TSTP Solution File: GRP191-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP191-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 10:37:55 EDT 2022
% Result : Unsatisfiable 6.20s 6.39s
% Output : CNFRefutation 6.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 76
% Syntax : Number of clauses : 314 ( 172 unt; 0 nHn; 157 RR)
% Number of literals : 517 ( 516 equ; 204 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 655 ( 43 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
multiply(identity,X) = X ).
cnf(left_inverse,axiom,
multiply(inverse(X),X) = identity ).
cnf(associativity,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ).
cnf(symmetry_of_glb,axiom,
greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ).
cnf(symmetry_of_lub,axiom,
least_upper_bound(X,Y) = least_upper_bound(Y,X) ).
cnf(associativity_of_glb,axiom,
greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) ).
cnf(associativity_of_lub,axiom,
least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) ).
cnf(idempotence_of_lub,axiom,
least_upper_bound(X,X) = X ).
cnf(lub_absorbtion,axiom,
least_upper_bound(X,greatest_lower_bound(X,Y)) = X ).
cnf(glb_absorbtion,axiom,
greatest_lower_bound(X,least_upper_bound(X,Y)) = X ).
cnf(monotony_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(p39b_1,hypothesis,
greatest_lower_bound(a,b) = b ).
cnf(prove_p39b,negated_conjecture,
greatest_lower_bound(inverse(a),inverse(b)) != inverse(a) ).
cnf(refute_0_0,plain,
greatest_lower_bound(inverse(a),least_upper_bound(inverse(a),inverse(b))) = inverse(a),
inference(subst,[],[glb_absorbtion:[bind(X,$fot(inverse(a))),bind(Y,$fot(inverse(b)))]]) ).
cnf(refute_0_1,plain,
multiply(multiply(inverse(X_60),X_60),X_61) = multiply(inverse(X_60),multiply(X_60,X_61)),
inference(subst,[],[associativity:[bind(X,$fot(inverse(X_60))),bind(Y,$fot(X_60)),bind(Z,$fot(X_61))]]) ).
cnf(refute_0_2,plain,
multiply(inverse(X_60),X_60) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_60))]]) ).
cnf(refute_0_3,plain,
( multiply(multiply(inverse(X_60),X_60),X_61) != multiply(inverse(X_60),multiply(X_60,X_61))
| multiply(inverse(X_60),X_60) != identity
| multiply(identity,X_61) = multiply(inverse(X_60),multiply(X_60,X_61)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_60),X_60),X_61),multiply(inverse(X_60),multiply(X_60,X_61))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_4,plain,
( multiply(multiply(inverse(X_60),X_60),X_61) != multiply(inverse(X_60),multiply(X_60,X_61))
| multiply(identity,X_61) = multiply(inverse(X_60),multiply(X_60,X_61)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_60),X_60),identity) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
multiply(identity,X_61) = multiply(inverse(X_60),multiply(X_60,X_61)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_60),X_60),X_61),multiply(inverse(X_60),multiply(X_60,X_61))) )],[refute_0_1,refute_0_4]) ).
cnf(refute_0_6,plain,
multiply(identity,X_61) = X_61,
inference(subst,[],[left_identity:[bind(X,$fot(X_61))]]) ).
cnf(refute_0_7,plain,
( multiply(identity,X_61) != X_61
| multiply(identity,X_61) != multiply(inverse(X_60),multiply(X_60,X_61))
| X_61 = multiply(inverse(X_60),multiply(X_60,X_61)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_61),multiply(inverse(X_60),multiply(X_60,X_61))) ),[0],$fot(X_61)]]) ).
cnf(refute_0_8,plain,
( multiply(identity,X_61) != multiply(inverse(X_60),multiply(X_60,X_61))
| X_61 = multiply(inverse(X_60),multiply(X_60,X_61)) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_61),X_61) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
X_61 = multiply(inverse(X_60),multiply(X_60,X_61)),
inference(resolve,[$cnf( $equal(multiply(identity,X_61),multiply(inverse(X_60),multiply(X_60,X_61))) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
X_63 = multiply(inverse(inverse(X_63)),multiply(inverse(X_63),X_63)),
inference(subst,[],[refute_0_9:[bind(X_60,$fot(inverse(X_63))),bind(X_61,$fot(X_63))]]) ).
cnf(refute_0_11,plain,
multiply(inverse(X_63),X_63) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_63))]]) ).
cnf(refute_0_12,plain,
( X_63 != multiply(inverse(inverse(X_63)),multiply(inverse(X_63),X_63))
| multiply(inverse(X_63),X_63) != identity
| X_63 = multiply(inverse(inverse(X_63)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(X_63,multiply(inverse(inverse(X_63)),multiply(inverse(X_63),X_63))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_13,plain,
( X_63 != multiply(inverse(inverse(X_63)),multiply(inverse(X_63),X_63))
| X_63 = multiply(inverse(inverse(X_63)),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_63),X_63),identity) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
X_63 = multiply(inverse(inverse(X_63)),identity),
inference(resolve,[$cnf( $equal(X_63,multiply(inverse(inverse(X_63)),multiply(inverse(X_63),X_63))) )],[refute_0_10,refute_0_13]) ).
cnf(refute_0_15,plain,
multiply(X_62,X_63) = multiply(inverse(inverse(X_62)),multiply(inverse(X_62),multiply(X_62,X_63))),
inference(subst,[],[refute_0_9:[bind(X_60,$fot(inverse(X_62))),bind(X_61,$fot(multiply(X_62,X_63)))]]) ).
cnf(refute_0_16,plain,
X_63 = multiply(inverse(X_62),multiply(X_62,X_63)),
inference(subst,[],[refute_0_9:[bind(X_60,$fot(X_62)),bind(X_61,$fot(X_63))]]) ).
cnf(refute_0_17,plain,
X0 = X0,
introduced(tautology,[refl,[$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( $equal(X0,X0) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
( X_63 != multiply(inverse(X_62),multiply(X_62,X_63))
| multiply(inverse(X_62),multiply(X_62,X_63)) = X_63 ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(X_63)),bind(Y0,$fot(multiply(inverse(X_62),multiply(X_62,X_63))))]]) ).
cnf(refute_0_21,plain,
multiply(inverse(X_62),multiply(X_62,X_63)) = X_63,
inference(resolve,[$cnf( $equal(X_63,multiply(inverse(X_62),multiply(X_62,X_63))) )],[refute_0_16,refute_0_20]) ).
cnf(refute_0_22,plain,
( multiply(X_62,X_63) != multiply(inverse(inverse(X_62)),multiply(inverse(X_62),multiply(X_62,X_63)))
| multiply(inverse(X_62),multiply(X_62,X_63)) != X_63
| multiply(X_62,X_63) = multiply(inverse(inverse(X_62)),X_63) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_62,X_63),multiply(inverse(inverse(X_62)),multiply(inverse(X_62),multiply(X_62,X_63)))) ),[1,1],$fot(X_63)]]) ).
cnf(refute_0_23,plain,
( multiply(X_62,X_63) != multiply(inverse(inverse(X_62)),multiply(inverse(X_62),multiply(X_62,X_63)))
| multiply(X_62,X_63) = multiply(inverse(inverse(X_62)),X_63) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_62),multiply(X_62,X_63)),X_63) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
multiply(X_62,X_63) = multiply(inverse(inverse(X_62)),X_63),
inference(resolve,[$cnf( $equal(multiply(X_62,X_63),multiply(inverse(inverse(X_62)),multiply(inverse(X_62),multiply(X_62,X_63)))) )],[refute_0_15,refute_0_23]) ).
cnf(refute_0_25,plain,
( multiply(X_62,X_63) != multiply(inverse(inverse(X_62)),X_63)
| multiply(inverse(inverse(X_62)),X_63) = multiply(X_62,X_63) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(X_62,X_63))),bind(Y0,$fot(multiply(inverse(inverse(X_62)),X_63)))]]) ).
cnf(refute_0_26,plain,
multiply(inverse(inverse(X_62)),X_63) = multiply(X_62,X_63),
inference(resolve,[$cnf( $equal(multiply(X_62,X_63),multiply(inverse(inverse(X_62)),X_63)) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
multiply(inverse(inverse(X_63)),identity) = multiply(X_63,identity),
inference(subst,[],[refute_0_26:[bind(X_62,$fot(X_63)),bind(X_63,$fot(identity))]]) ).
cnf(refute_0_28,plain,
( X_63 != multiply(inverse(inverse(X_63)),identity)
| multiply(inverse(inverse(X_63)),identity) != multiply(X_63,identity)
| X_63 = multiply(X_63,identity) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_63,multiply(X_63,identity)) ),[0],$fot(multiply(inverse(inverse(X_63)),identity))]]) ).
cnf(refute_0_29,plain,
( X_63 != multiply(inverse(inverse(X_63)),identity)
| X_63 = multiply(X_63,identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_63)),identity),multiply(X_63,identity)) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
X_63 = multiply(X_63,identity),
inference(resolve,[$cnf( $equal(X_63,multiply(inverse(inverse(X_63)),identity)) )],[refute_0_14,refute_0_29]) ).
cnf(refute_0_31,plain,
inverse(inverse(X_65)) = multiply(inverse(inverse(X_65)),identity),
inference(subst,[],[refute_0_30:[bind(X_63,$fot(inverse(inverse(X_65))))]]) ).
cnf(refute_0_32,plain,
multiply(X_65,identity) = multiply(inverse(inverse(X_65)),identity),
inference(subst,[],[refute_0_24:[bind(X_62,$fot(X_65)),bind(X_63,$fot(identity))]]) ).
cnf(refute_0_33,plain,
( multiply(X_65,identity) != multiply(inverse(inverse(X_65)),identity)
| multiply(inverse(inverse(X_65)),identity) = multiply(X_65,identity) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(X_65,identity))),bind(Y0,$fot(multiply(inverse(inverse(X_65)),identity)))]]) ).
cnf(refute_0_34,plain,
multiply(inverse(inverse(X_65)),identity) = multiply(X_65,identity),
inference(resolve,[$cnf( $equal(multiply(X_65,identity),multiply(inverse(inverse(X_65)),identity)) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
( multiply(inverse(inverse(X_65)),identity) != multiply(X_65,identity)
| inverse(inverse(X_65)) != multiply(inverse(inverse(X_65)),identity)
| inverse(inverse(X_65)) = multiply(X_65,identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_65)),multiply(inverse(inverse(X_65)),identity)) ),[1],$fot(multiply(X_65,identity))]]) ).
cnf(refute_0_36,plain,
( inverse(inverse(X_65)) != multiply(inverse(inverse(X_65)),identity)
| inverse(inverse(X_65)) = multiply(X_65,identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_65)),identity),multiply(X_65,identity)) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
inverse(inverse(X_65)) = multiply(X_65,identity),
inference(resolve,[$cnf( $equal(inverse(inverse(X_65)),multiply(inverse(inverse(X_65)),identity)) )],[refute_0_31,refute_0_36]) ).
cnf(refute_0_38,plain,
( X_63 != multiply(X_63,identity)
| multiply(X_63,identity) = X_63 ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(X_63)),bind(Y0,$fot(multiply(X_63,identity)))]]) ).
cnf(refute_0_39,plain,
multiply(X_63,identity) = X_63,
inference(resolve,[$cnf( $equal(X_63,multiply(X_63,identity)) )],[refute_0_30,refute_0_38]) ).
cnf(refute_0_40,plain,
multiply(X_65,identity) = X_65,
inference(subst,[],[refute_0_39:[bind(X_63,$fot(X_65))]]) ).
cnf(refute_0_41,plain,
( multiply(X_65,identity) != X_65
| inverse(inverse(X_65)) != multiply(X_65,identity)
| inverse(inverse(X_65)) = X_65 ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_65)),multiply(X_65,identity)) ),[1],$fot(X_65)]]) ).
cnf(refute_0_42,plain,
( inverse(inverse(X_65)) != multiply(X_65,identity)
| inverse(inverse(X_65)) = X_65 ),
inference(resolve,[$cnf( $equal(multiply(X_65,identity),X_65) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
inverse(inverse(X_65)) = X_65,
inference(resolve,[$cnf( $equal(inverse(inverse(X_65)),multiply(X_65,identity)) )],[refute_0_37,refute_0_42]) ).
cnf(refute_0_44,plain,
inverse(inverse(least_upper_bound(inverse(a),inverse(b)))) = least_upper_bound(inverse(a),inverse(b)),
inference(subst,[],[refute_0_43:[bind(X_65,$fot(least_upper_bound(inverse(a),inverse(b))))]]) ).
cnf(refute_0_45,plain,
X_61 = multiply(inverse(least_upper_bound(X_89,inverse(X_61))),multiply(least_upper_bound(X_89,inverse(X_61)),X_61)),
inference(subst,[],[refute_0_9:[bind(X_60,$fot(least_upper_bound(X_89,inverse(X_61))))]]) ).
cnf(refute_0_46,plain,
multiply(least_upper_bound(X_86,inverse(X_85)),X_85) = least_upper_bound(multiply(X_86,X_85),multiply(inverse(X_85),X_85)),
inference(subst,[],[monotony_lub2:[bind(X,$fot(X_85)),bind(Y,$fot(X_86)),bind(Z,$fot(inverse(X_85)))]]) ).
cnf(refute_0_47,plain,
multiply(inverse(X_85),X_85) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_85))]]) ).
cnf(refute_0_48,plain,
( multiply(inverse(X_85),X_85) != identity
| multiply(least_upper_bound(X_86,inverse(X_85)),X_85) != least_upper_bound(multiply(X_86,X_85),multiply(inverse(X_85),X_85))
| multiply(least_upper_bound(X_86,inverse(X_85)),X_85) = least_upper_bound(multiply(X_86,X_85),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_86,inverse(X_85)),X_85),least_upper_bound(multiply(X_86,X_85),multiply(inverse(X_85),X_85))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_49,plain,
( multiply(least_upper_bound(X_86,inverse(X_85)),X_85) != least_upper_bound(multiply(X_86,X_85),multiply(inverse(X_85),X_85))
| multiply(least_upper_bound(X_86,inverse(X_85)),X_85) = least_upper_bound(multiply(X_86,X_85),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_85),X_85),identity) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
multiply(least_upper_bound(X_86,inverse(X_85)),X_85) = least_upper_bound(multiply(X_86,X_85),identity),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_86,inverse(X_85)),X_85),least_upper_bound(multiply(X_86,X_85),multiply(inverse(X_85),X_85))) )],[refute_0_46,refute_0_49]) ).
