TSTP Solution File: GRP193-1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP193-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 10:37:56 EDT 2022
% Result : Unsatisfiable 1.75s 1.95s
% Output : CNFRefutation 1.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 41
% Syntax : Number of clauses : 142 ( 75 unt; 0 nHn; 115 RR)
% Number of literals : 240 ( 239 equ; 100 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 95 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
multiply(identity,X) = X ).
cnf(symmetry_of_glb,axiom,
greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ).
cnf(symmetry_of_lub,axiom,
least_upper_bound(X,Y) = least_upper_bound(Y,X) ).
cnf(associativity_of_glb,axiom,
greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) ).
cnf(lub_absorbtion,axiom,
least_upper_bound(X,greatest_lower_bound(X,Y)) = X ).
cnf(glb_absorbtion,axiom,
greatest_lower_bound(X,least_upper_bound(X,Y)) = X ).
cnf(monotony_glb2,axiom,
multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) ).
cnf(p8_9a_2,hypothesis,
least_upper_bound(identity,b) = b ).
cnf(p8_9a_4,hypothesis,
greatest_lower_bound(a,b) = identity ).
cnf(p8_9a_5,hypothesis,
least_upper_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)) ).
cnf(prove_p8_9a,negated_conjecture,
greatest_lower_bound(a,multiply(b,c)) != greatest_lower_bound(a,c) ).
cnf(refute_0_0,plain,
greatest_lower_bound(greatest_lower_bound(a,c),multiply(b,c)) = greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(greatest_lower_bound(a,c))),bind(Y,$fot(multiply(b,c)))]]) ).
cnf(refute_0_1,plain,
greatest_lower_bound(greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)),a) = greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c))),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)))),bind(Y,$fot(a))]]) ).
cnf(refute_0_2,plain,
greatest_lower_bound(X_12,least_upper_bound(X_12,X_13)) = X_12,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_12)),bind(Y,$fot(X_13))]]) ).
cnf(refute_0_3,plain,
least_upper_bound(X_13,X_12) = least_upper_bound(X_12,X_13),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_13)),bind(Y,$fot(X_12))]]) ).
cnf(refute_0_4,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_5,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_6,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
( least_upper_bound(X_13,X_12) != least_upper_bound(X_12,X_13)
| least_upper_bound(X_12,X_13) = least_upper_bound(X_13,X_12) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(least_upper_bound(X_13,X_12))),bind(Y0,$fot(least_upper_bound(X_12,X_13)))]]) ).
cnf(refute_0_8,plain,
least_upper_bound(X_12,X_13) = least_upper_bound(X_13,X_12),
inference(resolve,[$cnf( $equal(least_upper_bound(X_13,X_12),least_upper_bound(X_12,X_13)) )],[refute_0_3,refute_0_7]) ).
cnf(refute_0_9,plain,
( greatest_lower_bound(X_12,least_upper_bound(X_12,X_13)) != X_12
| least_upper_bound(X_12,X_13) != least_upper_bound(X_13,X_12)
| greatest_lower_bound(X_12,least_upper_bound(X_13,X_12)) = X_12 ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_12,least_upper_bound(X_12,X_13)),X_12) ),[0,1],$fot(least_upper_bound(X_13,X_12))]]) ).
cnf(refute_0_10,plain,
( greatest_lower_bound(X_12,least_upper_bound(X_12,X_13)) != X_12
| greatest_lower_bound(X_12,least_upper_bound(X_13,X_12)) = X_12 ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_12,X_13),least_upper_bound(X_13,X_12)) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
greatest_lower_bound(X_12,least_upper_bound(X_13,X_12)) = X_12,
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_12,least_upper_bound(X_12,X_13)),X_12) )],[refute_0_2,refute_0_10]) ).
cnf(refute_0_12,plain,
greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,multiply(b,c)))) = greatest_lower_bound(a,multiply(b,c)),
inference(subst,[],[refute_0_11:[bind(X_12,$fot(greatest_lower_bound(a,multiply(b,c)))),bind(X_13,$fot(greatest_lower_bound(a,c)))]]) ).
cnf(refute_0_13,plain,
( least_upper_bound(X,Y) != least_upper_bound(Y,X)
| least_upper_bound(Y,X) = least_upper_bound(X,Y) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(least_upper_bound(X,Y))),bind(Y0,$fot(least_upper_bound(Y,X)))]]) ).
cnf(refute_0_14,plain,
least_upper_bound(Y,X) = least_upper_bound(X,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(X,Y),least_upper_bound(Y,X)) )],[symmetry_of_lub,refute_0_13]) ).
