TSTP Solution File: GRP148-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP148-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n012.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 10:37:03 EDT 2022
% Result : Unsatisfiable 106.23s 106.46s
% Output : CNFRefutation 106.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 63
% Syntax : Number of clauses : 286 ( 157 unt; 0 nHn; 149 RR)
% Number of literals : 472 ( 471 equ; 189 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 : 472 ( 13 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_lub1c_1,hypothesis,
least_upper_bound(a,c) = c ).
cnf(ax_lub1c_2,hypothesis,
least_upper_bound(b,c) = c ).
cnf(prove_ax_lub1c,negated_conjecture,
greatest_lower_bound(least_upper_bound(a,b),c) != least_upper_bound(a,b) ).
cnf(refute_0_0,plain,
least_upper_bound(X_18,least_upper_bound(greatest_lower_bound(X_9,X_18),X_20)) = least_upper_bound(least_upper_bound(X_18,greatest_lower_bound(X_9,X_18)),X_20),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_18)),bind(Y,$fot(greatest_lower_bound(X_9,X_18))),bind(Z,$fot(X_20))]]) ).
cnf(refute_0_1,plain,
least_upper_bound(X_8,greatest_lower_bound(X_8,X_9)) = X_8,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_8)),bind(Y,$fot(X_9))]]) ).
cnf(refute_0_2,plain,
greatest_lower_bound(X_9,X_8) = greatest_lower_bound(X_8,X_9),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_9)),bind(Y,$fot(X_8))]]) ).
cnf(refute_0_3,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_4,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_5,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
( greatest_lower_bound(X_9,X_8) != greatest_lower_bound(X_8,X_9)
| greatest_lower_bound(X_8,X_9) = greatest_lower_bound(X_9,X_8) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(greatest_lower_bound(X_9,X_8))),bind(Y0,$fot(greatest_lower_bound(X_8,X_9)))]]) ).
cnf(refute_0_7,plain,
greatest_lower_bound(X_8,X_9) = greatest_lower_bound(X_9,X_8),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_9,X_8),greatest_lower_bound(X_8,X_9)) )],[refute_0_2,refute_0_6]) ).
cnf(refute_0_8,plain,
( greatest_lower_bound(X_8,X_9) != greatest_lower_bound(X_9,X_8)
| least_upper_bound(X_8,greatest_lower_bound(X_8,X_9)) != X_8
| least_upper_bound(X_8,greatest_lower_bound(X_9,X_8)) = X_8 ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_8,greatest_lower_bound(X_8,X_9)),X_8) ),[0,1],$fot(greatest_lower_bound(X_9,X_8))]]) ).
cnf(refute_0_9,plain,
( least_upper_bound(X_8,greatest_lower_bound(X_8,X_9)) != X_8
| least_upper_bound(X_8,greatest_lower_bound(X_9,X_8)) = X_8 ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_8,X_9),greatest_lower_bound(X_9,X_8)) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
least_upper_bound(X_8,greatest_lower_bound(X_9,X_8)) = X_8,
inference(resolve,[$cnf( $equal(least_upper_bound(X_8,greatest_lower_bound(X_8,X_9)),X_8) )],[refute_0_1,refute_0_9]) ).
cnf(refute_0_11,plain,
least_upper_bound(X_18,greatest_lower_bound(X_9,X_18)) = X_18,
inference(subst,[],[refute_0_10:[bind(X_8,$fot(X_18))]]) ).
cnf(refute_0_12,plain,
( least_upper_bound(X_18,greatest_lower_bound(X_9,X_18)) != X_18
| least_upper_bound(X_18,least_upper_bound(greatest_lower_bound(X_9,X_18),X_20)) != least_upper_bound(least_upper_bound(X_18,greatest_lower_bound(X_9,X_18)),X_20)
| least_upper_bound(X_18,least_upper_bound(greatest_lower_bound(X_9,X_18),X_20)) = least_upper_bound(X_18,X_20) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(greatest_lower_bound(X_9,X_18),X_20)),least_upper_bound(least_upper_bound(X_18,greatest_lower_bound(X_9,X_18)),X_20)) ),[1,0],$fot(X_18)]]) ).
cnf(refute_0_13,plain,
( least_upper_bound(X_18,least_upper_bound(greatest_lower_bound(X_9,X_18),X_20)) != least_upper_bound(least_upper_bound(X_18,greatest_lower_bound(X_9,X_18)),X_20)
| least_upper_bound(X_18,least_upper_bound(greatest_lower_bound(X_9,X_18),X_20)) = least_upper_bound(X_18,X_20) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,greatest_lower_bound(X_9,X_18)),X_18) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
least_upper_bound(X_18,least_upper_bound(greatest_lower_bound(X_9,X_18),X_20)) = least_upper_bound(X_18,X_20),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(greatest_lower_bound(X_9,X_18),X_20)),least_upper_bound(least_upper_bound(X_18,greatest_lower_bound(X_9,X_18)),X_20)) )],[refute_0_0,refute_0_13]) ).
cnf(refute_0_15,plain,
least_upper_bound(b,least_upper_bound(greatest_lower_bound(X_542,b),greatest_lower_bound(X_542,c))) = least_upper_bound(b,greatest_lower_bound(X_542,c)),
inference(subst,[],[refute_0_14:[bind(X_18,$fot(b)),bind(X_20,$fot(greatest_lower_bound(X_542,c))),bind(X_9,$fot(X_542))]]) ).
cnf(refute_0_16,plain,
least_upper_bound(greatest_lower_bound(c,X_47),greatest_lower_bound(b,greatest_lower_bound(c,X_47))) = greatest_lower_bound(c,X_47),
inference(subst,[],[refute_0_10:[bind(X_8,$fot(greatest_lower_bound(c,X_47))),bind(X_9,$fot(b))]]) ).
cnf(refute_0_17,plain,
greatest_lower_bound(b,greatest_lower_bound(c,X_45)) = greatest_lower_bound(greatest_lower_bound(b,c),X_45),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(b)),bind(Y,$fot(c)),bind(Z,$fot(X_45))]]) ).
cnf(refute_0_18,plain,
greatest_lower_bound(b,least_upper_bound(b,c)) = b,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(b)),bind(Y,$fot(c))]]) ).
cnf(refute_0_19,plain,
( greatest_lower_bound(b,least_upper_bound(b,c)) != b
| least_upper_bound(b,c) != c
| greatest_lower_bound(b,c) = b ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(b,c)),b) ),[0,1],$fot(c)]]) ).
cnf(refute_0_20,plain,
( greatest_lower_bound(b,least_upper_bound(b,c)) != b
| greatest_lower_bound(b,c) = b ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,c),c) )],[ax_lub1c_2,refute_0_19]) ).
cnf(refute_0_21,plain,
greatest_lower_bound(b,c) = b,
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(b,c)),b) )],[refute_0_18,refute_0_20]) ).
cnf(refute_0_22,plain,
( greatest_lower_bound(b,c) != b
| greatest_lower_bound(b,greatest_lower_bound(c,X_45)) != greatest_lower_bound(greatest_lower_bound(b,c),X_45)
| greatest_lower_bound(b,greatest_lower_bound(c,X_45)) = greatest_lower_bound(b,X_45) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(c,X_45)),greatest_lower_bound(greatest_lower_bound(b,c),X_45)) ),[1,0],$fot(b)]]) ).
cnf(refute_0_23,plain,
( greatest_lower_bound(b,greatest_lower_bound(c,X_45)) != greatest_lower_bound(greatest_lower_bound(b,c),X_45)
| greatest_lower_bound(b,greatest_lower_bound(c,X_45)) = greatest_lower_bound(b,X_45) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,c),b) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
greatest_lower_bound(b,greatest_lower_bound(c,X_45)) = greatest_lower_bound(b,X_45),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(c,X_45)),greatest_lower_bound(greatest_lower_bound(b,c),X_45)) )],[refute_0_17,refute_0_23]) ).
cnf(refute_0_25,plain,
greatest_lower_bound(b,greatest_lower_bound(c,X_47)) = greatest_lower_bound(b,X_47),
inference(subst,[],[refute_0_24:[bind(X_45,$fot(X_47))]]) ).
cnf(refute_0_26,plain,
( greatest_lower_bound(b,greatest_lower_bound(c,X_47)) != greatest_lower_bound(b,X_47)
| least_upper_bound(greatest_lower_bound(c,X_47),greatest_lower_bound(b,greatest_lower_bound(c,X_47))) != greatest_lower_bound(c,X_47)
| least_upper_bound(greatest_lower_bound(c,X_47),greatest_lower_bound(b,X_47)) = greatest_lower_bound(c,X_47) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(c,X_47),greatest_lower_bound(b,greatest_lower_bound(c,X_47))),greatest_lower_bound(c,X_47)) ),[0,1],$fot(greatest_lower_bound(b,X_47))]]) ).
cnf(refute_0_27,plain,
( least_upper_bound(greatest_lower_bound(c,X_47),greatest_lower_bound(b,greatest_lower_bound(c,X_47))) != greatest_lower_bound(c,X_47)
| least_upper_bound(greatest_lower_bound(c,X_47),greatest_lower_bound(b,X_47)) = greatest_lower_bound(c,X_47) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(c,X_47)),greatest_lower_bound(b,X_47)) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
least_upper_bound(greatest_lower_bound(c,X_47),greatest_lower_bound(b,X_47)) = greatest_lower_bound(c,X_47),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(c,X_47),greatest_lower_bound(b,greatest_lower_bound(c,X_47))),greatest_lower_bound(c,X_47)) )],[refute_0_16,refute_0_27]) ).
cnf(refute_0_29,plain,
( least_upper_bound(X,Y) != least_upper_bound(Y,X)
| least_upper_bound(Y,X) = least_upper_bound(X,Y) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(least_upper_bound(X,Y))),bind(Y0,$fot(least_upper_bound(Y,X)))]]) ).
cnf(refute_0_30,plain,
least_upper_bound(Y,X) = least_upper_bound(X,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(X,Y),least_upper_bound(Y,X)) )],[symmetry_of_lub,refute_0_29]) ).
cnf(refute_0_31,plain,
least_upper_bound(greatest_lower_bound(c,X_47),greatest_lower_bound(b,X_47)) = least_upper_bound(greatest_lower_bound(b,X_47),greatest_lower_bound(c,X_47)),
inference(subst,[],[refute_0_30:[bind(X,$fot(greatest_lower_bound(b,X_47))),bind(Y,$fot(greatest_lower_bound(c,X_47)))]]) ).
cnf(refute_0_32,plain,
( least_upper_bound(greatest_lower_bound(c,X_47),greatest_lower_bound(b,X_47)) != greatest_lower_bound(c,X_47)
| least_upper_bound(greatest_lower_bound(c,X_47),greatest_lower_bound(b,X_47)) != least_upper_bound(greatest_lower_bound(b,X_47),greatest_lower_bound(c,X_47))
| least_upper_bound(greatest_lower_bound(b,X_47),greatest_lower_bound(c,X_47)) = greatest_lower_bound(c,X_47) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(c,X_47),greatest_lower_bound(b,X_47)),greatest_lower_bound(c,X_47)) ),[0],$fot(least_upper_bound(greatest_lower_bound(b,X_47),greatest_lower_bound(c,X_47)))]]) ).
cnf(refute_0_33,plain,
( least_upper_bound(greatest_lower_bound(c,X_47),greatest_lower_bound(b,X_47)) != greatest_lower_bound(c,X_47)
| least_upper_bound(greatest_lower_bound(b,X_47),greatest_lower_bound(c,X_47)) = greatest_lower_bound(c,X_47) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(c,X_47),greatest_lower_bound(b,X_47)),least_upper_bound(greatest_lower_bound(b,X_47),greatest_lower_bound(c,X_47))) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
least_upper_bound(greatest_lower_bound(b,X_47),greatest_lower_bound(c,X_47)) = greatest_lower_bound(c,X_47),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(c,X_47),greatest_lower_bound(b,X_47)),greatest_lower_bound(c,X_47)) )],[refute_0_28,refute_0_33]) ).
cnf(refute_0_35,plain,
least_upper_bound(greatest_lower_bound(b,X_52),greatest_lower_bound(c,X_52)) = greatest_lower_bound(c,X_52),
inference(subst,[],[refute_0_34:[bind(X_47,$fot(X_52))]]) ).
cnf(refute_0_36,plain,
greatest_lower_bound(X_52,c) = greatest_lower_bound(c,X_52),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_52)),bind(Y,$fot(c))]]) ).
cnf(refute_0_37,plain,
( greatest_lower_bound(X_52,c) != greatest_lower_bound(c,X_52)
| greatest_lower_bound(c,X_52) = greatest_lower_bound(X_52,c) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(greatest_lower_bound(X_52,c))),bind(Y0,$fot(greatest_lower_bound(c,X_52)))]]) ).
cnf(refute_0_38,plain,
greatest_lower_bound(c,X_52) = greatest_lower_bound(X_52,c),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_52,c),greatest_lower_bound(c,X_52)) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
( greatest_lower_bound(c,X_52) != greatest_lower_bound(X_52,c)
| least_upper_bound(greatest_lower_bound(b,X_52),greatest_lower_bound(c,X_52)) != greatest_lower_bound(c,X_52)
| least_upper_bound(greatest_lower_bound(b,X_52),greatest_lower_bound(X_52,c)) = greatest_lower_bound(c,X_52) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(b,X_52),greatest_lower_bound(c,X_52)),greatest_lower_bound(c,X_52)) ),[0,1],$fot(greatest_lower_bound(X_52,c))]]) ).
cnf(refute_0_40,plain,
( least_upper_bound(greatest_lower_bound(b,X_52),greatest_lower_bound(c,X_52)) != greatest_lower_bound(c,X_52)
| least_upper_bound(greatest_lower_bound(b,X_52),greatest_lower_bound(X_52,c)) = greatest_lower_bound(c,X_52) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(c,X_52),greatest_lower_bound(X_52,c)) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
least_upper_bound(greatest_lower_bound(b,X_52),greatest_lower_bound(X_52,c)) = greatest_lower_bound(c,X_52),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(b,X_52),greatest_lower_bound(c,X_52)),greatest_lower_bound(c,X_52)) )],[refute_0_35,refute_0_40]) ).