cnf(refute_0_51,plain,
least_upper_bound(X_33,X_32) = least_upper_bound(X_32,X_33),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_33)),bind(Y,$fot(X_32))]]) ).
cnf(refute_0_52,plain,
least_upper_bound(multiply(X_86,X_85),identity) = least_upper_bound(identity,multiply(X_86,X_85)),
inference(subst,[],[refute_0_51:[bind(X_32,$fot(identity)),bind(X_33,$fot(multiply(X_86,X_85)))]]) ).
cnf(refute_0_53,plain,
( multiply(least_upper_bound(X_86,inverse(X_85)),X_85) != least_upper_bound(multiply(X_86,X_85),identity)
| least_upper_bound(multiply(X_86,X_85),identity) != least_upper_bound(identity,multiply(X_86,X_85))
| multiply(least_upper_bound(X_86,inverse(X_85)),X_85) = least_upper_bound(identity,multiply(X_86,X_85)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_86,inverse(X_85)),X_85),least_upper_bound(identity,multiply(X_86,X_85))) ),[0],$fot(least_upper_bound(multiply(X_86,X_85),identity))]]) ).
cnf(refute_0_54,plain,
( multiply(least_upper_bound(X_86,inverse(X_85)),X_85) != least_upper_bound(multiply(X_86,X_85),identity)
| multiply(least_upper_bound(X_86,inverse(X_85)),X_85) = least_upper_bound(identity,multiply(X_86,X_85)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_86,X_85),identity),least_upper_bound(identity,multiply(X_86,X_85))) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
multiply(least_upper_bound(X_86,inverse(X_85)),X_85) = least_upper_bound(identity,multiply(X_86,X_85)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_86,inverse(X_85)),X_85),least_upper_bound(multiply(X_86,X_85),identity)) )],[refute_0_50,refute_0_54]) ).
cnf(refute_0_56,plain,
multiply(least_upper_bound(X_89,inverse(X_61)),X_61) = least_upper_bound(identity,multiply(X_89,X_61)),
inference(subst,[],[refute_0_55:[bind(X_85,$fot(X_61)),bind(X_86,$fot(X_89))]]) ).
cnf(refute_0_57,plain,
( X_61 != multiply(inverse(least_upper_bound(X_89,inverse(X_61))),multiply(least_upper_bound(X_89,inverse(X_61)),X_61))
| multiply(least_upper_bound(X_89,inverse(X_61)),X_61) != least_upper_bound(identity,multiply(X_89,X_61))
| X_61 = multiply(inverse(least_upper_bound(X_89,inverse(X_61))),least_upper_bound(identity,multiply(X_89,X_61))) ),
introduced(tautology,[equality,[$cnf( $equal(X_61,multiply(inverse(least_upper_bound(X_89,inverse(X_61))),multiply(least_upper_bound(X_89,inverse(X_61)),X_61))) ),[1,1],$fot(least_upper_bound(identity,multiply(X_89,X_61)))]]) ).
cnf(refute_0_58,plain,
( X_61 != multiply(inverse(least_upper_bound(X_89,inverse(X_61))),multiply(least_upper_bound(X_89,inverse(X_61)),X_61))
| X_61 = multiply(inverse(least_upper_bound(X_89,inverse(X_61))),least_upper_bound(identity,multiply(X_89,X_61))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_89,inverse(X_61)),X_61),least_upper_bound(identity,multiply(X_89,X_61))) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
X_61 = multiply(inverse(least_upper_bound(X_89,inverse(X_61))),least_upper_bound(identity,multiply(X_89,X_61))),
inference(resolve,[$cnf( $equal(X_61,multiply(inverse(least_upper_bound(X_89,inverse(X_61))),multiply(least_upper_bound(X_89,inverse(X_61)),X_61))) )],[refute_0_45,refute_0_58]) ).
cnf(refute_0_60,plain,
b = multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_254,a)),inverse(b))),least_upper_bound(identity,multiply(inverse(least_upper_bound(X_254,a)),b))),
inference(subst,[],[refute_0_59:[bind(X_61,$fot(b)),bind(X_89,$fot(inverse(least_upper_bound(X_254,a))))]]) ).
cnf(refute_0_61,plain,
least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_253,a)),b))) = identity,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(identity)),bind(Y,$fot(multiply(inverse(least_upper_bound(X_253,a)),b)))]]) ).
cnf(refute_0_62,plain,
multiply(inverse(X_113),greatest_lower_bound(X_112,X_113)) = greatest_lower_bound(multiply(inverse(X_113),X_112),multiply(inverse(X_113),X_113)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(inverse(X_113))),bind(Y,$fot(X_112)),bind(Z,$fot(X_113))]]) ).
cnf(refute_0_63,plain,
multiply(inverse(X_113),X_113) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_113))]]) ).
cnf(refute_0_64,plain,
( multiply(inverse(X_113),X_113) != identity
| multiply(inverse(X_113),greatest_lower_bound(X_112,X_113)) != greatest_lower_bound(multiply(inverse(X_113),X_112),multiply(inverse(X_113),X_113))
| multiply(inverse(X_113),greatest_lower_bound(X_112,X_113)) = greatest_lower_bound(multiply(inverse(X_113),X_112),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_113),greatest_lower_bound(X_112,X_113)),greatest_lower_bound(multiply(inverse(X_113),X_112),multiply(inverse(X_113),X_113))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_65,plain,
( multiply(inverse(X_113),greatest_lower_bound(X_112,X_113)) != greatest_lower_bound(multiply(inverse(X_113),X_112),multiply(inverse(X_113),X_113))
| multiply(inverse(X_113),greatest_lower_bound(X_112,X_113)) = greatest_lower_bound(multiply(inverse(X_113),X_112),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_113),X_113),identity) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
multiply(inverse(X_113),greatest_lower_bound(X_112,X_113)) = greatest_lower_bound(multiply(inverse(X_113),X_112),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_113),greatest_lower_bound(X_112,X_113)),greatest_lower_bound(multiply(inverse(X_113),X_112),multiply(inverse(X_113),X_113))) )],[refute_0_62,refute_0_65]) ).
cnf(refute_0_67,plain,
( greatest_lower_bound(X,Y) != greatest_lower_bound(Y,X)
| greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(greatest_lower_bound(X,Y))),bind(Y0,$fot(greatest_lower_bound(Y,X)))]]) ).
cnf(refute_0_68,plain,
greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X)) )],[symmetry_of_glb,refute_0_67]) ).
cnf(refute_0_69,plain,
greatest_lower_bound(multiply(inverse(X_113),X_112),identity) = greatest_lower_bound(identity,multiply(inverse(X_113),X_112)),
inference(subst,[],[refute_0_68:[bind(X,$fot(identity)),bind(Y,$fot(multiply(inverse(X_113),X_112)))]]) ).
cnf(refute_0_70,plain,
( multiply(inverse(X_113),greatest_lower_bound(X_112,X_113)) != greatest_lower_bound(multiply(inverse(X_113),X_112),identity)
| greatest_lower_bound(multiply(inverse(X_113),X_112),identity) != greatest_lower_bound(identity,multiply(inverse(X_113),X_112))
| multiply(inverse(X_113),greatest_lower_bound(X_112,X_113)) = greatest_lower_bound(identity,multiply(inverse(X_113),X_112)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_113),greatest_lower_bound(X_112,X_113)),greatest_lower_bound(identity,multiply(inverse(X_113),X_112))) ),[0],$fot(greatest_lower_bound(multiply(inverse(X_113),X_112),identity))]]) ).
cnf(refute_0_71,plain,
( multiply(inverse(X_113),greatest_lower_bound(X_112,X_113)) != greatest_lower_bound(multiply(inverse(X_113),X_112),identity)
| multiply(inverse(X_113),greatest_lower_bound(X_112,X_113)) = greatest_lower_bound(identity,multiply(inverse(X_113),X_112)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(inverse(X_113),X_112),identity),greatest_lower_bound(identity,multiply(inverse(X_113),X_112))) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
multiply(inverse(X_113),greatest_lower_bound(X_112,X_113)) = greatest_lower_bound(identity,multiply(inverse(X_113),X_112)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_113),greatest_lower_bound(X_112,X_113)),greatest_lower_bound(multiply(inverse(X_113),X_112),identity)) )],[refute_0_66,refute_0_71]) ).
cnf(refute_0_73,plain,
multiply(inverse(least_upper_bound(X_49,a)),greatest_lower_bound(b,least_upper_bound(X_49,a))) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_49,a)),b)),
inference(subst,[],[refute_0_72:[bind(X_112,$fot(b)),bind(X_113,$fot(least_upper_bound(X_49,a)))]]) ).
cnf(refute_0_74,plain,
greatest_lower_bound(a,greatest_lower_bound(b,X_24)) = greatest_lower_bound(greatest_lower_bound(a,b),X_24),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(a)),bind(Y,$fot(b)),bind(Z,$fot(X_24))]]) ).
cnf(refute_0_75,plain,
( greatest_lower_bound(a,b) != b
| greatest_lower_bound(a,greatest_lower_bound(b,X_24)) != greatest_lower_bound(greatest_lower_bound(a,b),X_24)
| greatest_lower_bound(a,greatest_lower_bound(b,X_24)) = greatest_lower_bound(b,X_24) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(b,X_24)),greatest_lower_bound(greatest_lower_bound(a,b),X_24)) ),[1,0],$fot(b)]]) ).
cnf(refute_0_76,plain,
( greatest_lower_bound(a,greatest_lower_bound(b,X_24)) != greatest_lower_bound(greatest_lower_bound(a,b),X_24)
| greatest_lower_bound(a,greatest_lower_bound(b,X_24)) = greatest_lower_bound(b,X_24) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,b),b) )],[p39b_1,refute_0_75]) ).
cnf(refute_0_77,plain,
greatest_lower_bound(a,greatest_lower_bound(b,X_24)) = greatest_lower_bound(b,X_24),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(b,X_24)),greatest_lower_bound(greatest_lower_bound(a,b),X_24)) )],[refute_0_74,refute_0_76]) ).
cnf(refute_0_78,plain,
greatest_lower_bound(a,greatest_lower_bound(b,X_25)) = greatest_lower_bound(b,X_25),
inference(subst,[],[refute_0_77:[bind(X_24,$fot(X_25))]]) ).
cnf(refute_0_79,plain,
greatest_lower_bound(X_25,b) = greatest_lower_bound(b,X_25),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_25)),bind(Y,$fot(b))]]) ).
cnf(refute_0_80,plain,
( greatest_lower_bound(X_25,b) != greatest_lower_bound(b,X_25)
| greatest_lower_bound(b,X_25) = greatest_lower_bound(X_25,b) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(greatest_lower_bound(X_25,b))),bind(Y0,$fot(greatest_lower_bound(b,X_25)))]]) ).
cnf(refute_0_81,plain,
greatest_lower_bound(b,X_25) = greatest_lower_bound(X_25,b),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_25,b),greatest_lower_bound(b,X_25)) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
( greatest_lower_bound(a,greatest_lower_bound(b,X_25)) != greatest_lower_bound(b,X_25)
| greatest_lower_bound(b,X_25) != greatest_lower_bound(X_25,b)
| greatest_lower_bound(a,greatest_lower_bound(X_25,b)) = greatest_lower_bound(b,X_25) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(b,X_25)),greatest_lower_bound(b,X_25)) ),[0,1],$fot(greatest_lower_bound(X_25,b))]]) ).
cnf(refute_0_83,plain,
( greatest_lower_bound(a,greatest_lower_bound(b,X_25)) != greatest_lower_bound(b,X_25)
| greatest_lower_bound(a,greatest_lower_bound(X_25,b)) = greatest_lower_bound(b,X_25) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,X_25),greatest_lower_bound(X_25,b)) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
greatest_lower_bound(a,greatest_lower_bound(X_25,b)) = greatest_lower_bound(b,X_25),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(b,X_25)),greatest_lower_bound(b,X_25)) )],[refute_0_78,refute_0_83]) ).
cnf(refute_0_85,plain,
greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(X_49,a),b)) = greatest_lower_bound(b,least_upper_bound(X_49,a)),
inference(subst,[],[refute_0_84:[bind(X_25,$fot(least_upper_bound(X_49,a)))]]) ).
cnf(refute_0_86,plain,
greatest_lower_bound(X_22,greatest_lower_bound(least_upper_bound(X_11,X_22),X_24)) = greatest_lower_bound(greatest_lower_bound(X_22,least_upper_bound(X_11,X_22)),X_24),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_22)),bind(Y,$fot(least_upper_bound(X_11,X_22))),bind(Z,$fot(X_24))]]) ).
cnf(refute_0_87,plain,
greatest_lower_bound(X_10,least_upper_bound(X_10,X_11)) = X_10,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_10)),bind(Y,$fot(X_11))]]) ).
cnf(refute_0_88,plain,
least_upper_bound(X_11,X_10) = least_upper_bound(X_10,X_11),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_11)),bind(Y,$fot(X_10))]]) ).
cnf(refute_0_89,plain,
( least_upper_bound(X_11,X_10) != least_upper_bound(X_10,X_11)
| least_upper_bound(X_10,X_11) = least_upper_bound(X_11,X_10) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(least_upper_bound(X_11,X_10))),bind(Y0,$fot(least_upper_bound(X_10,X_11)))]]) ).
cnf(refute_0_90,plain,
least_upper_bound(X_10,X_11) = least_upper_bound(X_11,X_10),
inference(resolve,[$cnf( $equal(least_upper_bound(X_11,X_10),least_upper_bound(X_10,X_11)) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
( greatest_lower_bound(X_10,least_upper_bound(X_10,X_11)) != X_10
| least_upper_bound(X_10,X_11) != least_upper_bound(X_11,X_10)
| greatest_lower_bound(X_10,least_upper_bound(X_11,X_10)) = X_10 ),
introduced(tautology,[equality,[$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_92,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( $equal(least_upper_bound(X_10,X_11),least_upper_bound(X_11,X_10)) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
greatest_lower_bound(X_10,least_upper_bound(X_11,X_10)) = X_10,
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_10,least_upper_bound(X_10,X_11)),X_10) )],[refute_0_87,refute_0_92]) ).
