%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP147-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n013.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 10:37:02 EDT 2022
% Result : Unsatisfiable 1.22s 1.40s
% Output : CNFRefutation 1.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 65
% Syntax : Number of clauses : 286 ( 149 unt; 0 nHn; 145 RR)
% Number of literals : 483 ( 482 equ; 199 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 462 ( 26 sgn)
% Comments :
%------------------------------------------------------------------------------
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(associativity_of_lub,axiom,
least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_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(ax_lub1b_1,hypothesis,
greatest_lower_bound(a,c) = a ).
cnf(ax_lub1b_2,hypothesis,
greatest_lower_bound(b,c) = b ).
cnf(prove_ax_lub1b,negated_conjecture,
greatest_lower_bound(least_upper_bound(a,b),c) != least_upper_bound(a,b) ).
cnf(refute_0_0,plain,
greatest_lower_bound(X_8,least_upper_bound(X_8,X_9)) = X_8,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_8)),bind(Y,$fot(X_9))]]) ).
cnf(refute_0_1,plain,
least_upper_bound(X_9,X_8) = least_upper_bound(X_8,X_9),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_9)),bind(Y,$fot(X_8))]]) ).
cnf(refute_0_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( $equal(X0,X0) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( least_upper_bound(X_9,X_8) != least_upper_bound(X_8,X_9)
| least_upper_bound(X_8,X_9) = least_upper_bound(X_9,X_8) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(least_upper_bound(X_9,X_8))),bind(Y0,$fot(least_upper_bound(X_8,X_9)))]]) ).
cnf(refute_0_6,plain,
least_upper_bound(X_8,X_9) = least_upper_bound(X_9,X_8),
inference(resolve,[$cnf( $equal(least_upper_bound(X_9,X_8),least_upper_bound(X_8,X_9)) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
( greatest_lower_bound(X_8,least_upper_bound(X_8,X_9)) != X_8
| least_upper_bound(X_8,X_9) != least_upper_bound(X_9,X_8)
| greatest_lower_bound(X_8,least_upper_bound(X_9,X_8)) = X_8 ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_8,least_upper_bound(X_8,X_9)),X_8) ),[0,1],$fot(least_upper_bound(X_9,X_8))]]) ).
cnf(refute_0_8,plain,
( greatest_lower_bound(X_8,least_upper_bound(X_8,X_9)) != X_8
| greatest_lower_bound(X_8,least_upper_bound(X_9,X_8)) = X_8 ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_8,X_9),least_upper_bound(X_9,X_8)) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
greatest_lower_bound(X_8,least_upper_bound(X_9,X_8)) = X_8,
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_8,least_upper_bound(X_8,X_9)),X_8) )],[refute_0_0,refute_0_8]) ).
cnf(refute_0_10,plain,
greatest_lower_bound(least_upper_bound(X_37,b),least_upper_bound(c,least_upper_bound(X_37,b))) = least_upper_bound(X_37,b),
inference(subst,[],[refute_0_9:[bind(X_8,$fot(least_upper_bound(X_37,b))),bind(X_9,$fot(c))]]) ).
cnf(refute_0_11,plain,
least_upper_bound(X_10,greatest_lower_bound(X_10,X_11)) = X_10,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_10)),bind(Y,$fot(X_11))]]) ).
cnf(refute_0_12,plain,
greatest_lower_bound(X_11,X_10) = greatest_lower_bound(X_10,X_11),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_11)),bind(Y,$fot(X_10))]]) ).
cnf(refute_0_13,plain,
( greatest_lower_bound(X_11,X_10) != greatest_lower_bound(X_10,X_11)
| greatest_lower_bound(X_10,X_11) = greatest_lower_bound(X_11,X_10) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(greatest_lower_bound(X_11,X_10))),bind(Y0,$fot(greatest_lower_bound(X_10,X_11)))]]) ).
cnf(refute_0_14,plain,
greatest_lower_bound(X_10,X_11) = greatest_lower_bound(X_11,X_10),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_11,X_10),greatest_lower_bound(X_10,X_11)) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
( greatest_lower_bound(X_10,X_11) != greatest_lower_bound(X_11,X_10)
| least_upper_bound(X_10,greatest_lower_bound(X_10,X_11)) != X_10
| least_upper_bound(X_10,greatest_lower_bound(X_11,X_10)) = X_10 ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_10,greatest_lower_bound(X_10,X_11)),X_10) ),[0,1],$fot(greatest_lower_bound(X_11,X_10))]]) ).
cnf(refute_0_16,plain,
( least_upper_bound(X_10,greatest_lower_bound(X_10,X_11)) != X_10
| least_upper_bound(X_10,greatest_lower_bound(X_11,X_10)) = X_10 ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_10,X_11),greatest_lower_bound(X_11,X_10)) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
least_upper_bound(X_10,greatest_lower_bound(X_11,X_10)) = X_10,
inference(resolve,[$cnf( $equal(least_upper_bound(X_10,greatest_lower_bound(X_10,X_11)),X_10) )],[refute_0_11,refute_0_16]) ).
cnf(refute_0_18,plain,
least_upper_bound(least_upper_bound(c,X_31),greatest_lower_bound(b,least_upper_bound(c,X_31))) = least_upper_bound(c,X_31),
inference(subst,[],[refute_0_17:[bind(X_10,$fot(least_upper_bound(c,X_31))),bind(X_11,$fot(b))]]) ).
cnf(refute_0_19,plain,
greatest_lower_bound(b,greatest_lower_bound(c,X_28)) = greatest_lower_bound(greatest_lower_bound(b,c),X_28),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(b)),bind(Y,$fot(c)),bind(Z,$fot(X_28))]]) ).
cnf(refute_0_20,plain,
( greatest_lower_bound(b,c) != b
| greatest_lower_bound(b,greatest_lower_bound(c,X_28)) != greatest_lower_bound(greatest_lower_bound(b,c),X_28)
| greatest_lower_bound(b,greatest_lower_bound(c,X_28)) = greatest_lower_bound(b,X_28) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(c,X_28)),greatest_lower_bound(greatest_lower_bound(b,c),X_28)) ),[1,0],$fot(b)]]) ).
cnf(refute_0_21,plain,
( greatest_lower_bound(b,greatest_lower_bound(c,X_28)) != greatest_lower_bound(greatest_lower_bound(b,c),X_28)
| greatest_lower_bound(b,greatest_lower_bound(c,X_28)) = greatest_lower_bound(b,X_28) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,c),b) )],[ax_lub1b_2,refute_0_20]) ).
cnf(refute_0_22,plain,
greatest_lower_bound(b,greatest_lower_bound(c,X_28)) = greatest_lower_bound(b,X_28),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(c,X_28)),greatest_lower_bound(greatest_lower_bound(b,c),X_28)) )],[refute_0_19,refute_0_21]) ).
cnf(refute_0_23,plain,
greatest_lower_bound(b,greatest_lower_bound(c,least_upper_bound(c,Y))) = greatest_lower_bound(b,least_upper_bound(c,Y)),
inference(subst,[],[refute_0_22:[bind(X_28,$fot(least_upper_bound(c,Y)))]]) ).
cnf(refute_0_24,plain,
greatest_lower_bound(c,least_upper_bound(c,Y)) = c,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(c))]]) ).
cnf(refute_0_25,plain,
( greatest_lower_bound(b,greatest_lower_bound(c,least_upper_bound(c,Y))) != greatest_lower_bound(b,least_upper_bound(c,Y))
| greatest_lower_bound(c,least_upper_bound(c,Y)) != c
| greatest_lower_bound(b,c) = greatest_lower_bound(b,least_upper_bound(c,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(c,least_upper_bound(c,Y))),greatest_lower_bound(b,least_upper_bound(c,Y))) ),[0,1],$fot(c)]]) ).
cnf(refute_0_26,plain,
( greatest_lower_bound(b,greatest_lower_bound(c,least_upper_bound(c,Y))) != greatest_lower_bound(b,least_upper_bound(c,Y))
| greatest_lower_bound(b,c) = greatest_lower_bound(b,least_upper_bound(c,Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(c,least_upper_bound(c,Y)),c) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
greatest_lower_bound(b,c) = greatest_lower_bound(b,least_upper_bound(c,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(c,least_upper_bound(c,Y))),greatest_lower_bound(b,least_upper_bound(c,Y))) )],[refute_0_23,refute_0_26]) ).
cnf(refute_0_28,plain,
( greatest_lower_bound(b,c) != b
| greatest_lower_bound(b,c) != greatest_lower_bound(b,least_upper_bound(c,Y))
| b = greatest_lower_bound(b,least_upper_bound(c,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,c),greatest_lower_bound(b,least_upper_bound(c,Y))) ),[0],$fot(b)]]) ).
cnf(refute_0_29,plain,
( greatest_lower_bound(b,c) != greatest_lower_bound(b,least_upper_bound(c,Y))
| b = greatest_lower_bound(b,least_upper_bound(c,Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,c),b) )],[ax_lub1b_2,refute_0_28]) ).
cnf(refute_0_30,plain,
b = greatest_lower_bound(b,least_upper_bound(c,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,c),greatest_lower_bound(b,least_upper_bound(c,Y))) )],[refute_0_27,refute_0_29]) ).
cnf(refute_0_31,plain,
b = greatest_lower_bound(b,least_upper_bound(c,X_31)),
inference(subst,[],[refute_0_30:[bind(Y,$fot(X_31))]]) ).
cnf(refute_0_32,plain,
( b != greatest_lower_bound(b,least_upper_bound(c,X_31))
| greatest_lower_bound(b,least_upper_bound(c,X_31)) = b ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(b)),bind(Y0,$fot(greatest_lower_bound(b,least_upper_bound(c,X_31))))]]) ).
cnf(refute_0_33,plain,
greatest_lower_bound(b,least_upper_bound(c,X_31)) = b,
inference(resolve,[$cnf( $equal(b,greatest_lower_bound(b,least_upper_bound(c,X_31))) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
( greatest_lower_bound(b,least_upper_bound(c,X_31)) != b
| least_upper_bound(least_upper_bound(c,X_31),greatest_lower_bound(b,least_upper_bound(c,X_31))) != least_upper_bound(c,X_31)
| least_upper_bound(least_upper_bound(c,X_31),b) = least_upper_bound(c,X_31) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(c,X_31),greatest_lower_bound(b,least_upper_bound(c,X_31))),least_upper_bound(c,X_31)) ),[0,1],$fot(b)]]) ).
cnf(refute_0_35,plain,
( least_upper_bound(least_upper_bound(c,X_31),greatest_lower_bound(b,least_upper_bound(c,X_31))) != least_upper_bound(c,X_31)
| least_upper_bound(least_upper_bound(c,X_31),b) = least_upper_bound(c,X_31) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(c,X_31)),b) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
least_upper_bound(least_upper_bound(c,X_31),b) = least_upper_bound(c,X_31),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(c,X_31),greatest_lower_bound(b,least_upper_bound(c,X_31))),least_upper_bound(c,X_31)) )],[refute_0_18,refute_0_35]) ).
cnf(refute_0_37,plain,
( least_upper_bound(X,least_upper_bound(Y,Z)) != least_upper_bound(least_upper_bound(X,Y),Z)
| least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(Y,Z)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X,Y),Z)))]]) ).
cnf(refute_0_38,plain,
least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,Z)),least_upper_bound(least_upper_bound(X,Y),Z)) )],[associativity_of_lub,refute_0_37]) ).
cnf(refute_0_39,plain,
least_upper_bound(least_upper_bound(c,X_31),b) = least_upper_bound(c,least_upper_bound(X_31,b)),
inference(subst,[],[refute_0_38:[bind(X,$fot(c)),bind(Y,$fot(X_31)),bind(Z,$fot(b))]]) ).
cnf(refute_0_40,plain,
( least_upper_bound(least_upper_bound(c,X_31),b) != least_upper_bound(c,X_31)
| least_upper_bound(least_upper_bound(c,X_31),b) != least_upper_bound(c,least_upper_bound(X_31,b))
| least_upper_bound(c,least_upper_bound(X_31,b)) = least_upper_bound(c,X_31) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(c,X_31),b),least_upper_bound(c,X_31)) ),[0],$fot(least_upper_bound(c,least_upper_bound(X_31,b)))]]) ).
cnf(refute_0_41,plain,
( least_upper_bound(least_upper_bound(c,X_31),b) != least_upper_bound(c,X_31)
| least_upper_bound(c,least_upper_bound(X_31,b)) = least_upper_bound(c,X_31) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(c,X_31),b),least_upper_bound(c,least_upper_bound(X_31,b))) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
least_upper_bound(c,least_upper_bound(X_31,b)) = least_upper_bound(c,X_31),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(c,X_31),b),least_upper_bound(c,X_31)) )],[refute_0_36,refute_0_41]) ).
cnf(refute_0_43,plain,
least_upper_bound(c,least_upper_bound(X_37,b)) = least_upper_bound(c,X_37),
inference(subst,[],[refute_0_42:[bind(X_31,$fot(X_37))]]) ).
cnf(refute_0_44,plain,
( greatest_lower_bound(least_upper_bound(X_37,b),least_upper_bound(c,least_upper_bound(X_37,b))) != least_upper_bound(X_37,b)
| least_upper_bound(c,least_upper_bound(X_37,b)) != least_upper_bound(c,X_37)
| greatest_lower_bound(least_upper_bound(X_37,b),least_upper_bound(c,X_37)) = least_upper_bound(X_37,b) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_37,b),least_upper_bound(c,least_upper_bound(X_37,b))),least_upper_bound(X_37,b)) ),[0,1],$fot(least_upper_bound(c,X_37))]]) ).
cnf(refute_0_45,plain,
( greatest_lower_bound(least_upper_bound(X_37,b),least_upper_bound(c,least_upper_bound(X_37,b))) != least_upper_bound(X_37,b)
| greatest_lower_bound(least_upper_bound(X_37,b),least_upper_bound(c,X_37)) = least_upper_bound(X_37,b) ),
inference(resolve,[$cnf( $equal(least_upper_bound(c,least_upper_bound(X_37,b)),least_upper_bound(c,X_37)) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
greatest_lower_bound(least_upper_bound(X_37,b),least_upper_bound(c,X_37)) = least_upper_bound(X_37,b),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_37,b),least_upper_bound(c,least_upper_bound(X_37,b))),least_upper_bound(X_37,b)) )],[refute_0_10,refute_0_45]) ).
cnf(refute_0_47,plain,
greatest_lower_bound(least_upper_bound(greatest_lower_bound(a,X_32),b),least_upper_bound(c,greatest_lower_bound(a,X_32))) = least_upper_bound(greatest_lower_bound(a,X_32),b),
inference(subst,[],[refute_0_46:[bind(X_37,$fot(greatest_lower_bound(a,X_32)))]]) ).
cnf(refute_0_48,plain,
least_upper_bound(X,least_upper_bound(b,least_upper_bound(c,X_44))) = least_upper_bound(least_upper_bound(X,b),least_upper_bound(c,X_44)),
inference(subst,[],[associativity_of_lub:[bind(Y,$fot(b)),bind(Z,$fot(least_upper_bound(c,X_44)))]]) ).
