TSTP Solution File: GRP184-2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP184-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n022.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 10:37:48 EDT 2022
% Result : Unsatisfiable 7.03s 7.21s
% Output : CNFRefutation 7.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 45
% Syntax : Number of clauses : 167 ( 94 unt; 0 nHn; 79 RR)
% Number of literals : 273 ( 272 equ; 108 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; 2 con; 0-2 aty)
% Number of variables : 222 ( 0 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(monotony_lub1,axiom,
multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ).
cnf(monotony_glb1,axiom,
multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)) ).
cnf(monotony_lub2,axiom,
multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) ).
cnf(monotony_glb2,axiom,
multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) ).
cnf(p21_1,hypothesis,
inverse(identity) = identity ).
cnf(p21_2,hypothesis,
inverse(inverse(X)) = X ).
cnf(p21_3,hypothesis,
inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) ).
cnf(prove_p21,negated_conjecture,
multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) != multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)) ).
cnf(refute_0_0,plain,
multiply(least_upper_bound(X_88,identity),X_87) = least_upper_bound(multiply(X_88,X_87),multiply(identity,X_87)),
inference(subst,[],[monotony_lub2:[bind(X,$fot(X_87)),bind(Y,$fot(X_88)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_1,plain,
multiply(identity,X_87) = X_87,
inference(subst,[],[left_identity:[bind(X,$fot(X_87))]]) ).
cnf(refute_0_2,plain,
( multiply(identity,X_87) != X_87
| multiply(least_upper_bound(X_88,identity),X_87) != least_upper_bound(multiply(X_88,X_87),multiply(identity,X_87))
| multiply(least_upper_bound(X_88,identity),X_87) = least_upper_bound(multiply(X_88,X_87),X_87) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_88,identity),X_87),least_upper_bound(multiply(X_88,X_87),multiply(identity,X_87))) ),[1,1],$fot(X_87)]]) ).
cnf(refute_0_3,plain,
( multiply(least_upper_bound(X_88,identity),X_87) != least_upper_bound(multiply(X_88,X_87),multiply(identity,X_87))
| multiply(least_upper_bound(X_88,identity),X_87) = least_upper_bound(multiply(X_88,X_87),X_87) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_87),X_87) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
multiply(least_upper_bound(X_88,identity),X_87) = least_upper_bound(multiply(X_88,X_87),X_87),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_88,identity),X_87),least_upper_bound(multiply(X_88,X_87),multiply(identity,X_87))) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_6,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_7,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( least_upper_bound(X,Y) != least_upper_bound(Y,X)
| least_upper_bound(Y,X) = least_upper_bound(X,Y) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(least_upper_bound(X,Y))),bind(Y0,$fot(least_upper_bound(Y,X)))]]) ).
cnf(refute_0_9,plain,
least_upper_bound(Y,X) = least_upper_bound(X,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(X,Y),least_upper_bound(Y,X)) )],[symmetry_of_lub,refute_0_8]) ).
cnf(refute_0_10,plain,
least_upper_bound(multiply(X_88,X_87),X_87) = least_upper_bound(X_87,multiply(X_88,X_87)),
inference(subst,[],[refute_0_9:[bind(X,$fot(X_87)),bind(Y,$fot(multiply(X_88,X_87)))]]) ).
cnf(refute_0_11,plain,
( multiply(least_upper_bound(X_88,identity),X_87) != least_upper_bound(multiply(X_88,X_87),X_87)
| least_upper_bound(multiply(X_88,X_87),X_87) != least_upper_bound(X_87,multiply(X_88,X_87))
| multiply(least_upper_bound(X_88,identity),X_87) = least_upper_bound(X_87,multiply(X_88,X_87)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_88,identity),X_87),least_upper_bound(X_87,multiply(X_88,X_87))) ),[0],$fot(least_upper_bound(multiply(X_88,X_87),X_87))]]) ).
cnf(refute_0_12,plain,
( multiply(least_upper_bound(X_88,identity),X_87) != least_upper_bound(multiply(X_88,X_87),X_87)
| multiply(least_upper_bound(X_88,identity),X_87) = least_upper_bound(X_87,multiply(X_88,X_87)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_88,X_87),X_87),least_upper_bound(X_87,multiply(X_88,X_87))) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
multiply(least_upper_bound(X_88,identity),X_87) = least_upper_bound(X_87,multiply(X_88,X_87)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_88,identity),X_87),least_upper_bound(multiply(X_88,X_87),X_87)) )],[refute_0_4,refute_0_12]) ).
cnf(refute_0_14,plain,
multiply(least_upper_bound(X_88,identity),inverse(greatest_lower_bound(X_88,identity))) = least_upper_bound(inverse(greatest_lower_bound(X_88,identity)),multiply(X_88,inverse(greatest_lower_bound(X_88,identity)))),
inference(subst,[],[refute_0_13:[bind(X_87,$fot(inverse(greatest_lower_bound(X_88,identity))))]]) ).
cnf(refute_0_15,plain,
inverse(multiply(greatest_lower_bound(X_118,identity),inverse(X_118))) = multiply(inverse(inverse(X_118)),inverse(greatest_lower_bound(X_118,identity))),
inference(subst,[],[p21_3:[bind(X,$fot(greatest_lower_bound(X_118,identity))),bind(Y,$fot(inverse(X_118)))]]) ).
cnf(refute_0_16,plain,
multiply(greatest_lower_bound(X_98,identity),X_97) = greatest_lower_bound(multiply(X_98,X_97),multiply(identity,X_97)),
inference(subst,[],[monotony_glb2:[bind(X,$fot(X_97)),bind(Y,$fot(X_98)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_17,plain,
multiply(identity,X_97) = X_97,
inference(subst,[],[left_identity:[bind(X,$fot(X_97))]]) ).
cnf(refute_0_18,plain,
( multiply(greatest_lower_bound(X_98,identity),X_97) != greatest_lower_bound(multiply(X_98,X_97),multiply(identity,X_97))
| multiply(identity,X_97) != X_97
| multiply(greatest_lower_bound(X_98,identity),X_97) = greatest_lower_bound(multiply(X_98,X_97),X_97) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_98,identity),X_97),greatest_lower_bound(multiply(X_98,X_97),multiply(identity,X_97))) ),[1,1],$fot(X_97)]]) ).
cnf(refute_0_19,plain,
( multiply(greatest_lower_bound(X_98,identity),X_97) != greatest_lower_bound(multiply(X_98,X_97),multiply(identity,X_97))
| multiply(greatest_lower_bound(X_98,identity),X_97) = greatest_lower_bound(multiply(X_98,X_97),X_97) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_97),X_97) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
multiply(greatest_lower_bound(X_98,identity),X_97) = greatest_lower_bound(multiply(X_98,X_97),X_97),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_98,identity),X_97),greatest_lower_bound(multiply(X_98,X_97),multiply(identity,X_97))) )],[refute_0_16,refute_0_19]) ).
cnf(refute_0_21,plain,
( greatest_lower_bound(X,Y) != greatest_lower_bound(Y,X)
| greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(greatest_lower_bound(X,Y))),bind(Y0,$fot(greatest_lower_bound(Y,X)))]]) ).
cnf(refute_0_22,plain,
greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X)) )],[symmetry_of_glb,refute_0_21]) ).
