TSTP Solution File: GRP172-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP172-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n007.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 0.38s 0.60s
% Output : CNFRefutation 0.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 37
% Syntax : Number of clauses : 132 ( 75 unt; 0 nHn; 83 RR)
% Number of literals : 213 ( 212 equ; 82 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 131 ( 2 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(glb_absorbtion,axiom,
greatest_lower_bound(X,least_upper_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(p04b_1,hypothesis,
greatest_lower_bound(identity,a) = identity ).
cnf(p04b_2,hypothesis,
greatest_lower_bound(identity,b) = identity ).
cnf(prove_p04b,negated_conjecture,
greatest_lower_bound(identity,multiply(a,b)) != identity ).
cnf(refute_0_0,plain,
greatest_lower_bound(identity,least_upper_bound(identity,multiply(a,b))) = identity,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(identity)),bind(Y,$fot(multiply(a,b)))]]) ).
cnf(refute_0_1,plain,
multiply(X_75,least_upper_bound(X_76,inverse(X_75))) = least_upper_bound(multiply(X_75,X_76),multiply(X_75,inverse(X_75))),
inference(subst,[],[monotony_lub1:[bind(X,$fot(X_75)),bind(Y,$fot(X_76)),bind(Z,$fot(inverse(X_75)))]]) ).
cnf(refute_0_2,plain,
multiply(inverse(inverse(X_52)),inverse(X_52)) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(inverse(X_52)))]]) ).
cnf(refute_0_3,plain,
multiply(multiply(inverse(X_47),X_47),X_48) = multiply(inverse(X_47),multiply(X_47,X_48)),
inference(subst,[],[associativity:[bind(X,$fot(inverse(X_47))),bind(Y,$fot(X_47)),bind(Z,$fot(X_48))]]) ).
cnf(refute_0_4,plain,
multiply(inverse(X_47),X_47) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_47))]]) ).
cnf(refute_0_5,plain,
( multiply(multiply(inverse(X_47),X_47),X_48) != multiply(inverse(X_47),multiply(X_47,X_48))
| multiply(inverse(X_47),X_47) != identity
| multiply(identity,X_48) = multiply(inverse(X_47),multiply(X_47,X_48)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_47),X_47),X_48),multiply(inverse(X_47),multiply(X_47,X_48))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_6,plain,
( multiply(multiply(inverse(X_47),X_47),X_48) != multiply(inverse(X_47),multiply(X_47,X_48))
| multiply(identity,X_48) = multiply(inverse(X_47),multiply(X_47,X_48)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_47),X_47),identity) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
multiply(identity,X_48) = multiply(inverse(X_47),multiply(X_47,X_48)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_47),X_47),X_48),multiply(inverse(X_47),multiply(X_47,X_48))) )],[refute_0_3,refute_0_6]) ).
cnf(refute_0_8,plain,
multiply(identity,X_48) = X_48,
inference(subst,[],[left_identity:[bind(X,$fot(X_48))]]) ).
cnf(refute_0_9,plain,
( multiply(identity,X_48) != X_48
| multiply(identity,X_48) != multiply(inverse(X_47),multiply(X_47,X_48))
| X_48 = multiply(inverse(X_47),multiply(X_47,X_48)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_48),multiply(inverse(X_47),multiply(X_47,X_48))) ),[0],$fot(X_48)]]) ).
cnf(refute_0_10,plain,
( multiply(identity,X_48) != multiply(inverse(X_47),multiply(X_47,X_48))
| X_48 = multiply(inverse(X_47),multiply(X_47,X_48)) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_48),X_48) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
X_48 = multiply(inverse(X_47),multiply(X_47,X_48)),
inference(resolve,[$cnf( $equal(multiply(identity,X_48),multiply(inverse(X_47),multiply(X_47,X_48))) )],[refute_0_7,refute_0_10]) ).
cnf(refute_0_12,plain,
multiply(X_49,X_50) = multiply(inverse(inverse(X_49)),multiply(inverse(X_49),multiply(X_49,X_50))),
inference(subst,[],[refute_0_11:[bind(X_47,$fot(inverse(X_49))),bind(X_48,$fot(multiply(X_49,X_50)))]]) ).
