TSTP Solution File: GRP173-1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP173-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n017.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 10:37:18 EDT 2022
% Result : Unsatisfiable 0.61s 0.83s
% Output : CNFRefutation 0.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 55
% Syntax : Number of clauses : 219 ( 110 unt; 0 nHn; 148 RR)
% Number of literals : 374 ( 373 equ; 156 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 228 ( 0 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_lub,axiom,
least_upper_bound(X,Y) = least_upper_bound(Y,X) ).
cnf(associativity_of_lub,axiom,
least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) ).
cnf(monotony_lub1,axiom,
multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ).
cnf(monotony_lub2,axiom,
multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) ).
cnf(p05a_1,hypothesis,
least_upper_bound(identity,a) = identity ).
cnf(p05a_2,hypothesis,
least_upper_bound(identity,inverse(a)) = identity ).
cnf(prove_p05a,negated_conjecture,
identity != a ).
cnf(refute_0_0,plain,
multiply(inverse(X_52),least_upper_bound(X_51,X_52)) = least_upper_bound(multiply(inverse(X_52),X_51),multiply(inverse(X_52),X_52)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(inverse(X_52))),bind(Y,$fot(X_51)),bind(Z,$fot(X_52))]]) ).
cnf(refute_0_1,plain,
multiply(inverse(X_52),X_52) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_52))]]) ).
cnf(refute_0_2,plain,
( multiply(inverse(X_52),X_52) != identity
| multiply(inverse(X_52),least_upper_bound(X_51,X_52)) != least_upper_bound(multiply(inverse(X_52),X_51),multiply(inverse(X_52),X_52))
| multiply(inverse(X_52),least_upper_bound(X_51,X_52)) = least_upper_bound(multiply(inverse(X_52),X_51),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_52),least_upper_bound(X_51,X_52)),least_upper_bound(multiply(inverse(X_52),X_51),multiply(inverse(X_52),X_52))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_3,plain,
( multiply(inverse(X_52),least_upper_bound(X_51,X_52)) != least_upper_bound(multiply(inverse(X_52),X_51),multiply(inverse(X_52),X_52))
| multiply(inverse(X_52),least_upper_bound(X_51,X_52)) = least_upper_bound(multiply(inverse(X_52),X_51),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_52),X_52),identity) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
multiply(inverse(X_52),least_upper_bound(X_51,X_52)) = least_upper_bound(multiply(inverse(X_52),X_51),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_52),least_upper_bound(X_51,X_52)),least_upper_bound(multiply(inverse(X_52),X_51),multiply(inverse(X_52),X_52))) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_6,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_7,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( least_upper_bound(X,Y) != least_upper_bound(Y,X)
| least_upper_bound(Y,X) = least_upper_bound(X,Y) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(least_upper_bound(X,Y))),bind(Y0,$fot(least_upper_bound(Y,X)))]]) ).
cnf(refute_0_9,plain,
least_upper_bound(Y,X) = least_upper_bound(X,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(X,Y),least_upper_bound(Y,X)) )],[symmetry_of_lub,refute_0_8]) ).
cnf(refute_0_10,plain,
least_upper_bound(multiply(inverse(X_52),X_51),identity) = least_upper_bound(identity,multiply(inverse(X_52),X_51)),
inference(subst,[],[refute_0_9:[bind(X,$fot(identity)),bind(Y,$fot(multiply(inverse(X_52),X_51)))]]) ).
cnf(refute_0_11,plain,
( multiply(inverse(X_52),least_upper_bound(X_51,X_52)) != least_upper_bound(multiply(inverse(X_52),X_51),identity)
| least_upper_bound(multiply(inverse(X_52),X_51),identity) != least_upper_bound(identity,multiply(inverse(X_52),X_51))
| multiply(inverse(X_52),least_upper_bound(X_51,X_52)) = least_upper_bound(identity,multiply(inverse(X_52),X_51)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_52),least_upper_bound(X_51,X_52)),least_upper_bound(identity,multiply(inverse(X_52),X_51))) ),[0],$fot(least_upper_bound(multiply(inverse(X_52),X_51),identity))]]) ).
cnf(refute_0_12,plain,
( multiply(inverse(X_52),least_upper_bound(X_51,X_52)) != least_upper_bound(multiply(inverse(X_52),X_51),identity)
| multiply(inverse(X_52),least_upper_bound(X_51,X_52)) = least_upper_bound(identity,multiply(inverse(X_52),X_51)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(X_52),X_51),identity),least_upper_bound(identity,multiply(inverse(X_52),X_51))) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
multiply(inverse(X_52),least_upper_bound(X_51,X_52)) = least_upper_bound(identity,multiply(inverse(X_52),X_51)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_52),least_upper_bound(X_51,X_52)),least_upper_bound(multiply(inverse(X_52),X_51),identity)) )],[refute_0_4,refute_0_12]) ).
cnf(refute_0_14,plain,
multiply(inverse(multiply(inverse(inverse(a)),identity)),least_upper_bound(a,multiply(inverse(inverse(a)),identity))) = least_upper_bound(identity,multiply(inverse(multiply(inverse(inverse(a)),identity)),a)),
inference(subst,[],[refute_0_13:[bind(X_51,$fot(a)),bind(X_52,$fot(multiply(inverse(inverse(a)),identity)))]]) ).
cnf(refute_0_15,plain,
least_upper_bound(a,least_upper_bound(identity,X_16)) = least_upper_bound(least_upper_bound(a,identity),X_16),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(a)),bind(Y,$fot(identity)),bind(Z,$fot(X_16))]]) ).
cnf(refute_0_16,plain,
least_upper_bound(identity,a) = least_upper_bound(a,identity),
inference(subst,[],[refute_0_9:[bind(X,$fot(a)),bind(Y,$fot(identity))]]) ).
cnf(refute_0_17,plain,
( least_upper_bound(identity,a) != identity
| least_upper_bound(identity,a) != least_upper_bound(a,identity)
| least_upper_bound(a,identity) = identity ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,a),identity) ),[0],$fot(least_upper_bound(a,identity))]]) ).
cnf(refute_0_18,plain,
( least_upper_bound(identity,a) != identity
| least_upper_bound(a,identity) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,a),least_upper_bound(a,identity)) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
least_upper_bound(a,identity) = identity,
inference(resolve,[$cnf( $equal(least_upper_bound(identity,a),identity) )],[p05a_1,refute_0_18]) ).
cnf(refute_0_20,plain,
( least_upper_bound(a,identity) != identity
| least_upper_bound(a,least_upper_bound(identity,X_16)) != least_upper_bound(least_upper_bound(a,identity),X_16)
| least_upper_bound(a,least_upper_bound(identity,X_16)) = least_upper_bound(identity,X_16) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(a,least_upper_bound(identity,X_16)),least_upper_bound(least_upper_bound(a,identity),X_16)) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_21,plain,
( least_upper_bound(a,least_upper_bound(identity,X_16)) != least_upper_bound(least_upper_bound(a,identity),X_16)
| least_upper_bound(a,least_upper_bound(identity,X_16)) = least_upper_bound(identity,X_16) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,identity),identity) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
least_upper_bound(a,least_upper_bound(identity,X_16)) = least_upper_bound(identity,X_16),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(identity,X_16)),least_upper_bound(least_upper_bound(a,identity),X_16)) )],[refute_0_15,refute_0_21]) ).
cnf(refute_0_23,plain,
least_upper_bound(a,least_upper_bound(identity,multiply(inverse(inverse(a)),identity))) = least_upper_bound(identity,multiply(inverse(inverse(a)),identity)),
inference(subst,[],[refute_0_22:[bind(X_16,$fot(multiply(inverse(inverse(a)),identity)))]]) ).
cnf(refute_0_24,plain,
multiply(inverse(inverse(a)),least_upper_bound(identity,inverse(a))) = least_upper_bound(identity,multiply(inverse(inverse(a)),identity)),
inference(subst,[],[refute_0_13:[bind(X_51,$fot(identity)),bind(X_52,$fot(inverse(a)))]]) ).
cnf(refute_0_25,plain,
( multiply(inverse(inverse(a)),least_upper_bound(identity,inverse(a))) != least_upper_bound(identity,multiply(inverse(inverse(a)),identity))
| least_upper_bound(identity,inverse(a)) != identity
| multiply(inverse(inverse(a)),identity) = least_upper_bound(identity,multiply(inverse(inverse(a)),identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(a)),least_upper_bound(identity,inverse(a))),least_upper_bound(identity,multiply(inverse(inverse(a)),identity))) ),[0,1],$fot(identity)]]) ).
cnf(refute_0_26,plain,
( multiply(inverse(inverse(a)),least_upper_bound(identity,inverse(a))) != least_upper_bound(identity,multiply(inverse(inverse(a)),identity))
| multiply(inverse(inverse(a)),identity) = least_upper_bound(identity,multiply(inverse(inverse(a)),identity)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(a)),identity) )],[p05a_2,refute_0_25]) ).
cnf(refute_0_27,plain,
multiply(inverse(inverse(a)),identity) = least_upper_bound(identity,multiply(inverse(inverse(a)),identity)),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(a)),least_upper_bound(identity,inverse(a))),least_upper_bound(identity,multiply(inverse(inverse(a)),identity))) )],[refute_0_24,refute_0_26]) ).
