TSTP Solution File: GRP171-2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP171-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 10:37:17 EDT 2022
% Result : Unsatisfiable 0.79s 1.00s
% Output : CNFRefutation 0.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 45
% Syntax : Number of clauses : 170 ( 96 unt; 0 nHn; 102 RR)
% Number of literals : 275 ( 274 equ; 107 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 209 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
multiply(identity,X) = X ).
cnf(left_inverse,axiom,
multiply(inverse(X),X) = identity ).
cnf(associativity,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ).
cnf(symmetry_of_glb,axiom,
greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ).
cnf(symmetry_of_lub,axiom,
least_upper_bound(X,Y) = least_upper_bound(Y,X) ).
cnf(associativity_of_glb,axiom,
greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) ).
cnf(glb_absorbtion,axiom,
greatest_lower_bound(X,least_upper_bound(X,Y)) = X ).
cnf(monotony_glb1,axiom,
multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)) ).
cnf(monotony_glb2,axiom,
multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) ).
cnf(p04c_1,hypothesis,
least_upper_bound(identity,a) = a ).
cnf(p04c_2,hypothesis,
least_upper_bound(identity,b) = b ).
cnf(prove_p04c,negated_conjecture,
greatest_lower_bound(identity,multiply(a,b)) != identity ).
cnf(refute_0_0,plain,
multiply(inverse(X_36),greatest_lower_bound(X_35,X_36)) = greatest_lower_bound(multiply(inverse(X_36),X_35),multiply(inverse(X_36),X_36)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(inverse(X_36))),bind(Y,$fot(X_35)),bind(Z,$fot(X_36))]]) ).
cnf(refute_0_1,plain,
multiply(inverse(X_36),X_36) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_36))]]) ).
cnf(refute_0_2,plain,
( multiply(inverse(X_36),X_36) != identity
| multiply(inverse(X_36),greatest_lower_bound(X_35,X_36)) != greatest_lower_bound(multiply(inverse(X_36),X_35),multiply(inverse(X_36),X_36))
| multiply(inverse(X_36),greatest_lower_bound(X_35,X_36)) = greatest_lower_bound(multiply(inverse(X_36),X_35),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_36),greatest_lower_bound(X_35,X_36)),greatest_lower_bound(multiply(inverse(X_36),X_35),multiply(inverse(X_36),X_36))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_3,plain,
( multiply(inverse(X_36),greatest_lower_bound(X_35,X_36)) != greatest_lower_bound(multiply(inverse(X_36),X_35),multiply(inverse(X_36),X_36))
| multiply(inverse(X_36),greatest_lower_bound(X_35,X_36)) = greatest_lower_bound(multiply(inverse(X_36),X_35),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_36),X_36),identity) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
multiply(inverse(X_36),greatest_lower_bound(X_35,X_36)) = greatest_lower_bound(multiply(inverse(X_36),X_35),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_36),greatest_lower_bound(X_35,X_36)),greatest_lower_bound(multiply(inverse(X_36),X_35),multiply(inverse(X_36),X_36))) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
greatest_lower_bound(X_20,X_19) = greatest_lower_bound(X_19,X_20),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_20)),bind(Y,$fot(X_19))]]) ).
cnf(refute_0_6,plain,
greatest_lower_bound(multiply(inverse(X_36),X_35),identity) = greatest_lower_bound(identity,multiply(inverse(X_36),X_35)),
inference(subst,[],[refute_0_5:[bind(X_19,$fot(identity)),bind(X_20,$fot(multiply(inverse(X_36),X_35)))]]) ).
cnf(refute_0_7,plain,
( multiply(inverse(X_36),greatest_lower_bound(X_35,X_36)) != greatest_lower_bound(multiply(inverse(X_36),X_35),identity)
| greatest_lower_bound(multiply(inverse(X_36),X_35),identity) != greatest_lower_bound(identity,multiply(inverse(X_36),X_35))
| multiply(inverse(X_36),greatest_lower_bound(X_35,X_36)) = greatest_lower_bound(identity,multiply(inverse(X_36),X_35)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_36),greatest_lower_bound(X_35,X_36)),greatest_lower_bound(identity,multiply(inverse(X_36),X_35))) ),[0],$fot(greatest_lower_bound(multiply(inverse(X_36),X_35),identity))]]) ).
cnf(refute_0_8,plain,
( multiply(inverse(X_36),greatest_lower_bound(X_35,X_36)) != greatest_lower_bound(multiply(inverse(X_36),X_35),identity)
| multiply(inverse(X_36),greatest_lower_bound(X_35,X_36)) = greatest_lower_bound(identity,multiply(inverse(X_36),X_35)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(inverse(X_36),X_35),identity),greatest_lower_bound(identity,multiply(inverse(X_36),X_35))) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
multiply(inverse(X_36),greatest_lower_bound(X_35,X_36)) = greatest_lower_bound(identity,multiply(inverse(X_36),X_35)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_36),greatest_lower_bound(X_35,X_36)),greatest_lower_bound(multiply(inverse(X_36),X_35),identity)) )],[refute_0_4,refute_0_8]) ).
cnf(refute_0_10,plain,
multiply(inverse(greatest_lower_bound(identity,X_20)),greatest_lower_bound(b,greatest_lower_bound(identity,X_20))) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_20)),b)),
inference(subst,[],[refute_0_9:[bind(X_35,$fot(b)),bind(X_36,$fot(greatest_lower_bound(identity,X_20)))]]) ).
cnf(refute_0_11,plain,
greatest_lower_bound(b,greatest_lower_bound(identity,X_20)) = greatest_lower_bound(greatest_lower_bound(b,identity),X_20),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(b)),bind(Y,$fot(identity)),bind(Z,$fot(X_20))]]) ).
cnf(refute_0_12,plain,
greatest_lower_bound(X_8,least_upper_bound(X_8,X_9)) = X_8,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_8)),bind(Y,$fot(X_9))]]) ).
cnf(refute_0_13,plain,
least_upper_bound(X_9,X_8) = least_upper_bound(X_8,X_9),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_9)),bind(Y,$fot(X_8))]]) ).
cnf(refute_0_14,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_15,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_16,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
( least_upper_bound(X_9,X_8) != least_upper_bound(X_8,X_9)
| least_upper_bound(X_8,X_9) = least_upper_bound(X_9,X_8) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(least_upper_bound(X_9,X_8))),bind(Y0,$fot(least_upper_bound(X_8,X_9)))]]) ).
