TSTP Solution File: GRP172-2 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GRP172-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n020.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 10:37:17 EDT 2022

% Result   : Unsatisfiable 0.41s 0.59s
% Output   : CNFRefutation 0.41s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   28
%            Number of leaves      :   36
% Syntax   : Number of clauses     :  123 (  68 unt;   0 nHn;  83 RR)
%            Number of literals    :  201 ( 200 equ;  80 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    3 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :  110 (   1 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_lub,axiom,
    least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) ).

cnf(lub_absorbtion,axiom,
    least_upper_bound(X,greatest_lower_bound(X,Y)) = X ).

cnf(monotony_lub1,axiom,
    multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ).

cnf(p04d_1,hypothesis,
    greatest_lower_bound(identity,a) = identity ).

cnf(p04d_2,hypothesis,
    greatest_lower_bound(identity,b) = identity ).

cnf(prove_p04d,negated_conjecture,
    least_upper_bound(identity,multiply(a,b)) != multiply(a,b) ).

cnf(refute_0_0,plain,
    multiply(inverse(X_47),least_upper_bound(X_46,X_47)) = least_upper_bound(multiply(inverse(X_47),X_46),multiply(inverse(X_47),X_47)),
    inference(subst,[],[monotony_lub1:[bind(X,$fot(inverse(X_47))),bind(Y,$fot(X_46)),bind(Z,$fot(X_47))]]) ).

cnf(refute_0_1,plain,
    multiply(inverse(X_47),X_47) = identity,
    inference(subst,[],[left_inverse:[bind(X,$fot(X_47))]]) ).

cnf(refute_0_2,plain,
    ( multiply(inverse(X_47),X_47) != identity
    | multiply(inverse(X_47),least_upper_bound(X_46,X_47)) != least_upper_bound(multiply(inverse(X_47),X_46),multiply(inverse(X_47),X_47))
    | multiply(inverse(X_47),least_upper_bound(X_46,X_47)) = least_upper_bound(multiply(inverse(X_47),X_46),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_47),least_upper_bound(X_46,X_47)),least_upper_bound(multiply(inverse(X_47),X_46),multiply(inverse(X_47),X_47))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_3,plain,
    ( multiply(inverse(X_47),least_upper_bound(X_46,X_47)) != least_upper_bound(multiply(inverse(X_47),X_46),multiply(inverse(X_47),X_47))
    | multiply(inverse(X_47),least_upper_bound(X_46,X_47)) = least_upper_bound(multiply(inverse(X_47),X_46),identity) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_47),X_47),identity) )],[refute_0_1,refute_0_2]) ).

cnf(refute_0_4,plain,
    multiply(inverse(X_47),least_upper_bound(X_46,X_47)) = least_upper_bound(multiply(inverse(X_47),X_46),identity),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_47),least_upper_bound(X_46,X_47)),least_upper_bound(multiply(inverse(X_47),X_46),multiply(inverse(X_47),X_47))) )],[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_47),X_46),identity) = least_upper_bound(identity,multiply(inverse(X_47),X_46)),
    inference(subst,[],[refute_0_9:[bind(X,$fot(identity)),bind(Y,$fot(multiply(inverse(X_47),X_46)))]]) ).

cnf(refute_0_11,plain,
    ( multiply(inverse(X_47),least_upper_bound(X_46,X_47)) != least_upper_bound(multiply(inverse(X_47),X_46),identity)
    | least_upper_bound(multiply(inverse(X_47),X_46),identity) != least_upper_bound(identity,multiply(inverse(X_47),X_46))
    | multiply(inverse(X_47),least_upper_bound(X_46,X_47)) = least_upper_bound(identity,multiply(inverse(X_47),X_46)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_47),least_upper_bound(X_46,X_47)),least_upper_bound(identity,multiply(inverse(X_47),X_46))) ),[0],$fot(least_upper_bound(multiply(inverse(X_47),X_46),identity))]]) ).

cnf(refute_0_12,plain,
    ( multiply(inverse(X_47),least_upper_bound(X_46,X_47)) != least_upper_bound(multiply(inverse(X_47),X_46),identity)
    | multiply(inverse(X_47),least_upper_bound(X_46,X_47)) = least_upper_bound(identity,multiply(inverse(X_47),X_46)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(X_47),X_46),identity),least_upper_bound(identity,multiply(inverse(X_47),X_46))) )],[refute_0_10,refute_0_11]) ).