cnf(refute_0_28,plain,
( multiply(inverse(inverse(a)),identity) != least_upper_bound(identity,multiply(inverse(inverse(a)),identity))
| least_upper_bound(identity,multiply(inverse(inverse(a)),identity)) = multiply(inverse(inverse(a)),identity) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(multiply(inverse(inverse(a)),identity))),bind(Y0,$fot(least_upper_bound(identity,multiply(inverse(inverse(a)),identity))))]]) ).
cnf(refute_0_29,plain,
least_upper_bound(identity,multiply(inverse(inverse(a)),identity)) = multiply(inverse(inverse(a)),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(a)),identity),least_upper_bound(identity,multiply(inverse(inverse(a)),identity))) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
( least_upper_bound(a,least_upper_bound(identity,multiply(inverse(inverse(a)),identity))) != least_upper_bound(identity,multiply(inverse(inverse(a)),identity))
| least_upper_bound(identity,multiply(inverse(inverse(a)),identity)) != multiply(inverse(inverse(a)),identity)
| least_upper_bound(a,multiply(inverse(inverse(a)),identity)) = least_upper_bound(identity,multiply(inverse(inverse(a)),identity)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(a,least_upper_bound(identity,multiply(inverse(inverse(a)),identity))),least_upper_bound(identity,multiply(inverse(inverse(a)),identity))) ),[0,1],$fot(multiply(inverse(inverse(a)),identity))]]) ).
cnf(refute_0_31,plain,
( least_upper_bound(a,least_upper_bound(identity,multiply(inverse(inverse(a)),identity))) != least_upper_bound(identity,multiply(inverse(inverse(a)),identity))
| least_upper_bound(a,multiply(inverse(inverse(a)),identity)) = least_upper_bound(identity,multiply(inverse(inverse(a)),identity)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(inverse(a)),identity)),multiply(inverse(inverse(a)),identity)) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
least_upper_bound(a,multiply(inverse(inverse(a)),identity)) = least_upper_bound(identity,multiply(inverse(inverse(a)),identity)),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(identity,multiply(inverse(inverse(a)),identity))),least_upper_bound(identity,multiply(inverse(inverse(a)),identity))) )],[refute_0_23,refute_0_31]) ).
cnf(refute_0_33,plain,
( least_upper_bound(a,multiply(inverse(inverse(a)),identity)) != least_upper_bound(identity,multiply(inverse(inverse(a)),identity))
| least_upper_bound(identity,multiply(inverse(inverse(a)),identity)) != multiply(inverse(inverse(a)),identity)
| least_upper_bound(a,multiply(inverse(inverse(a)),identity)) = multiply(inverse(inverse(a)),identity) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(a,multiply(inverse(inverse(a)),identity)),multiply(inverse(inverse(a)),identity)) ),[0],$fot(least_upper_bound(identity,multiply(inverse(inverse(a)),identity)))]]) ).
cnf(refute_0_34,plain,
( least_upper_bound(a,multiply(inverse(inverse(a)),identity)) != least_upper_bound(identity,multiply(inverse(inverse(a)),identity))
| least_upper_bound(a,multiply(inverse(inverse(a)),identity)) = multiply(inverse(inverse(a)),identity) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(inverse(a)),identity)),multiply(inverse(inverse(a)),identity)) )],[refute_0_29,refute_0_33]) ).
cnf(refute_0_35,plain,
least_upper_bound(a,multiply(inverse(inverse(a)),identity)) = multiply(inverse(inverse(a)),identity),
inference(resolve,[$cnf( $equal(least_upper_bound(a,multiply(inverse(inverse(a)),identity)),least_upper_bound(identity,multiply(inverse(inverse(a)),identity))) )],[refute_0_32,refute_0_34]) ).
cnf(refute_0_36,plain,
( multiply(inverse(multiply(inverse(inverse(a)),identity)),least_upper_bound(a,multiply(inverse(inverse(a)),identity))) != least_upper_bound(identity,multiply(inverse(multiply(inverse(inverse(a)),identity)),a))
| least_upper_bound(a,multiply(inverse(inverse(a)),identity)) != multiply(inverse(inverse(a)),identity)
| multiply(inverse(multiply(inverse(inverse(a)),identity)),multiply(inverse(inverse(a)),identity)) = least_upper_bound(identity,multiply(inverse(multiply(inverse(inverse(a)),identity)),a)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(inverse(inverse(a)),identity)),least_upper_bound(a,multiply(inverse(inverse(a)),identity))),least_upper_bound(identity,multiply(inverse(multiply(inverse(inverse(a)),identity)),a))) ),[0,1],$fot(multiply(inverse(inverse(a)),identity))]]) ).
cnf(refute_0_37,plain,
( multiply(inverse(multiply(inverse(inverse(a)),identity)),least_upper_bound(a,multiply(inverse(inverse(a)),identity))) != least_upper_bound(identity,multiply(inverse(multiply(inverse(inverse(a)),identity)),a))
| multiply(inverse(multiply(inverse(inverse(a)),identity)),multiply(inverse(inverse(a)),identity)) = least_upper_bound(identity,multiply(inverse(multiply(inverse(inverse(a)),identity)),a)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,multiply(inverse(inverse(a)),identity)),multiply(inverse(inverse(a)),identity)) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
multiply(inverse(multiply(inverse(inverse(a)),identity)),multiply(inverse(inverse(a)),identity)) = least_upper_bound(identity,multiply(inverse(multiply(inverse(inverse(a)),identity)),a)),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(inverse(a)),identity)),least_upper_bound(a,multiply(inverse(inverse(a)),identity))),least_upper_bound(identity,multiply(inverse(multiply(inverse(inverse(a)),identity)),a))) )],[refute_0_14,refute_0_37]) ).
cnf(refute_0_39,plain,
multiply(inverse(multiply(inverse(inverse(a)),identity)),multiply(inverse(inverse(a)),identity)) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(multiply(inverse(inverse(a)),identity)))]]) ).
cnf(refute_0_40,plain,
( multiply(inverse(multiply(inverse(inverse(a)),identity)),multiply(inverse(inverse(a)),identity)) != identity
| multiply(inverse(multiply(inverse(inverse(a)),identity)),multiply(inverse(inverse(a)),identity)) != least_upper_bound(identity,multiply(inverse(multiply(inverse(inverse(a)),identity)),a))
| identity = least_upper_bound(identity,multiply(inverse(multiply(inverse(inverse(a)),identity)),a)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(inverse(inverse(a)),identity)),multiply(inverse(inverse(a)),identity)),least_upper_bound(identity,multiply(inverse(multiply(inverse(inverse(a)),identity)),a))) ),[0],$fot(identity)]]) ).
cnf(refute_0_41,plain,
( multiply(inverse(multiply(inverse(inverse(a)),identity)),multiply(inverse(inverse(a)),identity)) != least_upper_bound(identity,multiply(inverse(multiply(inverse(inverse(a)),identity)),a))
| identity = least_upper_bound(identity,multiply(inverse(multiply(inverse(inverse(a)),identity)),a)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(inverse(a)),identity)),multiply(inverse(inverse(a)),identity)),identity) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
identity = least_upper_bound(identity,multiply(inverse(multiply(inverse(inverse(a)),identity)),a)),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(inverse(a)),identity)),multiply(inverse(inverse(a)),identity)),least_upper_bound(identity,multiply(inverse(multiply(inverse(inverse(a)),identity)),a))) )],[refute_0_38,refute_0_41]) ).
cnf(refute_0_43,plain,
multiply(multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),identity),X_90) = multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),multiply(identity,X_90)),
inference(subst,[],[associativity:[bind(X,$fot(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))))),bind(Y,$fot(identity)),bind(Z,$fot(X_90))]]) ).
cnf(refute_0_44,plain,
multiply(inverse(multiply(inverse(inverse(a)),identity)),least_upper_bound(identity,multiply(inverse(inverse(a)),identity))) = least_upper_bound(identity,multiply(inverse(multiply(inverse(inverse(a)),identity)),identity)),
inference(subst,[],[refute_0_13:[bind(X_51,$fot(identity)),bind(X_52,$fot(multiply(inverse(inverse(a)),identity)))]]) ).
cnf(refute_0_45,plain,
( multiply(inverse(multiply(inverse(inverse(a)),identity)),least_upper_bound(identity,multiply(inverse(inverse(a)),identity))) != least_upper_bound(identity,multiply(inverse(multiply(inverse(inverse(a)),identity)),identity))
| least_upper_bound(identity,multiply(inverse(inverse(a)),identity)) != multiply(inverse(inverse(a)),identity)
| multiply(inverse(multiply(inverse(inverse(a)),identity)),multiply(inverse(inverse(a)),identity)) = least_upper_bound(identity,multiply(inverse(multiply(inverse(inverse(a)),identity)),identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(inverse(inverse(a)),identity)),least_upper_bound(identity,multiply(inverse(inverse(a)),identity))),least_upper_bound(identity,multiply(inverse(multiply(inverse(inverse(a)),identity)),identity))) ),[0,1],$fot(multiply(inverse(inverse(a)),identity))]]) ).
cnf(refute_0_46,plain,
( multiply(inverse(multiply(inverse(inverse(a)),identity)),least_upper_bound(identity,multiply(inverse(inverse(a)),identity))) != least_upper_bound(identity,multiply(inverse(multiply(inverse(inverse(a)),identity)),identity))
| multiply(inverse(multiply(inverse(inverse(a)),identity)),multiply(inverse(inverse(a)),identity)) = least_upper_bound(identity,multiply(inverse(multiply(inverse(inverse(a)),identity)),identity)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(inverse(a)),identity)),multiply(inverse(inverse(a)),identity)) )],[refute_0_29,refute_0_45]) ).