cnf(refute_0_15,plain,
least_upper_bound(greatest_lower_bound(a,multiply(b,c)),greatest_lower_bound(a,c)) = least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,multiply(b,c))),
inference(subst,[],[refute_0_14:[bind(X,$fot(greatest_lower_bound(a,c))),bind(Y,$fot(greatest_lower_bound(a,multiply(b,c))))]]) ).
cnf(refute_0_16,plain,
multiply(identity,greatest_lower_bound(a,c)) = greatest_lower_bound(a,c),
inference(subst,[],[left_identity:[bind(X,$fot(greatest_lower_bound(a,c)))]]) ).
cnf(refute_0_17,plain,
multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)) = multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)))]]) ).
cnf(refute_0_18,plain,
( multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)) != multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))
| greatest_lower_bound(a,b) != identity
| multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)) = multiply(identity,greatest_lower_bound(a,c)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_19,plain,
( greatest_lower_bound(a,b) != identity
| multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)) = multiply(identity,greatest_lower_bound(a,c)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)) = multiply(identity,greatest_lower_bound(a,c)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,b),identity) )],[p8_9a_4,refute_0_19]) ).
cnf(refute_0_21,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_22,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_6,refute_0_21]) ).
cnf(refute_0_23,plain,
( multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)) != multiply(identity,greatest_lower_bound(a,c))
| multiply(identity,greatest_lower_bound(a,c)) != greatest_lower_bound(a,c)
| multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)) = greatest_lower_bound(a,c) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)))),bind(Y0,$fot(multiply(identity,greatest_lower_bound(a,c)))),bind(Z0,$fot(greatest_lower_bound(a,c)))]]) ).
cnf(refute_0_24,plain,
( multiply(identity,greatest_lower_bound(a,c)) != greatest_lower_bound(a,c)
| multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)) = greatest_lower_bound(a,c) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),multiply(identity,greatest_lower_bound(a,c))) )],[refute_0_20,refute_0_23]) ).
cnf(refute_0_25,plain,
multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)) = greatest_lower_bound(a,c),
inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(a,c)),greatest_lower_bound(a,c)) )],[refute_0_16,refute_0_24]) ).
cnf(refute_0_26,plain,
least_upper_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = least_upper_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))),
introduced(tautology,[refl,[$fot(least_upper_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))))]]) ).
cnf(refute_0_27,plain,
( multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)) != greatest_lower_bound(a,c)
| least_upper_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) != least_upper_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)))
| least_upper_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = least_upper_bound(greatest_lower_bound(a,multiply(b,c)),greatest_lower_bound(a,c)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))),least_upper_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)))) ),[1,1],$fot(greatest_lower_bound(a,c))]]) ).
cnf(refute_0_28,plain,
( multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)) != greatest_lower_bound(a,c)
| least_upper_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = least_upper_bound(greatest_lower_bound(a,multiply(b,c)),greatest_lower_bound(a,c)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))),least_upper_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)))) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
least_upper_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = least_upper_bound(greatest_lower_bound(a,multiply(b,c)),greatest_lower_bound(a,c)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),greatest_lower_bound(a,c)) )],[refute_0_25,refute_0_28]) ).
cnf(refute_0_30,plain,
( least_upper_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) != least_upper_bound(greatest_lower_bound(a,multiply(b,c)),greatest_lower_bound(a,c))
| least_upper_bound(greatest_lower_bound(a,multiply(b,c)),greatest_lower_bound(a,c)) != least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,multiply(b,c)))
| least_upper_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,multiply(b,c))) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(a,multiply(b,c)),greatest_lower_bound(a,c)))),bind(Z0,$fot(least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,multiply(b,c)))))]]) ).
cnf(refute_0_31,plain,
( least_upper_bound(greatest_lower_bound(a,multiply(b,c)),greatest_lower_bound(a,c)) != least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,multiply(b,c)))
| least_upper_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,multiply(b,c))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))),least_upper_bound(greatest_lower_bound(a,multiply(b,c)),greatest_lower_bound(a,c))) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
least_upper_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,multiply(b,c))),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,multiply(b,c)),greatest_lower_bound(a,c)),least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,multiply(b,c)))) )],[refute_0_15,refute_0_31]) ).
cnf(refute_0_33,plain,
( least_upper_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) != multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))
| least_upper_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) != least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,multiply(b,c)))
| least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,multiply(b,c))) = multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) ),[0],$fot(least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,multiply(b,c))))]]) ).
cnf(refute_0_34,plain,
( least_upper_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) != multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))
| least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,multiply(b,c))) = multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))),least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,multiply(b,c)))) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
( multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)) != greatest_lower_bound(a,c)
| least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,multiply(b,c))) != multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))
| least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,multiply(b,c))) = greatest_lower_bound(a,c) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,multiply(b,c))),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) ),[1],$fot(greatest_lower_bound(a,c))]]) ).
