TSTP Solution File: GRP169-1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP169-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n026.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 10:37:14 EDT 2022
% Result : Unsatisfiable 0.55s 0.76s
% Output : CNFRefutation 0.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 47
% Syntax : Number of clauses : 193 ( 108 unt; 0 nHn; 109 RR)
% Number of literals : 313 ( 312 equ; 121 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 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 : 303 ( 5 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(idempotence_of_gld,axiom,
greatest_lower_bound(X,X) = X ).
cnf(lub_absorbtion,axiom,
least_upper_bound(X,greatest_lower_bound(X,Y)) = X ).
cnf(glb_absorbtion,axiom,
greatest_lower_bound(X,least_upper_bound(X,Y)) = X ).
cnf(monotony_glb1,axiom,
multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)) ).
cnf(monotony_glb2,axiom,
multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) ).
cnf(p02a_1,hypothesis,
least_upper_bound(inverse(a),inverse(b)) = inverse(b) ).
cnf(prove_p02a,negated_conjecture,
least_upper_bound(a,b) != a ).
cnf(refute_0_0,plain,
least_upper_bound(a,greatest_lower_bound(a,b)) = a,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(a)),bind(Y,$fot(b))]]) ).
cnf(refute_0_1,plain,
multiply(multiply(inverse(X_44),X_44),X_45) = multiply(inverse(X_44),multiply(X_44,X_45)),
inference(subst,[],[associativity:[bind(X,$fot(inverse(X_44))),bind(Y,$fot(X_44)),bind(Z,$fot(X_45))]]) ).
cnf(refute_0_2,plain,
multiply(inverse(X_44),X_44) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_44))]]) ).
cnf(refute_0_3,plain,
( multiply(multiply(inverse(X_44),X_44),X_45) != multiply(inverse(X_44),multiply(X_44,X_45))
| multiply(inverse(X_44),X_44) != identity
| multiply(identity,X_45) = multiply(inverse(X_44),multiply(X_44,X_45)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_44),X_44),X_45),multiply(inverse(X_44),multiply(X_44,X_45))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_4,plain,
( multiply(multiply(inverse(X_44),X_44),X_45) != multiply(inverse(X_44),multiply(X_44,X_45))
| multiply(identity,X_45) = multiply(inverse(X_44),multiply(X_44,X_45)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_44),X_44),identity) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
multiply(identity,X_45) = multiply(inverse(X_44),multiply(X_44,X_45)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_44),X_44),X_45),multiply(inverse(X_44),multiply(X_44,X_45))) )],[refute_0_1,refute_0_4]) ).
cnf(refute_0_6,plain,
multiply(identity,X_45) = X_45,
inference(subst,[],[left_identity:[bind(X,$fot(X_45))]]) ).
cnf(refute_0_7,plain,
( multiply(identity,X_45) != X_45
| multiply(identity,X_45) != multiply(inverse(X_44),multiply(X_44,X_45))
| X_45 = multiply(inverse(X_44),multiply(X_44,X_45)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_45),multiply(inverse(X_44),multiply(X_44,X_45))) ),[0],$fot(X_45)]]) ).
cnf(refute_0_8,plain,
( multiply(identity,X_45) != multiply(inverse(X_44),multiply(X_44,X_45))
| X_45 = multiply(inverse(X_44),multiply(X_44,X_45)) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_45),X_45) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
X_45 = multiply(inverse(X_44),multiply(X_44,X_45)),
inference(resolve,[$cnf( $equal(multiply(identity,X_45),multiply(inverse(X_44),multiply(X_44,X_45))) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
X_47 = multiply(inverse(inverse(X_47)),multiply(inverse(X_47),X_47)),
inference(subst,[],[refute_0_9:[bind(X_44,$fot(inverse(X_47))),bind(X_45,$fot(X_47))]]) ).
cnf(refute_0_11,plain,
multiply(inverse(X_47),X_47) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_47))]]) ).
cnf(refute_0_12,plain,
( X_47 != multiply(inverse(inverse(X_47)),multiply(inverse(X_47),X_47))
| multiply(inverse(X_47),X_47) != identity
| X_47 = multiply(inverse(inverse(X_47)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(X_47,multiply(inverse(inverse(X_47)),multiply(inverse(X_47),X_47))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_13,plain,
( X_47 != multiply(inverse(inverse(X_47)),multiply(inverse(X_47),X_47))
| X_47 = multiply(inverse(inverse(X_47)),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_47),X_47),identity) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
X_47 = multiply(inverse(inverse(X_47)),identity),
inference(resolve,[$cnf( $equal(X_47,multiply(inverse(inverse(X_47)),multiply(inverse(X_47),X_47))) )],[refute_0_10,refute_0_13]) ).
cnf(refute_0_15,plain,
multiply(X_46,X_47) = multiply(inverse(inverse(X_46)),multiply(inverse(X_46),multiply(X_46,X_47))),
inference(subst,[],[refute_0_9:[bind(X_44,$fot(inverse(X_46))),bind(X_45,$fot(multiply(X_46,X_47)))]]) ).
cnf(refute_0_16,plain,
X_47 = multiply(inverse(X_46),multiply(X_46,X_47)),
inference(subst,[],[refute_0_9:[bind(X_44,$fot(X_46)),bind(X_45,$fot(X_47))]]) ).
cnf(refute_0_17,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_18,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_19,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
( X_47 != multiply(inverse(X_46),multiply(X_46,X_47))
| multiply(inverse(X_46),multiply(X_46,X_47)) = X_47 ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(X_47)),bind(Y0,$fot(multiply(inverse(X_46),multiply(X_46,X_47))))]]) ).
cnf(refute_0_21,plain,
multiply(inverse(X_46),multiply(X_46,X_47)) = X_47,
inference(resolve,[$cnf( $equal(X_47,multiply(inverse(X_46),multiply(X_46,X_47))) )],[refute_0_16,refute_0_20]) ).
cnf(refute_0_22,plain,
( multiply(X_46,X_47) != multiply(inverse(inverse(X_46)),multiply(inverse(X_46),multiply(X_46,X_47)))
| multiply(inverse(X_46),multiply(X_46,X_47)) != X_47
| multiply(X_46,X_47) = multiply(inverse(inverse(X_46)),X_47) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_46,X_47),multiply(inverse(inverse(X_46)),multiply(inverse(X_46),multiply(X_46,X_47)))) ),[1,1],$fot(X_47)]]) ).
cnf(refute_0_23,plain,
( multiply(X_46,X_47) != multiply(inverse(inverse(X_46)),multiply(inverse(X_46),multiply(X_46,X_47)))
| multiply(X_46,X_47) = multiply(inverse(inverse(X_46)),X_47) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_46),multiply(X_46,X_47)),X_47) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
multiply(X_46,X_47) = multiply(inverse(inverse(X_46)),X_47),
inference(resolve,[$cnf( $equal(multiply(X_46,X_47),multiply(inverse(inverse(X_46)),multiply(inverse(X_46),multiply(X_46,X_47)))) )],[refute_0_15,refute_0_23]) ).
cnf(refute_0_25,plain,
( multiply(X_46,X_47) != multiply(inverse(inverse(X_46)),X_47)
| multiply(inverse(inverse(X_46)),X_47) = multiply(X_46,X_47) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(X_46,X_47))),bind(Y0,$fot(multiply(inverse(inverse(X_46)),X_47)))]]) ).
cnf(refute_0_26,plain,
multiply(inverse(inverse(X_46)),X_47) = multiply(X_46,X_47),
inference(resolve,[$cnf( $equal(multiply(X_46,X_47),multiply(inverse(inverse(X_46)),X_47)) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
multiply(inverse(inverse(X_47)),identity) = multiply(X_47,identity),
inference(subst,[],[refute_0_26:[bind(X_46,$fot(X_47)),bind(X_47,$fot(identity))]]) ).
cnf(refute_0_28,plain,
( X_47 != multiply(inverse(inverse(X_47)),identity)
| multiply(inverse(inverse(X_47)),identity) != multiply(X_47,identity)
| X_47 = multiply(X_47,identity) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_47,multiply(X_47,identity)) ),[0],$fot(multiply(inverse(inverse(X_47)),identity))]]) ).
