TSTP Solution File: GRP192-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP192-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 10:37:56 EDT 2022
% Result : Unsatisfiable 0.18s 0.42s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 35
% Syntax : Number of clauses : 112 ( 63 unt; 0 nHn; 53 RR)
% Number of literals : 184 ( 183 equ; 74 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 : 187 ( 28 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
multiply(identity,X) = X ).
cnf(left_inverse,axiom,
multiply(inverse(X),X) = identity ).
cnf(symmetry_of_glb,axiom,
greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ).
cnf(symmetry_of_lub,axiom,
least_upper_bound(X,Y) = least_upper_bound(Y,X) ).
cnf(associativity_of_glb,axiom,
greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) ).
cnf(lub_absorbtion,axiom,
least_upper_bound(X,greatest_lower_bound(X,Y)) = X ).
cnf(glb_absorbtion,axiom,
greatest_lower_bound(X,least_upper_bound(X,Y)) = X ).
cnf(monotony_glb1,axiom,
multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)) ).
cnf(monotony_glb2,axiom,
multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) ).
cnf(p40a_1,hypothesis,
least_upper_bound(identity,X) = X ).
cnf(prove_p40a,negated_conjecture,
multiply(a,b) != multiply(b,a) ).
cnf(refute_0_0,plain,
multiply(greatest_lower_bound(X_50,identity),X_49) = greatest_lower_bound(multiply(X_50,X_49),multiply(identity,X_49)),
inference(subst,[],[monotony_glb2:[bind(X,$fot(X_49)),bind(Y,$fot(X_50)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_1,plain,
multiply(identity,X_49) = X_49,
inference(subst,[],[left_identity:[bind(X,$fot(X_49))]]) ).
cnf(refute_0_2,plain,
( multiply(greatest_lower_bound(X_50,identity),X_49) != greatest_lower_bound(multiply(X_50,X_49),multiply(identity,X_49))
| multiply(identity,X_49) != X_49
| multiply(greatest_lower_bound(X_50,identity),X_49) = greatest_lower_bound(multiply(X_50,X_49),X_49) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_50,identity),X_49),greatest_lower_bound(multiply(X_50,X_49),multiply(identity,X_49))) ),[1,1],$fot(X_49)]]) ).
cnf(refute_0_3,plain,
( multiply(greatest_lower_bound(X_50,identity),X_49) != greatest_lower_bound(multiply(X_50,X_49),multiply(identity,X_49))
| multiply(greatest_lower_bound(X_50,identity),X_49) = greatest_lower_bound(multiply(X_50,X_49),X_49) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_49),X_49) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
multiply(greatest_lower_bound(X_50,identity),X_49) = greatest_lower_bound(multiply(X_50,X_49),X_49),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_50,identity),X_49),greatest_lower_bound(multiply(X_50,X_49),multiply(identity,X_49))) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
greatest_lower_bound(X,identity) = greatest_lower_bound(identity,X),
inference(subst,[],[symmetry_of_glb:[bind(Y,$fot(identity))]]) ).
cnf(refute_0_6,plain,
greatest_lower_bound(identity,least_upper_bound(identity,X_11)) = identity,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(identity)),bind(Y,$fot(X_11))]]) ).
cnf(refute_0_7,plain,
least_upper_bound(identity,X_11) = X_11,
inference(subst,[],[p40a_1:[bind(X,$fot(X_11))]]) ).
cnf(refute_0_8,plain,
( greatest_lower_bound(identity,least_upper_bound(identity,X_11)) != identity
| least_upper_bound(identity,X_11) != X_11
| greatest_lower_bound(identity,X_11) = identity ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(identity,X_11)),identity) ),[0,1],$fot(X_11)]]) ).
cnf(refute_0_9,plain,
( greatest_lower_bound(identity,least_upper_bound(identity,X_11)) != identity
| greatest_lower_bound(identity,X_11) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,X_11),X_11) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
greatest_lower_bound(identity,X_11) = identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(identity,X_11)),identity) )],[refute_0_6,refute_0_9]) ).
cnf(refute_0_11,plain,
greatest_lower_bound(identity,X) = identity,
inference(subst,[],[refute_0_10:[bind(X_11,$fot(X))]]) ).