cnf(refute_0_36,plain,
( least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,multiply(b,c))) != multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))
| least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,multiply(b,c))) = greatest_lower_bound(a,c) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),greatest_lower_bound(a,c)) )],[refute_0_25,refute_0_35]) ).
cnf(refute_0_37,plain,
( least_upper_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) != multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))
| least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,multiply(b,c))) = greatest_lower_bound(a,c) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,multiply(b,c))),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) )],[refute_0_34,refute_0_36]) ).
cnf(refute_0_38,plain,
least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,multiply(b,c))) = greatest_lower_bound(a,c),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) )],[p8_9a_5,refute_0_37]) ).
cnf(refute_0_39,plain,
( greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,multiply(b,c)))) != greatest_lower_bound(a,multiply(b,c))
| least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,multiply(b,c))) != greatest_lower_bound(a,c)
| greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),greatest_lower_bound(a,c)) = greatest_lower_bound(a,multiply(b,c)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,multiply(b,c)))),greatest_lower_bound(a,multiply(b,c))) ),[0,1],$fot(greatest_lower_bound(a,c))]]) ).
cnf(refute_0_40,plain,
( greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,multiply(b,c)))) != greatest_lower_bound(a,multiply(b,c))
| greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),greatest_lower_bound(a,c)) = greatest_lower_bound(a,multiply(b,c)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,multiply(b,c))),greatest_lower_bound(a,c)) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),greatest_lower_bound(a,c)) = greatest_lower_bound(a,multiply(b,c)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,multiply(b,c)))),greatest_lower_bound(a,multiply(b,c))) )],[refute_0_12,refute_0_40]) ).
cnf(refute_0_42,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,Z)) != greatest_lower_bound(greatest_lower_bound(X,Y),Z)
| greatest_lower_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(Y,Z)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X,Y),Z)))]]) ).
cnf(refute_0_43,plain,
greatest_lower_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(greatest_lower_bound(X,Y),Z)) )],[associativity_of_glb,refute_0_42]) ).
cnf(refute_0_44,plain,
greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),greatest_lower_bound(a,c)) = greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c))),
inference(subst,[],[refute_0_43:[bind(X,$fot(a)),bind(Y,$fot(multiply(b,c))),bind(Z,$fot(greatest_lower_bound(a,c)))]]) ).
cnf(refute_0_45,plain,
( greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),greatest_lower_bound(a,c)) != greatest_lower_bound(a,multiply(b,c))
| greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),greatest_lower_bound(a,c)) != greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)))
| greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c))) = greatest_lower_bound(a,multiply(b,c)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),greatest_lower_bound(a,c)),greatest_lower_bound(a,multiply(b,c))) ),[0],$fot(greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c))))]]) ).
cnf(refute_0_46,plain,
( greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),greatest_lower_bound(a,c)) != greatest_lower_bound(a,multiply(b,c))
| greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c))) = greatest_lower_bound(a,multiply(b,c)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),greatest_lower_bound(a,c)),greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)))) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c))) = greatest_lower_bound(a,multiply(b,c)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),greatest_lower_bound(a,c)),greatest_lower_bound(a,multiply(b,c))) )],[refute_0_41,refute_0_46]) ).
cnf(refute_0_48,plain,
( greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c))) != greatest_lower_bound(a,multiply(b,c))
| greatest_lower_bound(greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)),a) != greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)))
| greatest_lower_bound(greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)),a) = greatest_lower_bound(a,multiply(b,c)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)),a),greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)))) ),[1],$fot(greatest_lower_bound(a,multiply(b,c)))]]) ).
cnf(refute_0_49,plain,
( greatest_lower_bound(greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)),a) != greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)))
| greatest_lower_bound(greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)),a) = greatest_lower_bound(a,multiply(b,c)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c))),greatest_lower_bound(a,multiply(b,c))) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
greatest_lower_bound(greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)),a) = greatest_lower_bound(a,multiply(b,c)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)),a),greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)))) )],[refute_0_1,refute_0_49]) ).
cnf(refute_0_51,plain,
greatest_lower_bound(greatest_lower_bound(X_17,Y),least_upper_bound(X_17,greatest_lower_bound(X_17,Y))) = greatest_lower_bound(X_17,Y),
inference(subst,[],[refute_0_11:[bind(X_12,$fot(greatest_lower_bound(X_17,Y))),bind(X_13,$fot(X_17))]]) ).
cnf(refute_0_52,plain,
least_upper_bound(X_17,greatest_lower_bound(X_17,Y)) = X_17,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_17))]]) ).