cnf(refute_0_29,plain,
( X_47 != multiply(inverse(inverse(X_47)),identity)
| X_47 = multiply(X_47,identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_47)),identity),multiply(X_47,identity)) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
X_47 = multiply(X_47,identity),
inference(resolve,[$cnf( $equal(X_47,multiply(inverse(inverse(X_47)),identity)) )],[refute_0_14,refute_0_29]) ).
cnf(refute_0_31,plain,
inverse(inverse(X_49)) = multiply(inverse(inverse(X_49)),identity),
inference(subst,[],[refute_0_30:[bind(X_47,$fot(inverse(inverse(X_49))))]]) ).
cnf(refute_0_32,plain,
multiply(X_49,identity) = multiply(inverse(inverse(X_49)),identity),
inference(subst,[],[refute_0_24:[bind(X_46,$fot(X_49)),bind(X_47,$fot(identity))]]) ).
cnf(refute_0_33,plain,
( multiply(X_49,identity) != multiply(inverse(inverse(X_49)),identity)
| multiply(inverse(inverse(X_49)),identity) = multiply(X_49,identity) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(X_49,identity))),bind(Y0,$fot(multiply(inverse(inverse(X_49)),identity)))]]) ).
cnf(refute_0_34,plain,
multiply(inverse(inverse(X_49)),identity) = multiply(X_49,identity),
inference(resolve,[$cnf( $equal(multiply(X_49,identity),multiply(inverse(inverse(X_49)),identity)) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
( multiply(inverse(inverse(X_49)),identity) != multiply(X_49,identity)
| inverse(inverse(X_49)) != multiply(inverse(inverse(X_49)),identity)
| inverse(inverse(X_49)) = multiply(X_49,identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_49)),multiply(inverse(inverse(X_49)),identity)) ),[1],$fot(multiply(X_49,identity))]]) ).
cnf(refute_0_36,plain,
( inverse(inverse(X_49)) != multiply(inverse(inverse(X_49)),identity)
| inverse(inverse(X_49)) = multiply(X_49,identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_49)),identity),multiply(X_49,identity)) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
inverse(inverse(X_49)) = multiply(X_49,identity),
inference(resolve,[$cnf( $equal(inverse(inverse(X_49)),multiply(inverse(inverse(X_49)),identity)) )],[refute_0_31,refute_0_36]) ).
cnf(refute_0_38,plain,
( X_47 != multiply(X_47,identity)
| multiply(X_47,identity) = X_47 ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(X_47)),bind(Y0,$fot(multiply(X_47,identity)))]]) ).
cnf(refute_0_39,plain,
multiply(X_47,identity) = X_47,
inference(resolve,[$cnf( $equal(X_47,multiply(X_47,identity)) )],[refute_0_30,refute_0_38]) ).
cnf(refute_0_40,plain,
multiply(X_49,identity) = X_49,
inference(subst,[],[refute_0_39:[bind(X_47,$fot(X_49))]]) ).
cnf(refute_0_41,plain,
( multiply(X_49,identity) != X_49
| inverse(inverse(X_49)) != multiply(X_49,identity)
| inverse(inverse(X_49)) = X_49 ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_49)),multiply(X_49,identity)) ),[1],$fot(X_49)]]) ).
cnf(refute_0_42,plain,
( inverse(inverse(X_49)) != multiply(X_49,identity)
| inverse(inverse(X_49)) = X_49 ),
inference(resolve,[$cnf( $equal(multiply(X_49,identity),X_49) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
inverse(inverse(X_49)) = X_49,
inference(resolve,[$cnf( $equal(inverse(inverse(X_49)),multiply(X_49,identity)) )],[refute_0_37,refute_0_42]) ).
cnf(refute_0_44,plain,
inverse(inverse(greatest_lower_bound(a,b))) = greatest_lower_bound(a,b),
inference(subst,[],[refute_0_43:[bind(X_49,$fot(greatest_lower_bound(a,b)))]]) ).
cnf(refute_0_45,plain,
inverse(b) = multiply(inverse(greatest_lower_bound(a,b)),multiply(greatest_lower_bound(a,b),inverse(b))),
inference(subst,[],[refute_0_9:[bind(X_44,$fot(greatest_lower_bound(a,b))),bind(X_45,$fot(inverse(b)))]]) ).
cnf(refute_0_46,plain,
multiply(X_67,greatest_lower_bound(inverse(X_67),X_69)) = greatest_lower_bound(multiply(X_67,inverse(X_67)),multiply(X_67,X_69)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(X_67)),bind(Y,$fot(inverse(X_67))),bind(Z,$fot(X_69))]]) ).
cnf(refute_0_47,plain,
multiply(inverse(inverse(X_49)),inverse(X_49)) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(inverse(X_49)))]]) ).
cnf(refute_0_48,plain,
multiply(X_49,inverse(X_49)) = multiply(inverse(inverse(X_49)),inverse(X_49)),
inference(subst,[],[refute_0_24:[bind(X_46,$fot(X_49)),bind(X_47,$fot(inverse(X_49)))]]) ).
cnf(refute_0_49,plain,
( multiply(X_49,inverse(X_49)) != multiply(inverse(inverse(X_49)),inverse(X_49))
| multiply(inverse(inverse(X_49)),inverse(X_49)) = multiply(X_49,inverse(X_49)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(X_49,inverse(X_49)))),bind(Y0,$fot(multiply(inverse(inverse(X_49)),inverse(X_49))))]]) ).
cnf(refute_0_50,plain,
multiply(inverse(inverse(X_49)),inverse(X_49)) = multiply(X_49,inverse(X_49)),
inference(resolve,[$cnf( $equal(multiply(X_49,inverse(X_49)),multiply(inverse(inverse(X_49)),inverse(X_49))) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
( multiply(inverse(inverse(X_49)),inverse(X_49)) != multiply(X_49,inverse(X_49))
| multiply(inverse(inverse(X_49)),inverse(X_49)) != identity
| multiply(X_49,inverse(X_49)) = identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X_49)),inverse(X_49)),identity) ),[0],$fot(multiply(X_49,inverse(X_49)))]]) ).
cnf(refute_0_52,plain,
( multiply(inverse(inverse(X_49)),inverse(X_49)) != identity
| multiply(X_49,inverse(X_49)) = identity ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_49)),inverse(X_49)),multiply(X_49,inverse(X_49))) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
multiply(X_49,inverse(X_49)) = identity,
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_49)),inverse(X_49)),identity) )],[refute_0_47,refute_0_52]) ).
cnf(refute_0_54,plain,
multiply(X_67,inverse(X_67)) = identity,
inference(subst,[],[refute_0_53:[bind(X_49,$fot(X_67))]]) ).
cnf(refute_0_55,plain,
( multiply(X_67,greatest_lower_bound(inverse(X_67),X_69)) != greatest_lower_bound(multiply(X_67,inverse(X_67)),multiply(X_67,X_69))
| multiply(X_67,inverse(X_67)) != identity
| multiply(X_67,greatest_lower_bound(inverse(X_67),X_69)) = greatest_lower_bound(identity,multiply(X_67,X_69)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_67,greatest_lower_bound(inverse(X_67),X_69)),greatest_lower_bound(multiply(X_67,inverse(X_67)),multiply(X_67,X_69))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_56,plain,
( multiply(X_67,greatest_lower_bound(inverse(X_67),X_69)) != greatest_lower_bound(multiply(X_67,inverse(X_67)),multiply(X_67,X_69))
| multiply(X_67,greatest_lower_bound(inverse(X_67),X_69)) = greatest_lower_bound(identity,multiply(X_67,X_69)) ),
inference(resolve,[$cnf( $equal(multiply(X_67,inverse(X_67)),identity) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
multiply(X_67,greatest_lower_bound(inverse(X_67),X_69)) = greatest_lower_bound(identity,multiply(X_67,X_69)),
inference(resolve,[$cnf( $equal(multiply(X_67,greatest_lower_bound(inverse(X_67),X_69)),greatest_lower_bound(multiply(X_67,inverse(X_67)),multiply(X_67,X_69))) )],[refute_0_46,refute_0_56]) ).