cnf(refute_0_13,plain,
    multiply(inverse(X_47),least_upper_bound(X_46,X_47)) = least_upper_bound(identity,multiply(inverse(X_47),X_46)),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_47),least_upper_bound(X_46,X_47)),least_upper_bound(multiply(inverse(X_47),X_46),identity)) )],[refute_0_4,refute_0_12]) ).

cnf(refute_0_14,plain,
    multiply(inverse(inverse(a)),least_upper_bound(b,inverse(a))) = least_upper_bound(identity,multiply(inverse(inverse(a)),b)),
    inference(subst,[],[refute_0_13:[bind(X_46,$fot(b)),bind(X_47,$fot(inverse(a)))]]) ).

cnf(refute_0_15,plain,
    least_upper_bound(b,least_upper_bound(identity,X_37)) = least_upper_bound(least_upper_bound(b,identity),X_37),
    inference(subst,[],[associativity_of_lub:[bind(X,$fot(b)),bind(Y,$fot(identity)),bind(Z,$fot(X_37))]]) ).

cnf(refute_0_16,plain,
    least_upper_bound(b,greatest_lower_bound(b,identity)) = b,
    inference(subst,[],[lub_absorbtion:[bind(X,$fot(b)),bind(Y,$fot(identity))]]) ).

cnf(refute_0_17,plain,
    ( greatest_lower_bound(X,Y) != greatest_lower_bound(Y,X)
    | greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y) ),
    inference(subst,[],[refute_0_7:[bind(X0,$fot(greatest_lower_bound(X,Y))),bind(Y0,$fot(greatest_lower_bound(Y,X)))]]) ).

cnf(refute_0_18,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_17]) ).

cnf(refute_0_19,plain,
    greatest_lower_bound(identity,b) = greatest_lower_bound(b,identity),
    inference(subst,[],[refute_0_18:[bind(X,$fot(b)),bind(Y,$fot(identity))]]) ).

cnf(refute_0_20,plain,
    ( greatest_lower_bound(identity,b) != greatest_lower_bound(b,identity)
    | greatest_lower_bound(identity,b) != identity
    | greatest_lower_bound(b,identity) = identity ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,b),identity) ),[0],$fot(greatest_lower_bound(b,identity))]]) ).

cnf(refute_0_21,plain,
    ( greatest_lower_bound(identity,b) != identity
    | greatest_lower_bound(b,identity) = identity ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,b),greatest_lower_bound(b,identity)) )],[refute_0_19,refute_0_20]) ).

cnf(refute_0_22,plain,
    greatest_lower_bound(b,identity) = identity,
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,b),identity) )],[p04d_2,refute_0_21]) ).

cnf(refute_0_23,plain,
    ( greatest_lower_bound(b,identity) != identity
    | least_upper_bound(b,greatest_lower_bound(b,identity)) != b
    | least_upper_bound(b,identity) = b ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(b,identity)),b) ),[0,1],$fot(identity)]]) ).

cnf(refute_0_24,plain,
    ( least_upper_bound(b,greatest_lower_bound(b,identity)) != b
    | least_upper_bound(b,identity) = b ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,identity),identity) )],[refute_0_22,refute_0_23]) ).

cnf(refute_0_25,plain,
    least_upper_bound(b,identity) = b,
    inference(resolve,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(b,identity)),b) )],[refute_0_16,refute_0_24]) ).

cnf(refute_0_26,plain,
    ( least_upper_bound(b,identity) != b
    | least_upper_bound(b,least_upper_bound(identity,X_37)) != least_upper_bound(least_upper_bound(b,identity),X_37)
    | least_upper_bound(b,least_upper_bound(identity,X_37)) = least_upper_bound(b,X_37) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,least_upper_bound(identity,X_37)),least_upper_bound(least_upper_bound(b,identity),X_37)) ),[1,0],$fot(b)]]) ).

cnf(refute_0_27,plain,
    ( least_upper_bound(b,least_upper_bound(identity,X_37)) != least_upper_bound(least_upper_bound(b,identity),X_37)
    | least_upper_bound(b,least_upper_bound(identity,X_37)) = least_upper_bound(b,X_37) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,identity),b) )],[refute_0_25,refute_0_26]) ).

cnf(refute_0_28,plain,
    least_upper_bound(b,least_upper_bound(identity,X_37)) = least_upper_bound(b,X_37),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(identity,X_37)),least_upper_bound(least_upper_bound(b,identity),X_37)) )],[refute_0_15,refute_0_27]) ).