cnf(refute_0_12,plain,
( greatest_lower_bound(X,identity) != greatest_lower_bound(identity,X)
| greatest_lower_bound(identity,X) != identity
| greatest_lower_bound(X,identity) = identity ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X,identity),identity) ),[0],$fot(greatest_lower_bound(identity,X))]]) ).
cnf(refute_0_13,plain,
( greatest_lower_bound(X,identity) != greatest_lower_bound(identity,X)
| greatest_lower_bound(X,identity) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,X),identity) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
greatest_lower_bound(X,identity) = identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,identity),greatest_lower_bound(identity,X)) )],[refute_0_5,refute_0_13]) ).
cnf(refute_0_15,plain,
greatest_lower_bound(X_50,identity) = identity,
inference(subst,[],[refute_0_14:[bind(X,$fot(X_50))]]) ).
cnf(refute_0_16,plain,
multiply(greatest_lower_bound(X_50,identity),X_49) = multiply(greatest_lower_bound(X_50,identity),X_49),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(X_50,identity),X_49))]]) ).
cnf(refute_0_17,plain,
( multiply(greatest_lower_bound(X_50,identity),X_49) != multiply(greatest_lower_bound(X_50,identity),X_49)
| greatest_lower_bound(X_50,identity) != identity
| multiply(greatest_lower_bound(X_50,identity),X_49) = multiply(identity,X_49) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_50,identity),X_49),multiply(greatest_lower_bound(X_50,identity),X_49)) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_18,plain,
( greatest_lower_bound(X_50,identity) != identity
| multiply(greatest_lower_bound(X_50,identity),X_49) = multiply(identity,X_49) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_50,identity),X_49),multiply(greatest_lower_bound(X_50,identity),X_49)) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
multiply(greatest_lower_bound(X_50,identity),X_49) = multiply(identity,X_49),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_50,identity),identity) )],[refute_0_15,refute_0_18]) ).
cnf(refute_0_20,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_21,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_22,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_24,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( multiply(greatest_lower_bound(X_50,identity),X_49) != multiply(identity,X_49)
| multiply(identity,X_49) != X_49
| multiply(greatest_lower_bound(X_50,identity),X_49) = X_49 ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(multiply(greatest_lower_bound(X_50,identity),X_49))),bind(Y0,$fot(multiply(identity,X_49))),bind(Z0,$fot(X_49))]]) ).
cnf(refute_0_26,plain,
( multiply(identity,X_49) != X_49
| multiply(greatest_lower_bound(X_50,identity),X_49) = X_49 ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_50,identity),X_49),multiply(identity,X_49)) )],[refute_0_19,refute_0_25]) ).
cnf(refute_0_27,plain,
multiply(greatest_lower_bound(X_50,identity),X_49) = X_49,
inference(resolve,[$cnf( $equal(multiply(identity,X_49),X_49) )],[refute_0_1,refute_0_26]) ).
cnf(refute_0_28,plain,
( multiply(greatest_lower_bound(X_50,identity),X_49) != X_49
| multiply(greatest_lower_bound(X_50,identity),X_49) != greatest_lower_bound(multiply(X_50,X_49),X_49)
| X_49 = greatest_lower_bound(multiply(X_50,X_49),X_49) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_50,identity),X_49),greatest_lower_bound(multiply(X_50,X_49),X_49)) ),[0],$fot(X_49)]]) ).
cnf(refute_0_29,plain,
( multiply(greatest_lower_bound(X_50,identity),X_49) != greatest_lower_bound(multiply(X_50,X_49),X_49)
| X_49 = greatest_lower_bound(multiply(X_50,X_49),X_49) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_50,identity),X_49),X_49) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
( greatest_lower_bound(X,Y) != greatest_lower_bound(Y,X)
| greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(greatest_lower_bound(X,Y))),bind(Y0,$fot(greatest_lower_bound(Y,X)))]]) ).
cnf(refute_0_31,plain,
greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X)) )],[symmetry_of_glb,refute_0_30]) ).
cnf(refute_0_32,plain,
greatest_lower_bound(multiply(X_50,X_49),X_49) = greatest_lower_bound(X_49,multiply(X_50,X_49)),
inference(subst,[],[refute_0_31:[bind(X,$fot(X_49)),bind(Y,$fot(multiply(X_50,X_49)))]]) ).