cnf(refute_0_94,plain,
greatest_lower_bound(X_22,least_upper_bound(X_11,X_22)) = X_22,
inference(subst,[],[refute_0_93:[bind(X_10,$fot(X_22))]]) ).
cnf(refute_0_95,plain,
( greatest_lower_bound(X_22,greatest_lower_bound(least_upper_bound(X_11,X_22),X_24)) != greatest_lower_bound(greatest_lower_bound(X_22,least_upper_bound(X_11,X_22)),X_24)
| greatest_lower_bound(X_22,least_upper_bound(X_11,X_22)) != X_22
| greatest_lower_bound(X_22,greatest_lower_bound(least_upper_bound(X_11,X_22),X_24)) = greatest_lower_bound(X_22,X_24) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_22,greatest_lower_bound(least_upper_bound(X_11,X_22),X_24)),greatest_lower_bound(greatest_lower_bound(X_22,least_upper_bound(X_11,X_22)),X_24)) ),[1,0],$fot(X_22)]]) ).
cnf(refute_0_96,plain,
( greatest_lower_bound(X_22,greatest_lower_bound(least_upper_bound(X_11,X_22),X_24)) != greatest_lower_bound(greatest_lower_bound(X_22,least_upper_bound(X_11,X_22)),X_24)
| greatest_lower_bound(X_22,greatest_lower_bound(least_upper_bound(X_11,X_22),X_24)) = greatest_lower_bound(X_22,X_24) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_22,least_upper_bound(X_11,X_22)),X_22) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
greatest_lower_bound(X_22,greatest_lower_bound(least_upper_bound(X_11,X_22),X_24)) = greatest_lower_bound(X_22,X_24),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_22,greatest_lower_bound(least_upper_bound(X_11,X_22),X_24)),greatest_lower_bound(greatest_lower_bound(X_22,least_upper_bound(X_11,X_22)),X_24)) )],[refute_0_86,refute_0_96]) ).
cnf(refute_0_98,plain,
greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(X_49,a),b)) = greatest_lower_bound(a,b),
inference(subst,[],[refute_0_97:[bind(X_11,$fot(X_49)),bind(X_22,$fot(a)),bind(X_24,$fot(b))]]) ).
cnf(refute_0_99,plain,
( greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(X_49,a),b)) != greatest_lower_bound(a,b)
| greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(X_49,a),b)) != greatest_lower_bound(b,least_upper_bound(X_49,a))
| greatest_lower_bound(a,b) = greatest_lower_bound(b,least_upper_bound(X_49,a)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(X_49,a),b)),greatest_lower_bound(b,least_upper_bound(X_49,a))) ),[0],$fot(greatest_lower_bound(a,b))]]) ).
cnf(refute_0_100,plain,
( greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(X_49,a),b)) != greatest_lower_bound(b,least_upper_bound(X_49,a))
| greatest_lower_bound(a,b) = greatest_lower_bound(b,least_upper_bound(X_49,a)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(X_49,a),b)),greatest_lower_bound(a,b)) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
greatest_lower_bound(a,b) = greatest_lower_bound(b,least_upper_bound(X_49,a)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(X_49,a),b)),greatest_lower_bound(b,least_upper_bound(X_49,a))) )],[refute_0_85,refute_0_100]) ).
cnf(refute_0_102,plain,
( greatest_lower_bound(a,b) != b
| greatest_lower_bound(a,b) != greatest_lower_bound(b,least_upper_bound(X_49,a))
| b = greatest_lower_bound(b,least_upper_bound(X_49,a)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,b),greatest_lower_bound(b,least_upper_bound(X_49,a))) ),[0],$fot(b)]]) ).
cnf(refute_0_103,plain,
( greatest_lower_bound(a,b) != greatest_lower_bound(b,least_upper_bound(X_49,a))
| b = greatest_lower_bound(b,least_upper_bound(X_49,a)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,b),b) )],[p39b_1,refute_0_102]) ).
cnf(refute_0_104,plain,
b = greatest_lower_bound(b,least_upper_bound(X_49,a)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,b),greatest_lower_bound(b,least_upper_bound(X_49,a))) )],[refute_0_101,refute_0_103]) ).
cnf(refute_0_105,plain,
( b != greatest_lower_bound(b,least_upper_bound(X_49,a))
| greatest_lower_bound(b,least_upper_bound(X_49,a)) = b ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(b)),bind(Y0,$fot(greatest_lower_bound(b,least_upper_bound(X_49,a))))]]) ).
cnf(refute_0_106,plain,
greatest_lower_bound(b,least_upper_bound(X_49,a)) = b,
inference(resolve,[$cnf( $equal(b,greatest_lower_bound(b,least_upper_bound(X_49,a))) )],[refute_0_104,refute_0_105]) ).
cnf(refute_0_107,plain,
( multiply(inverse(least_upper_bound(X_49,a)),greatest_lower_bound(b,least_upper_bound(X_49,a))) != greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_49,a)),b))
| greatest_lower_bound(b,least_upper_bound(X_49,a)) != b
| multiply(inverse(least_upper_bound(X_49,a)),b) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_49,a)),b)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(X_49,a)),greatest_lower_bound(b,least_upper_bound(X_49,a))),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_49,a)),b))) ),[0,1],$fot(b)]]) ).
cnf(refute_0_108,plain,
( multiply(inverse(least_upper_bound(X_49,a)),greatest_lower_bound(b,least_upper_bound(X_49,a))) != greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_49,a)),b))
| multiply(inverse(least_upper_bound(X_49,a)),b) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_49,a)),b)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(X_49,a)),b) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
multiply(inverse(least_upper_bound(X_49,a)),b) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_49,a)),b)),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_49,a)),greatest_lower_bound(b,least_upper_bound(X_49,a))),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_49,a)),b))) )],[refute_0_73,refute_0_108]) ).
cnf(refute_0_110,plain,
multiply(inverse(least_upper_bound(X_253,a)),b) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_253,a)),b)),
inference(subst,[],[refute_0_109:[bind(X_49,$fot(X_253))]]) ).
cnf(refute_0_111,plain,
( multiply(inverse(least_upper_bound(X_253,a)),b) != greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_253,a)),b))
| greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_253,a)),b)) = multiply(inverse(least_upper_bound(X_253,a)),b) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(inverse(least_upper_bound(X_253,a)),b))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_253,a)),b))))]]) ).
cnf(refute_0_112,plain,
greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_253,a)),b)) = multiply(inverse(least_upper_bound(X_253,a)),b),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_253,a)),b),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_253,a)),b))) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
( greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_253,a)),b)) != multiply(inverse(least_upper_bound(X_253,a)),b)
| least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_253,a)),b))) != identity
| least_upper_bound(identity,multiply(inverse(least_upper_bound(X_253,a)),b)) = identity ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_253,a)),b))),identity) ),[0,1],$fot(multiply(inverse(least_upper_bound(X_253,a)),b))]]) ).
cnf(refute_0_114,plain,
( least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_253,a)),b))) != identity
| least_upper_bound(identity,multiply(inverse(least_upper_bound(X_253,a)),b)) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_253,a)),b)),multiply(inverse(least_upper_bound(X_253,a)),b)) )],[refute_0_112,refute_0_113]) ).
cnf(refute_0_115,plain,
least_upper_bound(identity,multiply(inverse(least_upper_bound(X_253,a)),b)) = identity,
inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_253,a)),b))),identity) )],[refute_0_61,refute_0_114]) ).
cnf(refute_0_116,plain,
least_upper_bound(identity,multiply(inverse(least_upper_bound(X_254,a)),b)) = identity,
inference(subst,[],[refute_0_115:[bind(X_253,$fot(X_254))]]) ).
cnf(refute_0_117,plain,
( b != multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_254,a)),inverse(b))),least_upper_bound(identity,multiply(inverse(least_upper_bound(X_254,a)),b)))
| least_upper_bound(identity,multiply(inverse(least_upper_bound(X_254,a)),b)) != identity
| b = multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_254,a)),inverse(b))),identity) ),
introduced(tautology,[equality,[$cnf( $equal(b,multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_254,a)),inverse(b))),least_upper_bound(identity,multiply(inverse(least_upper_bound(X_254,a)),b)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_118,plain,
( b != multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_254,a)),inverse(b))),least_upper_bound(identity,multiply(inverse(least_upper_bound(X_254,a)),b)))
| b = multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_254,a)),inverse(b))),identity) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(least_upper_bound(X_254,a)),b)),identity) )],[refute_0_116,refute_0_117]) ).
cnf(refute_0_119,plain,
b = multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_254,a)),inverse(b))),identity),
inference(resolve,[$cnf( $equal(b,multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_254,a)),inverse(b))),least_upper_bound(identity,multiply(inverse(least_upper_bound(X_254,a)),b)))) )],[refute_0_60,refute_0_118]) ).
cnf(refute_0_120,plain,
least_upper_bound(X_8,greatest_lower_bound(X_8,X_9)) = X_8,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_8)),bind(Y,$fot(X_9))]]) ).
cnf(refute_0_121,plain,
greatest_lower_bound(X_9,X_8) = greatest_lower_bound(X_8,X_9),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_9)),bind(Y,$fot(X_8))]]) ).
cnf(refute_0_122,plain,
( greatest_lower_bound(X_9,X_8) != greatest_lower_bound(X_8,X_9)
| greatest_lower_bound(X_8,X_9) = greatest_lower_bound(X_9,X_8) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(greatest_lower_bound(X_9,X_8))),bind(Y0,$fot(greatest_lower_bound(X_8,X_9)))]]) ).
cnf(refute_0_123,plain,
greatest_lower_bound(X_8,X_9) = greatest_lower_bound(X_9,X_8),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_9,X_8),greatest_lower_bound(X_8,X_9)) )],[refute_0_121,refute_0_122]) ).
cnf(refute_0_124,plain,
( greatest_lower_bound(X_8,X_9) != greatest_lower_bound(X_9,X_8)
| least_upper_bound(X_8,greatest_lower_bound(X_8,X_9)) != X_8
| least_upper_bound(X_8,greatest_lower_bound(X_9,X_8)) = X_8 ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_8,greatest_lower_bound(X_8,X_9)),X_8) ),[0,1],$fot(greatest_lower_bound(X_9,X_8))]]) ).
cnf(refute_0_125,plain,
( least_upper_bound(X_8,greatest_lower_bound(X_8,X_9)) != X_8
| least_upper_bound(X_8,greatest_lower_bound(X_9,X_8)) = X_8 ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_8,X_9),greatest_lower_bound(X_9,X_8)) )],[refute_0_123,refute_0_124]) ).
cnf(refute_0_126,plain,
least_upper_bound(X_8,greatest_lower_bound(X_9,X_8)) = X_8,
inference(resolve,[$cnf( $equal(least_upper_bound(X_8,greatest_lower_bound(X_8,X_9)),X_8) )],[refute_0_120,refute_0_125]) ).
cnf(refute_0_127,plain,
least_upper_bound(least_upper_bound(X_31,X_32),greatest_lower_bound(X_9,least_upper_bound(X_31,X_32))) = least_upper_bound(X_31,X_32),
inference(subst,[],[refute_0_126:[bind(X_8,$fot(least_upper_bound(X_31,X_32)))]]) ).
cnf(refute_0_128,plain,
least_upper_bound(X_31,least_upper_bound(X_32,greatest_lower_bound(X_9,least_upper_bound(X_31,X_32)))) = least_upper_bound(least_upper_bound(X_31,X_32),greatest_lower_bound(X_9,least_upper_bound(X_31,X_32))),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_31)),bind(Y,$fot(X_32)),bind(Z,$fot(greatest_lower_bound(X_9,least_upper_bound(X_31,X_32))))]]) ).
cnf(refute_0_129,plain,
( least_upper_bound(X_31,least_upper_bound(X_32,greatest_lower_bound(X_9,least_upper_bound(X_31,X_32)))) != least_upper_bound(least_upper_bound(X_31,X_32),greatest_lower_bound(X_9,least_upper_bound(X_31,X_32)))
| least_upper_bound(least_upper_bound(X_31,X_32),greatest_lower_bound(X_9,least_upper_bound(X_31,X_32))) = least_upper_bound(X_31,least_upper_bound(X_32,greatest_lower_bound(X_9,least_upper_bound(X_31,X_32)))) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(least_upper_bound(X_31,least_upper_bound(X_32,greatest_lower_bound(X_9,least_upper_bound(X_31,X_32)))))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X_31,X_32),greatest_lower_bound(X_9,least_upper_bound(X_31,X_32)))))]]) ).
cnf(refute_0_130,plain,
least_upper_bound(least_upper_bound(X_31,X_32),greatest_lower_bound(X_9,least_upper_bound(X_31,X_32))) = least_upper_bound(X_31,least_upper_bound(X_32,greatest_lower_bound(X_9,least_upper_bound(X_31,X_32)))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_31,least_upper_bound(X_32,greatest_lower_bound(X_9,least_upper_bound(X_31,X_32)))),least_upper_bound(least_upper_bound(X_31,X_32),greatest_lower_bound(X_9,least_upper_bound(X_31,X_32)))) )],[refute_0_128,refute_0_129]) ).
cnf(refute_0_131,plain,
( least_upper_bound(least_upper_bound(X_31,X_32),greatest_lower_bound(X_9,least_upper_bound(X_31,X_32))) != least_upper_bound(X_31,X_32)
| least_upper_bound(least_upper_bound(X_31,X_32),greatest_lower_bound(X_9,least_upper_bound(X_31,X_32))) != least_upper_bound(X_31,least_upper_bound(X_32,greatest_lower_bound(X_9,least_upper_bound(X_31,X_32))))
| least_upper_bound(X_31,least_upper_bound(X_32,greatest_lower_bound(X_9,least_upper_bound(X_31,X_32)))) = least_upper_bound(X_31,X_32) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_31,X_32),greatest_lower_bound(X_9,least_upper_bound(X_31,X_32))),least_upper_bound(X_31,X_32)) ),[0],$fot(least_upper_bound(X_31,least_upper_bound(X_32,greatest_lower_bound(X_9,least_upper_bound(X_31,X_32)))))]]) ).