cnf(refute_0_29,plain,
    least_upper_bound(b,least_upper_bound(identity,inverse(a))) = least_upper_bound(b,inverse(a)),
    inference(subst,[],[refute_0_28:[bind(X_37,$fot(inverse(a)))]]) ).

cnf(refute_0_30,plain,
    multiply(inverse(X_46),least_upper_bound(X_46,X_47)) = least_upper_bound(multiply(inverse(X_46),X_46),multiply(inverse(X_46),X_47)),
    inference(subst,[],[monotony_lub1:[bind(X,$fot(inverse(X_46))),bind(Y,$fot(X_46)),bind(Z,$fot(X_47))]]) ).

cnf(refute_0_31,plain,
    multiply(inverse(X_46),X_46) = identity,
    inference(subst,[],[left_inverse:[bind(X,$fot(X_46))]]) ).

cnf(refute_0_32,plain,
    ( multiply(inverse(X_46),X_46) != identity
    | multiply(inverse(X_46),least_upper_bound(X_46,X_47)) != least_upper_bound(multiply(inverse(X_46),X_46),multiply(inverse(X_46),X_47))
    | multiply(inverse(X_46),least_upper_bound(X_46,X_47)) = least_upper_bound(identity,multiply(inverse(X_46),X_47)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_46),least_upper_bound(X_46,X_47)),least_upper_bound(multiply(inverse(X_46),X_46),multiply(inverse(X_46),X_47))) ),[1,0],$fot(identity)]]) ).

cnf(refute_0_33,plain,
    ( multiply(inverse(X_46),least_upper_bound(X_46,X_47)) != least_upper_bound(multiply(inverse(X_46),X_46),multiply(inverse(X_46),X_47))
    | multiply(inverse(X_46),least_upper_bound(X_46,X_47)) = least_upper_bound(identity,multiply(inverse(X_46),X_47)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_46),X_46),identity) )],[refute_0_31,refute_0_32]) ).

cnf(refute_0_34,plain,
    multiply(inverse(X_46),least_upper_bound(X_46,X_47)) = least_upper_bound(identity,multiply(inverse(X_46),X_47)),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_46),least_upper_bound(X_46,X_47)),least_upper_bound(multiply(inverse(X_46),X_46),multiply(inverse(X_46),X_47))) )],[refute_0_30,refute_0_33]) ).

cnf(refute_0_35,plain,
    multiply(inverse(X_46),least_upper_bound(X_46,identity)) = least_upper_bound(identity,multiply(inverse(X_46),identity)),
    inference(subst,[],[refute_0_34:[bind(X_47,$fot(identity))]]) ).

cnf(refute_0_36,plain,
    multiply(multiply(inverse(X_67),X_67),X_68) = multiply(inverse(X_67),multiply(X_67,X_68)),
    inference(subst,[],[associativity:[bind(X,$fot(inverse(X_67))),bind(Y,$fot(X_67)),bind(Z,$fot(X_68))]]) ).

cnf(refute_0_37,plain,
    multiply(inverse(X_67),X_67) = identity,
    inference(subst,[],[left_inverse:[bind(X,$fot(X_67))]]) ).

cnf(refute_0_38,plain,
    ( multiply(multiply(inverse(X_67),X_67),X_68) != multiply(inverse(X_67),multiply(X_67,X_68))
    | multiply(inverse(X_67),X_67) != identity
    | multiply(identity,X_68) = multiply(inverse(X_67),multiply(X_67,X_68)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_67),X_67),X_68),multiply(inverse(X_67),multiply(X_67,X_68))) ),[0,0],$fot(identity)]]) ).

cnf(refute_0_39,plain,
    ( multiply(multiply(inverse(X_67),X_67),X_68) != multiply(inverse(X_67),multiply(X_67,X_68))
    | multiply(identity,X_68) = multiply(inverse(X_67),multiply(X_67,X_68)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_67),X_67),identity) )],[refute_0_37,refute_0_38]) ).

cnf(refute_0_40,plain,
    multiply(identity,X_68) = multiply(inverse(X_67),multiply(X_67,X_68)),
    inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_67),X_67),X_68),multiply(inverse(X_67),multiply(X_67,X_68))) )],[refute_0_36,refute_0_39]) ).

cnf(refute_0_41,plain,
    multiply(identity,X_68) = X_68,
    inference(subst,[],[left_identity:[bind(X,$fot(X_68))]]) ).

cnf(refute_0_42,plain,
    ( multiply(identity,X_68) != X_68
    | multiply(identity,X_68) != multiply(inverse(X_67),multiply(X_67,X_68))
    | X_68 = multiply(inverse(X_67),multiply(X_67,X_68)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_68),multiply(inverse(X_67),multiply(X_67,X_68))) ),[0],$fot(X_68)]]) ).

