TSTP Solution File: GRP193-2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP193-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n021.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 10:37:57 EDT 2022
% Result : Unsatisfiable 6.88s 7.04s
% Output : CNFRefutation 6.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 57
% Syntax : Number of clauses : 196 ( 102 unt; 0 nHn; 176 RR)
% Number of literals : 335 ( 334 equ; 141 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; 4 con; 0-2 aty)
% Number of variables : 71 ( 4 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_9b_2,hypothesis,
greatest_lower_bound(identity,b) = identity ).
cnf(p8_9b_4,hypothesis,
greatest_lower_bound(a,b) = identity ).
cnf(p8_9b_5,hypothesis,
greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = greatest_lower_bound(a,multiply(b,c)) ).
cnf(prove_p8_9b,negated_conjecture,
greatest_lower_bound(a,multiply(b,c)) != greatest_lower_bound(a,c) ).
cnf(refute_0_0,plain,
greatest_lower_bound(X_10,least_upper_bound(X_10,X_11)) = X_10,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_10)),bind(Y,$fot(X_11))]]) ).
cnf(refute_0_1,plain,
least_upper_bound(X_11,X_10) = least_upper_bound(X_10,X_11),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_11)),bind(Y,$fot(X_10))]]) ).
cnf(refute_0_2,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_3,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_4,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( least_upper_bound(X_11,X_10) != least_upper_bound(X_10,X_11)
| least_upper_bound(X_10,X_11) = least_upper_bound(X_11,X_10) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(least_upper_bound(X_11,X_10))),bind(Y0,$fot(least_upper_bound(X_10,X_11)))]]) ).
cnf(refute_0_6,plain,
least_upper_bound(X_10,X_11) = least_upper_bound(X_11,X_10),
inference(resolve,[$cnf( $equal(least_upper_bound(X_11,X_10),least_upper_bound(X_10,X_11)) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
( greatest_lower_bound(X_10,least_upper_bound(X_10,X_11)) != X_10
| least_upper_bound(X_10,X_11) != least_upper_bound(X_11,X_10)
| greatest_lower_bound(X_10,least_upper_bound(X_11,X_10)) = X_10 ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_10,least_upper_bound(X_10,X_11)),X_10) ),[0,1],$fot(least_upper_bound(X_11,X_10))]]) ).
cnf(refute_0_8,plain,
( greatest_lower_bound(X_10,least_upper_bound(X_10,X_11)) != X_10
| greatest_lower_bound(X_10,least_upper_bound(X_11,X_10)) = X_10 ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_10,X_11),least_upper_bound(X_11,X_10)) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
greatest_lower_bound(X_10,least_upper_bound(X_11,X_10)) = X_10,
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_10,least_upper_bound(X_10,X_11)),X_10) )],[refute_0_0,refute_0_8]) ).
cnf(refute_0_10,plain,
greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),least_upper_bound(c,greatest_lower_bound(a,multiply(b,c)))) = greatest_lower_bound(a,multiply(b,c)),
inference(subst,[],[refute_0_9:[bind(X_10,$fot(greatest_lower_bound(a,multiply(b,c)))),bind(X_11,$fot(c))]]) ).
cnf(refute_0_11,plain,
least_upper_bound(c,greatest_lower_bound(c,greatest_lower_bound(a,greatest_lower_bound(a,multiply(b,c))))) = c,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(c)),bind(Y,$fot(greatest_lower_bound(a,greatest_lower_bound(a,multiply(b,c)))))]]) ).
cnf(refute_0_12,plain,
greatest_lower_bound(greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c))),a) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c)))),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c))))),bind(Y,$fot(a))]]) ).
cnf(refute_0_13,plain,
greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))),a) = greatest_lower_bound(a,greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c)))),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))))),bind(Y,$fot(a))]]) ).
cnf(refute_0_14,plain,
greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(a,c)),multiply(b,c)) = greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,greatest_lower_bound(a,c))),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(greatest_lower_bound(a,greatest_lower_bound(a,c)))),bind(Y,$fot(multiply(b,c)))]]) ).
cnf(refute_0_15,plain,
greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c))) = greatest_lower_bound(greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)),a),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(a)),bind(Y,$fot(greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c))))]]) ).
cnf(refute_0_16,plain,
multiply(identity,greatest_lower_bound(a,c)) = greatest_lower_bound(a,c),
inference(subst,[],[left_identity:[bind(X,$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( $equal(greatest_lower_bound(a,b),identity) )],[p8_9b_4,refute_0_19]) ).
cnf(refute_0_21,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_22,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_4,refute_0_21]) ).
cnf(refute_0_23,plain,
( multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)) != multiply(identity,greatest_lower_bound(a,c))
| multiply(identity,greatest_lower_bound(a,c)) != greatest_lower_bound(a,c)
| multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)) = greatest_lower_bound(a,c) ),
inference(subst,[],[refute_0_22:[bind(X0,$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( $equal(multiply(identity,greatest_lower_bound(a,c)),greatest_lower_bound(a,c)) )],[refute_0_16,refute_0_24]) ).
cnf(refute_0_26,plain,
greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(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)
| greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) != greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)))
| greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))),greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)))) ),[1,1],$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)
| greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))),greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)))) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),greatest_lower_bound(a,c)) )],[refute_0_25,refute_0_28]) ).
cnf(refute_0_30,plain,
greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)))) = greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)))))]]) ).
cnf(refute_0_31,plain,
( greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) != greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c))
| greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)))) != greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))))
| greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)))) = greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)))),greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))))) ),[1,1],$fot(greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)))]]) ).
cnf(refute_0_32,plain,
( greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) != greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c))
| greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)))) = greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)))),greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))))) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)))) = greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))),greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c))) )],[refute_0_29,refute_0_32]) ).
cnf(refute_0_34,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,Z)) != greatest_lower_bound(greatest_lower_bound(X,Y),Z)
| greatest_lower_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(Y,Z)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X,Y),Z)))]]) ).
cnf(refute_0_35,plain,
greatest_lower_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(greatest_lower_bound(X,Y),Z)) )],[associativity_of_glb,refute_0_34]) ).