cnf(refute_0_132,plain,
( least_upper_bound(least_upper_bound(X_31,X_32),greatest_lower_bound(X_9,least_upper_bound(X_31,X_32))) != least_upper_bound(X_31,X_32)
| least_upper_bound(X_31,least_upper_bound(X_32,greatest_lower_bound(X_9,least_upper_bound(X_31,X_32)))) = least_upper_bound(X_31,X_32) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_31,X_32),greatest_lower_bound(X_9,least_upper_bound(X_31,X_32))),least_upper_bound(X_31,least_upper_bound(X_32,greatest_lower_bound(X_9,least_upper_bound(X_31,X_32))))) )],[refute_0_130,refute_0_131]) ).
cnf(refute_0_133,plain,
least_upper_bound(X_31,least_upper_bound(X_32,greatest_lower_bound(X_9,least_upper_bound(X_31,X_32)))) = least_upper_bound(X_31,X_32),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_31,X_32),greatest_lower_bound(X_9,least_upper_bound(X_31,X_32))),least_upper_bound(X_31,X_32)) )],[refute_0_127,refute_0_132]) ).
cnf(refute_0_134,plain,
least_upper_bound(X_31,least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),greatest_lower_bound(X_9,least_upper_bound(X_31,least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))))))) = least_upper_bound(X_31,least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)))),
inference(subst,[],[refute_0_133:[bind(X_32,$fot(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)))))]]) ).
cnf(refute_0_135,plain,
least_upper_bound(X_31,least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)))) = least_upper_bound(X_31,X_240),
inference(subst,[],[refute_0_133:[bind(X_32,$fot(X_240)),bind(X_9,$fot(X_241))]]) ).
cnf(refute_0_136,plain,
( least_upper_bound(X_31,least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)))) != least_upper_bound(X_31,X_240)
| least_upper_bound(X_31,least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),greatest_lower_bound(X_9,least_upper_bound(X_31,least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))))))) != least_upper_bound(X_31,least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))))
| least_upper_bound(X_31,least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240)))) = least_upper_bound(X_31,least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_31,least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),greatest_lower_bound(X_9,least_upper_bound(X_31,least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))))))),least_upper_bound(X_31,least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))))) ),[0,1,1,1],$fot(least_upper_bound(X_31,X_240))]]) ).
cnf(refute_0_137,plain,
( least_upper_bound(X_31,least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),greatest_lower_bound(X_9,least_upper_bound(X_31,least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))))))) != least_upper_bound(X_31,least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))))
| least_upper_bound(X_31,least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240)))) = least_upper_bound(X_31,least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_31,least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)))),least_upper_bound(X_31,X_240)) )],[refute_0_135,refute_0_136]) ).
cnf(refute_0_138,plain,
least_upper_bound(X_31,least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240)))) = least_upper_bound(X_31,least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_31,least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),greatest_lower_bound(X_9,least_upper_bound(X_31,least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))))))),least_upper_bound(X_31,least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))))) )],[refute_0_134,refute_0_137]) ).
cnf(refute_0_139,plain,
( least_upper_bound(X,least_upper_bound(Y,Z)) != least_upper_bound(least_upper_bound(X,Y),Z)
| least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(Y,Z)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X,Y),Z)))]]) ).
cnf(refute_0_140,plain,
least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,Z)),least_upper_bound(least_upper_bound(X,Y),Z)) )],[associativity_of_lub,refute_0_139]) ).
cnf(refute_0_141,plain,
least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240))) = least_upper_bound(X_240,least_upper_bound(greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240)))),
inference(subst,[],[refute_0_140:[bind(X,$fot(X_240)),bind(Y,$fot(greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)))),bind(Z,$fot(greatest_lower_bound(X_9,least_upper_bound(X_31,X_240))))]]) ).
cnf(refute_0_142,plain,
least_upper_bound(X_31,least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240)))) = least_upper_bound(X_31,least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240)))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_31,least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240)))))]]) ).
cnf(refute_0_143,plain,
( least_upper_bound(X_31,least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240)))) != least_upper_bound(X_31,least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240))))
| least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240))) != least_upper_bound(X_240,least_upper_bound(greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240))))
| least_upper_bound(X_31,least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240)))) = least_upper_bound(X_31,least_upper_bound(X_240,least_upper_bound(greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240))))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_31,least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240)))),least_upper_bound(X_31,least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240))))) ),[1,1],$fot(least_upper_bound(X_240,least_upper_bound(greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240)))))]]) ).
cnf(refute_0_144,plain,
( least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240))) != least_upper_bound(X_240,least_upper_bound(greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240))))
| least_upper_bound(X_31,least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240)))) = least_upper_bound(X_31,least_upper_bound(X_240,least_upper_bound(greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240))))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_31,least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240)))),least_upper_bound(X_31,least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240))))) )],[refute_0_142,refute_0_143]) ).
cnf(refute_0_145,plain,
least_upper_bound(X_31,least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240)))) = least_upper_bound(X_31,least_upper_bound(X_240,least_upper_bound(greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240))))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240))),least_upper_bound(X_240,least_upper_bound(greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240))))) )],[refute_0_141,refute_0_144]) ).
cnf(refute_0_146,plain,
( least_upper_bound(X_31,least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240)))) != least_upper_bound(X_31,least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))))
| least_upper_bound(X_31,least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240)))) != least_upper_bound(X_31,least_upper_bound(X_240,least_upper_bound(greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240)))))
| least_upper_bound(X_31,least_upper_bound(X_240,least_upper_bound(greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240))))) = least_upper_bound(X_31,least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_31,least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240)))),least_upper_bound(X_31,least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))))) ),[0],$fot(least_upper_bound(X_31,least_upper_bound(X_240,least_upper_bound(greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240))))))]]) ).
cnf(refute_0_147,plain,
( least_upper_bound(X_31,least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240)))) != least_upper_bound(X_31,least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))))
| least_upper_bound(X_31,least_upper_bound(X_240,least_upper_bound(greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240))))) = least_upper_bound(X_31,least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_31,least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240)))),least_upper_bound(X_31,least_upper_bound(X_240,least_upper_bound(greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240)))))) )],[refute_0_145,refute_0_146]) ).
cnf(refute_0_148,plain,
( least_upper_bound(X_31,least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)))) != least_upper_bound(X_31,X_240)
| least_upper_bound(X_31,least_upper_bound(X_240,least_upper_bound(greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240))))) != least_upper_bound(X_31,least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))))
| least_upper_bound(X_31,least_upper_bound(X_240,least_upper_bound(greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240))))) = least_upper_bound(X_31,X_240) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_31,least_upper_bound(X_240,least_upper_bound(greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240))))),least_upper_bound(X_31,least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))))) ),[1],$fot(least_upper_bound(X_31,X_240))]]) ).
cnf(refute_0_149,plain,
( least_upper_bound(X_31,least_upper_bound(X_240,least_upper_bound(greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240))))) != least_upper_bound(X_31,least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))))
| least_upper_bound(X_31,least_upper_bound(X_240,least_upper_bound(greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240))))) = least_upper_bound(X_31,X_240) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_31,least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)))),least_upper_bound(X_31,X_240)) )],[refute_0_135,refute_0_148]) ).
cnf(refute_0_150,plain,
( least_upper_bound(X_31,least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240)))) != least_upper_bound(X_31,least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))))
| least_upper_bound(X_31,least_upper_bound(X_240,least_upper_bound(greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240))))) = least_upper_bound(X_31,X_240) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_31,least_upper_bound(X_240,least_upper_bound(greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240))))),least_upper_bound(X_31,least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))))) )],[refute_0_147,refute_0_149]) ).
cnf(refute_0_151,plain,
least_upper_bound(X_31,least_upper_bound(X_240,least_upper_bound(greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240))))) = least_upper_bound(X_31,X_240),
inference(resolve,[$cnf( $equal(least_upper_bound(X_31,least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240)))),least_upper_bound(X_31,least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))))) )],[refute_0_138,refute_0_150]) ).
cnf(refute_0_152,plain,
least_upper_bound(X_8,greatest_lower_bound(greatest_lower_bound(X_22,X_23),X_8)) = X_8,
inference(subst,[],[refute_0_126:[bind(X_9,$fot(greatest_lower_bound(X_22,X_23)))]]) ).
cnf(refute_0_153,plain,
greatest_lower_bound(X_22,greatest_lower_bound(X_23,X_8)) = greatest_lower_bound(greatest_lower_bound(X_22,X_23),X_8),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_22)),bind(Y,$fot(X_23)),bind(Z,$fot(X_8))]]) ).
cnf(refute_0_154,plain,
( greatest_lower_bound(X_22,greatest_lower_bound(X_23,X_8)) != greatest_lower_bound(greatest_lower_bound(X_22,X_23),X_8)
| greatest_lower_bound(greatest_lower_bound(X_22,X_23),X_8) = greatest_lower_bound(X_22,greatest_lower_bound(X_23,X_8)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(greatest_lower_bound(X_22,greatest_lower_bound(X_23,X_8)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X_22,X_23),X_8)))]]) ).
cnf(refute_0_155,plain,
greatest_lower_bound(greatest_lower_bound(X_22,X_23),X_8) = greatest_lower_bound(X_22,greatest_lower_bound(X_23,X_8)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_22,greatest_lower_bound(X_23,X_8)),greatest_lower_bound(greatest_lower_bound(X_22,X_23),X_8)) )],[refute_0_153,refute_0_154]) ).
cnf(refute_0_156,plain,
( greatest_lower_bound(greatest_lower_bound(X_22,X_23),X_8) != greatest_lower_bound(X_22,greatest_lower_bound(X_23,X_8))
| least_upper_bound(X_8,greatest_lower_bound(greatest_lower_bound(X_22,X_23),X_8)) != X_8
| least_upper_bound(X_8,greatest_lower_bound(X_22,greatest_lower_bound(X_23,X_8))) = X_8 ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_8,greatest_lower_bound(greatest_lower_bound(X_22,X_23),X_8)),X_8) ),[0,1],$fot(greatest_lower_bound(X_22,greatest_lower_bound(X_23,X_8)))]]) ).
cnf(refute_0_157,plain,
( least_upper_bound(X_8,greatest_lower_bound(greatest_lower_bound(X_22,X_23),X_8)) != X_8
| least_upper_bound(X_8,greatest_lower_bound(X_22,greatest_lower_bound(X_23,X_8))) = X_8 ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_22,X_23),X_8),greatest_lower_bound(X_22,greatest_lower_bound(X_23,X_8))) )],[refute_0_155,refute_0_156]) ).
cnf(refute_0_158,plain,
least_upper_bound(X_8,greatest_lower_bound(X_22,greatest_lower_bound(X_23,X_8))) = X_8,
inference(resolve,[$cnf( $equal(least_upper_bound(X_8,greatest_lower_bound(greatest_lower_bound(X_22,X_23),X_8)),X_8) )],[refute_0_152,refute_0_157]) ).
cnf(refute_0_159,plain,
least_upper_bound(least_upper_bound(X_11,X_38),greatest_lower_bound(X_138,greatest_lower_bound(least_upper_bound(X_38,X_11),least_upper_bound(X_11,X_38)))) = least_upper_bound(X_11,X_38),
inference(subst,[],[refute_0_158:[bind(X_22,$fot(X_138)),bind(X_23,$fot(least_upper_bound(X_38,X_11))),bind(X_8,$fot(least_upper_bound(X_11,X_38)))]]) ).
cnf(refute_0_160,plain,
greatest_lower_bound(least_upper_bound(X_38,X_11),least_upper_bound(X_11,least_upper_bound(X_38,X_11))) = least_upper_bound(X_38,X_11),
inference(subst,[],[refute_0_93:[bind(X_10,$fot(least_upper_bound(X_38,X_11)))]]) ).
cnf(refute_0_161,plain,
least_upper_bound(least_upper_bound(X_19,Y),greatest_lower_bound(X_19,least_upper_bound(X_19,Y))) = least_upper_bound(X_19,Y),
inference(subst,[],[refute_0_126:[bind(X_8,$fot(least_upper_bound(X_19,Y))),bind(X_9,$fot(X_19))]]) ).
cnf(refute_0_162,plain,
greatest_lower_bound(X_19,least_upper_bound(X_19,Y)) = X_19,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_19))]]) ).
cnf(refute_0_163,plain,
( greatest_lower_bound(X_19,least_upper_bound(X_19,Y)) != X_19
| least_upper_bound(least_upper_bound(X_19,Y),greatest_lower_bound(X_19,least_upper_bound(X_19,Y))) != least_upper_bound(X_19,Y)
| least_upper_bound(least_upper_bound(X_19,Y),X_19) = least_upper_bound(X_19,Y) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_19,Y),greatest_lower_bound(X_19,least_upper_bound(X_19,Y))),least_upper_bound(X_19,Y)) ),[0,1],$fot(X_19)]]) ).
cnf(refute_0_164,plain,
( least_upper_bound(least_upper_bound(X_19,Y),greatest_lower_bound(X_19,least_upper_bound(X_19,Y))) != least_upper_bound(X_19,Y)
| least_upper_bound(least_upper_bound(X_19,Y),X_19) = least_upper_bound(X_19,Y) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_19,least_upper_bound(X_19,Y)),X_19) )],[refute_0_162,refute_0_163]) ).
cnf(refute_0_165,plain,
least_upper_bound(least_upper_bound(X_19,Y),X_19) = least_upper_bound(X_19,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_19,Y),greatest_lower_bound(X_19,least_upper_bound(X_19,Y))),least_upper_bound(X_19,Y)) )],[refute_0_161,refute_0_164]) ).
cnf(refute_0_166,plain,
least_upper_bound(least_upper_bound(X_19,Y),X_19) = least_upper_bound(X_19,least_upper_bound(Y,X_19)),
inference(subst,[],[refute_0_140:[bind(X,$fot(X_19)),bind(Z,$fot(X_19))]]) ).
