TSTP Solution File: GRP171-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP171-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n025.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 10:37:16 EDT 2022
% Result : Unsatisfiable 0.75s 0.91s
% Output : CNFRefutation 0.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 85
% Syntax : Number of clauses : 344 ( 182 unt; 0 nHn; 197 RR)
% Number of literals : 574 ( 573 equ; 232 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 595 ( 10 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(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(p04a_1,hypothesis,
least_upper_bound(identity,a) = a ).
cnf(p04a_2,hypothesis,
least_upper_bound(identity,b) = b ).
cnf(prove_p04a,negated_conjecture,
least_upper_bound(identity,multiply(a,b)) != multiply(a,b) ).
cnf(refute_0_0,plain,
multiply(inverse(X_35),least_upper_bound(X_34,X_35)) = least_upper_bound(multiply(inverse(X_35),X_34),multiply(inverse(X_35),X_35)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(inverse(X_35))),bind(Y,$fot(X_34)),bind(Z,$fot(X_35))]]) ).
cnf(refute_0_1,plain,
multiply(inverse(X_35),X_35) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_35))]]) ).
cnf(refute_0_2,plain,
( multiply(inverse(X_35),X_35) != identity
| multiply(inverse(X_35),least_upper_bound(X_34,X_35)) != least_upper_bound(multiply(inverse(X_35),X_34),multiply(inverse(X_35),X_35))
| multiply(inverse(X_35),least_upper_bound(X_34,X_35)) = least_upper_bound(multiply(inverse(X_35),X_34),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_35),least_upper_bound(X_34,X_35)),least_upper_bound(multiply(inverse(X_35),X_34),multiply(inverse(X_35),X_35))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_3,plain,
( multiply(inverse(X_35),least_upper_bound(X_34,X_35)) != least_upper_bound(multiply(inverse(X_35),X_34),multiply(inverse(X_35),X_35))
| multiply(inverse(X_35),least_upper_bound(X_34,X_35)) = least_upper_bound(multiply(inverse(X_35),X_34),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_35),X_35),identity) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
multiply(inverse(X_35),least_upper_bound(X_34,X_35)) = least_upper_bound(multiply(inverse(X_35),X_34),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_35),least_upper_bound(X_34,X_35)),least_upper_bound(multiply(inverse(X_35),X_34),multiply(inverse(X_35),X_35))) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_6,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_7,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( least_upper_bound(X,Y) != least_upper_bound(Y,X)
| least_upper_bound(Y,X) = least_upper_bound(X,Y) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(least_upper_bound(X,Y))),bind(Y0,$fot(least_upper_bound(Y,X)))]]) ).
cnf(refute_0_9,plain,
least_upper_bound(Y,X) = least_upper_bound(X,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(X,Y),least_upper_bound(Y,X)) )],[symmetry_of_lub,refute_0_8]) ).
cnf(refute_0_10,plain,
least_upper_bound(multiply(inverse(X_35),X_34),identity) = least_upper_bound(identity,multiply(inverse(X_35),X_34)),
inference(subst,[],[refute_0_9:[bind(X,$fot(identity)),bind(Y,$fot(multiply(inverse(X_35),X_34)))]]) ).
cnf(refute_0_11,plain,
( multiply(inverse(X_35),least_upper_bound(X_34,X_35)) != least_upper_bound(multiply(inverse(X_35),X_34),identity)
| least_upper_bound(multiply(inverse(X_35),X_34),identity) != least_upper_bound(identity,multiply(inverse(X_35),X_34))
| multiply(inverse(X_35),least_upper_bound(X_34,X_35)) = least_upper_bound(identity,multiply(inverse(X_35),X_34)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_35),least_upper_bound(X_34,X_35)),least_upper_bound(identity,multiply(inverse(X_35),X_34))) ),[0],$fot(least_upper_bound(multiply(inverse(X_35),X_34),identity))]]) ).
cnf(refute_0_12,plain,
( multiply(inverse(X_35),least_upper_bound(X_34,X_35)) != least_upper_bound(multiply(inverse(X_35),X_34),identity)
| multiply(inverse(X_35),least_upper_bound(X_34,X_35)) = least_upper_bound(identity,multiply(inverse(X_35),X_34)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(X_35),X_34),identity),least_upper_bound(identity,multiply(inverse(X_35),X_34))) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
multiply(inverse(X_35),least_upper_bound(X_34,X_35)) = least_upper_bound(identity,multiply(inverse(X_35),X_34)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_35),least_upper_bound(X_34,X_35)),least_upper_bound(multiply(inverse(X_35),X_34),identity)) )],[refute_0_4,refute_0_12]) ).
cnf(refute_0_14,plain,
multiply(inverse(inverse(a)),least_upper_bound(b,inverse(a))) = least_upper_bound(identity,multiply(inverse(inverse(a)),b)),
inference(subst,[],[refute_0_13:[bind(X_34,$fot(b)),bind(X_35,$fot(inverse(a)))]]) ).
cnf(refute_0_15,plain,
least_upper_bound(b,least_upper_bound(identity,X_22)) = least_upper_bound(least_upper_bound(b,identity),X_22),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(b)),bind(Y,$fot(identity)),bind(Z,$fot(X_22))]]) ).
cnf(refute_0_16,plain,
least_upper_bound(identity,b) = least_upper_bound(b,identity),
inference(subst,[],[refute_0_9:[bind(X,$fot(b)),bind(Y,$fot(identity))]]) ).
cnf(refute_0_17,plain,
( least_upper_bound(identity,b) != b
| least_upper_bound(identity,b) != least_upper_bound(b,identity)
| least_upper_bound(b,identity) = b ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,b),b) ),[0],$fot(least_upper_bound(b,identity))]]) ).
cnf(refute_0_18,plain,
( least_upper_bound(identity,b) != b
| least_upper_bound(b,identity) = b ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,b),least_upper_bound(b,identity)) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
least_upper_bound(b,identity) = b,
inference(resolve,[$cnf( $equal(least_upper_bound(identity,b),b) )],[p04a_2,refute_0_18]) ).
cnf(refute_0_20,plain,
( least_upper_bound(b,identity) != b
| least_upper_bound(b,least_upper_bound(identity,X_22)) != least_upper_bound(least_upper_bound(b,identity),X_22)
| least_upper_bound(b,least_upper_bound(identity,X_22)) = least_upper_bound(b,X_22) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,least_upper_bound(identity,X_22)),least_upper_bound(least_upper_bound(b,identity),X_22)) ),[1,0],$fot(b)]]) ).
cnf(refute_0_21,plain,
( least_upper_bound(b,least_upper_bound(identity,X_22)) != least_upper_bound(least_upper_bound(b,identity),X_22)
| least_upper_bound(b,least_upper_bound(identity,X_22)) = least_upper_bound(b,X_22) ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,identity),b) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
least_upper_bound(b,least_upper_bound(identity,X_22)) = least_upper_bound(b,X_22),
inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(identity,X_22)),least_upper_bound(least_upper_bound(b,identity),X_22)) )],[refute_0_15,refute_0_21]) ).
cnf(refute_0_23,plain,
least_upper_bound(b,least_upper_bound(identity,greatest_lower_bound(identity,Y))) = least_upper_bound(b,greatest_lower_bound(identity,Y)),
inference(subst,[],[refute_0_22:[bind(X_22,$fot(greatest_lower_bound(identity,Y)))]]) ).
cnf(refute_0_24,plain,
least_upper_bound(identity,greatest_lower_bound(identity,Y)) = identity,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(identity))]]) ).
cnf(refute_0_25,plain,
( least_upper_bound(b,least_upper_bound(identity,greatest_lower_bound(identity,Y))) != least_upper_bound(b,greatest_lower_bound(identity,Y))
| least_upper_bound(identity,greatest_lower_bound(identity,Y)) != identity
| least_upper_bound(b,identity) = least_upper_bound(b,greatest_lower_bound(identity,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,least_upper_bound(identity,greatest_lower_bound(identity,Y))),least_upper_bound(b,greatest_lower_bound(identity,Y))) ),[0,1],$fot(identity)]]) ).
cnf(refute_0_26,plain,
( least_upper_bound(b,least_upper_bound(identity,greatest_lower_bound(identity,Y))) != least_upper_bound(b,greatest_lower_bound(identity,Y))
| least_upper_bound(b,identity) = least_upper_bound(b,greatest_lower_bound(identity,Y)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(identity,Y)),identity) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
least_upper_bound(b,identity) = least_upper_bound(b,greatest_lower_bound(identity,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(identity,greatest_lower_bound(identity,Y))),least_upper_bound(b,greatest_lower_bound(identity,Y))) )],[refute_0_23,refute_0_26]) ).
cnf(refute_0_28,plain,
( least_upper_bound(b,identity) != b
| least_upper_bound(b,identity) != least_upper_bound(b,greatest_lower_bound(identity,Y))
| b = least_upper_bound(b,greatest_lower_bound(identity,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,identity),least_upper_bound(b,greatest_lower_bound(identity,Y))) ),[0],$fot(b)]]) ).
cnf(refute_0_29,plain,
( least_upper_bound(b,identity) != least_upper_bound(b,greatest_lower_bound(identity,Y))
| b = least_upper_bound(b,greatest_lower_bound(identity,Y)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,identity),b) )],[refute_0_19,refute_0_28]) ).
cnf(refute_0_30,plain,
b = least_upper_bound(b,greatest_lower_bound(identity,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(b,identity),least_upper_bound(b,greatest_lower_bound(identity,Y))) )],[refute_0_27,refute_0_29]) ).
cnf(refute_0_31,plain,
b = least_upper_bound(b,greatest_lower_bound(identity,inverse(a))),
inference(subst,[],[refute_0_30:[bind(Y,$fot(inverse(a)))]]) ).
cnf(refute_0_32,plain,
multiply(inverse(X_60),greatest_lower_bound(X_59,X_60)) = greatest_lower_bound(multiply(inverse(X_60),X_59),multiply(inverse(X_60),X_60)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(inverse(X_60))),bind(Y,$fot(X_59)),bind(Z,$fot(X_60))]]) ).
cnf(refute_0_33,plain,
multiply(inverse(X_60),X_60) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_60))]]) ).
cnf(refute_0_34,plain,
( multiply(inverse(X_60),X_60) != identity
| multiply(inverse(X_60),greatest_lower_bound(X_59,X_60)) != greatest_lower_bound(multiply(inverse(X_60),X_59),multiply(inverse(X_60),X_60))
| multiply(inverse(X_60),greatest_lower_bound(X_59,X_60)) = greatest_lower_bound(multiply(inverse(X_60),X_59),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_60),greatest_lower_bound(X_59,X_60)),greatest_lower_bound(multiply(inverse(X_60),X_59),multiply(inverse(X_60),X_60))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_35,plain,
( multiply(inverse(X_60),greatest_lower_bound(X_59,X_60)) != greatest_lower_bound(multiply(inverse(X_60),X_59),multiply(inverse(X_60),X_60))
| multiply(inverse(X_60),greatest_lower_bound(X_59,X_60)) = greatest_lower_bound(multiply(inverse(X_60),X_59),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_60),X_60),identity) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
multiply(inverse(X_60),greatest_lower_bound(X_59,X_60)) = greatest_lower_bound(multiply(inverse(X_60),X_59),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_60),greatest_lower_bound(X_59,X_60)),greatest_lower_bound(multiply(inverse(X_60),X_59),multiply(inverse(X_60),X_60))) )],[refute_0_32,refute_0_35]) ).
cnf(refute_0_37,plain,
( greatest_lower_bound(X,Y) != greatest_lower_bound(Y,X)
| greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(greatest_lower_bound(X,Y))),bind(Y0,$fot(greatest_lower_bound(Y,X)))]]) ).
cnf(refute_0_38,plain,
greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X)) )],[symmetry_of_glb,refute_0_37]) ).
cnf(refute_0_39,plain,
greatest_lower_bound(multiply(inverse(X_60),X_59),identity) = greatest_lower_bound(identity,multiply(inverse(X_60),X_59)),
inference(subst,[],[refute_0_38:[bind(X,$fot(identity)),bind(Y,$fot(multiply(inverse(X_60),X_59)))]]) ).
cnf(refute_0_40,plain,
( multiply(inverse(X_60),greatest_lower_bound(X_59,X_60)) != greatest_lower_bound(multiply(inverse(X_60),X_59),identity)
| greatest_lower_bound(multiply(inverse(X_60),X_59),identity) != greatest_lower_bound(identity,multiply(inverse(X_60),X_59))
| multiply(inverse(X_60),greatest_lower_bound(X_59,X_60)) = greatest_lower_bound(identity,multiply(inverse(X_60),X_59)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_60),greatest_lower_bound(X_59,X_60)),greatest_lower_bound(identity,multiply(inverse(X_60),X_59))) ),[0],$fot(greatest_lower_bound(multiply(inverse(X_60),X_59),identity))]]) ).
cnf(refute_0_41,plain,
( multiply(inverse(X_60),greatest_lower_bound(X_59,X_60)) != greatest_lower_bound(multiply(inverse(X_60),X_59),identity)
| multiply(inverse(X_60),greatest_lower_bound(X_59,X_60)) = greatest_lower_bound(identity,multiply(inverse(X_60),X_59)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(inverse(X_60),X_59),identity),greatest_lower_bound(identity,multiply(inverse(X_60),X_59))) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
multiply(inverse(X_60),greatest_lower_bound(X_59,X_60)) = greatest_lower_bound(identity,multiply(inverse(X_60),X_59)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_60),greatest_lower_bound(X_59,X_60)),greatest_lower_bound(multiply(inverse(X_60),X_59),identity)) )],[refute_0_36,refute_0_41]) ).
cnf(refute_0_43,plain,
multiply(inverse(a),greatest_lower_bound(identity,a)) = greatest_lower_bound(identity,multiply(inverse(a),identity)),
inference(subst,[],[refute_0_42:[bind(X_59,$fot(identity)),bind(X_60,$fot(a))]]) ).
cnf(refute_0_44,plain,
multiply(inverse(X_59),greatest_lower_bound(X_59,X_60)) = greatest_lower_bound(multiply(inverse(X_59),X_59),multiply(inverse(X_59),X_60)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(inverse(X_59))),bind(Y,$fot(X_59)),bind(Z,$fot(X_60))]]) ).
cnf(refute_0_45,plain,
multiply(inverse(X_59),X_59) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_59))]]) ).
cnf(refute_0_46,plain,
( multiply(inverse(X_59),X_59) != identity
| multiply(inverse(X_59),greatest_lower_bound(X_59,X_60)) != greatest_lower_bound(multiply(inverse(X_59),X_59),multiply(inverse(X_59),X_60))
| multiply(inverse(X_59),greatest_lower_bound(X_59,X_60)) = greatest_lower_bound(identity,multiply(inverse(X_59),X_60)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_59),greatest_lower_bound(X_59,X_60)),greatest_lower_bound(multiply(inverse(X_59),X_59),multiply(inverse(X_59),X_60))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_47,plain,
( multiply(inverse(X_59),greatest_lower_bound(X_59,X_60)) != greatest_lower_bound(multiply(inverse(X_59),X_59),multiply(inverse(X_59),X_60))
| multiply(inverse(X_59),greatest_lower_bound(X_59,X_60)) = greatest_lower_bound(identity,multiply(inverse(X_59),X_60)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_59),X_59),identity) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
multiply(inverse(X_59),greatest_lower_bound(X_59,X_60)) = greatest_lower_bound(identity,multiply(inverse(X_59),X_60)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_59),greatest_lower_bound(X_59,X_60)),greatest_lower_bound(multiply(inverse(X_59),X_59),multiply(inverse(X_59),X_60))) )],[refute_0_44,refute_0_47]) ).
cnf(refute_0_49,plain,
multiply(inverse(a),greatest_lower_bound(a,greatest_lower_bound(X_46,identity))) = greatest_lower_bound(identity,multiply(inverse(a),greatest_lower_bound(X_46,identity))),
inference(subst,[],[refute_0_48:[bind(X_59,$fot(a)),bind(X_60,$fot(greatest_lower_bound(X_46,identity)))]]) ).
cnf(refute_0_50,plain,
greatest_lower_bound(a,greatest_lower_bound(identity,X_45)) = greatest_lower_bound(greatest_lower_bound(a,identity),X_45),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(a)),bind(Y,$fot(identity)),bind(Z,$fot(X_45))]]) ).
cnf(refute_0_51,plain,
greatest_lower_bound(X_8,least_upper_bound(X_8,X_9)) = X_8,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_8)),bind(Y,$fot(X_9))]]) ).
cnf(refute_0_52,plain,
least_upper_bound(X_9,X_8) = least_upper_bound(X_8,X_9),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_9)),bind(Y,$fot(X_8))]]) ).