cnf(refute_0_42,plain,
least_upper_bound(greatest_lower_bound(b,X_53),greatest_lower_bound(X_53,c)) = greatest_lower_bound(c,X_53),
inference(subst,[],[refute_0_41:[bind(X_52,$fot(X_53))]]) ).
cnf(refute_0_43,plain,
greatest_lower_bound(X_53,b) = greatest_lower_bound(b,X_53),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_53)),bind(Y,$fot(b))]]) ).
cnf(refute_0_44,plain,
( greatest_lower_bound(X_53,b) != greatest_lower_bound(b,X_53)
| greatest_lower_bound(b,X_53) = greatest_lower_bound(X_53,b) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(greatest_lower_bound(X_53,b))),bind(Y0,$fot(greatest_lower_bound(b,X_53)))]]) ).
cnf(refute_0_45,plain,
greatest_lower_bound(b,X_53) = greatest_lower_bound(X_53,b),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_53,b),greatest_lower_bound(b,X_53)) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
( greatest_lower_bound(b,X_53) != greatest_lower_bound(X_53,b)
| least_upper_bound(greatest_lower_bound(b,X_53),greatest_lower_bound(X_53,c)) != greatest_lower_bound(c,X_53)
| least_upper_bound(greatest_lower_bound(X_53,b),greatest_lower_bound(X_53,c)) = greatest_lower_bound(c,X_53) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(b,X_53),greatest_lower_bound(X_53,c)),greatest_lower_bound(c,X_53)) ),[0,0],$fot(greatest_lower_bound(X_53,b))]]) ).
cnf(refute_0_47,plain,
( least_upper_bound(greatest_lower_bound(b,X_53),greatest_lower_bound(X_53,c)) != greatest_lower_bound(c,X_53)
| least_upper_bound(greatest_lower_bound(X_53,b),greatest_lower_bound(X_53,c)) = greatest_lower_bound(c,X_53) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,X_53),greatest_lower_bound(X_53,b)) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
least_upper_bound(greatest_lower_bound(X_53,b),greatest_lower_bound(X_53,c)) = greatest_lower_bound(c,X_53),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(b,X_53),greatest_lower_bound(X_53,c)),greatest_lower_bound(c,X_53)) )],[refute_0_42,refute_0_47]) ).
cnf(refute_0_49,plain,
least_upper_bound(greatest_lower_bound(X_542,b),greatest_lower_bound(X_542,c)) = greatest_lower_bound(c,X_542),
inference(subst,[],[refute_0_48:[bind(X_53,$fot(X_542))]]) ).
cnf(refute_0_50,plain,
( least_upper_bound(b,least_upper_bound(greatest_lower_bound(X_542,b),greatest_lower_bound(X_542,c))) != least_upper_bound(b,greatest_lower_bound(X_542,c))
| least_upper_bound(greatest_lower_bound(X_542,b),greatest_lower_bound(X_542,c)) != greatest_lower_bound(c,X_542)
| least_upper_bound(b,greatest_lower_bound(c,X_542)) = least_upper_bound(b,greatest_lower_bound(X_542,c)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,least_upper_bound(greatest_lower_bound(X_542,b),greatest_lower_bound(X_542,c))),least_upper_bound(b,greatest_lower_bound(X_542,c))) ),[0,1],$fot(greatest_lower_bound(c,X_542))]]) ).
cnf(refute_0_51,plain,
( least_upper_bound(b,least_upper_bound(greatest_lower_bound(X_542,b),greatest_lower_bound(X_542,c))) != least_upper_bound(b,greatest_lower_bound(X_542,c))
| least_upper_bound(b,greatest_lower_bound(c,X_542)) = least_upper_bound(b,greatest_lower_bound(X_542,c)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_542,b),greatest_lower_bound(X_542,c)),greatest_lower_bound(c,X_542)) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
least_upper_bound(b,greatest_lower_bound(c,X_542)) = least_upper_bound(b,greatest_lower_bound(X_542,c)),
inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(greatest_lower_bound(X_542,b),greatest_lower_bound(X_542,c))),least_upper_bound(b,greatest_lower_bound(X_542,c))) )],[refute_0_15,refute_0_51]) ).
cnf(refute_0_53,plain,
least_upper_bound(b,greatest_lower_bound(c,least_upper_bound(b,a))) = least_upper_bound(b,greatest_lower_bound(least_upper_bound(b,a),c)),
inference(subst,[],[refute_0_52:[bind(X_542,$fot(least_upper_bound(b,a)))]]) ).
cnf(refute_0_54,plain,
least_upper_bound(least_upper_bound(a,X_686),greatest_lower_bound(c,least_upper_bound(a,X_686))) = least_upper_bound(a,X_686),
inference(subst,[],[refute_0_10:[bind(X_8,$fot(least_upper_bound(a,X_686))),bind(X_9,$fot(c))]]) ).
cnf(refute_0_55,plain,
least_upper_bound(greatest_lower_bound(c,X_46),greatest_lower_bound(a,greatest_lower_bound(c,X_46))) = greatest_lower_bound(c,X_46),
inference(subst,[],[refute_0_10:[bind(X_8,$fot(greatest_lower_bound(c,X_46))),bind(X_9,$fot(a))]]) ).
cnf(refute_0_56,plain,
greatest_lower_bound(a,greatest_lower_bound(c,X_45)) = greatest_lower_bound(greatest_lower_bound(a,c),X_45),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(a)),bind(Y,$fot(c)),bind(Z,$fot(X_45))]]) ).
cnf(refute_0_57,plain,
greatest_lower_bound(a,least_upper_bound(a,c)) = a,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(a)),bind(Y,$fot(c))]]) ).
cnf(refute_0_58,plain,
( greatest_lower_bound(a,least_upper_bound(a,c)) != a
| least_upper_bound(a,c) != c
| greatest_lower_bound(a,c) = a ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,least_upper_bound(a,c)),a) ),[0,1],$fot(c)]]) ).
cnf(refute_0_59,plain,
( greatest_lower_bound(a,least_upper_bound(a,c)) != a
| greatest_lower_bound(a,c) = a ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,c),c) )],[ax_lub1c_1,refute_0_58]) ).
cnf(refute_0_60,plain,
greatest_lower_bound(a,c) = a,
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,least_upper_bound(a,c)),a) )],[refute_0_57,refute_0_59]) ).
cnf(refute_0_61,plain,
( greatest_lower_bound(a,c) != a
| greatest_lower_bound(a,greatest_lower_bound(c,X_45)) != greatest_lower_bound(greatest_lower_bound(a,c),X_45)
| greatest_lower_bound(a,greatest_lower_bound(c,X_45)) = greatest_lower_bound(a,X_45) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(c,X_45)),greatest_lower_bound(greatest_lower_bound(a,c),X_45)) ),[1,0],$fot(a)]]) ).
cnf(refute_0_62,plain,
( greatest_lower_bound(a,greatest_lower_bound(c,X_45)) != greatest_lower_bound(greatest_lower_bound(a,c),X_45)
| greatest_lower_bound(a,greatest_lower_bound(c,X_45)) = greatest_lower_bound(a,X_45) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,c),a) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
greatest_lower_bound(a,greatest_lower_bound(c,X_45)) = greatest_lower_bound(a,X_45),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(c,X_45)),greatest_lower_bound(greatest_lower_bound(a,c),X_45)) )],[refute_0_56,refute_0_62]) ).
cnf(refute_0_64,plain,
greatest_lower_bound(a,greatest_lower_bound(c,X_46)) = greatest_lower_bound(a,X_46),
inference(subst,[],[refute_0_63:[bind(X_45,$fot(X_46))]]) ).
cnf(refute_0_65,plain,
( greatest_lower_bound(a,greatest_lower_bound(c,X_46)) != greatest_lower_bound(a,X_46)
| least_upper_bound(greatest_lower_bound(c,X_46),greatest_lower_bound(a,greatest_lower_bound(c,X_46))) != greatest_lower_bound(c,X_46)
| least_upper_bound(greatest_lower_bound(c,X_46),greatest_lower_bound(a,X_46)) = greatest_lower_bound(c,X_46) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(c,X_46),greatest_lower_bound(a,greatest_lower_bound(c,X_46))),greatest_lower_bound(c,X_46)) ),[0,1],$fot(greatest_lower_bound(a,X_46))]]) ).
cnf(refute_0_66,plain,
( least_upper_bound(greatest_lower_bound(c,X_46),greatest_lower_bound(a,greatest_lower_bound(c,X_46))) != greatest_lower_bound(c,X_46)
| least_upper_bound(greatest_lower_bound(c,X_46),greatest_lower_bound(a,X_46)) = greatest_lower_bound(c,X_46) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(c,X_46)),greatest_lower_bound(a,X_46)) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
least_upper_bound(greatest_lower_bound(c,X_46),greatest_lower_bound(a,X_46)) = greatest_lower_bound(c,X_46),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(c,X_46),greatest_lower_bound(a,greatest_lower_bound(c,X_46))),greatest_lower_bound(c,X_46)) )],[refute_0_55,refute_0_66]) ).
cnf(refute_0_68,plain,
least_upper_bound(greatest_lower_bound(c,X_46),greatest_lower_bound(a,X_46)) = least_upper_bound(greatest_lower_bound(a,X_46),greatest_lower_bound(c,X_46)),
inference(subst,[],[refute_0_30:[bind(X,$fot(greatest_lower_bound(a,X_46))),bind(Y,$fot(greatest_lower_bound(c,X_46)))]]) ).
cnf(refute_0_69,plain,
( least_upper_bound(greatest_lower_bound(c,X_46),greatest_lower_bound(a,X_46)) != greatest_lower_bound(c,X_46)
| least_upper_bound(greatest_lower_bound(c,X_46),greatest_lower_bound(a,X_46)) != least_upper_bound(greatest_lower_bound(a,X_46),greatest_lower_bound(c,X_46))
| least_upper_bound(greatest_lower_bound(a,X_46),greatest_lower_bound(c,X_46)) = greatest_lower_bound(c,X_46) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(c,X_46),greatest_lower_bound(a,X_46)),greatest_lower_bound(c,X_46)) ),[0],$fot(least_upper_bound(greatest_lower_bound(a,X_46),greatest_lower_bound(c,X_46)))]]) ).
cnf(refute_0_70,plain,
( least_upper_bound(greatest_lower_bound(c,X_46),greatest_lower_bound(a,X_46)) != greatest_lower_bound(c,X_46)
| least_upper_bound(greatest_lower_bound(a,X_46),greatest_lower_bound(c,X_46)) = greatest_lower_bound(c,X_46) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(c,X_46),greatest_lower_bound(a,X_46)),least_upper_bound(greatest_lower_bound(a,X_46),greatest_lower_bound(c,X_46))) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
least_upper_bound(greatest_lower_bound(a,X_46),greatest_lower_bound(c,X_46)) = greatest_lower_bound(c,X_46),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(c,X_46),greatest_lower_bound(a,X_46)),greatest_lower_bound(c,X_46)) )],[refute_0_67,refute_0_70]) ).
cnf(refute_0_72,plain,
least_upper_bound(greatest_lower_bound(a,least_upper_bound(X_11,a)),greatest_lower_bound(c,least_upper_bound(X_11,a))) = greatest_lower_bound(c,least_upper_bound(X_11,a)),
inference(subst,[],[refute_0_71:[bind(X_46,$fot(least_upper_bound(X_11,a)))]]) ).
cnf(refute_0_73,plain,
greatest_lower_bound(X_10,least_upper_bound(X_10,X_11)) = X_10,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_10)),bind(Y,$fot(X_11))]]) ).
cnf(refute_0_74,plain,
least_upper_bound(X_11,X_10) = least_upper_bound(X_10,X_11),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_11)),bind(Y,$fot(X_10))]]) ).
cnf(refute_0_75,plain,
( least_upper_bound(X_11,X_10) != least_upper_bound(X_10,X_11)
| least_upper_bound(X_10,X_11) = least_upper_bound(X_11,X_10) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(least_upper_bound(X_11,X_10))),bind(Y0,$fot(least_upper_bound(X_10,X_11)))]]) ).
cnf(refute_0_76,plain,
least_upper_bound(X_10,X_11) = least_upper_bound(X_11,X_10),
inference(resolve,[$cnf( $equal(least_upper_bound(X_11,X_10),least_upper_bound(X_10,X_11)) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
( greatest_lower_bound(X_10,least_upper_bound(X_10,X_11)) != X_10
| least_upper_bound(X_10,X_11) != least_upper_bound(X_11,X_10)
| greatest_lower_bound(X_10,least_upper_bound(X_11,X_10)) = X_10 ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_10,least_upper_bound(X_10,X_11)),X_10) ),[0,1],$fot(least_upper_bound(X_11,X_10))]]) ).
cnf(refute_0_78,plain,
( greatest_lower_bound(X_10,least_upper_bound(X_10,X_11)) != X_10
| greatest_lower_bound(X_10,least_upper_bound(X_11,X_10)) = X_10 ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_10,X_11),least_upper_bound(X_11,X_10)) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
greatest_lower_bound(X_10,least_upper_bound(X_11,X_10)) = X_10,
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_10,least_upper_bound(X_10,X_11)),X_10) )],[refute_0_73,refute_0_78]) ).
cnf(refute_0_80,plain,
greatest_lower_bound(a,least_upper_bound(X_11,a)) = a,
inference(subst,[],[refute_0_79:[bind(X_10,$fot(a))]]) ).
cnf(refute_0_81,plain,
( greatest_lower_bound(a,least_upper_bound(X_11,a)) != a
| least_upper_bound(greatest_lower_bound(a,least_upper_bound(X_11,a)),greatest_lower_bound(c,least_upper_bound(X_11,a))) != greatest_lower_bound(c,least_upper_bound(X_11,a))
| least_upper_bound(a,greatest_lower_bound(c,least_upper_bound(X_11,a))) = greatest_lower_bound(c,least_upper_bound(X_11,a)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,least_upper_bound(X_11,a)),greatest_lower_bound(c,least_upper_bound(X_11,a))),greatest_lower_bound(c,least_upper_bound(X_11,a))) ),[0,0],$fot(a)]]) ).