cnf(refute_0_13,plain,
X_50 = multiply(inverse(X_49),multiply(X_49,X_50)),
inference(subst,[],[refute_0_11:[bind(X_47,$fot(X_49)),bind(X_48,$fot(X_50))]]) ).
cnf(refute_0_14,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_15,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_16,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
( X_50 != multiply(inverse(X_49),multiply(X_49,X_50))
| multiply(inverse(X_49),multiply(X_49,X_50)) = X_50 ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(X_50)),bind(Y0,$fot(multiply(inverse(X_49),multiply(X_49,X_50))))]]) ).
cnf(refute_0_18,plain,
multiply(inverse(X_49),multiply(X_49,X_50)) = X_50,
inference(resolve,[$cnf( $equal(X_50,multiply(inverse(X_49),multiply(X_49,X_50))) )],[refute_0_13,refute_0_17]) ).
cnf(refute_0_19,plain,
( multiply(X_49,X_50) != multiply(inverse(inverse(X_49)),multiply(inverse(X_49),multiply(X_49,X_50)))
| multiply(inverse(X_49),multiply(X_49,X_50)) != X_50
| multiply(X_49,X_50) = multiply(inverse(inverse(X_49)),X_50) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_49,X_50),multiply(inverse(inverse(X_49)),multiply(inverse(X_49),multiply(X_49,X_50)))) ),[1,1],$fot(X_50)]]) ).
cnf(refute_0_20,plain,
( multiply(X_49,X_50) != multiply(inverse(inverse(X_49)),multiply(inverse(X_49),multiply(X_49,X_50)))
| multiply(X_49,X_50) = multiply(inverse(inverse(X_49)),X_50) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_49),multiply(X_49,X_50)),X_50) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
multiply(X_49,X_50) = multiply(inverse(inverse(X_49)),X_50),
inference(resolve,[$cnf( $equal(multiply(X_49,X_50),multiply(inverse(inverse(X_49)),multiply(inverse(X_49),multiply(X_49,X_50)))) )],[refute_0_12,refute_0_20]) ).
cnf(refute_0_22,plain,
multiply(X_52,inverse(X_52)) = multiply(inverse(inverse(X_52)),inverse(X_52)),
inference(subst,[],[refute_0_21:[bind(X_49,$fot(X_52)),bind(X_50,$fot(inverse(X_52)))]]) ).
cnf(refute_0_23,plain,
( multiply(X_52,inverse(X_52)) != multiply(inverse(inverse(X_52)),inverse(X_52))
| multiply(inverse(inverse(X_52)),inverse(X_52)) = multiply(X_52,inverse(X_52)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(multiply(X_52,inverse(X_52)))),bind(Y0,$fot(multiply(inverse(inverse(X_52)),inverse(X_52))))]]) ).
cnf(refute_0_24,plain,
multiply(inverse(inverse(X_52)),inverse(X_52)) = multiply(X_52,inverse(X_52)),
inference(resolve,[$cnf( $equal(multiply(X_52,inverse(X_52)),multiply(inverse(inverse(X_52)),inverse(X_52))) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( multiply(inverse(inverse(X_52)),inverse(X_52)) != multiply(X_52,inverse(X_52))
| multiply(inverse(inverse(X_52)),inverse(X_52)) != identity
| multiply(X_52,inverse(X_52)) = identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X_52)),inverse(X_52)),identity) ),[0],$fot(multiply(X_52,inverse(X_52)))]]) ).
cnf(refute_0_26,plain,
( multiply(inverse(inverse(X_52)),inverse(X_52)) != identity
| multiply(X_52,inverse(X_52)) = identity ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_52)),inverse(X_52)),multiply(X_52,inverse(X_52))) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
multiply(X_52,inverse(X_52)) = identity,
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_52)),inverse(X_52)),identity) )],[refute_0_2,refute_0_26]) ).
cnf(refute_0_28,plain,
multiply(X_75,inverse(X_75)) = identity,
inference(subst,[],[refute_0_27:[bind(X_52,$fot(X_75))]]) ).