cnf(refute_0_18,plain,
least_upper_bound(X_8,X_9) = least_upper_bound(X_9,X_8),
inference(resolve,[$cnf( $equal(least_upper_bound(X_9,X_8),least_upper_bound(X_8,X_9)) )],[refute_0_13,refute_0_17]) ).
cnf(refute_0_19,plain,
( greatest_lower_bound(X_8,least_upper_bound(X_8,X_9)) != X_8
| least_upper_bound(X_8,X_9) != least_upper_bound(X_9,X_8)
| greatest_lower_bound(X_8,least_upper_bound(X_9,X_8)) = X_8 ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_8,least_upper_bound(X_8,X_9)),X_8) ),[0,1],$fot(least_upper_bound(X_9,X_8))]]) ).
cnf(refute_0_20,plain,
( greatest_lower_bound(X_8,least_upper_bound(X_8,X_9)) != X_8
| greatest_lower_bound(X_8,least_upper_bound(X_9,X_8)) = X_8 ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_8,X_9),least_upper_bound(X_9,X_8)) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
greatest_lower_bound(X_8,least_upper_bound(X_9,X_8)) = X_8,
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_8,least_upper_bound(X_8,X_9)),X_8) )],[refute_0_12,refute_0_20]) ).
cnf(refute_0_22,plain,
greatest_lower_bound(identity,least_upper_bound(b,identity)) = identity,
inference(subst,[],[refute_0_21:[bind(X_8,$fot(identity)),bind(X_9,$fot(b))]]) ).
cnf(refute_0_23,plain,
( least_upper_bound(X,Y) != least_upper_bound(Y,X)
| least_upper_bound(Y,X) = least_upper_bound(X,Y) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(least_upper_bound(X,Y))),bind(Y0,$fot(least_upper_bound(Y,X)))]]) ).
cnf(refute_0_24,plain,
least_upper_bound(Y,X) = least_upper_bound(X,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(X,Y),least_upper_bound(Y,X)) )],[symmetry_of_lub,refute_0_23]) ).
cnf(refute_0_25,plain,
least_upper_bound(identity,b) = least_upper_bound(b,identity),
inference(subst,[],[refute_0_24:[bind(X,$fot(b)),bind(Y,$fot(identity))]]) ).
cnf(refute_0_26,plain,
( least_upper_bound(identity,b) != b
| least_upper_bound(identity,b) != least_upper_bound(b,identity)
| least_upper_bound(b,identity) = b ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,b),b) ),[0],$fot(least_upper_bound(b,identity))]]) ).
cnf(refute_0_27,plain,
( least_upper_bound(identity,b) != b
| least_upper_bound(b,identity) = b ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,b),least_upper_bound(b,identity)) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
least_upper_bound(b,identity) = b,
inference(resolve,[$cnf( $equal(least_upper_bound(identity,b),b) )],[p04c_2,refute_0_27]) ).
cnf(refute_0_29,plain,
( greatest_lower_bound(identity,least_upper_bound(b,identity)) != identity
| least_upper_bound(b,identity) != b
| greatest_lower_bound(identity,b) = identity ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(b,identity)),identity) ),[0,1],$fot(b)]]) ).
cnf(refute_0_30,plain,
( greatest_lower_bound(identity,least_upper_bound(b,identity)) != identity
| greatest_lower_bound(identity,b) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,identity),b) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
greatest_lower_bound(identity,b) = identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(b,identity)),identity) )],[refute_0_22,refute_0_30]) ).
cnf(refute_0_32,plain,
( greatest_lower_bound(X,Y) != greatest_lower_bound(Y,X)
| greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(greatest_lower_bound(X,Y))),bind(Y0,$fot(greatest_lower_bound(Y,X)))]]) ).
cnf(refute_0_33,plain,
greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X)) )],[symmetry_of_glb,refute_0_32]) ).
cnf(refute_0_34,plain,
greatest_lower_bound(identity,b) = greatest_lower_bound(b,identity),
inference(subst,[],[refute_0_33:[bind(X,$fot(b)),bind(Y,$fot(identity))]]) ).
cnf(refute_0_35,plain,
( greatest_lower_bound(identity,b) != greatest_lower_bound(b,identity)
| greatest_lower_bound(identity,b) != identity
| greatest_lower_bound(b,identity) = identity ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,b),identity) ),[0],$fot(greatest_lower_bound(b,identity))]]) ).
cnf(refute_0_36,plain,
( greatest_lower_bound(identity,b) != identity
| greatest_lower_bound(b,identity) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,b),greatest_lower_bound(b,identity)) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
greatest_lower_bound(b,identity) = identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,b),identity) )],[refute_0_31,refute_0_36]) ).
cnf(refute_0_38,plain,
( greatest_lower_bound(b,greatest_lower_bound(identity,X_20)) != greatest_lower_bound(greatest_lower_bound(b,identity),X_20)
| greatest_lower_bound(b,identity) != identity
| greatest_lower_bound(b,greatest_lower_bound(identity,X_20)) = greatest_lower_bound(identity,X_20) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(identity,X_20)),greatest_lower_bound(greatest_lower_bound(b,identity),X_20)) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_39,plain,
( greatest_lower_bound(b,greatest_lower_bound(identity,X_20)) != greatest_lower_bound(greatest_lower_bound(b,identity),X_20)
| greatest_lower_bound(b,greatest_lower_bound(identity,X_20)) = greatest_lower_bound(identity,X_20) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,identity),identity) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
greatest_lower_bound(b,greatest_lower_bound(identity,X_20)) = greatest_lower_bound(identity,X_20),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(identity,X_20)),greatest_lower_bound(greatest_lower_bound(b,identity),X_20)) )],[refute_0_11,refute_0_39]) ).
cnf(refute_0_41,plain,
( multiply(inverse(greatest_lower_bound(identity,X_20)),greatest_lower_bound(b,greatest_lower_bound(identity,X_20))) != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_20)),b))
| greatest_lower_bound(b,greatest_lower_bound(identity,X_20)) != greatest_lower_bound(identity,X_20)
| multiply(inverse(greatest_lower_bound(identity,X_20)),greatest_lower_bound(identity,X_20)) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_20)),b)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_20)),greatest_lower_bound(b,greatest_lower_bound(identity,X_20))),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_20)),b))) ),[0,1],$fot(greatest_lower_bound(identity,X_20))]]) ).