cnf(refute_0_47,plain,
multiply(inverse(multiply(inverse(inverse(a)),identity)),multiply(inverse(inverse(a)),identity)) = least_upper_bound(identity,multiply(inverse(multiply(inverse(inverse(a)),identity)),identity)),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(inverse(a)),identity)),least_upper_bound(identity,multiply(inverse(inverse(a)),identity))),least_upper_bound(identity,multiply(inverse(multiply(inverse(inverse(a)),identity)),identity))) )],[refute_0_44,refute_0_46]) ).
cnf(refute_0_48,plain,
( multiply(inverse(multiply(inverse(inverse(a)),identity)),multiply(inverse(inverse(a)),identity)) != identity
| multiply(inverse(multiply(inverse(inverse(a)),identity)),multiply(inverse(inverse(a)),identity)) != least_upper_bound(identity,multiply(inverse(multiply(inverse(inverse(a)),identity)),identity))
| identity = least_upper_bound(identity,multiply(inverse(multiply(inverse(inverse(a)),identity)),identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(inverse(inverse(a)),identity)),multiply(inverse(inverse(a)),identity)),least_upper_bound(identity,multiply(inverse(multiply(inverse(inverse(a)),identity)),identity))) ),[0],$fot(identity)]]) ).
cnf(refute_0_49,plain,
( multiply(inverse(multiply(inverse(inverse(a)),identity)),multiply(inverse(inverse(a)),identity)) != least_upper_bound(identity,multiply(inverse(multiply(inverse(inverse(a)),identity)),identity))
| identity = least_upper_bound(identity,multiply(inverse(multiply(inverse(inverse(a)),identity)),identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(inverse(a)),identity)),multiply(inverse(inverse(a)),identity)),identity) )],[refute_0_39,refute_0_48]) ).
cnf(refute_0_50,plain,
identity = least_upper_bound(identity,multiply(inverse(multiply(inverse(inverse(a)),identity)),identity)),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(inverse(a)),identity)),multiply(inverse(inverse(a)),identity)),least_upper_bound(identity,multiply(inverse(multiply(inverse(inverse(a)),identity)),identity))) )],[refute_0_47,refute_0_49]) ).
cnf(refute_0_51,plain,
least_upper_bound(multiply(X_60,X_58),multiply(X_59,X_58)) = least_upper_bound(multiply(X_59,X_58),multiply(X_60,X_58)),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(multiply(X_60,X_58))),bind(Y,$fot(multiply(X_59,X_58)))]]) ).
cnf(refute_0_52,plain,
multiply(least_upper_bound(X_59,X_60),X_58) = least_upper_bound(multiply(X_59,X_58),multiply(X_60,X_58)),
inference(subst,[],[monotony_lub2:[bind(X,$fot(X_58)),bind(Y,$fot(X_59)),bind(Z,$fot(X_60))]]) ).
cnf(refute_0_53,plain,
( multiply(least_upper_bound(X_59,X_60),X_58) != least_upper_bound(multiply(X_59,X_58),multiply(X_60,X_58))
| least_upper_bound(multiply(X_59,X_58),multiply(X_60,X_58)) = multiply(least_upper_bound(X_59,X_60),X_58) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(multiply(least_upper_bound(X_59,X_60),X_58))),bind(Y0,$fot(least_upper_bound(multiply(X_59,X_58),multiply(X_60,X_58))))]]) ).
cnf(refute_0_54,plain,
least_upper_bound(multiply(X_59,X_58),multiply(X_60,X_58)) = multiply(least_upper_bound(X_59,X_60),X_58),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_59,X_60),X_58),least_upper_bound(multiply(X_59,X_58),multiply(X_60,X_58))) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
( least_upper_bound(multiply(X_59,X_58),multiply(X_60,X_58)) != multiply(least_upper_bound(X_59,X_60),X_58)
| least_upper_bound(multiply(X_60,X_58),multiply(X_59,X_58)) != least_upper_bound(multiply(X_59,X_58),multiply(X_60,X_58))
| least_upper_bound(multiply(X_60,X_58),multiply(X_59,X_58)) = multiply(least_upper_bound(X_59,X_60),X_58) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_60,X_58),multiply(X_59,X_58)),least_upper_bound(multiply(X_59,X_58),multiply(X_60,X_58))) ),[1],$fot(multiply(least_upper_bound(X_59,X_60),X_58))]]) ).
cnf(refute_0_56,plain,
( least_upper_bound(multiply(X_60,X_58),multiply(X_59,X_58)) != least_upper_bound(multiply(X_59,X_58),multiply(X_60,X_58))
| least_upper_bound(multiply(X_60,X_58),multiply(X_59,X_58)) = multiply(least_upper_bound(X_59,X_60),X_58) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_59,X_58),multiply(X_60,X_58)),multiply(least_upper_bound(X_59,X_60),X_58)) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
least_upper_bound(multiply(X_60,X_58),multiply(X_59,X_58)) = multiply(least_upper_bound(X_59,X_60),X_58),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_60,X_58),multiply(X_59,X_58)),least_upper_bound(multiply(X_59,X_58),multiply(X_60,X_58))) )],[refute_0_51,refute_0_56]) ).
cnf(refute_0_58,plain,
( multiply(least_upper_bound(Y,Z),X) != least_upper_bound(multiply(Y,X),multiply(Z,X))
| least_upper_bound(multiply(Y,X),multiply(Z,X)) = multiply(least_upper_bound(Y,Z),X) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(multiply(least_upper_bound(Y,Z),X))),bind(Y0,$fot(least_upper_bound(multiply(Y,X),multiply(Z,X))))]]) ).
cnf(refute_0_59,plain,
least_upper_bound(multiply(Y,X),multiply(Z,X)) = multiply(least_upper_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Y,X),multiply(Z,X))) )],[monotony_lub2,refute_0_58]) ).
cnf(refute_0_60,plain,
least_upper_bound(multiply(X_60,X_58),multiply(X_59,X_58)) = multiply(least_upper_bound(X_60,X_59),X_58),
inference(subst,[],[refute_0_59:[bind(X,$fot(X_58)),bind(Y,$fot(X_60)),bind(Z,$fot(X_59))]]) ).
cnf(refute_0_61,plain,
( least_upper_bound(multiply(X_60,X_58),multiply(X_59,X_58)) != multiply(least_upper_bound(X_59,X_60),X_58)
| least_upper_bound(multiply(X_60,X_58),multiply(X_59,X_58)) != multiply(least_upper_bound(X_60,X_59),X_58)
| multiply(least_upper_bound(X_60,X_59),X_58) = multiply(least_upper_bound(X_59,X_60),X_58) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_60,X_58),multiply(X_59,X_58)),multiply(least_upper_bound(X_59,X_60),X_58)) ),[0],$fot(multiply(least_upper_bound(X_60,X_59),X_58))]]) ).
cnf(refute_0_62,plain,
( least_upper_bound(multiply(X_60,X_58),multiply(X_59,X_58)) != multiply(least_upper_bound(X_59,X_60),X_58)
| multiply(least_upper_bound(X_60,X_59),X_58) = multiply(least_upper_bound(X_59,X_60),X_58) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_60,X_58),multiply(X_59,X_58)),multiply(least_upper_bound(X_60,X_59),X_58)) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
multiply(least_upper_bound(X_60,X_59),X_58) = multiply(least_upper_bound(X_59,X_60),X_58),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_60,X_58),multiply(X_59,X_58)),multiply(least_upper_bound(X_59,X_60),X_58)) )],[refute_0_57,refute_0_62]) ).
cnf(refute_0_64,plain,
( multiply(least_upper_bound(X_60,X_59),X_58) != multiply(least_upper_bound(X_59,X_60),X_58)
| multiply(least_upper_bound(X_59,X_60),X_58) = multiply(least_upper_bound(X_60,X_59),X_58) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(multiply(least_upper_bound(X_60,X_59),X_58))),bind(Y0,$fot(multiply(least_upper_bound(X_59,X_60),X_58)))]]) ).
cnf(refute_0_65,plain,
multiply(least_upper_bound(X_59,X_60),X_58) = multiply(least_upper_bound(X_60,X_59),X_58),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_60,X_59),X_58),multiply(least_upper_bound(X_59,X_60),X_58)) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
multiply(least_upper_bound(inverse(multiply(inverse(inverse(a)),identity)),identity),identity) = multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),identity),
inference(subst,[],[refute_0_65:[bind(X_58,$fot(identity)),bind(X_59,$fot(inverse(multiply(inverse(inverse(a)),identity)))),bind(X_60,$fot(identity))]]) ).
cnf(refute_0_67,plain,
multiply(least_upper_bound(X_59,identity),X_58) = least_upper_bound(multiply(X_59,X_58),multiply(identity,X_58)),
inference(subst,[],[monotony_lub2:[bind(X,$fot(X_58)),bind(Y,$fot(X_59)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_68,plain,
multiply(identity,X_58) = X_58,
inference(subst,[],[left_identity:[bind(X,$fot(X_58))]]) ).
cnf(refute_0_69,plain,
( multiply(identity,X_58) != X_58
| multiply(least_upper_bound(X_59,identity),X_58) != least_upper_bound(multiply(X_59,X_58),multiply(identity,X_58))
| multiply(least_upper_bound(X_59,identity),X_58) = least_upper_bound(multiply(X_59,X_58),X_58) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_59,identity),X_58),least_upper_bound(multiply(X_59,X_58),multiply(identity,X_58))) ),[1,1],$fot(X_58)]]) ).