cnf(refute_0_58,plain,
multiply(a,greatest_lower_bound(inverse(a),inverse(b))) = greatest_lower_bound(identity,multiply(a,inverse(b))),
inference(subst,[],[refute_0_57:[bind(X_67,$fot(a)),bind(X_69,$fot(inverse(b)))]]) ).
cnf(refute_0_59,plain,
greatest_lower_bound(inverse(a),least_upper_bound(inverse(a),inverse(b))) = inverse(a),
inference(subst,[],[glb_absorbtion:[bind(X,$fot(inverse(a))),bind(Y,$fot(inverse(b)))]]) ).
cnf(refute_0_60,plain,
( greatest_lower_bound(inverse(a),least_upper_bound(inverse(a),inverse(b))) != inverse(a)
| least_upper_bound(inverse(a),inverse(b)) != inverse(b)
| greatest_lower_bound(inverse(a),inverse(b)) = inverse(a) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(inverse(a),least_upper_bound(inverse(a),inverse(b))),inverse(a)) ),[0,1],$fot(inverse(b))]]) ).
cnf(refute_0_61,plain,
( greatest_lower_bound(inverse(a),least_upper_bound(inverse(a),inverse(b))) != inverse(a)
| greatest_lower_bound(inverse(a),inverse(b)) = inverse(a) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(a),inverse(b)),inverse(b)) )],[p02a_1,refute_0_60]) ).
cnf(refute_0_62,plain,
greatest_lower_bound(inverse(a),inverse(b)) = inverse(a),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(a),least_upper_bound(inverse(a),inverse(b))),inverse(a)) )],[refute_0_59,refute_0_61]) ).
cnf(refute_0_63,plain,
( multiply(a,greatest_lower_bound(inverse(a),inverse(b))) != greatest_lower_bound(identity,multiply(a,inverse(b)))
| greatest_lower_bound(inverse(a),inverse(b)) != inverse(a)
| multiply(a,inverse(a)) = greatest_lower_bound(identity,multiply(a,inverse(b))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(a,greatest_lower_bound(inverse(a),inverse(b))),greatest_lower_bound(identity,multiply(a,inverse(b)))) ),[0,1],$fot(inverse(a))]]) ).
cnf(refute_0_64,plain,
( multiply(a,greatest_lower_bound(inverse(a),inverse(b))) != greatest_lower_bound(identity,multiply(a,inverse(b)))
| multiply(a,inverse(a)) = greatest_lower_bound(identity,multiply(a,inverse(b))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(a),inverse(b)),inverse(a)) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
multiply(a,inverse(a)) = greatest_lower_bound(identity,multiply(a,inverse(b))),
inference(resolve,[$cnf( $equal(multiply(a,greatest_lower_bound(inverse(a),inverse(b))),greatest_lower_bound(identity,multiply(a,inverse(b)))) )],[refute_0_58,refute_0_64]) ).
cnf(refute_0_66,plain,
multiply(a,inverse(a)) = identity,
inference(subst,[],[refute_0_53:[bind(X_49,$fot(a))]]) ).
cnf(refute_0_67,plain,
( multiply(a,inverse(a)) != greatest_lower_bound(identity,multiply(a,inverse(b)))
| multiply(a,inverse(a)) != identity
| identity = greatest_lower_bound(identity,multiply(a,inverse(b))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(a,inverse(a)),greatest_lower_bound(identity,multiply(a,inverse(b)))) ),[0],$fot(identity)]]) ).
cnf(refute_0_68,plain,
( multiply(a,inverse(a)) != greatest_lower_bound(identity,multiply(a,inverse(b)))
| identity = greatest_lower_bound(identity,multiply(a,inverse(b))) ),
inference(resolve,[$cnf( $equal(multiply(a,inverse(a)),identity) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
identity = greatest_lower_bound(identity,multiply(a,inverse(b))),
inference(resolve,[$cnf( $equal(multiply(a,inverse(a)),greatest_lower_bound(identity,multiply(a,inverse(b)))) )],[refute_0_65,refute_0_68]) ).
cnf(refute_0_70,plain,
greatest_lower_bound(X_10,least_upper_bound(X_10,X_11)) = X_10,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_10)),bind(Y,$fot(X_11))]]) ).
cnf(refute_0_71,plain,
least_upper_bound(X_11,X_10) = least_upper_bound(X_10,X_11),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_11)),bind(Y,$fot(X_10))]]) ).
cnf(refute_0_72,plain,
( least_upper_bound(X_11,X_10) != least_upper_bound(X_10,X_11)
| least_upper_bound(X_10,X_11) = least_upper_bound(X_11,X_10) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(least_upper_bound(X_11,X_10))),bind(Y0,$fot(least_upper_bound(X_10,X_11)))]]) ).
cnf(refute_0_73,plain,
least_upper_bound(X_10,X_11) = least_upper_bound(X_11,X_10),
inference(resolve,[$cnf( $equal(least_upper_bound(X_11,X_10),least_upper_bound(X_10,X_11)) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
( greatest_lower_bound(X_10,least_upper_bound(X_10,X_11)) != X_10
| least_upper_bound(X_10,X_11) != least_upper_bound(X_11,X_10)
| greatest_lower_bound(X_10,least_upper_bound(X_11,X_10)) = X_10 ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_10,least_upper_bound(X_10,X_11)),X_10) ),[0,1],$fot(least_upper_bound(X_11,X_10))]]) ).
cnf(refute_0_75,plain,
( greatest_lower_bound(X_10,least_upper_bound(X_10,X_11)) != X_10
| greatest_lower_bound(X_10,least_upper_bound(X_11,X_10)) = X_10 ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_10,X_11),least_upper_bound(X_11,X_10)) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
greatest_lower_bound(X_10,least_upper_bound(X_11,X_10)) = X_10,
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_10,least_upper_bound(X_10,X_11)),X_10) )],[refute_0_70,refute_0_75]) ).
cnf(refute_0_77,plain,
greatest_lower_bound(greatest_lower_bound(X_19,Y),least_upper_bound(X_19,greatest_lower_bound(X_19,Y))) = greatest_lower_bound(X_19,Y),
inference(subst,[],[refute_0_76:[bind(X_10,$fot(greatest_lower_bound(X_19,Y))),bind(X_11,$fot(X_19))]]) ).
cnf(refute_0_78,plain,
least_upper_bound(X_19,greatest_lower_bound(X_19,Y)) = X_19,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_19))]]) ).
cnf(refute_0_79,plain,
( greatest_lower_bound(greatest_lower_bound(X_19,Y),least_upper_bound(X_19,greatest_lower_bound(X_19,Y))) != greatest_lower_bound(X_19,Y)
| least_upper_bound(X_19,greatest_lower_bound(X_19,Y)) != X_19
| greatest_lower_bound(greatest_lower_bound(X_19,Y),X_19) = greatest_lower_bound(X_19,Y) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_19,Y),least_upper_bound(X_19,greatest_lower_bound(X_19,Y))),greatest_lower_bound(X_19,Y)) ),[0,1],$fot(X_19)]]) ).
cnf(refute_0_80,plain,
( greatest_lower_bound(greatest_lower_bound(X_19,Y),least_upper_bound(X_19,greatest_lower_bound(X_19,Y))) != greatest_lower_bound(X_19,Y)
| greatest_lower_bound(greatest_lower_bound(X_19,Y),X_19) = greatest_lower_bound(X_19,Y) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,greatest_lower_bound(X_19,Y)),X_19) )],[refute_0_78,refute_0_79]) ).
cnf(refute_0_81,plain,
greatest_lower_bound(greatest_lower_bound(X_19,Y),X_19) = greatest_lower_bound(X_19,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_19,Y),least_upper_bound(X_19,greatest_lower_bound(X_19,Y))),greatest_lower_bound(X_19,Y)) )],[refute_0_77,refute_0_80]) ).
cnf(refute_0_82,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,Z)) != greatest_lower_bound(greatest_lower_bound(X,Y),Z)
| greatest_lower_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(Y,Z)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X,Y),Z)))]]) ).
