909]) ).
cnf(refute_0_911,plain,
( least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity))))) != least_upper_bound(identity,least_upper_bound(X_162,identity))
| least_upper_bound(identity,least_upper_bound(X_162,identity)) != least_upper_bound(identity,X_162)
| least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity))))) = least_upper_bound(identity,X_162) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity))))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(X_162,identity)))),bind(Z0,$fot(least_upper_bound(identity,X_162)))]]) ).
cnf(refute_0_912,plain,
( least_upper_bound(identity,least_upper_bound(X_162,identity)) != least_upper_bound(identity,X_162)
| least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity))))) = least_upper_bound(identity,X_162) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),least_upper_bound(identity,least_upper_bound(X_162,identity))) )],[refute_0_910,refute_0_911]) ).
cnf(refute_0_913,plain,
least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity))))) = least_upper_bound(identity,X_162),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_162,identity)),least_upper_bound(identity,X_162)) )],[refute_0_906,refute_0_912]) ).
cnf(refute_0_914,plain,
greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),multiply(X_303,identity)) = greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),multiply(X_303,identity)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),multiply(X_303,identity)))]]) ).
cnf(refute_0_915,plain,
( greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),multiply(X_303,identity)) != greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),multiply(X_303,identity))
| least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity))))) != least_upper_bound(identity,X_162)
| greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),multiply(X_303,identity)) = greatest_lower_bound(least_upper_bound(identity,X_162),multiply(X_303,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),multiply(X_303,identity)),greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),multiply(X_303,identity))) ),[1,0],$fot(least_upper_bound(identity,X_162))]]) ).
cnf(refute_0_916,plain,
( least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity))))) != least_upper_bound(identity,X_162)
| greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),multiply(X_303,identity)) = greatest_lower_bound(least_upper_bound(identity,X_162),multiply(X_303,identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),multiply(X_303,identity)),greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),multiply(X_303,identity))) )],[refute_0_914,refute_0_915]) ).
cnf(refute_0_917,plain,
greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),multiply(X_303,identity)) = greatest_lower_bound(least_upper_bound(identity,X_162),multiply(X_303,identity)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),least_upper_bound(identity,X_162)) )],[refute_0_913,refute_0_916]) ).
cnf(refute_0_918,plain,
( greatest_lower_bound(least_upper_bound(identity,X_162),multiply(X_303,identity)) != greatest_lower_bound(least_upper_bound(identity,X_162),X_303)
| greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),multiply(X_303,identity)) != greatest_lower_bound(least_upper_bound(identity,X_162),multiply(X_303,identity))
| greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),multiply(X_303,identity)) = greatest_lower_bound(least_upper_bound(identity,X_162),X_303) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),multiply(X_303,identity)))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(identity,X_162),multiply(X_303,identity)))),bind(Z0,$fot(greatest_lower_bound(least_upper_bound(identity,X_162),X_303)))]]) ).
cnf(refute_0_919,plain,
( greatest_lower_bound(least_upper_bound(identity,X_162),multiply(X_303,identity)) != greatest_lower_bound(least_upper_bound(identity,X_162),X_303)
| greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),multiply(X_303,identity)) = greatest_lower_bound(least_upper_bound(identity,X_162),X_303) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),multiply(X_303,identity)),greatest_lower_bound(least_upper_bound(identity,X_162),multiply(X_303,identity))) )],[refute_0_917,refute_0_918]) ).
cnf(refute_0_920,plain,
greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),multiply(X_303,identity)) = greatest_lower_bound(least_upper_bound(identity,X_162),X_303),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,X_162),multiply(X_303,identity)),greatest_lower_bound(least_upper_bound(identity,X_162),X_303)) )],[refute_0_905,refute_0_919]) ).
cnf(refute_0_921,plain,
( greatest_lower_bound(X_303,least_upper_bound(X_162,identity)) != greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),multiply(X_303,identity))
| greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),multiply(X_303,identity)) != greatest_lower_bound(least_upper_bound(identity,X_162),X_303)
| greatest_lower_bound(X_303,least_upper_bound(X_162,identity)) = greatest_lower_bound(least_upper_bound(identity,X_162),X_303) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_303,least_upper_bound(X_162,identity)),greatest_lower_bound(least_upper_bound(identity,X_162),X_303)) ),[0],$fot(greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),multiply(X_303,identity)))]]) ).
cnf(refute_0_922,plain,
( greatest_lower_bound(X_303,least_upper_bound(X_162,identity)) != greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),multiply(X_303,identity))
| greatest_lower_bound(X_303,least_upper_bound(X_162,identity)) = greatest_lower_bound(least_upper_bound(identity,X_162),X_303) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),multiply(X_303,identity)),greatest_lower_bound(least_upper_bound(identity,X_162),X_303)) )],[refute_0_920,refute_0_921]) ).
cnf(refute_0_923,plain,
( multiply(greatest_lower_bound(X_303,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))) != greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),multiply(X_303,identity))
| greatest_lower_bound(X_303,least_upper_bound(X_162,identity)) = greatest_lower_bound(least_upper_bound(identity,X_162),X_303) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_303,least_upper_bound(X_162,identity)),greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),multiply(X_303,identity))) )],[refute_0_900,refute_0_922]) ).
cnf(refute_0_924,plain,
greatest_lower_bound(X_303,least_upper_bound(X_162,identity)) = greatest_lower_bound(least_upper_bound(identity,X_162),X_303),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_303,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),least_upper_bound(identity,inverse(least_upper_bound(X_162,inverse(identity))))),greatest_lower_bound(least_upper_bound(identity,inverse(inverse(least_upper_bound(X_162,inverse(identity))))),multiply(X_303,identity))) )],[refute_0_871,refute_0_923]) ).
cnf(refute_0_925,plain,
greatest_lower_bound(X_305,least_upper_bound(least_upper_bound(identity,X_221),identity)) = greatest_lower_bound(least_upper_bound(identity,least_upper_bound(identity,X_221)),X_305),
inference(subst,[],[refute_0_924:[bind(X_162,$fot(least_upper_bound(identity,X_221))),bind(X_303,$fot(X_305))]]) ).
cnf(refute_0_926,plain,
multiply(least_upper_bound(X_77,X_78),inverse(X_77)) = least_upper_bound(multiply(X_77,inverse(X_77)),multiply(X_78,inverse(X_77))),
inference(subst,[],[monotony_lub2:[bind(X,$fot(inverse(X_77))),bind(Y,$fot(X_77)),bind(Z,$fot(X_78))]]) ).
cnf(refute_0_927,plain,
multiply(X_77,inverse(X_77)) = identity,
inference(subst,[],[refute_0_156:[bind(X,$fot(X_77))]]) ).
cnf(refute_0_928,plain,
( multiply(X_77,inverse(X_77)) != identity
| multiply(least_upper_bound(X_77,X_78),inverse(X_77)) != least_upper_bound(multiply(X_77,inverse(X_77)),multiply(X_78,inverse(X_77)))
| multiply(least_upper_bound(X_77,X_78),inverse(X_77)) = least_upper_bound(identity,multiply(X_78,inverse(X_77))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_77,X_78),inverse(X_77)),least_upper_bound(multiply(X_77,inverse(X_77)),multiply(X_78,inverse(X_77)))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_929,plain,
( multiply(least_upper_bound(X_77,X_78),inverse(X_77)) != least_upper_bound(multiply(X_77,inverse(X_77)),multiply(X_78,inverse(X_77)))
| multiply(least_upper_bound(X_77,X_78),inverse(X_77)) = least_upper_bound(identity,multiply(X_78,inverse(X_77))) ),
inference(resolve,[$cnf( $equal(multiply(X_77,inverse(X_77)),identity) )],[refute_0_927,refute_0_928]) ).
cnf(refute_0_930,plain,
multiply(least_upper_bound(X_77,X_78),inverse(X_77)) = least_upper_bound(identity,multiply(X_78,inverse(X_77))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_77,X_78),inverse(X_77)),least_upper_bound(multiply(X_77,inverse(X_77)),multiply(X_78,inverse(X_77)))) )],[refute_0_926,refute_0_929]) ).
cnf(refute_0_931,plain,
multiply(least_upper_bound(identity,least_upper_bound(X_18,X_221)),inverse(identity)) = least_upper_bound(identity,multiply(least_upper_bound(X_18,X_221),inverse(identity))),
inference(subst,[],[refute_0_930:[bind(X_77,$fot(identity)),bind(X_78,$fot(least_upper_bound(X_18,X_221)))]]) ).
cnf(refute_0_932,plain,
multiply(least_upper_bound(X_77,inverse(X_63)),least_upper_bound(identity,X_63)) = least_upper_bound(multiply(X_77,least_upper_bound(identity,X_63)),multiply(inverse(X_63),least_upper_bound(identity,X_63))),
inference(subst,[],[monotony_lub2:[bind(X,$fot(least_upper_bound(identity,X_63))),bind(Y,$fot(X_77)),bind(Z,$fot(inverse(X_63)))]]) ).
cnf(refute_0_933,plain,
( multiply(inverse(X_63),least_upper_bound(identity,X_63)) != least_upper_bound(identity,inverse(X_63))
| multiply(least_upper_bound(X_77,inverse(X_63)),least_upper_bound(identity,X_63)) != least_upper_bound(multiply(X_77,least_upper_bound(identity,X_63)),multiply(inverse(X_63),least_upper_bound(identity,X_63)))
| multiply(least_upper_bound(X_77,inverse(X_63)),least_upper_bound(identity,X_63)) = least_upper_bound(multiply(X_77,least_upper_bound(identity,X_63)),least_upper_bound(identity,inverse(X_63))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_77,inverse(X_63)),least_upper_bound(identity,X_63)),least_upper_bound(multiply(X_77,least_upper_bound(identity,X_63)),multiply(inverse(X_63),least_upper_bound(identity,X_63)))) ),[1,1],$fot(least_upper_bound(identity,inverse(X_63)))]]) ).
cnf(refute_0_934,plain,
( multiply(least_upper_bound(X_77,inverse(X_63)),least_upper_bound(identity,X_63)) != least_upper_bound(multiply(X_77,least_upper_bound(identity,X_63)),multiply(inverse(X_63),least_upper_bound(identity,X_63)))
| multiply(least_upper_bound(X_77,inverse(X_63)),least_upper_bound(identity,X_63)) = least_upper_bound(multiply(X_77,least_upper_bound(identity,X_63)),least_upper_bound(identity,inverse(X_63))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_63),least_upper_bound(identity,X_63)),least_upper_bound(identity,inverse(X_63))) )],[refute_0_134,refute_0_933]) ).
cnf(refute_0_935,plain,
multiply(least_upper_bound(X_77,inverse(X_63)),least_upper_bound(identity,X_63)) = least_upper_bound(multiply(X_77,least_upper_bound(identity,X_63)),least_upper_bound(identity,inverse(X_63))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_77,inverse(X_63)),least_upper_bound(identity,X_63)),least_upper_bound(multiply(X_77,least_upper_bound(identity,X_63)),multiply(inverse(X_63),least_upper_bound(identity,X_63)))) )],[refute_0_932,refute_0_934]) ).
cnf(refute_0_936,plain,
least_upper_bound(X_36,least_upper_bound(X_37,X_38)) = least_upper_bound(least_upper_bound(X_36,X_37),X_38),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_36)),bind(Y,$fot(X_37)),bind(Z,$fot(X_38))]]) ).
cnf(refute_0_937,plain,
least_upper_bound(X_38,X_37) = least_upper_bound(X_37,X_38),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_38)),bind(Y,$fot(X_37))]]) ).
cnf(refute_0_938,plain,
( least_upper_bound(X_38,X_37) != least_upper_bound(X_37,X_38)
| least_upper_bound(X_37,X_38) = least_upper_bound(X_38,X_37) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(least_upper_bound(X_38,X_37))),bind(Y0,$fot(least_upper_bound(X_37,X_38)))]]) ).
cnf(refute_0_939,plain,
least_upper_bound(X_37,X_38) = least_upper_bound(X_38,X_37),
inference(resolve,[$cnf( $equal(least_upper_bound(X_38,X_37),least_upper_bound(X_37,X_38)) )],[refute_0_937,refute_0_938]) ).
cnf(refute_0_940,plain,
( least_upper_bound(X_36,least_upper_bound(X_37,X_38)) != least_upper_bound(least_upper_bound(X_36,X_37),X_38)
| least_upper_bound(X_37,X_38) != least_upper_bound(X_38,X_37)
| least_upper_bound(X_36,least_upper_bound(X_38,X_37)) = least_upper_bound(least_upper_bound(X_36,X_37),X_38) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_36,least_upper_bound(X_37,X_38)),least_upper_bound(least_upper_bound(X_36,X_37),X_38)) ),[0,1],$fot(least_upper_bound(X_38,X_37))]]) ).
cnf(refute_0_941,plain,
( least_upper_bound(X_36,least_upper_bound(X_37,X_38)) != least_upper_bound(least_upper_bound(X_36,X_37),X_38)
| least_upper_bound(X_36,least_upper_bound(X_38,X_37)) = least_upper_bound(least_upper_bound(X_36,X_37),X_38) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_37,X_38),least_upper_bound(X_38,X_37)) )],[refute_0_939,refute_0_940]) ).
cnf(refute_0_942,plain,
least_upper_bound(X_36,least_upper_bound(X_38,X_37)) = least_upper_bound(least_upper_bound(X_36,X_37),X_38),
inference(resolve,[$cnf( $equal(least_upper_bound(X_36,least_upper_bound(X_37,X_38)),least_upper_bound(least_upper_bound(X_36,X_37),X_38)) )],[refute_0_936,refute_0_941]) ).
cnf(refute_0_943,plain,
least_upper_bound(least_upper_bound(X_36,X_37),X_38) = least_upper_bound(X_36,least_upper_bound(X_37,X_38)),
inference(subst,[],[refute_0_631:[bind(X,$fot(X_36)),bind(Y,$fot(X_37)),bind(Z,$fot(X_38))]]) ).
cnf(refute_0_944,plain,
( least_upper_bound(X_36,least_upper_bound(X_38,X_37)) != least_upper_bound(least_upper_bound(X_36,X_37),X_38)
| least_upper_bound(least_upper_bound(X_36,X_37),X_38) != least_upper_bound(X_36,least_upper_bound(X_37,X_38))
| least_upper_bound(X_36,least_upper_bound(X_38,X_37)) = least_upper_bound(X_36,least_upper_bound(X_37,X_38)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_36,least_upper_bound(X_38,X_37)),least_upper_bound(X_36,least_upper_bound(X_37,X_38))) ),[0],$fot(least_upper_bound(least_upper_bound(X_36,X_37),X_38))]]) ).
cnf(refute_0_945,plain,
( least_upper_bound(X_36,least_upper_bound(X_38,X_37)) != least_upper_bound(least_upper_bound(X_36,X_37),X_38)
| least_upper_bound(X_36,least_upper_bound(X_38,X_37)) = least_upper_bound(X_36,least_upper_bound(X_37,X_38)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_36,X_37),X_38),least_upper_bound(X_36,least_upper_bound(X_37,X_38))) )],[refute_0_943,refute_0_944]) ).
cnf(refute_0_946,plain,
least_upper_bound(X_36,least_upper_bound(X_38,X_37)) = least_upper_bound(X_36,least_upper_bound(X_37,X_38)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_36,least_upper_bound(X_38,X_37)),least_upper_bound(least_upper_bound(X_36,X_37),X_38)) )],[refute_0_942,refute_0_945]) ).
cnf(refute_0_947,plain,
( least_upper_bound(X_36,least_upper_bound(X_38,X_37)) != least_upper_bound(X_36,least_upper_bound(X_37,X_38))
| least_upper_bound(X_36,least_upper_bound(X_37,X_38)) = least_upper_bound(X_36,least_upper_bound(X_38,X_37)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(least_upper_bound(X_36,least_upper_bound(X_38,X_37)))),bind(Y0,$fot(least_upper_bound(X_36,least_upper_bound(X_37,X_38))))]]) ).
cnf(refute_0_948,plain,
least_upper_bound(X_36,least_upper_bound(X_37,X_38)) = least_upper_bound(X_36,least_upper_bound(X_38,X_37)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_36,least_upper_bound(X_38,X_37)),least_upper_bound(X_36,least_upper_bound(X_37,X_38))) )],[refute_0_946,refute_0_947]) ).
cnf(refute_0_949,plain,
least_upper_bound(identity,least_upper_bound(multiply(X_77,least_upper_bound(identity,X_63)),inverse(X_63))) = least_upper_bound(identity,least_upper_bound(inverse(X_63),multiply(X_77,least_upper_bound(identity,X_63)))),
inference(subst,[],[refute_0_948:[bind(X_36,$fot(identity)),bind(X_37,$fot(multiply(X_77,least_upper_bound(identity,X_63)))),bind(X_38,$fot(inverse(X_63)))]]) ).
cnf(refute_0_950,plain,
least_upper_bound(X_36,least_upper_bound(least_upper_bound(Y,X_36),X_38)) = least_upper_bound(least_upper_bound(X_36,least_upper_bound(Y,X_36)),X_38),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_36)),bind(Y,$fot(least_upper_bound(Y,X_36))),bind(Z,$fot(X_38))]]) ).
cnf(refute_0_951,plain,
least_upper_bound(X_36,least_upper_bound(Y,X_36)) = least_upper_bound(X_36,Y),
inference(subst,[],[refute_0_635:[bind(X_17,$fot(X_36))]]) ).
cnf(refute_0_952,plain,
( least_upper_bound(X_36,least_upper_bound(Y,X_36)) != least_upper_bound(X_36,Y)
| least_upper_bound(X_36,least_upper_bound(least_upper_bound(Y,X_36),X_38)) != least_upper_bound(least_upper_bound(X_36,least_upper_bound(Y,X_36)),X_38)
| least_upper_bound(X_36,least_upper_bound(least_upper_bound(Y,X_36),X_38)) = least_upper_bound(least_upper_bound(X_36,Y),X_38) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_36,least_upper_bound(least_upper_bound(Y,X_36),X_38)),least_upper_bound(least_upper_bound(X_36,least_upper_bound(Y,X_36)),X_38)) ),[1,0],$fot(least_upper_bound(X_36,Y))]]) ).
cnf(refute_0_953,plain,
( least_upper_bound(X_36,least_upper_bound(least_upper_bound(Y,X_36),X_38)) != least_upper_bound(least_upper_bound(X_36,least_upper_bound(Y,X_36)),X_38)
| least_upper_bound(X_36,least_upper_bound(least_upper_bound(Y,X_36),X_38)) = least_upper_bound(least_upper_bound(X_36,Y),X_38) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_36,least_upper_bound(Y,X_36)),least_upper_bound(X_36,Y)) )],[refute_0_951,refute_0_952]) ).
cnf(refute_0_954,plain,
least_upper_bound(X_36,least_upper_bound(least_upper_bound(Y,X_36),X_38)) = least_upper_bound(least_upper_bound(X_36,Y),X_38),
inference(resolve,[$cnf( $equal(least_upper_bound(X_36,least_upper_bound(least_upper_bound(Y,X_36),X_38)),least_upper_bound(least_upper_bound(X_36,least_upper_bound(Y,X_36)),X_38)) )],[refute_0_950,refute_0_953]) ).
cnf(refute_0_955,plain,
least_upper_bound(X_36,least_upper_bound(X_37,least_upper_bound(Y,X_37))) = least_upper_bound(least_upper_bound(X_36,X_37),least_upper_bound(Y,X_37)),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_36)),bind(Y,$fot(X_37)),bind(Z,$fot(least_upper_bound(Y,X_37)))]]) ).
cnf(refute_0_956,plain,
least_upper_bound(X_37,least_upper_bound(Y,X_37)) = least_upper_bound(X_37,Y),
inference(subst,[],[refute_0_635:[bind(X_17,$fot(X_37))]]) ).
cnf(refute_0_957,plain,
( least_upper_bound(X_36,least_upper_bound(X_37,least_upper_bound(Y,X_37))) != least_upper_bound(least_upper_bound(X_36,X_37),least_upper_bound(Y,X_37))
| least_upper_bound(X_37,least_upper_bound(Y,X_37)) != least_upper_bound(X_37,Y)
| least_upper_bound(X_36,least_upper_bound(X_37,Y)) = least_upper_bound(least_upper_bound(X_36,X_37),least_upper_bound(Y,X_37)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_36,least_upper_bound(X_37,least_upper_bound(Y,X_37))),least_upper_bound(least_upper_bound(X_36,X_37),least_upper_bound(Y,X_37))) ),[0,1],$fot(least_upper_bound(X_37,Y))]]) ).
cnf(refute_0_958,plain,
( least_upper_bound(X_36,least_upper_bound(X_37,least_upper_bound(Y,X_37))) != least_upper_bound(least_upper_bound(X_36,X_37),least_upper_bound(Y,X_37))
| least_upper_bound(X_36,least_upper_bound(X_37,Y)) = least_upper_bound(least_upper_bound(X_36,X_37),least_upper_bound(Y,X_37)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_37,least_upper_bound(Y,X_37)),least_upper_bound(X_37,Y)) )],[refute_0_956,refute_0_957]) ).
cnf(refute_0_959,plain,
least_upper_bound(X_36,least_upper_bound(X_37,Y)) = least_upper_bound(least_upper_bound(X_36,X_37),least_upper_bound(Y,X_37)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_36,least_upper_bound(X_37,least_upper_bound(Y,X_37))),least_upper_bound(least_upper_bound(X_36,X_37),least_upper_bound(Y,X_37))) )],[refute_0_955,refute_0_958]) ).
cnf(refute_0_960,plain,
least_upper_bound(least_upper_bound(X_36,X_37),Y) = least_upper_bound(X_36,least_upper_bound(X_37,Y)),
inference(subst,[],[refute_0_631:[bind(X,$fot(X_36)),bind(Y,$fot(X_37)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_961,plain,
least_upper_bound(X_37,least_upper_bound(least_upper_bound(X_36,X_37),Y)) = least_upper_bound(X_37,least_upper_bound(least_upper_bound(X_36,X_37),Y)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_37,least_upper_bound(least_upper_bound(X_36,X_37),Y)))]]) ).
cnf(refute_0_962,plain,
( least_upper_bound(X_37,least_upper_bound(least_upper_bound(X_36,X_37),Y)) != least_upper_bound(X_37,least_upper_bound(least_upper_bound(X_36,X_37),Y))
| least_upper_bound(least_upper_bound(X_36,X_37),Y) != least_upper_bound(X_36,least_upper_bound(X_37,Y))
| least_upper_bound(X_37,least_upper_bound(least_upper_bound(X_36,X_37),Y)) = least_upper_bound(X_37,least_upper_bound(X_36,least_upper_bound(X_37,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_37,least_upper_bound(least_upper_bound(X_36,X_37),Y)),least_upper_bound(X_37,least_upper_bound(least_upper_bound(X_36,X_37),Y))) ),[1,1],$fot(least_upper_bound(X_36,least_upper_bound(X_37,Y)))]]) ).
cnf(refute_0_963,plain,
( least_upper_bound(least_upper_bound(X_36,X_37),Y) != least_upper_bound(X_36,least_upper_bound(X_37,Y))
| least_upper_bound(X_37,least_upper_bound(least_upper_bound(X_36,X_37),Y)) = least_upper_bound(X_37,least_upper_bound(X_36,least_upper_bound(X_37,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_37,least_upper_bound(least_upper_bound(X_36,X_37),Y)),least_upper_bound(X_37,least_upper_bound(least_upper_bound(X_36,X_37),Y))) )],[refute_0_961,refute_0_962]) ).
cnf(refute_0_964,plain,
least_upper_bound(X_37,least_upper_bound(least_upper_bound(X_36,X_37),Y)) = least_upper_bound(X_37,least_upper_bound(X_36,least_upper_bound(X_37,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_36,X_37),Y),least_upper_bound(X_36,least_upper_bound(X_37,Y))) )],[refute_0_960,refute_0_963]) ).
cnf(refute_0_965,plain,
least_upper_bound(X,least_upper_bound(X_36,X_37)) = least_upper_bound(least_upper_bound(X_36,X_37),X),
inference(subst,[],[symmetry_of_lub:[bind(Y,$fot(least_upper_bound(X_36,X_37)))]]) ).
cnf(refute_0_966,plain,
least_upper_bound(X_36,least_upper_bound(X_37,X)) = least_upper_bound(least_upper_bound(X_36,X_37),X),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_36)),bind(Y,$fot(X_37)),bind(Z,$fot(X))]]) ).
cnf(refute_0_967,plain,
( least_upper_bound(X_36,least_upper_bound(X_37,X)) != least_upper_bound(least_upper_bound(X_36,X_37),X)
| least_upper_bound(least_upper_bound(X_36,X_37),X) = least_upper_bound(X_36,least_upper_bound(X_37,X)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(least_upper_bound(X_36,least_upper_bound(X_37,X)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X_36,X_37),X)))]]) ).
cnf(refute_0_968,plain,
least_upper_bound(least_upper_bound(X_36,X_37),X) = least_upper_bound(X_36,least_upper_bound(X_37,X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_36,least_upper_bound(X_37,X)),least_upper_bound(least_upper_bound(X_36,X_37),X)) )],[refute_0_966,refute_0_967]) ).
cnf(refute_0_969,plain,
( least_upper_bound(X,least_upper_bound(X_36,X_37)) != least_upper_bound(least_upper_bound(X_36,X_37),X)
| least_upper_bound(least_upper_bound(X_36,X_37),X) != least_upper_bound(X_36,least_upper_bound(X_37,X))
| least_upper_bound(X,least_upper_bound(X_36,X_37)) = least_upper_bound(X_36,least_upper_bound(X_37,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,least_upper_bound(X_36,X_37)),least_upper_bound(X_36,least_upper_bound(X_37,X))) ),[0],$fot(least_upper_bound(least_upper_bound(X_36,X_37),X))]]) ).
cnf(refute_0_970,plain,
( least_upper_bound(X,least_upper_bound(X_36,X_37)) != least_upper_bound(least_upper_bound(X_36,X_37),X)
| least_upper_bound(X,least_upper_bound(X_36,X_37)) = least_upper_bound(X_36,least_upper_bound(X_37,X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_36,X_37),X),least_upper_bound(X_36,least_upper_bound(X_37,X))) )],[refute_0_968,refute_0_969]) ).
cnf(refute_0_971,plain,
least_upper_bound(X,least_upper_bound(X_36,X_37)) = least_upper_bound(X_36,least_upper_bound(X_37,X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_36,X_37)),least_upper_bound(least_upper_bound(X_36,X_37),X)) )],[refute_0_965,refute_0_970]) ).
cnf(refute_0_972,plain,
( least_upper_bound(X,least_upper_bound(X_36,X_37)) != least_upper_bound(X_36,least_upper_bound(X_37,X))
| least_upper_bound(X_36,least_upper_bound(X_37,X)) = least_upper_bound(X,least_upper_bound(X_36,X_37)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(X_36,X_37)))),bind(Y0,$fot(least_upper_bound(X_36,least_upper_bound(X_37,X))))]]) ).
cnf(refute_0_973,plain,
least_upper_bound(X_36,least_upper_bound(X_37,X)) = least_upper_bound(X,least_upper_bound(X_36,X_37)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_36,X_37)),least_upper_bound(X_36,least_upper_bound(X_37,X))) )],[refute_0_971,refute_0_972]) ).
cnf(refute_0_974,plain,
least_upper_bound(least_upper_bound(X_36,X_37),least_upper_bound(Y,X_37)) = least_upper_bound(X_37,least_upper_bound(least_upper_bound(X_36,X_37),Y)),
inference(subst,[],[refute_0_973:[bind(X,$fot(X_37)),bind(X_36,$fot(least_upper_bound(X_36,X_37))),bind(X_37,$fot(Y))]]) ).
cnf(refute_0_975,plain,
( least_upper_bound(X_37,least_upper_bound(least_upper_bound(X_36,X_37),Y)) != least_upper_bound(X_37,least_upper_bound(X_36,least_upper_bound(X_37,Y)))
| least_upper_bound(least_upper_bound(X_36,X_37),least_upper_bound(Y,X_37)) != least_upper_bound(X_37,least_upper_bound(least_upper_bound(X_36,X_37),Y))
| least_upper_bound(least_upper_bound(X_36,X_37),least_upper_bound(Y,X_37)) = least_upper_bound(X_37,least_upper_bound(X_36,least_upper_bound(X_37,Y))) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_36,X_37),least_upper_bound(Y,X_37)))),bind(Y0,$fot(least_upper_bound(X_37,least_upper_bound(least_upper_bound(X_36,X_37),Y)))),bind(Z0,$fot(least_upper_bound(X_37,least_upper_bound(X_36,least_upper_bound(X_37,Y)))))]]) ).
cnf(refute_0_976,plain,
( least_upper_bound(X_37,least_upper_bound(least_upper_bound(X_36,X_37),Y)) != least_upper_bound(X_37,least_upper_bound(X_36,least_upper_bound(X_37,Y)))
| least_upper_bound(least_upper_bound(X_36,X_37),least_upper_bound(Y,X_37)) = least_upper_bound(X_37,least_upper_bound(X_36,least_upper_bound(X_37,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_36,X_37),least_upper_bound(Y,X_37)),least_upper_bound(X_37,least_upper_bound(least_upper_bound(X_36,X_37),Y))) )],[refute_0_974,refute_0_975]) ).
cnf(refute_0_977,plain,
least_upper_bound(least_upper_bound(X_36,X_37),least_upper_bound(Y,X_37)) = least_upper_bound(X_37,least_upper_bound(X_36,least_upper_bound(X_37,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_37,least_upper_bound(least_upper_bound(X_36,X_37),Y)),least_upper_bound(X_37,least_upper_bound(X_36,least_upper_bound(X_37,Y)))) )],[refute_0_964,refute_0_976]) ).
cnf(refute_0_978,plain,
( least_upper_bound(X_36,least_upper_bound(X_37,Y)) != least_upper_bound(least_upper_bound(X_36,X_37),least_upper_bound(Y,X_37))
| least_upper_bound(least_upper_bound(X_36,X_37),least_upper_bound(Y,X_37)) != least_upper_bound(X_37,least_upper_bound(X_36,least_upper_bound(X_37,Y)))
| least_upper_bound(X_36,least_upper_bound(X_37,Y)) = least_upper_bound(X_37,least_upper_bound(X_36,least_upper_bound(X_37,Y))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_36,least_upper_bound(X_37,Y)),least_upper_bound(X_37,least_upper_bound(X_36,least_upper_bound(X_37,Y)))) ),[0],$fot(least_upper_bound(least_upper_bound(X_36,X_37),least_upper_bound(Y,X_37)))]]) ).
cnf(refute_0_979,plain,
( least_upper_bound(X_36,least_upper_bound(X_37,Y)) != least_upper_bound(least_upper_bound(X_36,X_37),least_upper_bound(Y,X_37))
| least_upper_bound(X_36,least_upper_bound(X_37,Y)) = least_upper_bound(X_37,least_upper_bound(X_36,least_upper_bound(X_37,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_36,X_37),least_upper_bound(Y,X_37)),least_upper_bound(X_37,least_upper_bound(X_36,least_upper_bound(X_37,Y)))) )],[refute_0_977,refute_0_978]) ).
cnf(refute_0_980,plain,
least_upper_bound(X_36,least_upper_bound(X_37,Y)) = least_upper_bound(X_37,least_upper_bound(X_36,least_upper_bound(X_37,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_36,least_upper_bound(X_37,Y)),least_upper_bound(least_upper_bound(X_36,X_37),least_upper_bound(Y,X_37))) )],[refute_0_959,refute_0_979]) ).
cnf(refute_0_981,plain,
( least_upper_bound(X_36,least_upper_bound(X_37,Y)) != least_upper_bound(X_37,least_upper_bound(X_36,least_upper_bound(X_37,Y)))
| least_upper_bound(X_37,least_upper_bound(X_36,least_upper_bound(X_37,Y))) = least_upper_bound(X_36,least_upper_bound(X_37,Y)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(least_upper_bound(X_36,least_upper_bound(X_37,Y)))),bind(Y0,$fot(least_upper_bound(X_37,least_upper_bound(X_36,least_upper_bound(X_37,Y)))))]]) ).
cnf(refute_0_982,plain,
least_upper_bound(X_37,least_upper_bound(X_36,least_upper_bound(X_37,Y))) = least_upper_bound(X_36,least_upper_bound(X_37,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_36,least_upper_bound(X_37,Y)),least_upper_bound(X_37,least_upper_bound(X_36,least_upper_bound(X_37,Y)))) )],[refute_0_980,refute_0_981]) ).
cnf(refute_0_983,plain,
least_upper_bound(X_36,least_upper_bound(Y,least_upper_bound(X_36,X_38))) = least_upper_bound(Y,least_upper_bound(X_36,X_38)),
inference(subst,[],[refute_0_982:[bind(Y,$fot(X_38)),bind(X_36,$fot(Y)),bind(X_37,$fot(X_36))]]) ).
cnf(refute_0_984,plain,
least_upper_bound(least_upper_bound(Y,X_36),X_38) = least_upper_bound(Y,least_upper_bound(X_36,X_38)),
inference(subst,[],[refute_0_631:[bind(X,$fot(Y)),bind(Y,$fot(X_36)),bind(Z,$fot(X_38))]]) ).
cnf(refute_0_985,plain,
least_upper_bound(X_36,least_upper_bound(least_upper_bound(Y,X_36),X_38)) = least_upper_bound(X_36,least_upper_bound(least_upper_bound(Y,X_36),X_38)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_36,least_upper_bound(least_upper_bound(Y,X_36),X_38)))]]) ).
cnf(refute_0_986,plain,
( least_upper_bound(X_36,least_upper_bound(least_upper_bound(Y,X_36),X_38)) != least_upper_bound(X_36,least_upper_bound(least_upper_bound(Y,X_36),X_38))
| least_upper_bound(least_upper_bound(Y,X_36),X_38) != least_upper_bound(Y,least_upper_bound(X_36,X_38))
| least_upper_bound(X_36,least_upper_bound(least_upper_bound(Y,X_36),X_38)) = least_upper_bound(X_36,least_upper_bound(Y,least_upper_bound(X_36,X_38))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_36,least_upper_bound(least_upper_bound(Y,X_36),X_38)),least_upper_bound(X_36,least_upper_bound(least_upper_bound(Y,X_36),X_38))) ),[1,1],$fot(least_upper_bound(Y,least_upper_bound(X_36,X_38)))]]) ).
cnf(refute_0_987,plain,
( least_upper_bound(least_upper_bound(Y,X_36),X_38) != least_upper_bound(Y,least_upper_bound(X_36,X_38))
| least_upper_bound(X_36,least_upper_bound(least_upper_bound(Y,X_36),X_38)) = least_upper_bound(X_36,least_upper_bound(Y,least_upper_bound(X_36,X_38))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_36,least_upper_bound(least_upper_bound(Y,X_36),X_38)),least_upper_bound(X_36,least_upper_bound(least_upper_bound(Y,X_36),X_38))) )],[refute_0_985,refute_0_986]) ).
cnf(refute_0_988,plain,
least_upper_bound(X_36,least_upper_bound(least_upper_bound(Y,X_36),X_38)) = least_upper_bound(X_36,least_upper_bound(Y,least_upper_bound(X_36,X_38))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_36),X_38),least_upper_bound(Y,least_upper_bound(X_36,X_38))) )],[refute_0_984,refute_0_987]) ).
cnf(refute_0_989,plain,
( least_upper_bound(X_36,least_upper_bound(Y,least_upper_bound(X_36,X_38))) != least_upper_bound(Y,least_upper_bound(X_36,X_38))
| least_upper_bound(X_36,least_upper_bound(least_upper_bound(Y,X_36),X_38)) != least_upper_bound(X_36,least_upper_bound(Y,least_upper_bound(X_36,X_38)))
| least_upper_bound(X_36,least_upper_bound(least_upper_bound(Y,X_36),X_38)) = least_upper_bound(Y,least_upper_bound(X_36,X_38)) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(least_upper_bound(X_36,least_upper_bound(least_upper_bound(Y,X_36),X_38)))),bind(Y0,$fot(least_upper_bound(X_36,least_upper_bound(Y,least_upper_bound(X_36,X_38))))),bind(Z0,$fot(least_upper_bound(Y,least_upper_bound(X_36,X_38))))]]) ).
cnf(refute_0_990,plain,
( least_upper_bound(X_36,least_upper_bound(Y,least_upper_bound(X_36,X_38))) != least_upper_bound(Y,least_upper_bound(X_36,X_38))
| least_upper_bound(X_36,least_upper_bound(least_upper_bound(Y,X_36),X_38)) = least_upper_bound(Y,least_upper_bound(X_36,X_38)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_36,least_upper_bound(least_upper_bound(Y,X_36),X_38)),least_upper_bound(X_36,least_upper_bound(Y,least_upper_bound(X_36,X_38)))) )],[refute_0_988,refute_0_989]) ).
cnf(refute_0_991,plain,
least_upper_bound(X_36,least_upper_bound(least_upper_bound(Y,X_36),X_38)) = least_upper_bound(Y,least_upper_bound(X_36,X_38)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_36,least_upper_bound(Y,least_upper_bound(X_36,X_38))),least_upper_bound(Y,least_upper_bound(X_36,X_38))) )],[refute_0_983,refute_0_990]) ).
cnf(refute_0_992,plain,
( least_upper_bound(X_36,least_upper_bound(least_upper_bound(Y,X_36),X_38)) != least_upper_bound(Y,least_upper_bound(X_36,X_38))
| least_upper_bound(X_36,least_upper_bound(least_upper_bound(Y,X_36),X_38)) != least_upper_bound(least_upper_bound(X_36,Y),X_38)
| least_upper_bound(Y,least_upper_bound(X_36,X_38)) = least_upper_bound(least_upper_bound(X_36,Y),X_38) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_36,least_upper_bound(least_upper_bound(Y,X_36),X_38)),least_upper_bound(least_upper_bound(X_36,Y),X_38)) ),[0],$fot(least_upper_bound(Y,least_upper_bound(X_36,X_38)))]]) ).
cnf(refute_0_993,plain,
( least_upper_bound(X_36,least_upper_bound(least_upper_bound(Y,X_36),X_38)) != least_upper_bound(least_upper_bound(X_36,Y),X_38)
| least_upper_bound(Y,least_upper_bound(X_36,X_38)) = least_upper_bound(least_upper_bound(X_36,Y),X_38) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_36,least_upper_bound(least_upper_bound(Y,X_36),X_38)),least_upper_bound(Y,least_upper_bound(X_36,X_38))) )],[refute_0_991,refute_0_992]) ).
cnf(refute_0_994,plain,
least_upper_bound(least_upper_bound(X_36,Y),X_38) = least_upper_bound(X_36,least_upper_bound(Y,X_38)),
inference(subst,[],[refute_0_631:[bind(X,$fot(X_36)),bind(Z,$fot(X_38))]]) ).
cnf(refute_0_995,plain,
( least_upper_bound(Y,least_upper_bound(X_36,X_38)) != least_upper_bound(least_upper_bound(X_36,Y),X_38)
| least_upper_bound(least_upper_bound(X_36,Y),X_38) != least_upper_bound(X_36,least_upper_bound(Y,X_38))
| least_upper_bound(Y,least_upper_bound(X_36,X_38)) = least_upper_bound(X_36,least_upper_bound(Y,X_38)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(Y,least_upper_bound(X_36,X_38)),least_upper_bound(X_36,least_upper_bound(Y,X_38))) ),[0],$fot(least_upper_bound(least_upper_bound(X_36,Y),X_38))]]) ).
cnf(refute_0_996,plain,
( least_upper_bound(Y,least_upper_bound(X_36,X_38)) != least_upper_bound(least_upper_bound(X_36,Y),X_38)
| least_upper_bound(Y,least_upper_bound(X_36,X_38)) = least_upper_bound(X_36,least_upper_bound(Y,X_38)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_36,Y),X_38),least_upper_bound(X_36,least_upper_bound(Y,X_38))) )],[refute_0_994,refute_0_995]) ).
cnf(refute_0_997,plain,
( least_upper_bound(X_36,least_upper_bound(least_upper_bound(Y,X_36),X_38)) != least_upper_bound(least_upper_bound(X_36,Y),X_38)
| least_upper_bound(Y,least_upper_bound(X_36,X_38)) = least_upper_bound(X_36,least_upper_bound(Y,X_38)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_36,X_38)),least_upper_bound(least_upper_bound(X_36,Y),X_38)) )],[refute_0_993,refute_0_996]) ).
cnf(refute_0_998,plain,
least_upper_bound(Y,least_upper_bound(X_36,X_38)) = least_upper_bound(X_36,least_upper_bound(Y,X_38)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_36,least_upper_bound(least_upper_bound(Y,X_36),X_38)),least_upper_bound(least_upper_bound(X_36,Y),X_38)) )],[refute_0_954,refute_0_997]) ).
cnf(refute_0_999,plain,
( least_upper_bound(Y,least_upper_bound(X_36,X_38)) != least_upper_bound(X_36,least_upper_bound(Y,X_38))
| least_upper_bound(X_36,least_upper_bound(Y,X_38)) = least_upper_bound(Y,least_upper_bound(X_36,X_38)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(least_upper_bound(Y,least_upper_bound(X_36,X_38)))),bind(Y0,$fot(least_upper_bound(X_36,least_upper_bound(Y,X_38))))]]) ).
cnf(refute_0_1000,plain,
least_upper_bound(X_36,least_upper_bound(Y,X_38)) = least_upper_bound(Y,least_upper_bound(X_36,X_38)),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_36,X_38)),least_upper_bound(X_36,least_upper_bound(Y,X_38))) )],[refute_0_998,refute_0_999]) ).
cnf(refute_0_1001,plain,
least_upper_bound(multiply(X_77,least_upper_bound(identity,X_63)),least_upper_bound(identity,inverse(X_63))) = least_upper_bound(identity,least_upper_bound(multiply(X_77,least_upper_bound(identity,X_63)),inverse(X_63))),
inference(subst,[],[refute_0_1000:[bind(Y,$fot(identity)),bind(X_36,$fot(multiply(X_77,least_upper_bound(identity,X_63)))),bind(X_38,$fot(inverse(X_63)))]]) ).
cnf(refute_0_1002,plain,
( least_upper_bound(multiply(X_77,least_upper_bound(identity,X_63)),least_upper_bound(identity,inverse(X_63))) != least_upper_bound(identity,least_upper_bound(multiply(X_77,least_upper_bound(identity,X_63)),inverse(X_63)))
| least_upper_bound(identity,least_upper_bound(multiply(X_77,least_upper_bound(identity,X_63)),inverse(X_63))) != least_upper_bound(identity,least_upper_bound(inverse(X_63),multiply(X_77,least_upper_bound(identity,X_63))))
| least_upper_bound(multiply(X_77,least_upper_bound(identity,X_63)),least_upper_bound(identity,inverse(X_63))) = least_upper_bound(identity,least_upper_bound(inverse(X_63),multiply(X_77,least_upper_bound(identity,X_63)))) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(least_upper_bound(multiply(X_77,least_upper_bound(identity,X_63)),least_upper_bound(identity,inverse(X_63))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(multiply(X_77,least_upper_bound(identity,X_63)),inverse(X_63))))),bind(Z0,$fot(least_upper_bound(identity,least_upper_bound(inverse(X_63),multiply(X_77,least_upper_bound(identity,X_63))))))]]) ).
cnf(refute_0_1003,plain,
( least_upper_bound(identity,least_upper_bound(multiply(X_77,least_upper_bound(identity,X_63)),inverse(X_63))) != least_upper_bound(identity,least_upper_bound(inverse(X_63),multiply(X_77,least_upper_bound(identity,X_63))))
| least_upper_bound(multiply(X_77,least_upper_bound(identity,X_63)),least_upper_bound(identity,inverse(X_63))) = least_upper_bound(identity,least_upper_bound(inverse(X_63),multiply(X_77,least_upper_bound(identity,X_63)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_77,least_upper_bound(identity,X_63)),least_upper_bound(identity,inverse(X_63))),least_upper_bound(identity,least_upper_bound(multiply(X_77,least_upper_bound(identity,X_63)),inverse(X_63)))) )],[refute_0_1001,refute_0_1002]) ).
cnf(refute_0_1004,plain,
least_upper_bound(multiply(X_77,least_upper_bound(identity,X_63)),least_upper_bound(identity,inverse(X_63))) = least_upper_bound(identity,least_upper_bound(inverse(X_63),multiply(X_77,least_upper_bound(identity,X_63)))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(X_77,least_upper_bound(identity,X_63)),inverse(X_63))),least_upper_bound(identity,least_upper_bound(inverse(X_63),multiply(X_77,least_upper_bound(identity,X_63))))) )],[refute_0_949,refute_0_1003]) ).
cnf(refute_0_1005,plain,
( multiply(least_upper_bound(X_77,inverse(X_63)),least_upper_bound(identity,X_63)) != least_upper_bound(multiply(X_77,least_upper_bound(identity,X_63)),least_upper_bound(identity,inverse(X_63)))
| least_upper_bound(multiply(X_77,least_upper_bound(identity,X_63)),least_upper_bound(identity,inverse(X_63))) != least_upper_bound(identity,least_upper_bound(inverse(X_63),multiply(X_77,least_upper_bound(identity,X_63))))
| multiply(least_upper_bound(X_77,inverse(X_63)),least_upper_bound(identity,X_63)) = least_upper_bound(identity,least_upper_bound(inverse(X_63),multiply(X_77,least_upper_bound(identity,X_63)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_77,inverse(X_63)),least_upper_bound(identity,X_63)),least_upper_bound(identity,least_upper_bound(inverse(X_63),multiply(X_77,least_upper_bound(identity,X_63))))) ),[0],$fot(least_upper_bound(multiply(X_77,least_upper_bound(identity,X_63)),least_upper_bound(identity,inverse(X_63))))]]) ).
cnf(refute_0_1006,plain,
( multiply(least_upper_bound(X_77,inverse(X_63)),least_upper_bound(identity,X_63)) != least_upper_bound(multiply(X_77,least_upper_bound(identity,X_63)),least_upper_bound(identity,inverse(X_63)))
| multiply(least_upper_bound(X_77,inverse(X_63)),least_upper_bound(identity,X_63)) = least_upper_bound(identity,least_upper_bound(inverse(X_63),multiply(X_77,least_upper_bound(identity,X_63)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_77,least_upper_bound(identity,X_63)),least_upper_bound(identity,inverse(X_63))),least_upper_bound(identity,least_upper_bound(inverse(X_63),multiply(X_77,least_upper_bound(identity,X_63))))) )],[refute_0_1004,refute_0_1005]) ).
cnf(refute_0_1007,plain,
multiply(least_upper_bound(X_77,inverse(X_63)),least_upper_bound(identity,X_63)) = least_upper_bound(identity,least_upper_bound(inverse(X_63),multiply(X_77,least_upper_bound(identity,X_63)))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_77,inverse(X_63)),least_upper_bound(identity,X_63)),least_upper_bound(multiply(X_77,least_upper_bound(identity,X_63)),least_upper_bound(identity,inverse(X_63)))) )],[refute_0_935,refute_0_1006]) ).
cnf(refute_0_1008,plain,
multiply(least_upper_bound(X_221,inverse(inverse(least_upper_bound(identity,X_18)))),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))) = least_upper_bound(identity,least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))))),
inference(subst,[],[refute_0_1007:[bind(X_63,$fot(inverse(least_upper_bound(identity,X_18)))),bind(X_77,$fot(X_221))]]) ).
cnf(refute_0_1009,plain,
( multiply(least_upper_bound(X_221,inverse(inverse(least_upper_bound(identity,X_18)))),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))) != least_upper_bound(identity,least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,least_upper_bound(identity,inverse(least_upper_bound(identity,X_18))))))
| least_upper_bound(identity,inverse(least_upper_bound(identity,X_18))) != identity
| multiply(least_upper_bound(X_221,inverse(inverse(least_upper_bound(identity,X_18)))),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))) = least_upper_bound(identity,least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_221,inverse(inverse(least_upper_bound(identity,X_18)))),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))),least_upper_bound(identity,least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,least_upper_bound(identity,inverse(least_upper_bound(identity,X_18))))))) ),[1,1,1,1],$fot(identity)]]) ).
cnf(refute_0_1010,plain,
( multiply(least_upper_bound(X_221,inverse(inverse(least_upper_bound(identity,X_18)))),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))) != least_upper_bound(identity,least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,least_upper_bound(identity,inverse(least_upper_bound(identity,X_18))))))
| multiply(least_upper_bound(X_221,inverse(inverse(least_upper_bound(identity,X_18)))),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))) = least_upper_bound(identity,least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(least_upper_bound(identity,X_18))),identity) )],[refute_0_850,refute_0_1009]) ).
cnf(refute_0_1011,plain,
multiply(least_upper_bound(X_221,inverse(inverse(least_upper_bound(identity,X_18)))),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))) = least_upper_bound(identity,least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_221,inverse(inverse(least_upper_bound(identity,X_18)))),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))),least_upper_bound(identity,least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,least_upper_bound(identity,inverse(least_upper_bound(identity,X_18))))))) )],[refute_0_1008,refute_0_1010]) ).
cnf(refute_0_1012,plain,
multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),identity) = least_upper_bound(X_221,least_upper_bound(identity,X_18)),
inference(subst,[],[refute_0_564:[bind(X,$fot(least_upper_bound(X_221,least_upper_bound(identity,X_18))))]]) ).
cnf(refute_0_1013,plain,
multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))) = multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))))]]) ).
cnf(refute_0_1014,plain,
( multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))) != multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18))))
| least_upper_bound(identity,inverse(least_upper_bound(identity,X_18))) != identity
| multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))) = multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))),multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_1015,plain,
( least_upper_bound(identity,inverse(least_upper_bound(identity,X_18))) != identity
| multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))) = multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),identity) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))),multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18))))) )],[refute_0_1013,refute_0_1014]) ).
cnf(refute_0_1016,plain,
multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))) = multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),identity),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(least_upper_bound(identity,X_18))),identity) )],[refute_0_850,refute_0_1015]) ).
cnf(refute_0_1017,plain,
inverse(inverse(least_upper_bound(identity,X_18))) = least_upper_bound(identity,X_18),
inference(subst,[],[p19_2:[bind(X,$fot(least_upper_bound(identity,X_18)))]]) ).
cnf(refute_0_1018,plain,
least_upper_bound(X_221,inverse(inverse(least_upper_bound(identity,X_18)))) = least_upper_bound(X_221,inverse(inverse(least_upper_bound(identity,X_18)))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_221,inverse(inverse(least_upper_bound(identity,X_18)))))]]) ).
cnf(refute_0_1019,plain,
( inverse(inverse(least_upper_bound(identity,X_18))) != least_upper_bound(identity,X_18)
| least_upper_bound(X_221,inverse(inverse(least_upper_bound(identity,X_18)))) != least_upper_bound(X_221,inverse(inverse(least_upper_bound(identity,X_18))))
| least_upper_bound(X_221,inverse(inverse(least_upper_bound(identity,X_18)))) = least_upper_bound(X_221,least_upper_bound(identity,X_18)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_221,inverse(inverse(least_upper_bound(identity,X_18)))),least_upper_bound(X_221,inverse(inverse(least_upper_bound(identity,X_18))))) ),[1,1],$fot(least_upper_bound(identity,X_18))]]) ).
cnf(refute_0_1020,plain,
( inverse(inverse(least_upper_bound(identity,X_18))) != least_upper_bound(identity,X_18)
| least_upper_bound(X_221,inverse(inverse(least_upper_bound(identity,X_18)))) = least_upper_bound(X_221,least_upper_bound(identity,X_18)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_221,inverse(inverse(least_upper_bound(identity,X_18)))),least_upper_bound(X_221,inverse(inverse(least_upper_bound(identity,X_18))))) )],[refute_0_1018,refute_0_1019]) ).
cnf(refute_0_1021,plain,
least_upper_bound(X_221,inverse(inverse(least_upper_bound(identity,X_18)))) = least_upper_bound(X_221,least_upper_bound(identity,X_18)),
inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(identity,X_18))),least_upper_bound(identity,X_18)) )],[refute_0_1017,refute_0_1020]) ).
cnf(refute_0_1022,plain,
multiply(least_upper_bound(X_221,inverse(inverse(least_upper_bound(identity,X_18)))),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))) = multiply(least_upper_bound(X_221,inverse(inverse(least_upper_bound(identity,X_18)))),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(X_221,inverse(inverse(least_upper_bound(identity,X_18)))),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))))]]) ).
cnf(refute_0_1023,plain,
( multiply(least_upper_bound(X_221,inverse(inverse(least_upper_bound(identity,X_18)))),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))) != multiply(least_upper_bound(X_221,inverse(inverse(least_upper_bound(identity,X_18)))),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18))))
| least_upper_bound(X_221,inverse(inverse(least_upper_bound(identity,X_18)))) != least_upper_bound(X_221,least_upper_bound(identity,X_18))
| multiply(least_upper_bound(X_221,inverse(inverse(least_upper_bound(identity,X_18)))),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))) = multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_221,inverse(inverse(least_upper_bound(identity,X_18)))),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))),multiply(least_upper_bound(X_221,inverse(inverse(least_upper_bound(identity,X_18)))),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18))))) ),[1,0],$fot(least_upper_bound(X_221,least_upper_bound(identity,X_18)))]]) ).
cnf(refute_0_1024,plain,
( least_upper_bound(X_221,inverse(inverse(least_upper_bound(identity,X_18)))) != least_upper_bound(X_221,least_upper_bound(identity,X_18))
| multiply(least_upper_bound(X_221,inverse(inverse(least_upper_bound(identity,X_18)))),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))) = multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_221,inverse(inverse(least_upper_bound(identity,X_18)))),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))),multiply(least_upper_bound(X_221,inverse(inverse(least_upper_bound(identity,X_18)))),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18))))) )],[refute_0_1022,refute_0_1023]) ).
cnf(refute_0_1025,plain,
multiply(least_upper_bound(X_221,inverse(inverse(least_upper_bound(identity,X_18)))),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))) = multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_221,inverse(inverse(least_upper_bound(identity,X_18)))),least_upper_bound(X_221,least_upper_bound(identity,X_18))) )],[refute_0_1021,refute_0_1024]) ).
cnf(refute_0_1026,plain,
( multiply(least_upper_bound(X_221,inverse(inverse(least_upper_bound(identity,X_18)))),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))) != multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18))))
| multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))) != multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),identity)
| multiply(least_upper_bound(X_221,inverse(inverse(least_upper_bound(identity,X_18)))),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))) = multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),identity) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(multiply(least_upper_bound(X_221,inverse(inverse(least_upper_bound(identity,X_18)))),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))))),bind(Y0,$fot(multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))))),bind(Z0,$fot(multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),identity)))]]) ).
cnf(refute_0_1027,plain,
( multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))) != multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),identity)
| multiply(least_upper_bound(X_221,inverse(inverse(least_upper_bound(identity,X_18)))),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))) = multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),identity) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_221,inverse(inverse(least_upper_bound(identity,X_18)))),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))),multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18))))) )],[refute_0_1025,refute_0_1026]) ).
cnf(refute_0_1028,plain,
multiply(least_upper_bound(X_221,inverse(inverse(least_upper_bound(identity,X_18)))),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))) = multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),identity),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))),multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),identity)) )],[refute_0_1016,refute_0_1027]) ).
cnf(refute_0_1029,plain,
( multiply(least_upper_bound(X_221,inverse(inverse(least_upper_bound(identity,X_18)))),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))) != multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),identity)
| multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),identity) != least_upper_bound(X_221,least_upper_bound(identity,X_18))
| multiply(least_upper_bound(X_221,inverse(inverse(least_upper_bound(identity,X_18)))),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))) = least_upper_bound(X_221,least_upper_bound(identity,X_18)) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(multiply(least_upper_bound(X_221,inverse(inverse(least_upper_bound(identity,X_18)))),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))))),bind(Y0,$fot(multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),identity))),bind(Z0,$fot(least_upper_bound(X_221,least_upper_bound(identity,X_18))))]]) ).
cnf(refute_0_1030,plain,
( multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),identity) != least_upper_bound(X_221,least_upper_bound(identity,X_18))
| multiply(least_upper_bound(X_221,inverse(inverse(least_upper_bound(identity,X_18)))),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))) = least_upper_bound(X_221,least_upper_bound(identity,X_18)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_221,inverse(inverse(least_upper_bound(identity,X_18)))),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))),multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),identity)) )],[refute_0_1028,refute_0_1029]) ).
cnf(refute_0_1031,plain,
multiply(least_upper_bound(X_221,inverse(inverse(least_upper_bound(identity,X_18)))),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))) = least_upper_bound(X_221,least_upper_bound(identity,X_18)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),identity),least_upper_bound(X_221,least_upper_bound(identity,X_18))) )],[refute_0_1012,refute_0_1030]) ).
cnf(refute_0_1032,plain,
( multiply(least_upper_bound(X_221,inverse(inverse(least_upper_bound(identity,X_18)))),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))) != least_upper_bound(X_221,least_upper_bound(identity,X_18))
| multiply(least_upper_bound(X_221,inverse(inverse(least_upper_bound(identity,X_18)))),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))) != least_upper_bound(identity,least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity)))
| least_upper_bound(X_221,least_upper_bound(identity,X_18)) = least_upper_bound(identity,least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_221,inverse(inverse(least_upper_bound(identity,X_18)))),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))),least_upper_bound(identity,least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity)))) ),[0],$fot(least_upper_bound(X_221,least_upper_bound(identity,X_18)))]]) ).
cnf(refute_0_1033,plain,
( multiply(least_upper_bound(X_221,inverse(inverse(least_upper_bound(identity,X_18)))),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))) != least_upper_bound(identity,least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity)))
| least_upper_bound(X_221,least_upper_bound(identity,X_18)) = least_upper_bound(identity,least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_221,inverse(inverse(least_upper_bound(identity,X_18)))),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))),least_upper_bound(X_221,least_upper_bound(identity,X_18))) )],[refute_0_1031,refute_0_1032]) ).
cnf(refute_0_1034,plain,
least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_18,X_221))) = least_upper_bound(identity,least_upper_bound(X_18,X_221)),
inference(subst,[],[refute_0_642:[bind(X_18,$fot(least_upper_bound(X_18,X_221))),bind(X_19,$fot(identity))]]) ).
cnf(refute_0_1035,plain,
least_upper_bound(least_upper_bound(identity,X_18),X_221) = least_upper_bound(identity,least_upper_bound(X_18,X_221)),
inference(subst,[],[refute_0_631:[bind(X,$fot(identity)),bind(Y,$fot(X_18)),bind(Z,$fot(X_221))]]) ).
cnf(refute_0_1036,plain,
multiply(X_221,identity) = X_221,
inference(subst,[],[refute_0_564:[bind(X,$fot(X_221))]]) ).
cnf(refute_0_1037,plain,
least_upper_bound(least_upper_bound(identity,X_18),multiply(X_221,identity)) = least_upper_bound(least_upper_bound(identity,X_18),multiply(X_221,identity)),
introduced(tautology,[refl,[$fot(least_upper_bound(least_upper_bound(identity,X_18),multiply(X_221,identity)))]]) ).
cnf(refute_0_1038,plain,
( multiply(X_221,identity) != X_221
| least_upper_bound(least_upper_bound(identity,X_18),multiply(X_221,identity)) != least_upper_bound(least_upper_bound(identity,X_18),multiply(X_221,identity))
| least_upper_bound(least_upper_bound(identity,X_18),multiply(X_221,identity)) = least_upper_bound(least_upper_bound(identity,X_18),X_221) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(identity,X_18),multiply(X_221,identity)),least_upper_bound(least_upper_bound(identity,X_18),multiply(X_221,identity))) ),[1,1],$fot(X_221)]]) ).
cnf(refute_0_1039,plain,
( multiply(X_221,identity) != X_221
| least_upper_bound(least_upper_bound(identity,X_18),multiply(X_221,identity)) = least_upper_bound(least_upper_bound(identity,X_18),X_221) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(identity,X_18),multiply(X_221,identity)),least_upper_bound(least_upper_bound(identity,X_18),multiply(X_221,identity))) )],[refute_0_1037,refute_0_1038]) ).
cnf(refute_0_1040,plain,
least_upper_bound(least_upper_bound(identity,X_18),multiply(X_221,identity)) = least_upper_bound(least_upper_bound(identity,X_18),X_221),
inference(resolve,[$cnf( $equal(multiply(X_221,identity),X_221) )],[refute_0_1036,refute_0_1039]) ).
cnf(refute_0_1041,plain,
least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity)) = least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity)),
introduced(tautology,[refl,[$fot(least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity)))]]) ).
cnf(refute_0_1042,plain,
( inverse(inverse(least_upper_bound(identity,X_18))) != least_upper_bound(identity,X_18)
| least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity)) != least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity))
| least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity)) = least_upper_bound(least_upper_bound(identity,X_18),multiply(X_221,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity)),least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity))) ),[1,0],$fot(least_upper_bound(identity,X_18))]]) ).
cnf(refute_0_1043,plain,
( inverse(inverse(least_upper_bound(identity,X_18))) != least_upper_bound(identity,X_18)
| least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity)) = least_upper_bound(least_upper_bound(identity,X_18),multiply(X_221,identity)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity)),least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity))) )],[refute_0_1041,refute_0_1042]) ).
cnf(refute_0_1044,plain,
least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity)) = least_upper_bound(least_upper_bound(identity,X_18),multiply(X_221,identity)),
inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(identity,X_18))),least_upper_bound(identity,X_18)) )],[refute_0_1017,refute_0_1043]) ).
cnf(refute_0_1045,plain,
( least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity)) != least_upper_bound(least_upper_bound(identity,X_18),multiply(X_221,identity))
| least_upper_bound(least_upper_bound(identity,X_18),multiply(X_221,identity)) != least_upper_bound(least_upper_bound(identity,X_18),X_221)
| least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity)) = least_upper_bound(least_upper_bound(identity,X_18),X_221) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(identity,X_18),multiply(X_221,identity)))),bind(Z0,$fot(least_upper_bound(least_upper_bound(identity,X_18),X_221)))]]) ).
cnf(refute_0_1046,plain,
( least_upper_bound(least_upper_bound(identity,X_18),multiply(X_221,identity)) != least_upper_bound(least_upper_bound(identity,X_18),X_221)
| least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity)) = least_upper_bound(least_upper_bound(identity,X_18),X_221) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity)),least_upper_bound(least_upper_bound(identity,X_18),multiply(X_221,identity))) )],[refute_0_1044,refute_0_1045]) ).
cnf(refute_0_1047,plain,
least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity)) = least_upper_bound(least_upper_bound(identity,X_18),X_221),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(identity,X_18),multiply(X_221,identity)),least_upper_bound(least_upper_bound(identity,X_18),X_221)) )],[refute_0_1040,refute_0_1046]) ).
cnf(refute_0_1048,plain,
( least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity)) != least_upper_bound(least_upper_bound(identity,X_18),X_221)
| least_upper_bound(least_upper_bound(identity,X_18),X_221) != least_upper_bound(identity,least_upper_bound(X_18,X_221))
| least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity)) = least_upper_bound(identity,least_upper_bound(X_18,X_221)) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(identity,X_18),X_221))),bind(Z0,$fot(least_upper_bound(identity,least_upper_bound(X_18,X_221))))]]) ).
cnf(refute_0_1049,plain,
( least_upper_bound(least_upper_bound(identity,X_18),X_221) != least_upper_bound(identity,least_upper_bound(X_18,X_221))
| least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity)) = least_upper_bound(identity,least_upper_bound(X_18,X_221)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity)),least_upper_bound(least_upper_bound(identity,X_18),X_221)) )],[refute_0_1047,refute_0_1048]) ).
cnf(refute_0_1050,plain,
least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity)) = least_upper_bound(identity,least_upper_bound(X_18,X_221)),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(identity,X_18),X_221),least_upper_bound(identity,least_upper_bound(X_18,X_221))) )],[refute_0_1035,refute_0_1049]) ).
cnf(refute_0_1051,plain,
least_upper_bound(identity,least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity))) = least_upper_bound(identity,least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity))))]]) ).
cnf(refute_0_1052,plain,
( least_upper_bound(identity,least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity))) != least_upper_bound(identity,least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity)))
| least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity)) != least_upper_bound(identity,least_upper_bound(X_18,X_221))
| least_upper_bound(identity,least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity))) = least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_18,X_221))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity))),least_upper_bound(identity,least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity)))) ),[1,1],$fot(least_upper_bound(identity,least_upper_bound(X_18,X_221)))]]) ).
cnf(refute_0_1053,plain,
( least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity)) != least_upper_bound(identity,least_upper_bound(X_18,X_221))
| least_upper_bound(identity,least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity))) = least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_18,X_221))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity))),least_upper_bound(identity,least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity)))) )],[refute_0_1051,refute_0_1052]) ).
cnf(refute_0_1054,plain,
least_upper_bound(identity,least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity))) = least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_18,X_221))),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity)),least_upper_bound(identity,least_upper_bound(X_18,X_221))) )],[refute_0_1050,refute_0_1053]) ).
cnf(refute_0_1055,plain,
( least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_18,X_221))) != least_upper_bound(identity,least_upper_bound(X_18,X_221))
| least_upper_bound(identity,least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity))) != least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_18,X_221)))
| least_upper_bound(identity,least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity))) = least_upper_bound(identity,least_upper_bound(X_18,X_221)) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_18,X_221))))),bind(Z0,$fot(least_upper_bound(identity,least_upper_bound(X_18,X_221))))]]) ).
cnf(refute_0_1056,plain,
( least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_18,X_221))) != least_upper_bound(identity,least_upper_bound(X_18,X_221))
| least_upper_bound(identity,least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity))) = least_upper_bound(identity,least_upper_bound(X_18,X_221)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_18,X_221)))) )],[refute_0_1054,refute_0_1055]) ).
cnf(refute_0_1057,plain,
least_upper_bound(identity,least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity))) = least_upper_bound(identity,least_upper_bound(X_18,X_221)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_18,X_221))),least_upper_bound(identity,least_upper_bound(X_18,X_221))) )],[refute_0_1034,refute_0_1056]) ).
cnf(refute_0_1058,plain,
( least_upper_bound(X_221,least_upper_bound(identity,X_18)) != least_upper_bound(identity,least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity)))
| least_upper_bound(identity,least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity))) != least_upper_bound(identity,least_upper_bound(X_18,X_221))
| least_upper_bound(X_221,least_upper_bound(identity,X_18)) = least_upper_bound(identity,least_upper_bound(X_18,X_221)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_221,least_upper_bound(identity,X_18)),least_upper_bound(identity,least_upper_bound(X_18,X_221))) ),[0],$fot(least_upper_bound(identity,least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity))))]]) ).
cnf(refute_0_1059,plain,
( least_upper_bound(X_221,least_upper_bound(identity,X_18)) != least_upper_bound(identity,least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity)))
| least_upper_bound(X_221,least_upper_bound(identity,X_18)) = least_upper_bound(identity,least_upper_bound(X_18,X_221)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity))),least_upper_bound(identity,least_upper_bound(X_18,X_221))) )],[refute_0_1057,refute_0_1058]) ).
cnf(refute_0_1060,plain,
( multiply(least_upper_bound(X_221,inverse(inverse(least_upper_bound(identity,X_18)))),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))) != least_upper_bound(identity,least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity)))
| least_upper_bound(X_221,least_upper_bound(identity,X_18)) = least_upper_bound(identity,least_upper_bound(X_18,X_221)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_221,least_upper_bound(identity,X_18)),least_upper_bound(identity,least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity)))) )],[refute_0_1033,refute_0_1059]) ).
cnf(refute_0_1061,plain,
least_upper_bound(X_221,least_upper_bound(identity,X_18)) = least_upper_bound(identity,least_upper_bound(X_18,X_221)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_221,inverse(inverse(least_upper_bound(identity,X_18)))),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))),least_upper_bound(identity,least_upper_bound(inverse(inverse(least_upper_bound(identity,X_18))),multiply(X_221,identity)))) )],[refute_0_1011,refute_0_1060]) ).
cnf(refute_0_1062,plain,
( least_upper_bound(X_221,least_upper_bound(identity,X_18)) != least_upper_bound(identity,least_upper_bound(X_18,X_221))
| least_upper_bound(identity,least_upper_bound(X_18,X_221)) = least_upper_bound(X_221,least_upper_bound(identity,X_18)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(least_upper_bound(X_221,least_upper_bound(identity,X_18)))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(X_18,X_221))))]]) ).
cnf(refute_0_1063,plain,
least_upper_bound(identity,least_upper_bound(X_18,X_221)) = least_upper_bound(X_221,least_upper_bound(identity,X_18)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_221,least_upper_bound(identity,X_18)),least_upper_bound(identity,least_upper_bound(X_18,X_221))) )],[refute_0_1061,refute_0_1062]) ).
cnf(refute_0_1064,plain,
( multiply(least_upper_bound(identity,least_upper_bound(X_18,X_221)),inverse(identity)) != least_upper_bound(identity,multiply(least_upper_bound(X_18,X_221),inverse(identity)))
| least_upper_bound(identity,least_upper_bound(X_18,X_221)) != least_upper_bound(X_221,least_upper_bound(identity,X_18))
| multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),inverse(identity)) = least_upper_bound(identity,multiply(least_upper_bound(X_18,X_221),inverse(identity))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(X_18,X_221)),inverse(identity)),least_upper_bound(identity,multiply(least_upper_bound(X_18,X_221),inverse(identity)))) ),[0,0],$fot(least_upper_bound(X_221,least_upper_bound(identity,X_18)))]]) ).
cnf(refute_0_1065,plain,
( multiply(least_upper_bound(identity,least_upper_bound(X_18,X_221)),inverse(identity)) != least_upper_bound(identity,multiply(least_upper_bound(X_18,X_221),inverse(identity)))
| multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),inverse(identity)) = least_upper_bound(identity,multiply(least_upper_bound(X_18,X_221),inverse(identity))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_18,X_221)),least_upper_bound(X_221,least_upper_bound(identity,X_18))) )],[refute_0_1063,refute_0_1064]) ).
cnf(refute_0_1066,plain,
multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),inverse(identity)) = least_upper_bound(identity,multiply(least_upper_bound(X_18,X_221),inverse(identity))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(X_18,X_221)),inverse(identity)),least_upper_bound(identity,multiply(least_upper_bound(X_18,X_221),inverse(identity)))) )],[refute_0_931,refute_0_1065]) ).
cnf(refute_0_1067,plain,
multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),inverse(identity)) = multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),inverse(identity)),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),inverse(identity)))]]) ).
cnf(refute_0_1068,plain,
( multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),inverse(identity)) != multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),inverse(identity))
| inverse(identity) != identity
| multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),inverse(identity)) = multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),inverse(identity)),multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),inverse(identity))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_1069,plain,
( inverse(identity) != identity
| multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),inverse(identity)) = multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),identity) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),inverse(identity)),multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),inverse(identity))) )],[refute_0_1067,refute_0_1068]) ).
cnf(refute_0_1070,plain,
multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),inverse(identity)) = multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),identity),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[p19_1,refute_0_1069]) ).
cnf(refute_0_1071,plain,
( multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),identity) != least_upper_bound(X_221,least_upper_bound(identity,X_18))
| multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),inverse(identity)) != multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),identity)
| multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),inverse(identity)) = least_upper_bound(X_221,least_upper_bound(identity,X_18)) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),inverse(identity)))),bind(Y0,$fot(multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),identity))),bind(Z0,$fot(least_upper_bound(X_221,least_upper_bound(identity,X_18))))]]) ).
cnf(refute_0_1072,plain,
( multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),identity) != least_upper_bound(X_221,least_upper_bound(identity,X_18))
| multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),inverse(identity)) = least_upper_bound(X_221,least_upper_bound(identity,X_18)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),inverse(identity)),multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),identity)) )],[refute_0_1070,refute_0_1071]) ).
cnf(refute_0_1073,plain,
multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),inverse(identity)) = least_upper_bound(X_221,least_upper_bound(identity,X_18)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),identity),least_upper_bound(X_221,least_upper_bound(identity,X_18))) )],[refute_0_1012,refute_0_1072]) ).
cnf(refute_0_1074,plain,
( multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),inverse(identity)) != least_upper_bound(X_221,least_upper_bound(identity,X_18))
| multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),inverse(identity)) != least_upper_bound(identity,multiply(least_upper_bound(X_18,X_221),inverse(identity)))
| least_upper_bound(X_221,least_upper_bound(identity,X_18)) = least_upper_bound(identity,multiply(least_upper_bound(X_18,X_221),inverse(identity))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),inverse(identity)),least_upper_bound(identity,multiply(least_upper_bound(X_18,X_221),inverse(identity)))) ),[0],$fot(least_upper_bound(X_221,least_upper_bound(identity,X_18)))]]) ).
cnf(refute_0_1075,plain,
( multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),inverse(identity)) != least_upper_bound(identity,multiply(least_upper_bound(X_18,X_221),inverse(identity)))
| least_upper_bound(X_221,least_upper_bound(identity,X_18)) = least_upper_bound(identity,multiply(least_upper_bound(X_18,X_221),inverse(identity))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),inverse(identity)),least_upper_bound(X_221,least_upper_bound(identity,X_18))) )],[refute_0_1073,refute_0_1074]) ).
cnf(refute_0_1076,plain,
multiply(least_upper_bound(X_18,least_upper_bound(identity,X_221)),identity) = least_upper_bound(X_18,least_upper_bound(identity,X_221)),
inference(subst,[],[refute_0_564:[bind(X,$fot(least_upper_bound(X_18,least_upper_bound(identity,X_221))))]]) ).
cnf(refute_0_1077,plain,
multiply(least_upper_bound(X_18,least_upper_bound(identity,X_221)),inverse(identity)) = multiply(least_upper_bound(X_18,least_upper_bound(identity,X_221)),inverse(identity)),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(X_18,least_upper_bound(identity,X_221)),inverse(identity)))]]) ).
cnf(refute_0_1078,plain,
( multiply(least_upper_bound(X_18,least_upper_bound(identity,X_221)),inverse(identity)) != multiply(least_upper_bound(X_18,least_upper_bound(identity,X_221)),inverse(identity))
| inverse(identity) != identity
| multiply(least_upper_bound(X_18,least_upper_bound(identity,X_221)),inverse(identity)) = multiply(least_upper_bound(X_18,least_upper_bound(identity,X_221)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_18,least_upper_bound(identity,X_221)),inverse(identity)),multiply(least_upper_bound(X_18,least_upper_bound(identity,X_221)),inverse(identity))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_1079,plain,
( inverse(identity) != identity
| multiply(least_upper_bound(X_18,least_upper_bound(identity,X_221)),inverse(identity)) = multiply(least_upper_bound(X_18,least_upper_bound(identity,X_221)),identity) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_18,least_upper_bound(identity,X_221)),inverse(identity)),multiply(least_upper_bound(X_18,least_upper_bound(identity,X_221)),inverse(identity))) )],[refute_0_1077,refute_0_1078]) ).
cnf(refute_0_1080,plain,
multiply(least_upper_bound(X_18,least_upper_bound(identity,X_221)),inverse(identity)) = multiply(least_upper_bound(X_18,least_upper_bound(identity,X_221)),identity),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[p19_1,refute_0_1079]) ).
cnf(refute_0_1081,plain,
( multiply(least_upper_bound(X_18,least_upper_bound(identity,X_221)),identity) != least_upper_bound(X_18,least_upper_bound(identity,X_221))
| multiply(least_upper_bound(X_18,least_upper_bound(identity,X_221)),inverse(identity)) != multiply(least_upper_bound(X_18,least_upper_bound(identity,X_221)),identity)
| multiply(least_upper_bound(X_18,least_upper_bound(identity,X_221)),inverse(identity)) = least_upper_bound(X_18,least_upper_bound(identity,X_221)) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(multiply(least_upper_bound(X_18,least_upper_bound(identity,X_221)),inverse(identity)))),bind(Y0,$fot(multiply(least_upper_bound(X_18,least_upper_bound(identity,X_221)),identity))),bind(Z0,$fot(least_upper_bound(X_18,least_upper_bound(identity,X_221))))]]) ).
cnf(refute_0_1082,plain,
( multiply(least_upper_bound(X_18,least_upper_bound(identity,X_221)),identity) != least_upper_bound(X_18,least_upper_bound(identity,X_221))
| multiply(least_upper_bound(X_18,least_upper_bound(identity,X_221)),inverse(identity)) = least_upper_bound(X_18,least_upper_bound(identity,X_221)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_18,least_upper_bound(identity,X_221)),inverse(identity)),multiply(least_upper_bound(X_18,least_upper_bound(identity,X_221)),identity)) )],[refute_0_1080,refute_0_1081]) ).
cnf(refute_0_1083,plain,
multiply(least_upper_bound(X_18,least_upper_bound(identity,X_221)),inverse(identity)) = least_upper_bound(X_18,least_upper_bound(identity,X_221)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_18,least_upper_bound(identity,X_221)),identity),least_upper_bound(X_18,least_upper_bound(identity,X_221))) )],[refute_0_1076,refute_0_1082]) ).
cnf(refute_0_1084,plain,
multiply(least_upper_bound(Y,least_upper_bound(X_278,X_279)),inverse(X_278)) = least_upper_bound(multiply(Y,inverse(X_278)),multiply(least_upper_bound(X_278,X_279),inverse(X_278))),
inference(subst,[],[monotony_lub2:[bind(X,$fot(inverse(X_278))),bind(Z,$fot(least_upper_bound(X_278,X_279)))]]) ).
cnf(refute_0_1085,plain,
multiply(least_upper_bound(X_278,X_279),inverse(X_278)) = least_upper_bound(identity,multiply(X_279,inverse(X_278))),
inference(subst,[],[refute_0_930:[bind(X_77,$fot(X_278)),bind(X_78,$fot(X_279))]]) ).
cnf(refute_0_1086,plain,
( multiply(least_upper_bound(Y,least_upper_bound(X_278,X_279)),inverse(X_278)) != least_upper_bound(multiply(Y,inverse(X_278)),multiply(least_upper_bound(X_278,X_279),inverse(X_278)))
| multiply(least_upper_bound(X_278,X_279),inverse(X_278)) != least_upper_bound(identity,multiply(X_279,inverse(X_278)))
| multiply(least_upper_bound(Y,least_upper_bound(X_278,X_279)),inverse(X_278)) = least_upper_bound(multiply(Y,inverse(X_278)),least_upper_bound(identity,multiply(X_279,inverse(X_278)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(Y,least_upper_bound(X_278,X_279)),inverse(X_278)),least_upper_bound(multiply(Y,inverse(X_278)),multiply(least_upper_bound(X_278,X_279),inverse(X_278)))) ),[1,1],$fot(least_upper_bound(identity,multiply(X_279,inverse(X_278))))]]) ).
cnf(refute_0_1087,plain,
( multiply(least_upper_bound(Y,least_upper_bound(X_278,X_279)),inverse(X_278)) != least_upper_bound(multiply(Y,inverse(X_278)),multiply(least_upper_bound(X_278,X_279),inverse(X_278)))
| multiply(least_upper_bound(Y,least_upper_bound(X_278,X_279)),inverse(X_278)) = least_upper_bound(multiply(Y,inverse(X_278)),least_upper_bound(identity,multiply(X_279,inverse(X_278)))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_278,X_279),inverse(X_278)),least_upper_bound(identity,multiply(X_279,inverse(X_278)))) )],[refute_0_1085,refute_0_1086]) ).
cnf(refute_0_1088,plain,
multiply(least_upper_bound(Y,least_upper_bound(X_278,X_279)),inverse(X_278)) = least_upper_bound(multiply(Y,inverse(X_278)),least_upper_bound(identity,multiply(X_279,inverse(X_278)))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,least_upper_bound(X_278,X_279)),inverse(X_278)),least_upper_bound(multiply(Y,inverse(X_278)),multiply(least_upper_bound(X_278,X_279),inverse(X_278)))) )],[refute_0_1084,refute_0_1087]) ).
cnf(refute_0_1089,plain,
least_upper_bound(multiply(Y,inverse(X_278)),multiply(X_279,inverse(X_278))) = multiply(least_upper_bound(Y,X_279),inverse(X_278)),
inference(subst,[],[refute_0_662:[bind(X,$fot(inverse(X_278))),bind(Z,$fot(X_279))]]) ).
cnf(refute_0_1090,plain,
least_upper_bound(identity,least_upper_bound(multiply(Y,inverse(X_278)),multiply(X_279,inverse(X_278)))) = least_upper_bound(identity,least_upper_bound(multiply(Y,inverse(X_278)),multiply(X_279,inverse(X_278)))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,least_upper_bound(multiply(Y,inverse(X_278)),multiply(X_279,inverse(X_278)))))]]) ).
cnf(refute_0_1091,plain,
( least_upper_bound(multiply(Y,inverse(X_278)),multiply(X_279,inverse(X_278))) != multiply(least_upper_bound(Y,X_279),inverse(X_278))
| least_upper_bound(identity,least_upper_bound(multiply(Y,inverse(X_278)),multiply(X_279,inverse(X_278)))) != least_upper_bound(identity,least_upper_bound(multiply(Y,inverse(X_278)),multiply(X_279,inverse(X_278))))
| least_upper_bound(identity,least_upper_bound(multiply(Y,inverse(X_278)),multiply(X_279,inverse(X_278)))) = least_upper_bound(identity,multiply(least_upper_bound(Y,X_279),inverse(X_278))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(Y,inverse(X_278)),multiply(X_279,inverse(X_278)))),least_upper_bound(identity,least_upper_bound(multiply(Y,inverse(X_278)),multiply(X_279,inverse(X_278))))) ),[1,1],$fot(multiply(least_upper_bound(Y,X_279),inverse(X_278)))]]) ).
cnf(refute_0_1092,plain,
( least_upper_bound(multiply(Y,inverse(X_278)),multiply(X_279,inverse(X_278))) != multiply(least_upper_bound(Y,X_279),inverse(X_278))
| least_upper_bound(identity,least_upper_bound(multiply(Y,inverse(X_278)),multiply(X_279,inverse(X_278)))) = least_upper_bound(identity,multiply(least_upper_bound(Y,X_279),inverse(X_278))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(Y,inverse(X_278)),multiply(X_279,inverse(X_278)))),least_upper_bound(identity,least_upper_bound(multiply(Y,inverse(X_278)),multiply(X_279,inverse(X_278))))) )],[refute_0_1090,refute_0_1091]) ).
cnf(refute_0_1093,plain,
least_upper_bound(identity,least_upper_bound(multiply(Y,inverse(X_278)),multiply(X_279,inverse(X_278)))) = least_upper_bound(identity,multiply(least_upper_bound(Y,X_279),inverse(X_278))),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(Y,inverse(X_278)),multiply(X_279,inverse(X_278))),multiply(least_upper_bound(Y,X_279),inverse(X_278))) )],[refute_0_1089,refute_0_1092]) ).
cnf(refute_0_1094,plain,
least_upper_bound(X_36,least_upper_bound(greatest_lower_bound(X_15,X_36),X_38)) = least_upper_bound(least_upper_bound(X_36,greatest_lower_bound(X_15,X_36)),X_38),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_36)),bind(Y,$fot(greatest_lower_bound(X_15,X_36))),bind(Z,$fot(X_38))]]) ).
cnf(refute_0_1095,plain,
least_upper_bound(X_36,greatest_lower_bound(X_15,X_36)) = X_36,
inference(subst,[],[refute_0_270:[bind(X_14,$fot(X_36))]]) ).
cnf(refute_0_1096,plain,
( least_upper_bound(X_36,greatest_lower_bound(X_15,X_36)) != X_36
| least_upper_bound(X_36,least_upper_bound(greatest_lower_bound(X_15,X_36),X_38)) != least_upper_bound(least_upper_bound(X_36,greatest_lower_bound(X_15,X_36)),X_38)
| least_upper_bound(X_36,least_upper_bound(greatest_lower_bound(X_15,X_36),X_38)) = least_upper_bound(X_36,X_38) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_36,least_upper_bound(greatest_lower_bound(X_15,X_36),X_38)),least_upper_bound(least_upper_bound(X_36,greatest_lower_bound(X_15,X_36)),X_38)) ),[1,0],$fot(X_36)]]) ).
cnf(refute_0_1097,plain,
( least_upper_bound(X_36,least_upper_bound(greatest_lower_bound(X_15,X_36),X_38)) != least_upper_bound(least_upper_bound(X_36,greatest_lower_bound(X_15,X_36)),X_38)
| least_upper_bound(X_36,least_upper_bound(greatest_lower_bound(X_15,X_36),X_38)) = least_upper_bound(X_36,X_38) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_36,greatest_lower_bound(X_15,X_36)),X_36) )],[refute_0_1095,refute_0_1096]) ).
cnf(refute_0_1098,plain,
least_upper_bound(X_36,least_upper_bound(greatest_lower_bound(X_15,X_36),X_38)) = least_upper_bound(X_36,X_38),
inference(resolve,[$cnf( $equal(least_upper_bound(X_36,least_upper_bound(greatest_lower_bound(X_15,X_36),X_38)),least_upper_bound(least_upper_bound(X_36,greatest_lower_bound(X_15,X_36)),X_38)) )],[refute_0_1094,refute_0_1097]) ).
cnf(refute_0_1099,plain,
least_upper_bound(least_upper_bound(Y,X_18),least_upper_bound(greatest_lower_bound(least_upper_bound(X_18,Y),least_upper_bound(Y,X_18)),X_263)) = least_upper_bound(least_upper_bound(Y,X_18),X_263),
inference(subst,[],[refute_0_1098:[bind(X_15,$fot(least_upper_bound(X_18,Y))),bind(X_36,$fot(least_upper_bound(Y,X_18))),bind(X_38,$fot(X_263))]]) ).