cnf(refute_0_43,plain,
    ( multiply(identity,X_68) != multiply(inverse(X_67),multiply(X_67,X_68))
    | X_68 = multiply(inverse(X_67),multiply(X_67,X_68)) ),
    inference(resolve,[$cnf( $equal(multiply(identity,X_68),X_68) )],[refute_0_41,refute_0_42]) ).

cnf(refute_0_44,plain,
    X_68 = multiply(inverse(X_67),multiply(X_67,X_68)),
    inference(resolve,[$cnf( $equal(multiply(identity,X_68),multiply(inverse(X_67),multiply(X_67,X_68))) )],[refute_0_40,refute_0_43]) ).

cnf(refute_0_45,plain,
    X_70 = multiply(inverse(inverse(X_70)),multiply(inverse(X_70),X_70)),
    inference(subst,[],[refute_0_44:[bind(X_67,$fot(inverse(X_70))),bind(X_68,$fot(X_70))]]) ).

cnf(refute_0_46,plain,
    multiply(inverse(X_70),X_70) = identity,
    inference(subst,[],[left_inverse:[bind(X,$fot(X_70))]]) ).

cnf(refute_0_47,plain,
    ( X_70 != multiply(inverse(inverse(X_70)),multiply(inverse(X_70),X_70))
    | multiply(inverse(X_70),X_70) != identity
    | X_70 = multiply(inverse(inverse(X_70)),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(X_70,multiply(inverse(inverse(X_70)),multiply(inverse(X_70),X_70))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_48,plain,
    ( X_70 != multiply(inverse(inverse(X_70)),multiply(inverse(X_70),X_70))
    | X_70 = multiply(inverse(inverse(X_70)),identity) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_70),X_70),identity) )],[refute_0_46,refute_0_47]) ).

cnf(refute_0_49,plain,
    X_70 = multiply(inverse(inverse(X_70)),identity),
    inference(resolve,[$cnf( $equal(X_70,multiply(inverse(inverse(X_70)),multiply(inverse(X_70),X_70))) )],[refute_0_45,refute_0_48]) ).

cnf(refute_0_50,plain,
    multiply(X_69,X_70) = multiply(inverse(inverse(X_69)),multiply(inverse(X_69),multiply(X_69,X_70))),
    inference(subst,[],[refute_0_44:[bind(X_67,$fot(inverse(X_69))),bind(X_68,$fot(multiply(X_69,X_70)))]]) ).

cnf(refute_0_51,plain,
    X_70 = multiply(inverse(X_69),multiply(X_69,X_70)),
    inference(subst,[],[refute_0_44:[bind(X_67,$fot(X_69)),bind(X_68,$fot(X_70))]]) ).

cnf(refute_0_52,plain,
    ( X_70 != multiply(inverse(X_69),multiply(X_69,X_70))
    | multiply(inverse(X_69),multiply(X_69,X_70)) = X_70 ),
    inference(subst,[],[refute_0_7:[bind(X0,$fot(X_70)),bind(Y0,$fot(multiply(inverse(X_69),multiply(X_69,X_70))))]]) ).

cnf(refute_0_53,plain,
    multiply(inverse(X_69),multiply(X_69,X_70)) = X_70,
    inference(resolve,[$cnf( $equal(X_70,multiply(inverse(X_69),multiply(X_69,X_70))) )],[refute_0_51,refute_0_52]) ).

cnf(refute_0_54,plain,
    ( multiply(X_69,X_70) != multiply(inverse(inverse(X_69)),multiply(inverse(X_69),multiply(X_69,X_70)))
    | multiply(inverse(X_69),multiply(X_69,X_70)) != X_70
    | multiply(X_69,X_70) = multiply(inverse(inverse(X_69)),X_70) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_69,X_70),multiply(inverse(inverse(X_69)),multiply(inverse(X_69),multiply(X_69,X_70)))) ),[1,1],$fot(X_70)]]) ).

cnf(refute_0_55,plain,
    ( multiply(X_69,X_70) != multiply(inverse(inverse(X_69)),multiply(inverse(X_69),multiply(X_69,X_70)))
    | multiply(X_69,X_70) = multiply(inverse(inverse(X_69)),X_70) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_69),multiply(X_69,X_70)),X_70) )],[refute_0_53,refute_0_54]) ).