cnf(refute_0_42,plain,
( multiply(inverse(greatest_lower_bound(identity,X_20)),greatest_lower_bound(b,greatest_lower_bound(identity,X_20))) != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_20)),b))
| multiply(inverse(greatest_lower_bound(identity,X_20)),greatest_lower_bound(identity,X_20)) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_20)),b)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(identity,X_20)),greatest_lower_bound(identity,X_20)) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
multiply(inverse(greatest_lower_bound(identity,X_20)),greatest_lower_bound(identity,X_20)) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_20)),b)),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_20)),greatest_lower_bound(b,greatest_lower_bound(identity,X_20))),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_20)),b))) )],[refute_0_10,refute_0_42]) ).
cnf(refute_0_44,plain,
multiply(inverse(greatest_lower_bound(identity,X_20)),greatest_lower_bound(identity,X_20)) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(greatest_lower_bound(identity,X_20)))]]) ).
cnf(refute_0_45,plain,
( multiply(inverse(greatest_lower_bound(identity,X_20)),greatest_lower_bound(identity,X_20)) != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_20)),b))
| multiply(inverse(greatest_lower_bound(identity,X_20)),greatest_lower_bound(identity,X_20)) != identity
| identity = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_20)),b)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_20)),greatest_lower_bound(identity,X_20)),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_20)),b))) ),[0],$fot(identity)]]) ).
cnf(refute_0_46,plain,
( multiply(inverse(greatest_lower_bound(identity,X_20)),greatest_lower_bound(identity,X_20)) != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_20)),b))
| identity = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_20)),b)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_20)),greatest_lower_bound(identity,X_20)),identity) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
identity = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_20)),b)),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_20)),greatest_lower_bound(identity,X_20)),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_20)),b))) )],[refute_0_43,refute_0_46]) ).
cnf(refute_0_48,plain,
identity = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(a))),b)),
inference(subst,[],[refute_0_47:[bind(X_20,$fot(inverse(a)))]]) ).
cnf(refute_0_49,plain,
multiply(inverse(X_35),greatest_lower_bound(X_35,X_36)) = greatest_lower_bound(multiply(inverse(X_35),X_35),multiply(inverse(X_35),X_36)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(inverse(X_35))),bind(Y,$fot(X_35)),bind(Z,$fot(X_36))]]) ).
cnf(refute_0_50,plain,
multiply(inverse(X_35),X_35) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_35))]]) ).
cnf(refute_0_51,plain,
( multiply(inverse(X_35),X_35) != identity
| multiply(inverse(X_35),greatest_lower_bound(X_35,X_36)) != greatest_lower_bound(multiply(inverse(X_35),X_35),multiply(inverse(X_35),X_36))
| multiply(inverse(X_35),greatest_lower_bound(X_35,X_36)) = greatest_lower_bound(identity,multiply(inverse(X_35),X_36)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_35),greatest_lower_bound(X_35,X_36)),greatest_lower_bound(multiply(inverse(X_35),X_35),multiply(inverse(X_35),X_36))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_52,plain,
( multiply(inverse(X_35),greatest_lower_bound(X_35,X_36)) != greatest_lower_bound(multiply(inverse(X_35),X_35),multiply(inverse(X_35),X_36))
| multiply(inverse(X_35),greatest_lower_bound(X_35,X_36)) = greatest_lower_bound(identity,multiply(inverse(X_35),X_36)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_35),X_35),identity) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
multiply(inverse(X_35),greatest_lower_bound(X_35,X_36)) = greatest_lower_bound(identity,multiply(inverse(X_35),X_36)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_35),greatest_lower_bound(X_35,X_36)),greatest_lower_bound(multiply(inverse(X_35),X_35),multiply(inverse(X_35),X_36))) )],[refute_0_49,refute_0_52]) ).
cnf(refute_0_54,plain,
multiply(inverse(X_35),greatest_lower_bound(X_35,identity)) = greatest_lower_bound(identity,multiply(inverse(X_35),identity)),
inference(subst,[],[refute_0_53:[bind(X_36,$fot(identity))]]) ).
cnf(refute_0_55,plain,
multiply(greatest_lower_bound(X_40,identity),X_39) = greatest_lower_bound(multiply(X_40,X_39),multiply(identity,X_39)),
inference(subst,[],[monotony_glb2:[bind(X,$fot(X_39)),bind(Y,$fot(X_40)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_56,plain,
multiply(identity,X_39) = X_39,
inference(subst,[],[left_identity:[bind(X,$fot(X_39))]]) ).
cnf(refute_0_57,plain,
( multiply(greatest_lower_bound(X_40,identity),X_39) != greatest_lower_bound(multiply(X_40,X_39),multiply(identity,X_39))
| multiply(identity,X_39) != X_39
| multiply(greatest_lower_bound(X_40,identity),X_39) = greatest_lower_bound(multiply(X_40,X_39),X_39) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_40,identity),X_39),greatest_lower_bound(multiply(X_40,X_39),multiply(identity,X_39))) ),[1,1],$fot(X_39)]]) ).
cnf(refute_0_58,plain,
( multiply(greatest_lower_bound(X_40,identity),X_39) != greatest_lower_bound(multiply(X_40,X_39),multiply(identity,X_39))
| multiply(greatest_lower_bound(X_40,identity),X_39) = greatest_lower_bound(multiply(X_40,X_39),X_39) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_39),X_39) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
multiply(greatest_lower_bound(X_40,identity),X_39) = greatest_lower_bound(multiply(X_40,X_39),X_39),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_40,identity),X_39),greatest_lower_bound(multiply(X_40,X_39),multiply(identity,X_39))) )],[refute_0_55,refute_0_58]) ).
cnf(refute_0_60,plain,
greatest_lower_bound(multiply(X_40,X_39),X_39) = greatest_lower_bound(X_39,multiply(X_40,X_39)),
inference(subst,[],[refute_0_5:[bind(X_19,$fot(X_39)),bind(X_20,$fot(multiply(X_40,X_39)))]]) ).
cnf(refute_0_61,plain,
( multiply(greatest_lower_bound(X_40,identity),X_39) != greatest_lower_bound(multiply(X_40,X_39),X_39)
| greatest_lower_bound(multiply(X_40,X_39),X_39) != greatest_lower_bound(X_39,multiply(X_40,X_39))
| multiply(greatest_lower_bound(X_40,identity),X_39) = greatest_lower_bound(X_39,multiply(X_40,X_39)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_40,identity),X_39),greatest_lower_bound(X_39,multiply(X_40,X_39))) ),[0],$fot(greatest_lower_bound(multiply(X_40,X_39),X_39))]]) ).
