TSTP Solution File: GRP138-1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP138-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 10:36:59 EDT 2022
% Result : Unsatisfiable 10.47s 10.65s
% Output : CNFRefutation 10.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 111
% Syntax : Number of clauses : 465 ( 250 unt; 0 nHn; 230 RR)
% Number of literals : 773 ( 772 equ; 310 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 872 ( 31 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
multiply(identity,X) = X ).
cnf(left_inverse,axiom,
multiply(inverse(X),X) = identity ).
cnf(associativity,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ).
cnf(symmetry_of_glb,axiom,
greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ).
cnf(symmetry_of_lub,axiom,
least_upper_bound(X,Y) = least_upper_bound(Y,X) ).
cnf(associativity_of_glb,axiom,
greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) ).
cnf(associativity_of_lub,axiom,
least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) ).
cnf(idempotence_of_gld,axiom,
greatest_lower_bound(X,X) = X ).
cnf(lub_absorbtion,axiom,
least_upper_bound(X,greatest_lower_bound(X,Y)) = X ).
cnf(glb_absorbtion,axiom,
greatest_lower_bound(X,least_upper_bound(X,Y)) = X ).
cnf(monotony_lub1,axiom,
multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ).
cnf(monotony_glb1,axiom,
multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)) ).
cnf(monotony_lub2,axiom,
multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) ).
cnf(ax_glb1a_1,hypothesis,
least_upper_bound(a,c) = a ).
cnf(ax_glb1a_2,hypothesis,
least_upper_bound(b,c) = b ).
cnf(prove_ax_glb1a,negated_conjecture,
least_upper_bound(greatest_lower_bound(a,b),c) != greatest_lower_bound(a,b) ).
cnf(refute_0_0,plain,
least_upper_bound(X_10,greatest_lower_bound(X_10,X_11)) = X_10,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_10)),bind(Y,$fot(X_11))]]) ).
cnf(refute_0_1,plain,
greatest_lower_bound(X_11,X_10) = greatest_lower_bound(X_10,X_11),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_11)),bind(Y,$fot(X_10))]]) ).
cnf(refute_0_2,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_3,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_4,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( greatest_lower_bound(X_11,X_10) != greatest_lower_bound(X_10,X_11)
| greatest_lower_bound(X_10,X_11) = greatest_lower_bound(X_11,X_10) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(greatest_lower_bound(X_11,X_10))),bind(Y0,$fot(greatest_lower_bound(X_10,X_11)))]]) ).
cnf(refute_0_6,plain,
greatest_lower_bound(X_10,X_11) = greatest_lower_bound(X_11,X_10),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_11,X_10),greatest_lower_bound(X_10,X_11)) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
( greatest_lower_bound(X_10,X_11) != greatest_lower_bound(X_11,X_10)
| least_upper_bound(X_10,greatest_lower_bound(X_10,X_11)) != X_10
| least_upper_bound(X_10,greatest_lower_bound(X_11,X_10)) = X_10 ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_10,greatest_lower_bound(X_10,X_11)),X_10) ),[0,1],$fot(greatest_lower_bound(X_11,X_10))]]) ).
cnf(refute_0_8,plain,
( least_upper_bound(X_10,greatest_lower_bound(X_10,X_11)) != X_10
| least_upper_bound(X_10,greatest_lower_bound(X_11,X_10)) = X_10 ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_10,X_11),greatest_lower_bound(X_11,X_10)) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
least_upper_bound(X_10,greatest_lower_bound(X_11,X_10)) = X_10,
inference(resolve,[$cnf( $equal(least_upper_bound(X_10,greatest_lower_bound(X_10,X_11)),X_10) )],[refute_0_0,refute_0_8]) ).
cnf(refute_0_10,plain,
least_upper_bound(greatest_lower_bound(X_82,a),greatest_lower_bound(c,greatest_lower_bound(X_82,a))) = greatest_lower_bound(X_82,a),
inference(subst,[],[refute_0_9:[bind(X_10,$fot(greatest_lower_bound(X_82,a))),bind(X_11,$fot(c))]]) ).
cnf(refute_0_11,plain,
( greatest_lower_bound(X,least_upper_bound(X,Y)) != X
| least_upper_bound(X,Y) != least_upper_bound(Y,X)
| greatest_lower_bound(X,least_upper_bound(Y,X)) = X ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X,least_upper_bound(X,Y)),X) ),[0,1],$fot(least_upper_bound(Y,X))]]) ).
cnf(refute_0_12,plain,
( greatest_lower_bound(X,least_upper_bound(X,Y)) != X
| greatest_lower_bound(X,least_upper_bound(Y,X)) = X ),
inference(resolve,[$cnf( $equal(least_upper_bound(X,Y),least_upper_bound(Y,X)) )],[symmetry_of_lub,refute_0_11]) ).
cnf(refute_0_13,plain,
greatest_lower_bound(X,least_upper_bound(Y,X)) = X,
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,least_upper_bound(X,Y)),X) )],[glb_absorbtion,refute_0_12]) ).
cnf(refute_0_14,plain,
greatest_lower_bound(greatest_lower_bound(c,X_25),least_upper_bound(a,greatest_lower_bound(c,X_25))) = greatest_lower_bound(c,X_25),
inference(subst,[],[refute_0_13:[bind(X,$fot(greatest_lower_bound(c,X_25))),bind(Y,$fot(a))]]) ).
cnf(refute_0_15,plain,
least_upper_bound(a,least_upper_bound(c,X_20)) = least_upper_bound(least_upper_bound(a,c),X_20),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(a)),bind(Y,$fot(c)),bind(Z,$fot(X_20))]]) ).
cnf(refute_0_16,plain,
( least_upper_bound(a,c) != a
| least_upper_bound(a,least_upper_bound(c,X_20)) != least_upper_bound(least_upper_bound(a,c),X_20)
| least_upper_bound(a,least_upper_bound(c,X_20)) = least_upper_bound(a,X_20) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(a,least_upper_bound(c,X_20)),least_upper_bound(least_upper_bound(a,c),X_20)) ),[1,0],$fot(a)]]) ).
cnf(refute_0_17,plain,
( least_upper_bound(a,least_upper_bound(c,X_20)) != least_upper_bound(least_upper_bound(a,c),X_20)
| least_upper_bound(a,least_upper_bound(c,X_20)) = least_upper_bound(a,X_20) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,c),a) )],[ax_glb1a_1,refute_0_16]) ).
cnf(refute_0_18,plain,
least_upper_bound(a,least_upper_bound(c,X_20)) = least_upper_bound(a,X_20),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(c,X_20)),least_upper_bound(least_upper_bound(a,c),X_20)) )],[refute_0_15,refute_0_17]) ).
cnf(refute_0_19,plain,
least_upper_bound(a,least_upper_bound(c,greatest_lower_bound(c,Y))) = least_upper_bound(a,greatest_lower_bound(c,Y)),
inference(subst,[],[refute_0_18:[bind(X_20,$fot(greatest_lower_bound(c,Y)))]]) ).
cnf(refute_0_20,plain,
least_upper_bound(c,greatest_lower_bound(c,Y)) = c,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(c))]]) ).
cnf(refute_0_21,plain,
( least_upper_bound(a,least_upper_bound(c,greatest_lower_bound(c,Y))) != least_upper_bound(a,greatest_lower_bound(c,Y))
| least_upper_bound(c,greatest_lower_bound(c,Y)) != c
| least_upper_bound(a,c) = least_upper_bound(a,greatest_lower_bound(c,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(a,least_upper_bound(c,greatest_lower_bound(c,Y))),least_upper_bound(a,greatest_lower_bound(c,Y))) ),[0,1],$fot(c)]]) ).
cnf(refute_0_22,plain,
( least_upper_bound(a,least_upper_bound(c,greatest_lower_bound(c,Y))) != least_upper_bound(a,greatest_lower_bound(c,Y))
| least_upper_bound(a,c) = least_upper_bound(a,greatest_lower_bound(c,Y)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(c,greatest_lower_bound(c,Y)),c) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
least_upper_bound(a,c) = least_upper_bound(a,greatest_lower_bound(c,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(c,greatest_lower_bound(c,Y))),least_upper_bound(a,greatest_lower_bound(c,Y))) )],[refute_0_19,refute_0_22]) ).
cnf(refute_0_24,plain,
( least_upper_bound(a,c) != a
| least_upper_bound(a,c) != least_upper_bound(a,greatest_lower_bound(c,Y))
| a = least_upper_bound(a,greatest_lower_bound(c,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(a,c),least_upper_bound(a,greatest_lower_bound(c,Y))) ),[0],$fot(a)]]) ).
cnf(refute_0_25,plain,
( least_upper_bound(a,c) != least_upper_bound(a,greatest_lower_bound(c,Y))
| a = least_upper_bound(a,greatest_lower_bound(c,Y)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,c),a) )],[ax_glb1a_1,refute_0_24]) ).
cnf(refute_0_26,plain,
a = least_upper_bound(a,greatest_lower_bound(c,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(a,c),least_upper_bound(a,greatest_lower_bound(c,Y))) )],[refute_0_23,refute_0_25]) ).
cnf(refute_0_27,plain,
a = least_upper_bound(a,greatest_lower_bound(c,X_25)),
inference(subst,[],[refute_0_26:[bind(Y,$fot(X_25))]]) ).
cnf(refute_0_28,plain,
( a != least_upper_bound(a,greatest_lower_bound(c,X_25))
| least_upper_bound(a,greatest_lower_bound(c,X_25)) = a ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(a)),bind(Y0,$fot(least_upper_bound(a,greatest_lower_bound(c,X_25))))]]) ).
cnf(refute_0_29,plain,
least_upper_bound(a,greatest_lower_bound(c,X_25)) = a,
inference(resolve,[$cnf( $equal(a,least_upper_bound(a,greatest_lower_bound(c,X_25))) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
( greatest_lower_bound(greatest_lower_bound(c,X_25),least_upper_bound(a,greatest_lower_bound(c,X_25))) != greatest_lower_bound(c,X_25)
| least_upper_bound(a,greatest_lower_bound(c,X_25)) != a
| greatest_lower_bound(greatest_lower_bound(c,X_25),a) = greatest_lower_bound(c,X_25) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(c,X_25),least_upper_bound(a,greatest_lower_bound(c,X_25))),greatest_lower_bound(c,X_25)) ),[0,1],$fot(a)]]) ).
cnf(refute_0_31,plain,
( greatest_lower_bound(greatest_lower_bound(c,X_25),least_upper_bound(a,greatest_lower_bound(c,X_25))) != greatest_lower_bound(c,X_25)
| greatest_lower_bound(greatest_lower_bound(c,X_25),a) = greatest_lower_bound(c,X_25) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,greatest_lower_bound(c,X_25)),a) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
greatest_lower_bound(greatest_lower_bound(c,X_25),a) = greatest_lower_bound(c,X_25),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(c,X_25),least_upper_bound(a,greatest_lower_bound(c,X_25))),greatest_lower_bound(c,X_25)) )],[refute_0_14,refute_0_31]) ).
cnf(refute_0_33,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,Z)) != greatest_lower_bound(greatest_lower_bound(X,Y),Z)
| greatest_lower_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(Y,Z)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X,Y),Z)))]]) ).
cnf(refute_0_34,plain,
greatest_lower_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(greatest_lower_bound(X,Y),Z)) )],[associativity_of_glb,refute_0_33]) ).
cnf(refute_0_35,plain,
greatest_lower_bound(greatest_lower_bound(c,X_25),a) = greatest_lower_bound(c,greatest_lower_bound(X_25,a)),
inference(subst,[],[refute_0_34:[bind(X,$fot(c)),bind(Y,$fot(X_25)),bind(Z,$fot(a))]]) ).
cnf(refute_0_36,plain,
( greatest_lower_bound(greatest_lower_bound(c,X_25),a) != greatest_lower_bound(c,X_25)
| greatest_lower_bound(greatest_lower_bound(c,X_25),a) != greatest_lower_bound(c,greatest_lower_bound(X_25,a))
| greatest_lower_bound(c,greatest_lower_bound(X_25,a)) = greatest_lower_bound(c,X_25) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(c,X_25),a),greatest_lower_bound(c,X_25)) ),[0],$fot(greatest_lower_bound(c,greatest_lower_bound(X_25,a)))]]) ).
cnf(refute_0_37,plain,
( greatest_lower_bound(greatest_lower_bound(c,X_25),a) != greatest_lower_bound(c,X_25)
| greatest_lower_bound(c,greatest_lower_bound(X_25,a)) = greatest_lower_bound(c,X_25) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(c,X_25),a),greatest_lower_bound(c,greatest_lower_bound(X_25,a))) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
greatest_lower_bound(c,greatest_lower_bound(X_25,a)) = greatest_lower_bound(c,X_25),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(c,X_25),a),greatest_lower_bound(c,X_25)) )],[refute_0_32,refute_0_37]) ).
cnf(refute_0_39,plain,
greatest_lower_bound(c,greatest_lower_bound(X_82,a)) = greatest_lower_bound(c,X_82),
inference(subst,[],[refute_0_38:[bind(X_25,$fot(X_82))]]) ).
cnf(refute_0_40,plain,
( greatest_lower_bound(c,greatest_lower_bound(X_82,a)) != greatest_lower_bound(c,X_82)
| least_upper_bound(greatest_lower_bound(X_82,a),greatest_lower_bound(c,greatest_lower_bound(X_82,a))) != greatest_lower_bound(X_82,a)
| least_upper_bound(greatest_lower_bound(X_82,a),greatest_lower_bound(c,X_82)) = greatest_lower_bound(X_82,a) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_82,a),greatest_lower_bound(c,greatest_lower_bound(X_82,a))),greatest_lower_bound(X_82,a)) ),[0,1],$fot(greatest_lower_bound(c,X_82))]]) ).
cnf(refute_0_41,plain,
( least_upper_bound(greatest_lower_bound(X_82,a),greatest_lower_bound(c,greatest_lower_bound(X_82,a))) != greatest_lower_bound(X_82,a)
| least_upper_bound(greatest_lower_bound(X_82,a),greatest_lower_bound(c,X_82)) = greatest_lower_bound(X_82,a) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(c,greatest_lower_bound(X_82,a)),greatest_lower_bound(c,X_82)) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
least_upper_bound(greatest_lower_bound(X_82,a),greatest_lower_bound(c,X_82)) = greatest_lower_bound(X_82,a),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_82,a),greatest_lower_bound(c,greatest_lower_bound(X_82,a))),greatest_lower_bound(X_82,a)) )],[refute_0_10,refute_0_41]) ).
cnf(refute_0_43,plain,
least_upper_bound(greatest_lower_bound(X_248,a),greatest_lower_bound(c,X_248)) = greatest_lower_bound(X_248,a),
inference(subst,[],[refute_0_42:[bind(X_82,$fot(X_248))]]) ).
cnf(refute_0_44,plain,
greatest_lower_bound(X_248,c) = greatest_lower_bound(c,X_248),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_248)),bind(Y,$fot(c))]]) ).
cnf(refute_0_45,plain,
( greatest_lower_bound(X_248,c) != greatest_lower_bound(c,X_248)
| greatest_lower_bound(c,X_248) = greatest_lower_bound(X_248,c) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(greatest_lower_bound(X_248,c))),bind(Y0,$fot(greatest_lower_bound(c,X_248)))]]) ).
cnf(refute_0_46,plain,
greatest_lower_bound(c,X_248) = greatest_lower_bound(X_248,c),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_248,c),greatest_lower_bound(c,X_248)) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
( greatest_lower_bound(c,X_248) != greatest_lower_bound(X_248,c)
| least_upper_bound(greatest_lower_bound(X_248,a),greatest_lower_bound(c,X_248)) != greatest_lower_bound(X_248,a)
| least_upper_bound(greatest_lower_bound(X_248,a),greatest_lower_bound(X_248,c)) = greatest_lower_bound(X_248,a) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_248,a),greatest_lower_bound(c,X_248)),greatest_lower_bound(X_248,a)) ),[0,1],$fot(greatest_lower_bound(X_248,c))]]) ).
cnf(refute_0_48,plain,
( least_upper_bound(greatest_lower_bound(X_248,a),greatest_lower_bound(c,X_248)) != greatest_lower_bound(X_248,a)
| least_upper_bound(greatest_lower_bound(X_248,a),greatest_lower_bound(X_248,c)) = greatest_lower_bound(X_248,a) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(c,X_248),greatest_lower_bound(X_248,c)) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
least_upper_bound(greatest_lower_bound(X_248,a),greatest_lower_bound(X_248,c)) = greatest_lower_bound(X_248,a),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_248,a),greatest_lower_bound(c,X_248)),greatest_lower_bound(X_248,a)) )],[refute_0_43,refute_0_48]) ).
cnf(refute_0_50,plain,
least_upper_bound(greatest_lower_bound(b,a),greatest_lower_bound(b,c)) = greatest_lower_bound(b,a),
inference(subst,[],[refute_0_49:[bind(X_248,$fot(b))]]) ).
cnf(refute_0_51,plain,
greatest_lower_bound(c,least_upper_bound(b,c)) = c,
inference(subst,[],[refute_0_13:[bind(X,$fot(c)),bind(Y,$fot(b))]]) ).
cnf(refute_0_52,plain,
( greatest_lower_bound(c,least_upper_bound(b,c)) != c
| least_upper_bound(b,c) != b
| greatest_lower_bound(c,b) = c ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(c,least_upper_bound(b,c)),c) ),[0,1],$fot(b)]]) ).
cnf(refute_0_53,plain,
( greatest_lower_bound(c,least_upper_bound(b,c)) != c
| greatest_lower_bound(c,b) = c ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,c),b) )],[ax_glb1a_2,refute_0_52]) ).
cnf(refute_0_54,plain,
greatest_lower_bound(c,b) = c,
inference(resolve,[$cnf( $equal(greatest_lower_bound(c,least_upper_bound(b,c)),c) )],[refute_0_51,refute_0_53]) ).
cnf(refute_0_55,plain,
( greatest_lower_bound(X,Y) != greatest_lower_bound(Y,X)
| greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(greatest_lower_bound(X,Y))),bind(Y0,$fot(greatest_lower_bound(Y,X)))]]) ).
cnf(refute_0_56,plain,
greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X)) )],[symmetry_of_glb,refute_0_55]) ).
cnf(refute_0_57,plain,
greatest_lower_bound(c,b) = greatest_lower_bound(b,c),
inference(subst,[],[refute_0_56:[bind(X,$fot(b)),bind(Y,$fot(c))]]) ).
cnf(refute_0_58,plain,
( greatest_lower_bound(c,b) != c
| greatest_lower_bound(c,b) != greatest_lower_bound(b,c)
| greatest_lower_bound(b,c) = c ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(c,b),c) ),[0],$fot(greatest_lower_bound(b,c))]]) ).
cnf(refute_0_59,plain,
( greatest_lower_bound(c,b) != c
| greatest_lower_bound(b,c) = c ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(c,b),greatest_lower_bound(b,c)) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
greatest_lower_bound(b,c) = c,
inference(resolve,[$cnf( $equal(greatest_lower_bound(c,b),c) )],[refute_0_54,refute_0_59]) ).
cnf(refute_0_61,plain,
( greatest_lower_bound(b,c) != c
| least_upper_bound(greatest_lower_bound(b,a),greatest_lower_bound(b,c)) != greatest_lower_bound(b,a)
| least_upper_bound(greatest_lower_bound(b,a),c) = greatest_lower_bound(b,a) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(b,a),greatest_lower_bound(b,c)),greatest_lower_bound(b,a)) ),[0,1],$fot(c)]]) ).
cnf(refute_0_62,plain,
( least_upper_bound(greatest_lower_bound(b,a),greatest_lower_bound(b,c)) != greatest_lower_bound(b,a)
| least_upper_bound(greatest_lower_bound(b,a),c) = greatest_lower_bound(b,a) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,c),c) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
least_upper_bound(greatest_lower_bound(b,a),c) = greatest_lower_bound(b,a),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(b,a),greatest_lower_bound(b,c)),greatest_lower_bound(b,a)) )],[refute_0_50,refute_0_62]) ).
cnf(refute_0_64,plain,
least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_375,X_374),greatest_lower_bound(X_374,X_375))) = least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_375,X_374)),greatest_lower_bound(X_374,X_375)),
inference(subst,[],[associativity_of_lub:[bind(Y,$fot(greatest_lower_bound(X_375,X_374))),bind(Z,$fot(greatest_lower_bound(X_374,X_375)))]]) ).
cnf(refute_0_65,plain,
least_upper_bound(greatest_lower_bound(X_26,X_11),greatest_lower_bound(X_11,greatest_lower_bound(X_26,X_11))) = greatest_lower_bound(X_26,X_11),
inference(subst,[],[refute_0_9:[bind(X_10,$fot(greatest_lower_bound(X_26,X_11)))]]) ).
cnf(refute_0_66,plain,
greatest_lower_bound(greatest_lower_bound(X_13,Y),least_upper_bound(X_13,greatest_lower_bound(X_13,Y))) = greatest_lower_bound(X_13,Y),
inference(subst,[],[refute_0_13:[bind(X,$fot(greatest_lower_bound(X_13,Y))),bind(Y,$fot(X_13))]]) ).