cnf(refute_0_70,plain,
( multiply(least_upper_bound(X_59,identity),X_58) != least_upper_bound(multiply(X_59,X_58),multiply(identity,X_58))
| multiply(least_upper_bound(X_59,identity),X_58) = least_upper_bound(multiply(X_59,X_58),X_58) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_58),X_58) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
multiply(least_upper_bound(X_59,identity),X_58) = least_upper_bound(multiply(X_59,X_58),X_58),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_59,identity),X_58),least_upper_bound(multiply(X_59,X_58),multiply(identity,X_58))) )],[refute_0_67,refute_0_70]) ).
cnf(refute_0_72,plain,
least_upper_bound(multiply(X_59,X_58),X_58) = least_upper_bound(X_58,multiply(X_59,X_58)),
inference(subst,[],[refute_0_9:[bind(X,$fot(X_58)),bind(Y,$fot(multiply(X_59,X_58)))]]) ).
cnf(refute_0_73,plain,
( multiply(least_upper_bound(X_59,identity),X_58) != least_upper_bound(multiply(X_59,X_58),X_58)
| least_upper_bound(multiply(X_59,X_58),X_58) != least_upper_bound(X_58,multiply(X_59,X_58))
| multiply(least_upper_bound(X_59,identity),X_58) = least_upper_bound(X_58,multiply(X_59,X_58)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_59,identity),X_58),least_upper_bound(X_58,multiply(X_59,X_58))) ),[0],$fot(least_upper_bound(multiply(X_59,X_58),X_58))]]) ).
cnf(refute_0_74,plain,
( multiply(least_upper_bound(X_59,identity),X_58) != least_upper_bound(multiply(X_59,X_58),X_58)
| multiply(least_upper_bound(X_59,identity),X_58) = least_upper_bound(X_58,multiply(X_59,X_58)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_59,X_58),X_58),least_upper_bound(X_58,multiply(X_59,X_58))) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
multiply(least_upper_bound(X_59,identity),X_58) = least_upper_bound(X_58,multiply(X_59,X_58)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_59,identity),X_58),least_upper_bound(multiply(X_59,X_58),X_58)) )],[refute_0_71,refute_0_74]) ).
cnf(refute_0_76,plain,
( multiply(least_upper_bound(X_59,identity),X_58) != least_upper_bound(X_58,multiply(X_59,X_58))
| least_upper_bound(X_58,multiply(X_59,X_58)) = multiply(least_upper_bound(X_59,identity),X_58) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(multiply(least_upper_bound(X_59,identity),X_58))),bind(Y0,$fot(least_upper_bound(X_58,multiply(X_59,X_58))))]]) ).
cnf(refute_0_77,plain,
least_upper_bound(X_58,multiply(X_59,X_58)) = multiply(least_upper_bound(X_59,identity),X_58),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_59,identity),X_58),least_upper_bound(X_58,multiply(X_59,X_58))) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
least_upper_bound(identity,multiply(inverse(multiply(inverse(inverse(a)),identity)),identity)) = multiply(least_upper_bound(inverse(multiply(inverse(inverse(a)),identity)),identity),identity),
inference(subst,[],[refute_0_77:[bind(X_58,$fot(identity)),bind(X_59,$fot(inverse(multiply(inverse(inverse(a)),identity))))]]) ).
cnf(refute_0_79,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_80,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_7,refute_0_79]) ).
cnf(refute_0_81,plain,
( multiply(least_upper_bound(inverse(multiply(inverse(inverse(a)),identity)),identity),identity) != multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),identity)
| least_upper_bound(identity,multiply(inverse(multiply(inverse(inverse(a)),identity)),identity)) != multiply(least_upper_bound(inverse(multiply(inverse(inverse(a)),identity)),identity),identity)
| least_upper_bound(identity,multiply(inverse(multiply(inverse(inverse(a)),identity)),identity)) = multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),identity) ),
inference(subst,[],[refute_0_80:[bind(X0,$fot(least_upper_bound(identity,multiply(inverse(multiply(inverse(inverse(a)),identity)),identity)))),bind(Y0,$fot(multiply(least_upper_bound(inverse(multiply(inverse(inverse(a)),identity)),identity),identity))),bind(Z0,$fot(multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),identity)))]]) ).
cnf(refute_0_82,plain,
( multiply(least_upper_bound(inverse(multiply(inverse(inverse(a)),identity)),identity),identity) != multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),identity)
| least_upper_bound(identity,multiply(inverse(multiply(inverse(inverse(a)),identity)),identity)) = multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),identity) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(multiply(inverse(inverse(a)),identity)),identity)),multiply(least_upper_bound(inverse(multiply(inverse(inverse(a)),identity)),identity),identity)) )],[refute_0_78,refute_0_81]) ).
cnf(refute_0_83,plain,
least_upper_bound(identity,multiply(inverse(multiply(inverse(inverse(a)),identity)),identity)) = multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),identity),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(multiply(inverse(inverse(a)),identity)),identity),identity),multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),identity)) )],[refute_0_66,refute_0_82]) ).
cnf(refute_0_84,plain,
( identity != least_upper_bound(identity,multiply(inverse(multiply(inverse(inverse(a)),identity)),identity))
| least_upper_bound(identity,multiply(inverse(multiply(inverse(inverse(a)),identity)),identity)) != multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),identity)
| identity = multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),identity) ),
introduced(tautology,[equality,[$cnf( ~ $equal(identity,multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),identity)) ),[0],$fot(least_upper_bound(identity,multiply(inverse(multiply(inverse(inverse(a)),identity)),identity)))]]) ).
cnf(refute_0_85,plain,
( identity != least_upper_bound(identity,multiply(inverse(multiply(inverse(inverse(a)),identity)),identity))
| identity = multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),identity) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(multiply(inverse(inverse(a)),identity)),identity)),multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),identity)) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
identity = multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),identity),
inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,multiply(inverse(multiply(inverse(inverse(a)),identity)),identity))) )],[refute_0_50,refute_0_85]) ).
cnf(refute_0_87,plain,
( identity != multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),identity)
| multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),identity) = identity ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(identity)),bind(Y0,$fot(multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),identity)))]]) ).
cnf(refute_0_88,plain,
multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),identity) = identity,
inference(resolve,[$cnf( $equal(identity,multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),identity)) )],[refute_0_86,refute_0_87]) ).
cnf(refute_0_89,plain,
( multiply(multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),identity),X_90) != multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),multiply(identity,X_90))
| multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),identity) != identity
| multiply(identity,X_90) = multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),multiply(identity,X_90)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),identity),X_90),multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),multiply(identity,X_90))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_90,plain,
( multiply(multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),identity),X_90) != multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),multiply(identity,X_90))
| multiply(identity,X_90) = multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),multiply(identity,X_90)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),identity),identity) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
multiply(identity,X_90) = multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),multiply(identity,X_90)),
inference(resolve,[$cnf( $equal(multiply(multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),identity),X_90),multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),multiply(identity,X_90))) )],[refute_0_43,refute_0_90]) ).
cnf(refute_0_92,plain,
multiply(identity,X_90) = X_90,
inference(subst,[],[left_identity:[bind(X,$fot(X_90))]]) ).
cnf(refute_0_93,plain,
( multiply(identity,X_90) != X_90
| multiply(identity,X_90) != multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),multiply(identity,X_90))
| X_90 = multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),multiply(identity,X_90)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_90),multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),multiply(identity,X_90))) ),[0],$fot(X_90)]]) ).
cnf(refute_0_94,plain,
( multiply(identity,X_90) != multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),multiply(identity,X_90))
| X_90 = multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),multiply(identity,X_90)) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_90),X_90) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),multiply(identity,X_90)) = multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),multiply(identity,X_90)),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),multiply(identity,X_90)))]]) ).
cnf(refute_0_96,plain,
( multiply(identity,X_90) != X_90
| multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),multiply(identity,X_90)) != multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),multiply(identity,X_90))
| multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),multiply(identity,X_90)) = multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),X_90) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),multiply(identity,X_90)),multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),multiply(identity,X_90))) ),[1,1],$fot(X_90)]]) ).
cnf(refute_0_97,plain,
( multiply(identity,X_90) != X_90
| multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),multiply(identity,X_90)) = multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),X_90) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),multiply(identity,X_90)),multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),multiply(identity,X_90))) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),multiply(identity,X_90)) = multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),X_90),
inference(resolve,[$cnf( $equal(multiply(identity,X_90),X_90) )],[refute_0_92,refute_0_97]) ).
cnf(refute_0_99,plain,
( X_90 != multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),multiply(identity,X_90))
| multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),multiply(identity,X_90)) != multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),X_90)
| X_90 = multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),X_90) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_90,multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),X_90)) ),[0],$fot(multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),multiply(identity,X_90)))]]) ).
cnf(refute_0_100,plain,
( X_90 != multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),multiply(identity,X_90))
| X_90 = multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),X_90) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),multiply(identity,X_90)),multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),X_90)) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
( multiply(identity,X_90) != multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),multiply(identity,X_90))
| X_90 = multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),X_90) ),
inference(resolve,[$cnf( $equal(X_90,multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),multiply(identity,X_90))) )],[refute_0_94,refute_0_100]) ).