cnf(refute_0_29,plain,
( multiply(X_75,inverse(X_75)) != identity
| multiply(X_75,least_upper_bound(X_76,inverse(X_75))) != least_upper_bound(multiply(X_75,X_76),multiply(X_75,inverse(X_75)))
| multiply(X_75,least_upper_bound(X_76,inverse(X_75))) = least_upper_bound(multiply(X_75,X_76),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_75,least_upper_bound(X_76,inverse(X_75))),least_upper_bound(multiply(X_75,X_76),multiply(X_75,inverse(X_75)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_30,plain,
( multiply(X_75,least_upper_bound(X_76,inverse(X_75))) != least_upper_bound(multiply(X_75,X_76),multiply(X_75,inverse(X_75)))
| multiply(X_75,least_upper_bound(X_76,inverse(X_75))) = least_upper_bound(multiply(X_75,X_76),identity) ),
inference(resolve,[$cnf( $equal(multiply(X_75,inverse(X_75)),identity) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
multiply(X_75,least_upper_bound(X_76,inverse(X_75))) = least_upper_bound(multiply(X_75,X_76),identity),
inference(resolve,[$cnf( $equal(multiply(X_75,least_upper_bound(X_76,inverse(X_75))),least_upper_bound(multiply(X_75,X_76),multiply(X_75,inverse(X_75)))) )],[refute_0_1,refute_0_30]) ).
cnf(refute_0_32,plain,
( least_upper_bound(X,Y) != least_upper_bound(Y,X)
| least_upper_bound(Y,X) = least_upper_bound(X,Y) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(least_upper_bound(X,Y))),bind(Y0,$fot(least_upper_bound(Y,X)))]]) ).
cnf(refute_0_33,plain,
least_upper_bound(Y,X) = least_upper_bound(X,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(X,Y),least_upper_bound(Y,X)) )],[symmetry_of_lub,refute_0_32]) ).
cnf(refute_0_34,plain,
least_upper_bound(multiply(X_75,X_76),identity) = least_upper_bound(identity,multiply(X_75,X_76)),
inference(subst,[],[refute_0_33:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_75,X_76)))]]) ).
cnf(refute_0_35,plain,
( multiply(X_75,least_upper_bound(X_76,inverse(X_75))) != least_upper_bound(multiply(X_75,X_76),identity)
| least_upper_bound(multiply(X_75,X_76),identity) != least_upper_bound(identity,multiply(X_75,X_76))
| multiply(X_75,least_upper_bound(X_76,inverse(X_75))) = least_upper_bound(identity,multiply(X_75,X_76)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_75,least_upper_bound(X_76,inverse(X_75))),least_upper_bound(identity,multiply(X_75,X_76))) ),[0],$fot(least_upper_bound(multiply(X_75,X_76),identity))]]) ).
cnf(refute_0_36,plain,
( multiply(X_75,least_upper_bound(X_76,inverse(X_75))) != least_upper_bound(multiply(X_75,X_76),identity)
| multiply(X_75,least_upper_bound(X_76,inverse(X_75))) = least_upper_bound(identity,multiply(X_75,X_76)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_75,X_76),identity),least_upper_bound(identity,multiply(X_75,X_76))) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
multiply(X_75,least_upper_bound(X_76,inverse(X_75))) = least_upper_bound(identity,multiply(X_75,X_76)),
inference(resolve,[$cnf( $equal(multiply(X_75,least_upper_bound(X_76,inverse(X_75))),least_upper_bound(multiply(X_75,X_76),identity)) )],[refute_0_31,refute_0_36]) ).
cnf(refute_0_38,plain,
multiply(a,least_upper_bound(b,inverse(a))) = least_upper_bound(identity,multiply(a,b)),
inference(subst,[],[refute_0_37:[bind(X_75,$fot(a)),bind(X_76,$fot(b))]]) ).
cnf(refute_0_39,plain,
least_upper_bound(b,least_upper_bound(identity,X_60)) = least_upper_bound(least_upper_bound(b,identity),X_60),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(b)),bind(Y,$fot(identity)),bind(Z,$fot(X_60))]]) ).
cnf(refute_0_40,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_41,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_16:[bind(X0,$fot(greatest_lower_bound(X,Y))),bind(Y0,$fot(greatest_lower_bound(Y,X)))]]) ).