cnf(refute_0_53,plain,
( least_upper_bound(X_9,X_8) != least_upper_bound(X_8,X_9)
| least_upper_bound(X_8,X_9) = least_upper_bound(X_9,X_8) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(least_upper_bound(X_9,X_8))),bind(Y0,$fot(least_upper_bound(X_8,X_9)))]]) ).
cnf(refute_0_54,plain,
least_upper_bound(X_8,X_9) = least_upper_bound(X_9,X_8),
inference(resolve,[$cnf( $equal(least_upper_bound(X_9,X_8),least_upper_bound(X_8,X_9)) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
( greatest_lower_bound(X_8,least_upper_bound(X_8,X_9)) != X_8
| least_upper_bound(X_8,X_9) != least_upper_bound(X_9,X_8)
| greatest_lower_bound(X_8,least_upper_bound(X_9,X_8)) = X_8 ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_8,least_upper_bound(X_8,X_9)),X_8) ),[0,1],$fot(least_upper_bound(X_9,X_8))]]) ).
cnf(refute_0_56,plain,
( greatest_lower_bound(X_8,least_upper_bound(X_8,X_9)) != X_8
| greatest_lower_bound(X_8,least_upper_bound(X_9,X_8)) = X_8 ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_8,X_9),least_upper_bound(X_9,X_8)) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
greatest_lower_bound(X_8,least_upper_bound(X_9,X_8)) = X_8,
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_8,least_upper_bound(X_8,X_9)),X_8) )],[refute_0_51,refute_0_56]) ).
cnf(refute_0_58,plain,
greatest_lower_bound(identity,least_upper_bound(a,identity)) = identity,
inference(subst,[],[refute_0_57:[bind(X_8,$fot(identity)),bind(X_9,$fot(a))]]) ).
cnf(refute_0_59,plain,
least_upper_bound(identity,a) = least_upper_bound(a,identity),
inference(subst,[],[refute_0_9:[bind(X,$fot(a)),bind(Y,$fot(identity))]]) ).
cnf(refute_0_60,plain,
( least_upper_bound(identity,a) != a
| least_upper_bound(identity,a) != least_upper_bound(a,identity)
| least_upper_bound(a,identity) = a ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,a),a) ),[0],$fot(least_upper_bound(a,identity))]]) ).
cnf(refute_0_61,plain,
( least_upper_bound(identity,a) != a
| least_upper_bound(a,identity) = a ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,a),least_upper_bound(a,identity)) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
least_upper_bound(a,identity) = a,
inference(resolve,[$cnf( $equal(least_upper_bound(identity,a),a) )],[p04a_1,refute_0_61]) ).
cnf(refute_0_63,plain,
( greatest_lower_bound(identity,least_upper_bound(a,identity)) != identity
| least_upper_bound(a,identity) != a
| greatest_lower_bound(identity,a) = identity ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(a,identity)),identity) ),[0,1],$fot(a)]]) ).
cnf(refute_0_64,plain,
( greatest_lower_bound(identity,least_upper_bound(a,identity)) != identity
| greatest_lower_bound(identity,a) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,identity),a) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
greatest_lower_bound(identity,a) = identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(a,identity)),identity) )],[refute_0_58,refute_0_64]) ).
cnf(refute_0_66,plain,
greatest_lower_bound(identity,a) = greatest_lower_bound(a,identity),
inference(subst,[],[refute_0_38:[bind(X,$fot(a)),bind(Y,$fot(identity))]]) ).
cnf(refute_0_67,plain,
( greatest_lower_bound(identity,a) != greatest_lower_bound(a,identity)
| greatest_lower_bound(identity,a) != identity
| greatest_lower_bound(a,identity) = identity ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,a),identity) ),[0],$fot(greatest_lower_bound(a,identity))]]) ).
cnf(refute_0_68,plain,
( greatest_lower_bound(identity,a) != identity
| greatest_lower_bound(a,identity) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,a),greatest_lower_bound(a,identity)) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
greatest_lower_bound(a,identity) = identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,a),identity) )],[refute_0_65,refute_0_68]) ).
cnf(refute_0_70,plain,
( greatest_lower_bound(a,greatest_lower_bound(identity,X_45)) != greatest_lower_bound(greatest_lower_bound(a,identity),X_45)
| greatest_lower_bound(a,identity) != identity
| greatest_lower_bound(a,greatest_lower_bound(identity,X_45)) = greatest_lower_bound(identity,X_45) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(identity,X_45)),greatest_lower_bound(greatest_lower_bound(a,identity),X_45)) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_71,plain,
( greatest_lower_bound(a,greatest_lower_bound(identity,X_45)) != greatest_lower_bound(greatest_lower_bound(a,identity),X_45)
| greatest_lower_bound(a,greatest_lower_bound(identity,X_45)) = greatest_lower_bound(identity,X_45) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,identity),identity) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
greatest_lower_bound(a,greatest_lower_bound(identity,X_45)) = greatest_lower_bound(identity,X_45),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(identity,X_45)),greatest_lower_bound(greatest_lower_bound(a,identity),X_45)) )],[refute_0_50,refute_0_71]) ).
cnf(refute_0_73,plain,
greatest_lower_bound(a,greatest_lower_bound(identity,X_46)) = greatest_lower_bound(identity,X_46),
inference(subst,[],[refute_0_72:[bind(X_45,$fot(X_46))]]) ).
cnf(refute_0_74,plain,
greatest_lower_bound(X_46,identity) = greatest_lower_bound(identity,X_46),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_46)),bind(Y,$fot(identity))]]) ).
cnf(refute_0_75,plain,
( greatest_lower_bound(X_46,identity) != greatest_lower_bound(identity,X_46)
| greatest_lower_bound(identity,X_46) = greatest_lower_bound(X_46,identity) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(greatest_lower_bound(X_46,identity))),bind(Y0,$fot(greatest_lower_bound(identity,X_46)))]]) ).
cnf(refute_0_76,plain,
greatest_lower_bound(identity,X_46) = greatest_lower_bound(X_46,identity),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_46,identity),greatest_lower_bound(identity,X_46)) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
( greatest_lower_bound(a,greatest_lower_bound(identity,X_46)) != greatest_lower_bound(identity,X_46)
| greatest_lower_bound(identity,X_46) != greatest_lower_bound(X_46,identity)
| greatest_lower_bound(a,greatest_lower_bound(X_46,identity)) = greatest_lower_bound(identity,X_46) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(identity,X_46)),greatest_lower_bound(identity,X_46)) ),[0,1],$fot(greatest_lower_bound(X_46,identity))]]) ).
cnf(refute_0_78,plain,
( greatest_lower_bound(a,greatest_lower_bound(identity,X_46)) != greatest_lower_bound(identity,X_46)
| greatest_lower_bound(a,greatest_lower_bound(X_46,identity)) = greatest_lower_bound(identity,X_46) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,X_46),greatest_lower_bound(X_46,identity)) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
greatest_lower_bound(a,greatest_lower_bound(X_46,identity)) = greatest_lower_bound(identity,X_46),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(identity,X_46)),greatest_lower_bound(identity,X_46)) )],[refute_0_73,refute_0_78]) ).
cnf(refute_0_80,plain,
( multiply(inverse(a),greatest_lower_bound(a,greatest_lower_bound(X_46,identity))) != greatest_lower_bound(identity,multiply(inverse(a),greatest_lower_bound(X_46,identity)))
| greatest_lower_bound(a,greatest_lower_bound(X_46,identity)) != greatest_lower_bound(identity,X_46)
| multiply(inverse(a),greatest_lower_bound(identity,X_46)) = greatest_lower_bound(identity,multiply(inverse(a),greatest_lower_bound(X_46,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(a),greatest_lower_bound(a,greatest_lower_bound(X_46,identity))),greatest_lower_bound(identity,multiply(inverse(a),greatest_lower_bound(X_46,identity)))) ),[0,1],$fot(greatest_lower_bound(identity,X_46))]]) ).
cnf(refute_0_81,plain,
( multiply(inverse(a),greatest_lower_bound(a,greatest_lower_bound(X_46,identity))) != greatest_lower_bound(identity,multiply(inverse(a),greatest_lower_bound(X_46,identity)))
| multiply(inverse(a),greatest_lower_bound(identity,X_46)) = greatest_lower_bound(identity,multiply(inverse(a),greatest_lower_bound(X_46,identity))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(X_46,identity)),greatest_lower_bound(identity,X_46)) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
multiply(inverse(a),greatest_lower_bound(identity,X_46)) = greatest_lower_bound(identity,multiply(inverse(a),greatest_lower_bound(X_46,identity))),
inference(resolve,[$cnf( $equal(multiply(inverse(a),greatest_lower_bound(a,greatest_lower_bound(X_46,identity))),greatest_lower_bound(identity,multiply(inverse(a),greatest_lower_bound(X_46,identity)))) )],[refute_0_49,refute_0_81]) ).
cnf(refute_0_83,plain,
greatest_lower_bound(X_46,greatest_lower_bound(a,identity)) = greatest_lower_bound(X_46,greatest_lower_bound(a,identity)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X_46,greatest_lower_bound(a,identity)))]]) ).
cnf(refute_0_84,plain,
( greatest_lower_bound(X_46,greatest_lower_bound(a,identity)) != greatest_lower_bound(X_46,greatest_lower_bound(a,identity))
| greatest_lower_bound(a,identity) != identity
| greatest_lower_bound(X_46,greatest_lower_bound(a,identity)) = greatest_lower_bound(X_46,identity) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_46,greatest_lower_bound(a,identity)),greatest_lower_bound(X_46,greatest_lower_bound(a,identity))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_85,plain,
( greatest_lower_bound(a,identity) != identity
| greatest_lower_bound(X_46,greatest_lower_bound(a,identity)) = greatest_lower_bound(X_46,identity) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_46,greatest_lower_bound(a,identity)),greatest_lower_bound(X_46,greatest_lower_bound(a,identity))) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
greatest_lower_bound(X_46,greatest_lower_bound(a,identity)) = greatest_lower_bound(X_46,identity),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,identity),identity) )],[refute_0_69,refute_0_85]) ).
cnf(refute_0_87,plain,
multiply(inverse(a),greatest_lower_bound(X_46,greatest_lower_bound(a,identity))) = multiply(inverse(a),greatest_lower_bound(X_46,greatest_lower_bound(a,identity))),
introduced(tautology,[refl,[$fot(multiply(inverse(a),greatest_lower_bound(X_46,greatest_lower_bound(a,identity))))]]) ).
cnf(refute_0_88,plain,
( multiply(inverse(a),greatest_lower_bound(X_46,greatest_lower_bound(a,identity))) != multiply(inverse(a),greatest_lower_bound(X_46,greatest_lower_bound(a,identity)))
| greatest_lower_bound(X_46,greatest_lower_bound(a,identity)) != greatest_lower_bound(X_46,identity)
| multiply(inverse(a),greatest_lower_bound(X_46,greatest_lower_bound(a,identity))) = multiply(inverse(a),greatest_lower_bound(X_46,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(a),greatest_lower_bound(X_46,greatest_lower_bound(a,identity))),multiply(inverse(a),greatest_lower_bound(X_46,greatest_lower_bound(a,identity)))) ),[1,1],$fot(greatest_lower_bound(X_46,identity))]]) ).
cnf(refute_0_89,plain,
( greatest_lower_bound(X_46,greatest_lower_bound(a,identity)) != greatest_lower_bound(X_46,identity)
| multiply(inverse(a),greatest_lower_bound(X_46,greatest_lower_bound(a,identity))) = multiply(inverse(a),greatest_lower_bound(X_46,identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(a),greatest_lower_bound(X_46,greatest_lower_bound(a,identity))),multiply(inverse(a),greatest_lower_bound(X_46,greatest_lower_bound(a,identity)))) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
multiply(inverse(a),greatest_lower_bound(X_46,greatest_lower_bound(a,identity))) = multiply(inverse(a),greatest_lower_bound(X_46,identity)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_46,greatest_lower_bound(a,identity)),greatest_lower_bound(X_46,identity)) )],[refute_0_86,refute_0_89]) ).
cnf(refute_0_91,plain,
multiply(inverse(X_65),greatest_lower_bound(Y,greatest_lower_bound(X_65,X_66))) = greatest_lower_bound(multiply(inverse(X_65),Y),multiply(inverse(X_65),greatest_lower_bound(X_65,X_66))),
inference(subst,[],[monotony_glb1:[bind(X,$fot(inverse(X_65))),bind(Z,$fot(greatest_lower_bound(X_65,X_66)))]]) ).
cnf(refute_0_92,plain,
multiply(inverse(X_65),greatest_lower_bound(X_65,X_66)) = greatest_lower_bound(identity,multiply(inverse(X_65),X_66)),
inference(subst,[],[refute_0_48:[bind(X_59,$fot(X_65)),bind(X_60,$fot(X_66))]]) ).
cnf(refute_0_93,plain,
( multiply(inverse(X_65),greatest_lower_bound(Y,greatest_lower_bound(X_65,X_66))) != greatest_lower_bound(multiply(inverse(X_65),Y),multiply(inverse(X_65),greatest_lower_bound(X_65,X_66)))
| multiply(inverse(X_65),greatest_lower_bound(X_65,X_66)) != greatest_lower_bound(identity,multiply(inverse(X_65),X_66))
| multiply(inverse(X_65),greatest_lower_bound(Y,greatest_lower_bound(X_65,X_66))) = greatest_lower_bound(multiply(inverse(X_65),Y),greatest_lower_bound(identity,multiply(inverse(X_65),X_66))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_65),greatest_lower_bound(Y,greatest_lower_bound(X_65,X_66))),greatest_lower_bound(multiply(inverse(X_65),Y),multiply(inverse(X_65),greatest_lower_bound(X_65,X_66)))) ),[1,1],$fot(greatest_lower_bound(identity,multiply(inverse(X_65),X_66)))]]) ).
cnf(refute_0_94,plain,
( multiply(inverse(X_65),greatest_lower_bound(Y,greatest_lower_bound(X_65,X_66))) != greatest_lower_bound(multiply(inverse(X_65),Y),multiply(inverse(X_65),greatest_lower_bound(X_65,X_66)))
| multiply(inverse(X_65),greatest_lower_bound(Y,greatest_lower_bound(X_65,X_66))) = greatest_lower_bound(multiply(inverse(X_65),Y),greatest_lower_bound(identity,multiply(inverse(X_65),X_66))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_65),greatest_lower_bound(X_65,X_66)),greatest_lower_bound(identity,multiply(inverse(X_65),X_66))) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
multiply(inverse(X_65),greatest_lower_bound(Y,greatest_lower_bound(X_65,X_66))) = greatest_lower_bound(multiply(inverse(X_65),Y),greatest_lower_bound(identity,multiply(inverse(X_65),X_66))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_65),greatest_lower_bound(Y,greatest_lower_bound(X_65,X_66))),greatest_lower_bound(multiply(inverse(X_65),Y),multiply(inverse(X_65),greatest_lower_bound(X_65,X_66)))) )],[refute_0_91,refute_0_94]) ).
cnf(refute_0_96,plain,
( multiply(X,greatest_lower_bound(Y,Z)) != greatest_lower_bound(multiply(X,Y),multiply(X,Z))
| greatest_lower_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,greatest_lower_bound(Y,Z)) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(multiply(X,greatest_lower_bound(Y,Z)))),bind(Y0,$fot(greatest_lower_bound(multiply(X,Y),multiply(X,Z))))]]) ).
cnf(refute_0_97,plain,
greatest_lower_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) )],[monotony_glb1,refute_0_96]) ).
cnf(refute_0_98,plain,
greatest_lower_bound(multiply(inverse(X_65),Y),multiply(inverse(X_65),X_66)) = multiply(inverse(X_65),greatest_lower_bound(Y,X_66)),
inference(subst,[],[refute_0_97:[bind(X,$fot(inverse(X_65))),bind(Z,$fot(X_66))]]) ).
cnf(refute_0_99,plain,
greatest_lower_bound(identity,greatest_lower_bound(multiply(inverse(X_65),Y),multiply(inverse(X_65),X_66))) = greatest_lower_bound(identity,greatest_lower_bound(multiply(inverse(X_65),Y),multiply(inverse(X_65),X_66))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,greatest_lower_bound(multiply(inverse(X_65),Y),multiply(inverse(X_65),X_66))))]]) ).
cnf(refute_0_100,plain,
( greatest_lower_bound(multiply(inverse(X_65),Y),multiply(inverse(X_65),X_66)) != multiply(inverse(X_65),greatest_lower_bound(Y,X_66))
| greatest_lower_bound(identity,greatest_lower_bound(multiply(inverse(X_65),Y),multiply(inverse(X_65),X_66))) != greatest_lower_bound(identity,greatest_lower_bound(multiply(inverse(X_65),Y),multiply(inverse(X_65),X_66)))
| greatest_lower_bound(identity,greatest_lower_bound(multiply(inverse(X_65),Y),multiply(inverse(X_65),X_66))) = greatest_lower_bound(identity,multiply(inverse(X_65),greatest_lower_bound(Y,X_66))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(multiply(inverse(X_65),Y),multiply(inverse(X_65),X_66))),greatest_lower_bound(identity,greatest_lower_bound(multiply(inverse(X_65),Y),multiply(inverse(X_65),X_66)))) ),[1,1],$fot(multiply(inverse(X_65),greatest_lower_bound(Y,X_66)))]]) ).