cnf(refute_0_102,plain,
X_90 = multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),X_90),
inference(resolve,[$cnf( $equal(multiply(identity,X_90),multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),multiply(identity,X_90))) )],[refute_0_91,refute_0_101]) ).
cnf(refute_0_103,plain,
( X_90 != multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),X_90)
| multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),X_90) = X_90 ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(X_90)),bind(Y0,$fot(multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),X_90)))]]) ).
cnf(refute_0_104,plain,
multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),X_90) = X_90,
inference(resolve,[$cnf( $equal(X_90,multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),X_90)) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),a) = a,
inference(subst,[],[refute_0_104:[bind(X_90,$fot(a))]]) ).
cnf(refute_0_106,plain,
multiply(least_upper_bound(X_62,identity),X_61) = least_upper_bound(X_61,multiply(X_62,X_61)),
inference(subst,[],[refute_0_75:[bind(X_58,$fot(X_61)),bind(X_59,$fot(X_62))]]) ).
cnf(refute_0_107,plain,
least_upper_bound(identity,X_62) = least_upper_bound(X_62,identity),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(identity)),bind(Y,$fot(X_62))]]) ).
cnf(refute_0_108,plain,
( least_upper_bound(identity,X_62) != least_upper_bound(X_62,identity)
| least_upper_bound(X_62,identity) = least_upper_bound(identity,X_62) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(least_upper_bound(identity,X_62))),bind(Y0,$fot(least_upper_bound(X_62,identity)))]]) ).
cnf(refute_0_109,plain,
least_upper_bound(X_62,identity) = least_upper_bound(identity,X_62),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,X_62),least_upper_bound(X_62,identity)) )],[refute_0_107,refute_0_108]) ).
cnf(refute_0_110,plain,
( multiply(least_upper_bound(X_62,identity),X_61) != least_upper_bound(X_61,multiply(X_62,X_61))
| least_upper_bound(X_62,identity) != least_upper_bound(identity,X_62)
| multiply(least_upper_bound(identity,X_62),X_61) = least_upper_bound(X_61,multiply(X_62,X_61)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_62,identity),X_61),least_upper_bound(X_61,multiply(X_62,X_61))) ),[0,0],$fot(least_upper_bound(identity,X_62))]]) ).
cnf(refute_0_111,plain,
( multiply(least_upper_bound(X_62,identity),X_61) != least_upper_bound(X_61,multiply(X_62,X_61))
| multiply(least_upper_bound(identity,X_62),X_61) = least_upper_bound(X_61,multiply(X_62,X_61)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_62,identity),least_upper_bound(identity,X_62)) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
multiply(least_upper_bound(identity,X_62),X_61) = least_upper_bound(X_61,multiply(X_62,X_61)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_62,identity),X_61),least_upper_bound(X_61,multiply(X_62,X_61))) )],[refute_0_106,refute_0_111]) ).
cnf(refute_0_113,plain,
least_upper_bound(X_61,multiply(X_62,X_61)) = multiply(least_upper_bound(X_62,identity),X_61),
inference(subst,[],[refute_0_77:[bind(X_58,$fot(X_61)),bind(X_59,$fot(X_62))]]) ).
cnf(refute_0_114,plain,
( multiply(least_upper_bound(identity,X_62),X_61) != least_upper_bound(X_61,multiply(X_62,X_61))
| least_upper_bound(X_61,multiply(X_62,X_61)) != multiply(least_upper_bound(X_62,identity),X_61)
| multiply(least_upper_bound(identity,X_62),X_61) = multiply(least_upper_bound(X_62,identity),X_61) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(identity,X_62),X_61),multiply(least_upper_bound(X_62,identity),X_61)) ),[0],$fot(least_upper_bound(X_61,multiply(X_62,X_61)))]]) ).
cnf(refute_0_115,plain,
( multiply(least_upper_bound(identity,X_62),X_61) != least_upper_bound(X_61,multiply(X_62,X_61))
| multiply(least_upper_bound(identity,X_62),X_61) = multiply(least_upper_bound(X_62,identity),X_61) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_61,multiply(X_62,X_61)),multiply(least_upper_bound(X_62,identity),X_61)) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
multiply(least_upper_bound(identity,X_62),X_61) = multiply(least_upper_bound(X_62,identity),X_61),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_62),X_61),least_upper_bound(X_61,multiply(X_62,X_61))) )],[refute_0_112,refute_0_115]) ).
cnf(refute_0_117,plain,
( multiply(least_upper_bound(identity,X_62),X_61) != multiply(least_upper_bound(X_62,identity),X_61)
| multiply(least_upper_bound(X_62,identity),X_61) = multiply(least_upper_bound(identity,X_62),X_61) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(multiply(least_upper_bound(identity,X_62),X_61))),bind(Y0,$fot(multiply(least_upper_bound(X_62,identity),X_61)))]]) ).
cnf(refute_0_118,plain,
multiply(least_upper_bound(X_62,identity),X_61) = multiply(least_upper_bound(identity,X_62),X_61),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_62),X_61),multiply(least_upper_bound(X_62,identity),X_61)) )],[refute_0_116,refute_0_117]) ).
cnf(refute_0_119,plain,
multiply(least_upper_bound(inverse(multiply(inverse(inverse(a)),identity)),identity),a) = multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),a),
inference(subst,[],[refute_0_118:[bind(X_61,$fot(a)),bind(X_62,$fot(inverse(multiply(inverse(inverse(a)),identity))))]]) ).
cnf(refute_0_120,plain,
( multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),a) != a
| multiply(least_upper_bound(inverse(multiply(inverse(inverse(a)),identity)),identity),a) != multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),a)
| multiply(least_upper_bound(inverse(multiply(inverse(inverse(a)),identity)),identity),a) = a ),
inference(subst,[],[refute_0_80:[bind(X0,$fot(multiply(least_upper_bound(inverse(multiply(inverse(inverse(a)),identity)),identity),a))),bind(Y0,$fot(multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),a))),bind(Z0,$fot(a))]]) ).
cnf(refute_0_121,plain,
( multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),a) != a
| multiply(least_upper_bound(inverse(multiply(inverse(inverse(a)),identity)),identity),a) = a ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(multiply(inverse(inverse(a)),identity)),identity),a),multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),a)) )],[refute_0_119,refute_0_120]) ).
cnf(refute_0_122,plain,
multiply(least_upper_bound(inverse(multiply(inverse(inverse(a)),identity)),identity),a) = a,
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(multiply(inverse(inverse(a)),identity))),a),a) )],[refute_0_105,refute_0_121]) ).
cnf(refute_0_123,plain,
least_upper_bound(a,multiply(inverse(multiply(inverse(inverse(a)),identity)),a)) = multiply(least_upper_bound(inverse(multiply(inverse(inverse(a)),identity)),identity),a),
inference(subst,[],[refute_0_77:[bind(X_58,$fot(a)),bind(X_59,$fot(inverse(multiply(inverse(inverse(a)),identity))))]]) ).
cnf(refute_0_124,plain,
( multiply(least_upper_bound(inverse(multiply(inverse(inverse(a)),identity)),identity),a) != a
| least_upper_bound(a,multiply(inverse(multiply(inverse(inverse(a)),identity)),a)) != multiply(least_upper_bound(inverse(multiply(inverse(inverse(a)),identity)),identity),a)
| least_upper_bound(a,multiply(inverse(multiply(inverse(inverse(a)),identity)),a)) = a ),
inference(subst,[],[refute_0_80:[bind(X0,$fot(least_upper_bound(a,multiply(inverse(multiply(inverse(inverse(a)),identity)),a)))),bind(Y0,$fot(multiply(least_upper_bound(inverse(multiply(inverse(inverse(a)),identity)),identity),a))),bind(Z0,$fot(a))]]) ).
cnf(refute_0_125,plain,
( multiply(least_upper_bound(inverse(multiply(inverse(inverse(a)),identity)),identity),a) != a
| least_upper_bound(a,multiply(inverse(multiply(inverse(inverse(a)),identity)),a)) = a ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,multiply(inverse(multiply(inverse(inverse(a)),identity)),a)),multiply(least_upper_bound(inverse(multiply(inverse(inverse(a)),identity)),identity),a)) )],[refute_0_123,refute_0_124]) ).
cnf(refute_0_126,plain,
least_upper_bound(a,multiply(inverse(multiply(inverse(inverse(a)),identity)),a)) = a,
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(multiply(inverse(inverse(a)),identity)),identity),a),a) )],[refute_0_122,refute_0_125]) ).
cnf(refute_0_127,plain,
multiply(inverse(a),least_upper_bound(identity,Z)) = least_upper_bound(multiply(inverse(a),identity),multiply(inverse(a),Z)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(inverse(a))),bind(Y,$fot(identity))]]) ).
cnf(refute_0_128,plain,
multiply(least_upper_bound(inverse(X_77),identity),identity) = least_upper_bound(identity,multiply(inverse(X_77),identity)),
inference(subst,[],[refute_0_75:[bind(X_58,$fot(identity)),bind(X_59,$fot(inverse(X_77)))]]) ).
cnf(refute_0_129,plain,
multiply(inverse(X_51),least_upper_bound(X_51,X_52)) = least_upper_bound(multiply(inverse(X_51),X_51),multiply(inverse(X_51),X_52)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(inverse(X_51))),bind(Y,$fot(X_51)),bind(Z,$fot(X_52))]]) ).
cnf(refute_0_130,plain,
multiply(inverse(X_51),X_51) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_51))]]) ).