cnf(refute_0_49,plain,
least_upper_bound(c,least_upper_bound(X_42,b)) = least_upper_bound(least_upper_bound(c,X_42),b),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(c)),bind(Y,$fot(X_42)),bind(Z,$fot(b))]]) ).
cnf(refute_0_50,plain,
least_upper_bound(c,least_upper_bound(X_42,b)) = least_upper_bound(c,X_42),
inference(subst,[],[refute_0_42:[bind(X_31,$fot(X_42))]]) ).
cnf(refute_0_51,plain,
( least_upper_bound(c,least_upper_bound(X_42,b)) != least_upper_bound(c,X_42)
| least_upper_bound(c,least_upper_bound(X_42,b)) != least_upper_bound(least_upper_bound(c,X_42),b)
| least_upper_bound(c,X_42) = least_upper_bound(least_upper_bound(c,X_42),b) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(c,least_upper_bound(X_42,b)),least_upper_bound(least_upper_bound(c,X_42),b)) ),[0],$fot(least_upper_bound(c,X_42))]]) ).
cnf(refute_0_52,plain,
( least_upper_bound(c,least_upper_bound(X_42,b)) != least_upper_bound(least_upper_bound(c,X_42),b)
| least_upper_bound(c,X_42) = least_upper_bound(least_upper_bound(c,X_42),b) ),
inference(resolve,[$cnf( $equal(least_upper_bound(c,least_upper_bound(X_42,b)),least_upper_bound(c,X_42)) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
least_upper_bound(c,X_42) = least_upper_bound(least_upper_bound(c,X_42),b),
inference(resolve,[$cnf( $equal(least_upper_bound(c,least_upper_bound(X_42,b)),least_upper_bound(least_upper_bound(c,X_42),b)) )],[refute_0_49,refute_0_52]) ).
cnf(refute_0_54,plain,
least_upper_bound(X,least_upper_bound(X_41,X_42)) = least_upper_bound(least_upper_bound(X_41,X_42),X),
inference(subst,[],[symmetry_of_lub:[bind(Y,$fot(least_upper_bound(X_41,X_42)))]]) ).
cnf(refute_0_55,plain,
least_upper_bound(X_41,least_upper_bound(X_42,X)) = least_upper_bound(least_upper_bound(X_41,X_42),X),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_41)),bind(Y,$fot(X_42)),bind(Z,$fot(X))]]) ).
cnf(refute_0_56,plain,
( least_upper_bound(X_41,least_upper_bound(X_42,X)) != least_upper_bound(least_upper_bound(X_41,X_42),X)
| least_upper_bound(least_upper_bound(X_41,X_42),X) = least_upper_bound(X_41,least_upper_bound(X_42,X)) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(least_upper_bound(X_41,least_upper_bound(X_42,X)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X_41,X_42),X)))]]) ).
cnf(refute_0_57,plain,
least_upper_bound(least_upper_bound(X_41,X_42),X) = least_upper_bound(X_41,least_upper_bound(X_42,X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_41,least_upper_bound(X_42,X)),least_upper_bound(least_upper_bound(X_41,X_42),X)) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
( least_upper_bound(X,least_upper_bound(X_41,X_42)) != least_upper_bound(least_upper_bound(X_41,X_42),X)
| least_upper_bound(least_upper_bound(X_41,X_42),X) != least_upper_bound(X_41,least_upper_bound(X_42,X))
| least_upper_bound(X,least_upper_bound(X_41,X_42)) = least_upper_bound(X_41,least_upper_bound(X_42,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,least_upper_bound(X_41,X_42)),least_upper_bound(X_41,least_upper_bound(X_42,X))) ),[0],$fot(least_upper_bound(least_upper_bound(X_41,X_42),X))]]) ).
cnf(refute_0_59,plain,
( least_upper_bound(X,least_upper_bound(X_41,X_42)) != least_upper_bound(least_upper_bound(X_41,X_42),X)
| least_upper_bound(X,least_upper_bound(X_41,X_42)) = least_upper_bound(X_41,least_upper_bound(X_42,X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_41,X_42),X),least_upper_bound(X_41,least_upper_bound(X_42,X))) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
least_upper_bound(X,least_upper_bound(X_41,X_42)) = least_upper_bound(X_41,least_upper_bound(X_42,X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_41,X_42)),least_upper_bound(least_upper_bound(X_41,X_42),X)) )],[refute_0_54,refute_0_59]) ).
cnf(refute_0_61,plain,
( least_upper_bound(X,least_upper_bound(X_41,X_42)) != least_upper_bound(X_41,least_upper_bound(X_42,X))
| least_upper_bound(X_41,least_upper_bound(X_42,X)) = least_upper_bound(X,least_upper_bound(X_41,X_42)) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(X_41,X_42)))),bind(Y0,$fot(least_upper_bound(X_41,least_upper_bound(X_42,X))))]]) ).
cnf(refute_0_62,plain,
least_upper_bound(X_41,least_upper_bound(X_42,X)) = least_upper_bound(X,least_upper_bound(X_41,X_42)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_41,X_42)),least_upper_bound(X_41,least_upper_bound(X_42,X))) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
least_upper_bound(c,least_upper_bound(X_42,b)) = least_upper_bound(b,least_upper_bound(c,X_42)),
inference(subst,[],[refute_0_62:[bind(X,$fot(b)),bind(X_41,$fot(c))]]) ).
cnf(refute_0_64,plain,
least_upper_bound(least_upper_bound(c,X_42),b) = least_upper_bound(c,least_upper_bound(X_42,b)),
inference(subst,[],[refute_0_38:[bind(X,$fot(c)),bind(Y,$fot(X_42)),bind(Z,$fot(b))]]) ).
cnf(refute_0_65,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_66,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_4,refute_0_65]) ).
cnf(refute_0_67,plain,
( least_upper_bound(c,least_upper_bound(X_42,b)) != least_upper_bound(b,least_upper_bound(c,X_42))
| least_upper_bound(least_upper_bound(c,X_42),b) != least_upper_bound(c,least_upper_bound(X_42,b))
| least_upper_bound(least_upper_bound(c,X_42),b) = least_upper_bound(b,least_upper_bound(c,X_42)) ),
inference(subst,[],[refute_0_66:[bind(X0,$fot(least_upper_bound(least_upper_bound(c,X_42),b))),bind(Y0,$fot(least_upper_bound(c,least_upper_bound(X_42,b)))),bind(Z0,$fot(least_upper_bound(b,least_upper_bound(c,X_42))))]]) ).
cnf(refute_0_68,plain,
( least_upper_bound(c,least_upper_bound(X_42,b)) != least_upper_bound(b,least_upper_bound(c,X_42))
| least_upper_bound(least_upper_bound(c,X_42),b) = least_upper_bound(b,least_upper_bound(c,X_42)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(c,X_42),b),least_upper_bound(c,least_upper_bound(X_42,b))) )],[refute_0_64,refute_0_67]) ).
cnf(refute_0_69,plain,
least_upper_bound(least_upper_bound(c,X_42),b) = least_upper_bound(b,least_upper_bound(c,X_42)),
inference(resolve,[$cnf( $equal(least_upper_bound(c,least_upper_bound(X_42,b)),least_upper_bound(b,least_upper_bound(c,X_42))) )],[refute_0_63,refute_0_68]) ).
cnf(refute_0_70,plain,
( least_upper_bound(c,X_42) != least_upper_bound(least_upper_bound(c,X_42),b)
| least_upper_bound(least_upper_bound(c,X_42),b) != least_upper_bound(b,least_upper_bound(c,X_42))
| least_upper_bound(c,X_42) = least_upper_bound(b,least_upper_bound(c,X_42)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(c,X_42),least_upper_bound(b,least_upper_bound(c,X_42))) ),[0],$fot(least_upper_bound(least_upper_bound(c,X_42),b))]]) ).
cnf(refute_0_71,plain,
( least_upper_bound(c,X_42) != least_upper_bound(least_upper_bound(c,X_42),b)
| least_upper_bound(c,X_42) = least_upper_bound(b,least_upper_bound(c,X_42)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(c,X_42),b),least_upper_bound(b,least_upper_bound(c,X_42))) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
least_upper_bound(c,X_42) = least_upper_bound(b,least_upper_bound(c,X_42)),
inference(resolve,[$cnf( $equal(least_upper_bound(c,X_42),least_upper_bound(least_upper_bound(c,X_42),b)) )],[refute_0_53,refute_0_71]) ).
cnf(refute_0_73,plain,
least_upper_bound(c,X_44) = least_upper_bound(b,least_upper_bound(c,X_44)),
inference(subst,[],[refute_0_72:[bind(X_42,$fot(X_44))]]) ).
cnf(refute_0_74,plain,
( least_upper_bound(c,X_44) != least_upper_bound(b,least_upper_bound(c,X_44))
| least_upper_bound(b,least_upper_bound(c,X_44)) = least_upper_bound(c,X_44) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(least_upper_bound(c,X_44))),bind(Y0,$fot(least_upper_bound(b,least_upper_bound(c,X_44))))]]) ).
cnf(refute_0_75,plain,
least_upper_bound(b,least_upper_bound(c,X_44)) = least_upper_bound(c,X_44),
inference(resolve,[$cnf( $equal(least_upper_bound(c,X_44),least_upper_bound(b,least_upper_bound(c,X_44))) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
( least_upper_bound(X,least_upper_bound(b,least_upper_bound(c,X_44))) != least_upper_bound(least_upper_bound(X,b),least_upper_bound(c,X_44))
| least_upper_bound(b,least_upper_bound(c,X_44)) != least_upper_bound(c,X_44)
| least_upper_bound(X,least_upper_bound(c,X_44)) = least_upper_bound(least_upper_bound(X,b),least_upper_bound(c,X_44)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(b,least_upper_bound(c,X_44))),least_upper_bound(least_upper_bound(X,b),least_upper_bound(c,X_44))) ),[0,1],$fot(least_upper_bound(c,X_44))]]) ).
cnf(refute_0_77,plain,
( least_upper_bound(X,least_upper_bound(b,least_upper_bound(c,X_44))) != least_upper_bound(least_upper_bound(X,b),least_upper_bound(c,X_44))
| least_upper_bound(X,least_upper_bound(c,X_44)) = least_upper_bound(least_upper_bound(X,b),least_upper_bound(c,X_44)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(c,X_44)),least_upper_bound(c,X_44)) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
least_upper_bound(X,least_upper_bound(c,X_44)) = least_upper_bound(least_upper_bound(X,b),least_upper_bound(c,X_44)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(b,least_upper_bound(c,X_44))),least_upper_bound(least_upper_bound(X,b),least_upper_bound(c,X_44))) )],[refute_0_48,refute_0_77]) ).
cnf(refute_0_79,plain,
least_upper_bound(c,least_upper_bound(least_upper_bound(X_31,b),X_43)) = least_upper_bound(least_upper_bound(c,least_upper_bound(X_31,b)),X_43),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(c)),bind(Y,$fot(least_upper_bound(X_31,b))),bind(Z,$fot(X_43))]]) ).
cnf(refute_0_80,plain,
( least_upper_bound(c,least_upper_bound(X_31,b)) != least_upper_bound(c,X_31)
| least_upper_bound(c,least_upper_bound(least_upper_bound(X_31,b),X_43)) != least_upper_bound(least_upper_bound(c,least_upper_bound(X_31,b)),X_43)
| least_upper_bound(c,least_upper_bound(least_upper_bound(X_31,b),X_43)) = least_upper_bound(least_upper_bound(c,X_31),X_43) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(c,least_upper_bound(least_upper_bound(X_31,b),X_43)),least_upper_bound(least_upper_bound(c,least_upper_bound(X_31,b)),X_43)) ),[1,0],$fot(least_upper_bound(c,X_31))]]) ).
cnf(refute_0_81,plain,
( least_upper_bound(c,least_upper_bound(least_upper_bound(X_31,b),X_43)) != least_upper_bound(least_upper_bound(c,least_upper_bound(X_31,b)),X_43)
| least_upper_bound(c,least_upper_bound(least_upper_bound(X_31,b),X_43)) = least_upper_bound(least_upper_bound(c,X_31),X_43) ),
inference(resolve,[$cnf( $equal(least_upper_bound(c,least_upper_bound(X_31,b)),least_upper_bound(c,X_31)) )],[refute_0_42,refute_0_80]) ).
cnf(refute_0_82,plain,
least_upper_bound(c,least_upper_bound(least_upper_bound(X_31,b),X_43)) = least_upper_bound(least_upper_bound(c,X_31),X_43),
inference(resolve,[$cnf( $equal(least_upper_bound(c,least_upper_bound(least_upper_bound(X_31,b),X_43)),least_upper_bound(least_upper_bound(c,least_upper_bound(X_31,b)),X_43)) )],[refute_0_79,refute_0_81]) ).
cnf(refute_0_83,plain,
least_upper_bound(least_upper_bound(X_31,b),X_43) = least_upper_bound(X_31,least_upper_bound(b,X_43)),
inference(subst,[],[refute_0_38:[bind(X,$fot(X_31)),bind(Y,$fot(b)),bind(Z,$fot(X_43))]]) ).
cnf(refute_0_84,plain,
least_upper_bound(c,least_upper_bound(least_upper_bound(X_31,b),X_43)) = least_upper_bound(c,least_upper_bound(least_upper_bound(X_31,b),X_43)),
introduced(tautology,[refl,[$fot(least_upper_bound(c,least_upper_bound(least_upper_bound(X_31,b),X_43)))]]) ).
cnf(refute_0_85,plain,
( least_upper_bound(c,least_upper_bound(least_upper_bound(X_31,b),X_43)) != least_upper_bound(c,least_upper_bound(least_upper_bound(X_31,b),X_43))
| least_upper_bound(least_upper_bound(X_31,b),X_43) != least_upper_bound(X_31,least_upper_bound(b,X_43))
| least_upper_bound(c,least_upper_bound(least_upper_bound(X_31,b),X_43)) = least_upper_bound(c,least_upper_bound(X_31,least_upper_bound(b,X_43))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(c,least_upper_bound(least_upper_bound(X_31,b),X_43)),least_upper_bound(c,least_upper_bound(least_upper_bound(X_31,b),X_43))) ),[1,1],$fot(least_upper_bound(X_31,least_upper_bound(b,X_43)))]]) ).
cnf(refute_0_86,plain,
( least_upper_bound(least_upper_bound(X_31,b),X_43) != least_upper_bound(X_31,least_upper_bound(b,X_43))
| least_upper_bound(c,least_upper_bound(least_upper_bound(X_31,b),X_43)) = least_upper_bound(c,least_upper_bound(X_31,least_upper_bound(b,X_43))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(c,least_upper_bound(least_upper_bound(X_31,b),X_43)),least_upper_bound(c,least_upper_bound(least_upper_bound(X_31,b),X_43))) )],[refute_0_84,refute_0_85]) ).