cnf(refute_0_101,plain,
( greatest_lower_bound(multiply(inverse(X_65),Y),multiply(inverse(X_65),X_66)) != multiply(inverse(X_65),greatest_lower_bound(Y,X_66))
| greatest_lower_bound(identity,greatest_lower_bound(multiply(inverse(X_65),Y),multiply(inverse(X_65),X_66))) = greatest_lower_bound(identity,multiply(inverse(X_65),greatest_lower_bound(Y,X_66))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(multiply(inverse(X_65),Y),multiply(inverse(X_65),X_66))),greatest_lower_bound(identity,greatest_lower_bound(multiply(inverse(X_65),Y),multiply(inverse(X_65),X_66)))) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
greatest_lower_bound(identity,greatest_lower_bound(multiply(inverse(X_65),Y),multiply(inverse(X_65),X_66))) = greatest_lower_bound(identity,multiply(inverse(X_65),greatest_lower_bound(Y,X_66))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(inverse(X_65),Y),multiply(inverse(X_65),X_66)),multiply(inverse(X_65),greatest_lower_bound(Y,X_66))) )],[refute_0_98,refute_0_101]) ).
cnf(refute_0_103,plain,
greatest_lower_bound(X_43,greatest_lower_bound(greatest_lower_bound(Y,X_43),X_45)) = greatest_lower_bound(greatest_lower_bound(X_43,greatest_lower_bound(Y,X_43)),X_45),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_43)),bind(Y,$fot(greatest_lower_bound(Y,X_43))),bind(Z,$fot(X_45))]]) ).
cnf(refute_0_104,plain,
greatest_lower_bound(greatest_lower_bound(X_13,Y),least_upper_bound(X_13,greatest_lower_bound(X_13,Y))) = greatest_lower_bound(X_13,Y),
inference(subst,[],[refute_0_57:[bind(X_8,$fot(greatest_lower_bound(X_13,Y))),bind(X_9,$fot(X_13))]]) ).
cnf(refute_0_105,plain,
least_upper_bound(X_13,greatest_lower_bound(X_13,Y)) = X_13,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_13))]]) ).
cnf(refute_0_106,plain,
( greatest_lower_bound(greatest_lower_bound(X_13,Y),least_upper_bound(X_13,greatest_lower_bound(X_13,Y))) != greatest_lower_bound(X_13,Y)
| least_upper_bound(X_13,greatest_lower_bound(X_13,Y)) != X_13
| greatest_lower_bound(greatest_lower_bound(X_13,Y),X_13) = greatest_lower_bound(X_13,Y) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_13,Y),least_upper_bound(X_13,greatest_lower_bound(X_13,Y))),greatest_lower_bound(X_13,Y)) ),[0,1],$fot(X_13)]]) ).
cnf(refute_0_107,plain,
( greatest_lower_bound(greatest_lower_bound(X_13,Y),least_upper_bound(X_13,greatest_lower_bound(X_13,Y))) != greatest_lower_bound(X_13,Y)
| greatest_lower_bound(greatest_lower_bound(X_13,Y),X_13) = greatest_lower_bound(X_13,Y) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_13,greatest_lower_bound(X_13,Y)),X_13) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
greatest_lower_bound(greatest_lower_bound(X_13,Y),X_13) = greatest_lower_bound(X_13,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_13,Y),least_upper_bound(X_13,greatest_lower_bound(X_13,Y))),greatest_lower_bound(X_13,Y)) )],[refute_0_104,refute_0_107]) ).
cnf(refute_0_109,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,Z)) != greatest_lower_bound(greatest_lower_bound(X,Y),Z)
| greatest_lower_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(Y,Z)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X,Y),Z)))]]) ).
cnf(refute_0_110,plain,
greatest_lower_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(greatest_lower_bound(X,Y),Z)) )],[associativity_of_glb,refute_0_109]) ).
cnf(refute_0_111,plain,
greatest_lower_bound(greatest_lower_bound(X_13,Y),X_13) = greatest_lower_bound(X_13,greatest_lower_bound(Y,X_13)),
inference(subst,[],[refute_0_110:[bind(X,$fot(X_13)),bind(Z,$fot(X_13))]]) ).
cnf(refute_0_112,plain,
( greatest_lower_bound(greatest_lower_bound(X_13,Y),X_13) != greatest_lower_bound(X_13,Y)
| greatest_lower_bound(greatest_lower_bound(X_13,Y),X_13) != greatest_lower_bound(X_13,greatest_lower_bound(Y,X_13))
| greatest_lower_bound(X_13,greatest_lower_bound(Y,X_13)) = greatest_lower_bound(X_13,Y) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_13,Y),X_13),greatest_lower_bound(X_13,Y)) ),[0],$fot(greatest_lower_bound(X_13,greatest_lower_bound(Y,X_13)))]]) ).
cnf(refute_0_113,plain,
( greatest_lower_bound(greatest_lower_bound(X_13,Y),X_13) != greatest_lower_bound(X_13,Y)
| greatest_lower_bound(X_13,greatest_lower_bound(Y,X_13)) = greatest_lower_bound(X_13,Y) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_13,Y),X_13),greatest_lower_bound(X_13,greatest_lower_bound(Y,X_13))) )],[refute_0_111,refute_0_112]) ).
cnf(refute_0_114,plain,
greatest_lower_bound(X_13,greatest_lower_bound(Y,X_13)) = greatest_lower_bound(X_13,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_13,Y),X_13),greatest_lower_bound(X_13,Y)) )],[refute_0_108,refute_0_113]) ).
cnf(refute_0_115,plain,
greatest_lower_bound(X_43,greatest_lower_bound(Y,X_43)) = greatest_lower_bound(X_43,Y),
inference(subst,[],[refute_0_114:[bind(X_13,$fot(X_43))]]) ).
cnf(refute_0_116,plain,
( greatest_lower_bound(X_43,greatest_lower_bound(Y,X_43)) != greatest_lower_bound(X_43,Y)
| greatest_lower_bound(X_43,greatest_lower_bound(greatest_lower_bound(Y,X_43),X_45)) != greatest_lower_bound(greatest_lower_bound(X_43,greatest_lower_bound(Y,X_43)),X_45)
| greatest_lower_bound(X_43,greatest_lower_bound(greatest_lower_bound(Y,X_43),X_45)) = greatest_lower_bound(greatest_lower_bound(X_43,Y),X_45) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_43,greatest_lower_bound(greatest_lower_bound(Y,X_43),X_45)),greatest_lower_bound(greatest_lower_bound(X_43,greatest_lower_bound(Y,X_43)),X_45)) ),[1,0],$fot(greatest_lower_bound(X_43,Y))]]) ).
cnf(refute_0_117,plain,
( greatest_lower_bound(X_43,greatest_lower_bound(greatest_lower_bound(Y,X_43),X_45)) != greatest_lower_bound(greatest_lower_bound(X_43,greatest_lower_bound(Y,X_43)),X_45)
| greatest_lower_bound(X_43,greatest_lower_bound(greatest_lower_bound(Y,X_43),X_45)) = greatest_lower_bound(greatest_lower_bound(X_43,Y),X_45) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_43,greatest_lower_bound(Y,X_43)),greatest_lower_bound(X_43,Y)) )],[refute_0_115,refute_0_116]) ).
cnf(refute_0_118,plain,
greatest_lower_bound(X_43,greatest_lower_bound(greatest_lower_bound(Y,X_43),X_45)) = greatest_lower_bound(greatest_lower_bound(X_43,Y),X_45),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_43,greatest_lower_bound(greatest_lower_bound(Y,X_43),X_45)),greatest_lower_bound(greatest_lower_bound(X_43,greatest_lower_bound(Y,X_43)),X_45)) )],[refute_0_103,refute_0_117]) ).
cnf(refute_0_119,plain,
greatest_lower_bound(X_43,greatest_lower_bound(X_44,greatest_lower_bound(Y,X_44))) = greatest_lower_bound(greatest_lower_bound(X_43,X_44),greatest_lower_bound(Y,X_44)),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_43)),bind(Y,$fot(X_44)),bind(Z,$fot(greatest_lower_bound(Y,X_44)))]]) ).
cnf(refute_0_120,plain,
greatest_lower_bound(X_44,greatest_lower_bound(Y,X_44)) = greatest_lower_bound(X_44,Y),
inference(subst,[],[refute_0_114:[bind(X_13,$fot(X_44))]]) ).
cnf(refute_0_121,plain,
( greatest_lower_bound(X_43,greatest_lower_bound(X_44,greatest_lower_bound(Y,X_44))) != greatest_lower_bound(greatest_lower_bound(X_43,X_44),greatest_lower_bound(Y,X_44))
| greatest_lower_bound(X_44,greatest_lower_bound(Y,X_44)) != greatest_lower_bound(X_44,Y)
| greatest_lower_bound(X_43,greatest_lower_bound(X_44,Y)) = greatest_lower_bound(greatest_lower_bound(X_43,X_44),greatest_lower_bound(Y,X_44)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_43,greatest_lower_bound(X_44,greatest_lower_bound(Y,X_44))),greatest_lower_bound(greatest_lower_bound(X_43,X_44),greatest_lower_bound(Y,X_44))) ),[0,1],$fot(greatest_lower_bound(X_44,Y))]]) ).
cnf(refute_0_122,plain,
( greatest_lower_bound(X_43,greatest_lower_bound(X_44,greatest_lower_bound(Y,X_44))) != greatest_lower_bound(greatest_lower_bound(X_43,X_44),greatest_lower_bound(Y,X_44))
| greatest_lower_bound(X_43,greatest_lower_bound(X_44,Y)) = greatest_lower_bound(greatest_lower_bound(X_43,X_44),greatest_lower_bound(Y,X_44)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_44,greatest_lower_bound(Y,X_44)),greatest_lower_bound(X_44,Y)) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
greatest_lower_bound(X_43,greatest_lower_bound(X_44,Y)) = greatest_lower_bound(greatest_lower_bound(X_43,X_44),greatest_lower_bound(Y,X_44)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_43,greatest_lower_bound(X_44,greatest_lower_bound(Y,X_44))),greatest_lower_bound(greatest_lower_bound(X_43,X_44),greatest_lower_bound(Y,X_44))) )],[refute_0_119,refute_0_122]) ).
cnf(refute_0_124,plain,
greatest_lower_bound(greatest_lower_bound(X_43,X_44),Y) = greatest_lower_bound(X_43,greatest_lower_bound(X_44,Y)),
inference(subst,[],[refute_0_110:[bind(X,$fot(X_43)),bind(Y,$fot(X_44)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_125,plain,
greatest_lower_bound(X_44,greatest_lower_bound(greatest_lower_bound(X_43,X_44),Y)) = greatest_lower_bound(X_44,greatest_lower_bound(greatest_lower_bound(X_43,X_44),Y)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X_44,greatest_lower_bound(greatest_lower_bound(X_43,X_44),Y)))]]) ).
cnf(refute_0_126,plain,
( greatest_lower_bound(X_44,greatest_lower_bound(greatest_lower_bound(X_43,X_44),Y)) != greatest_lower_bound(X_44,greatest_lower_bound(greatest_lower_bound(X_43,X_44),Y))
| greatest_lower_bound(greatest_lower_bound(X_43,X_44),Y) != greatest_lower_bound(X_43,greatest_lower_bound(X_44,Y))
| greatest_lower_bound(X_44,greatest_lower_bound(greatest_lower_bound(X_43,X_44),Y)) = greatest_lower_bound(X_44,greatest_lower_bound(X_43,greatest_lower_bound(X_44,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_44,greatest_lower_bound(greatest_lower_bound(X_43,X_44),Y)),greatest_lower_bound(X_44,greatest_lower_bound(greatest_lower_bound(X_43,X_44),Y))) ),[1,1],$fot(greatest_lower_bound(X_43,greatest_lower_bound(X_44,Y)))]]) ).
cnf(refute_0_127,plain,
( greatest_lower_bound(greatest_lower_bound(X_43,X_44),Y) != greatest_lower_bound(X_43,greatest_lower_bound(X_44,Y))
| greatest_lower_bound(X_44,greatest_lower_bound(greatest_lower_bound(X_43,X_44),Y)) = greatest_lower_bound(X_44,greatest_lower_bound(X_43,greatest_lower_bound(X_44,Y))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_44,greatest_lower_bound(greatest_lower_bound(X_43,X_44),Y)),greatest_lower_bound(X_44,greatest_lower_bound(greatest_lower_bound(X_43,X_44),Y))) )],[refute_0_125,refute_0_126]) ).
cnf(refute_0_128,plain,
greatest_lower_bound(X_44,greatest_lower_bound(greatest_lower_bound(X_43,X_44),Y)) = greatest_lower_bound(X_44,greatest_lower_bound(X_43,greatest_lower_bound(X_44,Y))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_43,X_44),Y),greatest_lower_bound(X_43,greatest_lower_bound(X_44,Y))) )],[refute_0_124,refute_0_127]) ).
cnf(refute_0_129,plain,
greatest_lower_bound(X,greatest_lower_bound(X_43,X_44)) = greatest_lower_bound(greatest_lower_bound(X_43,X_44),X),
inference(subst,[],[symmetry_of_glb:[bind(Y,$fot(greatest_lower_bound(X_43,X_44)))]]) ).
cnf(refute_0_130,plain,
greatest_lower_bound(X_43,greatest_lower_bound(X_44,X)) = greatest_lower_bound(greatest_lower_bound(X_43,X_44),X),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_43)),bind(Y,$fot(X_44)),bind(Z,$fot(X))]]) ).
cnf(refute_0_131,plain,
( greatest_lower_bound(X_43,greatest_lower_bound(X_44,X)) != greatest_lower_bound(greatest_lower_bound(X_43,X_44),X)
| greatest_lower_bound(greatest_lower_bound(X_43,X_44),X) = greatest_lower_bound(X_43,greatest_lower_bound(X_44,X)) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(greatest_lower_bound(X_43,greatest_lower_bound(X_44,X)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X_43,X_44),X)))]]) ).
cnf(refute_0_132,plain,
greatest_lower_bound(greatest_lower_bound(X_43,X_44),X) = greatest_lower_bound(X_43,greatest_lower_bound(X_44,X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_43,greatest_lower_bound(X_44,X)),greatest_lower_bound(greatest_lower_bound(X_43,X_44),X)) )],[refute_0_130,refute_0_131]) ).
cnf(refute_0_133,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_43,X_44)) != greatest_lower_bound(greatest_lower_bound(X_43,X_44),X)
| greatest_lower_bound(greatest_lower_bound(X_43,X_44),X) != greatest_lower_bound(X_43,greatest_lower_bound(X_44,X))
| greatest_lower_bound(X,greatest_lower_bound(X_43,X_44)) = greatest_lower_bound(X_43,greatest_lower_bound(X_44,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X,greatest_lower_bound(X_43,X_44)),greatest_lower_bound(X_43,greatest_lower_bound(X_44,X))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_43,X_44),X))]]) ).
cnf(refute_0_134,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_43,X_44)) != greatest_lower_bound(greatest_lower_bound(X_43,X_44),X)
| greatest_lower_bound(X,greatest_lower_bound(X_43,X_44)) = greatest_lower_bound(X_43,greatest_lower_bound(X_44,X)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_43,X_44),X),greatest_lower_bound(X_43,greatest_lower_bound(X_44,X))) )],[refute_0_132,refute_0_133]) ).
cnf(refute_0_135,plain,
greatest_lower_bound(X,greatest_lower_bound(X_43,X_44)) = greatest_lower_bound(X_43,greatest_lower_bound(X_44,X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_43,X_44)),greatest_lower_bound(greatest_lower_bound(X_43,X_44),X)) )],[refute_0_129,refute_0_134]) ).
cnf(refute_0_136,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_43,X_44)) != greatest_lower_bound(X_43,greatest_lower_bound(X_44,X))
| greatest_lower_bound(X_43,greatest_lower_bound(X_44,X)) = greatest_lower_bound(X,greatest_lower_bound(X_43,X_44)) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(X_43,X_44)))),bind(Y0,$fot(greatest_lower_bound(X_43,greatest_lower_bound(X_44,X))))]]) ).
cnf(refute_0_137,plain,
greatest_lower_bound(X_43,greatest_lower_bound(X_44,X)) = greatest_lower_bound(X,greatest_lower_bound(X_43,X_44)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_43,X_44)),greatest_lower_bound(X_43,greatest_lower_bound(X_44,X))) )],[refute_0_135,refute_0_136]) ).