cnf(refute_0_53,plain,
( greatest_lower_bound(greatest_lower_bound(X_17,Y),least_upper_bound(X_17,greatest_lower_bound(X_17,Y))) != greatest_lower_bound(X_17,Y)
| least_upper_bound(X_17,greatest_lower_bound(X_17,Y)) != X_17
| greatest_lower_bound(greatest_lower_bound(X_17,Y),X_17) = greatest_lower_bound(X_17,Y) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_17,Y),least_upper_bound(X_17,greatest_lower_bound(X_17,Y))),greatest_lower_bound(X_17,Y)) ),[0,1],$fot(X_17)]]) ).
cnf(refute_0_54,plain,
( greatest_lower_bound(greatest_lower_bound(X_17,Y),least_upper_bound(X_17,greatest_lower_bound(X_17,Y))) != greatest_lower_bound(X_17,Y)
| greatest_lower_bound(greatest_lower_bound(X_17,Y),X_17) = greatest_lower_bound(X_17,Y) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,greatest_lower_bound(X_17,Y)),X_17) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
greatest_lower_bound(greatest_lower_bound(X_17,Y),X_17) = greatest_lower_bound(X_17,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_17,Y),least_upper_bound(X_17,greatest_lower_bound(X_17,Y))),greatest_lower_bound(X_17,Y)) )],[refute_0_51,refute_0_54]) ).
cnf(refute_0_56,plain,
greatest_lower_bound(greatest_lower_bound(X_17,Y),X_17) = greatest_lower_bound(X_17,greatest_lower_bound(Y,X_17)),
inference(subst,[],[refute_0_43:[bind(X,$fot(X_17)),bind(Z,$fot(X_17))]]) ).
cnf(refute_0_57,plain,
( greatest_lower_bound(greatest_lower_bound(X_17,Y),X_17) != greatest_lower_bound(X_17,Y)
| greatest_lower_bound(greatest_lower_bound(X_17,Y),X_17) != greatest_lower_bound(X_17,greatest_lower_bound(Y,X_17))
| greatest_lower_bound(X_17,greatest_lower_bound(Y,X_17)) = greatest_lower_bound(X_17,Y) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_17,Y),X_17),greatest_lower_bound(X_17,Y)) ),[0],$fot(greatest_lower_bound(X_17,greatest_lower_bound(Y,X_17)))]]) ).
cnf(refute_0_58,plain,
( greatest_lower_bound(greatest_lower_bound(X_17,Y),X_17) != greatest_lower_bound(X_17,Y)
| greatest_lower_bound(X_17,greatest_lower_bound(Y,X_17)) = greatest_lower_bound(X_17,Y) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_17,Y),X_17),greatest_lower_bound(X_17,greatest_lower_bound(Y,X_17))) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
greatest_lower_bound(X_17,greatest_lower_bound(Y,X_17)) = greatest_lower_bound(X_17,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_17,Y),X_17),greatest_lower_bound(X_17,Y)) )],[refute_0_55,refute_0_58]) ).
cnf(refute_0_60,plain,
greatest_lower_bound(a,greatest_lower_bound(c,a)) = greatest_lower_bound(a,c),
inference(subst,[],[refute_0_59:[bind(Y,$fot(c)),bind(X_17,$fot(a))]]) ).
cnf(refute_0_61,plain,
greatest_lower_bound(greatest_lower_bound(a,c),a) = greatest_lower_bound(a,greatest_lower_bound(c,a)),
inference(subst,[],[refute_0_43:[bind(X,$fot(a)),bind(Y,$fot(c)),bind(Z,$fot(a))]]) ).
cnf(refute_0_62,plain,
( greatest_lower_bound(a,greatest_lower_bound(c,a)) != greatest_lower_bound(a,c)
| greatest_lower_bound(greatest_lower_bound(a,c),a) != greatest_lower_bound(a,greatest_lower_bound(c,a))
| greatest_lower_bound(greatest_lower_bound(a,c),a) = greatest_lower_bound(a,c) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(a,c),a))),bind(Y0,$fot(greatest_lower_bound(a,greatest_lower_bound(c,a)))),bind(Z0,$fot(greatest_lower_bound(a,c)))]]) ).
cnf(refute_0_63,plain,
( greatest_lower_bound(a,greatest_lower_bound(c,a)) != greatest_lower_bound(a,c)
| greatest_lower_bound(greatest_lower_bound(a,c),a) = greatest_lower_bound(a,c) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,c),a),greatest_lower_bound(a,greatest_lower_bound(c,a))) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
greatest_lower_bound(greatest_lower_bound(a,c),a) = greatest_lower_bound(a,c),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(c,a)),greatest_lower_bound(a,c)) )],[refute_0_60,refute_0_63]) ).