cnf(refute_0_67,plain,
least_upper_bound(X_13,greatest_lower_bound(X_13,Y)) = X_13,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_13))]]) ).
cnf(refute_0_68,plain,
( greatest_lower_bound(greatest_lower_bound(X_13,Y),least_upper_bound(X_13,greatest_lower_bound(X_13,Y))) != greatest_lower_bound(X_13,Y)
| least_upper_bound(X_13,greatest_lower_bound(X_13,Y)) != X_13
| greatest_lower_bound(greatest_lower_bound(X_13,Y),X_13) = greatest_lower_bound(X_13,Y) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_13,Y),least_upper_bound(X_13,greatest_lower_bound(X_13,Y))),greatest_lower_bound(X_13,Y)) ),[0,1],$fot(X_13)]]) ).
cnf(refute_0_69,plain,
( greatest_lower_bound(greatest_lower_bound(X_13,Y),least_upper_bound(X_13,greatest_lower_bound(X_13,Y))) != greatest_lower_bound(X_13,Y)
| greatest_lower_bound(greatest_lower_bound(X_13,Y),X_13) = greatest_lower_bound(X_13,Y) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_13,greatest_lower_bound(X_13,Y)),X_13) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
greatest_lower_bound(greatest_lower_bound(X_13,Y),X_13) = greatest_lower_bound(X_13,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_13,Y),least_upper_bound(X_13,greatest_lower_bound(X_13,Y))),greatest_lower_bound(X_13,Y)) )],[refute_0_66,refute_0_69]) ).
cnf(refute_0_71,plain,
greatest_lower_bound(greatest_lower_bound(X_13,Y),X_13) = greatest_lower_bound(X_13,greatest_lower_bound(Y,X_13)),
inference(subst,[],[refute_0_34:[bind(X,$fot(X_13)),bind(Z,$fot(X_13))]]) ).
cnf(refute_0_72,plain,
( greatest_lower_bound(greatest_lower_bound(X_13,Y),X_13) != greatest_lower_bound(X_13,Y)
| greatest_lower_bound(greatest_lower_bound(X_13,Y),X_13) != greatest_lower_bound(X_13,greatest_lower_bound(Y,X_13))
| greatest_lower_bound(X_13,greatest_lower_bound(Y,X_13)) = greatest_lower_bound(X_13,Y) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_13,Y),X_13),greatest_lower_bound(X_13,Y)) ),[0],$fot(greatest_lower_bound(X_13,greatest_lower_bound(Y,X_13)))]]) ).
cnf(refute_0_73,plain,
( greatest_lower_bound(greatest_lower_bound(X_13,Y),X_13) != greatest_lower_bound(X_13,Y)
| greatest_lower_bound(X_13,greatest_lower_bound(Y,X_13)) = greatest_lower_bound(X_13,Y) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_13,Y),X_13),greatest_lower_bound(X_13,greatest_lower_bound(Y,X_13))) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
greatest_lower_bound(X_13,greatest_lower_bound(Y,X_13)) = greatest_lower_bound(X_13,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_13,Y),X_13),greatest_lower_bound(X_13,Y)) )],[refute_0_70,refute_0_73]) ).
cnf(refute_0_75,plain,
greatest_lower_bound(X_11,greatest_lower_bound(X_26,X_11)) = greatest_lower_bound(X_11,X_26),
inference(subst,[],[refute_0_74:[bind(Y,$fot(X_26)),bind(X_13,$fot(X_11))]]) ).
cnf(refute_0_76,plain,
( greatest_lower_bound(X_11,greatest_lower_bound(X_26,X_11)) != greatest_lower_bound(X_11,X_26)
| least_upper_bound(greatest_lower_bound(X_26,X_11),greatest_lower_bound(X_11,greatest_lower_bound(X_26,X_11))) != greatest_lower_bound(X_26,X_11)
| least_upper_bound(greatest_lower_bound(X_26,X_11),greatest_lower_bound(X_11,X_26)) = greatest_lower_bound(X_26,X_11) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_26,X_11),greatest_lower_bound(X_11,greatest_lower_bound(X_26,X_11))),greatest_lower_bound(X_26,X_11)) ),[0,1],$fot(greatest_lower_bound(X_11,X_26))]]) ).
cnf(refute_0_77,plain,
( least_upper_bound(greatest_lower_bound(X_26,X_11),greatest_lower_bound(X_11,greatest_lower_bound(X_26,X_11))) != greatest_lower_bound(X_26,X_11)
| least_upper_bound(greatest_lower_bound(X_26,X_11),greatest_lower_bound(X_11,X_26)) = greatest_lower_bound(X_26,X_11) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_11,greatest_lower_bound(X_26,X_11)),greatest_lower_bound(X_11,X_26)) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
least_upper_bound(greatest_lower_bound(X_26,X_11),greatest_lower_bound(X_11,X_26)) = greatest_lower_bound(X_26,X_11),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_26,X_11),greatest_lower_bound(X_11,greatest_lower_bound(X_26,X_11))),greatest_lower_bound(X_26,X_11)) )],[refute_0_65,refute_0_77]) ).
cnf(refute_0_79,plain,
least_upper_bound(greatest_lower_bound(X_375,X_374),greatest_lower_bound(X_374,X_375)) = greatest_lower_bound(X_375,X_374),
inference(subst,[],[refute_0_78:[bind(X_11,$fot(X_374)),bind(X_26,$fot(X_375))]]) ).
cnf(refute_0_80,plain,
( least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_375,X_374),greatest_lower_bound(X_374,X_375))) != least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_375,X_374)),greatest_lower_bound(X_374,X_375))
| least_upper_bound(greatest_lower_bound(X_375,X_374),greatest_lower_bound(X_374,X_375)) != greatest_lower_bound(X_375,X_374)
| least_upper_bound(X,greatest_lower_bound(X_375,X_374)) = least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_375,X_374)),greatest_lower_bound(X_374,X_375)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_375,X_374),greatest_lower_bound(X_374,X_375))),least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_375,X_374)),greatest_lower_bound(X_374,X_375))) ),[0,1],$fot(greatest_lower_bound(X_375,X_374))]]) ).
cnf(refute_0_81,plain,
( least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_375,X_374),greatest_lower_bound(X_374,X_375))) != least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_375,X_374)),greatest_lower_bound(X_374,X_375))
| least_upper_bound(X,greatest_lower_bound(X_375,X_374)) = least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_375,X_374)),greatest_lower_bound(X_374,X_375)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_375,X_374),greatest_lower_bound(X_374,X_375)),greatest_lower_bound(X_375,X_374)) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
least_upper_bound(X,greatest_lower_bound(X_375,X_374)) = least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_375,X_374)),greatest_lower_bound(X_374,X_375)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_375,X_374),greatest_lower_bound(X_374,X_375))),least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_375,X_374)),greatest_lower_bound(X_374,X_375))) )],[refute_0_64,refute_0_81]) ).
cnf(refute_0_83,plain,
least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) = least_upper_bound(least_upper_bound(X_18,least_upper_bound(Y,X_18)),X_20),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_18)),bind(Y,$fot(least_upper_bound(Y,X_18))),bind(Z,$fot(X_20))]]) ).
cnf(refute_0_84,plain,
least_upper_bound(least_upper_bound(X_15,Y),greatest_lower_bound(X_15,least_upper_bound(X_15,Y))) = least_upper_bound(X_15,Y),
inference(subst,[],[refute_0_9:[bind(X_10,$fot(least_upper_bound(X_15,Y))),bind(X_11,$fot(X_15))]]) ).
cnf(refute_0_85,plain,
greatest_lower_bound(X_15,least_upper_bound(X_15,Y)) = X_15,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_15))]]) ).
cnf(refute_0_86,plain,
( greatest_lower_bound(X_15,least_upper_bound(X_15,Y)) != X_15
| least_upper_bound(least_upper_bound(X_15,Y),greatest_lower_bound(X_15,least_upper_bound(X_15,Y))) != least_upper_bound(X_15,Y)
| least_upper_bound(least_upper_bound(X_15,Y),X_15) = least_upper_bound(X_15,Y) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_15,Y),greatest_lower_bound(X_15,least_upper_bound(X_15,Y))),least_upper_bound(X_15,Y)) ),[0,1],$fot(X_15)]]) ).
cnf(refute_0_87,plain,
( least_upper_bound(least_upper_bound(X_15,Y),greatest_lower_bound(X_15,least_upper_bound(X_15,Y))) != least_upper_bound(X_15,Y)
| least_upper_bound(least_upper_bound(X_15,Y),X_15) = least_upper_bound(X_15,Y) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_15,least_upper_bound(X_15,Y)),X_15) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
least_upper_bound(least_upper_bound(X_15,Y),X_15) = least_upper_bound(X_15,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_15,Y),greatest_lower_bound(X_15,least_upper_bound(X_15,Y))),least_upper_bound(X_15,Y)) )],[refute_0_84,refute_0_87]) ).
cnf(refute_0_89,plain,
( least_upper_bound(X,least_upper_bound(Y,Z)) != least_upper_bound(least_upper_bound(X,Y),Z)
| least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(Y,Z)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X,Y),Z)))]]) ).
cnf(refute_0_90,plain,
least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,Z)),least_upper_bound(least_upper_bound(X,Y),Z)) )],[associativity_of_lub,refute_0_89]) ).
cnf(refute_0_91,plain,
least_upper_bound(least_upper_bound(X_15,Y),X_15) = least_upper_bound(X_15,least_upper_bound(Y,X_15)),
inference(subst,[],[refute_0_90:[bind(X,$fot(X_15)),bind(Z,$fot(X_15))]]) ).
cnf(refute_0_92,plain,
( least_upper_bound(least_upper_bound(X_15,Y),X_15) != least_upper_bound(X_15,Y)
| least_upper_bound(least_upper_bound(X_15,Y),X_15) != least_upper_bound(X_15,least_upper_bound(Y,X_15))
| least_upper_bound(X_15,least_upper_bound(Y,X_15)) = least_upper_bound(X_15,Y) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_15,Y),X_15),least_upper_bound(X_15,Y)) ),[0],$fot(least_upper_bound(X_15,least_upper_bound(Y,X_15)))]]) ).
cnf(refute_0_93,plain,
( least_upper_bound(least_upper_bound(X_15,Y),X_15) != least_upper_bound(X_15,Y)
| least_upper_bound(X_15,least_upper_bound(Y,X_15)) = least_upper_bound(X_15,Y) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_15,Y),X_15),least_upper_bound(X_15,least_upper_bound(Y,X_15))) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
least_upper_bound(X_15,least_upper_bound(Y,X_15)) = least_upper_bound(X_15,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_15,Y),X_15),least_upper_bound(X_15,Y)) )],[refute_0_88,refute_0_93]) ).
cnf(refute_0_95,plain,
least_upper_bound(X_18,least_upper_bound(Y,X_18)) = least_upper_bound(X_18,Y),
inference(subst,[],[refute_0_94:[bind(X_15,$fot(X_18))]]) ).
cnf(refute_0_96,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_97,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( $equal(least_upper_bound(X_18,least_upper_bound(Y,X_18)),least_upper_bound(X_18,Y)) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) = least_upper_bound(least_upper_bound(X_18,Y),X_20),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)),least_upper_bound(least_upper_bound(X_18,least_upper_bound(Y,X_18)),X_20)) )],[refute_0_83,refute_0_97]) ).
cnf(refute_0_99,plain,
least_upper_bound(X_18,least_upper_bound(X_19,least_upper_bound(Y,X_19))) = least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_18)),bind(Y,$fot(X_19)),bind(Z,$fot(least_upper_bound(Y,X_19)))]]) ).
cnf(refute_0_100,plain,
least_upper_bound(X_19,least_upper_bound(Y,X_19)) = least_upper_bound(X_19,Y),
inference(subst,[],[refute_0_94:[bind(X_15,$fot(X_19))]]) ).
cnf(refute_0_101,plain,
( least_upper_bound(X_18,least_upper_bound(X_19,least_upper_bound(Y,X_19))) != least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19))
| least_upper_bound(X_19,least_upper_bound(Y,X_19)) != least_upper_bound(X_19,Y)
| least_upper_bound(X_18,least_upper_bound(X_19,Y)) = least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)) ),
introduced(tautology,[equality,[$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_102,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( $equal(least_upper_bound(X_19,least_upper_bound(Y,X_19)),least_upper_bound(X_19,Y)) )],[refute_0_100,refute_0_101]) ).
cnf(refute_0_103,plain,
least_upper_bound(X_18,least_upper_bound(X_19,Y)) = least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(X_19,least_upper_bound(Y,X_19))),least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19))) )],[refute_0_99,refute_0_102]) ).
cnf(refute_0_104,plain,
least_upper_bound(least_upper_bound(X_18,X_19),Y) = least_upper_bound(X_18,least_upper_bound(X_19,Y)),
inference(subst,[],[refute_0_90:[bind(X,$fot(X_18)),bind(Y,$fot(X_19)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_105,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,[$fot(least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)))]]) ).
cnf(refute_0_106,plain,
( least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)) != least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y))
| least_upper_bound(least_upper_bound(X_18,X_19),Y) != least_upper_bound(X_18,least_upper_bound(X_19,Y))
| least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)) = least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y))) ),
introduced(tautology,[equality,[$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_107,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( $equal(least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)),least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y))) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)) = least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_18,X_19),Y),least_upper_bound(X_18,least_upper_bound(X_19,Y))) )],[refute_0_104,refute_0_107]) ).
cnf(refute_0_109,plain,
least_upper_bound(X,least_upper_bound(X_18,X_19)) = least_upper_bound(least_upper_bound(X_18,X_19),X),
inference(subst,[],[symmetry_of_lub:[bind(Y,$fot(least_upper_bound(X_18,X_19)))]]) ).
cnf(refute_0_110,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,$fot(X))]]) ).
cnf(refute_0_111,plain,
( least_upper_bound(X_18,least_upper_bound(X_19,X)) != least_upper_bound(least_upper_bound(X_18,X_19),X)
| least_upper_bound(least_upper_bound(X_18,X_19),X) = least_upper_bound(X_18,least_upper_bound(X_19,X)) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(least_upper_bound(X_18,least_upper_bound(X_19,X)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X_18,X_19),X)))]]) ).
cnf(refute_0_112,plain,
least_upper_bound(least_upper_bound(X_18,X_19),X) = least_upper_bound(X_18,least_upper_bound(X_19,X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(X_19,X)),least_upper_bound(least_upper_bound(X_18,X_19),X)) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
( least_upper_bound(X,least_upper_bound(X_18,X_19)) != least_upper_bound(least_upper_bound(X_18,X_19),X)
| least_upper_bound(least_upper_bound(X_18,X_19),X) != least_upper_bound(X_18,least_upper_bound(X_19,X))
| least_upper_bound(X,least_upper_bound(X_18,X_19)) = least_upper_bound(X_18,least_upper_bound(X_19,X)) ),
introduced(tautology,[equality,[$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_114,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( $equal(least_upper_bound(least_upper_bound(X_18,X_19),X),least_upper_bound(X_18,least_upper_bound(X_19,X))) )],[refute_0_112,refute_0_113]) ).
cnf(refute_0_115,plain,
least_upper_bound(X,least_upper_bound(X_18,X_19)) = least_upper_bound(X_18,least_upper_bound(X_19,X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_18,X_19)),least_upper_bound(least_upper_bound(X_18,X_19),X)) )],[refute_0_109,refute_0_114]) ).
cnf(refute_0_116,plain,
( least_upper_bound(X,least_upper_bound(X_18,X_19)) != least_upper_bound(X_18,least_upper_bound(X_19,X))
| least_upper_bound(X_18,least_upper_bound(X_19,X)) = least_upper_bound(X,least_upper_bound(X_18,X_19)) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(X_18,X_19)))),bind(Y0,$fot(least_upper_bound(X_18,least_upper_bound(X_19,X))))]]) ).
cnf(refute_0_117,plain,
least_upper_bound(X_18,least_upper_bound(X_19,X)) = least_upper_bound(X,least_upper_bound(X_18,X_19)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_18,X_19)),least_upper_bound(X_18,least_upper_bound(X_19,X))) )],[refute_0_115,refute_0_116]) ).
cnf(refute_0_118,plain,
least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)) = least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)),
inference(subst,[],[refute_0_117:[bind(X,$fot(X_19)),bind(X_18,$fot(least_upper_bound(X_18,X_19))),bind(X_19,$fot(Y))]]) ).
cnf(refute_0_119,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_120,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_4,refute_0_119]) ).
cnf(refute_0_121,plain,
( least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)) != least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y)))
| least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)) != least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y))
| least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)) = least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y))) ),
inference(subst,[],[refute_0_120:[bind(X0,$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_122,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( $equal(least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)),least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y))) )],[refute_0_118,refute_0_121]) ).
cnf(refute_0_123,plain,
least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)) = least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)),least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y)))) )],[refute_0_108,refute_0_122]) ).
cnf(refute_0_124,plain,
( least_upper_bound(X_18,least_upper_bound(X_19,Y)) != least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19))
| least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)) != least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y)))
| least_upper_bound(X_18,least_upper_bound(X_19,Y)) = least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y))) ),
introduced(tautology,[equality,[$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_125,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( $equal(least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)),least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y)))) )],[refute_0_123,refute_0_124]) ).
cnf(refute_0_126,plain,
least_upper_bound(X_18,least_upper_bound(X_19,Y)) = least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(X_19,Y)),least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19))) )],[refute_0_103,refute_0_125]) ).
cnf(refute_0_127,plain,
( least_upper_bound(X_18,least_upper_bound(X_19,Y)) != least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y)))
| least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y))) = least_upper_bound(X_18,least_upper_bound(X_19,Y)) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(least_upper_bound(X_18,least_upper_bound(X_19,Y)))),bind(Y0,$fot(least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y)))))]]) ).
cnf(refute_0_128,plain,
least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y))) = least_upper_bound(X_18,least_upper_bound(X_19,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(X_19,Y)),least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y)))) )],[refute_0_126,refute_0_127]) ).
cnf(refute_0_129,plain,
least_upper_bound(X_18,least_upper_bound(Y,least_upper_bound(X_18,X_20))) = least_upper_bound(Y,least_upper_bound(X_18,X_20)),
inference(subst,[],[refute_0_128:[bind(Y,$fot(X_20)),bind(X_18,$fot(Y)),bind(X_19,$fot(X_18))]]) ).
cnf(refute_0_130,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_90:[bind(X,$fot(Y)),bind(Y,$fot(X_18)),bind(Z,$fot(X_20))]]) ).
cnf(refute_0_131,plain,
least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) = least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)))]]) ).
cnf(refute_0_132,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_133,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( $equal(least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)),least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20))) )],[refute_0_131,refute_0_132]) ).
cnf(refute_0_134,plain,
least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) = least_upper_bound(X_18,least_upper_bound(Y,least_upper_bound(X_18,X_20))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_18),X_20),least_upper_bound(Y,least_upper_bound(X_18,X_20))) )],[refute_0_130,refute_0_133]) ).
cnf(refute_0_135,plain,
( least_upper_bound(X_18,least_upper_bound(Y,least_upper_bound(X_18,X_20))) != least_upper_bound(Y,least_upper_bound(X_18,X_20))
| least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) != least_upper_bound(X_18,least_upper_bound(Y,least_upper_bound(X_18,X_20)))
| least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) = least_upper_bound(Y,least_upper_bound(X_18,X_20)) ),
inference(subst,[],[refute_0_120:[bind(X0,$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_136,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( $equal(least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)),least_upper_bound(X_18,least_upper_bound(Y,least_upper_bound(X_18,X_20)))) )],[refute_0_134,refute_0_135]) ).
cnf(refute_0_137,plain,
least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) = least_upper_bound(Y,least_upper_bound(X_18,X_20)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(Y,least_upper_bound(X_18,X_20))),least_upper_bound(Y,least_upper_bound(X_18,X_20))) )],[refute_0_129,refute_0_136]) ).
cnf(refute_0_138,plain,
( least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) != least_upper_bound(Y,least_upper_bound(X_18,X_20))
| least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) != least_upper_bound(least_upper_bound(X_18,Y),X_20)
| least_upper_bound(Y,least_upper_bound(X_18,X_20)) = least_upper_bound(least_upper_bound(X_18,Y),X_20) ),
introduced(tautology,[equality,[$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_139,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( $equal(least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)),least_upper_bound(Y,least_upper_bound(X_18,X_20))) )],[refute_0_137,refute_0_138]) ).
cnf(refute_0_140,plain,
least_upper_bound(least_upper_bound(X_18,Y),X_20) = least_upper_bound(X_18,least_upper_bound(Y,X_20)),
inference(subst,[],[refute_0_90:[bind(X,$fot(X_18)),bind(Z,$fot(X_20))]]) ).