cnf(refute_0_56,plain,
    multiply(X_69,X_70) = multiply(inverse(inverse(X_69)),X_70),
    inference(resolve,[$cnf( $equal(multiply(X_69,X_70),multiply(inverse(inverse(X_69)),multiply(inverse(X_69),multiply(X_69,X_70)))) )],[refute_0_50,refute_0_55]) ).

cnf(refute_0_57,plain,
    ( multiply(X_69,X_70) != multiply(inverse(inverse(X_69)),X_70)
    | multiply(inverse(inverse(X_69)),X_70) = multiply(X_69,X_70) ),
    inference(subst,[],[refute_0_7:[bind(X0,$fot(multiply(X_69,X_70))),bind(Y0,$fot(multiply(inverse(inverse(X_69)),X_70)))]]) ).

cnf(refute_0_58,plain,
    multiply(inverse(inverse(X_69)),X_70) = multiply(X_69,X_70),
    inference(resolve,[$cnf( $equal(multiply(X_69,X_70),multiply(inverse(inverse(X_69)),X_70)) )],[refute_0_56,refute_0_57]) ).

cnf(refute_0_59,plain,
    multiply(inverse(inverse(X_70)),identity) = multiply(X_70,identity),
    inference(subst,[],[refute_0_58:[bind(X_69,$fot(X_70)),bind(X_70,$fot(identity))]]) ).

cnf(refute_0_60,plain,
    ( X_70 != multiply(inverse(inverse(X_70)),identity)
    | multiply(inverse(inverse(X_70)),identity) != multiply(X_70,identity)
    | X_70 = multiply(X_70,identity) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(X_70,multiply(X_70,identity)) ),[0],$fot(multiply(inverse(inverse(X_70)),identity))]]) ).

cnf(refute_0_61,plain,
    ( X_70 != multiply(inverse(inverse(X_70)),identity)
    | X_70 = multiply(X_70,identity) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_70)),identity),multiply(X_70,identity)) )],[refute_0_59,refute_0_60]) ).

cnf(refute_0_62,plain,
    X_70 = multiply(X_70,identity),
    inference(resolve,[$cnf( $equal(X_70,multiply(inverse(inverse(X_70)),identity)) )],[refute_0_49,refute_0_61]) ).

cnf(refute_0_63,plain,
    inverse(X_46) = multiply(inverse(X_46),identity),
    inference(subst,[],[refute_0_62:[bind(X_70,$fot(inverse(X_46)))]]) ).

cnf(refute_0_64,plain,
    ( inverse(X_46) != multiply(inverse(X_46),identity)
    | multiply(inverse(X_46),identity) = inverse(X_46) ),
    inference(subst,[],[refute_0_7:[bind(X0,$fot(inverse(X_46))),bind(Y0,$fot(multiply(inverse(X_46),identity)))]]) ).

cnf(refute_0_65,plain,
    multiply(inverse(X_46),identity) = inverse(X_46),
    inference(resolve,[$cnf( $equal(inverse(X_46),multiply(inverse(X_46),identity)) )],[refute_0_63,refute_0_64]) ).

cnf(refute_0_66,plain,
    ( multiply(inverse(X_46),identity) != inverse(X_46)
    | multiply(inverse(X_46),least_upper_bound(X_46,identity)) != least_upper_bound(identity,multiply(inverse(X_46),identity))
    | multiply(inverse(X_46),least_upper_bound(X_46,identity)) = least_upper_bound(identity,inverse(X_46)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_46),least_upper_bound(X_46,identity)),least_upper_bound(identity,multiply(inverse(X_46),identity))) ),[1,1],$fot(inverse(X_46))]]) ).

cnf(refute_0_67,plain,
    ( multiply(inverse(X_46),least_upper_bound(X_46,identity)) != least_upper_bound(identity,multiply(inverse(X_46),identity))
    | multiply(inverse(X_46),least_upper_bound(X_46,identity)) = least_upper_bound(identity,inverse(X_46)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_46),identity),inverse(X_46)) )],[refute_0_65,refute_0_66]) ).

cnf(refute_0_68,plain,
    multiply(inverse(X_46),least_upper_bound(X_46,identity)) = least_upper_bound(identity,inverse(X_46)),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_46),least_upper_bound(X_46,identity)),least_upper_bound(identity,multiply(inverse(X_46),identity))) )],[refute_0_35,refute_0_67]) ).

cnf(refute_0_69,plain,
    multiply(inverse(a),least_upper_bound(a,identity)) = least_upper_bound(identity,inverse(a)),
    inference(subst,[],[refute_0_68:[bind(X_46,$fot(a))]]) ).