cnf(refute_0_33,plain,
( X_49 != greatest_lower_bound(multiply(X_50,X_49),X_49)
| greatest_lower_bound(multiply(X_50,X_49),X_49) != greatest_lower_bound(X_49,multiply(X_50,X_49))
| X_49 = greatest_lower_bound(X_49,multiply(X_50,X_49)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_49,greatest_lower_bound(X_49,multiply(X_50,X_49))) ),[0],$fot(greatest_lower_bound(multiply(X_50,X_49),X_49))]]) ).
cnf(refute_0_34,plain,
( X_49 != greatest_lower_bound(multiply(X_50,X_49),X_49)
| X_49 = greatest_lower_bound(X_49,multiply(X_50,X_49)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_50,X_49),X_49),greatest_lower_bound(X_49,multiply(X_50,X_49))) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
( multiply(greatest_lower_bound(X_50,identity),X_49) != greatest_lower_bound(multiply(X_50,X_49),X_49)
| X_49 = greatest_lower_bound(X_49,multiply(X_50,X_49)) ),
inference(resolve,[$cnf( $equal(X_49,greatest_lower_bound(multiply(X_50,X_49),X_49)) )],[refute_0_29,refute_0_34]) ).
cnf(refute_0_36,plain,
X_49 = greatest_lower_bound(X_49,multiply(X_50,X_49)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_50,identity),X_49),greatest_lower_bound(multiply(X_50,X_49),X_49)) )],[refute_0_4,refute_0_35]) ).
cnf(refute_0_37,plain,
X_52 = greatest_lower_bound(X_52,multiply(inverse(least_upper_bound(X_11,X_52)),X_52)),
inference(subst,[],[refute_0_36:[bind(X_49,$fot(X_52)),bind(X_50,$fot(inverse(least_upper_bound(X_11,X_52))))]]) ).
cnf(refute_0_38,plain,
multiply(inverse(X_36),greatest_lower_bound(X_35,X_36)) = greatest_lower_bound(multiply(inverse(X_36),X_35),multiply(inverse(X_36),X_36)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(inverse(X_36))),bind(Y,$fot(X_35)),bind(Z,$fot(X_36))]]) ).
cnf(refute_0_39,plain,
multiply(inverse(X_36),X_36) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_36))]]) ).
cnf(refute_0_40,plain,
( multiply(inverse(X_36),X_36) != identity
| multiply(inverse(X_36),greatest_lower_bound(X_35,X_36)) != greatest_lower_bound(multiply(inverse(X_36),X_35),multiply(inverse(X_36),X_36))
| multiply(inverse(X_36),greatest_lower_bound(X_35,X_36)) = greatest_lower_bound(multiply(inverse(X_36),X_35),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_36),greatest_lower_bound(X_35,X_36)),greatest_lower_bound(multiply(inverse(X_36),X_35),multiply(inverse(X_36),X_36))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_41,plain,
( multiply(inverse(X_36),greatest_lower_bound(X_35,X_36)) != greatest_lower_bound(multiply(inverse(X_36),X_35),multiply(inverse(X_36),X_36))
| multiply(inverse(X_36),greatest_lower_bound(X_35,X_36)) = greatest_lower_bound(multiply(inverse(X_36),X_35),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_36),X_36),identity) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
multiply(inverse(X_36),greatest_lower_bound(X_35,X_36)) = greatest_lower_bound(multiply(inverse(X_36),X_35),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_36),greatest_lower_bound(X_35,X_36)),greatest_lower_bound(multiply(inverse(X_36),X_35),multiply(inverse(X_36),X_36))) )],[refute_0_38,refute_0_41]) ).
cnf(refute_0_43,plain,
greatest_lower_bound(multiply(inverse(X_36),X_35),identity) = identity,
inference(subst,[],[refute_0_14:[bind(X,$fot(multiply(inverse(X_36),X_35)))]]) ).
cnf(refute_0_44,plain,
( multiply(inverse(X_36),greatest_lower_bound(X_35,X_36)) != greatest_lower_bound(multiply(inverse(X_36),X_35),identity)
| greatest_lower_bound(multiply(inverse(X_36),X_35),identity) != identity
| multiply(inverse(X_36),greatest_lower_bound(X_35,X_36)) = identity ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_36),greatest_lower_bound(X_35,X_36)),identity) ),[0],$fot(greatest_lower_bound(multiply(inverse(X_36),X_35),identity))]]) ).