cnf(refute_0_23,plain,
greatest_lower_bound(multiply(X_98,X_97),X_97) = greatest_lower_bound(X_97,multiply(X_98,X_97)),
inference(subst,[],[refute_0_22:[bind(X,$fot(X_97)),bind(Y,$fot(multiply(X_98,X_97)))]]) ).
cnf(refute_0_24,plain,
( multiply(greatest_lower_bound(X_98,identity),X_97) != greatest_lower_bound(multiply(X_98,X_97),X_97)
| greatest_lower_bound(multiply(X_98,X_97),X_97) != greatest_lower_bound(X_97,multiply(X_98,X_97))
| multiply(greatest_lower_bound(X_98,identity),X_97) = greatest_lower_bound(X_97,multiply(X_98,X_97)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_98,identity),X_97),greatest_lower_bound(X_97,multiply(X_98,X_97))) ),[0],$fot(greatest_lower_bound(multiply(X_98,X_97),X_97))]]) ).
cnf(refute_0_25,plain,
( multiply(greatest_lower_bound(X_98,identity),X_97) != greatest_lower_bound(multiply(X_98,X_97),X_97)
| multiply(greatest_lower_bound(X_98,identity),X_97) = greatest_lower_bound(X_97,multiply(X_98,X_97)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_98,X_97),X_97),greatest_lower_bound(X_97,multiply(X_98,X_97))) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
multiply(greatest_lower_bound(X_98,identity),X_97) = greatest_lower_bound(X_97,multiply(X_98,X_97)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_98,identity),X_97),greatest_lower_bound(multiply(X_98,X_97),X_97)) )],[refute_0_20,refute_0_25]) ).
cnf(refute_0_27,plain,
multiply(greatest_lower_bound(X_101,identity),inverse(X_101)) = greatest_lower_bound(inverse(X_101),multiply(X_101,inverse(X_101))),
inference(subst,[],[refute_0_26:[bind(X_97,$fot(inverse(X_101))),bind(X_98,$fot(X_101))]]) ).
cnf(refute_0_28,plain,
multiply(inverse(inverse(X_1)),inverse(X_1)) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(inverse(X_1)))]]) ).
cnf(refute_0_29,plain,
inverse(inverse(X_1)) = X_1,
inference(subst,[],[p21_2:[bind(X,$fot(X_1))]]) ).
cnf(refute_0_30,plain,
( multiply(inverse(inverse(X_1)),inverse(X_1)) != identity
| inverse(inverse(X_1)) != X_1
| multiply(X_1,inverse(X_1)) = identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X_1)),inverse(X_1)),identity) ),[0,0],$fot(X_1)]]) ).
cnf(refute_0_31,plain,
( multiply(inverse(inverse(X_1)),inverse(X_1)) != identity
| multiply(X_1,inverse(X_1)) = identity ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_1)),X_1) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
multiply(X_1,inverse(X_1)) = identity,
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_1)),inverse(X_1)),identity) )],[refute_0_28,refute_0_31]) ).
cnf(refute_0_33,plain,
multiply(X_101,inverse(X_101)) = identity,
inference(subst,[],[refute_0_32:[bind(X_1,$fot(X_101))]]) ).
cnf(refute_0_34,plain,
( multiply(X_101,inverse(X_101)) != identity
| multiply(greatest_lower_bound(X_101,identity),inverse(X_101)) != greatest_lower_bound(inverse(X_101),multiply(X_101,inverse(X_101)))
| multiply(greatest_lower_bound(X_101,identity),inverse(X_101)) = greatest_lower_bound(inverse(X_101),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_101,identity),inverse(X_101)),greatest_lower_bound(inverse(X_101),multiply(X_101,inverse(X_101)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_35,plain,
( multiply(greatest_lower_bound(X_101,identity),inverse(X_101)) != greatest_lower_bound(inverse(X_101),multiply(X_101,inverse(X_101)))
| multiply(greatest_lower_bound(X_101,identity),inverse(X_101)) = greatest_lower_bound(inverse(X_101),identity) ),
inference(resolve,[$cnf( $equal(multiply(X_101,inverse(X_101)),identity) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
multiply(greatest_lower_bound(X_101,identity),inverse(X_101)) = greatest_lower_bound(inverse(X_101),identity),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_101,identity),inverse(X_101)),greatest_lower_bound(inverse(X_101),multiply(X_101,inverse(X_101)))) )],[refute_0_27,refute_0_35]) ).
cnf(refute_0_37,plain,
greatest_lower_bound(inverse(X_101),identity) = greatest_lower_bound(identity,inverse(X_101)),
inference(subst,[],[refute_0_22:[bind(X,$fot(identity)),bind(Y,$fot(inverse(X_101)))]]) ).
cnf(refute_0_38,plain,
( multiply(greatest_lower_bound(X_101,identity),inverse(X_101)) != greatest_lower_bound(inverse(X_101),identity)
| greatest_lower_bound(inverse(X_101),identity) != greatest_lower_bound(identity,inverse(X_101))
| multiply(greatest_lower_bound(X_101,identity),inverse(X_101)) = greatest_lower_bound(identity,inverse(X_101)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_101,identity),inverse(X_101)),greatest_lower_bound(identity,inverse(X_101))) ),[0],$fot(greatest_lower_bound(inverse(X_101),identity))]]) ).
cnf(refute_0_39,plain,
( multiply(greatest_lower_bound(X_101,identity),inverse(X_101)) != greatest_lower_bound(inverse(X_101),identity)
| multiply(greatest_lower_bound(X_101,identity),inverse(X_101)) = greatest_lower_bound(identity,inverse(X_101)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_101),identity),greatest_lower_bound(identity,inverse(X_101))) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
multiply(greatest_lower_bound(X_101,identity),inverse(X_101)) = greatest_lower_bound(identity,inverse(X_101)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_101,identity),inverse(X_101)),greatest_lower_bound(inverse(X_101),identity)) )],[refute_0_36,refute_0_39]) ).
cnf(refute_0_41,plain,
multiply(greatest_lower_bound(X_118,identity),inverse(X_118)) = greatest_lower_bound(identity,inverse(X_118)),
inference(subst,[],[refute_0_40:[bind(X_101,$fot(X_118))]]) ).
cnf(refute_0_42,plain,
( multiply(greatest_lower_bound(X_118,identity),inverse(X_118)) != greatest_lower_bound(identity,inverse(X_118))
| inverse(multiply(greatest_lower_bound(X_118,identity),inverse(X_118))) != multiply(inverse(inverse(X_118)),inverse(greatest_lower_bound(X_118,identity)))
| inverse(greatest_lower_bound(identity,inverse(X_118))) = multiply(inverse(inverse(X_118)),inverse(greatest_lower_bound(X_118,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(greatest_lower_bound(X_118,identity),inverse(X_118))),multiply(inverse(inverse(X_118)),inverse(greatest_lower_bound(X_118,identity)))) ),[0,0],$fot(greatest_lower_bound(identity,inverse(X_118)))]]) ).