cnf(refute_0_70,plain,
    least_upper_bound(a,greatest_lower_bound(a,identity)) = a,
    inference(subst,[],[lub_absorbtion:[bind(X,$fot(a)),bind(Y,$fot(identity))]]) ).

cnf(refute_0_71,plain,
    greatest_lower_bound(identity,a) = greatest_lower_bound(a,identity),
    inference(subst,[],[refute_0_18:[bind(X,$fot(a)),bind(Y,$fot(identity))]]) ).

cnf(refute_0_72,plain,
    ( greatest_lower_bound(identity,a) != greatest_lower_bound(a,identity)
    | greatest_lower_bound(identity,a) != identity
    | greatest_lower_bound(a,identity) = identity ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,a),identity) ),[0],$fot(greatest_lower_bound(a,identity))]]) ).

cnf(refute_0_73,plain,
    ( greatest_lower_bound(identity,a) != identity
    | greatest_lower_bound(a,identity) = identity ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,a),greatest_lower_bound(a,identity)) )],[refute_0_71,refute_0_72]) ).

cnf(refute_0_74,plain,
    greatest_lower_bound(a,identity) = identity,
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,a),identity) )],[p04d_1,refute_0_73]) ).

cnf(refute_0_75,plain,
    ( greatest_lower_bound(a,identity) != identity
    | least_upper_bound(a,greatest_lower_bound(a,identity)) != a
    | least_upper_bound(a,identity) = a ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(a,greatest_lower_bound(a,identity)),a) ),[0,1],$fot(identity)]]) ).

cnf(refute_0_76,plain,
    ( least_upper_bound(a,greatest_lower_bound(a,identity)) != a
    | least_upper_bound(a,identity) = a ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,identity),identity) )],[refute_0_74,refute_0_75]) ).

cnf(refute_0_77,plain,
    least_upper_bound(a,identity) = a,
    inference(resolve,[$cnf( $equal(least_upper_bound(a,greatest_lower_bound(a,identity)),a) )],[refute_0_70,refute_0_76]) ).

cnf(refute_0_78,plain,
    ( multiply(inverse(a),least_upper_bound(a,identity)) != least_upper_bound(identity,inverse(a))
    | least_upper_bound(a,identity) != a
    | multiply(inverse(a),a) = least_upper_bound(identity,inverse(a)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(a),least_upper_bound(a,identity)),least_upper_bound(identity,inverse(a))) ),[0,1],$fot(a)]]) ).

cnf(refute_0_79,plain,
    ( multiply(inverse(a),least_upper_bound(a,identity)) != least_upper_bound(identity,inverse(a))
    | multiply(inverse(a),a) = least_upper_bound(identity,inverse(a)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(a,identity),a) )],[refute_0_77,refute_0_78]) ).

cnf(refute_0_80,plain,
    multiply(inverse(a),a) = least_upper_bound(identity,inverse(a)),
    inference(resolve,[$cnf( $equal(multiply(inverse(a),least_upper_bound(a,identity)),least_upper_bound(identity,inverse(a))) )],[refute_0_69,refute_0_79]) ).

cnf(refute_0_81,plain,
    multiply(inverse(a),a) = identity,
    inference(subst,[],[left_inverse:[bind(X,$fot(a))]]) ).

cnf(refute_0_82,plain,
    ( multiply(inverse(a),a) != identity
    | multiply(inverse(a),a) != least_upper_bound(identity,inverse(a))
    | identity = least_upper_bound(identity,inverse(a)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(a),a),least_upper_bound(identity,inverse(a))) ),[0],$fot(identity)]]) ).

cnf(refute_0_83,plain,
    ( multiply(inverse(a),a) != least_upper_bound(identity,inverse(a))
    | identity = least_upper_bound(identity,inverse(a)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(a),a),identity) )],[refute_0_81,refute_0_82]) ).

cnf(refute_0_84,plain,
    identity = least_upper_bound(identity,inverse(a)),
    inference(resolve,[$cnf( $equal(multiply(inverse(a),a),least_upper_bound(identity,inverse(a))) )],[refute_0_80,refute_0_83]) ).

cnf(refute_0_85,plain,
    ( identity != least_upper_bound(identity,inverse(a))
    | least_upper_bound(identity,inverse(a)) = identity ),
    inference(subst,[],[refute_0_7:[bind(X0,$fot(identity)),bind(Y0,$fot(least_upper_bound(identity,inverse(a))))]]) ).