cnf(refute_0_82,plain,
( least_upper_bound(greatest_lower_bound(a,least_upper_bound(X_11,a)),greatest_lower_bound(c,least_upper_bound(X_11,a))) != greatest_lower_bound(c,least_upper_bound(X_11,a))
| least_upper_bound(a,greatest_lower_bound(c,least_upper_bound(X_11,a))) = greatest_lower_bound(c,least_upper_bound(X_11,a)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,least_upper_bound(X_11,a)),a) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
least_upper_bound(a,greatest_lower_bound(c,least_upper_bound(X_11,a))) = greatest_lower_bound(c,least_upper_bound(X_11,a)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,least_upper_bound(X_11,a)),greatest_lower_bound(c,least_upper_bound(X_11,a))),greatest_lower_bound(c,least_upper_bound(X_11,a))) )],[refute_0_72,refute_0_82]) ).
cnf(refute_0_84,plain,
least_upper_bound(a,greatest_lower_bound(c,least_upper_bound(X_683,a))) = greatest_lower_bound(c,least_upper_bound(X_683,a)),
inference(subst,[],[refute_0_83:[bind(X_11,$fot(X_683))]]) ).
cnf(refute_0_85,plain,
least_upper_bound(a,X_683) = least_upper_bound(X_683,a),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(a)),bind(Y,$fot(X_683))]]) ).
cnf(refute_0_86,plain,
( least_upper_bound(a,X_683) != least_upper_bound(X_683,a)
| least_upper_bound(X_683,a) = least_upper_bound(a,X_683) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(least_upper_bound(a,X_683))),bind(Y0,$fot(least_upper_bound(X_683,a)))]]) ).
cnf(refute_0_87,plain,
least_upper_bound(X_683,a) = least_upper_bound(a,X_683),
inference(resolve,[$cnf( $equal(least_upper_bound(a,X_683),least_upper_bound(X_683,a)) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
( least_upper_bound(X_683,a) != least_upper_bound(a,X_683)
| least_upper_bound(a,greatest_lower_bound(c,least_upper_bound(X_683,a))) != greatest_lower_bound(c,least_upper_bound(X_683,a))
| least_upper_bound(a,greatest_lower_bound(c,least_upper_bound(a,X_683))) = greatest_lower_bound(c,least_upper_bound(X_683,a)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(a,greatest_lower_bound(c,least_upper_bound(X_683,a))),greatest_lower_bound(c,least_upper_bound(X_683,a))) ),[0,1,1],$fot(least_upper_bound(a,X_683))]]) ).
cnf(refute_0_89,plain,
( least_upper_bound(a,greatest_lower_bound(c,least_upper_bound(X_683,a))) != greatest_lower_bound(c,least_upper_bound(X_683,a))
| least_upper_bound(a,greatest_lower_bound(c,least_upper_bound(a,X_683))) = greatest_lower_bound(c,least_upper_bound(X_683,a)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_683,a),least_upper_bound(a,X_683)) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
least_upper_bound(a,greatest_lower_bound(c,least_upper_bound(a,X_683))) = greatest_lower_bound(c,least_upper_bound(X_683,a)),
inference(resolve,[$cnf( $equal(least_upper_bound(a,greatest_lower_bound(c,least_upper_bound(X_683,a))),greatest_lower_bound(c,least_upper_bound(X_683,a))) )],[refute_0_84,refute_0_89]) ).
cnf(refute_0_91,plain,
least_upper_bound(greatest_lower_bound(a,least_upper_bound(a,Y)),greatest_lower_bound(c,least_upper_bound(a,Y))) = greatest_lower_bound(c,least_upper_bound(a,Y)),
inference(subst,[],[refute_0_71:[bind(X_46,$fot(least_upper_bound(a,Y)))]]) ).
cnf(refute_0_92,plain,
greatest_lower_bound(a,least_upper_bound(a,Y)) = a,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(a))]]) ).
cnf(refute_0_93,plain,
( greatest_lower_bound(a,least_upper_bound(a,Y)) != a
| least_upper_bound(greatest_lower_bound(a,least_upper_bound(a,Y)),greatest_lower_bound(c,least_upper_bound(a,Y))) != greatest_lower_bound(c,least_upper_bound(a,Y))
| least_upper_bound(a,greatest_lower_bound(c,least_upper_bound(a,Y))) = greatest_lower_bound(c,least_upper_bound(a,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,least_upper_bound(a,Y)),greatest_lower_bound(c,least_upper_bound(a,Y))),greatest_lower_bound(c,least_upper_bound(a,Y))) ),[0,0],$fot(a)]]) ).
cnf(refute_0_94,plain,
( least_upper_bound(greatest_lower_bound(a,least_upper_bound(a,Y)),greatest_lower_bound(c,least_upper_bound(a,Y))) != greatest_lower_bound(c,least_upper_bound(a,Y))
| least_upper_bound(a,greatest_lower_bound(c,least_upper_bound(a,Y))) = greatest_lower_bound(c,least_upper_bound(a,Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,least_upper_bound(a,Y)),a) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
least_upper_bound(a,greatest_lower_bound(c,least_upper_bound(a,Y))) = greatest_lower_bound(c,least_upper_bound(a,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,least_upper_bound(a,Y)),greatest_lower_bound(c,least_upper_bound(a,Y))),greatest_lower_bound(c,least_upper_bound(a,Y))) )],[refute_0_91,refute_0_94]) ).
cnf(refute_0_96,plain,
least_upper_bound(a,greatest_lower_bound(c,least_upper_bound(a,X_683))) = greatest_lower_bound(c,least_upper_bound(a,X_683)),
inference(subst,[],[refute_0_95:[bind(Y,$fot(X_683))]]) ).
cnf(refute_0_97,plain,
( least_upper_bound(a,greatest_lower_bound(c,least_upper_bound(a,X_683))) != greatest_lower_bound(c,least_upper_bound(X_683,a))
| least_upper_bound(a,greatest_lower_bound(c,least_upper_bound(a,X_683))) != greatest_lower_bound(c,least_upper_bound(a,X_683))
| greatest_lower_bound(c,least_upper_bound(a,X_683)) = greatest_lower_bound(c,least_upper_bound(X_683,a)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(a,greatest_lower_bound(c,least_upper_bound(a,X_683))),greatest_lower_bound(c,least_upper_bound(X_683,a))) ),[0],$fot(greatest_lower_bound(c,least_upper_bound(a,X_683)))]]) ).
cnf(refute_0_98,plain,
( least_upper_bound(a,greatest_lower_bound(c,least_upper_bound(a,X_683))) != greatest_lower_bound(c,least_upper_bound(X_683,a))
| greatest_lower_bound(c,least_upper_bound(a,X_683)) = greatest_lower_bound(c,least_upper_bound(X_683,a)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,greatest_lower_bound(c,least_upper_bound(a,X_683))),greatest_lower_bound(c,least_upper_bound(a,X_683))) )],[refute_0_96,refute_0_97]) ).
cnf(refute_0_99,plain,
greatest_lower_bound(c,least_upper_bound(a,X_683)) = greatest_lower_bound(c,least_upper_bound(X_683,a)),
inference(resolve,[$cnf( $equal(least_upper_bound(a,greatest_lower_bound(c,least_upper_bound(a,X_683))),greatest_lower_bound(c,least_upper_bound(X_683,a))) )],[refute_0_90,refute_0_98]) ).
cnf(refute_0_100,plain,
greatest_lower_bound(c,least_upper_bound(a,X_686)) = greatest_lower_bound(c,least_upper_bound(X_686,a)),
inference(subst,[],[refute_0_99:[bind(X_683,$fot(X_686))]]) ).
cnf(refute_0_101,plain,
( greatest_lower_bound(c,least_upper_bound(a,X_686)) != greatest_lower_bound(c,least_upper_bound(X_686,a))
| least_upper_bound(least_upper_bound(a,X_686),greatest_lower_bound(c,least_upper_bound(a,X_686))) != least_upper_bound(a,X_686)
| least_upper_bound(least_upper_bound(a,X_686),greatest_lower_bound(c,least_upper_bound(X_686,a))) = least_upper_bound(a,X_686) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(a,X_686),greatest_lower_bound(c,least_upper_bound(a,X_686))),least_upper_bound(a,X_686)) ),[0,1],$fot(greatest_lower_bound(c,least_upper_bound(X_686,a)))]]) ).
cnf(refute_0_102,plain,
( least_upper_bound(least_upper_bound(a,X_686),greatest_lower_bound(c,least_upper_bound(a,X_686))) != least_upper_bound(a,X_686)
| least_upper_bound(least_upper_bound(a,X_686),greatest_lower_bound(c,least_upper_bound(X_686,a))) = least_upper_bound(a,X_686) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(c,least_upper_bound(a,X_686)),greatest_lower_bound(c,least_upper_bound(X_686,a))) )],[refute_0_100,refute_0_101]) ).
cnf(refute_0_103,plain,
least_upper_bound(least_upper_bound(a,X_686),greatest_lower_bound(c,least_upper_bound(X_686,a))) = least_upper_bound(a,X_686),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(a,X_686),greatest_lower_bound(c,least_upper_bound(a,X_686))),least_upper_bound(a,X_686)) )],[refute_0_54,refute_0_102]) ).
cnf(refute_0_104,plain,
least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) = least_upper_bound(least_upper_bound(X_18,least_upper_bound(Y,X_18)),X_20),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_18)),bind(Y,$fot(least_upper_bound(Y,X_18))),bind(Z,$fot(X_20))]]) ).
cnf(refute_0_105,plain,
least_upper_bound(least_upper_bound(X_13,Y),greatest_lower_bound(X_13,least_upper_bound(X_13,Y))) = least_upper_bound(X_13,Y),
inference(subst,[],[refute_0_10:[bind(X_8,$fot(least_upper_bound(X_13,Y))),bind(X_9,$fot(X_13))]]) ).
cnf(refute_0_106,plain,
greatest_lower_bound(X_13,least_upper_bound(X_13,Y)) = X_13,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_13))]]) ).
cnf(refute_0_107,plain,
( greatest_lower_bound(X_13,least_upper_bound(X_13,Y)) != X_13
| least_upper_bound(least_upper_bound(X_13,Y),greatest_lower_bound(X_13,least_upper_bound(X_13,Y))) != least_upper_bound(X_13,Y)
| least_upper_bound(least_upper_bound(X_13,Y),X_13) = least_upper_bound(X_13,Y) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_13,Y),greatest_lower_bound(X_13,least_upper_bound(X_13,Y))),least_upper_bound(X_13,Y)) ),[0,1],$fot(X_13)]]) ).
cnf(refute_0_108,plain,
( least_upper_bound(least_upper_bound(X_13,Y),greatest_lower_bound(X_13,least_upper_bound(X_13,Y))) != least_upper_bound(X_13,Y)
| least_upper_bound(least_upper_bound(X_13,Y),X_13) = least_upper_bound(X_13,Y) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_13,least_upper_bound(X_13,Y)),X_13) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
least_upper_bound(least_upper_bound(X_13,Y),X_13) = least_upper_bound(X_13,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_13,Y),greatest_lower_bound(X_13,least_upper_bound(X_13,Y))),least_upper_bound(X_13,Y)) )],[refute_0_105,refute_0_108]) ).
cnf(refute_0_110,plain,
( least_upper_bound(X,least_upper_bound(Y,Z)) != least_upper_bound(least_upper_bound(X,Y),Z)
| least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(Y,Z)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X,Y),Z)))]]) ).
cnf(refute_0_111,plain,
least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,Z)),least_upper_bound(least_upper_bound(X,Y),Z)) )],[associativity_of_lub,refute_0_110]) ).
cnf(refute_0_112,plain,
least_upper_bound(least_upper_bound(X_13,Y),X_13) = least_upper_bound(X_13,least_upper_bound(Y,X_13)),
inference(subst,[],[refute_0_111:[bind(X,$fot(X_13)),bind(Z,$fot(X_13))]]) ).
cnf(refute_0_113,plain,
( least_upper_bound(least_upper_bound(X_13,Y),X_13) != least_upper_bound(X_13,Y)
| least_upper_bound(least_upper_bound(X_13,Y),X_13) != least_upper_bound(X_13,least_upper_bound(Y,X_13))
| least_upper_bound(X_13,least_upper_bound(Y,X_13)) = least_upper_bound(X_13,Y) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_13,Y),X_13),least_upper_bound(X_13,Y)) ),[0],$fot(least_upper_bound(X_13,least_upper_bound(Y,X_13)))]]) ).
cnf(refute_0_114,plain,
( least_upper_bound(least_upper_bound(X_13,Y),X_13) != least_upper_bound(X_13,Y)
| least_upper_bound(X_13,least_upper_bound(Y,X_13)) = least_upper_bound(X_13,Y) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_13,Y),X_13),least_upper_bound(X_13,least_upper_bound(Y,X_13))) )],[refute_0_112,refute_0_113]) ).
cnf(refute_0_115,plain,
least_upper_bound(X_13,least_upper_bound(Y,X_13)) = least_upper_bound(X_13,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_13,Y),X_13),least_upper_bound(X_13,Y)) )],[refute_0_109,refute_0_114]) ).
cnf(refute_0_116,plain,
least_upper_bound(X_18,least_upper_bound(Y,X_18)) = least_upper_bound(X_18,Y),
inference(subst,[],[refute_0_115:[bind(X_13,$fot(X_18))]]) ).
cnf(refute_0_117,plain,
( least_upper_bound(X_18,least_upper_bound(Y,X_18)) != least_upper_bound(X_18,Y)
| least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) != least_upper_bound(least_upper_bound(X_18,least_upper_bound(Y,X_18)),X_20)
| least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) = least_upper_bound(least_upper_bound(X_18,Y),X_20) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)),least_upper_bound(least_upper_bound(X_18,least_upper_bound(Y,X_18)),X_20)) ),[1,0],$fot(least_upper_bound(X_18,Y))]]) ).