cnf(refute_0_62,plain,
( multiply(greatest_lower_bound(X_40,identity),X_39) != greatest_lower_bound(multiply(X_40,X_39),X_39)
| multiply(greatest_lower_bound(X_40,identity),X_39) = greatest_lower_bound(X_39,multiply(X_40,X_39)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_40,X_39),X_39),greatest_lower_bound(X_39,multiply(X_40,X_39))) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
multiply(greatest_lower_bound(X_40,identity),X_39) = greatest_lower_bound(X_39,multiply(X_40,X_39)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_40,identity),X_39),greatest_lower_bound(multiply(X_40,X_39),X_39)) )],[refute_0_59,refute_0_62]) ).
cnf(refute_0_64,plain,
multiply(greatest_lower_bound(inverse(X_35),identity),identity) = greatest_lower_bound(identity,multiply(inverse(X_35),identity)),
inference(subst,[],[refute_0_63:[bind(X_39,$fot(identity)),bind(X_40,$fot(inverse(X_35)))]]) ).
cnf(refute_0_65,plain,
( multiply(greatest_lower_bound(inverse(X_35),identity),identity) != greatest_lower_bound(identity,multiply(inverse(X_35),identity))
| greatest_lower_bound(identity,multiply(inverse(X_35),identity)) = multiply(greatest_lower_bound(inverse(X_35),identity),identity) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(multiply(greatest_lower_bound(inverse(X_35),identity),identity))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(inverse(X_35),identity))))]]) ).
cnf(refute_0_66,plain,
greatest_lower_bound(identity,multiply(inverse(X_35),identity)) = multiply(greatest_lower_bound(inverse(X_35),identity),identity),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_35),identity),identity),greatest_lower_bound(identity,multiply(inverse(X_35),identity))) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
( multiply(inverse(X_35),greatest_lower_bound(X_35,identity)) != greatest_lower_bound(identity,multiply(inverse(X_35),identity))
| greatest_lower_bound(identity,multiply(inverse(X_35),identity)) != multiply(greatest_lower_bound(inverse(X_35),identity),identity)
| multiply(inverse(X_35),greatest_lower_bound(X_35,identity)) = multiply(greatest_lower_bound(inverse(X_35),identity),identity) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_35),greatest_lower_bound(X_35,identity)),multiply(greatest_lower_bound(inverse(X_35),identity),identity)) ),[0],$fot(greatest_lower_bound(identity,multiply(inverse(X_35),identity)))]]) ).
cnf(refute_0_68,plain,
( multiply(inverse(X_35),greatest_lower_bound(X_35,identity)) != greatest_lower_bound(identity,multiply(inverse(X_35),identity))
| multiply(inverse(X_35),greatest_lower_bound(X_35,identity)) = multiply(greatest_lower_bound(inverse(X_35),identity),identity) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(X_35),identity)),multiply(greatest_lower_bound(inverse(X_35),identity),identity)) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
multiply(inverse(X_35),greatest_lower_bound(X_35,identity)) = multiply(greatest_lower_bound(inverse(X_35),identity),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_35),greatest_lower_bound(X_35,identity)),greatest_lower_bound(identity,multiply(inverse(X_35),identity))) )],[refute_0_54,refute_0_68]) ).
cnf(refute_0_70,plain,
greatest_lower_bound(multiply(X_41,X_39),multiply(X_40,X_39)) = greatest_lower_bound(multiply(X_40,X_39),multiply(X_41,X_39)),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(multiply(X_41,X_39))),bind(Y,$fot(multiply(X_40,X_39)))]]) ).
cnf(refute_0_71,plain,
multiply(greatest_lower_bound(X_40,X_41),X_39) = greatest_lower_bound(multiply(X_40,X_39),multiply(X_41,X_39)),
inference(subst,[],[monotony_glb2:[bind(X,$fot(X_39)),bind(Y,$fot(X_40)),bind(Z,$fot(X_41))]]) ).
cnf(refute_0_72,plain,
( multiply(greatest_lower_bound(X_40,X_41),X_39) != greatest_lower_bound(multiply(X_40,X_39),multiply(X_41,X_39))
| greatest_lower_bound(multiply(X_40,X_39),multiply(X_41,X_39)) = multiply(greatest_lower_bound(X_40,X_41),X_39) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(multiply(greatest_lower_bound(X_40,X_41),X_39))),bind(Y0,$fot(greatest_lower_bound(multiply(X_40,X_39),multiply(X_41,X_39))))]]) ).
cnf(refute_0_73,plain,
greatest_lower_bound(multiply(X_40,X_39),multiply(X_41,X_39)) = multiply(greatest_lower_bound(X_40,X_41),X_39),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_40,X_41),X_39),greatest_lower_bound(multiply(X_40,X_39),multiply(X_41,X_39))) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
( greatest_lower_bound(multiply(X_40,X_39),multiply(X_41,X_39)) != multiply(greatest_lower_bound(X_40,X_41),X_39)
| greatest_lower_bound(multiply(X_41,X_39),multiply(X_40,X_39)) != greatest_lower_bound(multiply(X_40,X_39),multiply(X_41,X_39))
| greatest_lower_bound(multiply(X_41,X_39),multiply(X_40,X_39)) = multiply(greatest_lower_bound(X_40,X_41),X_39) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_41,X_39),multiply(X_40,X_39)),greatest_lower_bound(multiply(X_40,X_39),multiply(X_41,X_39))) ),[1],$fot(multiply(greatest_lower_bound(X_40,X_41),X_39))]]) ).
cnf(refute_0_75,plain,
( greatest_lower_bound(multiply(X_41,X_39),multiply(X_40,X_39)) != greatest_lower_bound(multiply(X_40,X_39),multiply(X_41,X_39))
| greatest_lower_bound(multiply(X_41,X_39),multiply(X_40,X_39)) = multiply(greatest_lower_bound(X_40,X_41),X_39) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_40,X_39),multiply(X_41,X_39)),multiply(greatest_lower_bound(X_40,X_41),X_39)) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
greatest_lower_bound(multiply(X_41,X_39),multiply(X_40,X_39)) = multiply(greatest_lower_bound(X_40,X_41),X_39),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_41,X_39),multiply(X_40,X_39)),greatest_lower_bound(multiply(X_40,X_39),multiply(X_41,X_39))) )],[refute_0_70,refute_0_75]) ).