cnf(refute_0_36,plain,
greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)))),
inference(subst,[],[refute_0_35:[bind(X,$fot(a)),bind(Y,$fot(multiply(b,c))),bind(Z,$fot(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))))]]) ).
cnf(refute_0_37,plain,
( greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)))) != greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)))
| greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) != greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))))
| greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c))) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))))),bind(Y0,$fot(greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)))))),bind(Z0,$fot(greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)))))]]) ).
cnf(refute_0_38,plain,
( greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)))) != greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)))
| greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))),greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))))) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)))),greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)))) )],[refute_0_33,refute_0_38]) ).
cnf(refute_0_40,plain,
( greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) != greatest_lower_bound(a,multiply(b,c))
| greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) != greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)))
| greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c))) = greatest_lower_bound(a,multiply(b,c)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))),greatest_lower_bound(a,multiply(b,c))) ),[0],$fot(greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c))))]]) ).
cnf(refute_0_41,plain,
( greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),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( $equal(greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))),greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)))) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c))) = greatest_lower_bound(a,multiply(b,c)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))),greatest_lower_bound(a,multiply(b,c))) )],[p8_9b_5,refute_0_41]) ).
cnf(refute_0_43,plain,
( greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c))) != greatest_lower_bound(a,multiply(b,c))
| greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c))) != greatest_lower_bound(greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)),a)
| greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)),a) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c))),greatest_lower_bound(greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)),a)) ),[0],$fot(greatest_lower_bound(a,multiply(b,c)))]]) ).
cnf(refute_0_44,plain,
( 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)) = greatest_lower_bound(greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)),a) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c))),greatest_lower_bound(a,multiply(b,c))) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)),a),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c))),greatest_lower_bound(greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)),a)) )],[refute_0_15,refute_0_44]) ).
cnf(refute_0_46,plain,
( greatest_lower_bound(X,Y) != greatest_lower_bound(Y,X)
| greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(greatest_lower_bound(X,Y))),bind(Y0,$fot(greatest_lower_bound(Y,X)))]]) ).
cnf(refute_0_47,plain,
greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X)) )],[symmetry_of_glb,refute_0_46]) ).
cnf(refute_0_48,plain,
greatest_lower_bound(c,a) = greatest_lower_bound(a,c),
inference(subst,[],[refute_0_47:[bind(X,$fot(a)),bind(Y,$fot(c))]]) ).
cnf(refute_0_49,plain,
greatest_lower_bound(a,greatest_lower_bound(c,a)) = greatest_lower_bound(a,greatest_lower_bound(c,a)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(a,greatest_lower_bound(c,a)))]]) ).
cnf(refute_0_50,plain,
( greatest_lower_bound(a,greatest_lower_bound(c,a)) != greatest_lower_bound(a,greatest_lower_bound(c,a))
| greatest_lower_bound(c,a) != greatest_lower_bound(a,c)
| greatest_lower_bound(a,greatest_lower_bound(c,a)) = greatest_lower_bound(a,greatest_lower_bound(a,c)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(c,a)),greatest_lower_bound(a,greatest_lower_bound(c,a))) ),[1,1],$fot(greatest_lower_bound(a,c))]]) ).
cnf(refute_0_51,plain,
( greatest_lower_bound(c,a) != greatest_lower_bound(a,c)
| greatest_lower_bound(a,greatest_lower_bound(c,a)) = greatest_lower_bound(a,greatest_lower_bound(a,c)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(c,a)),greatest_lower_bound(a,greatest_lower_bound(c,a))) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
greatest_lower_bound(a,greatest_lower_bound(c,a)) = greatest_lower_bound(a,greatest_lower_bound(a,c)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(c,a),greatest_lower_bound(a,c)) )],[refute_0_48,refute_0_51]) ).
cnf(refute_0_53,plain,
greatest_lower_bound(greatest_lower_bound(a,c),a) = greatest_lower_bound(a,greatest_lower_bound(c,a)),
inference(subst,[],[refute_0_35:[bind(X,$fot(a)),bind(Y,$fot(c)),bind(Z,$fot(a))]]) ).
cnf(refute_0_54,plain,
( greatest_lower_bound(a,greatest_lower_bound(c,a)) != greatest_lower_bound(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,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,$fot(greatest_lower_bound(a,greatest_lower_bound(a,c))))]]) ).
cnf(refute_0_55,plain,
( greatest_lower_bound(a,greatest_lower_bound(c,a)) != greatest_lower_bound(a,greatest_lower_bound(a,c))
| greatest_lower_bound(greatest_lower_bound(a,c),a) = greatest_lower_bound(a,greatest_lower_bound(a,c)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,c),a),greatest_lower_bound(a,greatest_lower_bound(c,a))) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
greatest_lower_bound(greatest_lower_bound(a,c),a) = greatest_lower_bound(a,greatest_lower_bound(a,c)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(c,a)),greatest_lower_bound(a,greatest_lower_bound(a,c))) )],[refute_0_52,refute_0_55]) ).
cnf(refute_0_57,plain,
greatest_lower_bound(multiply(b,c),greatest_lower_bound(greatest_lower_bound(a,c),a)) = greatest_lower_bound(multiply(b,c),greatest_lower_bound(greatest_lower_bound(a,c),a)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(multiply(b,c),greatest_lower_bound(greatest_lower_bound(a,c),a)))]]) ).
cnf(refute_0_58,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,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,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,greatest_lower_bound(a,c)))]]) ).
cnf(refute_0_59,plain,
( greatest_lower_bound(greatest_lower_bound(a,c),a) != greatest_lower_bound(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,greatest_lower_bound(a,c))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(b,c),greatest_lower_bound(greatest_lower_bound(a,c),a)),greatest_lower_bound(multiply(b,c),greatest_lower_bound(greatest_lower_bound(a,c),a))) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
greatest_lower_bound(multiply(b,c),greatest_lower_bound(greatest_lower_bound(a,c),a)) = greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,greatest_lower_bound(a,c))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,c),a),greatest_lower_bound(a,greatest_lower_bound(a,c))) )],[refute_0_56,refute_0_59]) ).