cnf(refute_0_118,plain,
( least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) != least_upper_bound(least_upper_bound(X_18,least_upper_bound(Y,X_18)),X_20)
| least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) = least_upper_bound(least_upper_bound(X_18,Y),X_20) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(Y,X_18)),least_upper_bound(X_18,Y)) )],[refute_0_116,refute_0_117]) ).
cnf(refute_0_119,plain,
least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) = least_upper_bound(least_upper_bound(X_18,Y),X_20),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)),least_upper_bound(least_upper_bound(X_18,least_upper_bound(Y,X_18)),X_20)) )],[refute_0_104,refute_0_118]) ).
cnf(refute_0_120,plain,
least_upper_bound(X_18,least_upper_bound(X_19,least_upper_bound(Y,X_19))) = least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_18)),bind(Y,$fot(X_19)),bind(Z,$fot(least_upper_bound(Y,X_19)))]]) ).
cnf(refute_0_121,plain,
least_upper_bound(X_19,least_upper_bound(Y,X_19)) = least_upper_bound(X_19,Y),
inference(subst,[],[refute_0_115:[bind(X_13,$fot(X_19))]]) ).
cnf(refute_0_122,plain,
( least_upper_bound(X_18,least_upper_bound(X_19,least_upper_bound(Y,X_19))) != least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19))
| least_upper_bound(X_19,least_upper_bound(Y,X_19)) != least_upper_bound(X_19,Y)
| least_upper_bound(X_18,least_upper_bound(X_19,Y)) = least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(X_19,least_upper_bound(Y,X_19))),least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19))) ),[0,1],$fot(least_upper_bound(X_19,Y))]]) ).
cnf(refute_0_123,plain,
( least_upper_bound(X_18,least_upper_bound(X_19,least_upper_bound(Y,X_19))) != least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19))
| least_upper_bound(X_18,least_upper_bound(X_19,Y)) = least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,least_upper_bound(Y,X_19)),least_upper_bound(X_19,Y)) )],[refute_0_121,refute_0_122]) ).
cnf(refute_0_124,plain,
least_upper_bound(X_18,least_upper_bound(X_19,Y)) = least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(X_19,least_upper_bound(Y,X_19))),least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19))) )],[refute_0_120,refute_0_123]) ).
cnf(refute_0_125,plain,
least_upper_bound(least_upper_bound(X_18,X_19),Y) = least_upper_bound(X_18,least_upper_bound(X_19,Y)),
inference(subst,[],[refute_0_111:[bind(X,$fot(X_18)),bind(Y,$fot(X_19)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_126,plain,
least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)) = least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)))]]) ).
cnf(refute_0_127,plain,
( least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)) != least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y))
| least_upper_bound(least_upper_bound(X_18,X_19),Y) != least_upper_bound(X_18,least_upper_bound(X_19,Y))
| least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)) = least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)),least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y))) ),[1,1],$fot(least_upper_bound(X_18,least_upper_bound(X_19,Y)))]]) ).
cnf(refute_0_128,plain,
( least_upper_bound(least_upper_bound(X_18,X_19),Y) != least_upper_bound(X_18,least_upper_bound(X_19,Y))
| least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)) = least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)),least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y))) )],[refute_0_126,refute_0_127]) ).
cnf(refute_0_129,plain,
least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)) = least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_18,X_19),Y),least_upper_bound(X_18,least_upper_bound(X_19,Y))) )],[refute_0_125,refute_0_128]) ).
cnf(refute_0_130,plain,
least_upper_bound(X,least_upper_bound(X_18,X_19)) = least_upper_bound(least_upper_bound(X_18,X_19),X),
inference(subst,[],[symmetry_of_lub:[bind(Y,$fot(least_upper_bound(X_18,X_19)))]]) ).
cnf(refute_0_131,plain,
least_upper_bound(X_18,least_upper_bound(X_19,X)) = least_upper_bound(least_upper_bound(X_18,X_19),X),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_18)),bind(Y,$fot(X_19)),bind(Z,$fot(X))]]) ).
cnf(refute_0_132,plain,
( least_upper_bound(X_18,least_upper_bound(X_19,X)) != least_upper_bound(least_upper_bound(X_18,X_19),X)
| least_upper_bound(least_upper_bound(X_18,X_19),X) = least_upper_bound(X_18,least_upper_bound(X_19,X)) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(least_upper_bound(X_18,least_upper_bound(X_19,X)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X_18,X_19),X)))]]) ).
cnf(refute_0_133,plain,
least_upper_bound(least_upper_bound(X_18,X_19),X) = least_upper_bound(X_18,least_upper_bound(X_19,X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(X_19,X)),least_upper_bound(least_upper_bound(X_18,X_19),X)) )],[refute_0_131,refute_0_132]) ).
cnf(refute_0_134,plain,
( least_upper_bound(X,least_upper_bound(X_18,X_19)) != least_upper_bound(least_upper_bound(X_18,X_19),X)
| least_upper_bound(least_upper_bound(X_18,X_19),X) != least_upper_bound(X_18,least_upper_bound(X_19,X))
| least_upper_bound(X,least_upper_bound(X_18,X_19)) = least_upper_bound(X_18,least_upper_bound(X_19,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,least_upper_bound(X_18,X_19)),least_upper_bound(X_18,least_upper_bound(X_19,X))) ),[0],$fot(least_upper_bound(least_upper_bound(X_18,X_19),X))]]) ).
cnf(refute_0_135,plain,
( least_upper_bound(X,least_upper_bound(X_18,X_19)) != least_upper_bound(least_upper_bound(X_18,X_19),X)
| least_upper_bound(X,least_upper_bound(X_18,X_19)) = least_upper_bound(X_18,least_upper_bound(X_19,X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_18,X_19),X),least_upper_bound(X_18,least_upper_bound(X_19,X))) )],[refute_0_133,refute_0_134]) ).
cnf(refute_0_136,plain,
least_upper_bound(X,least_upper_bound(X_18,X_19)) = least_upper_bound(X_18,least_upper_bound(X_19,X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_18,X_19)),least_upper_bound(least_upper_bound(X_18,X_19),X)) )],[refute_0_130,refute_0_135]) ).
cnf(refute_0_137,plain,
( least_upper_bound(X,least_upper_bound(X_18,X_19)) != least_upper_bound(X_18,least_upper_bound(X_19,X))
| least_upper_bound(X_18,least_upper_bound(X_19,X)) = least_upper_bound(X,least_upper_bound(X_18,X_19)) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(X_18,X_19)))),bind(Y0,$fot(least_upper_bound(X_18,least_upper_bound(X_19,X))))]]) ).
cnf(refute_0_138,plain,
least_upper_bound(X_18,least_upper_bound(X_19,X)) = least_upper_bound(X,least_upper_bound(X_18,X_19)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_18,X_19)),least_upper_bound(X_18,least_upper_bound(X_19,X))) )],[refute_0_136,refute_0_137]) ).
cnf(refute_0_139,plain,
least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)) = least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)),
inference(subst,[],[refute_0_138:[bind(X,$fot(X_19)),bind(X_18,$fot(least_upper_bound(X_18,X_19))),bind(X_19,$fot(Y))]]) ).
cnf(refute_0_140,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_141,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_5,refute_0_140]) ).
cnf(refute_0_142,plain,
( least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)) != least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y)))
| least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)) != least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y))
| least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)) = least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y))) ),
inference(subst,[],[refute_0_141:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)))),bind(Y0,$fot(least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)))),bind(Z0,$fot(least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y)))))]]) ).
cnf(refute_0_143,plain,
( least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)) != least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y)))
| least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)) = least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)),least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y))) )],[refute_0_139,refute_0_142]) ).
cnf(refute_0_144,plain,
least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)) = least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)),least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y)))) )],[refute_0_129,refute_0_143]) ).
cnf(refute_0_145,plain,
( least_upper_bound(X_18,least_upper_bound(X_19,Y)) != least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19))
| least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)) != least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y)))
| least_upper_bound(X_18,least_upper_bound(X_19,Y)) = least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_18,least_upper_bound(X_19,Y)),least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y)))) ),[0],$fot(least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)))]]) ).
cnf(refute_0_146,plain,
( least_upper_bound(X_18,least_upper_bound(X_19,Y)) != least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19))
| least_upper_bound(X_18,least_upper_bound(X_19,Y)) = least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)),least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y)))) )],[refute_0_144,refute_0_145]) ).
cnf(refute_0_147,plain,
least_upper_bound(X_18,least_upper_bound(X_19,Y)) = least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(X_19,Y)),least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19))) )],[refute_0_124,refute_0_146]) ).
cnf(refute_0_148,plain,
( least_upper_bound(X_18,least_upper_bound(X_19,Y)) != least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y)))
| least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y))) = least_upper_bound(X_18,least_upper_bound(X_19,Y)) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(least_upper_bound(X_18,least_upper_bound(X_19,Y)))),bind(Y0,$fot(least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y)))))]]) ).
cnf(refute_0_149,plain,
least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y))) = least_upper_bound(X_18,least_upper_bound(X_19,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(X_19,Y)),least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y)))) )],[refute_0_147,refute_0_148]) ).
cnf(refute_0_150,plain,
least_upper_bound(X_18,least_upper_bound(Y,least_upper_bound(X_18,X_20))) = least_upper_bound(Y,least_upper_bound(X_18,X_20)),
inference(subst,[],[refute_0_149:[bind(Y,$fot(X_20)),bind(X_18,$fot(Y)),bind(X_19,$fot(X_18))]]) ).
cnf(refute_0_151,plain,
least_upper_bound(least_upper_bound(Y,X_18),X_20) = least_upper_bound(Y,least_upper_bound(X_18,X_20)),
inference(subst,[],[refute_0_111:[bind(X,$fot(Y)),bind(Y,$fot(X_18)),bind(Z,$fot(X_20))]]) ).
cnf(refute_0_152,plain,
least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) = least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)))]]) ).
cnf(refute_0_153,plain,
( least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) != least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20))
| least_upper_bound(least_upper_bound(Y,X_18),X_20) != least_upper_bound(Y,least_upper_bound(X_18,X_20))
| least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) = least_upper_bound(X_18,least_upper_bound(Y,least_upper_bound(X_18,X_20))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)),least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20))) ),[1,1],$fot(least_upper_bound(Y,least_upper_bound(X_18,X_20)))]]) ).
cnf(refute_0_154,plain,
( least_upper_bound(least_upper_bound(Y,X_18),X_20) != least_upper_bound(Y,least_upper_bound(X_18,X_20))
| least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) = least_upper_bound(X_18,least_upper_bound(Y,least_upper_bound(X_18,X_20))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)),least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20))) )],[refute_0_152,refute_0_153]) ).
cnf(refute_0_155,plain,
least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) = least_upper_bound(X_18,least_upper_bound(Y,least_upper_bound(X_18,X_20))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_18),X_20),least_upper_bound(Y,least_upper_bound(X_18,X_20))) )],[refute_0_151,refute_0_154]) ).
cnf(refute_0_156,plain,
( least_upper_bound(X_18,least_upper_bound(Y,least_upper_bound(X_18,X_20))) != least_upper_bound(Y,least_upper_bound(X_18,X_20))
| least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) != least_upper_bound(X_18,least_upper_bound(Y,least_upper_bound(X_18,X_20)))
| least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) = least_upper_bound(Y,least_upper_bound(X_18,X_20)) ),
inference(subst,[],[refute_0_141:[bind(X0,$fot(least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)))),bind(Y0,$fot(least_upper_bound(X_18,least_upper_bound(Y,least_upper_bound(X_18,X_20))))),bind(Z0,$fot(least_upper_bound(Y,least_upper_bound(X_18,X_20))))]]) ).
cnf(refute_0_157,plain,
( least_upper_bound(X_18,least_upper_bound(Y,least_upper_bound(X_18,X_20))) != least_upper_bound(Y,least_upper_bound(X_18,X_20))
| least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) = least_upper_bound(Y,least_upper_bound(X_18,X_20)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)),least_upper_bound(X_18,least_upper_bound(Y,least_upper_bound(X_18,X_20)))) )],[refute_0_155,refute_0_156]) ).
cnf(refute_0_158,plain,
least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) = least_upper_bound(Y,least_upper_bound(X_18,X_20)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(Y,least_upper_bound(X_18,X_20))),least_upper_bound(Y,least_upper_bound(X_18,X_20))) )],[refute_0_150,refute_0_157]) ).
cnf(refute_0_159,plain,
( least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) != least_upper_bound(Y,least_upper_bound(X_18,X_20))
| least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) != least_upper_bound(least_upper_bound(X_18,Y),X_20)
| least_upper_bound(Y,least_upper_bound(X_18,X_20)) = least_upper_bound(least_upper_bound(X_18,Y),X_20) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)),least_upper_bound(least_upper_bound(X_18,Y),X_20)) ),[0],$fot(least_upper_bound(Y,least_upper_bound(X_18,X_20)))]]) ).
cnf(refute_0_160,plain,
( least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) != least_upper_bound(least_upper_bound(X_18,Y),X_20)
| least_upper_bound(Y,least_upper_bound(X_18,X_20)) = least_upper_bound(least_upper_bound(X_18,Y),X_20) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)),least_upper_bound(Y,least_upper_bound(X_18,X_20))) )],[refute_0_158,refute_0_159]) ).
cnf(refute_0_161,plain,
least_upper_bound(least_upper_bound(X_18,Y),X_20) = least_upper_bound(X_18,least_upper_bound(Y,X_20)),
inference(subst,[],[refute_0_111:[bind(X,$fot(X_18)),bind(Z,$fot(X_20))]]) ).