cnf(refute_0_83,plain,
greatest_lower_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(greatest_lower_bound(X,Y),Z)) )],[associativity_of_glb,refute_0_82]) ).
cnf(refute_0_84,plain,
greatest_lower_bound(greatest_lower_bound(X_19,Y),X_19) = greatest_lower_bound(X_19,greatest_lower_bound(Y,X_19)),
inference(subst,[],[refute_0_83:[bind(X,$fot(X_19)),bind(Z,$fot(X_19))]]) ).
cnf(refute_0_85,plain,
( greatest_lower_bound(greatest_lower_bound(X_19,Y),X_19) != greatest_lower_bound(X_19,Y)
| greatest_lower_bound(greatest_lower_bound(X_19,Y),X_19) != greatest_lower_bound(X_19,greatest_lower_bound(Y,X_19))
| greatest_lower_bound(X_19,greatest_lower_bound(Y,X_19)) = greatest_lower_bound(X_19,Y) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_19,Y),X_19),greatest_lower_bound(X_19,Y)) ),[0],$fot(greatest_lower_bound(X_19,greatest_lower_bound(Y,X_19)))]]) ).
cnf(refute_0_86,plain,
( greatest_lower_bound(greatest_lower_bound(X_19,Y),X_19) != greatest_lower_bound(X_19,Y)
| greatest_lower_bound(X_19,greatest_lower_bound(Y,X_19)) = greatest_lower_bound(X_19,Y) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_19,Y),X_19),greatest_lower_bound(X_19,greatest_lower_bound(Y,X_19))) )],[refute_0_84,refute_0_85]) ).
cnf(refute_0_87,plain,
greatest_lower_bound(X_19,greatest_lower_bound(Y,X_19)) = greatest_lower_bound(X_19,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_19,Y),X_19),greatest_lower_bound(X_19,Y)) )],[refute_0_81,refute_0_86]) ).
cnf(refute_0_88,plain,
greatest_lower_bound(X_21,greatest_lower_bound(X_20,X_21)) = greatest_lower_bound(X_21,X_20),
inference(subst,[],[refute_0_87:[bind(Y,$fot(X_20)),bind(X_19,$fot(X_21))]]) ).
cnf(refute_0_89,plain,
greatest_lower_bound(X_21,X_20) = greatest_lower_bound(X_20,X_21),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_21)),bind(Y,$fot(X_20))]]) ).
cnf(refute_0_90,plain,
( greatest_lower_bound(X_21,X_20) != greatest_lower_bound(X_20,X_21)
| greatest_lower_bound(X_20,X_21) = greatest_lower_bound(X_21,X_20) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(greatest_lower_bound(X_21,X_20))),bind(Y0,$fot(greatest_lower_bound(X_20,X_21)))]]) ).
cnf(refute_0_91,plain,
greatest_lower_bound(X_20,X_21) = greatest_lower_bound(X_21,X_20),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_21,X_20),greatest_lower_bound(X_20,X_21)) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
( greatest_lower_bound(X_20,X_21) != greatest_lower_bound(X_21,X_20)
| greatest_lower_bound(X_21,greatest_lower_bound(X_20,X_21)) != greatest_lower_bound(X_21,X_20)
| greatest_lower_bound(X_21,greatest_lower_bound(X_21,X_20)) = greatest_lower_bound(X_21,X_20) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_21,greatest_lower_bound(X_20,X_21)),greatest_lower_bound(X_21,X_20)) ),[0,1],$fot(greatest_lower_bound(X_21,X_20))]]) ).
cnf(refute_0_93,plain,
( greatest_lower_bound(X_21,greatest_lower_bound(X_20,X_21)) != greatest_lower_bound(X_21,X_20)
| greatest_lower_bound(X_21,greatest_lower_bound(X_21,X_20)) = greatest_lower_bound(X_21,X_20) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_20,X_21),greatest_lower_bound(X_21,X_20)) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
greatest_lower_bound(X_21,greatest_lower_bound(X_21,X_20)) = greatest_lower_bound(X_21,X_20),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_21,greatest_lower_bound(X_20,X_21)),greatest_lower_bound(X_21,X_20)) )],[refute_0_88,refute_0_93]) ).
cnf(refute_0_95,plain,
greatest_lower_bound(multiply(X_85,X_84),greatest_lower_bound(multiply(X_85,X_84),multiply(X_86,X_84))) = greatest_lower_bound(multiply(X_85,X_84),multiply(X_86,X_84)),
inference(subst,[],[refute_0_94:[bind(X_20,$fot(multiply(X_86,X_84))),bind(X_21,$fot(multiply(X_85,X_84)))]]) ).
cnf(refute_0_96,plain,
multiply(greatest_lower_bound(X_85,X_86),X_84) = greatest_lower_bound(multiply(X_85,X_84),multiply(X_86,X_84)),
inference(subst,[],[monotony_glb2:[bind(X,$fot(X_84)),bind(Y,$fot(X_85)),bind(Z,$fot(X_86))]]) ).
cnf(refute_0_97,plain,
( multiply(greatest_lower_bound(X_85,X_86),X_84) != greatest_lower_bound(multiply(X_85,X_84),multiply(X_86,X_84))
| greatest_lower_bound(multiply(X_85,X_84),multiply(X_86,X_84)) = multiply(greatest_lower_bound(X_85,X_86),X_84) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(greatest_lower_bound(X_85,X_86),X_84))),bind(Y0,$fot(greatest_lower_bound(multiply(X_85,X_84),multiply(X_86,X_84))))]]) ).
cnf(refute_0_98,plain,
greatest_lower_bound(multiply(X_85,X_84),multiply(X_86,X_84)) = multiply(greatest_lower_bound(X_85,X_86),X_84),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_85,X_86),X_84),greatest_lower_bound(multiply(X_85,X_84),multiply(X_86,X_84))) )],[refute_0_96,refute_0_97]) ).
cnf(refute_0_99,plain,
( greatest_lower_bound(multiply(X_85,X_84),multiply(X_86,X_84)) != multiply(greatest_lower_bound(X_85,X_86),X_84)
| greatest_lower_bound(multiply(X_85,X_84),greatest_lower_bound(multiply(X_85,X_84),multiply(X_86,X_84))) != greatest_lower_bound(multiply(X_85,X_84),multiply(X_86,X_84))
| greatest_lower_bound(multiply(X_85,X_84),greatest_lower_bound(multiply(X_85,X_84),multiply(X_86,X_84))) = multiply(greatest_lower_bound(X_85,X_86),X_84) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_85,X_84),greatest_lower_bound(multiply(X_85,X_84),multiply(X_86,X_84))),greatest_lower_bound(multiply(X_85,X_84),multiply(X_86,X_84))) ),[1],$fot(multiply(greatest_lower_bound(X_85,X_86),X_84))]]) ).
cnf(refute_0_100,plain,
( greatest_lower_bound(multiply(X_85,X_84),greatest_lower_bound(multiply(X_85,X_84),multiply(X_86,X_84))) != greatest_lower_bound(multiply(X_85,X_84),multiply(X_86,X_84))
| greatest_lower_bound(multiply(X_85,X_84),greatest_lower_bound(multiply(X_85,X_84),multiply(X_86,X_84))) = multiply(greatest_lower_bound(X_85,X_86),X_84) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_85,X_84),multiply(X_86,X_84)),multiply(greatest_lower_bound(X_85,X_86),X_84)) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
greatest_lower_bound(multiply(X_85,X_84),greatest_lower_bound(multiply(X_85,X_84),multiply(X_86,X_84))) = multiply(greatest_lower_bound(X_85,X_86),X_84),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_85,X_84),greatest_lower_bound(multiply(X_85,X_84),multiply(X_86,X_84))),greatest_lower_bound(multiply(X_85,X_84),multiply(X_86,X_84))) )],[refute_0_95,refute_0_100]) ).
cnf(refute_0_102,plain,
greatest_lower_bound(X_85,X_85) = X_85,
inference(subst,[],[idempotence_of_gld:[bind(X,$fot(X_85))]]) ).
cnf(refute_0_103,plain,
greatest_lower_bound(X_86,greatest_lower_bound(X_85,X_85)) = greatest_lower_bound(X_86,greatest_lower_bound(X_85,X_85)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X_86,greatest_lower_bound(X_85,X_85)))]]) ).