cnf(refute_0_1100,plain,
( greatest_lower_bound(least_upper_bound(X_18,Y),least_upper_bound(Y,X_18)) != least_upper_bound(X_18,Y)
| least_upper_bound(least_upper_bound(Y,X_18),least_upper_bound(greatest_lower_bound(least_upper_bound(X_18,Y),least_upper_bound(Y,X_18)),X_263)) != least_upper_bound(least_upper_bound(Y,X_18),X_263)
| least_upper_bound(least_upper_bound(Y,X_18),least_upper_bound(least_upper_bound(X_18,Y),X_263)) = least_upper_bound(least_upper_bound(Y,X_18),X_263) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_18),least_upper_bound(greatest_lower_bound(least_upper_bound(X_18,Y),least_upper_bound(Y,X_18)),X_263)),least_upper_bound(least_upper_bound(Y,X_18),X_263)) ),[0,1,0],$fot(least_upper_bound(X_18,Y))]]) ).
cnf(refute_0_1101,plain,
( least_upper_bound(least_upper_bound(Y,X_18),least_upper_bound(greatest_lower_bound(least_upper_bound(X_18,Y),least_upper_bound(Y,X_18)),X_263)) != least_upper_bound(least_upper_bound(Y,X_18),X_263)
| least_upper_bound(least_upper_bound(Y,X_18),least_upper_bound(least_upper_bound(X_18,Y),X_263)) = least_upper_bound(least_upper_bound(Y,X_18),X_263) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_18,Y),least_upper_bound(Y,X_18)),least_upper_bound(X_18,Y)) )],[refute_0_659,refute_0_1100]) ).
cnf(refute_0_1102,plain,
least_upper_bound(least_upper_bound(Y,X_18),least_upper_bound(least_upper_bound(X_18,Y),X_263)) = least_upper_bound(least_upper_bound(Y,X_18),X_263),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_18),least_upper_bound(greatest_lower_bound(least_upper_bound(X_18,Y),least_upper_bound(Y,X_18)),X_263)),least_upper_bound(least_upper_bound(Y,X_18),X_263)) )],[refute_0_1099,refute_0_1101]) ).
cnf(refute_0_1103,plain,
least_upper_bound(Y,least_upper_bound(X_18,least_upper_bound(Y,X_263))) = least_upper_bound(X_18,least_upper_bound(Y,X_263)),
inference(subst,[],[refute_0_982:[bind(Y,$fot(X_263)),bind(X_36,$fot(X_18)),bind(X_37,$fot(Y))]]) ).
cnf(refute_0_1104,plain,
least_upper_bound(X_18,least_upper_bound(X_18,least_upper_bound(Y,X_263))) = least_upper_bound(X_18,least_upper_bound(Y,X_263)),
inference(subst,[],[refute_0_642:[bind(X_18,$fot(least_upper_bound(Y,X_263))),bind(X_19,$fot(X_18))]]) ).
cnf(refute_0_1105,plain,
least_upper_bound(least_upper_bound(X_18,Y),X_263) = least_upper_bound(X_18,least_upper_bound(Y,X_263)),
inference(subst,[],[refute_0_631:[bind(X,$fot(X_18)),bind(Z,$fot(X_263))]]) ).
cnf(refute_0_1106,plain,
least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,Y),X_263)) = least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,Y),X_263)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,Y),X_263)))]]) ).
cnf(refute_0_1107,plain,
( least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,Y),X_263)) != least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,Y),X_263))
| least_upper_bound(least_upper_bound(X_18,Y),X_263) != least_upper_bound(X_18,least_upper_bound(Y,X_263))
| least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,Y),X_263)) = least_upper_bound(X_18,least_upper_bound(X_18,least_upper_bound(Y,X_263))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,Y),X_263)),least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,Y),X_263))) ),[1,1],$fot(least_upper_bound(X_18,least_upper_bound(Y,X_263)))]]) ).
cnf(refute_0_1108,plain,
( least_upper_bound(least_upper_bound(X_18,Y),X_263) != least_upper_bound(X_18,least_upper_bound(Y,X_263))
| least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,Y),X_263)) = least_upper_bound(X_18,least_upper_bound(X_18,least_upper_bound(Y,X_263))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,Y),X_263)),least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,Y),X_263))) )],[refute_0_1106,refute_0_1107]) ).
cnf(refute_0_1109,plain,
least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,Y),X_263)) = least_upper_bound(X_18,least_upper_bound(X_18,least_upper_bound(Y,X_263))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_18,Y),X_263),least_upper_bound(X_18,least_upper_bound(Y,X_263))) )],[refute_0_1105,refute_0_1108]) ).
cnf(refute_0_1110,plain,
( least_upper_bound(X_18,least_upper_bound(X_18,least_upper_bound(Y,X_263))) != least_upper_bound(X_18,least_upper_bound(Y,X_263))
| least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,Y),X_263)) != least_upper_bound(X_18,least_upper_bound(X_18,least_upper_bound(Y,X_263)))
| least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,Y),X_263)) = least_upper_bound(X_18,least_upper_bound(Y,X_263)) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,Y),X_263)))),bind(Y0,$fot(least_upper_bound(X_18,least_upper_bound(X_18,least_upper_bound(Y,X_263))))),bind(Z0,$fot(least_upper_bound(X_18,least_upper_bound(Y,X_263))))]]) ).
cnf(refute_0_1111,plain,
( least_upper_bound(X_18,least_upper_bound(X_18,least_upper_bound(Y,X_263))) != least_upper_bound(X_18,least_upper_bound(Y,X_263))
| least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,Y),X_263)) = least_upper_bound(X_18,least_upper_bound(Y,X_263)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,Y),X_263)),least_upper_bound(X_18,least_upper_bound(X_18,least_upper_bound(Y,X_263)))) )],[refute_0_1109,refute_0_1110]) ).
cnf(refute_0_1112,plain,
least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,Y),X_263)) = least_upper_bound(X_18,least_upper_bound(Y,X_263)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(X_18,least_upper_bound(Y,X_263))),least_upper_bound(X_18,least_upper_bound(Y,X_263))) )],[refute_0_1104,refute_0_1111]) ).
cnf(refute_0_1113,plain,
least_upper_bound(Y,least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,Y),X_263))) = least_upper_bound(Y,least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,Y),X_263))),
introduced(tautology,[refl,[$fot(least_upper_bound(Y,least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,Y),X_263))))]]) ).
cnf(refute_0_1114,plain,
( least_upper_bound(Y,least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,Y),X_263))) != least_upper_bound(Y,least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,Y),X_263)))
| least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,Y),X_263)) != least_upper_bound(X_18,least_upper_bound(Y,X_263))
| least_upper_bound(Y,least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,Y),X_263))) = least_upper_bound(Y,least_upper_bound(X_18,least_upper_bound(Y,X_263))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,Y),X_263))),least_upper_bound(Y,least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,Y),X_263)))) ),[1,1],$fot(least_upper_bound(X_18,least_upper_bound(Y,X_263)))]]) ).
cnf(refute_0_1115,plain,
( least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,Y),X_263)) != least_upper_bound(X_18,least_upper_bound(Y,X_263))
| least_upper_bound(Y,least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,Y),X_263))) = least_upper_bound(Y,least_upper_bound(X_18,least_upper_bound(Y,X_263))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,Y),X_263))),least_upper_bound(Y,least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,Y),X_263)))) )],[refute_0_1113,refute_0_1114]) ).
cnf(refute_0_1116,plain,
least_upper_bound(Y,least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,Y),X_263))) = least_upper_bound(Y,least_upper_bound(X_18,least_upper_bound(Y,X_263))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,Y),X_263)),least_upper_bound(X_18,least_upper_bound(Y,X_263))) )],[refute_0_1112,refute_0_1115]) ).
cnf(refute_0_1117,plain,
( least_upper_bound(Y,least_upper_bound(X_18,least_upper_bound(Y,X_263))) != least_upper_bound(X_18,least_upper_bound(Y,X_263))
| least_upper_bound(Y,least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,Y),X_263))) != least_upper_bound(Y,least_upper_bound(X_18,least_upper_bound(Y,X_263)))
| least_upper_bound(Y,least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,Y),X_263))) = least_upper_bound(X_18,least_upper_bound(Y,X_263)) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(least_upper_bound(Y,least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,Y),X_263))))),bind(Y0,$fot(least_upper_bound(Y,least_upper_bound(X_18,least_upper_bound(Y,X_263))))),bind(Z0,$fot(least_upper_bound(X_18,least_upper_bound(Y,X_263))))]]) ).
cnf(refute_0_1118,plain,
( least_upper_bound(Y,least_upper_bound(X_18,least_upper_bound(Y,X_263))) != least_upper_bound(X_18,least_upper_bound(Y,X_263))
| least_upper_bound(Y,least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,Y),X_263))) = least_upper_bound(X_18,least_upper_bound(Y,X_263)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,Y),X_263))),least_upper_bound(Y,least_upper_bound(X_18,least_upper_bound(Y,X_263)))) )],[refute_0_1116,refute_0_1117]) ).
cnf(refute_0_1119,plain,
least_upper_bound(Y,least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,Y),X_263))) = least_upper_bound(X_18,least_upper_bound(Y,X_263)),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_18,least_upper_bound(Y,X_263))),least_upper_bound(X_18,least_upper_bound(Y,X_263))) )],[refute_0_1103,refute_0_1118]) ).
cnf(refute_0_1120,plain,
least_upper_bound(least_upper_bound(Y,X_18),least_upper_bound(least_upper_bound(X_18,Y),X_263)) = least_upper_bound(Y,least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,Y),X_263))),
inference(subst,[],[refute_0_631:[bind(X,$fot(Y)),bind(Y,$fot(X_18)),bind(Z,$fot(least_upper_bound(least_upper_bound(X_18,Y),X_263)))]]) ).
cnf(refute_0_1121,plain,
( least_upper_bound(Y,least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,Y),X_263))) != least_upper_bound(X_18,least_upper_bound(Y,X_263))
| least_upper_bound(least_upper_bound(Y,X_18),least_upper_bound(least_upper_bound(X_18,Y),X_263)) != least_upper_bound(Y,least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,Y),X_263)))
| least_upper_bound(least_upper_bound(Y,X_18),least_upper_bound(least_upper_bound(X_18,Y),X_263)) = least_upper_bound(X_18,least_upper_bound(Y,X_263)) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(least_upper_bound(least_upper_bound(Y,X_18),least_upper_bound(least_upper_bound(X_18,Y),X_263)))),bind(Y0,$fot(least_upper_bound(Y,least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,Y),X_263))))),bind(Z0,$fot(least_upper_bound(X_18,least_upper_bound(Y,X_263))))]]) ).
cnf(refute_0_1122,plain,
( least_upper_bound(Y,least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,Y),X_263))) != least_upper_bound(X_18,least_upper_bound(Y,X_263))
| least_upper_bound(least_upper_bound(Y,X_18),least_upper_bound(least_upper_bound(X_18,Y),X_263)) = least_upper_bound(X_18,least_upper_bound(Y,X_263)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_18),least_upper_bound(least_upper_bound(X_18,Y),X_263)),least_upper_bound(Y,least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,Y),X_263)))) )],[refute_0_1120,refute_0_1121]) ).
cnf(refute_0_1123,plain,
least_upper_bound(least_upper_bound(Y,X_18),least_upper_bound(least_upper_bound(X_18,Y),X_263)) = least_upper_bound(X_18,least_upper_bound(Y,X_263)),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_18,least_upper_bound(least_upper_bound(X_18,Y),X_263))),least_upper_bound(X_18,least_upper_bound(Y,X_263))) )],[refute_0_1119,refute_0_1122]) ).
cnf(refute_0_1124,plain,
( least_upper_bound(least_upper_bound(Y,X_18),least_upper_bound(least_upper_bound(X_18,Y),X_263)) != least_upper_bound(X_18,least_upper_bound(Y,X_263))
| least_upper_bound(least_upper_bound(Y,X_18),least_upper_bound(least_upper_bound(X_18,Y),X_263)) != least_upper_bound(least_upper_bound(Y,X_18),X_263)
| least_upper_bound(X_18,least_upper_bound(Y,X_263)) = least_upper_bound(least_upper_bound(Y,X_18),X_263) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_18),least_upper_bound(least_upper_bound(X_18,Y),X_263)),least_upper_bound(least_upper_bound(Y,X_18),X_263)) ),[0],$fot(least_upper_bound(X_18,least_upper_bound(Y,X_263)))]]) ).
cnf(refute_0_1125,plain,
( least_upper_bound(least_upper_bound(Y,X_18),least_upper_bound(least_upper_bound(X_18,Y),X_263)) != least_upper_bound(least_upper_bound(Y,X_18),X_263)
| least_upper_bound(X_18,least_upper_bound(Y,X_263)) = least_upper_bound(least_upper_bound(Y,X_18),X_263) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_18),least_upper_bound(least_upper_bound(X_18,Y),X_263)),least_upper_bound(X_18,least_upper_bound(Y,X_263))) )],[refute_0_1123,refute_0_1124]) ).
cnf(refute_0_1126,plain,
least_upper_bound(least_upper_bound(Y,X_18),X_263) = least_upper_bound(Y,least_upper_bound(X_18,X_263)),
inference(subst,[],[refute_0_631:[bind(X,$fot(Y)),bind(Y,$fot(X_18)),bind(Z,$fot(X_263))]]) ).
cnf(refute_0_1127,plain,
( least_upper_bound(X_18,least_upper_bound(Y,X_263)) != least_upper_bound(least_upper_bound(Y,X_18),X_263)
| least_upper_bound(least_upper_bound(Y,X_18),X_263) != least_upper_bound(Y,least_upper_bound(X_18,X_263))
| least_upper_bound(X_18,least_upper_bound(Y,X_263)) = least_upper_bound(Y,least_upper_bound(X_18,X_263)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_18,least_upper_bound(Y,X_263)),least_upper_bound(Y,least_upper_bound(X_18,X_263))) ),[0],$fot(least_upper_bound(least_upper_bound(Y,X_18),X_263))]]) ).
cnf(refute_0_1128,plain,
( least_upper_bound(X_18,least_upper_bound(Y,X_263)) != least_upper_bound(least_upper_bound(Y,X_18),X_263)
| least_upper_bound(X_18,least_upper_bound(Y,X_263)) = least_upper_bound(Y,least_upper_bound(X_18,X_263)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_18),X_263),least_upper_bound(Y,least_upper_bound(X_18,X_263))) )],[refute_0_1126,refute_0_1127]) ).
cnf(refute_0_1129,plain,
( least_upper_bound(least_upper_bound(Y,X_18),least_upper_bound(least_upper_bound(X_18,Y),X_263)) != least_upper_bound(least_upper_bound(Y,X_18),X_263)
| least_upper_bound(X_18,least_upper_bound(Y,X_263)) = least_upper_bound(Y,least_upper_bound(X_18,X_263)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(Y,X_263)),least_upper_bound(least_upper_bound(Y,X_18),X_263)) )],[refute_0_1125,refute_0_1128]) ).
cnf(refute_0_1130,plain,
least_upper_bound(X_18,least_upper_bound(Y,X_263)) = least_upper_bound(Y,least_upper_bound(X_18,X_263)),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_18),least_upper_bound(least_upper_bound(X_18,Y),X_263)),least_upper_bound(least_upper_bound(Y,X_18),X_263)) )],[refute_0_1102,refute_0_1129]) ).
cnf(refute_0_1131,plain,
( least_upper_bound(X_18,least_upper_bound(Y,X_263)) != least_upper_bound(Y,least_upper_bound(X_18,X_263))
| least_upper_bound(Y,least_upper_bound(X_18,X_263)) = least_upper_bound(X_18,least_upper_bound(Y,X_263)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(least_upper_bound(X_18,least_upper_bound(Y,X_263)))),bind(Y0,$fot(least_upper_bound(Y,least_upper_bound(X_18,X_263))))]]) ).
cnf(refute_0_1132,plain,
least_upper_bound(Y,least_upper_bound(X_18,X_263)) = least_upper_bound(X_18,least_upper_bound(Y,X_263)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(Y,X_263)),least_upper_bound(Y,least_upper_bound(X_18,X_263))) )],[refute_0_1130,refute_0_1131]) ).
cnf(refute_0_1133,plain,
least_upper_bound(multiply(Y,inverse(X_278)),least_upper_bound(identity,multiply(X_279,inverse(X_278)))) = least_upper_bound(identity,least_upper_bound(multiply(Y,inverse(X_278)),multiply(X_279,inverse(X_278)))),
inference(subst,[],[refute_0_1132:[bind(Y,$fot(multiply(Y,inverse(X_278)))),bind(X_18,$fot(identity)),bind(X_263,$fot(multiply(X_279,inverse(X_278))))]]) ).
cnf(refute_0_1134,plain,
( least_upper_bound(multiply(Y,inverse(X_278)),least_upper_bound(identity,multiply(X_279,inverse(X_278)))) != least_upper_bound(identity,least_upper_bound(multiply(Y,inverse(X_278)),multiply(X_279,inverse(X_278))))
| least_upper_bound(identity,least_upper_bound(multiply(Y,inverse(X_278)),multiply(X_279,inverse(X_278)))) != least_upper_bound(identity,multiply(least_upper_bound(Y,X_279),inverse(X_278)))
| least_upper_bound(multiply(Y,inverse(X_278)),least_upper_bound(identity,multiply(X_279,inverse(X_278)))) = least_upper_bound(identity,multiply(least_upper_bound(Y,X_279),inverse(X_278))) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(least_upper_bound(multiply(Y,inverse(X_278)),least_upper_bound(identity,multiply(X_279,inverse(X_278)))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(multiply(Y,inverse(X_278)),multiply(X_279,inverse(X_278)))))),bind(Z0,$fot(least_upper_bound(identity,multiply(least_upper_bound(Y,X_279),inverse(X_278)))))]]) ).
cnf(refute_0_1135,plain,
( least_upper_bound(identity,least_upper_bound(multiply(Y,inverse(X_278)),multiply(X_279,inverse(X_278)))) != least_upper_bound(identity,multiply(least_upper_bound(Y,X_279),inverse(X_278)))
| least_upper_bound(multiply(Y,inverse(X_278)),least_upper_bound(identity,multiply(X_279,inverse(X_278)))) = least_upper_bound(identity,multiply(least_upper_bound(Y,X_279),inverse(X_278))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(Y,inverse(X_278)),least_upper_bound(identity,multiply(X_279,inverse(X_278)))),least_upper_bound(identity,least_upper_bound(multiply(Y,inverse(X_278)),multiply(X_279,inverse(X_278))))) )],[refute_0_1133,refute_0_1134]) ).
cnf(refute_0_1136,plain,
least_upper_bound(multiply(Y,inverse(X_278)),least_upper_bound(identity,multiply(X_279,inverse(X_278)))) = least_upper_bound(identity,multiply(least_upper_bound(Y,X_279),inverse(X_278))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(Y,inverse(X_278)),multiply(X_279,inverse(X_278)))),least_upper_bound(identity,multiply(least_upper_bound(Y,X_279),inverse(X_278)))) )],[refute_0_1093,refute_0_1135]) ).
cnf(refute_0_1137,plain,
( multiply(least_upper_bound(Y,least_upper_bound(X_278,X_279)),inverse(X_278)) != least_upper_bound(multiply(Y,inverse(X_278)),least_upper_bound(identity,multiply(X_279,inverse(X_278))))
| least_upper_bound(multiply(Y,inverse(X_278)),least_upper_bound(identity,multiply(X_279,inverse(X_278)))) != least_upper_bound(identity,multiply(least_upper_bound(Y,X_279),inverse(X_278)))
| multiply(least_upper_bound(Y,least_upper_bound(X_278,X_279)),inverse(X_278)) = least_upper_bound(identity,multiply(least_upper_bound(Y,X_279),inverse(X_278))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(Y,least_upper_bound(X_278,X_279)),inverse(X_278)),least_upper_bound(identity,multiply(least_upper_bound(Y,X_279),inverse(X_278)))) ),[0],$fot(least_upper_bound(multiply(Y,inverse(X_278)),least_upper_bound(identity,multiply(X_279,inverse(X_278)))))]]) ).
cnf(refute_0_1138,plain,
( multiply(least_upper_bound(Y,least_upper_bound(X_278,X_279)),inverse(X_278)) != least_upper_bound(multiply(Y,inverse(X_278)),least_upper_bound(identity,multiply(X_279,inverse(X_278))))
| multiply(least_upper_bound(Y,least_upper_bound(X_278,X_279)),inverse(X_278)) = least_upper_bound(identity,multiply(least_upper_bound(Y,X_279),inverse(X_278))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(Y,inverse(X_278)),least_upper_bound(identity,multiply(X_279,inverse(X_278)))),least_upper_bound(identity,multiply(least_upper_bound(Y,X_279),inverse(X_278)))) )],[refute_0_1136,refute_0_1137]) ).
cnf(refute_0_1139,plain,
multiply(least_upper_bound(Y,least_upper_bound(X_278,X_279)),inverse(X_278)) = least_upper_bound(identity,multiply(least_upper_bound(Y,X_279),inverse(X_278))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,least_upper_bound(X_278,X_279)),inverse(X_278)),least_upper_bound(multiply(Y,inverse(X_278)),least_upper_bound(identity,multiply(X_279,inverse(X_278))))) )],[refute_0_1088,refute_0_1138]) ).
cnf(refute_0_1140,plain,
( multiply(least_upper_bound(Y,least_upper_bound(X_278,X_279)),inverse(X_278)) != least_upper_bound(identity,multiply(least_upper_bound(Y,X_279),inverse(X_278)))
| least_upper_bound(identity,multiply(least_upper_bound(Y,X_279),inverse(X_278))) = multiply(least_upper_bound(Y,least_upper_bound(X_278,X_279)),inverse(X_278)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(multiply(least_upper_bound(Y,least_upper_bound(X_278,X_279)),inverse(X_278)))),bind(Y0,$fot(least_upper_bound(identity,multiply(least_upper_bound(Y,X_279),inverse(X_278)))))]]) ).
cnf(refute_0_1141,plain,
least_upper_bound(identity,multiply(least_upper_bound(Y,X_279),inverse(X_278))) = multiply(least_upper_bound(Y,least_upper_bound(X_278,X_279)),inverse(X_278)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,least_upper_bound(X_278,X_279)),inverse(X_278)),least_upper_bound(identity,multiply(least_upper_bound(Y,X_279),inverse(X_278)))) )],[refute_0_1139,refute_0_1140]) ).
cnf(refute_0_1142,plain,
least_upper_bound(identity,multiply(least_upper_bound(X_18,X_221),inverse(identity))) = multiply(least_upper_bound(X_18,least_upper_bound(identity,X_221)),inverse(identity)),
inference(subst,[],[refute_0_1141:[bind(Y,$fot(X_18)),bind(X_278,$fot(identity)),bind(X_279,$fot(X_221))]]) ).
cnf(refute_0_1143,plain,
( multiply(least_upper_bound(X_18,least_upper_bound(identity,X_221)),inverse(identity)) != least_upper_bound(X_18,least_upper_bound(identity,X_221))
| least_upper_bound(identity,multiply(least_upper_bound(X_18,X_221),inverse(identity))) != multiply(least_upper_bound(X_18,least_upper_bound(identity,X_221)),inverse(identity))
| least_upper_bound(identity,multiply(least_upper_bound(X_18,X_221),inverse(identity))) = least_upper_bound(X_18,least_upper_bound(identity,X_221)) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(least_upper_bound(identity,multiply(least_upper_bound(X_18,X_221),inverse(identity))))),bind(Y0,$fot(multiply(least_upper_bound(X_18,least_upper_bound(identity,X_221)),inverse(identity)))),bind(Z0,$fot(least_upper_bound(X_18,least_upper_bound(identity,X_221))))]]) ).
cnf(refute_0_1144,plain,
( multiply(least_upper_bound(X_18,least_upper_bound(identity,X_221)),inverse(identity)) != least_upper_bound(X_18,least_upper_bound(identity,X_221))
| least_upper_bound(identity,multiply(least_upper_bound(X_18,X_221),inverse(identity))) = least_upper_bound(X_18,least_upper_bound(identity,X_221)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(least_upper_bound(X_18,X_221),inverse(identity))),multiply(least_upper_bound(X_18,least_upper_bound(identity,X_221)),inverse(identity))) )],[refute_0_1142,refute_0_1143]) ).
cnf(refute_0_1145,plain,
least_upper_bound(identity,multiply(least_upper_bound(X_18,X_221),inverse(identity))) = least_upper_bound(X_18,least_upper_bound(identity,X_221)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_18,least_upper_bound(identity,X_221)),inverse(identity)),least_upper_bound(X_18,least_upper_bound(identity,X_221))) )],[refute_0_1083,refute_0_1144]) ).
cnf(refute_0_1146,plain,
( least_upper_bound(X_221,least_upper_bound(identity,X_18)) != least_upper_bound(identity,multiply(least_upper_bound(X_18,X_221),inverse(identity)))
| least_upper_bound(identity,multiply(least_upper_bound(X_18,X_221),inverse(identity))) != least_upper_bound(X_18,least_upper_bound(identity,X_221))
| least_upper_bound(X_221,least_upper_bound(identity,X_18)) = least_upper_bound(X_18,least_upper_bound(identity,X_221)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_221,least_upper_bound(identity,X_18)),least_upper_bound(X_18,least_upper_bound(identity,X_221))) ),[0],$fot(least_upper_bound(identity,multiply(least_upper_bound(X_18,X_221),inverse(identity))))]]) ).
cnf(refute_0_1147,plain,
( least_upper_bound(X_221,least_upper_bound(identity,X_18)) != least_upper_bound(identity,multiply(least_upper_bound(X_18,X_221),inverse(identity)))
| least_upper_bound(X_221,least_upper_bound(identity,X_18)) = least_upper_bound(X_18,least_upper_bound(identity,X_221)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(least_upper_bound(X_18,X_221),inverse(identity))),least_upper_bound(X_18,least_upper_bound(identity,X_221))) )],[refute_0_1145,refute_0_1146]) ).
cnf(refute_0_1148,plain,
( multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),inverse(identity)) != least_upper_bound(identity,multiply(least_upper_bound(X_18,X_221),inverse(identity)))
| least_upper_bound(X_221,least_upper_bound(identity,X_18)) = least_upper_bound(X_18,least_upper_bound(identity,X_221)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_221,least_upper_bound(identity,X_18)),least_upper_bound(identity,multiply(least_upper_bound(X_18,X_221),inverse(identity)))) )],[refute_0_1075,refute_0_1147]) ).
cnf(refute_0_1149,plain,
least_upper_bound(X_221,least_upper_bound(identity,X_18)) = least_upper_bound(X_18,least_upper_bound(identity,X_221)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_221,least_upper_bound(identity,X_18)),inverse(identity)),least_upper_bound(identity,multiply(least_upper_bound(X_18,X_221),inverse(identity)))) )],[refute_0_1066,refute_0_1148]) ).
cnf(refute_0_1150,plain,
least_upper_bound(X_221,least_upper_bound(identity,identity)) = least_upper_bound(identity,least_upper_bound(identity,X_221)),
inference(subst,[],[refute_0_1149:[bind(X_18,$fot(identity))]]) ).
cnf(refute_0_1151,plain,
( least_upper_bound(X_221,least_upper_bound(identity,identity)) != least_upper_bound(identity,least_upper_bound(identity,X_221))
| least_upper_bound(identity,least_upper_bound(identity,X_221)) = least_upper_bound(X_221,least_upper_bound(identity,identity)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(least_upper_bound(X_221,least_upper_bound(identity,identity)))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(identity,X_221))))]]) ).
cnf(refute_0_1152,plain,
least_upper_bound(identity,least_upper_bound(identity,X_221)) = least_upper_bound(X_221,least_upper_bound(identity,identity)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_221,least_upper_bound(identity,identity)),least_upper_bound(identity,least_upper_bound(identity,X_221))) )],[refute_0_1150,refute_0_1151]) ).
cnf(refute_0_1153,plain,
( greatest_lower_bound(X_305,least_upper_bound(least_upper_bound(identity,X_221),identity)) != greatest_lower_bound(least_upper_bound(identity,least_upper_bound(identity,X_221)),X_305)
| least_upper_bound(identity,least_upper_bound(identity,X_221)) != least_upper_bound(X_221,least_upper_bound(identity,identity))
| greatest_lower_bound(X_305,least_upper_bound(least_upper_bound(identity,X_221),identity)) = greatest_lower_bound(least_upper_bound(X_221,least_upper_bound(identity,identity)),X_305) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_305,least_upper_bound(least_upper_bound(identity,X_221),identity)),greatest_lower_bound(least_upper_bound(identity,least_upper_bound(identity,X_221)),X_305)) ),[1,0],$fot(least_upper_bound(X_221,least_upper_bound(identity,identity)))]]) ).
cnf(refute_0_1154,plain,
( greatest_lower_bound(X_305,least_upper_bound(least_upper_bound(identity,X_221),identity)) != greatest_lower_bound(least_upper_bound(identity,least_upper_bound(identity,X_221)),X_305)
| greatest_lower_bound(X_305,least_upper_bound(least_upper_bound(identity,X_221),identity)) = greatest_lower_bound(least_upper_bound(X_221,least_upper_bound(identity,identity)),X_305) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(identity,X_221)),least_upper_bound(X_221,least_upper_bound(identity,identity))) )],[refute_0_1152,refute_0_1153]) ).
cnf(refute_0_1155,plain,
greatest_lower_bound(X_305,least_upper_bound(least_upper_bound(identity,X_221),identity)) = greatest_lower_bound(least_upper_bound(X_221,least_upper_bound(identity,identity)),X_305),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_305,least_upper_bound(least_upper_bound(identity,X_221),identity)),greatest_lower_bound(least_upper_bound(identity,least_upper_bound(identity,X_221)),X_305)) )],[refute_0_925,refute_0_1154]) ).
cnf(refute_0_1156,plain,
least_upper_bound(identity,least_upper_bound(identity,X_221)) = least_upper_bound(identity,X_221),
inference(subst,[],[refute_0_642:[bind(X_18,$fot(X_221)),bind(X_19,$fot(identity))]]) ).
cnf(refute_0_1157,plain,
greatest_lower_bound(X_305,least_upper_bound(identity,least_upper_bound(identity,X_221))) = greatest_lower_bound(X_305,least_upper_bound(identity,least_upper_bound(identity,X_221))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X_305,least_upper_bound(identity,least_upper_bound(identity,X_221))))]]) ).
cnf(refute_0_1158,plain,
( greatest_lower_bound(X_305,least_upper_bound(identity,least_upper_bound(identity,X_221))) != greatest_lower_bound(X_305,least_upper_bound(identity,least_upper_bound(identity,X_221)))
| least_upper_bound(identity,least_upper_bound(identity,X_221)) != least_upper_bound(identity,X_221)
| greatest_lower_bound(X_305,least_upper_bound(identity,least_upper_bound(identity,X_221))) = greatest_lower_bound(X_305,least_upper_bound(identity,X_221)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_305,least_upper_bound(identity,least_upper_bound(identity,X_221))),greatest_lower_bound(X_305,least_upper_bound(identity,least_upper_bound(identity,X_221)))) ),[1,1],$fot(least_upper_bound(identity,X_221))]]) ).
cnf(refute_0_1159,plain,
( least_upper_bound(identity,least_upper_bound(identity,X_221)) != least_upper_bound(identity,X_221)
| greatest_lower_bound(X_305,least_upper_bound(identity,least_upper_bound(identity,X_221))) = greatest_lower_bound(X_305,least_upper_bound(identity,X_221)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_305,least_upper_bound(identity,least_upper_bound(identity,X_221))),greatest_lower_bound(X_305,least_upper_bound(identity,least_upper_bound(identity,X_221)))) )],[refute_0_1157,refute_0_1158]) ).
cnf(refute_0_1160,plain,
greatest_lower_bound(X_305,least_upper_bound(identity,least_upper_bound(identity,X_221))) = greatest_lower_bound(X_305,least_upper_bound(identity,X_221)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(identity,X_221)),least_upper_bound(identity,X_221)) )],[refute_0_1156,refute_0_1159]) ).
cnf(refute_0_1161,plain,
greatest_lower_bound(greatest_lower_bound(X_15,X_41),greatest_lower_bound(X_40,X_41)) = greatest_lower_bound(X_40,greatest_lower_bound(X_41,greatest_lower_bound(X_15,X_41))),
inference(subst,[],[refute_0_321:[bind(X,$fot(greatest_lower_bound(X_15,X_41))),bind(Y,$fot(X_40)),bind(X_35,$fot(X_41))]]) ).
cnf(refute_0_1162,plain,
greatest_lower_bound(X_41,greatest_lower_bound(X_15,X_41)) = greatest_lower_bound(X_41,X_15),
inference(subst,[],[refute_0_229:[bind(Y,$fot(X_41))]]) ).
cnf(refute_0_1163,plain,
( greatest_lower_bound(X_41,greatest_lower_bound(X_15,X_41)) != greatest_lower_bound(X_41,X_15)
| greatest_lower_bound(greatest_lower_bound(X_15,X_41),greatest_lower_bound(X_40,X_41)) != greatest_lower_bound(X_40,greatest_lower_bound(X_41,greatest_lower_bound(X_15,X_41)))
| greatest_lower_bound(greatest_lower_bound(X_15,X_41),greatest_lower_bound(X_40,X_41)) = greatest_lower_bound(X_40,greatest_lower_bound(X_41,X_15)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_15,X_41),greatest_lower_bound(X_40,X_41)),greatest_lower_bound(X_40,greatest_lower_bound(X_41,greatest_lower_bound(X_15,X_41)))) ),[1,1],$fot(greatest_lower_bound(X_41,X_15))]]) ).
cnf(refute_0_1164,plain,
( greatest_lower_bound(greatest_lower_bound(X_15,X_41),greatest_lower_bound(X_40,X_41)) != greatest_lower_bound(X_40,greatest_lower_bound(X_41,greatest_lower_bound(X_15,X_41)))
| greatest_lower_bound(greatest_lower_bound(X_15,X_41),greatest_lower_bound(X_40,X_41)) = greatest_lower_bound(X_40,greatest_lower_bound(X_41,X_15)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_41,greatest_lower_bound(X_15,X_41)),greatest_lower_bound(X_41,X_15)) )],[refute_0_1162,refute_0_1163]) ).
cnf(refute_0_1165,plain,
greatest_lower_bound(greatest_lower_bound(X_15,X_41),greatest_lower_bound(X_40,X_41)) = greatest_lower_bound(X_40,greatest_lower_bound(X_41,X_15)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_15,X_41),greatest_lower_bound(X_40,X_41)),greatest_lower_bound(X_40,greatest_lower_bound(X_41,greatest_lower_bound(X_15,X_41)))) )],[refute_0_1161,refute_0_1164]) ).
cnf(refute_0_1166,plain,
greatest_lower_bound(X_41,greatest_lower_bound(X_40,greatest_lower_bound(X_15,X_41))) = greatest_lower_bound(X_40,greatest_lower_bound(X_15,X_41)),
inference(subst,[],[refute_0_285:[bind(Y,$fot(X_41)),bind(X_30,$fot(X_40)),bind(X_31,$fot(X_15))]]) ).
cnf(refute_0_1167,plain,
greatest_lower_bound(greatest_lower_bound(X_41,X_39),greatest_lower_bound(X_15,greatest_lower_bound(X_41,X_39))) = greatest_lower_bound(greatest_lower_bound(X_41,X_39),X_15),
inference(subst,[],[refute_0_229:[bind(Y,$fot(greatest_lower_bound(X_41,X_39)))]]) ).
cnf(refute_0_1168,plain,
greatest_lower_bound(X_39,greatest_lower_bound(X_15,X_41)) = greatest_lower_bound(X_15,greatest_lower_bound(X_41,X_39)),
inference(subst,[],[refute_0_321:[bind(X,$fot(X_39)),bind(Y,$fot(X_15)),bind(X_35,$fot(X_41))]]) ).
cnf(refute_0_1169,plain,
( greatest_lower_bound(X_39,greatest_lower_bound(X_15,X_41)) != greatest_lower_bound(X_15,greatest_lower_bound(X_41,X_39))
| greatest_lower_bound(X_15,greatest_lower_bound(X_41,X_39)) = greatest_lower_bound(X_39,greatest_lower_bound(X_15,X_41)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(greatest_lower_bound(X_39,greatest_lower_bound(X_15,X_41)))),bind(Y0,$fot(greatest_lower_bound(X_15,greatest_lower_bound(X_41,X_39))))]]) ).
cnf(refute_0_1170,plain,
greatest_lower_bound(X_15,greatest_lower_bound(X_41,X_39)) = greatest_lower_bound(X_39,greatest_lower_bound(X_15,X_41)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_39,greatest_lower_bound(X_15,X_41)),greatest_lower_bound(X_15,greatest_lower_bound(X_41,X_39))) )],[refute_0_1168,refute_0_1169]) ).
cnf(refute_0_1171,plain,
( greatest_lower_bound(X_15,greatest_lower_bound(X_41,X_39)) != greatest_lower_bound(X_39,greatest_lower_bound(X_15,X_41))
| greatest_lower_bound(greatest_lower_bound(X_41,X_39),greatest_lower_bound(X_15,greatest_lower_bound(X_41,X_39))) != greatest_lower_bound(greatest_lower_bound(X_41,X_39),X_15)
| greatest_lower_bound(greatest_lower_bound(X_41,X_39),greatest_lower_bound(X_39,greatest_lower_bound(X_15,X_41))) = greatest_lower_bound(greatest_lower_bound(X_41,X_39),X_15) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_41,X_39),greatest_lower_bound(X_15,greatest_lower_bound(X_41,X_39))),greatest_lower_bound(greatest_lower_bound(X_41,X_39),X_15)) ),[0,1],$fot(greatest_lower_bound(X_39,greatest_lower_bound(X_15,X_41)))]]) ).
cnf(refute_0_1172,plain,
( greatest_lower_bound(greatest_lower_bound(X_41,X_39),greatest_lower_bound(X_15,greatest_lower_bound(X_41,X_39))) != greatest_lower_bound(greatest_lower_bound(X_41,X_39),X_15)
| greatest_lower_bound(greatest_lower_bound(X_41,X_39),greatest_lower_bound(X_39,greatest_lower_bound(X_15,X_41))) = greatest_lower_bound(greatest_lower_bound(X_41,X_39),X_15) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_15,greatest_lower_bound(X_41,X_39)),greatest_lower_bound(X_39,greatest_lower_bound(X_15,X_41))) )],[refute_0_1170,refute_0_1171]) ).
cnf(refute_0_1173,plain,
greatest_lower_bound(greatest_lower_bound(X_41,X_39),greatest_lower_bound(X_39,greatest_lower_bound(X_15,X_41))) = greatest_lower_bound(greatest_lower_bound(X_41,X_39),X_15),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_41,X_39),greatest_lower_bound(X_15,greatest_lower_bound(X_41,X_39))),greatest_lower_bound(greatest_lower_bound(X_41,X_39),X_15)) )],[refute_0_1167,refute_0_1172]) ).
cnf(refute_0_1174,plain,
greatest_lower_bound(X_41,greatest_lower_bound(X_15,greatest_lower_bound(X_39,X_41))) = greatest_lower_bound(X_15,greatest_lower_bound(X_39,X_41)),
inference(subst,[],[refute_0_285:[bind(Y,$fot(X_41)),bind(X_30,$fot(X_15)),bind(X_31,$fot(X_39))]]) ).
cnf(refute_0_1175,plain,
greatest_lower_bound(X_39,greatest_lower_bound(X_41,X_39)) = greatest_lower_bound(X_39,X_41),
inference(subst,[],[refute_0_229:[bind(Y,$fot(X_39)),bind(X_15,$fot(X_41))]]) ).
cnf(refute_0_1176,plain,
greatest_lower_bound(X_15,greatest_lower_bound(X_39,greatest_lower_bound(X_41,X_39))) = greatest_lower_bound(X_15,greatest_lower_bound(X_39,greatest_lower_bound(X_41,X_39))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X_15,greatest_lower_bound(X_39,greatest_lower_bound(X_41,X_39))))]]) ).
cnf(refute_0_1177,plain,
( greatest_lower_bound(X_15,greatest_lower_bound(X_39,greatest_lower_bound(X_41,X_39))) != greatest_lower_bound(X_15,greatest_lower_bound(X_39,greatest_lower_bound(X_41,X_39)))
| greatest_lower_bound(X_39,greatest_lower_bound(X_41,X_39)) != greatest_lower_bound(X_39,X_41)
| greatest_lower_bound(X_15,greatest_lower_bound(X_39,greatest_lower_bound(X_41,X_39))) = greatest_lower_bound(X_15,greatest_lower_bound(X_39,X_41)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_15,greatest_lower_bound(X_39,greatest_lower_bound(X_41,X_39))),greatest_lower_bound(X_15,greatest_lower_bound(X_39,greatest_lower_bound(X_41,X_39)))) ),[1,1],$fot(greatest_lower_bound(X_39,X_41))]]) ).
cnf(refute_0_1178,plain,
( greatest_lower_bound(X_39,greatest_lower_bound(X_41,X_39)) != greatest_lower_bound(X_39,X_41)
| greatest_lower_bound(X_15,greatest_lower_bound(X_39,greatest_lower_bound(X_41,X_39))) = greatest_lower_bound(X_15,greatest_lower_bound(X_39,X_41)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_15,greatest_lower_bound(X_39,greatest_lower_bound(X_41,X_39))),greatest_lower_bound(X_15,greatest_lower_bound(X_39,greatest_lower_bound(X_41,X_39)))) )],[refute_0_1176,refute_0_1177]) ).
cnf(refute_0_1179,plain,
greatest_lower_bound(X_15,greatest_lower_bound(X_39,greatest_lower_bound(X_41,X_39))) = greatest_lower_bound(X_15,greatest_lower_bound(X_39,X_41)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_39,greatest_lower_bound(X_41,X_39)),greatest_lower_bound(X_39,X_41)) )],[refute_0_1175,refute_0_1178]) ).
cnf(refute_0_1180,plain,
greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_35,X),Z)) = greatest_lower_bound(greatest_lower_bound(X,greatest_lower_bound(X_35,X)),Z),
inference(subst,[],[associativity_of_glb:[bind(Y,$fot(greatest_lower_bound(X_35,X)))]]) ).
cnf(refute_0_1181,plain,
greatest_lower_bound(X,greatest_lower_bound(X_35,X)) = greatest_lower_bound(X,X_35),
inference(subst,[],[refute_0_229:[bind(Y,$fot(X)),bind(X_15,$fot(X_35))]]) ).
cnf(refute_0_1182,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_35,X)) != greatest_lower_bound(X,X_35)
| greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_35,X),Z)) != greatest_lower_bound(greatest_lower_bound(X,greatest_lower_bound(X_35,X)),Z)
| greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_35,X),Z)) = greatest_lower_bound(greatest_lower_bound(X,X_35),Z) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_35,X),Z)),greatest_lower_bound(greatest_lower_bound(X,greatest_lower_bound(X_35,X)),Z)) ),[1,0],$fot(greatest_lower_bound(X,X_35))]]) ).
cnf(refute_0_1183,plain,
( greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_35,X),Z)) != greatest_lower_bound(greatest_lower_bound(X,greatest_lower_bound(X_35,X)),Z)
| greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_35,X),Z)) = greatest_lower_bound(greatest_lower_bound(X,X_35),Z) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_35,X)),greatest_lower_bound(X,X_35)) )],[refute_0_1181,refute_0_1182]) ).
cnf(refute_0_1184,plain,
greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_35,X),Z)) = greatest_lower_bound(greatest_lower_bound(X,X_35),Z),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_35,X),Z)),greatest_lower_bound(greatest_lower_bound(X,greatest_lower_bound(X_35,X)),Z)) )],[refute_0_1180,refute_0_1183]) ).
cnf(refute_0_1185,plain,
greatest_lower_bound(X,greatest_lower_bound(X_35,greatest_lower_bound(X,Z))) = greatest_lower_bound(X,greatest_lower_bound(Z,X_35)),
inference(subst,[],[refute_0_297:[bind(Y,$fot(Z))]]) ).
cnf(refute_0_1186,plain,
greatest_lower_bound(greatest_lower_bound(X_35,X),Z) = greatest_lower_bound(X_35,greatest_lower_bound(X,Z)),
inference(subst,[],[refute_0_225:[bind(X,$fot(X_35)),bind(Y,$fot(X))]]) ).
cnf(refute_0_1187,plain,
greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_35,X),Z)) = greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_35,X),Z)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_35,X),Z)))]]) ).
cnf(refute_0_1188,plain,
( greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_35,X),Z)) != greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_35,X),Z))
| greatest_lower_bound(greatest_lower_bound(X_35,X),Z) != greatest_lower_bound(X_35,greatest_lower_bound(X,Z))
| greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_35,X),Z)) = greatest_lower_bound(X,greatest_lower_bound(X_35,greatest_lower_bound(X,Z))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_35,X),Z)),greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_35,X),Z))) ),[1,1],$fot(greatest_lower_bound(X_35,greatest_lower_bound(X,Z)))]]) ).
cnf(refute_0_1189,plain,
( greatest_lower_bound(greatest_lower_bound(X_35,X),Z) != greatest_lower_bound(X_35,greatest_lower_bound(X,Z))
| greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_35,X),Z)) = greatest_lower_bound(X,greatest_lower_bound(X_35,greatest_lower_bound(X,Z))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_35,X),Z)),greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_35,X),Z))) )],[refute_0_1187,refute_0_1188]) ).
cnf(refute_0_1190,plain,
greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_35,X),Z)) = greatest_lower_bound(X,greatest_lower_bound(X_35,greatest_lower_bound(X,Z))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_35,X),Z),greatest_lower_bound(X_35,greatest_lower_bound(X,Z))) )],[refute_0_1186,refute_0_1189]) ).
cnf(refute_0_1191,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_35,greatest_lower_bound(X,Z))) != greatest_lower_bound(X,greatest_lower_bound(Z,X_35))
| greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_35,X),Z)) != greatest_lower_bound(X,greatest_lower_bound(X_35,greatest_lower_bound(X,Z)))
| greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_35,X),Z)) = greatest_lower_bound(X,greatest_lower_bound(Z,X_35)) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_35,X),Z)))),bind(Y0,$fot(greatest_lower_bound(X,greatest_lower_bound(X_35,greatest_lower_bound(X,Z))))),bind(Z0,$fot(greatest_lower_bound(X,greatest_lower_bound(Z,X_35))))]]) ).
cnf(refute_0_1192,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_35,greatest_lower_bound(X,Z))) != greatest_lower_bound(X,greatest_lower_bound(Z,X_35))
| greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_35,X),Z)) = greatest_lower_bound(X,greatest_lower_bound(Z,X_35)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_35,X),Z)),greatest_lower_bound(X,greatest_lower_bound(X_35,greatest_lower_bound(X,Z)))) )],[refute_0_1190,refute_0_1191]) ).
cnf(refute_0_1193,plain,
greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_35,X),Z)) = greatest_lower_bound(X,greatest_lower_bound(Z,X_35)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_35,greatest_lower_bound(X,Z))),greatest_lower_bound(X,greatest_lower_bound(Z,X_35))) )],[refute_0_1185,refute_0_1192]) ).
cnf(refute_0_1194,plain,
( greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_35,X),Z)) != greatest_lower_bound(X,greatest_lower_bound(Z,X_35))
| greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_35,X),Z)) != greatest_lower_bound(greatest_lower_bound(X,X_35),Z)
| greatest_lower_bound(X,greatest_lower_bound(Z,X_35)) = greatest_lower_bound(greatest_lower_bound(X,X_35),Z) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_35,X),Z)),greatest_lower_bound(greatest_lower_bound(X,X_35),Z)) ),[0],$fot(greatest_lower_bound(X,greatest_lower_bound(Z,X_35)))]]) ).
cnf(refute_0_1195,plain,
( greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_35,X),Z)) != greatest_lower_bound(greatest_lower_bound(X,X_35),Z)
| greatest_lower_bound(X,greatest_lower_bound(Z,X_35)) = greatest_lower_bound(greatest_lower_bound(X,X_35),Z) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_35,X),Z)),greatest_lower_bound(X,greatest_lower_bound(Z,X_35))) )],[refute_0_1193,refute_0_1194]) ).
cnf(refute_0_1196,plain,
greatest_lower_bound(greatest_lower_bound(X,X_35),Z) = greatest_lower_bound(X,greatest_lower_bound(X_35,Z)),
inference(subst,[],[refute_0_225:[bind(Y,$fot(X_35))]]) ).
cnf(refute_0_1197,plain,
( greatest_lower_bound(X,greatest_lower_bound(Z,X_35)) != greatest_lower_bound(greatest_lower_bound(X,X_35),Z)
| greatest_lower_bound(greatest_lower_bound(X,X_35),Z) != greatest_lower_bound(X,greatest_lower_bound(X_35,Z))
| greatest_lower_bound(X,greatest_lower_bound(Z,X_35)) = greatest_lower_bound(X,greatest_lower_bound(X_35,Z)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X,greatest_lower_bound(Z,X_35)),greatest_lower_bound(X,greatest_lower_bound(X_35,Z))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X,X_35),Z))]]) ).
cnf(refute_0_1198,plain,
( greatest_lower_bound(X,greatest_lower_bound(Z,X_35)) != greatest_lower_bound(greatest_lower_bound(X,X_35),Z)
| greatest_lower_bound(X,greatest_lower_bound(Z,X_35)) = greatest_lower_bound(X,greatest_lower_bound(X_35,Z)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X,X_35),Z),greatest_lower_bound(X,greatest_lower_bound(X_35,Z))) )],[refute_0_1196,refute_0_1197]) ).
cnf(refute_0_1199,plain,
( greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_35,X),Z)) != greatest_lower_bound(greatest_lower_bound(X,X_35),Z)
| greatest_lower_bound(X,greatest_lower_bound(Z,X_35)) = greatest_lower_bound(X,greatest_lower_bound(X_35,Z)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Z,X_35)),greatest_lower_bound(greatest_lower_bound(X,X_35),Z)) )],[refute_0_1195,refute_0_1198]) ).
cnf(refute_0_1200,plain,
greatest_lower_bound(X,greatest_lower_bound(Z,X_35)) = greatest_lower_bound(X,greatest_lower_bound(X_35,Z)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_35,X),Z)),greatest_lower_bound(greatest_lower_bound(X,X_35),Z)) )],[refute_0_1184,refute_0_1199]) ).
cnf(refute_0_1201,plain,
( greatest_lower_bound(X,greatest_lower_bound(Z,X_35)) != greatest_lower_bound(X,greatest_lower_bound(X_35,Z))
| greatest_lower_bound(X,greatest_lower_bound(X_35,Z)) = greatest_lower_bound(X,greatest_lower_bound(Z,X_35)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(Z,X_35)))),bind(Y0,$fot(greatest_lower_bound(X,greatest_lower_bound(X_35,Z))))]]) ).
cnf(refute_0_1202,plain,
greatest_lower_bound(X,greatest_lower_bound(X_35,Z)) = greatest_lower_bound(X,greatest_lower_bound(Z,X_35)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Z,X_35)),greatest_lower_bound(X,greatest_lower_bound(X_35,Z))) )],[refute_0_1200,refute_0_1201]) ).
cnf(refute_0_1203,plain,
greatest_lower_bound(X_15,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X_39)) = greatest_lower_bound(X_15,greatest_lower_bound(X_39,greatest_lower_bound(X_41,X_39))),
inference(subst,[],[refute_0_1202:[bind(X,$fot(X_15)),bind(Z,$fot(X_39)),bind(X_35,$fot(greatest_lower_bound(X_41,X_39)))]]) ).
cnf(refute_0_1204,plain,
( greatest_lower_bound(X_15,greatest_lower_bound(X_39,greatest_lower_bound(X_41,X_39))) != greatest_lower_bound(X_15,greatest_lower_bound(X_39,X_41))
| greatest_lower_bound(X_15,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X_39)) != greatest_lower_bound(X_15,greatest_lower_bound(X_39,greatest_lower_bound(X_41,X_39)))
| greatest_lower_bound(X_15,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X_39)) = greatest_lower_bound(X_15,greatest_lower_bound(X_39,X_41)) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(greatest_lower_bound(X_15,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X_39)))),bind(Y0,$fot(greatest_lower_bound(X_15,greatest_lower_bound(X_39,greatest_lower_bound(X_41,X_39))))),bind(Z0,$fot(greatest_lower_bound(X_15,greatest_lower_bound(X_39,X_41))))]]) ).
cnf(refute_0_1205,plain,
( greatest_lower_bound(X_15,greatest_lower_bound(X_39,greatest_lower_bound(X_41,X_39))) != greatest_lower_bound(X_15,greatest_lower_bound(X_39,X_41))
| greatest_lower_bound(X_15,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X_39)) = greatest_lower_bound(X_15,greatest_lower_bound(X_39,X_41)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_15,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X_39)),greatest_lower_bound(X_15,greatest_lower_bound(X_39,greatest_lower_bound(X_41,X_39)))) )],[refute_0_1203,refute_0_1204]) ).
cnf(refute_0_1206,plain,
greatest_lower_bound(X_15,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X_39)) = greatest_lower_bound(X_15,greatest_lower_bound(X_39,X_41)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_15,greatest_lower_bound(X_39,greatest_lower_bound(X_41,X_39))),greatest_lower_bound(X_15,greatest_lower_bound(X_39,X_41))) )],[refute_0_1179,refute_0_1205]) ).
cnf(refute_0_1207,plain,
greatest_lower_bound(X_41,greatest_lower_bound(X_15,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X_39))) = greatest_lower_bound(X_41,greatest_lower_bound(X_15,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X_39))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X_41,greatest_lower_bound(X_15,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X_39))))]]) ).
cnf(refute_0_1208,plain,
( greatest_lower_bound(X_15,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X_39)) != greatest_lower_bound(X_15,greatest_lower_bound(X_39,X_41))
| greatest_lower_bound(X_41,greatest_lower_bound(X_15,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X_39))) != greatest_lower_bound(X_41,greatest_lower_bound(X_15,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X_39)))
| greatest_lower_bound(X_41,greatest_lower_bound(X_15,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X_39))) = greatest_lower_bound(X_41,greatest_lower_bound(X_15,greatest_lower_bound(X_39,X_41))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_41,greatest_lower_bound(X_15,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X_39))),greatest_lower_bound(X_41,greatest_lower_bound(X_15,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X_39)))) ),[1,1],$fot(greatest_lower_bound(X_15,greatest_lower_bound(X_39,X_41)))]]) ).
cnf(refute_0_1209,plain,
( greatest_lower_bound(X_15,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X_39)) != greatest_lower_bound(X_15,greatest_lower_bound(X_39,X_41))
| greatest_lower_bound(X_41,greatest_lower_bound(X_15,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X_39))) = greatest_lower_bound(X_41,greatest_lower_bound(X_15,greatest_lower_bound(X_39,X_41))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_41,greatest_lower_bound(X_15,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X_39))),greatest_lower_bound(X_41,greatest_lower_bound(X_15,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X_39)))) )],[refute_0_1207,refute_0_1208]) ).
cnf(refute_0_1210,plain,
greatest_lower_bound(X_41,greatest_lower_bound(X_15,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X_39))) = greatest_lower_bound(X_41,greatest_lower_bound(X_15,greatest_lower_bound(X_39,X_41))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_15,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X_39)),greatest_lower_bound(X_15,greatest_lower_bound(X_39,X_41))) )],[refute_0_1206,refute_0_1209]) ).
cnf(refute_0_1211,plain,
( greatest_lower_bound(X_41,greatest_lower_bound(X_15,greatest_lower_bound(X_39,X_41))) != greatest_lower_bound(X_15,greatest_lower_bound(X_39,X_41))
| greatest_lower_bound(X_41,greatest_lower_bound(X_15,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X_39))) != greatest_lower_bound(X_41,greatest_lower_bound(X_15,greatest_lower_bound(X_39,X_41)))
| greatest_lower_bound(X_41,greatest_lower_bound(X_15,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X_39))) = greatest_lower_bound(X_15,greatest_lower_bound(X_39,X_41)) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(greatest_lower_bound(X_41,greatest_lower_bound(X_15,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X_39))))),bind(Y0,$fot(greatest_lower_bound(X_41,greatest_lower_bound(X_15,greatest_lower_bound(X_39,X_41))))),bind(Z0,$fot(greatest_lower_bound(X_15,greatest_lower_bound(X_39,X_41))))]]) ).
cnf(refute_0_1212,plain,
( greatest_lower_bound(X_41,greatest_lower_bound(X_15,greatest_lower_bound(X_39,X_41))) != greatest_lower_bound(X_15,greatest_lower_bound(X_39,X_41))
| greatest_lower_bound(X_41,greatest_lower_bound(X_15,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X_39))) = greatest_lower_bound(X_15,greatest_lower_bound(X_39,X_41)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_41,greatest_lower_bound(X_15,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X_39))),greatest_lower_bound(X_41,greatest_lower_bound(X_15,greatest_lower_bound(X_39,X_41)))) )],[refute_0_1210,refute_0_1211]) ).
cnf(refute_0_1213,plain,
greatest_lower_bound(X_41,greatest_lower_bound(X_15,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X_39))) = greatest_lower_bound(X_15,greatest_lower_bound(X_39,X_41)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_41,greatest_lower_bound(X_15,greatest_lower_bound(X_39,X_41))),greatest_lower_bound(X_15,greatest_lower_bound(X_39,X_41))) )],[refute_0_1174,refute_0_1212]) ).
cnf(refute_0_1214,plain,
greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_41,X_39))) = greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X)),
inference(subst,[],[refute_0_321:[bind(X_35,$fot(greatest_lower_bound(X_41,X_39)))]]) ).
cnf(refute_0_1215,plain,
greatest_lower_bound(X_39,greatest_lower_bound(Y,X_41)) = greatest_lower_bound(Y,greatest_lower_bound(X_41,X_39)),
inference(subst,[],[refute_0_321:[bind(X,$fot(X_39)),bind(X_35,$fot(X_41))]]) ).
cnf(refute_0_1216,plain,
( greatest_lower_bound(X_39,greatest_lower_bound(Y,X_41)) != greatest_lower_bound(Y,greatest_lower_bound(X_41,X_39))
| greatest_lower_bound(Y,greatest_lower_bound(X_41,X_39)) = greatest_lower_bound(X_39,greatest_lower_bound(Y,X_41)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(greatest_lower_bound(X_39,greatest_lower_bound(Y,X_41)))),bind(Y0,$fot(greatest_lower_bound(Y,greatest_lower_bound(X_41,X_39))))]]) ).
cnf(refute_0_1217,plain,
greatest_lower_bound(Y,greatest_lower_bound(X_41,X_39)) = greatest_lower_bound(X_39,greatest_lower_bound(Y,X_41)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_39,greatest_lower_bound(Y,X_41)),greatest_lower_bound(Y,greatest_lower_bound(X_41,X_39))) )],[refute_0_1215,refute_0_1216]) ).
cnf(refute_0_1218,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_41,X_39))) != greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X))
| greatest_lower_bound(Y,greatest_lower_bound(X_41,X_39)) != greatest_lower_bound(X_39,greatest_lower_bound(Y,X_41))
| greatest_lower_bound(X,greatest_lower_bound(X_39,greatest_lower_bound(Y,X_41))) = greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_41,X_39))),greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X))) ),[0,1],$fot(greatest_lower_bound(X_39,greatest_lower_bound(Y,X_41)))]]) ).
cnf(refute_0_1219,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_41,X_39))) != greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X))
| greatest_lower_bound(X,greatest_lower_bound(X_39,greatest_lower_bound(Y,X_41))) = greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(X_41,X_39)),greatest_lower_bound(X_39,greatest_lower_bound(Y,X_41))) )],[refute_0_1217,refute_0_1218]) ).
cnf(refute_0_1220,plain,
greatest_lower_bound(X,greatest_lower_bound(X_39,greatest_lower_bound(Y,X_41))) = greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_41,X_39))),greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X))) )],[refute_0_1214,refute_0_1219]) ).
cnf(refute_0_1221,plain,
greatest_lower_bound(greatest_lower_bound(X_41,X_39),X) = greatest_lower_bound(X_41,greatest_lower_bound(X_39,X)),
inference(subst,[],[refute_0_225:[bind(X,$fot(X_41)),bind(Y,$fot(X_39)),bind(Z,$fot(X))]]) ).
cnf(refute_0_1222,plain,
greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X)) = greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X)))]]) ).
cnf(refute_0_1223,plain,
( greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X)) != greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X))
| greatest_lower_bound(greatest_lower_bound(X_41,X_39),X) != greatest_lower_bound(X_41,greatest_lower_bound(X_39,X))
| greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X)) = greatest_lower_bound(Y,greatest_lower_bound(X_41,greatest_lower_bound(X_39,X))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X)),greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X))) ),[1,1],$fot(greatest_lower_bound(X_41,greatest_lower_bound(X_39,X)))]]) ).
cnf(refute_0_1224,plain,
( greatest_lower_bound(greatest_lower_bound(X_41,X_39),X) != greatest_lower_bound(X_41,greatest_lower_bound(X_39,X))
| greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X)) = greatest_lower_bound(Y,greatest_lower_bound(X_41,greatest_lower_bound(X_39,X))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X)),greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X))) )],[refute_0_1222,refute_0_1223]) ).
cnf(refute_0_1225,plain,
greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X)) = greatest_lower_bound(Y,greatest_lower_bound(X_41,greatest_lower_bound(X_39,X))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_41,X_39),X),greatest_lower_bound(X_41,greatest_lower_bound(X_39,X))) )],[refute_0_1221,refute_0_1224]) ).
cnf(refute_0_1226,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_39,greatest_lower_bound(Y,X_41))) != greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X))
| greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X)) != greatest_lower_bound(Y,greatest_lower_bound(X_41,greatest_lower_bound(X_39,X)))
| greatest_lower_bound(X,greatest_lower_bound(X_39,greatest_lower_bound(Y,X_41))) = greatest_lower_bound(Y,greatest_lower_bound(X_41,greatest_lower_bound(X_39,X))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X,greatest_lower_bound(X_39,greatest_lower_bound(Y,X_41))),greatest_lower_bound(Y,greatest_lower_bound(X_41,greatest_lower_bound(X_39,X)))) ),[0],$fot(greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X)))]]) ).
cnf(refute_0_1227,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_39,greatest_lower_bound(Y,X_41))) != greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X))
| greatest_lower_bound(X,greatest_lower_bound(X_39,greatest_lower_bound(Y,X_41))) = greatest_lower_bound(Y,greatest_lower_bound(X_41,greatest_lower_bound(X_39,X))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X)),greatest_lower_bound(Y,greatest_lower_bound(X_41,greatest_lower_bound(X_39,X)))) )],[refute_0_1225,refute_0_1226]) ).
cnf(refute_0_1228,plain,
greatest_lower_bound(X,greatest_lower_bound(X_39,greatest_lower_bound(Y,X_41))) = greatest_lower_bound(Y,greatest_lower_bound(X_41,greatest_lower_bound(X_39,X))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_39,greatest_lower_bound(Y,X_41))),greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X))) )],[refute_0_1220,refute_0_1227]) ).
cnf(refute_0_1229,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_39,greatest_lower_bound(Y,X_41))) != greatest_lower_bound(Y,greatest_lower_bound(X_41,greatest_lower_bound(X_39,X)))
| greatest_lower_bound(Y,greatest_lower_bound(X_41,greatest_lower_bound(X_39,X))) = greatest_lower_bound(X,greatest_lower_bound(X_39,greatest_lower_bound(Y,X_41))) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(X_39,greatest_lower_bound(Y,X_41))))),bind(Y0,$fot(greatest_lower_bound(Y,greatest_lower_bound(X_41,greatest_lower_bound(X_39,X)))))]]) ).
cnf(refute_0_1230,plain,
greatest_lower_bound(Y,greatest_lower_bound(X_41,greatest_lower_bound(X_39,X))) = greatest_lower_bound(X,greatest_lower_bound(X_39,greatest_lower_bound(Y,X_41))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_39,greatest_lower_bound(Y,X_41))),greatest_lower_bound(Y,greatest_lower_bound(X_41,greatest_lower_bound(X_39,X)))) )],[refute_0_1228,refute_0_1229]) ).
cnf(refute_0_1231,plain,
greatest_lower_bound(greatest_lower_bound(X_41,X_39),greatest_lower_bound(X_39,greatest_lower_bound(X_15,X_41))) = greatest_lower_bound(X_41,greatest_lower_bound(X_15,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X_39))),
inference(subst,[],[refute_0_1230:[bind(X,$fot(X_41)),bind(Y,$fot(greatest_lower_bound(X_41,X_39))),bind(X_39,$fot(X_15)),bind(X_41,$fot(X_39))]]) ).
cnf(refute_0_1232,plain,
( greatest_lower_bound(X_41,greatest_lower_bound(X_15,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X_39))) != greatest_lower_bound(X_15,greatest_lower_bound(X_39,X_41))
| greatest_lower_bound(greatest_lower_bound(X_41,X_39),greatest_lower_bound(X_39,greatest_lower_bound(X_15,X_41))) != greatest_lower_bound(X_41,greatest_lower_bound(X_15,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X_39)))
| greatest_lower_bound(greatest_lower_bound(X_41,X_39),greatest_lower_bound(X_39,greatest_lower_bound(X_15,X_41))) = greatest_lower_bound(X_15,greatest_lower_bound(X_39,X_41)) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(X_41,X_39),greatest_lower_bound(X_39,greatest_lower_bound(X_15,X_41))))),bind(Y0,$fot(greatest_lower_bound(X_41,greatest_lower_bound(X_15,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X_39))))),bind(Z0,$fot(greatest_lower_bound(X_15,greatest_lower_bound(X_39,X_41))))]]) ).
cnf(refute_0_1233,plain,
( greatest_lower_bound(X_41,greatest_lower_bound(X_15,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X_39))) != greatest_lower_bound(X_15,greatest_lower_bound(X_39,X_41))
| greatest_lower_bound(greatest_lower_bound(X_41,X_39),greatest_lower_bound(X_39,greatest_lower_bound(X_15,X_41))) = greatest_lower_bound(X_15,greatest_lower_bound(X_39,X_41)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_41,X_39),greatest_lower_bound(X_39,greatest_lower_bound(X_15,X_41))),greatest_lower_bound(X_41,greatest_lower_bound(X_15,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X_39)))) )],[refute_0_1231,refute_0_1232]) ).
cnf(refute_0_1234,plain,
greatest_lower_bound(greatest_lower_bound(X_41,X_39),greatest_lower_bound(X_39,greatest_lower_bound(X_15,X_41))) = greatest_lower_bound(X_15,greatest_lower_bound(X_39,X_41)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_41,greatest_lower_bound(X_15,greatest_lower_bound(greatest_lower_bound(X_41,X_39),X_39))),greatest_lower_bound(X_15,greatest_lower_bound(X_39,X_41))) )],[refute_0_1213,refute_0_1233]) ).
cnf(refute_0_1235,plain,
( greatest_lower_bound(greatest_lower_bound(X_41,X_39),greatest_lower_bound(X_39,greatest_lower_bound(X_15,X_41))) != greatest_lower_bound(X_15,greatest_lower_bound(X_39,X_41))
| greatest_lower_bound(greatest_lower_bound(X_41,X_39),greatest_lower_bound(X_39,greatest_lower_bound(X_15,X_41))) != greatest_lower_bound(greatest_lower_bound(X_41,X_39),X_15)
| greatest_lower_bound(X_15,greatest_lower_bound(X_39,X_41)) = greatest_lower_bound(greatest_lower_bound(X_41,X_39),X_15) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_41,X_39),greatest_lower_bound(X_39,greatest_lower_bound(X_15,X_41))),greatest_lower_bound(greatest_lower_bound(X_41,X_39),X_15)) ),[0],$fot(greatest_lower_bound(X_15,greatest_lower_bound(X_39,X_41)))]]) ).
cnf(refute_0_1236,plain,
( greatest_lower_bound(greatest_lower_bound(X_41,X_39),greatest_lower_bound(X_39,greatest_lower_bound(X_15,X_41))) != greatest_lower_bound(greatest_lower_bound(X_41,X_39),X_15)
| greatest_lower_bound(X_15,greatest_lower_bound(X_39,X_41)) = greatest_lower_bound(greatest_lower_bound(X_41,X_39),X_15) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_41,X_39),greatest_lower_bound(X_39,greatest_lower_bound(X_15,X_41))),greatest_lower_bound(X_15,greatest_lower_bound(X_39,X_41))) )],[refute_0_1234,refute_0_1235]) ).
cnf(refute_0_1237,plain,
greatest_lower_bound(greatest_lower_bound(X_41,X_39),X_15) = greatest_lower_bound(X_41,greatest_lower_bound(X_39,X_15)),
inference(subst,[],[refute_0_225:[bind(X,$fot(X_41)),bind(Y,$fot(X_39)),bind(Z,$fot(X_15))]]) ).
cnf(refute_0_1238,plain,
( greatest_lower_bound(X_15,greatest_lower_bound(X_39,X_41)) != greatest_lower_bound(greatest_lower_bound(X_41,X_39),X_15)
| greatest_lower_bound(greatest_lower_bound(X_41,X_39),X_15) != greatest_lower_bound(X_41,greatest_lower_bound(X_39,X_15))
| greatest_lower_bound(X_15,greatest_lower_bound(X_39,X_41)) = greatest_lower_bound(X_41,greatest_lower_bound(X_39,X_15)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_15,greatest_lower_bound(X_39,X_41)),greatest_lower_bound(X_41,greatest_lower_bound(X_39,X_15))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_41,X_39),X_15))]]) ).
cnf(refute_0_1239,plain,
( greatest_lower_bound(X_15,greatest_lower_bound(X_39,X_41)) != greatest_lower_bound(greatest_lower_bound(X_41,X_39),X_15)
| greatest_lower_bound(X_15,greatest_lower_bound(X_39,X_41)) = greatest_lower_bound(X_41,greatest_lower_bound(X_39,X_15)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_41,X_39),X_15),greatest_lower_bound(X_41,greatest_lower_bound(X_39,X_15))) )],[refute_0_1237,refute_0_1238]) ).
cnf(refute_0_1240,plain,
( greatest_lower_bound(greatest_lower_bound(X_41,X_39),greatest_lower_bound(X_39,greatest_lower_bound(X_15,X_41))) != greatest_lower_bound(greatest_lower_bound(X_41,X_39),X_15)
| greatest_lower_bound(X_15,greatest_lower_bound(X_39,X_41)) = greatest_lower_bound(X_41,greatest_lower_bound(X_39,X_15)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_15,greatest_lower_bound(X_39,X_41)),greatest_lower_bound(greatest_lower_bound(X_41,X_39),X_15)) )],[refute_0_1236,refute_0_1239]) ).
cnf(refute_0_1241,plain,
greatest_lower_bound(X_15,greatest_lower_bound(X_39,X_41)) = greatest_lower_bound(X_41,greatest_lower_bound(X_39,X_15)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_41,X_39),greatest_lower_bound(X_39,greatest_lower_bound(X_15,X_41))),greatest_lower_bound(greatest_lower_bound(X_41,X_39),X_15)) )],[refute_0_1173,refute_0_1240]) ).
cnf(refute_0_1242,plain,
( greatest_lower_bound(X_15,greatest_lower_bound(X_39,X_41)) != greatest_lower_bound(X_41,greatest_lower_bound(X_39,X_15))
| greatest_lower_bound(X_41,greatest_lower_bound(X_39,X_15)) = greatest_lower_bound(X_15,greatest_lower_bound(X_39,X_41)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(greatest_lower_bound(X_15,greatest_lower_bound(X_39,X_41)))),bind(Y0,$fot(greatest_lower_bound(X_41,greatest_lower_bound(X_39,X_15))))]]) ).
cnf(refute_0_1243,plain,
greatest_lower_bound(X_41,greatest_lower_bound(X_39,X_15)) = greatest_lower_bound(X_15,greatest_lower_bound(X_39,X_41)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_15,greatest_lower_bound(X_39,X_41)),greatest_lower_bound(X_41,greatest_lower_bound(X_39,X_15))) )],[refute_0_1241,refute_0_1242]) ).
cnf(refute_0_1244,plain,
greatest_lower_bound(greatest_lower_bound(X_15,X_41),greatest_lower_bound(X_40,X_41)) = greatest_lower_bound(X_41,greatest_lower_bound(X_40,greatest_lower_bound(X_15,X_41))),
inference(subst,[],[refute_0_1243:[bind(X_15,$fot(X_41)),bind(X_39,$fot(X_40)),bind(X_41,$fot(greatest_lower_bound(X_15,X_41)))]]) ).
cnf(refute_0_1245,plain,
( greatest_lower_bound(X_41,greatest_lower_bound(X_40,greatest_lower_bound(X_15,X_41))) != greatest_lower_bound(X_40,greatest_lower_bound(X_15,X_41))
| greatest_lower_bound(greatest_lower_bound(X_15,X_41),greatest_lower_bound(X_40,X_41)) != greatest_lower_bound(X_41,greatest_lower_bound(X_40,greatest_lower_bound(X_15,X_41)))
| greatest_lower_bound(greatest_lower_bound(X_15,X_41),greatest_lower_bound(X_40,X_41)) = greatest_lower_bound(X_40,greatest_lower_bound(X_15,X_41)) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(X_15,X_41),greatest_lower_bound(X_40,X_41)))),bind(Y0,$fot(greatest_lower_bound(X_41,greatest_lower_bound(X_40,greatest_lower_bound(X_15,X_41))))),bind(Z0,$fot(greatest_lower_bound(X_40,greatest_lower_bound(X_15,X_41))))]]) ).
cnf(refute_0_1246,plain,
( greatest_lower_bound(X_41,greatest_lower_bound(X_40,greatest_lower_bound(X_15,X_41))) != greatest_lower_bound(X_40,greatest_lower_bound(X_15,X_41))
| greatest_lower_bound(greatest_lower_bound(X_15,X_41),greatest_lower_bound(X_40,X_41)) = greatest_lower_bound(X_40,greatest_lower_bound(X_15,X_41)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_15,X_41),greatest_lower_bound(X_40,X_41)),greatest_lower_bound(X_41,greatest_lower_bound(X_40,greatest_lower_bound(X_15,X_41)))) )],[refute_0_1244,refute_0_1245]) ).
cnf(refute_0_1247,plain,
greatest_lower_bound(greatest_lower_bound(X_15,X_41),greatest_lower_bound(X_40,X_41)) = greatest_lower_bound(X_40,greatest_lower_bound(X_15,X_41)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_41,greatest_lower_bound(X_40,greatest_lower_bound(X_15,X_41))),greatest_lower_bound(X_40,greatest_lower_bound(X_15,X_41))) )],[refute_0_1166,refute_0_1246]) ).
cnf(refute_0_1248,plain,
( greatest_lower_bound(greatest_lower_bound(X_15,X_41),greatest_lower_bound(X_40,X_41)) != greatest_lower_bound(X_40,greatest_lower_bound(X_15,X_41))
| greatest_lower_bound(greatest_lower_bound(X_15,X_41),greatest_lower_bound(X_40,X_41)) != greatest_lower_bound(X_40,greatest_lower_bound(X_41,X_15))
| greatest_lower_bound(X_40,greatest_lower_bound(X_15,X_41)) = greatest_lower_bound(X_40,greatest_lower_bound(X_41,X_15)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_15,X_41),greatest_lower_bound(X_40,X_41)),greatest_lower_bound(X_40,greatest_lower_bound(X_41,X_15))) ),[0],$fot(greatest_lower_bound(X_40,greatest_lower_bound(X_15,X_41)))]]) ).
cnf(refute_0_1249,plain,
( greatest_lower_bound(greatest_lower_bound(X_15,X_41),greatest_lower_bound(X_40,X_41)) != greatest_lower_bound(X_40,greatest_lower_bound(X_41,X_15))
| greatest_lower_bound(X_40,greatest_lower_bound(X_15,X_41)) = greatest_lower_bound(X_40,greatest_lower_bound(X_41,X_15)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_15,X_41),greatest_lower_bound(X_40,X_41)),greatest_lower_bound(X_40,greatest_lower_bound(X_15,X_41))) )],[refute_0_1247,refute_0_1248]) ).
cnf(refute_0_1250,plain,
greatest_lower_bound(X_40,greatest_lower_bound(X_15,X_41)) = greatest_lower_bound(X_40,greatest_lower_bound(X_41,X_15)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_15,X_41),greatest_lower_bound(X_40,X_41)),greatest_lower_bound(X_40,greatest_lower_bound(X_41,X_15))) )],[refute_0_1165,refute_0_1249]) ).
cnf(refute_0_1251,plain,
greatest_lower_bound(X_197,greatest_lower_bound(least_upper_bound(X_18,Y),least_upper_bound(Y,X_18))) = greatest_lower_bound(X_197,greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y))),
inference(subst,[],[refute_0_1250:[bind(X_15,$fot(least_upper_bound(X_18,Y))),bind(X_40,$fot(X_197)),bind(X_41,$fot(least_upper_bound(Y,X_18)))]]) ).
cnf(refute_0_1252,plain,
( greatest_lower_bound(X_197,greatest_lower_bound(least_upper_bound(X_18,Y),least_upper_bound(Y,X_18))) != greatest_lower_bound(X_197,greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)))
| greatest_lower_bound(least_upper_bound(X_18,Y),least_upper_bound(Y,X_18)) != least_upper_bound(X_18,Y)
| greatest_lower_bound(X_197,least_upper_bound(X_18,Y)) = greatest_lower_bound(X_197,greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_197,greatest_lower_bound(least_upper_bound(X_18,Y),least_upper_bound(Y,X_18))),greatest_lower_bound(X_197,greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)))) ),[0,1],$fot(least_upper_bound(X_18,Y))]]) ).
cnf(refute_0_1253,plain,
( greatest_lower_bound(X_197,greatest_lower_bound(least_upper_bound(X_18,Y),least_upper_bound(Y,X_18))) != greatest_lower_bound(X_197,greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)))
| greatest_lower_bound(X_197,least_upper_bound(X_18,Y)) = greatest_lower_bound(X_197,greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_18,Y),least_upper_bound(Y,X_18)),least_upper_bound(X_18,Y)) )],[refute_0_659,refute_0_1252]) ).
cnf(refute_0_1254,plain,
greatest_lower_bound(X_197,least_upper_bound(X_18,Y)) = greatest_lower_bound(X_197,greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_197,greatest_lower_bound(least_upper_bound(X_18,Y),least_upper_bound(Y,X_18))),greatest_lower_bound(X_197,greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)))) )],[refute_0_1251,refute_0_1253]) ).
cnf(refute_0_1255,plain,
greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)) = least_upper_bound(Y,X_18),
inference(subst,[],[refute_0_659:[bind(Y,$fot(X_18)),bind(X_18,$fot(Y))]]) ).
cnf(refute_0_1256,plain,
greatest_lower_bound(X_197,greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y))) = greatest_lower_bound(X_197,greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X_197,greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y))))]]) ).
cnf(refute_0_1257,plain,
( greatest_lower_bound(X_197,greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y))) != greatest_lower_bound(X_197,greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)))
| greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)) != least_upper_bound(Y,X_18)
| greatest_lower_bound(X_197,greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y))) = greatest_lower_bound(X_197,least_upper_bound(Y,X_18)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_197,greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y))),greatest_lower_bound(X_197,greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)))) ),[1,1],$fot(least_upper_bound(Y,X_18))]]) ).
cnf(refute_0_1258,plain,
( greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)) != least_upper_bound(Y,X_18)
| greatest_lower_bound(X_197,greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y))) = greatest_lower_bound(X_197,least_upper_bound(Y,X_18)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_197,greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y))),greatest_lower_bound(X_197,greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)))) )],[refute_0_1256,refute_0_1257]) ).
cnf(refute_0_1259,plain,
greatest_lower_bound(X_197,greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y))) = greatest_lower_bound(X_197,least_upper_bound(Y,X_18)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),least_upper_bound(Y,X_18)) )],[refute_0_1255,refute_0_1258]) ).
cnf(refute_0_1260,plain,
( greatest_lower_bound(X_197,greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y))) != greatest_lower_bound(X_197,least_upper_bound(Y,X_18))
| greatest_lower_bound(X_197,least_upper_bound(X_18,Y)) != greatest_lower_bound(X_197,greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)))
| greatest_lower_bound(X_197,least_upper_bound(X_18,Y)) = greatest_lower_bound(X_197,least_upper_bound(Y,X_18)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_197,least_upper_bound(X_18,Y)),greatest_lower_bound(X_197,greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)))) ),[1],$fot(greatest_lower_bound(X_197,least_upper_bound(Y,X_18)))]]) ).
cnf(refute_0_1261,plain,
( greatest_lower_bound(X_197,least_upper_bound(X_18,Y)) != greatest_lower_bound(X_197,greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)))
| greatest_lower_bound(X_197,least_upper_bound(X_18,Y)) = greatest_lower_bound(X_197,least_upper_bound(Y,X_18)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_197,greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y))),greatest_lower_bound(X_197,least_upper_bound(Y,X_18))) )],[refute_0_1259,refute_0_1260]) ).
cnf(refute_0_1262,plain,
greatest_lower_bound(X_197,least_upper_bound(X_18,Y)) = greatest_lower_bound(X_197,least_upper_bound(Y,X_18)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_197,least_upper_bound(X_18,Y)),greatest_lower_bound(X_197,greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)))) )],[refute_0_1254,refute_0_1261]) ).
cnf(refute_0_1263,plain,
( greatest_lower_bound(X_197,least_upper_bound(X_18,Y)) != greatest_lower_bound(X_197,least_upper_bound(Y,X_18))
| greatest_lower_bound(X_197,least_upper_bound(Y,X_18)) = greatest_lower_bound(X_197,least_upper_bound(X_18,Y)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(greatest_lower_bound(X_197,least_upper_bound(X_18,Y)))),bind(Y0,$fot(greatest_lower_bound(X_197,least_upper_bound(Y,X_18))))]]) ).
cnf(refute_0_1264,plain,
greatest_lower_bound(X_197,least_upper_bound(Y,X_18)) = greatest_lower_bound(X_197,least_upper_bound(X_18,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_197,least_upper_bound(X_18,Y)),greatest_lower_bound(X_197,least_upper_bound(Y,X_18))) )],[refute_0_1262,refute_0_1263]) ).
cnf(refute_0_1265,plain,
greatest_lower_bound(X_305,least_upper_bound(least_upper_bound(identity,X_221),identity)) = greatest_lower_bound(X_305,least_upper_bound(identity,least_upper_bound(identity,X_221))),
inference(subst,[],[refute_0_1264:[bind(Y,$fot(least_upper_bound(identity,X_221))),bind(X_18,$fot(identity)),bind(X_197,$fot(X_305))]]) ).
cnf(refute_0_1266,plain,
( greatest_lower_bound(X_305,least_upper_bound(identity,least_upper_bound(identity,X_221))) != greatest_lower_bound(X_305,least_upper_bound(identity,X_221))
| greatest_lower_bound(X_305,least_upper_bound(least_upper_bound(identity,X_221),identity)) != greatest_lower_bound(X_305,least_upper_bound(identity,least_upper_bound(identity,X_221)))
| greatest_lower_bound(X_305,least_upper_bound(least_upper_bound(identity,X_221),identity)) = greatest_lower_bound(X_305,least_upper_bound(identity,X_221)) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(greatest_lower_bound(X_305,least_upper_bound(least_upper_bound(identity,X_221),identity)))),bind(Y0,$fot(greatest_lower_bound(X_305,least_upper_bound(identity,least_upper_bound(identity,X_221))))),bind(Z0,$fot(greatest_lower_bound(X_305,least_upper_bound(identity,X_221))))]]) ).
cnf(refute_0_1267,plain,
( greatest_lower_bound(X_305,least_upper_bound(identity,least_upper_bound(identity,X_221))) != greatest_lower_bound(X_305,least_upper_bound(identity,X_221))
| greatest_lower_bound(X_305,least_upper_bound(least_upper_bound(identity,X_221),identity)) = greatest_lower_bound(X_305,least_upper_bound(identity,X_221)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_305,least_upper_bound(least_upper_bound(identity,X_221),identity)),greatest_lower_bound(X_305,least_upper_bound(identity,least_upper_bound(identity,X_221)))) )],[refute_0_1265,refute_0_1266]) ).
cnf(refute_0_1268,plain,
greatest_lower_bound(X_305,least_upper_bound(least_upper_bound(identity,X_221),identity)) = greatest_lower_bound(X_305,least_upper_bound(identity,X_221)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_305,least_upper_bound(identity,least_upper_bound(identity,X_221))),greatest_lower_bound(X_305,least_upper_bound(identity,X_221))) )],[refute_0_1160,refute_0_1267]) ).
cnf(refute_0_1269,plain,
( greatest_lower_bound(X_305,least_upper_bound(least_upper_bound(identity,X_221),identity)) != greatest_lower_bound(X_305,least_upper_bound(identity,X_221))
| greatest_lower_bound(X_305,least_upper_bound(least_upper_bound(identity,X_221),identity)) != greatest_lower_bound(least_upper_bound(X_221,least_upper_bound(identity,identity)),X_305)
| greatest_lower_bound(X_305,least_upper_bound(identity,X_221)) = greatest_lower_bound(least_upper_bound(X_221,least_upper_bound(identity,identity)),X_305) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_305,least_upper_bound(least_upper_bound(identity,X_221),identity)),greatest_lower_bound(least_upper_bound(X_221,least_upper_bound(identity,identity)),X_305)) ),[0],$fot(greatest_lower_bound(X_305,least_upper_bound(identity,X_221)))]]) ).
cnf(refute_0_1270,plain,
( greatest_lower_bound(X_305,least_upper_bound(least_upper_bound(identity,X_221),identity)) != greatest_lower_bound(least_upper_bound(X_221,least_upper_bound(identity,identity)),X_305)
| greatest_lower_bound(X_305,least_upper_bound(identity,X_221)) = greatest_lower_bound(least_upper_bound(X_221,least_upper_bound(identity,identity)),X_305) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_305,least_upper_bound(least_upper_bound(identity,X_221),identity)),greatest_lower_bound(X_305,least_upper_bound(identity,X_221))) )],[refute_0_1268,refute_0_1269]) ).
cnf(refute_0_1271,plain,
least_upper_bound(identity,identity) = identity,
inference(subst,[],[idempotence_of_lub:[bind(X,$fot(identity))]]) ).