cnf(refute_0_138,plain,
greatest_lower_bound(greatest_lower_bound(X_43,X_44),greatest_lower_bound(Y,X_44)) = greatest_lower_bound(X_44,greatest_lower_bound(greatest_lower_bound(X_43,X_44),Y)),
inference(subst,[],[refute_0_137:[bind(X,$fot(X_44)),bind(X_43,$fot(greatest_lower_bound(X_43,X_44))),bind(X_44,$fot(Y))]]) ).
cnf(refute_0_139,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_140,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_7,refute_0_139]) ).
cnf(refute_0_141,plain,
( greatest_lower_bound(X_44,greatest_lower_bound(greatest_lower_bound(X_43,X_44),Y)) != greatest_lower_bound(X_44,greatest_lower_bound(X_43,greatest_lower_bound(X_44,Y)))
| greatest_lower_bound(greatest_lower_bound(X_43,X_44),greatest_lower_bound(Y,X_44)) != greatest_lower_bound(X_44,greatest_lower_bound(greatest_lower_bound(X_43,X_44),Y))
| greatest_lower_bound(greatest_lower_bound(X_43,X_44),greatest_lower_bound(Y,X_44)) = greatest_lower_bound(X_44,greatest_lower_bound(X_43,greatest_lower_bound(X_44,Y))) ),
inference(subst,[],[refute_0_140:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(X_43,X_44),greatest_lower_bound(Y,X_44)))),bind(Y0,$fot(greatest_lower_bound(X_44,greatest_lower_bound(greatest_lower_bound(X_43,X_44),Y)))),bind(Z0,$fot(greatest_lower_bound(X_44,greatest_lower_bound(X_43,greatest_lower_bound(X_44,Y)))))]]) ).
cnf(refute_0_142,plain,
( greatest_lower_bound(X_44,greatest_lower_bound(greatest_lower_bound(X_43,X_44),Y)) != greatest_lower_bound(X_44,greatest_lower_bound(X_43,greatest_lower_bound(X_44,Y)))
| greatest_lower_bound(greatest_lower_bound(X_43,X_44),greatest_lower_bound(Y,X_44)) = greatest_lower_bound(X_44,greatest_lower_bound(X_43,greatest_lower_bound(X_44,Y))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_43,X_44),greatest_lower_bound(Y,X_44)),greatest_lower_bound(X_44,greatest_lower_bound(greatest_lower_bound(X_43,X_44),Y))) )],[refute_0_138,refute_0_141]) ).
cnf(refute_0_143,plain,
greatest_lower_bound(greatest_lower_bound(X_43,X_44),greatest_lower_bound(Y,X_44)) = greatest_lower_bound(X_44,greatest_lower_bound(X_43,greatest_lower_bound(X_44,Y))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_44,greatest_lower_bound(greatest_lower_bound(X_43,X_44),Y)),greatest_lower_bound(X_44,greatest_lower_bound(X_43,greatest_lower_bound(X_44,Y)))) )],[refute_0_128,refute_0_142]) ).
cnf(refute_0_144,plain,
( greatest_lower_bound(X_43,greatest_lower_bound(X_44,Y)) != greatest_lower_bound(greatest_lower_bound(X_43,X_44),greatest_lower_bound(Y,X_44))
| greatest_lower_bound(greatest_lower_bound(X_43,X_44),greatest_lower_bound(Y,X_44)) != greatest_lower_bound(X_44,greatest_lower_bound(X_43,greatest_lower_bound(X_44,Y)))
| greatest_lower_bound(X_43,greatest_lower_bound(X_44,Y)) = greatest_lower_bound(X_44,greatest_lower_bound(X_43,greatest_lower_bound(X_44,Y))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_43,greatest_lower_bound(X_44,Y)),greatest_lower_bound(X_44,greatest_lower_bound(X_43,greatest_lower_bound(X_44,Y)))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_43,X_44),greatest_lower_bound(Y,X_44)))]]) ).
cnf(refute_0_145,plain,
( greatest_lower_bound(X_43,greatest_lower_bound(X_44,Y)) != greatest_lower_bound(greatest_lower_bound(X_43,X_44),greatest_lower_bound(Y,X_44))
| greatest_lower_bound(X_43,greatest_lower_bound(X_44,Y)) = greatest_lower_bound(X_44,greatest_lower_bound(X_43,greatest_lower_bound(X_44,Y))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_43,X_44),greatest_lower_bound(Y,X_44)),greatest_lower_bound(X_44,greatest_lower_bound(X_43,greatest_lower_bound(X_44,Y)))) )],[refute_0_143,refute_0_144]) ).
cnf(refute_0_146,plain,
greatest_lower_bound(X_43,greatest_lower_bound(X_44,Y)) = greatest_lower_bound(X_44,greatest_lower_bound(X_43,greatest_lower_bound(X_44,Y))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_43,greatest_lower_bound(X_44,Y)),greatest_lower_bound(greatest_lower_bound(X_43,X_44),greatest_lower_bound(Y,X_44))) )],[refute_0_123,refute_0_145]) ).
cnf(refute_0_147,plain,
( greatest_lower_bound(X_43,greatest_lower_bound(X_44,Y)) != greatest_lower_bound(X_44,greatest_lower_bound(X_43,greatest_lower_bound(X_44,Y)))
| greatest_lower_bound(X_44,greatest_lower_bound(X_43,greatest_lower_bound(X_44,Y))) = greatest_lower_bound(X_43,greatest_lower_bound(X_44,Y)) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(greatest_lower_bound(X_43,greatest_lower_bound(X_44,Y)))),bind(Y0,$fot(greatest_lower_bound(X_44,greatest_lower_bound(X_43,greatest_lower_bound(X_44,Y)))))]]) ).
cnf(refute_0_148,plain,
greatest_lower_bound(X_44,greatest_lower_bound(X_43,greatest_lower_bound(X_44,Y))) = greatest_lower_bound(X_43,greatest_lower_bound(X_44,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_43,greatest_lower_bound(X_44,Y)),greatest_lower_bound(X_44,greatest_lower_bound(X_43,greatest_lower_bound(X_44,Y)))) )],[refute_0_146,refute_0_147]) ).
cnf(refute_0_149,plain,
greatest_lower_bound(X_43,greatest_lower_bound(Y,greatest_lower_bound(X_43,X_45))) = greatest_lower_bound(Y,greatest_lower_bound(X_43,X_45)),
inference(subst,[],[refute_0_148:[bind(Y,$fot(X_45)),bind(X_43,$fot(Y)),bind(X_44,$fot(X_43))]]) ).
cnf(refute_0_150,plain,
greatest_lower_bound(greatest_lower_bound(Y,X_43),X_45) = greatest_lower_bound(Y,greatest_lower_bound(X_43,X_45)),
inference(subst,[],[refute_0_110:[bind(X,$fot(Y)),bind(Y,$fot(X_43)),bind(Z,$fot(X_45))]]) ).
cnf(refute_0_151,plain,
greatest_lower_bound(X_43,greatest_lower_bound(greatest_lower_bound(Y,X_43),X_45)) = greatest_lower_bound(X_43,greatest_lower_bound(greatest_lower_bound(Y,X_43),X_45)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X_43,greatest_lower_bound(greatest_lower_bound(Y,X_43),X_45)))]]) ).
cnf(refute_0_152,plain,
( greatest_lower_bound(X_43,greatest_lower_bound(greatest_lower_bound(Y,X_43),X_45)) != greatest_lower_bound(X_43,greatest_lower_bound(greatest_lower_bound(Y,X_43),X_45))
| greatest_lower_bound(greatest_lower_bound(Y,X_43),X_45) != greatest_lower_bound(Y,greatest_lower_bound(X_43,X_45))
| greatest_lower_bound(X_43,greatest_lower_bound(greatest_lower_bound(Y,X_43),X_45)) = greatest_lower_bound(X_43,greatest_lower_bound(Y,greatest_lower_bound(X_43,X_45))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_43,greatest_lower_bound(greatest_lower_bound(Y,X_43),X_45)),greatest_lower_bound(X_43,greatest_lower_bound(greatest_lower_bound(Y,X_43),X_45))) ),[1,1],$fot(greatest_lower_bound(Y,greatest_lower_bound(X_43,X_45)))]]) ).
cnf(refute_0_153,plain,
( greatest_lower_bound(greatest_lower_bound(Y,X_43),X_45) != greatest_lower_bound(Y,greatest_lower_bound(X_43,X_45))
| greatest_lower_bound(X_43,greatest_lower_bound(greatest_lower_bound(Y,X_43),X_45)) = greatest_lower_bound(X_43,greatest_lower_bound(Y,greatest_lower_bound(X_43,X_45))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_43,greatest_lower_bound(greatest_lower_bound(Y,X_43),X_45)),greatest_lower_bound(X_43,greatest_lower_bound(greatest_lower_bound(Y,X_43),X_45))) )],[refute_0_151,refute_0_152]) ).
cnf(refute_0_154,plain,
greatest_lower_bound(X_43,greatest_lower_bound(greatest_lower_bound(Y,X_43),X_45)) = greatest_lower_bound(X_43,greatest_lower_bound(Y,greatest_lower_bound(X_43,X_45))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(Y,X_43),X_45),greatest_lower_bound(Y,greatest_lower_bound(X_43,X_45))) )],[refute_0_150,refute_0_153]) ).
cnf(refute_0_155,plain,
( greatest_lower_bound(X_43,greatest_lower_bound(Y,greatest_lower_bound(X_43,X_45))) != greatest_lower_bound(Y,greatest_lower_bound(X_43,X_45))
| greatest_lower_bound(X_43,greatest_lower_bound(greatest_lower_bound(Y,X_43),X_45)) != greatest_lower_bound(X_43,greatest_lower_bound(Y,greatest_lower_bound(X_43,X_45)))
| greatest_lower_bound(X_43,greatest_lower_bound(greatest_lower_bound(Y,X_43),X_45)) = greatest_lower_bound(Y,greatest_lower_bound(X_43,X_45)) ),
inference(subst,[],[refute_0_140:[bind(X0,$fot(greatest_lower_bound(X_43,greatest_lower_bound(greatest_lower_bound(Y,X_43),X_45)))),bind(Y0,$fot(greatest_lower_bound(X_43,greatest_lower_bound(Y,greatest_lower_bound(X_43,X_45))))),bind(Z0,$fot(greatest_lower_bound(Y,greatest_lower_bound(X_43,X_45))))]]) ).
cnf(refute_0_156,plain,
( greatest_lower_bound(X_43,greatest_lower_bound(Y,greatest_lower_bound(X_43,X_45))) != greatest_lower_bound(Y,greatest_lower_bound(X_43,X_45))
| greatest_lower_bound(X_43,greatest_lower_bound(greatest_lower_bound(Y,X_43),X_45)) = greatest_lower_bound(Y,greatest_lower_bound(X_43,X_45)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_43,greatest_lower_bound(greatest_lower_bound(Y,X_43),X_45)),greatest_lower_bound(X_43,greatest_lower_bound(Y,greatest_lower_bound(X_43,X_45)))) )],[refute_0_154,refute_0_155]) ).
cnf(refute_0_157,plain,
greatest_lower_bound(X_43,greatest_lower_bound(greatest_lower_bound(Y,X_43),X_45)) = greatest_lower_bound(Y,greatest_lower_bound(X_43,X_45)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_43,greatest_lower_bound(Y,greatest_lower_bound(X_43,X_45))),greatest_lower_bound(Y,greatest_lower_bound(X_43,X_45))) )],[refute_0_149,refute_0_156]) ).
cnf(refute_0_158,plain,
( greatest_lower_bound(X_43,greatest_lower_bound(greatest_lower_bound(Y,X_43),X_45)) != greatest_lower_bound(Y,greatest_lower_bound(X_43,X_45))
| greatest_lower_bound(X_43,greatest_lower_bound(greatest_lower_bound(Y,X_43),X_45)) != greatest_lower_bound(greatest_lower_bound(X_43,Y),X_45)
| greatest_lower_bound(Y,greatest_lower_bound(X_43,X_45)) = greatest_lower_bound(greatest_lower_bound(X_43,Y),X_45) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_43,greatest_lower_bound(greatest_lower_bound(Y,X_43),X_45)),greatest_lower_bound(greatest_lower_bound(X_43,Y),X_45)) ),[0],$fot(greatest_lower_bound(Y,greatest_lower_bound(X_43,X_45)))]]) ).
cnf(refute_0_159,plain,
( greatest_lower_bound(X_43,greatest_lower_bound(greatest_lower_bound(Y,X_43),X_45)) != greatest_lower_bound(greatest_lower_bound(X_43,Y),X_45)
| greatest_lower_bound(Y,greatest_lower_bound(X_43,X_45)) = greatest_lower_bound(greatest_lower_bound(X_43,Y),X_45) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_43,greatest_lower_bound(greatest_lower_bound(Y,X_43),X_45)),greatest_lower_bound(Y,greatest_lower_bound(X_43,X_45))) )],[refute_0_157,refute_0_158]) ).
cnf(refute_0_160,plain,
greatest_lower_bound(greatest_lower_bound(X_43,Y),X_45) = greatest_lower_bound(X_43,greatest_lower_bound(Y,X_45)),
inference(subst,[],[refute_0_110:[bind(X,$fot(X_43)),bind(Z,$fot(X_45))]]) ).
cnf(refute_0_161,plain,
( greatest_lower_bound(Y,greatest_lower_bound(X_43,X_45)) != greatest_lower_bound(greatest_lower_bound(X_43,Y),X_45)
| greatest_lower_bound(greatest_lower_bound(X_43,Y),X_45) != greatest_lower_bound(X_43,greatest_lower_bound(Y,X_45))
| greatest_lower_bound(Y,greatest_lower_bound(X_43,X_45)) = greatest_lower_bound(X_43,greatest_lower_bound(Y,X_45)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(Y,greatest_lower_bound(X_43,X_45)),greatest_lower_bound(X_43,greatest_lower_bound(Y,X_45))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_43,Y),X_45))]]) ).
cnf(refute_0_162,plain,
( greatest_lower_bound(Y,greatest_lower_bound(X_43,X_45)) != greatest_lower_bound(greatest_lower_bound(X_43,Y),X_45)
| greatest_lower_bound(Y,greatest_lower_bound(X_43,X_45)) = greatest_lower_bound(X_43,greatest_lower_bound(Y,X_45)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_43,Y),X_45),greatest_lower_bound(X_43,greatest_lower_bound(Y,X_45))) )],[refute_0_160,refute_0_161]) ).
cnf(refute_0_163,plain,
( greatest_lower_bound(X_43,greatest_lower_bound(greatest_lower_bound(Y,X_43),X_45)) != greatest_lower_bound(greatest_lower_bound(X_43,Y),X_45)
| greatest_lower_bound(Y,greatest_lower_bound(X_43,X_45)) = greatest_lower_bound(X_43,greatest_lower_bound(Y,X_45)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(X_43,X_45)),greatest_lower_bound(greatest_lower_bound(X_43,Y),X_45)) )],[refute_0_159,refute_0_162]) ).
cnf(refute_0_164,plain,
greatest_lower_bound(Y,greatest_lower_bound(X_43,X_45)) = greatest_lower_bound(X_43,greatest_lower_bound(Y,X_45)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_43,greatest_lower_bound(greatest_lower_bound(Y,X_43),X_45)),greatest_lower_bound(greatest_lower_bound(X_43,Y),X_45)) )],[refute_0_118,refute_0_163]) ).
cnf(refute_0_165,plain,
( greatest_lower_bound(Y,greatest_lower_bound(X_43,X_45)) != greatest_lower_bound(X_43,greatest_lower_bound(Y,X_45))
| greatest_lower_bound(X_43,greatest_lower_bound(Y,X_45)) = greatest_lower_bound(Y,greatest_lower_bound(X_43,X_45)) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(greatest_lower_bound(Y,greatest_lower_bound(X_43,X_45)))),bind(Y0,$fot(greatest_lower_bound(X_43,greatest_lower_bound(Y,X_45))))]]) ).
cnf(refute_0_166,plain,
greatest_lower_bound(X_43,greatest_lower_bound(Y,X_45)) = greatest_lower_bound(Y,greatest_lower_bound(X_43,X_45)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(X_43,X_45)),greatest_lower_bound(X_43,greatest_lower_bound(Y,X_45))) )],[refute_0_164,refute_0_165]) ).
cnf(refute_0_167,plain,
greatest_lower_bound(multiply(inverse(X_65),Y),greatest_lower_bound(identity,multiply(inverse(X_65),X_66))) = greatest_lower_bound(identity,greatest_lower_bound(multiply(inverse(X_65),Y),multiply(inverse(X_65),X_66))),
inference(subst,[],[refute_0_166:[bind(Y,$fot(identity)),bind(X_43,$fot(multiply(inverse(X_65),Y))),bind(X_45,$fot(multiply(inverse(X_65),X_66)))]]) ).