cnf(refute_0_104,plain,
( greatest_lower_bound(X_85,X_85) != X_85
| greatest_lower_bound(X_86,greatest_lower_bound(X_85,X_85)) != greatest_lower_bound(X_86,greatest_lower_bound(X_85,X_85))
| greatest_lower_bound(X_86,greatest_lower_bound(X_85,X_85)) = greatest_lower_bound(X_86,X_85) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_86,greatest_lower_bound(X_85,X_85)),greatest_lower_bound(X_86,greatest_lower_bound(X_85,X_85))) ),[1,1],$fot(X_85)]]) ).
cnf(refute_0_105,plain,
( greatest_lower_bound(X_85,X_85) != X_85
| greatest_lower_bound(X_86,greatest_lower_bound(X_85,X_85)) = greatest_lower_bound(X_86,X_85) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_86,greatest_lower_bound(X_85,X_85)),greatest_lower_bound(X_86,greatest_lower_bound(X_85,X_85))) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
greatest_lower_bound(X_86,greatest_lower_bound(X_85,X_85)) = greatest_lower_bound(X_86,X_85),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_85,X_85),X_85) )],[refute_0_102,refute_0_105]) ).
cnf(refute_0_107,plain,
multiply(greatest_lower_bound(X_86,greatest_lower_bound(X_85,X_85)),X_84) = multiply(greatest_lower_bound(X_86,greatest_lower_bound(X_85,X_85)),X_84),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(X_86,greatest_lower_bound(X_85,X_85)),X_84))]]) ).
cnf(refute_0_108,plain,
( multiply(greatest_lower_bound(X_86,greatest_lower_bound(X_85,X_85)),X_84) != multiply(greatest_lower_bound(X_86,greatest_lower_bound(X_85,X_85)),X_84)
| greatest_lower_bound(X_86,greatest_lower_bound(X_85,X_85)) != greatest_lower_bound(X_86,X_85)
| multiply(greatest_lower_bound(X_86,greatest_lower_bound(X_85,X_85)),X_84) = multiply(greatest_lower_bound(X_86,X_85),X_84) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_86,greatest_lower_bound(X_85,X_85)),X_84),multiply(greatest_lower_bound(X_86,greatest_lower_bound(X_85,X_85)),X_84)) ),[1,0],$fot(greatest_lower_bound(X_86,X_85))]]) ).
cnf(refute_0_109,plain,
( greatest_lower_bound(X_86,greatest_lower_bound(X_85,X_85)) != greatest_lower_bound(X_86,X_85)
| multiply(greatest_lower_bound(X_86,greatest_lower_bound(X_85,X_85)),X_84) = multiply(greatest_lower_bound(X_86,X_85),X_84) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_86,greatest_lower_bound(X_85,X_85)),X_84),multiply(greatest_lower_bound(X_86,greatest_lower_bound(X_85,X_85)),X_84)) )],[refute_0_107,refute_0_108]) ).
cnf(refute_0_110,plain,
multiply(greatest_lower_bound(X_86,greatest_lower_bound(X_85,X_85)),X_84) = multiply(greatest_lower_bound(X_86,X_85),X_84),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_86,greatest_lower_bound(X_85,X_85)),greatest_lower_bound(X_86,X_85)) )],[refute_0_106,refute_0_109]) ).
cnf(refute_0_111,plain,
( multiply(greatest_lower_bound(Y,Z),X) != greatest_lower_bound(multiply(Y,X),multiply(Z,X))
| greatest_lower_bound(multiply(Y,X),multiply(Z,X)) = multiply(greatest_lower_bound(Y,Z),X) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(greatest_lower_bound(Y,Z),X))),bind(Y0,$fot(greatest_lower_bound(multiply(Y,X),multiply(Z,X))))]]) ).
cnf(refute_0_112,plain,
greatest_lower_bound(multiply(Y,X),multiply(Z,X)) = multiply(greatest_lower_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Y,X),multiply(Z,X))) )],[monotony_glb2,refute_0_111]) ).
cnf(refute_0_113,plain,
greatest_lower_bound(multiply(X_86,X_84),multiply(greatest_lower_bound(X_85,X_85),X_84)) = multiply(greatest_lower_bound(X_86,greatest_lower_bound(X_85,X_85)),X_84),
inference(subst,[],[refute_0_112:[bind(X,$fot(X_84)),bind(Y,$fot(X_86)),bind(Z,$fot(greatest_lower_bound(X_85,X_85)))]]) ).
cnf(refute_0_114,plain,
greatest_lower_bound(X,greatest_lower_bound(X_24,X_25)) = greatest_lower_bound(greatest_lower_bound(X_24,X_25),X),
inference(subst,[],[symmetry_of_glb:[bind(Y,$fot(greatest_lower_bound(X_24,X_25)))]]) ).
cnf(refute_0_115,plain,
greatest_lower_bound(X_24,greatest_lower_bound(X_25,X)) = greatest_lower_bound(greatest_lower_bound(X_24,X_25),X),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_24)),bind(Y,$fot(X_25)),bind(Z,$fot(X))]]) ).
cnf(refute_0_116,plain,
( greatest_lower_bound(X_24,greatest_lower_bound(X_25,X)) != greatest_lower_bound(greatest_lower_bound(X_24,X_25),X)
| greatest_lower_bound(greatest_lower_bound(X_24,X_25),X) = greatest_lower_bound(X_24,greatest_lower_bound(X_25,X)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(greatest_lower_bound(X_24,greatest_lower_bound(X_25,X)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X_24,X_25),X)))]]) ).
cnf(refute_0_117,plain,
greatest_lower_bound(greatest_lower_bound(X_24,X_25),X) = greatest_lower_bound(X_24,greatest_lower_bound(X_25,X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_24,greatest_lower_bound(X_25,X)),greatest_lower_bound(greatest_lower_bound(X_24,X_25),X)) )],[refute_0_115,refute_0_116]) ).
cnf(refute_0_118,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_24,X_25)) != greatest_lower_bound(greatest_lower_bound(X_24,X_25),X)
| greatest_lower_bound(greatest_lower_bound(X_24,X_25),X) != greatest_lower_bound(X_24,greatest_lower_bound(X_25,X))
| greatest_lower_bound(X,greatest_lower_bound(X_24,X_25)) = greatest_lower_bound(X_24,greatest_lower_bound(X_25,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X,greatest_lower_bound(X_24,X_25)),greatest_lower_bound(X_24,greatest_lower_bound(X_25,X))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_24,X_25),X))]]) ).
cnf(refute_0_119,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_24,X_25)) != greatest_lower_bound(greatest_lower_bound(X_24,X_25),X)
| greatest_lower_bound(X,greatest_lower_bound(X_24,X_25)) = greatest_lower_bound(X_24,greatest_lower_bound(X_25,X)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_24,X_25),X),greatest_lower_bound(X_24,greatest_lower_bound(X_25,X))) )],[refute_0_117,refute_0_118]) ).
cnf(refute_0_120,plain,
greatest_lower_bound(X,greatest_lower_bound(X_24,X_25)) = greatest_lower_bound(X_24,greatest_lower_bound(X_25,X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_24,X_25)),greatest_lower_bound(greatest_lower_bound(X_24,X_25),X)) )],[refute_0_114,refute_0_119]) ).
cnf(refute_0_121,plain,
greatest_lower_bound(X,greatest_lower_bound(multiply(X_85,X_84),multiply(X_86,X_84))) = greatest_lower_bound(multiply(X_85,X_84),greatest_lower_bound(multiply(X_86,X_84),X)),
inference(subst,[],[refute_0_120:[bind(X_24,$fot(multiply(X_85,X_84))),bind(X_25,$fot(multiply(X_86,X_84)))]]) ).