cnf(refute_0_141,plain,
( least_upper_bound(Y,least_upper_bound(X_18,X_20)) != least_upper_bound(least_upper_bound(X_18,Y),X_20)
| least_upper_bound(least_upper_bound(X_18,Y),X_20) != least_upper_bound(X_18,least_upper_bound(Y,X_20))
| least_upper_bound(Y,least_upper_bound(X_18,X_20)) = least_upper_bound(X_18,least_upper_bound(Y,X_20)) ),
introduced(tautology,[equality,[$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_142,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( $equal(least_upper_bound(least_upper_bound(X_18,Y),X_20),least_upper_bound(X_18,least_upper_bound(Y,X_20))) )],[refute_0_140,refute_0_141]) ).
cnf(refute_0_143,plain,
( least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) != least_upper_bound(least_upper_bound(X_18,Y),X_20)
| least_upper_bound(Y,least_upper_bound(X_18,X_20)) = least_upper_bound(X_18,least_upper_bound(Y,X_20)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_18,X_20)),least_upper_bound(least_upper_bound(X_18,Y),X_20)) )],[refute_0_139,refute_0_142]) ).
cnf(refute_0_144,plain,
least_upper_bound(Y,least_upper_bound(X_18,X_20)) = least_upper_bound(X_18,least_upper_bound(Y,X_20)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)),least_upper_bound(least_upper_bound(X_18,Y),X_20)) )],[refute_0_98,refute_0_143]) ).
cnf(refute_0_145,plain,
least_upper_bound(greatest_lower_bound(X_375,X_374),least_upper_bound(X_18,greatest_lower_bound(X_374,X_375))) = least_upper_bound(X_18,least_upper_bound(greatest_lower_bound(X_375,X_374),greatest_lower_bound(X_374,X_375))),
inference(subst,[],[refute_0_144:[bind(Y,$fot(greatest_lower_bound(X_375,X_374))),bind(X_20,$fot(greatest_lower_bound(X_374,X_375)))]]) ).
cnf(refute_0_146,plain,
( least_upper_bound(greatest_lower_bound(X_375,X_374),greatest_lower_bound(X_374,X_375)) != greatest_lower_bound(X_375,X_374)
| least_upper_bound(greatest_lower_bound(X_375,X_374),least_upper_bound(X_18,greatest_lower_bound(X_374,X_375))) != least_upper_bound(X_18,least_upper_bound(greatest_lower_bound(X_375,X_374),greatest_lower_bound(X_374,X_375)))
| least_upper_bound(greatest_lower_bound(X_375,X_374),least_upper_bound(X_18,greatest_lower_bound(X_374,X_375))) = least_upper_bound(X_18,greatest_lower_bound(X_375,X_374)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_375,X_374),least_upper_bound(X_18,greatest_lower_bound(X_374,X_375))),least_upper_bound(X_18,least_upper_bound(greatest_lower_bound(X_375,X_374),greatest_lower_bound(X_374,X_375)))) ),[1,1],$fot(greatest_lower_bound(X_375,X_374))]]) ).
cnf(refute_0_147,plain,
( least_upper_bound(greatest_lower_bound(X_375,X_374),least_upper_bound(X_18,greatest_lower_bound(X_374,X_375))) != least_upper_bound(X_18,least_upper_bound(greatest_lower_bound(X_375,X_374),greatest_lower_bound(X_374,X_375)))
| least_upper_bound(greatest_lower_bound(X_375,X_374),least_upper_bound(X_18,greatest_lower_bound(X_374,X_375))) = least_upper_bound(X_18,greatest_lower_bound(X_375,X_374)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_375,X_374),greatest_lower_bound(X_374,X_375)),greatest_lower_bound(X_375,X_374)) )],[refute_0_79,refute_0_146]) ).
cnf(refute_0_148,plain,
least_upper_bound(greatest_lower_bound(X_375,X_374),least_upper_bound(X_18,greatest_lower_bound(X_374,X_375))) = least_upper_bound(X_18,greatest_lower_bound(X_375,X_374)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_375,X_374),least_upper_bound(X_18,greatest_lower_bound(X_374,X_375))),least_upper_bound(X_18,least_upper_bound(greatest_lower_bound(X_375,X_374),greatest_lower_bound(X_374,X_375)))) )],[refute_0_145,refute_0_147]) ).
cnf(refute_0_149,plain,
least_upper_bound(greatest_lower_bound(X_374,X_375),least_upper_bound(X,greatest_lower_bound(X_375,X_374))) = least_upper_bound(X,greatest_lower_bound(X_374,X_375)),
inference(subst,[],[refute_0_148:[bind(X_18,$fot(X)),bind(X_374,$fot(X_375)),bind(X_375,$fot(X_374))]]) ).
cnf(refute_0_150,plain,
multiply(multiply(inverse(X_96),X_96),X_97) = multiply(inverse(X_96),multiply(X_96,X_97)),
inference(subst,[],[associativity:[bind(X,$fot(inverse(X_96))),bind(Y,$fot(X_96)),bind(Z,$fot(X_97))]]) ).
cnf(refute_0_151,plain,
multiply(inverse(X_96),X_96) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_96))]]) ).
cnf(refute_0_152,plain,
( multiply(multiply(inverse(X_96),X_96),X_97) != multiply(inverse(X_96),multiply(X_96,X_97))
| multiply(inverse(X_96),X_96) != identity
| multiply(identity,X_97) = multiply(inverse(X_96),multiply(X_96,X_97)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_96),X_96),X_97),multiply(inverse(X_96),multiply(X_96,X_97))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_153,plain,
( multiply(multiply(inverse(X_96),X_96),X_97) != multiply(inverse(X_96),multiply(X_96,X_97))
| multiply(identity,X_97) = multiply(inverse(X_96),multiply(X_96,X_97)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_96),X_96),identity) )],[refute_0_151,refute_0_152]) ).
cnf(refute_0_154,plain,
multiply(identity,X_97) = multiply(inverse(X_96),multiply(X_96,X_97)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_96),X_96),X_97),multiply(inverse(X_96),multiply(X_96,X_97))) )],[refute_0_150,refute_0_153]) ).
cnf(refute_0_155,plain,
multiply(identity,X_97) = X_97,
inference(subst,[],[left_identity:[bind(X,$fot(X_97))]]) ).
cnf(refute_0_156,plain,
( multiply(identity,X_97) != X_97
| multiply(identity,X_97) != multiply(inverse(X_96),multiply(X_96,X_97))
| X_97 = multiply(inverse(X_96),multiply(X_96,X_97)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_97),multiply(inverse(X_96),multiply(X_96,X_97))) ),[0],$fot(X_97)]]) ).
cnf(refute_0_157,plain,
( multiply(identity,X_97) != multiply(inverse(X_96),multiply(X_96,X_97))
| X_97 = multiply(inverse(X_96),multiply(X_96,X_97)) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_97),X_97) )],[refute_0_155,refute_0_156]) ).
cnf(refute_0_158,plain,
X_97 = multiply(inverse(X_96),multiply(X_96,X_97)),
inference(resolve,[$cnf( $equal(multiply(identity,X_97),multiply(inverse(X_96),multiply(X_96,X_97))) )],[refute_0_154,refute_0_157]) ).
cnf(refute_0_159,plain,
X_97 = multiply(inverse(least_upper_bound(inverse(X_97),X_206)),multiply(least_upper_bound(inverse(X_97),X_206),X_97)),
inference(subst,[],[refute_0_158:[bind(X_96,$fot(least_upper_bound(inverse(X_97),X_206)))]]) ).
cnf(refute_0_160,plain,
multiply(least_upper_bound(inverse(X_60),X_62),X_60) = least_upper_bound(multiply(inverse(X_60),X_60),multiply(X_62,X_60)),
inference(subst,[],[monotony_lub2:[bind(X,$fot(X_60)),bind(Y,$fot(inverse(X_60))),bind(Z,$fot(X_62))]]) ).
cnf(refute_0_161,plain,
multiply(inverse(X_60),X_60) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_60))]]) ).
cnf(refute_0_162,plain,
( multiply(inverse(X_60),X_60) != identity
| multiply(least_upper_bound(inverse(X_60),X_62),X_60) != least_upper_bound(multiply(inverse(X_60),X_60),multiply(X_62,X_60))
| multiply(least_upper_bound(inverse(X_60),X_62),X_60) = least_upper_bound(identity,multiply(X_62,X_60)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(X_60),X_62),X_60),least_upper_bound(multiply(inverse(X_60),X_60),multiply(X_62,X_60))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_163,plain,
( multiply(least_upper_bound(inverse(X_60),X_62),X_60) != least_upper_bound(multiply(inverse(X_60),X_60),multiply(X_62,X_60))
| multiply(least_upper_bound(inverse(X_60),X_62),X_60) = least_upper_bound(identity,multiply(X_62,X_60)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_60),X_60),identity) )],[refute_0_161,refute_0_162]) ).
cnf(refute_0_164,plain,
multiply(least_upper_bound(inverse(X_60),X_62),X_60) = least_upper_bound(identity,multiply(X_62,X_60)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_60),X_62),X_60),least_upper_bound(multiply(inverse(X_60),X_60),multiply(X_62,X_60))) )],[refute_0_160,refute_0_163]) ).
cnf(refute_0_165,plain,
multiply(least_upper_bound(inverse(X_97),X_206),X_97) = least_upper_bound(identity,multiply(X_206,X_97)),
inference(subst,[],[refute_0_164:[bind(X_60,$fot(X_97)),bind(X_62,$fot(X_206))]]) ).
cnf(refute_0_166,plain,
( X_97 != multiply(inverse(least_upper_bound(inverse(X_97),X_206)),multiply(least_upper_bound(inverse(X_97),X_206),X_97))
| multiply(least_upper_bound(inverse(X_97),X_206),X_97) != least_upper_bound(identity,multiply(X_206,X_97))
| X_97 = multiply(inverse(least_upper_bound(inverse(X_97),X_206)),least_upper_bound(identity,multiply(X_206,X_97))) ),
introduced(tautology,[equality,[$cnf( $equal(X_97,multiply(inverse(least_upper_bound(inverse(X_97),X_206)),multiply(least_upper_bound(inverse(X_97),X_206),X_97))) ),[1,1],$fot(least_upper_bound(identity,multiply(X_206,X_97)))]]) ).
cnf(refute_0_167,plain,
( X_97 != multiply(inverse(least_upper_bound(inverse(X_97),X_206)),multiply(least_upper_bound(inverse(X_97),X_206),X_97))
| X_97 = multiply(inverse(least_upper_bound(inverse(X_97),X_206)),least_upper_bound(identity,multiply(X_206,X_97))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_97),X_206),X_97),least_upper_bound(identity,multiply(X_206,X_97))) )],[refute_0_165,refute_0_166]) ).
cnf(refute_0_168,plain,
X_97 = multiply(inverse(least_upper_bound(inverse(X_97),X_206)),least_upper_bound(identity,multiply(X_206,X_97))),
inference(resolve,[$cnf( $equal(X_97,multiply(inverse(least_upper_bound(inverse(X_97),X_206)),multiply(least_upper_bound(inverse(X_97),X_206),X_97))) )],[refute_0_159,refute_0_167]) ).
cnf(refute_0_169,plain,
least_upper_bound(X_40,X_41) = multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_40,X_41)),inverse(X_40))),least_upper_bound(identity,multiply(inverse(X_40),least_upper_bound(X_40,X_41)))),
inference(subst,[],[refute_0_168:[bind(X_206,$fot(inverse(X_40))),bind(X_97,$fot(least_upper_bound(X_40,X_41)))]]) ).
cnf(refute_0_170,plain,
multiply(inverse(X_40),least_upper_bound(X_40,X_41)) = least_upper_bound(multiply(inverse(X_40),X_40),multiply(inverse(X_40),X_41)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(inverse(X_40))),bind(Y,$fot(X_40)),bind(Z,$fot(X_41))]]) ).
cnf(refute_0_171,plain,
multiply(inverse(X_40),X_40) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_40))]]) ).
cnf(refute_0_172,plain,
( multiply(inverse(X_40),X_40) != identity
| multiply(inverse(X_40),least_upper_bound(X_40,X_41)) != least_upper_bound(multiply(inverse(X_40),X_40),multiply(inverse(X_40),X_41))
| multiply(inverse(X_40),least_upper_bound(X_40,X_41)) = least_upper_bound(identity,multiply(inverse(X_40),X_41)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_40),least_upper_bound(X_40,X_41)),least_upper_bound(multiply(inverse(X_40),X_40),multiply(inverse(X_40),X_41))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_173,plain,
( multiply(inverse(X_40),least_upper_bound(X_40,X_41)) != least_upper_bound(multiply(inverse(X_40),X_40),multiply(inverse(X_40),X_41))
| multiply(inverse(X_40),least_upper_bound(X_40,X_41)) = least_upper_bound(identity,multiply(inverse(X_40),X_41)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_40),X_40),identity) )],[refute_0_171,refute_0_172]) ).
cnf(refute_0_174,plain,
multiply(inverse(X_40),least_upper_bound(X_40,X_41)) = least_upper_bound(identity,multiply(inverse(X_40),X_41)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_40),least_upper_bound(X_40,X_41)),least_upper_bound(multiply(inverse(X_40),X_40),multiply(inverse(X_40),X_41))) )],[refute_0_170,refute_0_173]) ).
cnf(refute_0_175,plain,
( multiply(inverse(X_40),least_upper_bound(X_40,X_41)) != least_upper_bound(identity,multiply(inverse(X_40),X_41))
| least_upper_bound(X_40,X_41) != multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_40,X_41)),inverse(X_40))),least_upper_bound(identity,multiply(inverse(X_40),least_upper_bound(X_40,X_41))))
| least_upper_bound(X_40,X_41) = multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_40,X_41)),inverse(X_40))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_40),X_41)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_40,X_41),multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_40,X_41)),inverse(X_40))),least_upper_bound(identity,multiply(inverse(X_40),least_upper_bound(X_40,X_41))))) ),[1,1,1],$fot(least_upper_bound(identity,multiply(inverse(X_40),X_41)))]]) ).
cnf(refute_0_176,plain,
( least_upper_bound(X_40,X_41) != multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_40,X_41)),inverse(X_40))),least_upper_bound(identity,multiply(inverse(X_40),least_upper_bound(X_40,X_41))))
| least_upper_bound(X_40,X_41) = multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_40,X_41)),inverse(X_40))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_40),X_41)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_40),least_upper_bound(X_40,X_41)),least_upper_bound(identity,multiply(inverse(X_40),X_41))) )],[refute_0_174,refute_0_175]) ).
cnf(refute_0_177,plain,
least_upper_bound(X_40,X_41) = multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_40,X_41)),inverse(X_40))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_40),X_41)))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_40,X_41),multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_40,X_41)),inverse(X_40))),least_upper_bound(identity,multiply(inverse(X_40),least_upper_bound(X_40,X_41))))) )],[refute_0_169,refute_0_176]) ).
cnf(refute_0_178,plain,
least_upper_bound(X_17,least_upper_bound(X_16,X_17)) = least_upper_bound(X_17,X_16),
inference(subst,[],[refute_0_94:[bind(Y,$fot(X_16)),bind(X_15,$fot(X_17))]]) ).
cnf(refute_0_179,plain,
least_upper_bound(X_17,X_16) = least_upper_bound(X_16,X_17),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_17)),bind(Y,$fot(X_16))]]) ).
cnf(refute_0_180,plain,
( least_upper_bound(X_17,X_16) != least_upper_bound(X_16,X_17)
| least_upper_bound(X_16,X_17) = least_upper_bound(X_17,X_16) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(least_upper_bound(X_17,X_16))),bind(Y0,$fot(least_upper_bound(X_16,X_17)))]]) ).
cnf(refute_0_181,plain,
least_upper_bound(X_16,X_17) = least_upper_bound(X_17,X_16),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,X_16),least_upper_bound(X_16,X_17)) )],[refute_0_179,refute_0_180]) ).
cnf(refute_0_182,plain,
( least_upper_bound(X_16,X_17) != least_upper_bound(X_17,X_16)
| least_upper_bound(X_17,least_upper_bound(X_16,X_17)) != least_upper_bound(X_17,X_16)
| least_upper_bound(X_17,least_upper_bound(X_17,X_16)) = least_upper_bound(X_17,X_16) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_17,least_upper_bound(X_16,X_17)),least_upper_bound(X_17,X_16)) ),[0,1],$fot(least_upper_bound(X_17,X_16))]]) ).
cnf(refute_0_183,plain,
( least_upper_bound(X_17,least_upper_bound(X_16,X_17)) != least_upper_bound(X_17,X_16)
| least_upper_bound(X_17,least_upper_bound(X_17,X_16)) = least_upper_bound(X_17,X_16) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_16,X_17),least_upper_bound(X_17,X_16)) )],[refute_0_181,refute_0_182]) ).
cnf(refute_0_184,plain,
least_upper_bound(X_17,least_upper_bound(X_17,X_16)) = least_upper_bound(X_17,X_16),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,least_upper_bound(X_16,X_17)),least_upper_bound(X_17,X_16)) )],[refute_0_178,refute_0_183]) ).
cnf(refute_0_185,plain,
least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_40),X_41))) = least_upper_bound(identity,multiply(inverse(X_40),X_41)),
inference(subst,[],[refute_0_184:[bind(X_16,$fot(multiply(inverse(X_40),X_41))),bind(X_17,$fot(identity))]]) ).
cnf(refute_0_186,plain,
multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_40),X_41)))) = multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_40),X_41)))),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_40),X_41)))))]]) ).
cnf(refute_0_187,plain,
( multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_40),X_41)))) != multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_40),X_41))))
| least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_40),X_41))) != least_upper_bound(identity,multiply(inverse(X_40),X_41))
| multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_40),X_41)))) = multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,multiply(inverse(X_40),X_41))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_40),X_41)))),multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_40),X_41))))) ),[1,1],$fot(least_upper_bound(identity,multiply(inverse(X_40),X_41)))]]) ).
cnf(refute_0_188,plain,
( least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_40),X_41))) != least_upper_bound(identity,multiply(inverse(X_40),X_41))
| multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_40),X_41)))) = multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,multiply(inverse(X_40),X_41))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_40),X_41)))),multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_40),X_41))))) )],[refute_0_186,refute_0_187]) ).
cnf(refute_0_189,plain,
multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_40),X_41)))) = multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,multiply(inverse(X_40),X_41))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_40),X_41))),least_upper_bound(identity,multiply(inverse(X_40),X_41))) )],[refute_0_185,refute_0_188]) ).
cnf(refute_0_190,plain,
( least_upper_bound(X,Y) != least_upper_bound(Y,X)
| least_upper_bound(Y,X) = least_upper_bound(X,Y) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(least_upper_bound(X,Y))),bind(Y0,$fot(least_upper_bound(Y,X)))]]) ).
cnf(refute_0_191,plain,
least_upper_bound(Y,X) = least_upper_bound(X,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(X,Y),least_upper_bound(Y,X)) )],[symmetry_of_lub,refute_0_190]) ).
cnf(refute_0_192,plain,
least_upper_bound(inverse(least_upper_bound(X_40,X_41)),inverse(X_40)) = least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41))),
inference(subst,[],[refute_0_191:[bind(X,$fot(inverse(X_40))),bind(Y,$fot(inverse(least_upper_bound(X_40,X_41))))]]) ).
cnf(refute_0_193,plain,
inverse(least_upper_bound(inverse(least_upper_bound(X_40,X_41)),inverse(X_40))) = inverse(least_upper_bound(inverse(least_upper_bound(X_40,X_41)),inverse(X_40))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(inverse(least_upper_bound(X_40,X_41)),inverse(X_40))))]]) ).
cnf(refute_0_194,plain,
( inverse(least_upper_bound(inverse(least_upper_bound(X_40,X_41)),inverse(X_40))) != inverse(least_upper_bound(inverse(least_upper_bound(X_40,X_41)),inverse(X_40)))
| least_upper_bound(inverse(least_upper_bound(X_40,X_41)),inverse(X_40)) != least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))
| inverse(least_upper_bound(inverse(least_upper_bound(X_40,X_41)),inverse(X_40))) = inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(inverse(least_upper_bound(X_40,X_41)),inverse(X_40))),inverse(least_upper_bound(inverse(least_upper_bound(X_40,X_41)),inverse(X_40)))) ),[1,0],$fot(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41))))]]) ).
cnf(refute_0_195,plain,
( least_upper_bound(inverse(least_upper_bound(X_40,X_41)),inverse(X_40)) != least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))
| inverse(least_upper_bound(inverse(least_upper_bound(X_40,X_41)),inverse(X_40))) = inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(least_upper_bound(X_40,X_41)),inverse(X_40))),inverse(least_upper_bound(inverse(least_upper_bound(X_40,X_41)),inverse(X_40)))) )],[refute_0_193,refute_0_194]) ).
cnf(refute_0_196,plain,
inverse(least_upper_bound(inverse(least_upper_bound(X_40,X_41)),inverse(X_40))) = inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(X_40,X_41)),inverse(X_40)),least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))) )],[refute_0_192,refute_0_195]) ).
cnf(refute_0_197,plain,
multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_40,X_41)),inverse(X_40))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_40),X_41)))) = multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_40,X_41)),inverse(X_40))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_40),X_41)))),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_40,X_41)),inverse(X_40))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_40),X_41)))))]]) ).