cnf(refute_0_168,plain,
( greatest_lower_bound(multiply(inverse(X_65),Y),greatest_lower_bound(identity,multiply(inverse(X_65),X_66))) != greatest_lower_bound(identity,greatest_lower_bound(multiply(inverse(X_65),Y),multiply(inverse(X_65),X_66)))
| greatest_lower_bound(identity,greatest_lower_bound(multiply(inverse(X_65),Y),multiply(inverse(X_65),X_66))) != greatest_lower_bound(identity,multiply(inverse(X_65),greatest_lower_bound(Y,X_66)))
| greatest_lower_bound(multiply(inverse(X_65),Y),greatest_lower_bound(identity,multiply(inverse(X_65),X_66))) = greatest_lower_bound(identity,multiply(inverse(X_65),greatest_lower_bound(Y,X_66))) ),
inference(subst,[],[refute_0_140:[bind(X0,$fot(greatest_lower_bound(multiply(inverse(X_65),Y),greatest_lower_bound(identity,multiply(inverse(X_65),X_66))))),bind(Y0,$fot(greatest_lower_bound(identity,greatest_lower_bound(multiply(inverse(X_65),Y),multiply(inverse(X_65),X_66))))),bind(Z0,$fot(greatest_lower_bound(identity,multiply(inverse(X_65),greatest_lower_bound(Y,X_66)))))]]) ).
cnf(refute_0_169,plain,
( greatest_lower_bound(identity,greatest_lower_bound(multiply(inverse(X_65),Y),multiply(inverse(X_65),X_66))) != greatest_lower_bound(identity,multiply(inverse(X_65),greatest_lower_bound(Y,X_66)))
| greatest_lower_bound(multiply(inverse(X_65),Y),greatest_lower_bound(identity,multiply(inverse(X_65),X_66))) = greatest_lower_bound(identity,multiply(inverse(X_65),greatest_lower_bound(Y,X_66))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(inverse(X_65),Y),greatest_lower_bound(identity,multiply(inverse(X_65),X_66))),greatest_lower_bound(identity,greatest_lower_bound(multiply(inverse(X_65),Y),multiply(inverse(X_65),X_66)))) )],[refute_0_167,refute_0_168]) ).
cnf(refute_0_170,plain,
greatest_lower_bound(multiply(inverse(X_65),Y),greatest_lower_bound(identity,multiply(inverse(X_65),X_66))) = greatest_lower_bound(identity,multiply(inverse(X_65),greatest_lower_bound(Y,X_66))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(multiply(inverse(X_65),Y),multiply(inverse(X_65),X_66))),greatest_lower_bound(identity,multiply(inverse(X_65),greatest_lower_bound(Y,X_66)))) )],[refute_0_102,refute_0_169]) ).
cnf(refute_0_171,plain,
( multiply(inverse(X_65),greatest_lower_bound(Y,greatest_lower_bound(X_65,X_66))) != greatest_lower_bound(multiply(inverse(X_65),Y),greatest_lower_bound(identity,multiply(inverse(X_65),X_66)))
| greatest_lower_bound(multiply(inverse(X_65),Y),greatest_lower_bound(identity,multiply(inverse(X_65),X_66))) != greatest_lower_bound(identity,multiply(inverse(X_65),greatest_lower_bound(Y,X_66)))
| multiply(inverse(X_65),greatest_lower_bound(Y,greatest_lower_bound(X_65,X_66))) = greatest_lower_bound(identity,multiply(inverse(X_65),greatest_lower_bound(Y,X_66))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_65),greatest_lower_bound(Y,greatest_lower_bound(X_65,X_66))),greatest_lower_bound(identity,multiply(inverse(X_65),greatest_lower_bound(Y,X_66)))) ),[0],$fot(greatest_lower_bound(multiply(inverse(X_65),Y),greatest_lower_bound(identity,multiply(inverse(X_65),X_66))))]]) ).
cnf(refute_0_172,plain,
( multiply(inverse(X_65),greatest_lower_bound(Y,greatest_lower_bound(X_65,X_66))) != greatest_lower_bound(multiply(inverse(X_65),Y),greatest_lower_bound(identity,multiply(inverse(X_65),X_66)))
| multiply(inverse(X_65),greatest_lower_bound(Y,greatest_lower_bound(X_65,X_66))) = greatest_lower_bound(identity,multiply(inverse(X_65),greatest_lower_bound(Y,X_66))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(inverse(X_65),Y),greatest_lower_bound(identity,multiply(inverse(X_65),X_66))),greatest_lower_bound(identity,multiply(inverse(X_65),greatest_lower_bound(Y,X_66)))) )],[refute_0_170,refute_0_171]) ).
cnf(refute_0_173,plain,
multiply(inverse(X_65),greatest_lower_bound(Y,greatest_lower_bound(X_65,X_66))) = greatest_lower_bound(identity,multiply(inverse(X_65),greatest_lower_bound(Y,X_66))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_65),greatest_lower_bound(Y,greatest_lower_bound(X_65,X_66))),greatest_lower_bound(multiply(inverse(X_65),Y),greatest_lower_bound(identity,multiply(inverse(X_65),X_66)))) )],[refute_0_95,refute_0_172]) ).
cnf(refute_0_174,plain,
( multiply(inverse(X_65),greatest_lower_bound(Y,greatest_lower_bound(X_65,X_66))) != greatest_lower_bound(identity,multiply(inverse(X_65),greatest_lower_bound(Y,X_66)))
| greatest_lower_bound(identity,multiply(inverse(X_65),greatest_lower_bound(Y,X_66))) = multiply(inverse(X_65),greatest_lower_bound(Y,greatest_lower_bound(X_65,X_66))) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(multiply(inverse(X_65),greatest_lower_bound(Y,greatest_lower_bound(X_65,X_66))))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(inverse(X_65),greatest_lower_bound(Y,X_66)))))]]) ).
cnf(refute_0_175,plain,
greatest_lower_bound(identity,multiply(inverse(X_65),greatest_lower_bound(Y,X_66))) = multiply(inverse(X_65),greatest_lower_bound(Y,greatest_lower_bound(X_65,X_66))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_65),greatest_lower_bound(Y,greatest_lower_bound(X_65,X_66))),greatest_lower_bound(identity,multiply(inverse(X_65),greatest_lower_bound(Y,X_66)))) )],[refute_0_173,refute_0_174]) ).
cnf(refute_0_176,plain,
greatest_lower_bound(identity,multiply(inverse(a),greatest_lower_bound(X_46,identity))) = multiply(inverse(a),greatest_lower_bound(X_46,greatest_lower_bound(a,identity))),
inference(subst,[],[refute_0_175:[bind(Y,$fot(X_46)),bind(X_65,$fot(a)),bind(X_66,$fot(identity))]]) ).
cnf(refute_0_177,plain,
( multiply(inverse(a),greatest_lower_bound(X_46,greatest_lower_bound(a,identity))) != multiply(inverse(a),greatest_lower_bound(X_46,identity))
| greatest_lower_bound(identity,multiply(inverse(a),greatest_lower_bound(X_46,identity))) != multiply(inverse(a),greatest_lower_bound(X_46,greatest_lower_bound(a,identity)))
| greatest_lower_bound(identity,multiply(inverse(a),greatest_lower_bound(X_46,identity))) = multiply(inverse(a),greatest_lower_bound(X_46,identity)) ),
inference(subst,[],[refute_0_140:[bind(X0,$fot(greatest_lower_bound(identity,multiply(inverse(a),greatest_lower_bound(X_46,identity))))),bind(Y0,$fot(multiply(inverse(a),greatest_lower_bound(X_46,greatest_lower_bound(a,identity))))),bind(Z0,$fot(multiply(inverse(a),greatest_lower_bound(X_46,identity))))]]) ).
cnf(refute_0_178,plain,
( multiply(inverse(a),greatest_lower_bound(X_46,greatest_lower_bound(a,identity))) != multiply(inverse(a),greatest_lower_bound(X_46,identity))
| greatest_lower_bound(identity,multiply(inverse(a),greatest_lower_bound(X_46,identity))) = multiply(inverse(a),greatest_lower_bound(X_46,identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(a),greatest_lower_bound(X_46,identity))),multiply(inverse(a),greatest_lower_bound(X_46,greatest_lower_bound(a,identity)))) )],[refute_0_176,refute_0_177]) ).
cnf(refute_0_179,plain,
greatest_lower_bound(identity,multiply(inverse(a),greatest_lower_bound(X_46,identity))) = multiply(inverse(a),greatest_lower_bound(X_46,identity)),
inference(resolve,[$cnf( $equal(multiply(inverse(a),greatest_lower_bound(X_46,greatest_lower_bound(a,identity))),multiply(inverse(a),greatest_lower_bound(X_46,identity))) )],[refute_0_90,refute_0_178]) ).
cnf(refute_0_180,plain,
( multiply(inverse(a),greatest_lower_bound(identity,X_46)) != greatest_lower_bound(identity,multiply(inverse(a),greatest_lower_bound(X_46,identity)))
| greatest_lower_bound(identity,multiply(inverse(a),greatest_lower_bound(X_46,identity))) != multiply(inverse(a),greatest_lower_bound(X_46,identity))
| multiply(inverse(a),greatest_lower_bound(identity,X_46)) = multiply(inverse(a),greatest_lower_bound(X_46,identity)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(a),greatest_lower_bound(identity,X_46)),multiply(inverse(a),greatest_lower_bound(X_46,identity))) ),[0],$fot(greatest_lower_bound(identity,multiply(inverse(a),greatest_lower_bound(X_46,identity))))]]) ).
cnf(refute_0_181,plain,
( multiply(inverse(a),greatest_lower_bound(identity,X_46)) != greatest_lower_bound(identity,multiply(inverse(a),greatest_lower_bound(X_46,identity)))
| multiply(inverse(a),greatest_lower_bound(identity,X_46)) = multiply(inverse(a),greatest_lower_bound(X_46,identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(a),greatest_lower_bound(X_46,identity))),multiply(inverse(a),greatest_lower_bound(X_46,identity))) )],[refute_0_179,refute_0_180]) ).
cnf(refute_0_182,plain,
multiply(inverse(a),greatest_lower_bound(identity,X_46)) = multiply(inverse(a),greatest_lower_bound(X_46,identity)),
inference(resolve,[$cnf( $equal(multiply(inverse(a),greatest_lower_bound(identity,X_46)),greatest_lower_bound(identity,multiply(inverse(a),greatest_lower_bound(X_46,identity)))) )],[refute_0_82,refute_0_181]) ).
cnf(refute_0_183,plain,
multiply(inverse(a),greatest_lower_bound(identity,a)) = multiply(inverse(a),greatest_lower_bound(a,identity)),
inference(subst,[],[refute_0_182:[bind(X_46,$fot(a))]]) ).
cnf(refute_0_184,plain,
( multiply(inverse(a),greatest_lower_bound(identity,a)) != multiply(inverse(a),greatest_lower_bound(a,identity))
| multiply(inverse(a),greatest_lower_bound(identity,a)) != greatest_lower_bound(identity,multiply(inverse(a),identity))
| multiply(inverse(a),greatest_lower_bound(a,identity)) = greatest_lower_bound(identity,multiply(inverse(a),identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(a),greatest_lower_bound(identity,a)),greatest_lower_bound(identity,multiply(inverse(a),identity))) ),[0],$fot(multiply(inverse(a),greatest_lower_bound(a,identity)))]]) ).
cnf(refute_0_185,plain,
( multiply(inverse(a),greatest_lower_bound(identity,a)) != greatest_lower_bound(identity,multiply(inverse(a),identity))
| multiply(inverse(a),greatest_lower_bound(a,identity)) = greatest_lower_bound(identity,multiply(inverse(a),identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(a),greatest_lower_bound(identity,a)),multiply(inverse(a),greatest_lower_bound(a,identity))) )],[refute_0_183,refute_0_184]) ).
cnf(refute_0_186,plain,
multiply(inverse(a),greatest_lower_bound(a,identity)) = greatest_lower_bound(identity,multiply(inverse(a),identity)),
inference(resolve,[$cnf( $equal(multiply(inverse(a),greatest_lower_bound(identity,a)),greatest_lower_bound(identity,multiply(inverse(a),identity))) )],[refute_0_43,refute_0_185]) ).
cnf(refute_0_187,plain,
multiply(inverse(a),greatest_lower_bound(a,identity)) = multiply(inverse(a),greatest_lower_bound(a,identity)),
introduced(tautology,[refl,[$fot(multiply(inverse(a),greatest_lower_bound(a,identity)))]]) ).
cnf(refute_0_188,plain,
( multiply(inverse(a),greatest_lower_bound(a,identity)) != multiply(inverse(a),greatest_lower_bound(a,identity))
| greatest_lower_bound(a,identity) != identity
| multiply(inverse(a),greatest_lower_bound(a,identity)) = multiply(inverse(a),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(a),greatest_lower_bound(a,identity)),multiply(inverse(a),greatest_lower_bound(a,identity))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_189,plain,
( greatest_lower_bound(a,identity) != identity
| multiply(inverse(a),greatest_lower_bound(a,identity)) = multiply(inverse(a),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(a),greatest_lower_bound(a,identity)),multiply(inverse(a),greatest_lower_bound(a,identity))) )],[refute_0_187,refute_0_188]) ).
cnf(refute_0_190,plain,
multiply(inverse(a),greatest_lower_bound(a,identity)) = multiply(inverse(a),identity),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,identity),identity) )],[refute_0_69,refute_0_189]) ).
cnf(refute_0_191,plain,
( multiply(inverse(a),greatest_lower_bound(a,identity)) != multiply(inverse(a),identity)
| multiply(inverse(a),greatest_lower_bound(a,identity)) != greatest_lower_bound(identity,multiply(inverse(a),identity))
| multiply(inverse(a),identity) = greatest_lower_bound(identity,multiply(inverse(a),identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(a),greatest_lower_bound(a,identity)),greatest_lower_bound(identity,multiply(inverse(a),identity))) ),[0],$fot(multiply(inverse(a),identity))]]) ).
cnf(refute_0_192,plain,
( multiply(inverse(a),greatest_lower_bound(a,identity)) != greatest_lower_bound(identity,multiply(inverse(a),identity))
| multiply(inverse(a),identity) = greatest_lower_bound(identity,multiply(inverse(a),identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(a),greatest_lower_bound(a,identity)),multiply(inverse(a),identity)) )],[refute_0_190,refute_0_191]) ).
cnf(refute_0_193,plain,
least_upper_bound(X_10,greatest_lower_bound(X_10,X_11)) = X_10,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_10)),bind(Y,$fot(X_11))]]) ).
cnf(refute_0_194,plain,
greatest_lower_bound(X_11,X_10) = greatest_lower_bound(X_10,X_11),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_11)),bind(Y,$fot(X_10))]]) ).
cnf(refute_0_195,plain,
( greatest_lower_bound(X_11,X_10) != greatest_lower_bound(X_10,X_11)
| greatest_lower_bound(X_10,X_11) = greatest_lower_bound(X_11,X_10) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(greatest_lower_bound(X_11,X_10))),bind(Y0,$fot(greatest_lower_bound(X_10,X_11)))]]) ).
cnf(refute_0_196,plain,
greatest_lower_bound(X_10,X_11) = greatest_lower_bound(X_11,X_10),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_11,X_10),greatest_lower_bound(X_10,X_11)) )],[refute_0_194,refute_0_195]) ).
cnf(refute_0_197,plain,
( greatest_lower_bound(X_10,X_11) != greatest_lower_bound(X_11,X_10)
| least_upper_bound(X_10,greatest_lower_bound(X_10,X_11)) != X_10
| least_upper_bound(X_10,greatest_lower_bound(X_11,X_10)) = X_10 ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_10,greatest_lower_bound(X_10,X_11)),X_10) ),[0,1],$fot(greatest_lower_bound(X_11,X_10))]]) ).
cnf(refute_0_198,plain,
( least_upper_bound(X_10,greatest_lower_bound(X_10,X_11)) != X_10
| least_upper_bound(X_10,greatest_lower_bound(X_11,X_10)) = X_10 ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_10,X_11),greatest_lower_bound(X_11,X_10)) )],[refute_0_196,refute_0_197]) ).
cnf(refute_0_199,plain,
least_upper_bound(X_10,greatest_lower_bound(X_11,X_10)) = X_10,
inference(resolve,[$cnf( $equal(least_upper_bound(X_10,greatest_lower_bound(X_10,X_11)),X_10) )],[refute_0_193,refute_0_198]) ).
