%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP166-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n028.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 10:37:08 EDT 2022
% Result : Unsatisfiable 0.77s 0.95s
% Output : CNFRefutation 0.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 32
% Syntax : Number of clauses : 126 ( 68 unt; 0 nHn; 69 RR)
% Number of literals : 210 ( 209 equ; 86 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 192 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
multiply(identity,X) = X ).
cnf(left_inverse,axiom,
multiply(inverse(X),X) = identity ).
cnf(associativity,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ).
cnf(symmetry_of_glb,axiom,
greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ).
cnf(monotony_glb1,axiom,
multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)) ).
cnf(lat2b_2,hypothesis,
greatest_lower_bound(b,identity) = identity ).
cnf(prove_lat2b,negated_conjecture,
greatest_lower_bound(a,multiply(a,b)) != a ).
cnf(refute_0_0,plain,
multiply(multiply(inverse(X_87),X_87),X_88) = multiply(inverse(X_87),multiply(X_87,X_88)),
inference(subst,[],[associativity:[bind(X,$fot(inverse(X_87))),bind(Y,$fot(X_87)),bind(Z,$fot(X_88))]]) ).
cnf(refute_0_1,plain,
multiply(inverse(X_87),X_87) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_87))]]) ).
cnf(refute_0_2,plain,
( multiply(multiply(inverse(X_87),X_87),X_88) != multiply(inverse(X_87),multiply(X_87,X_88))
| multiply(inverse(X_87),X_87) != identity
| multiply(identity,X_88) = multiply(inverse(X_87),multiply(X_87,X_88)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_87),X_87),X_88),multiply(inverse(X_87),multiply(X_87,X_88))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_3,plain,
( multiply(multiply(inverse(X_87),X_87),X_88) != multiply(inverse(X_87),multiply(X_87,X_88))
| multiply(identity,X_88) = multiply(inverse(X_87),multiply(X_87,X_88)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_87),X_87),identity) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
multiply(identity,X_88) = multiply(inverse(X_87),multiply(X_87,X_88)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_87),X_87),X_88),multiply(inverse(X_87),multiply(X_87,X_88))) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
multiply(identity,X_88) = X_88,
inference(subst,[],[left_identity:[bind(X,$fot(X_88))]]) ).
cnf(refute_0_6,plain,
( multiply(identity,X_88) != X_88
| multiply(identity,X_88) != multiply(inverse(X_87),multiply(X_87,X_88))
| X_88 = multiply(inverse(X_87),multiply(X_87,X_88)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_88),multiply(inverse(X_87),multiply(X_87,X_88))) ),[0],$fot(X_88)]]) ).
cnf(refute_0_7,plain,
( multiply(identity,X_88) != multiply(inverse(X_87),multiply(X_87,X_88))
| X_88 = multiply(inverse(X_87),multiply(X_87,X_88)) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_88),X_88) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
X_88 = multiply(inverse(X_87),multiply(X_87,X_88)),
inference(resolve,[$cnf( $equal(multiply(identity,X_88),multiply(inverse(X_87),multiply(X_87,X_88))) )],[refute_0_4,refute_0_7]) ).
cnf(refute_0_9,plain,
X_111 = multiply(inverse(inverse(X_111)),multiply(inverse(X_111),X_111)),
inference(subst,[],[refute_0_8:[bind(X_87,$fot(inverse(X_111))),bind(X_88,$fot(X_111))]]) ).
cnf(refute_0_10,plain,
multiply(inverse(X_111),X_111) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_111))]]) ).
cnf(refute_0_11,plain,
( X_111 != multiply(inverse(inverse(X_111)),multiply(inverse(X_111),X_111))
| multiply(inverse(X_111),X_111) != identity
| X_111 = multiply(inverse(inverse(X_111)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(X_111,multiply(inverse(inverse(X_111)),multiply(inverse(X_111),X_111))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_12,plain,
( X_111 != multiply(inverse(inverse(X_111)),multiply(inverse(X_111),X_111))
| X_111 = multiply(inverse(inverse(X_111)),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_111),X_111),identity) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
X_111 = multiply(inverse(inverse(X_111)),identity),
inference(resolve,[$cnf( $equal(X_111,multiply(inverse(inverse(X_111)),multiply(inverse(X_111),X_111))) )],[refute_0_9,refute_0_12]) ).
cnf(refute_0_14,plain,
multiply(X_110,X_111) = multiply(inverse(inverse(X_110)),multiply(inverse(X_110),multiply(X_110,X_111))),
inference(subst,[],[refute_0_8:[bind(X_87,$fot(inverse(X_110))),bind(X_88,$fot(multiply(X_110,X_111)))]]) ).
cnf(refute_0_15,plain,
X_111 = multiply(inverse(X_110),multiply(X_110,X_111)),
inference(subst,[],[refute_0_8:[bind(X_87,$fot(X_110)),bind(X_88,$fot(X_111))]]) ).