cnf(refute_0_42,plain,
greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X)) )],[symmetry_of_glb,refute_0_41]) ).
cnf(refute_0_43,plain,
greatest_lower_bound(identity,b) = greatest_lower_bound(b,identity),
inference(subst,[],[refute_0_42:[bind(X,$fot(b)),bind(Y,$fot(identity))]]) ).
cnf(refute_0_44,plain,
( greatest_lower_bound(identity,b) != greatest_lower_bound(b,identity)
| greatest_lower_bound(identity,b) != identity
| greatest_lower_bound(b,identity) = identity ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,b),identity) ),[0],$fot(greatest_lower_bound(b,identity))]]) ).
cnf(refute_0_45,plain,
( greatest_lower_bound(identity,b) != identity
| greatest_lower_bound(b,identity) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,b),greatest_lower_bound(b,identity)) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
greatest_lower_bound(b,identity) = identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,b),identity) )],[p04b_2,refute_0_45]) ).
cnf(refute_0_47,plain,
( greatest_lower_bound(b,identity) != identity
| least_upper_bound(b,greatest_lower_bound(b,identity)) != b
| least_upper_bound(b,identity) = b ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(b,identity)),b) ),[0,1],$fot(identity)]]) ).
cnf(refute_0_48,plain,
( least_upper_bound(b,greatest_lower_bound(b,identity)) != b
| least_upper_bound(b,identity) = b ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,identity),identity) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
least_upper_bound(b,identity) = b,
inference(resolve,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(b,identity)),b) )],[refute_0_40,refute_0_48]) ).
cnf(refute_0_50,plain,
( least_upper_bound(b,identity) != b
| least_upper_bound(b,least_upper_bound(identity,X_60)) != least_upper_bound(least_upper_bound(b,identity),X_60)
| least_upper_bound(b,least_upper_bound(identity,X_60)) = least_upper_bound(b,X_60) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,least_upper_bound(identity,X_60)),least_upper_bound(least_upper_bound(b,identity),X_60)) ),[1,0],$fot(b)]]) ).
cnf(refute_0_51,plain,
( least_upper_bound(b,least_upper_bound(identity,X_60)) != least_upper_bound(least_upper_bound(b,identity),X_60)
| least_upper_bound(b,least_upper_bound(identity,X_60)) = least_upper_bound(b,X_60) ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,identity),b) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
least_upper_bound(b,least_upper_bound(identity,X_60)) = least_upper_bound(b,X_60),
inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(identity,X_60)),least_upper_bound(least_upper_bound(b,identity),X_60)) )],[refute_0_39,refute_0_51]) ).
cnf(refute_0_53,plain,
least_upper_bound(b,least_upper_bound(identity,inverse(a))) = least_upper_bound(b,inverse(a)),
inference(subst,[],[refute_0_52:[bind(X_60,$fot(inverse(a)))]]) ).
cnf(refute_0_54,plain,
multiply(X_75,least_upper_bound(X_76,identity)) = least_upper_bound(multiply(X_75,X_76),multiply(X_75,identity)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(X_75)),bind(Y,$fot(X_76)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_55,plain,
X_50 = multiply(inverse(inverse(X_50)),multiply(inverse(X_50),X_50)),
inference(subst,[],[refute_0_11:[bind(X_47,$fot(inverse(X_50))),bind(X_48,$fot(X_50))]]) ).
cnf(refute_0_56,plain,
multiply(inverse(X_50),X_50) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_50))]]) ).
cnf(refute_0_57,plain,
( X_50 != multiply(inverse(inverse(X_50)),multiply(inverse(X_50),X_50))
| multiply(inverse(X_50),X_50) != identity
| X_50 = multiply(inverse(inverse(X_50)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(X_50,multiply(inverse(inverse(X_50)),multiply(inverse(X_50),X_50))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_58,plain,
( X_50 != multiply(inverse(inverse(X_50)),multiply(inverse(X_50),X_50))
| X_50 = multiply(inverse(inverse(X_50)),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_50),X_50),identity) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
X_50 = multiply(inverse(inverse(X_50)),identity),
inference(resolve,[$cnf( $equal(X_50,multiply(inverse(inverse(X_50)),multiply(inverse(X_50),X_50))) )],[refute_0_55,refute_0_58]) ).