cnf(refute_0_200,plain,
least_upper_bound(greatest_lower_bound(X_27,X_11),greatest_lower_bound(X_11,greatest_lower_bound(X_27,X_11))) = greatest_lower_bound(X_27,X_11),
inference(subst,[],[refute_0_199:[bind(X_10,$fot(greatest_lower_bound(X_27,X_11)))]]) ).
cnf(refute_0_201,plain,
greatest_lower_bound(X_11,greatest_lower_bound(X_27,X_11)) = greatest_lower_bound(X_11,X_27),
inference(subst,[],[refute_0_114:[bind(Y,$fot(X_27)),bind(X_13,$fot(X_11))]]) ).
cnf(refute_0_202,plain,
( greatest_lower_bound(X_11,greatest_lower_bound(X_27,X_11)) != greatest_lower_bound(X_11,X_27)
| least_upper_bound(greatest_lower_bound(X_27,X_11),greatest_lower_bound(X_11,greatest_lower_bound(X_27,X_11))) != greatest_lower_bound(X_27,X_11)
| least_upper_bound(greatest_lower_bound(X_27,X_11),greatest_lower_bound(X_11,X_27)) = greatest_lower_bound(X_27,X_11) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_27,X_11),greatest_lower_bound(X_11,greatest_lower_bound(X_27,X_11))),greatest_lower_bound(X_27,X_11)) ),[0,1],$fot(greatest_lower_bound(X_11,X_27))]]) ).
cnf(refute_0_203,plain,
( least_upper_bound(greatest_lower_bound(X_27,X_11),greatest_lower_bound(X_11,greatest_lower_bound(X_27,X_11))) != greatest_lower_bound(X_27,X_11)
| least_upper_bound(greatest_lower_bound(X_27,X_11),greatest_lower_bound(X_11,X_27)) = greatest_lower_bound(X_27,X_11) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_11,greatest_lower_bound(X_27,X_11)),greatest_lower_bound(X_11,X_27)) )],[refute_0_201,refute_0_202]) ).
cnf(refute_0_204,plain,
least_upper_bound(greatest_lower_bound(X_27,X_11),greatest_lower_bound(X_11,X_27)) = greatest_lower_bound(X_27,X_11),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_27,X_11),greatest_lower_bound(X_11,greatest_lower_bound(X_27,X_11))),greatest_lower_bound(X_27,X_11)) )],[refute_0_200,refute_0_203]) ).
cnf(refute_0_205,plain,
least_upper_bound(greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68)),greatest_lower_bound(multiply(X_69,X_68),multiply(X_70,X_68))) = greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68)),
inference(subst,[],[refute_0_204:[bind(X_11,$fot(multiply(X_69,X_68))),bind(X_27,$fot(multiply(X_70,X_68)))]]) ).
cnf(refute_0_206,plain,
multiply(greatest_lower_bound(X_69,X_70),X_68) = greatest_lower_bound(multiply(X_69,X_68),multiply(X_70,X_68)),
inference(subst,[],[monotony_glb2:[bind(X,$fot(X_68)),bind(Y,$fot(X_69)),bind(Z,$fot(X_70))]]) ).
cnf(refute_0_207,plain,
( multiply(greatest_lower_bound(X_69,X_70),X_68) != greatest_lower_bound(multiply(X_69,X_68),multiply(X_70,X_68))
| greatest_lower_bound(multiply(X_69,X_68),multiply(X_70,X_68)) = multiply(greatest_lower_bound(X_69,X_70),X_68) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(multiply(greatest_lower_bound(X_69,X_70),X_68))),bind(Y0,$fot(greatest_lower_bound(multiply(X_69,X_68),multiply(X_70,X_68))))]]) ).
cnf(refute_0_208,plain,
greatest_lower_bound(multiply(X_69,X_68),multiply(X_70,X_68)) = multiply(greatest_lower_bound(X_69,X_70),X_68),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_69,X_70),X_68),greatest_lower_bound(multiply(X_69,X_68),multiply(X_70,X_68))) )],[refute_0_206,refute_0_207]) ).
cnf(refute_0_209,plain,
( greatest_lower_bound(multiply(X_69,X_68),multiply(X_70,X_68)) != multiply(greatest_lower_bound(X_69,X_70),X_68)
| least_upper_bound(greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68)),greatest_lower_bound(multiply(X_69,X_68),multiply(X_70,X_68))) != greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68))
| least_upper_bound(greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68)),multiply(greatest_lower_bound(X_69,X_70),X_68)) = greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68)),greatest_lower_bound(multiply(X_69,X_68),multiply(X_70,X_68))),greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68))) ),[0,1],$fot(multiply(greatest_lower_bound(X_69,X_70),X_68))]]) ).
cnf(refute_0_210,plain,
( least_upper_bound(greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68)),greatest_lower_bound(multiply(X_69,X_68),multiply(X_70,X_68))) != greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68))
| least_upper_bound(greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68)),multiply(greatest_lower_bound(X_69,X_70),X_68)) = greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_69,X_68),multiply(X_70,X_68)),multiply(greatest_lower_bound(X_69,X_70),X_68)) )],[refute_0_208,refute_0_209]) ).
cnf(refute_0_211,plain,
least_upper_bound(greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68)),multiply(greatest_lower_bound(X_69,X_70),X_68)) = greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68)),greatest_lower_bound(multiply(X_69,X_68),multiply(X_70,X_68))),greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68))) )],[refute_0_205,refute_0_210]) ).
cnf(refute_0_212,plain,
least_upper_bound(greatest_lower_bound(X_69,X_70),greatest_lower_bound(X_70,X_69)) = greatest_lower_bound(X_69,X_70),
inference(subst,[],[refute_0_204:[bind(X_11,$fot(X_70)),bind(X_27,$fot(X_69))]]) ).
cnf(refute_0_213,plain,
multiply(least_upper_bound(greatest_lower_bound(X_69,X_70),greatest_lower_bound(X_70,X_69)),X_68) = multiply(least_upper_bound(greatest_lower_bound(X_69,X_70),greatest_lower_bound(X_70,X_69)),X_68),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(greatest_lower_bound(X_69,X_70),greatest_lower_bound(X_70,X_69)),X_68))]]) ).
cnf(refute_0_214,plain,
( multiply(least_upper_bound(greatest_lower_bound(X_69,X_70),greatest_lower_bound(X_70,X_69)),X_68) != multiply(least_upper_bound(greatest_lower_bound(X_69,X_70),greatest_lower_bound(X_70,X_69)),X_68)
| least_upper_bound(greatest_lower_bound(X_69,X_70),greatest_lower_bound(X_70,X_69)) != greatest_lower_bound(X_69,X_70)
| multiply(least_upper_bound(greatest_lower_bound(X_69,X_70),greatest_lower_bound(X_70,X_69)),X_68) = multiply(greatest_lower_bound(X_69,X_70),X_68) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(X_69,X_70),greatest_lower_bound(X_70,X_69)),X_68),multiply(least_upper_bound(greatest_lower_bound(X_69,X_70),greatest_lower_bound(X_70,X_69)),X_68)) ),[1,0],$fot(greatest_lower_bound(X_69,X_70))]]) ).
cnf(refute_0_215,plain,
( least_upper_bound(greatest_lower_bound(X_69,X_70),greatest_lower_bound(X_70,X_69)) != greatest_lower_bound(X_69,X_70)
| multiply(least_upper_bound(greatest_lower_bound(X_69,X_70),greatest_lower_bound(X_70,X_69)),X_68) = multiply(greatest_lower_bound(X_69,X_70),X_68) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(X_69,X_70),greatest_lower_bound(X_70,X_69)),X_68),multiply(least_upper_bound(greatest_lower_bound(X_69,X_70),greatest_lower_bound(X_70,X_69)),X_68)) )],[refute_0_213,refute_0_214]) ).
cnf(refute_0_216,plain,
multiply(least_upper_bound(greatest_lower_bound(X_69,X_70),greatest_lower_bound(X_70,X_69)),X_68) = multiply(greatest_lower_bound(X_69,X_70),X_68),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_69,X_70),greatest_lower_bound(X_70,X_69)),greatest_lower_bound(X_69,X_70)) )],[refute_0_212,refute_0_215]) ).
cnf(refute_0_217,plain,
( multiply(least_upper_bound(Y,Z),X) != least_upper_bound(multiply(Y,X),multiply(Z,X))
| least_upper_bound(multiply(Y,X),multiply(Z,X)) = multiply(least_upper_bound(Y,Z),X) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(multiply(least_upper_bound(Y,Z),X))),bind(Y0,$fot(least_upper_bound(multiply(Y,X),multiply(Z,X))))]]) ).
cnf(refute_0_218,plain,
least_upper_bound(multiply(Y,X),multiply(Z,X)) = multiply(least_upper_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Y,X),multiply(Z,X))) )],[monotony_lub2,refute_0_217]) ).
cnf(refute_0_219,plain,
least_upper_bound(multiply(greatest_lower_bound(X_69,X_70),X_68),multiply(greatest_lower_bound(X_70,X_69),X_68)) = multiply(least_upper_bound(greatest_lower_bound(X_69,X_70),greatest_lower_bound(X_70,X_69)),X_68),
inference(subst,[],[refute_0_218:[bind(X,$fot(X_68)),bind(Y,$fot(greatest_lower_bound(X_69,X_70))),bind(Z,$fot(greatest_lower_bound(X_70,X_69)))]]) ).
cnf(refute_0_220,plain,
( multiply(least_upper_bound(greatest_lower_bound(X_69,X_70),greatest_lower_bound(X_70,X_69)),X_68) != multiply(greatest_lower_bound(X_69,X_70),X_68)
| least_upper_bound(multiply(greatest_lower_bound(X_69,X_70),X_68),multiply(greatest_lower_bound(X_70,X_69),X_68)) != multiply(least_upper_bound(greatest_lower_bound(X_69,X_70),greatest_lower_bound(X_70,X_69)),X_68)
| least_upper_bound(multiply(greatest_lower_bound(X_69,X_70),X_68),multiply(greatest_lower_bound(X_70,X_69),X_68)) = multiply(greatest_lower_bound(X_69,X_70),X_68) ),
inference(subst,[],[refute_0_140:[bind(X0,$fot(least_upper_bound(multiply(greatest_lower_bound(X_69,X_70),X_68),multiply(greatest_lower_bound(X_70,X_69),X_68)))),bind(Y0,$fot(multiply(least_upper_bound(greatest_lower_bound(X_69,X_70),greatest_lower_bound(X_70,X_69)),X_68))),bind(Z0,$fot(multiply(greatest_lower_bound(X_69,X_70),X_68)))]]) ).
cnf(refute_0_221,plain,
( multiply(least_upper_bound(greatest_lower_bound(X_69,X_70),greatest_lower_bound(X_70,X_69)),X_68) != multiply(greatest_lower_bound(X_69,X_70),X_68)
| least_upper_bound(multiply(greatest_lower_bound(X_69,X_70),X_68),multiply(greatest_lower_bound(X_70,X_69),X_68)) = multiply(greatest_lower_bound(X_69,X_70),X_68) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(X_69,X_70),X_68),multiply(greatest_lower_bound(X_70,X_69),X_68)),multiply(least_upper_bound(greatest_lower_bound(X_69,X_70),greatest_lower_bound(X_70,X_69)),X_68)) )],[refute_0_219,refute_0_220]) ).
cnf(refute_0_222,plain,
least_upper_bound(multiply(greatest_lower_bound(X_69,X_70),X_68),multiply(greatest_lower_bound(X_70,X_69),X_68)) = multiply(greatest_lower_bound(X_69,X_70),X_68),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(X_69,X_70),greatest_lower_bound(X_70,X_69)),X_68),multiply(greatest_lower_bound(X_69,X_70),X_68)) )],[refute_0_216,refute_0_221]) ).
cnf(refute_0_223,plain,
( multiply(greatest_lower_bound(Y,Z),X) != greatest_lower_bound(multiply(Y,X),multiply(Z,X))
| greatest_lower_bound(multiply(Y,X),multiply(Z,X)) = multiply(greatest_lower_bound(Y,Z),X) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(multiply(greatest_lower_bound(Y,Z),X))),bind(Y0,$fot(greatest_lower_bound(multiply(Y,X),multiply(Z,X))))]]) ).
cnf(refute_0_224,plain,
greatest_lower_bound(multiply(Y,X),multiply(Z,X)) = multiply(greatest_lower_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Y,X),multiply(Z,X))) )],[monotony_glb2,refute_0_223]) ).
cnf(refute_0_225,plain,
greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68)) = multiply(greatest_lower_bound(X_70,X_69),X_68),
inference(subst,[],[refute_0_224:[bind(X,$fot(X_68)),bind(Y,$fot(X_70)),bind(Z,$fot(X_69))]]) ).
cnf(refute_0_226,plain,
least_upper_bound(multiply(greatest_lower_bound(X_69,X_70),X_68),greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68))) = least_upper_bound(multiply(greatest_lower_bound(X_69,X_70),X_68),greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68))),
introduced(tautology,[refl,[$fot(least_upper_bound(multiply(greatest_lower_bound(X_69,X_70),X_68),greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68))))]]) ).
cnf(refute_0_227,plain,
( greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68)) != multiply(greatest_lower_bound(X_70,X_69),X_68)
| least_upper_bound(multiply(greatest_lower_bound(X_69,X_70),X_68),greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68))) != least_upper_bound(multiply(greatest_lower_bound(X_69,X_70),X_68),greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68)))
| least_upper_bound(multiply(greatest_lower_bound(X_69,X_70),X_68),greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68))) = least_upper_bound(multiply(greatest_lower_bound(X_69,X_70),X_68),multiply(greatest_lower_bound(X_70,X_69),X_68)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(X_69,X_70),X_68),greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68))),least_upper_bound(multiply(greatest_lower_bound(X_69,X_70),X_68),greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68)))) ),[1,1],$fot(multiply(greatest_lower_bound(X_70,X_69),X_68))]]) ).
cnf(refute_0_228,plain,
( greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68)) != multiply(greatest_lower_bound(X_70,X_69),X_68)
| least_upper_bound(multiply(greatest_lower_bound(X_69,X_70),X_68),greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68))) = least_upper_bound(multiply(greatest_lower_bound(X_69,X_70),X_68),multiply(greatest_lower_bound(X_70,X_69),X_68)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(X_69,X_70),X_68),greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68))),least_upper_bound(multiply(greatest_lower_bound(X_69,X_70),X_68),greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68)))) )],[refute_0_226,refute_0_227]) ).
cnf(refute_0_229,plain,
least_upper_bound(multiply(greatest_lower_bound(X_69,X_70),X_68),greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68))) = least_upper_bound(multiply(greatest_lower_bound(X_69,X_70),X_68),multiply(greatest_lower_bound(X_70,X_69),X_68)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68)),multiply(greatest_lower_bound(X_70,X_69),X_68)) )],[refute_0_225,refute_0_228]) ).
cnf(refute_0_230,plain,
( least_upper_bound(multiply(greatest_lower_bound(X_69,X_70),X_68),multiply(greatest_lower_bound(X_70,X_69),X_68)) != multiply(greatest_lower_bound(X_69,X_70),X_68)
| least_upper_bound(multiply(greatest_lower_bound(X_69,X_70),X_68),greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68))) != least_upper_bound(multiply(greatest_lower_bound(X_69,X_70),X_68),multiply(greatest_lower_bound(X_70,X_69),X_68))
| least_upper_bound(multiply(greatest_lower_bound(X_69,X_70),X_68),greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68))) = multiply(greatest_lower_bound(X_69,X_70),X_68) ),
inference(subst,[],[refute_0_140:[bind(X0,$fot(least_upper_bound(multiply(greatest_lower_bound(X_69,X_70),X_68),greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68))))),bind(Y0,$fot(least_upper_bound(multiply(greatest_lower_bound(X_69,X_70),X_68),multiply(greatest_lower_bound(X_70,X_69),X_68)))),bind(Z0,$fot(multiply(greatest_lower_bound(X_69,X_70),X_68)))]]) ).
cnf(refute_0_231,plain,
( least_upper_bound(multiply(greatest_lower_bound(X_69,X_70),X_68),multiply(greatest_lower_bound(X_70,X_69),X_68)) != multiply(greatest_lower_bound(X_69,X_70),X_68)
| least_upper_bound(multiply(greatest_lower_bound(X_69,X_70),X_68),greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68))) = multiply(greatest_lower_bound(X_69,X_70),X_68) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(X_69,X_70),X_68),greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68))),least_upper_bound(multiply(greatest_lower_bound(X_69,X_70),X_68),multiply(greatest_lower_bound(X_70,X_69),X_68))) )],[refute_0_229,refute_0_230]) ).