cnf(refute_0_65,plain,
greatest_lower_bound(multiply(b,c),greatest_lower_bound(greatest_lower_bound(a,c),a)) = greatest_lower_bound(multiply(b,c),greatest_lower_bound(greatest_lower_bound(a,c),a)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(multiply(b,c),greatest_lower_bound(greatest_lower_bound(a,c),a)))]]) ).
cnf(refute_0_66,plain,
( greatest_lower_bound(multiply(b,c),greatest_lower_bound(greatest_lower_bound(a,c),a)) != greatest_lower_bound(multiply(b,c),greatest_lower_bound(greatest_lower_bound(a,c),a))
| greatest_lower_bound(greatest_lower_bound(a,c),a) != greatest_lower_bound(a,c)
| greatest_lower_bound(multiply(b,c),greatest_lower_bound(greatest_lower_bound(a,c),a)) = greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(b,c),greatest_lower_bound(greatest_lower_bound(a,c),a)),greatest_lower_bound(multiply(b,c),greatest_lower_bound(greatest_lower_bound(a,c),a))) ),[1,1],$fot(greatest_lower_bound(a,c))]]) ).
cnf(refute_0_67,plain,
( greatest_lower_bound(greatest_lower_bound(a,c),a) != greatest_lower_bound(a,c)
| greatest_lower_bound(multiply(b,c),greatest_lower_bound(greatest_lower_bound(a,c),a)) = greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(b,c),greatest_lower_bound(greatest_lower_bound(a,c),a)),greatest_lower_bound(multiply(b,c),greatest_lower_bound(greatest_lower_bound(a,c),a))) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
greatest_lower_bound(multiply(b,c),greatest_lower_bound(greatest_lower_bound(a,c),a)) = greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,c),a),greatest_lower_bound(a,c)) )],[refute_0_64,refute_0_67]) ).
cnf(refute_0_69,plain,
greatest_lower_bound(greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)),a) = greatest_lower_bound(multiply(b,c),greatest_lower_bound(greatest_lower_bound(a,c),a)),
inference(subst,[],[refute_0_43:[bind(X,$fot(multiply(b,c))),bind(Y,$fot(greatest_lower_bound(a,c))),bind(Z,$fot(a))]]) ).
cnf(refute_0_70,plain,
( greatest_lower_bound(multiply(b,c),greatest_lower_bound(greatest_lower_bound(a,c),a)) != greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c))
| greatest_lower_bound(greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)),a) != greatest_lower_bound(multiply(b,c),greatest_lower_bound(greatest_lower_bound(a,c),a))
| greatest_lower_bound(greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)),a) = greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)),a))),bind(Y0,$fot(greatest_lower_bound(multiply(b,c),greatest_lower_bound(greatest_lower_bound(a,c),a)))),bind(Z0,$fot(greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c))))]]) ).
cnf(refute_0_71,plain,
( greatest_lower_bound(multiply(b,c),greatest_lower_bound(greatest_lower_bound(a,c),a)) != greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c))
| greatest_lower_bound(greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)),a) = greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)),a),greatest_lower_bound(multiply(b,c),greatest_lower_bound(greatest_lower_bound(a,c),a))) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
greatest_lower_bound(greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)),a) = greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(b,c),greatest_lower_bound(greatest_lower_bound(a,c),a)),greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c))) )],[refute_0_68,refute_0_71]) ).
cnf(refute_0_73,plain,
( greatest_lower_bound(greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)),a) != greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c))
| greatest_lower_bound(greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)),a) != greatest_lower_bound(a,multiply(b,c))
| greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)) = greatest_lower_bound(a,multiply(b,c)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)),a),greatest_lower_bound(a,multiply(b,c))) ),[0],$fot(greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)))]]) ).
cnf(refute_0_74,plain,
( greatest_lower_bound(greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)),a) != greatest_lower_bound(a,multiply(b,c))
| greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)) = greatest_lower_bound(a,multiply(b,c)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)),a),greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c))) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)) = greatest_lower_bound(a,multiply(b,c)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)),a),greatest_lower_bound(a,multiply(b,c))) )],[refute_0_50,refute_0_74]) ).
cnf(refute_0_76,plain,
( greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)) != greatest_lower_bound(a,multiply(b,c))
| greatest_lower_bound(greatest_lower_bound(a,c),multiply(b,c)) != greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c))
| greatest_lower_bound(greatest_lower_bound(a,c),multiply(b,c)) = greatest_lower_bound(a,multiply(b,c)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,c),multiply(b,c)),greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c))) ),[1],$fot(greatest_lower_bound(a,multiply(b,c)))]]) ).