cnf(refute_0_167,plain,
( least_upper_bound(least_upper_bound(X_19,Y),X_19) != least_upper_bound(X_19,Y)
| least_upper_bound(least_upper_bound(X_19,Y),X_19) != least_upper_bound(X_19,least_upper_bound(Y,X_19))
| least_upper_bound(X_19,least_upper_bound(Y,X_19)) = least_upper_bound(X_19,Y) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_19,Y),X_19),least_upper_bound(X_19,Y)) ),[0],$fot(least_upper_bound(X_19,least_upper_bound(Y,X_19)))]]) ).
cnf(refute_0_168,plain,
( least_upper_bound(least_upper_bound(X_19,Y),X_19) != least_upper_bound(X_19,Y)
| least_upper_bound(X_19,least_upper_bound(Y,X_19)) = least_upper_bound(X_19,Y) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_19,Y),X_19),least_upper_bound(X_19,least_upper_bound(Y,X_19))) )],[refute_0_166,refute_0_167]) ).
cnf(refute_0_169,plain,
least_upper_bound(X_19,least_upper_bound(Y,X_19)) = least_upper_bound(X_19,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_19,Y),X_19),least_upper_bound(X_19,Y)) )],[refute_0_165,refute_0_168]) ).
cnf(refute_0_170,plain,
least_upper_bound(X_11,least_upper_bound(X_38,X_11)) = least_upper_bound(X_11,X_38),
inference(subst,[],[refute_0_169:[bind(Y,$fot(X_38)),bind(X_19,$fot(X_11))]]) ).
cnf(refute_0_171,plain,
( greatest_lower_bound(least_upper_bound(X_38,X_11),least_upper_bound(X_11,least_upper_bound(X_38,X_11))) != least_upper_bound(X_38,X_11)
| least_upper_bound(X_11,least_upper_bound(X_38,X_11)) != least_upper_bound(X_11,X_38)
| greatest_lower_bound(least_upper_bound(X_38,X_11),least_upper_bound(X_11,X_38)) = least_upper_bound(X_38,X_11) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_38,X_11),least_upper_bound(X_11,least_upper_bound(X_38,X_11))),least_upper_bound(X_38,X_11)) ),[0,1],$fot(least_upper_bound(X_11,X_38))]]) ).
cnf(refute_0_172,plain,
( greatest_lower_bound(least_upper_bound(X_38,X_11),least_upper_bound(X_11,least_upper_bound(X_38,X_11))) != least_upper_bound(X_38,X_11)
| greatest_lower_bound(least_upper_bound(X_38,X_11),least_upper_bound(X_11,X_38)) = least_upper_bound(X_38,X_11) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_11,least_upper_bound(X_38,X_11)),least_upper_bound(X_11,X_38)) )],[refute_0_170,refute_0_171]) ).
cnf(refute_0_173,plain,
greatest_lower_bound(least_upper_bound(X_38,X_11),least_upper_bound(X_11,X_38)) = least_upper_bound(X_38,X_11),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_38,X_11),least_upper_bound(X_11,least_upper_bound(X_38,X_11))),least_upper_bound(X_38,X_11)) )],[refute_0_160,refute_0_172]) ).
cnf(refute_0_174,plain,
( greatest_lower_bound(least_upper_bound(X_38,X_11),least_upper_bound(X_11,X_38)) != least_upper_bound(X_38,X_11)
| least_upper_bound(least_upper_bound(X_11,X_38),greatest_lower_bound(X_138,greatest_lower_bound(least_upper_bound(X_38,X_11),least_upper_bound(X_11,X_38)))) != least_upper_bound(X_11,X_38)
| least_upper_bound(least_upper_bound(X_11,X_38),greatest_lower_bound(X_138,least_upper_bound(X_38,X_11))) = least_upper_bound(X_11,X_38) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_11,X_38),greatest_lower_bound(X_138,greatest_lower_bound(least_upper_bound(X_38,X_11),least_upper_bound(X_11,X_38)))),least_upper_bound(X_11,X_38)) ),[0,1,1],$fot(least_upper_bound(X_38,X_11))]]) ).
cnf(refute_0_175,plain,
( least_upper_bound(least_upper_bound(X_11,X_38),greatest_lower_bound(X_138,greatest_lower_bound(least_upper_bound(X_38,X_11),least_upper_bound(X_11,X_38)))) != least_upper_bound(X_11,X_38)
| least_upper_bound(least_upper_bound(X_11,X_38),greatest_lower_bound(X_138,least_upper_bound(X_38,X_11))) = least_upper_bound(X_11,X_38) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_38,X_11),least_upper_bound(X_11,X_38)),least_upper_bound(X_38,X_11)) )],[refute_0_173,refute_0_174]) ).
cnf(refute_0_176,plain,
least_upper_bound(least_upper_bound(X_11,X_38),greatest_lower_bound(X_138,least_upper_bound(X_38,X_11))) = least_upper_bound(X_11,X_38),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_11,X_38),greatest_lower_bound(X_138,greatest_lower_bound(least_upper_bound(X_38,X_11),least_upper_bound(X_11,X_38)))),least_upper_bound(X_11,X_38)) )],[refute_0_159,refute_0_175]) ).
cnf(refute_0_177,plain,
least_upper_bound(least_upper_bound(X_11,X_38),greatest_lower_bound(X_138,least_upper_bound(X_38,X_11))) = least_upper_bound(X_11,least_upper_bound(X_38,greatest_lower_bound(X_138,least_upper_bound(X_38,X_11)))),
inference(subst,[],[refute_0_140:[bind(X,$fot(X_11)),bind(Y,$fot(X_38)),bind(Z,$fot(greatest_lower_bound(X_138,least_upper_bound(X_38,X_11))))]]) ).
cnf(refute_0_178,plain,
( least_upper_bound(least_upper_bound(X_11,X_38),greatest_lower_bound(X_138,least_upper_bound(X_38,X_11))) != least_upper_bound(X_11,X_38)
| least_upper_bound(least_upper_bound(X_11,X_38),greatest_lower_bound(X_138,least_upper_bound(X_38,X_11))) != least_upper_bound(X_11,least_upper_bound(X_38,greatest_lower_bound(X_138,least_upper_bound(X_38,X_11))))
| least_upper_bound(X_11,least_upper_bound(X_38,greatest_lower_bound(X_138,least_upper_bound(X_38,X_11)))) = least_upper_bound(X_11,X_38) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_11,X_38),greatest_lower_bound(X_138,least_upper_bound(X_38,X_11))),least_upper_bound(X_11,X_38)) ),[0],$fot(least_upper_bound(X_11,least_upper_bound(X_38,greatest_lower_bound(X_138,least_upper_bound(X_38,X_11)))))]]) ).
cnf(refute_0_179,plain,
( least_upper_bound(least_upper_bound(X_11,X_38),greatest_lower_bound(X_138,least_upper_bound(X_38,X_11))) != least_upper_bound(X_11,X_38)
| least_upper_bound(X_11,least_upper_bound(X_38,greatest_lower_bound(X_138,least_upper_bound(X_38,X_11)))) = least_upper_bound(X_11,X_38) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_11,X_38),greatest_lower_bound(X_138,least_upper_bound(X_38,X_11))),least_upper_bound(X_11,least_upper_bound(X_38,greatest_lower_bound(X_138,least_upper_bound(X_38,X_11))))) )],[refute_0_177,refute_0_178]) ).
cnf(refute_0_180,plain,
least_upper_bound(X_11,least_upper_bound(X_38,greatest_lower_bound(X_138,least_upper_bound(X_38,X_11)))) = least_upper_bound(X_11,X_38),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_11,X_38),greatest_lower_bound(X_138,least_upper_bound(X_38,X_11))),least_upper_bound(X_11,X_38)) )],[refute_0_176,refute_0_179]) ).
cnf(refute_0_181,plain,
least_upper_bound(X_240,least_upper_bound(X_31,greatest_lower_bound(X_9,least_upper_bound(X_31,X_240)))) = least_upper_bound(X_240,X_31),
inference(subst,[],[refute_0_180:[bind(X_11,$fot(X_240)),bind(X_138,$fot(X_9)),bind(X_38,$fot(X_31))]]) ).
cnf(refute_0_182,plain,
least_upper_bound(X,least_upper_bound(X_31,X_32)) = least_upper_bound(least_upper_bound(X_31,X_32),X),
inference(subst,[],[symmetry_of_lub:[bind(Y,$fot(least_upper_bound(X_31,X_32)))]]) ).
cnf(refute_0_183,plain,
least_upper_bound(X_31,least_upper_bound(X_32,X)) = least_upper_bound(least_upper_bound(X_31,X_32),X),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_31)),bind(Y,$fot(X_32)),bind(Z,$fot(X))]]) ).
cnf(refute_0_184,plain,
( least_upper_bound(X_31,least_upper_bound(X_32,X)) != least_upper_bound(least_upper_bound(X_31,X_32),X)
| least_upper_bound(least_upper_bound(X_31,X_32),X) = least_upper_bound(X_31,least_upper_bound(X_32,X)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(least_upper_bound(X_31,least_upper_bound(X_32,X)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X_31,X_32),X)))]]) ).
cnf(refute_0_185,plain,
least_upper_bound(least_upper_bound(X_31,X_32),X) = least_upper_bound(X_31,least_upper_bound(X_32,X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_31,least_upper_bound(X_32,X)),least_upper_bound(least_upper_bound(X_31,X_32),X)) )],[refute_0_183,refute_0_184]) ).
cnf(refute_0_186,plain,
( least_upper_bound(X,least_upper_bound(X_31,X_32)) != least_upper_bound(least_upper_bound(X_31,X_32),X)
| least_upper_bound(least_upper_bound(X_31,X_32),X) != least_upper_bound(X_31,least_upper_bound(X_32,X))
| least_upper_bound(X,least_upper_bound(X_31,X_32)) = least_upper_bound(X_31,least_upper_bound(X_32,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,least_upper_bound(X_31,X_32)),least_upper_bound(X_31,least_upper_bound(X_32,X))) ),[0],$fot(least_upper_bound(least_upper_bound(X_31,X_32),X))]]) ).
cnf(refute_0_187,plain,
( least_upper_bound(X,least_upper_bound(X_31,X_32)) != least_upper_bound(least_upper_bound(X_31,X_32),X)
| least_upper_bound(X,least_upper_bound(X_31,X_32)) = least_upper_bound(X_31,least_upper_bound(X_32,X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_31,X_32),X),least_upper_bound(X_31,least_upper_bound(X_32,X))) )],[refute_0_185,refute_0_186]) ).
cnf(refute_0_188,plain,
least_upper_bound(X,least_upper_bound(X_31,X_32)) = least_upper_bound(X_31,least_upper_bound(X_32,X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_31,X_32)),least_upper_bound(least_upper_bound(X_31,X_32),X)) )],[refute_0_182,refute_0_187]) ).
cnf(refute_0_189,plain,
least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_38,Y))) = least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_38,Y)),
inference(subst,[],[associativity_of_lub:[bind(Z,$fot(least_upper_bound(X_38,Y)))]]) ).
cnf(refute_0_190,plain,
least_upper_bound(Y,least_upper_bound(X_38,Y)) = least_upper_bound(Y,X_38),
inference(subst,[],[refute_0_169:[bind(Y,$fot(X_38)),bind(X_19,$fot(Y))]]) ).
cnf(refute_0_191,plain,
( least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_38,Y))) != least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_38,Y))
| least_upper_bound(Y,least_upper_bound(X_38,Y)) != least_upper_bound(Y,X_38)
| least_upper_bound(X,least_upper_bound(Y,X_38)) = least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_38,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_38,Y))),least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_38,Y))) ),[0,1],$fot(least_upper_bound(Y,X_38))]]) ).
cnf(refute_0_192,plain,
( least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_38,Y))) != least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_38,Y))
| least_upper_bound(X,least_upper_bound(Y,X_38)) = least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_38,Y)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_38,Y)),least_upper_bound(Y,X_38)) )],[refute_0_190,refute_0_191]) ).
cnf(refute_0_193,plain,
least_upper_bound(X,least_upper_bound(Y,X_38)) = least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_38,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_38,Y))),least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_38,Y))) )],[refute_0_189,refute_0_192]) ).
cnf(refute_0_194,plain,
least_upper_bound(X,least_upper_bound(least_upper_bound(X_38,X),Z)) = least_upper_bound(least_upper_bound(X,least_upper_bound(X_38,X)),Z),
inference(subst,[],[associativity_of_lub:[bind(Y,$fot(least_upper_bound(X_38,X)))]]) ).
cnf(refute_0_195,plain,
least_upper_bound(X,least_upper_bound(X_38,X)) = least_upper_bound(X,X_38),
inference(subst,[],[refute_0_169:[bind(Y,$fot(X_38)),bind(X_19,$fot(X))]]) ).
cnf(refute_0_196,plain,
( least_upper_bound(X,least_upper_bound(X_38,X)) != least_upper_bound(X,X_38)
| least_upper_bound(X,least_upper_bound(least_upper_bound(X_38,X),Z)) != least_upper_bound(least_upper_bound(X,least_upper_bound(X_38,X)),Z)
| least_upper_bound(X,least_upper_bound(least_upper_bound(X_38,X),Z)) = least_upper_bound(least_upper_bound(X,X_38),Z) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(least_upper_bound(X_38,X),Z)),least_upper_bound(least_upper_bound(X,least_upper_bound(X_38,X)),Z)) ),[1,0],$fot(least_upper_bound(X,X_38))]]) ).
cnf(refute_0_197,plain,
( least_upper_bound(X,least_upper_bound(least_upper_bound(X_38,X),Z)) != least_upper_bound(least_upper_bound(X,least_upper_bound(X_38,X)),Z)
| least_upper_bound(X,least_upper_bound(least_upper_bound(X_38,X),Z)) = least_upper_bound(least_upper_bound(X,X_38),Z) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_38,X)),least_upper_bound(X,X_38)) )],[refute_0_195,refute_0_196]) ).