cnf(refute_0_86,plain,
    least_upper_bound(identity,inverse(a)) = identity,
    inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,inverse(a))) )],[refute_0_84,refute_0_85]) ).

cnf(refute_0_87,plain,
    ( least_upper_bound(b,least_upper_bound(identity,inverse(a))) != least_upper_bound(b,inverse(a))
    | least_upper_bound(identity,inverse(a)) != identity
    | least_upper_bound(b,identity) = least_upper_bound(b,inverse(a)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,least_upper_bound(identity,inverse(a))),least_upper_bound(b,inverse(a))) ),[0,1],$fot(identity)]]) ).

cnf(refute_0_88,plain,
    ( least_upper_bound(b,least_upper_bound(identity,inverse(a))) != least_upper_bound(b,inverse(a))
    | least_upper_bound(b,identity) = least_upper_bound(b,inverse(a)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(a)),identity) )],[refute_0_86,refute_0_87]) ).

cnf(refute_0_89,plain,
    least_upper_bound(b,identity) = least_upper_bound(b,inverse(a)),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(identity,inverse(a))),least_upper_bound(b,inverse(a))) )],[refute_0_29,refute_0_88]) ).

cnf(refute_0_90,plain,
    ( least_upper_bound(b,identity) != b
    | least_upper_bound(b,identity) != least_upper_bound(b,inverse(a))
    | b = least_upper_bound(b,inverse(a)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,identity),least_upper_bound(b,inverse(a))) ),[0],$fot(b)]]) ).

cnf(refute_0_91,plain,
    ( least_upper_bound(b,identity) != least_upper_bound(b,inverse(a))
    | b = least_upper_bound(b,inverse(a)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,identity),b) )],[refute_0_25,refute_0_90]) ).

cnf(refute_0_92,plain,
    b = least_upper_bound(b,inverse(a)),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,identity),least_upper_bound(b,inverse(a))) )],[refute_0_89,refute_0_91]) ).

cnf(refute_0_93,plain,
    ( b != least_upper_bound(b,inverse(a))
    | least_upper_bound(b,inverse(a)) = b ),
    inference(subst,[],[refute_0_7:[bind(X0,$fot(b)),bind(Y0,$fot(least_upper_bound(b,inverse(a))))]]) ).

cnf(refute_0_94,plain,
    least_upper_bound(b,inverse(a)) = b,
    inference(resolve,[$cnf( $equal(b,least_upper_bound(b,inverse(a))) )],[refute_0_92,refute_0_93]) ).

cnf(refute_0_95,plain,
    ( multiply(inverse(inverse(a)),least_upper_bound(b,inverse(a))) != least_upper_bound(identity,multiply(inverse(inverse(a)),b))
    | least_upper_bound(b,inverse(a)) != b
    | multiply(inverse(inverse(a)),b) = least_upper_bound(identity,multiply(inverse(inverse(a)),b)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(a)),least_upper_bound(b,inverse(a))),least_upper_bound(identity,multiply(inverse(inverse(a)),b))) ),[0,1],$fot(b)]]) ).

cnf(refute_0_96,plain,
    ( multiply(inverse(inverse(a)),least_upper_bound(b,inverse(a))) != least_upper_bound(identity,multiply(inverse(inverse(a)),b))
    | multiply(inverse(inverse(a)),b) = least_upper_bound(identity,multiply(inverse(inverse(a)),b)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,inverse(a)),b) )],[refute_0_94,refute_0_95]) ).

cnf(refute_0_97,plain,
    multiply(inverse(inverse(a)),b) = least_upper_bound(identity,multiply(inverse(inverse(a)),b)),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(a)),least_upper_bound(b,inverse(a))),least_upper_bound(identity,multiply(inverse(inverse(a)),b))) )],[refute_0_14,refute_0_96]) ).

cnf(refute_0_98,plain,
    multiply(inverse(inverse(a)),b) = multiply(a,b),
    inference(subst,[],[refute_0_58:[bind(X_69,$fot(a)),bind(X_70,$fot(b))]]) ).

cnf(refute_0_99,plain,
    ( multiply(inverse(inverse(a)),b) != multiply(a,b)
    | multiply(inverse(inverse(a)),b) != least_upper_bound(identity,multiply(inverse(inverse(a)),b))
    | multiply(a,b) = least_upper_bound(identity,multiply(inverse(inverse(a)),b)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(a)),b),least_upper_bound(identity,multiply(inverse(inverse(a)),b))) ),[0],$fot(multiply(a,b))]]) ).