cnf(refute_0_162,plain,
( least_upper_bound(Y,least_upper_bound(X_18,X_20)) != least_upper_bound(least_upper_bound(X_18,Y),X_20)
| least_upper_bound(least_upper_bound(X_18,Y),X_20) != least_upper_bound(X_18,least_upper_bound(Y,X_20))
| least_upper_bound(Y,least_upper_bound(X_18,X_20)) = least_upper_bound(X_18,least_upper_bound(Y,X_20)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(Y,least_upper_bound(X_18,X_20)),least_upper_bound(X_18,least_upper_bound(Y,X_20))) ),[0],$fot(least_upper_bound(least_upper_bound(X_18,Y),X_20))]]) ).
cnf(refute_0_163,plain,
( least_upper_bound(Y,least_upper_bound(X_18,X_20)) != least_upper_bound(least_upper_bound(X_18,Y),X_20)
| least_upper_bound(Y,least_upper_bound(X_18,X_20)) = least_upper_bound(X_18,least_upper_bound(Y,X_20)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_18,Y),X_20),least_upper_bound(X_18,least_upper_bound(Y,X_20))) )],[refute_0_161,refute_0_162]) ).
cnf(refute_0_164,plain,
( least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) != least_upper_bound(least_upper_bound(X_18,Y),X_20)
| least_upper_bound(Y,least_upper_bound(X_18,X_20)) = least_upper_bound(X_18,least_upper_bound(Y,X_20)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_18,X_20)),least_upper_bound(least_upper_bound(X_18,Y),X_20)) )],[refute_0_160,refute_0_163]) ).
cnf(refute_0_165,plain,
least_upper_bound(Y,least_upper_bound(X_18,X_20)) = least_upper_bound(X_18,least_upper_bound(Y,X_20)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)),least_upper_bound(least_upper_bound(X_18,Y),X_20)) )],[refute_0_119,refute_0_164]) ).
cnf(refute_0_166,plain,
least_upper_bound(a,least_upper_bound(X_18,greatest_lower_bound(c,least_upper_bound(X_683,a)))) = least_upper_bound(X_18,least_upper_bound(a,greatest_lower_bound(c,least_upper_bound(X_683,a)))),
inference(subst,[],[refute_0_165:[bind(Y,$fot(a)),bind(X_20,$fot(greatest_lower_bound(c,least_upper_bound(X_683,a))))]]) ).
cnf(refute_0_167,plain,
( least_upper_bound(a,greatest_lower_bound(c,least_upper_bound(X_683,a))) != greatest_lower_bound(c,least_upper_bound(X_683,a))
| least_upper_bound(a,least_upper_bound(X_18,greatest_lower_bound(c,least_upper_bound(X_683,a)))) != least_upper_bound(X_18,least_upper_bound(a,greatest_lower_bound(c,least_upper_bound(X_683,a))))
| least_upper_bound(a,least_upper_bound(X_18,greatest_lower_bound(c,least_upper_bound(X_683,a)))) = least_upper_bound(X_18,greatest_lower_bound(c,least_upper_bound(X_683,a))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(a,least_upper_bound(X_18,greatest_lower_bound(c,least_upper_bound(X_683,a)))),least_upper_bound(X_18,least_upper_bound(a,greatest_lower_bound(c,least_upper_bound(X_683,a))))) ),[1,1],$fot(greatest_lower_bound(c,least_upper_bound(X_683,a)))]]) ).
cnf(refute_0_168,plain,
( least_upper_bound(a,least_upper_bound(X_18,greatest_lower_bound(c,least_upper_bound(X_683,a)))) != least_upper_bound(X_18,least_upper_bound(a,greatest_lower_bound(c,least_upper_bound(X_683,a))))
| least_upper_bound(a,least_upper_bound(X_18,greatest_lower_bound(c,least_upper_bound(X_683,a)))) = least_upper_bound(X_18,greatest_lower_bound(c,least_upper_bound(X_683,a))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,greatest_lower_bound(c,least_upper_bound(X_683,a))),greatest_lower_bound(c,least_upper_bound(X_683,a))) )],[refute_0_84,refute_0_167]) ).
cnf(refute_0_169,plain,
least_upper_bound(a,least_upper_bound(X_18,greatest_lower_bound(c,least_upper_bound(X_683,a)))) = least_upper_bound(X_18,greatest_lower_bound(c,least_upper_bound(X_683,a))),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(X_18,greatest_lower_bound(c,least_upper_bound(X_683,a)))),least_upper_bound(X_18,least_upper_bound(a,greatest_lower_bound(c,least_upper_bound(X_683,a))))) )],[refute_0_166,refute_0_168]) ).
cnf(refute_0_170,plain,
least_upper_bound(a,least_upper_bound(X_686,greatest_lower_bound(c,least_upper_bound(X_686,a)))) = least_upper_bound(X_686,greatest_lower_bound(c,least_upper_bound(X_686,a))),
inference(subst,[],[refute_0_169:[bind(X_18,$fot(X_686)),bind(X_683,$fot(X_686))]]) ).
cnf(refute_0_171,plain,
least_upper_bound(least_upper_bound(a,X_686),greatest_lower_bound(c,least_upper_bound(X_686,a))) = least_upper_bound(a,least_upper_bound(X_686,greatest_lower_bound(c,least_upper_bound(X_686,a)))),
inference(subst,[],[refute_0_111:[bind(X,$fot(a)),bind(Y,$fot(X_686)),bind(Z,$fot(greatest_lower_bound(c,least_upper_bound(X_686,a))))]]) ).
cnf(refute_0_172,plain,
( least_upper_bound(a,least_upper_bound(X_686,greatest_lower_bound(c,least_upper_bound(X_686,a)))) != least_upper_bound(X_686,greatest_lower_bound(c,least_upper_bound(X_686,a)))
| least_upper_bound(least_upper_bound(a,X_686),greatest_lower_bound(c,least_upper_bound(X_686,a))) != least_upper_bound(a,least_upper_bound(X_686,greatest_lower_bound(c,least_upper_bound(X_686,a))))
| least_upper_bound(least_upper_bound(a,X_686),greatest_lower_bound(c,least_upper_bound(X_686,a))) = least_upper_bound(X_686,greatest_lower_bound(c,least_upper_bound(X_686,a))) ),
inference(subst,[],[refute_0_141:[bind(X0,$fot(least_upper_bound(least_upper_bound(a,X_686),greatest_lower_bound(c,least_upper_bound(X_686,a))))),bind(Y0,$fot(least_upper_bound(a,least_upper_bound(X_686,greatest_lower_bound(c,least_upper_bound(X_686,a)))))),bind(Z0,$fot(least_upper_bound(X_686,greatest_lower_bound(c,least_upper_bound(X_686,a)))))]]) ).
cnf(refute_0_173,plain,
( least_upper_bound(a,least_upper_bound(X_686,greatest_lower_bound(c,least_upper_bound(X_686,a)))) != least_upper_bound(X_686,greatest_lower_bound(c,least_upper_bound(X_686,a)))
| least_upper_bound(least_upper_bound(a,X_686),greatest_lower_bound(c,least_upper_bound(X_686,a))) = least_upper_bound(X_686,greatest_lower_bound(c,least_upper_bound(X_686,a))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(a,X_686),greatest_lower_bound(c,least_upper_bound(X_686,a))),least_upper_bound(a,least_upper_bound(X_686,greatest_lower_bound(c,least_upper_bound(X_686,a))))) )],[refute_0_171,refute_0_172]) ).
cnf(refute_0_174,plain,
least_upper_bound(least_upper_bound(a,X_686),greatest_lower_bound(c,least_upper_bound(X_686,a))) = least_upper_bound(X_686,greatest_lower_bound(c,least_upper_bound(X_686,a))),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(X_686,greatest_lower_bound(c,least_upper_bound(X_686,a)))),least_upper_bound(X_686,greatest_lower_bound(c,least_upper_bound(X_686,a)))) )],[refute_0_170,refute_0_173]) ).
cnf(refute_0_175,plain,
( least_upper_bound(least_upper_bound(a,X_686),greatest_lower_bound(c,least_upper_bound(X_686,a))) != least_upper_bound(X_686,greatest_lower_bound(c,least_upper_bound(X_686,a)))
| least_upper_bound(least_upper_bound(a,X_686),greatest_lower_bound(c,least_upper_bound(X_686,a))) != least_upper_bound(a,X_686)
| least_upper_bound(X_686,greatest_lower_bound(c,least_upper_bound(X_686,a))) = least_upper_bound(a,X_686) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(a,X_686),greatest_lower_bound(c,least_upper_bound(X_686,a))),least_upper_bound(a,X_686)) ),[0],$fot(least_upper_bound(X_686,greatest_lower_bound(c,least_upper_bound(X_686,a))))]]) ).
cnf(refute_0_176,plain,
( least_upper_bound(least_upper_bound(a,X_686),greatest_lower_bound(c,least_upper_bound(X_686,a))) != least_upper_bound(a,X_686)
| least_upper_bound(X_686,greatest_lower_bound(c,least_upper_bound(X_686,a))) = least_upper_bound(a,X_686) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(a,X_686),greatest_lower_bound(c,least_upper_bound(X_686,a))),least_upper_bound(X_686,greatest_lower_bound(c,least_upper_bound(X_686,a)))) )],[refute_0_174,refute_0_175]) ).
cnf(refute_0_177,plain,
least_upper_bound(X_686,greatest_lower_bound(c,least_upper_bound(X_686,a))) = least_upper_bound(a,X_686),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(a,X_686),greatest_lower_bound(c,least_upper_bound(X_686,a))),least_upper_bound(a,X_686)) )],[refute_0_103,refute_0_176]) ).
cnf(refute_0_178,plain,
least_upper_bound(b,greatest_lower_bound(c,least_upper_bound(b,a))) = least_upper_bound(a,b),
inference(subst,[],[refute_0_177:[bind(X_686,$fot(b))]]) ).
cnf(refute_0_179,plain,
( least_upper_bound(b,greatest_lower_bound(c,least_upper_bound(b,a))) != least_upper_bound(a,b)
| least_upper_bound(b,greatest_lower_bound(c,least_upper_bound(b,a))) != least_upper_bound(b,greatest_lower_bound(least_upper_bound(b,a),c))
| least_upper_bound(a,b) = least_upper_bound(b,greatest_lower_bound(least_upper_bound(b,a),c)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(c,least_upper_bound(b,a))),least_upper_bound(b,greatest_lower_bound(least_upper_bound(b,a),c))) ),[0],$fot(least_upper_bound(a,b))]]) ).
cnf(refute_0_180,plain,
( least_upper_bound(b,greatest_lower_bound(c,least_upper_bound(b,a))) != least_upper_bound(b,greatest_lower_bound(least_upper_bound(b,a),c))
| least_upper_bound(a,b) = least_upper_bound(b,greatest_lower_bound(least_upper_bound(b,a),c)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(c,least_upper_bound(b,a))),least_upper_bound(a,b)) )],[refute_0_178,refute_0_179]) ).
cnf(refute_0_181,plain,
least_upper_bound(a,b) = least_upper_bound(b,greatest_lower_bound(least_upper_bound(b,a),c)),
inference(resolve,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(c,least_upper_bound(b,a))),least_upper_bound(b,greatest_lower_bound(least_upper_bound(b,a),c))) )],[refute_0_53,refute_0_180]) ).
cnf(refute_0_182,plain,
least_upper_bound(greatest_lower_bound(b,least_upper_bound(X_11,b)),greatest_lower_bound(c,least_upper_bound(X_11,b))) = greatest_lower_bound(c,least_upper_bound(X_11,b)),
inference(subst,[],[refute_0_34:[bind(X_47,$fot(least_upper_bound(X_11,b)))]]) ).
cnf(refute_0_183,plain,
greatest_lower_bound(b,least_upper_bound(X_11,b)) = b,
inference(subst,[],[refute_0_79:[bind(X_10,$fot(b))]]) ).
cnf(refute_0_184,plain,
( greatest_lower_bound(b,least_upper_bound(X_11,b)) != b
| least_upper_bound(greatest_lower_bound(b,least_upper_bound(X_11,b)),greatest_lower_bound(c,least_upper_bound(X_11,b))) != greatest_lower_bound(c,least_upper_bound(X_11,b))
| least_upper_bound(b,greatest_lower_bound(c,least_upper_bound(X_11,b))) = greatest_lower_bound(c,least_upper_bound(X_11,b)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(b,least_upper_bound(X_11,b)),greatest_lower_bound(c,least_upper_bound(X_11,b))),greatest_lower_bound(c,least_upper_bound(X_11,b))) ),[0,0],$fot(b)]]) ).
cnf(refute_0_185,plain,
( least_upper_bound(greatest_lower_bound(b,least_upper_bound(X_11,b)),greatest_lower_bound(c,least_upper_bound(X_11,b))) != greatest_lower_bound(c,least_upper_bound(X_11,b))
| least_upper_bound(b,greatest_lower_bound(c,least_upper_bound(X_11,b))) = greatest_lower_bound(c,least_upper_bound(X_11,b)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(X_11,b)),b) )],[refute_0_183,refute_0_184]) ).
cnf(refute_0_186,plain,
least_upper_bound(b,greatest_lower_bound(c,least_upper_bound(X_11,b))) = greatest_lower_bound(c,least_upper_bound(X_11,b)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(b,least_upper_bound(X_11,b)),greatest_lower_bound(c,least_upper_bound(X_11,b))),greatest_lower_bound(c,least_upper_bound(X_11,b))) )],[refute_0_182,refute_0_185]) ).
cnf(refute_0_187,plain,
least_upper_bound(b,greatest_lower_bound(c,least_upper_bound(a,b))) = greatest_lower_bound(c,least_upper_bound(a,b)),
inference(subst,[],[refute_0_186:[bind(X_11,$fot(a))]]) ).
cnf(refute_0_188,plain,
least_upper_bound(X_550,least_upper_bound(greatest_lower_bound(a,X_50),greatest_lower_bound(X_50,c))) = least_upper_bound(greatest_lower_bound(a,X_50),least_upper_bound(X_550,greatest_lower_bound(X_50,c))),
inference(subst,[],[refute_0_165:[bind(Y,$fot(X_550)),bind(X_18,$fot(greatest_lower_bound(a,X_50))),bind(X_20,$fot(greatest_lower_bound(X_50,c)))]]) ).