cnf(refute_0_77,plain,
( multiply(greatest_lower_bound(Y,Z),X) != greatest_lower_bound(multiply(Y,X),multiply(Z,X))
| greatest_lower_bound(multiply(Y,X),multiply(Z,X)) = multiply(greatest_lower_bound(Y,Z),X) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(multiply(greatest_lower_bound(Y,Z),X))),bind(Y0,$fot(greatest_lower_bound(multiply(Y,X),multiply(Z,X))))]]) ).
cnf(refute_0_78,plain,
greatest_lower_bound(multiply(Y,X),multiply(Z,X)) = multiply(greatest_lower_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Y,X),multiply(Z,X))) )],[monotony_glb2,refute_0_77]) ).
cnf(refute_0_79,plain,
greatest_lower_bound(multiply(X_41,X_39),multiply(X_40,X_39)) = multiply(greatest_lower_bound(X_41,X_40),X_39),
inference(subst,[],[refute_0_78:[bind(X,$fot(X_39)),bind(Y,$fot(X_41)),bind(Z,$fot(X_40))]]) ).
cnf(refute_0_80,plain,
( greatest_lower_bound(multiply(X_41,X_39),multiply(X_40,X_39)) != multiply(greatest_lower_bound(X_40,X_41),X_39)
| greatest_lower_bound(multiply(X_41,X_39),multiply(X_40,X_39)) != multiply(greatest_lower_bound(X_41,X_40),X_39)
| multiply(greatest_lower_bound(X_41,X_40),X_39) = multiply(greatest_lower_bound(X_40,X_41),X_39) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_41,X_39),multiply(X_40,X_39)),multiply(greatest_lower_bound(X_40,X_41),X_39)) ),[0],$fot(multiply(greatest_lower_bound(X_41,X_40),X_39))]]) ).
cnf(refute_0_81,plain,
( greatest_lower_bound(multiply(X_41,X_39),multiply(X_40,X_39)) != multiply(greatest_lower_bound(X_40,X_41),X_39)
| multiply(greatest_lower_bound(X_41,X_40),X_39) = multiply(greatest_lower_bound(X_40,X_41),X_39) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_41,X_39),multiply(X_40,X_39)),multiply(greatest_lower_bound(X_41,X_40),X_39)) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
multiply(greatest_lower_bound(X_41,X_40),X_39) = multiply(greatest_lower_bound(X_40,X_41),X_39),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_41,X_39),multiply(X_40,X_39)),multiply(greatest_lower_bound(X_40,X_41),X_39)) )],[refute_0_76,refute_0_81]) ).
cnf(refute_0_83,plain,
( multiply(greatest_lower_bound(X_41,X_40),X_39) != multiply(greatest_lower_bound(X_40,X_41),X_39)
| multiply(greatest_lower_bound(X_40,X_41),X_39) = multiply(greatest_lower_bound(X_41,X_40),X_39) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(multiply(greatest_lower_bound(X_41,X_40),X_39))),bind(Y0,$fot(multiply(greatest_lower_bound(X_40,X_41),X_39)))]]) ).
cnf(refute_0_84,plain,
multiply(greatest_lower_bound(X_40,X_41),X_39) = multiply(greatest_lower_bound(X_41,X_40),X_39),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_41,X_40),X_39),multiply(greatest_lower_bound(X_40,X_41),X_39)) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
multiply(greatest_lower_bound(inverse(X_35),identity),identity) = multiply(greatest_lower_bound(identity,inverse(X_35)),identity),
inference(subst,[],[refute_0_84:[bind(X_39,$fot(identity)),bind(X_40,$fot(inverse(X_35))),bind(X_41,$fot(identity))]]) ).
cnf(refute_0_86,plain,
( multiply(greatest_lower_bound(inverse(X_35),identity),identity) != multiply(greatest_lower_bound(identity,inverse(X_35)),identity)
| multiply(inverse(X_35),greatest_lower_bound(X_35,identity)) != multiply(greatest_lower_bound(inverse(X_35),identity),identity)
| multiply(inverse(X_35),greatest_lower_bound(X_35,identity)) = multiply(greatest_lower_bound(identity,inverse(X_35)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_35),greatest_lower_bound(X_35,identity)),multiply(greatest_lower_bound(inverse(X_35),identity),identity)) ),[1],$fot(multiply(greatest_lower_bound(identity,inverse(X_35)),identity))]]) ).
cnf(refute_0_87,plain,
( multiply(inverse(X_35),greatest_lower_bound(X_35,identity)) != multiply(greatest_lower_bound(inverse(X_35),identity),identity)
| multiply(inverse(X_35),greatest_lower_bound(X_35,identity)) = multiply(greatest_lower_bound(identity,inverse(X_35)),identity) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_35),identity),identity),multiply(greatest_lower_bound(identity,inverse(X_35)),identity)) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
multiply(inverse(X_35),greatest_lower_bound(X_35,identity)) = multiply(greatest_lower_bound(identity,inverse(X_35)),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_35),greatest_lower_bound(X_35,identity)),multiply(greatest_lower_bound(inverse(X_35),identity),identity)) )],[refute_0_69,refute_0_87]) ).
cnf(refute_0_89,plain,
multiply(multiply(inverse(X_106),X_106),X_107) = multiply(inverse(X_106),multiply(X_106,X_107)),
inference(subst,[],[associativity:[bind(X,$fot(inverse(X_106))),bind(Y,$fot(X_106)),bind(Z,$fot(X_107))]]) ).
cnf(refute_0_90,plain,
multiply(inverse(X_106),X_106) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_106))]]) ).
cnf(refute_0_91,plain,
( multiply(multiply(inverse(X_106),X_106),X_107) != multiply(inverse(X_106),multiply(X_106,X_107))
| multiply(inverse(X_106),X_106) != identity
| multiply(identity,X_107) = multiply(inverse(X_106),multiply(X_106,X_107)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_106),X_106),X_107),multiply(inverse(X_106),multiply(X_106,X_107))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_92,plain,
( multiply(multiply(inverse(X_106),X_106),X_107) != multiply(inverse(X_106),multiply(X_106,X_107))
| multiply(identity,X_107) = multiply(inverse(X_106),multiply(X_106,X_107)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_106),X_106),identity) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
multiply(identity,X_107) = multiply(inverse(X_106),multiply(X_106,X_107)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_106),X_106),X_107),multiply(inverse(X_106),multiply(X_106,X_107))) )],[refute_0_89,refute_0_92]) ).