cnf(refute_0_198,plain,
( multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_40,X_41)),inverse(X_40))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_40),X_41)))) != multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_40,X_41)),inverse(X_40))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_40),X_41))))
| inverse(least_upper_bound(inverse(least_upper_bound(X_40,X_41)),inverse(X_40))) != inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41))))
| multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_40,X_41)),inverse(X_40))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_40),X_41)))) = multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_40),X_41)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_40,X_41)),inverse(X_40))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_40),X_41)))),multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_40,X_41)),inverse(X_40))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_40),X_41))))) ),[1,0],$fot(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))))]]) ).
cnf(refute_0_199,plain,
( inverse(least_upper_bound(inverse(least_upper_bound(X_40,X_41)),inverse(X_40))) != inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41))))
| multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_40,X_41)),inverse(X_40))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_40),X_41)))) = multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_40),X_41)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_40,X_41)),inverse(X_40))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_40),X_41)))),multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_40,X_41)),inverse(X_40))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_40),X_41))))) )],[refute_0_197,refute_0_198]) ).
cnf(refute_0_200,plain,
multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_40,X_41)),inverse(X_40))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_40),X_41)))) = multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_40),X_41)))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(least_upper_bound(X_40,X_41)),inverse(X_40))),inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41))))) )],[refute_0_196,refute_0_199]) ).
cnf(refute_0_201,plain,
( multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_40),X_41)))) != multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,multiply(inverse(X_40),X_41)))
| multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_40,X_41)),inverse(X_40))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_40),X_41)))) != multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_40),X_41))))
| multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_40,X_41)),inverse(X_40))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_40),X_41)))) = multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,multiply(inverse(X_40),X_41))) ),
inference(subst,[],[refute_0_120:[bind(X0,$fot(multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_40,X_41)),inverse(X_40))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_40),X_41)))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_40),X_41)))))),bind(Z0,$fot(multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,multiply(inverse(X_40),X_41)))))]]) ).
cnf(refute_0_202,plain,
( multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_40),X_41)))) != multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,multiply(inverse(X_40),X_41)))
| multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_40,X_41)),inverse(X_40))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_40),X_41)))) = multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,multiply(inverse(X_40),X_41))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_40,X_41)),inverse(X_40))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_40),X_41)))),multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_40),X_41))))) )],[refute_0_200,refute_0_201]) ).
cnf(refute_0_203,plain,
multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_40,X_41)),inverse(X_40))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_40),X_41)))) = multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,multiply(inverse(X_40),X_41))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_40),X_41)))),multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,multiply(inverse(X_40),X_41)))) )],[refute_0_189,refute_0_202]) ).
cnf(refute_0_204,plain,
( multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_40,X_41)),inverse(X_40))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_40),X_41)))) != multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,multiply(inverse(X_40),X_41)))
| least_upper_bound(X_40,X_41) != multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_40,X_41)),inverse(X_40))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_40),X_41))))
| least_upper_bound(X_40,X_41) = multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,multiply(inverse(X_40),X_41))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_40,X_41),multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_40,X_41)),inverse(X_40))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_40),X_41))))) ),[1],$fot(multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,multiply(inverse(X_40),X_41))))]]) ).
cnf(refute_0_205,plain,
( least_upper_bound(X_40,X_41) != multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_40,X_41)),inverse(X_40))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_40),X_41))))
| least_upper_bound(X_40,X_41) = multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,multiply(inverse(X_40),X_41))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_40,X_41)),inverse(X_40))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_40),X_41)))),multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,multiply(inverse(X_40),X_41)))) )],[refute_0_203,refute_0_204]) ).
cnf(refute_0_206,plain,
least_upper_bound(X_40,X_41) = multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,multiply(inverse(X_40),X_41))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_40,X_41),multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_40,X_41)),inverse(X_40))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_40),X_41))))) )],[refute_0_177,refute_0_205]) ).
cnf(refute_0_207,plain,
least_upper_bound(X_43,X_42) = multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_43,X_42)),inverse(X_42))),least_upper_bound(identity,multiply(inverse(X_42),least_upper_bound(X_43,X_42)))),
inference(subst,[],[refute_0_168:[bind(X_206,$fot(inverse(X_42))),bind(X_97,$fot(least_upper_bound(X_43,X_42)))]]) ).
cnf(refute_0_208,plain,
least_upper_bound(multiply(inverse(X_42),X_43),least_upper_bound(identity,multiply(inverse(X_42),X_43))) = least_upper_bound(multiply(inverse(X_42),X_43),identity),
inference(subst,[],[refute_0_94:[bind(Y,$fot(identity)),bind(X_15,$fot(multiply(inverse(X_42),X_43)))]]) ).
cnf(refute_0_209,plain,
multiply(inverse(X_42),least_upper_bound(X_42,X_43)) = least_upper_bound(identity,multiply(inverse(X_42),X_43)),
inference(subst,[],[refute_0_174:[bind(X_40,$fot(X_42)),bind(X_41,$fot(X_43))]]) ).
cnf(refute_0_210,plain,
( multiply(inverse(X_42),least_upper_bound(X_42,X_43)) != least_upper_bound(identity,multiply(inverse(X_42),X_43))
| least_upper_bound(identity,multiply(inverse(X_42),X_43)) = multiply(inverse(X_42),least_upper_bound(X_42,X_43)) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(multiply(inverse(X_42),least_upper_bound(X_42,X_43)))),bind(Y0,$fot(least_upper_bound(identity,multiply(inverse(X_42),X_43))))]]) ).
cnf(refute_0_211,plain,
least_upper_bound(identity,multiply(inverse(X_42),X_43)) = multiply(inverse(X_42),least_upper_bound(X_42,X_43)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_42),least_upper_bound(X_42,X_43)),least_upper_bound(identity,multiply(inverse(X_42),X_43))) )],[refute_0_209,refute_0_210]) ).
cnf(refute_0_212,plain,
( least_upper_bound(multiply(inverse(X_42),X_43),least_upper_bound(identity,multiply(inverse(X_42),X_43))) != least_upper_bound(multiply(inverse(X_42),X_43),identity)
| least_upper_bound(identity,multiply(inverse(X_42),X_43)) != multiply(inverse(X_42),least_upper_bound(X_42,X_43))
| least_upper_bound(multiply(inverse(X_42),X_43),multiply(inverse(X_42),least_upper_bound(X_42,X_43))) = least_upper_bound(multiply(inverse(X_42),X_43),identity) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(inverse(X_42),X_43),least_upper_bound(identity,multiply(inverse(X_42),X_43))),least_upper_bound(multiply(inverse(X_42),X_43),identity)) ),[0,1],$fot(multiply(inverse(X_42),least_upper_bound(X_42,X_43)))]]) ).
cnf(refute_0_213,plain,
( least_upper_bound(multiply(inverse(X_42),X_43),least_upper_bound(identity,multiply(inverse(X_42),X_43))) != least_upper_bound(multiply(inverse(X_42),X_43),identity)
| least_upper_bound(multiply(inverse(X_42),X_43),multiply(inverse(X_42),least_upper_bound(X_42,X_43))) = least_upper_bound(multiply(inverse(X_42),X_43),identity) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(X_42),X_43)),multiply(inverse(X_42),least_upper_bound(X_42,X_43))) )],[refute_0_211,refute_0_212]) ).
cnf(refute_0_214,plain,
least_upper_bound(multiply(inverse(X_42),X_43),multiply(inverse(X_42),least_upper_bound(X_42,X_43))) = least_upper_bound(multiply(inverse(X_42),X_43),identity),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(X_42),X_43),least_upper_bound(identity,multiply(inverse(X_42),X_43))),least_upper_bound(multiply(inverse(X_42),X_43),identity)) )],[refute_0_208,refute_0_213]) ).
cnf(refute_0_215,plain,
least_upper_bound(X_43,least_upper_bound(X_42,X_43)) = least_upper_bound(X_43,X_42),
inference(subst,[],[refute_0_94:[bind(Y,$fot(X_42)),bind(X_15,$fot(X_43))]]) ).
cnf(refute_0_216,plain,
multiply(inverse(X_42),least_upper_bound(X_43,least_upper_bound(X_42,X_43))) = multiply(inverse(X_42),least_upper_bound(X_43,least_upper_bound(X_42,X_43))),
introduced(tautology,[refl,[$fot(multiply(inverse(X_42),least_upper_bound(X_43,least_upper_bound(X_42,X_43))))]]) ).
cnf(refute_0_217,plain,
( multiply(inverse(X_42),least_upper_bound(X_43,least_upper_bound(X_42,X_43))) != multiply(inverse(X_42),least_upper_bound(X_43,least_upper_bound(X_42,X_43)))
| least_upper_bound(X_43,least_upper_bound(X_42,X_43)) != least_upper_bound(X_43,X_42)
| multiply(inverse(X_42),least_upper_bound(X_43,least_upper_bound(X_42,X_43))) = multiply(inverse(X_42),least_upper_bound(X_43,X_42)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_42),least_upper_bound(X_43,least_upper_bound(X_42,X_43))),multiply(inverse(X_42),least_upper_bound(X_43,least_upper_bound(X_42,X_43)))) ),[1,1],$fot(least_upper_bound(X_43,X_42))]]) ).
cnf(refute_0_218,plain,
( least_upper_bound(X_43,least_upper_bound(X_42,X_43)) != least_upper_bound(X_43,X_42)
| multiply(inverse(X_42),least_upper_bound(X_43,least_upper_bound(X_42,X_43))) = multiply(inverse(X_42),least_upper_bound(X_43,X_42)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_42),least_upper_bound(X_43,least_upper_bound(X_42,X_43))),multiply(inverse(X_42),least_upper_bound(X_43,least_upper_bound(X_42,X_43)))) )],[refute_0_216,refute_0_217]) ).
cnf(refute_0_219,plain,
multiply(inverse(X_42),least_upper_bound(X_43,least_upper_bound(X_42,X_43))) = multiply(inverse(X_42),least_upper_bound(X_43,X_42)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_43,least_upper_bound(X_42,X_43)),least_upper_bound(X_43,X_42)) )],[refute_0_215,refute_0_218]) ).
cnf(refute_0_220,plain,
( multiply(X,least_upper_bound(Y,Z)) != least_upper_bound(multiply(X,Y),multiply(X,Z))
| least_upper_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(multiply(X,least_upper_bound(Y,Z)))),bind(Y0,$fot(least_upper_bound(multiply(X,Y),multiply(X,Z))))]]) ).
cnf(refute_0_221,plain,
least_upper_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Y),multiply(X,Z))) )],[monotony_lub1,refute_0_220]) ).
cnf(refute_0_222,plain,
least_upper_bound(multiply(inverse(X_42),X_43),multiply(inverse(X_42),least_upper_bound(X_42,X_43))) = multiply(inverse(X_42),least_upper_bound(X_43,least_upper_bound(X_42,X_43))),
inference(subst,[],[refute_0_221:[bind(X,$fot(inverse(X_42))),bind(Y,$fot(X_43)),bind(Z,$fot(least_upper_bound(X_42,X_43)))]]) ).
cnf(refute_0_223,plain,
( multiply(inverse(X_42),least_upper_bound(X_43,least_upper_bound(X_42,X_43))) != multiply(inverse(X_42),least_upper_bound(X_43,X_42))
| least_upper_bound(multiply(inverse(X_42),X_43),multiply(inverse(X_42),least_upper_bound(X_42,X_43))) != multiply(inverse(X_42),least_upper_bound(X_43,least_upper_bound(X_42,X_43)))
| least_upper_bound(multiply(inverse(X_42),X_43),multiply(inverse(X_42),least_upper_bound(X_42,X_43))) = multiply(inverse(X_42),least_upper_bound(X_43,X_42)) ),
inference(subst,[],[refute_0_120:[bind(X0,$fot(least_upper_bound(multiply(inverse(X_42),X_43),multiply(inverse(X_42),least_upper_bound(X_42,X_43))))),bind(Y0,$fot(multiply(inverse(X_42),least_upper_bound(X_43,least_upper_bound(X_42,X_43))))),bind(Z0,$fot(multiply(inverse(X_42),least_upper_bound(X_43,X_42))))]]) ).
cnf(refute_0_224,plain,
( multiply(inverse(X_42),least_upper_bound(X_43,least_upper_bound(X_42,X_43))) != multiply(inverse(X_42),least_upper_bound(X_43,X_42))
| least_upper_bound(multiply(inverse(X_42),X_43),multiply(inverse(X_42),least_upper_bound(X_42,X_43))) = multiply(inverse(X_42),least_upper_bound(X_43,X_42)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(X_42),X_43),multiply(inverse(X_42),least_upper_bound(X_42,X_43))),multiply(inverse(X_42),least_upper_bound(X_43,least_upper_bound(X_42,X_43)))) )],[refute_0_222,refute_0_223]) ).
cnf(refute_0_225,plain,
least_upper_bound(multiply(inverse(X_42),X_43),multiply(inverse(X_42),least_upper_bound(X_42,X_43))) = multiply(inverse(X_42),least_upper_bound(X_43,X_42)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_42),least_upper_bound(X_43,least_upper_bound(X_42,X_43))),multiply(inverse(X_42),least_upper_bound(X_43,X_42))) )],[refute_0_219,refute_0_224]) ).
cnf(refute_0_226,plain,
( least_upper_bound(multiply(inverse(X_42),X_43),multiply(inverse(X_42),least_upper_bound(X_42,X_43))) != multiply(inverse(X_42),least_upper_bound(X_43,X_42))
| least_upper_bound(multiply(inverse(X_42),X_43),multiply(inverse(X_42),least_upper_bound(X_42,X_43))) != least_upper_bound(multiply(inverse(X_42),X_43),identity)
| multiply(inverse(X_42),least_upper_bound(X_43,X_42)) = least_upper_bound(multiply(inverse(X_42),X_43),identity) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(inverse(X_42),X_43),multiply(inverse(X_42),least_upper_bound(X_42,X_43))),least_upper_bound(multiply(inverse(X_42),X_43),identity)) ),[0],$fot(multiply(inverse(X_42),least_upper_bound(X_43,X_42)))]]) ).
cnf(refute_0_227,plain,
( least_upper_bound(multiply(inverse(X_42),X_43),multiply(inverse(X_42),least_upper_bound(X_42,X_43))) != least_upper_bound(multiply(inverse(X_42),X_43),identity)
| multiply(inverse(X_42),least_upper_bound(X_43,X_42)) = least_upper_bound(multiply(inverse(X_42),X_43),identity) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(X_42),X_43),multiply(inverse(X_42),least_upper_bound(X_42,X_43))),multiply(inverse(X_42),least_upper_bound(X_43,X_42))) )],[refute_0_225,refute_0_226]) ).
cnf(refute_0_228,plain,
least_upper_bound(multiply(inverse(X_42),X_43),identity) = least_upper_bound(identity,multiply(inverse(X_42),X_43)),
inference(subst,[],[refute_0_191:[bind(X,$fot(identity)),bind(Y,$fot(multiply(inverse(X_42),X_43)))]]) ).
cnf(refute_0_229,plain,
( multiply(inverse(X_42),least_upper_bound(X_43,X_42)) != least_upper_bound(multiply(inverse(X_42),X_43),identity)
| least_upper_bound(multiply(inverse(X_42),X_43),identity) != least_upper_bound(identity,multiply(inverse(X_42),X_43))
| multiply(inverse(X_42),least_upper_bound(X_43,X_42)) = least_upper_bound(identity,multiply(inverse(X_42),X_43)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_42),least_upper_bound(X_43,X_42)),least_upper_bound(identity,multiply(inverse(X_42),X_43))) ),[0],$fot(least_upper_bound(multiply(inverse(X_42),X_43),identity))]]) ).
cnf(refute_0_230,plain,
( multiply(inverse(X_42),least_upper_bound(X_43,X_42)) != least_upper_bound(multiply(inverse(X_42),X_43),identity)
| multiply(inverse(X_42),least_upper_bound(X_43,X_42)) = least_upper_bound(identity,multiply(inverse(X_42),X_43)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(X_42),X_43),identity),least_upper_bound(identity,multiply(inverse(X_42),X_43))) )],[refute_0_228,refute_0_229]) ).
cnf(refute_0_231,plain,
( least_upper_bound(multiply(inverse(X_42),X_43),multiply(inverse(X_42),least_upper_bound(X_42,X_43))) != least_upper_bound(multiply(inverse(X_42),X_43),identity)
| multiply(inverse(X_42),least_upper_bound(X_43,X_42)) = least_upper_bound(identity,multiply(inverse(X_42),X_43)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_42),least_upper_bound(X_43,X_42)),least_upper_bound(multiply(inverse(X_42),X_43),identity)) )],[refute_0_227,refute_0_230]) ).
cnf(refute_0_232,plain,
multiply(inverse(X_42),least_upper_bound(X_43,X_42)) = least_upper_bound(identity,multiply(inverse(X_42),X_43)),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(X_42),X_43),multiply(inverse(X_42),least_upper_bound(X_42,X_43))),least_upper_bound(multiply(inverse(X_42),X_43),identity)) )],[refute_0_214,refute_0_231]) ).
cnf(refute_0_233,plain,
( multiply(inverse(X_42),least_upper_bound(X_43,X_42)) != least_upper_bound(identity,multiply(inverse(X_42),X_43))
| least_upper_bound(X_43,X_42) != multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_43,X_42)),inverse(X_42))),least_upper_bound(identity,multiply(inverse(X_42),least_upper_bound(X_43,X_42))))
| least_upper_bound(X_43,X_42) = multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_43,X_42)),inverse(X_42))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_42),X_43)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_43,X_42),multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_43,X_42)),inverse(X_42))),least_upper_bound(identity,multiply(inverse(X_42),least_upper_bound(X_43,X_42))))) ),[1,1,1],$fot(least_upper_bound(identity,multiply(inverse(X_42),X_43)))]]) ).
cnf(refute_0_234,plain,
( least_upper_bound(X_43,X_42) != multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_43,X_42)),inverse(X_42))),least_upper_bound(identity,multiply(inverse(X_42),least_upper_bound(X_43,X_42))))
| least_upper_bound(X_43,X_42) = multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_43,X_42)),inverse(X_42))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_42),X_43)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_42),least_upper_bound(X_43,X_42)),least_upper_bound(identity,multiply(inverse(X_42),X_43))) )],[refute_0_232,refute_0_233]) ).
cnf(refute_0_235,plain,
least_upper_bound(X_43,X_42) = multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_43,X_42)),inverse(X_42))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_42),X_43)))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_43,X_42),multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_43,X_42)),inverse(X_42))),least_upper_bound(identity,multiply(inverse(X_42),least_upper_bound(X_43,X_42))))) )],[refute_0_207,refute_0_234]) ).
cnf(refute_0_236,plain,
least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_42),X_43))) = least_upper_bound(identity,multiply(inverse(X_42),X_43)),
inference(subst,[],[refute_0_184:[bind(X_16,$fot(multiply(inverse(X_42),X_43))),bind(X_17,$fot(identity))]]) ).
cnf(refute_0_237,plain,
multiply(inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_42),X_43)))) = multiply(inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_42),X_43)))),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_42),X_43)))))]]) ).
cnf(refute_0_238,plain,
( multiply(inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_42),X_43)))) != multiply(inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_42),X_43))))
| least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_42),X_43))) != least_upper_bound(identity,multiply(inverse(X_42),X_43))
| multiply(inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_42),X_43)))) = multiply(inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))),least_upper_bound(identity,multiply(inverse(X_42),X_43))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_42),X_43)))),multiply(inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_42),X_43))))) ),[1,1],$fot(least_upper_bound(identity,multiply(inverse(X_42),X_43)))]]) ).
cnf(refute_0_239,plain,
( least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_42),X_43))) != least_upper_bound(identity,multiply(inverse(X_42),X_43))
| multiply(inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_42),X_43)))) = multiply(inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))),least_upper_bound(identity,multiply(inverse(X_42),X_43))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_42),X_43)))),multiply(inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_42),X_43))))) )],[refute_0_237,refute_0_238]) ).
cnf(refute_0_240,plain,
multiply(inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_42),X_43)))) = multiply(inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))),least_upper_bound(identity,multiply(inverse(X_42),X_43))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_42),X_43))),least_upper_bound(identity,multiply(inverse(X_42),X_43))) )],[refute_0_236,refute_0_239]) ).
cnf(refute_0_241,plain,
least_upper_bound(inverse(least_upper_bound(X_43,X_42)),inverse(X_42)) = least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42))),
inference(subst,[],[refute_0_191:[bind(X,$fot(inverse(X_42))),bind(Y,$fot(inverse(least_upper_bound(X_43,X_42))))]]) ).
cnf(refute_0_242,plain,
inverse(least_upper_bound(inverse(least_upper_bound(X_43,X_42)),inverse(X_42))) = inverse(least_upper_bound(inverse(least_upper_bound(X_43,X_42)),inverse(X_42))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(inverse(least_upper_bound(X_43,X_42)),inverse(X_42))))]]) ).