cnf(refute_0_60,plain,
( multiply(X_49,X_50) != multiply(inverse(inverse(X_49)),X_50)
| multiply(inverse(inverse(X_49)),X_50) = multiply(X_49,X_50) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(multiply(X_49,X_50))),bind(Y0,$fot(multiply(inverse(inverse(X_49)),X_50)))]]) ).
cnf(refute_0_61,plain,
multiply(inverse(inverse(X_49)),X_50) = multiply(X_49,X_50),
inference(resolve,[$cnf( $equal(multiply(X_49,X_50),multiply(inverse(inverse(X_49)),X_50)) )],[refute_0_21,refute_0_60]) ).
cnf(refute_0_62,plain,
multiply(inverse(inverse(X_50)),identity) = multiply(X_50,identity),
inference(subst,[],[refute_0_61:[bind(X_49,$fot(X_50)),bind(X_50,$fot(identity))]]) ).
cnf(refute_0_63,plain,
( X_50 != multiply(inverse(inverse(X_50)),identity)
| multiply(inverse(inverse(X_50)),identity) != multiply(X_50,identity)
| X_50 = multiply(X_50,identity) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_50,multiply(X_50,identity)) ),[0],$fot(multiply(inverse(inverse(X_50)),identity))]]) ).
cnf(refute_0_64,plain,
( X_50 != multiply(inverse(inverse(X_50)),identity)
| X_50 = multiply(X_50,identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_50)),identity),multiply(X_50,identity)) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
X_50 = multiply(X_50,identity),
inference(resolve,[$cnf( $equal(X_50,multiply(inverse(inverse(X_50)),identity)) )],[refute_0_59,refute_0_64]) ).
cnf(refute_0_66,plain,
X_75 = multiply(X_75,identity),
inference(subst,[],[refute_0_65:[bind(X_50,$fot(X_75))]]) ).
cnf(refute_0_67,plain,
( X_75 != multiply(X_75,identity)
| multiply(X_75,identity) = X_75 ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(X_75)),bind(Y0,$fot(multiply(X_75,identity)))]]) ).
cnf(refute_0_68,plain,
multiply(X_75,identity) = X_75,
inference(resolve,[$cnf( $equal(X_75,multiply(X_75,identity)) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
( multiply(X_75,identity) != X_75
| multiply(X_75,least_upper_bound(X_76,identity)) != least_upper_bound(multiply(X_75,X_76),multiply(X_75,identity))
| multiply(X_75,least_upper_bound(X_76,identity)) = least_upper_bound(multiply(X_75,X_76),X_75) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_75,least_upper_bound(X_76,identity)),least_upper_bound(multiply(X_75,X_76),multiply(X_75,identity))) ),[1,1],$fot(X_75)]]) ).
cnf(refute_0_70,plain,
( multiply(X_75,least_upper_bound(X_76,identity)) != least_upper_bound(multiply(X_75,X_76),multiply(X_75,identity))
| multiply(X_75,least_upper_bound(X_76,identity)) = least_upper_bound(multiply(X_75,X_76),X_75) ),
inference(resolve,[$cnf( $equal(multiply(X_75,identity),X_75) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
multiply(X_75,least_upper_bound(X_76,identity)) = least_upper_bound(multiply(X_75,X_76),X_75),
inference(resolve,[$cnf( $equal(multiply(X_75,least_upper_bound(X_76,identity)),least_upper_bound(multiply(X_75,X_76),multiply(X_75,identity))) )],[refute_0_54,refute_0_70]) ).
cnf(refute_0_72,plain,
least_upper_bound(multiply(X_75,X_76),X_75) = least_upper_bound(X_75,multiply(X_75,X_76)),
inference(subst,[],[refute_0_33:[bind(X,$fot(X_75)),bind(Y,$fot(multiply(X_75,X_76)))]]) ).