cnf(refute_0_45,plain,
( multiply(inverse(X_36),greatest_lower_bound(X_35,X_36)) != greatest_lower_bound(multiply(inverse(X_36),X_35),identity)
| multiply(inverse(X_36),greatest_lower_bound(X_35,X_36)) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(inverse(X_36),X_35),identity),identity) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
multiply(inverse(X_36),greatest_lower_bound(X_35,X_36)) = identity,
inference(resolve,[$cnf( $equal(multiply(inverse(X_36),greatest_lower_bound(X_35,X_36)),greatest_lower_bound(multiply(inverse(X_36),X_35),identity)) )],[refute_0_42,refute_0_45]) ).
cnf(refute_0_47,plain,
multiply(inverse(least_upper_bound(X_11,X_37)),greatest_lower_bound(X_37,least_upper_bound(X_11,X_37))) = identity,
inference(subst,[],[refute_0_46:[bind(X_35,$fot(X_37)),bind(X_36,$fot(least_upper_bound(X_11,X_37)))]]) ).
cnf(refute_0_48,plain,
greatest_lower_bound(X_10,least_upper_bound(X_10,X_11)) = X_10,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_10)),bind(Y,$fot(X_11))]]) ).
cnf(refute_0_49,plain,
least_upper_bound(X_11,X_10) = least_upper_bound(X_10,X_11),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_11)),bind(Y,$fot(X_10))]]) ).
cnf(refute_0_50,plain,
( least_upper_bound(X_11,X_10) != least_upper_bound(X_10,X_11)
| least_upper_bound(X_10,X_11) = least_upper_bound(X_11,X_10) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(least_upper_bound(X_11,X_10))),bind(Y0,$fot(least_upper_bound(X_10,X_11)))]]) ).
cnf(refute_0_51,plain,
least_upper_bound(X_10,X_11) = least_upper_bound(X_11,X_10),
inference(resolve,[$cnf( $equal(least_upper_bound(X_11,X_10),least_upper_bound(X_10,X_11)) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
( greatest_lower_bound(X_10,least_upper_bound(X_10,X_11)) != X_10
| least_upper_bound(X_10,X_11) != least_upper_bound(X_11,X_10)
| greatest_lower_bound(X_10,least_upper_bound(X_11,X_10)) = X_10 ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_10,least_upper_bound(X_10,X_11)),X_10) ),[0,1],$fot(least_upper_bound(X_11,X_10))]]) ).
cnf(refute_0_53,plain,
( greatest_lower_bound(X_10,least_upper_bound(X_10,X_11)) != X_10
| greatest_lower_bound(X_10,least_upper_bound(X_11,X_10)) = X_10 ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_10,X_11),least_upper_bound(X_11,X_10)) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
greatest_lower_bound(X_10,least_upper_bound(X_11,X_10)) = X_10,
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_10,least_upper_bound(X_10,X_11)),X_10) )],[refute_0_48,refute_0_53]) ).
cnf(refute_0_55,plain,
greatest_lower_bound(X_37,least_upper_bound(X_11,X_37)) = X_37,
inference(subst,[],[refute_0_54:[bind(X_10,$fot(X_37))]]) ).
cnf(refute_0_56,plain,
( multiply(inverse(least_upper_bound(X_11,X_37)),greatest_lower_bound(X_37,least_upper_bound(X_11,X_37))) != identity
| greatest_lower_bound(X_37,least_upper_bound(X_11,X_37)) != X_37
| multiply(inverse(least_upper_bound(X_11,X_37)),X_37) = identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(X_11,X_37)),greatest_lower_bound(X_37,least_upper_bound(X_11,X_37))),identity) ),[0,1],$fot(X_37)]]) ).
cnf(refute_0_57,plain,
( multiply(inverse(least_upper_bound(X_11,X_37)),greatest_lower_bound(X_37,least_upper_bound(X_11,X_37))) != identity
| multiply(inverse(least_upper_bound(X_11,X_37)),X_37) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_37,least_upper_bound(X_11,X_37)),X_37) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
multiply(inverse(least_upper_bound(X_11,X_37)),X_37) = identity,
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_11,X_37)),greatest_lower_bound(X_37,least_upper_bound(X_11,X_37))),identity) )],[refute_0_47,refute_0_57]) ).