cnf(refute_0_243,plain,
( inverse(least_upper_bound(inverse(least_upper_bound(X_43,X_42)),inverse(X_42))) != inverse(least_upper_bound(inverse(least_upper_bound(X_43,X_42)),inverse(X_42)))
| least_upper_bound(inverse(least_upper_bound(X_43,X_42)),inverse(X_42)) != least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))
| inverse(least_upper_bound(inverse(least_upper_bound(X_43,X_42)),inverse(X_42))) = inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(inverse(least_upper_bound(X_43,X_42)),inverse(X_42))),inverse(least_upper_bound(inverse(least_upper_bound(X_43,X_42)),inverse(X_42)))) ),[1,0],$fot(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42))))]]) ).
cnf(refute_0_244,plain,
( least_upper_bound(inverse(least_upper_bound(X_43,X_42)),inverse(X_42)) != least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))
| inverse(least_upper_bound(inverse(least_upper_bound(X_43,X_42)),inverse(X_42))) = inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(least_upper_bound(X_43,X_42)),inverse(X_42))),inverse(least_upper_bound(inverse(least_upper_bound(X_43,X_42)),inverse(X_42)))) )],[refute_0_242,refute_0_243]) ).
cnf(refute_0_245,plain,
inverse(least_upper_bound(inverse(least_upper_bound(X_43,X_42)),inverse(X_42))) = inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(X_43,X_42)),inverse(X_42)),least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))) )],[refute_0_241,refute_0_244]) ).
cnf(refute_0_246,plain,
multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_43,X_42)),inverse(X_42))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_42),X_43)))) = multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_43,X_42)),inverse(X_42))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_42),X_43)))),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_43,X_42)),inverse(X_42))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_42),X_43)))))]]) ).
cnf(refute_0_247,plain,
( multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_43,X_42)),inverse(X_42))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_42),X_43)))) != multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_43,X_42)),inverse(X_42))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_42),X_43))))
| inverse(least_upper_bound(inverse(least_upper_bound(X_43,X_42)),inverse(X_42))) != inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42))))
| multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_43,X_42)),inverse(X_42))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_42),X_43)))) = multiply(inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_42),X_43)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_43,X_42)),inverse(X_42))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_42),X_43)))),multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_43,X_42)),inverse(X_42))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_42),X_43))))) ),[1,0],$fot(inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))))]]) ).
cnf(refute_0_248,plain,
( inverse(least_upper_bound(inverse(least_upper_bound(X_43,X_42)),inverse(X_42))) != inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42))))
| multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_43,X_42)),inverse(X_42))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_42),X_43)))) = multiply(inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_42),X_43)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_43,X_42)),inverse(X_42))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_42),X_43)))),multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_43,X_42)),inverse(X_42))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_42),X_43))))) )],[refute_0_246,refute_0_247]) ).
cnf(refute_0_249,plain,
multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_43,X_42)),inverse(X_42))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_42),X_43)))) = multiply(inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_42),X_43)))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(least_upper_bound(X_43,X_42)),inverse(X_42))),inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42))))) )],[refute_0_245,refute_0_248]) ).
cnf(refute_0_250,plain,
( multiply(inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_42),X_43)))) != multiply(inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))),least_upper_bound(identity,multiply(inverse(X_42),X_43)))
| multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_43,X_42)),inverse(X_42))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_42),X_43)))) != multiply(inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_42),X_43))))
| multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_43,X_42)),inverse(X_42))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_42),X_43)))) = multiply(inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))),least_upper_bound(identity,multiply(inverse(X_42),X_43))) ),
inference(subst,[],[refute_0_120:[bind(X0,$fot(multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_43,X_42)),inverse(X_42))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_42),X_43)))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_42),X_43)))))),bind(Z0,$fot(multiply(inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))),least_upper_bound(identity,multiply(inverse(X_42),X_43)))))]]) ).
cnf(refute_0_251,plain,
( multiply(inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_42),X_43)))) != multiply(inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))),least_upper_bound(identity,multiply(inverse(X_42),X_43)))
| multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_43,X_42)),inverse(X_42))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_42),X_43)))) = multiply(inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))),least_upper_bound(identity,multiply(inverse(X_42),X_43))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_43,X_42)),inverse(X_42))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_42),X_43)))),multiply(inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_42),X_43))))) )],[refute_0_249,refute_0_250]) ).
cnf(refute_0_252,plain,
multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_43,X_42)),inverse(X_42))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_42),X_43)))) = multiply(inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))),least_upper_bound(identity,multiply(inverse(X_42),X_43))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_42),X_43)))),multiply(inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))),least_upper_bound(identity,multiply(inverse(X_42),X_43)))) )],[refute_0_240,refute_0_251]) ).
cnf(refute_0_253,plain,
( multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_43,X_42)),inverse(X_42))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_42),X_43)))) != multiply(inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))),least_upper_bound(identity,multiply(inverse(X_42),X_43)))
| least_upper_bound(X_43,X_42) != multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_43,X_42)),inverse(X_42))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_42),X_43))))
| least_upper_bound(X_43,X_42) = multiply(inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))),least_upper_bound(identity,multiply(inverse(X_42),X_43))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_43,X_42),multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_43,X_42)),inverse(X_42))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_42),X_43))))) ),[1],$fot(multiply(inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))),least_upper_bound(identity,multiply(inverse(X_42),X_43))))]]) ).
cnf(refute_0_254,plain,
( least_upper_bound(X_43,X_42) != multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_43,X_42)),inverse(X_42))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_42),X_43))))
| least_upper_bound(X_43,X_42) = multiply(inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))),least_upper_bound(identity,multiply(inverse(X_42),X_43))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_43,X_42)),inverse(X_42))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_42),X_43)))),multiply(inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))),least_upper_bound(identity,multiply(inverse(X_42),X_43)))) )],[refute_0_252,refute_0_253]) ).
cnf(refute_0_255,plain,
least_upper_bound(X_43,X_42) = multiply(inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))),least_upper_bound(identity,multiply(inverse(X_42),X_43))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_43,X_42),multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_43,X_42)),inverse(X_42))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_42),X_43))))) )],[refute_0_235,refute_0_254]) ).
cnf(refute_0_256,plain,
X_276 = multiply(inverse(least_upper_bound(inverse(X_276),inverse(least_upper_bound(Y,X_276)))),least_upper_bound(identity,multiply(inverse(least_upper_bound(Y,X_276)),X_276))),
inference(subst,[],[refute_0_168:[bind(X_206,$fot(inverse(least_upper_bound(Y,X_276)))),bind(X_97,$fot(X_276))]]) ).
cnf(refute_0_257,plain,
multiply(inverse(X_42),least_upper_bound(X_42,greatest_lower_bound(X_11,X_42))) = least_upper_bound(identity,multiply(inverse(X_42),greatest_lower_bound(X_11,X_42))),
inference(subst,[],[refute_0_174:[bind(X_40,$fot(X_42)),bind(X_41,$fot(greatest_lower_bound(X_11,X_42)))]]) ).
cnf(refute_0_258,plain,
least_upper_bound(X_42,greatest_lower_bound(X_11,X_42)) = X_42,
inference(subst,[],[refute_0_9:[bind(X_10,$fot(X_42))]]) ).
cnf(refute_0_259,plain,
( multiply(inverse(X_42),least_upper_bound(X_42,greatest_lower_bound(X_11,X_42))) != least_upper_bound(identity,multiply(inverse(X_42),greatest_lower_bound(X_11,X_42)))
| least_upper_bound(X_42,greatest_lower_bound(X_11,X_42)) != X_42
| multiply(inverse(X_42),X_42) = least_upper_bound(identity,multiply(inverse(X_42),greatest_lower_bound(X_11,X_42))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_42),least_upper_bound(X_42,greatest_lower_bound(X_11,X_42))),least_upper_bound(identity,multiply(inverse(X_42),greatest_lower_bound(X_11,X_42)))) ),[0,1],$fot(X_42)]]) ).
cnf(refute_0_260,plain,
( multiply(inverse(X_42),least_upper_bound(X_42,greatest_lower_bound(X_11,X_42))) != least_upper_bound(identity,multiply(inverse(X_42),greatest_lower_bound(X_11,X_42)))
| multiply(inverse(X_42),X_42) = least_upper_bound(identity,multiply(inverse(X_42),greatest_lower_bound(X_11,X_42))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_42,greatest_lower_bound(X_11,X_42)),X_42) )],[refute_0_258,refute_0_259]) ).
cnf(refute_0_261,plain,
multiply(inverse(X_42),X_42) = least_upper_bound(identity,multiply(inverse(X_42),greatest_lower_bound(X_11,X_42))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_42),least_upper_bound(X_42,greatest_lower_bound(X_11,X_42))),least_upper_bound(identity,multiply(inverse(X_42),greatest_lower_bound(X_11,X_42)))) )],[refute_0_257,refute_0_260]) ).
cnf(refute_0_262,plain,
multiply(inverse(X_42),X_42) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_42))]]) ).
cnf(refute_0_263,plain,
( multiply(inverse(X_42),X_42) != identity
| multiply(inverse(X_42),X_42) != least_upper_bound(identity,multiply(inverse(X_42),greatest_lower_bound(X_11,X_42)))
| identity = least_upper_bound(identity,multiply(inverse(X_42),greatest_lower_bound(X_11,X_42))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_42),X_42),least_upper_bound(identity,multiply(inverse(X_42),greatest_lower_bound(X_11,X_42)))) ),[0],$fot(identity)]]) ).
cnf(refute_0_264,plain,
( multiply(inverse(X_42),X_42) != least_upper_bound(identity,multiply(inverse(X_42),greatest_lower_bound(X_11,X_42)))
| identity = least_upper_bound(identity,multiply(inverse(X_42),greatest_lower_bound(X_11,X_42))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_42),X_42),identity) )],[refute_0_262,refute_0_263]) ).
cnf(refute_0_265,plain,
identity = least_upper_bound(identity,multiply(inverse(X_42),greatest_lower_bound(X_11,X_42))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_42),X_42),least_upper_bound(identity,multiply(inverse(X_42),greatest_lower_bound(X_11,X_42)))) )],[refute_0_261,refute_0_264]) ).
cnf(refute_0_266,plain,
identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(Y,X_44)),greatest_lower_bound(X_44,least_upper_bound(Y,X_44)))),
inference(subst,[],[refute_0_265:[bind(X_11,$fot(X_44)),bind(X_42,$fot(least_upper_bound(Y,X_44)))]]) ).
cnf(refute_0_267,plain,
greatest_lower_bound(X_44,least_upper_bound(Y,X_44)) = X_44,
inference(subst,[],[refute_0_13:[bind(X,$fot(X_44))]]) ).
cnf(refute_0_268,plain,
( greatest_lower_bound(X_44,least_upper_bound(Y,X_44)) != X_44
| identity != least_upper_bound(identity,multiply(inverse(least_upper_bound(Y,X_44)),greatest_lower_bound(X_44,least_upper_bound(Y,X_44))))
| identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(Y,X_44)),X_44)) ),
introduced(tautology,[equality,[$cnf( $equal(identity,least_upper_bound(identity,multiply(inverse(least_upper_bound(Y,X_44)),greatest_lower_bound(X_44,least_upper_bound(Y,X_44))))) ),[1,1,1],$fot(X_44)]]) ).
cnf(refute_0_269,plain,
( identity != least_upper_bound(identity,multiply(inverse(least_upper_bound(Y,X_44)),greatest_lower_bound(X_44,least_upper_bound(Y,X_44))))
| identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(Y,X_44)),X_44)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_44,least_upper_bound(Y,X_44)),X_44) )],[refute_0_267,refute_0_268]) ).
cnf(refute_0_270,plain,
identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(Y,X_44)),X_44)),
inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,multiply(inverse(least_upper_bound(Y,X_44)),greatest_lower_bound(X_44,least_upper_bound(Y,X_44))))) )],[refute_0_266,refute_0_269]) ).
cnf(refute_0_271,plain,
identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(Y,X_276)),X_276)),
inference(subst,[],[refute_0_270:[bind(X_44,$fot(X_276))]]) ).
cnf(refute_0_272,plain,
( identity != least_upper_bound(identity,multiply(inverse(least_upper_bound(Y,X_276)),X_276))
| least_upper_bound(identity,multiply(inverse(least_upper_bound(Y,X_276)),X_276)) = identity ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(identity)),bind(Y0,$fot(least_upper_bound(identity,multiply(inverse(least_upper_bound(Y,X_276)),X_276))))]]) ).
cnf(refute_0_273,plain,
least_upper_bound(identity,multiply(inverse(least_upper_bound(Y,X_276)),X_276)) = identity,
inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,multiply(inverse(least_upper_bound(Y,X_276)),X_276))) )],[refute_0_271,refute_0_272]) ).
cnf(refute_0_274,plain,
( X_276 != multiply(inverse(least_upper_bound(inverse(X_276),inverse(least_upper_bound(Y,X_276)))),least_upper_bound(identity,multiply(inverse(least_upper_bound(Y,X_276)),X_276)))
| least_upper_bound(identity,multiply(inverse(least_upper_bound(Y,X_276)),X_276)) != identity
| X_276 = multiply(inverse(least_upper_bound(inverse(X_276),inverse(least_upper_bound(Y,X_276)))),identity) ),
introduced(tautology,[equality,[$cnf( $equal(X_276,multiply(inverse(least_upper_bound(inverse(X_276),inverse(least_upper_bound(Y,X_276)))),least_upper_bound(identity,multiply(inverse(least_upper_bound(Y,X_276)),X_276)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_275,plain,
( X_276 != multiply(inverse(least_upper_bound(inverse(X_276),inverse(least_upper_bound(Y,X_276)))),least_upper_bound(identity,multiply(inverse(least_upper_bound(Y,X_276)),X_276)))
| X_276 = multiply(inverse(least_upper_bound(inverse(X_276),inverse(least_upper_bound(Y,X_276)))),identity) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(least_upper_bound(Y,X_276)),X_276)),identity) )],[refute_0_273,refute_0_274]) ).
cnf(refute_0_276,plain,
X_276 = multiply(inverse(least_upper_bound(inverse(X_276),inverse(least_upper_bound(Y,X_276)))),identity),
inference(resolve,[$cnf( $equal(X_276,multiply(inverse(least_upper_bound(inverse(X_276),inverse(least_upper_bound(Y,X_276)))),least_upper_bound(identity,multiply(inverse(least_upper_bound(Y,X_276)),X_276)))) )],[refute_0_256,refute_0_275]) ).
cnf(refute_0_277,plain,
X_99 = multiply(inverse(inverse(X_99)),multiply(inverse(X_99),X_99)),
inference(subst,[],[refute_0_158:[bind(X_96,$fot(inverse(X_99))),bind(X_97,$fot(X_99))]]) ).
cnf(refute_0_278,plain,
multiply(inverse(X_99),X_99) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_99))]]) ).
cnf(refute_0_279,plain,
( X_99 != multiply(inverse(inverse(X_99)),multiply(inverse(X_99),X_99))
| multiply(inverse(X_99),X_99) != identity
| X_99 = multiply(inverse(inverse(X_99)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(X_99,multiply(inverse(inverse(X_99)),multiply(inverse(X_99),X_99))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_280,plain,
( X_99 != multiply(inverse(inverse(X_99)),multiply(inverse(X_99),X_99))
| X_99 = multiply(inverse(inverse(X_99)),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_99),X_99),identity) )],[refute_0_278,refute_0_279]) ).
cnf(refute_0_281,plain,
X_99 = multiply(inverse(inverse(X_99)),identity),
inference(resolve,[$cnf( $equal(X_99,multiply(inverse(inverse(X_99)),multiply(inverse(X_99),X_99))) )],[refute_0_277,refute_0_280]) ).
cnf(refute_0_282,plain,
multiply(X_98,X_99) = multiply(inverse(inverse(X_98)),multiply(inverse(X_98),multiply(X_98,X_99))),
inference(subst,[],[refute_0_158:[bind(X_96,$fot(inverse(X_98))),bind(X_97,$fot(multiply(X_98,X_99)))]]) ).
cnf(refute_0_283,plain,
X_99 = multiply(inverse(X_98),multiply(X_98,X_99)),
inference(subst,[],[refute_0_158:[bind(X_96,$fot(X_98)),bind(X_97,$fot(X_99))]]) ).
cnf(refute_0_284,plain,
( X_99 != multiply(inverse(X_98),multiply(X_98,X_99))
| multiply(inverse(X_98),multiply(X_98,X_99)) = X_99 ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(X_99)),bind(Y0,$fot(multiply(inverse(X_98),multiply(X_98,X_99))))]]) ).
cnf(refute_0_285,plain,
multiply(inverse(X_98),multiply(X_98,X_99)) = X_99,
inference(resolve,[$cnf( $equal(X_99,multiply(inverse(X_98),multiply(X_98,X_99))) )],[refute_0_283,refute_0_284]) ).
cnf(refute_0_286,plain,
( multiply(X_98,X_99) != multiply(inverse(inverse(X_98)),multiply(inverse(X_98),multiply(X_98,X_99)))
| multiply(inverse(X_98),multiply(X_98,X_99)) != X_99
| multiply(X_98,X_99) = multiply(inverse(inverse(X_98)),X_99) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_98,X_99),multiply(inverse(inverse(X_98)),multiply(inverse(X_98),multiply(X_98,X_99)))) ),[1,1],$fot(X_99)]]) ).
cnf(refute_0_287,plain,
( multiply(X_98,X_99) != multiply(inverse(inverse(X_98)),multiply(inverse(X_98),multiply(X_98,X_99)))
| multiply(X_98,X_99) = multiply(inverse(inverse(X_98)),X_99) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_98),multiply(X_98,X_99)),X_99) )],[refute_0_285,refute_0_286]) ).
cnf(refute_0_288,plain,
multiply(X_98,X_99) = multiply(inverse(inverse(X_98)),X_99),
inference(resolve,[$cnf( $equal(multiply(X_98,X_99),multiply(inverse(inverse(X_98)),multiply(inverse(X_98),multiply(X_98,X_99)))) )],[refute_0_282,refute_0_287]) ).
cnf(refute_0_289,plain,
( multiply(X_98,X_99) != multiply(inverse(inverse(X_98)),X_99)
| multiply(inverse(inverse(X_98)),X_99) = multiply(X_98,X_99) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(multiply(X_98,X_99))),bind(Y0,$fot(multiply(inverse(inverse(X_98)),X_99)))]]) ).
cnf(refute_0_290,plain,
multiply(inverse(inverse(X_98)),X_99) = multiply(X_98,X_99),
inference(resolve,[$cnf( $equal(multiply(X_98,X_99),multiply(inverse(inverse(X_98)),X_99)) )],[refute_0_288,refute_0_289]) ).
cnf(refute_0_291,plain,
multiply(inverse(inverse(X_99)),identity) = multiply(X_99,identity),
inference(subst,[],[refute_0_290:[bind(X_98,$fot(X_99)),bind(X_99,$fot(identity))]]) ).
cnf(refute_0_292,plain,
( X_99 != multiply(inverse(inverse(X_99)),identity)
| multiply(inverse(inverse(X_99)),identity) != multiply(X_99,identity)
| X_99 = multiply(X_99,identity) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_99,multiply(X_99,identity)) ),[0],$fot(multiply(inverse(inverse(X_99)),identity))]]) ).
cnf(refute_0_293,plain,
( X_99 != multiply(inverse(inverse(X_99)),identity)
| X_99 = multiply(X_99,identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_99)),identity),multiply(X_99,identity)) )],[refute_0_291,refute_0_292]) ).
cnf(refute_0_294,plain,
X_99 = multiply(X_99,identity),
inference(resolve,[$cnf( $equal(X_99,multiply(inverse(inverse(X_99)),identity)) )],[refute_0_281,refute_0_293]) ).
cnf(refute_0_295,plain,
( X_99 != multiply(X_99,identity)
| multiply(X_99,identity) = X_99 ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(X_99)),bind(Y0,$fot(multiply(X_99,identity)))]]) ).
cnf(refute_0_296,plain,
multiply(X_99,identity) = X_99,
inference(resolve,[$cnf( $equal(X_99,multiply(X_99,identity)) )],[refute_0_294,refute_0_295]) ).
cnf(refute_0_297,plain,
multiply(inverse(least_upper_bound(inverse(X_276),inverse(least_upper_bound(Y,X_276)))),identity) = inverse(least_upper_bound(inverse(X_276),inverse(least_upper_bound(Y,X_276)))),
inference(subst,[],[refute_0_296:[bind(X_99,$fot(inverse(least_upper_bound(inverse(X_276),inverse(least_upper_bound(Y,X_276))))))]]) ).
cnf(refute_0_298,plain,
( X_276 != multiply(inverse(least_upper_bound(inverse(X_276),inverse(least_upper_bound(Y,X_276)))),identity)
| multiply(inverse(least_upper_bound(inverse(X_276),inverse(least_upper_bound(Y,X_276)))),identity) != inverse(least_upper_bound(inverse(X_276),inverse(least_upper_bound(Y,X_276))))
| X_276 = inverse(least_upper_bound(inverse(X_276),inverse(least_upper_bound(Y,X_276)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_276,inverse(least_upper_bound(inverse(X_276),inverse(least_upper_bound(Y,X_276))))) ),[0],$fot(multiply(inverse(least_upper_bound(inverse(X_276),inverse(least_upper_bound(Y,X_276)))),identity))]]) ).