cnf(refute_0_1272,plain,
least_upper_bound(X_221,least_upper_bound(identity,identity)) = least_upper_bound(X_221,least_upper_bound(identity,identity)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_221,least_upper_bound(identity,identity)))]]) ).
cnf(refute_0_1273,plain,
( least_upper_bound(X_221,least_upper_bound(identity,identity)) != least_upper_bound(X_221,least_upper_bound(identity,identity))
| least_upper_bound(identity,identity) != identity
| least_upper_bound(X_221,least_upper_bound(identity,identity)) = least_upper_bound(X_221,identity) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_221,least_upper_bound(identity,identity)),least_upper_bound(X_221,least_upper_bound(identity,identity))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_1274,plain,
( least_upper_bound(identity,identity) != identity
| least_upper_bound(X_221,least_upper_bound(identity,identity)) = least_upper_bound(X_221,identity) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_221,least_upper_bound(identity,identity)),least_upper_bound(X_221,least_upper_bound(identity,identity))) )],[refute_0_1272,refute_0_1273]) ).
cnf(refute_0_1275,plain,
least_upper_bound(X_221,least_upper_bound(identity,identity)) = least_upper_bound(X_221,identity),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,identity),identity) )],[refute_0_1271,refute_0_1274]) ).
cnf(refute_0_1276,plain,
greatest_lower_bound(least_upper_bound(X_221,least_upper_bound(identity,identity)),X_305) = greatest_lower_bound(least_upper_bound(X_221,least_upper_bound(identity,identity)),X_305),
introduced(tautology,[refl,[$fot(greatest_lower_bound(least_upper_bound(X_221,least_upper_bound(identity,identity)),X_305))]]) ).
cnf(refute_0_1277,plain,
( greatest_lower_bound(least_upper_bound(X_221,least_upper_bound(identity,identity)),X_305) != greatest_lower_bound(least_upper_bound(X_221,least_upper_bound(identity,identity)),X_305)
| least_upper_bound(X_221,least_upper_bound(identity,identity)) != least_upper_bound(X_221,identity)
| greatest_lower_bound(least_upper_bound(X_221,least_upper_bound(identity,identity)),X_305) = greatest_lower_bound(least_upper_bound(X_221,identity),X_305) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_221,least_upper_bound(identity,identity)),X_305),greatest_lower_bound(least_upper_bound(X_221,least_upper_bound(identity,identity)),X_305)) ),[1,0],$fot(least_upper_bound(X_221,identity))]]) ).
cnf(refute_0_1278,plain,
( least_upper_bound(X_221,least_upper_bound(identity,identity)) != least_upper_bound(X_221,identity)
| greatest_lower_bound(least_upper_bound(X_221,least_upper_bound(identity,identity)),X_305) = greatest_lower_bound(least_upper_bound(X_221,identity),X_305) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_221,least_upper_bound(identity,identity)),X_305),greatest_lower_bound(least_upper_bound(X_221,least_upper_bound(identity,identity)),X_305)) )],[refute_0_1276,refute_0_1277]) ).
cnf(refute_0_1279,plain,
greatest_lower_bound(least_upper_bound(X_221,least_upper_bound(identity,identity)),X_305) = greatest_lower_bound(least_upper_bound(X_221,identity),X_305),
inference(resolve,[$cnf( $equal(least_upper_bound(X_221,least_upper_bound(identity,identity)),least_upper_bound(X_221,identity)) )],[refute_0_1275,refute_0_1278]) ).
cnf(refute_0_1280,plain,
( greatest_lower_bound(X_305,least_upper_bound(identity,X_221)) != greatest_lower_bound(least_upper_bound(X_221,least_upper_bound(identity,identity)),X_305)
| greatest_lower_bound(least_upper_bound(X_221,least_upper_bound(identity,identity)),X_305) != greatest_lower_bound(least_upper_bound(X_221,identity),X_305)
| greatest_lower_bound(X_305,least_upper_bound(identity,X_221)) = greatest_lower_bound(least_upper_bound(X_221,identity),X_305) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_305,least_upper_bound(identity,X_221)),greatest_lower_bound(least_upper_bound(X_221,identity),X_305)) ),[0],$fot(greatest_lower_bound(least_upper_bound(X_221,least_upper_bound(identity,identity)),X_305))]]) ).
cnf(refute_0_1281,plain,
( greatest_lower_bound(X_305,least_upper_bound(identity,X_221)) != greatest_lower_bound(least_upper_bound(X_221,least_upper_bound(identity,identity)),X_305)
| greatest_lower_bound(X_305,least_upper_bound(identity,X_221)) = greatest_lower_bound(least_upper_bound(X_221,identity),X_305) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_221,least_upper_bound(identity,identity)),X_305),greatest_lower_bound(least_upper_bound(X_221,identity),X_305)) )],[refute_0_1279,refute_0_1280]) ).
cnf(refute_0_1282,plain,
( greatest_lower_bound(X_305,least_upper_bound(least_upper_bound(identity,X_221),identity)) != greatest_lower_bound(least_upper_bound(X_221,least_upper_bound(identity,identity)),X_305)
| greatest_lower_bound(X_305,least_upper_bound(identity,X_221)) = greatest_lower_bound(least_upper_bound(X_221,identity),X_305) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_305,least_upper_bound(identity,X_221)),greatest_lower_bound(least_upper_bound(X_221,least_upper_bound(identity,identity)),X_305)) )],[refute_0_1270,refute_0_1281]) ).
cnf(refute_0_1283,plain,
greatest_lower_bound(X_305,least_upper_bound(identity,X_221)) = greatest_lower_bound(least_upper_bound(X_221,identity),X_305),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_305,least_upper_bound(least_upper_bound(identity,X_221),identity)),greatest_lower_bound(least_upper_bound(X_221,least_upper_bound(identity,identity)),X_305)) )],[refute_0_1155,refute_0_1282]) ).
cnf(refute_0_1284,plain,
greatest_lower_bound(least_upper_bound(identity,inverse(X)),least_upper_bound(identity,X)) = greatest_lower_bound(least_upper_bound(X,identity),least_upper_bound(identity,inverse(X))),
inference(subst,[],[refute_0_1283:[bind(X_221,$fot(X)),bind(X_305,$fot(least_upper_bound(identity,inverse(X))))]]) ).
cnf(refute_0_1285,plain,
( greatest_lower_bound(least_upper_bound(X,identity),least_upper_bound(identity,inverse(X))) != multiply(least_upper_bound(identity,X),greatest_lower_bound(identity,inverse(X)))
| greatest_lower_bound(least_upper_bound(identity,inverse(X)),least_upper_bound(identity,X)) != greatest_lower_bound(least_upper_bound(X,identity),least_upper_bound(identity,inverse(X)))
| greatest_lower_bound(least_upper_bound(identity,inverse(X)),least_upper_bound(identity,X)) = multiply(least_upper_bound(identity,X),greatest_lower_bound(identity,inverse(X))) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(identity,inverse(X)),least_upper_bound(identity,X)))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(X,identity),least_upper_bound(identity,inverse(X))))),bind(Z0,$fot(multiply(least_upper_bound(identity,X),greatest_lower_bound(identity,inverse(X)))))]]) ).
cnf(refute_0_1286,plain,
( greatest_lower_bound(least_upper_bound(X,identity),least_upper_bound(identity,inverse(X))) != multiply(least_upper_bound(identity,X),greatest_lower_bound(identity,inverse(X)))
| greatest_lower_bound(least_upper_bound(identity,inverse(X)),least_upper_bound(identity,X)) = multiply(least_upper_bound(identity,X),greatest_lower_bound(identity,inverse(X))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,inverse(X)),least_upper_bound(identity,X)),greatest_lower_bound(least_upper_bound(X,identity),least_upper_bound(identity,inverse(X)))) )],[refute_0_1284,refute_0_1285]) ).
cnf(refute_0_1287,plain,
greatest_lower_bound(least_upper_bound(identity,inverse(X)),least_upper_bound(identity,X)) = multiply(least_upper_bound(identity,X),greatest_lower_bound(identity,inverse(X))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X,identity),least_upper_bound(identity,inverse(X))),multiply(least_upper_bound(identity,X),greatest_lower_bound(identity,inverse(X)))) )],[refute_0_823,refute_0_1286]) ).
cnf(refute_0_1288,plain,
( multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,X)) != greatest_lower_bound(least_upper_bound(identity,inverse(X)),least_upper_bound(identity,X))
| greatest_lower_bound(least_upper_bound(identity,inverse(X)),least_upper_bound(identity,X)) != multiply(least_upper_bound(identity,X),greatest_lower_bound(identity,inverse(X)))
| multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,X)) = multiply(least_upper_bound(identity,X),greatest_lower_bound(identity,inverse(X))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,X)),multiply(least_upper_bound(identity,X),greatest_lower_bound(identity,inverse(X)))) ),[0],$fot(greatest_lower_bound(least_upper_bound(identity,inverse(X)),least_upper_bound(identity,X)))]]) ).
cnf(refute_0_1289,plain,
( multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,X)) != greatest_lower_bound(least_upper_bound(identity,inverse(X)),least_upper_bound(identity,X))
| multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,X)) = multiply(least_upper_bound(identity,X),greatest_lower_bound(identity,inverse(X))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,inverse(X)),least_upper_bound(identity,X)),multiply(least_upper_bound(identity,X),greatest_lower_bound(identity,inverse(X)))) )],[refute_0_1287,refute_0_1288]) ).
cnf(refute_0_1290,plain,
( multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,inverse(inverse(X)))) != greatest_lower_bound(least_upper_bound(identity,inverse(X)),least_upper_bound(identity,X))
| multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,X)) = multiply(least_upper_bound(identity,X),greatest_lower_bound(identity,inverse(X))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,X)),greatest_lower_bound(least_upper_bound(identity,inverse(X)),least_upper_bound(identity,X))) )],[refute_0_734,refute_0_1289]) ).
cnf(refute_0_1291,plain,
multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,X)) = multiply(least_upper_bound(identity,X),greatest_lower_bound(identity,inverse(X))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,inverse(inverse(X)))),greatest_lower_bound(least_upper_bound(identity,inverse(X)),least_upper_bound(identity,X))) )],[refute_0_724,refute_0_1290]) ).
cnf(refute_0_1292,plain,
multiply(least_upper_bound(identity,inverse(X_75)),greatest_lower_bound(identity,X_75)) = multiply(least_upper_bound(identity,X_75),greatest_lower_bound(identity,inverse(X_75))),
inference(subst,[],[refute_0_1291:[bind(X,$fot(X_75))]]) ).
cnf(refute_0_1293,plain,
( multiply(least_upper_bound(identity,inverse(X_75)),greatest_lower_bound(identity,X_75)) != multiply(least_upper_bound(identity,X_75),greatest_lower_bound(identity,inverse(X_75)))
| multiply(least_upper_bound(identity,inverse(X_75)),greatest_lower_bound(identity,X_75)) != least_upper_bound(greatest_lower_bound(identity,X_75),greatest_lower_bound(identity,inverse(X_75)))
| multiply(least_upper_bound(identity,X_75),greatest_lower_bound(identity,inverse(X_75))) = least_upper_bound(greatest_lower_bound(identity,X_75),greatest_lower_bound(identity,inverse(X_75))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_75)),greatest_lower_bound(identity,X_75)),least_upper_bound(greatest_lower_bound(identity,X_75),greatest_lower_bound(identity,inverse(X_75)))) ),[0],$fot(multiply(least_upper_bound(identity,X_75),greatest_lower_bound(identity,inverse(X_75))))]]) ).
cnf(refute_0_1294,plain,
( multiply(least_upper_bound(identity,inverse(X_75)),greatest_lower_bound(identity,X_75)) != least_upper_bound(greatest_lower_bound(identity,X_75),greatest_lower_bound(identity,inverse(X_75)))
| multiply(least_upper_bound(identity,X_75),greatest_lower_bound(identity,inverse(X_75))) = least_upper_bound(greatest_lower_bound(identity,X_75),greatest_lower_bound(identity,inverse(X_75))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_75)),greatest_lower_bound(identity,X_75)),multiply(least_upper_bound(identity,X_75),greatest_lower_bound(identity,inverse(X_75)))) )],[refute_0_1292,refute_0_1293]) ).
cnf(refute_0_1295,plain,
multiply(least_upper_bound(identity,X_75),greatest_lower_bound(identity,inverse(X_75))) = least_upper_bound(greatest_lower_bound(identity,X_75),greatest_lower_bound(identity,inverse(X_75))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_75)),greatest_lower_bound(identity,X_75)),least_upper_bound(greatest_lower_bound(identity,X_75),greatest_lower_bound(identity,inverse(X_75)))) )],[refute_0_714,refute_0_1294]) ).
cnf(refute_0_1296,plain,
( multiply(least_upper_bound(identity,X_75),greatest_lower_bound(identity,inverse(X_75))) != least_upper_bound(greatest_lower_bound(identity,X_75),greatest_lower_bound(identity,inverse(X_75)))
| least_upper_bound(greatest_lower_bound(identity,X_75),greatest_lower_bound(identity,inverse(X_75))) = multiply(least_upper_bound(identity,X_75),greatest_lower_bound(identity,inverse(X_75))) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(multiply(least_upper_bound(identity,X_75),greatest_lower_bound(identity,inverse(X_75))))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(identity,X_75),greatest_lower_bound(identity,inverse(X_75)))))]]) ).
cnf(refute_0_1297,plain,
least_upper_bound(greatest_lower_bound(identity,X_75),greatest_lower_bound(identity,inverse(X_75))) = multiply(least_upper_bound(identity,X_75),greatest_lower_bound(identity,inverse(X_75))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_75),greatest_lower_bound(identity,inverse(X_75))),least_upper_bound(greatest_lower_bound(identity,X_75),greatest_lower_bound(identity,inverse(X_75)))) )],[refute_0_1295,refute_0_1296]) ).
cnf(refute_0_1298,plain,
least_upper_bound(greatest_lower_bound(identity,X_309),greatest_lower_bound(identity,inverse(X_309))) = multiply(least_upper_bound(identity,X_309),greatest_lower_bound(identity,inverse(X_309))),
inference(subst,[],[refute_0_1297:[bind(X_75,$fot(X_309))]]) ).
cnf(refute_0_1299,plain,
( multiply(greatest_lower_bound(identity,X_309),least_upper_bound(identity,inverse(X_309))) != least_upper_bound(greatest_lower_bound(identity,X_309),greatest_lower_bound(identity,inverse(X_309)))
| least_upper_bound(greatest_lower_bound(identity,X_309),greatest_lower_bound(identity,inverse(X_309))) != multiply(least_upper_bound(identity,X_309),greatest_lower_bound(identity,inverse(X_309)))
| multiply(greatest_lower_bound(identity,X_309),least_upper_bound(identity,inverse(X_309))) = multiply(least_upper_bound(identity,X_309),greatest_lower_bound(identity,inverse(X_309))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(identity,X_309),least_upper_bound(identity,inverse(X_309))),multiply(least_upper_bound(identity,X_309),greatest_lower_bound(identity,inverse(X_309)))) ),[0],$fot(least_upper_bound(greatest_lower_bound(identity,X_309),greatest_lower_bound(identity,inverse(X_309))))]]) ).
cnf(refute_0_1300,plain,
( multiply(greatest_lower_bound(identity,X_309),least_upper_bound(identity,inverse(X_309))) != least_upper_bound(greatest_lower_bound(identity,X_309),greatest_lower_bound(identity,inverse(X_309)))
| multiply(greatest_lower_bound(identity,X_309),least_upper_bound(identity,inverse(X_309))) = multiply(least_upper_bound(identity,X_309),greatest_lower_bound(identity,inverse(X_309))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,X_309),greatest_lower_bound(identity,inverse(X_309))),multiply(least_upper_bound(identity,X_309),greatest_lower_bound(identity,inverse(X_309)))) )],[refute_0_1298,refute_0_1299]) ).
cnf(refute_0_1301,plain,
( multiply(greatest_lower_bound(identity,X_309),least_upper_bound(inverse(X_309),identity)) != least_upper_bound(greatest_lower_bound(identity,X_309),greatest_lower_bound(identity,inverse(X_309)))
| multiply(greatest_lower_bound(identity,X_309),least_upper_bound(identity,inverse(X_309))) = multiply(least_upper_bound(identity,X_309),greatest_lower_bound(identity,inverse(X_309))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_309),least_upper_bound(identity,inverse(X_309))),least_upper_bound(greatest_lower_bound(identity,X_309),greatest_lower_bound(identity,inverse(X_309)))) )],[refute_0_604,refute_0_1300]) ).
cnf(refute_0_1302,plain,
multiply(greatest_lower_bound(identity,X_309),least_upper_bound(identity,inverse(X_309))) = multiply(least_upper_bound(identity,X_309),greatest_lower_bound(identity,inverse(X_309))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_309),least_upper_bound(inverse(X_309),identity)),least_upper_bound(greatest_lower_bound(identity,X_309),greatest_lower_bound(identity,inverse(X_309)))) )],[refute_0_505,refute_0_1301]) ).
cnf(refute_0_1303,plain,
( multiply(greatest_lower_bound(identity,X_309),least_upper_bound(identity,inverse(X_309))) != multiply(least_upper_bound(identity,X_309),greatest_lower_bound(identity,inverse(X_309)))
| multiply(least_upper_bound(identity,X_309),greatest_lower_bound(identity,inverse(X_309))) = multiply(greatest_lower_bound(identity,X_309),least_upper_bound(identity,inverse(X_309))) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(multiply(greatest_lower_bound(identity,X_309),least_upper_bound(identity,inverse(X_309))))),bind(Y0,$fot(multiply(least_upper_bound(identity,X_309),greatest_lower_bound(identity,inverse(X_309)))))]]) ).
cnf(refute_0_1304,plain,
multiply(least_upper_bound(identity,X_309),greatest_lower_bound(identity,inverse(X_309))) = multiply(greatest_lower_bound(identity,X_309),least_upper_bound(identity,inverse(X_309))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_309),least_upper_bound(identity,inverse(X_309))),multiply(least_upper_bound(identity,X_309),greatest_lower_bound(identity,inverse(X_309)))) )],[refute_0_1302,refute_0_1303]) ).
cnf(refute_0_1305,plain,
multiply(least_upper_bound(identity,X_84),greatest_lower_bound(identity,inverse(X_84))) = multiply(greatest_lower_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))),
inference(subst,[],[refute_0_1304:[bind(X_309,$fot(X_84))]]) ).
cnf(refute_0_1306,plain,
( multiply(least_upper_bound(identity,X_84),greatest_lower_bound(identity,inverse(X_84))) != multiply(greatest_lower_bound(identity,X_84),least_upper_bound(identity,inverse(X_84)))
| multiply(least_upper_bound(identity,X_84),greatest_lower_bound(identity,inverse(X_84))) != multiply(greatest_lower_bound(identity,inverse(X_84)),least_upper_bound(identity,X_84))
| multiply(greatest_lower_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))) = multiply(greatest_lower_bound(identity,inverse(X_84)),least_upper_bound(identity,X_84)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,X_84),greatest_lower_bound(identity,inverse(X_84))),multiply(greatest_lower_bound(identity,inverse(X_84)),least_upper_bound(identity,X_84))) ),[0],$fot(multiply(greatest_lower_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))))]]) ).
cnf(refute_0_1307,plain,
( multiply(least_upper_bound(identity,X_84),greatest_lower_bound(identity,inverse(X_84))) != multiply(greatest_lower_bound(identity,inverse(X_84)),least_upper_bound(identity,X_84))
| multiply(greatest_lower_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))) = multiply(greatest_lower_bound(identity,inverse(X_84)),least_upper_bound(identity,X_84)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_84),greatest_lower_bound(identity,inverse(X_84))),multiply(greatest_lower_bound(identity,X_84),least_upper_bound(identity,inverse(X_84)))) )],[refute_0_1305,refute_0_1306]) ).
cnf(refute_0_1308,plain,
multiply(greatest_lower_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))) = multiply(greatest_lower_bound(identity,inverse(X_84)),least_upper_bound(identity,X_84)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_84),greatest_lower_bound(identity,inverse(X_84))),multiply(greatest_lower_bound(identity,inverse(X_84)),least_upper_bound(identity,X_84))) )],[refute_0_443,refute_0_1307]) ).
cnf(refute_0_1309,plain,
( multiply(greatest_lower_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))) != multiply(greatest_lower_bound(identity,inverse(X_84)),least_upper_bound(identity,X_84))
| multiply(greatest_lower_bound(identity,inverse(X_84)),least_upper_bound(identity,X_84)) = multiply(greatest_lower_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(multiply(greatest_lower_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))))),bind(Y0,$fot(multiply(greatest_lower_bound(identity,inverse(X_84)),least_upper_bound(identity,X_84))))]]) ).
cnf(refute_0_1310,plain,
multiply(greatest_lower_bound(identity,inverse(X_84)),least_upper_bound(identity,X_84)) = multiply(greatest_lower_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))),multiply(greatest_lower_bound(identity,inverse(X_84)),least_upper_bound(identity,X_84))) )],[refute_0_1308,refute_0_1309]) ).
cnf(refute_0_1311,plain,
multiply(greatest_lower_bound(identity,inverse(X_310)),least_upper_bound(identity,X_310)) = multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310))),
inference(subst,[],[refute_0_1310:[bind(X_84,$fot(X_310))]]) ).
cnf(refute_0_1312,plain,
inverse(multiply(greatest_lower_bound(identity,inverse(X_310)),least_upper_bound(identity,X_310))) = inverse(multiply(greatest_lower_bound(identity,inverse(X_310)),least_upper_bound(identity,X_310))),
introduced(tautology,[refl,[$fot(inverse(multiply(greatest_lower_bound(identity,inverse(X_310)),least_upper_bound(identity,X_310))))]]) ).
cnf(refute_0_1313,plain,
( multiply(greatest_lower_bound(identity,inverse(X_310)),least_upper_bound(identity,X_310)) != multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310)))
| inverse(multiply(greatest_lower_bound(identity,inverse(X_310)),least_upper_bound(identity,X_310))) != inverse(multiply(greatest_lower_bound(identity,inverse(X_310)),least_upper_bound(identity,X_310)))
| inverse(multiply(greatest_lower_bound(identity,inverse(X_310)),least_upper_bound(identity,X_310))) = inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(greatest_lower_bound(identity,inverse(X_310)),least_upper_bound(identity,X_310))),inverse(multiply(greatest_lower_bound(identity,inverse(X_310)),least_upper_bound(identity,X_310)))) ),[1,0],$fot(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310))))]]) ).
cnf(refute_0_1314,plain,
( multiply(greatest_lower_bound(identity,inverse(X_310)),least_upper_bound(identity,X_310)) != multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310)))
| inverse(multiply(greatest_lower_bound(identity,inverse(X_310)),least_upper_bound(identity,X_310))) = inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310)))) ),
inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(identity,inverse(X_310)),least_upper_bound(identity,X_310))),inverse(multiply(greatest_lower_bound(identity,inverse(X_310)),least_upper_bound(identity,X_310)))) )],[refute_0_1312,refute_0_1313]) ).
cnf(refute_0_1315,plain,
inverse(multiply(greatest_lower_bound(identity,inverse(X_310)),least_upper_bound(identity,X_310))) = inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310)))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(X_310)),least_upper_bound(identity,X_310)),multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310)))) )],[refute_0_1311,refute_0_1314]) ).
cnf(refute_0_1316,plain,
multiply(inverse(least_upper_bound(identity,X_310)),inverse(greatest_lower_bound(identity,inverse(X_310)))) = inverse(multiply(greatest_lower_bound(identity,inverse(X_310)),least_upper_bound(identity,X_310))),
inference(subst,[],[refute_0_100:[bind(X,$fot(greatest_lower_bound(identity,inverse(X_310)))),bind(Y,$fot(least_upper_bound(identity,X_310)))]]) ).
cnf(refute_0_1317,plain,
( multiply(inverse(least_upper_bound(identity,X_310)),inverse(greatest_lower_bound(identity,inverse(X_310)))) != inverse(multiply(greatest_lower_bound(identity,inverse(X_310)),least_upper_bound(identity,X_310)))
| inverse(multiply(greatest_lower_bound(identity,inverse(X_310)),least_upper_bound(identity,X_310))) != inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310))))
| multiply(inverse(least_upper_bound(identity,X_310)),inverse(greatest_lower_bound(identity,inverse(X_310)))) = inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310)))) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(multiply(inverse(least_upper_bound(identity,X_310)),inverse(greatest_lower_bound(identity,inverse(X_310)))))),bind(Y0,$fot(inverse(multiply(greatest_lower_bound(identity,inverse(X_310)),least_upper_bound(identity,X_310))))),bind(Z0,$fot(inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310))))))]]) ).
cnf(refute_0_1318,plain,
( inverse(multiply(greatest_lower_bound(identity,inverse(X_310)),least_upper_bound(identity,X_310))) != inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310))))
| multiply(inverse(least_upper_bound(identity,X_310)),inverse(greatest_lower_bound(identity,inverse(X_310)))) = inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_310)),inverse(greatest_lower_bound(identity,inverse(X_310)))),inverse(multiply(greatest_lower_bound(identity,inverse(X_310)),least_upper_bound(identity,X_310)))) )],[refute_0_1316,refute_0_1317]) ).
cnf(refute_0_1319,plain,
multiply(inverse(least_upper_bound(identity,X_310)),inverse(greatest_lower_bound(identity,inverse(X_310)))) = inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310)))),
inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(identity,inverse(X_310)),least_upper_bound(identity,X_310))),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310))))) )],[refute_0_1315,refute_0_1318]) ).
cnf(refute_0_1320,plain,
multiply(greatest_lower_bound(X_310,identity),multiply(inverse(least_upper_bound(identity,X_310)),inverse(greatest_lower_bound(identity,inverse(X_310))))) = multiply(greatest_lower_bound(X_310,identity),multiply(inverse(least_upper_bound(identity,X_310)),inverse(greatest_lower_bound(identity,inverse(X_310))))),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(X_310,identity),multiply(inverse(least_upper_bound(identity,X_310)),inverse(greatest_lower_bound(identity,inverse(X_310))))))]]) ).
cnf(refute_0_1321,plain,
( multiply(greatest_lower_bound(X_310,identity),multiply(inverse(least_upper_bound(identity,X_310)),inverse(greatest_lower_bound(identity,inverse(X_310))))) != multiply(greatest_lower_bound(X_310,identity),multiply(inverse(least_upper_bound(identity,X_310)),inverse(greatest_lower_bound(identity,inverse(X_310)))))
| multiply(inverse(least_upper_bound(identity,X_310)),inverse(greatest_lower_bound(identity,inverse(X_310)))) != inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310))))
| multiply(greatest_lower_bound(X_310,identity),multiply(inverse(least_upper_bound(identity,X_310)),inverse(greatest_lower_bound(identity,inverse(X_310))))) = multiply(greatest_lower_bound(X_310,identity),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_310,identity),multiply(inverse(least_upper_bound(identity,X_310)),inverse(greatest_lower_bound(identity,inverse(X_310))))),multiply(greatest_lower_bound(X_310,identity),multiply(inverse(least_upper_bound(identity,X_310)),inverse(greatest_lower_bound(identity,inverse(X_310)))))) ),[1,1],$fot(inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310)))))]]) ).
cnf(refute_0_1322,plain,
( multiply(inverse(least_upper_bound(identity,X_310)),inverse(greatest_lower_bound(identity,inverse(X_310)))) != inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310))))
| multiply(greatest_lower_bound(X_310,identity),multiply(inverse(least_upper_bound(identity,X_310)),inverse(greatest_lower_bound(identity,inverse(X_310))))) = multiply(greatest_lower_bound(X_310,identity),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310))))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_310,identity),multiply(inverse(least_upper_bound(identity,X_310)),inverse(greatest_lower_bound(identity,inverse(X_310))))),multiply(greatest_lower_bound(X_310,identity),multiply(inverse(least_upper_bound(identity,X_310)),inverse(greatest_lower_bound(identity,inverse(X_310)))))) )],[refute_0_1320,refute_0_1321]) ).
cnf(refute_0_1323,plain,
multiply(greatest_lower_bound(X_310,identity),multiply(inverse(least_upper_bound(identity,X_310)),inverse(greatest_lower_bound(identity,inverse(X_310))))) = multiply(greatest_lower_bound(X_310,identity),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310))))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_310)),inverse(greatest_lower_bound(identity,inverse(X_310)))),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310))))) )],[refute_0_1319,refute_0_1322]) ).
cnf(refute_0_1324,plain,
multiply(multiply(greatest_lower_bound(X_310,identity),inverse(least_upper_bound(identity,X_310))),inverse(greatest_lower_bound(identity,inverse(X_310)))) = multiply(greatest_lower_bound(X_310,identity),multiply(inverse(least_upper_bound(identity,X_310)),inverse(greatest_lower_bound(identity,inverse(X_310))))),
inference(subst,[],[associativity:[bind(X,$fot(greatest_lower_bound(X_310,identity))),bind(Y,$fot(inverse(least_upper_bound(identity,X_310)))),bind(Z,$fot(inverse(greatest_lower_bound(identity,inverse(X_310)))))]]) ).
cnf(refute_0_1325,plain,
( multiply(multiply(greatest_lower_bound(X_310,identity),inverse(least_upper_bound(identity,X_310))),inverse(greatest_lower_bound(identity,inverse(X_310)))) != multiply(greatest_lower_bound(X_310,identity),multiply(inverse(least_upper_bound(identity,X_310)),inverse(greatest_lower_bound(identity,inverse(X_310)))))
| multiply(greatest_lower_bound(X_310,identity),multiply(inverse(least_upper_bound(identity,X_310)),inverse(greatest_lower_bound(identity,inverse(X_310))))) != multiply(greatest_lower_bound(X_310,identity),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310)))))
| multiply(multiply(greatest_lower_bound(X_310,identity),inverse(least_upper_bound(identity,X_310))),inverse(greatest_lower_bound(identity,inverse(X_310)))) = multiply(greatest_lower_bound(X_310,identity),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310))))) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(multiply(multiply(greatest_lower_bound(X_310,identity),inverse(least_upper_bound(identity,X_310))),inverse(greatest_lower_bound(identity,inverse(X_310)))))),bind(Y0,$fot(multiply(greatest_lower_bound(X_310,identity),multiply(inverse(least_upper_bound(identity,X_310)),inverse(greatest_lower_bound(identity,inverse(X_310))))))),bind(Z0,$fot(multiply(greatest_lower_bound(X_310,identity),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310)))))))]]) ).
cnf(refute_0_1326,plain,
( multiply(greatest_lower_bound(X_310,identity),multiply(inverse(least_upper_bound(identity,X_310)),inverse(greatest_lower_bound(identity,inverse(X_310))))) != multiply(greatest_lower_bound(X_310,identity),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310)))))
| multiply(multiply(greatest_lower_bound(X_310,identity),inverse(least_upper_bound(identity,X_310))),inverse(greatest_lower_bound(identity,inverse(X_310)))) = multiply(greatest_lower_bound(X_310,identity),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310))))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(greatest_lower_bound(X_310,identity),inverse(least_upper_bound(identity,X_310))),inverse(greatest_lower_bound(identity,inverse(X_310)))),multiply(greatest_lower_bound(X_310,identity),multiply(inverse(least_upper_bound(identity,X_310)),inverse(greatest_lower_bound(identity,inverse(X_310)))))) )],[refute_0_1324,refute_0_1325]) ).
cnf(refute_0_1327,plain,
multiply(multiply(greatest_lower_bound(X_310,identity),inverse(least_upper_bound(identity,X_310))),inverse(greatest_lower_bound(identity,inverse(X_310)))) = multiply(greatest_lower_bound(X_310,identity),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310))))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_310,identity),multiply(inverse(least_upper_bound(identity,X_310)),inverse(greatest_lower_bound(identity,inverse(X_310))))),multiply(greatest_lower_bound(X_310,identity),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310)))))) )],[refute_0_1323,refute_0_1326]) ).
cnf(refute_0_1328,plain,
multiply(inverse(least_upper_bound(identity,X_68)),greatest_lower_bound(X_68,identity)) = greatest_lower_bound(inverse(least_upper_bound(identity,X_68)),multiply(inverse(least_upper_bound(identity,X_68)),X_68)),
inference(subst,[],[refute_0_57:[bind(X_67,$fot(inverse(least_upper_bound(identity,X_68))))]]) ).
cnf(refute_0_1329,plain,
inverse(multiply(inverse(X_64),least_upper_bound(identity,X_64))) = multiply(inverse(least_upper_bound(identity,X_64)),inverse(inverse(X_64))),
inference(subst,[],[p19_3:[bind(X,$fot(inverse(X_64))),bind(Y,$fot(least_upper_bound(identity,X_64)))]]) ).
cnf(refute_0_1330,plain,
( multiply(inverse(X_64),least_upper_bound(identity,X_64)) != least_upper_bound(identity,inverse(X_64))
| inverse(multiply(inverse(X_64),least_upper_bound(identity,X_64))) != multiply(inverse(least_upper_bound(identity,X_64)),inverse(inverse(X_64)))
| inverse(least_upper_bound(identity,inverse(X_64))) = multiply(inverse(least_upper_bound(identity,X_64)),inverse(inverse(X_64))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X_64),least_upper_bound(identity,X_64))),multiply(inverse(least_upper_bound(identity,X_64)),inverse(inverse(X_64)))) ),[0,0],$fot(least_upper_bound(identity,inverse(X_64)))]]) ).
cnf(refute_0_1331,plain,
( inverse(multiply(inverse(X_64),least_upper_bound(identity,X_64))) != multiply(inverse(least_upper_bound(identity,X_64)),inverse(inverse(X_64)))
| inverse(least_upper_bound(identity,inverse(X_64))) = multiply(inverse(least_upper_bound(identity,X_64)),inverse(inverse(X_64))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_64),least_upper_bound(identity,X_64)),least_upper_bound(identity,inverse(X_64))) )],[refute_0_135,refute_0_1330]) ).
cnf(refute_0_1332,plain,
inverse(least_upper_bound(identity,inverse(X_64))) = multiply(inverse(least_upper_bound(identity,X_64)),inverse(inverse(X_64))),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_64),least_upper_bound(identity,X_64))),multiply(inverse(least_upper_bound(identity,X_64)),inverse(inverse(X_64)))) )],[refute_0_1329,refute_0_1331]) ).
cnf(refute_0_1333,plain,
inverse(multiply(inverse(X_64),least_upper_bound(identity,X_64))) = multiply(inverse(least_upper_bound(identity,X_64)),X_64),
inference(subst,[],[refute_0_534:[bind(X,$fot(X_64)),bind(X_24,$fot(least_upper_bound(identity,X_64)))]]) ).
cnf(refute_0_1334,plain,
multiply(inverse(least_upper_bound(identity,X_64)),inverse(inverse(X_64))) = inverse(multiply(inverse(X_64),least_upper_bound(identity,X_64))),
inference(subst,[],[refute_0_100:[bind(X,$fot(inverse(X_64))),bind(Y,$fot(least_upper_bound(identity,X_64)))]]) ).
cnf(refute_0_1335,plain,
( multiply(inverse(least_upper_bound(identity,X_64)),inverse(inverse(X_64))) != inverse(multiply(inverse(X_64),least_upper_bound(identity,X_64)))
| inverse(multiply(inverse(X_64),least_upper_bound(identity,X_64))) != multiply(inverse(least_upper_bound(identity,X_64)),X_64)
| multiply(inverse(least_upper_bound(identity,X_64)),inverse(inverse(X_64))) = multiply(inverse(least_upper_bound(identity,X_64)),X_64) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(multiply(inverse(least_upper_bound(identity,X_64)),inverse(inverse(X_64))))),bind(Y0,$fot(inverse(multiply(inverse(X_64),least_upper_bound(identity,X_64))))),bind(Z0,$fot(multiply(inverse(least_upper_bound(identity,X_64)),X_64)))]]) ).
cnf(refute_0_1336,plain,
( inverse(multiply(inverse(X_64),least_upper_bound(identity,X_64))) != multiply(inverse(least_upper_bound(identity,X_64)),X_64)
| multiply(inverse(least_upper_bound(identity,X_64)),inverse(inverse(X_64))) = multiply(inverse(least_upper_bound(identity,X_64)),X_64) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_64)),inverse(inverse(X_64))),inverse(multiply(inverse(X_64),least_upper_bound(identity,X_64)))) )],[refute_0_1334,refute_0_1335]) ).
cnf(refute_0_1337,plain,
multiply(inverse(least_upper_bound(identity,X_64)),inverse(inverse(X_64))) = multiply(inverse(least_upper_bound(identity,X_64)),X_64),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_64),least_upper_bound(identity,X_64))),multiply(inverse(least_upper_bound(identity,X_64)),X_64)) )],[refute_0_1333,refute_0_1336]) ).
cnf(refute_0_1338,plain,
( multiply(inverse(least_upper_bound(identity,X_64)),inverse(inverse(X_64))) != multiply(inverse(least_upper_bound(identity,X_64)),X_64)
| inverse(least_upper_bound(identity,inverse(X_64))) != multiply(inverse(least_upper_bound(identity,X_64)),inverse(inverse(X_64)))
| inverse(least_upper_bound(identity,inverse(X_64))) = multiply(inverse(least_upper_bound(identity,X_64)),X_64) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_64))),multiply(inverse(least_upper_bound(identity,X_64)),inverse(inverse(X_64)))) ),[1],$fot(multiply(inverse(least_upper_bound(identity,X_64)),X_64))]]) ).
cnf(refute_0_1339,plain,
( inverse(least_upper_bound(identity,inverse(X_64))) != multiply(inverse(least_upper_bound(identity,X_64)),inverse(inverse(X_64)))
| inverse(least_upper_bound(identity,inverse(X_64))) = multiply(inverse(least_upper_bound(identity,X_64)),X_64) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_64)),inverse(inverse(X_64))),multiply(inverse(least_upper_bound(identity,X_64)),X_64)) )],[refute_0_1337,refute_0_1338]) ).
cnf(refute_0_1340,plain,
inverse(least_upper_bound(identity,inverse(X_64))) = multiply(inverse(least_upper_bound(identity,X_64)),X_64),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_64))),multiply(inverse(least_upper_bound(identity,X_64)),inverse(inverse(X_64)))) )],[refute_0_1332,refute_0_1339]) ).
cnf(refute_0_1341,plain,
inverse(least_upper_bound(identity,inverse(X_68))) = multiply(inverse(least_upper_bound(identity,X_68)),X_68),
inference(subst,[],[refute_0_1340:[bind(X_64,$fot(X_68))]]) ).
cnf(refute_0_1342,plain,
( inverse(least_upper_bound(identity,inverse(X_68))) != multiply(inverse(least_upper_bound(identity,X_68)),X_68)
| multiply(inverse(least_upper_bound(identity,X_68)),X_68) = inverse(least_upper_bound(identity,inverse(X_68))) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(inverse(least_upper_bound(identity,inverse(X_68))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(identity,X_68)),X_68)))]]) ).
cnf(refute_0_1343,plain,
multiply(inverse(least_upper_bound(identity,X_68)),X_68) = inverse(least_upper_bound(identity,inverse(X_68))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_68))),multiply(inverse(least_upper_bound(identity,X_68)),X_68)) )],[refute_0_1341,refute_0_1342]) ).
cnf(refute_0_1344,plain,
( multiply(inverse(least_upper_bound(identity,X_68)),X_68) != inverse(least_upper_bound(identity,inverse(X_68)))
| multiply(inverse(least_upper_bound(identity,X_68)),greatest_lower_bound(X_68,identity)) != greatest_lower_bound(inverse(least_upper_bound(identity,X_68)),multiply(inverse(least_upper_bound(identity,X_68)),X_68))
| multiply(inverse(least_upper_bound(identity,X_68)),greatest_lower_bound(X_68,identity)) = greatest_lower_bound(inverse(least_upper_bound(identity,X_68)),inverse(least_upper_bound(identity,inverse(X_68)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_68)),greatest_lower_bound(X_68,identity)),greatest_lower_bound(inverse(least_upper_bound(identity,X_68)),multiply(inverse(least_upper_bound(identity,X_68)),X_68))) ),[1,1],$fot(inverse(least_upper_bound(identity,inverse(X_68))))]]) ).
cnf(refute_0_1345,plain,
( multiply(inverse(least_upper_bound(identity,X_68)),greatest_lower_bound(X_68,identity)) != greatest_lower_bound(inverse(least_upper_bound(identity,X_68)),multiply(inverse(least_upper_bound(identity,X_68)),X_68))
| multiply(inverse(least_upper_bound(identity,X_68)),greatest_lower_bound(X_68,identity)) = greatest_lower_bound(inverse(least_upper_bound(identity,X_68)),inverse(least_upper_bound(identity,inverse(X_68)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_68)),X_68),inverse(least_upper_bound(identity,inverse(X_68)))) )],[refute_0_1343,refute_0_1344]) ).
cnf(refute_0_1346,plain,
multiply(inverse(least_upper_bound(identity,X_68)),greatest_lower_bound(X_68,identity)) = greatest_lower_bound(inverse(least_upper_bound(identity,X_68)),inverse(least_upper_bound(identity,inverse(X_68)))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_68)),greatest_lower_bound(X_68,identity)),greatest_lower_bound(inverse(least_upper_bound(identity,X_68)),multiply(inverse(least_upper_bound(identity,X_68)),X_68))) )],[refute_0_1328,refute_0_1345]) ).
cnf(refute_0_1347,plain,
multiply(greatest_lower_bound(X_87,identity),inverse(least_upper_bound(identity,X_87))) = greatest_lower_bound(inverse(least_upper_bound(identity,X_87)),multiply(X_87,inverse(least_upper_bound(identity,X_87)))),
inference(subst,[],[refute_0_45:[bind(X_86,$fot(inverse(least_upper_bound(identity,X_87))))]]) ).
cnf(refute_0_1348,plain,
inverse(multiply(least_upper_bound(identity,X_85),inverse(X_85))) = multiply(inverse(inverse(X_85)),inverse(least_upper_bound(identity,X_85))),
inference(subst,[],[p19_3:[bind(X,$fot(least_upper_bound(identity,X_85))),bind(Y,$fot(inverse(X_85)))]]) ).
cnf(refute_0_1349,plain,
multiply(least_upper_bound(identity,X_85),inverse(X_85)) = least_upper_bound(identity,inverse(X_85)),
inference(subst,[],[refute_0_200:[bind(X_84,$fot(X_85))]]) ).
cnf(refute_0_1350,plain,
( multiply(least_upper_bound(identity,X_85),inverse(X_85)) != least_upper_bound(identity,inverse(X_85))
| inverse(multiply(least_upper_bound(identity,X_85),inverse(X_85))) != multiply(inverse(inverse(X_85)),inverse(least_upper_bound(identity,X_85)))
| inverse(least_upper_bound(identity,inverse(X_85))) = multiply(inverse(inverse(X_85)),inverse(least_upper_bound(identity,X_85))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(least_upper_bound(identity,X_85),inverse(X_85))),multiply(inverse(inverse(X_85)),inverse(least_upper_bound(identity,X_85)))) ),[0,0],$fot(least_upper_bound(identity,inverse(X_85)))]]) ).
cnf(refute_0_1351,plain,
( inverse(multiply(least_upper_bound(identity,X_85),inverse(X_85))) != multiply(inverse(inverse(X_85)),inverse(least_upper_bound(identity,X_85)))
| inverse(least_upper_bound(identity,inverse(X_85))) = multiply(inverse(inverse(X_85)),inverse(least_upper_bound(identity,X_85))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_85),inverse(X_85)),least_upper_bound(identity,inverse(X_85))) )],[refute_0_1349,refute_0_1350]) ).
cnf(refute_0_1352,plain,
inverse(least_upper_bound(identity,inverse(X_85))) = multiply(inverse(inverse(X_85)),inverse(least_upper_bound(identity,X_85))),
inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(identity,X_85),inverse(X_85))),multiply(inverse(inverse(X_85)),inverse(least_upper_bound(identity,X_85)))) )],[refute_0_1348,refute_0_1351]) ).
cnf(refute_0_1353,plain,
inverse(multiply(least_upper_bound(identity,X_85),inverse(X_85))) = multiply(X_85,inverse(least_upper_bound(identity,X_85))),
inference(subst,[],[refute_0_107:[bind(X,$fot(X_85)),bind(X_23,$fot(least_upper_bound(identity,X_85)))]]) ).
cnf(refute_0_1354,plain,
multiply(inverse(inverse(X_85)),inverse(least_upper_bound(identity,X_85))) = inverse(multiply(least_upper_bound(identity,X_85),inverse(X_85))),
inference(subst,[],[refute_0_100:[bind(X,$fot(least_upper_bound(identity,X_85))),bind(Y,$fot(inverse(X_85)))]]) ).
cnf(refute_0_1355,plain,
( multiply(inverse(inverse(X_85)),inverse(least_upper_bound(identity,X_85))) != inverse(multiply(least_upper_bound(identity,X_85),inverse(X_85)))
| inverse(multiply(least_upper_bound(identity,X_85),inverse(X_85))) != multiply(X_85,inverse(least_upper_bound(identity,X_85)))
| multiply(inverse(inverse(X_85)),inverse(least_upper_bound(identity,X_85))) = multiply(X_85,inverse(least_upper_bound(identity,X_85))) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(multiply(inverse(inverse(X_85)),inverse(least_upper_bound(identity,X_85))))),bind(Y0,$fot(inverse(multiply(least_upper_bound(identity,X_85),inverse(X_85))))),bind(Z0,$fot(multiply(X_85,inverse(least_upper_bound(identity,X_85)))))]]) ).
cnf(refute_0_1356,plain,
( inverse(multiply(least_upper_bound(identity,X_85),inverse(X_85))) != multiply(X_85,inverse(least_upper_bound(identity,X_85)))
| multiply(inverse(inverse(X_85)),inverse(least_upper_bound(identity,X_85))) = multiply(X_85,inverse(least_upper_bound(identity,X_85))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_85)),inverse(least_upper_bound(identity,X_85))),inverse(multiply(least_upper_bound(identity,X_85),inverse(X_85)))) )],[refute_0_1354,refute_0_1355]) ).
cnf(refute_0_1357,plain,
multiply(inverse(inverse(X_85)),inverse(least_upper_bound(identity,X_85))) = multiply(X_85,inverse(least_upper_bound(identity,X_85))),
inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(identity,X_85),inverse(X_85))),multiply(X_85,inverse(least_upper_bound(identity,X_85)))) )],[refute_0_1353,refute_0_1356]) ).
cnf(refute_0_1358,plain,
( multiply(inverse(inverse(X_85)),inverse(least_upper_bound(identity,X_85))) != multiply(X_85,inverse(least_upper_bound(identity,X_85)))
| inverse(least_upper_bound(identity,inverse(X_85))) != multiply(inverse(inverse(X_85)),inverse(least_upper_bound(identity,X_85)))
| inverse(least_upper_bound(identity,inverse(X_85))) = multiply(X_85,inverse(least_upper_bound(identity,X_85))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_85))),multiply(inverse(inverse(X_85)),inverse(least_upper_bound(identity,X_85)))) ),[1],$fot(multiply(X_85,inverse(least_upper_bound(identity,X_85))))]]) ).
cnf(refute_0_1359,plain,
( inverse(least_upper_bound(identity,inverse(X_85))) != multiply(inverse(inverse(X_85)),inverse(least_upper_bound(identity,X_85)))
| inverse(least_upper_bound(identity,inverse(X_85))) = multiply(X_85,inverse(least_upper_bound(identity,X_85))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_85)),inverse(least_upper_bound(identity,X_85))),multiply(X_85,inverse(least_upper_bound(identity,X_85)))) )],[refute_0_1357,refute_0_1358]) ).
cnf(refute_0_1360,plain,
inverse(least_upper_bound(identity,inverse(X_85))) = multiply(X_85,inverse(least_upper_bound(identity,X_85))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_85))),multiply(inverse(inverse(X_85)),inverse(least_upper_bound(identity,X_85)))) )],[refute_0_1352,refute_0_1359]) ).
cnf(refute_0_1361,plain,
inverse(least_upper_bound(identity,inverse(X_87))) = multiply(X_87,inverse(least_upper_bound(identity,X_87))),
inference(subst,[],[refute_0_1360:[bind(X_85,$fot(X_87))]]) ).
cnf(refute_0_1362,plain,
( inverse(least_upper_bound(identity,inverse(X_87))) != multiply(X_87,inverse(least_upper_bound(identity,X_87)))
| multiply(X_87,inverse(least_upper_bound(identity,X_87))) = inverse(least_upper_bound(identity,inverse(X_87))) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(inverse(least_upper_bound(identity,inverse(X_87))))),bind(Y0,$fot(multiply(X_87,inverse(least_upper_bound(identity,X_87)))))]]) ).
cnf(refute_0_1363,plain,
multiply(X_87,inverse(least_upper_bound(identity,X_87))) = inverse(least_upper_bound(identity,inverse(X_87))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_87))),multiply(X_87,inverse(least_upper_bound(identity,X_87)))) )],[refute_0_1361,refute_0_1362]) ).
cnf(refute_0_1364,plain,
( multiply(X_87,inverse(least_upper_bound(identity,X_87))) != inverse(least_upper_bound(identity,inverse(X_87)))
| multiply(greatest_lower_bound(X_87,identity),inverse(least_upper_bound(identity,X_87))) != greatest_lower_bound(inverse(least_upper_bound(identity,X_87)),multiply(X_87,inverse(least_upper_bound(identity,X_87))))
| multiply(greatest_lower_bound(X_87,identity),inverse(least_upper_bound(identity,X_87))) = greatest_lower_bound(inverse(least_upper_bound(identity,X_87)),inverse(least_upper_bound(identity,inverse(X_87)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_87,identity),inverse(least_upper_bound(identity,X_87))),greatest_lower_bound(inverse(least_upper_bound(identity,X_87)),multiply(X_87,inverse(least_upper_bound(identity,X_87))))) ),[1,1],$fot(inverse(least_upper_bound(identity,inverse(X_87))))]]) ).
cnf(refute_0_1365,plain,
( multiply(greatest_lower_bound(X_87,identity),inverse(least_upper_bound(identity,X_87))) != greatest_lower_bound(inverse(least_upper_bound(identity,X_87)),multiply(X_87,inverse(least_upper_bound(identity,X_87))))
| multiply(greatest_lower_bound(X_87,identity),inverse(least_upper_bound(identity,X_87))) = greatest_lower_bound(inverse(least_upper_bound(identity,X_87)),inverse(least_upper_bound(identity,inverse(X_87)))) ),
inference(resolve,[$cnf( $equal(multiply(X_87,inverse(least_upper_bound(identity,X_87))),inverse(least_upper_bound(identity,inverse(X_87)))) )],[refute_0_1363,refute_0_1364]) ).
cnf(refute_0_1366,plain,
multiply(greatest_lower_bound(X_87,identity),inverse(least_upper_bound(identity,X_87))) = greatest_lower_bound(inverse(least_upper_bound(identity,X_87)),inverse(least_upper_bound(identity,inverse(X_87)))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_87,identity),inverse(least_upper_bound(identity,X_87))),greatest_lower_bound(inverse(least_upper_bound(identity,X_87)),multiply(X_87,inverse(least_upper_bound(identity,X_87))))) )],[refute_0_1347,refute_0_1365]) ).
cnf(refute_0_1367,plain,
( multiply(inverse(least_upper_bound(identity,X_68)),greatest_lower_bound(X_68,identity)) != greatest_lower_bound(inverse(least_upper_bound(identity,X_68)),inverse(least_upper_bound(identity,inverse(X_68))))
| greatest_lower_bound(inverse(least_upper_bound(identity,X_68)),inverse(least_upper_bound(identity,inverse(X_68)))) = multiply(inverse(least_upper_bound(identity,X_68)),greatest_lower_bound(X_68,identity)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(multiply(inverse(least_upper_bound(identity,X_68)),greatest_lower_bound(X_68,identity)))),bind(Y0,$fot(greatest_lower_bound(inverse(least_upper_bound(identity,X_68)),inverse(least_upper_bound(identity,inverse(X_68))))))]]) ).
cnf(refute_0_1368,plain,
greatest_lower_bound(inverse(least_upper_bound(identity,X_68)),inverse(least_upper_bound(identity,inverse(X_68)))) = multiply(inverse(least_upper_bound(identity,X_68)),greatest_lower_bound(X_68,identity)),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_68)),greatest_lower_bound(X_68,identity)),greatest_lower_bound(inverse(least_upper_bound(identity,X_68)),inverse(least_upper_bound(identity,inverse(X_68))))) )],[refute_0_1346,refute_0_1367]) ).
cnf(refute_0_1369,plain,
greatest_lower_bound(inverse(least_upper_bound(identity,X_87)),inverse(least_upper_bound(identity,inverse(X_87)))) = multiply(inverse(least_upper_bound(identity,X_87)),greatest_lower_bound(X_87,identity)),
inference(subst,[],[refute_0_1368:[bind(X_68,$fot(X_87))]]) ).
cnf(refute_0_1370,plain,
( multiply(greatest_lower_bound(X_87,identity),inverse(least_upper_bound(identity,X_87))) != greatest_lower_bound(inverse(least_upper_bound(identity,X_87)),inverse(least_upper_bound(identity,inverse(X_87))))
| greatest_lower_bound(inverse(least_upper_bound(identity,X_87)),inverse(least_upper_bound(identity,inverse(X_87)))) != multiply(inverse(least_upper_bound(identity,X_87)),greatest_lower_bound(X_87,identity))
| multiply(greatest_lower_bound(X_87,identity),inverse(least_upper_bound(identity,X_87))) = multiply(inverse(least_upper_bound(identity,X_87)),greatest_lower_bound(X_87,identity)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_87,identity),inverse(least_upper_bound(identity,X_87))),multiply(inverse(least_upper_bound(identity,X_87)),greatest_lower_bound(X_87,identity))) ),[0],$fot(greatest_lower_bound(inverse(least_upper_bound(identity,X_87)),inverse(least_upper_bound(identity,inverse(X_87)))))]]) ).
cnf(refute_0_1371,plain,
( multiply(greatest_lower_bound(X_87,identity),inverse(least_upper_bound(identity,X_87))) != greatest_lower_bound(inverse(least_upper_bound(identity,X_87)),inverse(least_upper_bound(identity,inverse(X_87))))
| multiply(greatest_lower_bound(X_87,identity),inverse(least_upper_bound(identity,X_87))) = multiply(inverse(least_upper_bound(identity,X_87)),greatest_lower_bound(X_87,identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(least_upper_bound(identity,X_87)),inverse(least_upper_bound(identity,inverse(X_87)))),multiply(inverse(least_upper_bound(identity,X_87)),greatest_lower_bound(X_87,identity))) )],[refute_0_1369,refute_0_1370]) ).
cnf(refute_0_1372,plain,
multiply(greatest_lower_bound(X_87,identity),inverse(least_upper_bound(identity,X_87))) = multiply(inverse(least_upper_bound(identity,X_87)),greatest_lower_bound(X_87,identity)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_87,identity),inverse(least_upper_bound(identity,X_87))),greatest_lower_bound(inverse(least_upper_bound(identity,X_87)),inverse(least_upper_bound(identity,inverse(X_87))))) )],[refute_0_1366,refute_0_1371]) ).
cnf(refute_0_1373,plain,
( multiply(greatest_lower_bound(X_87,identity),inverse(least_upper_bound(identity,X_87))) != multiply(inverse(least_upper_bound(identity,X_87)),greatest_lower_bound(X_87,identity))
| multiply(inverse(least_upper_bound(identity,X_87)),greatest_lower_bound(X_87,identity)) = multiply(greatest_lower_bound(X_87,identity),inverse(least_upper_bound(identity,X_87))) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(multiply(greatest_lower_bound(X_87,identity),inverse(least_upper_bound(identity,X_87))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(identity,X_87)),greatest_lower_bound(X_87,identity))))]]) ).
cnf(refute_0_1374,plain,
multiply(inverse(least_upper_bound(identity,X_87)),greatest_lower_bound(X_87,identity)) = multiply(greatest_lower_bound(X_87,identity),inverse(least_upper_bound(identity,X_87))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_87,identity),inverse(least_upper_bound(identity,X_87))),multiply(inverse(least_upper_bound(identity,X_87)),greatest_lower_bound(X_87,identity))) )],[refute_0_1372,refute_0_1373]) ).
cnf(refute_0_1375,plain,
multiply(inverse(least_upper_bound(identity,X_68)),greatest_lower_bound(X_68,identity)) = multiply(greatest_lower_bound(X_68,identity),inverse(least_upper_bound(identity,X_68))),
inference(subst,[],[refute_0_1374:[bind(X_87,$fot(X_68))]]) ).
cnf(refute_0_1376,plain,
( multiply(inverse(least_upper_bound(identity,X_68)),greatest_lower_bound(X_68,identity)) != multiply(greatest_lower_bound(X_68,identity),inverse(least_upper_bound(identity,X_68)))
| multiply(inverse(least_upper_bound(identity,X_68)),greatest_lower_bound(X_68,identity)) != greatest_lower_bound(inverse(least_upper_bound(identity,X_68)),inverse(least_upper_bound(identity,inverse(X_68))))
| multiply(greatest_lower_bound(X_68,identity),inverse(least_upper_bound(identity,X_68))) = greatest_lower_bound(inverse(least_upper_bound(identity,X_68)),inverse(least_upper_bound(identity,inverse(X_68)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_68)),greatest_lower_bound(X_68,identity)),greatest_lower_bound(inverse(least_upper_bound(identity,X_68)),inverse(least_upper_bound(identity,inverse(X_68))))) ),[0],$fot(multiply(greatest_lower_bound(X_68,identity),inverse(least_upper_bound(identity,X_68))))]]) ).
cnf(refute_0_1377,plain,
( multiply(inverse(least_upper_bound(identity,X_68)),greatest_lower_bound(X_68,identity)) != greatest_lower_bound(inverse(least_upper_bound(identity,X_68)),inverse(least_upper_bound(identity,inverse(X_68))))
| multiply(greatest_lower_bound(X_68,identity),inverse(least_upper_bound(identity,X_68))) = greatest_lower_bound(inverse(least_upper_bound(identity,X_68)),inverse(least_upper_bound(identity,inverse(X_68)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_68)),greatest_lower_bound(X_68,identity)),multiply(greatest_lower_bound(X_68,identity),inverse(least_upper_bound(identity,X_68)))) )],[refute_0_1375,refute_0_1376]) ).
cnf(refute_0_1378,plain,
multiply(greatest_lower_bound(X_68,identity),inverse(least_upper_bound(identity,X_68))) = greatest_lower_bound(inverse(least_upper_bound(identity,X_68)),inverse(least_upper_bound(identity,inverse(X_68)))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_68)),greatest_lower_bound(X_68,identity)),greatest_lower_bound(inverse(least_upper_bound(identity,X_68)),inverse(least_upper_bound(identity,inverse(X_68))))) )],[refute_0_1346,refute_0_1377]) ).
cnf(refute_0_1379,plain,
( multiply(greatest_lower_bound(X_68,identity),inverse(least_upper_bound(identity,X_68))) != greatest_lower_bound(inverse(least_upper_bound(identity,X_68)),inverse(least_upper_bound(identity,inverse(X_68))))
| greatest_lower_bound(inverse(least_upper_bound(identity,X_68)),inverse(least_upper_bound(identity,inverse(X_68)))) = multiply(greatest_lower_bound(X_68,identity),inverse(least_upper_bound(identity,X_68))) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(multiply(greatest_lower_bound(X_68,identity),inverse(least_upper_bound(identity,X_68))))),bind(Y0,$fot(greatest_lower_bound(inverse(least_upper_bound(identity,X_68)),inverse(least_upper_bound(identity,inverse(X_68))))))]]) ).
cnf(refute_0_1380,plain,
greatest_lower_bound(inverse(least_upper_bound(identity,X_68)),inverse(least_upper_bound(identity,inverse(X_68)))) = multiply(greatest_lower_bound(X_68,identity),inverse(least_upper_bound(identity,X_68))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_68,identity),inverse(least_upper_bound(identity,X_68))),greatest_lower_bound(inverse(least_upper_bound(identity,X_68)),inverse(least_upper_bound(identity,inverse(X_68))))) )],[refute_0_1378,refute_0_1379]) ).
cnf(refute_0_1381,plain,
greatest_lower_bound(inverse(least_upper_bound(identity,X_310)),inverse(least_upper_bound(identity,inverse(X_310)))) = multiply(greatest_lower_bound(X_310,identity),inverse(least_upper_bound(identity,X_310))),
inference(subst,[],[refute_0_1380:[bind(X_68,$fot(X_310))]]) ).
cnf(refute_0_1382,plain,
multiply(greatest_lower_bound(inverse(least_upper_bound(identity,X_310)),inverse(least_upper_bound(identity,inverse(X_310)))),inverse(greatest_lower_bound(identity,inverse(X_310)))) = multiply(greatest_lower_bound(inverse(least_upper_bound(identity,X_310)),inverse(least_upper_bound(identity,inverse(X_310)))),inverse(greatest_lower_bound(identity,inverse(X_310)))),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(inverse(least_upper_bound(identity,X_310)),inverse(least_upper_bound(identity,inverse(X_310)))),inverse(greatest_lower_bound(identity,inverse(X_310)))))]]) ).
cnf(refute_0_1383,plain,
( multiply(greatest_lower_bound(inverse(least_upper_bound(identity,X_310)),inverse(least_upper_bound(identity,inverse(X_310)))),inverse(greatest_lower_bound(identity,inverse(X_310)))) != multiply(greatest_lower_bound(inverse(least_upper_bound(identity,X_310)),inverse(least_upper_bound(identity,inverse(X_310)))),inverse(greatest_lower_bound(identity,inverse(X_310))))
| greatest_lower_bound(inverse(least_upper_bound(identity,X_310)),inverse(least_upper_bound(identity,inverse(X_310)))) != multiply(greatest_lower_bound(X_310,identity),inverse(least_upper_bound(identity,X_310)))
| multiply(greatest_lower_bound(inverse(least_upper_bound(identity,X_310)),inverse(least_upper_bound(identity,inverse(X_310)))),inverse(greatest_lower_bound(identity,inverse(X_310)))) = multiply(multiply(greatest_lower_bound(X_310,identity),inverse(least_upper_bound(identity,X_310))),inverse(greatest_lower_bound(identity,inverse(X_310)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(inverse(least_upper_bound(identity,X_310)),inverse(least_upper_bound(identity,inverse(X_310)))),inverse(greatest_lower_bound(identity,inverse(X_310)))),multiply(greatest_lower_bound(inverse(least_upper_bound(identity,X_310)),inverse(least_upper_bound(identity,inverse(X_310)))),inverse(greatest_lower_bound(identity,inverse(X_310))))) ),[1,0],$fot(multiply(greatest_lower_bound(X_310,identity),inverse(least_upper_bound(identity,X_310))))]]) ).
cnf(refute_0_1384,plain,
( greatest_lower_bound(inverse(least_upper_bound(identity,X_310)),inverse(least_upper_bound(identity,inverse(X_310)))) != multiply(greatest_lower_bound(X_310,identity),inverse(least_upper_bound(identity,X_310)))
| multiply(greatest_lower_bound(inverse(least_upper_bound(identity,X_310)),inverse(least_upper_bound(identity,inverse(X_310)))),inverse(greatest_lower_bound(identity,inverse(X_310)))) = multiply(multiply(greatest_lower_bound(X_310,identity),inverse(least_upper_bound(identity,X_310))),inverse(greatest_lower_bound(identity,inverse(X_310)))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(least_upper_bound(identity,X_310)),inverse(least_upper_bound(identity,inverse(X_310)))),inverse(greatest_lower_bound(identity,inverse(X_310)))),multiply(greatest_lower_bound(inverse(least_upper_bound(identity,X_310)),inverse(least_upper_bound(identity,inverse(X_310)))),inverse(greatest_lower_bound(identity,inverse(X_310))))) )],[refute_0_1382,refute_0_1383]) ).
cnf(refute_0_1385,plain,
multiply(greatest_lower_bound(inverse(least_upper_bound(identity,X_310)),inverse(least_upper_bound(identity,inverse(X_310)))),inverse(greatest_lower_bound(identity,inverse(X_310)))) = multiply(multiply(greatest_lower_bound(X_310,identity),inverse(least_upper_bound(identity,X_310))),inverse(greatest_lower_bound(identity,inverse(X_310)))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(least_upper_bound(identity,X_310)),inverse(least_upper_bound(identity,inverse(X_310)))),multiply(greatest_lower_bound(X_310,identity),inverse(least_upper_bound(identity,X_310)))) )],[refute_0_1381,refute_0_1384]) ).
cnf(refute_0_1386,plain,
( multiply(multiply(greatest_lower_bound(X_310,identity),inverse(least_upper_bound(identity,X_310))),inverse(greatest_lower_bound(identity,inverse(X_310)))) != multiply(greatest_lower_bound(X_310,identity),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310)))))
| multiply(greatest_lower_bound(inverse(least_upper_bound(identity,X_310)),inverse(least_upper_bound(identity,inverse(X_310)))),inverse(greatest_lower_bound(identity,inverse(X_310)))) != multiply(multiply(greatest_lower_bound(X_310,identity),inverse(least_upper_bound(identity,X_310))),inverse(greatest_lower_bound(identity,inverse(X_310))))
| multiply(greatest_lower_bound(inverse(least_upper_bound(identity,X_310)),inverse(least_upper_bound(identity,inverse(X_310)))),inverse(greatest_lower_bound(identity,inverse(X_310)))) = multiply(greatest_lower_bound(X_310,identity),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310))))) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(multiply(greatest_lower_bound(inverse(least_upper_bound(identity,X_310)),inverse(least_upper_bound(identity,inverse(X_310)))),inverse(greatest_lower_bound(identity,inverse(X_310)))))),bind(Y0,$fot(multiply(multiply(greatest_lower_bound(X_310,identity),inverse(least_upper_bound(identity,X_310))),inverse(greatest_lower_bound(identity,inverse(X_310)))))),bind(Z0,$fot(multiply(greatest_lower_bound(X_310,identity),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310)))))))]]) ).
cnf(refute_0_1387,plain,
( multiply(multiply(greatest_lower_bound(X_310,identity),inverse(least_upper_bound(identity,X_310))),inverse(greatest_lower_bound(identity,inverse(X_310)))) != multiply(greatest_lower_bound(X_310,identity),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310)))))
| multiply(greatest_lower_bound(inverse(least_upper_bound(identity,X_310)),inverse(least_upper_bound(identity,inverse(X_310)))),inverse(greatest_lower_bound(identity,inverse(X_310)))) = multiply(greatest_lower_bound(X_310,identity),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310))))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(least_upper_bound(identity,X_310)),inverse(least_upper_bound(identity,inverse(X_310)))),inverse(greatest_lower_bound(identity,inverse(X_310)))),multiply(multiply(greatest_lower_bound(X_310,identity),inverse(least_upper_bound(identity,X_310))),inverse(greatest_lower_bound(identity,inverse(X_310))))) )],[refute_0_1385,refute_0_1386]) ).
cnf(refute_0_1388,plain,
multiply(greatest_lower_bound(inverse(least_upper_bound(identity,X_310)),inverse(least_upper_bound(identity,inverse(X_310)))),inverse(greatest_lower_bound(identity,inverse(X_310)))) = multiply(greatest_lower_bound(X_310,identity),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310))))),
inference(resolve,[$cnf( $equal(multiply(multiply(greatest_lower_bound(X_310,identity),inverse(least_upper_bound(identity,X_310))),inverse(greatest_lower_bound(identity,inverse(X_310)))),multiply(greatest_lower_bound(X_310,identity),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310)))))) )],[refute_0_1327,refute_0_1387]) ).
cnf(refute_0_1389,plain,
inverse(multiply(X,Y)) = multiply(X_54,inverse(multiply(multiply(X,Y),X_54))),
inference(subst,[],[refute_0_117:[bind(X,$fot(multiply(X,Y))),bind(Y,$fot(X_54))]]) ).
cnf(refute_0_1390,plain,
multiply(multiply(X,Y),X_54) = multiply(X,multiply(Y,X_54)),
inference(subst,[],[associativity:[bind(Z,$fot(X_54))]]) ).
cnf(refute_0_1391,plain,
( multiply(multiply(X,Y),X_54) != multiply(X,multiply(Y,X_54))
| inverse(multiply(X,Y)) != multiply(X_54,inverse(multiply(multiply(X,Y),X_54)))
| inverse(multiply(X,Y)) = multiply(X_54,inverse(multiply(X,multiply(Y,X_54)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X,Y)),multiply(X_54,inverse(multiply(multiply(X,Y),X_54)))) ),[1,1,0],$fot(multiply(X,multiply(Y,X_54)))]]) ).
cnf(refute_0_1392,plain,
( inverse(multiply(X,Y)) != multiply(X_54,inverse(multiply(multiply(X,Y),X_54)))
| inverse(multiply(X,Y)) = multiply(X_54,inverse(multiply(X,multiply(Y,X_54)))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X,Y),X_54),multiply(X,multiply(Y,X_54))) )],[refute_0_1390,refute_0_1391]) ).
cnf(refute_0_1393,plain,
inverse(multiply(X,Y)) = multiply(X_54,inverse(multiply(X,multiply(Y,X_54)))),
inference(resolve,[$cnf( $equal(inverse(multiply(X,Y)),multiply(X_54,inverse(multiply(multiply(X,Y),X_54)))) )],[refute_0_1389,refute_0_1392]) ).
cnf(refute_0_1394,plain,
inverse(multiply(X,inverse(greatest_lower_bound(X_269,inverse(X_268))))) = multiply(greatest_lower_bound(identity,multiply(X_269,X_268)),inverse(multiply(X,multiply(inverse(greatest_lower_bound(X_269,inverse(X_268))),greatest_lower_bound(identity,multiply(X_269,X_268)))))),
inference(subst,[],[refute_0_1393:[bind(Y,$fot(inverse(greatest_lower_bound(X_269,inverse(X_268))))),bind(X_54,$fot(greatest_lower_bound(identity,multiply(X_269,X_268))))]]) ).
cnf(refute_0_1395,plain,
X_46 = multiply(inverse(greatest_lower_bound(X_92,inverse(X_46))),multiply(greatest_lower_bound(X_92,inverse(X_46)),X_46)),
inference(subst,[],[refute_0_97:[bind(X_45,$fot(greatest_lower_bound(X_92,inverse(X_46))))]]) ).
cnf(refute_0_1396,plain,
multiply(greatest_lower_bound(X_87,inverse(X_86)),X_86) = greatest_lower_bound(multiply(X_87,X_86),multiply(inverse(X_86),X_86)),
inference(subst,[],[monotony_glb2:[bind(X,$fot(X_86)),bind(Y,$fot(X_87)),bind(Z,$fot(inverse(X_86)))]]) ).
cnf(refute_0_1397,plain,
multiply(inverse(X_86),X_86) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_86))]]) ).
cnf(refute_0_1398,plain,
( multiply(greatest_lower_bound(X_87,inverse(X_86)),X_86) != greatest_lower_bound(multiply(X_87,X_86),multiply(inverse(X_86),X_86))
| multiply(inverse(X_86),X_86) != identity
| multiply(greatest_lower_bound(X_87,inverse(X_86)),X_86) = greatest_lower_bound(multiply(X_87,X_86),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_87,inverse(X_86)),X_86),greatest_lower_bound(multiply(X_87,X_86),multiply(inverse(X_86),X_86))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_1399,plain,
( multiply(greatest_lower_bound(X_87,inverse(X_86)),X_86) != greatest_lower_bound(multiply(X_87,X_86),multiply(inverse(X_86),X_86))
| multiply(greatest_lower_bound(X_87,inverse(X_86)),X_86) = greatest_lower_bound(multiply(X_87,X_86),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_86),X_86),identity) )],[refute_0_1397,refute_0_1398]) ).
cnf(refute_0_1400,plain,
multiply(greatest_lower_bound(X_87,inverse(X_86)),X_86) = greatest_lower_bound(multiply(X_87,X_86),identity),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_87,inverse(X_86)),X_86),greatest_lower_bound(multiply(X_87,X_86),multiply(inverse(X_86),X_86))) )],[refute_0_1396,refute_0_1399]) ).
cnf(refute_0_1401,plain,
greatest_lower_bound(multiply(X_87,X_86),identity) = greatest_lower_bound(identity,multiply(X_87,X_86)),
inference(subst,[],[refute_0_41:[bind(X_21,$fot(identity)),bind(X_22,$fot(multiply(X_87,X_86)))]]) ).
cnf(refute_0_1402,plain,
( multiply(greatest_lower_bound(X_87,inverse(X_86)),X_86) != greatest_lower_bound(multiply(X_87,X_86),identity)
| greatest_lower_bound(multiply(X_87,X_86),identity) != greatest_lower_bound(identity,multiply(X_87,X_86))
| multiply(greatest_lower_bound(X_87,inverse(X_86)),X_86) = greatest_lower_bound(identity,multiply(X_87,X_86)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_87,inverse(X_86)),X_86),greatest_lower_bound(identity,multiply(X_87,X_86))) ),[0],$fot(greatest_lower_bound(multiply(X_87,X_86),identity))]]) ).
cnf(refute_0_1403,plain,
( multiply(greatest_lower_bound(X_87,inverse(X_86)),X_86) != greatest_lower_bound(multiply(X_87,X_86),identity)
| multiply(greatest_lower_bound(X_87,inverse(X_86)),X_86) = greatest_lower_bound(identity,multiply(X_87,X_86)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_87,X_86),identity),greatest_lower_bound(identity,multiply(X_87,X_86))) )],[refute_0_1401,refute_0_1402]) ).
cnf(refute_0_1404,plain,
multiply(greatest_lower_bound(X_87,inverse(X_86)),X_86) = greatest_lower_bound(identity,multiply(X_87,X_86)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_87,inverse(X_86)),X_86),greatest_lower_bound(multiply(X_87,X_86),identity)) )],[refute_0_1400,refute_0_1403]) ).
cnf(refute_0_1405,plain,
multiply(greatest_lower_bound(X_92,inverse(X_46)),X_46) = greatest_lower_bound(identity,multiply(X_92,X_46)),
inference(subst,[],[refute_0_1404:[bind(X_86,$fot(X_46)),bind(X_87,$fot(X_92))]]) ).
cnf(refute_0_1406,plain,
( X_46 != multiply(inverse(greatest_lower_bound(X_92,inverse(X_46))),multiply(greatest_lower_bound(X_92,inverse(X_46)),X_46))
| multiply(greatest_lower_bound(X_92,inverse(X_46)),X_46) != greatest_lower_bound(identity,multiply(X_92,X_46))
| X_46 = multiply(inverse(greatest_lower_bound(X_92,inverse(X_46))),greatest_lower_bound(identity,multiply(X_92,X_46))) ),
introduced(tautology,[equality,[$cnf( $equal(X_46,multiply(inverse(greatest_lower_bound(X_92,inverse(X_46))),multiply(greatest_lower_bound(X_92,inverse(X_46)),X_46))) ),[1,1],$fot(greatest_lower_bound(identity,multiply(X_92,X_46)))]]) ).
cnf(refute_0_1407,plain,
( X_46 != multiply(inverse(greatest_lower_bound(X_92,inverse(X_46))),multiply(greatest_lower_bound(X_92,inverse(X_46)),X_46))
| X_46 = multiply(inverse(greatest_lower_bound(X_92,inverse(X_46))),greatest_lower_bound(identity,multiply(X_92,X_46))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_92,inverse(X_46)),X_46),greatest_lower_bound(identity,multiply(X_92,X_46))) )],[refute_0_1405,refute_0_1406]) ).
cnf(refute_0_1408,plain,
X_46 = multiply(inverse(greatest_lower_bound(X_92,inverse(X_46))),greatest_lower_bound(identity,multiply(X_92,X_46))),
inference(resolve,[$cnf( $equal(X_46,multiply(inverse(greatest_lower_bound(X_92,inverse(X_46))),multiply(greatest_lower_bound(X_92,inverse(X_46)),X_46))) )],[refute_0_1395,refute_0_1407]) ).
cnf(refute_0_1409,plain,
X_268 = multiply(inverse(greatest_lower_bound(X_269,inverse(X_268))),greatest_lower_bound(identity,multiply(X_269,X_268))),
inference(subst,[],[refute_0_1408:[bind(X_46,$fot(X_268)),bind(X_92,$fot(X_269))]]) ).
cnf(refute_0_1410,plain,
( X_268 != multiply(inverse(greatest_lower_bound(X_269,inverse(X_268))),greatest_lower_bound(identity,multiply(X_269,X_268)))
| multiply(inverse(greatest_lower_bound(X_269,inverse(X_268))),greatest_lower_bound(identity,multiply(X_269,X_268))) = X_268 ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(X_268)),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(X_269,inverse(X_268))),greatest_lower_bound(identity,multiply(X_269,X_268)))))]]) ).
cnf(refute_0_1411,plain,
multiply(inverse(greatest_lower_bound(X_269,inverse(X_268))),greatest_lower_bound(identity,multiply(X_269,X_268))) = X_268,
inference(resolve,[$cnf( $equal(X_268,multiply(inverse(greatest_lower_bound(X_269,inverse(X_268))),greatest_lower_bound(identity,multiply(X_269,X_268)))) )],[refute_0_1409,refute_0_1410]) ).
cnf(refute_0_1412,plain,
( multiply(inverse(greatest_lower_bound(X_269,inverse(X_268))),greatest_lower_bound(identity,multiply(X_269,X_268))) != X_268
| inverse(multiply(X,inverse(greatest_lower_bound(X_269,inverse(X_268))))) != multiply(greatest_lower_bound(identity,multiply(X_269,X_268)),inverse(multiply(X,multiply(inverse(greatest_lower_bound(X_269,inverse(X_268))),greatest_lower_bound(identity,multiply(X_269,X_268))))))
| inverse(multiply(X,inverse(greatest_lower_bound(X_269,inverse(X_268))))) = multiply(greatest_lower_bound(identity,multiply(X_269,X_268)),inverse(multiply(X,X_268))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X,inverse(greatest_lower_bound(X_269,inverse(X_268))))),multiply(greatest_lower_bound(identity,multiply(X_269,X_268)),inverse(multiply(X,multiply(inverse(greatest_lower_bound(X_269,inverse(X_268))),greatest_lower_bound(identity,multiply(X_269,X_268))))))) ),[1,1,0,1],$fot(X_268)]]) ).
cnf(refute_0_1413,plain,
( inverse(multiply(X,inverse(greatest_lower_bound(X_269,inverse(X_268))))) != multiply(greatest_lower_bound(identity,multiply(X_269,X_268)),inverse(multiply(X,multiply(inverse(greatest_lower_bound(X_269,inverse(X_268))),greatest_lower_bound(identity,multiply(X_269,X_268))))))
| inverse(multiply(X,inverse(greatest_lower_bound(X_269,inverse(X_268))))) = multiply(greatest_lower_bound(identity,multiply(X_269,X_268)),inverse(multiply(X,X_268))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_269,inverse(X_268))),greatest_lower_bound(identity,multiply(X_269,X_268))),X_268) )],[refute_0_1411,refute_0_1412]) ).
cnf(refute_0_1414,plain,
inverse(multiply(X,inverse(greatest_lower_bound(X_269,inverse(X_268))))) = multiply(greatest_lower_bound(identity,multiply(X_269,X_268)),inverse(multiply(X,X_268))),
inference(resolve,[$cnf( $equal(inverse(multiply(X,inverse(greatest_lower_bound(X_269,inverse(X_268))))),multiply(greatest_lower_bound(identity,multiply(X_269,X_268)),inverse(multiply(X,multiply(inverse(greatest_lower_bound(X_269,inverse(X_268))),greatest_lower_bound(identity,multiply(X_269,X_268))))))) )],[refute_0_1394,refute_0_1413]) ).
cnf(refute_0_1415,plain,
inverse(multiply(X,inverse(greatest_lower_bound(X_269,inverse(X_268))))) = multiply(greatest_lower_bound(X_269,inverse(X_268)),inverse(X)),
inference(subst,[],[refute_0_107:[bind(X,$fot(greatest_lower_bound(X_269,inverse(X_268)))),bind(X_23,$fot(X))]]) ).
cnf(refute_0_1416,plain,
( inverse(multiply(X,inverse(greatest_lower_bound(X_269,inverse(X_268))))) != multiply(greatest_lower_bound(X_269,inverse(X_268)),inverse(X))
| inverse(multiply(X,inverse(greatest_lower_bound(X_269,inverse(X_268))))) != multiply(greatest_lower_bound(identity,multiply(X_269,X_268)),inverse(multiply(X,X_268)))
| multiply(greatest_lower_bound(X_269,inverse(X_268)),inverse(X)) = multiply(greatest_lower_bound(identity,multiply(X_269,X_268)),inverse(multiply(X,X_268))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X,inverse(greatest_lower_bound(X_269,inverse(X_268))))),multiply(greatest_lower_bound(identity,multiply(X_269,X_268)),inverse(multiply(X,X_268)))) ),[0],$fot(multiply(greatest_lower_bound(X_269,inverse(X_268)),inverse(X)))]]) ).
cnf(refute_0_1417,plain,
( inverse(multiply(X,inverse(greatest_lower_bound(X_269,inverse(X_268))))) != multiply(greatest_lower_bound(identity,multiply(X_269,X_268)),inverse(multiply(X,X_268)))
| multiply(greatest_lower_bound(X_269,inverse(X_268)),inverse(X)) = multiply(greatest_lower_bound(identity,multiply(X_269,X_268)),inverse(multiply(X,X_268))) ),
inference(resolve,[$cnf( $equal(inverse(multiply(X,inverse(greatest_lower_bound(X_269,inverse(X_268))))),multiply(greatest_lower_bound(X_269,inverse(X_268)),inverse(X))) )],[refute_0_1415,refute_0_1416]) ).
cnf(refute_0_1418,plain,
inverse(multiply(X,inverse(greatest_lower_bound(inverse(X_230),X_231)))) = multiply(greatest_lower_bound(identity,multiply(X_231,X_230)),inverse(multiply(X,multiply(inverse(greatest_lower_bound(inverse(X_230),X_231)),greatest_lower_bound(identity,multiply(X_231,X_230)))))),
inference(subst,[],[refute_0_1393:[bind(Y,$fot(inverse(greatest_lower_bound(inverse(X_230),X_231)))),bind(X_54,$fot(greatest_lower_bound(identity,multiply(X_231,X_230))))]]) ).
cnf(refute_0_1419,plain,
X_46 = multiply(inverse(greatest_lower_bound(inverse(X_46),X_94)),multiply(greatest_lower_bound(inverse(X_46),X_94),X_46)),
inference(subst,[],[refute_0_97:[bind(X_45,$fot(greatest_lower_bound(inverse(X_46),X_94)))]]) ).
cnf(refute_0_1420,plain,
multiply(greatest_lower_bound(inverse(X_86),X_88),X_86) = greatest_lower_bound(multiply(inverse(X_86),X_86),multiply(X_88,X_86)),
inference(subst,[],[monotony_glb2:[bind(X,$fot(X_86)),bind(Y,$fot(inverse(X_86))),bind(Z,$fot(X_88))]]) ).
cnf(refute_0_1421,plain,
( multiply(greatest_lower_bound(inverse(X_86),X_88),X_86) != greatest_lower_bound(multiply(inverse(X_86),X_86),multiply(X_88,X_86))
| multiply(inverse(X_86),X_86) != identity
| multiply(greatest_lower_bound(inverse(X_86),X_88),X_86) = greatest_lower_bound(identity,multiply(X_88,X_86)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_86),X_88),X_86),greatest_lower_bound(multiply(inverse(X_86),X_86),multiply(X_88,X_86))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_1422,plain,
( multiply(greatest_lower_bound(inverse(X_86),X_88),X_86) != greatest_lower_bound(multiply(inverse(X_86),X_86),multiply(X_88,X_86))
| multiply(greatest_lower_bound(inverse(X_86),X_88),X_86) = greatest_lower_bound(identity,multiply(X_88,X_86)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_86),X_86),identity) )],[refute_0_1397,refute_0_1421]) ).
cnf(refute_0_1423,plain,
multiply(greatest_lower_bound(inverse(X_86),X_88),X_86) = greatest_lower_bound(identity,multiply(X_88,X_86)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_86),X_88),X_86),greatest_lower_bound(multiply(inverse(X_86),X_86),multiply(X_88,X_86))) )],[refute_0_1420,refute_0_1422]) ).
cnf(refute_0_1424,plain,
multiply(greatest_lower_bound(inverse(X_46),X_94),X_46) = greatest_lower_bound(identity,multiply(X_94,X_46)),
inference(subst,[],[refute_0_1423:[bind(X_86,$fot(X_46)),bind(X_88,$fot(X_94))]]) ).
cnf(refute_0_1425,plain,
( X_46 != multiply(inverse(greatest_lower_bound(inverse(X_46),X_94)),multiply(greatest_lower_bound(inverse(X_46),X_94),X_46))
| multiply(greatest_lower_bound(inverse(X_46),X_94),X_46) != greatest_lower_bound(identity,multiply(X_94,X_46))
| X_46 = multiply(inverse(greatest_lower_bound(inverse(X_46),X_94)),greatest_lower_bound(identity,multiply(X_94,X_46))) ),
introduced(tautology,[equality,[$cnf( $equal(X_46,multiply(inverse(greatest_lower_bound(inverse(X_46),X_94)),multiply(greatest_lower_bound(inverse(X_46),X_94),X_46))) ),[1,1],$fot(greatest_lower_bound(identity,multiply(X_94,X_46)))]]) ).
cnf(refute_0_1426,plain,
( X_46 != multiply(inverse(greatest_lower_bound(inverse(X_46),X_94)),multiply(greatest_lower_bound(inverse(X_46),X_94),X_46))
| X_46 = multiply(inverse(greatest_lower_bound(inverse(X_46),X_94)),greatest_lower_bound(identity,multiply(X_94,X_46))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_46),X_94),X_46),greatest_lower_bound(identity,multiply(X_94,X_46))) )],[refute_0_1424,refute_0_1425]) ).
cnf(refute_0_1427,plain,
X_46 = multiply(inverse(greatest_lower_bound(inverse(X_46),X_94)),greatest_lower_bound(identity,multiply(X_94,X_46))),
inference(resolve,[$cnf( $equal(X_46,multiply(inverse(greatest_lower_bound(inverse(X_46),X_94)),multiply(greatest_lower_bound(inverse(X_46),X_94),X_46))) )],[refute_0_1419,refute_0_1426]) ).