cnf(refute_0_77,plain,
( greatest_lower_bound(greatest_lower_bound(a,c),multiply(b,c)) != greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c))
| greatest_lower_bound(greatest_lower_bound(a,c),multiply(b,c)) = greatest_lower_bound(a,multiply(b,c)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)),greatest_lower_bound(a,multiply(b,c))) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
greatest_lower_bound(greatest_lower_bound(a,c),multiply(b,c)) = greatest_lower_bound(a,multiply(b,c)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,c),multiply(b,c)),greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c))) )],[refute_0_0,refute_0_77]) ).
cnf(refute_0_79,plain,
greatest_lower_bound(greatest_lower_bound(a,c),multiply(b,c)) = greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))),
inference(subst,[],[refute_0_43:[bind(X,$fot(a)),bind(Y,$fot(c)),bind(Z,$fot(multiply(b,c)))]]) ).
cnf(refute_0_80,plain,
( greatest_lower_bound(greatest_lower_bound(a,c),multiply(b,c)) != greatest_lower_bound(a,multiply(b,c))
| greatest_lower_bound(greatest_lower_bound(a,c),multiply(b,c)) != greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c)))
| greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))) = greatest_lower_bound(a,multiply(b,c)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,c),multiply(b,c)),greatest_lower_bound(a,multiply(b,c))) ),[0],$fot(greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))))]]) ).
cnf(refute_0_81,plain,
( greatest_lower_bound(greatest_lower_bound(a,c),multiply(b,c)) != greatest_lower_bound(a,multiply(b,c))
| greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))) = greatest_lower_bound(a,multiply(b,c)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,c),multiply(b,c)),greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c)))) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))) = greatest_lower_bound(a,multiply(b,c)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,c),multiply(b,c)),greatest_lower_bound(a,multiply(b,c))) )],[refute_0_78,refute_0_81]) ).
cnf(refute_0_83,plain,
multiply(identity,c) = c,
inference(subst,[],[left_identity:[bind(X,$fot(c))]]) ).
cnf(refute_0_84,plain,
greatest_lower_bound(identity,least_upper_bound(b,identity)) = identity,
inference(subst,[],[refute_0_11:[bind(X_12,$fot(identity)),bind(X_13,$fot(b))]]) ).
cnf(refute_0_85,plain,
least_upper_bound(identity,b) = least_upper_bound(b,identity),
inference(subst,[],[refute_0_14:[bind(X,$fot(b)),bind(Y,$fot(identity))]]) ).
cnf(refute_0_86,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_87,plain,
( least_upper_bound(identity,b) != b
| least_upper_bound(b,identity) = b ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,b),least_upper_bound(b,identity)) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
least_upper_bound(b,identity) = b,
inference(resolve,[$cnf( $equal(least_upper_bound(identity,b),b) )],[p8_9a_2,refute_0_87]) ).
cnf(refute_0_89,plain,
( greatest_lower_bound(identity,least_upper_bound(b,identity)) != identity
| least_upper_bound(b,identity) != b
| greatest_lower_bound(identity,b) = identity ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(b,identity)),identity) ),[0,1],$fot(b)]]) ).
cnf(refute_0_90,plain,
( greatest_lower_bound(identity,least_upper_bound(b,identity)) != identity
| greatest_lower_bound(identity,b) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,identity),b) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
greatest_lower_bound(identity,b) = identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(b,identity)),identity) )],[refute_0_84,refute_0_90]) ).
cnf(refute_0_92,plain,
( greatest_lower_bound(X,Y) != greatest_lower_bound(Y,X)
| greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(greatest_lower_bound(X,Y))),bind(Y0,$fot(greatest_lower_bound(Y,X)))]]) ).
cnf(refute_0_93,plain,
greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X)) )],[symmetry_of_glb,refute_0_92]) ).
cnf(refute_0_94,plain,
greatest_lower_bound(identity,b) = greatest_lower_bound(b,identity),
inference(subst,[],[refute_0_93:[bind(X,$fot(b)),bind(Y,$fot(identity))]]) ).
cnf(refute_0_95,plain,
( greatest_lower_bound(identity,b) != greatest_lower_bound(b,identity)
| greatest_lower_bound(identity,b) != identity
| greatest_lower_bound(b,identity) = identity ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,b),identity) ),[0],$fot(greatest_lower_bound(b,identity))]]) ).
cnf(refute_0_96,plain,
( greatest_lower_bound(identity,b) != identity
| greatest_lower_bound(b,identity) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,b),greatest_lower_bound(b,identity)) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
greatest_lower_bound(b,identity) = identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,b),identity) )],[refute_0_91,refute_0_96]) ).
cnf(refute_0_98,plain,
multiply(greatest_lower_bound(b,identity),c) = multiply(greatest_lower_bound(b,identity),c),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(b,identity),c))]]) ).