cnf(refute_0_73,plain,
( multiply(X_75,least_upper_bound(X_76,identity)) != least_upper_bound(multiply(X_75,X_76),X_75)
| least_upper_bound(multiply(X_75,X_76),X_75) != least_upper_bound(X_75,multiply(X_75,X_76))
| multiply(X_75,least_upper_bound(X_76,identity)) = least_upper_bound(X_75,multiply(X_75,X_76)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_75,least_upper_bound(X_76,identity)),least_upper_bound(X_75,multiply(X_75,X_76))) ),[0],$fot(least_upper_bound(multiply(X_75,X_76),X_75))]]) ).
cnf(refute_0_74,plain,
( multiply(X_75,least_upper_bound(X_76,identity)) != least_upper_bound(multiply(X_75,X_76),X_75)
| multiply(X_75,least_upper_bound(X_76,identity)) = least_upper_bound(X_75,multiply(X_75,X_76)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_75,X_76),X_75),least_upper_bound(X_75,multiply(X_75,X_76))) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
multiply(X_75,least_upper_bound(X_76,identity)) = least_upper_bound(X_75,multiply(X_75,X_76)),
inference(resolve,[$cnf( $equal(multiply(X_75,least_upper_bound(X_76,identity)),least_upper_bound(multiply(X_75,X_76),X_75)) )],[refute_0_71,refute_0_74]) ).
cnf(refute_0_76,plain,
multiply(inverse(X_87),least_upper_bound(X_87,identity)) = least_upper_bound(inverse(X_87),multiply(inverse(X_87),X_87)),
inference(subst,[],[refute_0_75:[bind(X_75,$fot(inverse(X_87))),bind(X_76,$fot(X_87))]]) ).
cnf(refute_0_77,plain,
multiply(inverse(X_87),X_87) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_87))]]) ).
cnf(refute_0_78,plain,
( multiply(inverse(X_87),X_87) != identity
| multiply(inverse(X_87),least_upper_bound(X_87,identity)) != least_upper_bound(inverse(X_87),multiply(inverse(X_87),X_87))
| multiply(inverse(X_87),least_upper_bound(X_87,identity)) = least_upper_bound(inverse(X_87),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_87),least_upper_bound(X_87,identity)),least_upper_bound(inverse(X_87),multiply(inverse(X_87),X_87))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_79,plain,
( multiply(inverse(X_87),least_upper_bound(X_87,identity)) != least_upper_bound(inverse(X_87),multiply(inverse(X_87),X_87))
| multiply(inverse(X_87),least_upper_bound(X_87,identity)) = least_upper_bound(inverse(X_87),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_87),X_87),identity) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
multiply(inverse(X_87),least_upper_bound(X_87,identity)) = least_upper_bound(inverse(X_87),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_87),least_upper_bound(X_87,identity)),least_upper_bound(inverse(X_87),multiply(inverse(X_87),X_87))) )],[refute_0_76,refute_0_79]) ).
cnf(refute_0_81,plain,
least_upper_bound(inverse(X_87),identity) = least_upper_bound(identity,inverse(X_87)),
inference(subst,[],[refute_0_33:[bind(X,$fot(identity)),bind(Y,$fot(inverse(X_87)))]]) ).
cnf(refute_0_82,plain,
( multiply(inverse(X_87),least_upper_bound(X_87,identity)) != least_upper_bound(inverse(X_87),identity)
| least_upper_bound(inverse(X_87),identity) != least_upper_bound(identity,inverse(X_87))
| multiply(inverse(X_87),least_upper_bound(X_87,identity)) = least_upper_bound(identity,inverse(X_87)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_87),least_upper_bound(X_87,identity)),least_upper_bound(identity,inverse(X_87))) ),[0],$fot(least_upper_bound(inverse(X_87),identity))]]) ).
cnf(refute_0_83,plain,
( multiply(inverse(X_87),least_upper_bound(X_87,identity)) != least_upper_bound(inverse(X_87),identity)
| multiply(inverse(X_87),least_upper_bound(X_87,identity)) = least_upper_bound(identity,inverse(X_87)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_87),identity),least_upper_bound(identity,inverse(X_87))) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
multiply(inverse(X_87),least_upper_bound(X_87,identity)) = least_upper_bound(identity,inverse(X_87)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_87),least_upper_bound(X_87,identity)),least_upper_bound(inverse(X_87),identity)) )],[refute_0_80,refute_0_83]) ).