cnf(refute_0_61,plain,
greatest_lower_bound(greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)),a) = greatest_lower_bound(multiply(b,c),greatest_lower_bound(greatest_lower_bound(a,c),a)),
inference(subst,[],[refute_0_35:[bind(X,$fot(multiply(b,c))),bind(Y,$fot(greatest_lower_bound(a,c))),bind(Z,$fot(a))]]) ).
cnf(refute_0_62,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,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,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,$fot(greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,greatest_lower_bound(a,c)))))]]) ).
cnf(refute_0_63,plain,
( greatest_lower_bound(multiply(b,c),greatest_lower_bound(greatest_lower_bound(a,c),a)) != greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,greatest_lower_bound(a,c)))
| greatest_lower_bound(greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)),a) = greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,greatest_lower_bound(a,c))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)),a),greatest_lower_bound(multiply(b,c),greatest_lower_bound(greatest_lower_bound(a,c),a))) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
greatest_lower_bound(greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)),a) = greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,greatest_lower_bound(a,c))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(b,c),greatest_lower_bound(greatest_lower_bound(a,c),a)),greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,greatest_lower_bound(a,c)))) )],[refute_0_60,refute_0_63]) ).
cnf(refute_0_65,plain,
( greatest_lower_bound(a,multiply(b,c)) != greatest_lower_bound(greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)),a)
| greatest_lower_bound(greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)),a) != greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,greatest_lower_bound(a,c)))
| greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,greatest_lower_bound(a,c))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(a,multiply(b,c)),greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,greatest_lower_bound(a,c)))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)),a))]]) ).
cnf(refute_0_66,plain,
( 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,multiply(b,c)) = greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,greatest_lower_bound(a,c))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)),a),greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,greatest_lower_bound(a,c)))) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,greatest_lower_bound(a,c))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,multiply(b,c)),greatest_lower_bound(greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)),a)) )],[refute_0_45,refute_0_66]) ).
cnf(refute_0_68,plain,
( greatest_lower_bound(a,multiply(b,c)) != greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,greatest_lower_bound(a,c)))
| greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,greatest_lower_bound(a,c))) = greatest_lower_bound(a,multiply(b,c)) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(greatest_lower_bound(a,multiply(b,c)))),bind(Y0,$fot(greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,greatest_lower_bound(a,c)))))]]) ).
cnf(refute_0_69,plain,
greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,greatest_lower_bound(a,c))) = greatest_lower_bound(a,multiply(b,c)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,multiply(b,c)),greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,greatest_lower_bound(a,c)))) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
( greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,greatest_lower_bound(a,c))) != greatest_lower_bound(a,multiply(b,c))
| greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(a,c)),multiply(b,c)) != greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,greatest_lower_bound(a,c)))
| greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(a,c)),multiply(b,c)) = greatest_lower_bound(a,multiply(b,c)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(a,c)),multiply(b,c)),greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,greatest_lower_bound(a,c)))) ),[1],$fot(greatest_lower_bound(a,multiply(b,c)))]]) ).
cnf(refute_0_71,plain,
( greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(a,c)),multiply(b,c)) != greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,greatest_lower_bound(a,c)))
| greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(a,c)),multiply(b,c)) = greatest_lower_bound(a,multiply(b,c)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,greatest_lower_bound(a,c))),greatest_lower_bound(a,multiply(b,c))) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(a,c)),multiply(b,c)) = greatest_lower_bound(a,multiply(b,c)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(a,c)),multiply(b,c)),greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,greatest_lower_bound(a,c)))) )],[refute_0_14,refute_0_71]) ).
cnf(refute_0_73,plain,
greatest_lower_bound(greatest_lower_bound(a,c),multiply(b,c)) = greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))),
inference(subst,[],[refute_0_35:[bind(X,$fot(a)),bind(Y,$fot(c)),bind(Z,$fot(multiply(b,c)))]]) ).
cnf(refute_0_74,plain,
greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(a,c),multiply(b,c))) = greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(a,c),multiply(b,c))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(a,c),multiply(b,c))))]]) ).
cnf(refute_0_75,plain,
( greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(a,c),multiply(b,c))) != greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(a,c),multiply(b,c)))
| greatest_lower_bound(greatest_lower_bound(a,c),multiply(b,c)) != greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c)))
| greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(a,c),multiply(b,c))) = greatest_lower_bound(a,greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c)))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(a,c),multiply(b,c))),greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(a,c),multiply(b,c)))) ),[1,1],$fot(greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))))]]) ).
cnf(refute_0_76,plain,
( 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(greatest_lower_bound(a,c),multiply(b,c))) = greatest_lower_bound(a,greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(a,c),multiply(b,c))),greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(a,c),multiply(b,c)))) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(a,c),multiply(b,c))) = greatest_lower_bound(a,greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c)))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,c),multiply(b,c)),greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c)))) )],[refute_0_73,refute_0_76]) ).
cnf(refute_0_78,plain,
greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(a,c)),multiply(b,c)) = greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(a,c),multiply(b,c))),
inference(subst,[],[refute_0_35:[bind(X,$fot(a)),bind(Y,$fot(greatest_lower_bound(a,c))),bind(Z,$fot(multiply(b,c)))]]) ).
cnf(refute_0_79,plain,
( greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(a,c),multiply(b,c))) != greatest_lower_bound(a,greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))))
| greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(a,c)),multiply(b,c)) != greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(a,c),multiply(b,c)))
| greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(a,c)),multiply(b,c)) = greatest_lower_bound(a,greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c)))) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(a,c)),multiply(b,c)))),bind(Y0,$fot(greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(a,c),multiply(b,c))))),bind(Z0,$fot(greatest_lower_bound(a,greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))))))]]) ).
cnf(refute_0_80,plain,
( greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(a,c),multiply(b,c))) != greatest_lower_bound(a,greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))))
| greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(a,c)),multiply(b,c)) = greatest_lower_bound(a,greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(a,c)),multiply(b,c)),greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(a,c),multiply(b,c)))) )],[refute_0_78,refute_0_79]) ).
cnf(refute_0_81,plain,
greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(a,c)),multiply(b,c)) = greatest_lower_bound(a,greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c)))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(a,c),multiply(b,c))),greatest_lower_bound(a,greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))))) )],[refute_0_77,refute_0_80]) ).