cnf(refute_0_299,plain,
( X_276 != multiply(inverse(least_upper_bound(inverse(X_276),inverse(least_upper_bound(Y,X_276)))),identity)
| X_276 = inverse(least_upper_bound(inverse(X_276),inverse(least_upper_bound(Y,X_276)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_276),inverse(least_upper_bound(Y,X_276)))),identity),inverse(least_upper_bound(inverse(X_276),inverse(least_upper_bound(Y,X_276))))) )],[refute_0_297,refute_0_298]) ).
cnf(refute_0_300,plain,
X_276 = inverse(least_upper_bound(inverse(X_276),inverse(least_upper_bound(Y,X_276)))),
inference(resolve,[$cnf( $equal(X_276,multiply(inverse(least_upper_bound(inverse(X_276),inverse(least_upper_bound(Y,X_276)))),identity)) )],[refute_0_276,refute_0_299]) ).
cnf(refute_0_301,plain,
( X_276 != inverse(least_upper_bound(inverse(X_276),inverse(least_upper_bound(Y,X_276))))
| inverse(least_upper_bound(inverse(X_276),inverse(least_upper_bound(Y,X_276)))) = X_276 ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(X_276)),bind(Y0,$fot(inverse(least_upper_bound(inverse(X_276),inverse(least_upper_bound(Y,X_276))))))]]) ).
cnf(refute_0_302,plain,
inverse(least_upper_bound(inverse(X_276),inverse(least_upper_bound(Y,X_276)))) = X_276,
inference(resolve,[$cnf( $equal(X_276,inverse(least_upper_bound(inverse(X_276),inverse(least_upper_bound(Y,X_276))))) )],[refute_0_300,refute_0_301]) ).
cnf(refute_0_303,plain,
inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))) = X_42,
inference(subst,[],[refute_0_302:[bind(Y,$fot(X_43)),bind(X_276,$fot(X_42))]]) ).
cnf(refute_0_304,plain,
multiply(inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))),least_upper_bound(identity,multiply(inverse(X_42),X_43))) = multiply(inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))),least_upper_bound(identity,multiply(inverse(X_42),X_43))),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))),least_upper_bound(identity,multiply(inverse(X_42),X_43))))]]) ).
cnf(refute_0_305,plain,
( multiply(inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))),least_upper_bound(identity,multiply(inverse(X_42),X_43))) != multiply(inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))),least_upper_bound(identity,multiply(inverse(X_42),X_43)))
| inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))) != X_42
| multiply(inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))),least_upper_bound(identity,multiply(inverse(X_42),X_43))) = multiply(X_42,least_upper_bound(identity,multiply(inverse(X_42),X_43))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))),least_upper_bound(identity,multiply(inverse(X_42),X_43))),multiply(inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))),least_upper_bound(identity,multiply(inverse(X_42),X_43)))) ),[1,0],$fot(X_42)]]) ).
cnf(refute_0_306,plain,
( inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))) != X_42
| multiply(inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))),least_upper_bound(identity,multiply(inverse(X_42),X_43))) = multiply(X_42,least_upper_bound(identity,multiply(inverse(X_42),X_43))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))),least_upper_bound(identity,multiply(inverse(X_42),X_43))),multiply(inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))),least_upper_bound(identity,multiply(inverse(X_42),X_43)))) )],[refute_0_304,refute_0_305]) ).
cnf(refute_0_307,plain,
multiply(inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))),least_upper_bound(identity,multiply(inverse(X_42),X_43))) = multiply(X_42,least_upper_bound(identity,multiply(inverse(X_42),X_43))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))),X_42) )],[refute_0_303,refute_0_306]) ).
cnf(refute_0_308,plain,
( multiply(inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))),least_upper_bound(identity,multiply(inverse(X_42),X_43))) != multiply(X_42,least_upper_bound(identity,multiply(inverse(X_42),X_43)))
| least_upper_bound(X_43,X_42) != multiply(inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))),least_upper_bound(identity,multiply(inverse(X_42),X_43)))
| least_upper_bound(X_43,X_42) = multiply(X_42,least_upper_bound(identity,multiply(inverse(X_42),X_43))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_43,X_42),multiply(inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))),least_upper_bound(identity,multiply(inverse(X_42),X_43)))) ),[1],$fot(multiply(X_42,least_upper_bound(identity,multiply(inverse(X_42),X_43))))]]) ).
cnf(refute_0_309,plain,
( least_upper_bound(X_43,X_42) != multiply(inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))),least_upper_bound(identity,multiply(inverse(X_42),X_43)))
| least_upper_bound(X_43,X_42) = multiply(X_42,least_upper_bound(identity,multiply(inverse(X_42),X_43))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))),least_upper_bound(identity,multiply(inverse(X_42),X_43))),multiply(X_42,least_upper_bound(identity,multiply(inverse(X_42),X_43)))) )],[refute_0_307,refute_0_308]) ).
cnf(refute_0_310,plain,
least_upper_bound(X_43,X_42) = multiply(X_42,least_upper_bound(identity,multiply(inverse(X_42),X_43))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_43,X_42),multiply(inverse(least_upper_bound(inverse(X_42),inverse(least_upper_bound(X_43,X_42)))),least_upper_bound(identity,multiply(inverse(X_42),X_43)))) )],[refute_0_255,refute_0_309]) ).
cnf(refute_0_311,plain,
( least_upper_bound(X_43,X_42) != multiply(X_42,least_upper_bound(identity,multiply(inverse(X_42),X_43)))
| multiply(X_42,least_upper_bound(identity,multiply(inverse(X_42),X_43))) = least_upper_bound(X_43,X_42) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(least_upper_bound(X_43,X_42))),bind(Y0,$fot(multiply(X_42,least_upper_bound(identity,multiply(inverse(X_42),X_43)))))]]) ).
cnf(refute_0_312,plain,
multiply(X_42,least_upper_bound(identity,multiply(inverse(X_42),X_43))) = least_upper_bound(X_43,X_42),
inference(resolve,[$cnf( $equal(least_upper_bound(X_43,X_42),multiply(X_42,least_upper_bound(identity,multiply(inverse(X_42),X_43)))) )],[refute_0_310,refute_0_311]) ).
cnf(refute_0_313,plain,
multiply(X_40,least_upper_bound(identity,multiply(inverse(X_40),X_41))) = least_upper_bound(X_41,X_40),
inference(subst,[],[refute_0_312:[bind(X_42,$fot(X_40)),bind(X_43,$fot(X_41))]]) ).
cnf(refute_0_314,plain,
X_276 = multiply(inverse(least_upper_bound(inverse(X_276),inverse(least_upper_bound(X_276,Y)))),least_upper_bound(identity,multiply(inverse(least_upper_bound(X_276,Y)),X_276))),
inference(subst,[],[refute_0_168:[bind(X_206,$fot(inverse(least_upper_bound(X_276,Y)))),bind(X_97,$fot(X_276))]]) ).
cnf(refute_0_315,plain,
identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_44,Y)),greatest_lower_bound(X_44,least_upper_bound(X_44,Y)))),
inference(subst,[],[refute_0_265:[bind(X_11,$fot(X_44)),bind(X_42,$fot(least_upper_bound(X_44,Y)))]]) ).
cnf(refute_0_316,plain,
greatest_lower_bound(X_44,least_upper_bound(X_44,Y)) = X_44,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_44))]]) ).
cnf(refute_0_317,plain,
( greatest_lower_bound(X_44,least_upper_bound(X_44,Y)) != X_44
| identity != least_upper_bound(identity,multiply(inverse(least_upper_bound(X_44,Y)),greatest_lower_bound(X_44,least_upper_bound(X_44,Y))))
| identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_44,Y)),X_44)) ),
introduced(tautology,[equality,[$cnf( $equal(identity,least_upper_bound(identity,multiply(inverse(least_upper_bound(X_44,Y)),greatest_lower_bound(X_44,least_upper_bound(X_44,Y))))) ),[1,1,1],$fot(X_44)]]) ).
cnf(refute_0_318,plain,
( identity != least_upper_bound(identity,multiply(inverse(least_upper_bound(X_44,Y)),greatest_lower_bound(X_44,least_upper_bound(X_44,Y))))
| identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_44,Y)),X_44)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_44,least_upper_bound(X_44,Y)),X_44) )],[refute_0_316,refute_0_317]) ).
cnf(refute_0_319,plain,
identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_44,Y)),X_44)),
inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,multiply(inverse(least_upper_bound(X_44,Y)),greatest_lower_bound(X_44,least_upper_bound(X_44,Y))))) )],[refute_0_315,refute_0_318]) ).
cnf(refute_0_320,plain,
identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_276,Y)),X_276)),
inference(subst,[],[refute_0_319:[bind(X_44,$fot(X_276))]]) ).
cnf(refute_0_321,plain,
( identity != least_upper_bound(identity,multiply(inverse(least_upper_bound(X_276,Y)),X_276))
| least_upper_bound(identity,multiply(inverse(least_upper_bound(X_276,Y)),X_276)) = identity ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(identity)),bind(Y0,$fot(least_upper_bound(identity,multiply(inverse(least_upper_bound(X_276,Y)),X_276))))]]) ).
cnf(refute_0_322,plain,
least_upper_bound(identity,multiply(inverse(least_upper_bound(X_276,Y)),X_276)) = identity,
inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,multiply(inverse(least_upper_bound(X_276,Y)),X_276))) )],[refute_0_320,refute_0_321]) ).
cnf(refute_0_323,plain,
( X_276 != multiply(inverse(least_upper_bound(inverse(X_276),inverse(least_upper_bound(X_276,Y)))),least_upper_bound(identity,multiply(inverse(least_upper_bound(X_276,Y)),X_276)))
| least_upper_bound(identity,multiply(inverse(least_upper_bound(X_276,Y)),X_276)) != identity
| X_276 = multiply(inverse(least_upper_bound(inverse(X_276),inverse(least_upper_bound(X_276,Y)))),identity) ),
introduced(tautology,[equality,[$cnf( $equal(X_276,multiply(inverse(least_upper_bound(inverse(X_276),inverse(least_upper_bound(X_276,Y)))),least_upper_bound(identity,multiply(inverse(least_upper_bound(X_276,Y)),X_276)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_324,plain,
( X_276 != multiply(inverse(least_upper_bound(inverse(X_276),inverse(least_upper_bound(X_276,Y)))),least_upper_bound(identity,multiply(inverse(least_upper_bound(X_276,Y)),X_276)))
| X_276 = multiply(inverse(least_upper_bound(inverse(X_276),inverse(least_upper_bound(X_276,Y)))),identity) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(least_upper_bound(X_276,Y)),X_276)),identity) )],[refute_0_322,refute_0_323]) ).
cnf(refute_0_325,plain,
X_276 = multiply(inverse(least_upper_bound(inverse(X_276),inverse(least_upper_bound(X_276,Y)))),identity),
inference(resolve,[$cnf( $equal(X_276,multiply(inverse(least_upper_bound(inverse(X_276),inverse(least_upper_bound(X_276,Y)))),least_upper_bound(identity,multiply(inverse(least_upper_bound(X_276,Y)),X_276)))) )],[refute_0_314,refute_0_324]) ).
cnf(refute_0_326,plain,
multiply(inverse(least_upper_bound(inverse(X_276),inverse(least_upper_bound(X_276,Y)))),identity) = inverse(least_upper_bound(inverse(X_276),inverse(least_upper_bound(X_276,Y)))),
inference(subst,[],[refute_0_296:[bind(X_99,$fot(inverse(least_upper_bound(inverse(X_276),inverse(least_upper_bound(X_276,Y))))))]]) ).
cnf(refute_0_327,plain,
( X_276 != multiply(inverse(least_upper_bound(inverse(X_276),inverse(least_upper_bound(X_276,Y)))),identity)
| multiply(inverse(least_upper_bound(inverse(X_276),inverse(least_upper_bound(X_276,Y)))),identity) != inverse(least_upper_bound(inverse(X_276),inverse(least_upper_bound(X_276,Y))))
| X_276 = inverse(least_upper_bound(inverse(X_276),inverse(least_upper_bound(X_276,Y)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_276,inverse(least_upper_bound(inverse(X_276),inverse(least_upper_bound(X_276,Y))))) ),[0],$fot(multiply(inverse(least_upper_bound(inverse(X_276),inverse(least_upper_bound(X_276,Y)))),identity))]]) ).
cnf(refute_0_328,plain,
( X_276 != multiply(inverse(least_upper_bound(inverse(X_276),inverse(least_upper_bound(X_276,Y)))),identity)
| X_276 = inverse(least_upper_bound(inverse(X_276),inverse(least_upper_bound(X_276,Y)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_276),inverse(least_upper_bound(X_276,Y)))),identity),inverse(least_upper_bound(inverse(X_276),inverse(least_upper_bound(X_276,Y))))) )],[refute_0_326,refute_0_327]) ).
cnf(refute_0_329,plain,
X_276 = inverse(least_upper_bound(inverse(X_276),inverse(least_upper_bound(X_276,Y)))),
inference(resolve,[$cnf( $equal(X_276,multiply(inverse(least_upper_bound(inverse(X_276),inverse(least_upper_bound(X_276,Y)))),identity)) )],[refute_0_325,refute_0_328]) ).
cnf(refute_0_330,plain,
( X_276 != inverse(least_upper_bound(inverse(X_276),inverse(least_upper_bound(X_276,Y))))
| inverse(least_upper_bound(inverse(X_276),inverse(least_upper_bound(X_276,Y)))) = X_276 ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(X_276)),bind(Y0,$fot(inverse(least_upper_bound(inverse(X_276),inverse(least_upper_bound(X_276,Y))))))]]) ).
cnf(refute_0_331,plain,
inverse(least_upper_bound(inverse(X_276),inverse(least_upper_bound(X_276,Y)))) = X_276,
inference(resolve,[$cnf( $equal(X_276,inverse(least_upper_bound(inverse(X_276),inverse(least_upper_bound(X_276,Y))))) )],[refute_0_329,refute_0_330]) ).
cnf(refute_0_332,plain,
inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))) = X_40,
inference(subst,[],[refute_0_331:[bind(Y,$fot(X_41)),bind(X_276,$fot(X_40))]]) ).
cnf(refute_0_333,plain,
multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,multiply(inverse(X_40),X_41))) = multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,multiply(inverse(X_40),X_41))),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,multiply(inverse(X_40),X_41))))]]) ).
cnf(refute_0_334,plain,
( multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,multiply(inverse(X_40),X_41))) != multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,multiply(inverse(X_40),X_41)))
| inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))) != X_40
| multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,multiply(inverse(X_40),X_41))) = multiply(X_40,least_upper_bound(identity,multiply(inverse(X_40),X_41))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,multiply(inverse(X_40),X_41))),multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,multiply(inverse(X_40),X_41)))) ),[1,0],$fot(X_40)]]) ).
cnf(refute_0_335,plain,
( inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))) != X_40
| multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,multiply(inverse(X_40),X_41))) = multiply(X_40,least_upper_bound(identity,multiply(inverse(X_40),X_41))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,multiply(inverse(X_40),X_41))),multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,multiply(inverse(X_40),X_41)))) )],[refute_0_333,refute_0_334]) ).
cnf(refute_0_336,plain,
multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,multiply(inverse(X_40),X_41))) = multiply(X_40,least_upper_bound(identity,multiply(inverse(X_40),X_41))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),X_40) )],[refute_0_332,refute_0_335]) ).
cnf(refute_0_337,plain,
( multiply(X_40,least_upper_bound(identity,multiply(inverse(X_40),X_41))) != least_upper_bound(X_41,X_40)
| multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,multiply(inverse(X_40),X_41))) != multiply(X_40,least_upper_bound(identity,multiply(inverse(X_40),X_41)))
| multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,multiply(inverse(X_40),X_41))) = least_upper_bound(X_41,X_40) ),
inference(subst,[],[refute_0_120:[bind(X0,$fot(multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,multiply(inverse(X_40),X_41))))),bind(Y0,$fot(multiply(X_40,least_upper_bound(identity,multiply(inverse(X_40),X_41))))),bind(Z0,$fot(least_upper_bound(X_41,X_40)))]]) ).
cnf(refute_0_338,plain,
( multiply(X_40,least_upper_bound(identity,multiply(inverse(X_40),X_41))) != least_upper_bound(X_41,X_40)
| multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,multiply(inverse(X_40),X_41))) = least_upper_bound(X_41,X_40) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,multiply(inverse(X_40),X_41))),multiply(X_40,least_upper_bound(identity,multiply(inverse(X_40),X_41)))) )],[refute_0_336,refute_0_337]) ).
cnf(refute_0_339,plain,
multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,multiply(inverse(X_40),X_41))) = least_upper_bound(X_41,X_40),
inference(resolve,[$cnf( $equal(multiply(X_40,least_upper_bound(identity,multiply(inverse(X_40),X_41))),least_upper_bound(X_41,X_40)) )],[refute_0_313,refute_0_338]) ).
cnf(refute_0_340,plain,
( multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,multiply(inverse(X_40),X_41))) != least_upper_bound(X_41,X_40)
| least_upper_bound(X_40,X_41) != multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,multiply(inverse(X_40),X_41)))
| least_upper_bound(X_40,X_41) = least_upper_bound(X_41,X_40) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_40,X_41),multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,multiply(inverse(X_40),X_41)))) ),[1],$fot(least_upper_bound(X_41,X_40))]]) ).
cnf(refute_0_341,plain,
( least_upper_bound(X_40,X_41) != multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,multiply(inverse(X_40),X_41)))
| least_upper_bound(X_40,X_41) = least_upper_bound(X_41,X_40) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,multiply(inverse(X_40),X_41))),least_upper_bound(X_41,X_40)) )],[refute_0_339,refute_0_340]) ).
cnf(refute_0_342,plain,
least_upper_bound(X_40,X_41) = least_upper_bound(X_41,X_40),
inference(resolve,[$cnf( $equal(least_upper_bound(X_40,X_41),multiply(inverse(least_upper_bound(inverse(X_40),inverse(least_upper_bound(X_40,X_41)))),least_upper_bound(identity,multiply(inverse(X_40),X_41)))) )],[refute_0_206,refute_0_341]) ).
cnf(refute_0_343,plain,
( least_upper_bound(X_40,X_41) != least_upper_bound(X_41,X_40)
| least_upper_bound(X_41,X_40) = least_upper_bound(X_40,X_41) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(least_upper_bound(X_40,X_41))),bind(Y0,$fot(least_upper_bound(X_41,X_40)))]]) ).
cnf(refute_0_344,plain,
least_upper_bound(X_41,X_40) = least_upper_bound(X_40,X_41),
inference(resolve,[$cnf( $equal(least_upper_bound(X_40,X_41),least_upper_bound(X_41,X_40)) )],[refute_0_342,refute_0_343]) ).
cnf(refute_0_345,plain,
least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_375,X_374)),greatest_lower_bound(X_374,X_375)) = least_upper_bound(greatest_lower_bound(X_374,X_375),least_upper_bound(X,greatest_lower_bound(X_375,X_374))),
inference(subst,[],[refute_0_344:[bind(X_40,$fot(greatest_lower_bound(X_374,X_375))),bind(X_41,$fot(least_upper_bound(X,greatest_lower_bound(X_375,X_374))))]]) ).
cnf(refute_0_346,plain,
( least_upper_bound(greatest_lower_bound(X_374,X_375),least_upper_bound(X,greatest_lower_bound(X_375,X_374))) != least_upper_bound(X,greatest_lower_bound(X_374,X_375))
| least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_375,X_374)),greatest_lower_bound(X_374,X_375)) != least_upper_bound(greatest_lower_bound(X_374,X_375),least_upper_bound(X,greatest_lower_bound(X_375,X_374)))
| least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_375,X_374)),greatest_lower_bound(X_374,X_375)) = least_upper_bound(X,greatest_lower_bound(X_374,X_375)) ),
inference(subst,[],[refute_0_120:[bind(X0,$fot(least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_375,X_374)),greatest_lower_bound(X_374,X_375)))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(X_374,X_375),least_upper_bound(X,greatest_lower_bound(X_375,X_374))))),bind(Z0,$fot(least_upper_bound(X,greatest_lower_bound(X_374,X_375))))]]) ).
cnf(refute_0_347,plain,
( least_upper_bound(greatest_lower_bound(X_374,X_375),least_upper_bound(X,greatest_lower_bound(X_375,X_374))) != least_upper_bound(X,greatest_lower_bound(X_374,X_375))
| least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_375,X_374)),greatest_lower_bound(X_374,X_375)) = least_upper_bound(X,greatest_lower_bound(X_374,X_375)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_375,X_374)),greatest_lower_bound(X_374,X_375)),least_upper_bound(greatest_lower_bound(X_374,X_375),least_upper_bound(X,greatest_lower_bound(X_375,X_374)))) )],[refute_0_345,refute_0_346]) ).