cnf(refute_0_94,plain,
multiply(identity,X_107) = X_107,
inference(subst,[],[left_identity:[bind(X,$fot(X_107))]]) ).
cnf(refute_0_95,plain,
( multiply(identity,X_107) != X_107
| multiply(identity,X_107) != multiply(inverse(X_106),multiply(X_106,X_107))
| X_107 = multiply(inverse(X_106),multiply(X_106,X_107)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_107),multiply(inverse(X_106),multiply(X_106,X_107))) ),[0],$fot(X_107)]]) ).
cnf(refute_0_96,plain,
( multiply(identity,X_107) != multiply(inverse(X_106),multiply(X_106,X_107))
| X_107 = multiply(inverse(X_106),multiply(X_106,X_107)) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_107),X_107) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
X_107 = multiply(inverse(X_106),multiply(X_106,X_107)),
inference(resolve,[$cnf( $equal(multiply(identity,X_107),multiply(inverse(X_106),multiply(X_106,X_107))) )],[refute_0_93,refute_0_96]) ).
cnf(refute_0_98,plain,
X_112 = multiply(inverse(inverse(X_112)),multiply(inverse(X_112),X_112)),
inference(subst,[],[refute_0_97:[bind(X_106,$fot(inverse(X_112))),bind(X_107,$fot(X_112))]]) ).
cnf(refute_0_99,plain,
multiply(inverse(X_112),X_112) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_112))]]) ).
cnf(refute_0_100,plain,
( X_112 != multiply(inverse(inverse(X_112)),multiply(inverse(X_112),X_112))
| multiply(inverse(X_112),X_112) != identity
| X_112 = multiply(inverse(inverse(X_112)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(X_112,multiply(inverse(inverse(X_112)),multiply(inverse(X_112),X_112))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_101,plain,
( X_112 != multiply(inverse(inverse(X_112)),multiply(inverse(X_112),X_112))
| X_112 = multiply(inverse(inverse(X_112)),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_112),X_112),identity) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
X_112 = multiply(inverse(inverse(X_112)),identity),
inference(resolve,[$cnf( $equal(X_112,multiply(inverse(inverse(X_112)),multiply(inverse(X_112),X_112))) )],[refute_0_98,refute_0_101]) ).
cnf(refute_0_103,plain,
multiply(X_111,X_112) = multiply(inverse(inverse(X_111)),multiply(inverse(X_111),multiply(X_111,X_112))),
inference(subst,[],[refute_0_97:[bind(X_106,$fot(inverse(X_111))),bind(X_107,$fot(multiply(X_111,X_112)))]]) ).
cnf(refute_0_104,plain,
X_112 = multiply(inverse(X_111),multiply(X_111,X_112)),
inference(subst,[],[refute_0_97:[bind(X_106,$fot(X_111)),bind(X_107,$fot(X_112))]]) ).
cnf(refute_0_105,plain,
( X_112 != multiply(inverse(X_111),multiply(X_111,X_112))
| multiply(inverse(X_111),multiply(X_111,X_112)) = X_112 ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(X_112)),bind(Y0,$fot(multiply(inverse(X_111),multiply(X_111,X_112))))]]) ).
cnf(refute_0_106,plain,
multiply(inverse(X_111),multiply(X_111,X_112)) = X_112,
inference(resolve,[$cnf( $equal(X_112,multiply(inverse(X_111),multiply(X_111,X_112))) )],[refute_0_104,refute_0_105]) ).
cnf(refute_0_107,plain,
( multiply(X_111,X_112) != multiply(inverse(inverse(X_111)),multiply(inverse(X_111),multiply(X_111,X_112)))
| multiply(inverse(X_111),multiply(X_111,X_112)) != X_112
| multiply(X_111,X_112) = multiply(inverse(inverse(X_111)),X_112) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_111,X_112),multiply(inverse(inverse(X_111)),multiply(inverse(X_111),multiply(X_111,X_112)))) ),[1,1],$fot(X_112)]]) ).
cnf(refute_0_108,plain,
( multiply(X_111,X_112) != multiply(inverse(inverse(X_111)),multiply(inverse(X_111),multiply(X_111,X_112)))
| multiply(X_111,X_112) = multiply(inverse(inverse(X_111)),X_112) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_111),multiply(X_111,X_112)),X_112) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
multiply(X_111,X_112) = multiply(inverse(inverse(X_111)),X_112),
inference(resolve,[$cnf( $equal(multiply(X_111,X_112),multiply(inverse(inverse(X_111)),multiply(inverse(X_111),multiply(X_111,X_112)))) )],[refute_0_103,refute_0_108]) ).
cnf(refute_0_110,plain,
( multiply(X_111,X_112) != multiply(inverse(inverse(X_111)),X_112)
| multiply(inverse(inverse(X_111)),X_112) = multiply(X_111,X_112) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(multiply(X_111,X_112))),bind(Y0,$fot(multiply(inverse(inverse(X_111)),X_112)))]]) ).
cnf(refute_0_111,plain,
multiply(inverse(inverse(X_111)),X_112) = multiply(X_111,X_112),
inference(resolve,[$cnf( $equal(multiply(X_111,X_112),multiply(inverse(inverse(X_111)),X_112)) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
multiply(inverse(inverse(X_112)),identity) = multiply(X_112,identity),
inference(subst,[],[refute_0_111:[bind(X_111,$fot(X_112)),bind(X_112,$fot(identity))]]) ).
cnf(refute_0_113,plain,
( X_112 != multiply(inverse(inverse(X_112)),identity)
| multiply(inverse(inverse(X_112)),identity) != multiply(X_112,identity)
| X_112 = multiply(X_112,identity) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_112,multiply(X_112,identity)) ),[0],$fot(multiply(inverse(inverse(X_112)),identity))]]) ).
cnf(refute_0_114,plain,
( X_112 != multiply(inverse(inverse(X_112)),identity)
| X_112 = multiply(X_112,identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_112)),identity),multiply(X_112,identity)) )],[refute_0_112,refute_0_113]) ).