cnf(refute_0_82,plain,
( greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(a,c)),multiply(b,c)) != greatest_lower_bound(a,multiply(b,c))
| greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(a,c)),multiply(b,c)) != greatest_lower_bound(a,greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))))
| greatest_lower_bound(a,greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c)))) = greatest_lower_bound(a,multiply(b,c)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(a,c)),multiply(b,c)),greatest_lower_bound(a,multiply(b,c))) ),[0],$fot(greatest_lower_bound(a,greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c)))))]]) ).
cnf(refute_0_83,plain,
( greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(a,c)),multiply(b,c)) != greatest_lower_bound(a,multiply(b,c))
| greatest_lower_bound(a,greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c)))) = greatest_lower_bound(a,multiply(b,c)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(a,c)),multiply(b,c)),greatest_lower_bound(a,greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))))) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
greatest_lower_bound(a,greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c)))) = greatest_lower_bound(a,multiply(b,c)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(a,c)),multiply(b,c)),greatest_lower_bound(a,multiply(b,c))) )],[refute_0_72,refute_0_83]) ).
cnf(refute_0_85,plain,
( greatest_lower_bound(a,greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c)))) != greatest_lower_bound(a,multiply(b,c))
| greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))),a) != greatest_lower_bound(a,greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))))
| greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))),a) = greatest_lower_bound(a,multiply(b,c)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))),a),greatest_lower_bound(a,greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))))) ),[1],$fot(greatest_lower_bound(a,multiply(b,c)))]]) ).
cnf(refute_0_86,plain,
( greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))),a) != greatest_lower_bound(a,greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))))
| greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))),a) = greatest_lower_bound(a,multiply(b,c)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c)))),greatest_lower_bound(a,multiply(b,c))) )],[refute_0_84,refute_0_85]) ).
cnf(refute_0_87,plain,
greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))),a) = greatest_lower_bound(a,multiply(b,c)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))),a),greatest_lower_bound(a,greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))))) )],[refute_0_13,refute_0_86]) ).
cnf(refute_0_88,plain,
greatest_lower_bound(multiply(b,c),a) = greatest_lower_bound(a,multiply(b,c)),
inference(subst,[],[refute_0_47:[bind(X,$fot(a)),bind(Y,$fot(multiply(b,c)))]]) ).
cnf(refute_0_89,plain,
greatest_lower_bound(c,greatest_lower_bound(multiply(b,c),a)) = greatest_lower_bound(c,greatest_lower_bound(multiply(b,c),a)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(c,greatest_lower_bound(multiply(b,c),a)))]]) ).
cnf(refute_0_90,plain,
( greatest_lower_bound(multiply(b,c),a) != greatest_lower_bound(a,multiply(b,c))
| greatest_lower_bound(c,greatest_lower_bound(multiply(b,c),a)) != greatest_lower_bound(c,greatest_lower_bound(multiply(b,c),a))
| greatest_lower_bound(c,greatest_lower_bound(multiply(b,c),a)) = greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(c,greatest_lower_bound(multiply(b,c),a)),greatest_lower_bound(c,greatest_lower_bound(multiply(b,c),a))) ),[1,1],$fot(greatest_lower_bound(a,multiply(b,c)))]]) ).
cnf(refute_0_91,plain,
( greatest_lower_bound(multiply(b,c),a) != greatest_lower_bound(a,multiply(b,c))
| greatest_lower_bound(c,greatest_lower_bound(multiply(b,c),a)) = greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(c,greatest_lower_bound(multiply(b,c),a)),greatest_lower_bound(c,greatest_lower_bound(multiply(b,c),a))) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
greatest_lower_bound(c,greatest_lower_bound(multiply(b,c),a)) = greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(b,c),a),greatest_lower_bound(a,multiply(b,c))) )],[refute_0_88,refute_0_91]) ).
cnf(refute_0_93,plain,
greatest_lower_bound(greatest_lower_bound(c,multiply(b,c)),a) = greatest_lower_bound(c,greatest_lower_bound(multiply(b,c),a)),
inference(subst,[],[refute_0_35:[bind(X,$fot(c)),bind(Y,$fot(multiply(b,c))),bind(Z,$fot(a))]]) ).
cnf(refute_0_94,plain,
( greatest_lower_bound(c,greatest_lower_bound(multiply(b,c),a)) != greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c)))
| greatest_lower_bound(greatest_lower_bound(c,multiply(b,c)),a) != greatest_lower_bound(c,greatest_lower_bound(multiply(b,c),a))
| greatest_lower_bound(greatest_lower_bound(c,multiply(b,c)),a) = greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c))) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(c,multiply(b,c)),a))),bind(Y0,$fot(greatest_lower_bound(c,greatest_lower_bound(multiply(b,c),a)))),bind(Z0,$fot(greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c)))))]]) ).
cnf(refute_0_95,plain,
( greatest_lower_bound(c,greatest_lower_bound(multiply(b,c),a)) != greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c)))
| greatest_lower_bound(greatest_lower_bound(c,multiply(b,c)),a) = greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(c,multiply(b,c)),a),greatest_lower_bound(c,greatest_lower_bound(multiply(b,c),a))) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
greatest_lower_bound(greatest_lower_bound(c,multiply(b,c)),a) = greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(c,greatest_lower_bound(multiply(b,c),a)),greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c)))) )],[refute_0_92,refute_0_95]) ).
cnf(refute_0_97,plain,
greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,multiply(b,c)),a)) = greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,multiply(b,c)),a)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,multiply(b,c)),a)))]]) ).
cnf(refute_0_98,plain,
( greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,multiply(b,c)),a)) != greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,multiply(b,c)),a))
| greatest_lower_bound(greatest_lower_bound(c,multiply(b,c)),a) != greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c)))
| greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,multiply(b,c)),a)) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c)))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,multiply(b,c)),a)),greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,multiply(b,c)),a))) ),[1,1],$fot(greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c))))]]) ).