cnf(refute_0_232,plain,
least_upper_bound(multiply(greatest_lower_bound(X_69,X_70),X_68),greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68))) = multiply(greatest_lower_bound(X_69,X_70),X_68),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(X_69,X_70),X_68),multiply(greatest_lower_bound(X_70,X_69),X_68)),multiply(greatest_lower_bound(X_69,X_70),X_68)) )],[refute_0_222,refute_0_231]) ).
cnf(refute_0_233,plain,
least_upper_bound(greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68)),multiply(greatest_lower_bound(X_69,X_70),X_68)) = least_upper_bound(multiply(greatest_lower_bound(X_69,X_70),X_68),greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68))),
inference(subst,[],[refute_0_9:[bind(X,$fot(multiply(greatest_lower_bound(X_69,X_70),X_68))),bind(Y,$fot(greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68))))]]) ).
cnf(refute_0_234,plain,
( least_upper_bound(multiply(greatest_lower_bound(X_69,X_70),X_68),greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68))) != multiply(greatest_lower_bound(X_69,X_70),X_68)
| least_upper_bound(greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68)),multiply(greatest_lower_bound(X_69,X_70),X_68)) != least_upper_bound(multiply(greatest_lower_bound(X_69,X_70),X_68),greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68)))
| least_upper_bound(greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68)),multiply(greatest_lower_bound(X_69,X_70),X_68)) = multiply(greatest_lower_bound(X_69,X_70),X_68) ),
inference(subst,[],[refute_0_140:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68)),multiply(greatest_lower_bound(X_69,X_70),X_68)))),bind(Y0,$fot(least_upper_bound(multiply(greatest_lower_bound(X_69,X_70),X_68),greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68))))),bind(Z0,$fot(multiply(greatest_lower_bound(X_69,X_70),X_68)))]]) ).
cnf(refute_0_235,plain,
( least_upper_bound(multiply(greatest_lower_bound(X_69,X_70),X_68),greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68))) != multiply(greatest_lower_bound(X_69,X_70),X_68)
| least_upper_bound(greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68)),multiply(greatest_lower_bound(X_69,X_70),X_68)) = multiply(greatest_lower_bound(X_69,X_70),X_68) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68)),multiply(greatest_lower_bound(X_69,X_70),X_68)),least_upper_bound(multiply(greatest_lower_bound(X_69,X_70),X_68),greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68)))) )],[refute_0_233,refute_0_234]) ).
cnf(refute_0_236,plain,
least_upper_bound(greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68)),multiply(greatest_lower_bound(X_69,X_70),X_68)) = multiply(greatest_lower_bound(X_69,X_70),X_68),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(X_69,X_70),X_68),greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68))),multiply(greatest_lower_bound(X_69,X_70),X_68)) )],[refute_0_232,refute_0_235]) ).
cnf(refute_0_237,plain,
( least_upper_bound(greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68)),multiply(greatest_lower_bound(X_69,X_70),X_68)) != multiply(greatest_lower_bound(X_69,X_70),X_68)
| least_upper_bound(greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68)),multiply(greatest_lower_bound(X_69,X_70),X_68)) != greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68))
| multiply(greatest_lower_bound(X_69,X_70),X_68) = greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68)),multiply(greatest_lower_bound(X_69,X_70),X_68)),greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68))) ),[0],$fot(multiply(greatest_lower_bound(X_69,X_70),X_68))]]) ).
cnf(refute_0_238,plain,
( least_upper_bound(greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68)),multiply(greatest_lower_bound(X_69,X_70),X_68)) != greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68))
| multiply(greatest_lower_bound(X_69,X_70),X_68) = greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68)),multiply(greatest_lower_bound(X_69,X_70),X_68)),multiply(greatest_lower_bound(X_69,X_70),X_68)) )],[refute_0_236,refute_0_237]) ).
cnf(refute_0_239,plain,
( multiply(greatest_lower_bound(X_69,X_70),X_68) != greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68))
| greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68)) != multiply(greatest_lower_bound(X_70,X_69),X_68)
| multiply(greatest_lower_bound(X_69,X_70),X_68) = multiply(greatest_lower_bound(X_70,X_69),X_68) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_69,X_70),X_68),multiply(greatest_lower_bound(X_70,X_69),X_68)) ),[0],$fot(greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68)))]]) ).
cnf(refute_0_240,plain,
( multiply(greatest_lower_bound(X_69,X_70),X_68) != greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68))
| multiply(greatest_lower_bound(X_69,X_70),X_68) = multiply(greatest_lower_bound(X_70,X_69),X_68) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68)),multiply(greatest_lower_bound(X_70,X_69),X_68)) )],[refute_0_225,refute_0_239]) ).
cnf(refute_0_241,plain,
( least_upper_bound(greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68)),multiply(greatest_lower_bound(X_69,X_70),X_68)) != greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68))
| multiply(greatest_lower_bound(X_69,X_70),X_68) = multiply(greatest_lower_bound(X_70,X_69),X_68) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_69,X_70),X_68),greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68))) )],[refute_0_238,refute_0_240]) ).
cnf(refute_0_242,plain,
multiply(greatest_lower_bound(X_69,X_70),X_68) = multiply(greatest_lower_bound(X_70,X_69),X_68),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68)),multiply(greatest_lower_bound(X_69,X_70),X_68)),greatest_lower_bound(multiply(X_70,X_68),multiply(X_69,X_68))) )],[refute_0_211,refute_0_241]) ).
cnf(refute_0_243,plain,
( multiply(greatest_lower_bound(X_69,X_70),X_68) != multiply(greatest_lower_bound(X_70,X_69),X_68)
| multiply(greatest_lower_bound(X_70,X_69),X_68) = multiply(greatest_lower_bound(X_69,X_70),X_68) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(multiply(greatest_lower_bound(X_69,X_70),X_68))),bind(Y0,$fot(multiply(greatest_lower_bound(X_70,X_69),X_68)))]]) ).
cnf(refute_0_244,plain,
multiply(greatest_lower_bound(X_70,X_69),X_68) = multiply(greatest_lower_bound(X_69,X_70),X_68),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_69,X_70),X_68),multiply(greatest_lower_bound(X_70,X_69),X_68)) )],[refute_0_242,refute_0_243]) ).
cnf(refute_0_245,plain,
multiply(greatest_lower_bound(inverse(a),identity),identity) = multiply(greatest_lower_bound(identity,inverse(a)),identity),
inference(subst,[],[refute_0_244:[bind(X_68,$fot(identity)),bind(X_69,$fot(identity)),bind(X_70,$fot(inverse(a)))]]) ).
cnf(refute_0_246,plain,
multiply(greatest_lower_bound(X_69,identity),X_68) = greatest_lower_bound(multiply(X_69,X_68),multiply(identity,X_68)),
inference(subst,[],[monotony_glb2:[bind(X,$fot(X_68)),bind(Y,$fot(X_69)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_247,plain,
multiply(identity,X_68) = X_68,
inference(subst,[],[left_identity:[bind(X,$fot(X_68))]]) ).
cnf(refute_0_248,plain,
( multiply(greatest_lower_bound(X_69,identity),X_68) != greatest_lower_bound(multiply(X_69,X_68),multiply(identity,X_68))
| multiply(identity,X_68) != X_68
| multiply(greatest_lower_bound(X_69,identity),X_68) = greatest_lower_bound(multiply(X_69,X_68),X_68) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_69,identity),X_68),greatest_lower_bound(multiply(X_69,X_68),multiply(identity,X_68))) ),[1,1],$fot(X_68)]]) ).
cnf(refute_0_249,plain,
( multiply(greatest_lower_bound(X_69,identity),X_68) != greatest_lower_bound(multiply(X_69,X_68),multiply(identity,X_68))
| multiply(greatest_lower_bound(X_69,identity),X_68) = greatest_lower_bound(multiply(X_69,X_68),X_68) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_68),X_68) )],[refute_0_247,refute_0_248]) ).
cnf(refute_0_250,plain,
multiply(greatest_lower_bound(X_69,identity),X_68) = greatest_lower_bound(multiply(X_69,X_68),X_68),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_69,identity),X_68),greatest_lower_bound(multiply(X_69,X_68),multiply(identity,X_68))) )],[refute_0_246,refute_0_249]) ).
cnf(refute_0_251,plain,
greatest_lower_bound(multiply(X_69,X_68),X_68) = greatest_lower_bound(X_68,multiply(X_69,X_68)),
inference(subst,[],[refute_0_38:[bind(X,$fot(X_68)),bind(Y,$fot(multiply(X_69,X_68)))]]) ).
cnf(refute_0_252,plain,
( multiply(greatest_lower_bound(X_69,identity),X_68) != greatest_lower_bound(multiply(X_69,X_68),X_68)
| greatest_lower_bound(multiply(X_69,X_68),X_68) != greatest_lower_bound(X_68,multiply(X_69,X_68))
| multiply(greatest_lower_bound(X_69,identity),X_68) = greatest_lower_bound(X_68,multiply(X_69,X_68)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_69,identity),X_68),greatest_lower_bound(X_68,multiply(X_69,X_68))) ),[0],$fot(greatest_lower_bound(multiply(X_69,X_68),X_68))]]) ).
cnf(refute_0_253,plain,
( multiply(greatest_lower_bound(X_69,identity),X_68) != greatest_lower_bound(multiply(X_69,X_68),X_68)
| multiply(greatest_lower_bound(X_69,identity),X_68) = greatest_lower_bound(X_68,multiply(X_69,X_68)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_69,X_68),X_68),greatest_lower_bound(X_68,multiply(X_69,X_68))) )],[refute_0_251,refute_0_252]) ).
cnf(refute_0_254,plain,
multiply(greatest_lower_bound(X_69,identity),X_68) = greatest_lower_bound(X_68,multiply(X_69,X_68)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_69,identity),X_68),greatest_lower_bound(multiply(X_69,X_68),X_68)) )],[refute_0_250,refute_0_253]) ).
cnf(refute_0_255,plain,
( multiply(greatest_lower_bound(X_69,identity),X_68) != greatest_lower_bound(X_68,multiply(X_69,X_68))
| greatest_lower_bound(X_68,multiply(X_69,X_68)) = multiply(greatest_lower_bound(X_69,identity),X_68) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(multiply(greatest_lower_bound(X_69,identity),X_68))),bind(Y0,$fot(greatest_lower_bound(X_68,multiply(X_69,X_68))))]]) ).
cnf(refute_0_256,plain,
greatest_lower_bound(X_68,multiply(X_69,X_68)) = multiply(greatest_lower_bound(X_69,identity),X_68),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_69,identity),X_68),greatest_lower_bound(X_68,multiply(X_69,X_68))) )],[refute_0_254,refute_0_255]) ).
cnf(refute_0_257,plain,
greatest_lower_bound(identity,multiply(inverse(a),identity)) = multiply(greatest_lower_bound(inverse(a),identity),identity),
inference(subst,[],[refute_0_256:[bind(X_68,$fot(identity)),bind(X_69,$fot(inverse(a)))]]) ).
cnf(refute_0_258,plain,
( multiply(greatest_lower_bound(inverse(a),identity),identity) != multiply(greatest_lower_bound(identity,inverse(a)),identity)
| greatest_lower_bound(identity,multiply(inverse(a),identity)) != multiply(greatest_lower_bound(inverse(a),identity),identity)
| greatest_lower_bound(identity,multiply(inverse(a),identity)) = multiply(greatest_lower_bound(identity,inverse(a)),identity) ),
inference(subst,[],[refute_0_140:[bind(X0,$fot(greatest_lower_bound(identity,multiply(inverse(a),identity)))),bind(Y0,$fot(multiply(greatest_lower_bound(inverse(a),identity),identity))),bind(Z0,$fot(multiply(greatest_lower_bound(identity,inverse(a)),identity)))]]) ).
cnf(refute_0_259,plain,
( multiply(greatest_lower_bound(inverse(a),identity),identity) != multiply(greatest_lower_bound(identity,inverse(a)),identity)
| greatest_lower_bound(identity,multiply(inverse(a),identity)) = multiply(greatest_lower_bound(identity,inverse(a)),identity) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(a),identity)),multiply(greatest_lower_bound(inverse(a),identity),identity)) )],[refute_0_257,refute_0_258]) ).
cnf(refute_0_260,plain,
greatest_lower_bound(identity,multiply(inverse(a),identity)) = multiply(greatest_lower_bound(identity,inverse(a)),identity),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(a),identity),identity),multiply(greatest_lower_bound(identity,inverse(a)),identity)) )],[refute_0_245,refute_0_259]) ).
cnf(refute_0_261,plain,
( multiply(inverse(a),identity) != greatest_lower_bound(identity,multiply(inverse(a),identity))
| greatest_lower_bound(identity,multiply(inverse(a),identity)) != multiply(greatest_lower_bound(identity,inverse(a)),identity)
| multiply(inverse(a),identity) = multiply(greatest_lower_bound(identity,inverse(a)),identity) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(a),identity),multiply(greatest_lower_bound(identity,inverse(a)),identity)) ),[0],$fot(greatest_lower_bound(identity,multiply(inverse(a),identity)))]]) ).
cnf(refute_0_262,plain,
( multiply(inverse(a),identity) != greatest_lower_bound(identity,multiply(inverse(a),identity))
| multiply(inverse(a),identity) = multiply(greatest_lower_bound(identity,inverse(a)),identity) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(a),identity)),multiply(greatest_lower_bound(identity,inverse(a)),identity)) )],[refute_0_260,refute_0_261]) ).
cnf(refute_0_263,plain,
( multiply(inverse(a),greatest_lower_bound(a,identity)) != greatest_lower_bound(identity,multiply(inverse(a),identity))
| multiply(inverse(a),identity) = multiply(greatest_lower_bound(identity,inverse(a)),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(a),identity),greatest_lower_bound(identity,multiply(inverse(a),identity))) )],[refute_0_192,refute_0_262]) ).
cnf(refute_0_264,plain,
multiply(inverse(a),identity) = multiply(greatest_lower_bound(identity,inverse(a)),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(a),greatest_lower_bound(a,identity)),greatest_lower_bound(identity,multiply(inverse(a),identity))) )],[refute_0_186,refute_0_263]) ).
cnf(refute_0_265,plain,
multiply(multiply(inverse(X_100),X_100),X_101) = multiply(inverse(X_100),multiply(X_100,X_101)),
inference(subst,[],[associativity:[bind(X,$fot(inverse(X_100))),bind(Y,$fot(X_100)),bind(Z,$fot(X_101))]]) ).
cnf(refute_0_266,plain,
multiply(inverse(X_100),X_100) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_100))]]) ).
cnf(refute_0_267,plain,
( multiply(multiply(inverse(X_100),X_100),X_101) != multiply(inverse(X_100),multiply(X_100,X_101))
| multiply(inverse(X_100),X_100) != identity
| multiply(identity,X_101) = multiply(inverse(X_100),multiply(X_100,X_101)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_100),X_100),X_101),multiply(inverse(X_100),multiply(X_100,X_101))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_268,plain,
( multiply(multiply(inverse(X_100),X_100),X_101) != multiply(inverse(X_100),multiply(X_100,X_101))
| multiply(identity,X_101) = multiply(inverse(X_100),multiply(X_100,X_101)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_100),X_100),identity) )],[refute_0_266,refute_0_267]) ).
cnf(refute_0_269,plain,
multiply(identity,X_101) = multiply(inverse(X_100),multiply(X_100,X_101)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_100),X_100),X_101),multiply(inverse(X_100),multiply(X_100,X_101))) )],[refute_0_265,refute_0_268]) ).
cnf(refute_0_270,plain,
multiply(identity,X_101) = X_101,
inference(subst,[],[left_identity:[bind(X,$fot(X_101))]]) ).
cnf(refute_0_271,plain,
( multiply(identity,X_101) != X_101
| multiply(identity,X_101) != multiply(inverse(X_100),multiply(X_100,X_101))
| X_101 = multiply(inverse(X_100),multiply(X_100,X_101)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_101),multiply(inverse(X_100),multiply(X_100,X_101))) ),[0],$fot(X_101)]]) ).
cnf(refute_0_272,plain,
( multiply(identity,X_101) != multiply(inverse(X_100),multiply(X_100,X_101))
| X_101 = multiply(inverse(X_100),multiply(X_100,X_101)) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_101),X_101) )],[refute_0_270,refute_0_271]) ).
cnf(refute_0_273,plain,
X_101 = multiply(inverse(X_100),multiply(X_100,X_101)),
inference(resolve,[$cnf( $equal(multiply(identity,X_101),multiply(inverse(X_100),multiply(X_100,X_101))) )],[refute_0_269,refute_0_272]) ).
cnf(refute_0_274,plain,
X_105 = multiply(inverse(inverse(X_105)),multiply(inverse(X_105),X_105)),
inference(subst,[],[refute_0_273:[bind(X_100,$fot(inverse(X_105))),bind(X_101,$fot(X_105))]]) ).