cnf(refute_0_85,plain,
multiply(inverse(a),least_upper_bound(a,identity)) = least_upper_bound(identity,inverse(a)),
inference(subst,[],[refute_0_84:[bind(X_87,$fot(a))]]) ).
cnf(refute_0_86,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_87,plain,
greatest_lower_bound(identity,a) = greatest_lower_bound(a,identity),
inference(subst,[],[refute_0_42:[bind(X,$fot(a)),bind(Y,$fot(identity))]]) ).
cnf(refute_0_88,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_89,plain,
( greatest_lower_bound(identity,a) != identity
| greatest_lower_bound(a,identity) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,a),greatest_lower_bound(a,identity)) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
greatest_lower_bound(a,identity) = identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,a),identity) )],[p04b_1,refute_0_89]) ).
cnf(refute_0_91,plain,
( greatest_lower_bound(a,identity) != identity
| least_upper_bound(a,greatest_lower_bound(a,identity)) != a
| least_upper_bound(a,identity) = a ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(a,greatest_lower_bound(a,identity)),a) ),[0,1],$fot(identity)]]) ).
cnf(refute_0_92,plain,
( least_upper_bound(a,greatest_lower_bound(a,identity)) != a
| least_upper_bound(a,identity) = a ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,identity),identity) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
least_upper_bound(a,identity) = a,
inference(resolve,[$cnf( $equal(least_upper_bound(a,greatest_lower_bound(a,identity)),a) )],[refute_0_86,refute_0_92]) ).
cnf(refute_0_94,plain,
( multiply(inverse(a),least_upper_bound(a,identity)) != least_upper_bound(identity,inverse(a))
| least_upper_bound(a,identity) != a
| multiply(inverse(a),a) = least_upper_bound(identity,inverse(a)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(a),least_upper_bound(a,identity)),least_upper_bound(identity,inverse(a))) ),[0,1],$fot(a)]]) ).
cnf(refute_0_95,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( $equal(least_upper_bound(a,identity),a) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
multiply(inverse(a),a) = least_upper_bound(identity,inverse(a)),
inference(resolve,[$cnf( $equal(multiply(inverse(a),least_upper_bound(a,identity)),least_upper_bound(identity,inverse(a))) )],[refute_0_85,refute_0_95]) ).
cnf(refute_0_97,plain,
multiply(inverse(a),a) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(a))]]) ).
cnf(refute_0_98,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_99,plain,
( multiply(inverse(a),a) != least_upper_bound(identity,inverse(a))
| identity = least_upper_bound(identity,inverse(a)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(a),a),identity) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
identity = least_upper_bound(identity,inverse(a)),
inference(resolve,[$cnf( $equal(multiply(inverse(a),a),least_upper_bound(identity,inverse(a))) )],[refute_0_96,refute_0_99]) ).
cnf(refute_0_101,plain,
( identity != least_upper_bound(identity,inverse(a))
| least_upper_bound(identity,inverse(a)) = identity ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(identity)),bind(Y0,$fot(least_upper_bound(identity,inverse(a))))]]) ).
cnf(refute_0_102,plain,
least_upper_bound(identity,inverse(a)) = identity,
inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,inverse(a))) )],[refute_0_100,refute_0_101]) ).
cnf(refute_0_103,plain,
( least_upper_bound(b,least_upper_bound(identity,inverse(a))) != least_upper_bound(b,inverse(a))
| least_upper_bound(identity,inverse(a)) != identity
| least_upper_bound(b,identity) = least_upper_bound(b,inverse(a)) ),
introduced(tautology,[equality,[$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_104,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( $equal(least_upper_bound(identity,inverse(a)),identity) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
least_upper_bound(b,identity) = least_upper_bound(b,inverse(a)),
inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(identity,inverse(a))),least_upper_bound(b,inverse(a))) )],[refute_0_53,refute_0_104]) ).
cnf(refute_0_106,plain,
( least_upper_bound(b,identity) != b
| least_upper_bound(b,identity) != least_upper_bound(b,inverse(a))
| b = least_upper_bound(b,inverse(a)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,identity),least_upper_bound(b,inverse(a))) ),[0],$fot(b)]]) ).