cnf(refute_0_43,plain,
( inverse(multiply(greatest_lower_bound(X_118,identity),inverse(X_118))) != multiply(inverse(inverse(X_118)),inverse(greatest_lower_bound(X_118,identity)))
| inverse(greatest_lower_bound(identity,inverse(X_118))) = multiply(inverse(inverse(X_118)),inverse(greatest_lower_bound(X_118,identity))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_118,identity),inverse(X_118)),greatest_lower_bound(identity,inverse(X_118))) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
inverse(greatest_lower_bound(identity,inverse(X_118))) = multiply(inverse(inverse(X_118)),inverse(greatest_lower_bound(X_118,identity))),
inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(X_118,identity),inverse(X_118))),multiply(inverse(inverse(X_118)),inverse(greatest_lower_bound(X_118,identity)))) )],[refute_0_15,refute_0_43]) ).
cnf(refute_0_45,plain,
inverse(multiply(X_29,inverse(X))) = multiply(inverse(inverse(X)),inverse(X_29)),
inference(subst,[],[p21_3:[bind(X,$fot(X_29)),bind(Y,$fot(inverse(X)))]]) ).
cnf(refute_0_46,plain,
( inverse(multiply(X_29,inverse(X))) != multiply(inverse(inverse(X)),inverse(X_29))
| inverse(inverse(X)) != X
| inverse(multiply(X_29,inverse(X))) = multiply(X,inverse(X_29)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_29,inverse(X))),multiply(inverse(inverse(X)),inverse(X_29))) ),[1,0],$fot(X)]]) ).
cnf(refute_0_47,plain,
( inverse(multiply(X_29,inverse(X))) != multiply(inverse(inverse(X)),inverse(X_29))
| inverse(multiply(X_29,inverse(X))) = multiply(X,inverse(X_29)) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p21_2,refute_0_46]) ).
cnf(refute_0_48,plain,
inverse(multiply(X_29,inverse(X))) = multiply(X,inverse(X_29)),
inference(resolve,[$cnf( $equal(inverse(multiply(X_29,inverse(X))),multiply(inverse(inverse(X)),inverse(X_29))) )],[refute_0_45,refute_0_47]) ).
cnf(refute_0_49,plain,
inverse(multiply(greatest_lower_bound(X_118,identity),inverse(X_118))) = multiply(X_118,inverse(greatest_lower_bound(X_118,identity))),
inference(subst,[],[refute_0_48:[bind(X,$fot(X_118)),bind(X_29,$fot(greatest_lower_bound(X_118,identity)))]]) ).
cnf(refute_0_50,plain,
( inverse(multiply(X,Y)) != multiply(inverse(Y),inverse(X))
| multiply(inverse(Y),inverse(X)) = inverse(multiply(X,Y)) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(inverse(multiply(X,Y)))),bind(Y0,$fot(multiply(inverse(Y),inverse(X))))]]) ).
cnf(refute_0_51,plain,
multiply(inverse(Y),inverse(X)) = inverse(multiply(X,Y)),
inference(resolve,[$cnf( $equal(inverse(multiply(X,Y)),multiply(inverse(Y),inverse(X))) )],[p21_3,refute_0_50]) ).
cnf(refute_0_52,plain,
multiply(inverse(inverse(X_118)),inverse(greatest_lower_bound(X_118,identity))) = inverse(multiply(greatest_lower_bound(X_118,identity),inverse(X_118))),
inference(subst,[],[refute_0_51:[bind(X,$fot(greatest_lower_bound(X_118,identity))),bind(Y,$fot(inverse(X_118)))]]) ).
cnf(refute_0_53,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_54,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_7,refute_0_53]) ).
cnf(refute_0_55,plain,
( multiply(inverse(inverse(X_118)),inverse(greatest_lower_bound(X_118,identity))) != inverse(multiply(greatest_lower_bound(X_118,identity),inverse(X_118)))
| inverse(multiply(greatest_lower_bound(X_118,identity),inverse(X_118))) != multiply(X_118,inverse(greatest_lower_bound(X_118,identity)))
| multiply(inverse(inverse(X_118)),inverse(greatest_lower_bound(X_118,identity))) = multiply(X_118,inverse(greatest_lower_bound(X_118,identity))) ),
inference(subst,[],[refute_0_54:[bind(X0,$fot(multiply(inverse(inverse(X_118)),inverse(greatest_lower_bound(X_118,identity))))),bind(Y0,$fot(inverse(multiply(greatest_lower_bound(X_118,identity),inverse(X_118))))),bind(Z0,$fot(multiply(X_118,inverse(greatest_lower_bound(X_118,identity)))))]]) ).
cnf(refute_0_56,plain,
( inverse(multiply(greatest_lower_bound(X_118,identity),inverse(X_118))) != multiply(X_118,inverse(greatest_lower_bound(X_118,identity)))
| multiply(inverse(inverse(X_118)),inverse(greatest_lower_bound(X_118,identity))) = multiply(X_118,inverse(greatest_lower_bound(X_118,identity))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_118)),inverse(greatest_lower_bound(X_118,identity))),inverse(multiply(greatest_lower_bound(X_118,identity),inverse(X_118)))) )],[refute_0_52,refute_0_55]) ).
cnf(refute_0_57,plain,
multiply(inverse(inverse(X_118)),inverse(greatest_lower_bound(X_118,identity))) = multiply(X_118,inverse(greatest_lower_bound(X_118,identity))),
inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(X_118,identity),inverse(X_118))),multiply(X_118,inverse(greatest_lower_bound(X_118,identity)))) )],[refute_0_49,refute_0_56]) ).
cnf(refute_0_58,plain,
( multiply(inverse(inverse(X_118)),inverse(greatest_lower_bound(X_118,identity))) != multiply(X_118,inverse(greatest_lower_bound(X_118,identity)))
| inverse(greatest_lower_bound(identity,inverse(X_118))) != multiply(inverse(inverse(X_118)),inverse(greatest_lower_bound(X_118,identity)))
| inverse(greatest_lower_bound(identity,inverse(X_118))) = multiply(X_118,inverse(greatest_lower_bound(X_118,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_118))),multiply(inverse(inverse(X_118)),inverse(greatest_lower_bound(X_118,identity)))) ),[1],$fot(multiply(X_118,inverse(greatest_lower_bound(X_118,identity))))]]) ).
cnf(refute_0_59,plain,
( inverse(greatest_lower_bound(identity,inverse(X_118))) != multiply(inverse(inverse(X_118)),inverse(greatest_lower_bound(X_118,identity)))
| inverse(greatest_lower_bound(identity,inverse(X_118))) = multiply(X_118,inverse(greatest_lower_bound(X_118,identity))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_118)),inverse(greatest_lower_bound(X_118,identity))),multiply(X_118,inverse(greatest_lower_bound(X_118,identity)))) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
inverse(greatest_lower_bound(identity,inverse(X_118))) = multiply(X_118,inverse(greatest_lower_bound(X_118,identity))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_118))),multiply(inverse(inverse(X_118)),inverse(greatest_lower_bound(X_118,identity)))) )],[refute_0_44,refute_0_59]) ).
cnf(refute_0_61,plain,
inverse(greatest_lower_bound(identity,inverse(X_88))) = multiply(X_88,inverse(greatest_lower_bound(X_88,identity))),
inference(subst,[],[refute_0_60:[bind(X_118,$fot(X_88))]]) ).