cnf(refute_0_16,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_17,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_18,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
( X_111 != multiply(inverse(X_110),multiply(X_110,X_111))
| multiply(inverse(X_110),multiply(X_110,X_111)) = X_111 ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(X_111)),bind(Y0,$fot(multiply(inverse(X_110),multiply(X_110,X_111))))]]) ).
cnf(refute_0_20,plain,
multiply(inverse(X_110),multiply(X_110,X_111)) = X_111,
inference(resolve,[$cnf( $equal(X_111,multiply(inverse(X_110),multiply(X_110,X_111))) )],[refute_0_15,refute_0_19]) ).
cnf(refute_0_21,plain,
( multiply(X_110,X_111) != multiply(inverse(inverse(X_110)),multiply(inverse(X_110),multiply(X_110,X_111)))
| multiply(inverse(X_110),multiply(X_110,X_111)) != X_111
| multiply(X_110,X_111) = multiply(inverse(inverse(X_110)),X_111) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_110,X_111),multiply(inverse(inverse(X_110)),multiply(inverse(X_110),multiply(X_110,X_111)))) ),[1,1],$fot(X_111)]]) ).
cnf(refute_0_22,plain,
( multiply(X_110,X_111) != multiply(inverse(inverse(X_110)),multiply(inverse(X_110),multiply(X_110,X_111)))
| multiply(X_110,X_111) = multiply(inverse(inverse(X_110)),X_111) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_110),multiply(X_110,X_111)),X_111) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
multiply(X_110,X_111) = multiply(inverse(inverse(X_110)),X_111),
inference(resolve,[$cnf( $equal(multiply(X_110,X_111),multiply(inverse(inverse(X_110)),multiply(inverse(X_110),multiply(X_110,X_111)))) )],[refute_0_14,refute_0_22]) ).
cnf(refute_0_24,plain,
( multiply(X_110,X_111) != multiply(inverse(inverse(X_110)),X_111)
| multiply(inverse(inverse(X_110)),X_111) = multiply(X_110,X_111) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(X_110,X_111))),bind(Y0,$fot(multiply(inverse(inverse(X_110)),X_111)))]]) ).
cnf(refute_0_25,plain,
multiply(inverse(inverse(X_110)),X_111) = multiply(X_110,X_111),
inference(resolve,[$cnf( $equal(multiply(X_110,X_111),multiply(inverse(inverse(X_110)),X_111)) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
multiply(inverse(inverse(X_111)),identity) = multiply(X_111,identity),
inference(subst,[],[refute_0_25:[bind(X_110,$fot(X_111)),bind(X_111,$fot(identity))]]) ).
cnf(refute_0_27,plain,
( X_111 != multiply(inverse(inverse(X_111)),identity)
| multiply(inverse(inverse(X_111)),identity) != multiply(X_111,identity)
| X_111 = multiply(X_111,identity) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_111,multiply(X_111,identity)) ),[0],$fot(multiply(inverse(inverse(X_111)),identity))]]) ).
cnf(refute_0_28,plain,
( X_111 != multiply(inverse(inverse(X_111)),identity)
| X_111 = multiply(X_111,identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_111)),identity),multiply(X_111,identity)) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
X_111 = multiply(X_111,identity),
inference(resolve,[$cnf( $equal(X_111,multiply(inverse(inverse(X_111)),identity)) )],[refute_0_13,refute_0_28]) ).
cnf(refute_0_30,plain,
( X_111 != multiply(X_111,identity)
| multiply(X_111,identity) = X_111 ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(X_111)),bind(Y0,$fot(multiply(X_111,identity)))]]) ).
cnf(refute_0_31,plain,
multiply(X_111,identity) = X_111,
inference(resolve,[$cnf( $equal(X_111,multiply(X_111,identity)) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
multiply(a,identity) = a,
inference(subst,[],[refute_0_31:[bind(X_111,$fot(a))]]) ).
cnf(refute_0_33,plain,
multiply(a,greatest_lower_bound(b,identity)) = multiply(a,greatest_lower_bound(b,identity)),
introduced(tautology,[refl,[$fot(multiply(a,greatest_lower_bound(b,identity)))]]) ).
cnf(refute_0_34,plain,
( multiply(a,greatest_lower_bound(b,identity)) != multiply(a,greatest_lower_bound(b,identity))
| greatest_lower_bound(b,identity) != identity
| multiply(a,greatest_lower_bound(b,identity)) = multiply(a,identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(a,greatest_lower_bound(b,identity)),multiply(a,greatest_lower_bound(b,identity))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_35,plain,
( greatest_lower_bound(b,identity) != identity
| multiply(a,greatest_lower_bound(b,identity)) = multiply(a,identity) ),
inference(resolve,[$cnf( $equal(multiply(a,greatest_lower_bound(b,identity)),multiply(a,greatest_lower_bound(b,identity))) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
multiply(a,greatest_lower_bound(b,identity)) = multiply(a,identity),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,identity),identity) )],[lat2b_2,refute_0_35]) ).
cnf(refute_0_37,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_38,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_18,refute_0_37]) ).