cnf(refute_0_59,plain,
multiply(inverse(least_upper_bound(X_11,X_52)),X_52) = identity,
inference(subst,[],[refute_0_58:[bind(X_37,$fot(X_52))]]) ).
cnf(refute_0_60,plain,
( X_52 != greatest_lower_bound(X_52,multiply(inverse(least_upper_bound(X_11,X_52)),X_52))
| multiply(inverse(least_upper_bound(X_11,X_52)),X_52) != identity
| X_52 = greatest_lower_bound(X_52,identity) ),
introduced(tautology,[equality,[$cnf( $equal(X_52,greatest_lower_bound(X_52,multiply(inverse(least_upper_bound(X_11,X_52)),X_52))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_61,plain,
( X_52 != greatest_lower_bound(X_52,multiply(inverse(least_upper_bound(X_11,X_52)),X_52))
| X_52 = greatest_lower_bound(X_52,identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_11,X_52)),X_52),identity) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
X_52 = greatest_lower_bound(X_52,identity),
inference(resolve,[$cnf( $equal(X_52,greatest_lower_bound(X_52,multiply(inverse(least_upper_bound(X_11,X_52)),X_52))) )],[refute_0_37,refute_0_61]) ).
cnf(refute_0_63,plain,
greatest_lower_bound(X_37,Y) = greatest_lower_bound(greatest_lower_bound(X_37,Y),multiply(inverse(greatest_lower_bound(Y,X_37)),greatest_lower_bound(X_37,Y))),
inference(subst,[],[refute_0_36:[bind(X_49,$fot(greatest_lower_bound(X_37,Y))),bind(X_50,$fot(inverse(greatest_lower_bound(Y,X_37))))]]) ).
cnf(refute_0_64,plain,
multiply(inverse(greatest_lower_bound(Y,X_37)),greatest_lower_bound(X_37,greatest_lower_bound(Y,X_37))) = identity,
inference(subst,[],[refute_0_46:[bind(X_35,$fot(X_37)),bind(X_36,$fot(greatest_lower_bound(Y,X_37)))]]) ).
cnf(refute_0_65,plain,
greatest_lower_bound(greatest_lower_bound(X_21,Y),least_upper_bound(X_21,greatest_lower_bound(X_21,Y))) = greatest_lower_bound(X_21,Y),
inference(subst,[],[refute_0_54:[bind(X_10,$fot(greatest_lower_bound(X_21,Y))),bind(X_11,$fot(X_21))]]) ).
cnf(refute_0_66,plain,
least_upper_bound(X_21,greatest_lower_bound(X_21,Y)) = X_21,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_21))]]) ).
cnf(refute_0_67,plain,
( greatest_lower_bound(greatest_lower_bound(X_21,Y),least_upper_bound(X_21,greatest_lower_bound(X_21,Y))) != greatest_lower_bound(X_21,Y)
| least_upper_bound(X_21,greatest_lower_bound(X_21,Y)) != X_21
| greatest_lower_bound(greatest_lower_bound(X_21,Y),X_21) = greatest_lower_bound(X_21,Y) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_21,Y),least_upper_bound(X_21,greatest_lower_bound(X_21,Y))),greatest_lower_bound(X_21,Y)) ),[0,1],$fot(X_21)]]) ).
cnf(refute_0_68,plain,
( greatest_lower_bound(greatest_lower_bound(X_21,Y),least_upper_bound(X_21,greatest_lower_bound(X_21,Y))) != greatest_lower_bound(X_21,Y)
| greatest_lower_bound(greatest_lower_bound(X_21,Y),X_21) = greatest_lower_bound(X_21,Y) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_21,greatest_lower_bound(X_21,Y)),X_21) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
greatest_lower_bound(greatest_lower_bound(X_21,Y),X_21) = greatest_lower_bound(X_21,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_21,Y),least_upper_bound(X_21,greatest_lower_bound(X_21,Y))),greatest_lower_bound(X_21,Y)) )],[refute_0_65,refute_0_68]) ).
cnf(refute_0_70,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,Z)) != greatest_lower_bound(greatest_lower_bound(X,Y),Z)
| greatest_lower_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(Y,Z)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X,Y),Z)))]]) ).
cnf(refute_0_71,plain,
greatest_lower_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(greatest_lower_bound(X,Y),Z)) )],[associativity_of_glb,refute_0_70]) ).