cnf(refute_0_62,plain,
( inverse(greatest_lower_bound(identity,inverse(X_88))) != multiply(X_88,inverse(greatest_lower_bound(X_88,identity)))
| multiply(X_88,inverse(greatest_lower_bound(X_88,identity))) = inverse(greatest_lower_bound(identity,inverse(X_88))) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(inverse(greatest_lower_bound(identity,inverse(X_88))))),bind(Y0,$fot(multiply(X_88,inverse(greatest_lower_bound(X_88,identity)))))]]) ).
cnf(refute_0_63,plain,
multiply(X_88,inverse(greatest_lower_bound(X_88,identity))) = inverse(greatest_lower_bound(identity,inverse(X_88))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_88))),multiply(X_88,inverse(greatest_lower_bound(X_88,identity)))) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
( multiply(X_88,inverse(greatest_lower_bound(X_88,identity))) != inverse(greatest_lower_bound(identity,inverse(X_88)))
| multiply(least_upper_bound(X_88,identity),inverse(greatest_lower_bound(X_88,identity))) != least_upper_bound(inverse(greatest_lower_bound(X_88,identity)),multiply(X_88,inverse(greatest_lower_bound(X_88,identity))))
| multiply(least_upper_bound(X_88,identity),inverse(greatest_lower_bound(X_88,identity))) = least_upper_bound(inverse(greatest_lower_bound(X_88,identity)),inverse(greatest_lower_bound(identity,inverse(X_88)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_88,identity),inverse(greatest_lower_bound(X_88,identity))),least_upper_bound(inverse(greatest_lower_bound(X_88,identity)),multiply(X_88,inverse(greatest_lower_bound(X_88,identity))))) ),[1,1],$fot(inverse(greatest_lower_bound(identity,inverse(X_88))))]]) ).
cnf(refute_0_65,plain,
( multiply(least_upper_bound(X_88,identity),inverse(greatest_lower_bound(X_88,identity))) != least_upper_bound(inverse(greatest_lower_bound(X_88,identity)),multiply(X_88,inverse(greatest_lower_bound(X_88,identity))))
| multiply(least_upper_bound(X_88,identity),inverse(greatest_lower_bound(X_88,identity))) = least_upper_bound(inverse(greatest_lower_bound(X_88,identity)),inverse(greatest_lower_bound(identity,inverse(X_88)))) ),
inference(resolve,[$cnf( $equal(multiply(X_88,inverse(greatest_lower_bound(X_88,identity))),inverse(greatest_lower_bound(identity,inverse(X_88)))) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
multiply(least_upper_bound(X_88,identity),inverse(greatest_lower_bound(X_88,identity))) = least_upper_bound(inverse(greatest_lower_bound(X_88,identity)),inverse(greatest_lower_bound(identity,inverse(X_88)))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_88,identity),inverse(greatest_lower_bound(X_88,identity))),least_upper_bound(inverse(greatest_lower_bound(X_88,identity)),multiply(X_88,inverse(greatest_lower_bound(X_88,identity))))) )],[refute_0_14,refute_0_65]) ).
cnf(refute_0_67,plain,
multiply(X_66,least_upper_bound(X_67,identity)) = least_upper_bound(multiply(X_66,X_67),multiply(X_66,identity)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(X_66)),bind(Y,$fot(X_67)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_68,plain,
inverse(multiply(identity,X_30)) = multiply(inverse(X_30),inverse(identity)),
inference(subst,[],[p21_3:[bind(X,$fot(identity)),bind(Y,$fot(X_30))]]) ).
cnf(refute_0_69,plain,
( inverse(multiply(identity,X_30)) != multiply(inverse(X_30),inverse(identity))
| inverse(identity) != identity
| inverse(multiply(identity,X_30)) = multiply(inverse(X_30),identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(identity,X_30)),multiply(inverse(X_30),inverse(identity))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_70,plain,
( inverse(multiply(identity,X_30)) != multiply(inverse(X_30),inverse(identity))
| inverse(multiply(identity,X_30)) = multiply(inverse(X_30),identity) ),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[p21_1,refute_0_69]) ).
cnf(refute_0_71,plain,
inverse(multiply(identity,X_30)) = multiply(inverse(X_30),identity),
inference(resolve,[$cnf( $equal(inverse(multiply(identity,X_30)),multiply(inverse(X_30),inverse(identity))) )],[refute_0_68,refute_0_70]) ).
cnf(refute_0_72,plain,
multiply(identity,X_30) = X_30,
inference(subst,[],[left_identity:[bind(X,$fot(X_30))]]) ).
cnf(refute_0_73,plain,
inverse(multiply(identity,X_30)) = inverse(multiply(identity,X_30)),
introduced(tautology,[refl,[$fot(inverse(multiply(identity,X_30)))]]) ).
cnf(refute_0_74,plain,
( multiply(identity,X_30) != X_30
| inverse(multiply(identity,X_30)) != inverse(multiply(identity,X_30))
| inverse(multiply(identity,X_30)) = inverse(X_30) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(identity,X_30)),inverse(multiply(identity,X_30))) ),[1,0],$fot(X_30)]]) ).
cnf(refute_0_75,plain,
( multiply(identity,X_30) != X_30
| inverse(multiply(identity,X_30)) = inverse(X_30) ),
inference(resolve,[$cnf( $equal(inverse(multiply(identity,X_30)),inverse(multiply(identity,X_30))) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
inverse(multiply(identity,X_30)) = inverse(X_30),
inference(resolve,[$cnf( $equal(multiply(identity,X_30),X_30) )],[refute_0_72,refute_0_75]) ).
cnf(refute_0_77,plain,
( inverse(multiply(identity,X_30)) != multiply(inverse(X_30),identity)
| inverse(multiply(identity,X_30)) != inverse(X_30)
| inverse(X_30) = multiply(inverse(X_30),identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(identity,X_30)),multiply(inverse(X_30),identity)) ),[0],$fot(inverse(X_30))]]) ).
cnf(refute_0_78,plain,
( inverse(multiply(identity,X_30)) != multiply(inverse(X_30),identity)
| inverse(X_30) = multiply(inverse(X_30),identity) ),
inference(resolve,[$cnf( $equal(inverse(multiply(identity,X_30)),inverse(X_30)) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
inverse(X_30) = multiply(inverse(X_30),identity),
inference(resolve,[$cnf( $equal(inverse(multiply(identity,X_30)),multiply(inverse(X_30),identity)) )],[refute_0_71,refute_0_78]) ).
cnf(refute_0_80,plain,
inverse(inverse(X)) = multiply(inverse(inverse(X)),identity),
inference(subst,[],[refute_0_79:[bind(X_30,$fot(inverse(X)))]]) ).
cnf(refute_0_81,plain,
( inverse(inverse(X)) != X
| inverse(inverse(X)) != multiply(inverse(inverse(X)),identity)
| inverse(inverse(X)) = multiply(X,identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X)),multiply(inverse(inverse(X)),identity)) ),[1,0],$fot(X)]]) ).
cnf(refute_0_82,plain,
( inverse(inverse(X)) != multiply(inverse(inverse(X)),identity)
| inverse(inverse(X)) = multiply(X,identity) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p21_2,refute_0_81]) ).
cnf(refute_0_83,plain,
inverse(inverse(X)) = multiply(X,identity),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),multiply(inverse(inverse(X)),identity)) )],[refute_0_80,refute_0_82]) ).