cnf(refute_0_99,plain,
( greatest_lower_bound(greatest_lower_bound(c,multiply(b,c)),a) != greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c)))
| greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,multiply(b,c)),a)) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,multiply(b,c)),a)),greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,multiply(b,c)),a))) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,multiply(b,c)),a)) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c)))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(c,multiply(b,c)),a),greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c)))) )],[refute_0_96,refute_0_99]) ).
cnf(refute_0_101,plain,
greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))),a) = greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,multiply(b,c)),a)),
inference(subst,[],[refute_0_35:[bind(X,$fot(a)),bind(Y,$fot(greatest_lower_bound(c,multiply(b,c)))),bind(Z,$fot(a))]]) ).
cnf(refute_0_102,plain,
( greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,multiply(b,c)),a)) != greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c))))
| greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))),a) != greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,multiply(b,c)),a))
| greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))),a) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c)))) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))),a))),bind(Y0,$fot(greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,multiply(b,c)),a)))),bind(Z0,$fot(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c))))))]]) ).
cnf(refute_0_103,plain,
( greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,multiply(b,c)),a)) != greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c))))
| greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))),a) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))),a),greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,multiply(b,c)),a))) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))),a) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c)))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,multiply(b,c)),a)),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c))))) )],[refute_0_100,refute_0_103]) ).
cnf(refute_0_105,plain,
( greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))),a) != greatest_lower_bound(a,multiply(b,c))
| greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))),a) != greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c))))
| greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c)))) = greatest_lower_bound(a,multiply(b,c)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))),a),greatest_lower_bound(a,multiply(b,c))) ),[0],$fot(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c)))))]]) ).
cnf(refute_0_106,plain,
( greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))),a) != greatest_lower_bound(a,multiply(b,c))
| greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c)))) = greatest_lower_bound(a,multiply(b,c)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))),a),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c))))) )],[refute_0_104,refute_0_105]) ).
cnf(refute_0_107,plain,
greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c)))) = greatest_lower_bound(a,multiply(b,c)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))),a),greatest_lower_bound(a,multiply(b,c))) )],[refute_0_87,refute_0_106]) ).
cnf(refute_0_108,plain,
( greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c)))) != greatest_lower_bound(a,multiply(b,c))
| greatest_lower_bound(greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c))),a) != greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c))))
| greatest_lower_bound(greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c))),a) = greatest_lower_bound(a,multiply(b,c)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c))),a),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c))))) ),[1],$fot(greatest_lower_bound(a,multiply(b,c)))]]) ).
cnf(refute_0_109,plain,
( greatest_lower_bound(greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c))),a) != greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c))))
| greatest_lower_bound(greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c))),a) = greatest_lower_bound(a,multiply(b,c)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c)))),greatest_lower_bound(a,multiply(b,c))) )],[refute_0_107,refute_0_108]) ).
cnf(refute_0_110,plain,
greatest_lower_bound(greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c))),a) = greatest_lower_bound(a,multiply(b,c)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c))),a),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c))))) )],[refute_0_12,refute_0_109]) ).
cnf(refute_0_111,plain,
greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),a)) = greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),a)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),a)))]]) ).
cnf(refute_0_112,plain,
( greatest_lower_bound(multiply(b,c),a) != greatest_lower_bound(a,multiply(b,c))
| greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),a)) != greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),a))
| greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),a)) = greatest_lower_bound(a,greatest_lower_bound(a,multiply(b,c))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),a)),greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),a))) ),[1,1],$fot(greatest_lower_bound(a,multiply(b,c)))]]) ).
cnf(refute_0_113,plain,
( greatest_lower_bound(multiply(b,c),a) != greatest_lower_bound(a,multiply(b,c))
| greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),a)) = greatest_lower_bound(a,greatest_lower_bound(a,multiply(b,c))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),a)),greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),a))) )],[refute_0_111,refute_0_112]) ).
cnf(refute_0_114,plain,
greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),a)) = greatest_lower_bound(a,greatest_lower_bound(a,multiply(b,c))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(b,c),a),greatest_lower_bound(a,multiply(b,c))) )],[refute_0_88,refute_0_113]) ).
cnf(refute_0_115,plain,
greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),a) = greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),a)),
inference(subst,[],[refute_0_35:[bind(X,$fot(a)),bind(Y,$fot(multiply(b,c))),bind(Z,$fot(a))]]) ).
cnf(refute_0_116,plain,
( greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),a)) != greatest_lower_bound(a,greatest_lower_bound(a,multiply(b,c)))
| greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),a) != greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),a))
| greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),a) = greatest_lower_bound(a,greatest_lower_bound(a,multiply(b,c))) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),a))),bind(Y0,$fot(greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),a)))),bind(Z0,$fot(greatest_lower_bound(a,greatest_lower_bound(a,multiply(b,c)))))]]) ).
cnf(refute_0_117,plain,
( greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),a)) != greatest_lower_bound(a,greatest_lower_bound(a,multiply(b,c)))
| greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),a) = greatest_lower_bound(a,greatest_lower_bound(a,multiply(b,c))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),a),greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),a))) )],[refute_0_115,refute_0_116]) ).
cnf(refute_0_118,plain,
greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),a) = greatest_lower_bound(a,greatest_lower_bound(a,multiply(b,c))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),a)),greatest_lower_bound(a,greatest_lower_bound(a,multiply(b,c)))) )],[refute_0_114,refute_0_117]) ).
cnf(refute_0_119,plain,
greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),a)) = greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),a)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),a)))]]) ).
cnf(refute_0_120,plain,
( greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),a)) != greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),a))
| greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),a) != greatest_lower_bound(a,greatest_lower_bound(a,multiply(b,c)))
| greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),a)) = greatest_lower_bound(c,greatest_lower_bound(a,greatest_lower_bound(a,multiply(b,c)))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),a)),greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),a))) ),[1,1],$fot(greatest_lower_bound(a,greatest_lower_bound(a,multiply(b,c))))]]) ).
cnf(refute_0_121,plain,
( greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),a) != greatest_lower_bound(a,greatest_lower_bound(a,multiply(b,c)))
| greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),a)) = greatest_lower_bound(c,greatest_lower_bound(a,greatest_lower_bound(a,multiply(b,c)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),a)),greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),a))) )],[refute_0_119,refute_0_120]) ).