cnf(refute_0_1428,plain,
X_230 = multiply(inverse(greatest_lower_bound(inverse(X_230),X_231)),greatest_lower_bound(identity,multiply(X_231,X_230))),
inference(subst,[],[refute_0_1427:[bind(X_46,$fot(X_230)),bind(X_94,$fot(X_231))]]) ).
cnf(refute_0_1429,plain,
( X_230 != multiply(inverse(greatest_lower_bound(inverse(X_230),X_231)),greatest_lower_bound(identity,multiply(X_231,X_230)))
| multiply(inverse(greatest_lower_bound(inverse(X_230),X_231)),greatest_lower_bound(identity,multiply(X_231,X_230))) = X_230 ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(X_230)),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(inverse(X_230),X_231)),greatest_lower_bound(identity,multiply(X_231,X_230)))))]]) ).
cnf(refute_0_1430,plain,
multiply(inverse(greatest_lower_bound(inverse(X_230),X_231)),greatest_lower_bound(identity,multiply(X_231,X_230))) = X_230,
inference(resolve,[$cnf( $equal(X_230,multiply(inverse(greatest_lower_bound(inverse(X_230),X_231)),greatest_lower_bound(identity,multiply(X_231,X_230)))) )],[refute_0_1428,refute_0_1429]) ).
cnf(refute_0_1431,plain,
( multiply(inverse(greatest_lower_bound(inverse(X_230),X_231)),greatest_lower_bound(identity,multiply(X_231,X_230))) != X_230
| inverse(multiply(X,inverse(greatest_lower_bound(inverse(X_230),X_231)))) != multiply(greatest_lower_bound(identity,multiply(X_231,X_230)),inverse(multiply(X,multiply(inverse(greatest_lower_bound(inverse(X_230),X_231)),greatest_lower_bound(identity,multiply(X_231,X_230))))))
| inverse(multiply(X,inverse(greatest_lower_bound(inverse(X_230),X_231)))) = multiply(greatest_lower_bound(identity,multiply(X_231,X_230)),inverse(multiply(X,X_230))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X,inverse(greatest_lower_bound(inverse(X_230),X_231)))),multiply(greatest_lower_bound(identity,multiply(X_231,X_230)),inverse(multiply(X,multiply(inverse(greatest_lower_bound(inverse(X_230),X_231)),greatest_lower_bound(identity,multiply(X_231,X_230))))))) ),[1,1,0,1],$fot(X_230)]]) ).
cnf(refute_0_1432,plain,
( inverse(multiply(X,inverse(greatest_lower_bound(inverse(X_230),X_231)))) != multiply(greatest_lower_bound(identity,multiply(X_231,X_230)),inverse(multiply(X,multiply(inverse(greatest_lower_bound(inverse(X_230),X_231)),greatest_lower_bound(identity,multiply(X_231,X_230))))))
| inverse(multiply(X,inverse(greatest_lower_bound(inverse(X_230),X_231)))) = multiply(greatest_lower_bound(identity,multiply(X_231,X_230)),inverse(multiply(X,X_230))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(X_230),X_231)),greatest_lower_bound(identity,multiply(X_231,X_230))),X_230) )],[refute_0_1430,refute_0_1431]) ).
cnf(refute_0_1433,plain,
inverse(multiply(X,inverse(greatest_lower_bound(inverse(X_230),X_231)))) = multiply(greatest_lower_bound(identity,multiply(X_231,X_230)),inverse(multiply(X,X_230))),
inference(resolve,[$cnf( $equal(inverse(multiply(X,inverse(greatest_lower_bound(inverse(X_230),X_231)))),multiply(greatest_lower_bound(identity,multiply(X_231,X_230)),inverse(multiply(X,multiply(inverse(greatest_lower_bound(inverse(X_230),X_231)),greatest_lower_bound(identity,multiply(X_231,X_230))))))) )],[refute_0_1418,refute_0_1432]) ).
cnf(refute_0_1434,plain,
inverse(multiply(X,inverse(greatest_lower_bound(inverse(X_230),X_231)))) = multiply(greatest_lower_bound(inverse(X_230),X_231),inverse(X)),
inference(subst,[],[refute_0_107:[bind(X,$fot(greatest_lower_bound(inverse(X_230),X_231))),bind(X_23,$fot(X))]]) ).
cnf(refute_0_1435,plain,
( inverse(multiply(X,inverse(greatest_lower_bound(inverse(X_230),X_231)))) != multiply(greatest_lower_bound(identity,multiply(X_231,X_230)),inverse(multiply(X,X_230)))
| inverse(multiply(X,inverse(greatest_lower_bound(inverse(X_230),X_231)))) != multiply(greatest_lower_bound(inverse(X_230),X_231),inverse(X))
| multiply(greatest_lower_bound(inverse(X_230),X_231),inverse(X)) = multiply(greatest_lower_bound(identity,multiply(X_231,X_230)),inverse(multiply(X,X_230))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X,inverse(greatest_lower_bound(inverse(X_230),X_231)))),multiply(greatest_lower_bound(identity,multiply(X_231,X_230)),inverse(multiply(X,X_230)))) ),[0],$fot(multiply(greatest_lower_bound(inverse(X_230),X_231),inverse(X)))]]) ).
cnf(refute_0_1436,plain,
( inverse(multiply(X,inverse(greatest_lower_bound(inverse(X_230),X_231)))) != multiply(greatest_lower_bound(identity,multiply(X_231,X_230)),inverse(multiply(X,X_230)))
| multiply(greatest_lower_bound(inverse(X_230),X_231),inverse(X)) = multiply(greatest_lower_bound(identity,multiply(X_231,X_230)),inverse(multiply(X,X_230))) ),
inference(resolve,[$cnf( $equal(inverse(multiply(X,inverse(greatest_lower_bound(inverse(X_230),X_231)))),multiply(greatest_lower_bound(inverse(X_230),X_231),inverse(X))) )],[refute_0_1434,refute_0_1435]) ).
cnf(refute_0_1437,plain,
multiply(greatest_lower_bound(inverse(X_230),X_231),inverse(X)) = multiply(greatest_lower_bound(identity,multiply(X_231,X_230)),inverse(multiply(X,X_230))),
inference(resolve,[$cnf( $equal(inverse(multiply(X,inverse(greatest_lower_bound(inverse(X_230),X_231)))),multiply(greatest_lower_bound(identity,multiply(X_231,X_230)),inverse(multiply(X,X_230)))) )],[refute_0_1433,refute_0_1436]) ).
cnf(refute_0_1438,plain,
( multiply(greatest_lower_bound(inverse(X_230),X_231),inverse(X)) != multiply(greatest_lower_bound(identity,multiply(X_231,X_230)),inverse(multiply(X,X_230)))
| multiply(greatest_lower_bound(identity,multiply(X_231,X_230)),inverse(multiply(X,X_230))) = multiply(greatest_lower_bound(inverse(X_230),X_231),inverse(X)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(multiply(greatest_lower_bound(inverse(X_230),X_231),inverse(X)))),bind(Y0,$fot(multiply(greatest_lower_bound(identity,multiply(X_231,X_230)),inverse(multiply(X,X_230)))))]]) ).
cnf(refute_0_1439,plain,
multiply(greatest_lower_bound(identity,multiply(X_231,X_230)),inverse(multiply(X,X_230))) = multiply(greatest_lower_bound(inverse(X_230),X_231),inverse(X)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_230),X_231),inverse(X)),multiply(greatest_lower_bound(identity,multiply(X_231,X_230)),inverse(multiply(X,X_230)))) )],[refute_0_1437,refute_0_1438]) ).
cnf(refute_0_1440,plain,
multiply(greatest_lower_bound(identity,multiply(X_269,X_268)),inverse(multiply(X,X_268))) = multiply(greatest_lower_bound(inverse(X_268),X_269),inverse(X)),
inference(subst,[],[refute_0_1439:[bind(X_230,$fot(X_268)),bind(X_231,$fot(X_269))]]) ).
cnf(refute_0_1441,plain,
( multiply(greatest_lower_bound(X_269,inverse(X_268)),inverse(X)) != multiply(greatest_lower_bound(identity,multiply(X_269,X_268)),inverse(multiply(X,X_268)))
| multiply(greatest_lower_bound(identity,multiply(X_269,X_268)),inverse(multiply(X,X_268))) != multiply(greatest_lower_bound(inverse(X_268),X_269),inverse(X))
| multiply(greatest_lower_bound(X_269,inverse(X_268)),inverse(X)) = multiply(greatest_lower_bound(inverse(X_268),X_269),inverse(X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_269,inverse(X_268)),inverse(X)),multiply(greatest_lower_bound(inverse(X_268),X_269),inverse(X))) ),[0],$fot(multiply(greatest_lower_bound(identity,multiply(X_269,X_268)),inverse(multiply(X,X_268))))]]) ).
cnf(refute_0_1442,plain,
( multiply(greatest_lower_bound(X_269,inverse(X_268)),inverse(X)) != multiply(greatest_lower_bound(identity,multiply(X_269,X_268)),inverse(multiply(X,X_268)))
| multiply(greatest_lower_bound(X_269,inverse(X_268)),inverse(X)) = multiply(greatest_lower_bound(inverse(X_268),X_269),inverse(X)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(X_269,X_268)),inverse(multiply(X,X_268))),multiply(greatest_lower_bound(inverse(X_268),X_269),inverse(X))) )],[refute_0_1440,refute_0_1441]) ).
cnf(refute_0_1443,plain,
( inverse(multiply(X,inverse(greatest_lower_bound(X_269,inverse(X_268))))) != multiply(greatest_lower_bound(identity,multiply(X_269,X_268)),inverse(multiply(X,X_268)))
| multiply(greatest_lower_bound(X_269,inverse(X_268)),inverse(X)) = multiply(greatest_lower_bound(inverse(X_268),X_269),inverse(X)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_269,inverse(X_268)),inverse(X)),multiply(greatest_lower_bound(identity,multiply(X_269,X_268)),inverse(multiply(X,X_268)))) )],[refute_0_1417,refute_0_1442]) ).
cnf(refute_0_1444,plain,
multiply(greatest_lower_bound(X_269,inverse(X_268)),inverse(X)) = multiply(greatest_lower_bound(inverse(X_268),X_269),inverse(X)),
inference(resolve,[$cnf( $equal(inverse(multiply(X,inverse(greatest_lower_bound(X_269,inverse(X_268))))),multiply(greatest_lower_bound(identity,multiply(X_269,X_268)),inverse(multiply(X,X_268)))) )],[refute_0_1414,refute_0_1443]) ).
cnf(refute_0_1445,plain,
multiply(greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_310))),inverse(least_upper_bound(identity,X_310))),inverse(greatest_lower_bound(identity,inverse(X_310)))) = multiply(greatest_lower_bound(inverse(least_upper_bound(identity,X_310)),inverse(least_upper_bound(identity,inverse(X_310)))),inverse(greatest_lower_bound(identity,inverse(X_310)))),
inference(subst,[],[refute_0_1444:[bind(X,$fot(greatest_lower_bound(identity,inverse(X_310)))),bind(X_268,$fot(least_upper_bound(identity,X_310))),bind(X_269,$fot(inverse(least_upper_bound(identity,inverse(X_310)))))]]) ).
cnf(refute_0_1446,plain,
( multiply(greatest_lower_bound(inverse(least_upper_bound(identity,X_310)),inverse(least_upper_bound(identity,inverse(X_310)))),inverse(greatest_lower_bound(identity,inverse(X_310)))) != multiply(greatest_lower_bound(X_310,identity),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310)))))
| multiply(greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_310))),inverse(least_upper_bound(identity,X_310))),inverse(greatest_lower_bound(identity,inverse(X_310)))) != multiply(greatest_lower_bound(inverse(least_upper_bound(identity,X_310)),inverse(least_upper_bound(identity,inverse(X_310)))),inverse(greatest_lower_bound(identity,inverse(X_310))))
| multiply(greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_310))),inverse(least_upper_bound(identity,X_310))),inverse(greatest_lower_bound(identity,inverse(X_310)))) = multiply(greatest_lower_bound(X_310,identity),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310))))) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(multiply(greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_310))),inverse(least_upper_bound(identity,X_310))),inverse(greatest_lower_bound(identity,inverse(X_310)))))),bind(Y0,$fot(multiply(greatest_lower_bound(inverse(least_upper_bound(identity,X_310)),inverse(least_upper_bound(identity,inverse(X_310)))),inverse(greatest_lower_bound(identity,inverse(X_310)))))),bind(Z0,$fot(multiply(greatest_lower_bound(X_310,identity),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310)))))))]]) ).
cnf(refute_0_1447,plain,
( multiply(greatest_lower_bound(inverse(least_upper_bound(identity,X_310)),inverse(least_upper_bound(identity,inverse(X_310)))),inverse(greatest_lower_bound(identity,inverse(X_310)))) != multiply(greatest_lower_bound(X_310,identity),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310)))))
| multiply(greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_310))),inverse(least_upper_bound(identity,X_310))),inverse(greatest_lower_bound(identity,inverse(X_310)))) = multiply(greatest_lower_bound(X_310,identity),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310))))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_310))),inverse(least_upper_bound(identity,X_310))),inverse(greatest_lower_bound(identity,inverse(X_310)))),multiply(greatest_lower_bound(inverse(least_upper_bound(identity,X_310)),inverse(least_upper_bound(identity,inverse(X_310)))),inverse(greatest_lower_bound(identity,inverse(X_310))))) )],[refute_0_1445,refute_0_1446]) ).
cnf(refute_0_1448,plain,
multiply(greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_310))),inverse(least_upper_bound(identity,X_310))),inverse(greatest_lower_bound(identity,inverse(X_310)))) = multiply(greatest_lower_bound(X_310,identity),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310))))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(least_upper_bound(identity,X_310)),inverse(least_upper_bound(identity,inverse(X_310)))),inverse(greatest_lower_bound(identity,inverse(X_310)))),multiply(greatest_lower_bound(X_310,identity),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310)))))) )],[refute_0_1388,refute_0_1447]) ).
cnf(refute_0_1449,plain,
( multiply(greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_310))),inverse(least_upper_bound(identity,X_310))),inverse(greatest_lower_bound(identity,inverse(X_310)))) != multiply(greatest_lower_bound(X_310,identity),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310)))))
| inverse(least_upper_bound(identity,inverse(X_310))) != multiply(greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_310))),inverse(least_upper_bound(identity,X_310))),inverse(greatest_lower_bound(identity,inverse(X_310))))
| inverse(least_upper_bound(identity,inverse(X_310))) = multiply(greatest_lower_bound(X_310,identity),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310))))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_310))),multiply(greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_310))),inverse(least_upper_bound(identity,X_310))),inverse(greatest_lower_bound(identity,inverse(X_310))))) ),[1],$fot(multiply(greatest_lower_bound(X_310,identity),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310))))))]]) ).
cnf(refute_0_1450,plain,
( inverse(least_upper_bound(identity,inverse(X_310))) != multiply(greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_310))),inverse(least_upper_bound(identity,X_310))),inverse(greatest_lower_bound(identity,inverse(X_310))))
| inverse(least_upper_bound(identity,inverse(X_310))) = multiply(greatest_lower_bound(X_310,identity),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310))))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_310))),inverse(least_upper_bound(identity,X_310))),inverse(greatest_lower_bound(identity,inverse(X_310)))),multiply(greatest_lower_bound(X_310,identity),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310)))))) )],[refute_0_1448,refute_0_1449]) ).
cnf(refute_0_1451,plain,
inverse(least_upper_bound(identity,inverse(X_310))) = multiply(greatest_lower_bound(X_310,identity),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310))))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_310))),multiply(greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_310))),inverse(least_upper_bound(identity,X_310))),inverse(greatest_lower_bound(identity,inverse(X_310))))) )],[refute_0_185,refute_0_1450]) ).
cnf(refute_0_1452,plain,
multiply(greatest_lower_bound(X_310,identity),identity) = greatest_lower_bound(X_310,identity),
inference(subst,[],[refute_0_564:[bind(X,$fot(greatest_lower_bound(X_310,identity)))]]) ).
cnf(refute_0_1453,plain,
multiply(inverse(greatest_lower_bound(X_15,X_62)),least_upper_bound(X_62,greatest_lower_bound(X_15,X_62))) = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_15,X_62)),X_62)),
inference(subst,[],[refute_0_127:[bind(X_56,$fot(X_62)),bind(X_57,$fot(greatest_lower_bound(X_15,X_62)))]]) ).
cnf(refute_0_1454,plain,
least_upper_bound(X_62,greatest_lower_bound(X_15,X_62)) = X_62,
inference(subst,[],[refute_0_270:[bind(X_14,$fot(X_62))]]) ).
cnf(refute_0_1455,plain,
( multiply(inverse(greatest_lower_bound(X_15,X_62)),least_upper_bound(X_62,greatest_lower_bound(X_15,X_62))) != least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_15,X_62)),X_62))
| least_upper_bound(X_62,greatest_lower_bound(X_15,X_62)) != X_62
| multiply(inverse(greatest_lower_bound(X_15,X_62)),X_62) = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_15,X_62)),X_62)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_15,X_62)),least_upper_bound(X_62,greatest_lower_bound(X_15,X_62))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_15,X_62)),X_62))) ),[0,1],$fot(X_62)]]) ).
cnf(refute_0_1456,plain,
( multiply(inverse(greatest_lower_bound(X_15,X_62)),least_upper_bound(X_62,greatest_lower_bound(X_15,X_62))) != least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_15,X_62)),X_62))
| multiply(inverse(greatest_lower_bound(X_15,X_62)),X_62) = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_15,X_62)),X_62)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_62,greatest_lower_bound(X_15,X_62)),X_62) )],[refute_0_1454,refute_0_1455]) ).
cnf(refute_0_1457,plain,
multiply(inverse(greatest_lower_bound(X_15,X_62)),X_62) = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_15,X_62)),X_62)),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_15,X_62)),least_upper_bound(X_62,greatest_lower_bound(X_15,X_62))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_15,X_62)),X_62))) )],[refute_0_1453,refute_0_1456]) ).
cnf(refute_0_1458,plain,
multiply(inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))) = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),
inference(subst,[],[refute_0_1457:[bind(X_15,$fot(identity)),bind(X_62,$fot(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))]]) ).
cnf(refute_0_1459,plain,
greatest_lower_bound(least_upper_bound(X_41,Y),greatest_lower_bound(X_40,X_41)) = greatest_lower_bound(X_40,greatest_lower_bound(X_41,least_upper_bound(X_41,Y))),
inference(subst,[],[refute_0_321:[bind(X,$fot(least_upper_bound(X_41,Y))),bind(Y,$fot(X_40)),bind(X_35,$fot(X_41))]]) ).
cnf(refute_0_1460,plain,
greatest_lower_bound(X_41,least_upper_bound(X_41,Y)) = X_41,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_41))]]) ).
cnf(refute_0_1461,plain,
( greatest_lower_bound(X_41,least_upper_bound(X_41,Y)) != X_41
| greatest_lower_bound(least_upper_bound(X_41,Y),greatest_lower_bound(X_40,X_41)) != greatest_lower_bound(X_40,greatest_lower_bound(X_41,least_upper_bound(X_41,Y)))
| greatest_lower_bound(least_upper_bound(X_41,Y),greatest_lower_bound(X_40,X_41)) = greatest_lower_bound(X_40,X_41) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_41,Y),greatest_lower_bound(X_40,X_41)),greatest_lower_bound(X_40,greatest_lower_bound(X_41,least_upper_bound(X_41,Y)))) ),[1,1],$fot(X_41)]]) ).
cnf(refute_0_1462,plain,
( greatest_lower_bound(least_upper_bound(X_41,Y),greatest_lower_bound(X_40,X_41)) != greatest_lower_bound(X_40,greatest_lower_bound(X_41,least_upper_bound(X_41,Y)))
| greatest_lower_bound(least_upper_bound(X_41,Y),greatest_lower_bound(X_40,X_41)) = greatest_lower_bound(X_40,X_41) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_41,least_upper_bound(X_41,Y)),X_41) )],[refute_0_1460,refute_0_1461]) ).
cnf(refute_0_1463,plain,
greatest_lower_bound(least_upper_bound(X_41,Y),greatest_lower_bound(X_40,X_41)) = greatest_lower_bound(X_40,X_41),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_41,Y),greatest_lower_bound(X_40,X_41)),greatest_lower_bound(X_40,greatest_lower_bound(X_41,least_upper_bound(X_41,Y)))) )],[refute_0_1459,refute_0_1462]) ).
cnf(refute_0_1464,plain,
greatest_lower_bound(least_upper_bound(X_41,Y),greatest_lower_bound(X_40,X_41)) = greatest_lower_bound(X_41,greatest_lower_bound(X_40,least_upper_bound(X_41,Y))),
inference(subst,[],[refute_0_1243:[bind(X_15,$fot(X_41)),bind(X_39,$fot(X_40)),bind(X_41,$fot(least_upper_bound(X_41,Y)))]]) ).
cnf(refute_0_1465,plain,
( greatest_lower_bound(least_upper_bound(X_41,Y),greatest_lower_bound(X_40,X_41)) != greatest_lower_bound(X_40,X_41)
| greatest_lower_bound(least_upper_bound(X_41,Y),greatest_lower_bound(X_40,X_41)) != greatest_lower_bound(X_41,greatest_lower_bound(X_40,least_upper_bound(X_41,Y)))
| greatest_lower_bound(X_41,greatest_lower_bound(X_40,least_upper_bound(X_41,Y))) = greatest_lower_bound(X_40,X_41) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_41,Y),greatest_lower_bound(X_40,X_41)),greatest_lower_bound(X_40,X_41)) ),[0],$fot(greatest_lower_bound(X_41,greatest_lower_bound(X_40,least_upper_bound(X_41,Y))))]]) ).
cnf(refute_0_1466,plain,
( greatest_lower_bound(least_upper_bound(X_41,Y),greatest_lower_bound(X_40,X_41)) != greatest_lower_bound(X_40,X_41)
| greatest_lower_bound(X_41,greatest_lower_bound(X_40,least_upper_bound(X_41,Y))) = greatest_lower_bound(X_40,X_41) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_41,Y),greatest_lower_bound(X_40,X_41)),greatest_lower_bound(X_41,greatest_lower_bound(X_40,least_upper_bound(X_41,Y)))) )],[refute_0_1464,refute_0_1465]) ).
cnf(refute_0_1467,plain,
greatest_lower_bound(X_41,greatest_lower_bound(X_40,least_upper_bound(X_41,Y))) = greatest_lower_bound(X_40,X_41),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_41,Y),greatest_lower_bound(X_40,X_41)),greatest_lower_bound(X_40,X_41)) )],[refute_0_1463,refute_0_1466]) ).
cnf(refute_0_1468,plain,
greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_306),least_upper_bound(identity,inverse(X_306)))) = greatest_lower_bound(least_upper_bound(identity,X_306),identity),
inference(subst,[],[refute_0_1467:[bind(Y,$fot(inverse(X_306))),bind(X_40,$fot(least_upper_bound(identity,X_306))),bind(X_41,$fot(identity))]]) ).
cnf(refute_0_1469,plain,
multiply(least_upper_bound(identity,X_306),greatest_lower_bound(identity,inverse(X_306))) = greatest_lower_bound(least_upper_bound(identity,X_306),least_upper_bound(identity,inverse(X_306))),
inference(subst,[],[refute_0_720:[bind(X_63,$fot(X_306))]]) ).
cnf(refute_0_1470,plain,
( multiply(least_upper_bound(identity,X_306),greatest_lower_bound(identity,inverse(X_306))) != greatest_lower_bound(least_upper_bound(identity,X_306),least_upper_bound(identity,inverse(X_306)))
| greatest_lower_bound(least_upper_bound(identity,X_306),least_upper_bound(identity,inverse(X_306))) = multiply(least_upper_bound(identity,X_306),greatest_lower_bound(identity,inverse(X_306))) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(multiply(least_upper_bound(identity,X_306),greatest_lower_bound(identity,inverse(X_306))))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(identity,X_306),least_upper_bound(identity,inverse(X_306)))))]]) ).
cnf(refute_0_1471,plain,
greatest_lower_bound(least_upper_bound(identity,X_306),least_upper_bound(identity,inverse(X_306))) = multiply(least_upper_bound(identity,X_306),greatest_lower_bound(identity,inverse(X_306))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_306),greatest_lower_bound(identity,inverse(X_306))),greatest_lower_bound(least_upper_bound(identity,X_306),least_upper_bound(identity,inverse(X_306)))) )],[refute_0_1469,refute_0_1470]) ).
cnf(refute_0_1472,plain,
( greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_306),least_upper_bound(identity,inverse(X_306)))) != greatest_lower_bound(least_upper_bound(identity,X_306),identity)
| greatest_lower_bound(least_upper_bound(identity,X_306),least_upper_bound(identity,inverse(X_306))) != multiply(least_upper_bound(identity,X_306),greatest_lower_bound(identity,inverse(X_306)))
| greatest_lower_bound(identity,multiply(least_upper_bound(identity,X_306),greatest_lower_bound(identity,inverse(X_306)))) = greatest_lower_bound(least_upper_bound(identity,X_306),identity) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_306),least_upper_bound(identity,inverse(X_306)))),greatest_lower_bound(least_upper_bound(identity,X_306),identity)) ),[0,1],$fot(multiply(least_upper_bound(identity,X_306),greatest_lower_bound(identity,inverse(X_306))))]]) ).
cnf(refute_0_1473,plain,
( greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_306),least_upper_bound(identity,inverse(X_306)))) != greatest_lower_bound(least_upper_bound(identity,X_306),identity)
| greatest_lower_bound(identity,multiply(least_upper_bound(identity,X_306),greatest_lower_bound(identity,inverse(X_306)))) = greatest_lower_bound(least_upper_bound(identity,X_306),identity) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,X_306),least_upper_bound(identity,inverse(X_306))),multiply(least_upper_bound(identity,X_306),greatest_lower_bound(identity,inverse(X_306)))) )],[refute_0_1471,refute_0_1472]) ).
cnf(refute_0_1474,plain,
greatest_lower_bound(identity,multiply(least_upper_bound(identity,X_306),greatest_lower_bound(identity,inverse(X_306)))) = greatest_lower_bound(least_upper_bound(identity,X_306),identity),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_306),least_upper_bound(identity,inverse(X_306)))),greatest_lower_bound(least_upper_bound(identity,X_306),identity)) )],[refute_0_1468,refute_0_1473]) ).
cnf(refute_0_1475,plain,
greatest_lower_bound(identity,least_upper_bound(X_306,identity)) = identity,
inference(subst,[],[refute_0_218:[bind(X,$fot(identity)),bind(Y,$fot(X_306))]]) ).
cnf(refute_0_1476,plain,
( greatest_lower_bound(X_303,least_upper_bound(X_162,identity)) != greatest_lower_bound(least_upper_bound(identity,X_162),X_303)
| greatest_lower_bound(least_upper_bound(identity,X_162),X_303) = greatest_lower_bound(X_303,least_upper_bound(X_162,identity)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(greatest_lower_bound(X_303,least_upper_bound(X_162,identity)))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(identity,X_162),X_303)))]]) ).
cnf(refute_0_1477,plain,
greatest_lower_bound(least_upper_bound(identity,X_162),X_303) = greatest_lower_bound(X_303,least_upper_bound(X_162,identity)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_303,least_upper_bound(X_162,identity)),greatest_lower_bound(least_upper_bound(identity,X_162),X_303)) )],[refute_0_924,refute_0_1476]) ).
cnf(refute_0_1478,plain,
greatest_lower_bound(least_upper_bound(identity,X_306),identity) = greatest_lower_bound(identity,least_upper_bound(X_306,identity)),
inference(subst,[],[refute_0_1477:[bind(X_162,$fot(X_306)),bind(X_303,$fot(identity))]]) ).
cnf(refute_0_1479,plain,
( greatest_lower_bound(identity,least_upper_bound(X_306,identity)) != identity
| greatest_lower_bound(least_upper_bound(identity,X_306),identity) != greatest_lower_bound(identity,least_upper_bound(X_306,identity))
| greatest_lower_bound(least_upper_bound(identity,X_306),identity) = identity ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(identity,X_306),identity))),bind(Y0,$fot(greatest_lower_bound(identity,least_upper_bound(X_306,identity)))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_1480,plain,
( greatest_lower_bound(identity,least_upper_bound(X_306,identity)) != identity
| greatest_lower_bound(least_upper_bound(identity,X_306),identity) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,X_306),identity),greatest_lower_bound(identity,least_upper_bound(X_306,identity))) )],[refute_0_1478,refute_0_1479]) ).
cnf(refute_0_1481,plain,
greatest_lower_bound(least_upper_bound(identity,X_306),identity) = identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(X_306,identity)),identity) )],[refute_0_1475,refute_0_1480]) ).
cnf(refute_0_1482,plain,
( greatest_lower_bound(identity,multiply(least_upper_bound(identity,X_306),greatest_lower_bound(identity,inverse(X_306)))) != greatest_lower_bound(least_upper_bound(identity,X_306),identity)
| greatest_lower_bound(least_upper_bound(identity,X_306),identity) != identity
| greatest_lower_bound(identity,multiply(least_upper_bound(identity,X_306),greatest_lower_bound(identity,inverse(X_306)))) = identity ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(identity,multiply(least_upper_bound(identity,X_306),greatest_lower_bound(identity,inverse(X_306)))),identity) ),[0],$fot(greatest_lower_bound(least_upper_bound(identity,X_306),identity))]]) ).
cnf(refute_0_1483,plain,
( greatest_lower_bound(identity,multiply(least_upper_bound(identity,X_306),greatest_lower_bound(identity,inverse(X_306)))) != greatest_lower_bound(least_upper_bound(identity,X_306),identity)
| greatest_lower_bound(identity,multiply(least_upper_bound(identity,X_306),greatest_lower_bound(identity,inverse(X_306)))) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,X_306),identity),identity) )],[refute_0_1481,refute_0_1482]) ).
cnf(refute_0_1484,plain,
greatest_lower_bound(identity,multiply(least_upper_bound(identity,X_306),greatest_lower_bound(identity,inverse(X_306)))) = identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(least_upper_bound(identity,X_306),greatest_lower_bound(identity,inverse(X_306)))),greatest_lower_bound(least_upper_bound(identity,X_306),identity)) )],[refute_0_1474,refute_0_1483]) ).
cnf(refute_0_1485,plain,
multiply(least_upper_bound(identity,X_306),greatest_lower_bound(identity,inverse(X_306))) = multiply(greatest_lower_bound(identity,X_306),least_upper_bound(identity,inverse(X_306))),
inference(subst,[],[refute_0_1304:[bind(X_309,$fot(X_306))]]) ).
cnf(refute_0_1486,plain,
greatest_lower_bound(identity,multiply(least_upper_bound(identity,X_306),greatest_lower_bound(identity,inverse(X_306)))) = greatest_lower_bound(identity,multiply(least_upper_bound(identity,X_306),greatest_lower_bound(identity,inverse(X_306)))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,multiply(least_upper_bound(identity,X_306),greatest_lower_bound(identity,inverse(X_306)))))]]) ).
cnf(refute_0_1487,plain,
( multiply(least_upper_bound(identity,X_306),greatest_lower_bound(identity,inverse(X_306))) != multiply(greatest_lower_bound(identity,X_306),least_upper_bound(identity,inverse(X_306)))
| greatest_lower_bound(identity,multiply(least_upper_bound(identity,X_306),greatest_lower_bound(identity,inverse(X_306)))) != greatest_lower_bound(identity,multiply(least_upper_bound(identity,X_306),greatest_lower_bound(identity,inverse(X_306))))
| greatest_lower_bound(identity,multiply(least_upper_bound(identity,X_306),greatest_lower_bound(identity,inverse(X_306)))) = greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_306),least_upper_bound(identity,inverse(X_306)))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(least_upper_bound(identity,X_306),greatest_lower_bound(identity,inverse(X_306)))),greatest_lower_bound(identity,multiply(least_upper_bound(identity,X_306),greatest_lower_bound(identity,inverse(X_306))))) ),[1,1],$fot(multiply(greatest_lower_bound(identity,X_306),least_upper_bound(identity,inverse(X_306))))]]) ).
cnf(refute_0_1488,plain,
( multiply(least_upper_bound(identity,X_306),greatest_lower_bound(identity,inverse(X_306))) != multiply(greatest_lower_bound(identity,X_306),least_upper_bound(identity,inverse(X_306)))
| greatest_lower_bound(identity,multiply(least_upper_bound(identity,X_306),greatest_lower_bound(identity,inverse(X_306)))) = greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_306),least_upper_bound(identity,inverse(X_306)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(least_upper_bound(identity,X_306),greatest_lower_bound(identity,inverse(X_306)))),greatest_lower_bound(identity,multiply(least_upper_bound(identity,X_306),greatest_lower_bound(identity,inverse(X_306))))) )],[refute_0_1486,refute_0_1487]) ).
cnf(refute_0_1489,plain,
greatest_lower_bound(identity,multiply(least_upper_bound(identity,X_306),greatest_lower_bound(identity,inverse(X_306)))) = greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_306),least_upper_bound(identity,inverse(X_306)))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_306),greatest_lower_bound(identity,inverse(X_306))),multiply(greatest_lower_bound(identity,X_306),least_upper_bound(identity,inverse(X_306)))) )],[refute_0_1485,refute_0_1488]) ).
cnf(refute_0_1490,plain,
( greatest_lower_bound(identity,multiply(least_upper_bound(identity,X_306),greatest_lower_bound(identity,inverse(X_306)))) != greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_306),least_upper_bound(identity,inverse(X_306))))
| greatest_lower_bound(identity,multiply(least_upper_bound(identity,X_306),greatest_lower_bound(identity,inverse(X_306)))) != identity
| greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_306),least_upper_bound(identity,inverse(X_306)))) = identity ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(least_upper_bound(identity,X_306),greatest_lower_bound(identity,inverse(X_306)))),identity) ),[0],$fot(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_306),least_upper_bound(identity,inverse(X_306)))))]]) ).
cnf(refute_0_1491,plain,
( greatest_lower_bound(identity,multiply(least_upper_bound(identity,X_306),greatest_lower_bound(identity,inverse(X_306)))) != identity
| greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_306),least_upper_bound(identity,inverse(X_306)))) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(least_upper_bound(identity,X_306),greatest_lower_bound(identity,inverse(X_306)))),greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_306),least_upper_bound(identity,inverse(X_306))))) )],[refute_0_1489,refute_0_1490]) ).
cnf(refute_0_1492,plain,
greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_306),least_upper_bound(identity,inverse(X_306)))) = identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(least_upper_bound(identity,X_306),greatest_lower_bound(identity,inverse(X_306)))),identity) )],[refute_0_1484,refute_0_1491]) ).
cnf(refute_0_1493,plain,
greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))) = identity,
inference(subst,[],[refute_0_1492:[bind(X_306,$fot(X_462))]]) ).
cnf(refute_0_1494,plain,
( multiply(inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))) != least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))
| greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))) != identity
| multiply(inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))) = least_upper_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))) ),[1,1,0,0],$fot(identity)]]) ).
cnf(refute_0_1495,plain,
( multiply(inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))) != least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))
| multiply(inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))) = least_upper_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity) )],[refute_0_1493,refute_0_1494]) ).
cnf(refute_0_1496,plain,
multiply(inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))) = least_upper_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))) )],[refute_0_1458,refute_0_1495]) ).
cnf(refute_0_1497,plain,
inverse(multiply(greatest_lower_bound(X_92,inverse(inverse(X))),inverse(X))) = multiply(X,inverse(greatest_lower_bound(X_92,inverse(inverse(X))))),
inference(subst,[],[refute_0_107:[bind(X_23,$fot(greatest_lower_bound(X_92,inverse(inverse(X)))))]]) ).
cnf(refute_0_1498,plain,
multiply(greatest_lower_bound(X_92,inverse(inverse(X))),inverse(X)) = greatest_lower_bound(identity,multiply(X_92,inverse(X))),
inference(subst,[],[refute_0_1404:[bind(X_86,$fot(inverse(X))),bind(X_87,$fot(X_92))]]) ).
cnf(refute_0_1499,plain,
( multiply(greatest_lower_bound(X_92,inverse(inverse(X))),inverse(X)) != greatest_lower_bound(identity,multiply(X_92,inverse(X)))
| inverse(multiply(greatest_lower_bound(X_92,inverse(inverse(X))),inverse(X))) != multiply(X,inverse(greatest_lower_bound(X_92,inverse(inverse(X)))))
| inverse(greatest_lower_bound(identity,multiply(X_92,inverse(X)))) = multiply(X,inverse(greatest_lower_bound(X_92,inverse(inverse(X))))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(greatest_lower_bound(X_92,inverse(inverse(X))),inverse(X))),multiply(X,inverse(greatest_lower_bound(X_92,inverse(inverse(X)))))) ),[0,0],$fot(greatest_lower_bound(identity,multiply(X_92,inverse(X))))]]) ).
cnf(refute_0_1500,plain,
( inverse(multiply(greatest_lower_bound(X_92,inverse(inverse(X))),inverse(X))) != multiply(X,inverse(greatest_lower_bound(X_92,inverse(inverse(X)))))
| inverse(greatest_lower_bound(identity,multiply(X_92,inverse(X)))) = multiply(X,inverse(greatest_lower_bound(X_92,inverse(inverse(X))))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_92,inverse(inverse(X))),inverse(X)),greatest_lower_bound(identity,multiply(X_92,inverse(X)))) )],[refute_0_1498,refute_0_1499]) ).
cnf(refute_0_1501,plain,
inverse(greatest_lower_bound(identity,multiply(X_92,inverse(X)))) = multiply(X,inverse(greatest_lower_bound(X_92,inverse(inverse(X))))),
inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(X_92,inverse(inverse(X))),inverse(X))),multiply(X,inverse(greatest_lower_bound(X_92,inverse(inverse(X)))))) )],[refute_0_1497,refute_0_1500]) ).
cnf(refute_0_1502,plain,
greatest_lower_bound(X_92,inverse(inverse(X))) = greatest_lower_bound(X_92,inverse(inverse(X))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X_92,inverse(inverse(X))))]]) ).
cnf(refute_0_1503,plain,
( greatest_lower_bound(X_92,inverse(inverse(X))) != greatest_lower_bound(X_92,inverse(inverse(X)))
| inverse(inverse(X)) != X
| greatest_lower_bound(X_92,inverse(inverse(X))) = greatest_lower_bound(X_92,X) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_92,inverse(inverse(X))),greatest_lower_bound(X_92,inverse(inverse(X)))) ),[1,1],$fot(X)]]) ).
cnf(refute_0_1504,plain,
( inverse(inverse(X)) != X
| greatest_lower_bound(X_92,inverse(inverse(X))) = greatest_lower_bound(X_92,X) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_92,inverse(inverse(X))),greatest_lower_bound(X_92,inverse(inverse(X)))) )],[refute_0_1502,refute_0_1503]) ).
cnf(refute_0_1505,plain,
greatest_lower_bound(X_92,inverse(inverse(X))) = greatest_lower_bound(X_92,X),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p19_2,refute_0_1504]) ).
cnf(refute_0_1506,plain,
inverse(greatest_lower_bound(X_92,inverse(inverse(X)))) = inverse(greatest_lower_bound(X_92,inverse(inverse(X)))),
introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(X_92,inverse(inverse(X)))))]]) ).
cnf(refute_0_1507,plain,
( greatest_lower_bound(X_92,inverse(inverse(X))) != greatest_lower_bound(X_92,X)
| inverse(greatest_lower_bound(X_92,inverse(inverse(X)))) != inverse(greatest_lower_bound(X_92,inverse(inverse(X))))
| inverse(greatest_lower_bound(X_92,inverse(inverse(X)))) = inverse(greatest_lower_bound(X_92,X)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X_92,inverse(inverse(X)))),inverse(greatest_lower_bound(X_92,inverse(inverse(X))))) ),[1,0],$fot(greatest_lower_bound(X_92,X))]]) ).
cnf(refute_0_1508,plain,
( greatest_lower_bound(X_92,inverse(inverse(X))) != greatest_lower_bound(X_92,X)
| inverse(greatest_lower_bound(X_92,inverse(inverse(X)))) = inverse(greatest_lower_bound(X_92,X)) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_92,inverse(inverse(X)))),inverse(greatest_lower_bound(X_92,inverse(inverse(X))))) )],[refute_0_1506,refute_0_1507]) ).
cnf(refute_0_1509,plain,
inverse(greatest_lower_bound(X_92,inverse(inverse(X)))) = inverse(greatest_lower_bound(X_92,X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_92,inverse(inverse(X))),greatest_lower_bound(X_92,X)) )],[refute_0_1505,refute_0_1508]) ).
cnf(refute_0_1510,plain,
multiply(X,inverse(greatest_lower_bound(X_92,inverse(inverse(X))))) = multiply(X,inverse(greatest_lower_bound(X_92,inverse(inverse(X))))),
introduced(tautology,[refl,[$fot(multiply(X,inverse(greatest_lower_bound(X_92,inverse(inverse(X))))))]]) ).
cnf(refute_0_1511,plain,
( multiply(X,inverse(greatest_lower_bound(X_92,inverse(inverse(X))))) != multiply(X,inverse(greatest_lower_bound(X_92,inverse(inverse(X)))))
| inverse(greatest_lower_bound(X_92,inverse(inverse(X)))) != inverse(greatest_lower_bound(X_92,X))
| multiply(X,inverse(greatest_lower_bound(X_92,inverse(inverse(X))))) = multiply(X,inverse(greatest_lower_bound(X_92,X))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X,inverse(greatest_lower_bound(X_92,inverse(inverse(X))))),multiply(X,inverse(greatest_lower_bound(X_92,inverse(inverse(X)))))) ),[1,1],$fot(inverse(greatest_lower_bound(X_92,X)))]]) ).
cnf(refute_0_1512,plain,
( inverse(greatest_lower_bound(X_92,inverse(inverse(X)))) != inverse(greatest_lower_bound(X_92,X))
| multiply(X,inverse(greatest_lower_bound(X_92,inverse(inverse(X))))) = multiply(X,inverse(greatest_lower_bound(X_92,X))) ),
inference(resolve,[$cnf( $equal(multiply(X,inverse(greatest_lower_bound(X_92,inverse(inverse(X))))),multiply(X,inverse(greatest_lower_bound(X_92,inverse(inverse(X)))))) )],[refute_0_1510,refute_0_1511]) ).
cnf(refute_0_1513,plain,
multiply(X,inverse(greatest_lower_bound(X_92,inverse(inverse(X))))) = multiply(X,inverse(greatest_lower_bound(X_92,X))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_92,inverse(inverse(X)))),inverse(greatest_lower_bound(X_92,X))) )],[refute_0_1509,refute_0_1512]) ).
cnf(refute_0_1514,plain,
( multiply(X,inverse(greatest_lower_bound(X_92,inverse(inverse(X))))) != multiply(X,inverse(greatest_lower_bound(X_92,X)))
| inverse(greatest_lower_bound(identity,multiply(X_92,inverse(X)))) != multiply(X,inverse(greatest_lower_bound(X_92,inverse(inverse(X)))))
| inverse(greatest_lower_bound(identity,multiply(X_92,inverse(X)))) = multiply(X,inverse(greatest_lower_bound(X_92,X))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(X_92,inverse(X)))),multiply(X,inverse(greatest_lower_bound(X_92,inverse(inverse(X)))))) ),[1],$fot(multiply(X,inverse(greatest_lower_bound(X_92,X))))]]) ).
cnf(refute_0_1515,plain,
( inverse(greatest_lower_bound(identity,multiply(X_92,inverse(X)))) != multiply(X,inverse(greatest_lower_bound(X_92,inverse(inverse(X)))))
| inverse(greatest_lower_bound(identity,multiply(X_92,inverse(X)))) = multiply(X,inverse(greatest_lower_bound(X_92,X))) ),
inference(resolve,[$cnf( $equal(multiply(X,inverse(greatest_lower_bound(X_92,inverse(inverse(X))))),multiply(X,inverse(greatest_lower_bound(X_92,X)))) )],[refute_0_1513,refute_0_1514]) ).
cnf(refute_0_1516,plain,
inverse(greatest_lower_bound(identity,multiply(X_92,inverse(X)))) = multiply(X,inverse(greatest_lower_bound(X_92,X))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(X_92,inverse(X)))),multiply(X,inverse(greatest_lower_bound(X_92,inverse(inverse(X)))))) )],[refute_0_1501,refute_0_1515]) ).
cnf(refute_0_1517,plain,
inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))))) = multiply(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))),
inference(subst,[],[refute_0_1516:[bind(X,$fot(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),bind(X_92,$fot(identity))]]) ).
cnf(refute_0_1518,plain,
( greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))) != identity
| inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))))) != multiply(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))))
| inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))))) = multiply(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))),inverse(identity)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))))),multiply(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))))) ),[1,1,0],$fot(identity)]]) ).
cnf(refute_0_1519,plain,
( inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))))) != multiply(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))))
| inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))))) = multiply(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))),inverse(identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity) )],[refute_0_1493,refute_0_1518]) ).
cnf(refute_0_1520,plain,
inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))))) = multiply(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))),inverse(identity)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))))),multiply(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))))) )],[refute_0_1517,refute_0_1519]) ).
cnf(refute_0_1521,plain,
multiply(identity,greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))) = greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),
inference(subst,[],[left_identity:[bind(X,$fot(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))))]]) ).
cnf(refute_0_1522,plain,
inverse(inverse(multiply(X_449,greatest_lower_bound(X_447,X_448)))) = multiply(inverse(multiply(greatest_lower_bound(X_448,X_447),inverse(multiply(X_449,greatest_lower_bound(X_447,X_448))))),greatest_lower_bound(X_448,X_447)),
inference(subst,[],[refute_0_542:[bind(X_47,$fot(greatest_lower_bound(X_448,X_447))),bind(X_48,$fot(inverse(multiply(X_449,greatest_lower_bound(X_447,X_448)))))]]) ).
cnf(refute_0_1523,plain,
inverse(multiply(X_227,multiply(greatest_lower_bound(X_183,X_184),inverse(greatest_lower_bound(X_184,X_183))))) = multiply(greatest_lower_bound(X_184,X_183),inverse(multiply(X_227,greatest_lower_bound(X_183,X_184)))),
inference(subst,[],[refute_0_522:[bind(X_23,$fot(X_227)),bind(X_32,$fot(greatest_lower_bound(X_183,X_184))),bind(X_33,$fot(greatest_lower_bound(X_184,X_183)))]]) ).
cnf(refute_0_1524,plain,
multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_183,X_184)),inverse(greatest_lower_bound(X_184,X_183)))),least_upper_bound(inverse(greatest_lower_bound(X_183,X_184)),inverse(greatest_lower_bound(X_184,X_183)))) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(least_upper_bound(inverse(greatest_lower_bound(X_183,X_184)),inverse(greatest_lower_bound(X_184,X_183)))))]]) ).
cnf(refute_0_1525,plain,
inverse(inverse(X_63)) = multiply(least_upper_bound(X_62,X_63),inverse(multiply(inverse(X_63),least_upper_bound(X_62,X_63)))),
inference(subst,[],[refute_0_117:[bind(X,$fot(inverse(X_63))),bind(Y,$fot(least_upper_bound(X_62,X_63)))]]) ).
cnf(refute_0_1526,plain,
multiply(inverse(X_63),least_upper_bound(X_62,X_63)) = least_upper_bound(identity,multiply(inverse(X_63),X_62)),
inference(subst,[],[refute_0_127:[bind(X_56,$fot(X_62)),bind(X_57,$fot(X_63))]]) ).
cnf(refute_0_1527,plain,
( multiply(inverse(X_63),least_upper_bound(X_62,X_63)) != least_upper_bound(identity,multiply(inverse(X_63),X_62))
| inverse(inverse(X_63)) != multiply(least_upper_bound(X_62,X_63),inverse(multiply(inverse(X_63),least_upper_bound(X_62,X_63))))
| inverse(inverse(X_63)) = multiply(least_upper_bound(X_62,X_63),inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_63)),multiply(least_upper_bound(X_62,X_63),inverse(multiply(inverse(X_63),least_upper_bound(X_62,X_63))))) ),[1,1,0],$fot(least_upper_bound(identity,multiply(inverse(X_63),X_62)))]]) ).
cnf(refute_0_1528,plain,
( inverse(inverse(X_63)) != multiply(least_upper_bound(X_62,X_63),inverse(multiply(inverse(X_63),least_upper_bound(X_62,X_63))))
| inverse(inverse(X_63)) = multiply(least_upper_bound(X_62,X_63),inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_63),least_upper_bound(X_62,X_63)),least_upper_bound(identity,multiply(inverse(X_63),X_62))) )],[refute_0_1526,refute_0_1527]) ).
cnf(refute_0_1529,plain,
inverse(inverse(X_63)) = multiply(least_upper_bound(X_62,X_63),inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))),
inference(resolve,[$cnf( $equal(inverse(inverse(X_63)),multiply(least_upper_bound(X_62,X_63),inverse(multiply(inverse(X_63),least_upper_bound(X_62,X_63))))) )],[refute_0_1525,refute_0_1528]) ).
cnf(refute_0_1530,plain,
inverse(inverse(X_63)) = X_63,
inference(subst,[],[p19_2:[bind(X,$fot(X_63))]]) ).
cnf(refute_0_1531,plain,
( inverse(inverse(X_63)) != X_63
| inverse(inverse(X_63)) != multiply(least_upper_bound(X_62,X_63),inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62))))
| X_63 = multiply(least_upper_bound(X_62,X_63),inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_63)),multiply(least_upper_bound(X_62,X_63),inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62))))) ),[0],$fot(X_63)]]) ).
cnf(refute_0_1532,plain,
( inverse(inverse(X_63)) != multiply(least_upper_bound(X_62,X_63),inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62))))
| X_63 = multiply(least_upper_bound(X_62,X_63),inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_63)),X_63) )],[refute_0_1530,refute_0_1531]) ).
cnf(refute_0_1533,plain,
X_63 = multiply(least_upper_bound(X_62,X_63),inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))),
inference(resolve,[$cnf( $equal(inverse(inverse(X_63)),multiply(least_upper_bound(X_62,X_63),inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62))))) )],[refute_0_1529,refute_0_1532]) ).
cnf(refute_0_1534,plain,
greatest_lower_bound(X_181,X_182) = multiply(least_upper_bound(greatest_lower_bound(X_182,X_181),greatest_lower_bound(X_181,X_182)),inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_181,X_182)),greatest_lower_bound(X_182,X_181))))),
inference(subst,[],[refute_0_1533:[bind(X_62,$fot(greatest_lower_bound(X_182,X_181))),bind(X_63,$fot(greatest_lower_bound(X_181,X_182)))]]) ).
cnf(refute_0_1535,plain,
least_upper_bound(greatest_lower_bound(X_35,X_15),greatest_lower_bound(X_15,greatest_lower_bound(X_35,X_15))) = greatest_lower_bound(X_35,X_15),
inference(subst,[],[refute_0_270:[bind(X_14,$fot(greatest_lower_bound(X_35,X_15)))]]) ).
cnf(refute_0_1536,plain,
greatest_lower_bound(X_15,greatest_lower_bound(X_35,X_15)) = greatest_lower_bound(X_15,X_35),
inference(subst,[],[refute_0_229:[bind(Y,$fot(X_15)),bind(X_15,$fot(X_35))]]) ).
cnf(refute_0_1537,plain,
( greatest_lower_bound(X_15,greatest_lower_bound(X_35,X_15)) != greatest_lower_bound(X_15,X_35)
| least_upper_bound(greatest_lower_bound(X_35,X_15),greatest_lower_bound(X_15,greatest_lower_bound(X_35,X_15))) != greatest_lower_bound(X_35,X_15)
| least_upper_bound(greatest_lower_bound(X_35,X_15),greatest_lower_bound(X_15,X_35)) = greatest_lower_bound(X_35,X_15) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_35,X_15),greatest_lower_bound(X_15,greatest_lower_bound(X_35,X_15))),greatest_lower_bound(X_35,X_15)) ),[0,1],$fot(greatest_lower_bound(X_15,X_35))]]) ).
cnf(refute_0_1538,plain,
( least_upper_bound(greatest_lower_bound(X_35,X_15),greatest_lower_bound(X_15,greatest_lower_bound(X_35,X_15))) != greatest_lower_bound(X_35,X_15)
| least_upper_bound(greatest_lower_bound(X_35,X_15),greatest_lower_bound(X_15,X_35)) = greatest_lower_bound(X_35,X_15) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_15,greatest_lower_bound(X_35,X_15)),greatest_lower_bound(X_15,X_35)) )],[refute_0_1536,refute_0_1537]) ).
cnf(refute_0_1539,plain,
least_upper_bound(greatest_lower_bound(X_35,X_15),greatest_lower_bound(X_15,X_35)) = greatest_lower_bound(X_35,X_15),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_35,X_15),greatest_lower_bound(X_15,greatest_lower_bound(X_35,X_15))),greatest_lower_bound(X_35,X_15)) )],[refute_0_1535,refute_0_1538]) ).
cnf(refute_0_1540,plain,
least_upper_bound(greatest_lower_bound(X_182,X_181),greatest_lower_bound(X_181,X_182)) = greatest_lower_bound(X_182,X_181),
inference(subst,[],[refute_0_1539:[bind(X_15,$fot(X_181)),bind(X_35,$fot(X_182))]]) ).
cnf(refute_0_1541,plain,
( greatest_lower_bound(X_181,X_182) != multiply(least_upper_bound(greatest_lower_bound(X_182,X_181),greatest_lower_bound(X_181,X_182)),inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_181,X_182)),greatest_lower_bound(X_182,X_181)))))
| least_upper_bound(greatest_lower_bound(X_182,X_181),greatest_lower_bound(X_181,X_182)) != greatest_lower_bound(X_182,X_181)
| greatest_lower_bound(X_181,X_182) = multiply(greatest_lower_bound(X_182,X_181),inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_181,X_182)),greatest_lower_bound(X_182,X_181))))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_181,X_182),multiply(least_upper_bound(greatest_lower_bound(X_182,X_181),greatest_lower_bound(X_181,X_182)),inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_181,X_182)),greatest_lower_bound(X_182,X_181)))))) ),[1,0],$fot(greatest_lower_bound(X_182,X_181))]]) ).
cnf(refute_0_1542,plain,
( greatest_lower_bound(X_181,X_182) != multiply(least_upper_bound(greatest_lower_bound(X_182,X_181),greatest_lower_bound(X_181,X_182)),inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_181,X_182)),greatest_lower_bound(X_182,X_181)))))
| greatest_lower_bound(X_181,X_182) = multiply(greatest_lower_bound(X_182,X_181),inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_181,X_182)),greatest_lower_bound(X_182,X_181))))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_182,X_181),greatest_lower_bound(X_181,X_182)),greatest_lower_bound(X_182,X_181)) )],[refute_0_1540,refute_0_1541]) ).
cnf(refute_0_1543,plain,
greatest_lower_bound(X_181,X_182) = multiply(greatest_lower_bound(X_182,X_181),inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_181,X_182)),greatest_lower_bound(X_182,X_181))))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_181,X_182),multiply(least_upper_bound(greatest_lower_bound(X_182,X_181),greatest_lower_bound(X_181,X_182)),inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_181,X_182)),greatest_lower_bound(X_182,X_181)))))) )],[refute_0_1534,refute_0_1542]) ).
cnf(refute_0_1544,plain,
inverse(least_upper_bound(X_80,inverse(Y))) = multiply(Y,inverse(multiply(least_upper_bound(X_80,inverse(Y)),Y))),
inference(subst,[],[refute_0_117:[bind(X,$fot(least_upper_bound(X_80,inverse(Y))))]]) ).
cnf(refute_0_1545,plain,
multiply(least_upper_bound(X_77,inverse(X_76)),X_76) = least_upper_bound(multiply(X_77,X_76),multiply(inverse(X_76),X_76)),
inference(subst,[],[monotony_lub2:[bind(X,$fot(X_76)),bind(Y,$fot(X_77)),bind(Z,$fot(inverse(X_76)))]]) ).
cnf(refute_0_1546,plain,
multiply(inverse(X_76),X_76) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_76))]]) ).
cnf(refute_0_1547,plain,
( multiply(inverse(X_76),X_76) != identity
| multiply(least_upper_bound(X_77,inverse(X_76)),X_76) != least_upper_bound(multiply(X_77,X_76),multiply(inverse(X_76),X_76))
| multiply(least_upper_bound(X_77,inverse(X_76)),X_76) = least_upper_bound(multiply(X_77,X_76),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_77,inverse(X_76)),X_76),least_upper_bound(multiply(X_77,X_76),multiply(inverse(X_76),X_76))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_1548,plain,
( multiply(least_upper_bound(X_77,inverse(X_76)),X_76) != least_upper_bound(multiply(X_77,X_76),multiply(inverse(X_76),X_76))
| multiply(least_upper_bound(X_77,inverse(X_76)),X_76) = least_upper_bound(multiply(X_77,X_76),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_76),X_76),identity) )],[refute_0_1546,refute_0_1547]) ).
cnf(refute_0_1549,plain,
multiply(least_upper_bound(X_77,inverse(X_76)),X_76) = least_upper_bound(multiply(X_77,X_76),identity),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_77,inverse(X_76)),X_76),least_upper_bound(multiply(X_77,X_76),multiply(inverse(X_76),X_76))) )],[refute_0_1545,refute_0_1548]) ).
cnf(refute_0_1550,plain,
least_upper_bound(multiply(X_77,X_76),identity) = least_upper_bound(identity,multiply(X_77,X_76)),
inference(subst,[],[refute_0_30:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_77,X_76)))]]) ).
cnf(refute_0_1551,plain,
( multiply(least_upper_bound(X_77,inverse(X_76)),X_76) != least_upper_bound(multiply(X_77,X_76),identity)
| least_upper_bound(multiply(X_77,X_76),identity) != least_upper_bound(identity,multiply(X_77,X_76))
| multiply(least_upper_bound(X_77,inverse(X_76)),X_76) = least_upper_bound(identity,multiply(X_77,X_76)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_77,inverse(X_76)),X_76),least_upper_bound(identity,multiply(X_77,X_76))) ),[0],$fot(least_upper_bound(multiply(X_77,X_76),identity))]]) ).
cnf(refute_0_1552,plain,
( multiply(least_upper_bound(X_77,inverse(X_76)),X_76) != least_upper_bound(multiply(X_77,X_76),identity)
| multiply(least_upper_bound(X_77,inverse(X_76)),X_76) = least_upper_bound(identity,multiply(X_77,X_76)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_77,X_76),identity),least_upper_bound(identity,multiply(X_77,X_76))) )],[refute_0_1550,refute_0_1551]) ).
cnf(refute_0_1553,plain,
multiply(least_upper_bound(X_77,inverse(X_76)),X_76) = least_upper_bound(identity,multiply(X_77,X_76)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_77,inverse(X_76)),X_76),least_upper_bound(multiply(X_77,X_76),identity)) )],[refute_0_1549,refute_0_1552]) ).
cnf(refute_0_1554,plain,
multiply(least_upper_bound(X_80,inverse(Y)),Y) = least_upper_bound(identity,multiply(X_80,Y)),
inference(subst,[],[refute_0_1553:[bind(X_76,$fot(Y)),bind(X_77,$fot(X_80))]]) ).
cnf(refute_0_1555,plain,
( multiply(least_upper_bound(X_80,inverse(Y)),Y) != least_upper_bound(identity,multiply(X_80,Y))
| inverse(least_upper_bound(X_80,inverse(Y))) != multiply(Y,inverse(multiply(least_upper_bound(X_80,inverse(Y)),Y)))
| inverse(least_upper_bound(X_80,inverse(Y))) = multiply(Y,inverse(least_upper_bound(identity,multiply(X_80,Y)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_80,inverse(Y))),multiply(Y,inverse(multiply(least_upper_bound(X_80,inverse(Y)),Y)))) ),[1,1,0],$fot(least_upper_bound(identity,multiply(X_80,Y)))]]) ).
cnf(refute_0_1556,plain,
( inverse(least_upper_bound(X_80,inverse(Y))) != multiply(Y,inverse(multiply(least_upper_bound(X_80,inverse(Y)),Y)))
| inverse(least_upper_bound(X_80,inverse(Y))) = multiply(Y,inverse(least_upper_bound(identity,multiply(X_80,Y)))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_80,inverse(Y)),Y),least_upper_bound(identity,multiply(X_80,Y))) )],[refute_0_1554,refute_0_1555]) ).
cnf(refute_0_1557,plain,
inverse(least_upper_bound(X_80,inverse(Y))) = multiply(Y,inverse(least_upper_bound(identity,multiply(X_80,Y)))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_80,inverse(Y))),multiply(Y,inverse(multiply(least_upper_bound(X_80,inverse(Y)),Y)))) )],[refute_0_1544,refute_0_1556]) ).
cnf(refute_0_1558,plain,
( inverse(least_upper_bound(X_80,inverse(Y))) != multiply(Y,inverse(least_upper_bound(identity,multiply(X_80,Y))))
| multiply(Y,inverse(least_upper_bound(identity,multiply(X_80,Y)))) = inverse(least_upper_bound(X_80,inverse(Y))) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(inverse(least_upper_bound(X_80,inverse(Y))))),bind(Y0,$fot(multiply(Y,inverse(least_upper_bound(identity,multiply(X_80,Y))))))]]) ).
cnf(refute_0_1559,plain,
multiply(Y,inverse(least_upper_bound(identity,multiply(X_80,Y)))) = inverse(least_upper_bound(X_80,inverse(Y))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_80,inverse(Y))),multiply(Y,inverse(least_upper_bound(identity,multiply(X_80,Y))))) )],[refute_0_1557,refute_0_1558]) ).
cnf(refute_0_1560,plain,
multiply(greatest_lower_bound(X_182,X_181),inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_181,X_182)),greatest_lower_bound(X_182,X_181))))) = inverse(least_upper_bound(inverse(greatest_lower_bound(X_181,X_182)),inverse(greatest_lower_bound(X_182,X_181)))),
inference(subst,[],[refute_0_1559:[bind(Y,$fot(greatest_lower_bound(X_182,X_181))),bind(X_80,$fot(inverse(greatest_lower_bound(X_181,X_182))))]]) ).
cnf(refute_0_1561,plain,
( multiply(greatest_lower_bound(X_182,X_181),inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_181,X_182)),greatest_lower_bound(X_182,X_181))))) != inverse(least_upper_bound(inverse(greatest_lower_bound(X_181,X_182)),inverse(greatest_lower_bound(X_182,X_181))))
| greatest_lower_bound(X_181,X_182) != multiply(greatest_lower_bound(X_182,X_181),inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_181,X_182)),greatest_lower_bound(X_182,X_181)))))
| greatest_lower_bound(X_181,X_182) = inverse(least_upper_bound(inverse(greatest_lower_bound(X_181,X_182)),inverse(greatest_lower_bound(X_182,X_181)))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_181,X_182),multiply(greatest_lower_bound(X_182,X_181),inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_181,X_182)),greatest_lower_bound(X_182,X_181)))))) ),[1],$fot(inverse(least_upper_bound(inverse(greatest_lower_bound(X_181,X_182)),inverse(greatest_lower_bound(X_182,X_181)))))]]) ).
cnf(refute_0_1562,plain,
( greatest_lower_bound(X_181,X_182) != multiply(greatest_lower_bound(X_182,X_181),inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_181,X_182)),greatest_lower_bound(X_182,X_181)))))
| greatest_lower_bound(X_181,X_182) = inverse(least_upper_bound(inverse(greatest_lower_bound(X_181,X_182)),inverse(greatest_lower_bound(X_182,X_181)))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_182,X_181),inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_181,X_182)),greatest_lower_bound(X_182,X_181))))),inverse(least_upper_bound(inverse(greatest_lower_bound(X_181,X_182)),inverse(greatest_lower_bound(X_182,X_181))))) )],[refute_0_1560,refute_0_1561]) ).
cnf(refute_0_1563,plain,
greatest_lower_bound(X_181,X_182) = inverse(least_upper_bound(inverse(greatest_lower_bound(X_181,X_182)),inverse(greatest_lower_bound(X_182,X_181)))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_181,X_182),multiply(greatest_lower_bound(X_182,X_181),inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_181,X_182)),greatest_lower_bound(X_182,X_181)))))) )],[refute_0_1543,refute_0_1562]) ).
cnf(refute_0_1564,plain,
greatest_lower_bound(X_183,X_184) = inverse(least_upper_bound(inverse(greatest_lower_bound(X_183,X_184)),inverse(greatest_lower_bound(X_184,X_183)))),
inference(subst,[],[refute_0_1563:[bind(X_181,$fot(X_183)),bind(X_182,$fot(X_184))]]) ).
cnf(refute_0_1565,plain,
( greatest_lower_bound(X_183,X_184) != inverse(least_upper_bound(inverse(greatest_lower_bound(X_183,X_184)),inverse(greatest_lower_bound(X_184,X_183))))
| inverse(least_upper_bound(inverse(greatest_lower_bound(X_183,X_184)),inverse(greatest_lower_bound(X_184,X_183)))) = greatest_lower_bound(X_183,X_184) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(greatest_lower_bound(X_183,X_184))),bind(Y0,$fot(inverse(least_upper_bound(inverse(greatest_lower_bound(X_183,X_184)),inverse(greatest_lower_bound(X_184,X_183))))))]]) ).
cnf(refute_0_1566,plain,
inverse(least_upper_bound(inverse(greatest_lower_bound(X_183,X_184)),inverse(greatest_lower_bound(X_184,X_183)))) = greatest_lower_bound(X_183,X_184),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_183,X_184),inverse(least_upper_bound(inverse(greatest_lower_bound(X_183,X_184)),inverse(greatest_lower_bound(X_184,X_183))))) )],[refute_0_1564,refute_0_1565]) ).
cnf(refute_0_1567,plain,
( multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_183,X_184)),inverse(greatest_lower_bound(X_184,X_183)))),least_upper_bound(inverse(greatest_lower_bound(X_183,X_184)),inverse(greatest_lower_bound(X_184,X_183)))) != identity
| inverse(least_upper_bound(inverse(greatest_lower_bound(X_183,X_184)),inverse(greatest_lower_bound(X_184,X_183)))) != greatest_lower_bound(X_183,X_184)
| multiply(greatest_lower_bound(X_183,X_184),least_upper_bound(inverse(greatest_lower_bound(X_183,X_184)),inverse(greatest_lower_bound(X_184,X_183)))) = identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_183,X_184)),inverse(greatest_lower_bound(X_184,X_183)))),least_upper_bound(inverse(greatest_lower_bound(X_183,X_184)),inverse(greatest_lower_bound(X_184,X_183)))),identity) ),[0,0],$fot(greatest_lower_bound(X_183,X_184))]]) ).
cnf(refute_0_1568,plain,
( multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_183,X_184)),inverse(greatest_lower_bound(X_184,X_183)))),least_upper_bound(inverse(greatest_lower_bound(X_183,X_184)),inverse(greatest_lower_bound(X_184,X_183)))) != identity
| multiply(greatest_lower_bound(X_183,X_184),least_upper_bound(inverse(greatest_lower_bound(X_183,X_184)),inverse(greatest_lower_bound(X_184,X_183)))) = identity ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(greatest_lower_bound(X_183,X_184)),inverse(greatest_lower_bound(X_184,X_183)))),greatest_lower_bound(X_183,X_184)) )],[refute_0_1566,refute_0_1567]) ).
cnf(refute_0_1569,plain,
multiply(greatest_lower_bound(X_183,X_184),least_upper_bound(inverse(greatest_lower_bound(X_183,X_184)),inverse(greatest_lower_bound(X_184,X_183)))) = identity,
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(greatest_lower_bound(X_183,X_184)),inverse(greatest_lower_bound(X_184,X_183)))),least_upper_bound(inverse(greatest_lower_bound(X_183,X_184)),inverse(greatest_lower_bound(X_184,X_183)))),identity) )],[refute_0_1524,refute_0_1568]) ).
cnf(refute_0_1570,plain,
multiply(least_upper_bound(greatest_lower_bound(X_182,X_181),greatest_lower_bound(X_181,X_182)),inverse(greatest_lower_bound(X_181,X_182))) = least_upper_bound(identity,multiply(greatest_lower_bound(X_182,X_181),inverse(greatest_lower_bound(X_181,X_182)))),
inference(subst,[],[refute_0_195:[bind(X_77,$fot(greatest_lower_bound(X_182,X_181))),bind(X_78,$fot(greatest_lower_bound(X_181,X_182)))]]) ).
cnf(refute_0_1571,plain,
( multiply(least_upper_bound(greatest_lower_bound(X_182,X_181),greatest_lower_bound(X_181,X_182)),inverse(greatest_lower_bound(X_181,X_182))) != least_upper_bound(identity,multiply(greatest_lower_bound(X_182,X_181),inverse(greatest_lower_bound(X_181,X_182))))
| least_upper_bound(greatest_lower_bound(X_182,X_181),greatest_lower_bound(X_181,X_182)) != greatest_lower_bound(X_182,X_181)
| multiply(greatest_lower_bound(X_182,X_181),inverse(greatest_lower_bound(X_181,X_182))) = least_upper_bound(identity,multiply(greatest_lower_bound(X_182,X_181),inverse(greatest_lower_bound(X_181,X_182)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(X_182,X_181),greatest_lower_bound(X_181,X_182)),inverse(greatest_lower_bound(X_181,X_182))),least_upper_bound(identity,multiply(greatest_lower_bound(X_182,X_181),inverse(greatest_lower_bound(X_181,X_182))))) ),[0,0],$fot(greatest_lower_bound(X_182,X_181))]]) ).
cnf(refute_0_1572,plain,
( multiply(least_upper_bound(greatest_lower_bound(X_182,X_181),greatest_lower_bound(X_181,X_182)),inverse(greatest_lower_bound(X_181,X_182))) != least_upper_bound(identity,multiply(greatest_lower_bound(X_182,X_181),inverse(greatest_lower_bound(X_181,X_182))))
| multiply(greatest_lower_bound(X_182,X_181),inverse(greatest_lower_bound(X_181,X_182))) = least_upper_bound(identity,multiply(greatest_lower_bound(X_182,X_181),inverse(greatest_lower_bound(X_181,X_182)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_182,X_181),greatest_lower_bound(X_181,X_182)),greatest_lower_bound(X_182,X_181)) )],[refute_0_1540,refute_0_1571]) ).
cnf(refute_0_1573,plain,
multiply(greatest_lower_bound(X_182,X_181),inverse(greatest_lower_bound(X_181,X_182))) = least_upper_bound(identity,multiply(greatest_lower_bound(X_182,X_181),inverse(greatest_lower_bound(X_181,X_182)))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(X_182,X_181),greatest_lower_bound(X_181,X_182)),inverse(greatest_lower_bound(X_181,X_182))),least_upper_bound(identity,multiply(greatest_lower_bound(X_182,X_181),inverse(greatest_lower_bound(X_181,X_182))))) )],[refute_0_1570,refute_0_1572]) ).
cnf(refute_0_1574,plain,
( multiply(greatest_lower_bound(X_182,X_181),inverse(greatest_lower_bound(X_181,X_182))) != least_upper_bound(identity,multiply(greatest_lower_bound(X_182,X_181),inverse(greatest_lower_bound(X_181,X_182))))
| least_upper_bound(identity,multiply(greatest_lower_bound(X_182,X_181),inverse(greatest_lower_bound(X_181,X_182)))) = multiply(greatest_lower_bound(X_182,X_181),inverse(greatest_lower_bound(X_181,X_182))) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(multiply(greatest_lower_bound(X_182,X_181),inverse(greatest_lower_bound(X_181,X_182))))),bind(Y0,$fot(least_upper_bound(identity,multiply(greatest_lower_bound(X_182,X_181),inverse(greatest_lower_bound(X_181,X_182))))))]]) ).
cnf(refute_0_1575,plain,
least_upper_bound(identity,multiply(greatest_lower_bound(X_182,X_181),inverse(greatest_lower_bound(X_181,X_182)))) = multiply(greatest_lower_bound(X_182,X_181),inverse(greatest_lower_bound(X_181,X_182))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_182,X_181),inverse(greatest_lower_bound(X_181,X_182))),least_upper_bound(identity,multiply(greatest_lower_bound(X_182,X_181),inverse(greatest_lower_bound(X_181,X_182))))) )],[refute_0_1573,refute_0_1574]) ).
cnf(refute_0_1576,plain,
least_upper_bound(identity,multiply(greatest_lower_bound(X_183,X_184),inverse(greatest_lower_bound(X_184,X_183)))) = multiply(greatest_lower_bound(X_183,X_184),inverse(greatest_lower_bound(X_184,X_183))),
inference(subst,[],[refute_0_1575:[bind(X_181,$fot(X_184)),bind(X_182,$fot(X_183))]]) ).
cnf(refute_0_1577,plain,
multiply(X_55,least_upper_bound(inverse(X_55),X_57)) = least_upper_bound(multiply(X_55,inverse(X_55)),multiply(X_55,X_57)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(X_55)),bind(Y,$fot(inverse(X_55))),bind(Z,$fot(X_57))]]) ).
cnf(refute_0_1578,plain,
( multiply(X_55,inverse(X_55)) != identity
| multiply(X_55,least_upper_bound(inverse(X_55),X_57)) != least_upper_bound(multiply(X_55,inverse(X_55)),multiply(X_55,X_57))
| multiply(X_55,least_upper_bound(inverse(X_55),X_57)) = least_upper_bound(identity,multiply(X_55,X_57)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_55,least_upper_bound(inverse(X_55),X_57)),least_upper_bound(multiply(X_55,inverse(X_55)),multiply(X_55,X_57))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_1579,plain,
( multiply(X_55,least_upper_bound(inverse(X_55),X_57)) != least_upper_bound(multiply(X_55,inverse(X_55)),multiply(X_55,X_57))
| multiply(X_55,least_upper_bound(inverse(X_55),X_57)) = least_upper_bound(identity,multiply(X_55,X_57)) ),
inference(resolve,[$cnf( $equal(multiply(X_55,inverse(X_55)),identity) )],[refute_0_545,refute_0_1578]) ).
cnf(refute_0_1580,plain,
multiply(X_55,least_upper_bound(inverse(X_55),X_57)) = least_upper_bound(identity,multiply(X_55,X_57)),
inference(resolve,[$cnf( $equal(multiply(X_55,least_upper_bound(inverse(X_55),X_57)),least_upper_bound(multiply(X_55,inverse(X_55)),multiply(X_55,X_57))) )],[refute_0_1577,refute_0_1579]) ).
cnf(refute_0_1581,plain,
multiply(greatest_lower_bound(X_183,X_184),least_upper_bound(inverse(greatest_lower_bound(X_183,X_184)),inverse(greatest_lower_bound(X_184,X_183)))) = least_upper_bound(identity,multiply(greatest_lower_bound(X_183,X_184),inverse(greatest_lower_bound(X_184,X_183)))),
inference(subst,[],[refute_0_1580:[bind(X_55,$fot(greatest_lower_bound(X_183,X_184))),bind(X_57,$fot(inverse(greatest_lower_bound(X_184,X_183))))]]) ).
cnf(refute_0_1582,plain,
( multiply(greatest_lower_bound(X_183,X_184),least_upper_bound(inverse(greatest_lower_bound(X_183,X_184)),inverse(greatest_lower_bound(X_184,X_183)))) != least_upper_bound(identity,multiply(greatest_lower_bound(X_183,X_184),inverse(greatest_lower_bound(X_184,X_183))))
| least_upper_bound(identity,multiply(greatest_lower_bound(X_183,X_184),inverse(greatest_lower_bound(X_184,X_183)))) != multiply(greatest_lower_bound(X_183,X_184),inverse(greatest_lower_bound(X_184,X_183)))
| multiply(greatest_lower_bound(X_183,X_184),least_upper_bound(inverse(greatest_lower_bound(X_183,X_184)),inverse(greatest_lower_bound(X_184,X_183)))) = multiply(greatest_lower_bound(X_183,X_184),inverse(greatest_lower_bound(X_184,X_183))) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(multiply(greatest_lower_bound(X_183,X_184),least_upper_bound(inverse(greatest_lower_bound(X_183,X_184)),inverse(greatest_lower_bound(X_184,X_183)))))),bind(Y0,$fot(least_upper_bound(identity,multiply(greatest_lower_bound(X_183,X_184),inverse(greatest_lower_bound(X_184,X_183)))))),bind(Z0,$fot(multiply(greatest_lower_bound(X_183,X_184),inverse(greatest_lower_bound(X_184,X_183)))))]]) ).
cnf(refute_0_1583,plain,
( least_upper_bound(identity,multiply(greatest_lower_bound(X_183,X_184),inverse(greatest_lower_bound(X_184,X_183)))) != multiply(greatest_lower_bound(X_183,X_184),inverse(greatest_lower_bound(X_184,X_183)))
| multiply(greatest_lower_bound(X_183,X_184),least_upper_bound(inverse(greatest_lower_bound(X_183,X_184)),inverse(greatest_lower_bound(X_184,X_183)))) = multiply(greatest_lower_bound(X_183,X_184),inverse(greatest_lower_bound(X_184,X_183))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_183,X_184),least_upper_bound(inverse(greatest_lower_bound(X_183,X_184)),inverse(greatest_lower_bound(X_184,X_183)))),least_upper_bound(identity,multiply(greatest_lower_bound(X_183,X_184),inverse(greatest_lower_bound(X_184,X_183))))) )],[refute_0_1581,refute_0_1582]) ).
cnf(refute_0_1584,plain,
multiply(greatest_lower_bound(X_183,X_184),least_upper_bound(inverse(greatest_lower_bound(X_183,X_184)),inverse(greatest_lower_bound(X_184,X_183)))) = multiply(greatest_lower_bound(X_183,X_184),inverse(greatest_lower_bound(X_184,X_183))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(greatest_lower_bound(X_183,X_184),inverse(greatest_lower_bound(X_184,X_183)))),multiply(greatest_lower_bound(X_183,X_184),inverse(greatest_lower_bound(X_184,X_183)))) )],[refute_0_1576,refute_0_1583]) ).
cnf(refute_0_1585,plain,
( multiply(greatest_lower_bound(X_183,X_184),least_upper_bound(inverse(greatest_lower_bound(X_183,X_184)),inverse(greatest_lower_bound(X_184,X_183)))) != multiply(greatest_lower_bound(X_183,X_184),inverse(greatest_lower_bound(X_184,X_183)))
| multiply(greatest_lower_bound(X_183,X_184),least_upper_bound(inverse(greatest_lower_bound(X_183,X_184)),inverse(greatest_lower_bound(X_184,X_183)))) != identity
| multiply(greatest_lower_bound(X_183,X_184),inverse(greatest_lower_bound(X_184,X_183))) = identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_183,X_184),least_upper_bound(inverse(greatest_lower_bound(X_183,X_184)),inverse(greatest_lower_bound(X_184,X_183)))),identity) ),[0],$fot(multiply(greatest_lower_bound(X_183,X_184),inverse(greatest_lower_bound(X_184,X_183))))]]) ).
cnf(refute_0_1586,plain,
( multiply(greatest_lower_bound(X_183,X_184),least_upper_bound(inverse(greatest_lower_bound(X_183,X_184)),inverse(greatest_lower_bound(X_184,X_183)))) != identity
| multiply(greatest_lower_bound(X_183,X_184),inverse(greatest_lower_bound(X_184,X_183))) = identity ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_183,X_184),least_upper_bound(inverse(greatest_lower_bound(X_183,X_184)),inverse(greatest_lower_bound(X_184,X_183)))),multiply(greatest_lower_bound(X_183,X_184),inverse(greatest_lower_bound(X_184,X_183)))) )],[refute_0_1584,refute_0_1585]) ).
cnf(refute_0_1587,plain,
multiply(greatest_lower_bound(X_183,X_184),inverse(greatest_lower_bound(X_184,X_183))) = identity,
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_183,X_184),least_upper_bound(inverse(greatest_lower_bound(X_183,X_184)),inverse(greatest_lower_bound(X_184,X_183)))),identity) )],[refute_0_1569,refute_0_1586]) ).
cnf(refute_0_1588,plain,
( multiply(greatest_lower_bound(X_183,X_184),inverse(greatest_lower_bound(X_184,X_183))) != identity
| inverse(multiply(X_227,multiply(greatest_lower_bound(X_183,X_184),inverse(greatest_lower_bound(X_184,X_183))))) != multiply(greatest_lower_bound(X_184,X_183),inverse(multiply(X_227,greatest_lower_bound(X_183,X_184))))
| inverse(multiply(X_227,identity)) = multiply(greatest_lower_bound(X_184,X_183),inverse(multiply(X_227,greatest_lower_bound(X_183,X_184)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_227,multiply(greatest_lower_bound(X_183,X_184),inverse(greatest_lower_bound(X_184,X_183))))),multiply(greatest_lower_bound(X_184,X_183),inverse(multiply(X_227,greatest_lower_bound(X_183,X_184))))) ),[0,0,1],$fot(identity)]]) ).
cnf(refute_0_1589,plain,
( inverse(multiply(X_227,multiply(greatest_lower_bound(X_183,X_184),inverse(greatest_lower_bound(X_184,X_183))))) != multiply(greatest_lower_bound(X_184,X_183),inverse(multiply(X_227,greatest_lower_bound(X_183,X_184))))
| inverse(multiply(X_227,identity)) = multiply(greatest_lower_bound(X_184,X_183),inverse(multiply(X_227,greatest_lower_bound(X_183,X_184)))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_183,X_184),inverse(greatest_lower_bound(X_184,X_183))),identity) )],[refute_0_1587,refute_0_1588]) ).
cnf(refute_0_1590,plain,
inverse(multiply(X_227,identity)) = multiply(greatest_lower_bound(X_184,X_183),inverse(multiply(X_227,greatest_lower_bound(X_183,X_184)))),
inference(resolve,[$cnf( $equal(inverse(multiply(X_227,multiply(greatest_lower_bound(X_183,X_184),inverse(greatest_lower_bound(X_184,X_183))))),multiply(greatest_lower_bound(X_184,X_183),inverse(multiply(X_227,greatest_lower_bound(X_183,X_184))))) )],[refute_0_1523,refute_0_1589]) ).
cnf(refute_0_1591,plain,
multiply(X_227,identity) = X_227,
inference(subst,[],[refute_0_564:[bind(X,$fot(X_227))]]) ).
cnf(refute_0_1592,plain,
inverse(multiply(X_227,identity)) = inverse(multiply(X_227,identity)),
introduced(tautology,[refl,[$fot(inverse(multiply(X_227,identity)))]]) ).
cnf(refute_0_1593,plain,
( multiply(X_227,identity) != X_227
| inverse(multiply(X_227,identity)) != inverse(multiply(X_227,identity))
| inverse(multiply(X_227,identity)) = inverse(X_227) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_227,identity)),inverse(multiply(X_227,identity))) ),[1,0],$fot(X_227)]]) ).
cnf(refute_0_1594,plain,
( multiply(X_227,identity) != X_227
| inverse(multiply(X_227,identity)) = inverse(X_227) ),
inference(resolve,[$cnf( $equal(inverse(multiply(X_227,identity)),inverse(multiply(X_227,identity))) )],[refute_0_1592,refute_0_1593]) ).
cnf(refute_0_1595,plain,
inverse(multiply(X_227,identity)) = inverse(X_227),
inference(resolve,[$cnf( $equal(multiply(X_227,identity),X_227) )],[refute_0_1591,refute_0_1594]) ).
cnf(refute_0_1596,plain,
( inverse(multiply(X_227,identity)) != multiply(greatest_lower_bound(X_184,X_183),inverse(multiply(X_227,greatest_lower_bound(X_183,X_184))))
| inverse(multiply(X_227,identity)) != inverse(X_227)
| inverse(X_227) = multiply(greatest_lower_bound(X_184,X_183),inverse(multiply(X_227,greatest_lower_bound(X_183,X_184)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_227,identity)),multiply(greatest_lower_bound(X_184,X_183),inverse(multiply(X_227,greatest_lower_bound(X_183,X_184))))) ),[0],$fot(inverse(X_227))]]) ).
cnf(refute_0_1597,plain,
( inverse(multiply(X_227,identity)) != multiply(greatest_lower_bound(X_184,X_183),inverse(multiply(X_227,greatest_lower_bound(X_183,X_184))))
| inverse(X_227) = multiply(greatest_lower_bound(X_184,X_183),inverse(multiply(X_227,greatest_lower_bound(X_183,X_184)))) ),
inference(resolve,[$cnf( $equal(inverse(multiply(X_227,identity)),inverse(X_227)) )],[refute_0_1595,refute_0_1596]) ).
cnf(refute_0_1598,plain,
inverse(X_227) = multiply(greatest_lower_bound(X_184,X_183),inverse(multiply(X_227,greatest_lower_bound(X_183,X_184)))),
inference(resolve,[$cnf( $equal(inverse(multiply(X_227,identity)),multiply(greatest_lower_bound(X_184,X_183),inverse(multiply(X_227,greatest_lower_bound(X_183,X_184))))) )],[refute_0_1590,refute_0_1597]) ).
cnf(refute_0_1599,plain,
inverse(X_449) = multiply(greatest_lower_bound(X_448,X_447),inverse(multiply(X_449,greatest_lower_bound(X_447,X_448)))),
inference(subst,[],[refute_0_1598:[bind(X_183,$fot(X_447)),bind(X_184,$fot(X_448)),bind(X_227,$fot(X_449))]]) ).
cnf(refute_0_1600,plain,
( inverse(X_449) != multiply(greatest_lower_bound(X_448,X_447),inverse(multiply(X_449,greatest_lower_bound(X_447,X_448))))
| multiply(greatest_lower_bound(X_448,X_447),inverse(multiply(X_449,greatest_lower_bound(X_447,X_448)))) = inverse(X_449) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(inverse(X_449))),bind(Y0,$fot(multiply(greatest_lower_bound(X_448,X_447),inverse(multiply(X_449,greatest_lower_bound(X_447,X_448))))))]]) ).