cnf(refute_0_72,plain,
greatest_lower_bound(greatest_lower_bound(X_21,Y),X_21) = greatest_lower_bound(X_21,greatest_lower_bound(Y,X_21)),
inference(subst,[],[refute_0_71:[bind(X,$fot(X_21)),bind(Z,$fot(X_21))]]) ).
cnf(refute_0_73,plain,
( greatest_lower_bound(greatest_lower_bound(X_21,Y),X_21) != greatest_lower_bound(X_21,Y)
| greatest_lower_bound(greatest_lower_bound(X_21,Y),X_21) != greatest_lower_bound(X_21,greatest_lower_bound(Y,X_21))
| greatest_lower_bound(X_21,greatest_lower_bound(Y,X_21)) = greatest_lower_bound(X_21,Y) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_21,Y),X_21),greatest_lower_bound(X_21,Y)) ),[0],$fot(greatest_lower_bound(X_21,greatest_lower_bound(Y,X_21)))]]) ).
cnf(refute_0_74,plain,
( greatest_lower_bound(greatest_lower_bound(X_21,Y),X_21) != greatest_lower_bound(X_21,Y)
| greatest_lower_bound(X_21,greatest_lower_bound(Y,X_21)) = greatest_lower_bound(X_21,Y) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_21,Y),X_21),greatest_lower_bound(X_21,greatest_lower_bound(Y,X_21))) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
greatest_lower_bound(X_21,greatest_lower_bound(Y,X_21)) = greatest_lower_bound(X_21,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_21,Y),X_21),greatest_lower_bound(X_21,Y)) )],[refute_0_69,refute_0_74]) ).
cnf(refute_0_76,plain,
greatest_lower_bound(X_37,greatest_lower_bound(Y,X_37)) = greatest_lower_bound(X_37,Y),
inference(subst,[],[refute_0_75:[bind(X_21,$fot(X_37))]]) ).
cnf(refute_0_77,plain,
( multiply(inverse(greatest_lower_bound(Y,X_37)),greatest_lower_bound(X_37,greatest_lower_bound(Y,X_37))) != identity
| greatest_lower_bound(X_37,greatest_lower_bound(Y,X_37)) != greatest_lower_bound(X_37,Y)
| multiply(inverse(greatest_lower_bound(Y,X_37)),greatest_lower_bound(X_37,Y)) = identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(Y,X_37)),greatest_lower_bound(X_37,greatest_lower_bound(Y,X_37))),identity) ),[0,1],$fot(greatest_lower_bound(X_37,Y))]]) ).
cnf(refute_0_78,plain,
( multiply(inverse(greatest_lower_bound(Y,X_37)),greatest_lower_bound(X_37,greatest_lower_bound(Y,X_37))) != identity
| multiply(inverse(greatest_lower_bound(Y,X_37)),greatest_lower_bound(X_37,Y)) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_37,greatest_lower_bound(Y,X_37)),greatest_lower_bound(X_37,Y)) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
multiply(inverse(greatest_lower_bound(Y,X_37)),greatest_lower_bound(X_37,Y)) = identity,
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(Y,X_37)),greatest_lower_bound(X_37,greatest_lower_bound(Y,X_37))),identity) )],[refute_0_64,refute_0_78]) ).
cnf(refute_0_80,plain,
( multiply(inverse(greatest_lower_bound(Y,X_37)),greatest_lower_bound(X_37,Y)) != identity
| greatest_lower_bound(X_37,Y) != greatest_lower_bound(greatest_lower_bound(X_37,Y),multiply(inverse(greatest_lower_bound(Y,X_37)),greatest_lower_bound(X_37,Y)))
| greatest_lower_bound(X_37,Y) = greatest_lower_bound(greatest_lower_bound(X_37,Y),identity) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_37,Y),greatest_lower_bound(greatest_lower_bound(X_37,Y),multiply(inverse(greatest_lower_bound(Y,X_37)),greatest_lower_bound(X_37,Y)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_81,plain,
( greatest_lower_bound(X_37,Y) != greatest_lower_bound(greatest_lower_bound(X_37,Y),multiply(inverse(greatest_lower_bound(Y,X_37)),greatest_lower_bound(X_37,Y)))
| greatest_lower_bound(X_37,Y) = greatest_lower_bound(greatest_lower_bound(X_37,Y),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(Y,X_37)),greatest_lower_bound(X_37,Y)),identity) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
greatest_lower_bound(X_37,Y) = greatest_lower_bound(greatest_lower_bound(X_37,Y),identity),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_37,Y),greatest_lower_bound(greatest_lower_bound(X_37,Y),multiply(inverse(greatest_lower_bound(Y,X_37)),greatest_lower_bound(X_37,Y)))) )],[refute_0_63,refute_0_81]) ).