cnf(refute_0_122,plain,
greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),a)) = greatest_lower_bound(c,greatest_lower_bound(a,greatest_lower_bound(a,multiply(b,c)))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),a),greatest_lower_bound(a,greatest_lower_bound(a,multiply(b,c)))) )],[refute_0_118,refute_0_121]) ).
cnf(refute_0_123,plain,
greatest_lower_bound(greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c))),a) = greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),a)),
inference(subst,[],[refute_0_35:[bind(X,$fot(c)),bind(Y,$fot(greatest_lower_bound(a,multiply(b,c)))),bind(Z,$fot(a))]]) ).
cnf(refute_0_124,plain,
( greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),a)) != greatest_lower_bound(c,greatest_lower_bound(a,greatest_lower_bound(a,multiply(b,c))))
| greatest_lower_bound(greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c))),a) != greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),a))
| greatest_lower_bound(greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c))),a) = greatest_lower_bound(c,greatest_lower_bound(a,greatest_lower_bound(a,multiply(b,c)))) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c))),a))),bind(Y0,$fot(greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),a)))),bind(Z0,$fot(greatest_lower_bound(c,greatest_lower_bound(a,greatest_lower_bound(a,multiply(b,c))))))]]) ).
cnf(refute_0_125,plain,
( greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),a)) != greatest_lower_bound(c,greatest_lower_bound(a,greatest_lower_bound(a,multiply(b,c))))
| greatest_lower_bound(greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c))),a) = greatest_lower_bound(c,greatest_lower_bound(a,greatest_lower_bound(a,multiply(b,c)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c))),a),greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),a))) )],[refute_0_123,refute_0_124]) ).
cnf(refute_0_126,plain,
greatest_lower_bound(greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c))),a) = greatest_lower_bound(c,greatest_lower_bound(a,greatest_lower_bound(a,multiply(b,c)))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),a)),greatest_lower_bound(c,greatest_lower_bound(a,greatest_lower_bound(a,multiply(b,c))))) )],[refute_0_122,refute_0_125]) ).
cnf(refute_0_127,plain,
( greatest_lower_bound(greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c))),a) != greatest_lower_bound(a,multiply(b,c))
| greatest_lower_bound(greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c))),a) != greatest_lower_bound(c,greatest_lower_bound(a,greatest_lower_bound(a,multiply(b,c))))
| greatest_lower_bound(c,greatest_lower_bound(a,greatest_lower_bound(a,multiply(b,c)))) = greatest_lower_bound(a,multiply(b,c)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c))),a),greatest_lower_bound(a,multiply(b,c))) ),[0],$fot(greatest_lower_bound(c,greatest_lower_bound(a,greatest_lower_bound(a,multiply(b,c)))))]]) ).
cnf(refute_0_128,plain,
( greatest_lower_bound(greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c))),a) != greatest_lower_bound(a,multiply(b,c))
| greatest_lower_bound(c,greatest_lower_bound(a,greatest_lower_bound(a,multiply(b,c)))) = greatest_lower_bound(a,multiply(b,c)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c))),a),greatest_lower_bound(c,greatest_lower_bound(a,greatest_lower_bound(a,multiply(b,c))))) )],[refute_0_126,refute_0_127]) ).
cnf(refute_0_129,plain,
greatest_lower_bound(c,greatest_lower_bound(a,greatest_lower_bound(a,multiply(b,c)))) = greatest_lower_bound(a,multiply(b,c)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(c,greatest_lower_bound(a,multiply(b,c))),a),greatest_lower_bound(a,multiply(b,c))) )],[refute_0_110,refute_0_128]) ).
cnf(refute_0_130,plain,
( greatest_lower_bound(c,greatest_lower_bound(a,greatest_lower_bound(a,multiply(b,c)))) != greatest_lower_bound(a,multiply(b,c))
| least_upper_bound(c,greatest_lower_bound(c,greatest_lower_bound(a,greatest_lower_bound(a,multiply(b,c))))) != c
| least_upper_bound(c,greatest_lower_bound(a,multiply(b,c))) = c ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(c,greatest_lower_bound(c,greatest_lower_bound(a,greatest_lower_bound(a,multiply(b,c))))),c) ),[0,1],$fot(greatest_lower_bound(a,multiply(b,c)))]]) ).
cnf(refute_0_131,plain,
( least_upper_bound(c,greatest_lower_bound(c,greatest_lower_bound(a,greatest_lower_bound(a,multiply(b,c))))) != c
| least_upper_bound(c,greatest_lower_bound(a,multiply(b,c))) = c ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(c,greatest_lower_bound(a,greatest_lower_bound(a,multiply(b,c)))),greatest_lower_bound(a,multiply(b,c))) )],[refute_0_129,refute_0_130]) ).
cnf(refute_0_132,plain,
least_upper_bound(c,greatest_lower_bound(a,multiply(b,c))) = c,
inference(resolve,[$cnf( $equal(least_upper_bound(c,greatest_lower_bound(c,greatest_lower_bound(a,greatest_lower_bound(a,multiply(b,c))))),c) )],[refute_0_11,refute_0_131]) ).
cnf(refute_0_133,plain,
( greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),least_upper_bound(c,greatest_lower_bound(a,multiply(b,c)))) != greatest_lower_bound(a,multiply(b,c))
| least_upper_bound(c,greatest_lower_bound(a,multiply(b,c))) != c
| greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),c) = greatest_lower_bound(a,multiply(b,c)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),least_upper_bound(c,greatest_lower_bound(a,multiply(b,c)))),greatest_lower_bound(a,multiply(b,c))) ),[0,1],$fot(c)]]) ).
cnf(refute_0_134,plain,
( greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),least_upper_bound(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)),c) = greatest_lower_bound(a,multiply(b,c)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(c,greatest_lower_bound(a,multiply(b,c))),c) )],[refute_0_132,refute_0_133]) ).
cnf(refute_0_135,plain,
greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),c) = greatest_lower_bound(a,multiply(b,c)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),least_upper_bound(c,greatest_lower_bound(a,multiply(b,c)))),greatest_lower_bound(a,multiply(b,c))) )],[refute_0_10,refute_0_134]) ).