cnf(refute_0_1601,plain,
multiply(greatest_lower_bound(X_448,X_447),inverse(multiply(X_449,greatest_lower_bound(X_447,X_448)))) = inverse(X_449),
inference(resolve,[$cnf( $equal(inverse(X_449),multiply(greatest_lower_bound(X_448,X_447),inverse(multiply(X_449,greatest_lower_bound(X_447,X_448))))) )],[refute_0_1599,refute_0_1600]) ).
cnf(refute_0_1602,plain,
( multiply(greatest_lower_bound(X_448,X_447),inverse(multiply(X_449,greatest_lower_bound(X_447,X_448)))) != inverse(X_449)
| inverse(inverse(multiply(X_449,greatest_lower_bound(X_447,X_448)))) != multiply(inverse(multiply(greatest_lower_bound(X_448,X_447),inverse(multiply(X_449,greatest_lower_bound(X_447,X_448))))),greatest_lower_bound(X_448,X_447))
| inverse(inverse(multiply(X_449,greatest_lower_bound(X_447,X_448)))) = multiply(inverse(inverse(X_449)),greatest_lower_bound(X_448,X_447)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(multiply(X_449,greatest_lower_bound(X_447,X_448)))),multiply(inverse(multiply(greatest_lower_bound(X_448,X_447),inverse(multiply(X_449,greatest_lower_bound(X_447,X_448))))),greatest_lower_bound(X_448,X_447))) ),[1,0,0],$fot(inverse(X_449))]]) ).
cnf(refute_0_1603,plain,
( inverse(inverse(multiply(X_449,greatest_lower_bound(X_447,X_448)))) != multiply(inverse(multiply(greatest_lower_bound(X_448,X_447),inverse(multiply(X_449,greatest_lower_bound(X_447,X_448))))),greatest_lower_bound(X_448,X_447))
| inverse(inverse(multiply(X_449,greatest_lower_bound(X_447,X_448)))) = multiply(inverse(inverse(X_449)),greatest_lower_bound(X_448,X_447)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_448,X_447),inverse(multiply(X_449,greatest_lower_bound(X_447,X_448)))),inverse(X_449)) )],[refute_0_1601,refute_0_1602]) ).
cnf(refute_0_1604,plain,
inverse(inverse(multiply(X_449,greatest_lower_bound(X_447,X_448)))) = multiply(inverse(inverse(X_449)),greatest_lower_bound(X_448,X_447)),
inference(resolve,[$cnf( $equal(inverse(inverse(multiply(X_449,greatest_lower_bound(X_447,X_448)))),multiply(inverse(multiply(greatest_lower_bound(X_448,X_447),inverse(multiply(X_449,greatest_lower_bound(X_447,X_448))))),greatest_lower_bound(X_448,X_447))) )],[refute_0_1522,refute_0_1603]) ).
cnf(refute_0_1605,plain,
inverse(inverse(multiply(X_449,greatest_lower_bound(X_447,X_448)))) = multiply(X_449,greatest_lower_bound(X_447,X_448)),
inference(subst,[],[p19_2:[bind(X,$fot(multiply(X_449,greatest_lower_bound(X_447,X_448))))]]) ).
cnf(refute_0_1606,plain,
( inverse(inverse(multiply(X_449,greatest_lower_bound(X_447,X_448)))) != multiply(X_449,greatest_lower_bound(X_447,X_448))
| inverse(inverse(multiply(X_449,greatest_lower_bound(X_447,X_448)))) != multiply(inverse(inverse(X_449)),greatest_lower_bound(X_448,X_447))
| multiply(X_449,greatest_lower_bound(X_447,X_448)) = multiply(inverse(inverse(X_449)),greatest_lower_bound(X_448,X_447)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(multiply(X_449,greatest_lower_bound(X_447,X_448)))),multiply(inverse(inverse(X_449)),greatest_lower_bound(X_448,X_447))) ),[0],$fot(multiply(X_449,greatest_lower_bound(X_447,X_448)))]]) ).
cnf(refute_0_1607,plain,
( inverse(inverse(multiply(X_449,greatest_lower_bound(X_447,X_448)))) != multiply(inverse(inverse(X_449)),greatest_lower_bound(X_448,X_447))
| multiply(X_449,greatest_lower_bound(X_447,X_448)) = multiply(inverse(inverse(X_449)),greatest_lower_bound(X_448,X_447)) ),
inference(resolve,[$cnf( $equal(inverse(inverse(multiply(X_449,greatest_lower_bound(X_447,X_448)))),multiply(X_449,greatest_lower_bound(X_447,X_448))) )],[refute_0_1605,refute_0_1606]) ).
cnf(refute_0_1608,plain,
inverse(inverse(X_449)) = X_449,
inference(subst,[],[p19_2:[bind(X,$fot(X_449))]]) ).
cnf(refute_0_1609,plain,
multiply(inverse(inverse(X_449)),greatest_lower_bound(X_448,X_447)) = multiply(inverse(inverse(X_449)),greatest_lower_bound(X_448,X_447)),
introduced(tautology,[refl,[$fot(multiply(inverse(inverse(X_449)),greatest_lower_bound(X_448,X_447)))]]) ).
cnf(refute_0_1610,plain,
( multiply(inverse(inverse(X_449)),greatest_lower_bound(X_448,X_447)) != multiply(inverse(inverse(X_449)),greatest_lower_bound(X_448,X_447))
| inverse(inverse(X_449)) != X_449
| multiply(inverse(inverse(X_449)),greatest_lower_bound(X_448,X_447)) = multiply(X_449,greatest_lower_bound(X_448,X_447)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X_449)),greatest_lower_bound(X_448,X_447)),multiply(inverse(inverse(X_449)),greatest_lower_bound(X_448,X_447))) ),[1,0],$fot(X_449)]]) ).
cnf(refute_0_1611,plain,
( inverse(inverse(X_449)) != X_449
| multiply(inverse(inverse(X_449)),greatest_lower_bound(X_448,X_447)) = multiply(X_449,greatest_lower_bound(X_448,X_447)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_449)),greatest_lower_bound(X_448,X_447)),multiply(inverse(inverse(X_449)),greatest_lower_bound(X_448,X_447))) )],[refute_0_1609,refute_0_1610]) ).
cnf(refute_0_1612,plain,
multiply(inverse(inverse(X_449)),greatest_lower_bound(X_448,X_447)) = multiply(X_449,greatest_lower_bound(X_448,X_447)),
inference(resolve,[$cnf( $equal(inverse(inverse(X_449)),X_449) )],[refute_0_1608,refute_0_1611]) ).
cnf(refute_0_1613,plain,
( multiply(X_449,greatest_lower_bound(X_447,X_448)) != multiply(inverse(inverse(X_449)),greatest_lower_bound(X_448,X_447))
| multiply(inverse(inverse(X_449)),greatest_lower_bound(X_448,X_447)) != multiply(X_449,greatest_lower_bound(X_448,X_447))
| multiply(X_449,greatest_lower_bound(X_447,X_448)) = multiply(X_449,greatest_lower_bound(X_448,X_447)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_449,greatest_lower_bound(X_447,X_448)),multiply(X_449,greatest_lower_bound(X_448,X_447))) ),[0],$fot(multiply(inverse(inverse(X_449)),greatest_lower_bound(X_448,X_447)))]]) ).
cnf(refute_0_1614,plain,
( multiply(X_449,greatest_lower_bound(X_447,X_448)) != multiply(inverse(inverse(X_449)),greatest_lower_bound(X_448,X_447))
| multiply(X_449,greatest_lower_bound(X_447,X_448)) = multiply(X_449,greatest_lower_bound(X_448,X_447)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_449)),greatest_lower_bound(X_448,X_447)),multiply(X_449,greatest_lower_bound(X_448,X_447))) )],[refute_0_1612,refute_0_1613]) ).
cnf(refute_0_1615,plain,
( inverse(inverse(multiply(X_449,greatest_lower_bound(X_447,X_448)))) != multiply(inverse(inverse(X_449)),greatest_lower_bound(X_448,X_447))
| multiply(X_449,greatest_lower_bound(X_447,X_448)) = multiply(X_449,greatest_lower_bound(X_448,X_447)) ),
inference(resolve,[$cnf( $equal(multiply(X_449,greatest_lower_bound(X_447,X_448)),multiply(inverse(inverse(X_449)),greatest_lower_bound(X_448,X_447))) )],[refute_0_1607,refute_0_1614]) ).
cnf(refute_0_1616,plain,
multiply(X_449,greatest_lower_bound(X_447,X_448)) = multiply(X_449,greatest_lower_bound(X_448,X_447)),
inference(resolve,[$cnf( $equal(inverse(inverse(multiply(X_449,greatest_lower_bound(X_447,X_448)))),multiply(inverse(inverse(X_449)),greatest_lower_bound(X_448,X_447))) )],[refute_0_1604,refute_0_1615]) ).
cnf(refute_0_1617,plain,
( multiply(X_449,greatest_lower_bound(X_447,X_448)) != multiply(X_449,greatest_lower_bound(X_448,X_447))
| multiply(X_449,greatest_lower_bound(X_448,X_447)) = multiply(X_449,greatest_lower_bound(X_447,X_448)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(multiply(X_449,greatest_lower_bound(X_447,X_448)))),bind(Y0,$fot(multiply(X_449,greatest_lower_bound(X_448,X_447))))]]) ).
cnf(refute_0_1618,plain,
multiply(X_449,greatest_lower_bound(X_448,X_447)) = multiply(X_449,greatest_lower_bound(X_447,X_448)),
inference(resolve,[$cnf( $equal(multiply(X_449,greatest_lower_bound(X_447,X_448)),multiply(X_449,greatest_lower_bound(X_448,X_447))) )],[refute_0_1616,refute_0_1617]) ).
cnf(refute_0_1619,plain,
multiply(identity,greatest_lower_bound(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity)) = multiply(identity,greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))),
inference(subst,[],[refute_0_1618:[bind(X_447,$fot(identity)),bind(X_448,$fot(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))),bind(X_449,$fot(identity))]]) ).
cnf(refute_0_1620,plain,
( multiply(identity,greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))) != greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))
| multiply(identity,greatest_lower_bound(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity)) != multiply(identity,greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))))
| multiply(identity,greatest_lower_bound(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity)) = greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(multiply(identity,greatest_lower_bound(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity)))),bind(Y0,$fot(multiply(identity,greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))))),bind(Z0,$fot(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))))]]) ).
cnf(refute_0_1621,plain,
( multiply(identity,greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))) != greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))
| multiply(identity,greatest_lower_bound(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity)) = greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))) ),
inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity)),multiply(identity,greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))))) )],[refute_0_1619,refute_0_1620]) ).
cnf(refute_0_1622,plain,
multiply(identity,greatest_lower_bound(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity)) = greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),
inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))),greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))) )],[refute_0_1521,refute_0_1621]) ).
cnf(refute_0_1623,plain,
greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))) = multiply(identity,greatest_lower_bound(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity)),
inference(subst,[],[refute_0_342:[bind(X_67,$fot(identity)),bind(X_68,$fot(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))))]]) ).
cnf(refute_0_1624,plain,
( multiply(identity,greatest_lower_bound(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity)) != greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))
| greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))) != multiply(identity,greatest_lower_bound(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity))
| greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))) = greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))))),bind(Y0,$fot(multiply(identity,greatest_lower_bound(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity)))),bind(Z0,$fot(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))))]]) ).
cnf(refute_0_1625,plain,
( multiply(identity,greatest_lower_bound(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity)) != greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))
| greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))) = greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))),multiply(identity,greatest_lower_bound(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity))) )],[refute_0_1623,refute_0_1624]) ).
cnf(refute_0_1626,plain,
greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))) = greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),
inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity)),greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))) )],[refute_0_1622,refute_0_1625]) ).
cnf(refute_0_1627,plain,
inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))))) = inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))))),
introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))))))]]) ).
cnf(refute_0_1628,plain,
( greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))) != greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))
| inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))))) != inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))))
| inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))))) = inverse(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))))),inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))))) ),[1,0],$fot(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))))]]) ).
cnf(refute_0_1629,plain,
( greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))) != greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))
| inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))))) = inverse(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))))),inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))))) )],[refute_0_1627,refute_0_1628]) ).
cnf(refute_0_1630,plain,
inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))))) = inverse(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))),greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))) )],[refute_0_1626,refute_0_1629]) ).
cnf(refute_0_1631,plain,
( inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))))) != multiply(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))),inverse(identity))
| inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))))) != inverse(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))))
| inverse(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))) = multiply(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))),inverse(identity)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))))),multiply(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))),inverse(identity))) ),[0],$fot(inverse(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))))]]) ).
cnf(refute_0_1632,plain,
( inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))))) != multiply(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))),inverse(identity))
| inverse(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))) = multiply(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))),inverse(identity)) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))))),inverse(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))))) )],[refute_0_1630,refute_0_1631]) ).
cnf(refute_0_1633,plain,
multiply(identity,X_462) = X_462,
inference(subst,[],[left_identity:[bind(X,$fot(X_462))]]) ).
cnf(refute_0_1634,plain,
inverse(multiply(identity,X_462)) = inverse(multiply(identity,X_462)),
introduced(tautology,[refl,[$fot(inverse(multiply(identity,X_462)))]]) ).
cnf(refute_0_1635,plain,
( multiply(identity,X_462) != X_462
| inverse(multiply(identity,X_462)) != inverse(multiply(identity,X_462))
| inverse(multiply(identity,X_462)) = inverse(X_462) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(identity,X_462)),inverse(multiply(identity,X_462))) ),[1,0],$fot(X_462)]]) ).
cnf(refute_0_1636,plain,
( multiply(identity,X_462) != X_462
| inverse(multiply(identity,X_462)) = inverse(X_462) ),
inference(resolve,[$cnf( $equal(inverse(multiply(identity,X_462)),inverse(multiply(identity,X_462))) )],[refute_0_1634,refute_0_1635]) ).
cnf(refute_0_1637,plain,
inverse(multiply(identity,X_462)) = inverse(X_462),
inference(resolve,[$cnf( $equal(multiply(identity,X_462),X_462) )],[refute_0_1633,refute_0_1636]) ).
cnf(refute_0_1638,plain,
least_upper_bound(identity,inverse(multiply(identity,X_462))) = least_upper_bound(identity,inverse(multiply(identity,X_462))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,inverse(multiply(identity,X_462))))]]) ).
cnf(refute_0_1639,plain,
( inverse(multiply(identity,X_462)) != inverse(X_462)
| least_upper_bound(identity,inverse(multiply(identity,X_462))) != least_upper_bound(identity,inverse(multiply(identity,X_462)))
| least_upper_bound(identity,inverse(multiply(identity,X_462))) = least_upper_bound(identity,inverse(X_462)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,inverse(multiply(identity,X_462))),least_upper_bound(identity,inverse(multiply(identity,X_462)))) ),[1,1],$fot(inverse(X_462))]]) ).
cnf(refute_0_1640,plain,
( inverse(multiply(identity,X_462)) != inverse(X_462)
| least_upper_bound(identity,inverse(multiply(identity,X_462))) = least_upper_bound(identity,inverse(X_462)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(multiply(identity,X_462))),least_upper_bound(identity,inverse(multiply(identity,X_462)))) )],[refute_0_1638,refute_0_1639]) ).
cnf(refute_0_1641,plain,
least_upper_bound(identity,inverse(multiply(identity,X_462))) = least_upper_bound(identity,inverse(X_462)),
inference(resolve,[$cnf( $equal(inverse(multiply(identity,X_462)),inverse(X_462)) )],[refute_0_1637,refute_0_1640]) ).
cnf(refute_0_1642,plain,
inverse(multiply(X_227,multiply(X_228,inverse(least_upper_bound(identity,multiply(X_227,X_228)))))) = multiply(least_upper_bound(identity,multiply(X_227,X_228)),inverse(multiply(X_227,X_228))),
inference(subst,[],[refute_0_522:[bind(X_23,$fot(X_227)),bind(X_32,$fot(X_228)),bind(X_33,$fot(least_upper_bound(identity,multiply(X_227,X_228))))]]) ).
cnf(refute_0_1643,plain,
multiply(least_upper_bound(identity,multiply(X_227,X_228)),inverse(multiply(X_227,X_228))) = least_upper_bound(identity,inverse(multiply(X_227,X_228))),
inference(subst,[],[refute_0_200:[bind(X_84,$fot(multiply(X_227,X_228)))]]) ).
cnf(refute_0_1644,plain,
( multiply(least_upper_bound(identity,multiply(X_227,X_228)),inverse(multiply(X_227,X_228))) != least_upper_bound(identity,inverse(multiply(X_227,X_228)))
| inverse(multiply(X_227,multiply(X_228,inverse(least_upper_bound(identity,multiply(X_227,X_228)))))) != multiply(least_upper_bound(identity,multiply(X_227,X_228)),inverse(multiply(X_227,X_228)))
| inverse(multiply(X_227,multiply(X_228,inverse(least_upper_bound(identity,multiply(X_227,X_228)))))) = least_upper_bound(identity,inverse(multiply(X_227,X_228))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_227,multiply(X_228,inverse(least_upper_bound(identity,multiply(X_227,X_228)))))),multiply(least_upper_bound(identity,multiply(X_227,X_228)),inverse(multiply(X_227,X_228)))) ),[1],$fot(least_upper_bound(identity,inverse(multiply(X_227,X_228))))]]) ).
cnf(refute_0_1645,plain,
( inverse(multiply(X_227,multiply(X_228,inverse(least_upper_bound(identity,multiply(X_227,X_228)))))) != multiply(least_upper_bound(identity,multiply(X_227,X_228)),inverse(multiply(X_227,X_228)))
| inverse(multiply(X_227,multiply(X_228,inverse(least_upper_bound(identity,multiply(X_227,X_228)))))) = least_upper_bound(identity,inverse(multiply(X_227,X_228))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(X_227,X_228)),inverse(multiply(X_227,X_228))),least_upper_bound(identity,inverse(multiply(X_227,X_228)))) )],[refute_0_1643,refute_0_1644]) ).
cnf(refute_0_1646,plain,
inverse(multiply(X_227,multiply(X_228,inverse(least_upper_bound(identity,multiply(X_227,X_228)))))) = least_upper_bound(identity,inverse(multiply(X_227,X_228))),
inference(resolve,[$cnf( $equal(inverse(multiply(X_227,multiply(X_228,inverse(least_upper_bound(identity,multiply(X_227,X_228)))))),multiply(least_upper_bound(identity,multiply(X_227,X_228)),inverse(multiply(X_227,X_228)))) )],[refute_0_1642,refute_0_1645]) ).
cnf(refute_0_1647,plain,
inverse(multiply(X,inverse(least_upper_bound(X_206,inverse(X_205))))) = multiply(least_upper_bound(identity,multiply(X_206,X_205)),inverse(multiply(X,multiply(inverse(least_upper_bound(X_206,inverse(X_205))),least_upper_bound(identity,multiply(X_206,X_205)))))),
inference(subst,[],[refute_0_1393:[bind(Y,$fot(inverse(least_upper_bound(X_206,inverse(X_205))))),bind(X_54,$fot(least_upper_bound(identity,multiply(X_206,X_205))))]]) ).
cnf(refute_0_1648,plain,
X_46 = multiply(inverse(least_upper_bound(X_80,inverse(X_46))),multiply(least_upper_bound(X_80,inverse(X_46)),X_46)),
inference(subst,[],[refute_0_97:[bind(X_45,$fot(least_upper_bound(X_80,inverse(X_46))))]]) ).
cnf(refute_0_1649,plain,
multiply(least_upper_bound(X_80,inverse(X_46)),X_46) = least_upper_bound(identity,multiply(X_80,X_46)),
inference(subst,[],[refute_0_1553:[bind(X_76,$fot(X_46)),bind(X_77,$fot(X_80))]]) ).
cnf(refute_0_1650,plain,
( X_46 != multiply(inverse(least_upper_bound(X_80,inverse(X_46))),multiply(least_upper_bound(X_80,inverse(X_46)),X_46))
| multiply(least_upper_bound(X_80,inverse(X_46)),X_46) != least_upper_bound(identity,multiply(X_80,X_46))
| X_46 = multiply(inverse(least_upper_bound(X_80,inverse(X_46))),least_upper_bound(identity,multiply(X_80,X_46))) ),
introduced(tautology,[equality,[$cnf( $equal(X_46,multiply(inverse(least_upper_bound(X_80,inverse(X_46))),multiply(least_upper_bound(X_80,inverse(X_46)),X_46))) ),[1,1],$fot(least_upper_bound(identity,multiply(X_80,X_46)))]]) ).
cnf(refute_0_1651,plain,
( X_46 != multiply(inverse(least_upper_bound(X_80,inverse(X_46))),multiply(least_upper_bound(X_80,inverse(X_46)),X_46))
| X_46 = multiply(inverse(least_upper_bound(X_80,inverse(X_46))),least_upper_bound(identity,multiply(X_80,X_46))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_80,inverse(X_46)),X_46),least_upper_bound(identity,multiply(X_80,X_46))) )],[refute_0_1649,refute_0_1650]) ).
cnf(refute_0_1652,plain,
X_46 = multiply(inverse(least_upper_bound(X_80,inverse(X_46))),least_upper_bound(identity,multiply(X_80,X_46))),
inference(resolve,[$cnf( $equal(X_46,multiply(inverse(least_upper_bound(X_80,inverse(X_46))),multiply(least_upper_bound(X_80,inverse(X_46)),X_46))) )],[refute_0_1648,refute_0_1651]) ).
cnf(refute_0_1653,plain,
X_205 = multiply(inverse(least_upper_bound(X_206,inverse(X_205))),least_upper_bound(identity,multiply(X_206,X_205))),
inference(subst,[],[refute_0_1652:[bind(X_46,$fot(X_205)),bind(X_80,$fot(X_206))]]) ).
cnf(refute_0_1654,plain,
( X_205 != multiply(inverse(least_upper_bound(X_206,inverse(X_205))),least_upper_bound(identity,multiply(X_206,X_205)))
| multiply(inverse(least_upper_bound(X_206,inverse(X_205))),least_upper_bound(identity,multiply(X_206,X_205))) = X_205 ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(X_205)),bind(Y0,$fot(multiply(inverse(least_upper_bound(X_206,inverse(X_205))),least_upper_bound(identity,multiply(X_206,X_205)))))]]) ).
cnf(refute_0_1655,plain,
multiply(inverse(least_upper_bound(X_206,inverse(X_205))),least_upper_bound(identity,multiply(X_206,X_205))) = X_205,
inference(resolve,[$cnf( $equal(X_205,multiply(inverse(least_upper_bound(X_206,inverse(X_205))),least_upper_bound(identity,multiply(X_206,X_205)))) )],[refute_0_1653,refute_0_1654]) ).
cnf(refute_0_1656,plain,
( multiply(inverse(least_upper_bound(X_206,inverse(X_205))),least_upper_bound(identity,multiply(X_206,X_205))) != X_205
| inverse(multiply(X,inverse(least_upper_bound(X_206,inverse(X_205))))) != multiply(least_upper_bound(identity,multiply(X_206,X_205)),inverse(multiply(X,multiply(inverse(least_upper_bound(X_206,inverse(X_205))),least_upper_bound(identity,multiply(X_206,X_205))))))
| inverse(multiply(X,inverse(least_upper_bound(X_206,inverse(X_205))))) = multiply(least_upper_bound(identity,multiply(X_206,X_205)),inverse(multiply(X,X_205))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X,inverse(least_upper_bound(X_206,inverse(X_205))))),multiply(least_upper_bound(identity,multiply(X_206,X_205)),inverse(multiply(X,multiply(inverse(least_upper_bound(X_206,inverse(X_205))),least_upper_bound(identity,multiply(X_206,X_205))))))) ),[1,1,0,1],$fot(X_205)]]) ).
cnf(refute_0_1657,plain,
( inverse(multiply(X,inverse(least_upper_bound(X_206,inverse(X_205))))) != multiply(least_upper_bound(identity,multiply(X_206,X_205)),inverse(multiply(X,multiply(inverse(least_upper_bound(X_206,inverse(X_205))),least_upper_bound(identity,multiply(X_206,X_205))))))
| inverse(multiply(X,inverse(least_upper_bound(X_206,inverse(X_205))))) = multiply(least_upper_bound(identity,multiply(X_206,X_205)),inverse(multiply(X,X_205))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_206,inverse(X_205))),least_upper_bound(identity,multiply(X_206,X_205))),X_205) )],[refute_0_1655,refute_0_1656]) ).
cnf(refute_0_1658,plain,
inverse(multiply(X,inverse(least_upper_bound(X_206,inverse(X_205))))) = multiply(least_upper_bound(identity,multiply(X_206,X_205)),inverse(multiply(X,X_205))),
inference(resolve,[$cnf( $equal(inverse(multiply(X,inverse(least_upper_bound(X_206,inverse(X_205))))),multiply(least_upper_bound(identity,multiply(X_206,X_205)),inverse(multiply(X,multiply(inverse(least_upper_bound(X_206,inverse(X_205))),least_upper_bound(identity,multiply(X_206,X_205))))))) )],[refute_0_1647,refute_0_1657]) ).
cnf(refute_0_1659,plain,
inverse(multiply(X,inverse(least_upper_bound(X_206,inverse(X_205))))) = multiply(least_upper_bound(X_206,inverse(X_205)),inverse(X)),
inference(subst,[],[refute_0_107:[bind(X,$fot(least_upper_bound(X_206,inverse(X_205)))),bind(X_23,$fot(X))]]) ).
cnf(refute_0_1660,plain,
( inverse(multiply(X,inverse(least_upper_bound(X_206,inverse(X_205))))) != multiply(least_upper_bound(X_206,inverse(X_205)),inverse(X))
| inverse(multiply(X,inverse(least_upper_bound(X_206,inverse(X_205))))) != multiply(least_upper_bound(identity,multiply(X_206,X_205)),inverse(multiply(X,X_205)))
| multiply(least_upper_bound(X_206,inverse(X_205)),inverse(X)) = multiply(least_upper_bound(identity,multiply(X_206,X_205)),inverse(multiply(X,X_205))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X,inverse(least_upper_bound(X_206,inverse(X_205))))),multiply(least_upper_bound(identity,multiply(X_206,X_205)),inverse(multiply(X,X_205)))) ),[0],$fot(multiply(least_upper_bound(X_206,inverse(X_205)),inverse(X)))]]) ).
cnf(refute_0_1661,plain,
( inverse(multiply(X,inverse(least_upper_bound(X_206,inverse(X_205))))) != multiply(least_upper_bound(identity,multiply(X_206,X_205)),inverse(multiply(X,X_205)))
| multiply(least_upper_bound(X_206,inverse(X_205)),inverse(X)) = multiply(least_upper_bound(identity,multiply(X_206,X_205)),inverse(multiply(X,X_205))) ),
inference(resolve,[$cnf( $equal(inverse(multiply(X,inverse(least_upper_bound(X_206,inverse(X_205))))),multiply(least_upper_bound(X_206,inverse(X_205)),inverse(X))) )],[refute_0_1659,refute_0_1660]) ).
cnf(refute_0_1662,plain,
multiply(least_upper_bound(X_206,inverse(X_205)),inverse(X)) = multiply(least_upper_bound(identity,multiply(X_206,X_205)),inverse(multiply(X,X_205))),
inference(resolve,[$cnf( $equal(inverse(multiply(X,inverse(least_upper_bound(X_206,inverse(X_205))))),multiply(least_upper_bound(identity,multiply(X_206,X_205)),inverse(multiply(X,X_205)))) )],[refute_0_1658,refute_0_1661]) ).
cnf(refute_0_1663,plain,
( multiply(least_upper_bound(X_206,inverse(X_205)),inverse(X)) != multiply(least_upper_bound(identity,multiply(X_206,X_205)),inverse(multiply(X,X_205)))
| multiply(least_upper_bound(identity,multiply(X_206,X_205)),inverse(multiply(X,X_205))) = multiply(least_upper_bound(X_206,inverse(X_205)),inverse(X)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(multiply(least_upper_bound(X_206,inverse(X_205)),inverse(X)))),bind(Y0,$fot(multiply(least_upper_bound(identity,multiply(X_206,X_205)),inverse(multiply(X,X_205)))))]]) ).
cnf(refute_0_1664,plain,
multiply(least_upper_bound(identity,multiply(X_206,X_205)),inverse(multiply(X,X_205))) = multiply(least_upper_bound(X_206,inverse(X_205)),inverse(X)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_206,inverse(X_205)),inverse(X)),multiply(least_upper_bound(identity,multiply(X_206,X_205)),inverse(multiply(X,X_205)))) )],[refute_0_1662,refute_0_1663]) ).
cnf(refute_0_1665,plain,
multiply(least_upper_bound(identity,multiply(X_227,X_228)),inverse(multiply(X_227,X_228))) = multiply(least_upper_bound(X_227,inverse(X_228)),inverse(X_227)),
inference(subst,[],[refute_0_1664:[bind(X,$fot(X_227)),bind(X_205,$fot(X_228)),bind(X_206,$fot(X_227))]]) ).
cnf(refute_0_1666,plain,
( multiply(least_upper_bound(identity,multiply(X_227,X_228)),inverse(multiply(X_227,X_228))) != multiply(least_upper_bound(X_227,inverse(X_228)),inverse(X_227))
| inverse(multiply(X_227,multiply(X_228,inverse(least_upper_bound(identity,multiply(X_227,X_228)))))) != multiply(least_upper_bound(identity,multiply(X_227,X_228)),inverse(multiply(X_227,X_228)))
| inverse(multiply(X_227,multiply(X_228,inverse(least_upper_bound(identity,multiply(X_227,X_228)))))) = multiply(least_upper_bound(X_227,inverse(X_228)),inverse(X_227)) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(inverse(multiply(X_227,multiply(X_228,inverse(least_upper_bound(identity,multiply(X_227,X_228)))))))),bind(Y0,$fot(multiply(least_upper_bound(identity,multiply(X_227,X_228)),inverse(multiply(X_227,X_228))))),bind(Z0,$fot(multiply(least_upper_bound(X_227,inverse(X_228)),inverse(X_227))))]]) ).
cnf(refute_0_1667,plain,
( multiply(least_upper_bound(identity,multiply(X_227,X_228)),inverse(multiply(X_227,X_228))) != multiply(least_upper_bound(X_227,inverse(X_228)),inverse(X_227))
| inverse(multiply(X_227,multiply(X_228,inverse(least_upper_bound(identity,multiply(X_227,X_228)))))) = multiply(least_upper_bound(X_227,inverse(X_228)),inverse(X_227)) ),
inference(resolve,[$cnf( $equal(inverse(multiply(X_227,multiply(X_228,inverse(least_upper_bound(identity,multiply(X_227,X_228)))))),multiply(least_upper_bound(identity,multiply(X_227,X_228)),inverse(multiply(X_227,X_228)))) )],[refute_0_1642,refute_0_1666]) ).
cnf(refute_0_1668,plain,
inverse(multiply(X_227,multiply(X_228,inverse(least_upper_bound(identity,multiply(X_227,X_228)))))) = multiply(least_upper_bound(X_227,inverse(X_228)),inverse(X_227)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(X_227,X_228)),inverse(multiply(X_227,X_228))),multiply(least_upper_bound(X_227,inverse(X_228)),inverse(X_227))) )],[refute_0_1665,refute_0_1667]) ).
cnf(refute_0_1669,plain,
( inverse(multiply(X_227,multiply(X_228,inverse(least_upper_bound(identity,multiply(X_227,X_228)))))) != multiply(least_upper_bound(X_227,inverse(X_228)),inverse(X_227))
| inverse(multiply(X_227,multiply(X_228,inverse(least_upper_bound(identity,multiply(X_227,X_228)))))) != least_upper_bound(identity,inverse(multiply(X_227,X_228)))
| multiply(least_upper_bound(X_227,inverse(X_228)),inverse(X_227)) = least_upper_bound(identity,inverse(multiply(X_227,X_228))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_227,multiply(X_228,inverse(least_upper_bound(identity,multiply(X_227,X_228)))))),least_upper_bound(identity,inverse(multiply(X_227,X_228)))) ),[0],$fot(multiply(least_upper_bound(X_227,inverse(X_228)),inverse(X_227)))]]) ).
cnf(refute_0_1670,plain,
( inverse(multiply(X_227,multiply(X_228,inverse(least_upper_bound(identity,multiply(X_227,X_228)))))) != least_upper_bound(identity,inverse(multiply(X_227,X_228)))
| multiply(least_upper_bound(X_227,inverse(X_228)),inverse(X_227)) = least_upper_bound(identity,inverse(multiply(X_227,X_228))) ),
inference(resolve,[$cnf( $equal(inverse(multiply(X_227,multiply(X_228,inverse(least_upper_bound(identity,multiply(X_227,X_228)))))),multiply(least_upper_bound(X_227,inverse(X_228)),inverse(X_227))) )],[refute_0_1668,refute_0_1669]) ).
cnf(refute_0_1671,plain,
multiply(least_upper_bound(X_227,inverse(X_228)),inverse(X_227)) = least_upper_bound(identity,inverse(multiply(X_227,X_228))),
inference(resolve,[$cnf( $equal(inverse(multiply(X_227,multiply(X_228,inverse(least_upper_bound(identity,multiply(X_227,X_228)))))),least_upper_bound(identity,inverse(multiply(X_227,X_228)))) )],[refute_0_1646,refute_0_1670]) ).
cnf(refute_0_1672,plain,
multiply(least_upper_bound(identity,inverse(X_462)),inverse(identity)) = least_upper_bound(identity,inverse(multiply(identity,X_462))),
inference(subst,[],[refute_0_1671:[bind(X_227,$fot(identity)),bind(X_228,$fot(X_462))]]) ).
cnf(refute_0_1673,plain,
( multiply(least_upper_bound(identity,inverse(X_462)),inverse(identity)) != least_upper_bound(identity,inverse(multiply(identity,X_462)))
| least_upper_bound(identity,inverse(multiply(identity,X_462))) != least_upper_bound(identity,inverse(X_462))
| multiply(least_upper_bound(identity,inverse(X_462)),inverse(identity)) = least_upper_bound(identity,inverse(X_462)) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(multiply(least_upper_bound(identity,inverse(X_462)),inverse(identity)))),bind(Y0,$fot(least_upper_bound(identity,inverse(multiply(identity,X_462))))),bind(Z0,$fot(least_upper_bound(identity,inverse(X_462))))]]) ).
cnf(refute_0_1674,plain,
( least_upper_bound(identity,inverse(multiply(identity,X_462))) != least_upper_bound(identity,inverse(X_462))
| multiply(least_upper_bound(identity,inverse(X_462)),inverse(identity)) = least_upper_bound(identity,inverse(X_462)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_462)),inverse(identity)),least_upper_bound(identity,inverse(multiply(identity,X_462)))) )],[refute_0_1672,refute_0_1673]) ).
cnf(refute_0_1675,plain,
multiply(least_upper_bound(identity,inverse(X_462)),inverse(identity)) = least_upper_bound(identity,inverse(X_462)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(multiply(identity,X_462))),least_upper_bound(identity,inverse(X_462))) )],[refute_0_1641,refute_0_1674]) ).
cnf(refute_0_1676,plain,
multiply(greatest_lower_bound(identity,X_462),multiply(least_upper_bound(identity,inverse(X_462)),inverse(identity))) = multiply(greatest_lower_bound(identity,X_462),multiply(least_upper_bound(identity,inverse(X_462)),inverse(identity))),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(identity,X_462),multiply(least_upper_bound(identity,inverse(X_462)),inverse(identity))))]]) ).
cnf(refute_0_1677,plain,
( multiply(greatest_lower_bound(identity,X_462),multiply(least_upper_bound(identity,inverse(X_462)),inverse(identity))) != multiply(greatest_lower_bound(identity,X_462),multiply(least_upper_bound(identity,inverse(X_462)),inverse(identity)))
| multiply(least_upper_bound(identity,inverse(X_462)),inverse(identity)) != least_upper_bound(identity,inverse(X_462))
| multiply(greatest_lower_bound(identity,X_462),multiply(least_upper_bound(identity,inverse(X_462)),inverse(identity))) = multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_462),multiply(least_upper_bound(identity,inverse(X_462)),inverse(identity))),multiply(greatest_lower_bound(identity,X_462),multiply(least_upper_bound(identity,inverse(X_462)),inverse(identity)))) ),[1,1],$fot(least_upper_bound(identity,inverse(X_462)))]]) ).
cnf(refute_0_1678,plain,
( multiply(least_upper_bound(identity,inverse(X_462)),inverse(identity)) != least_upper_bound(identity,inverse(X_462))
| multiply(greatest_lower_bound(identity,X_462),multiply(least_upper_bound(identity,inverse(X_462)),inverse(identity))) = multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_462),multiply(least_upper_bound(identity,inverse(X_462)),inverse(identity))),multiply(greatest_lower_bound(identity,X_462),multiply(least_upper_bound(identity,inverse(X_462)),inverse(identity)))) )],[refute_0_1676,refute_0_1677]) ).
cnf(refute_0_1679,plain,
multiply(greatest_lower_bound(identity,X_462),multiply(least_upper_bound(identity,inverse(X_462)),inverse(identity))) = multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_462)),inverse(identity)),least_upper_bound(identity,inverse(X_462))) )],[refute_0_1675,refute_0_1678]) ).
cnf(refute_0_1680,plain,
multiply(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))),inverse(identity)) = multiply(greatest_lower_bound(identity,X_462),multiply(least_upper_bound(identity,inverse(X_462)),inverse(identity))),
inference(subst,[],[associativity:[bind(X,$fot(greatest_lower_bound(identity,X_462))),bind(Y,$fot(least_upper_bound(identity,inverse(X_462)))),bind(Z,$fot(inverse(identity)))]]) ).
cnf(refute_0_1681,plain,
( multiply(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))),inverse(identity)) != multiply(greatest_lower_bound(identity,X_462),multiply(least_upper_bound(identity,inverse(X_462)),inverse(identity)))
| multiply(greatest_lower_bound(identity,X_462),multiply(least_upper_bound(identity,inverse(X_462)),inverse(identity))) != multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))
| multiply(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))),inverse(identity)) = multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(multiply(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))),inverse(identity)))),bind(Y0,$fot(multiply(greatest_lower_bound(identity,X_462),multiply(least_upper_bound(identity,inverse(X_462)),inverse(identity))))),bind(Z0,$fot(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))]]) ).
cnf(refute_0_1682,plain,
( multiply(greatest_lower_bound(identity,X_462),multiply(least_upper_bound(identity,inverse(X_462)),inverse(identity))) != multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))
| multiply(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))),inverse(identity)) = multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))),inverse(identity)),multiply(greatest_lower_bound(identity,X_462),multiply(least_upper_bound(identity,inverse(X_462)),inverse(identity)))) )],[refute_0_1680,refute_0_1681]) ).
cnf(refute_0_1683,plain,
multiply(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))),inverse(identity)) = multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_462),multiply(least_upper_bound(identity,inverse(X_462)),inverse(identity))),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))) )],[refute_0_1679,refute_0_1682]) ).
cnf(refute_0_1684,plain,
( multiply(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))),inverse(identity)) != multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))
| inverse(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))) != multiply(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))),inverse(identity))
| inverse(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))) = multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))),multiply(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))),inverse(identity))) ),[1],$fot(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))]]) ).
cnf(refute_0_1685,plain,
( inverse(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))) != multiply(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))),inverse(identity))
| inverse(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))) = multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))),inverse(identity)),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))) )],[refute_0_1683,refute_0_1684]) ).
cnf(refute_0_1686,plain,
( inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))))) != multiply(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))),inverse(identity))
| inverse(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))) = multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))),multiply(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))),inverse(identity))) )],[refute_0_1632,refute_0_1685]) ).
cnf(refute_0_1687,plain,
inverse(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))) = multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))))),multiply(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))),inverse(identity))) )],[refute_0_1520,refute_0_1686]) ).
cnf(refute_0_1688,plain,
multiply(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),identity) = greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),
inference(subst,[],[refute_0_564:[bind(X,$fot(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))))]]) ).
cnf(refute_0_1689,plain,
inverse(inverse(multiply(greatest_lower_bound(X_447,X_448),X_48))) = multiply(greatest_lower_bound(X_448,X_447),inverse(multiply(inverse(multiply(greatest_lower_bound(X_447,X_448),X_48)),greatest_lower_bound(X_447,X_448)))),
inference(subst,[],[refute_0_1598:[bind(X_183,$fot(X_447)),bind(X_184,$fot(X_448)),bind(X_227,$fot(inverse(multiply(greatest_lower_bound(X_447,X_448),X_48))))]]) ).
cnf(refute_0_1690,plain,
inverse(X_48) = multiply(inverse(multiply(greatest_lower_bound(X_447,X_448),X_48)),greatest_lower_bound(X_447,X_448)),
inference(subst,[],[refute_0_542:[bind(X_47,$fot(greatest_lower_bound(X_447,X_448)))]]) ).
cnf(refute_0_1691,plain,
( inverse(X_48) != multiply(inverse(multiply(greatest_lower_bound(X_447,X_448),X_48)),greatest_lower_bound(X_447,X_448))
| multiply(inverse(multiply(greatest_lower_bound(X_447,X_448),X_48)),greatest_lower_bound(X_447,X_448)) = inverse(X_48) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(inverse(X_48))),bind(Y0,$fot(multiply(inverse(multiply(greatest_lower_bound(X_447,X_448),X_48)),greatest_lower_bound(X_447,X_448))))]]) ).
cnf(refute_0_1692,plain,
multiply(inverse(multiply(greatest_lower_bound(X_447,X_448),X_48)),greatest_lower_bound(X_447,X_448)) = inverse(X_48),
inference(resolve,[$cnf( $equal(inverse(X_48),multiply(inverse(multiply(greatest_lower_bound(X_447,X_448),X_48)),greatest_lower_bound(X_447,X_448))) )],[refute_0_1690,refute_0_1691]) ).
cnf(refute_0_1693,plain,
( multiply(inverse(multiply(greatest_lower_bound(X_447,X_448),X_48)),greatest_lower_bound(X_447,X_448)) != inverse(X_48)
| inverse(inverse(multiply(greatest_lower_bound(X_447,X_448),X_48))) != multiply(greatest_lower_bound(X_448,X_447),inverse(multiply(inverse(multiply(greatest_lower_bound(X_447,X_448),X_48)),greatest_lower_bound(X_447,X_448))))
| inverse(inverse(multiply(greatest_lower_bound(X_447,X_448),X_48))) = multiply(greatest_lower_bound(X_448,X_447),inverse(inverse(X_48))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(multiply(greatest_lower_bound(X_447,X_448),X_48))),multiply(greatest_lower_bound(X_448,X_447),inverse(multiply(inverse(multiply(greatest_lower_bound(X_447,X_448),X_48)),greatest_lower_bound(X_447,X_448))))) ),[1,1,0],$fot(inverse(X_48))]]) ).
cnf(refute_0_1694,plain,
( inverse(inverse(multiply(greatest_lower_bound(X_447,X_448),X_48))) != multiply(greatest_lower_bound(X_448,X_447),inverse(multiply(inverse(multiply(greatest_lower_bound(X_447,X_448),X_48)),greatest_lower_bound(X_447,X_448))))
| inverse(inverse(multiply(greatest_lower_bound(X_447,X_448),X_48))) = multiply(greatest_lower_bound(X_448,X_447),inverse(inverse(X_48))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(greatest_lower_bound(X_447,X_448),X_48)),greatest_lower_bound(X_447,X_448)),inverse(X_48)) )],[refute_0_1692,refute_0_1693]) ).
cnf(refute_0_1695,plain,
inverse(inverse(multiply(greatest_lower_bound(X_447,X_448),X_48))) = multiply(greatest_lower_bound(X_448,X_447),inverse(inverse(X_48))),
inference(resolve,[$cnf( $equal(inverse(inverse(multiply(greatest_lower_bound(X_447,X_448),X_48))),multiply(greatest_lower_bound(X_448,X_447),inverse(multiply(inverse(multiply(greatest_lower_bound(X_447,X_448),X_48)),greatest_lower_bound(X_447,X_448))))) )],[refute_0_1689,refute_0_1694]) ).
cnf(refute_0_1696,plain,
inverse(inverse(multiply(greatest_lower_bound(X_447,X_448),X_48))) = multiply(greatest_lower_bound(X_447,X_448),X_48),
inference(subst,[],[p19_2:[bind(X,$fot(multiply(greatest_lower_bound(X_447,X_448),X_48)))]]) ).
cnf(refute_0_1697,plain,
( inverse(inverse(multiply(greatest_lower_bound(X_447,X_448),X_48))) != multiply(greatest_lower_bound(X_447,X_448),X_48)
| inverse(inverse(multiply(greatest_lower_bound(X_447,X_448),X_48))) != multiply(greatest_lower_bound(X_448,X_447),inverse(inverse(X_48)))
| multiply(greatest_lower_bound(X_447,X_448),X_48) = multiply(greatest_lower_bound(X_448,X_447),inverse(inverse(X_48))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(multiply(greatest_lower_bound(X_447,X_448),X_48))),multiply(greatest_lower_bound(X_448,X_447),inverse(inverse(X_48)))) ),[0],$fot(multiply(greatest_lower_bound(X_447,X_448),X_48))]]) ).
cnf(refute_0_1698,plain,
( inverse(inverse(multiply(greatest_lower_bound(X_447,X_448),X_48))) != multiply(greatest_lower_bound(X_448,X_447),inverse(inverse(X_48)))
| multiply(greatest_lower_bound(X_447,X_448),X_48) = multiply(greatest_lower_bound(X_448,X_447),inverse(inverse(X_48))) ),
inference(resolve,[$cnf( $equal(inverse(inverse(multiply(greatest_lower_bound(X_447,X_448),X_48))),multiply(greatest_lower_bound(X_447,X_448),X_48)) )],[refute_0_1696,refute_0_1697]) ).
cnf(refute_0_1699,plain,
inverse(inverse(X_48)) = X_48,
inference(subst,[],[p19_2:[bind(X,$fot(X_48))]]) ).
cnf(refute_0_1700,plain,
multiply(greatest_lower_bound(X_448,X_447),inverse(inverse(X_48))) = multiply(greatest_lower_bound(X_448,X_447),inverse(inverse(X_48))),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(X_448,X_447),inverse(inverse(X_48))))]]) ).
cnf(refute_0_1701,plain,
( multiply(greatest_lower_bound(X_448,X_447),inverse(inverse(X_48))) != multiply(greatest_lower_bound(X_448,X_447),inverse(inverse(X_48)))
| inverse(inverse(X_48)) != X_48
| multiply(greatest_lower_bound(X_448,X_447),inverse(inverse(X_48))) = multiply(greatest_lower_bound(X_448,X_447),X_48) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_448,X_447),inverse(inverse(X_48))),multiply(greatest_lower_bound(X_448,X_447),inverse(inverse(X_48)))) ),[1,1],$fot(X_48)]]) ).
cnf(refute_0_1702,plain,
( inverse(inverse(X_48)) != X_48
| multiply(greatest_lower_bound(X_448,X_447),inverse(inverse(X_48))) = multiply(greatest_lower_bound(X_448,X_447),X_48) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_448,X_447),inverse(inverse(X_48))),multiply(greatest_lower_bound(X_448,X_447),inverse(inverse(X_48)))) )],[refute_0_1700,refute_0_1701]) ).
cnf(refute_0_1703,plain,
multiply(greatest_lower_bound(X_448,X_447),inverse(inverse(X_48))) = multiply(greatest_lower_bound(X_448,X_447),X_48),
inference(resolve,[$cnf( $equal(inverse(inverse(X_48)),X_48) )],[refute_0_1699,refute_0_1702]) ).
cnf(refute_0_1704,plain,
( multiply(greatest_lower_bound(X_447,X_448),X_48) != multiply(greatest_lower_bound(X_448,X_447),inverse(inverse(X_48)))
| multiply(greatest_lower_bound(X_448,X_447),inverse(inverse(X_48))) != multiply(greatest_lower_bound(X_448,X_447),X_48)
| multiply(greatest_lower_bound(X_447,X_448),X_48) = multiply(greatest_lower_bound(X_448,X_447),X_48) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_447,X_448),X_48),multiply(greatest_lower_bound(X_448,X_447),X_48)) ),[0],$fot(multiply(greatest_lower_bound(X_448,X_447),inverse(inverse(X_48))))]]) ).
cnf(refute_0_1705,plain,
( multiply(greatest_lower_bound(X_447,X_448),X_48) != multiply(greatest_lower_bound(X_448,X_447),inverse(inverse(X_48)))
| multiply(greatest_lower_bound(X_447,X_448),X_48) = multiply(greatest_lower_bound(X_448,X_447),X_48) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_448,X_447),inverse(inverse(X_48))),multiply(greatest_lower_bound(X_448,X_447),X_48)) )],[refute_0_1703,refute_0_1704]) ).
cnf(refute_0_1706,plain,
( inverse(inverse(multiply(greatest_lower_bound(X_447,X_448),X_48))) != multiply(greatest_lower_bound(X_448,X_447),inverse(inverse(X_48)))
| multiply(greatest_lower_bound(X_447,X_448),X_48) = multiply(greatest_lower_bound(X_448,X_447),X_48) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_447,X_448),X_48),multiply(greatest_lower_bound(X_448,X_447),inverse(inverse(X_48)))) )],[refute_0_1698,refute_0_1705]) ).
cnf(refute_0_1707,plain,
multiply(greatest_lower_bound(X_447,X_448),X_48) = multiply(greatest_lower_bound(X_448,X_447),X_48),
inference(resolve,[$cnf( $equal(inverse(inverse(multiply(greatest_lower_bound(X_447,X_448),X_48))),multiply(greatest_lower_bound(X_448,X_447),inverse(inverse(X_48)))) )],[refute_0_1695,refute_0_1706]) ).
cnf(refute_0_1708,plain,
( multiply(greatest_lower_bound(X_447,X_448),X_48) != multiply(greatest_lower_bound(X_448,X_447),X_48)
| multiply(greatest_lower_bound(X_448,X_447),X_48) = multiply(greatest_lower_bound(X_447,X_448),X_48) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(multiply(greatest_lower_bound(X_447,X_448),X_48))),bind(Y0,$fot(multiply(greatest_lower_bound(X_448,X_447),X_48)))]]) ).
cnf(refute_0_1709,plain,
multiply(greatest_lower_bound(X_448,X_447),X_48) = multiply(greatest_lower_bound(X_447,X_448),X_48),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_447,X_448),X_48),multiply(greatest_lower_bound(X_448,X_447),X_48)) )],[refute_0_1707,refute_0_1708]) ).
cnf(refute_0_1710,plain,
multiply(greatest_lower_bound(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity),identity) = multiply(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),identity),
inference(subst,[],[refute_0_1709:[bind(X_447,$fot(identity)),bind(X_448,$fot(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))),bind(X_48,$fot(identity))]]) ).
cnf(refute_0_1711,plain,
( multiply(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),identity) != greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))
| multiply(greatest_lower_bound(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity),identity) != multiply(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),identity)
| multiply(greatest_lower_bound(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity),identity) = greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(multiply(greatest_lower_bound(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity),identity))),bind(Y0,$fot(multiply(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),identity))),bind(Z0,$fot(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))))]]) ).
cnf(refute_0_1712,plain,
( multiply(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),identity) != greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))
| multiply(greatest_lower_bound(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity),identity) = greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity),identity),multiply(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),identity)) )],[refute_0_1710,refute_0_1711]) ).
cnf(refute_0_1713,plain,
multiply(greatest_lower_bound(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity),identity) = greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),identity),greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))) )],[refute_0_1688,refute_0_1712]) ).
cnf(refute_0_1714,plain,
greatest_lower_bound(identity,multiply(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity)) = multiply(greatest_lower_bound(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity),identity),
inference(subst,[],[refute_0_410:[bind(X_86,$fot(identity)),bind(X_87,$fot(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))))]]) ).
cnf(refute_0_1715,plain,
( multiply(greatest_lower_bound(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity),identity) != greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))
| greatest_lower_bound(identity,multiply(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity)) != multiply(greatest_lower_bound(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity),identity)
| greatest_lower_bound(identity,multiply(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity)) = greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(greatest_lower_bound(identity,multiply(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity)))),bind(Y0,$fot(multiply(greatest_lower_bound(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity),identity))),bind(Z0,$fot(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))))]]) ).
cnf(refute_0_1716,plain,
( multiply(greatest_lower_bound(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity),identity) != greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))
| greatest_lower_bound(identity,multiply(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity)) = greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity)),multiply(greatest_lower_bound(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity),identity)) )],[refute_0_1714,refute_0_1715]) ).
cnf(refute_0_1717,plain,
greatest_lower_bound(identity,multiply(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity)) = greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity),identity),greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))) )],[refute_0_1713,refute_0_1716]) ).
cnf(refute_0_1718,plain,
inverse(greatest_lower_bound(identity,multiply(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity))) = inverse(greatest_lower_bound(identity,multiply(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity))),
introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(identity,multiply(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity))))]]) ).
cnf(refute_0_1719,plain,
( greatest_lower_bound(identity,multiply(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity)) != greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))
| inverse(greatest_lower_bound(identity,multiply(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity))) != inverse(greatest_lower_bound(identity,multiply(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity)))
| inverse(greatest_lower_bound(identity,multiply(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity))) = inverse(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity))),inverse(greatest_lower_bound(identity,multiply(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity)))) ),[1,0],$fot(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))))]]) ).
cnf(refute_0_1720,plain,
( greatest_lower_bound(identity,multiply(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity)) != greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))
| inverse(greatest_lower_bound(identity,multiply(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity))) = inverse(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity))),inverse(greatest_lower_bound(identity,multiply(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity)))) )],[refute_0_1718,refute_0_1719]) ).
cnf(refute_0_1721,plain,
inverse(greatest_lower_bound(identity,multiply(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity))) = inverse(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity)),greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))) )],[refute_0_1717,refute_0_1720]) ).
cnf(refute_0_1722,plain,
( inverse(greatest_lower_bound(identity,multiply(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity))) != inverse(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))))
| inverse(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))) != multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))
| inverse(greatest_lower_bound(identity,multiply(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity))) = multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(inverse(greatest_lower_bound(identity,multiply(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity))))),bind(Y0,$fot(inverse(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))))),bind(Z0,$fot(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))]]) ).
cnf(refute_0_1723,plain,
( inverse(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))) != multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))
| inverse(greatest_lower_bound(identity,multiply(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity))) = multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity))),inverse(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))))) )],[refute_0_1721,refute_0_1722]) ).
cnf(refute_0_1724,plain,
inverse(greatest_lower_bound(identity,multiply(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity))) = multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))) )],[refute_0_1687,refute_0_1723]) ).
cnf(refute_0_1725,plain,
multiply(least_upper_bound(identity,X_84),least_upper_bound(inverse(X_84),identity)) = least_upper_bound(least_upper_bound(identity,X_84),multiply(least_upper_bound(identity,X_84),inverse(X_84))),
inference(subst,[],[refute_0_34:[bind(X_55,$fot(least_upper_bound(identity,X_84))),bind(X_56,$fot(inverse(X_84)))]]) ).
cnf(refute_0_1726,plain,
( multiply(least_upper_bound(identity,X_84),inverse(X_84)) != least_upper_bound(identity,inverse(X_84))
| multiply(least_upper_bound(identity,X_84),least_upper_bound(inverse(X_84),identity)) != least_upper_bound(least_upper_bound(identity,X_84),multiply(least_upper_bound(identity,X_84),inverse(X_84)))
| multiply(least_upper_bound(identity,X_84),least_upper_bound(inverse(X_84),identity)) = least_upper_bound(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,X_84),least_upper_bound(inverse(X_84),identity)),least_upper_bound(least_upper_bound(identity,X_84),multiply(least_upper_bound(identity,X_84),inverse(X_84)))) ),[1,1],$fot(least_upper_bound(identity,inverse(X_84)))]]) ).
cnf(refute_0_1727,plain,
( multiply(least_upper_bound(identity,X_84),least_upper_bound(inverse(X_84),identity)) != least_upper_bound(least_upper_bound(identity,X_84),multiply(least_upper_bound(identity,X_84),inverse(X_84)))
| multiply(least_upper_bound(identity,X_84),least_upper_bound(inverse(X_84),identity)) = least_upper_bound(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_84),inverse(X_84)),least_upper_bound(identity,inverse(X_84))) )],[refute_0_200,refute_0_1726]) ).
cnf(refute_0_1728,plain,
multiply(least_upper_bound(identity,X_84),least_upper_bound(inverse(X_84),identity)) = least_upper_bound(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_84),least_upper_bound(inverse(X_84),identity)),least_upper_bound(least_upper_bound(identity,X_84),multiply(least_upper_bound(identity,X_84),inverse(X_84)))) )],[refute_0_1725,refute_0_1727]) ).
cnf(refute_0_1729,plain,
least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_19,X_105))) = least_upper_bound(X_19,multiply(X_19,X_105)),
inference(subst,[],[refute_0_642:[bind(X_18,$fot(multiply(X_19,X_105)))]]) ).
cnf(refute_0_1730,plain,
multiply(X_19,least_upper_bound(X_105,identity)) = least_upper_bound(X_19,multiply(X_19,X_105)),
inference(subst,[],[refute_0_34:[bind(X_55,$fot(X_19)),bind(X_56,$fot(X_105))]]) ).
cnf(refute_0_1731,plain,
( multiply(X_19,least_upper_bound(X_105,identity)) != least_upper_bound(X_19,multiply(X_19,X_105))
| least_upper_bound(X_19,multiply(X_19,X_105)) = multiply(X_19,least_upper_bound(X_105,identity)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(multiply(X_19,least_upper_bound(X_105,identity)))),bind(Y0,$fot(least_upper_bound(X_19,multiply(X_19,X_105))))]]) ).
cnf(refute_0_1732,plain,
least_upper_bound(X_19,multiply(X_19,X_105)) = multiply(X_19,least_upper_bound(X_105,identity)),
inference(resolve,[$cnf( $equal(multiply(X_19,least_upper_bound(X_105,identity)),least_upper_bound(X_19,multiply(X_19,X_105))) )],[refute_0_1730,refute_0_1731]) ).
cnf(refute_0_1733,plain,
( least_upper_bound(X_19,multiply(X_19,X_105)) != multiply(X_19,least_upper_bound(X_105,identity))
| least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_19,X_105))) != least_upper_bound(X_19,multiply(X_19,X_105))
| least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_105,identity))) = least_upper_bound(X_19,multiply(X_19,X_105)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_19,X_105))),least_upper_bound(X_19,multiply(X_19,X_105))) ),[0,1],$fot(multiply(X_19,least_upper_bound(X_105,identity)))]]) ).
cnf(refute_0_1734,plain,
( least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_19,X_105))) != least_upper_bound(X_19,multiply(X_19,X_105))
| least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_105,identity))) = least_upper_bound(X_19,multiply(X_19,X_105)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,multiply(X_19,X_105)),multiply(X_19,least_upper_bound(X_105,identity))) )],[refute_0_1732,refute_0_1733]) ).
cnf(refute_0_1735,plain,
least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_105,identity))) = least_upper_bound(X_19,multiply(X_19,X_105)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_19,X_105))),least_upper_bound(X_19,multiply(X_19,X_105))) )],[refute_0_1729,refute_0_1734]) ).
cnf(refute_0_1736,plain,
least_upper_bound(identity,least_upper_bound(X_105,identity)) = least_upper_bound(identity,X_105),
inference(subst,[],[refute_0_635:[bind(Y,$fot(X_105)),bind(X_17,$fot(identity))]]) ).
cnf(refute_0_1737,plain,
multiply(X_19,least_upper_bound(identity,least_upper_bound(X_105,identity))) = multiply(X_19,least_upper_bound(identity,least_upper_bound(X_105,identity))),
introduced(tautology,[refl,[$fot(multiply(X_19,least_upper_bound(identity,least_upper_bound(X_105,identity))))]]) ).
cnf(refute_0_1738,plain,
( multiply(X_19,least_upper_bound(identity,least_upper_bound(X_105,identity))) != multiply(X_19,least_upper_bound(identity,least_upper_bound(X_105,identity)))
| least_upper_bound(identity,least_upper_bound(X_105,identity)) != least_upper_bound(identity,X_105)
| multiply(X_19,least_upper_bound(identity,least_upper_bound(X_105,identity))) = multiply(X_19,least_upper_bound(identity,X_105)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_19,least_upper_bound(identity,least_upper_bound(X_105,identity))),multiply(X_19,least_upper_bound(identity,least_upper_bound(X_105,identity)))) ),[1,1],$fot(least_upper_bound(identity,X_105))]]) ).
cnf(refute_0_1739,plain,
( least_upper_bound(identity,least_upper_bound(X_105,identity)) != least_upper_bound(identity,X_105)
| multiply(X_19,least_upper_bound(identity,least_upper_bound(X_105,identity))) = multiply(X_19,least_upper_bound(identity,X_105)) ),
inference(resolve,[$cnf( $equal(multiply(X_19,least_upper_bound(identity,least_upper_bound(X_105,identity))),multiply(X_19,least_upper_bound(identity,least_upper_bound(X_105,identity)))) )],[refute_0_1737,refute_0_1738]) ).
cnf(refute_0_1740,plain,
multiply(X_19,least_upper_bound(identity,least_upper_bound(X_105,identity))) = multiply(X_19,least_upper_bound(identity,X_105)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_105,identity)),least_upper_bound(identity,X_105)) )],[refute_0_1736,refute_0_1739]) ).
cnf(refute_0_1741,plain,
multiply(X_19,least_upper_bound(least_upper_bound(X_105,identity),identity)) = multiply(X_19,least_upper_bound(identity,least_upper_bound(X_105,identity))),
inference(subst,[],[refute_0_760:[bind(X_55,$fot(X_19)),bind(X_56,$fot(least_upper_bound(X_105,identity))),bind(X_57,$fot(identity))]]) ).
cnf(refute_0_1742,plain,
( multiply(X_55,least_upper_bound(X_56,identity)) != least_upper_bound(X_55,multiply(X_55,X_56))
| least_upper_bound(X_55,multiply(X_55,X_56)) = multiply(X_55,least_upper_bound(X_56,identity)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(multiply(X_55,least_upper_bound(X_56,identity)))),bind(Y0,$fot(least_upper_bound(X_55,multiply(X_55,X_56))))]]) ).
cnf(refute_0_1743,plain,
least_upper_bound(X_55,multiply(X_55,X_56)) = multiply(X_55,least_upper_bound(X_56,identity)),
inference(resolve,[$cnf( $equal(multiply(X_55,least_upper_bound(X_56,identity)),least_upper_bound(X_55,multiply(X_55,X_56))) )],[refute_0_34,refute_0_1742]) ).
cnf(refute_0_1744,plain,
least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_105,identity))) = multiply(X_19,least_upper_bound(least_upper_bound(X_105,identity),identity)),
inference(subst,[],[refute_0_1743:[bind(X_55,$fot(X_19)),bind(X_56,$fot(least_upper_bound(X_105,identity)))]]) ).
cnf(refute_0_1745,plain,
( multiply(X_19,least_upper_bound(least_upper_bound(X_105,identity),identity)) != multiply(X_19,least_upper_bound(identity,least_upper_bound(X_105,identity)))
| least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_105,identity))) != multiply(X_19,least_upper_bound(least_upper_bound(X_105,identity),identity))
| least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_105,identity))) = multiply(X_19,least_upper_bound(identity,least_upper_bound(X_105,identity))) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_105,identity))))),bind(Y0,$fot(multiply(X_19,least_upper_bound(least_upper_bound(X_105,identity),identity)))),bind(Z0,$fot(multiply(X_19,least_upper_bound(identity,least_upper_bound(X_105,identity)))))]]) ).
cnf(refute_0_1746,plain,
( multiply(X_19,least_upper_bound(least_upper_bound(X_105,identity),identity)) != multiply(X_19,least_upper_bound(identity,least_upper_bound(X_105,identity)))
| least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_105,identity))) = multiply(X_19,least_upper_bound(identity,least_upper_bound(X_105,identity))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_105,identity))),multiply(X_19,least_upper_bound(least_upper_bound(X_105,identity),identity))) )],[refute_0_1744,refute_0_1745]) ).
cnf(refute_0_1747,plain,
least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_105,identity))) = multiply(X_19,least_upper_bound(identity,least_upper_bound(X_105,identity))),
inference(resolve,[$cnf( $equal(multiply(X_19,least_upper_bound(least_upper_bound(X_105,identity),identity)),multiply(X_19,least_upper_bound(identity,least_upper_bound(X_105,identity)))) )],[refute_0_1741,refute_0_1746]) ).
cnf(refute_0_1748,plain,
( multiply(X_19,least_upper_bound(identity,least_upper_bound(X_105,identity))) != multiply(X_19,least_upper_bound(identity,X_105))
| least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_105,identity))) != multiply(X_19,least_upper_bound(identity,least_upper_bound(X_105,identity)))
| least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_105,identity))) = multiply(X_19,least_upper_bound(identity,X_105)) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_105,identity))))),bind(Y0,$fot(multiply(X_19,least_upper_bound(identity,least_upper_bound(X_105,identity))))),bind(Z0,$fot(multiply(X_19,least_upper_bound(identity,X_105))))]]) ).
cnf(refute_0_1749,plain,
( multiply(X_19,least_upper_bound(identity,least_upper_bound(X_105,identity))) != multiply(X_19,least_upper_bound(identity,X_105))
| least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_105,identity))) = multiply(X_19,least_upper_bound(identity,X_105)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_105,identity))),multiply(X_19,least_upper_bound(identity,least_upper_bound(X_105,identity)))) )],[refute_0_1747,refute_0_1748]) ).
cnf(refute_0_1750,plain,
least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_105,identity))) = multiply(X_19,least_upper_bound(identity,X_105)),
inference(resolve,[$cnf( $equal(multiply(X_19,least_upper_bound(identity,least_upper_bound(X_105,identity))),multiply(X_19,least_upper_bound(identity,X_105))) )],[refute_0_1740,refute_0_1749]) ).
cnf(refute_0_1751,plain,
( least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_105,identity))) != multiply(X_19,least_upper_bound(identity,X_105))
| least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_105,identity))) != least_upper_bound(X_19,multiply(X_19,X_105))
| multiply(X_19,least_upper_bound(identity,X_105)) = least_upper_bound(X_19,multiply(X_19,X_105)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_105,identity))),least_upper_bound(X_19,multiply(X_19,X_105))) ),[0],$fot(multiply(X_19,least_upper_bound(identity,X_105)))]]) ).
cnf(refute_0_1752,plain,
( least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_105,identity))) != least_upper_bound(X_19,multiply(X_19,X_105))
| multiply(X_19,least_upper_bound(identity,X_105)) = least_upper_bound(X_19,multiply(X_19,X_105)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_105,identity))),multiply(X_19,least_upper_bound(identity,X_105))) )],[refute_0_1750,refute_0_1751]) ).
cnf(refute_0_1753,plain,
( multiply(X_19,least_upper_bound(identity,X_105)) != least_upper_bound(X_19,multiply(X_19,X_105))
| least_upper_bound(X_19,multiply(X_19,X_105)) != multiply(X_19,least_upper_bound(X_105,identity))
| multiply(X_19,least_upper_bound(identity,X_105)) = multiply(X_19,least_upper_bound(X_105,identity)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_19,least_upper_bound(identity,X_105)),multiply(X_19,least_upper_bound(X_105,identity))) ),[0],$fot(least_upper_bound(X_19,multiply(X_19,X_105)))]]) ).
cnf(refute_0_1754,plain,
( multiply(X_19,least_upper_bound(identity,X_105)) != least_upper_bound(X_19,multiply(X_19,X_105))
| multiply(X_19,least_upper_bound(identity,X_105)) = multiply(X_19,least_upper_bound(X_105,identity)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,multiply(X_19,X_105)),multiply(X_19,least_upper_bound(X_105,identity))) )],[refute_0_1732,refute_0_1753]) ).
cnf(refute_0_1755,plain,
( least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_105,identity))) != least_upper_bound(X_19,multiply(X_19,X_105))
| multiply(X_19,least_upper_bound(identity,X_105)) = multiply(X_19,least_upper_bound(X_105,identity)) ),
inference(resolve,[$cnf( $equal(multiply(X_19,least_upper_bound(identity,X_105)),least_upper_bound(X_19,multiply(X_19,X_105))) )],[refute_0_1752,refute_0_1754]) ).
cnf(refute_0_1756,plain,
multiply(X_19,least_upper_bound(identity,X_105)) = multiply(X_19,least_upper_bound(X_105,identity)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_105,identity))),least_upper_bound(X_19,multiply(X_19,X_105))) )],[refute_0_1735,refute_0_1755]) ).
cnf(refute_0_1757,plain,
( multiply(X_19,least_upper_bound(identity,X_105)) != multiply(X_19,least_upper_bound(X_105,identity))
| multiply(X_19,least_upper_bound(X_105,identity)) = multiply(X_19,least_upper_bound(identity,X_105)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(multiply(X_19,least_upper_bound(identity,X_105)))),bind(Y0,$fot(multiply(X_19,least_upper_bound(X_105,identity))))]]) ).
cnf(refute_0_1758,plain,
multiply(X_19,least_upper_bound(X_105,identity)) = multiply(X_19,least_upper_bound(identity,X_105)),
inference(resolve,[$cnf( $equal(multiply(X_19,least_upper_bound(identity,X_105)),multiply(X_19,least_upper_bound(X_105,identity))) )],[refute_0_1756,refute_0_1757]) ).
cnf(refute_0_1759,plain,
multiply(least_upper_bound(identity,X_84),least_upper_bound(inverse(X_84),identity)) = multiply(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))),
inference(subst,[],[refute_0_1758:[bind(X_105,$fot(inverse(X_84))),bind(X_19,$fot(least_upper_bound(identity,X_84)))]]) ).
cnf(refute_0_1760,plain,
( multiply(least_upper_bound(identity,X_84),least_upper_bound(inverse(X_84),identity)) != multiply(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84)))
| multiply(least_upper_bound(identity,X_84),least_upper_bound(inverse(X_84),identity)) != least_upper_bound(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84)))
| multiply(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))) = least_upper_bound(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,X_84),least_upper_bound(inverse(X_84),identity)),least_upper_bound(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84)))) ),[0],$fot(multiply(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))))]]) ).
cnf(refute_0_1761,plain,
( multiply(least_upper_bound(identity,X_84),least_upper_bound(inverse(X_84),identity)) != least_upper_bound(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84)))
| multiply(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))) = least_upper_bound(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_84),least_upper_bound(inverse(X_84),identity)),multiply(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84)))) )],[refute_0_1759,refute_0_1760]) ).
cnf(refute_0_1762,plain,
least_upper_bound(identity,least_upper_bound(inverse(X_84),X_84)) = least_upper_bound(identity,least_upper_bound(X_84,inverse(X_84))),
inference(subst,[],[refute_0_948:[bind(X_36,$fot(identity)),bind(X_37,$fot(inverse(X_84))),bind(X_38,$fot(X_84))]]) ).
cnf(refute_0_1763,plain,
least_upper_bound(inverse(X_84),least_upper_bound(identity,X_84)) = least_upper_bound(identity,least_upper_bound(inverse(X_84),X_84)),
inference(subst,[],[refute_0_1000:[bind(Y,$fot(identity)),bind(X_36,$fot(inverse(X_84))),bind(X_38,$fot(X_84))]]) ).
cnf(refute_0_1764,plain,
( least_upper_bound(identity,least_upper_bound(inverse(X_84),X_84)) != least_upper_bound(identity,least_upper_bound(X_84,inverse(X_84)))
| least_upper_bound(inverse(X_84),least_upper_bound(identity,X_84)) != least_upper_bound(identity,least_upper_bound(inverse(X_84),X_84))
| least_upper_bound(inverse(X_84),least_upper_bound(identity,X_84)) = least_upper_bound(identity,least_upper_bound(X_84,inverse(X_84))) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(least_upper_bound(inverse(X_84),least_upper_bound(identity,X_84)))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(inverse(X_84),X_84)))),bind(Z0,$fot(least_upper_bound(identity,least_upper_bound(X_84,inverse(X_84)))))]]) ).
cnf(refute_0_1765,plain,
( least_upper_bound(identity,least_upper_bound(inverse(X_84),X_84)) != least_upper_bound(identity,least_upper_bound(X_84,inverse(X_84)))
| least_upper_bound(inverse(X_84),least_upper_bound(identity,X_84)) = least_upper_bound(identity,least_upper_bound(X_84,inverse(X_84))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_84),least_upper_bound(identity,X_84)),least_upper_bound(identity,least_upper_bound(inverse(X_84),X_84))) )],[refute_0_1763,refute_0_1764]) ).
cnf(refute_0_1766,plain,
least_upper_bound(inverse(X_84),least_upper_bound(identity,X_84)) = least_upper_bound(identity,least_upper_bound(X_84,inverse(X_84))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_84),X_84)),least_upper_bound(identity,least_upper_bound(X_84,inverse(X_84)))) )],[refute_0_1762,refute_0_1765]) ).
cnf(refute_0_1767,plain,
least_upper_bound(identity,least_upper_bound(inverse(X_84),least_upper_bound(identity,X_84))) = least_upper_bound(inverse(X_84),least_upper_bound(identity,X_84)),
inference(subst,[],[refute_0_982:[bind(Y,$fot(X_84)),bind(X_36,$fot(inverse(X_84))),bind(X_37,$fot(identity))]]) ).
cnf(refute_0_1768,plain,
( least_upper_bound(identity,least_upper_bound(inverse(X_84),least_upper_bound(identity,X_84))) != least_upper_bound(inverse(X_84),least_upper_bound(identity,X_84))
| least_upper_bound(inverse(X_84),least_upper_bound(identity,X_84)) != least_upper_bound(identity,least_upper_bound(X_84,inverse(X_84)))
| least_upper_bound(identity,least_upper_bound(inverse(X_84),least_upper_bound(identity,X_84))) = least_upper_bound(identity,least_upper_bound(X_84,inverse(X_84))) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(inverse(X_84),least_upper_bound(identity,X_84))))),bind(Y0,$fot(least_upper_bound(inverse(X_84),least_upper_bound(identity,X_84)))),bind(Z0,$fot(least_upper_bound(identity,least_upper_bound(X_84,inverse(X_84)))))]]) ).
cnf(refute_0_1769,plain,
( least_upper_bound(inverse(X_84),least_upper_bound(identity,X_84)) != least_upper_bound(identity,least_upper_bound(X_84,inverse(X_84)))
| least_upper_bound(identity,least_upper_bound(inverse(X_84),least_upper_bound(identity,X_84))) = least_upper_bound(identity,least_upper_bound(X_84,inverse(X_84))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_84),least_upper_bound(identity,X_84))),least_upper_bound(inverse(X_84),least_upper_bound(identity,X_84))) )],[refute_0_1767,refute_0_1768]) ).
cnf(refute_0_1770,plain,
least_upper_bound(identity,least_upper_bound(inverse(X_84),least_upper_bound(identity,X_84))) = least_upper_bound(identity,least_upper_bound(X_84,inverse(X_84))),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_84),least_upper_bound(identity,X_84)),least_upper_bound(identity,least_upper_bound(X_84,inverse(X_84)))) )],[refute_0_1766,refute_0_1769]) ).
cnf(refute_0_1771,plain,
least_upper_bound(identity,least_upper_bound(least_upper_bound(identity,X_84),inverse(X_84))) = least_upper_bound(identity,least_upper_bound(inverse(X_84),least_upper_bound(identity,X_84))),
inference(subst,[],[refute_0_948:[bind(X_36,$fot(identity)),bind(X_37,$fot(least_upper_bound(identity,X_84))),bind(X_38,$fot(inverse(X_84)))]]) ).
cnf(refute_0_1772,plain,
( least_upper_bound(identity,least_upper_bound(inverse(X_84),least_upper_bound(identity,X_84))) != least_upper_bound(identity,least_upper_bound(X_84,inverse(X_84)))
| least_upper_bound(identity,least_upper_bound(least_upper_bound(identity,X_84),inverse(X_84))) != least_upper_bound(identity,least_upper_bound(inverse(X_84),least_upper_bound(identity,X_84)))
| least_upper_bound(identity,least_upper_bound(least_upper_bound(identity,X_84),inverse(X_84))) = least_upper_bound(identity,least_upper_bound(X_84,inverse(X_84))) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(least_upper_bound(identity,X_84),inverse(X_84))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(inverse(X_84),least_upper_bound(identity,X_84))))),bind(Z0,$fot(least_upper_bound(identity,least_upper_bound(X_84,inverse(X_84)))))]]) ).
cnf(refute_0_1773,plain,
( least_upper_bound(identity,least_upper_bound(inverse(X_84),least_upper_bound(identity,X_84))) != least_upper_bound(identity,least_upper_bound(X_84,inverse(X_84)))
| least_upper_bound(identity,least_upper_bound(least_upper_bound(identity,X_84),inverse(X_84))) = least_upper_bound(identity,least_upper_bound(X_84,inverse(X_84))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(least_upper_bound(identity,X_84),inverse(X_84))),least_upper_bound(identity,least_upper_bound(inverse(X_84),least_upper_bound(identity,X_84)))) )],[refute_0_1771,refute_0_1772]) ).
cnf(refute_0_1774,plain,
least_upper_bound(identity,least_upper_bound(least_upper_bound(identity,X_84),inverse(X_84))) = least_upper_bound(identity,least_upper_bound(X_84,inverse(X_84))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_84),least_upper_bound(identity,X_84))),least_upper_bound(identity,least_upper_bound(X_84,inverse(X_84)))) )],[refute_0_1770,refute_0_1773]) ).
cnf(refute_0_1775,plain,
least_upper_bound(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))) = least_upper_bound(identity,least_upper_bound(least_upper_bound(identity,X_84),inverse(X_84))),
inference(subst,[],[refute_0_1000:[bind(Y,$fot(identity)),bind(X_36,$fot(least_upper_bound(identity,X_84))),bind(X_38,$fot(inverse(X_84)))]]) ).
cnf(refute_0_1776,plain,
( least_upper_bound(identity,least_upper_bound(least_upper_bound(identity,X_84),inverse(X_84))) != least_upper_bound(identity,least_upper_bound(X_84,inverse(X_84)))
| least_upper_bound(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))) != least_upper_bound(identity,least_upper_bound(least_upper_bound(identity,X_84),inverse(X_84)))
| least_upper_bound(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))) = least_upper_bound(identity,least_upper_bound(X_84,inverse(X_84))) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(least_upper_bound(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(least_upper_bound(identity,X_84),inverse(X_84))))),bind(Z0,$fot(least_upper_bound(identity,least_upper_bound(X_84,inverse(X_84)))))]]) ).
cnf(refute_0_1777,plain,
( least_upper_bound(identity,least_upper_bound(least_upper_bound(identity,X_84),inverse(X_84))) != least_upper_bound(identity,least_upper_bound(X_84,inverse(X_84)))
| least_upper_bound(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))) = least_upper_bound(identity,least_upper_bound(X_84,inverse(X_84))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))),least_upper_bound(identity,least_upper_bound(least_upper_bound(identity,X_84),inverse(X_84)))) )],[refute_0_1775,refute_0_1776]) ).
cnf(refute_0_1778,plain,
least_upper_bound(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))) = least_upper_bound(identity,least_upper_bound(X_84,inverse(X_84))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(least_upper_bound(identity,X_84),inverse(X_84))),least_upper_bound(identity,least_upper_bound(X_84,inverse(X_84)))) )],[refute_0_1774,refute_0_1777]) ).
cnf(refute_0_1779,plain,
( multiply(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))) != least_upper_bound(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84)))
| least_upper_bound(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))) != least_upper_bound(identity,least_upper_bound(X_84,inverse(X_84)))
| multiply(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))) = least_upper_bound(identity,least_upper_bound(X_84,inverse(X_84))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))),least_upper_bound(identity,least_upper_bound(X_84,inverse(X_84)))) ),[0],$fot(least_upper_bound(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))))]]) ).
cnf(refute_0_1780,plain,
( multiply(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))) != least_upper_bound(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84)))
| multiply(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))) = least_upper_bound(identity,least_upper_bound(X_84,inverse(X_84))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))),least_upper_bound(identity,least_upper_bound(X_84,inverse(X_84)))) )],[refute_0_1778,refute_0_1779]) ).
cnf(refute_0_1781,plain,
( multiply(least_upper_bound(identity,X_84),least_upper_bound(inverse(X_84),identity)) != least_upper_bound(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84)))
| multiply(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))) = least_upper_bound(identity,least_upper_bound(X_84,inverse(X_84))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))),least_upper_bound(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84)))) )],[refute_0_1761,refute_0_1780]) ).
cnf(refute_0_1782,plain,
multiply(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))) = least_upper_bound(identity,least_upper_bound(X_84,inverse(X_84))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_84),least_upper_bound(inverse(X_84),identity)),least_upper_bound(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84)))) )],[refute_0_1728,refute_0_1781]) ).
cnf(refute_0_1783,plain,
least_upper_bound(identity,least_upper_bound(X_84,inverse(X_84))) = least_upper_bound(X_84,least_upper_bound(inverse(X_84),identity)),
inference(subst,[],[refute_0_971:[bind(X,$fot(identity)),bind(X_36,$fot(X_84)),bind(X_37,$fot(inverse(X_84)))]]) ).
cnf(refute_0_1784,plain,
( multiply(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))) != least_upper_bound(identity,least_upper_bound(X_84,inverse(X_84)))
| least_upper_bound(identity,least_upper_bound(X_84,inverse(X_84))) != least_upper_bound(X_84,least_upper_bound(inverse(X_84),identity))
| multiply(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))) = least_upper_bound(X_84,least_upper_bound(inverse(X_84),identity)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))),least_upper_bound(X_84,least_upper_bound(inverse(X_84),identity))) ),[0],$fot(least_upper_bound(identity,least_upper_bound(X_84,inverse(X_84))))]]) ).
cnf(refute_0_1785,plain,
( multiply(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))) != least_upper_bound(identity,least_upper_bound(X_84,inverse(X_84)))
| multiply(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))) = least_upper_bound(X_84,least_upper_bound(inverse(X_84),identity)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_84,inverse(X_84))),least_upper_bound(X_84,least_upper_bound(inverse(X_84),identity))) )],[refute_0_1783,refute_0_1784]) ).
cnf(refute_0_1786,plain,
multiply(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))) = least_upper_bound(X_84,least_upper_bound(inverse(X_84),identity)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))),least_upper_bound(identity,least_upper_bound(X_84,inverse(X_84)))) )],[refute_0_1782,refute_0_1785]) ).
cnf(refute_0_1787,plain,
( multiply(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))) != least_upper_bound(X_84,least_upper_bound(inverse(X_84),identity))
| multiply(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))) != least_upper_bound(identity,least_upper_bound(X_84,inverse(X_84)))
| least_upper_bound(identity,least_upper_bound(X_84,inverse(X_84))) = least_upper_bound(X_84,least_upper_bound(inverse(X_84),identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))),least_upper_bound(X_84,least_upper_bound(inverse(X_84),identity))) ),[0],$fot(least_upper_bound(identity,least_upper_bound(X_84,inverse(X_84))))]]) ).
cnf(refute_0_1788,plain,
( multiply(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))) != least_upper_bound(X_84,least_upper_bound(inverse(X_84),identity))
| least_upper_bound(identity,least_upper_bound(X_84,inverse(X_84))) = least_upper_bound(X_84,least_upper_bound(inverse(X_84),identity)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))),least_upper_bound(identity,least_upper_bound(X_84,inverse(X_84)))) )],[refute_0_1782,refute_0_1787]) ).
cnf(refute_0_1789,plain,
least_upper_bound(least_upper_bound(X_129,least_upper_bound(X_130,X_15)),greatest_lower_bound(X_15,least_upper_bound(X_129,least_upper_bound(X_130,X_15)))) = least_upper_bound(X_129,least_upper_bound(X_130,X_15)),
inference(subst,[],[refute_0_270:[bind(X_14,$fot(least_upper_bound(X_129,least_upper_bound(X_130,X_15))))]]) ).
cnf(refute_0_1790,plain,
greatest_lower_bound(X,least_upper_bound(least_upper_bound(X_36,X_37),X)) = X,
inference(subst,[],[refute_0_218:[bind(Y,$fot(least_upper_bound(X_36,X_37)))]]) ).
cnf(refute_0_1791,plain,
( greatest_lower_bound(X,least_upper_bound(least_upper_bound(X_36,X_37),X)) != X
| least_upper_bound(least_upper_bound(X_36,X_37),X) != least_upper_bound(X_36,least_upper_bound(X_37,X))
| greatest_lower_bound(X,least_upper_bound(X_36,least_upper_bound(X_37,X))) = X ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X,least_upper_bound(least_upper_bound(X_36,X_37),X)),X) ),[0,1],$fot(least_upper_bound(X_36,least_upper_bound(X_37,X)))]]) ).
cnf(refute_0_1792,plain,
( greatest_lower_bound(X,least_upper_bound(least_upper_bound(X_36,X_37),X)) != X
| greatest_lower_bound(X,least_upper_bound(X_36,least_upper_bound(X_37,X))) = X ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_36,X_37),X),least_upper_bound(X_36,least_upper_bound(X_37,X))) )],[refute_0_968,refute_0_1791]) ).
cnf(refute_0_1793,plain,
greatest_lower_bound(X,least_upper_bound(X_36,least_upper_bound(X_37,X))) = X,
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,least_upper_bound(least_upper_bound(X_36,X_37),X)),X) )],[refute_0_1790,refute_0_1792]) ).
cnf(refute_0_1794,plain,
greatest_lower_bound(X_15,least_upper_bound(X_129,least_upper_bound(X_130,X_15))) = X_15,
inference(subst,[],[refute_0_1793:[bind(X,$fot(X_15)),bind(X_36,$fot(X_129)),bind(X_37,$fot(X_130))]]) ).