cnf(refute_0_84,plain,
( inverse(inverse(X)) != X
| inverse(inverse(X)) != multiply(X,identity)
| X = multiply(X,identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X)),multiply(X,identity)) ),[0],$fot(X)]]) ).
cnf(refute_0_85,plain,
( inverse(inverse(X)) != multiply(X,identity)
| X = multiply(X,identity) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p21_2,refute_0_84]) ).
cnf(refute_0_86,plain,
X = multiply(X,identity),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),multiply(X,identity)) )],[refute_0_83,refute_0_85]) ).
cnf(refute_0_87,plain,
X_66 = multiply(X_66,identity),
inference(subst,[],[refute_0_86:[bind(X,$fot(X_66))]]) ).
cnf(refute_0_88,plain,
( X_66 != multiply(X_66,identity)
| multiply(X_66,identity) = X_66 ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(X_66)),bind(Y0,$fot(multiply(X_66,identity)))]]) ).
cnf(refute_0_89,plain,
multiply(X_66,identity) = X_66,
inference(resolve,[$cnf( $equal(X_66,multiply(X_66,identity)) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
( multiply(X_66,identity) != X_66
| multiply(X_66,least_upper_bound(X_67,identity)) != least_upper_bound(multiply(X_66,X_67),multiply(X_66,identity))
| multiply(X_66,least_upper_bound(X_67,identity)) = least_upper_bound(multiply(X_66,X_67),X_66) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_66,least_upper_bound(X_67,identity)),least_upper_bound(multiply(X_66,X_67),multiply(X_66,identity))) ),[1,1],$fot(X_66)]]) ).
cnf(refute_0_91,plain,
( multiply(X_66,least_upper_bound(X_67,identity)) != least_upper_bound(multiply(X_66,X_67),multiply(X_66,identity))
| multiply(X_66,least_upper_bound(X_67,identity)) = least_upper_bound(multiply(X_66,X_67),X_66) ),
inference(resolve,[$cnf( $equal(multiply(X_66,identity),X_66) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
multiply(X_66,least_upper_bound(X_67,identity)) = least_upper_bound(multiply(X_66,X_67),X_66),
inference(resolve,[$cnf( $equal(multiply(X_66,least_upper_bound(X_67,identity)),least_upper_bound(multiply(X_66,X_67),multiply(X_66,identity))) )],[refute_0_67,refute_0_91]) ).
cnf(refute_0_93,plain,
least_upper_bound(multiply(X_66,X_67),X_66) = least_upper_bound(X_66,multiply(X_66,X_67)),
inference(subst,[],[refute_0_9:[bind(X,$fot(X_66)),bind(Y,$fot(multiply(X_66,X_67)))]]) ).
cnf(refute_0_94,plain,
( multiply(X_66,least_upper_bound(X_67,identity)) != least_upper_bound(multiply(X_66,X_67),X_66)
| least_upper_bound(multiply(X_66,X_67),X_66) != least_upper_bound(X_66,multiply(X_66,X_67))
| multiply(X_66,least_upper_bound(X_67,identity)) = least_upper_bound(X_66,multiply(X_66,X_67)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_66,least_upper_bound(X_67,identity)),least_upper_bound(X_66,multiply(X_66,X_67))) ),[0],$fot(least_upper_bound(multiply(X_66,X_67),X_66))]]) ).
cnf(refute_0_95,plain,
( multiply(X_66,least_upper_bound(X_67,identity)) != least_upper_bound(multiply(X_66,X_67),X_66)
| multiply(X_66,least_upper_bound(X_67,identity)) = least_upper_bound(X_66,multiply(X_66,X_67)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_66,X_67),X_66),least_upper_bound(X_66,multiply(X_66,X_67))) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
multiply(X_66,least_upper_bound(X_67,identity)) = least_upper_bound(X_66,multiply(X_66,X_67)),
inference(resolve,[$cnf( $equal(multiply(X_66,least_upper_bound(X_67,identity)),least_upper_bound(multiply(X_66,X_67),X_66)) )],[refute_0_92,refute_0_95]) ).
cnf(refute_0_97,plain,
multiply(inverse(greatest_lower_bound(X_67,identity)),least_upper_bound(X_67,identity)) = least_upper_bound(inverse(greatest_lower_bound(X_67,identity)),multiply(inverse(greatest_lower_bound(X_67,identity)),X_67)),
inference(subst,[],[refute_0_96:[bind(X_66,$fot(inverse(greatest_lower_bound(X_67,identity))))]]) ).
cnf(refute_0_98,plain,
inverse(multiply(inverse(X_132),greatest_lower_bound(X_132,identity))) = multiply(inverse(greatest_lower_bound(X_132,identity)),inverse(inverse(X_132))),
inference(subst,[],[p21_3:[bind(X,$fot(inverse(X_132))),bind(Y,$fot(greatest_lower_bound(X_132,identity)))]]) ).
cnf(refute_0_99,plain,
multiply(X_82,greatest_lower_bound(X_83,identity)) = greatest_lower_bound(multiply(X_82,X_83),multiply(X_82,identity)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(X_82)),bind(Y,$fot(X_83)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_100,plain,
X_82 = multiply(X_82,identity),
inference(subst,[],[refute_0_86:[bind(X,$fot(X_82))]]) ).
cnf(refute_0_101,plain,
( X_82 != multiply(X_82,identity)
| multiply(X_82,identity) = X_82 ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(X_82)),bind(Y0,$fot(multiply(X_82,identity)))]]) ).
cnf(refute_0_102,plain,
multiply(X_82,identity) = X_82,
inference(resolve,[$cnf( $equal(X_82,multiply(X_82,identity)) )],[refute_0_100,refute_0_101]) ).
cnf(refute_0_103,plain,
( multiply(X_82,greatest_lower_bound(X_83,identity)) != greatest_lower_bound(multiply(X_82,X_83),multiply(X_82,identity))
| multiply(X_82,identity) != X_82
| multiply(X_82,greatest_lower_bound(X_83,identity)) = greatest_lower_bound(multiply(X_82,X_83),X_82) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_82,greatest_lower_bound(X_83,identity)),greatest_lower_bound(multiply(X_82,X_83),multiply(X_82,identity))) ),[1,1],$fot(X_82)]]) ).
cnf(refute_0_104,plain,
( multiply(X_82,greatest_lower_bound(X_83,identity)) != greatest_lower_bound(multiply(X_82,X_83),multiply(X_82,identity))
| multiply(X_82,greatest_lower_bound(X_83,identity)) = greatest_lower_bound(multiply(X_82,X_83),X_82) ),
inference(resolve,[$cnf( $equal(multiply(X_82,identity),X_82) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
multiply(X_82,greatest_lower_bound(X_83,identity)) = greatest_lower_bound(multiply(X_82,X_83),X_82),
inference(resolve,[$cnf( $equal(multiply(X_82,greatest_lower_bound(X_83,identity)),greatest_lower_bound(multiply(X_82,X_83),multiply(X_82,identity))) )],[refute_0_99,refute_0_104]) ).
cnf(refute_0_106,plain,
greatest_lower_bound(multiply(X_82,X_83),X_82) = greatest_lower_bound(X_82,multiply(X_82,X_83)),
inference(subst,[],[refute_0_22:[bind(X,$fot(X_82)),bind(Y,$fot(multiply(X_82,X_83)))]]) ).