cnf(refute_0_99,plain,
( multiply(greatest_lower_bound(b,identity),c) != multiply(greatest_lower_bound(b,identity),c)
| greatest_lower_bound(b,identity) != identity
| multiply(greatest_lower_bound(b,identity),c) = multiply(identity,c) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(b,identity),c),multiply(greatest_lower_bound(b,identity),c)) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_100,plain,
( greatest_lower_bound(b,identity) != identity
| multiply(greatest_lower_bound(b,identity),c) = multiply(identity,c) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(b,identity),c),multiply(greatest_lower_bound(b,identity),c)) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
multiply(greatest_lower_bound(b,identity),c) = multiply(identity,c),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,identity),identity) )],[refute_0_97,refute_0_100]) ).
cnf(refute_0_102,plain,
( multiply(greatest_lower_bound(b,identity),c) != multiply(identity,c)
| multiply(identity,c) != c
| multiply(greatest_lower_bound(b,identity),c) = c ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(multiply(greatest_lower_bound(b,identity),c))),bind(Y0,$fot(multiply(identity,c))),bind(Z0,$fot(c))]]) ).
cnf(refute_0_103,plain,
( multiply(identity,c) != c
| multiply(greatest_lower_bound(b,identity),c) = c ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(b,identity),c),multiply(identity,c)) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
multiply(greatest_lower_bound(b,identity),c) = c,
inference(resolve,[$cnf( $equal(multiply(identity,c),c) )],[refute_0_83,refute_0_103]) ).
cnf(refute_0_105,plain,
multiply(greatest_lower_bound(X_158,identity),X_157) = greatest_lower_bound(multiply(X_158,X_157),multiply(identity,X_157)),
inference(subst,[],[monotony_glb2:[bind(X,$fot(X_157)),bind(Y,$fot(X_158)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_106,plain,
multiply(identity,X_157) = X_157,
inference(subst,[],[left_identity:[bind(X,$fot(X_157))]]) ).
cnf(refute_0_107,plain,
( multiply(greatest_lower_bound(X_158,identity),X_157) != greatest_lower_bound(multiply(X_158,X_157),multiply(identity,X_157))
| multiply(identity,X_157) != X_157
| multiply(greatest_lower_bound(X_158,identity),X_157) = greatest_lower_bound(multiply(X_158,X_157),X_157) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_158,identity),X_157),greatest_lower_bound(multiply(X_158,X_157),multiply(identity,X_157))) ),[1,1],$fot(X_157)]]) ).
cnf(refute_0_108,plain,
( multiply(greatest_lower_bound(X_158,identity),X_157) != greatest_lower_bound(multiply(X_158,X_157),multiply(identity,X_157))
| multiply(greatest_lower_bound(X_158,identity),X_157) = greatest_lower_bound(multiply(X_158,X_157),X_157) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_157),X_157) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
multiply(greatest_lower_bound(X_158,identity),X_157) = greatest_lower_bound(multiply(X_158,X_157),X_157),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_158,identity),X_157),greatest_lower_bound(multiply(X_158,X_157),multiply(identity,X_157))) )],[refute_0_105,refute_0_108]) ).
cnf(refute_0_110,plain,
greatest_lower_bound(X_52,X_51) = greatest_lower_bound(X_51,X_52),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_52)),bind(Y,$fot(X_51))]]) ).
cnf(refute_0_111,plain,
greatest_lower_bound(multiply(X_158,X_157),X_157) = greatest_lower_bound(X_157,multiply(X_158,X_157)),
inference(subst,[],[refute_0_110:[bind(X_51,$fot(X_157)),bind(X_52,$fot(multiply(X_158,X_157)))]]) ).
cnf(refute_0_112,plain,
( multiply(greatest_lower_bound(X_158,identity),X_157) != greatest_lower_bound(multiply(X_158,X_157),X_157)
| greatest_lower_bound(multiply(X_158,X_157),X_157) != greatest_lower_bound(X_157,multiply(X_158,X_157))
| multiply(greatest_lower_bound(X_158,identity),X_157) = greatest_lower_bound(X_157,multiply(X_158,X_157)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_158,identity),X_157),greatest_lower_bound(X_157,multiply(X_158,X_157))) ),[0],$fot(greatest_lower_bound(multiply(X_158,X_157),X_157))]]) ).
cnf(refute_0_113,plain,
( multiply(greatest_lower_bound(X_158,identity),X_157) != greatest_lower_bound(multiply(X_158,X_157),X_157)
| multiply(greatest_lower_bound(X_158,identity),X_157) = greatest_lower_bound(X_157,multiply(X_158,X_157)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_158,X_157),X_157),greatest_lower_bound(X_157,multiply(X_158,X_157))) )],[refute_0_111,refute_0_112]) ).