cnf(refute_0_39,plain,
( multiply(a,greatest_lower_bound(b,identity)) != multiply(a,identity)
| multiply(a,identity) != a
| multiply(a,greatest_lower_bound(b,identity)) = a ),
inference(subst,[],[refute_0_38:[bind(X0,$fot(multiply(a,greatest_lower_bound(b,identity)))),bind(Y0,$fot(multiply(a,identity))),bind(Z0,$fot(a))]]) ).
cnf(refute_0_40,plain,
( multiply(a,identity) != a
| multiply(a,greatest_lower_bound(b,identity)) = a ),
inference(resolve,[$cnf( $equal(multiply(a,greatest_lower_bound(b,identity)),multiply(a,identity)) )],[refute_0_36,refute_0_39]) ).
cnf(refute_0_41,plain,
multiply(a,greatest_lower_bound(b,identity)) = a,
inference(resolve,[$cnf( $equal(multiply(a,identity),a) )],[refute_0_32,refute_0_40]) ).
cnf(refute_0_42,plain,
multiply(X,greatest_lower_bound(Y,identity)) = greatest_lower_bound(multiply(X,Y),multiply(X,identity)),
inference(subst,[],[monotony_glb1:[bind(Z,$fot(identity))]]) ).
cnf(refute_0_43,plain,
X = multiply(X,identity),
inference(subst,[],[refute_0_29:[bind(X_111,$fot(X))]]) ).
cnf(refute_0_44,plain,
( X != multiply(X,identity)
| multiply(X,identity) = X ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(X)),bind(Y0,$fot(multiply(X,identity)))]]) ).
cnf(refute_0_45,plain,
multiply(X,identity) = X,
inference(resolve,[$cnf( $equal(X,multiply(X,identity)) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
( multiply(X,greatest_lower_bound(Y,identity)) != greatest_lower_bound(multiply(X,Y),multiply(X,identity))
| multiply(X,identity) != X
| multiply(X,greatest_lower_bound(Y,identity)) = greatest_lower_bound(multiply(X,Y),X) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X,greatest_lower_bound(Y,identity)),greatest_lower_bound(multiply(X,Y),multiply(X,identity))) ),[1,1],$fot(X)]]) ).
cnf(refute_0_47,plain,
( multiply(X,greatest_lower_bound(Y,identity)) != greatest_lower_bound(multiply(X,Y),multiply(X,identity))
| multiply(X,greatest_lower_bound(Y,identity)) = greatest_lower_bound(multiply(X,Y),X) ),
inference(resolve,[$cnf( $equal(multiply(X,identity),X) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
multiply(X,greatest_lower_bound(Y,identity)) = greatest_lower_bound(multiply(X,Y),X),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(Y,identity)),greatest_lower_bound(multiply(X,Y),multiply(X,identity))) )],[refute_0_42,refute_0_47]) ).
cnf(refute_0_49,plain,
multiply(X,greatest_lower_bound(identity,Z)) = greatest_lower_bound(multiply(X,identity),multiply(X,Z)),
inference(subst,[],[monotony_glb1:[bind(Y,$fot(identity))]]) ).
cnf(refute_0_50,plain,
( multiply(X,greatest_lower_bound(identity,Z)) != greatest_lower_bound(multiply(X,identity),multiply(X,Z))
| multiply(X,identity) != X
| multiply(X,greatest_lower_bound(identity,Z)) = greatest_lower_bound(X,multiply(X,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X,greatest_lower_bound(identity,Z)),greatest_lower_bound(multiply(X,identity),multiply(X,Z))) ),[1,0],$fot(X)]]) ).
cnf(refute_0_51,plain,
( multiply(X,greatest_lower_bound(identity,Z)) != greatest_lower_bound(multiply(X,identity),multiply(X,Z))
| multiply(X,greatest_lower_bound(identity,Z)) = greatest_lower_bound(X,multiply(X,Z)) ),
inference(resolve,[$cnf( $equal(multiply(X,identity),X) )],[refute_0_45,refute_0_50]) ).
cnf(refute_0_52,plain,
multiply(X,greatest_lower_bound(identity,Z)) = greatest_lower_bound(X,multiply(X,Z)),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(identity,Z)),greatest_lower_bound(multiply(X,identity),multiply(X,Z))) )],[refute_0_49,refute_0_51]) ).
cnf(refute_0_53,plain,
( multiply(X,greatest_lower_bound(identity,Z)) != greatest_lower_bound(X,multiply(X,Z))
| greatest_lower_bound(X,multiply(X,Z)) = multiply(X,greatest_lower_bound(identity,Z)) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(X,greatest_lower_bound(identity,Z)))),bind(Y0,$fot(greatest_lower_bound(X,multiply(X,Z))))]]) ).
cnf(refute_0_54,plain,
greatest_lower_bound(X,multiply(X,Z)) = multiply(X,greatest_lower_bound(identity,Z)),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(identity,Z)),greatest_lower_bound(X,multiply(X,Z))) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
greatest_lower_bound(X,multiply(X,Y)) = multiply(X,greatest_lower_bound(identity,Y)),
inference(subst,[],[refute_0_54:[bind(Z,$fot(Y))]]) ).