cnf(refute_0_107,plain,
( multiply(X_82,greatest_lower_bound(X_83,identity)) != greatest_lower_bound(multiply(X_82,X_83),X_82)
| greatest_lower_bound(multiply(X_82,X_83),X_82) != greatest_lower_bound(X_82,multiply(X_82,X_83))
| multiply(X_82,greatest_lower_bound(X_83,identity)) = greatest_lower_bound(X_82,multiply(X_82,X_83)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_82,greatest_lower_bound(X_83,identity)),greatest_lower_bound(X_82,multiply(X_82,X_83))) ),[0],$fot(greatest_lower_bound(multiply(X_82,X_83),X_82))]]) ).
cnf(refute_0_108,plain,
( multiply(X_82,greatest_lower_bound(X_83,identity)) != greatest_lower_bound(multiply(X_82,X_83),X_82)
| multiply(X_82,greatest_lower_bound(X_83,identity)) = greatest_lower_bound(X_82,multiply(X_82,X_83)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_82,X_83),X_82),greatest_lower_bound(X_82,multiply(X_82,X_83))) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
multiply(X_82,greatest_lower_bound(X_83,identity)) = greatest_lower_bound(X_82,multiply(X_82,X_83)),
inference(resolve,[$cnf( $equal(multiply(X_82,greatest_lower_bound(X_83,identity)),greatest_lower_bound(multiply(X_82,X_83),X_82)) )],[refute_0_105,refute_0_108]) ).
cnf(refute_0_110,plain,
multiply(inverse(X_131),greatest_lower_bound(X_131,identity)) = greatest_lower_bound(inverse(X_131),multiply(inverse(X_131),X_131)),
inference(subst,[],[refute_0_109:[bind(X_82,$fot(inverse(X_131))),bind(X_83,$fot(X_131))]]) ).
cnf(refute_0_111,plain,
multiply(inverse(X_131),X_131) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_131))]]) ).
cnf(refute_0_112,plain,
( multiply(inverse(X_131),X_131) != identity
| multiply(inverse(X_131),greatest_lower_bound(X_131,identity)) != greatest_lower_bound(inverse(X_131),multiply(inverse(X_131),X_131))
| multiply(inverse(X_131),greatest_lower_bound(X_131,identity)) = greatest_lower_bound(inverse(X_131),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_131),greatest_lower_bound(X_131,identity)),greatest_lower_bound(inverse(X_131),multiply(inverse(X_131),X_131))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_113,plain,
( multiply(inverse(X_131),greatest_lower_bound(X_131,identity)) != greatest_lower_bound(inverse(X_131),multiply(inverse(X_131),X_131))
| multiply(inverse(X_131),greatest_lower_bound(X_131,identity)) = greatest_lower_bound(inverse(X_131),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_131),X_131),identity) )],[refute_0_111,refute_0_112]) ).
cnf(refute_0_114,plain,
multiply(inverse(X_131),greatest_lower_bound(X_131,identity)) = greatest_lower_bound(inverse(X_131),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_131),greatest_lower_bound(X_131,identity)),greatest_lower_bound(inverse(X_131),multiply(inverse(X_131),X_131))) )],[refute_0_110,refute_0_113]) ).
cnf(refute_0_115,plain,
greatest_lower_bound(inverse(X_131),identity) = greatest_lower_bound(identity,inverse(X_131)),
inference(subst,[],[refute_0_22:[bind(X,$fot(identity)),bind(Y,$fot(inverse(X_131)))]]) ).
cnf(refute_0_116,plain,
( multiply(inverse(X_131),greatest_lower_bound(X_131,identity)) != greatest_lower_bound(inverse(X_131),identity)
| greatest_lower_bound(inverse(X_131),identity) != greatest_lower_bound(identity,inverse(X_131))
| multiply(inverse(X_131),greatest_lower_bound(X_131,identity)) = greatest_lower_bound(identity,inverse(X_131)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_131),greatest_lower_bound(X_131,identity)),greatest_lower_bound(identity,inverse(X_131))) ),[0],$fot(greatest_lower_bound(inverse(X_131),identity))]]) ).
cnf(refute_0_117,plain,
( multiply(inverse(X_131),greatest_lower_bound(X_131,identity)) != greatest_lower_bound(inverse(X_131),identity)
| multiply(inverse(X_131),greatest_lower_bound(X_131,identity)) = greatest_lower_bound(identity,inverse(X_131)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_131),identity),greatest_lower_bound(identity,inverse(X_131))) )],[refute_0_115,refute_0_116]) ).
cnf(refute_0_118,plain,
multiply(inverse(X_131),greatest_lower_bound(X_131,identity)) = greatest_lower_bound(identity,inverse(X_131)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_131),greatest_lower_bound(X_131,identity)),greatest_lower_bound(inverse(X_131),identity)) )],[refute_0_114,refute_0_117]) ).
cnf(refute_0_119,plain,
multiply(inverse(X_132),greatest_lower_bound(X_132,identity)) = greatest_lower_bound(identity,inverse(X_132)),
inference(subst,[],[refute_0_118:[bind(X_131,$fot(X_132))]]) ).
cnf(refute_0_120,plain,
( multiply(inverse(X_132),greatest_lower_bound(X_132,identity)) != greatest_lower_bound(identity,inverse(X_132))
| inverse(multiply(inverse(X_132),greatest_lower_bound(X_132,identity))) != multiply(inverse(greatest_lower_bound(X_132,identity)),inverse(inverse(X_132)))
| inverse(greatest_lower_bound(identity,inverse(X_132))) = multiply(inverse(greatest_lower_bound(X_132,identity)),inverse(inverse(X_132))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X_132),greatest_lower_bound(X_132,identity))),multiply(inverse(greatest_lower_bound(X_132,identity)),inverse(inverse(X_132)))) ),[0,0],$fot(greatest_lower_bound(identity,inverse(X_132)))]]) ).
cnf(refute_0_121,plain,
( inverse(multiply(inverse(X_132),greatest_lower_bound(X_132,identity))) != multiply(inverse(greatest_lower_bound(X_132,identity)),inverse(inverse(X_132)))
| inverse(greatest_lower_bound(identity,inverse(X_132))) = multiply(inverse(greatest_lower_bound(X_132,identity)),inverse(inverse(X_132))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_132),greatest_lower_bound(X_132,identity)),greatest_lower_bound(identity,inverse(X_132))) )],[refute_0_119,refute_0_120]) ).
cnf(refute_0_122,plain,
inverse(greatest_lower_bound(identity,inverse(X_132))) = multiply(inverse(greatest_lower_bound(X_132,identity)),inverse(inverse(X_132))),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_132),greatest_lower_bound(X_132,identity))),multiply(inverse(greatest_lower_bound(X_132,identity)),inverse(inverse(X_132)))) )],[refute_0_98,refute_0_121]) ).
cnf(refute_0_123,plain,
inverse(multiply(inverse(X),X_30)) = multiply(inverse(X_30),inverse(inverse(X))),
inference(subst,[],[p21_3:[bind(X,$fot(inverse(X))),bind(Y,$fot(X_30))]]) ).
cnf(refute_0_124,plain,
( inverse(multiply(inverse(X),X_30)) != multiply(inverse(X_30),inverse(inverse(X)))
| inverse(inverse(X)) != X
| inverse(multiply(inverse(X),X_30)) = multiply(inverse(X_30),X) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X),X_30)),multiply(inverse(X_30),inverse(inverse(X)))) ),[1,1],$fot(X)]]) ).