cnf(refute_0_198,plain,
least_upper_bound(X,least_upper_bound(least_upper_bound(X_38,X),Z)) = least_upper_bound(least_upper_bound(X,X_38),Z),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(least_upper_bound(X_38,X),Z)),least_upper_bound(least_upper_bound(X,least_upper_bound(X_38,X)),Z)) )],[refute_0_194,refute_0_197]) ).
cnf(refute_0_199,plain,
least_upper_bound(least_upper_bound(X_38,X),Z) = least_upper_bound(X_38,least_upper_bound(X,Z)),
inference(subst,[],[refute_0_140:[bind(X,$fot(X_38)),bind(Y,$fot(X))]]) ).
cnf(refute_0_200,plain,
least_upper_bound(X,least_upper_bound(least_upper_bound(X_38,X),Z)) = least_upper_bound(X,least_upper_bound(least_upper_bound(X_38,X),Z)),
introduced(tautology,[refl,[$fot(least_upper_bound(X,least_upper_bound(least_upper_bound(X_38,X),Z)))]]) ).
cnf(refute_0_201,plain,
( least_upper_bound(X,least_upper_bound(least_upper_bound(X_38,X),Z)) != least_upper_bound(X,least_upper_bound(least_upper_bound(X_38,X),Z))
| least_upper_bound(least_upper_bound(X_38,X),Z) != least_upper_bound(X_38,least_upper_bound(X,Z))
| least_upper_bound(X,least_upper_bound(least_upper_bound(X_38,X),Z)) = least_upper_bound(X,least_upper_bound(X_38,least_upper_bound(X,Z))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(least_upper_bound(X_38,X),Z)),least_upper_bound(X,least_upper_bound(least_upper_bound(X_38,X),Z))) ),[1,1],$fot(least_upper_bound(X_38,least_upper_bound(X,Z)))]]) ).
cnf(refute_0_202,plain,
( least_upper_bound(least_upper_bound(X_38,X),Z) != least_upper_bound(X_38,least_upper_bound(X,Z))
| least_upper_bound(X,least_upper_bound(least_upper_bound(X_38,X),Z)) = least_upper_bound(X,least_upper_bound(X_38,least_upper_bound(X,Z))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(least_upper_bound(X_38,X),Z)),least_upper_bound(X,least_upper_bound(least_upper_bound(X_38,X),Z))) )],[refute_0_200,refute_0_201]) ).
cnf(refute_0_203,plain,
least_upper_bound(X,least_upper_bound(least_upper_bound(X_38,X),Z)) = least_upper_bound(X,least_upper_bound(X_38,least_upper_bound(X,Z))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_38,X),Z),least_upper_bound(X_38,least_upper_bound(X,Z))) )],[refute_0_199,refute_0_202]) ).
cnf(refute_0_204,plain,
( least_upper_bound(X,least_upper_bound(least_upper_bound(X_38,X),Z)) != least_upper_bound(X,least_upper_bound(X_38,least_upper_bound(X,Z)))
| least_upper_bound(X,least_upper_bound(least_upper_bound(X_38,X),Z)) != least_upper_bound(least_upper_bound(X,X_38),Z)
| least_upper_bound(X,least_upper_bound(X_38,least_upper_bound(X,Z))) = least_upper_bound(least_upper_bound(X,X_38),Z) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(least_upper_bound(X_38,X),Z)),least_upper_bound(least_upper_bound(X,X_38),Z)) ),[0],$fot(least_upper_bound(X,least_upper_bound(X_38,least_upper_bound(X,Z))))]]) ).
cnf(refute_0_205,plain,
( least_upper_bound(X,least_upper_bound(least_upper_bound(X_38,X),Z)) != least_upper_bound(least_upper_bound(X,X_38),Z)
| least_upper_bound(X,least_upper_bound(X_38,least_upper_bound(X,Z))) = least_upper_bound(least_upper_bound(X,X_38),Z) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(least_upper_bound(X_38,X),Z)),least_upper_bound(X,least_upper_bound(X_38,least_upper_bound(X,Z)))) )],[refute_0_203,refute_0_204]) ).
cnf(refute_0_206,plain,
least_upper_bound(least_upper_bound(X,X_38),Z) = least_upper_bound(X,least_upper_bound(X_38,Z)),
inference(subst,[],[refute_0_140:[bind(Y,$fot(X_38))]]) ).
cnf(refute_0_207,plain,
( least_upper_bound(X,least_upper_bound(X_38,least_upper_bound(X,Z))) != least_upper_bound(least_upper_bound(X,X_38),Z)
| least_upper_bound(least_upper_bound(X,X_38),Z) != least_upper_bound(X,least_upper_bound(X_38,Z))
| least_upper_bound(X,least_upper_bound(X_38,least_upper_bound(X,Z))) = least_upper_bound(X,least_upper_bound(X_38,Z)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,least_upper_bound(X_38,least_upper_bound(X,Z))),least_upper_bound(X,least_upper_bound(X_38,Z))) ),[0],$fot(least_upper_bound(least_upper_bound(X,X_38),Z))]]) ).
cnf(refute_0_208,plain,
( least_upper_bound(X,least_upper_bound(X_38,least_upper_bound(X,Z))) != least_upper_bound(least_upper_bound(X,X_38),Z)
| least_upper_bound(X,least_upper_bound(X_38,least_upper_bound(X,Z))) = least_upper_bound(X,least_upper_bound(X_38,Z)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X,X_38),Z),least_upper_bound(X,least_upper_bound(X_38,Z))) )],[refute_0_206,refute_0_207]) ).
cnf(refute_0_209,plain,
( least_upper_bound(X,least_upper_bound(least_upper_bound(X_38,X),Z)) != least_upper_bound(least_upper_bound(X,X_38),Z)
| least_upper_bound(X,least_upper_bound(X_38,least_upper_bound(X,Z))) = least_upper_bound(X,least_upper_bound(X_38,Z)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_38,least_upper_bound(X,Z))),least_upper_bound(least_upper_bound(X,X_38),Z)) )],[refute_0_205,refute_0_208]) ).
cnf(refute_0_210,plain,
least_upper_bound(X,least_upper_bound(X_38,least_upper_bound(X,Z))) = least_upper_bound(X,least_upper_bound(X_38,Z)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(least_upper_bound(X_38,X),Z)),least_upper_bound(least_upper_bound(X,X_38),Z)) )],[refute_0_198,refute_0_209]) ).
cnf(refute_0_211,plain,
least_upper_bound(Y,least_upper_bound(X,least_upper_bound(Y,X_38))) = least_upper_bound(Y,least_upper_bound(X,X_38)),
inference(subst,[],[refute_0_210:[bind(X,$fot(Y)),bind(Z,$fot(X_38)),bind(X_38,$fot(X))]]) ).
cnf(refute_0_212,plain,
least_upper_bound(least_upper_bound(X,Y),X_38) = least_upper_bound(X,least_upper_bound(Y,X_38)),
inference(subst,[],[refute_0_140:[bind(Z,$fot(X_38))]]) ).
cnf(refute_0_213,plain,
least_upper_bound(Y,least_upper_bound(least_upper_bound(X,Y),X_38)) = least_upper_bound(Y,least_upper_bound(least_upper_bound(X,Y),X_38)),
introduced(tautology,[refl,[$fot(least_upper_bound(Y,least_upper_bound(least_upper_bound(X,Y),X_38)))]]) ).
cnf(refute_0_214,plain,
( least_upper_bound(Y,least_upper_bound(least_upper_bound(X,Y),X_38)) != least_upper_bound(Y,least_upper_bound(least_upper_bound(X,Y),X_38))
| least_upper_bound(least_upper_bound(X,Y),X_38) != least_upper_bound(X,least_upper_bound(Y,X_38))
| least_upper_bound(Y,least_upper_bound(least_upper_bound(X,Y),X_38)) = least_upper_bound(Y,least_upper_bound(X,least_upper_bound(Y,X_38))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(least_upper_bound(X,Y),X_38)),least_upper_bound(Y,least_upper_bound(least_upper_bound(X,Y),X_38))) ),[1,1],$fot(least_upper_bound(X,least_upper_bound(Y,X_38)))]]) ).
cnf(refute_0_215,plain,
( least_upper_bound(least_upper_bound(X,Y),X_38) != least_upper_bound(X,least_upper_bound(Y,X_38))
| least_upper_bound(Y,least_upper_bound(least_upper_bound(X,Y),X_38)) = least_upper_bound(Y,least_upper_bound(X,least_upper_bound(Y,X_38))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(least_upper_bound(X,Y),X_38)),least_upper_bound(Y,least_upper_bound(least_upper_bound(X,Y),X_38))) )],[refute_0_213,refute_0_214]) ).
cnf(refute_0_216,plain,
least_upper_bound(Y,least_upper_bound(least_upper_bound(X,Y),X_38)) = least_upper_bound(Y,least_upper_bound(X,least_upper_bound(Y,X_38))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X,Y),X_38),least_upper_bound(X,least_upper_bound(Y,X_38))) )],[refute_0_212,refute_0_215]) ).
cnf(refute_0_217,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_218,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_19,refute_0_217]) ).
cnf(refute_0_219,plain,
( least_upper_bound(Y,least_upper_bound(X,least_upper_bound(Y,X_38))) != least_upper_bound(Y,least_upper_bound(X,X_38))
| least_upper_bound(Y,least_upper_bound(least_upper_bound(X,Y),X_38)) != least_upper_bound(Y,least_upper_bound(X,least_upper_bound(Y,X_38)))
| least_upper_bound(Y,least_upper_bound(least_upper_bound(X,Y),X_38)) = least_upper_bound(Y,least_upper_bound(X,X_38)) ),
inference(subst,[],[refute_0_218:[bind(X0,$fot(least_upper_bound(Y,least_upper_bound(least_upper_bound(X,Y),X_38)))),bind(Y0,$fot(least_upper_bound(Y,least_upper_bound(X,least_upper_bound(Y,X_38))))),bind(Z0,$fot(least_upper_bound(Y,least_upper_bound(X,X_38))))]]) ).
cnf(refute_0_220,plain,
( least_upper_bound(Y,least_upper_bound(X,least_upper_bound(Y,X_38))) != least_upper_bound(Y,least_upper_bound(X,X_38))
| least_upper_bound(Y,least_upper_bound(least_upper_bound(X,Y),X_38)) = least_upper_bound(Y,least_upper_bound(X,X_38)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(least_upper_bound(X,Y),X_38)),least_upper_bound(Y,least_upper_bound(X,least_upper_bound(Y,X_38)))) )],[refute_0_216,refute_0_219]) ).
cnf(refute_0_221,plain,
least_upper_bound(Y,least_upper_bound(least_upper_bound(X,Y),X_38)) = least_upper_bound(Y,least_upper_bound(X,X_38)),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X,least_upper_bound(Y,X_38))),least_upper_bound(Y,least_upper_bound(X,X_38))) )],[refute_0_211,refute_0_220]) ).
cnf(refute_0_222,plain,
( least_upper_bound(X,least_upper_bound(X_31,X_32)) != least_upper_bound(X_31,least_upper_bound(X_32,X))
| least_upper_bound(X_31,least_upper_bound(X_32,X)) = least_upper_bound(X,least_upper_bound(X_31,X_32)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(X_31,X_32)))),bind(Y0,$fot(least_upper_bound(X_31,least_upper_bound(X_32,X))))]]) ).
cnf(refute_0_223,plain,
least_upper_bound(X_31,least_upper_bound(X_32,X)) = least_upper_bound(X,least_upper_bound(X_31,X_32)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_31,X_32)),least_upper_bound(X_31,least_upper_bound(X_32,X))) )],[refute_0_188,refute_0_222]) ).
cnf(refute_0_224,plain,
least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_38,Y)) = least_upper_bound(Y,least_upper_bound(least_upper_bound(X,Y),X_38)),
inference(subst,[],[refute_0_223:[bind(X,$fot(Y)),bind(X_31,$fot(least_upper_bound(X,Y))),bind(X_32,$fot(X_38))]]) ).
cnf(refute_0_225,plain,
( least_upper_bound(Y,least_upper_bound(least_upper_bound(X,Y),X_38)) != least_upper_bound(Y,least_upper_bound(X,X_38))
| least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_38,Y)) != least_upper_bound(Y,least_upper_bound(least_upper_bound(X,Y),X_38))
| least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_38,Y)) = least_upper_bound(Y,least_upper_bound(X,X_38)) ),
inference(subst,[],[refute_0_218:[bind(X0,$fot(least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_38,Y)))),bind(Y0,$fot(least_upper_bound(Y,least_upper_bound(least_upper_bound(X,Y),X_38)))),bind(Z0,$fot(least_upper_bound(Y,least_upper_bound(X,X_38))))]]) ).
cnf(refute_0_226,plain,
( least_upper_bound(Y,least_upper_bound(least_upper_bound(X,Y),X_38)) != least_upper_bound(Y,least_upper_bound(X,X_38))
| least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_38,Y)) = least_upper_bound(Y,least_upper_bound(X,X_38)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_38,Y)),least_upper_bound(Y,least_upper_bound(least_upper_bound(X,Y),X_38))) )],[refute_0_224,refute_0_225]) ).
cnf(refute_0_227,plain,
least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_38,Y)) = least_upper_bound(Y,least_upper_bound(X,X_38)),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(least_upper_bound(X,Y),X_38)),least_upper_bound(Y,least_upper_bound(X,X_38))) )],[refute_0_221,refute_0_226]) ).
cnf(refute_0_228,plain,
( least_upper_bound(X,least_upper_bound(Y,X_38)) != least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_38,Y))
| least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_38,Y)) != least_upper_bound(Y,least_upper_bound(X,X_38))
| least_upper_bound(X,least_upper_bound(Y,X_38)) = least_upper_bound(Y,least_upper_bound(X,X_38)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,least_upper_bound(Y,X_38)),least_upper_bound(Y,least_upper_bound(X,X_38))) ),[0],$fot(least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_38,Y)))]]) ).