cnf(refute_0_122,plain,
( greatest_lower_bound(X,greatest_lower_bound(multiply(X_85,X_84),multiply(X_86,X_84))) != greatest_lower_bound(multiply(X_85,X_84),greatest_lower_bound(multiply(X_86,X_84),X))
| greatest_lower_bound(multiply(X_85,X_84),multiply(X_86,X_84)) != multiply(greatest_lower_bound(X_85,X_86),X_84)
| greatest_lower_bound(X,multiply(greatest_lower_bound(X_85,X_86),X_84)) = greatest_lower_bound(multiply(X_85,X_84),greatest_lower_bound(multiply(X_86,X_84),X)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(multiply(X_85,X_84),multiply(X_86,X_84))),greatest_lower_bound(multiply(X_85,X_84),greatest_lower_bound(multiply(X_86,X_84),X))) ),[0,1],$fot(multiply(greatest_lower_bound(X_85,X_86),X_84))]]) ).
cnf(refute_0_123,plain,
( greatest_lower_bound(X,greatest_lower_bound(multiply(X_85,X_84),multiply(X_86,X_84))) != greatest_lower_bound(multiply(X_85,X_84),greatest_lower_bound(multiply(X_86,X_84),X))
| greatest_lower_bound(X,multiply(greatest_lower_bound(X_85,X_86),X_84)) = greatest_lower_bound(multiply(X_85,X_84),greatest_lower_bound(multiply(X_86,X_84),X)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_85,X_84),multiply(X_86,X_84)),multiply(greatest_lower_bound(X_85,X_86),X_84)) )],[refute_0_98,refute_0_122]) ).
cnf(refute_0_124,plain,
greatest_lower_bound(X,multiply(greatest_lower_bound(X_85,X_86),X_84)) = greatest_lower_bound(multiply(X_85,X_84),greatest_lower_bound(multiply(X_86,X_84),X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(multiply(X_85,X_84),multiply(X_86,X_84))),greatest_lower_bound(multiply(X_85,X_84),greatest_lower_bound(multiply(X_86,X_84),X))) )],[refute_0_121,refute_0_123]) ).
cnf(refute_0_125,plain,
( greatest_lower_bound(X,multiply(greatest_lower_bound(X_85,X_86),X_84)) != greatest_lower_bound(multiply(X_85,X_84),greatest_lower_bound(multiply(X_86,X_84),X))
| greatest_lower_bound(multiply(X_85,X_84),greatest_lower_bound(multiply(X_86,X_84),X)) = greatest_lower_bound(X,multiply(greatest_lower_bound(X_85,X_86),X_84)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(greatest_lower_bound(X,multiply(greatest_lower_bound(X_85,X_86),X_84)))),bind(Y0,$fot(greatest_lower_bound(multiply(X_85,X_84),greatest_lower_bound(multiply(X_86,X_84),X))))]]) ).
cnf(refute_0_126,plain,
greatest_lower_bound(multiply(X_85,X_84),greatest_lower_bound(multiply(X_86,X_84),X)) = greatest_lower_bound(X,multiply(greatest_lower_bound(X_85,X_86),X_84)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,multiply(greatest_lower_bound(X_85,X_86),X_84)),greatest_lower_bound(multiply(X_85,X_84),greatest_lower_bound(multiply(X_86,X_84),X))) )],[refute_0_124,refute_0_125]) ).
cnf(refute_0_127,plain,
greatest_lower_bound(multiply(X_85,X_84),greatest_lower_bound(multiply(X_85,X_84),multiply(X_86,X_84))) = greatest_lower_bound(multiply(X_86,X_84),multiply(greatest_lower_bound(X_85,X_85),X_84)),
inference(subst,[],[refute_0_126:[bind(X,$fot(multiply(X_86,X_84))),bind(X_86,$fot(X_85))]]) ).
cnf(refute_0_128,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_129,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_19,refute_0_128]) ).
cnf(refute_0_130,plain,
( greatest_lower_bound(multiply(X_85,X_84),greatest_lower_bound(multiply(X_85,X_84),multiply(X_86,X_84))) != greatest_lower_bound(multiply(X_86,X_84),multiply(greatest_lower_bound(X_85,X_85),X_84))
| greatest_lower_bound(multiply(X_86,X_84),multiply(greatest_lower_bound(X_85,X_85),X_84)) != multiply(greatest_lower_bound(X_86,greatest_lower_bound(X_85,X_85)),X_84)
| greatest_lower_bound(multiply(X_85,X_84),greatest_lower_bound(multiply(X_85,X_84),multiply(X_86,X_84))) = multiply(greatest_lower_bound(X_86,greatest_lower_bound(X_85,X_85)),X_84) ),
inference(subst,[],[refute_0_129:[bind(X0,$fot(greatest_lower_bound(multiply(X_85,X_84),greatest_lower_bound(multiply(X_85,X_84),multiply(X_86,X_84))))),bind(Y0,$fot(greatest_lower_bound(multiply(X_86,X_84),multiply(greatest_lower_bound(X_85,X_85),X_84)))),bind(Z0,$fot(multiply(greatest_lower_bound(X_86,greatest_lower_bound(X_85,X_85)),X_84)))]]) ).
cnf(refute_0_131,plain,
( greatest_lower_bound(multiply(X_86,X_84),multiply(greatest_lower_bound(X_85,X_85),X_84)) != multiply(greatest_lower_bound(X_86,greatest_lower_bound(X_85,X_85)),X_84)
| greatest_lower_bound(multiply(X_85,X_84),greatest_lower_bound(multiply(X_85,X_84),multiply(X_86,X_84))) = multiply(greatest_lower_bound(X_86,greatest_lower_bound(X_85,X_85)),X_84) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_85,X_84),greatest_lower_bound(multiply(X_85,X_84),multiply(X_86,X_84))),greatest_lower_bound(multiply(X_86,X_84),multiply(greatest_lower_bound(X_85,X_85),X_84))) )],[refute_0_127,refute_0_130]) ).
cnf(refute_0_132,plain,
greatest_lower_bound(multiply(X_85,X_84),greatest_lower_bound(multiply(X_85,X_84),multiply(X_86,X_84))) = multiply(greatest_lower_bound(X_86,greatest_lower_bound(X_85,X_85)),X_84),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_86,X_84),multiply(greatest_lower_bound(X_85,X_85),X_84)),multiply(greatest_lower_bound(X_86,greatest_lower_bound(X_85,X_85)),X_84)) )],[refute_0_113,refute_0_131]) ).
cnf(refute_0_133,plain,
( multiply(greatest_lower_bound(X_86,greatest_lower_bound(X_85,X_85)),X_84) != multiply(greatest_lower_bound(X_86,X_85),X_84)
| greatest_lower_bound(multiply(X_85,X_84),greatest_lower_bound(multiply(X_85,X_84),multiply(X_86,X_84))) != multiply(greatest_lower_bound(X_86,greatest_lower_bound(X_85,X_85)),X_84)
| greatest_lower_bound(multiply(X_85,X_84),greatest_lower_bound(multiply(X_85,X_84),multiply(X_86,X_84))) = multiply(greatest_lower_bound(X_86,X_85),X_84) ),
inference(subst,[],[refute_0_129:[bind(X0,$fot(greatest_lower_bound(multiply(X_85,X_84),greatest_lower_bound(multiply(X_85,X_84),multiply(X_86,X_84))))),bind(Y0,$fot(multiply(greatest_lower_bound(X_86,greatest_lower_bound(X_85,X_85)),X_84))),bind(Z0,$fot(multiply(greatest_lower_bound(X_86,X_85),X_84)))]]) ).
cnf(refute_0_134,plain,
( multiply(greatest_lower_bound(X_86,greatest_lower_bound(X_85,X_85)),X_84) != multiply(greatest_lower_bound(X_86,X_85),X_84)
| greatest_lower_bound(multiply(X_85,X_84),greatest_lower_bound(multiply(X_85,X_84),multiply(X_86,X_84))) = multiply(greatest_lower_bound(X_86,X_85),X_84) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_85,X_84),greatest_lower_bound(multiply(X_85,X_84),multiply(X_86,X_84))),multiply(greatest_lower_bound(X_86,greatest_lower_bound(X_85,X_85)),X_84)) )],[refute_0_132,refute_0_133]) ).