cnf(refute_0_125,plain,
( inverse(multiply(inverse(X),X_30)) != multiply(inverse(X_30),inverse(inverse(X)))
| inverse(multiply(inverse(X),X_30)) = multiply(inverse(X_30),X) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p21_2,refute_0_124]) ).
cnf(refute_0_126,plain,
inverse(multiply(inverse(X),X_30)) = multiply(inverse(X_30),X),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X),X_30)),multiply(inverse(X_30),inverse(inverse(X)))) )],[refute_0_123,refute_0_125]) ).
cnf(refute_0_127,plain,
inverse(multiply(inverse(X_132),greatest_lower_bound(X_132,identity))) = multiply(inverse(greatest_lower_bound(X_132,identity)),X_132),
inference(subst,[],[refute_0_126:[bind(X,$fot(X_132)),bind(X_30,$fot(greatest_lower_bound(X_132,identity)))]]) ).
cnf(refute_0_128,plain,
multiply(inverse(greatest_lower_bound(X_132,identity)),inverse(inverse(X_132))) = inverse(multiply(inverse(X_132),greatest_lower_bound(X_132,identity))),
inference(subst,[],[refute_0_51:[bind(X,$fot(inverse(X_132))),bind(Y,$fot(greatest_lower_bound(X_132,identity)))]]) ).
cnf(refute_0_129,plain,
( multiply(inverse(greatest_lower_bound(X_132,identity)),inverse(inverse(X_132))) != inverse(multiply(inverse(X_132),greatest_lower_bound(X_132,identity)))
| inverse(multiply(inverse(X_132),greatest_lower_bound(X_132,identity))) != multiply(inverse(greatest_lower_bound(X_132,identity)),X_132)
| multiply(inverse(greatest_lower_bound(X_132,identity)),inverse(inverse(X_132))) = multiply(inverse(greatest_lower_bound(X_132,identity)),X_132) ),
inference(subst,[],[refute_0_54:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(X_132,identity)),inverse(inverse(X_132))))),bind(Y0,$fot(inverse(multiply(inverse(X_132),greatest_lower_bound(X_132,identity))))),bind(Z0,$fot(multiply(inverse(greatest_lower_bound(X_132,identity)),X_132)))]]) ).
cnf(refute_0_130,plain,
( inverse(multiply(inverse(X_132),greatest_lower_bound(X_132,identity))) != multiply(inverse(greatest_lower_bound(X_132,identity)),X_132)
| multiply(inverse(greatest_lower_bound(X_132,identity)),inverse(inverse(X_132))) = multiply(inverse(greatest_lower_bound(X_132,identity)),X_132) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_132,identity)),inverse(inverse(X_132))),inverse(multiply(inverse(X_132),greatest_lower_bound(X_132,identity)))) )],[refute_0_128,refute_0_129]) ).
cnf(refute_0_131,plain,
multiply(inverse(greatest_lower_bound(X_132,identity)),inverse(inverse(X_132))) = multiply(inverse(greatest_lower_bound(X_132,identity)),X_132),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_132),greatest_lower_bound(X_132,identity))),multiply(inverse(greatest_lower_bound(X_132,identity)),X_132)) )],[refute_0_127,refute_0_130]) ).
cnf(refute_0_132,plain,
( multiply(inverse(greatest_lower_bound(X_132,identity)),inverse(inverse(X_132))) != multiply(inverse(greatest_lower_bound(X_132,identity)),X_132)
| inverse(greatest_lower_bound(identity,inverse(X_132))) != multiply(inverse(greatest_lower_bound(X_132,identity)),inverse(inverse(X_132)))
| inverse(greatest_lower_bound(identity,inverse(X_132))) = multiply(inverse(greatest_lower_bound(X_132,identity)),X_132) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_132))),multiply(inverse(greatest_lower_bound(X_132,identity)),inverse(inverse(X_132)))) ),[1],$fot(multiply(inverse(greatest_lower_bound(X_132,identity)),X_132))]]) ).
cnf(refute_0_133,plain,
( inverse(greatest_lower_bound(identity,inverse(X_132))) != multiply(inverse(greatest_lower_bound(X_132,identity)),inverse(inverse(X_132)))
| inverse(greatest_lower_bound(identity,inverse(X_132))) = multiply(inverse(greatest_lower_bound(X_132,identity)),X_132) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_132,identity)),inverse(inverse(X_132))),multiply(inverse(greatest_lower_bound(X_132,identity)),X_132)) )],[refute_0_131,refute_0_132]) ).
cnf(refute_0_134,plain,
inverse(greatest_lower_bound(identity,inverse(X_132))) = multiply(inverse(greatest_lower_bound(X_132,identity)),X_132),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_132))),multiply(inverse(greatest_lower_bound(X_132,identity)),inverse(inverse(X_132)))) )],[refute_0_122,refute_0_133]) ).
cnf(refute_0_135,plain,
inverse(greatest_lower_bound(identity,inverse(X_67))) = multiply(inverse(greatest_lower_bound(X_67,identity)),X_67),
inference(subst,[],[refute_0_134:[bind(X_132,$fot(X_67))]]) ).
cnf(refute_0_136,plain,
( inverse(greatest_lower_bound(identity,inverse(X_67))) != multiply(inverse(greatest_lower_bound(X_67,identity)),X_67)
| multiply(inverse(greatest_lower_bound(X_67,identity)),X_67) = inverse(greatest_lower_bound(identity,inverse(X_67))) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(inverse(greatest_lower_bound(identity,inverse(X_67))))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(X_67,identity)),X_67)))]]) ).
cnf(refute_0_137,plain,
multiply(inverse(greatest_lower_bound(X_67,identity)),X_67) = inverse(greatest_lower_bound(identity,inverse(X_67))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_67))),multiply(inverse(greatest_lower_bound(X_67,identity)),X_67)) )],[refute_0_135,refute_0_136]) ).
cnf(refute_0_138,plain,
( multiply(inverse(greatest_lower_bound(X_67,identity)),X_67) != inverse(greatest_lower_bound(identity,inverse(X_67)))
| multiply(inverse(greatest_lower_bound(X_67,identity)),least_upper_bound(X_67,identity)) != least_upper_bound(inverse(greatest_lower_bound(X_67,identity)),multiply(inverse(greatest_lower_bound(X_67,identity)),X_67))
| multiply(inverse(greatest_lower_bound(X_67,identity)),least_upper_bound(X_67,identity)) = least_upper_bound(inverse(greatest_lower_bound(X_67,identity)),inverse(greatest_lower_bound(identity,inverse(X_67)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_67,identity)),least_upper_bound(X_67,identity)),least_upper_bound(inverse(greatest_lower_bound(X_67,identity)),multiply(inverse(greatest_lower_bound(X_67,identity)),X_67))) ),[1,1],$fot(inverse(greatest_lower_bound(identity,inverse(X_67))))]]) ).