cnf(refute_0_136,plain,
greatest_lower_bound(multiply(b,c),c) = greatest_lower_bound(c,multiply(b,c)),
inference(subst,[],[refute_0_47:[bind(X,$fot(c)),bind(Y,$fot(multiply(b,c)))]]) ).
cnf(refute_0_137,plain,
greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),c)) = greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),c)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),c)))]]) ).
cnf(refute_0_138,plain,
( greatest_lower_bound(multiply(b,c),c) != greatest_lower_bound(c,multiply(b,c))
| greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),c)) != greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),c))
| greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),c)) = greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),c)),greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),c))) ),[1,1],$fot(greatest_lower_bound(c,multiply(b,c)))]]) ).
cnf(refute_0_139,plain,
( greatest_lower_bound(multiply(b,c),c) != greatest_lower_bound(c,multiply(b,c))
| greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),c)) = greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),c)),greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),c))) )],[refute_0_137,refute_0_138]) ).
cnf(refute_0_140,plain,
greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),c)) = greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(b,c),c),greatest_lower_bound(c,multiply(b,c))) )],[refute_0_136,refute_0_139]) ).
cnf(refute_0_141,plain,
greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),c) = greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),c)),
inference(subst,[],[refute_0_35:[bind(X,$fot(a)),bind(Y,$fot(multiply(b,c))),bind(Z,$fot(c))]]) ).
cnf(refute_0_142,plain,
( greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),c)) != greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c)))
| greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),c) != greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),c))
| greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),c) = greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),c))),bind(Y0,$fot(greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),c)))),bind(Z0,$fot(greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c)))))]]) ).
cnf(refute_0_143,plain,
( greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),c)) != greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c)))
| greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),c) = greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),c),greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),c))) )],[refute_0_141,refute_0_142]) ).
cnf(refute_0_144,plain,
greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),c) = greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),c)),greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c)))) )],[refute_0_140,refute_0_143]) ).
cnf(refute_0_145,plain,
( greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),c) != greatest_lower_bound(a,multiply(b,c))
| greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),c) != greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c)))
| greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))) = greatest_lower_bound(a,multiply(b,c)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),c),greatest_lower_bound(a,multiply(b,c))) ),[0],$fot(greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))))]]) ).
cnf(refute_0_146,plain,
( greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),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( $equal(greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),c),greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c)))) )],[refute_0_144,refute_0_145]) ).
cnf(refute_0_147,plain,
greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))) = greatest_lower_bound(a,multiply(b,c)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),c),greatest_lower_bound(a,multiply(b,c))) )],[refute_0_135,refute_0_146]) ).
cnf(refute_0_148,plain,
multiply(identity,c) = c,
inference(subst,[],[left_identity:[bind(X,$fot(c))]]) ).
cnf(refute_0_149,plain,
greatest_lower_bound(identity,b) = greatest_lower_bound(b,identity),
inference(subst,[],[refute_0_47:[bind(X,$fot(b)),bind(Y,$fot(identity))]]) ).
cnf(refute_0_150,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_151,plain,
( greatest_lower_bound(identity,b) != identity
| greatest_lower_bound(b,identity) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,b),greatest_lower_bound(b,identity)) )],[refute_0_149,refute_0_150]) ).
cnf(refute_0_152,plain,
greatest_lower_bound(b,identity) = identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,b),identity) )],[p8_9b_2,refute_0_151]) ).
cnf(refute_0_153,plain,
multiply(greatest_lower_bound(b,identity),c) = multiply(greatest_lower_bound(b,identity),c),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(b,identity),c))]]) ).
cnf(refute_0_154,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_155,plain,
( greatest_lower_bound(b,identity) != identity
| multiply(greatest_lower_bound(b,identity),c) = multiply(identity,c) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(b,identity),c),multiply(greatest_lower_bound(b,identity),c)) )],[refute_0_153,refute_0_154]) ).
cnf(refute_0_156,plain,
multiply(greatest_lower_bound(b,identity),c) = multiply(identity,c),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,identity),identity) )],[refute_0_152,refute_0_155]) ).
cnf(refute_0_157,plain,
( multiply(greatest_lower_bound(b,identity),c) != multiply(identity,c)
| multiply(identity,c) != c
| multiply(greatest_lower_bound(b,identity),c) = c ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(multiply(greatest_lower_bound(b,identity),c))),bind(Y0,$fot(multiply(identity,c))),bind(Z0,$fot(c))]]) ).
cnf(refute_0_158,plain,
( multiply(identity,c) != c
| multiply(greatest_lower_bound(b,identity),c) = c ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(b,identity),c),multiply(identity,c)) )],[refute_0_156,refute_0_157]) ).
cnf(refute_0_159,plain,
multiply(greatest_lower_bound(b,identity),c) = c,
inference(resolve,[$cnf( $equal(multiply(identity,c),c) )],[refute_0_148,refute_0_158]) ).
cnf(refute_0_160,plain,
multiply(greatest_lower_bound(X_251,identity),X_250) = greatest_lower_bound(multiply(X_251,X_250),multiply(identity,X_250)),
inference(subst,[],[monotony_glb2:[bind(X,$fot(X_250)),bind(Y,$fot(X_251)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_161,plain,
multiply(identity,X_250) = X_250,
inference(subst,[],[left_identity:[bind(X,$fot(X_250))]]) ).
cnf(refute_0_162,plain,
( multiply(greatest_lower_bound(X_251,identity),X_250) != greatest_lower_bound(multiply(X_251,X_250),multiply(identity,X_250))
| multiply(identity,X_250) != X_250
| multiply(greatest_lower_bound(X_251,identity),X_250) = greatest_lower_bound(multiply(X_251,X_250),X_250) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_251,identity),X_250),greatest_lower_bound(multiply(X_251,X_250),multiply(identity,X_250))) ),[1,1],$fot(X_250)]]) ).
cnf(refute_0_163,plain,
( multiply(greatest_lower_bound(X_251,identity),X_250) != greatest_lower_bound(multiply(X_251,X_250),multiply(identity,X_250))
| multiply(greatest_lower_bound(X_251,identity),X_250) = greatest_lower_bound(multiply(X_251,X_250),X_250) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_250),X_250) )],[refute_0_161,refute_0_162]) ).