cnf(refute_0_189,plain,
least_upper_bound(greatest_lower_bound(a,X_50),greatest_lower_bound(c,X_50)) = greatest_lower_bound(c,X_50),
inference(subst,[],[refute_0_71:[bind(X_46,$fot(X_50))]]) ).
cnf(refute_0_190,plain,
greatest_lower_bound(X_50,c) = greatest_lower_bound(c,X_50),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_50)),bind(Y,$fot(c))]]) ).
cnf(refute_0_191,plain,
( greatest_lower_bound(X_50,c) != greatest_lower_bound(c,X_50)
| greatest_lower_bound(c,X_50) = greatest_lower_bound(X_50,c) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(greatest_lower_bound(X_50,c))),bind(Y0,$fot(greatest_lower_bound(c,X_50)))]]) ).
cnf(refute_0_192,plain,
greatest_lower_bound(c,X_50) = greatest_lower_bound(X_50,c),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_50,c),greatest_lower_bound(c,X_50)) )],[refute_0_190,refute_0_191]) ).
cnf(refute_0_193,plain,
( greatest_lower_bound(c,X_50) != greatest_lower_bound(X_50,c)
| least_upper_bound(greatest_lower_bound(a,X_50),greatest_lower_bound(c,X_50)) != greatest_lower_bound(c,X_50)
| least_upper_bound(greatest_lower_bound(a,X_50),greatest_lower_bound(X_50,c)) = greatest_lower_bound(c,X_50) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,X_50),greatest_lower_bound(c,X_50)),greatest_lower_bound(c,X_50)) ),[0,1],$fot(greatest_lower_bound(X_50,c))]]) ).
cnf(refute_0_194,plain,
( least_upper_bound(greatest_lower_bound(a,X_50),greatest_lower_bound(c,X_50)) != greatest_lower_bound(c,X_50)
| least_upper_bound(greatest_lower_bound(a,X_50),greatest_lower_bound(X_50,c)) = greatest_lower_bound(c,X_50) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(c,X_50),greatest_lower_bound(X_50,c)) )],[refute_0_192,refute_0_193]) ).
cnf(refute_0_195,plain,
least_upper_bound(greatest_lower_bound(a,X_50),greatest_lower_bound(X_50,c)) = greatest_lower_bound(c,X_50),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,X_50),greatest_lower_bound(c,X_50)),greatest_lower_bound(c,X_50)) )],[refute_0_189,refute_0_194]) ).
cnf(refute_0_196,plain,
( least_upper_bound(X_550,least_upper_bound(greatest_lower_bound(a,X_50),greatest_lower_bound(X_50,c))) != least_upper_bound(greatest_lower_bound(a,X_50),least_upper_bound(X_550,greatest_lower_bound(X_50,c)))
| least_upper_bound(greatest_lower_bound(a,X_50),greatest_lower_bound(X_50,c)) != greatest_lower_bound(c,X_50)
| least_upper_bound(X_550,greatest_lower_bound(c,X_50)) = least_upper_bound(greatest_lower_bound(a,X_50),least_upper_bound(X_550,greatest_lower_bound(X_50,c))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_550,least_upper_bound(greatest_lower_bound(a,X_50),greatest_lower_bound(X_50,c))),least_upper_bound(greatest_lower_bound(a,X_50),least_upper_bound(X_550,greatest_lower_bound(X_50,c)))) ),[0,1],$fot(greatest_lower_bound(c,X_50))]]) ).
cnf(refute_0_197,plain,
( least_upper_bound(X_550,least_upper_bound(greatest_lower_bound(a,X_50),greatest_lower_bound(X_50,c))) != least_upper_bound(greatest_lower_bound(a,X_50),least_upper_bound(X_550,greatest_lower_bound(X_50,c)))
| least_upper_bound(X_550,greatest_lower_bound(c,X_50)) = least_upper_bound(greatest_lower_bound(a,X_50),least_upper_bound(X_550,greatest_lower_bound(X_50,c))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,X_50),greatest_lower_bound(X_50,c)),greatest_lower_bound(c,X_50)) )],[refute_0_195,refute_0_196]) ).
cnf(refute_0_198,plain,
least_upper_bound(X_550,greatest_lower_bound(c,X_50)) = least_upper_bound(greatest_lower_bound(a,X_50),least_upper_bound(X_550,greatest_lower_bound(X_50,c))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_550,least_upper_bound(greatest_lower_bound(a,X_50),greatest_lower_bound(X_50,c))),least_upper_bound(greatest_lower_bound(a,X_50),least_upper_bound(X_550,greatest_lower_bound(X_50,c)))) )],[refute_0_188,refute_0_197]) ).
cnf(refute_0_199,plain,
least_upper_bound(greatest_lower_bound(a,X_48),least_upper_bound(X_238,greatest_lower_bound(X_48,c))) = least_upper_bound(X_238,least_upper_bound(greatest_lower_bound(X_48,c),greatest_lower_bound(a,X_48))),
inference(subst,[],[refute_0_136:[bind(X,$fot(greatest_lower_bound(a,X_48))),bind(X_18,$fot(X_238)),bind(X_19,$fot(greatest_lower_bound(X_48,c)))]]) ).
cnf(refute_0_200,plain,
least_upper_bound(greatest_lower_bound(X_48,c),greatest_lower_bound(a,greatest_lower_bound(X_48,c))) = greatest_lower_bound(X_48,c),
inference(subst,[],[refute_0_10:[bind(X_8,$fot(greatest_lower_bound(X_48,c))),bind(X_9,$fot(a))]]) ).
cnf(refute_0_201,plain,
greatest_lower_bound(X_46,c) = greatest_lower_bound(c,X_46),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_46)),bind(Y,$fot(c))]]) ).
cnf(refute_0_202,plain,
( greatest_lower_bound(X_46,c) != greatest_lower_bound(c,X_46)
| greatest_lower_bound(c,X_46) = greatest_lower_bound(X_46,c) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(greatest_lower_bound(X_46,c))),bind(Y0,$fot(greatest_lower_bound(c,X_46)))]]) ).
cnf(refute_0_203,plain,
greatest_lower_bound(c,X_46) = greatest_lower_bound(X_46,c),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_46,c),greatest_lower_bound(c,X_46)) )],[refute_0_201,refute_0_202]) ).
cnf(refute_0_204,plain,
( greatest_lower_bound(a,greatest_lower_bound(c,X_46)) != greatest_lower_bound(a,X_46)
| greatest_lower_bound(c,X_46) != greatest_lower_bound(X_46,c)
| greatest_lower_bound(a,greatest_lower_bound(X_46,c)) = greatest_lower_bound(a,X_46) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(c,X_46)),greatest_lower_bound(a,X_46)) ),[0,1],$fot(greatest_lower_bound(X_46,c))]]) ).
cnf(refute_0_205,plain,
( greatest_lower_bound(a,greatest_lower_bound(c,X_46)) != greatest_lower_bound(a,X_46)
| greatest_lower_bound(a,greatest_lower_bound(X_46,c)) = greatest_lower_bound(a,X_46) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(c,X_46),greatest_lower_bound(X_46,c)) )],[refute_0_203,refute_0_204]) ).
cnf(refute_0_206,plain,
greatest_lower_bound(a,greatest_lower_bound(X_46,c)) = greatest_lower_bound(a,X_46),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(c,X_46)),greatest_lower_bound(a,X_46)) )],[refute_0_64,refute_0_205]) ).
cnf(refute_0_207,plain,
greatest_lower_bound(a,greatest_lower_bound(X_48,c)) = greatest_lower_bound(a,X_48),
inference(subst,[],[refute_0_206:[bind(X_46,$fot(X_48))]]) ).
cnf(refute_0_208,plain,
( greatest_lower_bound(a,greatest_lower_bound(X_48,c)) != greatest_lower_bound(a,X_48)
| least_upper_bound(greatest_lower_bound(X_48,c),greatest_lower_bound(a,greatest_lower_bound(X_48,c))) != greatest_lower_bound(X_48,c)
| least_upper_bound(greatest_lower_bound(X_48,c),greatest_lower_bound(a,X_48)) = greatest_lower_bound(X_48,c) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_48,c),greatest_lower_bound(a,greatest_lower_bound(X_48,c))),greatest_lower_bound(X_48,c)) ),[0,1],$fot(greatest_lower_bound(a,X_48))]]) ).
cnf(refute_0_209,plain,
( least_upper_bound(greatest_lower_bound(X_48,c),greatest_lower_bound(a,greatest_lower_bound(X_48,c))) != greatest_lower_bound(X_48,c)
| least_upper_bound(greatest_lower_bound(X_48,c),greatest_lower_bound(a,X_48)) = greatest_lower_bound(X_48,c) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(X_48,c)),greatest_lower_bound(a,X_48)) )],[refute_0_207,refute_0_208]) ).
cnf(refute_0_210,plain,
least_upper_bound(greatest_lower_bound(X_48,c),greatest_lower_bound(a,X_48)) = greatest_lower_bound(X_48,c),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_48,c),greatest_lower_bound(a,greatest_lower_bound(X_48,c))),greatest_lower_bound(X_48,c)) )],[refute_0_200,refute_0_209]) ).
cnf(refute_0_211,plain,
( least_upper_bound(greatest_lower_bound(X_48,c),greatest_lower_bound(a,X_48)) != greatest_lower_bound(X_48,c)
| least_upper_bound(greatest_lower_bound(a,X_48),least_upper_bound(X_238,greatest_lower_bound(X_48,c))) != least_upper_bound(X_238,least_upper_bound(greatest_lower_bound(X_48,c),greatest_lower_bound(a,X_48)))
| least_upper_bound(greatest_lower_bound(a,X_48),least_upper_bound(X_238,greatest_lower_bound(X_48,c))) = least_upper_bound(X_238,greatest_lower_bound(X_48,c)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,X_48),least_upper_bound(X_238,greatest_lower_bound(X_48,c))),least_upper_bound(X_238,least_upper_bound(greatest_lower_bound(X_48,c),greatest_lower_bound(a,X_48)))) ),[1,1],$fot(greatest_lower_bound(X_48,c))]]) ).
cnf(refute_0_212,plain,
( least_upper_bound(greatest_lower_bound(a,X_48),least_upper_bound(X_238,greatest_lower_bound(X_48,c))) != least_upper_bound(X_238,least_upper_bound(greatest_lower_bound(X_48,c),greatest_lower_bound(a,X_48)))
| least_upper_bound(greatest_lower_bound(a,X_48),least_upper_bound(X_238,greatest_lower_bound(X_48,c))) = least_upper_bound(X_238,greatest_lower_bound(X_48,c)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_48,c),greatest_lower_bound(a,X_48)),greatest_lower_bound(X_48,c)) )],[refute_0_210,refute_0_211]) ).
cnf(refute_0_213,plain,
least_upper_bound(greatest_lower_bound(a,X_48),least_upper_bound(X_238,greatest_lower_bound(X_48,c))) = least_upper_bound(X_238,greatest_lower_bound(X_48,c)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,X_48),least_upper_bound(X_238,greatest_lower_bound(X_48,c))),least_upper_bound(X_238,least_upper_bound(greatest_lower_bound(X_48,c),greatest_lower_bound(a,X_48)))) )],[refute_0_199,refute_0_212]) ).
cnf(refute_0_214,plain,
least_upper_bound(greatest_lower_bound(a,X_50),least_upper_bound(X_550,greatest_lower_bound(X_50,c))) = least_upper_bound(X_550,greatest_lower_bound(X_50,c)),
inference(subst,[],[refute_0_213:[bind(X_238,$fot(X_550)),bind(X_48,$fot(X_50))]]) ).
cnf(refute_0_215,plain,
( least_upper_bound(X_550,greatest_lower_bound(c,X_50)) != least_upper_bound(greatest_lower_bound(a,X_50),least_upper_bound(X_550,greatest_lower_bound(X_50,c)))
| least_upper_bound(greatest_lower_bound(a,X_50),least_upper_bound(X_550,greatest_lower_bound(X_50,c))) != least_upper_bound(X_550,greatest_lower_bound(X_50,c))
| least_upper_bound(X_550,greatest_lower_bound(c,X_50)) = least_upper_bound(X_550,greatest_lower_bound(X_50,c)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_550,greatest_lower_bound(c,X_50)),least_upper_bound(X_550,greatest_lower_bound(X_50,c))) ),[0],$fot(least_upper_bound(greatest_lower_bound(a,X_50),least_upper_bound(X_550,greatest_lower_bound(X_50,c))))]]) ).
cnf(refute_0_216,plain,
( least_upper_bound(X_550,greatest_lower_bound(c,X_50)) != least_upper_bound(greatest_lower_bound(a,X_50),least_upper_bound(X_550,greatest_lower_bound(X_50,c)))
| least_upper_bound(X_550,greatest_lower_bound(c,X_50)) = least_upper_bound(X_550,greatest_lower_bound(X_50,c)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,X_50),least_upper_bound(X_550,greatest_lower_bound(X_50,c))),least_upper_bound(X_550,greatest_lower_bound(X_50,c))) )],[refute_0_214,refute_0_215]) ).
cnf(refute_0_217,plain,
least_upper_bound(X_550,greatest_lower_bound(c,X_50)) = least_upper_bound(X_550,greatest_lower_bound(X_50,c)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_550,greatest_lower_bound(c,X_50)),least_upper_bound(greatest_lower_bound(a,X_50),least_upper_bound(X_550,greatest_lower_bound(X_50,c)))) )],[refute_0_198,refute_0_216]) ).
cnf(refute_0_218,plain,
least_upper_bound(X_550,greatest_lower_bound(c,least_upper_bound(a,X_686))) = least_upper_bound(X_550,greatest_lower_bound(least_upper_bound(a,X_686),c)),
inference(subst,[],[refute_0_217:[bind(X_50,$fot(least_upper_bound(a,X_686)))]]) ).