cnf(refute_0_348,plain,
least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_375,X_374)),greatest_lower_bound(X_374,X_375)) = least_upper_bound(X,greatest_lower_bound(X_374,X_375)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_374,X_375),least_upper_bound(X,greatest_lower_bound(X_375,X_374))),least_upper_bound(X,greatest_lower_bound(X_374,X_375))) )],[refute_0_149,refute_0_347]) ).
cnf(refute_0_349,plain,
( least_upper_bound(X,greatest_lower_bound(X_375,X_374)) != least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_375,X_374)),greatest_lower_bound(X_374,X_375))
| least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_375,X_374)),greatest_lower_bound(X_374,X_375)) != least_upper_bound(X,greatest_lower_bound(X_374,X_375))
| least_upper_bound(X,greatest_lower_bound(X_375,X_374)) = least_upper_bound(X,greatest_lower_bound(X_374,X_375)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,greatest_lower_bound(X_375,X_374)),least_upper_bound(X,greatest_lower_bound(X_374,X_375))) ),[0],$fot(least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_375,X_374)),greatest_lower_bound(X_374,X_375)))]]) ).
cnf(refute_0_350,plain,
( least_upper_bound(X,greatest_lower_bound(X_375,X_374)) != least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_375,X_374)),greatest_lower_bound(X_374,X_375))
| least_upper_bound(X,greatest_lower_bound(X_375,X_374)) = least_upper_bound(X,greatest_lower_bound(X_374,X_375)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_375,X_374)),greatest_lower_bound(X_374,X_375)),least_upper_bound(X,greatest_lower_bound(X_374,X_375))) )],[refute_0_348,refute_0_349]) ).
cnf(refute_0_351,plain,
least_upper_bound(X,greatest_lower_bound(X_375,X_374)) = least_upper_bound(X,greatest_lower_bound(X_374,X_375)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,greatest_lower_bound(X_375,X_374)),least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_375,X_374)),greatest_lower_bound(X_374,X_375))) )],[refute_0_82,refute_0_350]) ).
cnf(refute_0_352,plain,
( least_upper_bound(X,greatest_lower_bound(X_375,X_374)) != least_upper_bound(X,greatest_lower_bound(X_374,X_375))
| least_upper_bound(X,greatest_lower_bound(X_374,X_375)) = least_upper_bound(X,greatest_lower_bound(X_375,X_374)) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(least_upper_bound(X,greatest_lower_bound(X_375,X_374)))),bind(Y0,$fot(least_upper_bound(X,greatest_lower_bound(X_374,X_375))))]]) ).
cnf(refute_0_353,plain,
least_upper_bound(X,greatest_lower_bound(X_374,X_375)) = least_upper_bound(X,greatest_lower_bound(X_375,X_374)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,greatest_lower_bound(X_375,X_374)),least_upper_bound(X,greatest_lower_bound(X_374,X_375))) )],[refute_0_351,refute_0_352]) ).
cnf(refute_0_354,plain,
least_upper_bound(c,greatest_lower_bound(b,a)) = least_upper_bound(c,greatest_lower_bound(a,b)),
inference(subst,[],[refute_0_353:[bind(X,$fot(c)),bind(X_374,$fot(b)),bind(X_375,$fot(a))]]) ).
cnf(refute_0_355,plain,
least_upper_bound(X_32,c) = least_upper_bound(c,X_32),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_32)),bind(Y,$fot(c))]]) ).
cnf(refute_0_356,plain,
least_upper_bound(greatest_lower_bound(b,a),c) = least_upper_bound(c,greatest_lower_bound(b,a)),
inference(subst,[],[refute_0_355:[bind(X_32,$fot(greatest_lower_bound(b,a)))]]) ).
cnf(refute_0_357,plain,
( least_upper_bound(c,greatest_lower_bound(b,a)) != least_upper_bound(c,greatest_lower_bound(a,b))
| least_upper_bound(greatest_lower_bound(b,a),c) != least_upper_bound(c,greatest_lower_bound(b,a))
| least_upper_bound(greatest_lower_bound(b,a),c) = least_upper_bound(c,greatest_lower_bound(a,b)) ),
inference(subst,[],[refute_0_120:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(b,a),c))),bind(Y0,$fot(least_upper_bound(c,greatest_lower_bound(b,a)))),bind(Z0,$fot(least_upper_bound(c,greatest_lower_bound(a,b))))]]) ).
cnf(refute_0_358,plain,
( least_upper_bound(c,greatest_lower_bound(b,a)) != least_upper_bound(c,greatest_lower_bound(a,b))
| least_upper_bound(greatest_lower_bound(b,a),c) = least_upper_bound(c,greatest_lower_bound(a,b)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(b,a),c),least_upper_bound(c,greatest_lower_bound(b,a))) )],[refute_0_356,refute_0_357]) ).
cnf(refute_0_359,plain,
least_upper_bound(greatest_lower_bound(b,a),c) = least_upper_bound(c,greatest_lower_bound(a,b)),
inference(resolve,[$cnf( $equal(least_upper_bound(c,greatest_lower_bound(b,a)),least_upper_bound(c,greatest_lower_bound(a,b))) )],[refute_0_354,refute_0_358]) ).
cnf(refute_0_360,plain,
( least_upper_bound(greatest_lower_bound(b,a),c) != greatest_lower_bound(b,a)
| least_upper_bound(greatest_lower_bound(b,a),c) != least_upper_bound(c,greatest_lower_bound(a,b))
| least_upper_bound(c,greatest_lower_bound(a,b)) = greatest_lower_bound(b,a) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(b,a),c),greatest_lower_bound(b,a)) ),[0],$fot(least_upper_bound(c,greatest_lower_bound(a,b)))]]) ).
cnf(refute_0_361,plain,
( least_upper_bound(greatest_lower_bound(b,a),c) != greatest_lower_bound(b,a)
| least_upper_bound(c,greatest_lower_bound(a,b)) = greatest_lower_bound(b,a) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(b,a),c),least_upper_bound(c,greatest_lower_bound(a,b))) )],[refute_0_359,refute_0_360]) ).
cnf(refute_0_362,plain,
greatest_lower_bound(X_54,X_55) = multiply(inverse(inverse(X_55)),multiply(inverse(X_55),greatest_lower_bound(X_54,X_55))),
inference(subst,[],[refute_0_158:[bind(X_96,$fot(inverse(X_55))),bind(X_97,$fot(greatest_lower_bound(X_54,X_55)))]]) ).
cnf(refute_0_363,plain,
multiply(inverse(X_55),greatest_lower_bound(X_54,X_55)) = greatest_lower_bound(multiply(inverse(X_55),X_54),multiply(inverse(X_55),X_55)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(inverse(X_55))),bind(Y,$fot(X_54)),bind(Z,$fot(X_55))]]) ).
cnf(refute_0_364,plain,
multiply(inverse(X_55),X_55) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_55))]]) ).
cnf(refute_0_365,plain,
( multiply(inverse(X_55),X_55) != identity
| multiply(inverse(X_55),greatest_lower_bound(X_54,X_55)) != greatest_lower_bound(multiply(inverse(X_55),X_54),multiply(inverse(X_55),X_55))
| multiply(inverse(X_55),greatest_lower_bound(X_54,X_55)) = greatest_lower_bound(multiply(inverse(X_55),X_54),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_55),greatest_lower_bound(X_54,X_55)),greatest_lower_bound(multiply(inverse(X_55),X_54),multiply(inverse(X_55),X_55))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_366,plain,
( multiply(inverse(X_55),greatest_lower_bound(X_54,X_55)) != greatest_lower_bound(multiply(inverse(X_55),X_54),multiply(inverse(X_55),X_55))
| multiply(inverse(X_55),greatest_lower_bound(X_54,X_55)) = greatest_lower_bound(multiply(inverse(X_55),X_54),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_55),X_55),identity) )],[refute_0_364,refute_0_365]) ).
cnf(refute_0_367,plain,
multiply(inverse(X_55),greatest_lower_bound(X_54,X_55)) = greatest_lower_bound(multiply(inverse(X_55),X_54),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_55),greatest_lower_bound(X_54,X_55)),greatest_lower_bound(multiply(inverse(X_55),X_54),multiply(inverse(X_55),X_55))) )],[refute_0_363,refute_0_366]) ).
cnf(refute_0_368,plain,
greatest_lower_bound(multiply(inverse(X_55),X_54),identity) = greatest_lower_bound(identity,multiply(inverse(X_55),X_54)),
inference(subst,[],[refute_0_56:[bind(X,$fot(identity)),bind(Y,$fot(multiply(inverse(X_55),X_54)))]]) ).
cnf(refute_0_369,plain,
( multiply(inverse(X_55),greatest_lower_bound(X_54,X_55)) != greatest_lower_bound(multiply(inverse(X_55),X_54),identity)
| greatest_lower_bound(multiply(inverse(X_55),X_54),identity) != greatest_lower_bound(identity,multiply(inverse(X_55),X_54))
| multiply(inverse(X_55),greatest_lower_bound(X_54,X_55)) = greatest_lower_bound(identity,multiply(inverse(X_55),X_54)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_55),greatest_lower_bound(X_54,X_55)),greatest_lower_bound(identity,multiply(inverse(X_55),X_54))) ),[0],$fot(greatest_lower_bound(multiply(inverse(X_55),X_54),identity))]]) ).
cnf(refute_0_370,plain,
( multiply(inverse(X_55),greatest_lower_bound(X_54,X_55)) != greatest_lower_bound(multiply(inverse(X_55),X_54),identity)
| multiply(inverse(X_55),greatest_lower_bound(X_54,X_55)) = greatest_lower_bound(identity,multiply(inverse(X_55),X_54)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(inverse(X_55),X_54),identity),greatest_lower_bound(identity,multiply(inverse(X_55),X_54))) )],[refute_0_368,refute_0_369]) ).
cnf(refute_0_371,plain,
multiply(inverse(X_55),greatest_lower_bound(X_54,X_55)) = greatest_lower_bound(identity,multiply(inverse(X_55),X_54)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_55),greatest_lower_bound(X_54,X_55)),greatest_lower_bound(multiply(inverse(X_55),X_54),identity)) )],[refute_0_367,refute_0_370]) ).
cnf(refute_0_372,plain,
( multiply(inverse(X_55),greatest_lower_bound(X_54,X_55)) != greatest_lower_bound(identity,multiply(inverse(X_55),X_54))
| greatest_lower_bound(X_54,X_55) != multiply(inverse(inverse(X_55)),multiply(inverse(X_55),greatest_lower_bound(X_54,X_55)))
| greatest_lower_bound(X_54,X_55) = multiply(inverse(inverse(X_55)),greatest_lower_bound(identity,multiply(inverse(X_55),X_54))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_54,X_55),multiply(inverse(inverse(X_55)),multiply(inverse(X_55),greatest_lower_bound(X_54,X_55)))) ),[1,1],$fot(greatest_lower_bound(identity,multiply(inverse(X_55),X_54)))]]) ).
cnf(refute_0_373,plain,
( greatest_lower_bound(X_54,X_55) != multiply(inverse(inverse(X_55)),multiply(inverse(X_55),greatest_lower_bound(X_54,X_55)))
| greatest_lower_bound(X_54,X_55) = multiply(inverse(inverse(X_55)),greatest_lower_bound(identity,multiply(inverse(X_55),X_54))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_55),greatest_lower_bound(X_54,X_55)),greatest_lower_bound(identity,multiply(inverse(X_55),X_54))) )],[refute_0_371,refute_0_372]) ).
cnf(refute_0_374,plain,
greatest_lower_bound(X_54,X_55) = multiply(inverse(inverse(X_55)),greatest_lower_bound(identity,multiply(inverse(X_55),X_54))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_54,X_55),multiply(inverse(inverse(X_55)),multiply(inverse(X_55),greatest_lower_bound(X_54,X_55)))) )],[refute_0_362,refute_0_373]) ).
cnf(refute_0_375,plain,
greatest_lower_bound(X_54,X_55) = multiply(inverse(inverse(X_54)),multiply(inverse(X_54),greatest_lower_bound(X_54,X_55))),
inference(subst,[],[refute_0_158:[bind(X_96,$fot(inverse(X_54))),bind(X_97,$fot(greatest_lower_bound(X_54,X_55)))]]) ).
cnf(refute_0_376,plain,
multiply(inverse(X_54),greatest_lower_bound(X_54,X_55)) = greatest_lower_bound(multiply(inverse(X_54),X_54),multiply(inverse(X_54),X_55)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(inverse(X_54))),bind(Y,$fot(X_54)),bind(Z,$fot(X_55))]]) ).
cnf(refute_0_377,plain,
multiply(inverse(X_54),X_54) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_54))]]) ).
cnf(refute_0_378,plain,
( multiply(inverse(X_54),X_54) != identity
| multiply(inverse(X_54),greatest_lower_bound(X_54,X_55)) != greatest_lower_bound(multiply(inverse(X_54),X_54),multiply(inverse(X_54),X_55))
| multiply(inverse(X_54),greatest_lower_bound(X_54,X_55)) = greatest_lower_bound(identity,multiply(inverse(X_54),X_55)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_54),greatest_lower_bound(X_54,X_55)),greatest_lower_bound(multiply(inverse(X_54),X_54),multiply(inverse(X_54),X_55))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_379,plain,
( multiply(inverse(X_54),greatest_lower_bound(X_54,X_55)) != greatest_lower_bound(multiply(inverse(X_54),X_54),multiply(inverse(X_54),X_55))
| multiply(inverse(X_54),greatest_lower_bound(X_54,X_55)) = greatest_lower_bound(identity,multiply(inverse(X_54),X_55)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_54),X_54),identity) )],[refute_0_377,refute_0_378]) ).
cnf(refute_0_380,plain,
multiply(inverse(X_54),greatest_lower_bound(X_54,X_55)) = greatest_lower_bound(identity,multiply(inverse(X_54),X_55)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_54),greatest_lower_bound(X_54,X_55)),greatest_lower_bound(multiply(inverse(X_54),X_54),multiply(inverse(X_54),X_55))) )],[refute_0_376,refute_0_379]) ).
cnf(refute_0_381,plain,
( multiply(inverse(X_54),greatest_lower_bound(X_54,X_55)) != greatest_lower_bound(identity,multiply(inverse(X_54),X_55))
| greatest_lower_bound(X_54,X_55) != multiply(inverse(inverse(X_54)),multiply(inverse(X_54),greatest_lower_bound(X_54,X_55)))
| greatest_lower_bound(X_54,X_55) = multiply(inverse(inverse(X_54)),greatest_lower_bound(identity,multiply(inverse(X_54),X_55))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_54,X_55),multiply(inverse(inverse(X_54)),multiply(inverse(X_54),greatest_lower_bound(X_54,X_55)))) ),[1,1],$fot(greatest_lower_bound(identity,multiply(inverse(X_54),X_55)))]]) ).
cnf(refute_0_382,plain,
( greatest_lower_bound(X_54,X_55) != multiply(inverse(inverse(X_54)),multiply(inverse(X_54),greatest_lower_bound(X_54,X_55)))
| greatest_lower_bound(X_54,X_55) = multiply(inverse(inverse(X_54)),greatest_lower_bound(identity,multiply(inverse(X_54),X_55))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_54),greatest_lower_bound(X_54,X_55)),greatest_lower_bound(identity,multiply(inverse(X_54),X_55))) )],[refute_0_380,refute_0_381]) ).
cnf(refute_0_383,plain,
greatest_lower_bound(X_54,X_55) = multiply(inverse(inverse(X_54)),greatest_lower_bound(identity,multiply(inverse(X_54),X_55))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_54,X_55),multiply(inverse(inverse(X_54)),multiply(inverse(X_54),greatest_lower_bound(X_54,X_55)))) )],[refute_0_375,refute_0_382]) ).
cnf(refute_0_384,plain,
multiply(inverse(inverse(X_54)),identity) = multiply(X_54,identity),
inference(subst,[],[refute_0_290:[bind(X_98,$fot(X_54)),bind(X_99,$fot(identity))]]) ).
cnf(refute_0_385,plain,
greatest_lower_bound(multiply(inverse(inverse(X_54)),identity),X_55) = greatest_lower_bound(multiply(inverse(inverse(X_54)),identity),X_55),
introduced(tautology,[refl,[$fot(greatest_lower_bound(multiply(inverse(inverse(X_54)),identity),X_55))]]) ).
cnf(refute_0_386,plain,
( multiply(inverse(inverse(X_54)),identity) != multiply(X_54,identity)
| greatest_lower_bound(multiply(inverse(inverse(X_54)),identity),X_55) != greatest_lower_bound(multiply(inverse(inverse(X_54)),identity),X_55)
| greatest_lower_bound(multiply(inverse(inverse(X_54)),identity),X_55) = greatest_lower_bound(multiply(X_54,identity),X_55) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(inverse(inverse(X_54)),identity),X_55),greatest_lower_bound(multiply(inverse(inverse(X_54)),identity),X_55)) ),[1,0],$fot(multiply(X_54,identity))]]) ).
cnf(refute_0_387,plain,
( multiply(inverse(inverse(X_54)),identity) != multiply(X_54,identity)
| greatest_lower_bound(multiply(inverse(inverse(X_54)),identity),X_55) = greatest_lower_bound(multiply(X_54,identity),X_55) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(inverse(inverse(X_54)),identity),X_55),greatest_lower_bound(multiply(inverse(inverse(X_54)),identity),X_55)) )],[refute_0_385,refute_0_386]) ).
cnf(refute_0_388,plain,
greatest_lower_bound(multiply(inverse(inverse(X_54)),identity),X_55) = greatest_lower_bound(multiply(X_54,identity),X_55),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_54)),identity),multiply(X_54,identity)) )],[refute_0_384,refute_0_387]) ).
cnf(refute_0_389,plain,
multiply(inverse(X_98),greatest_lower_bound(Y,multiply(X_98,X_99))) = greatest_lower_bound(multiply(inverse(X_98),Y),multiply(inverse(X_98),multiply(X_98,X_99))),
inference(subst,[],[monotony_glb1:[bind(X,$fot(inverse(X_98))),bind(Z,$fot(multiply(X_98,X_99)))]]) ).
cnf(refute_0_390,plain,
( multiply(inverse(X_98),multiply(X_98,X_99)) != X_99
| multiply(inverse(X_98),greatest_lower_bound(Y,multiply(X_98,X_99))) != greatest_lower_bound(multiply(inverse(X_98),Y),multiply(inverse(X_98),multiply(X_98,X_99)))
| multiply(inverse(X_98),greatest_lower_bound(Y,multiply(X_98,X_99))) = greatest_lower_bound(multiply(inverse(X_98),Y),X_99) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_98),greatest_lower_bound(Y,multiply(X_98,X_99))),greatest_lower_bound(multiply(inverse(X_98),Y),multiply(inverse(X_98),multiply(X_98,X_99)))) ),[1,1],$fot(X_99)]]) ).
cnf(refute_0_391,plain,
( multiply(inverse(X_98),greatest_lower_bound(Y,multiply(X_98,X_99))) != greatest_lower_bound(multiply(inverse(X_98),Y),multiply(inverse(X_98),multiply(X_98,X_99)))
| multiply(inverse(X_98),greatest_lower_bound(Y,multiply(X_98,X_99))) = greatest_lower_bound(multiply(inverse(X_98),Y),X_99) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_98),multiply(X_98,X_99)),X_99) )],[refute_0_285,refute_0_390]) ).
cnf(refute_0_392,plain,
multiply(inverse(X_98),greatest_lower_bound(Y,multiply(X_98,X_99))) = greatest_lower_bound(multiply(inverse(X_98),Y),X_99),
inference(resolve,[$cnf( $equal(multiply(inverse(X_98),greatest_lower_bound(Y,multiply(X_98,X_99))),greatest_lower_bound(multiply(inverse(X_98),Y),multiply(inverse(X_98),multiply(X_98,X_99)))) )],[refute_0_389,refute_0_391]) ).
cnf(refute_0_393,plain,
multiply(inverse(inverse(X_54)),greatest_lower_bound(identity,multiply(inverse(X_54),X_55))) = greatest_lower_bound(multiply(inverse(inverse(X_54)),identity),X_55),
inference(subst,[],[refute_0_392:[bind(Y,$fot(identity)),bind(X_98,$fot(inverse(X_54))),bind(X_99,$fot(X_55))]]) ).
cnf(refute_0_394,plain,
( multiply(inverse(inverse(X_54)),greatest_lower_bound(identity,multiply(inverse(X_54),X_55))) != greatest_lower_bound(multiply(inverse(inverse(X_54)),identity),X_55)
| greatest_lower_bound(multiply(inverse(inverse(X_54)),identity),X_55) != greatest_lower_bound(multiply(X_54,identity),X_55)
| multiply(inverse(inverse(X_54)),greatest_lower_bound(identity,multiply(inverse(X_54),X_55))) = greatest_lower_bound(multiply(X_54,identity),X_55) ),
inference(subst,[],[refute_0_120:[bind(X0,$fot(multiply(inverse(inverse(X_54)),greatest_lower_bound(identity,multiply(inverse(X_54),X_55))))),bind(Y0,$fot(greatest_lower_bound(multiply(inverse(inverse(X_54)),identity),X_55))),bind(Z0,$fot(greatest_lower_bound(multiply(X_54,identity),X_55)))]]) ).