cnf(refute_0_135,plain,
greatest_lower_bound(multiply(X_85,X_84),greatest_lower_bound(multiply(X_85,X_84),multiply(X_86,X_84))) = multiply(greatest_lower_bound(X_86,X_85),X_84),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_86,greatest_lower_bound(X_85,X_85)),X_84),multiply(greatest_lower_bound(X_86,X_85),X_84)) )],[refute_0_110,refute_0_134]) ).
cnf(refute_0_136,plain,
( greatest_lower_bound(multiply(X_85,X_84),greatest_lower_bound(multiply(X_85,X_84),multiply(X_86,X_84))) != multiply(greatest_lower_bound(X_85,X_86),X_84)
| greatest_lower_bound(multiply(X_85,X_84),greatest_lower_bound(multiply(X_85,X_84),multiply(X_86,X_84))) != multiply(greatest_lower_bound(X_86,X_85),X_84)
| multiply(greatest_lower_bound(X_86,X_85),X_84) = multiply(greatest_lower_bound(X_85,X_86),X_84) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_85,X_84),greatest_lower_bound(multiply(X_85,X_84),multiply(X_86,X_84))),multiply(greatest_lower_bound(X_85,X_86),X_84)) ),[0],$fot(multiply(greatest_lower_bound(X_86,X_85),X_84))]]) ).
cnf(refute_0_137,plain,
( greatest_lower_bound(multiply(X_85,X_84),greatest_lower_bound(multiply(X_85,X_84),multiply(X_86,X_84))) != multiply(greatest_lower_bound(X_85,X_86),X_84)
| multiply(greatest_lower_bound(X_86,X_85),X_84) = multiply(greatest_lower_bound(X_85,X_86),X_84) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_85,X_84),greatest_lower_bound(multiply(X_85,X_84),multiply(X_86,X_84))),multiply(greatest_lower_bound(X_86,X_85),X_84)) )],[refute_0_135,refute_0_136]) ).
cnf(refute_0_138,plain,
multiply(greatest_lower_bound(X_86,X_85),X_84) = multiply(greatest_lower_bound(X_85,X_86),X_84),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_85,X_84),greatest_lower_bound(multiply(X_85,X_84),multiply(X_86,X_84))),multiply(greatest_lower_bound(X_85,X_86),X_84)) )],[refute_0_101,refute_0_137]) ).
cnf(refute_0_139,plain,
( multiply(greatest_lower_bound(X_86,X_85),X_84) != multiply(greatest_lower_bound(X_85,X_86),X_84)
| multiply(greatest_lower_bound(X_85,X_86),X_84) = multiply(greatest_lower_bound(X_86,X_85),X_84) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(greatest_lower_bound(X_86,X_85),X_84))),bind(Y0,$fot(multiply(greatest_lower_bound(X_85,X_86),X_84)))]]) ).
cnf(refute_0_140,plain,
multiply(greatest_lower_bound(X_85,X_86),X_84) = multiply(greatest_lower_bound(X_86,X_85),X_84),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_86,X_85),X_84),multiply(greatest_lower_bound(X_85,X_86),X_84)) )],[refute_0_138,refute_0_139]) ).
cnf(refute_0_141,plain,
multiply(greatest_lower_bound(b,a),inverse(b)) = multiply(greatest_lower_bound(a,b),inverse(b)),
inference(subst,[],[refute_0_140:[bind(X_84,$fot(inverse(b))),bind(X_85,$fot(b)),bind(X_86,$fot(a))]]) ).
cnf(refute_0_142,plain,
multiply(greatest_lower_bound(X_85,X_86),inverse(X_85)) = greatest_lower_bound(multiply(X_85,inverse(X_85)),multiply(X_86,inverse(X_85))),
inference(subst,[],[monotony_glb2:[bind(X,$fot(inverse(X_85))),bind(Y,$fot(X_85)),bind(Z,$fot(X_86))]]) ).
cnf(refute_0_143,plain,
multiply(X_85,inverse(X_85)) = identity,
inference(subst,[],[refute_0_53:[bind(X_49,$fot(X_85))]]) ).
cnf(refute_0_144,plain,
( multiply(X_85,inverse(X_85)) != identity
| multiply(greatest_lower_bound(X_85,X_86),inverse(X_85)) != greatest_lower_bound(multiply(X_85,inverse(X_85)),multiply(X_86,inverse(X_85)))
| multiply(greatest_lower_bound(X_85,X_86),inverse(X_85)) = greatest_lower_bound(identity,multiply(X_86,inverse(X_85))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_85,X_86),inverse(X_85)),greatest_lower_bound(multiply(X_85,inverse(X_85)),multiply(X_86,inverse(X_85)))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_145,plain,
( multiply(greatest_lower_bound(X_85,X_86),inverse(X_85)) != greatest_lower_bound(multiply(X_85,inverse(X_85)),multiply(X_86,inverse(X_85)))
| multiply(greatest_lower_bound(X_85,X_86),inverse(X_85)) = greatest_lower_bound(identity,multiply(X_86,inverse(X_85))) ),
inference(resolve,[$cnf( $equal(multiply(X_85,inverse(X_85)),identity) )],[refute_0_143,refute_0_144]) ).
cnf(refute_0_146,plain,
multiply(greatest_lower_bound(X_85,X_86),inverse(X_85)) = greatest_lower_bound(identity,multiply(X_86,inverse(X_85))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_85,X_86),inverse(X_85)),greatest_lower_bound(multiply(X_85,inverse(X_85)),multiply(X_86,inverse(X_85)))) )],[refute_0_142,refute_0_145]) ).
cnf(refute_0_147,plain,
( multiply(greatest_lower_bound(X_85,X_86),inverse(X_85)) != greatest_lower_bound(identity,multiply(X_86,inverse(X_85)))
| greatest_lower_bound(identity,multiply(X_86,inverse(X_85))) = multiply(greatest_lower_bound(X_85,X_86),inverse(X_85)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(greatest_lower_bound(X_85,X_86),inverse(X_85)))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(X_86,inverse(X_85)))))]]) ).
cnf(refute_0_148,plain,
greatest_lower_bound(identity,multiply(X_86,inverse(X_85))) = multiply(greatest_lower_bound(X_85,X_86),inverse(X_85)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_85,X_86),inverse(X_85)),greatest_lower_bound(identity,multiply(X_86,inverse(X_85)))) )],[refute_0_146,refute_0_147]) ).
cnf(refute_0_149,plain,
greatest_lower_bound(identity,multiply(a,inverse(b))) = multiply(greatest_lower_bound(b,a),inverse(b)),
inference(subst,[],[refute_0_148:[bind(X_85,$fot(b)),bind(X_86,$fot(a))]]) ).
cnf(refute_0_150,plain,
( multiply(greatest_lower_bound(b,a),inverse(b)) != multiply(greatest_lower_bound(a,b),inverse(b))
| greatest_lower_bound(identity,multiply(a,inverse(b))) != multiply(greatest_lower_bound(b,a),inverse(b))
| greatest_lower_bound(identity,multiply(a,inverse(b))) = multiply(greatest_lower_bound(a,b),inverse(b)) ),
inference(subst,[],[refute_0_129:[bind(X0,$fot(greatest_lower_bound(identity,multiply(a,inverse(b))))),bind(Y0,$fot(multiply(greatest_lower_bound(b,a),inverse(b)))),bind(Z0,$fot(multiply(greatest_lower_bound(a,b),inverse(b))))]]) ).
cnf(refute_0_151,plain,
( multiply(greatest_lower_bound(b,a),inverse(b)) != multiply(greatest_lower_bound(a,b),inverse(b))
| greatest_lower_bound(identity,multiply(a,inverse(b))) = multiply(greatest_lower_bound(a,b),inverse(b)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(a,inverse(b))),multiply(greatest_lower_bound(b,a),inverse(b))) )],[refute_0_149,refute_0_150]) ).
cnf(refute_0_152,plain,
greatest_lower_bound(identity,multiply(a,inverse(b))) = multiply(greatest_lower_bound(a,b),inverse(b)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(b,a),inverse(b)),multiply(greatest_lower_bound(a,b),inverse(b))) )],[refute_0_141,refute_0_151]) ).