cnf(refute_0_219,plain,
( greatest_lower_bound(c,least_upper_bound(a,X_686)) != greatest_lower_bound(c,least_upper_bound(X_686,a))
| least_upper_bound(X_550,greatest_lower_bound(c,least_upper_bound(a,X_686))) != least_upper_bound(X_550,greatest_lower_bound(least_upper_bound(a,X_686),c))
| least_upper_bound(X_550,greatest_lower_bound(c,least_upper_bound(X_686,a))) = least_upper_bound(X_550,greatest_lower_bound(least_upper_bound(a,X_686),c)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_550,greatest_lower_bound(c,least_upper_bound(a,X_686))),least_upper_bound(X_550,greatest_lower_bound(least_upper_bound(a,X_686),c))) ),[0,1],$fot(greatest_lower_bound(c,least_upper_bound(X_686,a)))]]) ).
cnf(refute_0_220,plain,
( least_upper_bound(X_550,greatest_lower_bound(c,least_upper_bound(a,X_686))) != least_upper_bound(X_550,greatest_lower_bound(least_upper_bound(a,X_686),c))
| least_upper_bound(X_550,greatest_lower_bound(c,least_upper_bound(X_686,a))) = least_upper_bound(X_550,greatest_lower_bound(least_upper_bound(a,X_686),c)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(c,least_upper_bound(a,X_686)),greatest_lower_bound(c,least_upper_bound(X_686,a))) )],[refute_0_100,refute_0_219]) ).
cnf(refute_0_221,plain,
least_upper_bound(X_550,greatest_lower_bound(c,least_upper_bound(X_686,a))) = least_upper_bound(X_550,greatest_lower_bound(least_upper_bound(a,X_686),c)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_550,greatest_lower_bound(c,least_upper_bound(a,X_686))),least_upper_bound(X_550,greatest_lower_bound(least_upper_bound(a,X_686),c))) )],[refute_0_218,refute_0_220]) ).
cnf(refute_0_222,plain,
least_upper_bound(greatest_lower_bound(X_619,X_618),least_upper_bound(X_18,greatest_lower_bound(X_618,X_619))) = least_upper_bound(X_18,least_upper_bound(greatest_lower_bound(X_618,X_619),greatest_lower_bound(X_619,X_618))),
inference(subst,[],[refute_0_136:[bind(X,$fot(greatest_lower_bound(X_619,X_618))),bind(X_19,$fot(greatest_lower_bound(X_618,X_619)))]]) ).
cnf(refute_0_223,plain,
least_upper_bound(greatest_lower_bound(X_206,X_9),greatest_lower_bound(X_9,greatest_lower_bound(X_206,X_9))) = greatest_lower_bound(X_206,X_9),
inference(subst,[],[refute_0_10:[bind(X_8,$fot(greatest_lower_bound(X_206,X_9)))]]) ).
cnf(refute_0_224,plain,
greatest_lower_bound(greatest_lower_bound(X_30,Y),least_upper_bound(X_30,greatest_lower_bound(X_30,Y))) = greatest_lower_bound(X_30,Y),
inference(subst,[],[refute_0_79:[bind(X_10,$fot(greatest_lower_bound(X_30,Y))),bind(X_11,$fot(X_30))]]) ).
cnf(refute_0_225,plain,
least_upper_bound(X_30,greatest_lower_bound(X_30,Y)) = X_30,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_30))]]) ).
cnf(refute_0_226,plain,
( greatest_lower_bound(greatest_lower_bound(X_30,Y),least_upper_bound(X_30,greatest_lower_bound(X_30,Y))) != greatest_lower_bound(X_30,Y)
| least_upper_bound(X_30,greatest_lower_bound(X_30,Y)) != X_30
| greatest_lower_bound(greatest_lower_bound(X_30,Y),X_30) = greatest_lower_bound(X_30,Y) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_30,Y),least_upper_bound(X_30,greatest_lower_bound(X_30,Y))),greatest_lower_bound(X_30,Y)) ),[0,1],$fot(X_30)]]) ).
cnf(refute_0_227,plain,
( greatest_lower_bound(greatest_lower_bound(X_30,Y),least_upper_bound(X_30,greatest_lower_bound(X_30,Y))) != greatest_lower_bound(X_30,Y)
| greatest_lower_bound(greatest_lower_bound(X_30,Y),X_30) = greatest_lower_bound(X_30,Y) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_30,greatest_lower_bound(X_30,Y)),X_30) )],[refute_0_225,refute_0_226]) ).
cnf(refute_0_228,plain,
greatest_lower_bound(greatest_lower_bound(X_30,Y),X_30) = greatest_lower_bound(X_30,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_30,Y),least_upper_bound(X_30,greatest_lower_bound(X_30,Y))),greatest_lower_bound(X_30,Y)) )],[refute_0_224,refute_0_227]) ).
cnf(refute_0_229,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,Z)) != greatest_lower_bound(greatest_lower_bound(X,Y),Z)
| greatest_lower_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(Y,Z)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X,Y),Z)))]]) ).
cnf(refute_0_230,plain,
greatest_lower_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(greatest_lower_bound(X,Y),Z)) )],[associativity_of_glb,refute_0_229]) ).
cnf(refute_0_231,plain,
greatest_lower_bound(greatest_lower_bound(X_30,Y),X_30) = greatest_lower_bound(X_30,greatest_lower_bound(Y,X_30)),
inference(subst,[],[refute_0_230:[bind(X,$fot(X_30)),bind(Z,$fot(X_30))]]) ).
cnf(refute_0_232,plain,
( greatest_lower_bound(greatest_lower_bound(X_30,Y),X_30) != greatest_lower_bound(X_30,Y)
| greatest_lower_bound(greatest_lower_bound(X_30,Y),X_30) != greatest_lower_bound(X_30,greatest_lower_bound(Y,X_30))
| greatest_lower_bound(X_30,greatest_lower_bound(Y,X_30)) = greatest_lower_bound(X_30,Y) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_30,Y),X_30),greatest_lower_bound(X_30,Y)) ),[0],$fot(greatest_lower_bound(X_30,greatest_lower_bound(Y,X_30)))]]) ).
cnf(refute_0_233,plain,
( greatest_lower_bound(greatest_lower_bound(X_30,Y),X_30) != greatest_lower_bound(X_30,Y)
| greatest_lower_bound(X_30,greatest_lower_bound(Y,X_30)) = greatest_lower_bound(X_30,Y) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_30,Y),X_30),greatest_lower_bound(X_30,greatest_lower_bound(Y,X_30))) )],[refute_0_231,refute_0_232]) ).
cnf(refute_0_234,plain,
greatest_lower_bound(X_30,greatest_lower_bound(Y,X_30)) = greatest_lower_bound(X_30,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_30,Y),X_30),greatest_lower_bound(X_30,Y)) )],[refute_0_228,refute_0_233]) ).
cnf(refute_0_235,plain,
greatest_lower_bound(X_9,greatest_lower_bound(X_206,X_9)) = greatest_lower_bound(X_9,X_206),
inference(subst,[],[refute_0_234:[bind(Y,$fot(X_206)),bind(X_30,$fot(X_9))]]) ).
cnf(refute_0_236,plain,
( greatest_lower_bound(X_9,greatest_lower_bound(X_206,X_9)) != greatest_lower_bound(X_9,X_206)
| least_upper_bound(greatest_lower_bound(X_206,X_9),greatest_lower_bound(X_9,greatest_lower_bound(X_206,X_9))) != greatest_lower_bound(X_206,X_9)
| least_upper_bound(greatest_lower_bound(X_206,X_9),greatest_lower_bound(X_9,X_206)) = greatest_lower_bound(X_206,X_9) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_206,X_9),greatest_lower_bound(X_9,greatest_lower_bound(X_206,X_9))),greatest_lower_bound(X_206,X_9)) ),[0,1],$fot(greatest_lower_bound(X_9,X_206))]]) ).
cnf(refute_0_237,plain,
( least_upper_bound(greatest_lower_bound(X_206,X_9),greatest_lower_bound(X_9,greatest_lower_bound(X_206,X_9))) != greatest_lower_bound(X_206,X_9)
| least_upper_bound(greatest_lower_bound(X_206,X_9),greatest_lower_bound(X_9,X_206)) = greatest_lower_bound(X_206,X_9) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_9,greatest_lower_bound(X_206,X_9)),greatest_lower_bound(X_9,X_206)) )],[refute_0_235,refute_0_236]) ).
cnf(refute_0_238,plain,
least_upper_bound(greatest_lower_bound(X_206,X_9),greatest_lower_bound(X_9,X_206)) = greatest_lower_bound(X_206,X_9),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_206,X_9),greatest_lower_bound(X_9,greatest_lower_bound(X_206,X_9))),greatest_lower_bound(X_206,X_9)) )],[refute_0_223,refute_0_237]) ).
cnf(refute_0_239,plain,
least_upper_bound(greatest_lower_bound(X_618,X_619),greatest_lower_bound(X_619,X_618)) = greatest_lower_bound(X_618,X_619),
inference(subst,[],[refute_0_238:[bind(X_206,$fot(X_618)),bind(X_9,$fot(X_619))]]) ).
cnf(refute_0_240,plain,
( least_upper_bound(greatest_lower_bound(X_618,X_619),greatest_lower_bound(X_619,X_618)) != greatest_lower_bound(X_618,X_619)
| least_upper_bound(greatest_lower_bound(X_619,X_618),least_upper_bound(X_18,greatest_lower_bound(X_618,X_619))) != least_upper_bound(X_18,least_upper_bound(greatest_lower_bound(X_618,X_619),greatest_lower_bound(X_619,X_618)))
| least_upper_bound(greatest_lower_bound(X_619,X_618),least_upper_bound(X_18,greatest_lower_bound(X_618,X_619))) = least_upper_bound(X_18,greatest_lower_bound(X_618,X_619)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_619,X_618),least_upper_bound(X_18,greatest_lower_bound(X_618,X_619))),least_upper_bound(X_18,least_upper_bound(greatest_lower_bound(X_618,X_619),greatest_lower_bound(X_619,X_618)))) ),[1,1],$fot(greatest_lower_bound(X_618,X_619))]]) ).
cnf(refute_0_241,plain,
( least_upper_bound(greatest_lower_bound(X_619,X_618),least_upper_bound(X_18,greatest_lower_bound(X_618,X_619))) != least_upper_bound(X_18,least_upper_bound(greatest_lower_bound(X_618,X_619),greatest_lower_bound(X_619,X_618)))
| least_upper_bound(greatest_lower_bound(X_619,X_618),least_upper_bound(X_18,greatest_lower_bound(X_618,X_619))) = least_upper_bound(X_18,greatest_lower_bound(X_618,X_619)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_618,X_619),greatest_lower_bound(X_619,X_618)),greatest_lower_bound(X_618,X_619)) )],[refute_0_239,refute_0_240]) ).
cnf(refute_0_242,plain,
least_upper_bound(greatest_lower_bound(X_619,X_618),least_upper_bound(X_18,greatest_lower_bound(X_618,X_619))) = least_upper_bound(X_18,greatest_lower_bound(X_618,X_619)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_619,X_618),least_upper_bound(X_18,greatest_lower_bound(X_618,X_619))),least_upper_bound(X_18,least_upper_bound(greatest_lower_bound(X_618,X_619),greatest_lower_bound(X_619,X_618)))) )],[refute_0_222,refute_0_241]) ).
cnf(refute_0_243,plain,
least_upper_bound(greatest_lower_bound(X_618,X_619),least_upper_bound(X_18,greatest_lower_bound(X_619,X_618))) = least_upper_bound(X_18,least_upper_bound(greatest_lower_bound(X_618,X_619),greatest_lower_bound(X_619,X_618))),
inference(subst,[],[refute_0_165:[bind(Y,$fot(greatest_lower_bound(X_618,X_619))),bind(X_20,$fot(greatest_lower_bound(X_619,X_618)))]]) ).
cnf(refute_0_244,plain,
( least_upper_bound(greatest_lower_bound(X_618,X_619),greatest_lower_bound(X_619,X_618)) != greatest_lower_bound(X_618,X_619)
| least_upper_bound(greatest_lower_bound(X_618,X_619),least_upper_bound(X_18,greatest_lower_bound(X_619,X_618))) != least_upper_bound(X_18,least_upper_bound(greatest_lower_bound(X_618,X_619),greatest_lower_bound(X_619,X_618)))
| least_upper_bound(greatest_lower_bound(X_618,X_619),least_upper_bound(X_18,greatest_lower_bound(X_619,X_618))) = least_upper_bound(X_18,greatest_lower_bound(X_618,X_619)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_618,X_619),least_upper_bound(X_18,greatest_lower_bound(X_619,X_618))),least_upper_bound(X_18,least_upper_bound(greatest_lower_bound(X_618,X_619),greatest_lower_bound(X_619,X_618)))) ),[1,1],$fot(greatest_lower_bound(X_618,X_619))]]) ).
cnf(refute_0_245,plain,
( least_upper_bound(greatest_lower_bound(X_618,X_619),least_upper_bound(X_18,greatest_lower_bound(X_619,X_618))) != least_upper_bound(X_18,least_upper_bound(greatest_lower_bound(X_618,X_619),greatest_lower_bound(X_619,X_618)))
| least_upper_bound(greatest_lower_bound(X_618,X_619),least_upper_bound(X_18,greatest_lower_bound(X_619,X_618))) = least_upper_bound(X_18,greatest_lower_bound(X_618,X_619)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_618,X_619),greatest_lower_bound(X_619,X_618)),greatest_lower_bound(X_618,X_619)) )],[refute_0_239,refute_0_244]) ).
cnf(refute_0_246,plain,
least_upper_bound(greatest_lower_bound(X_618,X_619),least_upper_bound(X_18,greatest_lower_bound(X_619,X_618))) = least_upper_bound(X_18,greatest_lower_bound(X_618,X_619)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_618,X_619),least_upper_bound(X_18,greatest_lower_bound(X_619,X_618))),least_upper_bound(X_18,least_upper_bound(greatest_lower_bound(X_618,X_619),greatest_lower_bound(X_619,X_618)))) )],[refute_0_243,refute_0_245]) ).