cnf(refute_0_1795,plain,
( greatest_lower_bound(X_15,least_upper_bound(X_129,least_upper_bound(X_130,X_15))) != X_15
| least_upper_bound(least_upper_bound(X_129,least_upper_bound(X_130,X_15)),greatest_lower_bound(X_15,least_upper_bound(X_129,least_upper_bound(X_130,X_15)))) != least_upper_bound(X_129,least_upper_bound(X_130,X_15))
| least_upper_bound(least_upper_bound(X_129,least_upper_bound(X_130,X_15)),X_15) = least_upper_bound(X_129,least_upper_bound(X_130,X_15)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_129,least_upper_bound(X_130,X_15)),greatest_lower_bound(X_15,least_upper_bound(X_129,least_upper_bound(X_130,X_15)))),least_upper_bound(X_129,least_upper_bound(X_130,X_15))) ),[0,1],$fot(X_15)]]) ).
cnf(refute_0_1796,plain,
( least_upper_bound(least_upper_bound(X_129,least_upper_bound(X_130,X_15)),greatest_lower_bound(X_15,least_upper_bound(X_129,least_upper_bound(X_130,X_15)))) != least_upper_bound(X_129,least_upper_bound(X_130,X_15))
| least_upper_bound(least_upper_bound(X_129,least_upper_bound(X_130,X_15)),X_15) = least_upper_bound(X_129,least_upper_bound(X_130,X_15)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_15,least_upper_bound(X_129,least_upper_bound(X_130,X_15))),X_15) )],[refute_0_1794,refute_0_1795]) ).
cnf(refute_0_1797,plain,
least_upper_bound(least_upper_bound(X_129,least_upper_bound(X_130,X_15)),X_15) = least_upper_bound(X_129,least_upper_bound(X_130,X_15)),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_129,least_upper_bound(X_130,X_15)),greatest_lower_bound(X_15,least_upper_bound(X_129,least_upper_bound(X_130,X_15)))),least_upper_bound(X_129,least_upper_bound(X_130,X_15))) )],[refute_0_1789,refute_0_1796]) ).
cnf(refute_0_1798,plain,
least_upper_bound(X_15,least_upper_bound(X_130,X_15)) = least_upper_bound(X_15,X_130),
inference(subst,[],[refute_0_635:[bind(Y,$fot(X_130)),bind(X_17,$fot(X_15))]]) ).
cnf(refute_0_1799,plain,
least_upper_bound(X_129,least_upper_bound(X_15,least_upper_bound(X_130,X_15))) = least_upper_bound(X_129,least_upper_bound(X_15,least_upper_bound(X_130,X_15))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_129,least_upper_bound(X_15,least_upper_bound(X_130,X_15))))]]) ).
cnf(refute_0_1800,plain,
( least_upper_bound(X_129,least_upper_bound(X_15,least_upper_bound(X_130,X_15))) != least_upper_bound(X_129,least_upper_bound(X_15,least_upper_bound(X_130,X_15)))
| least_upper_bound(X_15,least_upper_bound(X_130,X_15)) != least_upper_bound(X_15,X_130)
| least_upper_bound(X_129,least_upper_bound(X_15,least_upper_bound(X_130,X_15))) = least_upper_bound(X_129,least_upper_bound(X_15,X_130)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_129,least_upper_bound(X_15,least_upper_bound(X_130,X_15))),least_upper_bound(X_129,least_upper_bound(X_15,least_upper_bound(X_130,X_15)))) ),[1,1],$fot(least_upper_bound(X_15,X_130))]]) ).
cnf(refute_0_1801,plain,
( least_upper_bound(X_15,least_upper_bound(X_130,X_15)) != least_upper_bound(X_15,X_130)
| least_upper_bound(X_129,least_upper_bound(X_15,least_upper_bound(X_130,X_15))) = least_upper_bound(X_129,least_upper_bound(X_15,X_130)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_129,least_upper_bound(X_15,least_upper_bound(X_130,X_15))),least_upper_bound(X_129,least_upper_bound(X_15,least_upper_bound(X_130,X_15)))) )],[refute_0_1799,refute_0_1800]) ).
cnf(refute_0_1802,plain,
least_upper_bound(X_129,least_upper_bound(X_15,least_upper_bound(X_130,X_15))) = least_upper_bound(X_129,least_upper_bound(X_15,X_130)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_15,least_upper_bound(X_130,X_15)),least_upper_bound(X_15,X_130)) )],[refute_0_1798,refute_0_1801]) ).
cnf(refute_0_1803,plain,
least_upper_bound(X_129,least_upper_bound(least_upper_bound(X_130,X_15),X_15)) = least_upper_bound(X_129,least_upper_bound(X_15,least_upper_bound(X_130,X_15))),
inference(subst,[],[refute_0_948:[bind(X_36,$fot(X_129)),bind(X_37,$fot(least_upper_bound(X_130,X_15))),bind(X_38,$fot(X_15))]]) ).
cnf(refute_0_1804,plain,
least_upper_bound(least_upper_bound(X_129,least_upper_bound(X_130,X_15)),X_15) = least_upper_bound(X_129,least_upper_bound(least_upper_bound(X_130,X_15),X_15)),
inference(subst,[],[refute_0_631:[bind(X,$fot(X_129)),bind(Y,$fot(least_upper_bound(X_130,X_15))),bind(Z,$fot(X_15))]]) ).
cnf(refute_0_1805,plain,
( least_upper_bound(X_129,least_upper_bound(least_upper_bound(X_130,X_15),X_15)) != least_upper_bound(X_129,least_upper_bound(X_15,least_upper_bound(X_130,X_15)))
| least_upper_bound(least_upper_bound(X_129,least_upper_bound(X_130,X_15)),X_15) != least_upper_bound(X_129,least_upper_bound(least_upper_bound(X_130,X_15),X_15))
| least_upper_bound(least_upper_bound(X_129,least_upper_bound(X_130,X_15)),X_15) = least_upper_bound(X_129,least_upper_bound(X_15,least_upper_bound(X_130,X_15))) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_129,least_upper_bound(X_130,X_15)),X_15))),bind(Y0,$fot(least_upper_bound(X_129,least_upper_bound(least_upper_bound(X_130,X_15),X_15)))),bind(Z0,$fot(least_upper_bound(X_129,least_upper_bound(X_15,least_upper_bound(X_130,X_15)))))]]) ).
cnf(refute_0_1806,plain,
( least_upper_bound(X_129,least_upper_bound(least_upper_bound(X_130,X_15),X_15)) != least_upper_bound(X_129,least_upper_bound(X_15,least_upper_bound(X_130,X_15)))
| least_upper_bound(least_upper_bound(X_129,least_upper_bound(X_130,X_15)),X_15) = least_upper_bound(X_129,least_upper_bound(X_15,least_upper_bound(X_130,X_15))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_129,least_upper_bound(X_130,X_15)),X_15),least_upper_bound(X_129,least_upper_bound(least_upper_bound(X_130,X_15),X_15))) )],[refute_0_1804,refute_0_1805]) ).
cnf(refute_0_1807,plain,
least_upper_bound(least_upper_bound(X_129,least_upper_bound(X_130,X_15)),X_15) = least_upper_bound(X_129,least_upper_bound(X_15,least_upper_bound(X_130,X_15))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_129,least_upper_bound(least_upper_bound(X_130,X_15),X_15)),least_upper_bound(X_129,least_upper_bound(X_15,least_upper_bound(X_130,X_15)))) )],[refute_0_1803,refute_0_1806]) ).
cnf(refute_0_1808,plain,
( least_upper_bound(X_129,least_upper_bound(X_15,least_upper_bound(X_130,X_15))) != least_upper_bound(X_129,least_upper_bound(X_15,X_130))
| least_upper_bound(least_upper_bound(X_129,least_upper_bound(X_130,X_15)),X_15) != least_upper_bound(X_129,least_upper_bound(X_15,least_upper_bound(X_130,X_15)))
| least_upper_bound(least_upper_bound(X_129,least_upper_bound(X_130,X_15)),X_15) = least_upper_bound(X_129,least_upper_bound(X_15,X_130)) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_129,least_upper_bound(X_130,X_15)),X_15))),bind(Y0,$fot(least_upper_bound(X_129,least_upper_bound(X_15,least_upper_bound(X_130,X_15))))),bind(Z0,$fot(least_upper_bound(X_129,least_upper_bound(X_15,X_130))))]]) ).
cnf(refute_0_1809,plain,
( least_upper_bound(X_129,least_upper_bound(X_15,least_upper_bound(X_130,X_15))) != least_upper_bound(X_129,least_upper_bound(X_15,X_130))
| least_upper_bound(least_upper_bound(X_129,least_upper_bound(X_130,X_15)),X_15) = least_upper_bound(X_129,least_upper_bound(X_15,X_130)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_129,least_upper_bound(X_130,X_15)),X_15),least_upper_bound(X_129,least_upper_bound(X_15,least_upper_bound(X_130,X_15)))) )],[refute_0_1807,refute_0_1808]) ).
cnf(refute_0_1810,plain,
least_upper_bound(least_upper_bound(X_129,least_upper_bound(X_130,X_15)),X_15) = least_upper_bound(X_129,least_upper_bound(X_15,X_130)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_129,least_upper_bound(X_15,least_upper_bound(X_130,X_15))),least_upper_bound(X_129,least_upper_bound(X_15,X_130))) )],[refute_0_1802,refute_0_1809]) ).
cnf(refute_0_1811,plain,
( least_upper_bound(least_upper_bound(X_129,least_upper_bound(X_130,X_15)),X_15) != least_upper_bound(X_129,least_upper_bound(X_130,X_15))
| least_upper_bound(least_upper_bound(X_129,least_upper_bound(X_130,X_15)),X_15) != least_upper_bound(X_129,least_upper_bound(X_15,X_130))
| least_upper_bound(X_129,least_upper_bound(X_15,X_130)) = least_upper_bound(X_129,least_upper_bound(X_130,X_15)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_129,least_upper_bound(X_130,X_15)),X_15),least_upper_bound(X_129,least_upper_bound(X_130,X_15))) ),[0],$fot(least_upper_bound(X_129,least_upper_bound(X_15,X_130)))]]) ).
cnf(refute_0_1812,plain,
( least_upper_bound(least_upper_bound(X_129,least_upper_bound(X_130,X_15)),X_15) != least_upper_bound(X_129,least_upper_bound(X_130,X_15))
| least_upper_bound(X_129,least_upper_bound(X_15,X_130)) = least_upper_bound(X_129,least_upper_bound(X_130,X_15)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_129,least_upper_bound(X_130,X_15)),X_15),least_upper_bound(X_129,least_upper_bound(X_15,X_130))) )],[refute_0_1810,refute_0_1811]) ).
cnf(refute_0_1813,plain,
least_upper_bound(X_129,least_upper_bound(X_15,X_130)) = least_upper_bound(X_129,least_upper_bound(X_130,X_15)),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_129,least_upper_bound(X_130,X_15)),X_15),least_upper_bound(X_129,least_upper_bound(X_130,X_15))) )],[refute_0_1797,refute_0_1812]) ).
cnf(refute_0_1814,plain,
( least_upper_bound(X_129,least_upper_bound(X_15,X_130)) != least_upper_bound(X_129,least_upper_bound(X_130,X_15))
| least_upper_bound(X_129,least_upper_bound(X_130,X_15)) = least_upper_bound(X_129,least_upper_bound(X_15,X_130)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(least_upper_bound(X_129,least_upper_bound(X_15,X_130)))),bind(Y0,$fot(least_upper_bound(X_129,least_upper_bound(X_130,X_15))))]]) ).
cnf(refute_0_1815,plain,
least_upper_bound(X_129,least_upper_bound(X_130,X_15)) = least_upper_bound(X_129,least_upper_bound(X_15,X_130)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_129,least_upper_bound(X_15,X_130)),least_upper_bound(X_129,least_upper_bound(X_130,X_15))) )],[refute_0_1813,refute_0_1814]) ).
cnf(refute_0_1816,plain,
least_upper_bound(X_84,least_upper_bound(inverse(X_84),identity)) = least_upper_bound(X_84,least_upper_bound(identity,inverse(X_84))),
inference(subst,[],[refute_0_1815:[bind(X_129,$fot(X_84)),bind(X_130,$fot(inverse(X_84))),bind(X_15,$fot(identity))]]) ).
cnf(refute_0_1817,plain,
( least_upper_bound(X_84,least_upper_bound(inverse(X_84),identity)) != least_upper_bound(X_84,least_upper_bound(identity,inverse(X_84)))
| least_upper_bound(identity,least_upper_bound(X_84,inverse(X_84))) != least_upper_bound(X_84,least_upper_bound(inverse(X_84),identity))
| least_upper_bound(identity,least_upper_bound(X_84,inverse(X_84))) = least_upper_bound(X_84,least_upper_bound(identity,inverse(X_84))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_84,inverse(X_84))),least_upper_bound(X_84,least_upper_bound(inverse(X_84),identity))) ),[1],$fot(least_upper_bound(X_84,least_upper_bound(identity,inverse(X_84))))]]) ).
cnf(refute_0_1818,plain,
( least_upper_bound(identity,least_upper_bound(X_84,inverse(X_84))) != least_upper_bound(X_84,least_upper_bound(inverse(X_84),identity))
| least_upper_bound(identity,least_upper_bound(X_84,inverse(X_84))) = least_upper_bound(X_84,least_upper_bound(identity,inverse(X_84))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_84,least_upper_bound(inverse(X_84),identity)),least_upper_bound(X_84,least_upper_bound(identity,inverse(X_84)))) )],[refute_0_1816,refute_0_1817]) ).
cnf(refute_0_1819,plain,
( multiply(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))) != least_upper_bound(X_84,least_upper_bound(inverse(X_84),identity))
| least_upper_bound(identity,least_upper_bound(X_84,inverse(X_84))) = least_upper_bound(X_84,least_upper_bound(identity,inverse(X_84))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_84,inverse(X_84))),least_upper_bound(X_84,least_upper_bound(inverse(X_84),identity))) )],[refute_0_1788,refute_0_1818]) ).
cnf(refute_0_1820,plain,
least_upper_bound(identity,least_upper_bound(X_84,inverse(X_84))) = least_upper_bound(X_84,least_upper_bound(identity,inverse(X_84))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_84),least_upper_bound(identity,inverse(X_84))),least_upper_bound(X_84,least_upper_bound(inverse(X_84),identity))) )],[refute_0_1786,refute_0_1819]) ).
cnf(refute_0_1821,plain,
least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71))))) = least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71))))),
inference(subst,[],[refute_0_1820:[bind(X_84,$fot(greatest_lower_bound(identity,multiply(inverse(X),X_71))))]]) ).
cnf(refute_0_1822,plain,
inverse(multiply(inverse(X),greatest_lower_bound(X_71,inverse(inverse(X))))) = multiply(inverse(greatest_lower_bound(X_71,inverse(inverse(X)))),X),
inference(subst,[],[refute_0_534:[bind(X_24,$fot(greatest_lower_bound(X_71,inverse(inverse(X)))))]]) ).
cnf(refute_0_1823,plain,
multiply(X_67,greatest_lower_bound(X_68,inverse(X_67))) = greatest_lower_bound(multiply(X_67,X_68),multiply(X_67,inverse(X_67))),
inference(subst,[],[monotony_glb1:[bind(X,$fot(X_67)),bind(Y,$fot(X_68)),bind(Z,$fot(inverse(X_67)))]]) ).
cnf(refute_0_1824,plain,
( multiply(X_67,greatest_lower_bound(X_68,inverse(X_67))) != greatest_lower_bound(multiply(X_67,X_68),multiply(X_67,inverse(X_67)))
| multiply(X_67,inverse(X_67)) != identity
| multiply(X_67,greatest_lower_bound(X_68,inverse(X_67))) = greatest_lower_bound(multiply(X_67,X_68),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_67,greatest_lower_bound(X_68,inverse(X_67))),greatest_lower_bound(multiply(X_67,X_68),multiply(X_67,inverse(X_67)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_1825,plain,
( multiply(X_67,greatest_lower_bound(X_68,inverse(X_67))) != greatest_lower_bound(multiply(X_67,X_68),multiply(X_67,inverse(X_67)))
| multiply(X_67,greatest_lower_bound(X_68,inverse(X_67))) = greatest_lower_bound(multiply(X_67,X_68),identity) ),
inference(resolve,[$cnf( $equal(multiply(X_67,inverse(X_67)),identity) )],[refute_0_157,refute_0_1824]) ).
cnf(refute_0_1826,plain,
multiply(X_67,greatest_lower_bound(X_68,inverse(X_67))) = greatest_lower_bound(multiply(X_67,X_68),identity),
inference(resolve,[$cnf( $equal(multiply(X_67,greatest_lower_bound(X_68,inverse(X_67))),greatest_lower_bound(multiply(X_67,X_68),multiply(X_67,inverse(X_67)))) )],[refute_0_1823,refute_0_1825]) ).
cnf(refute_0_1827,plain,
greatest_lower_bound(multiply(X_67,X_68),identity) = greatest_lower_bound(identity,multiply(X_67,X_68)),
inference(subst,[],[refute_0_41:[bind(X_21,$fot(identity)),bind(X_22,$fot(multiply(X_67,X_68)))]]) ).
cnf(refute_0_1828,plain,
( multiply(X_67,greatest_lower_bound(X_68,inverse(X_67))) != greatest_lower_bound(multiply(X_67,X_68),identity)
| greatest_lower_bound(multiply(X_67,X_68),identity) != greatest_lower_bound(identity,multiply(X_67,X_68))
| multiply(X_67,greatest_lower_bound(X_68,inverse(X_67))) = greatest_lower_bound(identity,multiply(X_67,X_68)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_67,greatest_lower_bound(X_68,inverse(X_67))),greatest_lower_bound(identity,multiply(X_67,X_68))) ),[0],$fot(greatest_lower_bound(multiply(X_67,X_68),identity))]]) ).
cnf(refute_0_1829,plain,
( multiply(X_67,greatest_lower_bound(X_68,inverse(X_67))) != greatest_lower_bound(multiply(X_67,X_68),identity)
| multiply(X_67,greatest_lower_bound(X_68,inverse(X_67))) = greatest_lower_bound(identity,multiply(X_67,X_68)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_67,X_68),identity),greatest_lower_bound(identity,multiply(X_67,X_68))) )],[refute_0_1827,refute_0_1828]) ).
cnf(refute_0_1830,plain,
multiply(X_67,greatest_lower_bound(X_68,inverse(X_67))) = greatest_lower_bound(identity,multiply(X_67,X_68)),
inference(resolve,[$cnf( $equal(multiply(X_67,greatest_lower_bound(X_68,inverse(X_67))),greatest_lower_bound(multiply(X_67,X_68),identity)) )],[refute_0_1826,refute_0_1829]) ).
cnf(refute_0_1831,plain,
multiply(inverse(X),greatest_lower_bound(X_71,inverse(inverse(X)))) = greatest_lower_bound(identity,multiply(inverse(X),X_71)),
inference(subst,[],[refute_0_1830:[bind(X_67,$fot(inverse(X))),bind(X_68,$fot(X_71))]]) ).
cnf(refute_0_1832,plain,
( multiply(inverse(X),greatest_lower_bound(X_71,inverse(inverse(X)))) != greatest_lower_bound(identity,multiply(inverse(X),X_71))
| inverse(multiply(inverse(X),greatest_lower_bound(X_71,inverse(inverse(X))))) != multiply(inverse(greatest_lower_bound(X_71,inverse(inverse(X)))),X)
| inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71))) = multiply(inverse(greatest_lower_bound(X_71,inverse(inverse(X)))),X) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X),greatest_lower_bound(X_71,inverse(inverse(X))))),multiply(inverse(greatest_lower_bound(X_71,inverse(inverse(X)))),X)) ),[0,0],$fot(greatest_lower_bound(identity,multiply(inverse(X),X_71)))]]) ).
cnf(refute_0_1833,plain,
( inverse(multiply(inverse(X),greatest_lower_bound(X_71,inverse(inverse(X))))) != multiply(inverse(greatest_lower_bound(X_71,inverse(inverse(X)))),X)
| inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71))) = multiply(inverse(greatest_lower_bound(X_71,inverse(inverse(X)))),X) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X),greatest_lower_bound(X_71,inverse(inverse(X)))),greatest_lower_bound(identity,multiply(inverse(X),X_71))) )],[refute_0_1831,refute_0_1832]) ).
cnf(refute_0_1834,plain,
inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71))) = multiply(inverse(greatest_lower_bound(X_71,inverse(inverse(X)))),X),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X),greatest_lower_bound(X_71,inverse(inverse(X))))),multiply(inverse(greatest_lower_bound(X_71,inverse(inverse(X)))),X)) )],[refute_0_1822,refute_0_1833]) ).
cnf(refute_0_1835,plain,
greatest_lower_bound(X_71,inverse(inverse(X))) = greatest_lower_bound(X_71,inverse(inverse(X))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X_71,inverse(inverse(X))))]]) ).
cnf(refute_0_1836,plain,
( greatest_lower_bound(X_71,inverse(inverse(X))) != greatest_lower_bound(X_71,inverse(inverse(X)))
| inverse(inverse(X)) != X
| greatest_lower_bound(X_71,inverse(inverse(X))) = greatest_lower_bound(X_71,X) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_71,inverse(inverse(X))),greatest_lower_bound(X_71,inverse(inverse(X)))) ),[1,1],$fot(X)]]) ).
cnf(refute_0_1837,plain,
( inverse(inverse(X)) != X
| greatest_lower_bound(X_71,inverse(inverse(X))) = greatest_lower_bound(X_71,X) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_71,inverse(inverse(X))),greatest_lower_bound(X_71,inverse(inverse(X)))) )],[refute_0_1835,refute_0_1836]) ).
cnf(refute_0_1838,plain,
greatest_lower_bound(X_71,inverse(inverse(X))) = greatest_lower_bound(X_71,X),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p19_2,refute_0_1837]) ).
cnf(refute_0_1839,plain,
inverse(greatest_lower_bound(X_71,inverse(inverse(X)))) = inverse(greatest_lower_bound(X_71,inverse(inverse(X)))),
introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(X_71,inverse(inverse(X)))))]]) ).
cnf(refute_0_1840,plain,
( greatest_lower_bound(X_71,inverse(inverse(X))) != greatest_lower_bound(X_71,X)
| inverse(greatest_lower_bound(X_71,inverse(inverse(X)))) != inverse(greatest_lower_bound(X_71,inverse(inverse(X))))
| inverse(greatest_lower_bound(X_71,inverse(inverse(X)))) = inverse(greatest_lower_bound(X_71,X)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X_71,inverse(inverse(X)))),inverse(greatest_lower_bound(X_71,inverse(inverse(X))))) ),[1,0],$fot(greatest_lower_bound(X_71,X))]]) ).
cnf(refute_0_1841,plain,
( greatest_lower_bound(X_71,inverse(inverse(X))) != greatest_lower_bound(X_71,X)
| inverse(greatest_lower_bound(X_71,inverse(inverse(X)))) = inverse(greatest_lower_bound(X_71,X)) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_71,inverse(inverse(X)))),inverse(greatest_lower_bound(X_71,inverse(inverse(X))))) )],[refute_0_1839,refute_0_1840]) ).
cnf(refute_0_1842,plain,
inverse(greatest_lower_bound(X_71,inverse(inverse(X)))) = inverse(greatest_lower_bound(X_71,X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_71,inverse(inverse(X))),greatest_lower_bound(X_71,X)) )],[refute_0_1838,refute_0_1841]) ).
cnf(refute_0_1843,plain,
multiply(inverse(greatest_lower_bound(X_71,inverse(inverse(X)))),X) = multiply(inverse(greatest_lower_bound(X_71,inverse(inverse(X)))),X),
introduced(tautology,[refl,[$fot(multiply(inverse(greatest_lower_bound(X_71,inverse(inverse(X)))),X))]]) ).
cnf(refute_0_1844,plain,
( multiply(inverse(greatest_lower_bound(X_71,inverse(inverse(X)))),X) != multiply(inverse(greatest_lower_bound(X_71,inverse(inverse(X)))),X)
| inverse(greatest_lower_bound(X_71,inverse(inverse(X)))) != inverse(greatest_lower_bound(X_71,X))
| multiply(inverse(greatest_lower_bound(X_71,inverse(inverse(X)))),X) = multiply(inverse(greatest_lower_bound(X_71,X)),X) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_71,inverse(inverse(X)))),X),multiply(inverse(greatest_lower_bound(X_71,inverse(inverse(X)))),X)) ),[1,0],$fot(inverse(greatest_lower_bound(X_71,X)))]]) ).
cnf(refute_0_1845,plain,
( inverse(greatest_lower_bound(X_71,inverse(inverse(X)))) != inverse(greatest_lower_bound(X_71,X))
| multiply(inverse(greatest_lower_bound(X_71,inverse(inverse(X)))),X) = multiply(inverse(greatest_lower_bound(X_71,X)),X) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_71,inverse(inverse(X)))),X),multiply(inverse(greatest_lower_bound(X_71,inverse(inverse(X)))),X)) )],[refute_0_1843,refute_0_1844]) ).
cnf(refute_0_1846,plain,
multiply(inverse(greatest_lower_bound(X_71,inverse(inverse(X)))),X) = multiply(inverse(greatest_lower_bound(X_71,X)),X),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_71,inverse(inverse(X)))),inverse(greatest_lower_bound(X_71,X))) )],[refute_0_1842,refute_0_1845]) ).
cnf(refute_0_1847,plain,
( multiply(inverse(greatest_lower_bound(X_71,inverse(inverse(X)))),X) != multiply(inverse(greatest_lower_bound(X_71,X)),X)
| inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71))) != multiply(inverse(greatest_lower_bound(X_71,inverse(inverse(X)))),X)
| inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71))) = multiply(inverse(greatest_lower_bound(X_71,X)),X) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71))),multiply(inverse(greatest_lower_bound(X_71,inverse(inverse(X)))),X)) ),[1],$fot(multiply(inverse(greatest_lower_bound(X_71,X)),X))]]) ).
cnf(refute_0_1848,plain,
( inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71))) != multiply(inverse(greatest_lower_bound(X_71,inverse(inverse(X)))),X)
| inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71))) = multiply(inverse(greatest_lower_bound(X_71,X)),X) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_71,inverse(inverse(X)))),X),multiply(inverse(greatest_lower_bound(X_71,X)),X)) )],[refute_0_1846,refute_0_1847]) ).
cnf(refute_0_1849,plain,
inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71))) = multiply(inverse(greatest_lower_bound(X_71,X)),X),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71))),multiply(inverse(greatest_lower_bound(X_71,inverse(inverse(X)))),X)) )],[refute_0_1834,refute_0_1848]) ).
cnf(refute_0_1850,plain,
( inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71))) != multiply(inverse(greatest_lower_bound(X_71,X)),X)
| least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71))))) != least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71)))))
| least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),multiply(inverse(greatest_lower_bound(X_71,X)),X))) = least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71))))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71))))),least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71)))))) ),[0,1,1],$fot(multiply(inverse(greatest_lower_bound(X_71,X)),X))]]) ).
cnf(refute_0_1851,plain,
( least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71))))) != least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71)))))
| least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),multiply(inverse(greatest_lower_bound(X_71,X)),X))) = least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71))))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71))),multiply(inverse(greatest_lower_bound(X_71,X)),X)) )],[refute_0_1849,refute_0_1850]) ).
cnf(refute_0_1852,plain,
least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),multiply(inverse(greatest_lower_bound(X_71,X)),X))) = least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71))))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71))))),least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71)))))) )],[refute_0_1821,refute_0_1851]) ).
cnf(refute_0_1853,plain,
( multiply(inverse(greatest_lower_bound(X_15,X_62)),X_62) != least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_15,X_62)),X_62))
| least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_15,X_62)),X_62)) = multiply(inverse(greatest_lower_bound(X_15,X_62)),X_62) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(X_15,X_62)),X_62))),bind(Y0,$fot(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_15,X_62)),X_62))))]]) ).
cnf(refute_0_1854,plain,
least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_15,X_62)),X_62)) = multiply(inverse(greatest_lower_bound(X_15,X_62)),X_62),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_15,X_62)),X_62),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_15,X_62)),X_62))) )],[refute_0_1457,refute_0_1853]) ).
cnf(refute_0_1855,plain,
least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_71,X)),X)) = multiply(inverse(greatest_lower_bound(X_71,X)),X),
inference(subst,[],[refute_0_1854:[bind(X_15,$fot(X_71)),bind(X_62,$fot(X))]]) ).
cnf(refute_0_1856,plain,
least_upper_bound(X_36,least_upper_bound(greatest_lower_bound(X_36,Y),X_38)) = least_upper_bound(least_upper_bound(X_36,greatest_lower_bound(X_36,Y)),X_38),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_36)),bind(Y,$fot(greatest_lower_bound(X_36,Y))),bind(Z,$fot(X_38))]]) ).
cnf(refute_0_1857,plain,
least_upper_bound(X_36,greatest_lower_bound(X_36,Y)) = X_36,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_36))]]) ).
cnf(refute_0_1858,plain,
( least_upper_bound(X_36,greatest_lower_bound(X_36,Y)) != X_36
| least_upper_bound(X_36,least_upper_bound(greatest_lower_bound(X_36,Y),X_38)) != least_upper_bound(least_upper_bound(X_36,greatest_lower_bound(X_36,Y)),X_38)
| least_upper_bound(X_36,least_upper_bound(greatest_lower_bound(X_36,Y),X_38)) = least_upper_bound(X_36,X_38) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_36,least_upper_bound(greatest_lower_bound(X_36,Y),X_38)),least_upper_bound(least_upper_bound(X_36,greatest_lower_bound(X_36,Y)),X_38)) ),[1,0],$fot(X_36)]]) ).
cnf(refute_0_1859,plain,
( least_upper_bound(X_36,least_upper_bound(greatest_lower_bound(X_36,Y),X_38)) != least_upper_bound(least_upper_bound(X_36,greatest_lower_bound(X_36,Y)),X_38)
| least_upper_bound(X_36,least_upper_bound(greatest_lower_bound(X_36,Y),X_38)) = least_upper_bound(X_36,X_38) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_36,greatest_lower_bound(X_36,Y)),X_36) )],[refute_0_1857,refute_0_1858]) ).
cnf(refute_0_1860,plain,
least_upper_bound(X_36,least_upper_bound(greatest_lower_bound(X_36,Y),X_38)) = least_upper_bound(X_36,X_38),
inference(resolve,[$cnf( $equal(least_upper_bound(X_36,least_upper_bound(greatest_lower_bound(X_36,Y),X_38)),least_upper_bound(least_upper_bound(X_36,greatest_lower_bound(X_36,Y)),X_38)) )],[refute_0_1856,refute_0_1859]) ).
cnf(refute_0_1861,plain,
least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),multiply(inverse(greatest_lower_bound(X_71,X)),X))) = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_71,X)),X)),
inference(subst,[],[refute_0_1860:[bind(Y,$fot(multiply(inverse(X),X_71))),bind(X_36,$fot(identity)),bind(X_38,$fot(multiply(inverse(greatest_lower_bound(X_71,X)),X)))]]) ).
cnf(refute_0_1862,plain,
( least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_71,X)),X)) != multiply(inverse(greatest_lower_bound(X_71,X)),X)
| least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),multiply(inverse(greatest_lower_bound(X_71,X)),X))) != least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_71,X)),X))
| least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),multiply(inverse(greatest_lower_bound(X_71,X)),X))) = multiply(inverse(greatest_lower_bound(X_71,X)),X) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),multiply(inverse(greatest_lower_bound(X_71,X)),X))))),bind(Y0,$fot(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_71,X)),X)))),bind(Z0,$fot(multiply(inverse(greatest_lower_bound(X_71,X)),X)))]]) ).
cnf(refute_0_1863,plain,
( least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_71,X)),X)) != multiply(inverse(greatest_lower_bound(X_71,X)),X)
| least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),multiply(inverse(greatest_lower_bound(X_71,X)),X))) = multiply(inverse(greatest_lower_bound(X_71,X)),X) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),multiply(inverse(greatest_lower_bound(X_71,X)),X))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_71,X)),X))) )],[refute_0_1861,refute_0_1862]) ).
cnf(refute_0_1864,plain,
least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),multiply(inverse(greatest_lower_bound(X_71,X)),X))) = multiply(inverse(greatest_lower_bound(X_71,X)),X),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_71,X)),X)),multiply(inverse(greatest_lower_bound(X_71,X)),X)) )],[refute_0_1855,refute_0_1863]) ).
cnf(refute_0_1865,plain,
( least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),multiply(inverse(greatest_lower_bound(X_71,X)),X))) != multiply(inverse(greatest_lower_bound(X_71,X)),X)
| least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),multiply(inverse(greatest_lower_bound(X_71,X)),X))) != least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71)))))
| multiply(inverse(greatest_lower_bound(X_71,X)),X) = least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71))))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),multiply(inverse(greatest_lower_bound(X_71,X)),X))),least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71)))))) ),[0],$fot(multiply(inverse(greatest_lower_bound(X_71,X)),X))]]) ).
cnf(refute_0_1866,plain,
( least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),multiply(inverse(greatest_lower_bound(X_71,X)),X))) != least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71)))))
| multiply(inverse(greatest_lower_bound(X_71,X)),X) = least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71))))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),multiply(inverse(greatest_lower_bound(X_71,X)),X))),multiply(inverse(greatest_lower_bound(X_71,X)),X)) )],[refute_0_1864,refute_0_1865]) ).
cnf(refute_0_1867,plain,
least_upper_bound(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(X_256,identity)) = least_upper_bound(X_256,least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y)))),
inference(subst,[],[refute_0_971:[bind(X,$fot(inverse(greatest_lower_bound(identity,Y)))),bind(X_36,$fot(X_256)),bind(X_37,$fot(identity))]]) ).
cnf(refute_0_1868,plain,
multiply(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(identity,greatest_lower_bound(identity,Y))) = least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y))),
inference(subst,[],[refute_0_134:[bind(X_63,$fot(greatest_lower_bound(identity,Y)))]]) ).
cnf(refute_0_1869,plain,
least_upper_bound(identity,greatest_lower_bound(identity,Y)) = identity,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(identity))]]) ).
cnf(refute_0_1870,plain,
( multiply(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(identity,greatest_lower_bound(identity,Y))) != least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y)))
| least_upper_bound(identity,greatest_lower_bound(identity,Y)) != identity
| multiply(inverse(greatest_lower_bound(identity,Y)),identity) = least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(identity,greatest_lower_bound(identity,Y))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y)))) ),[0,1],$fot(identity)]]) ).
cnf(refute_0_1871,plain,
( multiply(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(identity,greatest_lower_bound(identity,Y))) != least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y)))
| multiply(inverse(greatest_lower_bound(identity,Y)),identity) = least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(identity,Y)),identity) )],[refute_0_1869,refute_0_1870]) ).
cnf(refute_0_1872,plain,
multiply(inverse(greatest_lower_bound(identity,Y)),identity) = least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y))),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(identity,greatest_lower_bound(identity,Y))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y)))) )],[refute_0_1868,refute_0_1871]) ).
cnf(refute_0_1873,plain,
multiply(inverse(greatest_lower_bound(identity,Y)),identity) = inverse(greatest_lower_bound(identity,Y)),
inference(subst,[],[refute_0_564:[bind(X,$fot(inverse(greatest_lower_bound(identity,Y))))]]) ).
cnf(refute_0_1874,plain,
( multiply(inverse(greatest_lower_bound(identity,Y)),identity) != inverse(greatest_lower_bound(identity,Y))
| multiply(inverse(greatest_lower_bound(identity,Y)),identity) != least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y)))
| inverse(greatest_lower_bound(identity,Y)) = least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,Y)),identity),least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y)))) ),[0],$fot(inverse(greatest_lower_bound(identity,Y)))]]) ).
cnf(refute_0_1875,plain,
( multiply(inverse(greatest_lower_bound(identity,Y)),identity) != least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y)))
| inverse(greatest_lower_bound(identity,Y)) = least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,Y)),identity),inverse(greatest_lower_bound(identity,Y))) )],[refute_0_1873,refute_0_1874]) ).
cnf(refute_0_1876,plain,
inverse(greatest_lower_bound(identity,Y)) = least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y))),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,Y)),identity),least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y)))) )],[refute_0_1872,refute_0_1875]) ).
cnf(refute_0_1877,plain,
( inverse(greatest_lower_bound(identity,Y)) != least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y)))
| least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y))) = inverse(greatest_lower_bound(identity,Y)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(inverse(greatest_lower_bound(identity,Y)))),bind(Y0,$fot(least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y)))))]]) ).
cnf(refute_0_1878,plain,
least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y))) = inverse(greatest_lower_bound(identity,Y)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y)))) )],[refute_0_1876,refute_0_1877]) ).
cnf(refute_0_1879,plain,
( least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y))) != inverse(greatest_lower_bound(identity,Y))
| least_upper_bound(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(X_256,identity)) != least_upper_bound(X_256,least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y))))
| least_upper_bound(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(X_256,identity)) = least_upper_bound(X_256,inverse(greatest_lower_bound(identity,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(X_256,identity)),least_upper_bound(X_256,least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y))))) ),[1,1],$fot(inverse(greatest_lower_bound(identity,Y)))]]) ).
cnf(refute_0_1880,plain,
( least_upper_bound(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(X_256,identity)) != least_upper_bound(X_256,least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y))))
| least_upper_bound(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(X_256,identity)) = least_upper_bound(X_256,inverse(greatest_lower_bound(identity,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y))),inverse(greatest_lower_bound(identity,Y))) )],[refute_0_1878,refute_0_1879]) ).
cnf(refute_0_1881,plain,
least_upper_bound(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(X_256,identity)) = least_upper_bound(X_256,inverse(greatest_lower_bound(identity,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(X_256,identity)),least_upper_bound(X_256,least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y))))) )],[refute_0_1867,refute_0_1880]) ).
cnf(refute_0_1882,plain,
least_upper_bound(X_255,least_upper_bound(X_256,least_upper_bound(Y,X_256))) = least_upper_bound(X_256,least_upper_bound(least_upper_bound(Y,X_256),X_255)),
inference(subst,[],[refute_0_971:[bind(X,$fot(X_255)),bind(X_36,$fot(X_256)),bind(X_37,$fot(least_upper_bound(Y,X_256)))]]) ).
cnf(refute_0_1883,plain,
least_upper_bound(X_256,least_upper_bound(Y,X_256)) = least_upper_bound(X_256,Y),
inference(subst,[],[refute_0_635:[bind(X_17,$fot(X_256))]]) ).
cnf(refute_0_1884,plain,
( least_upper_bound(X_255,least_upper_bound(X_256,least_upper_bound(Y,X_256))) != least_upper_bound(X_256,least_upper_bound(least_upper_bound(Y,X_256),X_255))
| least_upper_bound(X_256,least_upper_bound(Y,X_256)) != least_upper_bound(X_256,Y)
| least_upper_bound(X_255,least_upper_bound(X_256,Y)) = least_upper_bound(X_256,least_upper_bound(least_upper_bound(Y,X_256),X_255)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_255,least_upper_bound(X_256,least_upper_bound(Y,X_256))),least_upper_bound(X_256,least_upper_bound(least_upper_bound(Y,X_256),X_255))) ),[0,1],$fot(least_upper_bound(X_256,Y))]]) ).
cnf(refute_0_1885,plain,
( least_upper_bound(X_255,least_upper_bound(X_256,least_upper_bound(Y,X_256))) != least_upper_bound(X_256,least_upper_bound(least_upper_bound(Y,X_256),X_255))
| least_upper_bound(X_255,least_upper_bound(X_256,Y)) = least_upper_bound(X_256,least_upper_bound(least_upper_bound(Y,X_256),X_255)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_256,least_upper_bound(Y,X_256)),least_upper_bound(X_256,Y)) )],[refute_0_1883,refute_0_1884]) ).
cnf(refute_0_1886,plain,
least_upper_bound(X_255,least_upper_bound(X_256,Y)) = least_upper_bound(X_256,least_upper_bound(least_upper_bound(Y,X_256),X_255)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_255,least_upper_bound(X_256,least_upper_bound(Y,X_256))),least_upper_bound(X_256,least_upper_bound(least_upper_bound(Y,X_256),X_255))) )],[refute_0_1882,refute_0_1885]) ).
cnf(refute_0_1887,plain,
least_upper_bound(X_256,least_upper_bound(Y,least_upper_bound(X_256,X_255))) = least_upper_bound(Y,least_upper_bound(X_256,X_255)),
inference(subst,[],[refute_0_982:[bind(Y,$fot(X_255)),bind(X_36,$fot(Y)),bind(X_37,$fot(X_256))]]) ).
cnf(refute_0_1888,plain,
least_upper_bound(least_upper_bound(Y,X_256),X_255) = least_upper_bound(Y,least_upper_bound(X_256,X_255)),
inference(subst,[],[refute_0_631:[bind(X,$fot(Y)),bind(Y,$fot(X_256)),bind(Z,$fot(X_255))]]) ).
cnf(refute_0_1889,plain,
least_upper_bound(X_256,least_upper_bound(least_upper_bound(Y,X_256),X_255)) = least_upper_bound(X_256,least_upper_bound(least_upper_bound(Y,X_256),X_255)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_256,least_upper_bound(least_upper_bound(Y,X_256),X_255)))]]) ).
cnf(refute_0_1890,plain,
( least_upper_bound(X_256,least_upper_bound(least_upper_bound(Y,X_256),X_255)) != least_upper_bound(X_256,least_upper_bound(least_upper_bound(Y,X_256),X_255))
| least_upper_bound(least_upper_bound(Y,X_256),X_255) != least_upper_bound(Y,least_upper_bound(X_256,X_255))
| least_upper_bound(X_256,least_upper_bound(least_upper_bound(Y,X_256),X_255)) = least_upper_bound(X_256,least_upper_bound(Y,least_upper_bound(X_256,X_255))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_256,least_upper_bound(least_upper_bound(Y,X_256),X_255)),least_upper_bound(X_256,least_upper_bound(least_upper_bound(Y,X_256),X_255))) ),[1,1],$fot(least_upper_bound(Y,least_upper_bound(X_256,X_255)))]]) ).
cnf(refute_0_1891,plain,
( least_upper_bound(least_upper_bound(Y,X_256),X_255) != least_upper_bound(Y,least_upper_bound(X_256,X_255))
| least_upper_bound(X_256,least_upper_bound(least_upper_bound(Y,X_256),X_255)) = least_upper_bound(X_256,least_upper_bound(Y,least_upper_bound(X_256,X_255))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_256,least_upper_bound(least_upper_bound(Y,X_256),X_255)),least_upper_bound(X_256,least_upper_bound(least_upper_bound(Y,X_256),X_255))) )],[refute_0_1889,refute_0_1890]) ).
cnf(refute_0_1892,plain,
least_upper_bound(X_256,least_upper_bound(least_upper_bound(Y,X_256),X_255)) = least_upper_bound(X_256,least_upper_bound(Y,least_upper_bound(X_256,X_255))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_256),X_255),least_upper_bound(Y,least_upper_bound(X_256,X_255))) )],[refute_0_1888,refute_0_1891]) ).
cnf(refute_0_1893,plain,
( least_upper_bound(X_256,least_upper_bound(Y,least_upper_bound(X_256,X_255))) != least_upper_bound(Y,least_upper_bound(X_256,X_255))
| least_upper_bound(X_256,least_upper_bound(least_upper_bound(Y,X_256),X_255)) != least_upper_bound(X_256,least_upper_bound(Y,least_upper_bound(X_256,X_255)))
| least_upper_bound(X_256,least_upper_bound(least_upper_bound(Y,X_256),X_255)) = least_upper_bound(Y,least_upper_bound(X_256,X_255)) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(least_upper_bound(X_256,least_upper_bound(least_upper_bound(Y,X_256),X_255)))),bind(Y0,$fot(least_upper_bound(X_256,least_upper_bound(Y,least_upper_bound(X_256,X_255))))),bind(Z0,$fot(least_upper_bound(Y,least_upper_bound(X_256,X_255))))]]) ).
cnf(refute_0_1894,plain,
( least_upper_bound(X_256,least_upper_bound(Y,least_upper_bound(X_256,X_255))) != least_upper_bound(Y,least_upper_bound(X_256,X_255))
| least_upper_bound(X_256,least_upper_bound(least_upper_bound(Y,X_256),X_255)) = least_upper_bound(Y,least_upper_bound(X_256,X_255)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_256,least_upper_bound(least_upper_bound(Y,X_256),X_255)),least_upper_bound(X_256,least_upper_bound(Y,least_upper_bound(X_256,X_255)))) )],[refute_0_1892,refute_0_1893]) ).
cnf(refute_0_1895,plain,
least_upper_bound(X_256,least_upper_bound(least_upper_bound(Y,X_256),X_255)) = least_upper_bound(Y,least_upper_bound(X_256,X_255)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_256,least_upper_bound(Y,least_upper_bound(X_256,X_255))),least_upper_bound(Y,least_upper_bound(X_256,X_255))) )],[refute_0_1887,refute_0_1894]) ).
cnf(refute_0_1896,plain,
( least_upper_bound(X_255,least_upper_bound(X_256,Y)) != least_upper_bound(X_256,least_upper_bound(least_upper_bound(Y,X_256),X_255))
| least_upper_bound(X_256,least_upper_bound(least_upper_bound(Y,X_256),X_255)) != least_upper_bound(Y,least_upper_bound(X_256,X_255))
| least_upper_bound(X_255,least_upper_bound(X_256,Y)) = least_upper_bound(Y,least_upper_bound(X_256,X_255)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_255,least_upper_bound(X_256,Y)),least_upper_bound(Y,least_upper_bound(X_256,X_255))) ),[0],$fot(least_upper_bound(X_256,least_upper_bound(least_upper_bound(Y,X_256),X_255)))]]) ).
cnf(refute_0_1897,plain,
( least_upper_bound(X_255,least_upper_bound(X_256,Y)) != least_upper_bound(X_256,least_upper_bound(least_upper_bound(Y,X_256),X_255))
| least_upper_bound(X_255,least_upper_bound(X_256,Y)) = least_upper_bound(Y,least_upper_bound(X_256,X_255)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_256,least_upper_bound(least_upper_bound(Y,X_256),X_255)),least_upper_bound(Y,least_upper_bound(X_256,X_255))) )],[refute_0_1895,refute_0_1896]) ).
cnf(refute_0_1898,plain,
least_upper_bound(X_255,least_upper_bound(X_256,Y)) = least_upper_bound(Y,least_upper_bound(X_256,X_255)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_255,least_upper_bound(X_256,Y)),least_upper_bound(X_256,least_upper_bound(least_upper_bound(Y,X_256),X_255))) )],[refute_0_1886,refute_0_1897]) ).
cnf(refute_0_1899,plain,
( least_upper_bound(X_255,least_upper_bound(X_256,Y)) != least_upper_bound(Y,least_upper_bound(X_256,X_255))
| least_upper_bound(Y,least_upper_bound(X_256,X_255)) = least_upper_bound(X_255,least_upper_bound(X_256,Y)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(least_upper_bound(X_255,least_upper_bound(X_256,Y)))),bind(Y0,$fot(least_upper_bound(Y,least_upper_bound(X_256,X_255))))]]) ).
cnf(refute_0_1900,plain,
least_upper_bound(Y,least_upper_bound(X_256,X_255)) = least_upper_bound(X_255,least_upper_bound(X_256,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_255,least_upper_bound(X_256,Y)),least_upper_bound(Y,least_upper_bound(X_256,X_255))) )],[refute_0_1898,refute_0_1899]) ).
cnf(refute_0_1901,plain,
least_upper_bound(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(X_256,identity)) = least_upper_bound(identity,least_upper_bound(X_256,inverse(greatest_lower_bound(identity,Y)))),
inference(subst,[],[refute_0_1900:[bind(Y,$fot(inverse(greatest_lower_bound(identity,Y)))),bind(X_255,$fot(identity))]]) ).
cnf(refute_0_1902,plain,
( least_upper_bound(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(X_256,identity)) != least_upper_bound(X_256,inverse(greatest_lower_bound(identity,Y)))
| least_upper_bound(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(X_256,identity)) != least_upper_bound(identity,least_upper_bound(X_256,inverse(greatest_lower_bound(identity,Y))))
| least_upper_bound(identity,least_upper_bound(X_256,inverse(greatest_lower_bound(identity,Y)))) = least_upper_bound(X_256,inverse(greatest_lower_bound(identity,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(X_256,identity)),least_upper_bound(X_256,inverse(greatest_lower_bound(identity,Y)))) ),[0],$fot(least_upper_bound(identity,least_upper_bound(X_256,inverse(greatest_lower_bound(identity,Y)))))]]) ).
cnf(refute_0_1903,plain,
( least_upper_bound(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(X_256,identity)) != least_upper_bound(X_256,inverse(greatest_lower_bound(identity,Y)))
| least_upper_bound(identity,least_upper_bound(X_256,inverse(greatest_lower_bound(identity,Y)))) = least_upper_bound(X_256,inverse(greatest_lower_bound(identity,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(X_256,identity)),least_upper_bound(identity,least_upper_bound(X_256,inverse(greatest_lower_bound(identity,Y))))) )],[refute_0_1901,refute_0_1902]) ).
cnf(refute_0_1904,plain,
least_upper_bound(identity,least_upper_bound(X_256,inverse(greatest_lower_bound(identity,Y)))) = least_upper_bound(X_256,inverse(greatest_lower_bound(identity,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(X_256,identity)),least_upper_bound(X_256,inverse(greatest_lower_bound(identity,Y)))) )],[refute_0_1881,refute_0_1903]) ).
cnf(refute_0_1905,plain,
least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71))))) = least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71)))),
inference(subst,[],[refute_0_1904:[bind(Y,$fot(multiply(inverse(X),X_71))),bind(X_256,$fot(greatest_lower_bound(identity,multiply(inverse(X),X_71))))]]) ).
cnf(refute_0_1906,plain,
least_upper_bound(least_upper_bound(Y,X_257),least_upper_bound(X_256,X_257)) = least_upper_bound(X_256,least_upper_bound(X_257,least_upper_bound(Y,X_257))),
inference(subst,[],[refute_0_971:[bind(X,$fot(least_upper_bound(Y,X_257))),bind(X_36,$fot(X_256)),bind(X_37,$fot(X_257))]]) ).
cnf(refute_0_1907,plain,
least_upper_bound(X_257,least_upper_bound(Y,X_257)) = least_upper_bound(X_257,Y),
inference(subst,[],[refute_0_635:[bind(X_17,$fot(X_257))]]) ).
cnf(refute_0_1908,plain,
( least_upper_bound(X_257,least_upper_bound(Y,X_257)) != least_upper_bound(X_257,Y)
| least_upper_bound(least_upper_bound(Y,X_257),least_upper_bound(X_256,X_257)) != least_upper_bound(X_256,least_upper_bound(X_257,least_upper_bound(Y,X_257)))
| least_upper_bound(least_upper_bound(Y,X_257),least_upper_bound(X_256,X_257)) = least_upper_bound(X_256,least_upper_bound(X_257,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_257),least_upper_bound(X_256,X_257)),least_upper_bound(X_256,least_upper_bound(X_257,least_upper_bound(Y,X_257)))) ),[1,1],$fot(least_upper_bound(X_257,Y))]]) ).
cnf(refute_0_1909,plain,
( least_upper_bound(least_upper_bound(Y,X_257),least_upper_bound(X_256,X_257)) != least_upper_bound(X_256,least_upper_bound(X_257,least_upper_bound(Y,X_257)))
| least_upper_bound(least_upper_bound(Y,X_257),least_upper_bound(X_256,X_257)) = least_upper_bound(X_256,least_upper_bound(X_257,Y)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_257,least_upper_bound(Y,X_257)),least_upper_bound(X_257,Y)) )],[refute_0_1907,refute_0_1908]) ).
cnf(refute_0_1910,plain,
least_upper_bound(least_upper_bound(Y,X_257),least_upper_bound(X_256,X_257)) = least_upper_bound(X_256,least_upper_bound(X_257,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_257),least_upper_bound(X_256,X_257)),least_upper_bound(X_256,least_upper_bound(X_257,least_upper_bound(Y,X_257)))) )],[refute_0_1906,refute_0_1909]) ).
cnf(refute_0_1911,plain,
least_upper_bound(X_17,least_upper_bound(least_upper_bound(X_36,X_37),X_17)) = least_upper_bound(X_17,least_upper_bound(X_36,X_37)),
inference(subst,[],[refute_0_635:[bind(Y,$fot(least_upper_bound(X_36,X_37)))]]) ).
cnf(refute_0_1912,plain,
least_upper_bound(X_36,least_upper_bound(X_37,X_17)) = least_upper_bound(least_upper_bound(X_36,X_37),X_17),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_36)),bind(Y,$fot(X_37)),bind(Z,$fot(X_17))]]) ).
cnf(refute_0_1913,plain,
( least_upper_bound(X_36,least_upper_bound(X_37,X_17)) != least_upper_bound(least_upper_bound(X_36,X_37),X_17)
| least_upper_bound(least_upper_bound(X_36,X_37),X_17) = least_upper_bound(X_36,least_upper_bound(X_37,X_17)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(least_upper_bound(X_36,least_upper_bound(X_37,X_17)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X_36,X_37),X_17)))]]) ).
cnf(refute_0_1914,plain,
least_upper_bound(least_upper_bound(X_36,X_37),X_17) = least_upper_bound(X_36,least_upper_bound(X_37,X_17)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_36,least_upper_bound(X_37,X_17)),least_upper_bound(least_upper_bound(X_36,X_37),X_17)) )],[refute_0_1912,refute_0_1913]) ).
cnf(refute_0_1915,plain,
( least_upper_bound(X_17,least_upper_bound(least_upper_bound(X_36,X_37),X_17)) != least_upper_bound(X_17,least_upper_bound(X_36,X_37))
| least_upper_bound(least_upper_bound(X_36,X_37),X_17) != least_upper_bound(X_36,least_upper_bound(X_37,X_17))
| least_upper_bound(X_17,least_upper_bound(X_36,least_upper_bound(X_37,X_17))) = least_upper_bound(X_17,least_upper_bound(X_36,X_37)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_17,least_upper_bound(least_upper_bound(X_36,X_37),X_17)),least_upper_bound(X_17,least_upper_bound(X_36,X_37))) ),[0,1],$fot(least_upper_bound(X_36,least_upper_bound(X_37,X_17)))]]) ).
cnf(refute_0_1916,plain,
( least_upper_bound(X_17,least_upper_bound(least_upper_bound(X_36,X_37),X_17)) != least_upper_bound(X_17,least_upper_bound(X_36,X_37))
| least_upper_bound(X_17,least_upper_bound(X_36,least_upper_bound(X_37,X_17))) = least_upper_bound(X_17,least_upper_bound(X_36,X_37)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_36,X_37),X_17),least_upper_bound(X_36,least_upper_bound(X_37,X_17))) )],[refute_0_1914,refute_0_1915]) ).
cnf(refute_0_1917,plain,
least_upper_bound(X_17,least_upper_bound(X_36,least_upper_bound(X_37,X_17))) = least_upper_bound(X_17,least_upper_bound(X_36,X_37)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,least_upper_bound(least_upper_bound(X_36,X_37),X_17)),least_upper_bound(X_17,least_upper_bound(X_36,X_37))) )],[refute_0_1911,refute_0_1916]) ).
cnf(refute_0_1918,plain,
least_upper_bound(X_257,least_upper_bound(X_256,least_upper_bound(Y,X_257))) = least_upper_bound(X_257,least_upper_bound(X_256,Y)),
inference(subst,[],[refute_0_1917:[bind(X_17,$fot(X_257)),bind(X_36,$fot(X_256)),bind(X_37,$fot(Y))]]) ).
cnf(refute_0_1919,plain,
least_upper_bound(least_upper_bound(Y,X_257),least_upper_bound(X_256,X_257)) = least_upper_bound(X_257,least_upper_bound(X_256,least_upper_bound(Y,X_257))),
inference(subst,[],[refute_0_1900:[bind(Y,$fot(least_upper_bound(Y,X_257))),bind(X_255,$fot(X_257))]]) ).
cnf(refute_0_1920,plain,
( least_upper_bound(X_257,least_upper_bound(X_256,least_upper_bound(Y,X_257))) != least_upper_bound(X_257,least_upper_bound(X_256,Y))
| least_upper_bound(least_upper_bound(Y,X_257),least_upper_bound(X_256,X_257)) != least_upper_bound(X_257,least_upper_bound(X_256,least_upper_bound(Y,X_257)))
| least_upper_bound(least_upper_bound(Y,X_257),least_upper_bound(X_256,X_257)) = least_upper_bound(X_257,least_upper_bound(X_256,Y)) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(least_upper_bound(least_upper_bound(Y,X_257),least_upper_bound(X_256,X_257)))),bind(Y0,$fot(least_upper_bound(X_257,least_upper_bound(X_256,least_upper_bound(Y,X_257))))),bind(Z0,$fot(least_upper_bound(X_257,least_upper_bound(X_256,Y))))]]) ).
cnf(refute_0_1921,plain,
( least_upper_bound(X_257,least_upper_bound(X_256,least_upper_bound(Y,X_257))) != least_upper_bound(X_257,least_upper_bound(X_256,Y))
| least_upper_bound(least_upper_bound(Y,X_257),least_upper_bound(X_256,X_257)) = least_upper_bound(X_257,least_upper_bound(X_256,Y)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_257),least_upper_bound(X_256,X_257)),least_upper_bound(X_257,least_upper_bound(X_256,least_upper_bound(Y,X_257)))) )],[refute_0_1919,refute_0_1920]) ).
cnf(refute_0_1922,plain,
least_upper_bound(least_upper_bound(Y,X_257),least_upper_bound(X_256,X_257)) = least_upper_bound(X_257,least_upper_bound(X_256,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_257,least_upper_bound(X_256,least_upper_bound(Y,X_257))),least_upper_bound(X_257,least_upper_bound(X_256,Y))) )],[refute_0_1918,refute_0_1921]) ).
cnf(refute_0_1923,plain,
( least_upper_bound(least_upper_bound(Y,X_257),least_upper_bound(X_256,X_257)) != least_upper_bound(X_256,least_upper_bound(X_257,Y))
| least_upper_bound(least_upper_bound(Y,X_257),least_upper_bound(X_256,X_257)) != least_upper_bound(X_257,least_upper_bound(X_256,Y))
| least_upper_bound(X_257,least_upper_bound(X_256,Y)) = least_upper_bound(X_256,least_upper_bound(X_257,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_257),least_upper_bound(X_256,X_257)),least_upper_bound(X_256,least_upper_bound(X_257,Y))) ),[0],$fot(least_upper_bound(X_257,least_upper_bound(X_256,Y)))]]) ).
cnf(refute_0_1924,plain,
( least_upper_bound(least_upper_bound(Y,X_257),least_upper_bound(X_256,X_257)) != least_upper_bound(X_256,least_upper_bound(X_257,Y))
| least_upper_bound(X_257,least_upper_bound(X_256,Y)) = least_upper_bound(X_256,least_upper_bound(X_257,Y)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_257),least_upper_bound(X_256,X_257)),least_upper_bound(X_257,least_upper_bound(X_256,Y))) )],[refute_0_1922,refute_0_1923]) ).
cnf(refute_0_1925,plain,
least_upper_bound(X_257,least_upper_bound(X_256,Y)) = least_upper_bound(X_256,least_upper_bound(X_257,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_257),least_upper_bound(X_256,X_257)),least_upper_bound(X_256,least_upper_bound(X_257,Y))) )],[refute_0_1910,refute_0_1924]) ).
cnf(refute_0_1926,plain,
( least_upper_bound(X_257,least_upper_bound(X_256,Y)) != least_upper_bound(X_256,least_upper_bound(X_257,Y))
| least_upper_bound(X_256,least_upper_bound(X_257,Y)) = least_upper_bound(X_257,least_upper_bound(X_256,Y)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(least_upper_bound(X_257,least_upper_bound(X_256,Y)))),bind(Y0,$fot(least_upper_bound(X_256,least_upper_bound(X_257,Y))))]]) ).
cnf(refute_0_1927,plain,
least_upper_bound(X_256,least_upper_bound(X_257,Y)) = least_upper_bound(X_257,least_upper_bound(X_256,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_257,least_upper_bound(X_256,Y)),least_upper_bound(X_256,least_upper_bound(X_257,Y))) )],[refute_0_1925,refute_0_1926]) ).
cnf(refute_0_1928,plain,
least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71))))) = least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71))))),
inference(subst,[],[refute_0_1927:[bind(Y,$fot(inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71))))),bind(X_256,$fot(greatest_lower_bound(identity,multiply(inverse(X),X_71)))),bind(X_257,$fot(identity))]]) ).
cnf(refute_0_1929,plain,
( least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71))))) != least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71)))))
| least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71))))) != least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71))))
| least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71))))) = least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71)))) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71))))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71))))))),bind(Z0,$fot(least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71))))))]]) ).
cnf(refute_0_1930,plain,
( least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71))))) != least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71))))
| least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71))))) = least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71))))),least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71)))))) )],[refute_0_1928,refute_0_1929]) ).
cnf(refute_0_1931,plain,
least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71))))) = least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71)))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71))))),least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71))))) )],[refute_0_1905,refute_0_1930]) ).
cnf(refute_0_1932,plain,
( multiply(inverse(greatest_lower_bound(X_71,X)),X) != least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71)))))
| least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71))))) != least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71))))
| multiply(inverse(greatest_lower_bound(X_71,X)),X) = least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(greatest_lower_bound(X_71,X)),X),least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71))))) ),[0],$fot(least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71))))))]]) ).
cnf(refute_0_1933,plain,
( multiply(inverse(greatest_lower_bound(X_71,X)),X) != least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71)))))
| multiply(inverse(greatest_lower_bound(X_71,X)),X) = least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71))))),least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71))))) )],[refute_0_1931,refute_0_1932]) ).
cnf(refute_0_1934,plain,
( least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),multiply(inverse(greatest_lower_bound(X_71,X)),X))) != least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71)))))
| multiply(inverse(greatest_lower_bound(X_71,X)),X) = least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_71,X)),X),least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71)))))) )],[refute_0_1866,refute_0_1933]) ).
cnf(refute_0_1935,plain,
multiply(inverse(greatest_lower_bound(X_71,X)),X) = least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71)))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),multiply(inverse(greatest_lower_bound(X_71,X)),X))),least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71)))))) )],[refute_0_1852,refute_0_1934]) ).
cnf(refute_0_1936,plain,
inverse(multiply(X,greatest_lower_bound(identity,multiply(inverse(X),X_237)))) = multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X),X_237))),inverse(X)),
inference(subst,[],[p19_3:[bind(Y,$fot(greatest_lower_bound(identity,multiply(inverse(X),X_237))))]]) ).
cnf(refute_0_1937,plain,
inverse(greatest_lower_bound(X_71,inverse(X_47))) = multiply(inverse(multiply(X_47,greatest_lower_bound(X_71,inverse(X_47)))),X_47),
inference(subst,[],[refute_0_542:[bind(X_48,$fot(greatest_lower_bound(X_71,inverse(X_47))))]]) ).
cnf(refute_0_1938,plain,
multiply(X_47,greatest_lower_bound(X_71,inverse(X_47))) = greatest_lower_bound(identity,multiply(X_47,X_71)),
inference(subst,[],[refute_0_1830:[bind(X_67,$fot(X_47)),bind(X_68,$fot(X_71))]]) ).
cnf(refute_0_1939,plain,
( multiply(X_47,greatest_lower_bound(X_71,inverse(X_47))) != greatest_lower_bound(identity,multiply(X_47,X_71))
| inverse(greatest_lower_bound(X_71,inverse(X_47))) != multiply(inverse(multiply(X_47,greatest_lower_bound(X_71,inverse(X_47)))),X_47)
| inverse(greatest_lower_bound(X_71,inverse(X_47))) = multiply(inverse(greatest_lower_bound(identity,multiply(X_47,X_71))),X_47) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X_71,inverse(X_47))),multiply(inverse(multiply(X_47,greatest_lower_bound(X_71,inverse(X_47)))),X_47)) ),[1,0,0],$fot(greatest_lower_bound(identity,multiply(X_47,X_71)))]]) ).
cnf(refute_0_1940,plain,
( inverse(greatest_lower_bound(X_71,inverse(X_47))) != multiply(inverse(multiply(X_47,greatest_lower_bound(X_71,inverse(X_47)))),X_47)
| inverse(greatest_lower_bound(X_71,inverse(X_47))) = multiply(inverse(greatest_lower_bound(identity,multiply(X_47,X_71))),X_47) ),
inference(resolve,[$cnf( $equal(multiply(X_47,greatest_lower_bound(X_71,inverse(X_47))),greatest_lower_bound(identity,multiply(X_47,X_71))) )],[refute_0_1938,refute_0_1939]) ).
cnf(refute_0_1941,plain,
inverse(greatest_lower_bound(X_71,inverse(X_47))) = multiply(inverse(greatest_lower_bound(identity,multiply(X_47,X_71))),X_47),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_71,inverse(X_47))),multiply(inverse(multiply(X_47,greatest_lower_bound(X_71,inverse(X_47)))),X_47)) )],[refute_0_1937,refute_0_1940]) ).
cnf(refute_0_1942,plain,
inverse(greatest_lower_bound(X_237,inverse(inverse(X)))) = multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X),X_237))),inverse(X)),
inference(subst,[],[refute_0_1941:[bind(X_47,$fot(inverse(X))),bind(X_71,$fot(X_237))]]) ).
cnf(refute_0_1943,plain,
( inverse(greatest_lower_bound(X_237,inverse(inverse(X)))) != multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X),X_237))),inverse(X))
| multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X),X_237))),inverse(X)) = inverse(greatest_lower_bound(X_237,inverse(inverse(X)))) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(inverse(greatest_lower_bound(X_237,inverse(inverse(X)))))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X),X_237))),inverse(X))))]]) ).
cnf(refute_0_1944,plain,
multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X),X_237))),inverse(X)) = inverse(greatest_lower_bound(X_237,inverse(inverse(X)))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_237,inverse(inverse(X)))),multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X),X_237))),inverse(X))) )],[refute_0_1942,refute_0_1943]) ).
cnf(refute_0_1945,plain,
( multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X),X_237))),inverse(X)) != inverse(greatest_lower_bound(X_237,inverse(inverse(X))))
| inverse(multiply(X,greatest_lower_bound(identity,multiply(inverse(X),X_237)))) != multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X),X_237))),inverse(X))
| inverse(multiply(X,greatest_lower_bound(identity,multiply(inverse(X),X_237)))) = inverse(greatest_lower_bound(X_237,inverse(inverse(X)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X,greatest_lower_bound(identity,multiply(inverse(X),X_237)))),multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X),X_237))),inverse(X))) ),[1],$fot(inverse(greatest_lower_bound(X_237,inverse(inverse(X)))))]]) ).
cnf(refute_0_1946,plain,
( inverse(multiply(X,greatest_lower_bound(identity,multiply(inverse(X),X_237)))) != multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X),X_237))),inverse(X))
| inverse(multiply(X,greatest_lower_bound(identity,multiply(inverse(X),X_237)))) = inverse(greatest_lower_bound(X_237,inverse(inverse(X)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X),X_237))),inverse(X)),inverse(greatest_lower_bound(X_237,inverse(inverse(X))))) )],[refute_0_1944,refute_0_1945]) ).
cnf(refute_0_1947,plain,
inverse(multiply(X,greatest_lower_bound(identity,multiply(inverse(X),X_237)))) = inverse(greatest_lower_bound(X_237,inverse(inverse(X)))),
inference(resolve,[$cnf( $equal(inverse(multiply(X,greatest_lower_bound(identity,multiply(inverse(X),X_237)))),multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X),X_237))),inverse(X))) )],[refute_0_1936,refute_0_1946]) ).
cnf(refute_0_1948,plain,
greatest_lower_bound(multiply(X,identity),X_237) = greatest_lower_bound(multiply(X,identity),X_237),
introduced(tautology,[refl,[$fot(greatest_lower_bound(multiply(X,identity),X_237))]]) ).
cnf(refute_0_1949,plain,
( multiply(X,identity) != X
| greatest_lower_bound(multiply(X,identity),X_237) != greatest_lower_bound(multiply(X,identity),X_237)
| greatest_lower_bound(multiply(X,identity),X_237) = greatest_lower_bound(X,X_237) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X,identity),X_237),greatest_lower_bound(multiply(X,identity),X_237)) ),[1,0],$fot(X)]]) ).
cnf(refute_0_1950,plain,
( multiply(X,identity) != X
| greatest_lower_bound(multiply(X,identity),X_237) = greatest_lower_bound(X,X_237) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,identity),X_237),greatest_lower_bound(multiply(X,identity),X_237)) )],[refute_0_1948,refute_0_1949]) ).
cnf(refute_0_1951,plain,
greatest_lower_bound(multiply(X,identity),X_237) = greatest_lower_bound(X,X_237),
inference(resolve,[$cnf( $equal(multiply(X,identity),X) )],[refute_0_564,refute_0_1950]) ).
cnf(refute_0_1952,plain,
multiply(X_67,greatest_lower_bound(X_68,multiply(inverse(X_67),X_46))) = greatest_lower_bound(multiply(X_67,X_68),multiply(X_67,multiply(inverse(X_67),X_46))),
inference(subst,[],[monotony_glb1:[bind(X,$fot(X_67)),bind(Y,$fot(X_68)),bind(Z,$fot(multiply(inverse(X_67),X_46)))]]) ).
cnf(refute_0_1953,plain,
multiply(multiply(X_44,inverse(X_44)),X_46) = multiply(X_44,multiply(inverse(X_44),X_46)),
inference(subst,[],[associativity:[bind(X,$fot(X_44)),bind(Y,$fot(inverse(X_44))),bind(Z,$fot(X_46))]]) ).
cnf(refute_0_1954,plain,
multiply(X_44,inverse(X_44)) = identity,
inference(subst,[],[refute_0_156:[bind(X,$fot(X_44))]]) ).
cnf(refute_0_1955,plain,
( multiply(X_44,inverse(X_44)) != identity
| multiply(multiply(X_44,inverse(X_44)),X_46) != multiply(X_44,multiply(inverse(X_44),X_46))
| multiply(identity,X_46) = multiply(X_44,multiply(inverse(X_44),X_46)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_44,inverse(X_44)),X_46),multiply(X_44,multiply(inverse(X_44),X_46))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_1956,plain,
( multiply(multiply(X_44,inverse(X_44)),X_46) != multiply(X_44,multiply(inverse(X_44),X_46))
| multiply(identity,X_46) = multiply(X_44,multiply(inverse(X_44),X_46)) ),
inference(resolve,[$cnf( $equal(multiply(X_44,inverse(X_44)),identity) )],[refute_0_1954,refute_0_1955]) ).
cnf(refute_0_1957,plain,
multiply(identity,X_46) = multiply(X_44,multiply(inverse(X_44),X_46)),
inference(resolve,[$cnf( $equal(multiply(multiply(X_44,inverse(X_44)),X_46),multiply(X_44,multiply(inverse(X_44),X_46))) )],[refute_0_1953,refute_0_1956]) ).
cnf(refute_0_1958,plain,
( multiply(identity,X_46) != X_46
| multiply(identity,X_46) != multiply(X_44,multiply(inverse(X_44),X_46))
| X_46 = multiply(X_44,multiply(inverse(X_44),X_46)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_46),multiply(X_44,multiply(inverse(X_44),X_46))) ),[0],$fot(X_46)]]) ).
cnf(refute_0_1959,plain,
( multiply(identity,X_46) != multiply(X_44,multiply(inverse(X_44),X_46))
| X_46 = multiply(X_44,multiply(inverse(X_44),X_46)) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_46),X_46) )],[refute_0_94,refute_0_1958]) ).
cnf(refute_0_1960,plain,
X_46 = multiply(X_44,multiply(inverse(X_44),X_46)),
inference(resolve,[$cnf( $equal(multiply(identity,X_46),multiply(X_44,multiply(inverse(X_44),X_46))) )],[refute_0_1957,refute_0_1959]) ).
cnf(refute_0_1961,plain,
X_46 = multiply(X_67,multiply(inverse(X_67),X_46)),
inference(subst,[],[refute_0_1960:[bind(X_44,$fot(X_67))]]) ).
cnf(refute_0_1962,plain,
( X_46 != multiply(X_67,multiply(inverse(X_67),X_46))
| multiply(X_67,multiply(inverse(X_67),X_46)) = X_46 ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(X_46)),bind(Y0,$fot(multiply(X_67,multiply(inverse(X_67),X_46))))]]) ).
cnf(refute_0_1963,plain,
multiply(X_67,multiply(inverse(X_67),X_46)) = X_46,
inference(resolve,[$cnf( $equal(X_46,multiply(X_67,multiply(inverse(X_67),X_46))) )],[refute_0_1961,refute_0_1962]) ).
cnf(refute_0_1964,plain,
( multiply(X_67,multiply(inverse(X_67),X_46)) != X_46
| multiply(X_67,greatest_lower_bound(X_68,multiply(inverse(X_67),X_46))) != greatest_lower_bound(multiply(X_67,X_68),multiply(X_67,multiply(inverse(X_67),X_46)))
| multiply(X_67,greatest_lower_bound(X_68,multiply(inverse(X_67),X_46))) = greatest_lower_bound(multiply(X_67,X_68),X_46) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_67,greatest_lower_bound(X_68,multiply(inverse(X_67),X_46))),greatest_lower_bound(multiply(X_67,X_68),multiply(X_67,multiply(inverse(X_67),X_46)))) ),[1,1],$fot(X_46)]]) ).
cnf(refute_0_1965,plain,
( multiply(X_67,greatest_lower_bound(X_68,multiply(inverse(X_67),X_46))) != greatest_lower_bound(multiply(X_67,X_68),multiply(X_67,multiply(inverse(X_67),X_46)))
| multiply(X_67,greatest_lower_bound(X_68,multiply(inverse(X_67),X_46))) = greatest_lower_bound(multiply(X_67,X_68),X_46) ),
inference(resolve,[$cnf( $equal(multiply(X_67,multiply(inverse(X_67),X_46)),X_46) )],[refute_0_1963,refute_0_1964]) ).
cnf(refute_0_1966,plain,
multiply(X_67,greatest_lower_bound(X_68,multiply(inverse(X_67),X_46))) = greatest_lower_bound(multiply(X_67,X_68),X_46),
inference(resolve,[$cnf( $equal(multiply(X_67,greatest_lower_bound(X_68,multiply(inverse(X_67),X_46))),greatest_lower_bound(multiply(X_67,X_68),multiply(X_67,multiply(inverse(X_67),X_46)))) )],[refute_0_1952,refute_0_1965]) ).
cnf(refute_0_1967,plain,
multiply(X,greatest_lower_bound(identity,multiply(inverse(X),X_237))) = greatest_lower_bound(multiply(X,identity),X_237),
inference(subst,[],[refute_0_1966:[bind(X_46,$fot(X_237)),bind(X_67,$fot(X)),bind(X_68,$fot(identity))]]) ).
cnf(refute_0_1968,plain,
( multiply(X,greatest_lower_bound(identity,multiply(inverse(X),X_237))) != greatest_lower_bound(multiply(X,identity),X_237)
| greatest_lower_bound(multiply(X,identity),X_237) != greatest_lower_bound(X,X_237)
| multiply(X,greatest_lower_bound(identity,multiply(inverse(X),X_237))) = greatest_lower_bound(X,X_237) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(multiply(X,greatest_lower_bound(identity,multiply(inverse(X),X_237))))),bind(Y0,$fot(greatest_lower_bound(multiply(X,identity),X_237))),bind(Z0,$fot(greatest_lower_bound(X,X_237)))]]) ).
cnf(refute_0_1969,plain,
( greatest_lower_bound(multiply(X,identity),X_237) != greatest_lower_bound(X,X_237)
| multiply(X,greatest_lower_bound(identity,multiply(inverse(X),X_237))) = greatest_lower_bound(X,X_237) ),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(identity,multiply(inverse(X),X_237))),greatest_lower_bound(multiply(X,identity),X_237)) )],[refute_0_1967,refute_0_1968]) ).
cnf(refute_0_1970,plain,
multiply(X,greatest_lower_bound(identity,multiply(inverse(X),X_237))) = greatest_lower_bound(X,X_237),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,identity),X_237),greatest_lower_bound(X,X_237)) )],[refute_0_1951,refute_0_1969]) ).
cnf(refute_0_1971,plain,
inverse(multiply(X,greatest_lower_bound(identity,multiply(inverse(X),X_237)))) = inverse(multiply(X,greatest_lower_bound(identity,multiply(inverse(X),X_237)))),
introduced(tautology,[refl,[$fot(inverse(multiply(X,greatest_lower_bound(identity,multiply(inverse(X),X_237)))))]]) ).
cnf(refute_0_1972,plain,
( multiply(X,greatest_lower_bound(identity,multiply(inverse(X),X_237))) != greatest_lower_bound(X,X_237)
| inverse(multiply(X,greatest_lower_bound(identity,multiply(inverse(X),X_237)))) != inverse(multiply(X,greatest_lower_bound(identity,multiply(inverse(X),X_237))))
| inverse(multiply(X,greatest_lower_bound(identity,multiply(inverse(X),X_237)))) = inverse(greatest_lower_bound(X,X_237)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X,greatest_lower_bound(identity,multiply(inverse(X),X_237)))),inverse(multiply(X,greatest_lower_bound(identity,multiply(inverse(X),X_237))))) ),[1,0],$fot(greatest_lower_bound(X,X_237))]]) ).
cnf(refute_0_1973,plain,
( multiply(X,greatest_lower_bound(identity,multiply(inverse(X),X_237))) != greatest_lower_bound(X,X_237)
| inverse(multiply(X,greatest_lower_bound(identity,multiply(inverse(X),X_237)))) = inverse(greatest_lower_bound(X,X_237)) ),
inference(resolve,[$cnf( $equal(inverse(multiply(X,greatest_lower_bound(identity,multiply(inverse(X),X_237)))),inverse(multiply(X,greatest_lower_bound(identity,multiply(inverse(X),X_237))))) )],[refute_0_1971,refute_0_1972]) ).
cnf(refute_0_1974,plain,
inverse(multiply(X,greatest_lower_bound(identity,multiply(inverse(X),X_237)))) = inverse(greatest_lower_bound(X,X_237)),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(identity,multiply(inverse(X),X_237))),greatest_lower_bound(X,X_237)) )],[refute_0_1970,refute_0_1973]) ).
cnf(refute_0_1975,plain,
( inverse(multiply(X,greatest_lower_bound(identity,multiply(inverse(X),X_237)))) != inverse(greatest_lower_bound(X,X_237))
| inverse(multiply(X,greatest_lower_bound(identity,multiply(inverse(X),X_237)))) != inverse(greatest_lower_bound(X_237,inverse(inverse(X))))
| inverse(greatest_lower_bound(X,X_237)) = inverse(greatest_lower_bound(X_237,inverse(inverse(X)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X,greatest_lower_bound(identity,multiply(inverse(X),X_237)))),inverse(greatest_lower_bound(X_237,inverse(inverse(X))))) ),[0],$fot(inverse(greatest_lower_bound(X,X_237)))]]) ).
cnf(refute_0_1976,plain,
( inverse(multiply(X,greatest_lower_bound(identity,multiply(inverse(X),X_237)))) != inverse(greatest_lower_bound(X_237,inverse(inverse(X))))
| inverse(greatest_lower_bound(X,X_237)) = inverse(greatest_lower_bound(X_237,inverse(inverse(X)))) ),
inference(resolve,[$cnf( $equal(inverse(multiply(X,greatest_lower_bound(identity,multiply(inverse(X),X_237)))),inverse(greatest_lower_bound(X,X_237))) )],[refute_0_1974,refute_0_1975]) ).
cnf(refute_0_1977,plain,
greatest_lower_bound(X_237,inverse(inverse(X))) = greatest_lower_bound(X_237,inverse(inverse(X))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X_237,inverse(inverse(X))))]]) ).
cnf(refute_0_1978,plain,
( greatest_lower_bound(X_237,inverse(inverse(X))) != greatest_lower_bound(X_237,inverse(inverse(X)))
| inverse(inverse(X)) != X
| greatest_lower_bound(X_237,inverse(inverse(X))) = greatest_lower_bound(X_237,X) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_237,inverse(inverse(X))),greatest_lower_bound(X_237,inverse(inverse(X)))) ),[1,1],$fot(X)]]) ).
cnf(refute_0_1979,plain,
( inverse(inverse(X)) != X
| greatest_lower_bound(X_237,inverse(inverse(X))) = greatest_lower_bound(X_237,X) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_237,inverse(inverse(X))),greatest_lower_bound(X_237,inverse(inverse(X)))) )],[refute_0_1977,refute_0_1978]) ).
cnf(refute_0_1980,plain,
greatest_lower_bound(X_237,inverse(inverse(X))) = greatest_lower_bound(X_237,X),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p19_2,refute_0_1979]) ).
cnf(refute_0_1981,plain,
inverse(greatest_lower_bound(X_237,inverse(inverse(X)))) = inverse(greatest_lower_bound(X_237,inverse(inverse(X)))),
introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(X_237,inverse(inverse(X)))))]]) ).
cnf(refute_0_1982,plain,
( greatest_lower_bound(X_237,inverse(inverse(X))) != greatest_lower_bound(X_237,X)
| inverse(greatest_lower_bound(X_237,inverse(inverse(X)))) != inverse(greatest_lower_bound(X_237,inverse(inverse(X))))
| inverse(greatest_lower_bound(X_237,inverse(inverse(X)))) = inverse(greatest_lower_bound(X_237,X)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X_237,inverse(inverse(X)))),inverse(greatest_lower_bound(X_237,inverse(inverse(X))))) ),[1,0],$fot(greatest_lower_bound(X_237,X))]]) ).
cnf(refute_0_1983,plain,
( greatest_lower_bound(X_237,inverse(inverse(X))) != greatest_lower_bound(X_237,X)
| inverse(greatest_lower_bound(X_237,inverse(inverse(X)))) = inverse(greatest_lower_bound(X_237,X)) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_237,inverse(inverse(X)))),inverse(greatest_lower_bound(X_237,inverse(inverse(X))))) )],[refute_0_1981,refute_0_1982]) ).
cnf(refute_0_1984,plain,
inverse(greatest_lower_bound(X_237,inverse(inverse(X)))) = inverse(greatest_lower_bound(X_237,X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_237,inverse(inverse(X))),greatest_lower_bound(X_237,X)) )],[refute_0_1980,refute_0_1983]) ).
cnf(refute_0_1985,plain,
( inverse(greatest_lower_bound(X,X_237)) != inverse(greatest_lower_bound(X_237,inverse(inverse(X))))
| inverse(greatest_lower_bound(X_237,inverse(inverse(X)))) != inverse(greatest_lower_bound(X_237,X))
| inverse(greatest_lower_bound(X,X_237)) = inverse(greatest_lower_bound(X_237,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(inverse(greatest_lower_bound(X,X_237)),inverse(greatest_lower_bound(X_237,X))) ),[0],$fot(inverse(greatest_lower_bound(X_237,inverse(inverse(X)))))]]) ).
cnf(refute_0_1986,plain,
( inverse(greatest_lower_bound(X,X_237)) != inverse(greatest_lower_bound(X_237,inverse(inverse(X))))
| inverse(greatest_lower_bound(X,X_237)) = inverse(greatest_lower_bound(X_237,X)) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_237,inverse(inverse(X)))),inverse(greatest_lower_bound(X_237,X))) )],[refute_0_1984,refute_0_1985]) ).
cnf(refute_0_1987,plain,
( inverse(multiply(X,greatest_lower_bound(identity,multiply(inverse(X),X_237)))) != inverse(greatest_lower_bound(X_237,inverse(inverse(X))))
| inverse(greatest_lower_bound(X,X_237)) = inverse(greatest_lower_bound(X_237,X)) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X,X_237)),inverse(greatest_lower_bound(X_237,inverse(inverse(X))))) )],[refute_0_1976,refute_0_1986]) ).
cnf(refute_0_1988,plain,
inverse(greatest_lower_bound(X,X_237)) = inverse(greatest_lower_bound(X_237,X)),
inference(resolve,[$cnf( $equal(inverse(multiply(X,greatest_lower_bound(identity,multiply(inverse(X),X_237)))),inverse(greatest_lower_bound(X_237,inverse(inverse(X))))) )],[refute_0_1947,refute_0_1987]) ).
cnf(refute_0_1989,plain,
( inverse(greatest_lower_bound(X,X_237)) != inverse(greatest_lower_bound(X_237,X))
| inverse(greatest_lower_bound(X_237,X)) = inverse(greatest_lower_bound(X,X_237)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(inverse(greatest_lower_bound(X,X_237)))),bind(Y0,$fot(inverse(greatest_lower_bound(X_237,X))))]]) ).
cnf(refute_0_1990,plain,
inverse(greatest_lower_bound(X_237,X)) = inverse(greatest_lower_bound(X,X_237)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X,X_237)),inverse(greatest_lower_bound(X_237,X))) )],[refute_0_1988,refute_0_1989]) ).
cnf(refute_0_1991,plain,
inverse(greatest_lower_bound(multiply(inverse(X),X_71),identity)) = inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71))),
inference(subst,[],[refute_0_1990:[bind(X,$fot(identity)),bind(X_237,$fot(multiply(inverse(X),X_71)))]]) ).
cnf(refute_0_1992,plain,
least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_95),inverse(greatest_lower_bound(identity,X_95)))) = least_upper_bound(greatest_lower_bound(identity,X_95),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_95)))),
inference(subst,[],[refute_0_1820:[bind(X_84,$fot(greatest_lower_bound(identity,X_95)))]]) ).
cnf(refute_0_1993,plain,
inverse(greatest_lower_bound(X_95,identity)) = multiply(inverse(X_95),inverse(multiply(greatest_lower_bound(X_95,identity),inverse(X_95)))),
inference(subst,[],[refute_0_117:[bind(X,$fot(greatest_lower_bound(X_95,identity))),bind(Y,$fot(inverse(X_95)))]]) ).
cnf(refute_0_1994,plain,
( multiply(greatest_lower_bound(X_95,identity),inverse(X_95)) != greatest_lower_bound(identity,inverse(X_95))
| inverse(greatest_lower_bound(X_95,identity)) != multiply(inverse(X_95),inverse(multiply(greatest_lower_bound(X_95,identity),inverse(X_95))))
| inverse(greatest_lower_bound(X_95,identity)) = multiply(inverse(X_95),inverse(greatest_lower_bound(identity,inverse(X_95)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X_95,identity)),multiply(inverse(X_95),inverse(multiply(greatest_lower_bound(X_95,identity),inverse(X_95))))) ),[1,1,0],$fot(greatest_lower_bound(identity,inverse(X_95)))]]) ).