cnf(refute_0_100,plain,
    ( multiply(inverse(inverse(a)),b) != least_upper_bound(identity,multiply(inverse(inverse(a)),b))
    | multiply(a,b) = least_upper_bound(identity,multiply(inverse(inverse(a)),b)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(a)),b),multiply(a,b)) )],[refute_0_98,refute_0_99]) ).

cnf(refute_0_101,plain,
    least_upper_bound(identity,multiply(inverse(inverse(a)),b)) = least_upper_bound(identity,multiply(inverse(inverse(a)),b)),
    introduced(tautology,[refl,[$fot(least_upper_bound(identity,multiply(inverse(inverse(a)),b)))]]) ).

cnf(refute_0_102,plain,
    ( multiply(inverse(inverse(a)),b) != multiply(a,b)
    | least_upper_bound(identity,multiply(inverse(inverse(a)),b)) != least_upper_bound(identity,multiply(inverse(inverse(a)),b))
    | least_upper_bound(identity,multiply(inverse(inverse(a)),b)) = least_upper_bound(identity,multiply(a,b)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(inverse(a)),b)),least_upper_bound(identity,multiply(inverse(inverse(a)),b))) ),[1,1],$fot(multiply(a,b))]]) ).

cnf(refute_0_103,plain,
    ( multiply(inverse(inverse(a)),b) != multiply(a,b)
    | least_upper_bound(identity,multiply(inverse(inverse(a)),b)) = least_upper_bound(identity,multiply(a,b)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(inverse(a)),b)),least_upper_bound(identity,multiply(inverse(inverse(a)),b))) )],[refute_0_101,refute_0_102]) ).

cnf(refute_0_104,plain,
    least_upper_bound(identity,multiply(inverse(inverse(a)),b)) = least_upper_bound(identity,multiply(a,b)),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(a)),b),multiply(a,b)) )],[refute_0_98,refute_0_103]) ).

cnf(refute_0_105,plain,
    ( multiply(a,b) != least_upper_bound(identity,multiply(inverse(inverse(a)),b))
    | least_upper_bound(identity,multiply(inverse(inverse(a)),b)) != least_upper_bound(identity,multiply(a,b))
    | multiply(a,b) = least_upper_bound(identity,multiply(a,b)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(a,b),least_upper_bound(identity,multiply(a,b))) ),[0],$fot(least_upper_bound(identity,multiply(inverse(inverse(a)),b)))]]) ).

cnf(refute_0_106,plain,
    ( multiply(a,b) != least_upper_bound(identity,multiply(inverse(inverse(a)),b))
    | multiply(a,b) = least_upper_bound(identity,multiply(a,b)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(inverse(a)),b)),least_upper_bound(identity,multiply(a,b))) )],[refute_0_104,refute_0_105]) ).

cnf(refute_0_107,plain,
    ( multiply(inverse(inverse(a)),b) != least_upper_bound(identity,multiply(inverse(inverse(a)),b))
    | multiply(a,b) = least_upper_bound(identity,multiply(a,b)) ),
    inference(resolve,[$cnf( $equal(multiply(a,b),least_upper_bound(identity,multiply(inverse(inverse(a)),b))) )],[refute_0_100,refute_0_106]) ).

cnf(refute_0_108,plain,
    multiply(a,b) = least_upper_bound(identity,multiply(a,b)),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(a)),b),least_upper_bound(identity,multiply(inverse(inverse(a)),b))) )],[refute_0_97,refute_0_107]) ).

cnf(refute_0_109,plain,
    ( multiply(a,b) != least_upper_bound(identity,multiply(a,b))
    | least_upper_bound(identity,multiply(a,b)) = multiply(a,b) ),
    inference(subst,[],[refute_0_7:[bind(X0,$fot(multiply(a,b))),bind(Y0,$fot(least_upper_bound(identity,multiply(a,b))))]]) ).

cnf(refute_0_110,plain,
    multiply(a,b) != least_upper_bound(identity,multiply(a,b)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(a,b)),multiply(a,b)) )],[refute_0_109,prove_p04d]) ).

cnf(refute_0_111,plain,
    $false,
    inference(resolve,[$cnf( $equal(multiply(a,b),least_upper_bound(identity,multiply(a,b))) )],[refute_0_108,refute_0_110]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GRP172-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.13  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n020.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Mon Jun 13 19:31:05 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.41/0.59  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.41/0.59  
% 0.41/0.59  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.41/0.60  
%------------------------------------------------------------------------------