cnf(refute_0_56,plain,
greatest_lower_bound(X_61,X_62) = multiply(inverse(inverse(X_62)),multiply(inverse(X_62),greatest_lower_bound(X_61,X_62))),
inference(subst,[],[refute_0_8:[bind(X_87,$fot(inverse(X_62))),bind(X_88,$fot(greatest_lower_bound(X_61,X_62)))]]) ).
cnf(refute_0_57,plain,
multiply(inverse(X_62),greatest_lower_bound(X_61,X_62)) = greatest_lower_bound(multiply(inverse(X_62),X_61),multiply(inverse(X_62),X_62)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(inverse(X_62))),bind(Y,$fot(X_61)),bind(Z,$fot(X_62))]]) ).
cnf(refute_0_58,plain,
multiply(inverse(X_62),X_62) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_62))]]) ).
cnf(refute_0_59,plain,
( multiply(inverse(X_62),X_62) != identity
| multiply(inverse(X_62),greatest_lower_bound(X_61,X_62)) != greatest_lower_bound(multiply(inverse(X_62),X_61),multiply(inverse(X_62),X_62))
| multiply(inverse(X_62),greatest_lower_bound(X_61,X_62)) = greatest_lower_bound(multiply(inverse(X_62),X_61),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_62),greatest_lower_bound(X_61,X_62)),greatest_lower_bound(multiply(inverse(X_62),X_61),multiply(inverse(X_62),X_62))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_60,plain,
( multiply(inverse(X_62),greatest_lower_bound(X_61,X_62)) != greatest_lower_bound(multiply(inverse(X_62),X_61),multiply(inverse(X_62),X_62))
| multiply(inverse(X_62),greatest_lower_bound(X_61,X_62)) = greatest_lower_bound(multiply(inverse(X_62),X_61),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_62),X_62),identity) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
multiply(inverse(X_62),greatest_lower_bound(X_61,X_62)) = greatest_lower_bound(multiply(inverse(X_62),X_61),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_62),greatest_lower_bound(X_61,X_62)),greatest_lower_bound(multiply(inverse(X_62),X_61),multiply(inverse(X_62),X_62))) )],[refute_0_57,refute_0_60]) ).
cnf(refute_0_62,plain,
( greatest_lower_bound(X,Y) != greatest_lower_bound(Y,X)
| greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X,Y))),bind(Y0,$fot(greatest_lower_bound(Y,X)))]]) ).
cnf(refute_0_63,plain,
greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X)) )],[symmetry_of_glb,refute_0_62]) ).
cnf(refute_0_64,plain,
greatest_lower_bound(multiply(inverse(X_62),X_61),identity) = greatest_lower_bound(identity,multiply(inverse(X_62),X_61)),
inference(subst,[],[refute_0_63:[bind(X,$fot(identity)),bind(Y,$fot(multiply(inverse(X_62),X_61)))]]) ).
cnf(refute_0_65,plain,
( multiply(inverse(X_62),greatest_lower_bound(X_61,X_62)) != greatest_lower_bound(multiply(inverse(X_62),X_61),identity)
| greatest_lower_bound(multiply(inverse(X_62),X_61),identity) != greatest_lower_bound(identity,multiply(inverse(X_62),X_61))
| multiply(inverse(X_62),greatest_lower_bound(X_61,X_62)) = greatest_lower_bound(identity,multiply(inverse(X_62),X_61)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_62),greatest_lower_bound(X_61,X_62)),greatest_lower_bound(identity,multiply(inverse(X_62),X_61))) ),[0],$fot(greatest_lower_bound(multiply(inverse(X_62),X_61),identity))]]) ).
cnf(refute_0_66,plain,
( multiply(inverse(X_62),greatest_lower_bound(X_61,X_62)) != greatest_lower_bound(multiply(inverse(X_62),X_61),identity)
| multiply(inverse(X_62),greatest_lower_bound(X_61,X_62)) = greatest_lower_bound(identity,multiply(inverse(X_62),X_61)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(inverse(X_62),X_61),identity),greatest_lower_bound(identity,multiply(inverse(X_62),X_61))) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
multiply(inverse(X_62),greatest_lower_bound(X_61,X_62)) = greatest_lower_bound(identity,multiply(inverse(X_62),X_61)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_62),greatest_lower_bound(X_61,X_62)),greatest_lower_bound(multiply(inverse(X_62),X_61),identity)) )],[refute_0_61,refute_0_66]) ).