cnf(refute_0_153,plain,
( greatest_lower_bound(identity,multiply(a,inverse(b))) != multiply(greatest_lower_bound(a,b),inverse(b))
| identity != greatest_lower_bound(identity,multiply(a,inverse(b)))
| identity = multiply(greatest_lower_bound(a,b),inverse(b)) ),
introduced(tautology,[equality,[$cnf( $equal(identity,greatest_lower_bound(identity,multiply(a,inverse(b)))) ),[1],$fot(multiply(greatest_lower_bound(a,b),inverse(b)))]]) ).
cnf(refute_0_154,plain,
( identity != greatest_lower_bound(identity,multiply(a,inverse(b)))
| identity = multiply(greatest_lower_bound(a,b),inverse(b)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(a,inverse(b))),multiply(greatest_lower_bound(a,b),inverse(b))) )],[refute_0_152,refute_0_153]) ).
cnf(refute_0_155,plain,
identity = multiply(greatest_lower_bound(a,b),inverse(b)),
inference(resolve,[$cnf( $equal(identity,greatest_lower_bound(identity,multiply(a,inverse(b)))) )],[refute_0_69,refute_0_154]) ).
cnf(refute_0_156,plain,
( identity != multiply(greatest_lower_bound(a,b),inverse(b))
| multiply(greatest_lower_bound(a,b),inverse(b)) = identity ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(identity)),bind(Y0,$fot(multiply(greatest_lower_bound(a,b),inverse(b))))]]) ).
cnf(refute_0_157,plain,
multiply(greatest_lower_bound(a,b),inverse(b)) = identity,
inference(resolve,[$cnf( $equal(identity,multiply(greatest_lower_bound(a,b),inverse(b))) )],[refute_0_155,refute_0_156]) ).
cnf(refute_0_158,plain,
( multiply(greatest_lower_bound(a,b),inverse(b)) != identity
| inverse(b) != multiply(inverse(greatest_lower_bound(a,b)),multiply(greatest_lower_bound(a,b),inverse(b)))
| inverse(b) = multiply(inverse(greatest_lower_bound(a,b)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(b),multiply(inverse(greatest_lower_bound(a,b)),multiply(greatest_lower_bound(a,b),inverse(b)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_159,plain,
( inverse(b) != multiply(inverse(greatest_lower_bound(a,b)),multiply(greatest_lower_bound(a,b),inverse(b)))
| inverse(b) = multiply(inverse(greatest_lower_bound(a,b)),identity) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(a,b),inverse(b)),identity) )],[refute_0_157,refute_0_158]) ).
cnf(refute_0_160,plain,
inverse(b) = multiply(inverse(greatest_lower_bound(a,b)),identity),
inference(resolve,[$cnf( $equal(inverse(b),multiply(inverse(greatest_lower_bound(a,b)),multiply(greatest_lower_bound(a,b),inverse(b)))) )],[refute_0_45,refute_0_159]) ).
cnf(refute_0_161,plain,
multiply(inverse(greatest_lower_bound(a,b)),identity) = inverse(greatest_lower_bound(a,b)),
inference(subst,[],[refute_0_39:[bind(X_47,$fot(inverse(greatest_lower_bound(a,b))))]]) ).
cnf(refute_0_162,plain,
( multiply(inverse(greatest_lower_bound(a,b)),identity) != inverse(greatest_lower_bound(a,b))
| inverse(b) != multiply(inverse(greatest_lower_bound(a,b)),identity)
| inverse(b) = inverse(greatest_lower_bound(a,b)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(b),multiply(inverse(greatest_lower_bound(a,b)),identity)) ),[1],$fot(inverse(greatest_lower_bound(a,b)))]]) ).
cnf(refute_0_163,plain,
( inverse(b) != multiply(inverse(greatest_lower_bound(a,b)),identity)
| inverse(b) = inverse(greatest_lower_bound(a,b)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(a,b)),identity),inverse(greatest_lower_bound(a,b))) )],[refute_0_161,refute_0_162]) ).
cnf(refute_0_164,plain,
inverse(b) = inverse(greatest_lower_bound(a,b)),
inference(resolve,[$cnf( $equal(inverse(b),multiply(inverse(greatest_lower_bound(a,b)),identity)) )],[refute_0_160,refute_0_163]) ).
cnf(refute_0_165,plain,
( inverse(b) != inverse(greatest_lower_bound(a,b))
| inverse(greatest_lower_bound(a,b)) = inverse(b) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(inverse(b))),bind(Y0,$fot(inverse(greatest_lower_bound(a,b))))]]) ).
cnf(refute_0_166,plain,
inverse(greatest_lower_bound(a,b)) = inverse(b),
inference(resolve,[$cnf( $equal(inverse(b),inverse(greatest_lower_bound(a,b))) )],[refute_0_164,refute_0_165]) ).
cnf(refute_0_167,plain,
( inverse(greatest_lower_bound(a,b)) != inverse(b)
| inverse(inverse(greatest_lower_bound(a,b))) != greatest_lower_bound(a,b)
| inverse(inverse(b)) = greatest_lower_bound(a,b) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(greatest_lower_bound(a,b))),greatest_lower_bound(a,b)) ),[0,0],$fot(inverse(b))]]) ).
cnf(refute_0_168,plain,
( inverse(inverse(greatest_lower_bound(a,b))) != greatest_lower_bound(a,b)
| inverse(inverse(b)) = greatest_lower_bound(a,b) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(a,b)),inverse(b)) )],[refute_0_166,refute_0_167]) ).
cnf(refute_0_169,plain,
inverse(inverse(b)) = greatest_lower_bound(a,b),
inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(a,b))),greatest_lower_bound(a,b)) )],[refute_0_44,refute_0_168]) ).
cnf(refute_0_170,plain,
inverse(inverse(b)) = b,
inference(subst,[],[refute_0_43:[bind(X_49,$fot(b))]]) ).
cnf(refute_0_171,plain,
( inverse(inverse(b)) != b
| inverse(inverse(b)) != greatest_lower_bound(a,b)
| b = greatest_lower_bound(a,b) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(b)),greatest_lower_bound(a,b)) ),[0],$fot(b)]]) ).
cnf(refute_0_172,plain,
( inverse(inverse(b)) != greatest_lower_bound(a,b)
| b = greatest_lower_bound(a,b) ),
inference(resolve,[$cnf( $equal(inverse(inverse(b)),b) )],[refute_0_170,refute_0_171]) ).
cnf(refute_0_173,plain,
b = greatest_lower_bound(a,b),
inference(resolve,[$cnf( $equal(inverse(inverse(b)),greatest_lower_bound(a,b)) )],[refute_0_169,refute_0_172]) ).
cnf(refute_0_174,plain,
( b != greatest_lower_bound(a,b)
| greatest_lower_bound(a,b) = b ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(b)),bind(Y0,$fot(greatest_lower_bound(a,b)))]]) ).
cnf(refute_0_175,plain,
greatest_lower_bound(a,b) = b,
inference(resolve,[$cnf( $equal(b,greatest_lower_bound(a,b)) )],[refute_0_173,refute_0_174]) ).
cnf(refute_0_176,plain,
( greatest_lower_bound(a,b) != b
| least_upper_bound(a,greatest_lower_bound(a,b)) != a
| least_upper_bound(a,b) = a ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(a,greatest_lower_bound(a,b)),a) ),[0,1],$fot(b)]]) ).
cnf(refute_0_177,plain,
( least_upper_bound(a,greatest_lower_bound(a,b)) != a
| least_upper_bound(a,b) = a ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,b),b) )],[refute_0_175,refute_0_176]) ).
cnf(refute_0_178,plain,
least_upper_bound(a,b) = a,
inference(resolve,[$cnf( $equal(least_upper_bound(a,greatest_lower_bound(a,b)),a) )],[refute_0_0,refute_0_177]) ).
cnf(refute_0_179,plain,
$false,
inference(resolve,[$cnf( $equal(least_upper_bound(a,b),a) )],[refute_0_178,prove_p02a]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP169-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n026.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 13 15:45:36 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.55/0.76 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.55/0.76
% 0.55/0.76 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.61/0.78
%------------------------------------------------------------------------------