cnf(refute_0_115,plain,
X_112 = multiply(X_112,identity),
inference(resolve,[$cnf( $equal(X_112,multiply(inverse(inverse(X_112)),identity)) )],[refute_0_102,refute_0_114]) ).
cnf(refute_0_116,plain,
( X_112 != multiply(X_112,identity)
| multiply(X_112,identity) = X_112 ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(X_112)),bind(Y0,$fot(multiply(X_112,identity)))]]) ).
cnf(refute_0_117,plain,
multiply(X_112,identity) = X_112,
inference(resolve,[$cnf( $equal(X_112,multiply(X_112,identity)) )],[refute_0_115,refute_0_116]) ).
cnf(refute_0_118,plain,
multiply(greatest_lower_bound(identity,inverse(X_35)),identity) = greatest_lower_bound(identity,inverse(X_35)),
inference(subst,[],[refute_0_117:[bind(X_112,$fot(greatest_lower_bound(identity,inverse(X_35))))]]) ).
cnf(refute_0_119,plain,
( multiply(greatest_lower_bound(identity,inverse(X_35)),identity) != greatest_lower_bound(identity,inverse(X_35))
| multiply(inverse(X_35),greatest_lower_bound(X_35,identity)) != multiply(greatest_lower_bound(identity,inverse(X_35)),identity)
| multiply(inverse(X_35),greatest_lower_bound(X_35,identity)) = greatest_lower_bound(identity,inverse(X_35)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_35),greatest_lower_bound(X_35,identity)),multiply(greatest_lower_bound(identity,inverse(X_35)),identity)) ),[1],$fot(greatest_lower_bound(identity,inverse(X_35)))]]) ).
cnf(refute_0_120,plain,
( multiply(inverse(X_35),greatest_lower_bound(X_35,identity)) != multiply(greatest_lower_bound(identity,inverse(X_35)),identity)
| multiply(inverse(X_35),greatest_lower_bound(X_35,identity)) = greatest_lower_bound(identity,inverse(X_35)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(X_35)),identity),greatest_lower_bound(identity,inverse(X_35))) )],[refute_0_118,refute_0_119]) ).
cnf(refute_0_121,plain,
multiply(inverse(X_35),greatest_lower_bound(X_35,identity)) = greatest_lower_bound(identity,inverse(X_35)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_35),greatest_lower_bound(X_35,identity)),multiply(greatest_lower_bound(identity,inverse(X_35)),identity)) )],[refute_0_88,refute_0_120]) ).
cnf(refute_0_122,plain,
multiply(inverse(a),greatest_lower_bound(a,identity)) = greatest_lower_bound(identity,inverse(a)),
inference(subst,[],[refute_0_121:[bind(X_35,$fot(a))]]) ).
cnf(refute_0_123,plain,
greatest_lower_bound(identity,least_upper_bound(a,identity)) = identity,
inference(subst,[],[refute_0_21:[bind(X_8,$fot(identity)),bind(X_9,$fot(a))]]) ).
cnf(refute_0_124,plain,
least_upper_bound(identity,a) = least_upper_bound(a,identity),
inference(subst,[],[refute_0_24:[bind(X,$fot(a)),bind(Y,$fot(identity))]]) ).
cnf(refute_0_125,plain,
( least_upper_bound(identity,a) != a
| least_upper_bound(identity,a) != least_upper_bound(a,identity)
| least_upper_bound(a,identity) = a ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,a),a) ),[0],$fot(least_upper_bound(a,identity))]]) ).
cnf(refute_0_126,plain,
( least_upper_bound(identity,a) != a
| least_upper_bound(a,identity) = a ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,a),least_upper_bound(a,identity)) )],[refute_0_124,refute_0_125]) ).
cnf(refute_0_127,plain,
least_upper_bound(a,identity) = a,
inference(resolve,[$cnf( $equal(least_upper_bound(identity,a),a) )],[p04c_1,refute_0_126]) ).
cnf(refute_0_128,plain,
( greatest_lower_bound(identity,least_upper_bound(a,identity)) != identity
| least_upper_bound(a,identity) != a
| greatest_lower_bound(identity,a) = identity ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(a,identity)),identity) ),[0,1],$fot(a)]]) ).
cnf(refute_0_129,plain,
( greatest_lower_bound(identity,least_upper_bound(a,identity)) != identity
| greatest_lower_bound(identity,a) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,identity),a) )],[refute_0_127,refute_0_128]) ).
cnf(refute_0_130,plain,
greatest_lower_bound(identity,a) = identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(a,identity)),identity) )],[refute_0_123,refute_0_129]) ).
cnf(refute_0_131,plain,
greatest_lower_bound(identity,a) = greatest_lower_bound(a,identity),
inference(subst,[],[refute_0_33:[bind(X,$fot(a)),bind(Y,$fot(identity))]]) ).
cnf(refute_0_132,plain,
( greatest_lower_bound(identity,a) != greatest_lower_bound(a,identity)
| greatest_lower_bound(identity,a) != identity
| greatest_lower_bound(a,identity) = identity ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,a),identity) ),[0],$fot(greatest_lower_bound(a,identity))]]) ).
cnf(refute_0_133,plain,
( greatest_lower_bound(identity,a) != identity
| greatest_lower_bound(a,identity) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,a),greatest_lower_bound(a,identity)) )],[refute_0_131,refute_0_132]) ).
cnf(refute_0_134,plain,
greatest_lower_bound(a,identity) = identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,a),identity) )],[refute_0_130,refute_0_133]) ).
cnf(refute_0_135,plain,
( multiply(inverse(a),greatest_lower_bound(a,identity)) != greatest_lower_bound(identity,inverse(a))
| greatest_lower_bound(a,identity) != identity
| multiply(inverse(a),identity) = greatest_lower_bound(identity,inverse(a)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(a),greatest_lower_bound(a,identity)),greatest_lower_bound(identity,inverse(a))) ),[0,1],$fot(identity)]]) ).
cnf(refute_0_136,plain,
( multiply(inverse(a),greatest_lower_bound(a,identity)) != greatest_lower_bound(identity,inverse(a))
| multiply(inverse(a),identity) = greatest_lower_bound(identity,inverse(a)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,identity),identity) )],[refute_0_134,refute_0_135]) ).
cnf(refute_0_137,plain,
multiply(inverse(a),identity) = greatest_lower_bound(identity,inverse(a)),
inference(resolve,[$cnf( $equal(multiply(inverse(a),greatest_lower_bound(a,identity)),greatest_lower_bound(identity,inverse(a))) )],[refute_0_122,refute_0_136]) ).