cnf(refute_0_87,plain,
least_upper_bound(c,least_upper_bound(least_upper_bound(X_31,b),X_43)) = least_upper_bound(c,least_upper_bound(X_31,least_upper_bound(b,X_43))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_31,b),X_43),least_upper_bound(X_31,least_upper_bound(b,X_43))) )],[refute_0_83,refute_0_86]) ).
cnf(refute_0_88,plain,
( least_upper_bound(c,least_upper_bound(least_upper_bound(X_31,b),X_43)) != least_upper_bound(c,least_upper_bound(X_31,least_upper_bound(b,X_43)))
| least_upper_bound(c,least_upper_bound(least_upper_bound(X_31,b),X_43)) != least_upper_bound(least_upper_bound(c,X_31),X_43)
| least_upper_bound(c,least_upper_bound(X_31,least_upper_bound(b,X_43))) = least_upper_bound(least_upper_bound(c,X_31),X_43) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(c,least_upper_bound(least_upper_bound(X_31,b),X_43)),least_upper_bound(least_upper_bound(c,X_31),X_43)) ),[0],$fot(least_upper_bound(c,least_upper_bound(X_31,least_upper_bound(b,X_43))))]]) ).
cnf(refute_0_89,plain,
( least_upper_bound(c,least_upper_bound(least_upper_bound(X_31,b),X_43)) != least_upper_bound(least_upper_bound(c,X_31),X_43)
| least_upper_bound(c,least_upper_bound(X_31,least_upper_bound(b,X_43))) = least_upper_bound(least_upper_bound(c,X_31),X_43) ),
inference(resolve,[$cnf( $equal(least_upper_bound(c,least_upper_bound(least_upper_bound(X_31,b),X_43)),least_upper_bound(c,least_upper_bound(X_31,least_upper_bound(b,X_43)))) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
least_upper_bound(least_upper_bound(c,X_31),X_43) = least_upper_bound(c,least_upper_bound(X_31,X_43)),
inference(subst,[],[refute_0_38:[bind(X,$fot(c)),bind(Y,$fot(X_31)),bind(Z,$fot(X_43))]]) ).
cnf(refute_0_91,plain,
( least_upper_bound(c,least_upper_bound(X_31,least_upper_bound(b,X_43))) != least_upper_bound(least_upper_bound(c,X_31),X_43)
| least_upper_bound(least_upper_bound(c,X_31),X_43) != least_upper_bound(c,least_upper_bound(X_31,X_43))
| least_upper_bound(c,least_upper_bound(X_31,least_upper_bound(b,X_43))) = least_upper_bound(c,least_upper_bound(X_31,X_43)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(c,least_upper_bound(X_31,least_upper_bound(b,X_43))),least_upper_bound(c,least_upper_bound(X_31,X_43))) ),[0],$fot(least_upper_bound(least_upper_bound(c,X_31),X_43))]]) ).
cnf(refute_0_92,plain,
( least_upper_bound(c,least_upper_bound(X_31,least_upper_bound(b,X_43))) != least_upper_bound(least_upper_bound(c,X_31),X_43)
| least_upper_bound(c,least_upper_bound(X_31,least_upper_bound(b,X_43))) = least_upper_bound(c,least_upper_bound(X_31,X_43)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(c,X_31),X_43),least_upper_bound(c,least_upper_bound(X_31,X_43))) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
( least_upper_bound(c,least_upper_bound(least_upper_bound(X_31,b),X_43)) != least_upper_bound(least_upper_bound(c,X_31),X_43)
| least_upper_bound(c,least_upper_bound(X_31,least_upper_bound(b,X_43))) = least_upper_bound(c,least_upper_bound(X_31,X_43)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(c,least_upper_bound(X_31,least_upper_bound(b,X_43))),least_upper_bound(least_upper_bound(c,X_31),X_43)) )],[refute_0_89,refute_0_92]) ).
cnf(refute_0_94,plain,
least_upper_bound(c,least_upper_bound(X_31,least_upper_bound(b,X_43))) = least_upper_bound(c,least_upper_bound(X_31,X_43)),
inference(resolve,[$cnf( $equal(least_upper_bound(c,least_upper_bound(least_upper_bound(X_31,b),X_43)),least_upper_bound(least_upper_bound(c,X_31),X_43)) )],[refute_0_82,refute_0_93]) ).
cnf(refute_0_95,plain,
least_upper_bound(c,least_upper_bound(X,least_upper_bound(b,X_44))) = least_upper_bound(c,least_upper_bound(X,X_44)),
inference(subst,[],[refute_0_94:[bind(X_31,$fot(X)),bind(X_43,$fot(X_44))]]) ).
cnf(refute_0_96,plain,
least_upper_bound(least_upper_bound(X,b),X_44) = least_upper_bound(X,least_upper_bound(b,X_44)),
inference(subst,[],[refute_0_38:[bind(Y,$fot(b)),bind(Z,$fot(X_44))]]) ).
cnf(refute_0_97,plain,
least_upper_bound(c,least_upper_bound(least_upper_bound(X,b),X_44)) = least_upper_bound(c,least_upper_bound(least_upper_bound(X,b),X_44)),
introduced(tautology,[refl,[$fot(least_upper_bound(c,least_upper_bound(least_upper_bound(X,b),X_44)))]]) ).
cnf(refute_0_98,plain,
( least_upper_bound(c,least_upper_bound(least_upper_bound(X,b),X_44)) != least_upper_bound(c,least_upper_bound(least_upper_bound(X,b),X_44))
| least_upper_bound(least_upper_bound(X,b),X_44) != least_upper_bound(X,least_upper_bound(b,X_44))
| least_upper_bound(c,least_upper_bound(least_upper_bound(X,b),X_44)) = least_upper_bound(c,least_upper_bound(X,least_upper_bound(b,X_44))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(c,least_upper_bound(least_upper_bound(X,b),X_44)),least_upper_bound(c,least_upper_bound(least_upper_bound(X,b),X_44))) ),[1,1],$fot(least_upper_bound(X,least_upper_bound(b,X_44)))]]) ).
cnf(refute_0_99,plain,
( least_upper_bound(least_upper_bound(X,b),X_44) != least_upper_bound(X,least_upper_bound(b,X_44))
| least_upper_bound(c,least_upper_bound(least_upper_bound(X,b),X_44)) = least_upper_bound(c,least_upper_bound(X,least_upper_bound(b,X_44))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(c,least_upper_bound(least_upper_bound(X,b),X_44)),least_upper_bound(c,least_upper_bound(least_upper_bound(X,b),X_44))) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
least_upper_bound(c,least_upper_bound(least_upper_bound(X,b),X_44)) = least_upper_bound(c,least_upper_bound(X,least_upper_bound(b,X_44))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X,b),X_44),least_upper_bound(X,least_upper_bound(b,X_44))) )],[refute_0_96,refute_0_99]) ).
cnf(refute_0_101,plain,
( least_upper_bound(c,least_upper_bound(X,least_upper_bound(b,X_44))) != least_upper_bound(c,least_upper_bound(X,X_44))
| least_upper_bound(c,least_upper_bound(least_upper_bound(X,b),X_44)) != least_upper_bound(c,least_upper_bound(X,least_upper_bound(b,X_44)))
| least_upper_bound(c,least_upper_bound(least_upper_bound(X,b),X_44)) = least_upper_bound(c,least_upper_bound(X,X_44)) ),
inference(subst,[],[refute_0_66:[bind(X0,$fot(least_upper_bound(c,least_upper_bound(least_upper_bound(X,b),X_44)))),bind(Y0,$fot(least_upper_bound(c,least_upper_bound(X,least_upper_bound(b,X_44))))),bind(Z0,$fot(least_upper_bound(c,least_upper_bound(X,X_44))))]]) ).
cnf(refute_0_102,plain,
( least_upper_bound(c,least_upper_bound(X,least_upper_bound(b,X_44))) != least_upper_bound(c,least_upper_bound(X,X_44))
| least_upper_bound(c,least_upper_bound(least_upper_bound(X,b),X_44)) = least_upper_bound(c,least_upper_bound(X,X_44)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(c,least_upper_bound(least_upper_bound(X,b),X_44)),least_upper_bound(c,least_upper_bound(X,least_upper_bound(b,X_44)))) )],[refute_0_100,refute_0_101]) ).
cnf(refute_0_103,plain,
least_upper_bound(c,least_upper_bound(least_upper_bound(X,b),X_44)) = least_upper_bound(c,least_upper_bound(X,X_44)),
inference(resolve,[$cnf( $equal(least_upper_bound(c,least_upper_bound(X,least_upper_bound(b,X_44))),least_upper_bound(c,least_upper_bound(X,X_44))) )],[refute_0_95,refute_0_102]) ).
cnf(refute_0_104,plain,
least_upper_bound(X_41,least_upper_bound(least_upper_bound(Y,X_41),X_43)) = least_upper_bound(least_upper_bound(X_41,least_upper_bound(Y,X_41)),X_43),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_41)),bind(Y,$fot(least_upper_bound(Y,X_41))),bind(Z,$fot(X_43))]]) ).
cnf(refute_0_105,plain,
least_upper_bound(least_upper_bound(X_19,Y),greatest_lower_bound(X_19,least_upper_bound(X_19,Y))) = least_upper_bound(X_19,Y),
inference(subst,[],[refute_0_17:[bind(X_10,$fot(least_upper_bound(X_19,Y))),bind(X_11,$fot(X_19))]]) ).
cnf(refute_0_106,plain,
greatest_lower_bound(X_19,least_upper_bound(X_19,Y)) = X_19,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_19))]]) ).
cnf(refute_0_107,plain,
( greatest_lower_bound(X_19,least_upper_bound(X_19,Y)) != X_19
| least_upper_bound(least_upper_bound(X_19,Y),greatest_lower_bound(X_19,least_upper_bound(X_19,Y))) != least_upper_bound(X_19,Y)
| least_upper_bound(least_upper_bound(X_19,Y),X_19) = least_upper_bound(X_19,Y) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_19,Y),greatest_lower_bound(X_19,least_upper_bound(X_19,Y))),least_upper_bound(X_19,Y)) ),[0,1],$fot(X_19)]]) ).
cnf(refute_0_108,plain,
( least_upper_bound(least_upper_bound(X_19,Y),greatest_lower_bound(X_19,least_upper_bound(X_19,Y))) != least_upper_bound(X_19,Y)
| least_upper_bound(least_upper_bound(X_19,Y),X_19) = least_upper_bound(X_19,Y) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_19,least_upper_bound(X_19,Y)),X_19) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
least_upper_bound(least_upper_bound(X_19,Y),X_19) = least_upper_bound(X_19,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_19,Y),greatest_lower_bound(X_19,least_upper_bound(X_19,Y))),least_upper_bound(X_19,Y)) )],[refute_0_105,refute_0_108]) ).
cnf(refute_0_110,plain,
least_upper_bound(least_upper_bound(X_19,Y),X_19) = least_upper_bound(X_19,least_upper_bound(Y,X_19)),
inference(subst,[],[refute_0_38:[bind(X,$fot(X_19)),bind(Z,$fot(X_19))]]) ).
cnf(refute_0_111,plain,
( least_upper_bound(least_upper_bound(X_19,Y),X_19) != least_upper_bound(X_19,Y)
| least_upper_bound(least_upper_bound(X_19,Y),X_19) != least_upper_bound(X_19,least_upper_bound(Y,X_19))
| least_upper_bound(X_19,least_upper_bound(Y,X_19)) = least_upper_bound(X_19,Y) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_19,Y),X_19),least_upper_bound(X_19,Y)) ),[0],$fot(least_upper_bound(X_19,least_upper_bound(Y,X_19)))]]) ).
cnf(refute_0_112,plain,
( least_upper_bound(least_upper_bound(X_19,Y),X_19) != least_upper_bound(X_19,Y)
| least_upper_bound(X_19,least_upper_bound(Y,X_19)) = least_upper_bound(X_19,Y) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_19,Y),X_19),least_upper_bound(X_19,least_upper_bound(Y,X_19))) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
least_upper_bound(X_19,least_upper_bound(Y,X_19)) = least_upper_bound(X_19,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_19,Y),X_19),least_upper_bound(X_19,Y)) )],[refute_0_109,refute_0_112]) ).
cnf(refute_0_114,plain,
least_upper_bound(X_41,least_upper_bound(Y,X_41)) = least_upper_bound(X_41,Y),
inference(subst,[],[refute_0_113:[bind(X_19,$fot(X_41))]]) ).
cnf(refute_0_115,plain,
( least_upper_bound(X_41,least_upper_bound(Y,X_41)) != least_upper_bound(X_41,Y)
| least_upper_bound(X_41,least_upper_bound(least_upper_bound(Y,X_41),X_43)) != least_upper_bound(least_upper_bound(X_41,least_upper_bound(Y,X_41)),X_43)
| least_upper_bound(X_41,least_upper_bound(least_upper_bound(Y,X_41),X_43)) = least_upper_bound(least_upper_bound(X_41,Y),X_43) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_41,least_upper_bound(least_upper_bound(Y,X_41),X_43)),least_upper_bound(least_upper_bound(X_41,least_upper_bound(Y,X_41)),X_43)) ),[1,0],$fot(least_upper_bound(X_41,Y))]]) ).
cnf(refute_0_116,plain,
( least_upper_bound(X_41,least_upper_bound(least_upper_bound(Y,X_41),X_43)) != least_upper_bound(least_upper_bound(X_41,least_upper_bound(Y,X_41)),X_43)
| least_upper_bound(X_41,least_upper_bound(least_upper_bound(Y,X_41),X_43)) = least_upper_bound(least_upper_bound(X_41,Y),X_43) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_41,least_upper_bound(Y,X_41)),least_upper_bound(X_41,Y)) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
least_upper_bound(X_41,least_upper_bound(least_upper_bound(Y,X_41),X_43)) = least_upper_bound(least_upper_bound(X_41,Y),X_43),
inference(resolve,[$cnf( $equal(least_upper_bound(X_41,least_upper_bound(least_upper_bound(Y,X_41),X_43)),least_upper_bound(least_upper_bound(X_41,least_upper_bound(Y,X_41)),X_43)) )],[refute_0_104,refute_0_116]) ).
cnf(refute_0_118,plain,
least_upper_bound(X_41,least_upper_bound(X_42,least_upper_bound(Y,X_42))) = least_upper_bound(least_upper_bound(X_41,X_42),least_upper_bound(Y,X_42)),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_41)),bind(Y,$fot(X_42)),bind(Z,$fot(least_upper_bound(Y,X_42)))]]) ).
cnf(refute_0_119,plain,
least_upper_bound(X_42,least_upper_bound(Y,X_42)) = least_upper_bound(X_42,Y),
inference(subst,[],[refute_0_113:[bind(X_19,$fot(X_42))]]) ).