cnf(refute_0_139,plain,
( multiply(inverse(greatest_lower_bound(X_67,identity)),least_upper_bound(X_67,identity)) != least_upper_bound(inverse(greatest_lower_bound(X_67,identity)),multiply(inverse(greatest_lower_bound(X_67,identity)),X_67))
| multiply(inverse(greatest_lower_bound(X_67,identity)),least_upper_bound(X_67,identity)) = least_upper_bound(inverse(greatest_lower_bound(X_67,identity)),inverse(greatest_lower_bound(identity,inverse(X_67)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_67,identity)),X_67),inverse(greatest_lower_bound(identity,inverse(X_67)))) )],[refute_0_137,refute_0_138]) ).
cnf(refute_0_140,plain,
multiply(inverse(greatest_lower_bound(X_67,identity)),least_upper_bound(X_67,identity)) = least_upper_bound(inverse(greatest_lower_bound(X_67,identity)),inverse(greatest_lower_bound(identity,inverse(X_67)))),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_67,identity)),least_upper_bound(X_67,identity)),least_upper_bound(inverse(greatest_lower_bound(X_67,identity)),multiply(inverse(greatest_lower_bound(X_67,identity)),X_67))) )],[refute_0_97,refute_0_139]) ).
cnf(refute_0_141,plain,
( multiply(inverse(greatest_lower_bound(X_67,identity)),least_upper_bound(X_67,identity)) != least_upper_bound(inverse(greatest_lower_bound(X_67,identity)),inverse(greatest_lower_bound(identity,inverse(X_67))))
| least_upper_bound(inverse(greatest_lower_bound(X_67,identity)),inverse(greatest_lower_bound(identity,inverse(X_67)))) = multiply(inverse(greatest_lower_bound(X_67,identity)),least_upper_bound(X_67,identity)) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(X_67,identity)),least_upper_bound(X_67,identity)))),bind(Y0,$fot(least_upper_bound(inverse(greatest_lower_bound(X_67,identity)),inverse(greatest_lower_bound(identity,inverse(X_67))))))]]) ).
cnf(refute_0_142,plain,
least_upper_bound(inverse(greatest_lower_bound(X_67,identity)),inverse(greatest_lower_bound(identity,inverse(X_67)))) = multiply(inverse(greatest_lower_bound(X_67,identity)),least_upper_bound(X_67,identity)),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_67,identity)),least_upper_bound(X_67,identity)),least_upper_bound(inverse(greatest_lower_bound(X_67,identity)),inverse(greatest_lower_bound(identity,inverse(X_67))))) )],[refute_0_140,refute_0_141]) ).
cnf(refute_0_143,plain,
least_upper_bound(inverse(greatest_lower_bound(X_88,identity)),inverse(greatest_lower_bound(identity,inverse(X_88)))) = multiply(inverse(greatest_lower_bound(X_88,identity)),least_upper_bound(X_88,identity)),
inference(subst,[],[refute_0_142:[bind(X_67,$fot(X_88))]]) ).
cnf(refute_0_144,plain,
( multiply(least_upper_bound(X_88,identity),inverse(greatest_lower_bound(X_88,identity))) != least_upper_bound(inverse(greatest_lower_bound(X_88,identity)),inverse(greatest_lower_bound(identity,inverse(X_88))))
| least_upper_bound(inverse(greatest_lower_bound(X_88,identity)),inverse(greatest_lower_bound(identity,inverse(X_88)))) != multiply(inverse(greatest_lower_bound(X_88,identity)),least_upper_bound(X_88,identity))
| multiply(least_upper_bound(X_88,identity),inverse(greatest_lower_bound(X_88,identity))) = multiply(inverse(greatest_lower_bound(X_88,identity)),least_upper_bound(X_88,identity)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_88,identity),inverse(greatest_lower_bound(X_88,identity))),multiply(inverse(greatest_lower_bound(X_88,identity)),least_upper_bound(X_88,identity))) ),[0],$fot(least_upper_bound(inverse(greatest_lower_bound(X_88,identity)),inverse(greatest_lower_bound(identity,inverse(X_88)))))]]) ).
cnf(refute_0_145,plain,
( multiply(least_upper_bound(X_88,identity),inverse(greatest_lower_bound(X_88,identity))) != least_upper_bound(inverse(greatest_lower_bound(X_88,identity)),inverse(greatest_lower_bound(identity,inverse(X_88))))
| multiply(least_upper_bound(X_88,identity),inverse(greatest_lower_bound(X_88,identity))) = multiply(inverse(greatest_lower_bound(X_88,identity)),least_upper_bound(X_88,identity)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(X_88,identity)),inverse(greatest_lower_bound(identity,inverse(X_88)))),multiply(inverse(greatest_lower_bound(X_88,identity)),least_upper_bound(X_88,identity))) )],[refute_0_143,refute_0_144]) ).
cnf(refute_0_146,plain,
multiply(least_upper_bound(X_88,identity),inverse(greatest_lower_bound(X_88,identity))) = multiply(inverse(greatest_lower_bound(X_88,identity)),least_upper_bound(X_88,identity)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_88,identity),inverse(greatest_lower_bound(X_88,identity))),least_upper_bound(inverse(greatest_lower_bound(X_88,identity)),inverse(greatest_lower_bound(identity,inverse(X_88))))) )],[refute_0_66,refute_0_145]) ).
cnf(refute_0_147,plain,
( multiply(least_upper_bound(X_88,identity),inverse(greatest_lower_bound(X_88,identity))) != multiply(inverse(greatest_lower_bound(X_88,identity)),least_upper_bound(X_88,identity))
| multiply(inverse(greatest_lower_bound(X_88,identity)),least_upper_bound(X_88,identity)) = multiply(least_upper_bound(X_88,identity),inverse(greatest_lower_bound(X_88,identity))) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(multiply(least_upper_bound(X_88,identity),inverse(greatest_lower_bound(X_88,identity))))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(X_88,identity)),least_upper_bound(X_88,identity))))]]) ).
cnf(refute_0_148,plain,
multiply(inverse(greatest_lower_bound(X_88,identity)),least_upper_bound(X_88,identity)) = multiply(least_upper_bound(X_88,identity),inverse(greatest_lower_bound(X_88,identity))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_88,identity),inverse(greatest_lower_bound(X_88,identity))),multiply(inverse(greatest_lower_bound(X_88,identity)),least_upper_bound(X_88,identity))) )],[refute_0_146,refute_0_147]) ).
cnf(refute_0_149,plain,
multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)) = multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))),
inference(subst,[],[refute_0_148:[bind(X_88,$fot(a))]]) ).
cnf(refute_0_150,plain,
( multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)) != multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity)))
| multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) != multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity)))
| multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) = multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))),multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity))) ),[1],$fot(multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))))]]) ).
cnf(refute_0_151,plain,
( multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) != multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity)))
| multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) = multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)),multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity)))) )],[refute_0_149,refute_0_150]) ).
cnf(refute_0_152,plain,
multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) != multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))),multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity))) )],[refute_0_151,prove_p21]) ).
cnf(refute_0_153,plain,
multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) = multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))))]]) ).
cnf(refute_0_154,plain,
$false,
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))),multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity)))) )],[refute_0_153,refute_0_152]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GRP184-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.04/0.14 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n022.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jun 13 09:08:03 EDT 2022
% 0.13/0.36 % CPUTime :
% 0.13/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 7.03/7.21 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.03/7.21
% 7.03/7.21 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.07/7.22
%------------------------------------------------------------------------------