cnf(refute_0_68,plain,
( multiply(inverse(X_62),greatest_lower_bound(X_61,X_62)) != greatest_lower_bound(identity,multiply(inverse(X_62),X_61))
| greatest_lower_bound(X_61,X_62) != multiply(inverse(inverse(X_62)),multiply(inverse(X_62),greatest_lower_bound(X_61,X_62)))
| greatest_lower_bound(X_61,X_62) = multiply(inverse(inverse(X_62)),greatest_lower_bound(identity,multiply(inverse(X_62),X_61))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_61,X_62),multiply(inverse(inverse(X_62)),multiply(inverse(X_62),greatest_lower_bound(X_61,X_62)))) ),[1,1],$fot(greatest_lower_bound(identity,multiply(inverse(X_62),X_61)))]]) ).
cnf(refute_0_69,plain,
( greatest_lower_bound(X_61,X_62) != multiply(inverse(inverse(X_62)),multiply(inverse(X_62),greatest_lower_bound(X_61,X_62)))
| greatest_lower_bound(X_61,X_62) = multiply(inverse(inverse(X_62)),greatest_lower_bound(identity,multiply(inverse(X_62),X_61))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_62),greatest_lower_bound(X_61,X_62)),greatest_lower_bound(identity,multiply(inverse(X_62),X_61))) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
greatest_lower_bound(X_61,X_62) = multiply(inverse(inverse(X_62)),greatest_lower_bound(identity,multiply(inverse(X_62),X_61))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_61,X_62),multiply(inverse(inverse(X_62)),multiply(inverse(X_62),greatest_lower_bound(X_61,X_62)))) )],[refute_0_56,refute_0_69]) ).
cnf(refute_0_71,plain,
multiply(inverse(inverse(X_62)),identity) = multiply(X_62,identity),
inference(subst,[],[refute_0_25:[bind(X_110,$fot(X_62)),bind(X_111,$fot(identity))]]) ).
cnf(refute_0_72,plain,
greatest_lower_bound(multiply(inverse(inverse(X_62)),identity),X_61) = greatest_lower_bound(multiply(inverse(inverse(X_62)),identity),X_61),
introduced(tautology,[refl,[$fot(greatest_lower_bound(multiply(inverse(inverse(X_62)),identity),X_61))]]) ).
cnf(refute_0_73,plain,
( multiply(inverse(inverse(X_62)),identity) != multiply(X_62,identity)
| greatest_lower_bound(multiply(inverse(inverse(X_62)),identity),X_61) != greatest_lower_bound(multiply(inverse(inverse(X_62)),identity),X_61)
| greatest_lower_bound(multiply(inverse(inverse(X_62)),identity),X_61) = greatest_lower_bound(multiply(X_62,identity),X_61) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(inverse(inverse(X_62)),identity),X_61),greatest_lower_bound(multiply(inverse(inverse(X_62)),identity),X_61)) ),[1,0],$fot(multiply(X_62,identity))]]) ).
cnf(refute_0_74,plain,
( multiply(inverse(inverse(X_62)),identity) != multiply(X_62,identity)
| greatest_lower_bound(multiply(inverse(inverse(X_62)),identity),X_61) = greatest_lower_bound(multiply(X_62,identity),X_61) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(inverse(inverse(X_62)),identity),X_61),greatest_lower_bound(multiply(inverse(inverse(X_62)),identity),X_61)) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
greatest_lower_bound(multiply(inverse(inverse(X_62)),identity),X_61) = greatest_lower_bound(multiply(X_62,identity),X_61),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_62)),identity),multiply(X_62,identity)) )],[refute_0_71,refute_0_74]) ).
cnf(refute_0_76,plain,
multiply(inverse(X_110),greatest_lower_bound(Y,multiply(X_110,X_111))) = greatest_lower_bound(multiply(inverse(X_110),Y),multiply(inverse(X_110),multiply(X_110,X_111))),
inference(subst,[],[monotony_glb1:[bind(X,$fot(inverse(X_110))),bind(Z,$fot(multiply(X_110,X_111)))]]) ).
cnf(refute_0_77,plain,
( multiply(inverse(X_110),multiply(X_110,X_111)) != X_111
| multiply(inverse(X_110),greatest_lower_bound(Y,multiply(X_110,X_111))) != greatest_lower_bound(multiply(inverse(X_110),Y),multiply(inverse(X_110),multiply(X_110,X_111)))
| multiply(inverse(X_110),greatest_lower_bound(Y,multiply(X_110,X_111))) = greatest_lower_bound(multiply(inverse(X_110),Y),X_111) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_110),greatest_lower_bound(Y,multiply(X_110,X_111))),greatest_lower_bound(multiply(inverse(X_110),Y),multiply(inverse(X_110),multiply(X_110,X_111)))) ),[1,1],$fot(X_111)]]) ).
cnf(refute_0_78,plain,
( multiply(inverse(X_110),greatest_lower_bound(Y,multiply(X_110,X_111))) != greatest_lower_bound(multiply(inverse(X_110),Y),multiply(inverse(X_110),multiply(X_110,X_111)))
| multiply(inverse(X_110),greatest_lower_bound(Y,multiply(X_110,X_111))) = greatest_lower_bound(multiply(inverse(X_110),Y),X_111) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_110),multiply(X_110,X_111)),X_111) )],[refute_0_20,refute_0_77]) ).