cnf(refute_0_138,plain,
multiply(inverse(a),identity) = inverse(a),
inference(subst,[],[refute_0_117:[bind(X_112,$fot(inverse(a)))]]) ).
cnf(refute_0_139,plain,
( multiply(inverse(a),identity) != greatest_lower_bound(identity,inverse(a))
| multiply(inverse(a),identity) != inverse(a)
| inverse(a) = greatest_lower_bound(identity,inverse(a)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(a),identity),greatest_lower_bound(identity,inverse(a))) ),[0],$fot(inverse(a))]]) ).
cnf(refute_0_140,plain,
( multiply(inverse(a),identity) != greatest_lower_bound(identity,inverse(a))
| inverse(a) = greatest_lower_bound(identity,inverse(a)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(a),identity),inverse(a)) )],[refute_0_138,refute_0_139]) ).
cnf(refute_0_141,plain,
inverse(a) = greatest_lower_bound(identity,inverse(a)),
inference(resolve,[$cnf( $equal(multiply(inverse(a),identity),greatest_lower_bound(identity,inverse(a))) )],[refute_0_137,refute_0_140]) ).
cnf(refute_0_142,plain,
( inverse(a) != greatest_lower_bound(identity,inverse(a))
| greatest_lower_bound(identity,inverse(a)) = inverse(a) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(inverse(a))),bind(Y0,$fot(greatest_lower_bound(identity,inverse(a))))]]) ).
cnf(refute_0_143,plain,
greatest_lower_bound(identity,inverse(a)) = inverse(a),
inference(resolve,[$cnf( $equal(inverse(a),greatest_lower_bound(identity,inverse(a))) )],[refute_0_141,refute_0_142]) ).
cnf(refute_0_144,plain,
( greatest_lower_bound(identity,inverse(a)) != inverse(a)
| identity != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(a))),b))
| identity = greatest_lower_bound(identity,multiply(inverse(inverse(a)),b)) ),
introduced(tautology,[equality,[$cnf( $equal(identity,greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(a))),b))) ),[1,1,0,0],$fot(inverse(a))]]) ).
cnf(refute_0_145,plain,
( identity != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(a))),b))
| identity = greatest_lower_bound(identity,multiply(inverse(inverse(a)),b)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(a)),inverse(a)) )],[refute_0_143,refute_0_144]) ).
cnf(refute_0_146,plain,
identity = greatest_lower_bound(identity,multiply(inverse(inverse(a)),b)),
inference(resolve,[$cnf( $equal(identity,greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(a))),b))) )],[refute_0_48,refute_0_145]) ).
cnf(refute_0_147,plain,
multiply(inverse(inverse(a)),b) = multiply(a,b),
inference(subst,[],[refute_0_111:[bind(X_111,$fot(a)),bind(X_112,$fot(b))]]) ).
cnf(refute_0_148,plain,
greatest_lower_bound(identity,multiply(inverse(inverse(a)),b)) = greatest_lower_bound(identity,multiply(inverse(inverse(a)),b)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,multiply(inverse(inverse(a)),b)))]]) ).
cnf(refute_0_149,plain,
( multiply(inverse(inverse(a)),b) != multiply(a,b)
| greatest_lower_bound(identity,multiply(inverse(inverse(a)),b)) != greatest_lower_bound(identity,multiply(inverse(inverse(a)),b))
| greatest_lower_bound(identity,multiply(inverse(inverse(a)),b)) = greatest_lower_bound(identity,multiply(a,b)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(inverse(a)),b)),greatest_lower_bound(identity,multiply(inverse(inverse(a)),b))) ),[1,1],$fot(multiply(a,b))]]) ).
cnf(refute_0_150,plain,
( multiply(inverse(inverse(a)),b) != multiply(a,b)
| greatest_lower_bound(identity,multiply(inverse(inverse(a)),b)) = greatest_lower_bound(identity,multiply(a,b)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(inverse(a)),b)),greatest_lower_bound(identity,multiply(inverse(inverse(a)),b))) )],[refute_0_148,refute_0_149]) ).
cnf(refute_0_151,plain,
greatest_lower_bound(identity,multiply(inverse(inverse(a)),b)) = greatest_lower_bound(identity,multiply(a,b)),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(a)),b),multiply(a,b)) )],[refute_0_147,refute_0_150]) ).
cnf(refute_0_152,plain,
( greatest_lower_bound(identity,multiply(inverse(inverse(a)),b)) != greatest_lower_bound(identity,multiply(a,b))
| identity != greatest_lower_bound(identity,multiply(inverse(inverse(a)),b))
| identity = greatest_lower_bound(identity,multiply(a,b)) ),
introduced(tautology,[equality,[$cnf( $equal(identity,greatest_lower_bound(identity,multiply(inverse(inverse(a)),b))) ),[1],$fot(greatest_lower_bound(identity,multiply(a,b)))]]) ).
cnf(refute_0_153,plain,
( identity != greatest_lower_bound(identity,multiply(inverse(inverse(a)),b))
| identity = greatest_lower_bound(identity,multiply(a,b)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(inverse(a)),b)),greatest_lower_bound(identity,multiply(a,b))) )],[refute_0_151,refute_0_152]) ).
cnf(refute_0_154,plain,
identity = greatest_lower_bound(identity,multiply(a,b)),
inference(resolve,[$cnf( $equal(identity,greatest_lower_bound(identity,multiply(inverse(inverse(a)),b))) )],[refute_0_146,refute_0_153]) ).
cnf(refute_0_155,plain,
( identity != greatest_lower_bound(identity,multiply(a,b))
| greatest_lower_bound(identity,multiply(a,b)) = identity ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(identity)),bind(Y0,$fot(greatest_lower_bound(identity,multiply(a,b))))]]) ).
cnf(refute_0_156,plain,
identity != greatest_lower_bound(identity,multiply(a,b)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(a,b)),identity) )],[refute_0_155,prove_p04c]) ).
cnf(refute_0_157,plain,
$false,
inference(resolve,[$cnf( $equal(identity,greatest_lower_bound(identity,multiply(a,b))) )],[refute_0_154,refute_0_156]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP171-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.13/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n023.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jun 13 08:46:51 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.79/1.00 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.79/1.00
% 0.79/1.00 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.85/1.01
%------------------------------------------------------------------------------