cnf(refute_0_120,plain,
( least_upper_bound(X_41,least_upper_bound(X_42,least_upper_bound(Y,X_42))) != least_upper_bound(least_upper_bound(X_41,X_42),least_upper_bound(Y,X_42))
| least_upper_bound(X_42,least_upper_bound(Y,X_42)) != least_upper_bound(X_42,Y)
| least_upper_bound(X_41,least_upper_bound(X_42,Y)) = least_upper_bound(least_upper_bound(X_41,X_42),least_upper_bound(Y,X_42)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_41,least_upper_bound(X_42,least_upper_bound(Y,X_42))),least_upper_bound(least_upper_bound(X_41,X_42),least_upper_bound(Y,X_42))) ),[0,1],$fot(least_upper_bound(X_42,Y))]]) ).
cnf(refute_0_121,plain,
( least_upper_bound(X_41,least_upper_bound(X_42,least_upper_bound(Y,X_42))) != least_upper_bound(least_upper_bound(X_41,X_42),least_upper_bound(Y,X_42))
| least_upper_bound(X_41,least_upper_bound(X_42,Y)) = least_upper_bound(least_upper_bound(X_41,X_42),least_upper_bound(Y,X_42)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_42,least_upper_bound(Y,X_42)),least_upper_bound(X_42,Y)) )],[refute_0_119,refute_0_120]) ).
cnf(refute_0_122,plain,
least_upper_bound(X_41,least_upper_bound(X_42,Y)) = least_upper_bound(least_upper_bound(X_41,X_42),least_upper_bound(Y,X_42)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_41,least_upper_bound(X_42,least_upper_bound(Y,X_42))),least_upper_bound(least_upper_bound(X_41,X_42),least_upper_bound(Y,X_42))) )],[refute_0_118,refute_0_121]) ).
cnf(refute_0_123,plain,
least_upper_bound(least_upper_bound(X_41,X_42),Y) = least_upper_bound(X_41,least_upper_bound(X_42,Y)),
inference(subst,[],[refute_0_38:[bind(X,$fot(X_41)),bind(Y,$fot(X_42)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_124,plain,
least_upper_bound(X_42,least_upper_bound(least_upper_bound(X_41,X_42),Y)) = least_upper_bound(X_42,least_upper_bound(least_upper_bound(X_41,X_42),Y)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_42,least_upper_bound(least_upper_bound(X_41,X_42),Y)))]]) ).
cnf(refute_0_125,plain,
( least_upper_bound(X_42,least_upper_bound(least_upper_bound(X_41,X_42),Y)) != least_upper_bound(X_42,least_upper_bound(least_upper_bound(X_41,X_42),Y))
| least_upper_bound(least_upper_bound(X_41,X_42),Y) != least_upper_bound(X_41,least_upper_bound(X_42,Y))
| least_upper_bound(X_42,least_upper_bound(least_upper_bound(X_41,X_42),Y)) = least_upper_bound(X_42,least_upper_bound(X_41,least_upper_bound(X_42,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_42,least_upper_bound(least_upper_bound(X_41,X_42),Y)),least_upper_bound(X_42,least_upper_bound(least_upper_bound(X_41,X_42),Y))) ),[1,1],$fot(least_upper_bound(X_41,least_upper_bound(X_42,Y)))]]) ).
cnf(refute_0_126,plain,
( least_upper_bound(least_upper_bound(X_41,X_42),Y) != least_upper_bound(X_41,least_upper_bound(X_42,Y))
| least_upper_bound(X_42,least_upper_bound(least_upper_bound(X_41,X_42),Y)) = least_upper_bound(X_42,least_upper_bound(X_41,least_upper_bound(X_42,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_42,least_upper_bound(least_upper_bound(X_41,X_42),Y)),least_upper_bound(X_42,least_upper_bound(least_upper_bound(X_41,X_42),Y))) )],[refute_0_124,refute_0_125]) ).
cnf(refute_0_127,plain,
least_upper_bound(X_42,least_upper_bound(least_upper_bound(X_41,X_42),Y)) = least_upper_bound(X_42,least_upper_bound(X_41,least_upper_bound(X_42,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_41,X_42),Y),least_upper_bound(X_41,least_upper_bound(X_42,Y))) )],[refute_0_123,refute_0_126]) ).
cnf(refute_0_128,plain,
least_upper_bound(least_upper_bound(X_41,X_42),least_upper_bound(Y,X_42)) = least_upper_bound(X_42,least_upper_bound(least_upper_bound(X_41,X_42),Y)),
inference(subst,[],[refute_0_62:[bind(X,$fot(X_42)),bind(X_41,$fot(least_upper_bound(X_41,X_42))),bind(X_42,$fot(Y))]]) ).
cnf(refute_0_129,plain,
( least_upper_bound(X_42,least_upper_bound(least_upper_bound(X_41,X_42),Y)) != least_upper_bound(X_42,least_upper_bound(X_41,least_upper_bound(X_42,Y)))
| least_upper_bound(least_upper_bound(X_41,X_42),least_upper_bound(Y,X_42)) != least_upper_bound(X_42,least_upper_bound(least_upper_bound(X_41,X_42),Y))
| least_upper_bound(least_upper_bound(X_41,X_42),least_upper_bound(Y,X_42)) = least_upper_bound(X_42,least_upper_bound(X_41,least_upper_bound(X_42,Y))) ),
inference(subst,[],[refute_0_66:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_41,X_42),least_upper_bound(Y,X_42)))),bind(Y0,$fot(least_upper_bound(X_42,least_upper_bound(least_upper_bound(X_41,X_42),Y)))),bind(Z0,$fot(least_upper_bound(X_42,least_upper_bound(X_41,least_upper_bound(X_42,Y)))))]]) ).
cnf(refute_0_130,plain,
( least_upper_bound(X_42,least_upper_bound(least_upper_bound(X_41,X_42),Y)) != least_upper_bound(X_42,least_upper_bound(X_41,least_upper_bound(X_42,Y)))
| least_upper_bound(least_upper_bound(X_41,X_42),least_upper_bound(Y,X_42)) = least_upper_bound(X_42,least_upper_bound(X_41,least_upper_bound(X_42,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_41,X_42),least_upper_bound(Y,X_42)),least_upper_bound(X_42,least_upper_bound(least_upper_bound(X_41,X_42),Y))) )],[refute_0_128,refute_0_129]) ).
cnf(refute_0_131,plain,
least_upper_bound(least_upper_bound(X_41,X_42),least_upper_bound(Y,X_42)) = least_upper_bound(X_42,least_upper_bound(X_41,least_upper_bound(X_42,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_42,least_upper_bound(least_upper_bound(X_41,X_42),Y)),least_upper_bound(X_42,least_upper_bound(X_41,least_upper_bound(X_42,Y)))) )],[refute_0_127,refute_0_130]) ).
cnf(refute_0_132,plain,
( least_upper_bound(X_41,least_upper_bound(X_42,Y)) != least_upper_bound(least_upper_bound(X_41,X_42),least_upper_bound(Y,X_42))
| least_upper_bound(least_upper_bound(X_41,X_42),least_upper_bound(Y,X_42)) != least_upper_bound(X_42,least_upper_bound(X_41,least_upper_bound(X_42,Y)))
| least_upper_bound(X_41,least_upper_bound(X_42,Y)) = least_upper_bound(X_42,least_upper_bound(X_41,least_upper_bound(X_42,Y))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_41,least_upper_bound(X_42,Y)),least_upper_bound(X_42,least_upper_bound(X_41,least_upper_bound(X_42,Y)))) ),[0],$fot(least_upper_bound(least_upper_bound(X_41,X_42),least_upper_bound(Y,X_42)))]]) ).
cnf(refute_0_133,plain,
( least_upper_bound(X_41,least_upper_bound(X_42,Y)) != least_upper_bound(least_upper_bound(X_41,X_42),least_upper_bound(Y,X_42))
| least_upper_bound(X_41,least_upper_bound(X_42,Y)) = least_upper_bound(X_42,least_upper_bound(X_41,least_upper_bound(X_42,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_41,X_42),least_upper_bound(Y,X_42)),least_upper_bound(X_42,least_upper_bound(X_41,least_upper_bound(X_42,Y)))) )],[refute_0_131,refute_0_132]) ).
cnf(refute_0_134,plain,
least_upper_bound(X_41,least_upper_bound(X_42,Y)) = least_upper_bound(X_42,least_upper_bound(X_41,least_upper_bound(X_42,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_41,least_upper_bound(X_42,Y)),least_upper_bound(least_upper_bound(X_41,X_42),least_upper_bound(Y,X_42))) )],[refute_0_122,refute_0_133]) ).
cnf(refute_0_135,plain,
( least_upper_bound(X_41,least_upper_bound(X_42,Y)) != least_upper_bound(X_42,least_upper_bound(X_41,least_upper_bound(X_42,Y)))
| least_upper_bound(X_42,least_upper_bound(X_41,least_upper_bound(X_42,Y))) = least_upper_bound(X_41,least_upper_bound(X_42,Y)) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(least_upper_bound(X_41,least_upper_bound(X_42,Y)))),bind(Y0,$fot(least_upper_bound(X_42,least_upper_bound(X_41,least_upper_bound(X_42,Y)))))]]) ).
cnf(refute_0_136,plain,
least_upper_bound(X_42,least_upper_bound(X_41,least_upper_bound(X_42,Y))) = least_upper_bound(X_41,least_upper_bound(X_42,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_41,least_upper_bound(X_42,Y)),least_upper_bound(X_42,least_upper_bound(X_41,least_upper_bound(X_42,Y)))) )],[refute_0_134,refute_0_135]) ).
cnf(refute_0_137,plain,
least_upper_bound(X_41,least_upper_bound(Y,least_upper_bound(X_41,X_43))) = least_upper_bound(Y,least_upper_bound(X_41,X_43)),
inference(subst,[],[refute_0_136:[bind(Y,$fot(X_43)),bind(X_41,$fot(Y)),bind(X_42,$fot(X_41))]]) ).
cnf(refute_0_138,plain,
least_upper_bound(least_upper_bound(Y,X_41),X_43) = least_upper_bound(Y,least_upper_bound(X_41,X_43)),
inference(subst,[],[refute_0_38:[bind(X,$fot(Y)),bind(Y,$fot(X_41)),bind(Z,$fot(X_43))]]) ).
cnf(refute_0_139,plain,
least_upper_bound(X_41,least_upper_bound(least_upper_bound(Y,X_41),X_43)) = least_upper_bound(X_41,least_upper_bound(least_upper_bound(Y,X_41),X_43)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_41,least_upper_bound(least_upper_bound(Y,X_41),X_43)))]]) ).
cnf(refute_0_140,plain,
( least_upper_bound(X_41,least_upper_bound(least_upper_bound(Y,X_41),X_43)) != least_upper_bound(X_41,least_upper_bound(least_upper_bound(Y,X_41),X_43))
| least_upper_bound(least_upper_bound(Y,X_41),X_43) != least_upper_bound(Y,least_upper_bound(X_41,X_43))
| least_upper_bound(X_41,least_upper_bound(least_upper_bound(Y,X_41),X_43)) = least_upper_bound(X_41,least_upper_bound(Y,least_upper_bound(X_41,X_43))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_41,least_upper_bound(least_upper_bound(Y,X_41),X_43)),least_upper_bound(X_41,least_upper_bound(least_upper_bound(Y,X_41),X_43))) ),[1,1],$fot(least_upper_bound(Y,least_upper_bound(X_41,X_43)))]]) ).
cnf(refute_0_141,plain,
( least_upper_bound(least_upper_bound(Y,X_41),X_43) != least_upper_bound(Y,least_upper_bound(X_41,X_43))
| least_upper_bound(X_41,least_upper_bound(least_upper_bound(Y,X_41),X_43)) = least_upper_bound(X_41,least_upper_bound(Y,least_upper_bound(X_41,X_43))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_41,least_upper_bound(least_upper_bound(Y,X_41),X_43)),least_upper_bound(X_41,least_upper_bound(least_upper_bound(Y,X_41),X_43))) )],[refute_0_139,refute_0_140]) ).
cnf(refute_0_142,plain,
least_upper_bound(X_41,least_upper_bound(least_upper_bound(Y,X_41),X_43)) = least_upper_bound(X_41,least_upper_bound(Y,least_upper_bound(X_41,X_43))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_41),X_43),least_upper_bound(Y,least_upper_bound(X_41,X_43))) )],[refute_0_138,refute_0_141]) ).
cnf(refute_0_143,plain,
( least_upper_bound(X_41,least_upper_bound(Y,least_upper_bound(X_41,X_43))) != least_upper_bound(Y,least_upper_bound(X_41,X_43))
| least_upper_bound(X_41,least_upper_bound(least_upper_bound(Y,X_41),X_43)) != least_upper_bound(X_41,least_upper_bound(Y,least_upper_bound(X_41,X_43)))
| least_upper_bound(X_41,least_upper_bound(least_upper_bound(Y,X_41),X_43)) = least_upper_bound(Y,least_upper_bound(X_41,X_43)) ),
inference(subst,[],[refute_0_66:[bind(X0,$fot(least_upper_bound(X_41,least_upper_bound(least_upper_bound(Y,X_41),X_43)))),bind(Y0,$fot(least_upper_bound(X_41,least_upper_bound(Y,least_upper_bound(X_41,X_43))))),bind(Z0,$fot(least_upper_bound(Y,least_upper_bound(X_41,X_43))))]]) ).
cnf(refute_0_144,plain,
( least_upper_bound(X_41,least_upper_bound(Y,least_upper_bound(X_41,X_43))) != least_upper_bound(Y,least_upper_bound(X_41,X_43))
| least_upper_bound(X_41,least_upper_bound(least_upper_bound(Y,X_41),X_43)) = least_upper_bound(Y,least_upper_bound(X_41,X_43)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_41,least_upper_bound(least_upper_bound(Y,X_41),X_43)),least_upper_bound(X_41,least_upper_bound(Y,least_upper_bound(X_41,X_43)))) )],[refute_0_142,refute_0_143]) ).
cnf(refute_0_145,plain,
least_upper_bound(X_41,least_upper_bound(least_upper_bound(Y,X_41),X_43)) = least_upper_bound(Y,least_upper_bound(X_41,X_43)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_41,least_upper_bound(Y,least_upper_bound(X_41,X_43))),least_upper_bound(Y,least_upper_bound(X_41,X_43))) )],[refute_0_137,refute_0_144]) ).
cnf(refute_0_146,plain,
( least_upper_bound(X_41,least_upper_bound(least_upper_bound(Y,X_41),X_43)) != least_upper_bound(Y,least_upper_bound(X_41,X_43))
| least_upper_bound(X_41,least_upper_bound(least_upper_bound(Y,X_41),X_43)) != least_upper_bound(least_upper_bound(X_41,Y),X_43)
| least_upper_bound(Y,least_upper_bound(X_41,X_43)) = least_upper_bound(least_upper_bound(X_41,Y),X_43) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_41,least_upper_bound(least_upper_bound(Y,X_41),X_43)),least_upper_bound(least_upper_bound(X_41,Y),X_43)) ),[0],$fot(least_upper_bound(Y,least_upper_bound(X_41,X_43)))]]) ).