cnf(refute_0_107,plain,
( least_upper_bound(b,identity) != least_upper_bound(b,inverse(a))
| b = least_upper_bound(b,inverse(a)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,identity),b) )],[refute_0_49,refute_0_106]) ).
cnf(refute_0_108,plain,
b = least_upper_bound(b,inverse(a)),
inference(resolve,[$cnf( $equal(least_upper_bound(b,identity),least_upper_bound(b,inverse(a))) )],[refute_0_105,refute_0_107]) ).
cnf(refute_0_109,plain,
( b != least_upper_bound(b,inverse(a))
| least_upper_bound(b,inverse(a)) = b ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(b)),bind(Y0,$fot(least_upper_bound(b,inverse(a))))]]) ).
cnf(refute_0_110,plain,
least_upper_bound(b,inverse(a)) = b,
inference(resolve,[$cnf( $equal(b,least_upper_bound(b,inverse(a))) )],[refute_0_108,refute_0_109]) ).
cnf(refute_0_111,plain,
( multiply(a,least_upper_bound(b,inverse(a))) != least_upper_bound(identity,multiply(a,b))
| least_upper_bound(b,inverse(a)) != b
| multiply(a,b) = least_upper_bound(identity,multiply(a,b)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(a,least_upper_bound(b,inverse(a))),least_upper_bound(identity,multiply(a,b))) ),[0,1],$fot(b)]]) ).
cnf(refute_0_112,plain,
( multiply(a,least_upper_bound(b,inverse(a))) != least_upper_bound(identity,multiply(a,b))
| multiply(a,b) = least_upper_bound(identity,multiply(a,b)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,inverse(a)),b) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
multiply(a,b) = least_upper_bound(identity,multiply(a,b)),
inference(resolve,[$cnf( $equal(multiply(a,least_upper_bound(b,inverse(a))),least_upper_bound(identity,multiply(a,b))) )],[refute_0_38,refute_0_112]) ).
cnf(refute_0_114,plain,
( multiply(a,b) != least_upper_bound(identity,multiply(a,b))
| least_upper_bound(identity,multiply(a,b)) = multiply(a,b) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(multiply(a,b))),bind(Y0,$fot(least_upper_bound(identity,multiply(a,b))))]]) ).
cnf(refute_0_115,plain,
least_upper_bound(identity,multiply(a,b)) = multiply(a,b),
inference(resolve,[$cnf( $equal(multiply(a,b),least_upper_bound(identity,multiply(a,b))) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
( greatest_lower_bound(identity,least_upper_bound(identity,multiply(a,b))) != identity
| least_upper_bound(identity,multiply(a,b)) != multiply(a,b)
| greatest_lower_bound(identity,multiply(a,b)) = identity ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(identity,multiply(a,b))),identity) ),[0,1],$fot(multiply(a,b))]]) ).
cnf(refute_0_117,plain,
( greatest_lower_bound(identity,least_upper_bound(identity,multiply(a,b))) != identity
| greatest_lower_bound(identity,multiply(a,b)) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(a,b)),multiply(a,b)) )],[refute_0_115,refute_0_116]) ).
cnf(refute_0_118,plain,
greatest_lower_bound(identity,multiply(a,b)) = identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(identity,multiply(a,b))),identity) )],[refute_0_0,refute_0_117]) ).
cnf(refute_0_119,plain,
$false,
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(a,b)),identity) )],[refute_0_118,prove_p04b]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : GRP172-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.06/0.07 % Command : metis --show proof --show saturation %s
% 0.06/0.25 % Computer : n007.cluster.edu
% 0.06/0.25 % Model : x86_64 x86_64
% 0.06/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.25 % Memory : 8042.1875MB
% 0.06/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.25 % CPULimit : 300
% 0.06/0.25 % WCLimit : 600
% 0.06/0.25 % DateTime : Tue Jun 14 13:27:54 EDT 2022
% 0.06/0.25 % CPUTime :
% 0.06/0.26 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.38/0.60 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.38/0.60
% 0.38/0.60 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.38/0.61
%------------------------------------------------------------------------------