cnf(refute_0_131,plain,
( multiply(inverse(X_51),X_51) != identity
| multiply(inverse(X_51),least_upper_bound(X_51,X_52)) != least_upper_bound(multiply(inverse(X_51),X_51),multiply(inverse(X_51),X_52))
| multiply(inverse(X_51),least_upper_bound(X_51,X_52)) = least_upper_bound(identity,multiply(inverse(X_51),X_52)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_51),least_upper_bound(X_51,X_52)),least_upper_bound(multiply(inverse(X_51),X_51),multiply(inverse(X_51),X_52))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_132,plain,
( multiply(inverse(X_51),least_upper_bound(X_51,X_52)) != least_upper_bound(multiply(inverse(X_51),X_51),multiply(inverse(X_51),X_52))
| multiply(inverse(X_51),least_upper_bound(X_51,X_52)) = least_upper_bound(identity,multiply(inverse(X_51),X_52)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_51),X_51),identity) )],[refute_0_130,refute_0_131]) ).
cnf(refute_0_133,plain,
multiply(inverse(X_51),least_upper_bound(X_51,X_52)) = least_upper_bound(identity,multiply(inverse(X_51),X_52)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_51),least_upper_bound(X_51,X_52)),least_upper_bound(multiply(inverse(X_51),X_51),multiply(inverse(X_51),X_52))) )],[refute_0_129,refute_0_132]) ).
cnf(refute_0_134,plain,
multiply(inverse(X_77),least_upper_bound(X_77,identity)) = least_upper_bound(identity,multiply(inverse(X_77),identity)),
inference(subst,[],[refute_0_133:[bind(X_51,$fot(X_77)),bind(X_52,$fot(identity))]]) ).
cnf(refute_0_135,plain,
( multiply(inverse(X_77),least_upper_bound(X_77,identity)) != least_upper_bound(identity,multiply(inverse(X_77),identity))
| least_upper_bound(identity,multiply(inverse(X_77),identity)) = multiply(inverse(X_77),least_upper_bound(X_77,identity)) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(multiply(inverse(X_77),least_upper_bound(X_77,identity)))),bind(Y0,$fot(least_upper_bound(identity,multiply(inverse(X_77),identity))))]]) ).
cnf(refute_0_136,plain,
least_upper_bound(identity,multiply(inverse(X_77),identity)) = multiply(inverse(X_77),least_upper_bound(X_77,identity)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_77),least_upper_bound(X_77,identity)),least_upper_bound(identity,multiply(inverse(X_77),identity))) )],[refute_0_134,refute_0_135]) ).
cnf(refute_0_137,plain,
( multiply(least_upper_bound(inverse(X_77),identity),identity) != least_upper_bound(identity,multiply(inverse(X_77),identity))
| least_upper_bound(identity,multiply(inverse(X_77),identity)) != multiply(inverse(X_77),least_upper_bound(X_77,identity))
| multiply(least_upper_bound(inverse(X_77),identity),identity) = multiply(inverse(X_77),least_upper_bound(X_77,identity)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(inverse(X_77),identity),identity),multiply(inverse(X_77),least_upper_bound(X_77,identity))) ),[0],$fot(least_upper_bound(identity,multiply(inverse(X_77),identity)))]]) ).
cnf(refute_0_138,plain,
( multiply(least_upper_bound(inverse(X_77),identity),identity) != least_upper_bound(identity,multiply(inverse(X_77),identity))
| multiply(least_upper_bound(inverse(X_77),identity),identity) = multiply(inverse(X_77),least_upper_bound(X_77,identity)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(X_77),identity)),multiply(inverse(X_77),least_upper_bound(X_77,identity))) )],[refute_0_136,refute_0_137]) ).
cnf(refute_0_139,plain,
multiply(least_upper_bound(inverse(X_77),identity),identity) = multiply(inverse(X_77),least_upper_bound(X_77,identity)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_77),identity),identity),least_upper_bound(identity,multiply(inverse(X_77),identity))) )],[refute_0_128,refute_0_138]) ).
cnf(refute_0_140,plain,
multiply(least_upper_bound(inverse(X_77),identity),identity) = multiply(least_upper_bound(identity,inverse(X_77)),identity),
inference(subst,[],[refute_0_118:[bind(X_61,$fot(identity)),bind(X_62,$fot(inverse(X_77)))]]) ).
cnf(refute_0_141,plain,
( multiply(least_upper_bound(inverse(X_77),identity),identity) != multiply(inverse(X_77),least_upper_bound(X_77,identity))
| multiply(least_upper_bound(inverse(X_77),identity),identity) != multiply(least_upper_bound(identity,inverse(X_77)),identity)
| multiply(least_upper_bound(identity,inverse(X_77)),identity) = multiply(inverse(X_77),least_upper_bound(X_77,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(X_77),identity),identity),multiply(inverse(X_77),least_upper_bound(X_77,identity))) ),[0],$fot(multiply(least_upper_bound(identity,inverse(X_77)),identity))]]) ).
cnf(refute_0_142,plain,
( multiply(least_upper_bound(inverse(X_77),identity),identity) != multiply(inverse(X_77),least_upper_bound(X_77,identity))
| multiply(least_upper_bound(identity,inverse(X_77)),identity) = multiply(inverse(X_77),least_upper_bound(X_77,identity)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_77),identity),identity),multiply(least_upper_bound(identity,inverse(X_77)),identity)) )],[refute_0_140,refute_0_141]) ).
cnf(refute_0_143,plain,
multiply(least_upper_bound(identity,inverse(X_77)),identity) = multiply(inverse(X_77),least_upper_bound(X_77,identity)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_77),identity),identity),multiply(inverse(X_77),least_upper_bound(X_77,identity))) )],[refute_0_139,refute_0_142]) ).
cnf(refute_0_144,plain,
multiply(least_upper_bound(identity,inverse(a)),identity) = multiply(inverse(a),least_upper_bound(a,identity)),
inference(subst,[],[refute_0_143:[bind(X_77,$fot(a))]]) ).
cnf(refute_0_145,plain,
( multiply(least_upper_bound(identity,inverse(a)),identity) != multiply(inverse(a),least_upper_bound(a,identity))
| least_upper_bound(identity,inverse(a)) != identity
| multiply(identity,identity) = multiply(inverse(a),least_upper_bound(a,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(a)),identity),multiply(inverse(a),least_upper_bound(a,identity))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_146,plain,
( multiply(least_upper_bound(identity,inverse(a)),identity) != multiply(inverse(a),least_upper_bound(a,identity))
| multiply(identity,identity) = multiply(inverse(a),least_upper_bound(a,identity)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(a)),identity) )],[p05a_2,refute_0_145]) ).
cnf(refute_0_147,plain,
multiply(identity,identity) = multiply(inverse(a),least_upper_bound(a,identity)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(a)),identity),multiply(inverse(a),least_upper_bound(a,identity))) )],[refute_0_144,refute_0_146]) ).
cnf(refute_0_148,plain,
multiply(identity,identity) = identity,
inference(subst,[],[left_identity:[bind(X,$fot(identity))]]) ).
cnf(refute_0_149,plain,
( multiply(identity,identity) != multiply(inverse(a),least_upper_bound(a,identity))
| multiply(identity,identity) != identity
| identity = multiply(inverse(a),least_upper_bound(a,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,identity),multiply(inverse(a),least_upper_bound(a,identity))) ),[0],$fot(identity)]]) ).
cnf(refute_0_150,plain,
( multiply(identity,identity) != multiply(inverse(a),least_upper_bound(a,identity))
| identity = multiply(inverse(a),least_upper_bound(a,identity)) ),
inference(resolve,[$cnf( $equal(multiply(identity,identity),identity) )],[refute_0_148,refute_0_149]) ).
cnf(refute_0_151,plain,
multiply(inverse(a),least_upper_bound(a,identity)) = multiply(inverse(a),least_upper_bound(a,identity)),
introduced(tautology,[refl,[$fot(multiply(inverse(a),least_upper_bound(a,identity)))]]) ).
cnf(refute_0_152,plain,
( multiply(inverse(a),least_upper_bound(a,identity)) != multiply(inverse(a),least_upper_bound(a,identity))
| least_upper_bound(a,identity) != identity
| multiply(inverse(a),least_upper_bound(a,identity)) = multiply(inverse(a),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(a),least_upper_bound(a,identity)),multiply(inverse(a),least_upper_bound(a,identity))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_153,plain,
( least_upper_bound(a,identity) != identity
| multiply(inverse(a),least_upper_bound(a,identity)) = multiply(inverse(a),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(a),least_upper_bound(a,identity)),multiply(inverse(a),least_upper_bound(a,identity))) )],[refute_0_151,refute_0_152]) ).
cnf(refute_0_154,plain,
multiply(inverse(a),least_upper_bound(a,identity)) = multiply(inverse(a),identity),
inference(resolve,[$cnf( $equal(least_upper_bound(a,identity),identity) )],[refute_0_19,refute_0_153]) ).
cnf(refute_0_155,plain,
( multiply(inverse(a),least_upper_bound(a,identity)) != multiply(inverse(a),identity)
| identity != multiply(inverse(a),least_upper_bound(a,identity))
| identity = multiply(inverse(a),identity) ),
introduced(tautology,[equality,[$cnf( $equal(identity,multiply(inverse(a),least_upper_bound(a,identity))) ),[1],$fot(multiply(inverse(a),identity))]]) ).