cnf(refute_0_147,plain,
( least_upper_bound(X_41,least_upper_bound(least_upper_bound(Y,X_41),X_43)) != least_upper_bound(least_upper_bound(X_41,Y),X_43)
| least_upper_bound(Y,least_upper_bound(X_41,X_43)) = least_upper_bound(least_upper_bound(X_41,Y),X_43) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_41,least_upper_bound(least_upper_bound(Y,X_41),X_43)),least_upper_bound(Y,least_upper_bound(X_41,X_43))) )],[refute_0_145,refute_0_146]) ).
cnf(refute_0_148,plain,
least_upper_bound(least_upper_bound(X_41,Y),X_43) = least_upper_bound(X_41,least_upper_bound(Y,X_43)),
inference(subst,[],[refute_0_38:[bind(X,$fot(X_41)),bind(Z,$fot(X_43))]]) ).
cnf(refute_0_149,plain,
( least_upper_bound(Y,least_upper_bound(X_41,X_43)) != least_upper_bound(least_upper_bound(X_41,Y),X_43)
| least_upper_bound(least_upper_bound(X_41,Y),X_43) != least_upper_bound(X_41,least_upper_bound(Y,X_43))
| least_upper_bound(Y,least_upper_bound(X_41,X_43)) = least_upper_bound(X_41,least_upper_bound(Y,X_43)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(Y,least_upper_bound(X_41,X_43)),least_upper_bound(X_41,least_upper_bound(Y,X_43))) ),[0],$fot(least_upper_bound(least_upper_bound(X_41,Y),X_43))]]) ).
cnf(refute_0_150,plain,
( least_upper_bound(Y,least_upper_bound(X_41,X_43)) != least_upper_bound(least_upper_bound(X_41,Y),X_43)
| least_upper_bound(Y,least_upper_bound(X_41,X_43)) = least_upper_bound(X_41,least_upper_bound(Y,X_43)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_41,Y),X_43),least_upper_bound(X_41,least_upper_bound(Y,X_43))) )],[refute_0_148,refute_0_149]) ).
cnf(refute_0_151,plain,
( least_upper_bound(X_41,least_upper_bound(least_upper_bound(Y,X_41),X_43)) != least_upper_bound(least_upper_bound(X_41,Y),X_43)
| least_upper_bound(Y,least_upper_bound(X_41,X_43)) = least_upper_bound(X_41,least_upper_bound(Y,X_43)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_41,X_43)),least_upper_bound(least_upper_bound(X_41,Y),X_43)) )],[refute_0_147,refute_0_150]) ).
cnf(refute_0_152,plain,
least_upper_bound(Y,least_upper_bound(X_41,X_43)) = least_upper_bound(X_41,least_upper_bound(Y,X_43)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_41,least_upper_bound(least_upper_bound(Y,X_41),X_43)),least_upper_bound(least_upper_bound(X_41,Y),X_43)) )],[refute_0_117,refute_0_151]) ).
cnf(refute_0_153,plain,
( least_upper_bound(Y,least_upper_bound(X_41,X_43)) != least_upper_bound(X_41,least_upper_bound(Y,X_43))
| least_upper_bound(X_41,least_upper_bound(Y,X_43)) = least_upper_bound(Y,least_upper_bound(X_41,X_43)) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(least_upper_bound(Y,least_upper_bound(X_41,X_43)))),bind(Y0,$fot(least_upper_bound(X_41,least_upper_bound(Y,X_43))))]]) ).
cnf(refute_0_154,plain,
least_upper_bound(X_41,least_upper_bound(Y,X_43)) = least_upper_bound(Y,least_upper_bound(X_41,X_43)),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_41,X_43)),least_upper_bound(X_41,least_upper_bound(Y,X_43))) )],[refute_0_152,refute_0_153]) ).
cnf(refute_0_155,plain,
least_upper_bound(least_upper_bound(X,b),least_upper_bound(c,X_44)) = least_upper_bound(c,least_upper_bound(least_upper_bound(X,b),X_44)),
inference(subst,[],[refute_0_154:[bind(Y,$fot(c)),bind(X_41,$fot(least_upper_bound(X,b))),bind(X_43,$fot(X_44))]]) ).
cnf(refute_0_156,plain,
( least_upper_bound(c,least_upper_bound(least_upper_bound(X,b),X_44)) != least_upper_bound(c,least_upper_bound(X,X_44))
| least_upper_bound(least_upper_bound(X,b),least_upper_bound(c,X_44)) != least_upper_bound(c,least_upper_bound(least_upper_bound(X,b),X_44))
| least_upper_bound(least_upper_bound(X,b),least_upper_bound(c,X_44)) = least_upper_bound(c,least_upper_bound(X,X_44)) ),
inference(subst,[],[refute_0_66:[bind(X0,$fot(least_upper_bound(least_upper_bound(X,b),least_upper_bound(c,X_44)))),bind(Y0,$fot(least_upper_bound(c,least_upper_bound(least_upper_bound(X,b),X_44)))),bind(Z0,$fot(least_upper_bound(c,least_upper_bound(X,X_44))))]]) ).
cnf(refute_0_157,plain,
( least_upper_bound(c,least_upper_bound(least_upper_bound(X,b),X_44)) != least_upper_bound(c,least_upper_bound(X,X_44))
| least_upper_bound(least_upper_bound(X,b),least_upper_bound(c,X_44)) = least_upper_bound(c,least_upper_bound(X,X_44)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X,b),least_upper_bound(c,X_44)),least_upper_bound(c,least_upper_bound(least_upper_bound(X,b),X_44))) )],[refute_0_155,refute_0_156]) ).
cnf(refute_0_158,plain,
least_upper_bound(least_upper_bound(X,b),least_upper_bound(c,X_44)) = least_upper_bound(c,least_upper_bound(X,X_44)),
inference(resolve,[$cnf( $equal(least_upper_bound(c,least_upper_bound(least_upper_bound(X,b),X_44)),least_upper_bound(c,least_upper_bound(X,X_44))) )],[refute_0_103,refute_0_157]) ).
cnf(refute_0_159,plain,
( least_upper_bound(X,least_upper_bound(c,X_44)) != least_upper_bound(least_upper_bound(X,b),least_upper_bound(c,X_44))
| least_upper_bound(least_upper_bound(X,b),least_upper_bound(c,X_44)) != least_upper_bound(c,least_upper_bound(X,X_44))
| least_upper_bound(X,least_upper_bound(c,X_44)) = least_upper_bound(c,least_upper_bound(X,X_44)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,least_upper_bound(c,X_44)),least_upper_bound(c,least_upper_bound(X,X_44))) ),[0],$fot(least_upper_bound(least_upper_bound(X,b),least_upper_bound(c,X_44)))]]) ).
cnf(refute_0_160,plain,
( least_upper_bound(X,least_upper_bound(c,X_44)) != least_upper_bound(least_upper_bound(X,b),least_upper_bound(c,X_44))
| least_upper_bound(X,least_upper_bound(c,X_44)) = least_upper_bound(c,least_upper_bound(X,X_44)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X,b),least_upper_bound(c,X_44)),least_upper_bound(c,least_upper_bound(X,X_44))) )],[refute_0_158,refute_0_159]) ).
cnf(refute_0_161,plain,
least_upper_bound(X,least_upper_bound(c,X_44)) = least_upper_bound(c,least_upper_bound(X,X_44)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(c,X_44)),least_upper_bound(least_upper_bound(X,b),least_upper_bound(c,X_44))) )],[refute_0_78,refute_0_160]) ).
cnf(refute_0_162,plain,
least_upper_bound(greatest_lower_bound(a,X_32),least_upper_bound(c,greatest_lower_bound(c,X_32))) = least_upper_bound(c,least_upper_bound(greatest_lower_bound(a,X_32),greatest_lower_bound(c,X_32))),
inference(subst,[],[refute_0_161:[bind(X,$fot(greatest_lower_bound(a,X_32))),bind(X_44,$fot(greatest_lower_bound(c,X_32)))]]) ).
cnf(refute_0_163,plain,
least_upper_bound(greatest_lower_bound(c,X_32),greatest_lower_bound(a,greatest_lower_bound(c,X_32))) = greatest_lower_bound(c,X_32),
inference(subst,[],[refute_0_17:[bind(X_10,$fot(greatest_lower_bound(c,X_32))),bind(X_11,$fot(a))]]) ).
cnf(refute_0_164,plain,
greatest_lower_bound(a,greatest_lower_bound(c,X_28)) = greatest_lower_bound(greatest_lower_bound(a,c),X_28),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(a)),bind(Y,$fot(c)),bind(Z,$fot(X_28))]]) ).
cnf(refute_0_165,plain,
( greatest_lower_bound(a,c) != a
| greatest_lower_bound(a,greatest_lower_bound(c,X_28)) != greatest_lower_bound(greatest_lower_bound(a,c),X_28)
| greatest_lower_bound(a,greatest_lower_bound(c,X_28)) = greatest_lower_bound(a,X_28) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(c,X_28)),greatest_lower_bound(greatest_lower_bound(a,c),X_28)) ),[1,0],$fot(a)]]) ).
cnf(refute_0_166,plain,
( greatest_lower_bound(a,greatest_lower_bound(c,X_28)) != greatest_lower_bound(greatest_lower_bound(a,c),X_28)
| greatest_lower_bound(a,greatest_lower_bound(c,X_28)) = greatest_lower_bound(a,X_28) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,c),a) )],[ax_lub1b_1,refute_0_165]) ).
cnf(refute_0_167,plain,
greatest_lower_bound(a,greatest_lower_bound(c,X_28)) = greatest_lower_bound(a,X_28),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(c,X_28)),greatest_lower_bound(greatest_lower_bound(a,c),X_28)) )],[refute_0_164,refute_0_166]) ).
cnf(refute_0_168,plain,
greatest_lower_bound(a,greatest_lower_bound(c,X_32)) = greatest_lower_bound(a,X_32),
inference(subst,[],[refute_0_167:[bind(X_28,$fot(X_32))]]) ).
cnf(refute_0_169,plain,
( greatest_lower_bound(a,greatest_lower_bound(c,X_32)) != greatest_lower_bound(a,X_32)
| least_upper_bound(greatest_lower_bound(c,X_32),greatest_lower_bound(a,greatest_lower_bound(c,X_32))) != greatest_lower_bound(c,X_32)
| least_upper_bound(greatest_lower_bound(c,X_32),greatest_lower_bound(a,X_32)) = greatest_lower_bound(c,X_32) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(c,X_32),greatest_lower_bound(a,greatest_lower_bound(c,X_32))),greatest_lower_bound(c,X_32)) ),[0,1],$fot(greatest_lower_bound(a,X_32))]]) ).
cnf(refute_0_170,plain,
( least_upper_bound(greatest_lower_bound(c,X_32),greatest_lower_bound(a,greatest_lower_bound(c,X_32))) != greatest_lower_bound(c,X_32)
| least_upper_bound(greatest_lower_bound(c,X_32),greatest_lower_bound(a,X_32)) = greatest_lower_bound(c,X_32) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(c,X_32)),greatest_lower_bound(a,X_32)) )],[refute_0_168,refute_0_169]) ).
cnf(refute_0_171,plain,
least_upper_bound(greatest_lower_bound(c,X_32),greatest_lower_bound(a,X_32)) = greatest_lower_bound(c,X_32),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(c,X_32),greatest_lower_bound(a,greatest_lower_bound(c,X_32))),greatest_lower_bound(c,X_32)) )],[refute_0_163,refute_0_170]) ).
cnf(refute_0_172,plain,
( least_upper_bound(X,Y) != least_upper_bound(Y,X)
| least_upper_bound(Y,X) = least_upper_bound(X,Y) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(least_upper_bound(X,Y))),bind(Y0,$fot(least_upper_bound(Y,X)))]]) ).
cnf(refute_0_173,plain,
least_upper_bound(Y,X) = least_upper_bound(X,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(X,Y),least_upper_bound(Y,X)) )],[symmetry_of_lub,refute_0_172]) ).
cnf(refute_0_174,plain,
least_upper_bound(greatest_lower_bound(c,X_32),greatest_lower_bound(a,X_32)) = least_upper_bound(greatest_lower_bound(a,X_32),greatest_lower_bound(c,X_32)),
inference(subst,[],[refute_0_173:[bind(X,$fot(greatest_lower_bound(a,X_32))),bind(Y,$fot(greatest_lower_bound(c,X_32)))]]) ).
cnf(refute_0_175,plain,
( least_upper_bound(greatest_lower_bound(c,X_32),greatest_lower_bound(a,X_32)) != greatest_lower_bound(c,X_32)
| least_upper_bound(greatest_lower_bound(c,X_32),greatest_lower_bound(a,X_32)) != least_upper_bound(greatest_lower_bound(a,X_32),greatest_lower_bound(c,X_32))
| least_upper_bound(greatest_lower_bound(a,X_32),greatest_lower_bound(c,X_32)) = greatest_lower_bound(c,X_32) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(c,X_32),greatest_lower_bound(a,X_32)),greatest_lower_bound(c,X_32)) ),[0],$fot(least_upper_bound(greatest_lower_bound(a,X_32),greatest_lower_bound(c,X_32)))]]) ).
cnf(refute_0_176,plain,
( least_upper_bound(greatest_lower_bound(c,X_32),greatest_lower_bound(a,X_32)) != greatest_lower_bound(c,X_32)
| least_upper_bound(greatest_lower_bound(a,X_32),greatest_lower_bound(c,X_32)) = greatest_lower_bound(c,X_32) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(c,X_32),greatest_lower_bound(a,X_32)),least_upper_bound(greatest_lower_bound(a,X_32),greatest_lower_bound(c,X_32))) )],[refute_0_174,refute_0_175]) ).
cnf(refute_0_177,plain,
least_upper_bound(greatest_lower_bound(a,X_32),greatest_lower_bound(c,X_32)) = greatest_lower_bound(c,X_32),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(c,X_32),greatest_lower_bound(a,X_32)),greatest_lower_bound(c,X_32)) )],[refute_0_171,refute_0_176]) ).
cnf(refute_0_178,plain,
( least_upper_bound(greatest_lower_bound(a,X_32),greatest_lower_bound(c,X_32)) != greatest_lower_bound(c,X_32)
| least_upper_bound(greatest_lower_bound(a,X_32),least_upper_bound(c,greatest_lower_bound(c,X_32))) != least_upper_bound(c,least_upper_bound(greatest_lower_bound(a,X_32),greatest_lower_bound(c,X_32)))
| least_upper_bound(greatest_lower_bound(a,X_32),least_upper_bound(c,greatest_lower_bound(c,X_32))) = least_upper_bound(c,greatest_lower_bound(c,X_32)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,X_32),least_upper_bound(c,greatest_lower_bound(c,X_32))),least_upper_bound(c,least_upper_bound(greatest_lower_bound(a,X_32),greatest_lower_bound(c,X_32)))) ),[1,1],$fot(greatest_lower_bound(c,X_32))]]) ).