cnf(refute_0_247,plain,
least_upper_bound(greatest_lower_bound(X_619,X_618),least_upper_bound(X_18,greatest_lower_bound(X_618,X_619))) = least_upper_bound(X_18,greatest_lower_bound(X_619,X_618)),
inference(subst,[],[refute_0_246:[bind(X_618,$fot(X_619)),bind(X_619,$fot(X_618))]]) ).
cnf(refute_0_248,plain,
( least_upper_bound(greatest_lower_bound(X_619,X_618),least_upper_bound(X_18,greatest_lower_bound(X_618,X_619))) != least_upper_bound(X_18,greatest_lower_bound(X_618,X_619))
| least_upper_bound(greatest_lower_bound(X_619,X_618),least_upper_bound(X_18,greatest_lower_bound(X_618,X_619))) != least_upper_bound(X_18,greatest_lower_bound(X_619,X_618))
| least_upper_bound(X_18,greatest_lower_bound(X_619,X_618)) = least_upper_bound(X_18,greatest_lower_bound(X_618,X_619)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_619,X_618),least_upper_bound(X_18,greatest_lower_bound(X_618,X_619))),least_upper_bound(X_18,greatest_lower_bound(X_618,X_619))) ),[0],$fot(least_upper_bound(X_18,greatest_lower_bound(X_619,X_618)))]]) ).
cnf(refute_0_249,plain,
( least_upper_bound(greatest_lower_bound(X_619,X_618),least_upper_bound(X_18,greatest_lower_bound(X_618,X_619))) != least_upper_bound(X_18,greatest_lower_bound(X_618,X_619))
| least_upper_bound(X_18,greatest_lower_bound(X_619,X_618)) = least_upper_bound(X_18,greatest_lower_bound(X_618,X_619)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_619,X_618),least_upper_bound(X_18,greatest_lower_bound(X_618,X_619))),least_upper_bound(X_18,greatest_lower_bound(X_619,X_618))) )],[refute_0_247,refute_0_248]) ).
cnf(refute_0_250,plain,
least_upper_bound(X_18,greatest_lower_bound(X_619,X_618)) = least_upper_bound(X_18,greatest_lower_bound(X_618,X_619)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_619,X_618),least_upper_bound(X_18,greatest_lower_bound(X_618,X_619))),least_upper_bound(X_18,greatest_lower_bound(X_618,X_619))) )],[refute_0_242,refute_0_249]) ).
cnf(refute_0_251,plain,
( least_upper_bound(X_18,greatest_lower_bound(X_619,X_618)) != least_upper_bound(X_18,greatest_lower_bound(X_618,X_619))
| least_upper_bound(X_18,greatest_lower_bound(X_618,X_619)) = least_upper_bound(X_18,greatest_lower_bound(X_619,X_618)) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(least_upper_bound(X_18,greatest_lower_bound(X_619,X_618)))),bind(Y0,$fot(least_upper_bound(X_18,greatest_lower_bound(X_618,X_619))))]]) ).
cnf(refute_0_252,plain,
least_upper_bound(X_18,greatest_lower_bound(X_618,X_619)) = least_upper_bound(X_18,greatest_lower_bound(X_619,X_618)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,greatest_lower_bound(X_619,X_618)),least_upper_bound(X_18,greatest_lower_bound(X_618,X_619))) )],[refute_0_250,refute_0_251]) ).
cnf(refute_0_253,plain,
least_upper_bound(X_550,greatest_lower_bound(least_upper_bound(a,X_686),c)) = least_upper_bound(X_550,greatest_lower_bound(c,least_upper_bound(a,X_686))),
inference(subst,[],[refute_0_252:[bind(X_18,$fot(X_550)),bind(X_618,$fot(least_upper_bound(a,X_686))),bind(X_619,$fot(c))]]) ).
cnf(refute_0_254,plain,
( least_upper_bound(X_550,greatest_lower_bound(c,least_upper_bound(X_686,a))) != least_upper_bound(X_550,greatest_lower_bound(least_upper_bound(a,X_686),c))
| least_upper_bound(X_550,greatest_lower_bound(least_upper_bound(a,X_686),c)) != least_upper_bound(X_550,greatest_lower_bound(c,least_upper_bound(a,X_686)))
| least_upper_bound(X_550,greatest_lower_bound(c,least_upper_bound(X_686,a))) = least_upper_bound(X_550,greatest_lower_bound(c,least_upper_bound(a,X_686))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_550,greatest_lower_bound(c,least_upper_bound(X_686,a))),least_upper_bound(X_550,greatest_lower_bound(c,least_upper_bound(a,X_686)))) ),[0],$fot(least_upper_bound(X_550,greatest_lower_bound(least_upper_bound(a,X_686),c)))]]) ).
cnf(refute_0_255,plain,
( least_upper_bound(X_550,greatest_lower_bound(c,least_upper_bound(X_686,a))) != least_upper_bound(X_550,greatest_lower_bound(least_upper_bound(a,X_686),c))
| least_upper_bound(X_550,greatest_lower_bound(c,least_upper_bound(X_686,a))) = least_upper_bound(X_550,greatest_lower_bound(c,least_upper_bound(a,X_686))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_550,greatest_lower_bound(least_upper_bound(a,X_686),c)),least_upper_bound(X_550,greatest_lower_bound(c,least_upper_bound(a,X_686)))) )],[refute_0_253,refute_0_254]) ).
cnf(refute_0_256,plain,
least_upper_bound(X_550,greatest_lower_bound(c,least_upper_bound(X_686,a))) = least_upper_bound(X_550,greatest_lower_bound(c,least_upper_bound(a,X_686))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_550,greatest_lower_bound(c,least_upper_bound(X_686,a))),least_upper_bound(X_550,greatest_lower_bound(least_upper_bound(a,X_686),c))) )],[refute_0_221,refute_0_255]) ).
cnf(refute_0_257,plain,
least_upper_bound(b,greatest_lower_bound(c,least_upper_bound(b,a))) = least_upper_bound(b,greatest_lower_bound(c,least_upper_bound(a,b))),
inference(subst,[],[refute_0_256:[bind(X_550,$fot(b)),bind(X_686,$fot(b))]]) ).
cnf(refute_0_258,plain,
( least_upper_bound(b,greatest_lower_bound(c,least_upper_bound(a,b))) != greatest_lower_bound(c,least_upper_bound(a,b))
| least_upper_bound(b,greatest_lower_bound(c,least_upper_bound(b,a))) != least_upper_bound(b,greatest_lower_bound(c,least_upper_bound(a,b)))
| least_upper_bound(b,greatest_lower_bound(c,least_upper_bound(b,a))) = greatest_lower_bound(c,least_upper_bound(a,b)) ),
inference(subst,[],[refute_0_141:[bind(X0,$fot(least_upper_bound(b,greatest_lower_bound(c,least_upper_bound(b,a))))),bind(Y0,$fot(least_upper_bound(b,greatest_lower_bound(c,least_upper_bound(a,b))))),bind(Z0,$fot(greatest_lower_bound(c,least_upper_bound(a,b))))]]) ).
cnf(refute_0_259,plain,
( least_upper_bound(b,greatest_lower_bound(c,least_upper_bound(a,b))) != greatest_lower_bound(c,least_upper_bound(a,b))
| least_upper_bound(b,greatest_lower_bound(c,least_upper_bound(b,a))) = greatest_lower_bound(c,least_upper_bound(a,b)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(c,least_upper_bound(b,a))),least_upper_bound(b,greatest_lower_bound(c,least_upper_bound(a,b)))) )],[refute_0_257,refute_0_258]) ).
cnf(refute_0_260,plain,
least_upper_bound(b,greatest_lower_bound(c,least_upper_bound(b,a))) = greatest_lower_bound(c,least_upper_bound(a,b)),
inference(resolve,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(c,least_upper_bound(a,b))),greatest_lower_bound(c,least_upper_bound(a,b))) )],[refute_0_187,refute_0_259]) ).
cnf(refute_0_261,plain,
least_upper_bound(b,greatest_lower_bound(least_upper_bound(b,a),c)) = least_upper_bound(b,greatest_lower_bound(c,least_upper_bound(b,a))),
inference(subst,[],[refute_0_252:[bind(X_18,$fot(b)),bind(X_618,$fot(least_upper_bound(b,a))),bind(X_619,$fot(c))]]) ).
cnf(refute_0_262,plain,
( least_upper_bound(b,greatest_lower_bound(c,least_upper_bound(b,a))) != greatest_lower_bound(c,least_upper_bound(a,b))
| least_upper_bound(b,greatest_lower_bound(least_upper_bound(b,a),c)) != least_upper_bound(b,greatest_lower_bound(c,least_upper_bound(b,a)))
| least_upper_bound(b,greatest_lower_bound(least_upper_bound(b,a),c)) = greatest_lower_bound(c,least_upper_bound(a,b)) ),
inference(subst,[],[refute_0_141:[bind(X0,$fot(least_upper_bound(b,greatest_lower_bound(least_upper_bound(b,a),c)))),bind(Y0,$fot(least_upper_bound(b,greatest_lower_bound(c,least_upper_bound(b,a))))),bind(Z0,$fot(greatest_lower_bound(c,least_upper_bound(a,b))))]]) ).
cnf(refute_0_263,plain,
( least_upper_bound(b,greatest_lower_bound(c,least_upper_bound(b,a))) != greatest_lower_bound(c,least_upper_bound(a,b))
| least_upper_bound(b,greatest_lower_bound(least_upper_bound(b,a),c)) = greatest_lower_bound(c,least_upper_bound(a,b)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(least_upper_bound(b,a),c)),least_upper_bound(b,greatest_lower_bound(c,least_upper_bound(b,a)))) )],[refute_0_261,refute_0_262]) ).
cnf(refute_0_264,plain,
least_upper_bound(b,greatest_lower_bound(least_upper_bound(b,a),c)) = greatest_lower_bound(c,least_upper_bound(a,b)),
inference(resolve,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(c,least_upper_bound(b,a))),greatest_lower_bound(c,least_upper_bound(a,b))) )],[refute_0_260,refute_0_263]) ).
cnf(refute_0_265,plain,
( least_upper_bound(a,b) != least_upper_bound(b,greatest_lower_bound(least_upper_bound(b,a),c))
| least_upper_bound(b,greatest_lower_bound(least_upper_bound(b,a),c)) != greatest_lower_bound(c,least_upper_bound(a,b))
| least_upper_bound(a,b) = greatest_lower_bound(c,least_upper_bound(a,b)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(a,b),greatest_lower_bound(c,least_upper_bound(a,b))) ),[0],$fot(least_upper_bound(b,greatest_lower_bound(least_upper_bound(b,a),c)))]]) ).
cnf(refute_0_266,plain,
( least_upper_bound(a,b) != least_upper_bound(b,greatest_lower_bound(least_upper_bound(b,a),c))
| least_upper_bound(a,b) = greatest_lower_bound(c,least_upper_bound(a,b)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(least_upper_bound(b,a),c)),greatest_lower_bound(c,least_upper_bound(a,b))) )],[refute_0_264,refute_0_265]) ).
cnf(refute_0_267,plain,
least_upper_bound(a,b) = greatest_lower_bound(c,least_upper_bound(a,b)),
inference(resolve,[$cnf( $equal(least_upper_bound(a,b),least_upper_bound(b,greatest_lower_bound(least_upper_bound(b,a),c))) )],[refute_0_181,refute_0_266]) ).
cnf(refute_0_268,plain,
( greatest_lower_bound(X,Y) != greatest_lower_bound(Y,X)
| greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(greatest_lower_bound(X,Y))),bind(Y0,$fot(greatest_lower_bound(Y,X)))]]) ).
cnf(refute_0_269,plain,
greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X)) )],[symmetry_of_glb,refute_0_268]) ).
cnf(refute_0_270,plain,
greatest_lower_bound(least_upper_bound(a,b),c) = greatest_lower_bound(c,least_upper_bound(a,b)),
inference(subst,[],[refute_0_269:[bind(X,$fot(c)),bind(Y,$fot(least_upper_bound(a,b)))]]) ).
cnf(refute_0_271,plain,
( greatest_lower_bound(c,least_upper_bound(a,b)) != least_upper_bound(a,b)
| greatest_lower_bound(least_upper_bound(a,b),c) != greatest_lower_bound(c,least_upper_bound(a,b))
| greatest_lower_bound(least_upper_bound(a,b),c) = least_upper_bound(a,b) ),
introduced(tautology,[equality,[$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_272,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( $equal(greatest_lower_bound(least_upper_bound(a,b),c),greatest_lower_bound(c,least_upper_bound(a,b))) )],[refute_0_270,refute_0_271]) ).
cnf(refute_0_273,plain,
greatest_lower_bound(c,least_upper_bound(a,b)) != least_upper_bound(a,b),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,b),c),least_upper_bound(a,b)) )],[refute_0_272,prove_ax_lub1c]) ).
cnf(refute_0_274,plain,
( least_upper_bound(a,b) != greatest_lower_bound(c,least_upper_bound(a,b))
| greatest_lower_bound(c,least_upper_bound(a,b)) = least_upper_bound(a,b) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(least_upper_bound(a,b))),bind(Y0,$fot(greatest_lower_bound(c,least_upper_bound(a,b))))]]) ).
cnf(refute_0_275,plain,
least_upper_bound(a,b) != greatest_lower_bound(c,least_upper_bound(a,b)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(c,least_upper_bound(a,b)),least_upper_bound(a,b)) )],[refute_0_274,refute_0_273]) ).
cnf(refute_0_276,plain,
$false,
inference(resolve,[$cnf( $equal(least_upper_bound(a,b),greatest_lower_bound(c,least_upper_bound(a,b))) )],[refute_0_267,refute_0_275]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP148-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.04/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % 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 05:55:55 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 106.23/106.46 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 106.23/106.46
% 106.23/106.46 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 106.23/106.48
%------------------------------------------------------------------------------