cnf(refute_0_79,plain,
multiply(inverse(X_110),greatest_lower_bound(Y,multiply(X_110,X_111))) = greatest_lower_bound(multiply(inverse(X_110),Y),X_111),
inference(resolve,[$cnf( $equal(multiply(inverse(X_110),greatest_lower_bound(Y,multiply(X_110,X_111))),greatest_lower_bound(multiply(inverse(X_110),Y),multiply(inverse(X_110),multiply(X_110,X_111)))) )],[refute_0_76,refute_0_78]) ).
cnf(refute_0_80,plain,
multiply(inverse(inverse(X_62)),greatest_lower_bound(identity,multiply(inverse(X_62),X_61))) = greatest_lower_bound(multiply(inverse(inverse(X_62)),identity),X_61),
inference(subst,[],[refute_0_79:[bind(Y,$fot(identity)),bind(X_110,$fot(inverse(X_62))),bind(X_111,$fot(X_61))]]) ).
cnf(refute_0_81,plain,
( multiply(inverse(inverse(X_62)),greatest_lower_bound(identity,multiply(inverse(X_62),X_61))) != greatest_lower_bound(multiply(inverse(inverse(X_62)),identity),X_61)
| greatest_lower_bound(multiply(inverse(inverse(X_62)),identity),X_61) != greatest_lower_bound(multiply(X_62,identity),X_61)
| multiply(inverse(inverse(X_62)),greatest_lower_bound(identity,multiply(inverse(X_62),X_61))) = greatest_lower_bound(multiply(X_62,identity),X_61) ),
inference(subst,[],[refute_0_38:[bind(X0,$fot(multiply(inverse(inverse(X_62)),greatest_lower_bound(identity,multiply(inverse(X_62),X_61))))),bind(Y0,$fot(greatest_lower_bound(multiply(inverse(inverse(X_62)),identity),X_61))),bind(Z0,$fot(greatest_lower_bound(multiply(X_62,identity),X_61)))]]) ).
cnf(refute_0_82,plain,
( greatest_lower_bound(multiply(inverse(inverse(X_62)),identity),X_61) != greatest_lower_bound(multiply(X_62,identity),X_61)
| multiply(inverse(inverse(X_62)),greatest_lower_bound(identity,multiply(inverse(X_62),X_61))) = greatest_lower_bound(multiply(X_62,identity),X_61) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_62)),greatest_lower_bound(identity,multiply(inverse(X_62),X_61))),greatest_lower_bound(multiply(inverse(inverse(X_62)),identity),X_61)) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
multiply(inverse(inverse(X_62)),greatest_lower_bound(identity,multiply(inverse(X_62),X_61))) = greatest_lower_bound(multiply(X_62,identity),X_61),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(inverse(inverse(X_62)),identity),X_61),greatest_lower_bound(multiply(X_62,identity),X_61)) )],[refute_0_75,refute_0_82]) ).
cnf(refute_0_84,plain,
( multiply(inverse(inverse(X_62)),greatest_lower_bound(identity,multiply(inverse(X_62),X_61))) != greatest_lower_bound(multiply(X_62,identity),X_61)
| greatest_lower_bound(X_61,X_62) != multiply(inverse(inverse(X_62)),greatest_lower_bound(identity,multiply(inverse(X_62),X_61)))
| greatest_lower_bound(X_61,X_62) = greatest_lower_bound(multiply(X_62,identity),X_61) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_61,X_62),multiply(inverse(inverse(X_62)),greatest_lower_bound(identity,multiply(inverse(X_62),X_61)))) ),[1],$fot(greatest_lower_bound(multiply(X_62,identity),X_61))]]) ).
cnf(refute_0_85,plain,
( greatest_lower_bound(X_61,X_62) != multiply(inverse(inverse(X_62)),greatest_lower_bound(identity,multiply(inverse(X_62),X_61)))
| greatest_lower_bound(X_61,X_62) = greatest_lower_bound(multiply(X_62,identity),X_61) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_62)),greatest_lower_bound(identity,multiply(inverse(X_62),X_61))),greatest_lower_bound(multiply(X_62,identity),X_61)) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
greatest_lower_bound(X_61,X_62) = greatest_lower_bound(multiply(X_62,identity),X_61),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_61,X_62),multiply(inverse(inverse(X_62)),greatest_lower_bound(identity,multiply(inverse(X_62),X_61)))) )],[refute_0_70,refute_0_85]) ).
cnf(refute_0_87,plain,
multiply(X_62,identity) = X_62,
inference(subst,[],[refute_0_31:[bind(X_111,$fot(X_62))]]) ).
cnf(refute_0_88,plain,
greatest_lower_bound(multiply(X_62,identity),X_61) = greatest_lower_bound(multiply(X_62,identity),X_61),
introduced(tautology,[refl,[$fot(greatest_lower_bound(multiply(X_62,identity),X_61))]]) ).