cnf(refute_0_179,plain,
( least_upper_bound(greatest_lower_bound(a,X_32),least_upper_bound(c,greatest_lower_bound(c,X_32))) != least_upper_bound(c,least_upper_bound(greatest_lower_bound(a,X_32),greatest_lower_bound(c,X_32)))
| least_upper_bound(greatest_lower_bound(a,X_32),least_upper_bound(c,greatest_lower_bound(c,X_32))) = least_upper_bound(c,greatest_lower_bound(c,X_32)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,X_32),greatest_lower_bound(c,X_32)),greatest_lower_bound(c,X_32)) )],[refute_0_177,refute_0_178]) ).
cnf(refute_0_180,plain,
least_upper_bound(greatest_lower_bound(a,X_32),least_upper_bound(c,greatest_lower_bound(c,X_32))) = least_upper_bound(c,greatest_lower_bound(c,X_32)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,X_32),least_upper_bound(c,greatest_lower_bound(c,X_32))),least_upper_bound(c,least_upper_bound(greatest_lower_bound(a,X_32),greatest_lower_bound(c,X_32)))) )],[refute_0_162,refute_0_179]) ).
cnf(refute_0_181,plain,
least_upper_bound(greatest_lower_bound(a,X_32),c) = least_upper_bound(c,greatest_lower_bound(a,X_32)),
inference(subst,[],[refute_0_173:[bind(X,$fot(c)),bind(Y,$fot(greatest_lower_bound(a,X_32)))]]) ).
cnf(refute_0_182,plain,
least_upper_bound(X_50,least_upper_bound(c,greatest_lower_bound(c,Y))) = least_upper_bound(c,least_upper_bound(X_50,greatest_lower_bound(c,Y))),
inference(subst,[],[refute_0_161:[bind(X,$fot(X_50)),bind(X_44,$fot(greatest_lower_bound(c,Y)))]]) ).
cnf(refute_0_183,plain,
least_upper_bound(c,greatest_lower_bound(c,Y)) = c,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(c))]]) ).
cnf(refute_0_184,plain,
( least_upper_bound(X_50,least_upper_bound(c,greatest_lower_bound(c,Y))) != least_upper_bound(c,least_upper_bound(X_50,greatest_lower_bound(c,Y)))
| least_upper_bound(c,greatest_lower_bound(c,Y)) != c
| least_upper_bound(X_50,c) = least_upper_bound(c,least_upper_bound(X_50,greatest_lower_bound(c,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_50,least_upper_bound(c,greatest_lower_bound(c,Y))),least_upper_bound(c,least_upper_bound(X_50,greatest_lower_bound(c,Y)))) ),[0,1],$fot(c)]]) ).
cnf(refute_0_185,plain,
( least_upper_bound(X_50,least_upper_bound(c,greatest_lower_bound(c,Y))) != least_upper_bound(c,least_upper_bound(X_50,greatest_lower_bound(c,Y)))
| least_upper_bound(X_50,c) = least_upper_bound(c,least_upper_bound(X_50,greatest_lower_bound(c,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(c,greatest_lower_bound(c,Y)),c) )],[refute_0_183,refute_0_184]) ).
cnf(refute_0_186,plain,
least_upper_bound(X_50,c) = least_upper_bound(c,least_upper_bound(X_50,greatest_lower_bound(c,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_50,least_upper_bound(c,greatest_lower_bound(c,Y))),least_upper_bound(c,least_upper_bound(X_50,greatest_lower_bound(c,Y)))) )],[refute_0_182,refute_0_185]) ).
cnf(refute_0_187,plain,
( least_upper_bound(X_50,c) != least_upper_bound(c,least_upper_bound(X_50,greatest_lower_bound(c,Y)))
| least_upper_bound(c,least_upper_bound(X_50,greatest_lower_bound(c,Y))) = least_upper_bound(X_50,c) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(least_upper_bound(X_50,c))),bind(Y0,$fot(least_upper_bound(c,least_upper_bound(X_50,greatest_lower_bound(c,Y)))))]]) ).
cnf(refute_0_188,plain,
least_upper_bound(c,least_upper_bound(X_50,greatest_lower_bound(c,Y))) = least_upper_bound(X_50,c),
inference(resolve,[$cnf( $equal(least_upper_bound(X_50,c),least_upper_bound(c,least_upper_bound(X_50,greatest_lower_bound(c,Y)))) )],[refute_0_186,refute_0_187]) ).
cnf(refute_0_189,plain,
least_upper_bound(c,least_upper_bound(greatest_lower_bound(a,X_32),greatest_lower_bound(c,X_32))) = least_upper_bound(greatest_lower_bound(a,X_32),c),
inference(subst,[],[refute_0_188:[bind(Y,$fot(X_32)),bind(X_50,$fot(greatest_lower_bound(a,X_32)))]]) ).
cnf(refute_0_190,plain,
( least_upper_bound(c,least_upper_bound(greatest_lower_bound(a,X_32),greatest_lower_bound(c,X_32))) != least_upper_bound(greatest_lower_bound(a,X_32),c)
| least_upper_bound(greatest_lower_bound(a,X_32),c) != least_upper_bound(c,greatest_lower_bound(a,X_32))
| least_upper_bound(c,least_upper_bound(greatest_lower_bound(a,X_32),greatest_lower_bound(c,X_32))) = least_upper_bound(c,greatest_lower_bound(a,X_32)) ),
inference(subst,[],[refute_0_66:[bind(X0,$fot(least_upper_bound(c,least_upper_bound(greatest_lower_bound(a,X_32),greatest_lower_bound(c,X_32))))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(a,X_32),c))),bind(Z0,$fot(least_upper_bound(c,greatest_lower_bound(a,X_32))))]]) ).
cnf(refute_0_191,plain,
( least_upper_bound(greatest_lower_bound(a,X_32),c) != least_upper_bound(c,greatest_lower_bound(a,X_32))
| least_upper_bound(c,least_upper_bound(greatest_lower_bound(a,X_32),greatest_lower_bound(c,X_32))) = least_upper_bound(c,greatest_lower_bound(a,X_32)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(c,least_upper_bound(greatest_lower_bound(a,X_32),greatest_lower_bound(c,X_32))),least_upper_bound(greatest_lower_bound(a,X_32),c)) )],[refute_0_189,refute_0_190]) ).
cnf(refute_0_192,plain,
least_upper_bound(c,least_upper_bound(greatest_lower_bound(a,X_32),greatest_lower_bound(c,X_32))) = least_upper_bound(c,greatest_lower_bound(a,X_32)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,X_32),c),least_upper_bound(c,greatest_lower_bound(a,X_32))) )],[refute_0_181,refute_0_191]) ).
cnf(refute_0_193,plain,
( least_upper_bound(c,least_upper_bound(greatest_lower_bound(a,X_32),greatest_lower_bound(c,X_32))) != least_upper_bound(c,greatest_lower_bound(a,X_32))
| least_upper_bound(greatest_lower_bound(a,X_32),least_upper_bound(c,greatest_lower_bound(c,X_32))) != least_upper_bound(c,least_upper_bound(greatest_lower_bound(a,X_32),greatest_lower_bound(c,X_32)))
| least_upper_bound(greatest_lower_bound(a,X_32),least_upper_bound(c,greatest_lower_bound(c,X_32))) = least_upper_bound(c,greatest_lower_bound(a,X_32)) ),
inference(subst,[],[refute_0_66:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(a,X_32),least_upper_bound(c,greatest_lower_bound(c,X_32))))),bind(Y0,$fot(least_upper_bound(c,least_upper_bound(greatest_lower_bound(a,X_32),greatest_lower_bound(c,X_32))))),bind(Z0,$fot(least_upper_bound(c,greatest_lower_bound(a,X_32))))]]) ).
cnf(refute_0_194,plain,
( least_upper_bound(c,least_upper_bound(greatest_lower_bound(a,X_32),greatest_lower_bound(c,X_32))) != least_upper_bound(c,greatest_lower_bound(a,X_32))
| least_upper_bound(greatest_lower_bound(a,X_32),least_upper_bound(c,greatest_lower_bound(c,X_32))) = least_upper_bound(c,greatest_lower_bound(a,X_32)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,X_32),least_upper_bound(c,greatest_lower_bound(c,X_32))),least_upper_bound(c,least_upper_bound(greatest_lower_bound(a,X_32),greatest_lower_bound(c,X_32)))) )],[refute_0_162,refute_0_193]) ).
cnf(refute_0_195,plain,
least_upper_bound(greatest_lower_bound(a,X_32),least_upper_bound(c,greatest_lower_bound(c,X_32))) = least_upper_bound(c,greatest_lower_bound(a,X_32)),
inference(resolve,[$cnf( $equal(least_upper_bound(c,least_upper_bound(greatest_lower_bound(a,X_32),greatest_lower_bound(c,X_32))),least_upper_bound(c,greatest_lower_bound(a,X_32))) )],[refute_0_192,refute_0_194]) ).
cnf(refute_0_196,plain,
( least_upper_bound(greatest_lower_bound(a,X_32),least_upper_bound(c,greatest_lower_bound(c,X_32))) != least_upper_bound(c,greatest_lower_bound(a,X_32))
| least_upper_bound(greatest_lower_bound(a,X_32),least_upper_bound(c,greatest_lower_bound(c,X_32))) != least_upper_bound(c,greatest_lower_bound(c,X_32))
| least_upper_bound(c,greatest_lower_bound(a,X_32)) = least_upper_bound(c,greatest_lower_bound(c,X_32)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,X_32),least_upper_bound(c,greatest_lower_bound(c,X_32))),least_upper_bound(c,greatest_lower_bound(c,X_32))) ),[0],$fot(least_upper_bound(c,greatest_lower_bound(a,X_32)))]]) ).
cnf(refute_0_197,plain,
( least_upper_bound(greatest_lower_bound(a,X_32),least_upper_bound(c,greatest_lower_bound(c,X_32))) != least_upper_bound(c,greatest_lower_bound(c,X_32))
| least_upper_bound(c,greatest_lower_bound(a,X_32)) = least_upper_bound(c,greatest_lower_bound(c,X_32)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,X_32),least_upper_bound(c,greatest_lower_bound(c,X_32))),least_upper_bound(c,greatest_lower_bound(a,X_32))) )],[refute_0_195,refute_0_196]) ).
cnf(refute_0_198,plain,
least_upper_bound(c,greatest_lower_bound(c,X_32)) = c,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(c)),bind(Y,$fot(X_32))]]) ).
cnf(refute_0_199,plain,
( least_upper_bound(c,greatest_lower_bound(a,X_32)) != least_upper_bound(c,greatest_lower_bound(c,X_32))
| least_upper_bound(c,greatest_lower_bound(c,X_32)) != c
| least_upper_bound(c,greatest_lower_bound(a,X_32)) = c ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(c,greatest_lower_bound(a,X_32)),c) ),[0],$fot(least_upper_bound(c,greatest_lower_bound(c,X_32)))]]) ).
cnf(refute_0_200,plain,
( least_upper_bound(c,greatest_lower_bound(a,X_32)) != least_upper_bound(c,greatest_lower_bound(c,X_32))
| least_upper_bound(c,greatest_lower_bound(a,X_32)) = c ),
inference(resolve,[$cnf( $equal(least_upper_bound(c,greatest_lower_bound(c,X_32)),c) )],[refute_0_198,refute_0_199]) ).
cnf(refute_0_201,plain,
( least_upper_bound(greatest_lower_bound(a,X_32),least_upper_bound(c,greatest_lower_bound(c,X_32))) != least_upper_bound(c,greatest_lower_bound(c,X_32))
| least_upper_bound(c,greatest_lower_bound(a,X_32)) = c ),
inference(resolve,[$cnf( $equal(least_upper_bound(c,greatest_lower_bound(a,X_32)),least_upper_bound(c,greatest_lower_bound(c,X_32))) )],[refute_0_197,refute_0_200]) ).
cnf(refute_0_202,plain,
least_upper_bound(c,greatest_lower_bound(a,X_32)) = c,
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,X_32),least_upper_bound(c,greatest_lower_bound(c,X_32))),least_upper_bound(c,greatest_lower_bound(c,X_32))) )],[refute_0_180,refute_0_201]) ).
cnf(refute_0_203,plain,
( greatest_lower_bound(least_upper_bound(greatest_lower_bound(a,X_32),b),least_upper_bound(c,greatest_lower_bound(a,X_32))) != least_upper_bound(greatest_lower_bound(a,X_32),b)
| least_upper_bound(c,greatest_lower_bound(a,X_32)) != c
| greatest_lower_bound(least_upper_bound(greatest_lower_bound(a,X_32),b),c) = least_upper_bound(greatest_lower_bound(a,X_32),b) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(greatest_lower_bound(a,X_32),b),least_upper_bound(c,greatest_lower_bound(a,X_32))),least_upper_bound(greatest_lower_bound(a,X_32),b)) ),[0,1],$fot(c)]]) ).
cnf(refute_0_204,plain,
( greatest_lower_bound(least_upper_bound(greatest_lower_bound(a,X_32),b),least_upper_bound(c,greatest_lower_bound(a,X_32))) != least_upper_bound(greatest_lower_bound(a,X_32),b)
| greatest_lower_bound(least_upper_bound(greatest_lower_bound(a,X_32),b),c) = least_upper_bound(greatest_lower_bound(a,X_32),b) ),
inference(resolve,[$cnf( $equal(least_upper_bound(c,greatest_lower_bound(a,X_32)),c) )],[refute_0_202,refute_0_203]) ).
cnf(refute_0_205,plain,
greatest_lower_bound(least_upper_bound(greatest_lower_bound(a,X_32),b),c) = least_upper_bound(greatest_lower_bound(a,X_32),b),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(greatest_lower_bound(a,X_32),b),least_upper_bound(c,greatest_lower_bound(a,X_32))),least_upper_bound(greatest_lower_bound(a,X_32),b)) )],[refute_0_47,refute_0_204]) ).
cnf(refute_0_206,plain,
least_upper_bound(greatest_lower_bound(c,X_29),greatest_lower_bound(b,greatest_lower_bound(c,X_29))) = greatest_lower_bound(c,X_29),
inference(subst,[],[refute_0_17:[bind(X_10,$fot(greatest_lower_bound(c,X_29))),bind(X_11,$fot(b))]]) ).
cnf(refute_0_207,plain,
greatest_lower_bound(b,greatest_lower_bound(c,X_29)) = greatest_lower_bound(b,X_29),
inference(subst,[],[refute_0_22:[bind(X_28,$fot(X_29))]]) ).
cnf(refute_0_208,plain,
( greatest_lower_bound(b,greatest_lower_bound(c,X_29)) != greatest_lower_bound(b,X_29)
| least_upper_bound(greatest_lower_bound(c,X_29),greatest_lower_bound(b,greatest_lower_bound(c,X_29))) != greatest_lower_bound(c,X_29)
| least_upper_bound(greatest_lower_bound(c,X_29),greatest_lower_bound(b,X_29)) = greatest_lower_bound(c,X_29) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(c,X_29),greatest_lower_bound(b,greatest_lower_bound(c,X_29))),greatest_lower_bound(c,X_29)) ),[0,1],$fot(greatest_lower_bound(b,X_29))]]) ).