cnf(refute_0_395,plain,
( greatest_lower_bound(multiply(inverse(inverse(X_54)),identity),X_55) != greatest_lower_bound(multiply(X_54,identity),X_55)
| multiply(inverse(inverse(X_54)),greatest_lower_bound(identity,multiply(inverse(X_54),X_55))) = greatest_lower_bound(multiply(X_54,identity),X_55) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_54)),greatest_lower_bound(identity,multiply(inverse(X_54),X_55))),greatest_lower_bound(multiply(inverse(inverse(X_54)),identity),X_55)) )],[refute_0_393,refute_0_394]) ).
cnf(refute_0_396,plain,
multiply(inverse(inverse(X_54)),greatest_lower_bound(identity,multiply(inverse(X_54),X_55))) = greatest_lower_bound(multiply(X_54,identity),X_55),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(inverse(inverse(X_54)),identity),X_55),greatest_lower_bound(multiply(X_54,identity),X_55)) )],[refute_0_388,refute_0_395]) ).
cnf(refute_0_397,plain,
( multiply(inverse(inverse(X_54)),greatest_lower_bound(identity,multiply(inverse(X_54),X_55))) != greatest_lower_bound(multiply(X_54,identity),X_55)
| greatest_lower_bound(X_54,X_55) != multiply(inverse(inverse(X_54)),greatest_lower_bound(identity,multiply(inverse(X_54),X_55)))
| greatest_lower_bound(X_54,X_55) = greatest_lower_bound(multiply(X_54,identity),X_55) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_54,X_55),multiply(inverse(inverse(X_54)),greatest_lower_bound(identity,multiply(inverse(X_54),X_55)))) ),[1],$fot(greatest_lower_bound(multiply(X_54,identity),X_55))]]) ).
cnf(refute_0_398,plain,
( greatest_lower_bound(X_54,X_55) != multiply(inverse(inverse(X_54)),greatest_lower_bound(identity,multiply(inverse(X_54),X_55)))
| greatest_lower_bound(X_54,X_55) = greatest_lower_bound(multiply(X_54,identity),X_55) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_54)),greatest_lower_bound(identity,multiply(inverse(X_54),X_55))),greatest_lower_bound(multiply(X_54,identity),X_55)) )],[refute_0_396,refute_0_397]) ).
cnf(refute_0_399,plain,
greatest_lower_bound(X_54,X_55) = greatest_lower_bound(multiply(X_54,identity),X_55),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_54,X_55),multiply(inverse(inverse(X_54)),greatest_lower_bound(identity,multiply(inverse(X_54),X_55)))) )],[refute_0_383,refute_0_398]) ).
cnf(refute_0_400,plain,
( greatest_lower_bound(X_54,X_55) != greatest_lower_bound(multiply(X_54,identity),X_55)
| greatest_lower_bound(multiply(X_54,identity),X_55) = greatest_lower_bound(X_54,X_55) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(greatest_lower_bound(X_54,X_55))),bind(Y0,$fot(greatest_lower_bound(multiply(X_54,identity),X_55)))]]) ).
cnf(refute_0_401,plain,
greatest_lower_bound(multiply(X_54,identity),X_55) = greatest_lower_bound(X_54,X_55),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_54,X_55),greatest_lower_bound(multiply(X_54,identity),X_55)) )],[refute_0_399,refute_0_400]) ).
cnf(refute_0_402,plain,
greatest_lower_bound(multiply(inverse(inverse(X_55)),identity),X_54) = greatest_lower_bound(inverse(inverse(X_55)),X_54),
inference(subst,[],[refute_0_401:[bind(X_54,$fot(inverse(inverse(X_55)))),bind(X_55,$fot(X_54))]]) ).
cnf(refute_0_403,plain,
multiply(inverse(inverse(X_55)),greatest_lower_bound(identity,multiply(inverse(X_55),X_54))) = greatest_lower_bound(multiply(inverse(inverse(X_55)),identity),X_54),
inference(subst,[],[refute_0_392:[bind(Y,$fot(identity)),bind(X_98,$fot(inverse(X_55))),bind(X_99,$fot(X_54))]]) ).
cnf(refute_0_404,plain,
( multiply(inverse(inverse(X_55)),greatest_lower_bound(identity,multiply(inverse(X_55),X_54))) != greatest_lower_bound(multiply(inverse(inverse(X_55)),identity),X_54)
| greatest_lower_bound(multiply(inverse(inverse(X_55)),identity),X_54) != greatest_lower_bound(inverse(inverse(X_55)),X_54)
| multiply(inverse(inverse(X_55)),greatest_lower_bound(identity,multiply(inverse(X_55),X_54))) = greatest_lower_bound(inverse(inverse(X_55)),X_54) ),
inference(subst,[],[refute_0_120:[bind(X0,$fot(multiply(inverse(inverse(X_55)),greatest_lower_bound(identity,multiply(inverse(X_55),X_54))))),bind(Y0,$fot(greatest_lower_bound(multiply(inverse(inverse(X_55)),identity),X_54))),bind(Z0,$fot(greatest_lower_bound(inverse(inverse(X_55)),X_54)))]]) ).
cnf(refute_0_405,plain,
( greatest_lower_bound(multiply(inverse(inverse(X_55)),identity),X_54) != greatest_lower_bound(inverse(inverse(X_55)),X_54)
| multiply(inverse(inverse(X_55)),greatest_lower_bound(identity,multiply(inverse(X_55),X_54))) = greatest_lower_bound(inverse(inverse(X_55)),X_54) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_55)),greatest_lower_bound(identity,multiply(inverse(X_55),X_54))),greatest_lower_bound(multiply(inverse(inverse(X_55)),identity),X_54)) )],[refute_0_403,refute_0_404]) ).
cnf(refute_0_406,plain,
multiply(inverse(inverse(X_55)),greatest_lower_bound(identity,multiply(inverse(X_55),X_54))) = greatest_lower_bound(inverse(inverse(X_55)),X_54),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(inverse(inverse(X_55)),identity),X_54),greatest_lower_bound(inverse(inverse(X_55)),X_54)) )],[refute_0_402,refute_0_405]) ).
cnf(refute_0_407,plain,
( multiply(inverse(inverse(X_55)),greatest_lower_bound(identity,multiply(inverse(X_55),X_54))) != greatest_lower_bound(inverse(inverse(X_55)),X_54)
| greatest_lower_bound(X_54,X_55) != multiply(inverse(inverse(X_55)),greatest_lower_bound(identity,multiply(inverse(X_55),X_54)))
| greatest_lower_bound(X_54,X_55) = greatest_lower_bound(inverse(inverse(X_55)),X_54) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_54,X_55),multiply(inverse(inverse(X_55)),greatest_lower_bound(identity,multiply(inverse(X_55),X_54)))) ),[1],$fot(greatest_lower_bound(inverse(inverse(X_55)),X_54))]]) ).
cnf(refute_0_408,plain,
( greatest_lower_bound(X_54,X_55) != multiply(inverse(inverse(X_55)),greatest_lower_bound(identity,multiply(inverse(X_55),X_54)))
| greatest_lower_bound(X_54,X_55) = greatest_lower_bound(inverse(inverse(X_55)),X_54) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_55)),greatest_lower_bound(identity,multiply(inverse(X_55),X_54))),greatest_lower_bound(inverse(inverse(X_55)),X_54)) )],[refute_0_406,refute_0_407]) ).
cnf(refute_0_409,plain,
greatest_lower_bound(X_54,X_55) = greatest_lower_bound(inverse(inverse(X_55)),X_54),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_54,X_55),multiply(inverse(inverse(X_55)),greatest_lower_bound(identity,multiply(inverse(X_55),X_54)))) )],[refute_0_374,refute_0_408]) ).
cnf(refute_0_410,plain,
greatest_lower_bound(inverse(inverse(X_102)),inverse(inverse(X_102))) = inverse(inverse(X_102)),
inference(subst,[],[idempotence_of_gld:[bind(X,$fot(inverse(inverse(X_102))))]]) ).
cnf(refute_0_411,plain,
greatest_lower_bound(inverse(inverse(X_102)),X_102) = greatest_lower_bound(inverse(inverse(X_102)),inverse(inverse(X_102))),
inference(subst,[],[refute_0_409:[bind(X_54,$fot(inverse(inverse(X_102)))),bind(X_55,$fot(X_102))]]) ).
cnf(refute_0_412,plain,
( greatest_lower_bound(inverse(inverse(X_102)),X_102) != greatest_lower_bound(inverse(inverse(X_102)),inverse(inverse(X_102)))
| greatest_lower_bound(inverse(inverse(X_102)),inverse(inverse(X_102))) = greatest_lower_bound(inverse(inverse(X_102)),X_102) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(greatest_lower_bound(inverse(inverse(X_102)),X_102))),bind(Y0,$fot(greatest_lower_bound(inverse(inverse(X_102)),inverse(inverse(X_102)))))]]) ).
cnf(refute_0_413,plain,
greatest_lower_bound(inverse(inverse(X_102)),inverse(inverse(X_102))) = greatest_lower_bound(inverse(inverse(X_102)),X_102),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(inverse(X_102)),X_102),greatest_lower_bound(inverse(inverse(X_102)),inverse(inverse(X_102)))) )],[refute_0_411,refute_0_412]) ).
cnf(refute_0_414,plain,
( greatest_lower_bound(inverse(inverse(X_102)),inverse(inverse(X_102))) != greatest_lower_bound(inverse(inverse(X_102)),X_102)
| greatest_lower_bound(inverse(inverse(X_102)),inverse(inverse(X_102))) != inverse(inverse(X_102))
| greatest_lower_bound(inverse(inverse(X_102)),X_102) = inverse(inverse(X_102)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(inverse(inverse(X_102)),inverse(inverse(X_102))),inverse(inverse(X_102))) ),[0],$fot(greatest_lower_bound(inverse(inverse(X_102)),X_102))]]) ).
cnf(refute_0_415,plain,
( greatest_lower_bound(inverse(inverse(X_102)),inverse(inverse(X_102))) != inverse(inverse(X_102))
| greatest_lower_bound(inverse(inverse(X_102)),X_102) = inverse(inverse(X_102)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(inverse(X_102)),inverse(inverse(X_102))),greatest_lower_bound(inverse(inverse(X_102)),X_102)) )],[refute_0_413,refute_0_414]) ).
cnf(refute_0_416,plain,
greatest_lower_bound(inverse(inverse(X_102)),X_102) = inverse(inverse(X_102)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(inverse(X_102)),inverse(inverse(X_102))),inverse(inverse(X_102))) )],[refute_0_410,refute_0_415]) ).
cnf(refute_0_417,plain,
greatest_lower_bound(X_102,X_102) = X_102,
inference(subst,[],[idempotence_of_gld:[bind(X,$fot(X_102))]]) ).
cnf(refute_0_418,plain,
( greatest_lower_bound(X_54,X_55) != greatest_lower_bound(inverse(inverse(X_55)),X_54)
| greatest_lower_bound(inverse(inverse(X_55)),X_54) = greatest_lower_bound(X_54,X_55) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(greatest_lower_bound(X_54,X_55))),bind(Y0,$fot(greatest_lower_bound(inverse(inverse(X_55)),X_54)))]]) ).
cnf(refute_0_419,plain,
greatest_lower_bound(inverse(inverse(X_55)),X_54) = greatest_lower_bound(X_54,X_55),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_54,X_55),greatest_lower_bound(inverse(inverse(X_55)),X_54)) )],[refute_0_409,refute_0_418]) ).
cnf(refute_0_420,plain,
greatest_lower_bound(inverse(inverse(X_102)),X_102) = greatest_lower_bound(X_102,X_102),
inference(subst,[],[refute_0_419:[bind(X_54,$fot(X_102)),bind(X_55,$fot(X_102))]]) ).
cnf(refute_0_421,plain,
( greatest_lower_bound(X_102,X_102) != X_102
| greatest_lower_bound(inverse(inverse(X_102)),X_102) != greatest_lower_bound(X_102,X_102)
| greatest_lower_bound(inverse(inverse(X_102)),X_102) = X_102 ),
inference(subst,[],[refute_0_120:[bind(X0,$fot(greatest_lower_bound(inverse(inverse(X_102)),X_102))),bind(Y0,$fot(greatest_lower_bound(X_102,X_102))),bind(Z0,$fot(X_102))]]) ).
cnf(refute_0_422,plain,
( greatest_lower_bound(X_102,X_102) != X_102
| greatest_lower_bound(inverse(inverse(X_102)),X_102) = X_102 ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(inverse(X_102)),X_102),greatest_lower_bound(X_102,X_102)) )],[refute_0_420,refute_0_421]) ).
cnf(refute_0_423,plain,
greatest_lower_bound(inverse(inverse(X_102)),X_102) = X_102,
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_102,X_102),X_102) )],[refute_0_417,refute_0_422]) ).
cnf(refute_0_424,plain,
( greatest_lower_bound(inverse(inverse(X_102)),X_102) != X_102
| greatest_lower_bound(inverse(inverse(X_102)),X_102) != inverse(inverse(X_102))
| X_102 = inverse(inverse(X_102)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(inverse(inverse(X_102)),X_102),inverse(inverse(X_102))) ),[0],$fot(X_102)]]) ).
cnf(refute_0_425,plain,
( greatest_lower_bound(inverse(inverse(X_102)),X_102) != inverse(inverse(X_102))
| X_102 = inverse(inverse(X_102)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(inverse(X_102)),X_102),X_102) )],[refute_0_423,refute_0_424]) ).
cnf(refute_0_426,plain,
X_102 = inverse(inverse(X_102)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(inverse(X_102)),X_102),inverse(inverse(X_102))) )],[refute_0_416,refute_0_425]) ).
cnf(refute_0_427,plain,
( X_102 != inverse(inverse(X_102))
| inverse(inverse(X_102)) = X_102 ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(X_102)),bind(Y0,$fot(inverse(inverse(X_102))))]]) ).
cnf(refute_0_428,plain,
inverse(inverse(X_102)) = X_102,
inference(resolve,[$cnf( $equal(X_102,inverse(inverse(X_102))) )],[refute_0_426,refute_0_427]) ).
cnf(refute_0_429,plain,
inverse(inverse(X_55)) = X_55,
inference(subst,[],[refute_0_428:[bind(X_102,$fot(X_55))]]) ).
cnf(refute_0_430,plain,
greatest_lower_bound(inverse(inverse(X_55)),X_54) = greatest_lower_bound(inverse(inverse(X_55)),X_54),
introduced(tautology,[refl,[$fot(greatest_lower_bound(inverse(inverse(X_55)),X_54))]]) ).
cnf(refute_0_431,plain,
( greatest_lower_bound(inverse(inverse(X_55)),X_54) != greatest_lower_bound(inverse(inverse(X_55)),X_54)
| inverse(inverse(X_55)) != X_55
| greatest_lower_bound(inverse(inverse(X_55)),X_54) = greatest_lower_bound(X_55,X_54) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(inverse(inverse(X_55)),X_54),greatest_lower_bound(inverse(inverse(X_55)),X_54)) ),[1,0],$fot(X_55)]]) ).
cnf(refute_0_432,plain,
( inverse(inverse(X_55)) != X_55
| greatest_lower_bound(inverse(inverse(X_55)),X_54) = greatest_lower_bound(X_55,X_54) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(inverse(X_55)),X_54),greatest_lower_bound(inverse(inverse(X_55)),X_54)) )],[refute_0_430,refute_0_431]) ).
cnf(refute_0_433,plain,
greatest_lower_bound(inverse(inverse(X_55)),X_54) = greatest_lower_bound(X_55,X_54),
inference(resolve,[$cnf( $equal(inverse(inverse(X_55)),X_55) )],[refute_0_429,refute_0_432]) ).
cnf(refute_0_434,plain,
( greatest_lower_bound(X_54,X_55) != greatest_lower_bound(inverse(inverse(X_55)),X_54)
| greatest_lower_bound(inverse(inverse(X_55)),X_54) != greatest_lower_bound(X_55,X_54)
| greatest_lower_bound(X_54,X_55) = greatest_lower_bound(X_55,X_54) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_54,X_55),greatest_lower_bound(X_55,X_54)) ),[0],$fot(greatest_lower_bound(inverse(inverse(X_55)),X_54))]]) ).
cnf(refute_0_435,plain,
( greatest_lower_bound(X_54,X_55) != greatest_lower_bound(inverse(inverse(X_55)),X_54)
| greatest_lower_bound(X_54,X_55) = greatest_lower_bound(X_55,X_54) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(inverse(X_55)),X_54),greatest_lower_bound(X_55,X_54)) )],[refute_0_433,refute_0_434]) ).
cnf(refute_0_436,plain,
greatest_lower_bound(X_54,X_55) = greatest_lower_bound(X_55,X_54),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_54,X_55),greatest_lower_bound(inverse(inverse(X_55)),X_54)) )],[refute_0_409,refute_0_435]) ).
cnf(refute_0_437,plain,
( greatest_lower_bound(X_54,X_55) != greatest_lower_bound(X_55,X_54)
| greatest_lower_bound(X_55,X_54) = greatest_lower_bound(X_54,X_55) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(greatest_lower_bound(X_54,X_55))),bind(Y0,$fot(greatest_lower_bound(X_55,X_54)))]]) ).
cnf(refute_0_438,plain,
greatest_lower_bound(X_55,X_54) = greatest_lower_bound(X_54,X_55),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_54,X_55),greatest_lower_bound(X_55,X_54)) )],[refute_0_436,refute_0_437]) ).
cnf(refute_0_439,plain,
greatest_lower_bound(b,a) = greatest_lower_bound(a,b),
inference(subst,[],[refute_0_438:[bind(X_54,$fot(a)),bind(X_55,$fot(b))]]) ).
cnf(refute_0_440,plain,
( greatest_lower_bound(b,a) != greatest_lower_bound(a,b)
| least_upper_bound(c,greatest_lower_bound(a,b)) != greatest_lower_bound(b,a)
| least_upper_bound(c,greatest_lower_bound(a,b)) = greatest_lower_bound(a,b) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(c,greatest_lower_bound(a,b)),greatest_lower_bound(b,a)) ),[1],$fot(greatest_lower_bound(a,b))]]) ).
cnf(refute_0_441,plain,
( least_upper_bound(c,greatest_lower_bound(a,b)) != greatest_lower_bound(b,a)
| least_upper_bound(c,greatest_lower_bound(a,b)) = greatest_lower_bound(a,b) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,a),greatest_lower_bound(a,b)) )],[refute_0_439,refute_0_440]) ).
cnf(refute_0_442,plain,
( least_upper_bound(greatest_lower_bound(b,a),c) != greatest_lower_bound(b,a)
| least_upper_bound(c,greatest_lower_bound(a,b)) = greatest_lower_bound(a,b) ),
inference(resolve,[$cnf( $equal(least_upper_bound(c,greatest_lower_bound(a,b)),greatest_lower_bound(b,a)) )],[refute_0_361,refute_0_441]) ).
cnf(refute_0_443,plain,
least_upper_bound(c,greatest_lower_bound(a,b)) = greatest_lower_bound(a,b),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(b,a),c),greatest_lower_bound(b,a)) )],[refute_0_63,refute_0_442]) ).
cnf(refute_0_444,plain,
least_upper_bound(greatest_lower_bound(a,b),c) = least_upper_bound(c,greatest_lower_bound(a,b)),
inference(subst,[],[refute_0_191:[bind(X,$fot(c)),bind(Y,$fot(greatest_lower_bound(a,b)))]]) ).
cnf(refute_0_445,plain,
( least_upper_bound(c,greatest_lower_bound(a,b)) != greatest_lower_bound(a,b)
| least_upper_bound(greatest_lower_bound(a,b),c) != least_upper_bound(c,greatest_lower_bound(a,b))
| least_upper_bound(greatest_lower_bound(a,b),c) = greatest_lower_bound(a,b) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,b),c),least_upper_bound(c,greatest_lower_bound(a,b))) ),[1],$fot(greatest_lower_bound(a,b))]]) ).
cnf(refute_0_446,plain,
( least_upper_bound(c,greatest_lower_bound(a,b)) != greatest_lower_bound(a,b)
| least_upper_bound(greatest_lower_bound(a,b),c) = greatest_lower_bound(a,b) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,b),c),least_upper_bound(c,greatest_lower_bound(a,b))) )],[refute_0_444,refute_0_445]) ).
cnf(refute_0_447,plain,
least_upper_bound(c,greatest_lower_bound(a,b)) != greatest_lower_bound(a,b),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,b),c),greatest_lower_bound(a,b)) )],[refute_0_446,prove_ax_glb1a]) ).
cnf(refute_0_448,plain,
$false,
inference(resolve,[$cnf( $equal(least_upper_bound(c,greatest_lower_bound(a,b)),greatest_lower_bound(a,b)) )],[refute_0_443,refute_0_447]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP138-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 21:05:51 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 10.47/10.65 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.47/10.65
% 10.47/10.65 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 10.51/10.71
%------------------------------------------------------------------------------