cnf(refute_0_1995,plain,
( inverse(greatest_lower_bound(X_95,identity)) != multiply(inverse(X_95),inverse(multiply(greatest_lower_bound(X_95,identity),inverse(X_95))))
| inverse(greatest_lower_bound(X_95,identity)) = multiply(inverse(X_95),inverse(greatest_lower_bound(identity,inverse(X_95)))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_95,identity),inverse(X_95)),greatest_lower_bound(identity,inverse(X_95))) )],[refute_0_455,refute_0_1994]) ).
cnf(refute_0_1996,plain,
inverse(greatest_lower_bound(X_95,identity)) = multiply(inverse(X_95),inverse(greatest_lower_bound(identity,inverse(X_95)))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_95,identity)),multiply(inverse(X_95),inverse(multiply(greatest_lower_bound(X_95,identity),inverse(X_95))))) )],[refute_0_1993,refute_0_1995]) ).
cnf(refute_0_1997,plain,
inverse(inverse(X_95)) = X_95,
inference(subst,[],[p19_2:[bind(X,$fot(X_95))]]) ).
cnf(refute_0_1998,plain,
greatest_lower_bound(identity,inverse(inverse(X_95))) = greatest_lower_bound(identity,inverse(inverse(X_95))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,inverse(inverse(X_95))))]]) ).
cnf(refute_0_1999,plain,
( greatest_lower_bound(identity,inverse(inverse(X_95))) != greatest_lower_bound(identity,inverse(inverse(X_95)))
| inverse(inverse(X_95)) != X_95
| greatest_lower_bound(identity,inverse(inverse(X_95))) = greatest_lower_bound(identity,X_95) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,inverse(inverse(X_95))),greatest_lower_bound(identity,inverse(inverse(X_95)))) ),[1,1],$fot(X_95)]]) ).
cnf(refute_0_2000,plain,
( inverse(inverse(X_95)) != X_95
| greatest_lower_bound(identity,inverse(inverse(X_95))) = greatest_lower_bound(identity,X_95) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(inverse(X_95))),greatest_lower_bound(identity,inverse(inverse(X_95)))) )],[refute_0_1998,refute_0_1999]) ).
cnf(refute_0_2001,plain,
greatest_lower_bound(identity,inverse(inverse(X_95))) = greatest_lower_bound(identity,X_95),
inference(resolve,[$cnf( $equal(inverse(inverse(X_95)),X_95) )],[refute_0_1997,refute_0_2000]) ).
cnf(refute_0_2002,plain,
multiply(identity,greatest_lower_bound(identity,inverse(inverse(X_95)))) = greatest_lower_bound(identity,inverse(inverse(X_95))),
inference(subst,[],[left_identity:[bind(X,$fot(greatest_lower_bound(identity,inverse(inverse(X_95)))))]]) ).
cnf(refute_0_2003,plain,
greatest_lower_bound(multiply(X_67,X_69),multiply(X_67,X_68)) = greatest_lower_bound(multiply(X_67,X_68),multiply(X_67,X_69)),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(multiply(X_67,X_69))),bind(Y,$fot(multiply(X_67,X_68)))]]) ).
cnf(refute_0_2004,plain,
multiply(X_67,greatest_lower_bound(X_68,X_69)) = greatest_lower_bound(multiply(X_67,X_68),multiply(X_67,X_69)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(X_67)),bind(Y,$fot(X_68)),bind(Z,$fot(X_69))]]) ).
cnf(refute_0_2005,plain,
( multiply(X_67,greatest_lower_bound(X_68,X_69)) != greatest_lower_bound(multiply(X_67,X_68),multiply(X_67,X_69))
| greatest_lower_bound(multiply(X_67,X_68),multiply(X_67,X_69)) = multiply(X_67,greatest_lower_bound(X_68,X_69)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(multiply(X_67,greatest_lower_bound(X_68,X_69)))),bind(Y0,$fot(greatest_lower_bound(multiply(X_67,X_68),multiply(X_67,X_69))))]]) ).
cnf(refute_0_2006,plain,
greatest_lower_bound(multiply(X_67,X_68),multiply(X_67,X_69)) = multiply(X_67,greatest_lower_bound(X_68,X_69)),
inference(resolve,[$cnf( $equal(multiply(X_67,greatest_lower_bound(X_68,X_69)),greatest_lower_bound(multiply(X_67,X_68),multiply(X_67,X_69))) )],[refute_0_2004,refute_0_2005]) ).
cnf(refute_0_2007,plain,
( greatest_lower_bound(multiply(X_67,X_68),multiply(X_67,X_69)) != multiply(X_67,greatest_lower_bound(X_68,X_69))
| greatest_lower_bound(multiply(X_67,X_69),multiply(X_67,X_68)) != greatest_lower_bound(multiply(X_67,X_68),multiply(X_67,X_69))
| greatest_lower_bound(multiply(X_67,X_69),multiply(X_67,X_68)) = multiply(X_67,greatest_lower_bound(X_68,X_69)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_67,X_69),multiply(X_67,X_68)),greatest_lower_bound(multiply(X_67,X_68),multiply(X_67,X_69))) ),[1],$fot(multiply(X_67,greatest_lower_bound(X_68,X_69)))]]) ).
cnf(refute_0_2008,plain,
( greatest_lower_bound(multiply(X_67,X_69),multiply(X_67,X_68)) != greatest_lower_bound(multiply(X_67,X_68),multiply(X_67,X_69))
| greatest_lower_bound(multiply(X_67,X_69),multiply(X_67,X_68)) = multiply(X_67,greatest_lower_bound(X_68,X_69)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_67,X_68),multiply(X_67,X_69)),multiply(X_67,greatest_lower_bound(X_68,X_69))) )],[refute_0_2006,refute_0_2007]) ).
cnf(refute_0_2009,plain,
greatest_lower_bound(multiply(X_67,X_69),multiply(X_67,X_68)) = multiply(X_67,greatest_lower_bound(X_68,X_69)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_67,X_69),multiply(X_67,X_68)),greatest_lower_bound(multiply(X_67,X_68),multiply(X_67,X_69))) )],[refute_0_2003,refute_0_2008]) ).
cnf(refute_0_2010,plain,
greatest_lower_bound(multiply(X_67,X_69),multiply(X_67,X_68)) = multiply(X_67,greatest_lower_bound(X_69,X_68)),
inference(subst,[],[refute_0_237:[bind(X,$fot(X_67)),bind(Y,$fot(X_69)),bind(Z,$fot(X_68))]]) ).
cnf(refute_0_2011,plain,
( greatest_lower_bound(multiply(X_67,X_69),multiply(X_67,X_68)) != multiply(X_67,greatest_lower_bound(X_68,X_69))
| greatest_lower_bound(multiply(X_67,X_69),multiply(X_67,X_68)) != multiply(X_67,greatest_lower_bound(X_69,X_68))
| multiply(X_67,greatest_lower_bound(X_69,X_68)) = multiply(X_67,greatest_lower_bound(X_68,X_69)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_67,X_69),multiply(X_67,X_68)),multiply(X_67,greatest_lower_bound(X_68,X_69))) ),[0],$fot(multiply(X_67,greatest_lower_bound(X_69,X_68)))]]) ).
cnf(refute_0_2012,plain,
( greatest_lower_bound(multiply(X_67,X_69),multiply(X_67,X_68)) != multiply(X_67,greatest_lower_bound(X_68,X_69))
| multiply(X_67,greatest_lower_bound(X_69,X_68)) = multiply(X_67,greatest_lower_bound(X_68,X_69)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_67,X_69),multiply(X_67,X_68)),multiply(X_67,greatest_lower_bound(X_69,X_68))) )],[refute_0_2010,refute_0_2011]) ).
cnf(refute_0_2013,plain,
multiply(X_67,greatest_lower_bound(X_69,X_68)) = multiply(X_67,greatest_lower_bound(X_68,X_69)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_67,X_69),multiply(X_67,X_68)),multiply(X_67,greatest_lower_bound(X_68,X_69))) )],[refute_0_2009,refute_0_2012]) ).
cnf(refute_0_2014,plain,
( multiply(X_67,greatest_lower_bound(X_69,X_68)) != multiply(X_67,greatest_lower_bound(X_68,X_69))
| multiply(X_67,greatest_lower_bound(X_68,X_69)) = multiply(X_67,greatest_lower_bound(X_69,X_68)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(multiply(X_67,greatest_lower_bound(X_69,X_68)))),bind(Y0,$fot(multiply(X_67,greatest_lower_bound(X_68,X_69))))]]) ).
cnf(refute_0_2015,plain,
multiply(X_67,greatest_lower_bound(X_68,X_69)) = multiply(X_67,greatest_lower_bound(X_69,X_68)),
inference(resolve,[$cnf( $equal(multiply(X_67,greatest_lower_bound(X_69,X_68)),multiply(X_67,greatest_lower_bound(X_68,X_69))) )],[refute_0_2013,refute_0_2014]) ).
cnf(refute_0_2016,plain,
multiply(identity,greatest_lower_bound(inverse(inverse(X_95)),identity)) = multiply(identity,greatest_lower_bound(identity,inverse(inverse(X_95)))),
inference(subst,[],[refute_0_2015:[bind(X_67,$fot(identity)),bind(X_68,$fot(inverse(inverse(X_95)))),bind(X_69,$fot(identity))]]) ).
cnf(refute_0_2017,plain,
( multiply(identity,greatest_lower_bound(identity,inverse(inverse(X_95)))) != greatest_lower_bound(identity,inverse(inverse(X_95)))
| multiply(identity,greatest_lower_bound(inverse(inverse(X_95)),identity)) != multiply(identity,greatest_lower_bound(identity,inverse(inverse(X_95))))
| multiply(identity,greatest_lower_bound(inverse(inverse(X_95)),identity)) = greatest_lower_bound(identity,inverse(inverse(X_95))) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(multiply(identity,greatest_lower_bound(inverse(inverse(X_95)),identity)))),bind(Y0,$fot(multiply(identity,greatest_lower_bound(identity,inverse(inverse(X_95)))))),bind(Z0,$fot(greatest_lower_bound(identity,inverse(inverse(X_95)))))]]) ).
cnf(refute_0_2018,plain,
( multiply(identity,greatest_lower_bound(identity,inverse(inverse(X_95)))) != greatest_lower_bound(identity,inverse(inverse(X_95)))
| multiply(identity,greatest_lower_bound(inverse(inverse(X_95)),identity)) = greatest_lower_bound(identity,inverse(inverse(X_95))) ),
inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(inverse(inverse(X_95)),identity)),multiply(identity,greatest_lower_bound(identity,inverse(inverse(X_95))))) )],[refute_0_2016,refute_0_2017]) ).
cnf(refute_0_2019,plain,
multiply(identity,greatest_lower_bound(inverse(inverse(X_95)),identity)) = greatest_lower_bound(identity,inverse(inverse(X_95))),
inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(identity,inverse(inverse(X_95)))),greatest_lower_bound(identity,inverse(inverse(X_95)))) )],[refute_0_2002,refute_0_2018]) ).
cnf(refute_0_2020,plain,
greatest_lower_bound(identity,multiply(identity,inverse(inverse(X_95)))) = multiply(identity,greatest_lower_bound(inverse(inverse(X_95)),identity)),
inference(subst,[],[refute_0_342:[bind(X_67,$fot(identity)),bind(X_68,$fot(inverse(inverse(X_95))))]]) ).
cnf(refute_0_2021,plain,
( multiply(identity,greatest_lower_bound(inverse(inverse(X_95)),identity)) != greatest_lower_bound(identity,inverse(inverse(X_95)))
| greatest_lower_bound(identity,multiply(identity,inverse(inverse(X_95)))) != multiply(identity,greatest_lower_bound(inverse(inverse(X_95)),identity))
| greatest_lower_bound(identity,multiply(identity,inverse(inverse(X_95)))) = greatest_lower_bound(identity,inverse(inverse(X_95))) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(greatest_lower_bound(identity,multiply(identity,inverse(inverse(X_95)))))),bind(Y0,$fot(multiply(identity,greatest_lower_bound(inverse(inverse(X_95)),identity)))),bind(Z0,$fot(greatest_lower_bound(identity,inverse(inverse(X_95)))))]]) ).
cnf(refute_0_2022,plain,
( multiply(identity,greatest_lower_bound(inverse(inverse(X_95)),identity)) != greatest_lower_bound(identity,inverse(inverse(X_95)))
| greatest_lower_bound(identity,multiply(identity,inverse(inverse(X_95)))) = greatest_lower_bound(identity,inverse(inverse(X_95))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(identity,inverse(inverse(X_95)))),multiply(identity,greatest_lower_bound(inverse(inverse(X_95)),identity))) )],[refute_0_2020,refute_0_2021]) ).
cnf(refute_0_2023,plain,
greatest_lower_bound(identity,multiply(identity,inverse(inverse(X_95)))) = greatest_lower_bound(identity,inverse(inverse(X_95))),
inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(inverse(inverse(X_95)),identity)),greatest_lower_bound(identity,inverse(inverse(X_95)))) )],[refute_0_2019,refute_0_2022]) ).
cnf(refute_0_2024,plain,
( greatest_lower_bound(identity,multiply(identity,inverse(inverse(X_95)))) != greatest_lower_bound(identity,inverse(inverse(X_95)))
| greatest_lower_bound(identity,inverse(inverse(X_95))) != greatest_lower_bound(identity,X_95)
| greatest_lower_bound(identity,multiply(identity,inverse(inverse(X_95)))) = greatest_lower_bound(identity,X_95) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(greatest_lower_bound(identity,multiply(identity,inverse(inverse(X_95)))))),bind(Y0,$fot(greatest_lower_bound(identity,inverse(inverse(X_95))))),bind(Z0,$fot(greatest_lower_bound(identity,X_95)))]]) ).
cnf(refute_0_2025,plain,
( greatest_lower_bound(identity,inverse(inverse(X_95))) != greatest_lower_bound(identity,X_95)
| greatest_lower_bound(identity,multiply(identity,inverse(inverse(X_95)))) = greatest_lower_bound(identity,X_95) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(identity,inverse(inverse(X_95)))),greatest_lower_bound(identity,inverse(inverse(X_95)))) )],[refute_0_2023,refute_0_2024]) ).
cnf(refute_0_2026,plain,
greatest_lower_bound(identity,multiply(identity,inverse(inverse(X_95)))) = greatest_lower_bound(identity,X_95),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(inverse(X_95))),greatest_lower_bound(identity,X_95)) )],[refute_0_2001,refute_0_2025]) ).
cnf(refute_0_2027,plain,
inverse(greatest_lower_bound(identity,multiply(identity,inverse(inverse(X_95))))) = inverse(greatest_lower_bound(identity,multiply(identity,inverse(inverse(X_95))))),
introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(identity,multiply(identity,inverse(inverse(X_95))))))]]) ).
cnf(refute_0_2028,plain,
( greatest_lower_bound(identity,multiply(identity,inverse(inverse(X_95)))) != greatest_lower_bound(identity,X_95)
| inverse(greatest_lower_bound(identity,multiply(identity,inverse(inverse(X_95))))) != inverse(greatest_lower_bound(identity,multiply(identity,inverse(inverse(X_95)))))
| inverse(greatest_lower_bound(identity,multiply(identity,inverse(inverse(X_95))))) = inverse(greatest_lower_bound(identity,X_95)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(identity,inverse(inverse(X_95))))),inverse(greatest_lower_bound(identity,multiply(identity,inverse(inverse(X_95)))))) ),[1,0],$fot(greatest_lower_bound(identity,X_95))]]) ).
cnf(refute_0_2029,plain,
( greatest_lower_bound(identity,multiply(identity,inverse(inverse(X_95)))) != greatest_lower_bound(identity,X_95)
| inverse(greatest_lower_bound(identity,multiply(identity,inverse(inverse(X_95))))) = inverse(greatest_lower_bound(identity,X_95)) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(identity,inverse(inverse(X_95))))),inverse(greatest_lower_bound(identity,multiply(identity,inverse(inverse(X_95)))))) )],[refute_0_2027,refute_0_2028]) ).
cnf(refute_0_2030,plain,
inverse(greatest_lower_bound(identity,multiply(identity,inverse(inverse(X_95))))) = inverse(greatest_lower_bound(identity,X_95)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(identity,inverse(inverse(X_95)))),greatest_lower_bound(identity,X_95)) )],[refute_0_2026,refute_0_2029]) ).
cnf(refute_0_2031,plain,
( inverse(greatest_lower_bound(identity,multiply(X_92,inverse(X)))) != multiply(X,inverse(greatest_lower_bound(X_92,X)))
| multiply(X,inverse(greatest_lower_bound(X_92,X))) = inverse(greatest_lower_bound(identity,multiply(X_92,inverse(X)))) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(inverse(greatest_lower_bound(identity,multiply(X_92,inverse(X)))))),bind(Y0,$fot(multiply(X,inverse(greatest_lower_bound(X_92,X)))))]]) ).
cnf(refute_0_2032,plain,
multiply(X,inverse(greatest_lower_bound(X_92,X))) = inverse(greatest_lower_bound(identity,multiply(X_92,inverse(X)))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(X_92,inverse(X)))),multiply(X,inverse(greatest_lower_bound(X_92,X)))) )],[refute_0_1516,refute_0_2031]) ).
cnf(refute_0_2033,plain,
multiply(inverse(X_95),inverse(greatest_lower_bound(identity,inverse(X_95)))) = inverse(greatest_lower_bound(identity,multiply(identity,inverse(inverse(X_95))))),
inference(subst,[],[refute_0_2032:[bind(X,$fot(inverse(X_95))),bind(X_92,$fot(identity))]]) ).
cnf(refute_0_2034,plain,
( multiply(inverse(X_95),inverse(greatest_lower_bound(identity,inverse(X_95)))) != inverse(greatest_lower_bound(identity,multiply(identity,inverse(inverse(X_95)))))
| inverse(greatest_lower_bound(identity,multiply(identity,inverse(inverse(X_95))))) != inverse(greatest_lower_bound(identity,X_95))
| multiply(inverse(X_95),inverse(greatest_lower_bound(identity,inverse(X_95)))) = inverse(greatest_lower_bound(identity,X_95)) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(multiply(inverse(X_95),inverse(greatest_lower_bound(identity,inverse(X_95)))))),bind(Y0,$fot(inverse(greatest_lower_bound(identity,multiply(identity,inverse(inverse(X_95))))))),bind(Z0,$fot(inverse(greatest_lower_bound(identity,X_95))))]]) ).
cnf(refute_0_2035,plain,
( inverse(greatest_lower_bound(identity,multiply(identity,inverse(inverse(X_95))))) != inverse(greatest_lower_bound(identity,X_95))
| multiply(inverse(X_95),inverse(greatest_lower_bound(identity,inverse(X_95)))) = inverse(greatest_lower_bound(identity,X_95)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_95),inverse(greatest_lower_bound(identity,inverse(X_95)))),inverse(greatest_lower_bound(identity,multiply(identity,inverse(inverse(X_95)))))) )],[refute_0_2033,refute_0_2034]) ).
cnf(refute_0_2036,plain,
multiply(inverse(X_95),inverse(greatest_lower_bound(identity,inverse(X_95)))) = inverse(greatest_lower_bound(identity,X_95)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(identity,inverse(inverse(X_95))))),inverse(greatest_lower_bound(identity,X_95))) )],[refute_0_2030,refute_0_2035]) ).
cnf(refute_0_2037,plain,
( multiply(inverse(X_95),inverse(greatest_lower_bound(identity,inverse(X_95)))) != inverse(greatest_lower_bound(identity,X_95))
| inverse(greatest_lower_bound(X_95,identity)) != multiply(inverse(X_95),inverse(greatest_lower_bound(identity,inverse(X_95))))
| inverse(greatest_lower_bound(X_95,identity)) = inverse(greatest_lower_bound(identity,X_95)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X_95,identity)),multiply(inverse(X_95),inverse(greatest_lower_bound(identity,inverse(X_95))))) ),[1],$fot(inverse(greatest_lower_bound(identity,X_95)))]]) ).
cnf(refute_0_2038,plain,
( inverse(greatest_lower_bound(X_95,identity)) != multiply(inverse(X_95),inverse(greatest_lower_bound(identity,inverse(X_95))))
| inverse(greatest_lower_bound(X_95,identity)) = inverse(greatest_lower_bound(identity,X_95)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_95),inverse(greatest_lower_bound(identity,inverse(X_95)))),inverse(greatest_lower_bound(identity,X_95))) )],[refute_0_2036,refute_0_2037]) ).
cnf(refute_0_2039,plain,
inverse(greatest_lower_bound(X_95,identity)) = inverse(greatest_lower_bound(identity,X_95)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_95,identity)),multiply(inverse(X_95),inverse(greatest_lower_bound(identity,inverse(X_95))))) )],[refute_0_1996,refute_0_2038]) ).
cnf(refute_0_2040,plain,
( inverse(greatest_lower_bound(X_95,identity)) != inverse(greatest_lower_bound(identity,X_95))
| inverse(greatest_lower_bound(identity,X_95)) = inverse(greatest_lower_bound(X_95,identity)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(inverse(greatest_lower_bound(X_95,identity)))),bind(Y0,$fot(inverse(greatest_lower_bound(identity,X_95))))]]) ).
cnf(refute_0_2041,plain,
inverse(greatest_lower_bound(identity,X_95)) = inverse(greatest_lower_bound(X_95,identity)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_95,identity)),inverse(greatest_lower_bound(identity,X_95))) )],[refute_0_2039,refute_0_2040]) ).
cnf(refute_0_2042,plain,
( inverse(greatest_lower_bound(identity,X_95)) != inverse(greatest_lower_bound(X_95,identity))
| least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_95),inverse(greatest_lower_bound(identity,X_95)))) != least_upper_bound(greatest_lower_bound(identity,X_95),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_95))))
| least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_95),inverse(greatest_lower_bound(X_95,identity)))) = least_upper_bound(greatest_lower_bound(identity,X_95),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_95)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_95),inverse(greatest_lower_bound(identity,X_95)))),least_upper_bound(greatest_lower_bound(identity,X_95),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_95))))) ),[0,1,1],$fot(inverse(greatest_lower_bound(X_95,identity)))]]) ).
cnf(refute_0_2043,plain,
( least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_95),inverse(greatest_lower_bound(identity,X_95)))) != least_upper_bound(greatest_lower_bound(identity,X_95),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_95))))
| least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_95),inverse(greatest_lower_bound(X_95,identity)))) = least_upper_bound(greatest_lower_bound(identity,X_95),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_95)))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,X_95)),inverse(greatest_lower_bound(X_95,identity))) )],[refute_0_2041,refute_0_2042]) ).
cnf(refute_0_2044,plain,
least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_95),inverse(greatest_lower_bound(X_95,identity)))) = least_upper_bound(greatest_lower_bound(identity,X_95),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_95)))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_95),inverse(greatest_lower_bound(identity,X_95)))),least_upper_bound(greatest_lower_bound(identity,X_95),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_95))))) )],[refute_0_1992,refute_0_2043]) ).
cnf(refute_0_2045,plain,
multiply(inverse(greatest_lower_bound(X_15,identity)),least_upper_bound(identity,greatest_lower_bound(X_15,identity))) = least_upper_bound(identity,inverse(greatest_lower_bound(X_15,identity))),
inference(subst,[],[refute_0_134:[bind(X_63,$fot(greatest_lower_bound(X_15,identity)))]]) ).
cnf(refute_0_2046,plain,
least_upper_bound(identity,greatest_lower_bound(X_15,identity)) = identity,
inference(subst,[],[refute_0_270:[bind(X_14,$fot(identity))]]) ).
cnf(refute_0_2047,plain,
( multiply(inverse(greatest_lower_bound(X_15,identity)),least_upper_bound(identity,greatest_lower_bound(X_15,identity))) != least_upper_bound(identity,inverse(greatest_lower_bound(X_15,identity)))
| least_upper_bound(identity,greatest_lower_bound(X_15,identity)) != identity
| multiply(inverse(greatest_lower_bound(X_15,identity)),identity) = least_upper_bound(identity,inverse(greatest_lower_bound(X_15,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_15,identity)),least_upper_bound(identity,greatest_lower_bound(X_15,identity))),least_upper_bound(identity,inverse(greatest_lower_bound(X_15,identity)))) ),[0,1],$fot(identity)]]) ).
cnf(refute_0_2048,plain,
( multiply(inverse(greatest_lower_bound(X_15,identity)),least_upper_bound(identity,greatest_lower_bound(X_15,identity))) != least_upper_bound(identity,inverse(greatest_lower_bound(X_15,identity)))
| multiply(inverse(greatest_lower_bound(X_15,identity)),identity) = least_upper_bound(identity,inverse(greatest_lower_bound(X_15,identity))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(X_15,identity)),identity) )],[refute_0_2046,refute_0_2047]) ).
cnf(refute_0_2049,plain,
multiply(inverse(greatest_lower_bound(X_15,identity)),identity) = least_upper_bound(identity,inverse(greatest_lower_bound(X_15,identity))),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_15,identity)),least_upper_bound(identity,greatest_lower_bound(X_15,identity))),least_upper_bound(identity,inverse(greatest_lower_bound(X_15,identity)))) )],[refute_0_2045,refute_0_2048]) ).
cnf(refute_0_2050,plain,
multiply(inverse(greatest_lower_bound(X_15,identity)),identity) = inverse(greatest_lower_bound(X_15,identity)),
inference(subst,[],[refute_0_564:[bind(X,$fot(inverse(greatest_lower_bound(X_15,identity))))]]) ).
cnf(refute_0_2051,plain,
( multiply(inverse(greatest_lower_bound(X_15,identity)),identity) != inverse(greatest_lower_bound(X_15,identity))
| multiply(inverse(greatest_lower_bound(X_15,identity)),identity) != least_upper_bound(identity,inverse(greatest_lower_bound(X_15,identity)))
| inverse(greatest_lower_bound(X_15,identity)) = least_upper_bound(identity,inverse(greatest_lower_bound(X_15,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_15,identity)),identity),least_upper_bound(identity,inverse(greatest_lower_bound(X_15,identity)))) ),[0],$fot(inverse(greatest_lower_bound(X_15,identity)))]]) ).
cnf(refute_0_2052,plain,
( multiply(inverse(greatest_lower_bound(X_15,identity)),identity) != least_upper_bound(identity,inverse(greatest_lower_bound(X_15,identity)))
| inverse(greatest_lower_bound(X_15,identity)) = least_upper_bound(identity,inverse(greatest_lower_bound(X_15,identity))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_15,identity)),identity),inverse(greatest_lower_bound(X_15,identity))) )],[refute_0_2050,refute_0_2051]) ).
cnf(refute_0_2053,plain,
inverse(greatest_lower_bound(X_15,identity)) = least_upper_bound(identity,inverse(greatest_lower_bound(X_15,identity))),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_15,identity)),identity),least_upper_bound(identity,inverse(greatest_lower_bound(X_15,identity)))) )],[refute_0_2049,refute_0_2052]) ).
cnf(refute_0_2054,plain,
( inverse(greatest_lower_bound(X_15,identity)) != least_upper_bound(identity,inverse(greatest_lower_bound(X_15,identity)))
| least_upper_bound(identity,inverse(greatest_lower_bound(X_15,identity))) = inverse(greatest_lower_bound(X_15,identity)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(inverse(greatest_lower_bound(X_15,identity)))),bind(Y0,$fot(least_upper_bound(identity,inverse(greatest_lower_bound(X_15,identity)))))]]) ).
cnf(refute_0_2055,plain,
least_upper_bound(identity,inverse(greatest_lower_bound(X_15,identity))) = inverse(greatest_lower_bound(X_15,identity)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_15,identity)),least_upper_bound(identity,inverse(greatest_lower_bound(X_15,identity)))) )],[refute_0_2053,refute_0_2054]) ).
cnf(refute_0_2056,plain,
least_upper_bound(identity,inverse(greatest_lower_bound(X_95,identity))) = inverse(greatest_lower_bound(X_95,identity)),
inference(subst,[],[refute_0_2055:[bind(X_15,$fot(X_95))]]) ).
cnf(refute_0_2057,plain,
least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_95),inverse(greatest_lower_bound(X_95,identity)))) = least_upper_bound(identity,inverse(greatest_lower_bound(X_95,identity))),
inference(subst,[],[refute_0_1860:[bind(Y,$fot(X_95)),bind(X_36,$fot(identity)),bind(X_38,$fot(inverse(greatest_lower_bound(X_95,identity))))]]) ).
cnf(refute_0_2058,plain,
( least_upper_bound(identity,inverse(greatest_lower_bound(X_95,identity))) != inverse(greatest_lower_bound(X_95,identity))
| least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_95),inverse(greatest_lower_bound(X_95,identity)))) != least_upper_bound(identity,inverse(greatest_lower_bound(X_95,identity)))
| least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_95),inverse(greatest_lower_bound(X_95,identity)))) = inverse(greatest_lower_bound(X_95,identity)) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_95),inverse(greatest_lower_bound(X_95,identity)))))),bind(Y0,$fot(least_upper_bound(identity,inverse(greatest_lower_bound(X_95,identity))))),bind(Z0,$fot(inverse(greatest_lower_bound(X_95,identity))))]]) ).
cnf(refute_0_2059,plain,
( least_upper_bound(identity,inverse(greatest_lower_bound(X_95,identity))) != inverse(greatest_lower_bound(X_95,identity))
| least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_95),inverse(greatest_lower_bound(X_95,identity)))) = inverse(greatest_lower_bound(X_95,identity)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_95),inverse(greatest_lower_bound(X_95,identity)))),least_upper_bound(identity,inverse(greatest_lower_bound(X_95,identity)))) )],[refute_0_2057,refute_0_2058]) ).
cnf(refute_0_2060,plain,
least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_95),inverse(greatest_lower_bound(X_95,identity)))) = inverse(greatest_lower_bound(X_95,identity)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(greatest_lower_bound(X_95,identity))),inverse(greatest_lower_bound(X_95,identity))) )],[refute_0_2056,refute_0_2059]) ).
cnf(refute_0_2061,plain,
( least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_95),inverse(greatest_lower_bound(X_95,identity)))) != inverse(greatest_lower_bound(X_95,identity))
| least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_95),inverse(greatest_lower_bound(X_95,identity)))) != least_upper_bound(greatest_lower_bound(identity,X_95),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_95))))
| inverse(greatest_lower_bound(X_95,identity)) = least_upper_bound(greatest_lower_bound(identity,X_95),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_95)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_95),inverse(greatest_lower_bound(X_95,identity)))),least_upper_bound(greatest_lower_bound(identity,X_95),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_95))))) ),[0],$fot(inverse(greatest_lower_bound(X_95,identity)))]]) ).
cnf(refute_0_2062,plain,
( least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_95),inverse(greatest_lower_bound(X_95,identity)))) != least_upper_bound(greatest_lower_bound(identity,X_95),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_95))))
| inverse(greatest_lower_bound(X_95,identity)) = least_upper_bound(greatest_lower_bound(identity,X_95),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_95)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_95),inverse(greatest_lower_bound(X_95,identity)))),inverse(greatest_lower_bound(X_95,identity))) )],[refute_0_2060,refute_0_2061]) ).
cnf(refute_0_2063,plain,
least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_95),inverse(greatest_lower_bound(identity,X_95)))) = least_upper_bound(greatest_lower_bound(identity,X_95),inverse(greatest_lower_bound(identity,X_95))),
inference(subst,[],[refute_0_1904:[bind(Y,$fot(X_95)),bind(X_256,$fot(greatest_lower_bound(identity,X_95)))]]) ).
cnf(refute_0_2064,plain,
least_upper_bound(greatest_lower_bound(identity,X_95),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_95)))) = least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_95),inverse(greatest_lower_bound(identity,X_95)))),
inference(subst,[],[refute_0_1927:[bind(Y,$fot(inverse(greatest_lower_bound(identity,X_95)))),bind(X_256,$fot(greatest_lower_bound(identity,X_95))),bind(X_257,$fot(identity))]]) ).
cnf(refute_0_2065,plain,
( least_upper_bound(greatest_lower_bound(identity,X_95),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_95)))) != least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_95),inverse(greatest_lower_bound(identity,X_95))))
| least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_95),inverse(greatest_lower_bound(identity,X_95)))) != least_upper_bound(greatest_lower_bound(identity,X_95),inverse(greatest_lower_bound(identity,X_95)))
| least_upper_bound(greatest_lower_bound(identity,X_95),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_95)))) = least_upper_bound(greatest_lower_bound(identity,X_95),inverse(greatest_lower_bound(identity,X_95))) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(identity,X_95),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_95)))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_95),inverse(greatest_lower_bound(identity,X_95)))))),bind(Z0,$fot(least_upper_bound(greatest_lower_bound(identity,X_95),inverse(greatest_lower_bound(identity,X_95)))))]]) ).
cnf(refute_0_2066,plain,
( least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_95),inverse(greatest_lower_bound(identity,X_95)))) != least_upper_bound(greatest_lower_bound(identity,X_95),inverse(greatest_lower_bound(identity,X_95)))
| least_upper_bound(greatest_lower_bound(identity,X_95),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_95)))) = least_upper_bound(greatest_lower_bound(identity,X_95),inverse(greatest_lower_bound(identity,X_95))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,X_95),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_95)))),least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_95),inverse(greatest_lower_bound(identity,X_95))))) )],[refute_0_2064,refute_0_2065]) ).
cnf(refute_0_2067,plain,
least_upper_bound(greatest_lower_bound(identity,X_95),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_95)))) = least_upper_bound(greatest_lower_bound(identity,X_95),inverse(greatest_lower_bound(identity,X_95))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_95),inverse(greatest_lower_bound(identity,X_95)))),least_upper_bound(greatest_lower_bound(identity,X_95),inverse(greatest_lower_bound(identity,X_95)))) )],[refute_0_2063,refute_0_2066]) ).
cnf(refute_0_2068,plain,
( inverse(greatest_lower_bound(X_95,identity)) != least_upper_bound(greatest_lower_bound(identity,X_95),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_95))))
| least_upper_bound(greatest_lower_bound(identity,X_95),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_95)))) != least_upper_bound(greatest_lower_bound(identity,X_95),inverse(greatest_lower_bound(identity,X_95)))
| inverse(greatest_lower_bound(X_95,identity)) = least_upper_bound(greatest_lower_bound(identity,X_95),inverse(greatest_lower_bound(identity,X_95))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(inverse(greatest_lower_bound(X_95,identity)),least_upper_bound(greatest_lower_bound(identity,X_95),inverse(greatest_lower_bound(identity,X_95)))) ),[0],$fot(least_upper_bound(greatest_lower_bound(identity,X_95),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_95)))))]]) ).
cnf(refute_0_2069,plain,
( inverse(greatest_lower_bound(X_95,identity)) != least_upper_bound(greatest_lower_bound(identity,X_95),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_95))))
| inverse(greatest_lower_bound(X_95,identity)) = least_upper_bound(greatest_lower_bound(identity,X_95),inverse(greatest_lower_bound(identity,X_95))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,X_95),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_95)))),least_upper_bound(greatest_lower_bound(identity,X_95),inverse(greatest_lower_bound(identity,X_95)))) )],[refute_0_2067,refute_0_2068]) ).
cnf(refute_0_2070,plain,
( least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_95),inverse(greatest_lower_bound(X_95,identity)))) != least_upper_bound(greatest_lower_bound(identity,X_95),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_95))))
| inverse(greatest_lower_bound(X_95,identity)) = least_upper_bound(greatest_lower_bound(identity,X_95),inverse(greatest_lower_bound(identity,X_95))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_95,identity)),least_upper_bound(greatest_lower_bound(identity,X_95),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_95))))) )],[refute_0_2062,refute_0_2069]) ).
cnf(refute_0_2071,plain,
inverse(greatest_lower_bound(X_95,identity)) = least_upper_bound(greatest_lower_bound(identity,X_95),inverse(greatest_lower_bound(identity,X_95))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_95),inverse(greatest_lower_bound(X_95,identity)))),least_upper_bound(greatest_lower_bound(identity,X_95),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_95))))) )],[refute_0_2044,refute_0_2070]) ).
cnf(refute_0_2072,plain,
( inverse(greatest_lower_bound(X_95,identity)) != least_upper_bound(greatest_lower_bound(identity,X_95),inverse(greatest_lower_bound(identity,X_95)))
| least_upper_bound(greatest_lower_bound(identity,X_95),inverse(greatest_lower_bound(identity,X_95))) = inverse(greatest_lower_bound(X_95,identity)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(inverse(greatest_lower_bound(X_95,identity)))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(identity,X_95),inverse(greatest_lower_bound(identity,X_95)))))]]) ).
cnf(refute_0_2073,plain,
least_upper_bound(greatest_lower_bound(identity,X_95),inverse(greatest_lower_bound(identity,X_95))) = inverse(greatest_lower_bound(X_95,identity)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_95,identity)),least_upper_bound(greatest_lower_bound(identity,X_95),inverse(greatest_lower_bound(identity,X_95)))) )],[refute_0_2071,refute_0_2072]) ).
cnf(refute_0_2074,plain,
least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71)))) = inverse(greatest_lower_bound(multiply(inverse(X),X_71),identity)),
inference(subst,[],[refute_0_2073:[bind(X_95,$fot(multiply(inverse(X),X_71)))]]) ).
cnf(refute_0_2075,plain,
( inverse(greatest_lower_bound(multiply(inverse(X),X_71),identity)) != inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71)))
| least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71)))) != inverse(greatest_lower_bound(multiply(inverse(X),X_71),identity))
| least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71)))) = inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71))) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71)))))),bind(Y0,$fot(inverse(greatest_lower_bound(multiply(inverse(X),X_71),identity)))),bind(Z0,$fot(inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71)))))]]) ).
cnf(refute_0_2076,plain,
( inverse(greatest_lower_bound(multiply(inverse(X),X_71),identity)) != inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71)))
| least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71)))) = inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71)))),inverse(greatest_lower_bound(multiply(inverse(X),X_71),identity))) )],[refute_0_2074,refute_0_2075]) ).
cnf(refute_0_2077,plain,
least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71)))) = inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(multiply(inverse(X),X_71),identity)),inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71)))) )],[refute_0_1991,refute_0_2076]) ).
cnf(refute_0_2078,plain,
( multiply(inverse(greatest_lower_bound(X_71,X)),X) != least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71))))
| least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71)))) != inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71)))
| multiply(inverse(greatest_lower_bound(X_71,X)),X) = inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(greatest_lower_bound(X_71,X)),X),inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71)))) ),[0],$fot(least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71)))))]]) ).
cnf(refute_0_2079,plain,
( multiply(inverse(greatest_lower_bound(X_71,X)),X) != least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71))))
| multiply(inverse(greatest_lower_bound(X_71,X)),X) = inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71)))),inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71)))) )],[refute_0_2077,refute_0_2078]) ).
cnf(refute_0_2080,plain,
multiply(inverse(greatest_lower_bound(X_71,X)),X) = inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71))),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_71,X)),X),least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X),X_71)),inverse(greatest_lower_bound(identity,multiply(inverse(X),X_71))))) )],[refute_0_1935,refute_0_2079]) ).
cnf(refute_0_2081,plain,
multiply(inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))) = inverse(greatest_lower_bound(identity,multiply(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity))),
inference(subst,[],[refute_0_2080:[bind(X,$fot(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),bind(X_71,$fot(identity))]]) ).
cnf(refute_0_2082,plain,
( multiply(inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))) != inverse(greatest_lower_bound(identity,multiply(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity)))
| inverse(greatest_lower_bound(identity,multiply(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity))) != multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))
| multiply(inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))) = multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))),bind(Y0,$fot(inverse(greatest_lower_bound(identity,multiply(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity))))),bind(Z0,$fot(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))]]) ).
cnf(refute_0_2083,plain,
( inverse(greatest_lower_bound(identity,multiply(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity))) != multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))
| multiply(inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))) = multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),inverse(greatest_lower_bound(identity,multiply(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity)))) )],[refute_0_2081,refute_0_2082]) ).
cnf(refute_0_2084,plain,
multiply(inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))) = multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity))),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))) )],[refute_0_1724,refute_0_2083]) ).
cnf(refute_0_2085,plain,
( multiply(inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))) != multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))
| multiply(inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))) != least_upper_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))
| multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))) = least_upper_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),least_upper_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))) ),[0],$fot(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))]]) ).
cnf(refute_0_2086,plain,
( multiply(inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))) != least_upper_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))
| multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))) = least_upper_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))) )],[refute_0_2084,refute_0_2085]) ).
cnf(refute_0_2087,plain,
multiply(identity,identity) = identity,
inference(subst,[],[refute_0_564:[bind(X,$fot(identity))]]) ).
cnf(refute_0_2088,plain,
least_upper_bound(identity,greatest_lower_bound(identity,X_462)) = identity,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(identity)),bind(Y,$fot(X_462))]]) ).
cnf(refute_0_2089,plain,
multiply(X_104,least_upper_bound(least_upper_bound(inverse(X_104),X_57),identity)) = least_upper_bound(X_104,multiply(X_104,least_upper_bound(inverse(X_104),X_57))),
inference(subst,[],[refute_0_34:[bind(X_55,$fot(X_104)),bind(X_56,$fot(least_upper_bound(inverse(X_104),X_57)))]]) ).
cnf(refute_0_2090,plain,
multiply(X_104,least_upper_bound(inverse(X_104),X_57)) = least_upper_bound(identity,multiply(X_104,X_57)),
inference(subst,[],[refute_0_1580:[bind(X_55,$fot(X_104))]]) ).
cnf(refute_0_2091,plain,
( multiply(X_104,least_upper_bound(inverse(X_104),X_57)) != least_upper_bound(identity,multiply(X_104,X_57))
| multiply(X_104,least_upper_bound(least_upper_bound(inverse(X_104),X_57),identity)) != least_upper_bound(X_104,multiply(X_104,least_upper_bound(inverse(X_104),X_57)))
| multiply(X_104,least_upper_bound(least_upper_bound(inverse(X_104),X_57),identity)) = least_upper_bound(X_104,least_upper_bound(identity,multiply(X_104,X_57))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_104,least_upper_bound(least_upper_bound(inverse(X_104),X_57),identity)),least_upper_bound(X_104,multiply(X_104,least_upper_bound(inverse(X_104),X_57)))) ),[1,1],$fot(least_upper_bound(identity,multiply(X_104,X_57)))]]) ).
cnf(refute_0_2092,plain,
( multiply(X_104,least_upper_bound(least_upper_bound(inverse(X_104),X_57),identity)) != least_upper_bound(X_104,multiply(X_104,least_upper_bound(inverse(X_104),X_57)))
| multiply(X_104,least_upper_bound(least_upper_bound(inverse(X_104),X_57),identity)) = least_upper_bound(X_104,least_upper_bound(identity,multiply(X_104,X_57))) ),
inference(resolve,[$cnf( $equal(multiply(X_104,least_upper_bound(inverse(X_104),X_57)),least_upper_bound(identity,multiply(X_104,X_57))) )],[refute_0_2090,refute_0_2091]) ).
cnf(refute_0_2093,plain,
multiply(X_104,least_upper_bound(least_upper_bound(inverse(X_104),X_57),identity)) = least_upper_bound(X_104,least_upper_bound(identity,multiply(X_104,X_57))),
inference(resolve,[$cnf( $equal(multiply(X_104,least_upper_bound(least_upper_bound(inverse(X_104),X_57),identity)),least_upper_bound(X_104,multiply(X_104,least_upper_bound(inverse(X_104),X_57)))) )],[refute_0_2089,refute_0_2092]) ).
cnf(refute_0_2094,plain,
multiply(X,least_upper_bound(least_upper_bound(X_59,inverse(X)),Z)) = least_upper_bound(multiply(X,least_upper_bound(X_59,inverse(X))),multiply(X,Z)),
inference(subst,[],[monotony_lub1:[bind(Y,$fot(least_upper_bound(X_59,inverse(X))))]]) ).
cnf(refute_0_2095,plain,
multiply(X,least_upper_bound(X_59,inverse(X))) = least_upper_bound(identity,multiply(X,X_59)),
inference(subst,[],[refute_0_552:[bind(X_55,$fot(X)),bind(X_56,$fot(X_59))]]) ).
cnf(refute_0_2096,plain,
( multiply(X,least_upper_bound(X_59,inverse(X))) != least_upper_bound(identity,multiply(X,X_59))
| multiply(X,least_upper_bound(least_upper_bound(X_59,inverse(X)),Z)) != least_upper_bound(multiply(X,least_upper_bound(X_59,inverse(X))),multiply(X,Z))
| multiply(X,least_upper_bound(least_upper_bound(X_59,inverse(X)),Z)) = least_upper_bound(least_upper_bound(identity,multiply(X,X_59)),multiply(X,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X,least_upper_bound(least_upper_bound(X_59,inverse(X)),Z)),least_upper_bound(multiply(X,least_upper_bound(X_59,inverse(X))),multiply(X,Z))) ),[1,0],$fot(least_upper_bound(identity,multiply(X,X_59)))]]) ).
cnf(refute_0_2097,plain,
( multiply(X,least_upper_bound(least_upper_bound(X_59,inverse(X)),Z)) != least_upper_bound(multiply(X,least_upper_bound(X_59,inverse(X))),multiply(X,Z))
| multiply(X,least_upper_bound(least_upper_bound(X_59,inverse(X)),Z)) = least_upper_bound(least_upper_bound(identity,multiply(X,X_59)),multiply(X,Z)) ),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(X_59,inverse(X))),least_upper_bound(identity,multiply(X,X_59))) )],[refute_0_2095,refute_0_2096]) ).
cnf(refute_0_2098,plain,
multiply(X,least_upper_bound(least_upper_bound(X_59,inverse(X)),Z)) = least_upper_bound(least_upper_bound(identity,multiply(X,X_59)),multiply(X,Z)),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(least_upper_bound(X_59,inverse(X)),Z)),least_upper_bound(multiply(X,least_upper_bound(X_59,inverse(X))),multiply(X,Z))) )],[refute_0_2094,refute_0_2097]) ).
cnf(refute_0_2099,plain,
least_upper_bound(least_upper_bound(X_59,inverse(X)),Z) = least_upper_bound(X_59,least_upper_bound(inverse(X),Z)),
inference(subst,[],[refute_0_631:[bind(X,$fot(X_59)),bind(Y,$fot(inverse(X)))]]) ).
cnf(refute_0_2100,plain,
multiply(X,least_upper_bound(least_upper_bound(X_59,inverse(X)),Z)) = multiply(X,least_upper_bound(least_upper_bound(X_59,inverse(X)),Z)),
introduced(tautology,[refl,[$fot(multiply(X,least_upper_bound(least_upper_bound(X_59,inverse(X)),Z)))]]) ).
cnf(refute_0_2101,plain,
( multiply(X,least_upper_bound(least_upper_bound(X_59,inverse(X)),Z)) != multiply(X,least_upper_bound(least_upper_bound(X_59,inverse(X)),Z))
| least_upper_bound(least_upper_bound(X_59,inverse(X)),Z) != least_upper_bound(X_59,least_upper_bound(inverse(X),Z))
| multiply(X,least_upper_bound(least_upper_bound(X_59,inverse(X)),Z)) = multiply(X,least_upper_bound(X_59,least_upper_bound(inverse(X),Z))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X,least_upper_bound(least_upper_bound(X_59,inverse(X)),Z)),multiply(X,least_upper_bound(least_upper_bound(X_59,inverse(X)),Z))) ),[1,1],$fot(least_upper_bound(X_59,least_upper_bound(inverse(X),Z)))]]) ).
cnf(refute_0_2102,plain,
( least_upper_bound(least_upper_bound(X_59,inverse(X)),Z) != least_upper_bound(X_59,least_upper_bound(inverse(X),Z))
| multiply(X,least_upper_bound(least_upper_bound(X_59,inverse(X)),Z)) = multiply(X,least_upper_bound(X_59,least_upper_bound(inverse(X),Z))) ),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(least_upper_bound(X_59,inverse(X)),Z)),multiply(X,least_upper_bound(least_upper_bound(X_59,inverse(X)),Z))) )],[refute_0_2100,refute_0_2101]) ).
cnf(refute_0_2103,plain,
multiply(X,least_upper_bound(least_upper_bound(X_59,inverse(X)),Z)) = multiply(X,least_upper_bound(X_59,least_upper_bound(inverse(X),Z))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_59,inverse(X)),Z),least_upper_bound(X_59,least_upper_bound(inverse(X),Z))) )],[refute_0_2099,refute_0_2102]) ).
cnf(refute_0_2104,plain,
( multiply(X,least_upper_bound(least_upper_bound(X_59,inverse(X)),Z)) != multiply(X,least_upper_bound(X_59,least_upper_bound(inverse(X),Z)))
| multiply(X,least_upper_bound(least_upper_bound(X_59,inverse(X)),Z)) != least_upper_bound(least_upper_bound(identity,multiply(X,X_59)),multiply(X,Z))
| multiply(X,least_upper_bound(X_59,least_upper_bound(inverse(X),Z))) = least_upper_bound(least_upper_bound(identity,multiply(X,X_59)),multiply(X,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X,least_upper_bound(least_upper_bound(X_59,inverse(X)),Z)),least_upper_bound(least_upper_bound(identity,multiply(X,X_59)),multiply(X,Z))) ),[0],$fot(multiply(X,least_upper_bound(X_59,least_upper_bound(inverse(X),Z))))]]) ).
cnf(refute_0_2105,plain,
( multiply(X,least_upper_bound(least_upper_bound(X_59,inverse(X)),Z)) != least_upper_bound(least_upper_bound(identity,multiply(X,X_59)),multiply(X,Z))
| multiply(X,least_upper_bound(X_59,least_upper_bound(inverse(X),Z))) = least_upper_bound(least_upper_bound(identity,multiply(X,X_59)),multiply(X,Z)) ),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(least_upper_bound(X_59,inverse(X)),Z)),multiply(X,least_upper_bound(X_59,least_upper_bound(inverse(X),Z)))) )],[refute_0_2103,refute_0_2104]) ).
cnf(refute_0_2106,plain,
least_upper_bound(multiply(X,X_59),multiply(X,Z)) = multiply(X,least_upper_bound(X_59,Z)),
inference(subst,[],[refute_0_754:[bind(Y,$fot(X_59))]]) ).
cnf(refute_0_2107,plain,
least_upper_bound(identity,least_upper_bound(multiply(X,X_59),multiply(X,Z))) = least_upper_bound(identity,least_upper_bound(multiply(X,X_59),multiply(X,Z))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,least_upper_bound(multiply(X,X_59),multiply(X,Z))))]]) ).
cnf(refute_0_2108,plain,
( least_upper_bound(multiply(X,X_59),multiply(X,Z)) != multiply(X,least_upper_bound(X_59,Z))
| least_upper_bound(identity,least_upper_bound(multiply(X,X_59),multiply(X,Z))) != least_upper_bound(identity,least_upper_bound(multiply(X,X_59),multiply(X,Z)))
| least_upper_bound(identity,least_upper_bound(multiply(X,X_59),multiply(X,Z))) = least_upper_bound(identity,multiply(X,least_upper_bound(X_59,Z))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(X,X_59),multiply(X,Z))),least_upper_bound(identity,least_upper_bound(multiply(X,X_59),multiply(X,Z)))) ),[1,1],$fot(multiply(X,least_upper_bound(X_59,Z)))]]) ).
cnf(refute_0_2109,plain,
( least_upper_bound(multiply(X,X_59),multiply(X,Z)) != multiply(X,least_upper_bound(X_59,Z))
| least_upper_bound(identity,least_upper_bound(multiply(X,X_59),multiply(X,Z))) = least_upper_bound(identity,multiply(X,least_upper_bound(X_59,Z))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(X,X_59),multiply(X,Z))),least_upper_bound(identity,least_upper_bound(multiply(X,X_59),multiply(X,Z)))) )],[refute_0_2107,refute_0_2108]) ).
cnf(refute_0_2110,plain,
least_upper_bound(identity,least_upper_bound(multiply(X,X_59),multiply(X,Z))) = least_upper_bound(identity,multiply(X,least_upper_bound(X_59,Z))),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,X_59),multiply(X,Z)),multiply(X,least_upper_bound(X_59,Z))) )],[refute_0_2106,refute_0_2109]) ).
cnf(refute_0_2111,plain,
least_upper_bound(least_upper_bound(identity,multiply(X,X_59)),multiply(X,Z)) = least_upper_bound(identity,least_upper_bound(multiply(X,X_59),multiply(X,Z))),
inference(subst,[],[refute_0_631:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X,X_59))),bind(Z,$fot(multiply(X,Z)))]]) ).
cnf(refute_0_2112,plain,
( least_upper_bound(identity,least_upper_bound(multiply(X,X_59),multiply(X,Z))) != least_upper_bound(identity,multiply(X,least_upper_bound(X_59,Z)))
| least_upper_bound(least_upper_bound(identity,multiply(X,X_59)),multiply(X,Z)) != least_upper_bound(identity,least_upper_bound(multiply(X,X_59),multiply(X,Z)))
| least_upper_bound(least_upper_bound(identity,multiply(X,X_59)),multiply(X,Z)) = least_upper_bound(identity,multiply(X,least_upper_bound(X_59,Z))) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(least_upper_bound(least_upper_bound(identity,multiply(X,X_59)),multiply(X,Z)))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(multiply(X,X_59),multiply(X,Z))))),bind(Z0,$fot(least_upper_bound(identity,multiply(X,least_upper_bound(X_59,Z)))))]]) ).
cnf(refute_0_2113,plain,
( least_upper_bound(identity,least_upper_bound(multiply(X,X_59),multiply(X,Z))) != least_upper_bound(identity,multiply(X,least_upper_bound(X_59,Z)))
| least_upper_bound(least_upper_bound(identity,multiply(X,X_59)),multiply(X,Z)) = least_upper_bound(identity,multiply(X,least_upper_bound(X_59,Z))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(identity,multiply(X,X_59)),multiply(X,Z)),least_upper_bound(identity,least_upper_bound(multiply(X,X_59),multiply(X,Z)))) )],[refute_0_2111,refute_0_2112]) ).
cnf(refute_0_2114,plain,
least_upper_bound(least_upper_bound(identity,multiply(X,X_59)),multiply(X,Z)) = least_upper_bound(identity,multiply(X,least_upper_bound(X_59,Z))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(X,X_59),multiply(X,Z))),least_upper_bound(identity,multiply(X,least_upper_bound(X_59,Z)))) )],[refute_0_2110,refute_0_2113]) ).
cnf(refute_0_2115,plain,
( multiply(X,least_upper_bound(X_59,least_upper_bound(inverse(X),Z))) != least_upper_bound(least_upper_bound(identity,multiply(X,X_59)),multiply(X,Z))
| least_upper_bound(least_upper_bound(identity,multiply(X,X_59)),multiply(X,Z)) != least_upper_bound(identity,multiply(X,least_upper_bound(X_59,Z)))
| multiply(X,least_upper_bound(X_59,least_upper_bound(inverse(X),Z))) = least_upper_bound(identity,multiply(X,least_upper_bound(X_59,Z))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X,least_upper_bound(X_59,least_upper_bound(inverse(X),Z))),least_upper_bound(identity,multiply(X,least_upper_bound(X_59,Z)))) ),[0],$fot(least_upper_bound(least_upper_bound(identity,multiply(X,X_59)),multiply(X,Z)))]]) ).
cnf(refute_0_2116,plain,
( multiply(X,least_upper_bound(X_59,least_upper_bound(inverse(X),Z))) != least_upper_bound(least_upper_bound(identity,multiply(X,X_59)),multiply(X,Z))
| multiply(X,least_upper_bound(X_59,least_upper_bound(inverse(X),Z))) = least_upper_bound(identity,multiply(X,least_upper_bound(X_59,Z))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(identity,multiply(X,X_59)),multiply(X,Z)),least_upper_bound(identity,multiply(X,least_upper_bound(X_59,Z)))) )],[refute_0_2114,refute_0_2115]) ).
cnf(refute_0_2117,plain,
( multiply(X,least_upper_bound(least_upper_bound(X_59,inverse(X)),Z)) != least_upper_bound(least_upper_bound(identity,multiply(X,X_59)),multiply(X,Z))
| multiply(X,least_upper_bound(X_59,least_upper_bound(inverse(X),Z))) = least_upper_bound(identity,multiply(X,least_upper_bound(X_59,Z))) ),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(X_59,least_upper_bound(inverse(X),Z))),least_upper_bound(least_upper_bound(identity,multiply(X,X_59)),multiply(X,Z))) )],[refute_0_2105,refute_0_2116]) ).
cnf(refute_0_2118,plain,
multiply(X,least_upper_bound(X_59,least_upper_bound(inverse(X),Z))) = least_upper_bound(identity,multiply(X,least_upper_bound(X_59,Z))),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(least_upper_bound(X_59,inverse(X)),Z)),least_upper_bound(least_upper_bound(identity,multiply(X,X_59)),multiply(X,Z))) )],[refute_0_2098,refute_0_2117]) ).
cnf(refute_0_2119,plain,
multiply(X_104,least_upper_bound(identity,least_upper_bound(inverse(X_104),X_57))) = least_upper_bound(identity,multiply(X_104,least_upper_bound(identity,X_57))),
inference(subst,[],[refute_0_2118:[bind(X,$fot(X_104)),bind(Z,$fot(X_57)),bind(X_59,$fot(identity))]]) ).
cnf(refute_0_2120,plain,
multiply(X_104,least_upper_bound(least_upper_bound(inverse(X_104),X_57),identity)) = multiply(X_104,least_upper_bound(identity,least_upper_bound(inverse(X_104),X_57))),
inference(subst,[],[refute_0_1758:[bind(X_105,$fot(least_upper_bound(inverse(X_104),X_57))),bind(X_19,$fot(X_104))]]) ).
cnf(refute_0_2121,plain,
( multiply(X_104,least_upper_bound(identity,least_upper_bound(inverse(X_104),X_57))) != least_upper_bound(identity,multiply(X_104,least_upper_bound(identity,X_57)))
| multiply(X_104,least_upper_bound(least_upper_bound(inverse(X_104),X_57),identity)) != multiply(X_104,least_upper_bound(identity,least_upper_bound(inverse(X_104),X_57)))
| multiply(X_104,least_upper_bound(least_upper_bound(inverse(X_104),X_57),identity)) = least_upper_bound(identity,multiply(X_104,least_upper_bound(identity,X_57))) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(multiply(X_104,least_upper_bound(least_upper_bound(inverse(X_104),X_57),identity)))),bind(Y0,$fot(multiply(X_104,least_upper_bound(identity,least_upper_bound(inverse(X_104),X_57))))),bind(Z0,$fot(least_upper_bound(identity,multiply(X_104,least_upper_bound(identity,X_57)))))]]) ).
cnf(refute_0_2122,plain,
( multiply(X_104,least_upper_bound(identity,least_upper_bound(inverse(X_104),X_57))) != least_upper_bound(identity,multiply(X_104,least_upper_bound(identity,X_57)))
| multiply(X_104,least_upper_bound(least_upper_bound(inverse(X_104),X_57),identity)) = least_upper_bound(identity,multiply(X_104,least_upper_bound(identity,X_57))) ),
inference(resolve,[$cnf( $equal(multiply(X_104,least_upper_bound(least_upper_bound(inverse(X_104),X_57),identity)),multiply(X_104,least_upper_bound(identity,least_upper_bound(inverse(X_104),X_57)))) )],[refute_0_2120,refute_0_2121]) ).
cnf(refute_0_2123,plain,
multiply(X_104,least_upper_bound(least_upper_bound(inverse(X_104),X_57),identity)) = least_upper_bound(identity,multiply(X_104,least_upper_bound(identity,X_57))),
inference(resolve,[$cnf( $equal(multiply(X_104,least_upper_bound(identity,least_upper_bound(inverse(X_104),X_57))),least_upper_bound(identity,multiply(X_104,least_upper_bound(identity,X_57)))) )],[refute_0_2119,refute_0_2122]) ).
cnf(refute_0_2124,plain,
( multiply(X_104,least_upper_bound(least_upper_bound(inverse(X_104),X_57),identity)) != least_upper_bound(X_104,least_upper_bound(identity,multiply(X_104,X_57)))
| multiply(X_104,least_upper_bound(least_upper_bound(inverse(X_104),X_57),identity)) != least_upper_bound(identity,multiply(X_104,least_upper_bound(identity,X_57)))
| least_upper_bound(identity,multiply(X_104,least_upper_bound(identity,X_57))) = least_upper_bound(X_104,least_upper_bound(identity,multiply(X_104,X_57))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_104,least_upper_bound(least_upper_bound(inverse(X_104),X_57),identity)),least_upper_bound(X_104,least_upper_bound(identity,multiply(X_104,X_57)))) ),[0],$fot(least_upper_bound(identity,multiply(X_104,least_upper_bound(identity,X_57))))]]) ).
cnf(refute_0_2125,plain,
( multiply(X_104,least_upper_bound(least_upper_bound(inverse(X_104),X_57),identity)) != least_upper_bound(X_104,least_upper_bound(identity,multiply(X_104,X_57)))
| least_upper_bound(identity,multiply(X_104,least_upper_bound(identity,X_57))) = least_upper_bound(X_104,least_upper_bound(identity,multiply(X_104,X_57))) ),
inference(resolve,[$cnf( $equal(multiply(X_104,least_upper_bound(least_upper_bound(inverse(X_104),X_57),identity)),least_upper_bound(identity,multiply(X_104,least_upper_bound(identity,X_57)))) )],[refute_0_2123,refute_0_2124]) ).
cnf(refute_0_2126,plain,
least_upper_bound(identity,multiply(X_104,least_upper_bound(identity,X_57))) = least_upper_bound(X_104,least_upper_bound(identity,multiply(X_104,X_57))),
inference(resolve,[$cnf( $equal(multiply(X_104,least_upper_bound(least_upper_bound(inverse(X_104),X_57),identity)),least_upper_bound(X_104,least_upper_bound(identity,multiply(X_104,X_57)))) )],[refute_0_2093,refute_0_2125]) ).
cnf(refute_0_2127,plain,
least_upper_bound(identity,multiply(greatest_lower_bound(X_92,X),least_upper_bound(identity,inverse(X)))) = least_upper_bound(greatest_lower_bound(X_92,X),least_upper_bound(identity,multiply(greatest_lower_bound(X_92,X),inverse(X)))),
inference(subst,[],[refute_0_2126:[bind(X_104,$fot(greatest_lower_bound(X_92,X))),bind(X_57,$fot(inverse(X)))]]) ).
cnf(refute_0_2128,plain,
( multiply(greatest_lower_bound(X_92,inverse(inverse(X))),inverse(X)) != greatest_lower_bound(identity,multiply(X_92,inverse(X)))
| inverse(inverse(X)) != X
| multiply(greatest_lower_bound(X_92,X),inverse(X)) = greatest_lower_bound(identity,multiply(X_92,inverse(X))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_92,inverse(inverse(X))),inverse(X)),greatest_lower_bound(identity,multiply(X_92,inverse(X)))) ),[0,0,1],$fot(X)]]) ).
cnf(refute_0_2129,plain,
( multiply(greatest_lower_bound(X_92,inverse(inverse(X))),inverse(X)) != greatest_lower_bound(identity,multiply(X_92,inverse(X)))
| multiply(greatest_lower_bound(X_92,X),inverse(X)) = greatest_lower_bound(identity,multiply(X_92,inverse(X))) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p19_2,refute_0_2128]) ).
cnf(refute_0_2130,plain,
multiply(greatest_lower_bound(X_92,X),inverse(X)) = greatest_lower_bound(identity,multiply(X_92,inverse(X))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_92,inverse(inverse(X))),inverse(X)),greatest_lower_bound(identity,multiply(X_92,inverse(X)))) )],[refute_0_1498,refute_0_2129]) ).
cnf(refute_0_2131,plain,
( multiply(greatest_lower_bound(X_92,X),inverse(X)) != greatest_lower_bound(identity,multiply(X_92,inverse(X)))
| least_upper_bound(identity,multiply(greatest_lower_bound(X_92,X),least_upper_bound(identity,inverse(X)))) != least_upper_bound(greatest_lower_bound(X_92,X),least_upper_bound(identity,multiply(greatest_lower_bound(X_92,X),inverse(X))))
| least_upper_bound(identity,multiply(greatest_lower_bound(X_92,X),least_upper_bound(identity,inverse(X)))) = least_upper_bound(greatest_lower_bound(X_92,X),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_92,inverse(X))))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(greatest_lower_bound(X_92,X),least_upper_bound(identity,inverse(X)))),least_upper_bound(greatest_lower_bound(X_92,X),least_upper_bound(identity,multiply(greatest_lower_bound(X_92,X),inverse(X))))) ),[1,1,1],$fot(greatest_lower_bound(identity,multiply(X_92,inverse(X))))]]) ).
cnf(refute_0_2132,plain,
( least_upper_bound(identity,multiply(greatest_lower_bound(X_92,X),least_upper_bound(identity,inverse(X)))) != least_upper_bound(greatest_lower_bound(X_92,X),least_upper_bound(identity,multiply(greatest_lower_bound(X_92,X),inverse(X))))
| least_upper_bound(identity,multiply(greatest_lower_bound(X_92,X),least_upper_bound(identity,inverse(X)))) = least_upper_bound(greatest_lower_bound(X_92,X),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_92,inverse(X))))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_92,X),inverse(X)),greatest_lower_bound(identity,multiply(X_92,inverse(X)))) )],[refute_0_2130,refute_0_2131]) ).
cnf(refute_0_2133,plain,
least_upper_bound(identity,multiply(greatest_lower_bound(X_92,X),least_upper_bound(identity,inverse(X)))) = least_upper_bound(greatest_lower_bound(X_92,X),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_92,inverse(X))))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(greatest_lower_bound(X_92,X),least_upper_bound(identity,inverse(X)))),least_upper_bound(greatest_lower_bound(X_92,X),least_upper_bound(identity,multiply(greatest_lower_bound(X_92,X),inverse(X))))) )],[refute_0_2127,refute_0_2132]) ).
cnf(refute_0_2134,plain,
least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),least_upper_bound(Y,least_upper_bound(greatest_lower_bound(Y,X_134),X_136))) = least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),Y),
inference(subst,[],[refute_0_635:[bind(X_17,$fot(least_upper_bound(greatest_lower_bound(Y,X_134),X_136)))]]) ).
cnf(refute_0_2135,plain,
least_upper_bound(Y,least_upper_bound(greatest_lower_bound(Y,X_134),X_136)) = least_upper_bound(Y,X_136),
inference(subst,[],[refute_0_1860:[bind(Y,$fot(X_134)),bind(X_36,$fot(Y)),bind(X_38,$fot(X_136))]]) ).
cnf(refute_0_2136,plain,
( least_upper_bound(Y,least_upper_bound(greatest_lower_bound(Y,X_134),X_136)) != least_upper_bound(Y,X_136)
| least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),least_upper_bound(Y,least_upper_bound(greatest_lower_bound(Y,X_134),X_136))) != least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),Y)
| least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),least_upper_bound(Y,X_136)) = least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),Y) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),least_upper_bound(Y,least_upper_bound(greatest_lower_bound(Y,X_134),X_136))),least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),Y)) ),[0,1],$fot(least_upper_bound(Y,X_136))]]) ).
cnf(refute_0_2137,plain,
( least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),least_upper_bound(Y,least_upper_bound(greatest_lower_bound(Y,X_134),X_136))) != least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),Y)
| least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),least_upper_bound(Y,X_136)) = least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),Y) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(greatest_lower_bound(Y,X_134),X_136)),least_upper_bound(Y,X_136)) )],[refute_0_2135,refute_0_2136]) ).
cnf(refute_0_2138,plain,
least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),least_upper_bound(Y,X_136)) = least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),Y),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),least_upper_bound(Y,least_upper_bound(greatest_lower_bound(Y,X_134),X_136))),least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),Y)) )],[refute_0_2134,refute_0_2137]) ).
cnf(refute_0_2139,plain,
least_upper_bound(X_136,least_upper_bound(greatest_lower_bound(Y,X_134),X_136)) = least_upper_bound(X_136,greatest_lower_bound(Y,X_134)),
inference(subst,[],[refute_0_635:[bind(Y,$fot(greatest_lower_bound(Y,X_134))),bind(X_17,$fot(X_136))]]) ).
cnf(refute_0_2140,plain,
least_upper_bound(Y,least_upper_bound(X_136,least_upper_bound(greatest_lower_bound(Y,X_134),X_136))) = least_upper_bound(Y,least_upper_bound(X_136,least_upper_bound(greatest_lower_bound(Y,X_134),X_136))),
introduced(tautology,[refl,[$fot(least_upper_bound(Y,least_upper_bound(X_136,least_upper_bound(greatest_lower_bound(Y,X_134),X_136))))]]) ).
cnf(refute_0_2141,plain,
( least_upper_bound(Y,least_upper_bound(X_136,least_upper_bound(greatest_lower_bound(Y,X_134),X_136))) != least_upper_bound(Y,least_upper_bound(X_136,least_upper_bound(greatest_lower_bound(Y,X_134),X_136)))
| least_upper_bound(X_136,least_upper_bound(greatest_lower_bound(Y,X_134),X_136)) != least_upper_bound(X_136,greatest_lower_bound(Y,X_134))
| least_upper_bound(Y,least_upper_bound(X_136,least_upper_bound(greatest_lower_bound(Y,X_134),X_136))) = least_upper_bound(Y,least_upper_bound(X_136,greatest_lower_bound(Y,X_134))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_136,least_upper_bound(greatest_lower_bound(Y,X_134),X_136))),least_upper_bound(Y,least_upper_bound(X_136,least_upper_bound(greatest_lower_bound(Y,X_134),X_136)))) ),[1,1],$fot(least_upper_bound(X_136,greatest_lower_bound(Y,X_134)))]]) ).
cnf(refute_0_2142,plain,
( least_upper_bound(X_136,least_upper_bound(greatest_lower_bound(Y,X_134),X_136)) != least_upper_bound(X_136,greatest_lower_bound(Y,X_134))
| least_upper_bound(Y,least_upper_bound(X_136,least_upper_bound(greatest_lower_bound(Y,X_134),X_136))) = least_upper_bound(Y,least_upper_bound(X_136,greatest_lower_bound(Y,X_134))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_136,least_upper_bound(greatest_lower_bound(Y,X_134),X_136))),least_upper_bound(Y,least_upper_bound(X_136,least_upper_bound(greatest_lower_bound(Y,X_134),X_136)))) )],[refute_0_2140,refute_0_2141]) ).
cnf(refute_0_2143,plain,
least_upper_bound(Y,least_upper_bound(X_136,least_upper_bound(greatest_lower_bound(Y,X_134),X_136))) = least_upper_bound(Y,least_upper_bound(X_136,greatest_lower_bound(Y,X_134))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_136,least_upper_bound(greatest_lower_bound(Y,X_134),X_136)),least_upper_bound(X_136,greatest_lower_bound(Y,X_134))) )],[refute_0_2139,refute_0_2142]) ).
cnf(refute_0_2144,plain,
least_upper_bound(Y,least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),X_136)) = least_upper_bound(Y,least_upper_bound(X_136,least_upper_bound(greatest_lower_bound(Y,X_134),X_136))),
inference(subst,[],[refute_0_1815:[bind(X_129,$fot(Y)),bind(X_130,$fot(least_upper_bound(greatest_lower_bound(Y,X_134),X_136))),bind(X_15,$fot(X_136))]]) ).
cnf(refute_0_2145,plain,
least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),least_upper_bound(Y,X_136)) = least_upper_bound(Y,least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),X_136)),
inference(subst,[],[refute_0_1000:[bind(X_36,$fot(least_upper_bound(greatest_lower_bound(Y,X_134),X_136))),bind(X_38,$fot(X_136))]]) ).
cnf(refute_0_2146,plain,
( least_upper_bound(Y,least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),X_136)) != least_upper_bound(Y,least_upper_bound(X_136,least_upper_bound(greatest_lower_bound(Y,X_134),X_136)))
| least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),least_upper_bound(Y,X_136)) != least_upper_bound(Y,least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),X_136))
| least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),least_upper_bound(Y,X_136)) = least_upper_bound(Y,least_upper_bound(X_136,least_upper_bound(greatest_lower_bound(Y,X_134),X_136))) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),least_upper_bound(Y,X_136)))),bind(Y0,$fot(least_upper_bound(Y,least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),X_136)))),bind(Z0,$fot(least_upper_bound(Y,least_upper_bound(X_136,least_upper_bound(greatest_lower_bound(Y,X_134),X_136)))))]]) ).
cnf(refute_0_2147,plain,
( least_upper_bound(Y,least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),X_136)) != least_upper_bound(Y,least_upper_bound(X_136,least_upper_bound(greatest_lower_bound(Y,X_134),X_136)))
| least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),least_upper_bound(Y,X_136)) = least_upper_bound(Y,least_upper_bound(X_136,least_upper_bound(greatest_lower_bound(Y,X_134),X_136))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),least_upper_bound(Y,X_136)),least_upper_bound(Y,least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),X_136))) )],[refute_0_2145,refute_0_2146]) ).
cnf(refute_0_2148,plain,
least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),least_upper_bound(Y,X_136)) = least_upper_bound(Y,least_upper_bound(X_136,least_upper_bound(greatest_lower_bound(Y,X_134),X_136))),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),X_136)),least_upper_bound(Y,least_upper_bound(X_136,least_upper_bound(greatest_lower_bound(Y,X_134),X_136)))) )],[refute_0_2144,refute_0_2147]) ).
cnf(refute_0_2149,plain,
( least_upper_bound(Y,least_upper_bound(X_136,least_upper_bound(greatest_lower_bound(Y,X_134),X_136))) != least_upper_bound(Y,least_upper_bound(X_136,greatest_lower_bound(Y,X_134)))
| least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),least_upper_bound(Y,X_136)) != least_upper_bound(Y,least_upper_bound(X_136,least_upper_bound(greatest_lower_bound(Y,X_134),X_136)))
| least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),least_upper_bound(Y,X_136)) = least_upper_bound(Y,least_upper_bound(X_136,greatest_lower_bound(Y,X_134))) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),least_upper_bound(Y,X_136)))),bind(Y0,$fot(least_upper_bound(Y,least_upper_bound(X_136,least_upper_bound(greatest_lower_bound(Y,X_134),X_136))))),bind(Z0,$fot(least_upper_bound(Y,least_upper_bound(X_136,greatest_lower_bound(Y,X_134)))))]]) ).
cnf(refute_0_2150,plain,
( least_upper_bound(Y,least_upper_bound(X_136,least_upper_bound(greatest_lower_bound(Y,X_134),X_136))) != least_upper_bound(Y,least_upper_bound(X_136,greatest_lower_bound(Y,X_134)))
| least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),least_upper_bound(Y,X_136)) = least_upper_bound(Y,least_upper_bound(X_136,greatest_lower_bound(Y,X_134))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),least_upper_bound(Y,X_136)),least_upper_bound(Y,least_upper_bound(X_136,least_upper_bound(greatest_lower_bound(Y,X_134),X_136)))) )],[refute_0_2148,refute_0_2149]) ).
cnf(refute_0_2151,plain,
least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),least_upper_bound(Y,X_136)) = least_upper_bound(Y,least_upper_bound(X_136,greatest_lower_bound(Y,X_134))),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_136,least_upper_bound(greatest_lower_bound(Y,X_134),X_136))),least_upper_bound(Y,least_upper_bound(X_136,greatest_lower_bound(Y,X_134)))) )],[refute_0_2143,refute_0_2150]) ).
cnf(refute_0_2152,plain,
( least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),least_upper_bound(Y,X_136)) != least_upper_bound(Y,least_upper_bound(X_136,greatest_lower_bound(Y,X_134)))
| least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),least_upper_bound(Y,X_136)) != least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),Y)
| least_upper_bound(Y,least_upper_bound(X_136,greatest_lower_bound(Y,X_134))) = least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),Y) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),least_upper_bound(Y,X_136)),least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),Y)) ),[0],$fot(least_upper_bound(Y,least_upper_bound(X_136,greatest_lower_bound(Y,X_134))))]]) ).
cnf(refute_0_2153,plain,
( least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),least_upper_bound(Y,X_136)) != least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),Y)
| least_upper_bound(Y,least_upper_bound(X_136,greatest_lower_bound(Y,X_134))) = least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),Y) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),least_upper_bound(Y,X_136)),least_upper_bound(Y,least_upper_bound(X_136,greatest_lower_bound(Y,X_134)))) )],[refute_0_2151,refute_0_2152]) ).
cnf(refute_0_2154,plain,
least_upper_bound(greatest_lower_bound(Y,X_134),least_upper_bound(X_136,Y)) = least_upper_bound(Y,least_upper_bound(greatest_lower_bound(Y,X_134),X_136)),
inference(subst,[],[refute_0_973:[bind(X,$fot(Y)),bind(X_36,$fot(greatest_lower_bound(Y,X_134))),bind(X_37,$fot(X_136))]]) ).
cnf(refute_0_2155,plain,
( least_upper_bound(Y,least_upper_bound(greatest_lower_bound(Y,X_134),X_136)) != least_upper_bound(Y,X_136)
| least_upper_bound(greatest_lower_bound(Y,X_134),least_upper_bound(X_136,Y)) != least_upper_bound(Y,least_upper_bound(greatest_lower_bound(Y,X_134),X_136))
| least_upper_bound(greatest_lower_bound(Y,X_134),least_upper_bound(X_136,Y)) = least_upper_bound(Y,X_136) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(Y,X_134),least_upper_bound(X_136,Y)))),bind(Y0,$fot(least_upper_bound(Y,least_upper_bound(greatest_lower_bound(Y,X_134),X_136)))),bind(Z0,$fot(least_upper_bound(Y,X_136)))]]) ).
cnf(refute_0_2156,plain,
( least_upper_bound(Y,least_upper_bound(greatest_lower_bound(Y,X_134),X_136)) != least_upper_bound(Y,X_136)
| least_upper_bound(greatest_lower_bound(Y,X_134),least_upper_bound(X_136,Y)) = least_upper_bound(Y,X_136) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(Y,X_134),least_upper_bound(X_136,Y)),least_upper_bound(Y,least_upper_bound(greatest_lower_bound(Y,X_134),X_136))) )],[refute_0_2154,refute_0_2155]) ).
cnf(refute_0_2157,plain,
least_upper_bound(greatest_lower_bound(Y,X_134),least_upper_bound(X_136,Y)) = least_upper_bound(Y,X_136),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(greatest_lower_bound(Y,X_134),X_136)),least_upper_bound(Y,X_136)) )],[refute_0_2135,refute_0_2156]) ).
cnf(refute_0_2158,plain,
least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),Y) = least_upper_bound(greatest_lower_bound(Y,X_134),least_upper_bound(X_136,Y)),
inference(subst,[],[refute_0_631:[bind(X,$fot(greatest_lower_bound(Y,X_134))),bind(Y,$fot(X_136)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_2159,plain,
( least_upper_bound(greatest_lower_bound(Y,X_134),least_upper_bound(X_136,Y)) != least_upper_bound(Y,X_136)
| least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),Y) != least_upper_bound(greatest_lower_bound(Y,X_134),least_upper_bound(X_136,Y))
| least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),Y) = least_upper_bound(Y,X_136) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),Y))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(Y,X_134),least_upper_bound(X_136,Y)))),bind(Z0,$fot(least_upper_bound(Y,X_136)))]]) ).
cnf(refute_0_2160,plain,
( least_upper_bound(greatest_lower_bound(Y,X_134),least_upper_bound(X_136,Y)) != least_upper_bound(Y,X_136)
| least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),Y) = least_upper_bound(Y,X_136) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),Y),least_upper_bound(greatest_lower_bound(Y,X_134),least_upper_bound(X_136,Y))) )],[refute_0_2158,refute_0_2159]) ).
cnf(refute_0_2161,plain,
least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),Y) = least_upper_bound(Y,X_136),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(Y,X_134),least_upper_bound(X_136,Y)),least_upper_bound(Y,X_136)) )],[refute_0_2157,refute_0_2160]) ).
cnf(refute_0_2162,plain,
( least_upper_bound(Y,least_upper_bound(X_136,greatest_lower_bound(Y,X_134))) != least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),Y)
| least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),Y) != least_upper_bound(Y,X_136)
| least_upper_bound(Y,least_upper_bound(X_136,greatest_lower_bound(Y,X_134))) = least_upper_bound(Y,X_136) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(Y,least_upper_bound(X_136,greatest_lower_bound(Y,X_134))),least_upper_bound(Y,X_136)) ),[0],$fot(least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),Y))]]) ).
cnf(refute_0_2163,plain,
( least_upper_bound(Y,least_upper_bound(X_136,greatest_lower_bound(Y,X_134))) != least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),Y)
| least_upper_bound(Y,least_upper_bound(X_136,greatest_lower_bound(Y,X_134))) = least_upper_bound(Y,X_136) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),Y),least_upper_bound(Y,X_136)) )],[refute_0_2161,refute_0_2162]) ).
cnf(refute_0_2164,plain,
( least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),least_upper_bound(Y,X_136)) != least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),Y)
| least_upper_bound(Y,least_upper_bound(X_136,greatest_lower_bound(Y,X_134))) = least_upper_bound(Y,X_136) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_136,greatest_lower_bound(Y,X_134))),least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),Y)) )],[refute_0_2153,refute_0_2163]) ).
cnf(refute_0_2165,plain,
least_upper_bound(Y,least_upper_bound(X_136,greatest_lower_bound(Y,X_134))) = least_upper_bound(Y,X_136),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),least_upper_bound(Y,X_136)),least_upper_bound(least_upper_bound(greatest_lower_bound(Y,X_134),X_136),Y)) )],[refute_0_2138,refute_0_2164]) ).
cnf(refute_0_2166,plain,
least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_92,X),greatest_lower_bound(identity,multiply(X_92,inverse(X))))) = least_upper_bound(identity,greatest_lower_bound(X_92,X)),
inference(subst,[],[refute_0_2165:[bind(Y,$fot(identity)),bind(X_134,$fot(multiply(X_92,inverse(X)))),bind(X_136,$fot(greatest_lower_bound(X_92,X)))]]) ).
cnf(refute_0_2167,plain,
least_upper_bound(greatest_lower_bound(X_92,X),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_92,inverse(X))))) = least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_92,X),greatest_lower_bound(identity,multiply(X_92,inverse(X))))),
inference(subst,[],[refute_0_1132:[bind(Y,$fot(greatest_lower_bound(X_92,X))),bind(X_18,$fot(identity)),bind(X_263,$fot(greatest_lower_bound(identity,multiply(X_92,inverse(X)))))]]) ).
cnf(refute_0_2168,plain,
( least_upper_bound(greatest_lower_bound(X_92,X),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_92,inverse(X))))) != least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_92,X),greatest_lower_bound(identity,multiply(X_92,inverse(X)))))
| least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_92,X),greatest_lower_bound(identity,multiply(X_92,inverse(X))))) != least_upper_bound(identity,greatest_lower_bound(X_92,X))
| least_upper_bound(greatest_lower_bound(X_92,X),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_92,inverse(X))))) = least_upper_bound(identity,greatest_lower_bound(X_92,X)) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(X_92,X),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_92,inverse(X))))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_92,X),greatest_lower_bound(identity,multiply(X_92,inverse(X))))))),bind(Z0,$fot(least_upper_bound(identity,greatest_lower_bound(X_92,X))))]]) ).
cnf(refute_0_2169,plain,
( least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_92,X),greatest_lower_bound(identity,multiply(X_92,inverse(X))))) != least_upper_bound(identity,greatest_lower_bound(X_92,X))
| least_upper_bound(greatest_lower_bound(X_92,X),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_92,inverse(X))))) = least_upper_bound(identity,greatest_lower_bound(X_92,X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_92,X),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_92,inverse(X))))),least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_92,X),greatest_lower_bound(identity,multiply(X_92,inverse(X)))))) )],[refute_0_2167,refute_0_2168]) ).
cnf(refute_0_2170,plain,
least_upper_bound(greatest_lower_bound(X_92,X),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_92,inverse(X))))) = least_upper_bound(identity,greatest_lower_bound(X_92,X)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_92,X),greatest_lower_bound(identity,multiply(X_92,inverse(X))))),least_upper_bound(identity,greatest_lower_bound(X_92,X))) )],[refute_0_2166,refute_0_2169]) ).
cnf(refute_0_2171,plain,
( least_upper_bound(greatest_lower_bound(X_92,X),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_92,inverse(X))))) != least_upper_bound(identity,greatest_lower_bound(X_92,X))
| least_upper_bound(identity,multiply(greatest_lower_bound(X_92,X),least_upper_bound(identity,inverse(X)))) != least_upper_bound(greatest_lower_bound(X_92,X),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_92,inverse(X)))))
| least_upper_bound(identity,multiply(greatest_lower_bound(X_92,X),least_upper_bound(identity,inverse(X)))) = least_upper_bound(identity,greatest_lower_bound(X_92,X)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(greatest_lower_bound(X_92,X),least_upper_bound(identity,inverse(X)))),least_upper_bound(greatest_lower_bound(X_92,X),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_92,inverse(X)))))) ),[1],$fot(least_upper_bound(identity,greatest_lower_bound(X_92,X)))]]) ).
cnf(refute_0_2172,plain,
( least_upper_bound(identity,multiply(greatest_lower_bound(X_92,X),least_upper_bound(identity,inverse(X)))) != least_upper_bound(greatest_lower_bound(X_92,X),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_92,inverse(X)))))
| least_upper_bound(identity,multiply(greatest_lower_bound(X_92,X),least_upper_bound(identity,inverse(X)))) = least_upper_bound(identity,greatest_lower_bound(X_92,X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_92,X),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_92,inverse(X))))),least_upper_bound(identity,greatest_lower_bound(X_92,X))) )],[refute_0_2170,refute_0_2171]) ).