cnf(refute_0_89,plain,
( multiply(X_62,identity) != X_62
| greatest_lower_bound(multiply(X_62,identity),X_61) != greatest_lower_bound(multiply(X_62,identity),X_61)
| greatest_lower_bound(multiply(X_62,identity),X_61) = greatest_lower_bound(X_62,X_61) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_62,identity),X_61),greatest_lower_bound(multiply(X_62,identity),X_61)) ),[1,0],$fot(X_62)]]) ).
cnf(refute_0_90,plain,
( multiply(X_62,identity) != X_62
| greatest_lower_bound(multiply(X_62,identity),X_61) = greatest_lower_bound(X_62,X_61) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_62,identity),X_61),greatest_lower_bound(multiply(X_62,identity),X_61)) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
greatest_lower_bound(multiply(X_62,identity),X_61) = greatest_lower_bound(X_62,X_61),
inference(resolve,[$cnf( $equal(multiply(X_62,identity),X_62) )],[refute_0_87,refute_0_90]) ).
cnf(refute_0_92,plain,
( greatest_lower_bound(X_61,X_62) != greatest_lower_bound(multiply(X_62,identity),X_61)
| greatest_lower_bound(multiply(X_62,identity),X_61) != greatest_lower_bound(X_62,X_61)
| greatest_lower_bound(X_61,X_62) = greatest_lower_bound(X_62,X_61) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_61,X_62),greatest_lower_bound(X_62,X_61)) ),[0],$fot(greatest_lower_bound(multiply(X_62,identity),X_61))]]) ).
cnf(refute_0_93,plain,
( greatest_lower_bound(X_61,X_62) != greatest_lower_bound(multiply(X_62,identity),X_61)
| greatest_lower_bound(X_61,X_62) = greatest_lower_bound(X_62,X_61) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_62,identity),X_61),greatest_lower_bound(X_62,X_61)) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
greatest_lower_bound(X_61,X_62) = greatest_lower_bound(X_62,X_61),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_61,X_62),greatest_lower_bound(multiply(X_62,identity),X_61)) )],[refute_0_86,refute_0_93]) ).
cnf(refute_0_95,plain,
( greatest_lower_bound(X_61,X_62) != greatest_lower_bound(X_62,X_61)
| greatest_lower_bound(X_62,X_61) = greatest_lower_bound(X_61,X_62) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X_61,X_62))),bind(Y0,$fot(greatest_lower_bound(X_62,X_61)))]]) ).
cnf(refute_0_96,plain,
greatest_lower_bound(X_62,X_61) = greatest_lower_bound(X_61,X_62),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_61,X_62),greatest_lower_bound(X_62,X_61)) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
greatest_lower_bound(multiply(X,Y),X) = greatest_lower_bound(X,multiply(X,Y)),
inference(subst,[],[refute_0_96:[bind(X_61,$fot(X)),bind(X_62,$fot(multiply(X,Y)))]]) ).
cnf(refute_0_98,plain,
( greatest_lower_bound(X,multiply(X,Y)) != multiply(X,greatest_lower_bound(identity,Y))
| greatest_lower_bound(multiply(X,Y),X) != greatest_lower_bound(X,multiply(X,Y))
| greatest_lower_bound(multiply(X,Y),X) = multiply(X,greatest_lower_bound(identity,Y)) ),
inference(subst,[],[refute_0_38:[bind(X0,$fot(greatest_lower_bound(multiply(X,Y),X))),bind(Y0,$fot(greatest_lower_bound(X,multiply(X,Y)))),bind(Z0,$fot(multiply(X,greatest_lower_bound(identity,Y))))]]) ).
cnf(refute_0_99,plain,
( greatest_lower_bound(X,multiply(X,Y)) != multiply(X,greatest_lower_bound(identity,Y))
| greatest_lower_bound(multiply(X,Y),X) = multiply(X,greatest_lower_bound(identity,Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,Y),X),greatest_lower_bound(X,multiply(X,Y))) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
greatest_lower_bound(multiply(X,Y),X) = multiply(X,greatest_lower_bound(identity,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,multiply(X,Y)),multiply(X,greatest_lower_bound(identity,Y))) )],[refute_0_55,refute_0_99]) ).
cnf(refute_0_101,plain,
( multiply(X,greatest_lower_bound(Y,identity)) != greatest_lower_bound(multiply(X,Y),X)
| greatest_lower_bound(multiply(X,Y),X) != multiply(X,greatest_lower_bound(identity,Y))
| multiply(X,greatest_lower_bound(Y,identity)) = multiply(X,greatest_lower_bound(identity,Y)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X,greatest_lower_bound(Y,identity)),multiply(X,greatest_lower_bound(identity,Y))) ),[0],$fot(greatest_lower_bound(multiply(X,Y),X))]]) ).
cnf(refute_0_102,plain,
( multiply(X,greatest_lower_bound(Y,identity)) != greatest_lower_bound(multiply(X,Y),X)
| multiply(X,greatest_lower_bound(Y,identity)) = multiply(X,greatest_lower_bound(identity,Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,Y),X),multiply(X,greatest_lower_bound(identity,Y))) )],[refute_0_100,refute_0_101]) ).