cnf(refute_0_229,plain,
( least_upper_bound(X,least_upper_bound(Y,X_38)) != least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_38,Y))
| least_upper_bound(X,least_upper_bound(Y,X_38)) = least_upper_bound(Y,least_upper_bound(X,X_38)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_38,Y)),least_upper_bound(Y,least_upper_bound(X,X_38))) )],[refute_0_227,refute_0_228]) ).
cnf(refute_0_230,plain,
least_upper_bound(X,least_upper_bound(Y,X_38)) = least_upper_bound(Y,least_upper_bound(X,X_38)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,X_38)),least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_38,Y))) )],[refute_0_193,refute_0_229]) ).
cnf(refute_0_231,plain,
least_upper_bound(X_31,least_upper_bound(X_32,X)) = least_upper_bound(X_32,least_upper_bound(X_31,X)),
inference(subst,[],[refute_0_230:[bind(X,$fot(X_31)),bind(Y,$fot(X_32)),bind(X_38,$fot(X))]]) ).
cnf(refute_0_232,plain,
( least_upper_bound(X,least_upper_bound(X_31,X_32)) != least_upper_bound(X_31,least_upper_bound(X_32,X))
| least_upper_bound(X_31,least_upper_bound(X_32,X)) != least_upper_bound(X_32,least_upper_bound(X_31,X))
| least_upper_bound(X,least_upper_bound(X_31,X_32)) = least_upper_bound(X_32,least_upper_bound(X_31,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,least_upper_bound(X_31,X_32)),least_upper_bound(X_32,least_upper_bound(X_31,X))) ),[0],$fot(least_upper_bound(X_31,least_upper_bound(X_32,X)))]]) ).
cnf(refute_0_233,plain,
( least_upper_bound(X,least_upper_bound(X_31,X_32)) != least_upper_bound(X_31,least_upper_bound(X_32,X))
| least_upper_bound(X,least_upper_bound(X_31,X_32)) = least_upper_bound(X_32,least_upper_bound(X_31,X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_31,least_upper_bound(X_32,X)),least_upper_bound(X_32,least_upper_bound(X_31,X))) )],[refute_0_231,refute_0_232]) ).
cnf(refute_0_234,plain,
least_upper_bound(X,least_upper_bound(X_31,X_32)) = least_upper_bound(X_32,least_upper_bound(X_31,X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_31,X_32)),least_upper_bound(X_31,least_upper_bound(X_32,X))) )],[refute_0_188,refute_0_233]) ).
cnf(refute_0_235,plain,
( least_upper_bound(X,least_upper_bound(X_31,X_32)) != least_upper_bound(X_32,least_upper_bound(X_31,X))
| least_upper_bound(X_32,least_upper_bound(X_31,X)) = least_upper_bound(X,least_upper_bound(X_31,X_32)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(X_31,X_32)))),bind(Y0,$fot(least_upper_bound(X_32,least_upper_bound(X_31,X))))]]) ).
cnf(refute_0_236,plain,
least_upper_bound(X_32,least_upper_bound(X_31,X)) = least_upper_bound(X,least_upper_bound(X_31,X_32)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_31,X_32)),least_upper_bound(X_32,least_upper_bound(X_31,X))) )],[refute_0_234,refute_0_235]) ).
cnf(refute_0_237,plain,
least_upper_bound(greatest_lower_bound(X_9,least_upper_bound(X_31,X_240)),least_upper_bound(X_31,X_240)) = least_upper_bound(X_240,least_upper_bound(X_31,greatest_lower_bound(X_9,least_upper_bound(X_31,X_240)))),
inference(subst,[],[refute_0_236:[bind(X,$fot(X_240)),bind(X_32,$fot(greatest_lower_bound(X_9,least_upper_bound(X_31,X_240))))]]) ).
cnf(refute_0_238,plain,
( least_upper_bound(X_240,least_upper_bound(X_31,greatest_lower_bound(X_9,least_upper_bound(X_31,X_240)))) != least_upper_bound(X_240,X_31)
| least_upper_bound(greatest_lower_bound(X_9,least_upper_bound(X_31,X_240)),least_upper_bound(X_31,X_240)) != least_upper_bound(X_240,least_upper_bound(X_31,greatest_lower_bound(X_9,least_upper_bound(X_31,X_240))))
| least_upper_bound(greatest_lower_bound(X_9,least_upper_bound(X_31,X_240)),least_upper_bound(X_31,X_240)) = least_upper_bound(X_240,X_31) ),
inference(subst,[],[refute_0_218:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(X_9,least_upper_bound(X_31,X_240)),least_upper_bound(X_31,X_240)))),bind(Y0,$fot(least_upper_bound(X_240,least_upper_bound(X_31,greatest_lower_bound(X_9,least_upper_bound(X_31,X_240)))))),bind(Z0,$fot(least_upper_bound(X_240,X_31)))]]) ).
cnf(refute_0_239,plain,
( least_upper_bound(X_240,least_upper_bound(X_31,greatest_lower_bound(X_9,least_upper_bound(X_31,X_240)))) != least_upper_bound(X_240,X_31)
| least_upper_bound(greatest_lower_bound(X_9,least_upper_bound(X_31,X_240)),least_upper_bound(X_31,X_240)) = least_upper_bound(X_240,X_31) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_9,least_upper_bound(X_31,X_240)),least_upper_bound(X_31,X_240)),least_upper_bound(X_240,least_upper_bound(X_31,greatest_lower_bound(X_9,least_upper_bound(X_31,X_240))))) )],[refute_0_237,refute_0_238]) ).
cnf(refute_0_240,plain,
least_upper_bound(greatest_lower_bound(X_9,least_upper_bound(X_31,X_240)),least_upper_bound(X_31,X_240)) = least_upper_bound(X_240,X_31),
inference(resolve,[$cnf( $equal(least_upper_bound(X_240,least_upper_bound(X_31,greatest_lower_bound(X_9,least_upper_bound(X_31,X_240)))),least_upper_bound(X_240,X_31)) )],[refute_0_181,refute_0_239]) ).
cnf(refute_0_241,plain,
least_upper_bound(X,least_upper_bound(X_31,least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))))) = least_upper_bound(X_31,least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),X)),
inference(subst,[],[refute_0_188:[bind(X_32,$fot(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)))))]]) ).
cnf(refute_0_242,plain,
( least_upper_bound(X,least_upper_bound(X_31,least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))))) != least_upper_bound(X_31,least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),X))
| least_upper_bound(X_31,least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)))) != least_upper_bound(X_31,X_240)
| least_upper_bound(X,least_upper_bound(X_31,X_240)) = least_upper_bound(X_31,least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),X)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_31,least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))))),least_upper_bound(X_31,least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),X))) ),[0,1],$fot(least_upper_bound(X_31,X_240))]]) ).
cnf(refute_0_243,plain,
( least_upper_bound(X,least_upper_bound(X_31,least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))))) != least_upper_bound(X_31,least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),X))
| least_upper_bound(X,least_upper_bound(X_31,X_240)) = least_upper_bound(X_31,least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_31,least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)))),least_upper_bound(X_31,X_240)) )],[refute_0_135,refute_0_242]) ).
cnf(refute_0_244,plain,
least_upper_bound(X,least_upper_bound(X_31,X_240)) = least_upper_bound(X_31,least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_31,least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))))),least_upper_bound(X_31,least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),X))) )],[refute_0_241,refute_0_243]) ).
cnf(refute_0_245,plain,
least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),X) = least_upper_bound(X_240,least_upper_bound(greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)),X)),
inference(subst,[],[refute_0_140:[bind(X,$fot(X_240)),bind(Y,$fot(greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)))),bind(Z,$fot(X))]]) ).
cnf(refute_0_246,plain,
least_upper_bound(X_31,least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),X)) = least_upper_bound(X_31,least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),X)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_31,least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),X)))]]) ).
cnf(refute_0_247,plain,
( least_upper_bound(X_31,least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),X)) != least_upper_bound(X_31,least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),X))
| least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),X) != least_upper_bound(X_240,least_upper_bound(greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)),X))
| least_upper_bound(X_31,least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),X)) = least_upper_bound(X_31,least_upper_bound(X_240,least_upper_bound(greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)),X))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_31,least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),X)),least_upper_bound(X_31,least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),X))) ),[1,1],$fot(least_upper_bound(X_240,least_upper_bound(greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)),X)))]]) ).
cnf(refute_0_248,plain,
( least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),X) != least_upper_bound(X_240,least_upper_bound(greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)),X))
| least_upper_bound(X_31,least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),X)) = least_upper_bound(X_31,least_upper_bound(X_240,least_upper_bound(greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)),X))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_31,least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),X)),least_upper_bound(X_31,least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),X))) )],[refute_0_246,refute_0_247]) ).
cnf(refute_0_249,plain,
least_upper_bound(X_31,least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),X)) = least_upper_bound(X_31,least_upper_bound(X_240,least_upper_bound(greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)),X))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),X),least_upper_bound(X_240,least_upper_bound(greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)),X))) )],[refute_0_245,refute_0_248]) ).
cnf(refute_0_250,plain,
( least_upper_bound(X,least_upper_bound(X_31,X_240)) != least_upper_bound(X_31,least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),X))
| least_upper_bound(X_31,least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),X)) != least_upper_bound(X_31,least_upper_bound(X_240,least_upper_bound(greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)),X)))
| least_upper_bound(X,least_upper_bound(X_31,X_240)) = least_upper_bound(X_31,least_upper_bound(X_240,least_upper_bound(greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)),X))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,least_upper_bound(X_31,X_240)),least_upper_bound(X_31,least_upper_bound(X_240,least_upper_bound(greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)),X)))) ),[0],$fot(least_upper_bound(X_31,least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),X)))]]) ).
cnf(refute_0_251,plain,
( least_upper_bound(X,least_upper_bound(X_31,X_240)) != least_upper_bound(X_31,least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),X))
| least_upper_bound(X,least_upper_bound(X_31,X_240)) = least_upper_bound(X_31,least_upper_bound(X_240,least_upper_bound(greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)),X))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_31,least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),X)),least_upper_bound(X_31,least_upper_bound(X_240,least_upper_bound(greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)),X)))) )],[refute_0_249,refute_0_250]) ).
cnf(refute_0_252,plain,
least_upper_bound(X,least_upper_bound(X_31,X_240)) = least_upper_bound(X_31,least_upper_bound(X_240,least_upper_bound(greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)),X))),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_31,X_240)),least_upper_bound(X_31,least_upper_bound(least_upper_bound(X_240,greatest_lower_bound(X_241,least_upper_bound(X_31,X_240))),X))) )],[refute_0_244,refute_0_251]) ).
cnf(refute_0_253,plain,
( least_upper_bound(X,least_upper_bound(X_31,X_240)) != least_upper_bound(X_31,least_upper_bound(X_240,least_upper_bound(greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)),X)))
| least_upper_bound(X_31,least_upper_bound(X_240,least_upper_bound(greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)),X))) = least_upper_bound(X,least_upper_bound(X_31,X_240)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(X_31,X_240)))),bind(Y0,$fot(least_upper_bound(X_31,least_upper_bound(X_240,least_upper_bound(greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)),X)))))]]) ).
cnf(refute_0_254,plain,
least_upper_bound(X_31,least_upper_bound(X_240,least_upper_bound(greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)),X))) = least_upper_bound(X,least_upper_bound(X_31,X_240)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_31,X_240)),least_upper_bound(X_31,least_upper_bound(X_240,least_upper_bound(greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)),X)))) )],[refute_0_252,refute_0_253]) ).
cnf(refute_0_255,plain,
least_upper_bound(X_31,least_upper_bound(X_240,least_upper_bound(greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240))))) = least_upper_bound(greatest_lower_bound(X_9,least_upper_bound(X_31,X_240)),least_upper_bound(X_31,X_240)),
inference(subst,[],[refute_0_254:[bind(X,$fot(greatest_lower_bound(X_9,least_upper_bound(X_31,X_240))))]]) ).
cnf(refute_0_256,plain,
( least_upper_bound(X_31,least_upper_bound(X_240,least_upper_bound(greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240))))) != least_upper_bound(greatest_lower_bound(X_9,least_upper_bound(X_31,X_240)),least_upper_bound(X_31,X_240))
| least_upper_bound(greatest_lower_bound(X_9,least_upper_bound(X_31,X_240)),least_upper_bound(X_31,X_240)) != least_upper_bound(X_240,X_31)
| least_upper_bound(X_31,least_upper_bound(X_240,least_upper_bound(greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240))))) = least_upper_bound(X_240,X_31) ),
inference(subst,[],[refute_0_218:[bind(X0,$fot(least_upper_bound(X_31,least_upper_bound(X_240,least_upper_bound(greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240))))))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(X_9,least_upper_bound(X_31,X_240)),least_upper_bound(X_31,X_240)))),bind(Z0,$fot(least_upper_bound(X_240,X_31)))]]) ).
cnf(refute_0_257,plain,
( least_upper_bound(greatest_lower_bound(X_9,least_upper_bound(X_31,X_240)),least_upper_bound(X_31,X_240)) != least_upper_bound(X_240,X_31)
| least_upper_bound(X_31,least_upper_bound(X_240,least_upper_bound(greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240))))) = least_upper_bound(X_240,X_31) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_31,least_upper_bound(X_240,least_upper_bound(greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240))))),least_upper_bound(greatest_lower_bound(X_9,least_upper_bound(X_31,X_240)),least_upper_bound(X_31,X_240))) )],[refute_0_255,refute_0_256]) ).
cnf(refute_0_258,plain,
least_upper_bound(X_31,least_upper_bound(X_240,least_upper_bound(greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240))))) = least_upper_bound(X_240,X_31),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_9,least_upper_bound(X_31,X_240)),least_upper_bound(X_31,X_240)),least_upper_bound(X_240,X_31)) )],[refute_0_240,refute_0_257]) ).
cnf(refute_0_259,plain,
( least_upper_bound(X_31,least_upper_bound(X_240,least_upper_bound(greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240))))) != least_upper_bound(X_240,X_31)
| least_upper_bound(X_31,least_upper_bound(X_240,least_upper_bound(greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240))))) != least_upper_bound(X_31,X_240)
| least_upper_bound(X_240,X_31) = least_upper_bound(X_31,X_240) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_31,least_upper_bound(X_240,least_upper_bound(greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240))))),least_upper_bound(X_31,X_240)) ),[0],$fot(least_upper_bound(X_240,X_31))]]) ).