cnf(refute_0_2173,plain,
least_upper_bound(identity,multiply(greatest_lower_bound(X_92,X),least_upper_bound(identity,inverse(X)))) = least_upper_bound(identity,greatest_lower_bound(X_92,X)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(greatest_lower_bound(X_92,X),least_upper_bound(identity,inverse(X)))),least_upper_bound(greatest_lower_bound(X_92,X),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_92,inverse(X)))))) )],[refute_0_2133,refute_0_2172]) ).
cnf(refute_0_2174,plain,
least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))) = least_upper_bound(identity,greatest_lower_bound(identity,X_462)),
inference(subst,[],[refute_0_2173:[bind(X,$fot(X_462)),bind(X_92,$fot(identity))]]) ).
cnf(refute_0_2175,plain,
( least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))) != least_upper_bound(identity,greatest_lower_bound(identity,X_462))
| least_upper_bound(identity,greatest_lower_bound(identity,X_462)) != identity
| least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))) = identity ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))),bind(Y0,$fot(least_upper_bound(identity,greatest_lower_bound(identity,X_462)))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_2176,plain,
( least_upper_bound(identity,greatest_lower_bound(identity,X_462)) != identity
| least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),least_upper_bound(identity,greatest_lower_bound(identity,X_462))) )],[refute_0_2174,refute_0_2175]) ).
cnf(refute_0_2177,plain,
least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))) = identity,
inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(identity,X_462)),identity) )],[refute_0_2088,refute_0_2176]) ).
cnf(refute_0_2178,plain,
multiply(identity,least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))) = multiply(identity,least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),
introduced(tautology,[refl,[$fot(multiply(identity,least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))))]]) ).
cnf(refute_0_2179,plain,
( multiply(identity,least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))) != multiply(identity,least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))
| least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))) != identity
| multiply(identity,least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))) = multiply(identity,identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),multiply(identity,least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_2180,plain,
( least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))) != identity
| multiply(identity,least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))) = multiply(identity,identity) ),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),multiply(identity,least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))) )],[refute_0_2178,refute_0_2179]) ).
cnf(refute_0_2181,plain,
multiply(identity,least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))) = multiply(identity,identity),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),identity) )],[refute_0_2177,refute_0_2180]) ).
cnf(refute_0_2182,plain,
multiply(inverse(identity),least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))) = multiply(inverse(identity),least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),
introduced(tautology,[refl,[$fot(multiply(inverse(identity),least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))))]]) ).
cnf(refute_0_2183,plain,
( multiply(inverse(identity),least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))) != multiply(inverse(identity),least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))
| inverse(identity) != identity
| multiply(inverse(identity),least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))) = multiply(identity,least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),multiply(inverse(identity),least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_2184,plain,
( inverse(identity) != identity
| multiply(inverse(identity),least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))) = multiply(identity,least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),multiply(inverse(identity),least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))) )],[refute_0_2182,refute_0_2183]) ).
cnf(refute_0_2185,plain,
multiply(inverse(identity),least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))) = multiply(identity,least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[p19_1,refute_0_2184]) ).
cnf(refute_0_2186,plain,
( multiply(identity,least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))) != multiply(identity,identity)
| multiply(inverse(identity),least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))) != multiply(identity,least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))
| multiply(inverse(identity),least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))) = multiply(identity,identity) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(multiply(inverse(identity),least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))))),bind(Y0,$fot(multiply(identity,least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))))),bind(Z0,$fot(multiply(identity,identity)))]]) ).
cnf(refute_0_2187,plain,
( multiply(identity,least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))) != multiply(identity,identity)
| multiply(inverse(identity),least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))) = multiply(identity,identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),multiply(identity,least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))) )],[refute_0_2185,refute_0_2186]) ).
cnf(refute_0_2188,plain,
multiply(inverse(identity),least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))) = multiply(identity,identity),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),multiply(identity,identity)) )],[refute_0_2181,refute_0_2187]) ).
cnf(refute_0_2189,plain,
( multiply(identity,identity) != identity
| multiply(inverse(identity),least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))) != multiply(identity,identity)
| multiply(inverse(identity),least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))) = identity ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(multiply(inverse(identity),least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))))),bind(Y0,$fot(multiply(identity,identity))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_2190,plain,
( multiply(identity,identity) != identity
| multiply(inverse(identity),least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))) = identity ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),multiply(identity,identity)) )],[refute_0_2188,refute_0_2189]) ).
cnf(refute_0_2191,plain,
multiply(inverse(identity),least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))) = identity,
inference(resolve,[$cnf( $equal(multiply(identity,identity),identity) )],[refute_0_2087,refute_0_2190]) ).
cnf(refute_0_2192,plain,
multiply(inverse(X_56),least_upper_bound(X_56,X_57)) = least_upper_bound(multiply(inverse(X_56),X_56),multiply(inverse(X_56),X_57)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(inverse(X_56))),bind(Y,$fot(X_56)),bind(Z,$fot(X_57))]]) ).
cnf(refute_0_2193,plain,
multiply(inverse(X_56),X_56) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_56))]]) ).
cnf(refute_0_2194,plain,
( multiply(inverse(X_56),X_56) != identity
| multiply(inverse(X_56),least_upper_bound(X_56,X_57)) != least_upper_bound(multiply(inverse(X_56),X_56),multiply(inverse(X_56),X_57))
| multiply(inverse(X_56),least_upper_bound(X_56,X_57)) = least_upper_bound(identity,multiply(inverse(X_56),X_57)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_56),least_upper_bound(X_56,X_57)),least_upper_bound(multiply(inverse(X_56),X_56),multiply(inverse(X_56),X_57))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_2195,plain,
( multiply(inverse(X_56),least_upper_bound(X_56,X_57)) != least_upper_bound(multiply(inverse(X_56),X_56),multiply(inverse(X_56),X_57))
| multiply(inverse(X_56),least_upper_bound(X_56,X_57)) = least_upper_bound(identity,multiply(inverse(X_56),X_57)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_56),X_56),identity) )],[refute_0_2193,refute_0_2194]) ).
cnf(refute_0_2196,plain,
multiply(inverse(X_56),least_upper_bound(X_56,X_57)) = least_upper_bound(identity,multiply(inverse(X_56),X_57)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_56),least_upper_bound(X_56,X_57)),least_upper_bound(multiply(inverse(X_56),X_56),multiply(inverse(X_56),X_57))) )],[refute_0_2192,refute_0_2195]) ).
cnf(refute_0_2197,plain,
multiply(inverse(X_57),least_upper_bound(X_57,X_56)) = least_upper_bound(identity,multiply(inverse(X_57),X_56)),
inference(subst,[],[refute_0_2196:[bind(X_56,$fot(X_57)),bind(X_57,$fot(X_56))]]) ).
cnf(refute_0_2198,plain,
( multiply(inverse(X_57),least_upper_bound(X_57,X_56)) != least_upper_bound(identity,multiply(inverse(X_57),X_56))
| least_upper_bound(identity,multiply(inverse(X_57),X_56)) = multiply(inverse(X_57),least_upper_bound(X_57,X_56)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(multiply(inverse(X_57),least_upper_bound(X_57,X_56)))),bind(Y0,$fot(least_upper_bound(identity,multiply(inverse(X_57),X_56))))]]) ).
cnf(refute_0_2199,plain,
least_upper_bound(identity,multiply(inverse(X_57),X_56)) = multiply(inverse(X_57),least_upper_bound(X_57,X_56)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_57),least_upper_bound(X_57,X_56)),least_upper_bound(identity,multiply(inverse(X_57),X_56))) )],[refute_0_2197,refute_0_2198]) ).
cnf(refute_0_2200,plain,
( multiply(inverse(X_57),least_upper_bound(X_56,X_57)) != least_upper_bound(identity,multiply(inverse(X_57),X_56))
| least_upper_bound(identity,multiply(inverse(X_57),X_56)) != multiply(inverse(X_57),least_upper_bound(X_57,X_56))
| multiply(inverse(X_57),least_upper_bound(X_56,X_57)) = multiply(inverse(X_57),least_upper_bound(X_57,X_56)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_57),least_upper_bound(X_56,X_57)),multiply(inverse(X_57),least_upper_bound(X_57,X_56))) ),[0],$fot(least_upper_bound(identity,multiply(inverse(X_57),X_56)))]]) ).
cnf(refute_0_2201,plain,
( multiply(inverse(X_57),least_upper_bound(X_56,X_57)) != least_upper_bound(identity,multiply(inverse(X_57),X_56))
| multiply(inverse(X_57),least_upper_bound(X_56,X_57)) = multiply(inverse(X_57),least_upper_bound(X_57,X_56)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(X_57),X_56)),multiply(inverse(X_57),least_upper_bound(X_57,X_56))) )],[refute_0_2199,refute_0_2200]) ).
cnf(refute_0_2202,plain,
multiply(inverse(X_57),least_upper_bound(X_56,X_57)) = multiply(inverse(X_57),least_upper_bound(X_57,X_56)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_57),least_upper_bound(X_56,X_57)),least_upper_bound(identity,multiply(inverse(X_57),X_56))) )],[refute_0_127,refute_0_2201]) ).
cnf(refute_0_2203,plain,
multiply(inverse(identity),least_upper_bound(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))),identity)) = multiply(inverse(identity),least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),
inference(subst,[],[refute_0_2202:[bind(X_56,$fot(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),bind(X_57,$fot(identity))]]) ).
cnf(refute_0_2204,plain,
inverse(X_48) = multiply(inverse(multiply(greatest_lower_bound(inverse(X_48),X_94),X_48)),greatest_lower_bound(inverse(X_48),X_94)),
inference(subst,[],[refute_0_542:[bind(X_47,$fot(greatest_lower_bound(inverse(X_48),X_94)))]]) ).
cnf(refute_0_2205,plain,
multiply(greatest_lower_bound(inverse(X_48),X_94),X_48) = greatest_lower_bound(identity,multiply(X_94,X_48)),
inference(subst,[],[refute_0_1423:[bind(X_86,$fot(X_48)),bind(X_88,$fot(X_94))]]) ).
cnf(refute_0_2206,plain,
( multiply(greatest_lower_bound(inverse(X_48),X_94),X_48) != greatest_lower_bound(identity,multiply(X_94,X_48))
| inverse(X_48) != multiply(inverse(multiply(greatest_lower_bound(inverse(X_48),X_94),X_48)),greatest_lower_bound(inverse(X_48),X_94))
| inverse(X_48) = multiply(inverse(greatest_lower_bound(identity,multiply(X_94,X_48))),greatest_lower_bound(inverse(X_48),X_94)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(X_48),multiply(inverse(multiply(greatest_lower_bound(inverse(X_48),X_94),X_48)),greatest_lower_bound(inverse(X_48),X_94))) ),[1,0,0],$fot(greatest_lower_bound(identity,multiply(X_94,X_48)))]]) ).
cnf(refute_0_2207,plain,
( inverse(X_48) != multiply(inverse(multiply(greatest_lower_bound(inverse(X_48),X_94),X_48)),greatest_lower_bound(inverse(X_48),X_94))
| inverse(X_48) = multiply(inverse(greatest_lower_bound(identity,multiply(X_94,X_48))),greatest_lower_bound(inverse(X_48),X_94)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_48),X_94),X_48),greatest_lower_bound(identity,multiply(X_94,X_48))) )],[refute_0_2205,refute_0_2206]) ).
cnf(refute_0_2208,plain,
inverse(X_48) = multiply(inverse(greatest_lower_bound(identity,multiply(X_94,X_48))),greatest_lower_bound(inverse(X_48),X_94)),
inference(resolve,[$cnf( $equal(inverse(X_48),multiply(inverse(multiply(greatest_lower_bound(inverse(X_48),X_94),X_48)),greatest_lower_bound(inverse(X_48),X_94))) )],[refute_0_2204,refute_0_2207]) ).
cnf(refute_0_2209,plain,
inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))) = multiply(inverse(greatest_lower_bound(identity,multiply(least_upper_bound(X_62,X_63),inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))))),greatest_lower_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))),least_upper_bound(X_62,X_63))),
inference(subst,[],[refute_0_2208:[bind(X_48,$fot(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62))))),bind(X_94,$fot(least_upper_bound(X_62,X_63)))]]) ).
cnf(refute_0_2210,plain,
( X_63 != multiply(least_upper_bound(X_62,X_63),inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62))))
| multiply(least_upper_bound(X_62,X_63),inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))) = X_63 ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(X_63)),bind(Y0,$fot(multiply(least_upper_bound(X_62,X_63),inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62))))))]]) ).
cnf(refute_0_2211,plain,
multiply(least_upper_bound(X_62,X_63),inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))) = X_63,
inference(resolve,[$cnf( $equal(X_63,multiply(least_upper_bound(X_62,X_63),inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62))))) )],[refute_0_1533,refute_0_2210]) ).
cnf(refute_0_2212,plain,
( multiply(least_upper_bound(X_62,X_63),inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))) != X_63
| inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))) != multiply(inverse(greatest_lower_bound(identity,multiply(least_upper_bound(X_62,X_63),inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))))),greatest_lower_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))),least_upper_bound(X_62,X_63)))
| inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))) = multiply(inverse(greatest_lower_bound(identity,X_63)),greatest_lower_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))),least_upper_bound(X_62,X_63))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))),multiply(inverse(greatest_lower_bound(identity,multiply(least_upper_bound(X_62,X_63),inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))))),greatest_lower_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))),least_upper_bound(X_62,X_63)))) ),[1,0,0,1],$fot(X_63)]]) ).
cnf(refute_0_2213,plain,
( inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))) != multiply(inverse(greatest_lower_bound(identity,multiply(least_upper_bound(X_62,X_63),inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))))),greatest_lower_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))),least_upper_bound(X_62,X_63)))
| inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))) = multiply(inverse(greatest_lower_bound(identity,X_63)),greatest_lower_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))),least_upper_bound(X_62,X_63))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_62,X_63),inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))),X_63) )],[refute_0_2211,refute_0_2212]) ).
cnf(refute_0_2214,plain,
inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))) = multiply(inverse(greatest_lower_bound(identity,X_63)),greatest_lower_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))),least_upper_bound(X_62,X_63))),
inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))),multiply(inverse(greatest_lower_bound(identity,multiply(least_upper_bound(X_62,X_63),inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))))),greatest_lower_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))),least_upper_bound(X_62,X_63)))) )],[refute_0_2209,refute_0_2213]) ).
cnf(refute_0_2215,plain,
inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))) = least_upper_bound(identity,multiply(inverse(X_63),X_62)),
inference(subst,[],[p19_2:[bind(X,$fot(least_upper_bound(identity,multiply(inverse(X_63),X_62))))]]) ).
cnf(refute_0_2216,plain,
( inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))) != multiply(inverse(greatest_lower_bound(identity,X_63)),greatest_lower_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))),least_upper_bound(X_62,X_63)))
| inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))) != least_upper_bound(identity,multiply(inverse(X_63),X_62))
| least_upper_bound(identity,multiply(inverse(X_63),X_62)) = multiply(inverse(greatest_lower_bound(identity,X_63)),greatest_lower_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))),least_upper_bound(X_62,X_63))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))),multiply(inverse(greatest_lower_bound(identity,X_63)),greatest_lower_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))),least_upper_bound(X_62,X_63)))) ),[0],$fot(least_upper_bound(identity,multiply(inverse(X_63),X_62)))]]) ).
cnf(refute_0_2217,plain,
( inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))) != multiply(inverse(greatest_lower_bound(identity,X_63)),greatest_lower_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))),least_upper_bound(X_62,X_63)))
| least_upper_bound(identity,multiply(inverse(X_63),X_62)) = multiply(inverse(greatest_lower_bound(identity,X_63)),greatest_lower_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))),least_upper_bound(X_62,X_63))) ),
inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))),least_upper_bound(identity,multiply(inverse(X_63),X_62))) )],[refute_0_2215,refute_0_2216]) ).
cnf(refute_0_2218,plain,
multiply(greatest_lower_bound(inverse(X_57),identity),least_upper_bound(X_56,X_57)) = greatest_lower_bound(least_upper_bound(X_56,X_57),multiply(inverse(X_57),least_upper_bound(X_56,X_57))),
inference(subst,[],[refute_0_45:[bind(X_86,$fot(least_upper_bound(X_56,X_57))),bind(X_87,$fot(inverse(X_57)))]]) ).
cnf(refute_0_2219,plain,
( multiply(greatest_lower_bound(inverse(X_57),identity),least_upper_bound(X_56,X_57)) != greatest_lower_bound(least_upper_bound(X_56,X_57),multiply(inverse(X_57),least_upper_bound(X_56,X_57)))
| multiply(inverse(X_57),least_upper_bound(X_56,X_57)) != least_upper_bound(identity,multiply(inverse(X_57),X_56))
| multiply(greatest_lower_bound(inverse(X_57),identity),least_upper_bound(X_56,X_57)) = greatest_lower_bound(least_upper_bound(X_56,X_57),least_upper_bound(identity,multiply(inverse(X_57),X_56))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_57),identity),least_upper_bound(X_56,X_57)),greatest_lower_bound(least_upper_bound(X_56,X_57),multiply(inverse(X_57),least_upper_bound(X_56,X_57)))) ),[1,1],$fot(least_upper_bound(identity,multiply(inverse(X_57),X_56)))]]) ).
cnf(refute_0_2220,plain,
( multiply(greatest_lower_bound(inverse(X_57),identity),least_upper_bound(X_56,X_57)) != greatest_lower_bound(least_upper_bound(X_56,X_57),multiply(inverse(X_57),least_upper_bound(X_56,X_57)))
| multiply(greatest_lower_bound(inverse(X_57),identity),least_upper_bound(X_56,X_57)) = greatest_lower_bound(least_upper_bound(X_56,X_57),least_upper_bound(identity,multiply(inverse(X_57),X_56))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_57),least_upper_bound(X_56,X_57)),least_upper_bound(identity,multiply(inverse(X_57),X_56))) )],[refute_0_127,refute_0_2219]) ).
cnf(refute_0_2221,plain,
multiply(greatest_lower_bound(inverse(X_57),identity),least_upper_bound(X_56,X_57)) = greatest_lower_bound(least_upper_bound(X_56,X_57),least_upper_bound(identity,multiply(inverse(X_57),X_56))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_57),identity),least_upper_bound(X_56,X_57)),greatest_lower_bound(least_upper_bound(X_56,X_57),multiply(inverse(X_57),least_upper_bound(X_56,X_57)))) )],[refute_0_2218,refute_0_2220]) ).
cnf(refute_0_2222,plain,
multiply(greatest_lower_bound(inverse(X_57),identity),least_upper_bound(X_56,X_57)) = multiply(greatest_lower_bound(identity,inverse(X_57)),least_upper_bound(X_56,X_57)),
inference(subst,[],[refute_0_432:[bind(Y,$fot(least_upper_bound(X_56,X_57))),bind(X_90,$fot(inverse(X_57)))]]) ).
cnf(refute_0_2223,plain,
( multiply(greatest_lower_bound(inverse(X_57),identity),least_upper_bound(X_56,X_57)) != multiply(greatest_lower_bound(identity,inverse(X_57)),least_upper_bound(X_56,X_57))
| multiply(greatest_lower_bound(inverse(X_57),identity),least_upper_bound(X_56,X_57)) != greatest_lower_bound(least_upper_bound(X_56,X_57),least_upper_bound(identity,multiply(inverse(X_57),X_56)))
| multiply(greatest_lower_bound(identity,inverse(X_57)),least_upper_bound(X_56,X_57)) = greatest_lower_bound(least_upper_bound(X_56,X_57),least_upper_bound(identity,multiply(inverse(X_57),X_56))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_57),identity),least_upper_bound(X_56,X_57)),greatest_lower_bound(least_upper_bound(X_56,X_57),least_upper_bound(identity,multiply(inverse(X_57),X_56)))) ),[0],$fot(multiply(greatest_lower_bound(identity,inverse(X_57)),least_upper_bound(X_56,X_57)))]]) ).
cnf(refute_0_2224,plain,
( multiply(greatest_lower_bound(inverse(X_57),identity),least_upper_bound(X_56,X_57)) != greatest_lower_bound(least_upper_bound(X_56,X_57),least_upper_bound(identity,multiply(inverse(X_57),X_56)))
| multiply(greatest_lower_bound(identity,inverse(X_57)),least_upper_bound(X_56,X_57)) = greatest_lower_bound(least_upper_bound(X_56,X_57),least_upper_bound(identity,multiply(inverse(X_57),X_56))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_57),identity),least_upper_bound(X_56,X_57)),multiply(greatest_lower_bound(identity,inverse(X_57)),least_upper_bound(X_56,X_57))) )],[refute_0_2222,refute_0_2223]) ).
cnf(refute_0_2225,plain,
multiply(greatest_lower_bound(identity,inverse(X_57)),least_upper_bound(X_56,X_57)) = greatest_lower_bound(least_upper_bound(X_56,X_57),least_upper_bound(identity,multiply(inverse(X_57),X_56))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_57),identity),least_upper_bound(X_56,X_57)),greatest_lower_bound(least_upper_bound(X_56,X_57),least_upper_bound(identity,multiply(inverse(X_57),X_56)))) )],[refute_0_2221,refute_0_2224]) ).
cnf(refute_0_2226,plain,
( multiply(greatest_lower_bound(identity,inverse(X_57)),least_upper_bound(X_56,X_57)) != greatest_lower_bound(least_upper_bound(X_56,X_57),least_upper_bound(identity,multiply(inverse(X_57),X_56)))
| greatest_lower_bound(least_upper_bound(X_56,X_57),least_upper_bound(identity,multiply(inverse(X_57),X_56))) = multiply(greatest_lower_bound(identity,inverse(X_57)),least_upper_bound(X_56,X_57)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(multiply(greatest_lower_bound(identity,inverse(X_57)),least_upper_bound(X_56,X_57)))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(X_56,X_57),least_upper_bound(identity,multiply(inverse(X_57),X_56)))))]]) ).
cnf(refute_0_2227,plain,
greatest_lower_bound(least_upper_bound(X_56,X_57),least_upper_bound(identity,multiply(inverse(X_57),X_56))) = multiply(greatest_lower_bound(identity,inverse(X_57)),least_upper_bound(X_56,X_57)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(X_57)),least_upper_bound(X_56,X_57)),greatest_lower_bound(least_upper_bound(X_56,X_57),least_upper_bound(identity,multiply(inverse(X_57),X_56)))) )],[refute_0_2225,refute_0_2226]) ).
cnf(refute_0_2228,plain,
greatest_lower_bound(least_upper_bound(X_62,X_63),least_upper_bound(identity,multiply(inverse(X_63),X_62))) = multiply(greatest_lower_bound(identity,inverse(X_63)),least_upper_bound(X_62,X_63)),
inference(subst,[],[refute_0_2227:[bind(X_56,$fot(X_62)),bind(X_57,$fot(X_63))]]) ).
cnf(refute_0_2229,plain,
greatest_lower_bound(least_upper_bound(X_62,X_63),inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62))))) = greatest_lower_bound(least_upper_bound(X_62,X_63),inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62))))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(least_upper_bound(X_62,X_63),inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62))))))]]) ).
cnf(refute_0_2230,plain,
( greatest_lower_bound(least_upper_bound(X_62,X_63),inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62))))) != greatest_lower_bound(least_upper_bound(X_62,X_63),inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))))
| inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))) != least_upper_bound(identity,multiply(inverse(X_63),X_62))
| greatest_lower_bound(least_upper_bound(X_62,X_63),inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62))))) = greatest_lower_bound(least_upper_bound(X_62,X_63),least_upper_bound(identity,multiply(inverse(X_63),X_62))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_62,X_63),inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62))))),greatest_lower_bound(least_upper_bound(X_62,X_63),inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))))) ),[1,1],$fot(least_upper_bound(identity,multiply(inverse(X_63),X_62)))]]) ).
cnf(refute_0_2231,plain,
( inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))) != least_upper_bound(identity,multiply(inverse(X_63),X_62))
| greatest_lower_bound(least_upper_bound(X_62,X_63),inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62))))) = greatest_lower_bound(least_upper_bound(X_62,X_63),least_upper_bound(identity,multiply(inverse(X_63),X_62))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_62,X_63),inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62))))),greatest_lower_bound(least_upper_bound(X_62,X_63),inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))))) )],[refute_0_2229,refute_0_2230]) ).
cnf(refute_0_2232,plain,
greatest_lower_bound(least_upper_bound(X_62,X_63),inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62))))) = greatest_lower_bound(least_upper_bound(X_62,X_63),least_upper_bound(identity,multiply(inverse(X_63),X_62))),
inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))),least_upper_bound(identity,multiply(inverse(X_63),X_62))) )],[refute_0_2215,refute_0_2231]) ).
cnf(refute_0_2233,plain,
( greatest_lower_bound(least_upper_bound(X_62,X_63),inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62))))) != greatest_lower_bound(least_upper_bound(X_62,X_63),least_upper_bound(identity,multiply(inverse(X_63),X_62)))
| greatest_lower_bound(least_upper_bound(X_62,X_63),least_upper_bound(identity,multiply(inverse(X_63),X_62))) != multiply(greatest_lower_bound(identity,inverse(X_63)),least_upper_bound(X_62,X_63))
| greatest_lower_bound(least_upper_bound(X_62,X_63),inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62))))) = multiply(greatest_lower_bound(identity,inverse(X_63)),least_upper_bound(X_62,X_63)) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(X_62,X_63),inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62))))))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(X_62,X_63),least_upper_bound(identity,multiply(inverse(X_63),X_62))))),bind(Z0,$fot(multiply(greatest_lower_bound(identity,inverse(X_63)),least_upper_bound(X_62,X_63))))]]) ).
cnf(refute_0_2234,plain,
( greatest_lower_bound(least_upper_bound(X_62,X_63),least_upper_bound(identity,multiply(inverse(X_63),X_62))) != multiply(greatest_lower_bound(identity,inverse(X_63)),least_upper_bound(X_62,X_63))
| greatest_lower_bound(least_upper_bound(X_62,X_63),inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62))))) = multiply(greatest_lower_bound(identity,inverse(X_63)),least_upper_bound(X_62,X_63)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_62,X_63),inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62))))),greatest_lower_bound(least_upper_bound(X_62,X_63),least_upper_bound(identity,multiply(inverse(X_63),X_62)))) )],[refute_0_2232,refute_0_2233]) ).
cnf(refute_0_2235,plain,
greatest_lower_bound(least_upper_bound(X_62,X_63),inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62))))) = multiply(greatest_lower_bound(identity,inverse(X_63)),least_upper_bound(X_62,X_63)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_62,X_63),least_upper_bound(identity,multiply(inverse(X_63),X_62))),multiply(greatest_lower_bound(identity,inverse(X_63)),least_upper_bound(X_62,X_63))) )],[refute_0_2228,refute_0_2234]) ).
cnf(refute_0_2236,plain,
multiply(inverse(greatest_lower_bound(identity,X_63)),greatest_lower_bound(least_upper_bound(X_62,X_63),inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))))) = multiply(inverse(greatest_lower_bound(identity,X_63)),greatest_lower_bound(least_upper_bound(X_62,X_63),inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))))),
introduced(tautology,[refl,[$fot(multiply(inverse(greatest_lower_bound(identity,X_63)),greatest_lower_bound(least_upper_bound(X_62,X_63),inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))))))]]) ).
cnf(refute_0_2237,plain,
( multiply(inverse(greatest_lower_bound(identity,X_63)),greatest_lower_bound(least_upper_bound(X_62,X_63),inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))))) != multiply(inverse(greatest_lower_bound(identity,X_63)),greatest_lower_bound(least_upper_bound(X_62,X_63),inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62))))))
| greatest_lower_bound(least_upper_bound(X_62,X_63),inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62))))) != multiply(greatest_lower_bound(identity,inverse(X_63)),least_upper_bound(X_62,X_63))
| multiply(inverse(greatest_lower_bound(identity,X_63)),greatest_lower_bound(least_upper_bound(X_62,X_63),inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))))) = multiply(inverse(greatest_lower_bound(identity,X_63)),multiply(greatest_lower_bound(identity,inverse(X_63)),least_upper_bound(X_62,X_63))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_63)),greatest_lower_bound(least_upper_bound(X_62,X_63),inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))))),multiply(inverse(greatest_lower_bound(identity,X_63)),greatest_lower_bound(least_upper_bound(X_62,X_63),inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62))))))) ),[1,1],$fot(multiply(greatest_lower_bound(identity,inverse(X_63)),least_upper_bound(X_62,X_63)))]]) ).
cnf(refute_0_2238,plain,
( greatest_lower_bound(least_upper_bound(X_62,X_63),inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62))))) != multiply(greatest_lower_bound(identity,inverse(X_63)),least_upper_bound(X_62,X_63))
| multiply(inverse(greatest_lower_bound(identity,X_63)),greatest_lower_bound(least_upper_bound(X_62,X_63),inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))))) = multiply(inverse(greatest_lower_bound(identity,X_63)),multiply(greatest_lower_bound(identity,inverse(X_63)),least_upper_bound(X_62,X_63))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_63)),greatest_lower_bound(least_upper_bound(X_62,X_63),inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))))),multiply(inverse(greatest_lower_bound(identity,X_63)),greatest_lower_bound(least_upper_bound(X_62,X_63),inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62))))))) )],[refute_0_2236,refute_0_2237]) ).
cnf(refute_0_2239,plain,
multiply(inverse(greatest_lower_bound(identity,X_63)),greatest_lower_bound(least_upper_bound(X_62,X_63),inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))))) = multiply(inverse(greatest_lower_bound(identity,X_63)),multiply(greatest_lower_bound(identity,inverse(X_63)),least_upper_bound(X_62,X_63))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_62,X_63),inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62))))),multiply(greatest_lower_bound(identity,inverse(X_63)),least_upper_bound(X_62,X_63))) )],[refute_0_2235,refute_0_2238]) ).
cnf(refute_0_2240,plain,
multiply(X_251,least_upper_bound(greatest_lower_bound(X_35,X_15),greatest_lower_bound(X_15,X_35))) = multiply(X_251,least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15))),
inference(subst,[],[refute_0_807:[bind(X,$fot(X_251)),bind(Y,$fot(greatest_lower_bound(X_35,X_15))),bind(Z,$fot(greatest_lower_bound(X_15,X_35)))]]) ).
cnf(refute_0_2241,plain,
( multiply(X_251,least_upper_bound(greatest_lower_bound(X_35,X_15),greatest_lower_bound(X_15,X_35))) != multiply(X_251,least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15)))
| least_upper_bound(greatest_lower_bound(X_35,X_15),greatest_lower_bound(X_15,X_35)) != greatest_lower_bound(X_35,X_15)
| multiply(X_251,greatest_lower_bound(X_35,X_15)) = multiply(X_251,least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_251,least_upper_bound(greatest_lower_bound(X_35,X_15),greatest_lower_bound(X_15,X_35))),multiply(X_251,least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15)))) ),[0,1],$fot(greatest_lower_bound(X_35,X_15))]]) ).
cnf(refute_0_2242,plain,
( multiply(X_251,least_upper_bound(greatest_lower_bound(X_35,X_15),greatest_lower_bound(X_15,X_35))) != multiply(X_251,least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15)))
| multiply(X_251,greatest_lower_bound(X_35,X_15)) = multiply(X_251,least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_35,X_15),greatest_lower_bound(X_15,X_35)),greatest_lower_bound(X_35,X_15)) )],[refute_0_1539,refute_0_2241]) ).
cnf(refute_0_2243,plain,
multiply(X_251,greatest_lower_bound(X_35,X_15)) = multiply(X_251,least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15))),
inference(resolve,[$cnf( $equal(multiply(X_251,least_upper_bound(greatest_lower_bound(X_35,X_15),greatest_lower_bound(X_15,X_35))),multiply(X_251,least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15)))) )],[refute_0_2240,refute_0_2242]) ).
cnf(refute_0_2244,plain,
least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15)) = greatest_lower_bound(X_15,X_35),
inference(subst,[],[refute_0_1539:[bind(X_15,$fot(X_35)),bind(X_35,$fot(X_15))]]) ).
cnf(refute_0_2245,plain,
multiply(X_251,least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15))) = multiply(X_251,least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15))),
introduced(tautology,[refl,[$fot(multiply(X_251,least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15))))]]) ).
cnf(refute_0_2246,plain,
( multiply(X_251,least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15))) != multiply(X_251,least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15)))
| least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15)) != greatest_lower_bound(X_15,X_35)
| multiply(X_251,least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15))) = multiply(X_251,greatest_lower_bound(X_15,X_35)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_251,least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15))),multiply(X_251,least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15)))) ),[1,1],$fot(greatest_lower_bound(X_15,X_35))]]) ).
cnf(refute_0_2247,plain,
( least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15)) != greatest_lower_bound(X_15,X_35)
| multiply(X_251,least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15))) = multiply(X_251,greatest_lower_bound(X_15,X_35)) ),
inference(resolve,[$cnf( $equal(multiply(X_251,least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15))),multiply(X_251,least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15)))) )],[refute_0_2245,refute_0_2246]) ).
cnf(refute_0_2248,plain,
multiply(X_251,least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15))) = multiply(X_251,greatest_lower_bound(X_15,X_35)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15)),greatest_lower_bound(X_15,X_35)) )],[refute_0_2244,refute_0_2247]) ).
cnf(refute_0_2249,plain,
( multiply(X_251,greatest_lower_bound(X_35,X_15)) != multiply(X_251,least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15)))
| multiply(X_251,least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15))) != multiply(X_251,greatest_lower_bound(X_15,X_35))
| multiply(X_251,greatest_lower_bound(X_35,X_15)) = multiply(X_251,greatest_lower_bound(X_15,X_35)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_251,greatest_lower_bound(X_35,X_15)),multiply(X_251,greatest_lower_bound(X_15,X_35))) ),[0],$fot(multiply(X_251,least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15))))]]) ).
cnf(refute_0_2250,plain,
( multiply(X_251,greatest_lower_bound(X_35,X_15)) != multiply(X_251,least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15)))
| multiply(X_251,greatest_lower_bound(X_35,X_15)) = multiply(X_251,greatest_lower_bound(X_15,X_35)) ),
inference(resolve,[$cnf( $equal(multiply(X_251,least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15))),multiply(X_251,greatest_lower_bound(X_15,X_35))) )],[refute_0_2248,refute_0_2249]) ).
cnf(refute_0_2251,plain,
multiply(X_251,greatest_lower_bound(X_35,X_15)) = multiply(X_251,greatest_lower_bound(X_15,X_35)),
inference(resolve,[$cnf( $equal(multiply(X_251,greatest_lower_bound(X_35,X_15)),multiply(X_251,least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15)))) )],[refute_0_2243,refute_0_2250]) ).
cnf(refute_0_2252,plain,
( multiply(X_251,greatest_lower_bound(X_35,X_15)) != multiply(X_251,greatest_lower_bound(X_15,X_35))
| multiply(X_251,greatest_lower_bound(X_15,X_35)) = multiply(X_251,greatest_lower_bound(X_35,X_15)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(multiply(X_251,greatest_lower_bound(X_35,X_15)))),bind(Y0,$fot(multiply(X_251,greatest_lower_bound(X_15,X_35))))]]) ).
cnf(refute_0_2253,plain,
multiply(X_251,greatest_lower_bound(X_15,X_35)) = multiply(X_251,greatest_lower_bound(X_35,X_15)),
inference(resolve,[$cnf( $equal(multiply(X_251,greatest_lower_bound(X_35,X_15)),multiply(X_251,greatest_lower_bound(X_15,X_35))) )],[refute_0_2251,refute_0_2252]) ).
cnf(refute_0_2254,plain,
multiply(inverse(greatest_lower_bound(identity,X_63)),greatest_lower_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))),least_upper_bound(X_62,X_63))) = multiply(inverse(greatest_lower_bound(identity,X_63)),greatest_lower_bound(least_upper_bound(X_62,X_63),inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))))),
inference(subst,[],[refute_0_2253:[bind(X_15,$fot(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))))),bind(X_251,$fot(inverse(greatest_lower_bound(identity,X_63)))),bind(X_35,$fot(least_upper_bound(X_62,X_63)))]]) ).
cnf(refute_0_2255,plain,
( multiply(inverse(greatest_lower_bound(identity,X_63)),greatest_lower_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))),least_upper_bound(X_62,X_63))) != multiply(inverse(greatest_lower_bound(identity,X_63)),greatest_lower_bound(least_upper_bound(X_62,X_63),inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62))))))
| multiply(inverse(greatest_lower_bound(identity,X_63)),greatest_lower_bound(least_upper_bound(X_62,X_63),inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))))) != multiply(inverse(greatest_lower_bound(identity,X_63)),multiply(greatest_lower_bound(identity,inverse(X_63)),least_upper_bound(X_62,X_63)))
| multiply(inverse(greatest_lower_bound(identity,X_63)),greatest_lower_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))),least_upper_bound(X_62,X_63))) = multiply(inverse(greatest_lower_bound(identity,X_63)),multiply(greatest_lower_bound(identity,inverse(X_63)),least_upper_bound(X_62,X_63))) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(identity,X_63)),greatest_lower_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))),least_upper_bound(X_62,X_63))))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(identity,X_63)),greatest_lower_bound(least_upper_bound(X_62,X_63),inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))))))),bind(Z0,$fot(multiply(inverse(greatest_lower_bound(identity,X_63)),multiply(greatest_lower_bound(identity,inverse(X_63)),least_upper_bound(X_62,X_63)))))]]) ).
cnf(refute_0_2256,plain,
( multiply(inverse(greatest_lower_bound(identity,X_63)),greatest_lower_bound(least_upper_bound(X_62,X_63),inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))))) != multiply(inverse(greatest_lower_bound(identity,X_63)),multiply(greatest_lower_bound(identity,inverse(X_63)),least_upper_bound(X_62,X_63)))
| multiply(inverse(greatest_lower_bound(identity,X_63)),greatest_lower_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))),least_upper_bound(X_62,X_63))) = multiply(inverse(greatest_lower_bound(identity,X_63)),multiply(greatest_lower_bound(identity,inverse(X_63)),least_upper_bound(X_62,X_63))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_63)),greatest_lower_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))),least_upper_bound(X_62,X_63))),multiply(inverse(greatest_lower_bound(identity,X_63)),greatest_lower_bound(least_upper_bound(X_62,X_63),inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62))))))) )],[refute_0_2254,refute_0_2255]) ).
cnf(refute_0_2257,plain,
multiply(inverse(greatest_lower_bound(identity,X_63)),greatest_lower_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))),least_upper_bound(X_62,X_63))) = multiply(inverse(greatest_lower_bound(identity,X_63)),multiply(greatest_lower_bound(identity,inverse(X_63)),least_upper_bound(X_62,X_63))),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_63)),greatest_lower_bound(least_upper_bound(X_62,X_63),inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))))),multiply(inverse(greatest_lower_bound(identity,X_63)),multiply(greatest_lower_bound(identity,inverse(X_63)),least_upper_bound(X_62,X_63)))) )],[refute_0_2239,refute_0_2256]) ).
cnf(refute_0_2258,plain,
( multiply(inverse(greatest_lower_bound(identity,X_63)),greatest_lower_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))),least_upper_bound(X_62,X_63))) != multiply(inverse(greatest_lower_bound(identity,X_63)),multiply(greatest_lower_bound(identity,inverse(X_63)),least_upper_bound(X_62,X_63)))
| least_upper_bound(identity,multiply(inverse(X_63),X_62)) != multiply(inverse(greatest_lower_bound(identity,X_63)),greatest_lower_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))),least_upper_bound(X_62,X_63)))
| least_upper_bound(identity,multiply(inverse(X_63),X_62)) = multiply(inverse(greatest_lower_bound(identity,X_63)),multiply(greatest_lower_bound(identity,inverse(X_63)),least_upper_bound(X_62,X_63))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(X_63),X_62)),multiply(inverse(greatest_lower_bound(identity,X_63)),greatest_lower_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))),least_upper_bound(X_62,X_63)))) ),[1],$fot(multiply(inverse(greatest_lower_bound(identity,X_63)),multiply(greatest_lower_bound(identity,inverse(X_63)),least_upper_bound(X_62,X_63))))]]) ).
cnf(refute_0_2259,plain,
( least_upper_bound(identity,multiply(inverse(X_63),X_62)) != multiply(inverse(greatest_lower_bound(identity,X_63)),greatest_lower_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))),least_upper_bound(X_62,X_63)))
| least_upper_bound(identity,multiply(inverse(X_63),X_62)) = multiply(inverse(greatest_lower_bound(identity,X_63)),multiply(greatest_lower_bound(identity,inverse(X_63)),least_upper_bound(X_62,X_63))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_63)),greatest_lower_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))),least_upper_bound(X_62,X_63))),multiply(inverse(greatest_lower_bound(identity,X_63)),multiply(greatest_lower_bound(identity,inverse(X_63)),least_upper_bound(X_62,X_63)))) )],[refute_0_2257,refute_0_2258]) ).
cnf(refute_0_2260,plain,
( inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))) != multiply(inverse(greatest_lower_bound(identity,X_63)),greatest_lower_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))),least_upper_bound(X_62,X_63)))
| least_upper_bound(identity,multiply(inverse(X_63),X_62)) = multiply(inverse(greatest_lower_bound(identity,X_63)),multiply(greatest_lower_bound(identity,inverse(X_63)),least_upper_bound(X_62,X_63))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(X_63),X_62)),multiply(inverse(greatest_lower_bound(identity,X_63)),greatest_lower_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))),least_upper_bound(X_62,X_63)))) )],[refute_0_2217,refute_0_2259]) ).
cnf(refute_0_2261,plain,
least_upper_bound(identity,multiply(inverse(X_63),X_62)) = multiply(inverse(greatest_lower_bound(identity,X_63)),multiply(greatest_lower_bound(identity,inverse(X_63)),least_upper_bound(X_62,X_63))),
inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))),multiply(inverse(greatest_lower_bound(identity,X_63)),greatest_lower_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_63),X_62)))),least_upper_bound(X_62,X_63)))) )],[refute_0_2214,refute_0_2260]) ).
cnf(refute_0_2262,plain,
inverse(multiply(inverse(X_318),X_46)) = multiply(inverse(greatest_lower_bound(identity,multiply(X_318,multiply(inverse(X_318),X_46)))),greatest_lower_bound(inverse(multiply(inverse(X_318),X_46)),X_318)),
inference(subst,[],[refute_0_2208:[bind(X_48,$fot(multiply(inverse(X_318),X_46))),bind(X_94,$fot(X_318))]]) ).
cnf(refute_0_2263,plain,
X_46 = multiply(X_318,multiply(inverse(X_318),X_46)),
inference(subst,[],[refute_0_1960:[bind(X_44,$fot(X_318))]]) ).
cnf(refute_0_2264,plain,
( X_46 != multiply(X_318,multiply(inverse(X_318),X_46))
| multiply(X_318,multiply(inverse(X_318),X_46)) = X_46 ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(X_46)),bind(Y0,$fot(multiply(X_318,multiply(inverse(X_318),X_46))))]]) ).
cnf(refute_0_2265,plain,
multiply(X_318,multiply(inverse(X_318),X_46)) = X_46,
inference(resolve,[$cnf( $equal(X_46,multiply(X_318,multiply(inverse(X_318),X_46))) )],[refute_0_2263,refute_0_2264]) ).
cnf(refute_0_2266,plain,
( multiply(X_318,multiply(inverse(X_318),X_46)) != X_46
| inverse(multiply(inverse(X_318),X_46)) != multiply(inverse(greatest_lower_bound(identity,multiply(X_318,multiply(inverse(X_318),X_46)))),greatest_lower_bound(inverse(multiply(inverse(X_318),X_46)),X_318))
| inverse(multiply(inverse(X_318),X_46)) = multiply(inverse(greatest_lower_bound(identity,X_46)),greatest_lower_bound(inverse(multiply(inverse(X_318),X_46)),X_318)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X_318),X_46)),multiply(inverse(greatest_lower_bound(identity,multiply(X_318,multiply(inverse(X_318),X_46)))),greatest_lower_bound(inverse(multiply(inverse(X_318),X_46)),X_318))) ),[1,0,0,1],$fot(X_46)]]) ).
cnf(refute_0_2267,plain,
( inverse(multiply(inverse(X_318),X_46)) != multiply(inverse(greatest_lower_bound(identity,multiply(X_318,multiply(inverse(X_318),X_46)))),greatest_lower_bound(inverse(multiply(inverse(X_318),X_46)),X_318))
| inverse(multiply(inverse(X_318),X_46)) = multiply(inverse(greatest_lower_bound(identity,X_46)),greatest_lower_bound(inverse(multiply(inverse(X_318),X_46)),X_318)) ),
inference(resolve,[$cnf( $equal(multiply(X_318,multiply(inverse(X_318),X_46)),X_46) )],[refute_0_2265,refute_0_2266]) ).
cnf(refute_0_2268,plain,
inverse(multiply(inverse(X_318),X_46)) = multiply(inverse(greatest_lower_bound(identity,X_46)),greatest_lower_bound(inverse(multiply(inverse(X_318),X_46)),X_318)),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_318),X_46)),multiply(inverse(greatest_lower_bound(identity,multiply(X_318,multiply(inverse(X_318),X_46)))),greatest_lower_bound(inverse(multiply(inverse(X_318),X_46)),X_318))) )],[refute_0_2262,refute_0_2267]) ).
cnf(refute_0_2269,plain,
inverse(multiply(inverse(X_318),X_46)) = multiply(inverse(X_46),X_318),
inference(subst,[],[refute_0_534:[bind(X,$fot(X_318)),bind(X_24,$fot(X_46))]]) ).
cnf(refute_0_2270,plain,
( inverse(multiply(inverse(X_318),X_46)) != multiply(inverse(X_46),X_318)
| inverse(multiply(inverse(X_318),X_46)) != multiply(inverse(greatest_lower_bound(identity,X_46)),greatest_lower_bound(inverse(multiply(inverse(X_318),X_46)),X_318))
| multiply(inverse(X_46),X_318) = multiply(inverse(greatest_lower_bound(identity,X_46)),greatest_lower_bound(inverse(multiply(inverse(X_318),X_46)),X_318)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X_318),X_46)),multiply(inverse(greatest_lower_bound(identity,X_46)),greatest_lower_bound(inverse(multiply(inverse(X_318),X_46)),X_318))) ),[0],$fot(multiply(inverse(X_46),X_318))]]) ).
cnf(refute_0_2271,plain,
( inverse(multiply(inverse(X_318),X_46)) != multiply(inverse(greatest_lower_bound(identity,X_46)),greatest_lower_bound(inverse(multiply(inverse(X_318),X_46)),X_318))
| multiply(inverse(X_46),X_318) = multiply(inverse(greatest_lower_bound(identity,X_46)),greatest_lower_bound(inverse(multiply(inverse(X_318),X_46)),X_318)) ),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_318),X_46)),multiply(inverse(X_46),X_318)) )],[refute_0_2269,refute_0_2270]) ).
cnf(refute_0_2272,plain,
multiply(least_upper_bound(greatest_lower_bound(X_35,X_15),greatest_lower_bound(X_15,X_35)),X_248) = multiply(least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15)),X_248),
inference(subst,[],[refute_0_692:[bind(X,$fot(X_248)),bind(Y,$fot(greatest_lower_bound(X_35,X_15))),bind(Z,$fot(greatest_lower_bound(X_15,X_35)))]]) ).
cnf(refute_0_2273,plain,
( multiply(least_upper_bound(greatest_lower_bound(X_35,X_15),greatest_lower_bound(X_15,X_35)),X_248) != multiply(least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15)),X_248)
| least_upper_bound(greatest_lower_bound(X_35,X_15),greatest_lower_bound(X_15,X_35)) != greatest_lower_bound(X_35,X_15)
| multiply(greatest_lower_bound(X_35,X_15),X_248) = multiply(least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15)),X_248) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(X_35,X_15),greatest_lower_bound(X_15,X_35)),X_248),multiply(least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15)),X_248)) ),[0,0],$fot(greatest_lower_bound(X_35,X_15))]]) ).
cnf(refute_0_2274,plain,
( multiply(least_upper_bound(greatest_lower_bound(X_35,X_15),greatest_lower_bound(X_15,X_35)),X_248) != multiply(least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15)),X_248)
| multiply(greatest_lower_bound(X_35,X_15),X_248) = multiply(least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15)),X_248) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_35,X_15),greatest_lower_bound(X_15,X_35)),greatest_lower_bound(X_35,X_15)) )],[refute_0_1539,refute_0_2273]) ).
cnf(refute_0_2275,plain,
multiply(greatest_lower_bound(X_35,X_15),X_248) = multiply(least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15)),X_248),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(X_35,X_15),greatest_lower_bound(X_15,X_35)),X_248),multiply(least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15)),X_248)) )],[refute_0_2272,refute_0_2274]) ).
cnf(refute_0_2276,plain,
multiply(least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15)),X_248) = multiply(least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15)),X_248),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15)),X_248))]]) ).
cnf(refute_0_2277,plain,
( multiply(least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15)),X_248) != multiply(least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15)),X_248)
| least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15)) != greatest_lower_bound(X_15,X_35)
| multiply(least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15)),X_248) = multiply(greatest_lower_bound(X_15,X_35),X_248) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15)),X_248),multiply(least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15)),X_248)) ),[1,0],$fot(greatest_lower_bound(X_15,X_35))]]) ).
cnf(refute_0_2278,plain,
( least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15)) != greatest_lower_bound(X_15,X_35)
| multiply(least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15)),X_248) = multiply(greatest_lower_bound(X_15,X_35),X_248) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15)),X_248),multiply(least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15)),X_248)) )],[refute_0_2276,refute_0_2277]) ).
cnf(refute_0_2279,plain,
multiply(least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15)),X_248) = multiply(greatest_lower_bound(X_15,X_35),X_248),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15)),greatest_lower_bound(X_15,X_35)) )],[refute_0_2244,refute_0_2278]) ).
cnf(refute_0_2280,plain,
( multiply(greatest_lower_bound(X_35,X_15),X_248) != multiply(least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15)),X_248)
| multiply(least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15)),X_248) != multiply(greatest_lower_bound(X_15,X_35),X_248)
| multiply(greatest_lower_bound(X_35,X_15),X_248) = multiply(greatest_lower_bound(X_15,X_35),X_248) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_35,X_15),X_248),multiply(greatest_lower_bound(X_15,X_35),X_248)) ),[0],$fot(multiply(least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15)),X_248))]]) ).
cnf(refute_0_2281,plain,
( multiply(greatest_lower_bound(X_35,X_15),X_248) != multiply(least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15)),X_248)
| multiply(greatest_lower_bound(X_35,X_15),X_248) = multiply(greatest_lower_bound(X_15,X_35),X_248) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15)),X_248),multiply(greatest_lower_bound(X_15,X_35),X_248)) )],[refute_0_2279,refute_0_2280]) ).
cnf(refute_0_2282,plain,
multiply(greatest_lower_bound(X_35,X_15),X_248) = multiply(greatest_lower_bound(X_15,X_35),X_248),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_35,X_15),X_248),multiply(least_upper_bound(greatest_lower_bound(X_15,X_35),greatest_lower_bound(X_35,X_15)),X_248)) )],[refute_0_2275,refute_0_2281]) ).
cnf(refute_0_2283,plain,
( multiply(greatest_lower_bound(X_35,X_15),X_248) != multiply(greatest_lower_bound(X_15,X_35),X_248)
| multiply(greatest_lower_bound(X_15,X_35),X_248) = multiply(greatest_lower_bound(X_35,X_15),X_248) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(multiply(greatest_lower_bound(X_35,X_15),X_248))),bind(Y0,$fot(multiply(greatest_lower_bound(X_15,X_35),X_248)))]]) ).
cnf(refute_0_2284,plain,
multiply(greatest_lower_bound(X_15,X_35),X_248) = multiply(greatest_lower_bound(X_35,X_15),X_248),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_35,X_15),X_248),multiply(greatest_lower_bound(X_15,X_35),X_248)) )],[refute_0_2282,refute_0_2283]) ).
cnf(refute_0_2285,plain,
multiply(greatest_lower_bound(inverse(X_46),identity),X_318) = multiply(greatest_lower_bound(identity,inverse(X_46)),X_318),
inference(subst,[],[refute_0_2284:[bind(X_15,$fot(inverse(X_46))),bind(X_248,$fot(X_318)),bind(X_35,$fot(identity))]]) ).
cnf(refute_0_2286,plain,
greatest_lower_bound(X_318,multiply(inverse(X_46),X_318)) = multiply(greatest_lower_bound(inverse(X_46),identity),X_318),
inference(subst,[],[refute_0_410:[bind(X_86,$fot(X_318)),bind(X_87,$fot(inverse(X_46)))]]) ).
cnf(refute_0_2287,plain,
( multiply(greatest_lower_bound(inverse(X_46),identity),X_318) != multiply(greatest_lower_bound(identity,inverse(X_46)),X_318)
| greatest_lower_bound(X_318,multiply(inverse(X_46),X_318)) != multiply(greatest_lower_bound(inverse(X_46),identity),X_318)
| greatest_lower_bound(X_318,multiply(inverse(X_46),X_318)) = multiply(greatest_lower_bound(identity,inverse(X_46)),X_318) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(greatest_lower_bound(X_318,multiply(inverse(X_46),X_318)))),bind(Y0,$fot(multiply(greatest_lower_bound(inverse(X_46),identity),X_318))),bind(Z0,$fot(multiply(greatest_lower_bound(identity,inverse(X_46)),X_318)))]]) ).
cnf(refute_0_2288,plain,
( multiply(greatest_lower_bound(inverse(X_46),identity),X_318) != multiply(greatest_lower_bound(identity,inverse(X_46)),X_318)
| greatest_lower_bound(X_318,multiply(inverse(X_46),X_318)) = multiply(greatest_lower_bound(identity,inverse(X_46)),X_318) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_318,multiply(inverse(X_46),X_318)),multiply(greatest_lower_bound(inverse(X_46),identity),X_318)) )],[refute_0_2286,refute_0_2287]) ).
cnf(refute_0_2289,plain,
greatest_lower_bound(X_318,multiply(inverse(X_46),X_318)) = multiply(greatest_lower_bound(identity,inverse(X_46)),X_318),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_46),identity),X_318),multiply(greatest_lower_bound(identity,inverse(X_46)),X_318)) )],[refute_0_2285,refute_0_2288]) ).
cnf(refute_0_2290,plain,
greatest_lower_bound(X_318,inverse(multiply(inverse(X_318),X_46))) = greatest_lower_bound(X_318,inverse(multiply(inverse(X_318),X_46))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X_318,inverse(multiply(inverse(X_318),X_46))))]]) ).
cnf(refute_0_2291,plain,
( greatest_lower_bound(X_318,inverse(multiply(inverse(X_318),X_46))) != greatest_lower_bound(X_318,inverse(multiply(inverse(X_318),X_46)))
| inverse(multiply(inverse(X_318),X_46)) != multiply(inverse(X_46),X_318)
| greatest_lower_bound(X_318,inverse(multiply(inverse(X_318),X_46))) = greatest_lower_bound(X_318,multiply(inverse(X_46),X_318)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_318,inverse(multiply(inverse(X_318),X_46))),greatest_lower_bound(X_318,inverse(multiply(inverse(X_318),X_46)))) ),[1,1],$fot(multiply(inverse(X_46),X_318))]]) ).
cnf(refute_0_2292,plain,
( inverse(multiply(inverse(X_318),X_46)) != multiply(inverse(X_46),X_318)
| greatest_lower_bound(X_318,inverse(multiply(inverse(X_318),X_46))) = greatest_lower_bound(X_318,multiply(inverse(X_46),X_318)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_318,inverse(multiply(inverse(X_318),X_46))),greatest_lower_bound(X_318,inverse(multiply(inverse(X_318),X_46)))) )],[refute_0_2290,refute_0_2291]) ).
cnf(refute_0_2293,plain,
greatest_lower_bound(X_318,inverse(multiply(inverse(X_318),X_46))) = greatest_lower_bound(X_318,multiply(inverse(X_46),X_318)),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_318),X_46)),multiply(inverse(X_46),X_318)) )],[refute_0_2269,refute_0_2292]) ).
cnf(refute_0_2294,plain,
( greatest_lower_bound(X_318,multiply(inverse(X_46),X_318)) != multiply(greatest_lower_bound(identity,inverse(X_46)),X_318)
| greatest_lower_bound(X_318,inverse(multiply(inverse(X_318),X_46))) != greatest_lower_bound(X_318,multiply(inverse(X_46),X_318))
| greatest_lower_bound(X_318,inverse(multiply(inverse(X_318),X_46))) = multiply(greatest_lower_bound(identity,inverse(X_46)),X_318) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(greatest_lower_bound(X_318,inverse(multiply(inverse(X_318),X_46))))),bind(Y0,$fot(greatest_lower_bound(X_318,multiply(inverse(X_46),X_318)))),bind(Z0,$fot(multiply(greatest_lower_bound(identity,inverse(X_46)),X_318)))]]) ).
cnf(refute_0_2295,plain,
( greatest_lower_bound(X_318,multiply(inverse(X_46),X_318)) != multiply(greatest_lower_bound(identity,inverse(X_46)),X_318)
| greatest_lower_bound(X_318,inverse(multiply(inverse(X_318),X_46))) = multiply(greatest_lower_bound(identity,inverse(X_46)),X_318) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_318,inverse(multiply(inverse(X_318),X_46))),greatest_lower_bound(X_318,multiply(inverse(X_46),X_318))) )],[refute_0_2293,refute_0_2294]) ).
cnf(refute_0_2296,plain,
greatest_lower_bound(X_318,inverse(multiply(inverse(X_318),X_46))) = multiply(greatest_lower_bound(identity,inverse(X_46)),X_318),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_318,multiply(inverse(X_46),X_318)),multiply(greatest_lower_bound(identity,inverse(X_46)),X_318)) )],[refute_0_2289,refute_0_2295]) ).
cnf(refute_0_2297,plain,
multiply(inverse(greatest_lower_bound(identity,X_46)),greatest_lower_bound(X_318,inverse(multiply(inverse(X_318),X_46)))) = multiply(inverse(greatest_lower_bound(identity,X_46)),greatest_lower_bound(X_318,inverse(multiply(inverse(X_318),X_46)))),
introduced(tautology,[refl,[$fot(multiply(inverse(greatest_lower_bound(identity,X_46)),greatest_lower_bound(X_318,inverse(multiply(inverse(X_318),X_46)))))]]) ).
cnf(refute_0_2298,plain,
( multiply(inverse(greatest_lower_bound(identity,X_46)),greatest_lower_bound(X_318,inverse(multiply(inverse(X_318),X_46)))) != multiply(inverse(greatest_lower_bound(identity,X_46)),greatest_lower_bound(X_318,inverse(multiply(inverse(X_318),X_46))))
| greatest_lower_bound(X_318,inverse(multiply(inverse(X_318),X_46))) != multiply(greatest_lower_bound(identity,inverse(X_46)),X_318)
| multiply(inverse(greatest_lower_bound(identity,X_46)),greatest_lower_bound(X_318,inverse(multiply(inverse(X_318),X_46)))) = multiply(inverse(greatest_lower_bound(identity,X_46)),multiply(greatest_lower_bound(identity,inverse(X_46)),X_318)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_46)),greatest_lower_bound(X_318,inverse(multiply(inverse(X_318),X_46)))),multiply(inverse(greatest_lower_bound(identity,X_46)),greatest_lower_bound(X_318,inverse(multiply(inverse(X_318),X_46))))) ),[1,1],$fot(multiply(greatest_lower_bound(identity,inverse(X_46)),X_318))]]) ).
cnf(refute_0_2299,plain,
( greatest_lower_bound(X_318,inverse(multiply(inverse(X_318),X_46))) != multiply(greatest_lower_bound(identity,inverse(X_46)),X_318)
| multiply(inverse(greatest_lower_bound(identity,X_46)),greatest_lower_bound(X_318,inverse(multiply(inverse(X_318),X_46)))) = multiply(inverse(greatest_lower_bound(identity,X_46)),multiply(greatest_lower_bound(identity,inverse(X_46)),X_318)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_46)),greatest_lower_bound(X_318,inverse(multiply(inverse(X_318),X_46)))),multiply(inverse(greatest_lower_bound(identity,X_46)),greatest_lower_bound(X_318,inverse(multiply(inverse(X_318),X_46))))) )],[refute_0_2297,refute_0_2298]) ).
cnf(refute_0_2300,plain,
multiply(inverse(greatest_lower_bound(identity,X_46)),greatest_lower_bound(X_318,inverse(multiply(inverse(X_318),X_46)))) = multiply(inverse(greatest_lower_bound(identity,X_46)),multiply(greatest_lower_bound(identity,inverse(X_46)),X_318)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_318,inverse(multiply(inverse(X_318),X_46))),multiply(greatest_lower_bound(identity,inverse(X_46)),X_318)) )],[refute_0_2296,refute_0_2299]) ).
cnf(refute_0_2301,plain,
multiply(inverse(greatest_lower_bound(identity,X_46)),greatest_lower_bound(inverse(multiply(inverse(X_318),X_46)),X_318)) = multiply(inverse(greatest_lower_bound(identity,X_46)),greatest_lower_bound(X_318,inverse(multiply(inverse(X_318),X_46)))),
inference(subst,[],[refute_0_2253:[bind(X_15,$fot(inverse(multiply(inverse(X_318),X_46)))),bind(X_251,$fot(inverse(greatest_lower_bound(identity,X_46)))),bind(X_35,$fot(X_318))]]) ).
cnf(refute_0_2302,plain,
( multiply(inverse(greatest_lower_bound(identity,X_46)),greatest_lower_bound(X_318,inverse(multiply(inverse(X_318),X_46)))) != multiply(inverse(greatest_lower_bound(identity,X_46)),multiply(greatest_lower_bound(identity,inverse(X_46)),X_318))
| multiply(inverse(greatest_lower_bound(identity,X_46)),greatest_lower_bound(inverse(multiply(inverse(X_318),X_46)),X_318)) != multiply(inverse(greatest_lower_bound(identity,X_46)),greatest_lower_bound(X_318,inverse(multiply(inverse(X_318),X_46))))
| multiply(inverse(greatest_lower_bound(identity,X_46)),greatest_lower_bound(inverse(multiply(inverse(X_318),X_46)),X_318)) = multiply(inverse(greatest_lower_bound(identity,X_46)),multiply(greatest_lower_bound(identity,inverse(X_46)),X_318)) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(identity,X_46)),greatest_lower_bound(inverse(multiply(inverse(X_318),X_46)),X_318)))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(identity,X_46)),greatest_lower_bound(X_318,inverse(multiply(inverse(X_318),X_46)))))),bind(Z0,$fot(multiply(inverse(greatest_lower_bound(identity,X_46)),multiply(greatest_lower_bound(identity,inverse(X_46)),X_318))))]]) ).
cnf(refute_0_2303,plain,
( multiply(inverse(greatest_lower_bound(identity,X_46)),greatest_lower_bound(X_318,inverse(multiply(inverse(X_318),X_46)))) != multiply(inverse(greatest_lower_bound(identity,X_46)),multiply(greatest_lower_bound(identity,inverse(X_46)),X_318))
| multiply(inverse(greatest_lower_bound(identity,X_46)),greatest_lower_bound(inverse(multiply(inverse(X_318),X_46)),X_318)) = multiply(inverse(greatest_lower_bound(identity,X_46)),multiply(greatest_lower_bound(identity,inverse(X_46)),X_318)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_46)),greatest_lower_bound(inverse(multiply(inverse(X_318),X_46)),X_318)),multiply(inverse(greatest_lower_bound(identity,X_46)),greatest_lower_bound(X_318,inverse(multiply(inverse(X_318),X_46))))) )],[refute_0_2301,refute_0_2302]) ).
cnf(refute_0_2304,plain,
multiply(inverse(greatest_lower_bound(identity,X_46)),greatest_lower_bound(inverse(multiply(inverse(X_318),X_46)),X_318)) = multiply(inverse(greatest_lower_bound(identity,X_46)),multiply(greatest_lower_bound(identity,inverse(X_46)),X_318)),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_46)),greatest_lower_bound(X_318,inverse(multiply(inverse(X_318),X_46)))),multiply(inverse(greatest_lower_bound(identity,X_46)),multiply(greatest_lower_bound(identity,inverse(X_46)),X_318))) )],[refute_0_2300,refute_0_2303]) ).
cnf(refute_0_2305,plain,
( multiply(inverse(X_46),X_318) != multiply(inverse(greatest_lower_bound(identity,X_46)),greatest_lower_bound(inverse(multiply(inverse(X_318),X_46)),X_318))
| multiply(inverse(greatest_lower_bound(identity,X_46)),greatest_lower_bound(inverse(multiply(inverse(X_318),X_46)),X_318)) != multiply(inverse(greatest_lower_bound(identity,X_46)),multiply(greatest_lower_bound(identity,inverse(X_46)),X_318))
| multiply(inverse(X_46),X_318) = multiply(inverse(greatest_lower_bound(identity,X_46)),multiply(greatest_lower_bound(identity,inverse(X_46)),X_318)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_46),X_318),multiply(inverse(greatest_lower_bound(identity,X_46)),multiply(greatest_lower_bound(identity,inverse(X_46)),X_318))) ),[0],$fot(multiply(inverse(greatest_lower_bound(identity,X_46)),greatest_lower_bound(inverse(multiply(inverse(X_318),X_46)),X_318)))]]) ).
cnf(refute_0_2306,plain,
( multiply(inverse(X_46),X_318) != multiply(inverse(greatest_lower_bound(identity,X_46)),greatest_lower_bound(inverse(multiply(inverse(X_318),X_46)),X_318))
| multiply(inverse(X_46),X_318) = multiply(inverse(greatest_lower_bound(identity,X_46)),multiply(greatest_lower_bound(identity,inverse(X_46)),X_318)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_46)),greatest_lower_bound(inverse(multiply(inverse(X_318),X_46)),X_318)),multiply(inverse(greatest_lower_bound(identity,X_46)),multiply(greatest_lower_bound(identity,inverse(X_46)),X_318))) )],[refute_0_2304,refute_0_2305]) ).
cnf(refute_0_2307,plain,
( inverse(multiply(inverse(X_318),X_46)) != multiply(inverse(greatest_lower_bound(identity,X_46)),greatest_lower_bound(inverse(multiply(inverse(X_318),X_46)),X_318))
| multiply(inverse(X_46),X_318) = multiply(inverse(greatest_lower_bound(identity,X_46)),multiply(greatest_lower_bound(identity,inverse(X_46)),X_318)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_46),X_318),multiply(inverse(greatest_lower_bound(identity,X_46)),greatest_lower_bound(inverse(multiply(inverse(X_318),X_46)),X_318))) )],[refute_0_2271,refute_0_2306]) ).
cnf(refute_0_2308,plain,
multiply(inverse(X_46),X_318) = multiply(inverse(greatest_lower_bound(identity,X_46)),multiply(greatest_lower_bound(identity,inverse(X_46)),X_318)),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_318),X_46)),multiply(inverse(greatest_lower_bound(identity,X_46)),greatest_lower_bound(inverse(multiply(inverse(X_318),X_46)),X_318))) )],[refute_0_2268,refute_0_2307]) ).
cnf(refute_0_2309,plain,
( multiply(inverse(X_46),X_318) != multiply(inverse(greatest_lower_bound(identity,X_46)),multiply(greatest_lower_bound(identity,inverse(X_46)),X_318))
| multiply(inverse(greatest_lower_bound(identity,X_46)),multiply(greatest_lower_bound(identity,inverse(X_46)),X_318)) = multiply(inverse(X_46),X_318) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(multiply(inverse(X_46),X_318))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(identity,X_46)),multiply(greatest_lower_bound(identity,inverse(X_46)),X_318))))]]) ).
cnf(refute_0_2310,plain,
multiply(inverse(greatest_lower_bound(identity,X_46)),multiply(greatest_lower_bound(identity,inverse(X_46)),X_318)) = multiply(inverse(X_46),X_318),
inference(resolve,[$cnf( $equal(multiply(inverse(X_46),X_318),multiply(inverse(greatest_lower_bound(identity,X_46)),multiply(greatest_lower_bound(identity,inverse(X_46)),X_318))) )],[refute_0_2308,refute_0_2309]) ).
cnf(refute_0_2311,plain,
multiply(inverse(greatest_lower_bound(identity,X_63)),multiply(greatest_lower_bound(identity,inverse(X_63)),least_upper_bound(X_62,X_63))) = multiply(inverse(X_63),least_upper_bound(X_62,X_63)),
inference(subst,[],[refute_0_2310:[bind(X_318,$fot(least_upper_bound(X_62,X_63))),bind(X_46,$fot(X_63))]]) ).
cnf(refute_0_2312,plain,
( multiply(inverse(greatest_lower_bound(identity,X_63)),multiply(greatest_lower_bound(identity,inverse(X_63)),least_upper_bound(X_62,X_63))) != multiply(inverse(X_63),least_upper_bound(X_62,X_63))
| least_upper_bound(identity,multiply(inverse(X_63),X_62)) != multiply(inverse(greatest_lower_bound(identity,X_63)),multiply(greatest_lower_bound(identity,inverse(X_63)),least_upper_bound(X_62,X_63)))
| least_upper_bound(identity,multiply(inverse(X_63),X_62)) = multiply(inverse(X_63),least_upper_bound(X_62,X_63)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(X_63),X_62)),multiply(inverse(greatest_lower_bound(identity,X_63)),multiply(greatest_lower_bound(identity,inverse(X_63)),least_upper_bound(X_62,X_63)))) ),[1],$fot(multiply(inverse(X_63),least_upper_bound(X_62,X_63)))]]) ).
cnf(refute_0_2313,plain,
( least_upper_bound(identity,multiply(inverse(X_63),X_62)) != multiply(inverse(greatest_lower_bound(identity,X_63)),multiply(greatest_lower_bound(identity,inverse(X_63)),least_upper_bound(X_62,X_63)))
| least_upper_bound(identity,multiply(inverse(X_63),X_62)) = multiply(inverse(X_63),least_upper_bound(X_62,X_63)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_63)),multiply(greatest_lower_bound(identity,inverse(X_63)),least_upper_bound(X_62,X_63))),multiply(inverse(X_63),least_upper_bound(X_62,X_63))) )],[refute_0_2311,refute_0_2312]) ).
cnf(refute_0_2314,plain,
least_upper_bound(identity,multiply(inverse(X_63),X_62)) = multiply(inverse(X_63),least_upper_bound(X_62,X_63)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(X_63),X_62)),multiply(inverse(greatest_lower_bound(identity,X_63)),multiply(greatest_lower_bound(identity,inverse(X_63)),least_upper_bound(X_62,X_63)))) )],[refute_0_2261,refute_0_2313]) ).
cnf(refute_0_2315,plain,
least_upper_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))) = multiply(inverse(identity),least_upper_bound(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))),identity)),
inference(subst,[],[refute_0_2314:[bind(X_62,$fot(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),bind(X_63,$fot(identity))]]) ).
cnf(refute_0_2316,plain,
( multiply(inverse(identity),least_upper_bound(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))),identity)) != multiply(inverse(identity),least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))
| least_upper_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))) != multiply(inverse(identity),least_upper_bound(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))),identity))
| least_upper_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))) = multiply(inverse(identity),least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(least_upper_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))))),bind(Y0,$fot(multiply(inverse(identity),least_upper_bound(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))),identity)))),bind(Z0,$fot(multiply(inverse(identity),least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))))]]) ).
cnf(refute_0_2317,plain,
( multiply(inverse(identity),least_upper_bound(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))),identity)) != multiply(inverse(identity),least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))
| least_upper_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))) = multiply(inverse(identity),least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),multiply(inverse(identity),least_upper_bound(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))),identity))) )],[refute_0_2315,refute_0_2316]) ).
cnf(refute_0_2318,plain,
least_upper_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))) = multiply(inverse(identity),least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))),identity)),multiply(inverse(identity),least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))) )],[refute_0_2203,refute_0_2317]) ).
cnf(refute_0_2319,plain,
( multiply(inverse(identity),least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))) != identity
| least_upper_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))) != multiply(inverse(identity),least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))
| least_upper_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))) = identity ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(least_upper_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))))),bind(Y0,$fot(multiply(inverse(identity),least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_2320,plain,
( multiply(inverse(identity),least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))) != identity
| least_upper_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),multiply(inverse(identity),least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))) )],[refute_0_2318,refute_0_2319]) ).
cnf(refute_0_2321,plain,
least_upper_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))) = identity,
inference(resolve,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),identity) )],[refute_0_2191,refute_0_2320]) ).
cnf(refute_0_2322,plain,
( multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))) != least_upper_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))
| least_upper_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))) != identity
| multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))) = identity ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))),identity) ),[0],$fot(least_upper_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))))]]) ).
cnf(refute_0_2323,plain,
( multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))) != least_upper_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))
| multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),identity) )],[refute_0_2321,refute_0_2322]) ).
cnf(refute_0_2324,plain,
( multiply(inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))) != least_upper_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))
| multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))) = identity ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))),least_upper_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))) )],[refute_0_2086,refute_0_2323]) ).
cnf(refute_0_2325,plain,
multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))) = identity,
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462))))),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))),least_upper_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(identity,X_462),least_upper_bound(identity,inverse(X_462)))))) )],[refute_0_1496,refute_0_2324]) ).
cnf(refute_0_2326,plain,
multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310))) = identity,
inference(subst,[],[refute_0_2325:[bind(X_462,$fot(X_310))]]) ).
cnf(refute_0_2327,plain,
inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310)))) = inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310)))),
introduced(tautology,[refl,[$fot(inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310)))))]]) ).
cnf(refute_0_2328,plain,
( multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310))) != identity
| inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310)))) != inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310))))
| inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310)))) = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310)))),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310))))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_2329,plain,
( multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310))) != identity
| inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310)))) = inverse(identity) ),
inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310)))),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310))))) )],[refute_0_2327,refute_0_2328]) ).
cnf(refute_0_2330,plain,
inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310)))) = inverse(identity),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310))),identity) )],[refute_0_2326,refute_0_2329]) ).
cnf(refute_0_2331,plain,
( inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310)))) != inverse(identity)
| inverse(identity) != identity
| inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310)))) = identity ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310)))))),bind(Y0,$fot(inverse(identity))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_2332,plain,
( inverse(identity) != identity
| inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310)))) = identity ),
inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310)))),inverse(identity)) )],[refute_0_2330,refute_0_2331]) ).
cnf(refute_0_2333,plain,
inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310)))) = identity,
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[p19_1,refute_0_2332]) ).
cnf(refute_0_2334,plain,
multiply(greatest_lower_bound(X_310,identity),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310))))) = multiply(greatest_lower_bound(X_310,identity),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310))))),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(X_310,identity),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310))))))]]) ).
cnf(refute_0_2335,plain,
( multiply(greatest_lower_bound(X_310,identity),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310))))) != multiply(greatest_lower_bound(X_310,identity),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310)))))
| inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310)))) != identity
| multiply(greatest_lower_bound(X_310,identity),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310))))) = multiply(greatest_lower_bound(X_310,identity),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_310,identity),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310))))),multiply(greatest_lower_bound(X_310,identity),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310)))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_2336,plain,
( inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310)))) != identity
| multiply(greatest_lower_bound(X_310,identity),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310))))) = multiply(greatest_lower_bound(X_310,identity),identity) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_310,identity),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310))))),multiply(greatest_lower_bound(X_310,identity),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310)))))) )],[refute_0_2334,refute_0_2335]) ).
cnf(refute_0_2337,plain,
multiply(greatest_lower_bound(X_310,identity),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310))))) = multiply(greatest_lower_bound(X_310,identity),identity),
inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310)))),identity) )],[refute_0_2333,refute_0_2336]) ).
cnf(refute_0_2338,plain,
( multiply(greatest_lower_bound(X_310,identity),identity) != greatest_lower_bound(X_310,identity)
| multiply(greatest_lower_bound(X_310,identity),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310))))) != multiply(greatest_lower_bound(X_310,identity),identity)
| multiply(greatest_lower_bound(X_310,identity),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310))))) = greatest_lower_bound(X_310,identity) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(multiply(greatest_lower_bound(X_310,identity),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310))))))),bind(Y0,$fot(multiply(greatest_lower_bound(X_310,identity),identity))),bind(Z0,$fot(greatest_lower_bound(X_310,identity)))]]) ).
cnf(refute_0_2339,plain,
( multiply(greatest_lower_bound(X_310,identity),identity) != greatest_lower_bound(X_310,identity)
| multiply(greatest_lower_bound(X_310,identity),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310))))) = greatest_lower_bound(X_310,identity) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_310,identity),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310))))),multiply(greatest_lower_bound(X_310,identity),identity)) )],[refute_0_2337,refute_0_2338]) ).
cnf(refute_0_2340,plain,
multiply(greatest_lower_bound(X_310,identity),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310))))) = greatest_lower_bound(X_310,identity),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_310,identity),identity),greatest_lower_bound(X_310,identity)) )],[refute_0_1452,refute_0_2339]) ).
cnf(refute_0_2341,plain,
( multiply(greatest_lower_bound(X_310,identity),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310))))) != greatest_lower_bound(X_310,identity)
| inverse(least_upper_bound(identity,inverse(X_310))) != multiply(greatest_lower_bound(X_310,identity),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310)))))
| inverse(least_upper_bound(identity,inverse(X_310))) = greatest_lower_bound(X_310,identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_310))),multiply(greatest_lower_bound(X_310,identity),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310)))))) ),[1],$fot(greatest_lower_bound(X_310,identity))]]) ).
cnf(refute_0_2342,plain,
( inverse(least_upper_bound(identity,inverse(X_310))) != multiply(greatest_lower_bound(X_310,identity),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310)))))
| inverse(least_upper_bound(identity,inverse(X_310))) = greatest_lower_bound(X_310,identity) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_310,identity),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310))))),greatest_lower_bound(X_310,identity)) )],[refute_0_2340,refute_0_2341]) ).
cnf(refute_0_2343,plain,
inverse(least_upper_bound(identity,inverse(X_310))) = greatest_lower_bound(X_310,identity),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_310))),multiply(greatest_lower_bound(X_310,identity),inverse(multiply(greatest_lower_bound(identity,X_310),least_upper_bound(identity,inverse(X_310)))))) )],[refute_0_1451,refute_0_2342]) ).
cnf(refute_0_2344,plain,
inverse(least_upper_bound(identity,inverse(X_99))) = greatest_lower_bound(X_99,identity),
inference(subst,[],[refute_0_2343:[bind(X_310,$fot(X_99))]]) ).
cnf(refute_0_2345,plain,
multiply(least_upper_bound(X_99,identity),inverse(least_upper_bound(identity,inverse(X_99)))) = multiply(least_upper_bound(X_99,identity),inverse(least_upper_bound(identity,inverse(X_99)))),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(X_99,identity),inverse(least_upper_bound(identity,inverse(X_99)))))]]) ).
cnf(refute_0_2346,plain,
( multiply(least_upper_bound(X_99,identity),inverse(least_upper_bound(identity,inverse(X_99)))) != multiply(least_upper_bound(X_99,identity),inverse(least_upper_bound(identity,inverse(X_99))))
| inverse(least_upper_bound(identity,inverse(X_99))) != greatest_lower_bound(X_99,identity)
| multiply(least_upper_bound(X_99,identity),inverse(least_upper_bound(identity,inverse(X_99)))) = multiply(least_upper_bound(X_99,identity),greatest_lower_bound(X_99,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_99,identity),inverse(least_upper_bound(identity,inverse(X_99)))),multiply(least_upper_bound(X_99,identity),inverse(least_upper_bound(identity,inverse(X_99))))) ),[1,1],$fot(greatest_lower_bound(X_99,identity))]]) ).
cnf(refute_0_2347,plain,
( inverse(least_upper_bound(identity,inverse(X_99))) != greatest_lower_bound(X_99,identity)
| multiply(least_upper_bound(X_99,identity),inverse(least_upper_bound(identity,inverse(X_99)))) = multiply(least_upper_bound(X_99,identity),greatest_lower_bound(X_99,identity)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_99,identity),inverse(least_upper_bound(identity,inverse(X_99)))),multiply(least_upper_bound(X_99,identity),inverse(least_upper_bound(identity,inverse(X_99))))) )],[refute_0_2345,refute_0_2346]) ).
cnf(refute_0_2348,plain,
multiply(least_upper_bound(X_99,identity),inverse(least_upper_bound(identity,inverse(X_99)))) = multiply(least_upper_bound(X_99,identity),greatest_lower_bound(X_99,identity)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_99))),greatest_lower_bound(X_99,identity)) )],[refute_0_2344,refute_0_2347]) ).
cnf(refute_0_2349,plain,
( multiply(least_upper_bound(X_99,identity),greatest_lower_bound(X_99,identity)) != multiply(greatest_lower_bound(X_99,identity),least_upper_bound(X_99,identity))
| multiply(least_upper_bound(X_99,identity),inverse(least_upper_bound(identity,inverse(X_99)))) != multiply(least_upper_bound(X_99,identity),greatest_lower_bound(X_99,identity))
| multiply(least_upper_bound(X_99,identity),inverse(least_upper_bound(identity,inverse(X_99)))) = multiply(greatest_lower_bound(X_99,identity),least_upper_bound(X_99,identity)) ),
inference(subst,[],[refute_0_111:[bind(X0,$fot(multiply(least_upper_bound(X_99,identity),inverse(least_upper_bound(identity,inverse(X_99)))))),bind(Y0,$fot(multiply(least_upper_bound(X_99,identity),greatest_lower_bound(X_99,identity)))),bind(Z0,$fot(multiply(greatest_lower_bound(X_99,identity),least_upper_bound(X_99,identity))))]]) ).
cnf(refute_0_2350,plain,
( multiply(least_upper_bound(X_99,identity),greatest_lower_bound(X_99,identity)) != multiply(greatest_lower_bound(X_99,identity),least_upper_bound(X_99,identity))
| multiply(least_upper_bound(X_99,identity),inverse(least_upper_bound(identity,inverse(X_99)))) = multiply(greatest_lower_bound(X_99,identity),least_upper_bound(X_99,identity)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_99,identity),inverse(least_upper_bound(identity,inverse(X_99)))),multiply(least_upper_bound(X_99,identity),greatest_lower_bound(X_99,identity))) )],[refute_0_2348,refute_0_2349]) ).
cnf(refute_0_2351,plain,
multiply(least_upper_bound(X_99,identity),inverse(least_upper_bound(identity,inverse(X_99)))) = multiply(greatest_lower_bound(X_99,identity),least_upper_bound(X_99,identity)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_99,identity),greatest_lower_bound(X_99,identity)),multiply(greatest_lower_bound(X_99,identity),least_upper_bound(X_99,identity))) )],[refute_0_150,refute_0_2350]) ).
cnf(refute_0_2352,plain,
( X_99 != multiply(least_upper_bound(X_99,identity),inverse(least_upper_bound(identity,inverse(X_99))))
| multiply(least_upper_bound(X_99,identity),inverse(least_upper_bound(identity,inverse(X_99)))) != multiply(greatest_lower_bound(X_99,identity),least_upper_bound(X_99,identity))
| X_99 = multiply(greatest_lower_bound(X_99,identity),least_upper_bound(X_99,identity)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_99,multiply(greatest_lower_bound(X_99,identity),least_upper_bound(X_99,identity))) ),[0],$fot(multiply(least_upper_bound(X_99,identity),inverse(least_upper_bound(identity,inverse(X_99)))))]]) ).
cnf(refute_0_2353,plain,
( X_99 != multiply(least_upper_bound(X_99,identity),inverse(least_upper_bound(identity,inverse(X_99))))
| X_99 = multiply(greatest_lower_bound(X_99,identity),least_upper_bound(X_99,identity)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_99,identity),inverse(least_upper_bound(identity,inverse(X_99)))),multiply(greatest_lower_bound(X_99,identity),least_upper_bound(X_99,identity))) )],[refute_0_2351,refute_0_2352]) ).
cnf(refute_0_2354,plain,
X_99 = multiply(greatest_lower_bound(X_99,identity),least_upper_bound(X_99,identity)),
inference(resolve,[$cnf( $equal(X_99,multiply(least_upper_bound(X_99,identity),inverse(least_upper_bound(identity,inverse(X_99))))) )],[refute_0_149,refute_0_2353]) ).
cnf(refute_0_2355,plain,
( X_99 != multiply(greatest_lower_bound(X_99,identity),least_upper_bound(X_99,identity))
| multiply(greatest_lower_bound(X_99,identity),least_upper_bound(X_99,identity)) = X_99 ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(X_99)),bind(Y0,$fot(multiply(greatest_lower_bound(X_99,identity),least_upper_bound(X_99,identity))))]]) ).
cnf(refute_0_2356,plain,
multiply(greatest_lower_bound(X_99,identity),least_upper_bound(X_99,identity)) = X_99,
inference(resolve,[$cnf( $equal(X_99,multiply(greatest_lower_bound(X_99,identity),least_upper_bound(X_99,identity))) )],[refute_0_2354,refute_0_2355]) ).
cnf(refute_0_2357,plain,
multiply(greatest_lower_bound(a,identity),least_upper_bound(a,identity)) = a,
inference(subst,[],[refute_0_2356:[bind(X_99,$fot(a))]]) ).
cnf(refute_0_2358,plain,
( multiply(greatest_lower_bound(a,identity),least_upper_bound(a,identity)) != a
| a != a
| a = multiply(greatest_lower_bound(a,identity),least_upper_bound(a,identity)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(a,multiply(greatest_lower_bound(a,identity),least_upper_bound(a,identity))) ),[1],$fot(a)]]) ).
cnf(refute_0_2359,plain,
( a != a
| a = multiply(greatest_lower_bound(a,identity),least_upper_bound(a,identity)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(a,identity),least_upper_bound(a,identity)),a) )],[refute_0_2357,refute_0_2358]) ).
cnf(refute_0_2360,plain,
a != a,
inference(resolve,[$cnf( $equal(a,multiply(greatest_lower_bound(a,identity),least_upper_bound(a,identity))) )],[refute_0_2359,refute_0_88]) ).
cnf(refute_0_2361,plain,
a = a,
introduced(tautology,[refl,[$fot(a)]]) ).
cnf(refute_0_2362,plain,
$false,
inference(resolve,[$cnf( $equal(a,a) )],[refute_0_2361,refute_0_2360]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP167-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n019.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Mon Jun 13 19:33:54 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 56.85/57.03 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 56.85/57.03
% 56.85/57.03 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 57.16/57.36
%------------------------------------------------------------------------------