cnf(refute_0_103,plain,
multiply(X,greatest_lower_bound(Y,identity)) = multiply(X,greatest_lower_bound(identity,Y)),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(Y,identity)),greatest_lower_bound(multiply(X,Y),X)) )],[refute_0_48,refute_0_102]) ).
cnf(refute_0_104,plain,
( multiply(X,greatest_lower_bound(Y,identity)) != multiply(X,greatest_lower_bound(identity,Y))
| multiply(X,greatest_lower_bound(identity,Y)) = multiply(X,greatest_lower_bound(Y,identity)) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(X,greatest_lower_bound(Y,identity)))),bind(Y0,$fot(multiply(X,greatest_lower_bound(identity,Y))))]]) ).
cnf(refute_0_105,plain,
multiply(X,greatest_lower_bound(identity,Y)) = multiply(X,greatest_lower_bound(Y,identity)),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(Y,identity)),multiply(X,greatest_lower_bound(identity,Y))) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
multiply(a,greatest_lower_bound(identity,b)) = multiply(a,greatest_lower_bound(b,identity)),
inference(subst,[],[refute_0_105:[bind(X,$fot(a)),bind(Y,$fot(b))]]) ).
cnf(refute_0_107,plain,
greatest_lower_bound(a,multiply(a,b)) = multiply(a,greatest_lower_bound(identity,b)),
inference(subst,[],[refute_0_54:[bind(X,$fot(a)),bind(Z,$fot(b))]]) ).
cnf(refute_0_108,plain,
( multiply(a,greatest_lower_bound(identity,b)) != multiply(a,greatest_lower_bound(b,identity))
| greatest_lower_bound(a,multiply(a,b)) != multiply(a,greatest_lower_bound(identity,b))
| greatest_lower_bound(a,multiply(a,b)) = multiply(a,greatest_lower_bound(b,identity)) ),
inference(subst,[],[refute_0_38:[bind(X0,$fot(greatest_lower_bound(a,multiply(a,b)))),bind(Y0,$fot(multiply(a,greatest_lower_bound(identity,b)))),bind(Z0,$fot(multiply(a,greatest_lower_bound(b,identity))))]]) ).
cnf(refute_0_109,plain,
( multiply(a,greatest_lower_bound(identity,b)) != multiply(a,greatest_lower_bound(b,identity))
| greatest_lower_bound(a,multiply(a,b)) = multiply(a,greatest_lower_bound(b,identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,multiply(a,b)),multiply(a,greatest_lower_bound(identity,b))) )],[refute_0_107,refute_0_108]) ).
cnf(refute_0_110,plain,
greatest_lower_bound(a,multiply(a,b)) = multiply(a,greatest_lower_bound(b,identity)),
inference(resolve,[$cnf( $equal(multiply(a,greatest_lower_bound(identity,b)),multiply(a,greatest_lower_bound(b,identity))) )],[refute_0_106,refute_0_109]) ).
cnf(refute_0_111,plain,
( multiply(a,greatest_lower_bound(b,identity)) != a
| greatest_lower_bound(a,multiply(a,b)) != multiply(a,greatest_lower_bound(b,identity))
| greatest_lower_bound(a,multiply(a,b)) = a ),
inference(subst,[],[refute_0_38:[bind(X0,$fot(greatest_lower_bound(a,multiply(a,b)))),bind(Y0,$fot(multiply(a,greatest_lower_bound(b,identity)))),bind(Z0,$fot(a))]]) ).
cnf(refute_0_112,plain,
( multiply(a,greatest_lower_bound(b,identity)) != a
| greatest_lower_bound(a,multiply(a,b)) = a ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,multiply(a,b)),multiply(a,greatest_lower_bound(b,identity))) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
greatest_lower_bound(a,multiply(a,b)) = a,
inference(resolve,[$cnf( $equal(multiply(a,greatest_lower_bound(b,identity)),a) )],[refute_0_41,refute_0_112]) ).
cnf(refute_0_114,plain,
( a != a
| greatest_lower_bound(a,multiply(a,b)) != a
| greatest_lower_bound(a,multiply(a,b)) = a ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,multiply(a,b)),a) ),[0,0],$fot(a)]]) ).
cnf(refute_0_115,plain,
( a != a
| greatest_lower_bound(a,multiply(a,b)) = a ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,multiply(a,b)),a) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
a != a,
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,multiply(a,b)),a) )],[refute_0_115,prove_lat2b]) ).
cnf(refute_0_117,plain,
a = a,
introduced(tautology,[refl,[$fot(a)]]) ).
cnf(refute_0_118,plain,
$false,
inference(resolve,[$cnf( $equal(a,a) )],[refute_0_117,refute_0_116]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP166-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 19:27:53 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.77/0.95 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.77/0.95
% 0.77/0.95 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.77/0.96
%------------------------------------------------------------------------------