cnf(refute_0_260,plain,
( least_upper_bound(X_31,least_upper_bound(X_240,least_upper_bound(greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240))))) != least_upper_bound(X_31,X_240)
| least_upper_bound(X_240,X_31) = least_upper_bound(X_31,X_240) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_31,least_upper_bound(X_240,least_upper_bound(greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240))))),least_upper_bound(X_240,X_31)) )],[refute_0_258,refute_0_259]) ).
cnf(refute_0_261,plain,
least_upper_bound(X_240,X_31) = least_upper_bound(X_31,X_240),
inference(resolve,[$cnf( $equal(least_upper_bound(X_31,least_upper_bound(X_240,least_upper_bound(greatest_lower_bound(X_241,least_upper_bound(X_31,X_240)),greatest_lower_bound(X_9,least_upper_bound(X_31,X_240))))),least_upper_bound(X_31,X_240)) )],[refute_0_151,refute_0_260]) ).
cnf(refute_0_262,plain,
( least_upper_bound(X_240,X_31) != least_upper_bound(X_31,X_240)
| least_upper_bound(X_31,X_240) = least_upper_bound(X_240,X_31) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(least_upper_bound(X_240,X_31))),bind(Y0,$fot(least_upper_bound(X_31,X_240)))]]) ).
cnf(refute_0_263,plain,
least_upper_bound(X_31,X_240) = least_upper_bound(X_240,X_31),
inference(resolve,[$cnf( $equal(least_upper_bound(X_240,X_31),least_upper_bound(X_31,X_240)) )],[refute_0_261,refute_0_262]) ).
cnf(refute_0_264,plain,
least_upper_bound(inverse(least_upper_bound(X_254,a)),inverse(b)) = least_upper_bound(inverse(b),inverse(least_upper_bound(X_254,a))),
inference(subst,[],[refute_0_263:[bind(X_240,$fot(inverse(b))),bind(X_31,$fot(inverse(least_upper_bound(X_254,a))))]]) ).
cnf(refute_0_265,plain,
inverse(least_upper_bound(inverse(least_upper_bound(X_254,a)),inverse(b))) = inverse(least_upper_bound(inverse(least_upper_bound(X_254,a)),inverse(b))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(inverse(least_upper_bound(X_254,a)),inverse(b))))]]) ).
cnf(refute_0_266,plain,
( inverse(least_upper_bound(inverse(least_upper_bound(X_254,a)),inverse(b))) != inverse(least_upper_bound(inverse(least_upper_bound(X_254,a)),inverse(b)))
| least_upper_bound(inverse(least_upper_bound(X_254,a)),inverse(b)) != least_upper_bound(inverse(b),inverse(least_upper_bound(X_254,a)))
| inverse(least_upper_bound(inverse(least_upper_bound(X_254,a)),inverse(b))) = inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(X_254,a)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(inverse(least_upper_bound(X_254,a)),inverse(b))),inverse(least_upper_bound(inverse(least_upper_bound(X_254,a)),inverse(b)))) ),[1,0],$fot(least_upper_bound(inverse(b),inverse(least_upper_bound(X_254,a))))]]) ).
cnf(refute_0_267,plain,
( least_upper_bound(inverse(least_upper_bound(X_254,a)),inverse(b)) != least_upper_bound(inverse(b),inverse(least_upper_bound(X_254,a)))
| inverse(least_upper_bound(inverse(least_upper_bound(X_254,a)),inverse(b))) = inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(X_254,a)))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(least_upper_bound(X_254,a)),inverse(b))),inverse(least_upper_bound(inverse(least_upper_bound(X_254,a)),inverse(b)))) )],[refute_0_265,refute_0_266]) ).
cnf(refute_0_268,plain,
inverse(least_upper_bound(inverse(least_upper_bound(X_254,a)),inverse(b))) = inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(X_254,a)))),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(X_254,a)),inverse(b)),least_upper_bound(inverse(b),inverse(least_upper_bound(X_254,a)))) )],[refute_0_264,refute_0_267]) ).
cnf(refute_0_269,plain,
multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_254,a)),inverse(b))),identity) = inverse(least_upper_bound(inverse(least_upper_bound(X_254,a)),inverse(b))),
inference(subst,[],[refute_0_39:[bind(X_63,$fot(inverse(least_upper_bound(inverse(least_upper_bound(X_254,a)),inverse(b)))))]]) ).
cnf(refute_0_270,plain,
( multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_254,a)),inverse(b))),identity) != inverse(least_upper_bound(inverse(least_upper_bound(X_254,a)),inverse(b)))
| inverse(least_upper_bound(inverse(least_upper_bound(X_254,a)),inverse(b))) != inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(X_254,a))))
| multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_254,a)),inverse(b))),identity) = inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(X_254,a)))) ),
inference(subst,[],[refute_0_218:[bind(X0,$fot(multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_254,a)),inverse(b))),identity))),bind(Y0,$fot(inverse(least_upper_bound(inverse(least_upper_bound(X_254,a)),inverse(b))))),bind(Z0,$fot(inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(X_254,a))))))]]) ).
cnf(refute_0_271,plain,
( inverse(least_upper_bound(inverse(least_upper_bound(X_254,a)),inverse(b))) != inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(X_254,a))))
| multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_254,a)),inverse(b))),identity) = inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(X_254,a)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_254,a)),inverse(b))),identity),inverse(least_upper_bound(inverse(least_upper_bound(X_254,a)),inverse(b)))) )],[refute_0_269,refute_0_270]) ).
cnf(refute_0_272,plain,
multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_254,a)),inverse(b))),identity) = inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(X_254,a)))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(least_upper_bound(X_254,a)),inverse(b))),inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(X_254,a))))) )],[refute_0_268,refute_0_271]) ).
cnf(refute_0_273,plain,
( multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_254,a)),inverse(b))),identity) != inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(X_254,a))))
| b != multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_254,a)),inverse(b))),identity)
| b = inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(X_254,a)))) ),
introduced(tautology,[equality,[$cnf( $equal(b,multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_254,a)),inverse(b))),identity)) ),[1],$fot(inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(X_254,a)))))]]) ).
cnf(refute_0_274,plain,
( b != multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_254,a)),inverse(b))),identity)
| b = inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(X_254,a)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_254,a)),inverse(b))),identity),inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(X_254,a))))) )],[refute_0_272,refute_0_273]) ).
cnf(refute_0_275,plain,
b = inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(X_254,a)))),
inference(resolve,[$cnf( $equal(b,multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_254,a)),inverse(b))),identity)) )],[refute_0_119,refute_0_274]) ).
cnf(refute_0_276,plain,
b = inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(a,a)))),
inference(subst,[],[refute_0_275:[bind(X_254,$fot(a))]]) ).
cnf(refute_0_277,plain,
least_upper_bound(a,a) = a,
inference(subst,[],[idempotence_of_lub:[bind(X,$fot(a))]]) ).
cnf(refute_0_278,plain,
( b != inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(a,a))))
| least_upper_bound(a,a) != a
| b = inverse(least_upper_bound(inverse(b),inverse(a))) ),
introduced(tautology,[equality,[$cnf( $equal(b,inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(a,a))))) ),[1,0,1,0],$fot(a)]]) ).
cnf(refute_0_279,plain,
( b != inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(a,a))))
| b = inverse(least_upper_bound(inverse(b),inverse(a))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,a),a) )],[refute_0_277,refute_0_278]) ).
cnf(refute_0_280,plain,
b = inverse(least_upper_bound(inverse(b),inverse(a))),
inference(resolve,[$cnf( $equal(b,inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(a,a))))) )],[refute_0_276,refute_0_279]) ).
cnf(refute_0_281,plain,
least_upper_bound(inverse(b),inverse(a)) = least_upper_bound(inverse(a),inverse(b)),
inference(subst,[],[refute_0_263:[bind(X_240,$fot(inverse(a))),bind(X_31,$fot(inverse(b)))]]) ).
cnf(refute_0_282,plain,
inverse(least_upper_bound(inverse(b),inverse(a))) = inverse(least_upper_bound(inverse(b),inverse(a))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(inverse(b),inverse(a))))]]) ).
cnf(refute_0_283,plain,
( inverse(least_upper_bound(inverse(b),inverse(a))) != inverse(least_upper_bound(inverse(b),inverse(a)))
| least_upper_bound(inverse(b),inverse(a)) != least_upper_bound(inverse(a),inverse(b))
| inverse(least_upper_bound(inverse(b),inverse(a))) = inverse(least_upper_bound(inverse(a),inverse(b))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(inverse(b),inverse(a))),inverse(least_upper_bound(inverse(b),inverse(a)))) ),[1,0],$fot(least_upper_bound(inverse(a),inverse(b)))]]) ).
cnf(refute_0_284,plain,
( least_upper_bound(inverse(b),inverse(a)) != least_upper_bound(inverse(a),inverse(b))
| inverse(least_upper_bound(inverse(b),inverse(a))) = inverse(least_upper_bound(inverse(a),inverse(b))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(b),inverse(a))),inverse(least_upper_bound(inverse(b),inverse(a)))) )],[refute_0_282,refute_0_283]) ).
cnf(refute_0_285,plain,
inverse(least_upper_bound(inverse(b),inverse(a))) = inverse(least_upper_bound(inverse(a),inverse(b))),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(b),inverse(a)),least_upper_bound(inverse(a),inverse(b))) )],[refute_0_281,refute_0_284]) ).
cnf(refute_0_286,plain,
( b != inverse(least_upper_bound(inverse(b),inverse(a)))
| inverse(least_upper_bound(inverse(b),inverse(a))) != inverse(least_upper_bound(inverse(a),inverse(b)))
| b = inverse(least_upper_bound(inverse(a),inverse(b))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(b,inverse(least_upper_bound(inverse(a),inverse(b)))) ),[0],$fot(inverse(least_upper_bound(inverse(b),inverse(a))))]]) ).
cnf(refute_0_287,plain,
( b != inverse(least_upper_bound(inverse(b),inverse(a)))
| b = inverse(least_upper_bound(inverse(a),inverse(b))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(b),inverse(a))),inverse(least_upper_bound(inverse(a),inverse(b)))) )],[refute_0_285,refute_0_286]) ).
cnf(refute_0_288,plain,
b = inverse(least_upper_bound(inverse(a),inverse(b))),
inference(resolve,[$cnf( $equal(b,inverse(least_upper_bound(inverse(b),inverse(a)))) )],[refute_0_280,refute_0_287]) ).
cnf(refute_0_289,plain,
( b != inverse(least_upper_bound(inverse(a),inverse(b)))
| inverse(least_upper_bound(inverse(a),inverse(b))) = b ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(b)),bind(Y0,$fot(inverse(least_upper_bound(inverse(a),inverse(b)))))]]) ).
cnf(refute_0_290,plain,
inverse(least_upper_bound(inverse(a),inverse(b))) = b,
inference(resolve,[$cnf( $equal(b,inverse(least_upper_bound(inverse(a),inverse(b)))) )],[refute_0_288,refute_0_289]) ).
cnf(refute_0_291,plain,
( inverse(inverse(least_upper_bound(inverse(a),inverse(b)))) != least_upper_bound(inverse(a),inverse(b))
| inverse(least_upper_bound(inverse(a),inverse(b))) != b
| inverse(b) = least_upper_bound(inverse(a),inverse(b)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(least_upper_bound(inverse(a),inverse(b)))),least_upper_bound(inverse(a),inverse(b))) ),[0,0],$fot(b)]]) ).
cnf(refute_0_292,plain,
( inverse(inverse(least_upper_bound(inverse(a),inverse(b)))) != least_upper_bound(inverse(a),inverse(b))
| inverse(b) = least_upper_bound(inverse(a),inverse(b)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(a),inverse(b))),b) )],[refute_0_290,refute_0_291]) ).
cnf(refute_0_293,plain,
inverse(b) = least_upper_bound(inverse(a),inverse(b)),
inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(inverse(a),inverse(b)))),least_upper_bound(inverse(a),inverse(b))) )],[refute_0_44,refute_0_292]) ).
cnf(refute_0_294,plain,
( inverse(b) != least_upper_bound(inverse(a),inverse(b))
| least_upper_bound(inverse(a),inverse(b)) = inverse(b) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(inverse(b))),bind(Y0,$fot(least_upper_bound(inverse(a),inverse(b))))]]) ).
cnf(refute_0_295,plain,
least_upper_bound(inverse(a),inverse(b)) = inverse(b),
inference(resolve,[$cnf( $equal(inverse(b),least_upper_bound(inverse(a),inverse(b))) )],[refute_0_293,refute_0_294]) ).
cnf(refute_0_296,plain,
( greatest_lower_bound(inverse(a),least_upper_bound(inverse(a),inverse(b))) != inverse(a)
| least_upper_bound(inverse(a),inverse(b)) != inverse(b)
| greatest_lower_bound(inverse(a),inverse(b)) = inverse(a) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(inverse(a),least_upper_bound(inverse(a),inverse(b))),inverse(a)) ),[0,1],$fot(inverse(b))]]) ).
cnf(refute_0_297,plain,
( greatest_lower_bound(inverse(a),least_upper_bound(inverse(a),inverse(b))) != inverse(a)
| greatest_lower_bound(inverse(a),inverse(b)) = inverse(a) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(a),inverse(b)),inverse(b)) )],[refute_0_295,refute_0_296]) ).
cnf(refute_0_298,plain,
greatest_lower_bound(inverse(a),inverse(b)) = inverse(a),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(a),least_upper_bound(inverse(a),inverse(b))),inverse(a)) )],[refute_0_0,refute_0_297]) ).
cnf(refute_0_299,plain,
$false,
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(a),inverse(b)),inverse(a)) )],[refute_0_298,prove_p39b]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GRP191-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.04/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.35 % Computer : n022.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Mon Jun 13 23:10:33 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 6.20/6.39 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.20/6.39
% 6.20/6.39 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.20/6.42
%------------------------------------------------------------------------------