cnf(refute_0_209,plain,
( least_upper_bound(greatest_lower_bound(c,X_29),greatest_lower_bound(b,greatest_lower_bound(c,X_29))) != greatest_lower_bound(c,X_29)
| least_upper_bound(greatest_lower_bound(c,X_29),greatest_lower_bound(b,X_29)) = greatest_lower_bound(c,X_29) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(c,X_29)),greatest_lower_bound(b,X_29)) )],[refute_0_207,refute_0_208]) ).
cnf(refute_0_210,plain,
least_upper_bound(greatest_lower_bound(c,X_29),greatest_lower_bound(b,X_29)) = greatest_lower_bound(c,X_29),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(c,X_29),greatest_lower_bound(b,greatest_lower_bound(c,X_29))),greatest_lower_bound(c,X_29)) )],[refute_0_206,refute_0_209]) ).
cnf(refute_0_211,plain,
least_upper_bound(greatest_lower_bound(c,X_29),greatest_lower_bound(b,X_29)) = least_upper_bound(greatest_lower_bound(b,X_29),greatest_lower_bound(c,X_29)),
inference(subst,[],[refute_0_173:[bind(X,$fot(greatest_lower_bound(b,X_29))),bind(Y,$fot(greatest_lower_bound(c,X_29)))]]) ).
cnf(refute_0_212,plain,
( least_upper_bound(greatest_lower_bound(c,X_29),greatest_lower_bound(b,X_29)) != greatest_lower_bound(c,X_29)
| least_upper_bound(greatest_lower_bound(c,X_29),greatest_lower_bound(b,X_29)) != least_upper_bound(greatest_lower_bound(b,X_29),greatest_lower_bound(c,X_29))
| least_upper_bound(greatest_lower_bound(b,X_29),greatest_lower_bound(c,X_29)) = greatest_lower_bound(c,X_29) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(c,X_29),greatest_lower_bound(b,X_29)),greatest_lower_bound(c,X_29)) ),[0],$fot(least_upper_bound(greatest_lower_bound(b,X_29),greatest_lower_bound(c,X_29)))]]) ).
cnf(refute_0_213,plain,
( least_upper_bound(greatest_lower_bound(c,X_29),greatest_lower_bound(b,X_29)) != greatest_lower_bound(c,X_29)
| least_upper_bound(greatest_lower_bound(b,X_29),greatest_lower_bound(c,X_29)) = greatest_lower_bound(c,X_29) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(c,X_29),greatest_lower_bound(b,X_29)),least_upper_bound(greatest_lower_bound(b,X_29),greatest_lower_bound(c,X_29))) )],[refute_0_211,refute_0_212]) ).
cnf(refute_0_214,plain,
least_upper_bound(greatest_lower_bound(b,X_29),greatest_lower_bound(c,X_29)) = greatest_lower_bound(c,X_29),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(c,X_29),greatest_lower_bound(b,X_29)),greatest_lower_bound(c,X_29)) )],[refute_0_210,refute_0_213]) ).
cnf(refute_0_215,plain,
least_upper_bound(greatest_lower_bound(b,least_upper_bound(b,Y)),greatest_lower_bound(c,least_upper_bound(b,Y))) = greatest_lower_bound(c,least_upper_bound(b,Y)),
inference(subst,[],[refute_0_214:[bind(X_29,$fot(least_upper_bound(b,Y)))]]) ).
cnf(refute_0_216,plain,
greatest_lower_bound(b,least_upper_bound(b,Y)) = b,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(b))]]) ).
cnf(refute_0_217,plain,
( greatest_lower_bound(b,least_upper_bound(b,Y)) != b
| least_upper_bound(greatest_lower_bound(b,least_upper_bound(b,Y)),greatest_lower_bound(c,least_upper_bound(b,Y))) != greatest_lower_bound(c,least_upper_bound(b,Y))
| least_upper_bound(b,greatest_lower_bound(c,least_upper_bound(b,Y))) = greatest_lower_bound(c,least_upper_bound(b,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(b,least_upper_bound(b,Y)),greatest_lower_bound(c,least_upper_bound(b,Y))),greatest_lower_bound(c,least_upper_bound(b,Y))) ),[0,0],$fot(b)]]) ).
cnf(refute_0_218,plain,
( least_upper_bound(greatest_lower_bound(b,least_upper_bound(b,Y)),greatest_lower_bound(c,least_upper_bound(b,Y))) != greatest_lower_bound(c,least_upper_bound(b,Y))
| least_upper_bound(b,greatest_lower_bound(c,least_upper_bound(b,Y))) = greatest_lower_bound(c,least_upper_bound(b,Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(b,Y)),b) )],[refute_0_216,refute_0_217]) ).
cnf(refute_0_219,plain,
least_upper_bound(b,greatest_lower_bound(c,least_upper_bound(b,Y))) = greatest_lower_bound(c,least_upper_bound(b,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(b,least_upper_bound(b,Y)),greatest_lower_bound(c,least_upper_bound(b,Y))),greatest_lower_bound(c,least_upper_bound(b,Y))) )],[refute_0_215,refute_0_218]) ).
cnf(refute_0_220,plain,
least_upper_bound(b,greatest_lower_bound(c,least_upper_bound(b,X_57))) = greatest_lower_bound(c,least_upper_bound(b,X_57)),
inference(subst,[],[refute_0_219:[bind(Y,$fot(X_57))]]) ).
cnf(refute_0_221,plain,
least_upper_bound(X_57,b) = least_upper_bound(b,X_57),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_57)),bind(Y,$fot(b))]]) ).
cnf(refute_0_222,plain,
( least_upper_bound(X_57,b) != least_upper_bound(b,X_57)
| least_upper_bound(b,X_57) = least_upper_bound(X_57,b) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(least_upper_bound(X_57,b))),bind(Y0,$fot(least_upper_bound(b,X_57)))]]) ).
cnf(refute_0_223,plain,
least_upper_bound(b,X_57) = least_upper_bound(X_57,b),
inference(resolve,[$cnf( $equal(least_upper_bound(X_57,b),least_upper_bound(b,X_57)) )],[refute_0_221,refute_0_222]) ).
cnf(refute_0_224,plain,
( least_upper_bound(b,X_57) != least_upper_bound(X_57,b)
| least_upper_bound(b,greatest_lower_bound(c,least_upper_bound(b,X_57))) != greatest_lower_bound(c,least_upper_bound(b,X_57))
| least_upper_bound(b,greatest_lower_bound(c,least_upper_bound(X_57,b))) = greatest_lower_bound(c,least_upper_bound(b,X_57)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(c,least_upper_bound(b,X_57))),greatest_lower_bound(c,least_upper_bound(b,X_57))) ),[0,1,1],$fot(least_upper_bound(X_57,b))]]) ).
cnf(refute_0_225,plain,
( least_upper_bound(b,greatest_lower_bound(c,least_upper_bound(b,X_57))) != greatest_lower_bound(c,least_upper_bound(b,X_57))
| least_upper_bound(b,greatest_lower_bound(c,least_upper_bound(X_57,b))) = greatest_lower_bound(c,least_upper_bound(b,X_57)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,X_57),least_upper_bound(X_57,b)) )],[refute_0_223,refute_0_224]) ).
cnf(refute_0_226,plain,
least_upper_bound(b,greatest_lower_bound(c,least_upper_bound(X_57,b))) = greatest_lower_bound(c,least_upper_bound(b,X_57)),
inference(resolve,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(c,least_upper_bound(b,X_57))),greatest_lower_bound(c,least_upper_bound(b,X_57))) )],[refute_0_220,refute_0_225]) ).
cnf(refute_0_227,plain,
least_upper_bound(greatest_lower_bound(b,least_upper_bound(X_9,b)),greatest_lower_bound(c,least_upper_bound(X_9,b))) = greatest_lower_bound(c,least_upper_bound(X_9,b)),
inference(subst,[],[refute_0_214:[bind(X_29,$fot(least_upper_bound(X_9,b)))]]) ).
cnf(refute_0_228,plain,
greatest_lower_bound(b,least_upper_bound(X_9,b)) = b,
inference(subst,[],[refute_0_9:[bind(X_8,$fot(b))]]) ).
cnf(refute_0_229,plain,
( greatest_lower_bound(b,least_upper_bound(X_9,b)) != b
| least_upper_bound(greatest_lower_bound(b,least_upper_bound(X_9,b)),greatest_lower_bound(c,least_upper_bound(X_9,b))) != greatest_lower_bound(c,least_upper_bound(X_9,b))
| least_upper_bound(b,greatest_lower_bound(c,least_upper_bound(X_9,b))) = greatest_lower_bound(c,least_upper_bound(X_9,b)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(b,least_upper_bound(X_9,b)),greatest_lower_bound(c,least_upper_bound(X_9,b))),greatest_lower_bound(c,least_upper_bound(X_9,b))) ),[0,0],$fot(b)]]) ).
cnf(refute_0_230,plain,
( least_upper_bound(greatest_lower_bound(b,least_upper_bound(X_9,b)),greatest_lower_bound(c,least_upper_bound(X_9,b))) != greatest_lower_bound(c,least_upper_bound(X_9,b))
| least_upper_bound(b,greatest_lower_bound(c,least_upper_bound(X_9,b))) = greatest_lower_bound(c,least_upper_bound(X_9,b)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(X_9,b)),b) )],[refute_0_228,refute_0_229]) ).
cnf(refute_0_231,plain,
least_upper_bound(b,greatest_lower_bound(c,least_upper_bound(X_9,b))) = greatest_lower_bound(c,least_upper_bound(X_9,b)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(b,least_upper_bound(X_9,b)),greatest_lower_bound(c,least_upper_bound(X_9,b))),greatest_lower_bound(c,least_upper_bound(X_9,b))) )],[refute_0_227,refute_0_230]) ).
cnf(refute_0_232,plain,
least_upper_bound(b,greatest_lower_bound(c,least_upper_bound(X_57,b))) = greatest_lower_bound(c,least_upper_bound(X_57,b)),
inference(subst,[],[refute_0_231:[bind(X_9,$fot(X_57))]]) ).
cnf(refute_0_233,plain,
( least_upper_bound(b,greatest_lower_bound(c,least_upper_bound(X_57,b))) != greatest_lower_bound(c,least_upper_bound(X_57,b))
| least_upper_bound(b,greatest_lower_bound(c,least_upper_bound(X_57,b))) != greatest_lower_bound(c,least_upper_bound(b,X_57))
| greatest_lower_bound(c,least_upper_bound(X_57,b)) = greatest_lower_bound(c,least_upper_bound(b,X_57)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(c,least_upper_bound(X_57,b))),greatest_lower_bound(c,least_upper_bound(b,X_57))) ),[0],$fot(greatest_lower_bound(c,least_upper_bound(X_57,b)))]]) ).
cnf(refute_0_234,plain,
( least_upper_bound(b,greatest_lower_bound(c,least_upper_bound(X_57,b))) != greatest_lower_bound(c,least_upper_bound(b,X_57))
| greatest_lower_bound(c,least_upper_bound(X_57,b)) = greatest_lower_bound(c,least_upper_bound(b,X_57)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(c,least_upper_bound(X_57,b))),greatest_lower_bound(c,least_upper_bound(X_57,b))) )],[refute_0_232,refute_0_233]) ).
cnf(refute_0_235,plain,
greatest_lower_bound(c,least_upper_bound(X_57,b)) = greatest_lower_bound(c,least_upper_bound(b,X_57)),
inference(resolve,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(c,least_upper_bound(X_57,b))),greatest_lower_bound(c,least_upper_bound(b,X_57))) )],[refute_0_226,refute_0_234]) ).
cnf(refute_0_236,plain,
greatest_lower_bound(c,least_upper_bound(greatest_lower_bound(a,X_32),b)) = greatest_lower_bound(c,least_upper_bound(b,greatest_lower_bound(a,X_32))),
inference(subst,[],[refute_0_235:[bind(X_57,$fot(greatest_lower_bound(a,X_32)))]]) ).
cnf(refute_0_237,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_238,plain,
greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X)) )],[symmetry_of_glb,refute_0_237]) ).
cnf(refute_0_239,plain,
greatest_lower_bound(least_upper_bound(greatest_lower_bound(a,X_32),b),c) = greatest_lower_bound(c,least_upper_bound(greatest_lower_bound(a,X_32),b)),
inference(subst,[],[refute_0_238:[bind(X,$fot(c)),bind(Y,$fot(least_upper_bound(greatest_lower_bound(a,X_32),b)))]]) ).
cnf(refute_0_240,plain,
( greatest_lower_bound(c,least_upper_bound(greatest_lower_bound(a,X_32),b)) != greatest_lower_bound(c,least_upper_bound(b,greatest_lower_bound(a,X_32)))
| greatest_lower_bound(least_upper_bound(greatest_lower_bound(a,X_32),b),c) != greatest_lower_bound(c,least_upper_bound(greatest_lower_bound(a,X_32),b))
| greatest_lower_bound(least_upper_bound(greatest_lower_bound(a,X_32),b),c) = greatest_lower_bound(c,least_upper_bound(b,greatest_lower_bound(a,X_32))) ),
inference(subst,[],[refute_0_66:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(greatest_lower_bound(a,X_32),b),c))),bind(Y0,$fot(greatest_lower_bound(c,least_upper_bound(greatest_lower_bound(a,X_32),b)))),bind(Z0,$fot(greatest_lower_bound(c,least_upper_bound(b,greatest_lower_bound(a,X_32)))))]]) ).
cnf(refute_0_241,plain,
( greatest_lower_bound(c,least_upper_bound(greatest_lower_bound(a,X_32),b)) != greatest_lower_bound(c,least_upper_bound(b,greatest_lower_bound(a,X_32)))
| greatest_lower_bound(least_upper_bound(greatest_lower_bound(a,X_32),b),c) = greatest_lower_bound(c,least_upper_bound(b,greatest_lower_bound(a,X_32))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(greatest_lower_bound(a,X_32),b),c),greatest_lower_bound(c,least_upper_bound(greatest_lower_bound(a,X_32),b))) )],[refute_0_239,refute_0_240]) ).
cnf(refute_0_242,plain,
greatest_lower_bound(least_upper_bound(greatest_lower_bound(a,X_32),b),c) = greatest_lower_bound(c,least_upper_bound(b,greatest_lower_bound(a,X_32))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(c,least_upper_bound(greatest_lower_bound(a,X_32),b)),greatest_lower_bound(c,least_upper_bound(b,greatest_lower_bound(a,X_32)))) )],[refute_0_236,refute_0_241]) ).