cnf(refute_0_156,plain,
( identity != multiply(inverse(a),least_upper_bound(a,identity))
| identity = multiply(inverse(a),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(a),least_upper_bound(a,identity)),multiply(inverse(a),identity)) )],[refute_0_154,refute_0_155]) ).
cnf(refute_0_157,plain,
( multiply(identity,identity) != multiply(inverse(a),least_upper_bound(a,identity))
| identity = multiply(inverse(a),identity) ),
inference(resolve,[$cnf( $equal(identity,multiply(inverse(a),least_upper_bound(a,identity))) )],[refute_0_150,refute_0_156]) ).
cnf(refute_0_158,plain,
identity = multiply(inverse(a),identity),
inference(resolve,[$cnf( $equal(multiply(identity,identity),multiply(inverse(a),least_upper_bound(a,identity))) )],[refute_0_147,refute_0_157]) ).
cnf(refute_0_159,plain,
( identity != multiply(inverse(a),identity)
| multiply(inverse(a),identity) = identity ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(identity)),bind(Y0,$fot(multiply(inverse(a),identity)))]]) ).
cnf(refute_0_160,plain,
multiply(inverse(a),identity) = identity,
inference(resolve,[$cnf( $equal(identity,multiply(inverse(a),identity)) )],[refute_0_158,refute_0_159]) ).
cnf(refute_0_161,plain,
( multiply(inverse(a),identity) != identity
| multiply(inverse(a),least_upper_bound(identity,Z)) != least_upper_bound(multiply(inverse(a),identity),multiply(inverse(a),Z))
| multiply(inverse(a),least_upper_bound(identity,Z)) = least_upper_bound(identity,multiply(inverse(a),Z)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(a),least_upper_bound(identity,Z)),least_upper_bound(multiply(inverse(a),identity),multiply(inverse(a),Z))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_162,plain,
( multiply(inverse(a),least_upper_bound(identity,Z)) != least_upper_bound(multiply(inverse(a),identity),multiply(inverse(a),Z))
| multiply(inverse(a),least_upper_bound(identity,Z)) = least_upper_bound(identity,multiply(inverse(a),Z)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(a),identity),identity) )],[refute_0_160,refute_0_161]) ).
cnf(refute_0_163,plain,
multiply(inverse(a),least_upper_bound(identity,Z)) = least_upper_bound(identity,multiply(inverse(a),Z)),
inference(resolve,[$cnf( $equal(multiply(inverse(a),least_upper_bound(identity,Z)),least_upper_bound(multiply(inverse(a),identity),multiply(inverse(a),Z))) )],[refute_0_127,refute_0_162]) ).
cnf(refute_0_164,plain,
multiply(inverse(X_54),least_upper_bound(X_53,X_54)) = least_upper_bound(identity,multiply(inverse(X_54),X_53)),
inference(subst,[],[refute_0_13:[bind(X_51,$fot(X_53)),bind(X_52,$fot(X_54))]]) ).
cnf(refute_0_165,plain,
least_upper_bound(X_54,X_53) = least_upper_bound(X_53,X_54),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_54)),bind(Y,$fot(X_53))]]) ).
cnf(refute_0_166,plain,
( least_upper_bound(X_54,X_53) != least_upper_bound(X_53,X_54)
| least_upper_bound(X_53,X_54) = least_upper_bound(X_54,X_53) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(least_upper_bound(X_54,X_53))),bind(Y0,$fot(least_upper_bound(X_53,X_54)))]]) ).
cnf(refute_0_167,plain,
least_upper_bound(X_53,X_54) = least_upper_bound(X_54,X_53),
inference(resolve,[$cnf( $equal(least_upper_bound(X_54,X_53),least_upper_bound(X_53,X_54)) )],[refute_0_165,refute_0_166]) ).
cnf(refute_0_168,plain,
( multiply(inverse(X_54),least_upper_bound(X_53,X_54)) != least_upper_bound(identity,multiply(inverse(X_54),X_53))
| least_upper_bound(X_53,X_54) != least_upper_bound(X_54,X_53)
| multiply(inverse(X_54),least_upper_bound(X_54,X_53)) = least_upper_bound(identity,multiply(inverse(X_54),X_53)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_54),least_upper_bound(X_53,X_54)),least_upper_bound(identity,multiply(inverse(X_54),X_53))) ),[0,1],$fot(least_upper_bound(X_54,X_53))]]) ).
cnf(refute_0_169,plain,
( multiply(inverse(X_54),least_upper_bound(X_53,X_54)) != least_upper_bound(identity,multiply(inverse(X_54),X_53))
| multiply(inverse(X_54),least_upper_bound(X_54,X_53)) = least_upper_bound(identity,multiply(inverse(X_54),X_53)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_53,X_54),least_upper_bound(X_54,X_53)) )],[refute_0_167,refute_0_168]) ).
cnf(refute_0_170,plain,
multiply(inverse(X_54),least_upper_bound(X_54,X_53)) = least_upper_bound(identity,multiply(inverse(X_54),X_53)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_54),least_upper_bound(X_53,X_54)),least_upper_bound(identity,multiply(inverse(X_54),X_53))) )],[refute_0_164,refute_0_169]) ).
cnf(refute_0_171,plain,
( multiply(inverse(X_54),least_upper_bound(X_54,X_53)) != least_upper_bound(identity,multiply(inverse(X_54),X_53))
| least_upper_bound(identity,multiply(inverse(X_54),X_53)) = multiply(inverse(X_54),least_upper_bound(X_54,X_53)) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(multiply(inverse(X_54),least_upper_bound(X_54,X_53)))),bind(Y0,$fot(least_upper_bound(identity,multiply(inverse(X_54),X_53))))]]) ).
cnf(refute_0_172,plain,
least_upper_bound(identity,multiply(inverse(X_54),X_53)) = multiply(inverse(X_54),least_upper_bound(X_54,X_53)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_54),least_upper_bound(X_54,X_53)),least_upper_bound(identity,multiply(inverse(X_54),X_53))) )],[refute_0_170,refute_0_171]) ).
cnf(refute_0_173,plain,
least_upper_bound(identity,multiply(inverse(a),Z)) = multiply(inverse(a),least_upper_bound(a,Z)),
inference(subst,[],[refute_0_172:[bind(X_53,$fot(Z)),bind(X_54,$fot(a))]]) ).
cnf(refute_0_174,plain,
( multiply(inverse(a),least_upper_bound(identity,Z)) != least_upper_bound(identity,multiply(inverse(a),Z))
| least_upper_bound(identity,multiply(inverse(a),Z)) != multiply(inverse(a),least_upper_bound(a,Z))
| multiply(inverse(a),least_upper_bound(identity,Z)) = multiply(inverse(a),least_upper_bound(a,Z)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(a),least_upper_bound(identity,Z)),multiply(inverse(a),least_upper_bound(a,Z))) ),[0],$fot(least_upper_bound(identity,multiply(inverse(a),Z)))]]) ).
cnf(refute_0_175,plain,
( multiply(inverse(a),least_upper_bound(identity,Z)) != least_upper_bound(identity,multiply(inverse(a),Z))
| multiply(inverse(a),least_upper_bound(identity,Z)) = multiply(inverse(a),least_upper_bound(a,Z)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(a),Z)),multiply(inverse(a),least_upper_bound(a,Z))) )],[refute_0_173,refute_0_174]) ).
cnf(refute_0_176,plain,
multiply(inverse(a),least_upper_bound(identity,Z)) = multiply(inverse(a),least_upper_bound(a,Z)),
inference(resolve,[$cnf( $equal(multiply(inverse(a),least_upper_bound(identity,Z)),least_upper_bound(identity,multiply(inverse(a),Z))) )],[refute_0_163,refute_0_175]) ).
cnf(refute_0_177,plain,
multiply(multiply(inverse(a),identity),X_90) = multiply(inverse(a),multiply(identity,X_90)),
inference(subst,[],[associativity:[bind(X,$fot(inverse(a))),bind(Y,$fot(identity)),bind(Z,$fot(X_90))]]) ).
cnf(refute_0_178,plain,
( multiply(multiply(inverse(a),identity),X_90) != multiply(inverse(a),multiply(identity,X_90))
| multiply(inverse(a),identity) != identity
| multiply(identity,X_90) = multiply(inverse(a),multiply(identity,X_90)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(a),identity),X_90),multiply(inverse(a),multiply(identity,X_90))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_179,plain,
( multiply(multiply(inverse(a),identity),X_90) != multiply(inverse(a),multiply(identity,X_90))
| multiply(identity,X_90) = multiply(inverse(a),multiply(identity,X_90)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(a),identity),identity) )],[refute_0_160,refute_0_178]) ).
cnf(refute_0_180,plain,
multiply(identity,X_90) = multiply(inverse(a),multiply(identity,X_90)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(a),identity),X_90),multiply(inverse(a),multiply(identity,X_90))) )],[refute_0_177,refute_0_179]) ).
cnf(refute_0_181,plain,
( multiply(identity,X_90) != X_90
| multiply(identity,X_90) != multiply(inverse(a),multiply(identity,X_90))
| X_90 = multiply(inverse(a),multiply(identity,X_90)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_90),multiply(inverse(a),multiply(identity,X_90))) ),[0],$fot(X_90)]]) ).
cnf(refute_0_182,plain,
( multiply(identity,X_90) != multiply(inverse(a),multiply(identity,X_90))
| X_90 = multiply(inverse(a),multiply(identity,X_90)) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_90),X_90) )],[refute_0_92,refute_0_181]) ).