cnf(refute_0_164,plain,
multiply(greatest_lower_bound(X_251,identity),X_250) = greatest_lower_bound(multiply(X_251,X_250),X_250),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_251,identity),X_250),greatest_lower_bound(multiply(X_251,X_250),multiply(identity,X_250))) )],[refute_0_160,refute_0_163]) ).
cnf(refute_0_165,plain,
greatest_lower_bound(multiply(X_251,X_250),X_250) = greatest_lower_bound(X_250,multiply(X_251,X_250)),
inference(subst,[],[refute_0_47:[bind(X,$fot(X_250)),bind(Y,$fot(multiply(X_251,X_250)))]]) ).
cnf(refute_0_166,plain,
( multiply(greatest_lower_bound(X_251,identity),X_250) != greatest_lower_bound(multiply(X_251,X_250),X_250)
| greatest_lower_bound(multiply(X_251,X_250),X_250) != greatest_lower_bound(X_250,multiply(X_251,X_250))
| multiply(greatest_lower_bound(X_251,identity),X_250) = greatest_lower_bound(X_250,multiply(X_251,X_250)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_251,identity),X_250),greatest_lower_bound(X_250,multiply(X_251,X_250))) ),[0],$fot(greatest_lower_bound(multiply(X_251,X_250),X_250))]]) ).
cnf(refute_0_167,plain,
( multiply(greatest_lower_bound(X_251,identity),X_250) != greatest_lower_bound(multiply(X_251,X_250),X_250)
| multiply(greatest_lower_bound(X_251,identity),X_250) = greatest_lower_bound(X_250,multiply(X_251,X_250)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_251,X_250),X_250),greatest_lower_bound(X_250,multiply(X_251,X_250))) )],[refute_0_165,refute_0_166]) ).
cnf(refute_0_168,plain,
multiply(greatest_lower_bound(X_251,identity),X_250) = greatest_lower_bound(X_250,multiply(X_251,X_250)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_251,identity),X_250),greatest_lower_bound(multiply(X_251,X_250),X_250)) )],[refute_0_164,refute_0_167]) ).
cnf(refute_0_169,plain,
( multiply(greatest_lower_bound(X_251,identity),X_250) != greatest_lower_bound(X_250,multiply(X_251,X_250))
| greatest_lower_bound(X_250,multiply(X_251,X_250)) = multiply(greatest_lower_bound(X_251,identity),X_250) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(multiply(greatest_lower_bound(X_251,identity),X_250))),bind(Y0,$fot(greatest_lower_bound(X_250,multiply(X_251,X_250))))]]) ).
cnf(refute_0_170,plain,
greatest_lower_bound(X_250,multiply(X_251,X_250)) = multiply(greatest_lower_bound(X_251,identity),X_250),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_251,identity),X_250),greatest_lower_bound(X_250,multiply(X_251,X_250))) )],[refute_0_168,refute_0_169]) ).
cnf(refute_0_171,plain,
greatest_lower_bound(c,multiply(b,c)) = multiply(greatest_lower_bound(b,identity),c),
inference(subst,[],[refute_0_170:[bind(X_250,$fot(c)),bind(X_251,$fot(b))]]) ).
cnf(refute_0_172,plain,
( multiply(greatest_lower_bound(b,identity),c) != c
| greatest_lower_bound(c,multiply(b,c)) != multiply(greatest_lower_bound(b,identity),c)
| greatest_lower_bound(c,multiply(b,c)) = c ),
inference(subst,[],[refute_0_22:[bind(X0,$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_173,plain,
( multiply(greatest_lower_bound(b,identity),c) != c
| greatest_lower_bound(c,multiply(b,c)) = c ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(c,multiply(b,c)),multiply(greatest_lower_bound(b,identity),c)) )],[refute_0_171,refute_0_172]) ).
cnf(refute_0_174,plain,
greatest_lower_bound(c,multiply(b,c)) = c,
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(b,identity),c),c) )],[refute_0_159,refute_0_173]) ).
cnf(refute_0_175,plain,
greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))) = greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))))]]) ).
cnf(refute_0_176,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_177,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( $equal(greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))),greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c)))) )],[refute_0_175,refute_0_176]) ).
cnf(refute_0_178,plain,
greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))) = greatest_lower_bound(a,c),
inference(resolve,[$cnf( $equal(greatest_lower_bound(c,multiply(b,c)),c) )],[refute_0_174,refute_0_177]) ).
cnf(refute_0_179,plain,
( greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))) != greatest_lower_bound(a,multiply(b,c))
| greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))) != greatest_lower_bound(a,c)
| greatest_lower_bound(a,c) = greatest_lower_bound(a,multiply(b,c)) ),
introduced(tautology,[equality,[$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_180,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( $equal(greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))),greatest_lower_bound(a,c)) )],[refute_0_178,refute_0_179]) ).
cnf(refute_0_181,plain,
greatest_lower_bound(a,c) = greatest_lower_bound(a,multiply(b,c)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))),greatest_lower_bound(a,multiply(b,c))) )],[refute_0_147,refute_0_180]) ).
cnf(refute_0_182,plain,
( greatest_lower_bound(a,c) != greatest_lower_bound(a,multiply(b,c))
| greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(a,c) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(greatest_lower_bound(a,c))),bind(Y0,$fot(greatest_lower_bound(a,multiply(b,c))))]]) ).
cnf(refute_0_183,plain,
greatest_lower_bound(a,c) != greatest_lower_bound(a,multiply(b,c)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,multiply(b,c)),greatest_lower_bound(a,c)) )],[refute_0_182,prove_p8_9b]) ).
cnf(refute_0_184,plain,
$false,
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,c),greatest_lower_bound(a,multiply(b,c))) )],[refute_0_181,refute_0_183]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14 % Problem : GRP193-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.14/0.14 % Command : metis --show proof --show saturation %s
% 0.14/0.36 % Computer : n021.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Tue Jun 14 09:04:58 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 6.88/7.04 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.88/7.04
% 6.88/7.04 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.88/7.06
%------------------------------------------------------------------------------