cnf(refute_0_243,plain,
( greatest_lower_bound(least_upper_bound(greatest_lower_bound(a,X_32),b),c) != greatest_lower_bound(c,least_upper_bound(b,greatest_lower_bound(a,X_32)))
| greatest_lower_bound(least_upper_bound(greatest_lower_bound(a,X_32),b),c) != least_upper_bound(greatest_lower_bound(a,X_32),b)
| greatest_lower_bound(c,least_upper_bound(b,greatest_lower_bound(a,X_32))) = least_upper_bound(greatest_lower_bound(a,X_32),b) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(greatest_lower_bound(a,X_32),b),c),least_upper_bound(greatest_lower_bound(a,X_32),b)) ),[0],$fot(greatest_lower_bound(c,least_upper_bound(b,greatest_lower_bound(a,X_32))))]]) ).
cnf(refute_0_244,plain,
( greatest_lower_bound(least_upper_bound(greatest_lower_bound(a,X_32),b),c) != least_upper_bound(greatest_lower_bound(a,X_32),b)
| greatest_lower_bound(c,least_upper_bound(b,greatest_lower_bound(a,X_32))) = least_upper_bound(greatest_lower_bound(a,X_32),b) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(greatest_lower_bound(a,X_32),b),c),greatest_lower_bound(c,least_upper_bound(b,greatest_lower_bound(a,X_32)))) )],[refute_0_242,refute_0_243]) ).
cnf(refute_0_245,plain,
least_upper_bound(greatest_lower_bound(a,X_32),b) = least_upper_bound(b,greatest_lower_bound(a,X_32)),
inference(subst,[],[refute_0_173:[bind(X,$fot(b)),bind(Y,$fot(greatest_lower_bound(a,X_32)))]]) ).
cnf(refute_0_246,plain,
( greatest_lower_bound(c,least_upper_bound(b,greatest_lower_bound(a,X_32))) != least_upper_bound(greatest_lower_bound(a,X_32),b)
| least_upper_bound(greatest_lower_bound(a,X_32),b) != least_upper_bound(b,greatest_lower_bound(a,X_32))
| greatest_lower_bound(c,least_upper_bound(b,greatest_lower_bound(a,X_32))) = least_upper_bound(b,greatest_lower_bound(a,X_32)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(c,least_upper_bound(b,greatest_lower_bound(a,X_32))),least_upper_bound(b,greatest_lower_bound(a,X_32))) ),[0],$fot(least_upper_bound(greatest_lower_bound(a,X_32),b))]]) ).
cnf(refute_0_247,plain,
( greatest_lower_bound(c,least_upper_bound(b,greatest_lower_bound(a,X_32))) != least_upper_bound(greatest_lower_bound(a,X_32),b)
| greatest_lower_bound(c,least_upper_bound(b,greatest_lower_bound(a,X_32))) = least_upper_bound(b,greatest_lower_bound(a,X_32)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,X_32),b),least_upper_bound(b,greatest_lower_bound(a,X_32))) )],[refute_0_245,refute_0_246]) ).
cnf(refute_0_248,plain,
( greatest_lower_bound(least_upper_bound(greatest_lower_bound(a,X_32),b),c) != least_upper_bound(greatest_lower_bound(a,X_32),b)
| greatest_lower_bound(c,least_upper_bound(b,greatest_lower_bound(a,X_32))) = least_upper_bound(b,greatest_lower_bound(a,X_32)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(c,least_upper_bound(b,greatest_lower_bound(a,X_32))),least_upper_bound(greatest_lower_bound(a,X_32),b)) )],[refute_0_244,refute_0_247]) ).
cnf(refute_0_249,plain,
greatest_lower_bound(c,least_upper_bound(b,greatest_lower_bound(a,X_32))) = least_upper_bound(b,greatest_lower_bound(a,X_32)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(greatest_lower_bound(a,X_32),b),c),least_upper_bound(greatest_lower_bound(a,X_32),b)) )],[refute_0_205,refute_0_248]) ).
cnf(refute_0_250,plain,
greatest_lower_bound(c,least_upper_bound(b,greatest_lower_bound(a,least_upper_bound(X_9,a)))) = least_upper_bound(b,greatest_lower_bound(a,least_upper_bound(X_9,a))),
inference(subst,[],[refute_0_249:[bind(X_32,$fot(least_upper_bound(X_9,a)))]]) ).
cnf(refute_0_251,plain,
greatest_lower_bound(a,least_upper_bound(X_9,a)) = a,
inference(subst,[],[refute_0_9:[bind(X_8,$fot(a))]]) ).
cnf(refute_0_252,plain,
( greatest_lower_bound(a,least_upper_bound(X_9,a)) != a
| greatest_lower_bound(c,least_upper_bound(b,greatest_lower_bound(a,least_upper_bound(X_9,a)))) != least_upper_bound(b,greatest_lower_bound(a,least_upper_bound(X_9,a)))
| greatest_lower_bound(c,least_upper_bound(b,a)) = least_upper_bound(b,greatest_lower_bound(a,least_upper_bound(X_9,a))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(c,least_upper_bound(b,greatest_lower_bound(a,least_upper_bound(X_9,a)))),least_upper_bound(b,greatest_lower_bound(a,least_upper_bound(X_9,a)))) ),[0,1,1],$fot(a)]]) ).
cnf(refute_0_253,plain,
( greatest_lower_bound(c,least_upper_bound(b,greatest_lower_bound(a,least_upper_bound(X_9,a)))) != least_upper_bound(b,greatest_lower_bound(a,least_upper_bound(X_9,a)))
| greatest_lower_bound(c,least_upper_bound(b,a)) = least_upper_bound(b,greatest_lower_bound(a,least_upper_bound(X_9,a))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,least_upper_bound(X_9,a)),a) )],[refute_0_251,refute_0_252]) ).
cnf(refute_0_254,plain,
greatest_lower_bound(c,least_upper_bound(b,a)) = least_upper_bound(b,greatest_lower_bound(a,least_upper_bound(X_9,a))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(c,least_upper_bound(b,greatest_lower_bound(a,least_upper_bound(X_9,a)))),least_upper_bound(b,greatest_lower_bound(a,least_upper_bound(X_9,a)))) )],[refute_0_250,refute_0_253]) ).
cnf(refute_0_255,plain,
( greatest_lower_bound(c,least_upper_bound(X_57,b)) != greatest_lower_bound(c,least_upper_bound(b,X_57))
| greatest_lower_bound(c,least_upper_bound(b,X_57)) = greatest_lower_bound(c,least_upper_bound(X_57,b)) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(greatest_lower_bound(c,least_upper_bound(X_57,b)))),bind(Y0,$fot(greatest_lower_bound(c,least_upper_bound(b,X_57))))]]) ).
cnf(refute_0_256,plain,
greatest_lower_bound(c,least_upper_bound(b,X_57)) = greatest_lower_bound(c,least_upper_bound(X_57,b)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(c,least_upper_bound(X_57,b)),greatest_lower_bound(c,least_upper_bound(b,X_57))) )],[refute_0_235,refute_0_255]) ).
cnf(refute_0_257,plain,
greatest_lower_bound(c,least_upper_bound(b,a)) = greatest_lower_bound(c,least_upper_bound(a,b)),
inference(subst,[],[refute_0_256:[bind(X_57,$fot(a))]]) ).
cnf(refute_0_258,plain,
( greatest_lower_bound(c,least_upper_bound(b,a)) != greatest_lower_bound(c,least_upper_bound(a,b))
| greatest_lower_bound(c,least_upper_bound(b,a)) != least_upper_bound(b,greatest_lower_bound(a,least_upper_bound(X_9,a)))
| greatest_lower_bound(c,least_upper_bound(a,b)) = least_upper_bound(b,greatest_lower_bound(a,least_upper_bound(X_9,a))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(c,least_upper_bound(b,a)),least_upper_bound(b,greatest_lower_bound(a,least_upper_bound(X_9,a)))) ),[0],$fot(greatest_lower_bound(c,least_upper_bound(a,b)))]]) ).
cnf(refute_0_259,plain,
( greatest_lower_bound(c,least_upper_bound(b,a)) != least_upper_bound(b,greatest_lower_bound(a,least_upper_bound(X_9,a)))
| greatest_lower_bound(c,least_upper_bound(a,b)) = least_upper_bound(b,greatest_lower_bound(a,least_upper_bound(X_9,a))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(c,least_upper_bound(b,a)),greatest_lower_bound(c,least_upper_bound(a,b))) )],[refute_0_257,refute_0_258]) ).
cnf(refute_0_260,plain,
least_upper_bound(b,a) = least_upper_bound(a,b),
inference(subst,[],[refute_0_173:[bind(X,$fot(a)),bind(Y,$fot(b))]]) ).
cnf(refute_0_261,plain,
least_upper_bound(b,greatest_lower_bound(a,least_upper_bound(X_9,a))) = least_upper_bound(b,greatest_lower_bound(a,least_upper_bound(X_9,a))),
introduced(tautology,[refl,[$fot(least_upper_bound(b,greatest_lower_bound(a,least_upper_bound(X_9,a))))]]) ).
cnf(refute_0_262,plain,
( greatest_lower_bound(a,least_upper_bound(X_9,a)) != a
| least_upper_bound(b,greatest_lower_bound(a,least_upper_bound(X_9,a))) != least_upper_bound(b,greatest_lower_bound(a,least_upper_bound(X_9,a)))
| least_upper_bound(b,greatest_lower_bound(a,least_upper_bound(X_9,a))) = least_upper_bound(b,a) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(a,least_upper_bound(X_9,a))),least_upper_bound(b,greatest_lower_bound(a,least_upper_bound(X_9,a)))) ),[1,1],$fot(a)]]) ).
cnf(refute_0_263,plain,
( greatest_lower_bound(a,least_upper_bound(X_9,a)) != a
| least_upper_bound(b,greatest_lower_bound(a,least_upper_bound(X_9,a))) = least_upper_bound(b,a) ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(a,least_upper_bound(X_9,a))),least_upper_bound(b,greatest_lower_bound(a,least_upper_bound(X_9,a)))) )],[refute_0_261,refute_0_262]) ).
cnf(refute_0_264,plain,
least_upper_bound(b,greatest_lower_bound(a,least_upper_bound(X_9,a))) = least_upper_bound(b,a),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,least_upper_bound(X_9,a)),a) )],[refute_0_251,refute_0_263]) ).
cnf(refute_0_265,plain,
( least_upper_bound(b,a) != least_upper_bound(a,b)
| least_upper_bound(b,greatest_lower_bound(a,least_upper_bound(X_9,a))) != least_upper_bound(b,a)
| least_upper_bound(b,greatest_lower_bound(a,least_upper_bound(X_9,a))) = least_upper_bound(a,b) ),
inference(subst,[],[refute_0_66:[bind(X0,$fot(least_upper_bound(b,greatest_lower_bound(a,least_upper_bound(X_9,a))))),bind(Y0,$fot(least_upper_bound(b,a))),bind(Z0,$fot(least_upper_bound(a,b)))]]) ).
cnf(refute_0_266,plain,
( least_upper_bound(b,a) != least_upper_bound(a,b)
| least_upper_bound(b,greatest_lower_bound(a,least_upper_bound(X_9,a))) = least_upper_bound(a,b) ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(a,least_upper_bound(X_9,a))),least_upper_bound(b,a)) )],[refute_0_264,refute_0_265]) ).
cnf(refute_0_267,plain,
least_upper_bound(b,greatest_lower_bound(a,least_upper_bound(X_9,a))) = least_upper_bound(a,b),
inference(resolve,[$cnf( $equal(least_upper_bound(b,a),least_upper_bound(a,b)) )],[refute_0_260,refute_0_266]) ).
cnf(refute_0_268,plain,
( greatest_lower_bound(c,least_upper_bound(a,b)) != least_upper_bound(b,greatest_lower_bound(a,least_upper_bound(X_9,a)))
| least_upper_bound(b,greatest_lower_bound(a,least_upper_bound(X_9,a))) != least_upper_bound(a,b)
| greatest_lower_bound(c,least_upper_bound(a,b)) = least_upper_bound(a,b) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(c,least_upper_bound(a,b)),least_upper_bound(a,b)) ),[0],$fot(least_upper_bound(b,greatest_lower_bound(a,least_upper_bound(X_9,a))))]]) ).
cnf(refute_0_269,plain,
( greatest_lower_bound(c,least_upper_bound(a,b)) != least_upper_bound(b,greatest_lower_bound(a,least_upper_bound(X_9,a)))
| greatest_lower_bound(c,least_upper_bound(a,b)) = least_upper_bound(a,b) ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(a,least_upper_bound(X_9,a))),least_upper_bound(a,b)) )],[refute_0_267,refute_0_268]) ).
cnf(refute_0_270,plain,
( greatest_lower_bound(c,least_upper_bound(b,a)) != least_upper_bound(b,greatest_lower_bound(a,least_upper_bound(X_9,a)))
| greatest_lower_bound(c,least_upper_bound(a,b)) = least_upper_bound(a,b) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(c,least_upper_bound(a,b)),least_upper_bound(b,greatest_lower_bound(a,least_upper_bound(X_9,a)))) )],[refute_0_259,refute_0_269]) ).
cnf(refute_0_271,plain,
greatest_lower_bound(c,least_upper_bound(a,b)) = least_upper_bound(a,b),
inference(resolve,[$cnf( $equal(greatest_lower_bound(c,least_upper_bound(b,a)),least_upper_bound(b,greatest_lower_bound(a,least_upper_bound(X_9,a)))) )],[refute_0_254,refute_0_270]) ).
cnf(refute_0_272,plain,
greatest_lower_bound(least_upper_bound(a,b),c) = greatest_lower_bound(c,least_upper_bound(a,b)),
inference(subst,[],[refute_0_238:[bind(X,$fot(c)),bind(Y,$fot(least_upper_bound(a,b)))]]) ).
cnf(refute_0_273,plain,
( greatest_lower_bound(c,least_upper_bound(a,b)) != least_upper_bound(a,b)
| greatest_lower_bound(least_upper_bound(a,b),c) != greatest_lower_bound(c,least_upper_bound(a,b))
| greatest_lower_bound(least_upper_bound(a,b),c) = least_upper_bound(a,b) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,b),c),greatest_lower_bound(c,least_upper_bound(a,b))) ),[1],$fot(least_upper_bound(a,b))]]) ).
cnf(refute_0_274,plain,
( greatest_lower_bound(c,least_upper_bound(a,b)) != least_upper_bound(a,b)
| greatest_lower_bound(least_upper_bound(a,b),c) = least_upper_bound(a,b) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,b),c),greatest_lower_bound(c,least_upper_bound(a,b))) )],[refute_0_272,refute_0_273]) ).
cnf(refute_0_275,plain,
greatest_lower_bound(c,least_upper_bound(a,b)) != least_upper_bound(a,b),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,b),c),least_upper_bound(a,b)) )],[refute_0_274,prove_ax_lub1b]) ).
cnf(refute_0_276,plain,
$false,
inference(resolve,[$cnf( $equal(greatest_lower_bound(c,least_upper_bound(a,b)),least_upper_bound(a,b)) )],[refute_0_271,refute_0_275]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP147-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n013.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 16:34:14 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.22/1.40 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.22/1.40
% 1.22/1.40 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.22/1.42
%------------------------------------------------------------------------------