cnf(refute_0_83,plain,
greatest_lower_bound(greatest_lower_bound(X_37,Y),identity) = identity,
inference(subst,[],[refute_0_14:[bind(X,$fot(greatest_lower_bound(X_37,Y)))]]) ).
cnf(refute_0_84,plain,
( greatest_lower_bound(X_37,Y) != greatest_lower_bound(greatest_lower_bound(X_37,Y),identity)
| greatest_lower_bound(greatest_lower_bound(X_37,Y),identity) != identity
| greatest_lower_bound(X_37,Y) = identity ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_37,Y),identity) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_37,Y),identity))]]) ).
cnf(refute_0_85,plain,
( greatest_lower_bound(X_37,Y) != greatest_lower_bound(greatest_lower_bound(X_37,Y),identity)
| greatest_lower_bound(X_37,Y) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_37,Y),identity),identity) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
greatest_lower_bound(X_37,Y) = identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_37,Y),greatest_lower_bound(greatest_lower_bound(X_37,Y),identity)) )],[refute_0_82,refute_0_85]) ).
cnf(refute_0_87,plain,
greatest_lower_bound(X_52,identity) = identity,
inference(subst,[],[refute_0_86:[bind(Y,$fot(identity)),bind(X_37,$fot(X_52))]]) ).
cnf(refute_0_88,plain,
( X_52 != greatest_lower_bound(X_52,identity)
| greatest_lower_bound(X_52,identity) != identity
| X_52 = identity ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_52,identity) ),[0],$fot(greatest_lower_bound(X_52,identity))]]) ).
cnf(refute_0_89,plain,
( X_52 != greatest_lower_bound(X_52,identity)
| X_52 = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_52,identity),identity) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
X_52 = identity,
inference(resolve,[$cnf( $equal(X_52,greatest_lower_bound(X_52,identity)) )],[refute_0_62,refute_0_89]) ).
cnf(refute_0_91,plain,
multiply(a,b) = identity,
inference(subst,[],[refute_0_90:[bind(X_52,$fot(multiply(a,b)))]]) ).
cnf(refute_0_92,plain,
( multiply(a,b) != identity
| identity != multiply(b,a)
| multiply(a,b) = multiply(b,a) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(a,b),multiply(b,a)) ),[0],$fot(identity)]]) ).
cnf(refute_0_93,plain,
( identity != multiply(b,a)
| multiply(a,b) = multiply(b,a) ),
inference(resolve,[$cnf( $equal(multiply(a,b),identity) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
multiply(b,a) = identity,
inference(subst,[],[refute_0_90:[bind(X_52,$fot(multiply(b,a)))]]) ).
cnf(refute_0_95,plain,
( multiply(b,a) != identity
| identity != identity
| identity = multiply(b,a) ),
introduced(tautology,[equality,[$cnf( ~ $equal(identity,multiply(b,a)) ),[1],$fot(identity)]]) ).
cnf(refute_0_96,plain,
( identity != identity
| identity = multiply(b,a) ),
inference(resolve,[$cnf( $equal(multiply(b,a),identity) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
( identity != identity
| multiply(a,b) = multiply(b,a) ),
inference(resolve,[$cnf( $equal(identity,multiply(b,a)) )],[refute_0_96,refute_0_93]) ).
cnf(refute_0_98,plain,
identity != identity,
inference(resolve,[$cnf( $equal(multiply(a,b),multiply(b,a)) )],[refute_0_97,prove_p40a]) ).
cnf(refute_0_99,plain,
identity = identity,
introduced(tautology,[refl,[$fot(identity)]]) ).
cnf(refute_0_100,plain,
$false,
inference(resolve,[$cnf( $equal(identity,identity) )],[refute_0_99,refute_0_98]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP192-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n025.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 : Tue Jun 14 06:42:24 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.42 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.42
% 0.18/0.42 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.18/0.43
%------------------------------------------------------------------------------