cnf(refute_0_275,plain,
multiply(inverse(X_105),X_105) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_105))]]) ).
cnf(refute_0_276,plain,
( X_105 != multiply(inverse(inverse(X_105)),multiply(inverse(X_105),X_105))
| multiply(inverse(X_105),X_105) != identity
| X_105 = multiply(inverse(inverse(X_105)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(X_105,multiply(inverse(inverse(X_105)),multiply(inverse(X_105),X_105))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_277,plain,
( X_105 != multiply(inverse(inverse(X_105)),multiply(inverse(X_105),X_105))
| X_105 = multiply(inverse(inverse(X_105)),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_105),X_105),identity) )],[refute_0_275,refute_0_276]) ).
cnf(refute_0_278,plain,
X_105 = multiply(inverse(inverse(X_105)),identity),
inference(resolve,[$cnf( $equal(X_105,multiply(inverse(inverse(X_105)),multiply(inverse(X_105),X_105))) )],[refute_0_274,refute_0_277]) ).
cnf(refute_0_279,plain,
multiply(X_104,X_105) = multiply(inverse(inverse(X_104)),multiply(inverse(X_104),multiply(X_104,X_105))),
inference(subst,[],[refute_0_273:[bind(X_100,$fot(inverse(X_104))),bind(X_101,$fot(multiply(X_104,X_105)))]]) ).
cnf(refute_0_280,plain,
X_105 = multiply(inverse(X_104),multiply(X_104,X_105)),
inference(subst,[],[refute_0_273:[bind(X_100,$fot(X_104)),bind(X_101,$fot(X_105))]]) ).
cnf(refute_0_281,plain,
( X_105 != multiply(inverse(X_104),multiply(X_104,X_105))
| multiply(inverse(X_104),multiply(X_104,X_105)) = X_105 ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(X_105)),bind(Y0,$fot(multiply(inverse(X_104),multiply(X_104,X_105))))]]) ).
cnf(refute_0_282,plain,
multiply(inverse(X_104),multiply(X_104,X_105)) = X_105,
inference(resolve,[$cnf( $equal(X_105,multiply(inverse(X_104),multiply(X_104,X_105))) )],[refute_0_280,refute_0_281]) ).
cnf(refute_0_283,plain,
( multiply(X_104,X_105) != multiply(inverse(inverse(X_104)),multiply(inverse(X_104),multiply(X_104,X_105)))
| multiply(inverse(X_104),multiply(X_104,X_105)) != X_105
| multiply(X_104,X_105) = multiply(inverse(inverse(X_104)),X_105) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_104,X_105),multiply(inverse(inverse(X_104)),multiply(inverse(X_104),multiply(X_104,X_105)))) ),[1,1],$fot(X_105)]]) ).
cnf(refute_0_284,plain,
( multiply(X_104,X_105) != multiply(inverse(inverse(X_104)),multiply(inverse(X_104),multiply(X_104,X_105)))
| multiply(X_104,X_105) = multiply(inverse(inverse(X_104)),X_105) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_104),multiply(X_104,X_105)),X_105) )],[refute_0_282,refute_0_283]) ).
cnf(refute_0_285,plain,
multiply(X_104,X_105) = multiply(inverse(inverse(X_104)),X_105),
inference(resolve,[$cnf( $equal(multiply(X_104,X_105),multiply(inverse(inverse(X_104)),multiply(inverse(X_104),multiply(X_104,X_105)))) )],[refute_0_279,refute_0_284]) ).
cnf(refute_0_286,plain,
( multiply(X_104,X_105) != multiply(inverse(inverse(X_104)),X_105)
| multiply(inverse(inverse(X_104)),X_105) = multiply(X_104,X_105) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(multiply(X_104,X_105))),bind(Y0,$fot(multiply(inverse(inverse(X_104)),X_105)))]]) ).
cnf(refute_0_287,plain,
multiply(inverse(inverse(X_104)),X_105) = multiply(X_104,X_105),
inference(resolve,[$cnf( $equal(multiply(X_104,X_105),multiply(inverse(inverse(X_104)),X_105)) )],[refute_0_285,refute_0_286]) ).
cnf(refute_0_288,plain,
multiply(inverse(inverse(X_105)),identity) = multiply(X_105,identity),
inference(subst,[],[refute_0_287:[bind(X_104,$fot(X_105)),bind(X_105,$fot(identity))]]) ).
cnf(refute_0_289,plain,
( X_105 != multiply(inverse(inverse(X_105)),identity)
| multiply(inverse(inverse(X_105)),identity) != multiply(X_105,identity)
| X_105 = multiply(X_105,identity) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_105,multiply(X_105,identity)) ),[0],$fot(multiply(inverse(inverse(X_105)),identity))]]) ).
cnf(refute_0_290,plain,
( X_105 != multiply(inverse(inverse(X_105)),identity)
| X_105 = multiply(X_105,identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_105)),identity),multiply(X_105,identity)) )],[refute_0_288,refute_0_289]) ).
cnf(refute_0_291,plain,
X_105 = multiply(X_105,identity),
inference(resolve,[$cnf( $equal(X_105,multiply(inverse(inverse(X_105)),identity)) )],[refute_0_278,refute_0_290]) ).
cnf(refute_0_292,plain,
greatest_lower_bound(identity,inverse(a)) = multiply(greatest_lower_bound(identity,inverse(a)),identity),
inference(subst,[],[refute_0_291:[bind(X_105,$fot(greatest_lower_bound(identity,inverse(a))))]]) ).
cnf(refute_0_293,plain,
( greatest_lower_bound(identity,inverse(a)) != multiply(greatest_lower_bound(identity,inverse(a)),identity)
| multiply(greatest_lower_bound(identity,inverse(a)),identity) = greatest_lower_bound(identity,inverse(a)) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(greatest_lower_bound(identity,inverse(a)))),bind(Y0,$fot(multiply(greatest_lower_bound(identity,inverse(a)),identity)))]]) ).
cnf(refute_0_294,plain,
multiply(greatest_lower_bound(identity,inverse(a)),identity) = greatest_lower_bound(identity,inverse(a)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(a)),multiply(greatest_lower_bound(identity,inverse(a)),identity)) )],[refute_0_292,refute_0_293]) ).
cnf(refute_0_295,plain,
( multiply(greatest_lower_bound(identity,inverse(a)),identity) != greatest_lower_bound(identity,inverse(a))
| multiply(inverse(a),identity) != multiply(greatest_lower_bound(identity,inverse(a)),identity)
| multiply(inverse(a),identity) = greatest_lower_bound(identity,inverse(a)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(a),identity),multiply(greatest_lower_bound(identity,inverse(a)),identity)) ),[1],$fot(greatest_lower_bound(identity,inverse(a)))]]) ).
cnf(refute_0_296,plain,
( multiply(inverse(a),identity) != multiply(greatest_lower_bound(identity,inverse(a)),identity)
| multiply(inverse(a),identity) = greatest_lower_bound(identity,inverse(a)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(a)),identity),greatest_lower_bound(identity,inverse(a))) )],[refute_0_294,refute_0_295]) ).
cnf(refute_0_297,plain,
multiply(inverse(a),identity) = greatest_lower_bound(identity,inverse(a)),
inference(resolve,[$cnf( $equal(multiply(inverse(a),identity),multiply(greatest_lower_bound(identity,inverse(a)),identity)) )],[refute_0_264,refute_0_296]) ).
cnf(refute_0_298,plain,
( X_105 != multiply(X_105,identity)
| multiply(X_105,identity) = X_105 ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(X_105)),bind(Y0,$fot(multiply(X_105,identity)))]]) ).
cnf(refute_0_299,plain,
multiply(X_105,identity) = X_105,
inference(resolve,[$cnf( $equal(X_105,multiply(X_105,identity)) )],[refute_0_291,refute_0_298]) ).
cnf(refute_0_300,plain,
multiply(inverse(a),identity) = inverse(a),
inference(subst,[],[refute_0_299:[bind(X_105,$fot(inverse(a)))]]) ).
cnf(refute_0_301,plain,
( multiply(inverse(a),identity) != greatest_lower_bound(identity,inverse(a))
| multiply(inverse(a),identity) != inverse(a)
| inverse(a) = greatest_lower_bound(identity,inverse(a)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(a),identity),greatest_lower_bound(identity,inverse(a))) ),[0],$fot(inverse(a))]]) ).
cnf(refute_0_302,plain,
( multiply(inverse(a),identity) != greatest_lower_bound(identity,inverse(a))
| inverse(a) = greatest_lower_bound(identity,inverse(a)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(a),identity),inverse(a)) )],[refute_0_300,refute_0_301]) ).
cnf(refute_0_303,plain,
inverse(a) = greatest_lower_bound(identity,inverse(a)),
inference(resolve,[$cnf( $equal(multiply(inverse(a),identity),greatest_lower_bound(identity,inverse(a))) )],[refute_0_297,refute_0_302]) ).
cnf(refute_0_304,plain,
( inverse(a) != greatest_lower_bound(identity,inverse(a))
| greatest_lower_bound(identity,inverse(a)) = inverse(a) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(inverse(a))),bind(Y0,$fot(greatest_lower_bound(identity,inverse(a))))]]) ).
cnf(refute_0_305,plain,
greatest_lower_bound(identity,inverse(a)) = inverse(a),
inference(resolve,[$cnf( $equal(inverse(a),greatest_lower_bound(identity,inverse(a))) )],[refute_0_303,refute_0_304]) ).
cnf(refute_0_306,plain,
( b != least_upper_bound(b,greatest_lower_bound(identity,inverse(a)))
| greatest_lower_bound(identity,inverse(a)) != inverse(a)
| b = least_upper_bound(b,inverse(a)) ),
introduced(tautology,[equality,[$cnf( $equal(b,least_upper_bound(b,greatest_lower_bound(identity,inverse(a)))) ),[1,1],$fot(inverse(a))]]) ).
cnf(refute_0_307,plain,
( b != least_upper_bound(b,greatest_lower_bound(identity,inverse(a)))
| b = least_upper_bound(b,inverse(a)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(a)),inverse(a)) )],[refute_0_305,refute_0_306]) ).
cnf(refute_0_308,plain,
b = least_upper_bound(b,inverse(a)),
inference(resolve,[$cnf( $equal(b,least_upper_bound(b,greatest_lower_bound(identity,inverse(a)))) )],[refute_0_31,refute_0_307]) ).
cnf(refute_0_309,plain,
( b != least_upper_bound(b,inverse(a))
| least_upper_bound(b,inverse(a)) = b ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(b)),bind(Y0,$fot(least_upper_bound(b,inverse(a))))]]) ).
cnf(refute_0_310,plain,
least_upper_bound(b,inverse(a)) = b,
inference(resolve,[$cnf( $equal(b,least_upper_bound(b,inverse(a))) )],[refute_0_308,refute_0_309]) ).
cnf(refute_0_311,plain,
( multiply(inverse(inverse(a)),least_upper_bound(b,inverse(a))) != least_upper_bound(identity,multiply(inverse(inverse(a)),b))
| least_upper_bound(b,inverse(a)) != b
| multiply(inverse(inverse(a)),b) = least_upper_bound(identity,multiply(inverse(inverse(a)),b)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(a)),least_upper_bound(b,inverse(a))),least_upper_bound(identity,multiply(inverse(inverse(a)),b))) ),[0,1],$fot(b)]]) ).
cnf(refute_0_312,plain,
( multiply(inverse(inverse(a)),least_upper_bound(b,inverse(a))) != least_upper_bound(identity,multiply(inverse(inverse(a)),b))
| multiply(inverse(inverse(a)),b) = least_upper_bound(identity,multiply(inverse(inverse(a)),b)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,inverse(a)),b) )],[refute_0_310,refute_0_311]) ).
cnf(refute_0_313,plain,
multiply(inverse(inverse(a)),b) = least_upper_bound(identity,multiply(inverse(inverse(a)),b)),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(a)),least_upper_bound(b,inverse(a))),least_upper_bound(identity,multiply(inverse(inverse(a)),b))) )],[refute_0_14,refute_0_312]) ).
cnf(refute_0_314,plain,
multiply(inverse(inverse(a)),b) = multiply(a,b),
inference(subst,[],[refute_0_287:[bind(X_104,$fot(a)),bind(X_105,$fot(b))]]) ).
cnf(refute_0_315,plain,
( multiply(inverse(inverse(a)),b) != multiply(a,b)
| multiply(inverse(inverse(a)),b) != least_upper_bound(identity,multiply(inverse(inverse(a)),b))
| multiply(a,b) = least_upper_bound(identity,multiply(inverse(inverse(a)),b)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(a)),b),least_upper_bound(identity,multiply(inverse(inverse(a)),b))) ),[0],$fot(multiply(a,b))]]) ).
cnf(refute_0_316,plain,
( multiply(inverse(inverse(a)),b) != least_upper_bound(identity,multiply(inverse(inverse(a)),b))
| multiply(a,b) = least_upper_bound(identity,multiply(inverse(inverse(a)),b)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(a)),b),multiply(a,b)) )],[refute_0_314,refute_0_315]) ).
cnf(refute_0_317,plain,
least_upper_bound(identity,multiply(inverse(inverse(a)),b)) = least_upper_bound(identity,multiply(inverse(inverse(a)),b)),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,multiply(inverse(inverse(a)),b)))]]) ).
cnf(refute_0_318,plain,
( multiply(inverse(inverse(a)),b) != multiply(a,b)
| least_upper_bound(identity,multiply(inverse(inverse(a)),b)) != least_upper_bound(identity,multiply(inverse(inverse(a)),b))
| least_upper_bound(identity,multiply(inverse(inverse(a)),b)) = least_upper_bound(identity,multiply(a,b)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(inverse(a)),b)),least_upper_bound(identity,multiply(inverse(inverse(a)),b))) ),[1,1],$fot(multiply(a,b))]]) ).
cnf(refute_0_319,plain,
( multiply(inverse(inverse(a)),b) != multiply(a,b)
| least_upper_bound(identity,multiply(inverse(inverse(a)),b)) = least_upper_bound(identity,multiply(a,b)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(inverse(a)),b)),least_upper_bound(identity,multiply(inverse(inverse(a)),b))) )],[refute_0_317,refute_0_318]) ).
cnf(refute_0_320,plain,
least_upper_bound(identity,multiply(inverse(inverse(a)),b)) = least_upper_bound(identity,multiply(a,b)),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(a)),b),multiply(a,b)) )],[refute_0_314,refute_0_319]) ).
cnf(refute_0_321,plain,
( multiply(a,b) != least_upper_bound(identity,multiply(inverse(inverse(a)),b))
| least_upper_bound(identity,multiply(inverse(inverse(a)),b)) != least_upper_bound(identity,multiply(a,b))
| multiply(a,b) = least_upper_bound(identity,multiply(a,b)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(a,b),least_upper_bound(identity,multiply(a,b))) ),[0],$fot(least_upper_bound(identity,multiply(inverse(inverse(a)),b)))]]) ).
cnf(refute_0_322,plain,
( multiply(a,b) != least_upper_bound(identity,multiply(inverse(inverse(a)),b))
| multiply(a,b) = least_upper_bound(identity,multiply(a,b)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(inverse(a)),b)),least_upper_bound(identity,multiply(a,b))) )],[refute_0_320,refute_0_321]) ).
cnf(refute_0_323,plain,
( multiply(inverse(inverse(a)),b) != least_upper_bound(identity,multiply(inverse(inverse(a)),b))
| multiply(a,b) = least_upper_bound(identity,multiply(a,b)) ),
inference(resolve,[$cnf( $equal(multiply(a,b),least_upper_bound(identity,multiply(inverse(inverse(a)),b))) )],[refute_0_316,refute_0_322]) ).
cnf(refute_0_324,plain,
multiply(a,b) = least_upper_bound(identity,multiply(a,b)),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(a)),b),least_upper_bound(identity,multiply(inverse(inverse(a)),b))) )],[refute_0_313,refute_0_323]) ).
cnf(refute_0_325,plain,
( multiply(a,b) != least_upper_bound(identity,multiply(a,b))
| least_upper_bound(identity,multiply(a,b)) = multiply(a,b) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(multiply(a,b))),bind(Y0,$fot(least_upper_bound(identity,multiply(a,b))))]]) ).
cnf(refute_0_326,plain,
multiply(a,b) != least_upper_bound(identity,multiply(a,b)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(a,b)),multiply(a,b)) )],[refute_0_325,prove_p04a]) ).
cnf(refute_0_327,plain,
$false,
inference(resolve,[$cnf( $equal(multiply(a,b),least_upper_bound(identity,multiply(a,b))) )],[refute_0_324,refute_0_326]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP171-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n025.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jun 13 22:38:24 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.75/0.91 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.75/0.91
% 0.75/0.91 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.78/0.94
%------------------------------------------------------------------------------