cnf(refute_0_183,plain,
multiply(inverse(a),multiply(identity,X_90)) = multiply(inverse(a),multiply(identity,X_90)),
introduced(tautology,[refl,[$fot(multiply(inverse(a),multiply(identity,X_90)))]]) ).
cnf(refute_0_184,plain,
( multiply(identity,X_90) != X_90
| multiply(inverse(a),multiply(identity,X_90)) != multiply(inverse(a),multiply(identity,X_90))
| multiply(inverse(a),multiply(identity,X_90)) = multiply(inverse(a),X_90) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(a),multiply(identity,X_90)),multiply(inverse(a),multiply(identity,X_90))) ),[1,1],$fot(X_90)]]) ).
cnf(refute_0_185,plain,
( multiply(identity,X_90) != X_90
| multiply(inverse(a),multiply(identity,X_90)) = multiply(inverse(a),X_90) ),
inference(resolve,[$cnf( $equal(multiply(inverse(a),multiply(identity,X_90)),multiply(inverse(a),multiply(identity,X_90))) )],[refute_0_183,refute_0_184]) ).
cnf(refute_0_186,plain,
multiply(inverse(a),multiply(identity,X_90)) = multiply(inverse(a),X_90),
inference(resolve,[$cnf( $equal(multiply(identity,X_90),X_90) )],[refute_0_92,refute_0_185]) ).
cnf(refute_0_187,plain,
( X_90 != multiply(inverse(a),multiply(identity,X_90))
| multiply(inverse(a),multiply(identity,X_90)) != multiply(inverse(a),X_90)
| X_90 = multiply(inverse(a),X_90) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_90,multiply(inverse(a),X_90)) ),[0],$fot(multiply(inverse(a),multiply(identity,X_90)))]]) ).
cnf(refute_0_188,plain,
( X_90 != multiply(inverse(a),multiply(identity,X_90))
| X_90 = multiply(inverse(a),X_90) ),
inference(resolve,[$cnf( $equal(multiply(inverse(a),multiply(identity,X_90)),multiply(inverse(a),X_90)) )],[refute_0_186,refute_0_187]) ).
cnf(refute_0_189,plain,
( multiply(identity,X_90) != multiply(inverse(a),multiply(identity,X_90))
| X_90 = multiply(inverse(a),X_90) ),
inference(resolve,[$cnf( $equal(X_90,multiply(inverse(a),multiply(identity,X_90))) )],[refute_0_182,refute_0_188]) ).
cnf(refute_0_190,plain,
X_90 = multiply(inverse(a),X_90),
inference(resolve,[$cnf( $equal(multiply(identity,X_90),multiply(inverse(a),multiply(identity,X_90))) )],[refute_0_180,refute_0_189]) ).
cnf(refute_0_191,plain,
( X_90 != multiply(inverse(a),X_90)
| multiply(inverse(a),X_90) = X_90 ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(X_90)),bind(Y0,$fot(multiply(inverse(a),X_90)))]]) ).
cnf(refute_0_192,plain,
multiply(inverse(a),X_90) = X_90,
inference(resolve,[$cnf( $equal(X_90,multiply(inverse(a),X_90)) )],[refute_0_190,refute_0_191]) ).
cnf(refute_0_193,plain,
multiply(inverse(a),least_upper_bound(identity,Z)) = least_upper_bound(identity,Z),
inference(subst,[],[refute_0_192:[bind(X_90,$fot(least_upper_bound(identity,Z)))]]) ).
cnf(refute_0_194,plain,
( multiply(inverse(a),least_upper_bound(identity,Z)) != multiply(inverse(a),least_upper_bound(a,Z))
| multiply(inverse(a),least_upper_bound(identity,Z)) != least_upper_bound(identity,Z)
| least_upper_bound(identity,Z) = multiply(inverse(a),least_upper_bound(a,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(a),least_upper_bound(identity,Z)),multiply(inverse(a),least_upper_bound(a,Z))) ),[0],$fot(least_upper_bound(identity,Z))]]) ).
cnf(refute_0_195,plain,
( multiply(inverse(a),least_upper_bound(identity,Z)) != multiply(inverse(a),least_upper_bound(a,Z))
| least_upper_bound(identity,Z) = multiply(inverse(a),least_upper_bound(a,Z)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(a),least_upper_bound(identity,Z)),least_upper_bound(identity,Z)) )],[refute_0_193,refute_0_194]) ).
cnf(refute_0_196,plain,
multiply(inverse(a),least_upper_bound(a,Z)) = least_upper_bound(a,Z),
inference(subst,[],[refute_0_192:[bind(X_90,$fot(least_upper_bound(a,Z)))]]) ).
cnf(refute_0_197,plain,
( multiply(inverse(a),least_upper_bound(a,Z)) != least_upper_bound(a,Z)
| least_upper_bound(identity,Z) != multiply(inverse(a),least_upper_bound(a,Z))
| least_upper_bound(identity,Z) = least_upper_bound(a,Z) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,Z),multiply(inverse(a),least_upper_bound(a,Z))) ),[1],$fot(least_upper_bound(a,Z))]]) ).
cnf(refute_0_198,plain,
( least_upper_bound(identity,Z) != multiply(inverse(a),least_upper_bound(a,Z))
| least_upper_bound(identity,Z) = least_upper_bound(a,Z) ),
inference(resolve,[$cnf( $equal(multiply(inverse(a),least_upper_bound(a,Z)),least_upper_bound(a,Z)) )],[refute_0_196,refute_0_197]) ).
cnf(refute_0_199,plain,
( multiply(inverse(a),least_upper_bound(identity,Z)) != multiply(inverse(a),least_upper_bound(a,Z))
| least_upper_bound(identity,Z) = least_upper_bound(a,Z) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,Z),multiply(inverse(a),least_upper_bound(a,Z))) )],[refute_0_195,refute_0_198]) ).
cnf(refute_0_200,plain,
least_upper_bound(identity,Z) = least_upper_bound(a,Z),
inference(resolve,[$cnf( $equal(multiply(inverse(a),least_upper_bound(identity,Z)),multiply(inverse(a),least_upper_bound(a,Z))) )],[refute_0_176,refute_0_199]) ).
cnf(refute_0_201,plain,
least_upper_bound(identity,multiply(inverse(multiply(inverse(inverse(a)),identity)),a)) = least_upper_bound(a,multiply(inverse(multiply(inverse(inverse(a)),identity)),a)),
inference(subst,[],[refute_0_200:[bind(Z,$fot(multiply(inverse(multiply(inverse(inverse(a)),identity)),a)))]]) ).
cnf(refute_0_202,plain,
( least_upper_bound(a,multiply(inverse(multiply(inverse(inverse(a)),identity)),a)) != a
| least_upper_bound(identity,multiply(inverse(multiply(inverse(inverse(a)),identity)),a)) != least_upper_bound(a,multiply(inverse(multiply(inverse(inverse(a)),identity)),a))
| least_upper_bound(identity,multiply(inverse(multiply(inverse(inverse(a)),identity)),a)) = a ),
inference(subst,[],[refute_0_80:[bind(X0,$fot(least_upper_bound(identity,multiply(inverse(multiply(inverse(inverse(a)),identity)),a)))),bind(Y0,$fot(least_upper_bound(a,multiply(inverse(multiply(inverse(inverse(a)),identity)),a)))),bind(Z0,$fot(a))]]) ).
cnf(refute_0_203,plain,
( least_upper_bound(a,multiply(inverse(multiply(inverse(inverse(a)),identity)),a)) != a
| least_upper_bound(identity,multiply(inverse(multiply(inverse(inverse(a)),identity)),a)) = a ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(multiply(inverse(inverse(a)),identity)),a)),least_upper_bound(a,multiply(inverse(multiply(inverse(inverse(a)),identity)),a))) )],[refute_0_201,refute_0_202]) ).
cnf(refute_0_204,plain,
least_upper_bound(identity,multiply(inverse(multiply(inverse(inverse(a)),identity)),a)) = a,
inference(resolve,[$cnf( $equal(least_upper_bound(a,multiply(inverse(multiply(inverse(inverse(a)),identity)),a)),a) )],[refute_0_126,refute_0_203]) ).
cnf(refute_0_205,plain,
( identity != least_upper_bound(identity,multiply(inverse(multiply(inverse(inverse(a)),identity)),a))
| least_upper_bound(identity,multiply(inverse(multiply(inverse(inverse(a)),identity)),a)) != a
| identity = a ),
introduced(tautology,[equality,[$cnf( ~ $equal(identity,a) ),[0],$fot(least_upper_bound(identity,multiply(inverse(multiply(inverse(inverse(a)),identity)),a)))]]) ).
cnf(refute_0_206,plain,
( identity != least_upper_bound(identity,multiply(inverse(multiply(inverse(inverse(a)),identity)),a))
| identity = a ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(multiply(inverse(inverse(a)),identity)),a)),a) )],[refute_0_204,refute_0_205]) ).
cnf(refute_0_207,plain,
identity = a,
inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,multiply(inverse(multiply(inverse(inverse(a)),identity)),a))) )],[refute_0_42,refute_0_206]) ).
cnf(refute_0_208,plain,
$false,
inference(resolve,[$cnf( $equal(identity,a) )],[refute_0_207,prove_p05a]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP173-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 18:38:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.61/0.83 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.61/0.83
% 0.61/0.83 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.61/0.85
%------------------------------------------------------------------------------