cnf(refute_0_114,plain,
multiply(greatest_lower_bound(X_158,identity),X_157) = greatest_lower_bound(X_157,multiply(X_158,X_157)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_158,identity),X_157),greatest_lower_bound(multiply(X_158,X_157),X_157)) )],[refute_0_109,refute_0_113]) ).
cnf(refute_0_115,plain,
( multiply(greatest_lower_bound(X_158,identity),X_157) != greatest_lower_bound(X_157,multiply(X_158,X_157))
| greatest_lower_bound(X_157,multiply(X_158,X_157)) = multiply(greatest_lower_bound(X_158,identity),X_157) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(multiply(greatest_lower_bound(X_158,identity),X_157))),bind(Y0,$fot(greatest_lower_bound(X_157,multiply(X_158,X_157))))]]) ).
cnf(refute_0_116,plain,
greatest_lower_bound(X_157,multiply(X_158,X_157)) = multiply(greatest_lower_bound(X_158,identity),X_157),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_158,identity),X_157),greatest_lower_bound(X_157,multiply(X_158,X_157))) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
greatest_lower_bound(c,multiply(b,c)) = multiply(greatest_lower_bound(b,identity),c),
inference(subst,[],[refute_0_116:[bind(X_157,$fot(c)),bind(X_158,$fot(b))]]) ).
cnf(refute_0_118,plain,
( multiply(greatest_lower_bound(b,identity),c) != c
| greatest_lower_bound(c,multiply(b,c)) != multiply(greatest_lower_bound(b,identity),c)
| greatest_lower_bound(c,multiply(b,c)) = c ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(greatest_lower_bound(c,multiply(b,c)))),bind(Y0,$fot(multiply(greatest_lower_bound(b,identity),c))),bind(Z0,$fot(c))]]) ).
cnf(refute_0_119,plain,
( multiply(greatest_lower_bound(b,identity),c) != c
| greatest_lower_bound(c,multiply(b,c)) = c ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(c,multiply(b,c)),multiply(greatest_lower_bound(b,identity),c)) )],[refute_0_117,refute_0_118]) ).
cnf(refute_0_120,plain,
greatest_lower_bound(c,multiply(b,c)) = c,
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(b,identity),c),c) )],[refute_0_104,refute_0_119]) ).
cnf(refute_0_121,plain,
greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))) = greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))))]]) ).
cnf(refute_0_122,plain,
( greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))) != greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c)))
| greatest_lower_bound(c,multiply(b,c)) != c
| greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))) = greatest_lower_bound(a,c) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))),greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c)))) ),[1,1],$fot(c)]]) ).
cnf(refute_0_123,plain,
( greatest_lower_bound(c,multiply(b,c)) != c
| greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))) = greatest_lower_bound(a,c) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))),greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c)))) )],[refute_0_121,refute_0_122]) ).
cnf(refute_0_124,plain,
greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))) = greatest_lower_bound(a,c),
inference(resolve,[$cnf( $equal(greatest_lower_bound(c,multiply(b,c)),c) )],[refute_0_120,refute_0_123]) ).
cnf(refute_0_125,plain,
( greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))) != greatest_lower_bound(a,multiply(b,c))
| greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))) != greatest_lower_bound(a,c)
| greatest_lower_bound(a,c) = greatest_lower_bound(a,multiply(b,c)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))),greatest_lower_bound(a,multiply(b,c))) ),[0],$fot(greatest_lower_bound(a,c))]]) ).
cnf(refute_0_126,plain,
( greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))) != greatest_lower_bound(a,multiply(b,c))
| greatest_lower_bound(a,c) = greatest_lower_bound(a,multiply(b,c)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))),greatest_lower_bound(a,c)) )],[refute_0_124,refute_0_125]) ).
cnf(refute_0_127,plain,
greatest_lower_bound(a,c) = greatest_lower_bound(a,multiply(b,c)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))),greatest_lower_bound(a,multiply(b,c))) )],[refute_0_82,refute_0_126]) ).
cnf(refute_0_128,plain,
( greatest_lower_bound(a,c) != greatest_lower_bound(a,multiply(b,c))
| greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(a,c) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(greatest_lower_bound(a,c))),bind(Y0,$fot(greatest_lower_bound(a,multiply(b,c))))]]) ).
cnf(refute_0_129,plain,
greatest_lower_bound(a,c) != greatest_lower_bound(a,multiply(b,c)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,multiply(b,c)),greatest_lower_bound(a,c)) )],[refute_0_128,prove_p8_9a]) ).
cnf(refute_0_130,plain,
$false,
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,c),greatest_lower_bound(a,multiply(b,c))) )],[refute_0_127,refute_0_129]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP193-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 06:02:39 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.75/1.95 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.75/1.95
% 1.75/1.95 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 1.75/1.96
%------------------------------------------------------------------------------