TSTP Solution File: GRP181-4 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP181-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 10:37:40 EDT 2022
% Result : Unsatisfiable 19.04s 19.30s
% Output : CNFRefutation 19.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 69
% Syntax : Number of clauses : 277 ( 148 unt; 0 nHn; 157 RR)
% Number of literals : 461 ( 460 equ; 185 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 : 380 ( 0 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(monotony_lub1,axiom,
multiply(X,least_upper_bound(Y,Z)) = least_upper_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(monotony_glb2,axiom,
multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) ).
cnf(p12x_1,hypothesis,
inverse(identity) = identity ).
cnf(p12x_2,hypothesis,
inverse(inverse(X)) = X ).
cnf(p12x_3,hypothesis,
inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) ).
cnf(p12x_4,hypothesis,
greatest_lower_bound(a,c) = greatest_lower_bound(b,c) ).
cnf(p12x_5,hypothesis,
least_upper_bound(a,c) = least_upper_bound(b,c) ).
cnf(p12x_6,hypothesis,
inverse(greatest_lower_bound(X,Y)) = least_upper_bound(inverse(X),inverse(Y)) ).
cnf(p12x_7,hypothesis,
inverse(least_upper_bound(X,Y)) = greatest_lower_bound(inverse(X),inverse(Y)) ).
cnf(prove_p12x,negated_conjecture,
a != b ).
cnf(refute_0_0,plain,
inverse(inverse(b)) = b,
inference(subst,[],[p12x_2:[bind(X,$fot(b))]]) ).
cnf(refute_0_1,plain,
multiply(multiply(inverse(X_153),X_153),X_154) = multiply(inverse(X_153),multiply(X_153,X_154)),
inference(subst,[],[associativity:[bind(X,$fot(inverse(X_153))),bind(Y,$fot(X_153)),bind(Z,$fot(X_154))]]) ).
cnf(refute_0_2,plain,
multiply(inverse(X_153),X_153) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_153))]]) ).
cnf(refute_0_3,plain,
( multiply(multiply(inverse(X_153),X_153),X_154) != multiply(inverse(X_153),multiply(X_153,X_154))
| multiply(inverse(X_153),X_153) != identity
| multiply(identity,X_154) = multiply(inverse(X_153),multiply(X_153,X_154)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_153),X_153),X_154),multiply(inverse(X_153),multiply(X_153,X_154))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_4,plain,
( multiply(multiply(inverse(X_153),X_153),X_154) != multiply(inverse(X_153),multiply(X_153,X_154))
| multiply(identity,X_154) = multiply(inverse(X_153),multiply(X_153,X_154)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_153),X_153),identity) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
multiply(identity,X_154) = multiply(inverse(X_153),multiply(X_153,X_154)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_153),X_153),X_154),multiply(inverse(X_153),multiply(X_153,X_154))) )],[refute_0_1,refute_0_4]) ).
cnf(refute_0_6,plain,
multiply(identity,X_154) = X_154,
inference(subst,[],[left_identity:[bind(X,$fot(X_154))]]) ).
cnf(refute_0_7,plain,
( multiply(identity,X_154) != X_154
| multiply(identity,X_154) != multiply(inverse(X_153),multiply(X_153,X_154))
| X_154 = multiply(inverse(X_153),multiply(X_153,X_154)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_154),multiply(inverse(X_153),multiply(X_153,X_154))) ),[0],$fot(X_154)]]) ).
cnf(refute_0_8,plain,
( multiply(identity,X_154) != multiply(inverse(X_153),multiply(X_153,X_154))
| X_154 = multiply(inverse(X_153),multiply(X_153,X_154)) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_154),X_154) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
X_154 = multiply(inverse(X_153),multiply(X_153,X_154)),
inference(resolve,[$cnf( $equal(multiply(identity,X_154),multiply(inverse(X_153),multiply(X_153,X_154))) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
inverse(X) = multiply(inverse(inverse(Y)),multiply(inverse(Y),inverse(X))),
inference(subst,[],[refute_0_9:[bind(X_153,$fot(inverse(Y))),bind(X_154,$fot(inverse(X)))]]) ).
cnf(refute_0_11,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_12,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_13,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( inverse(multiply(X,Y)) != multiply(inverse(Y),inverse(X))
| multiply(inverse(Y),inverse(X)) = inverse(multiply(X,Y)) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(inverse(multiply(X,Y)))),bind(Y0,$fot(multiply(inverse(Y),inverse(X))))]]) ).
cnf(refute_0_15,plain,
multiply(inverse(Y),inverse(X)) = inverse(multiply(X,Y)),
inference(resolve,[$cnf( $equal(inverse(multiply(X,Y)),multiply(inverse(Y),inverse(X))) )],[p12x_3,refute_0_14]) ).
cnf(refute_0_16,plain,
( multiply(inverse(Y),inverse(X)) != inverse(multiply(X,Y))
| inverse(X) != multiply(inverse(inverse(Y)),multiply(inverse(Y),inverse(X)))
| inverse(X) = multiply(inverse(inverse(Y)),inverse(multiply(X,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(X),multiply(inverse(inverse(Y)),multiply(inverse(Y),inverse(X)))) ),[1,1],$fot(inverse(multiply(X,Y)))]]) ).
cnf(refute_0_17,plain,
( inverse(X) != multiply(inverse(inverse(Y)),multiply(inverse(Y),inverse(X)))
| inverse(X) = multiply(inverse(inverse(Y)),inverse(multiply(X,Y))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(Y),inverse(X)),inverse(multiply(X,Y))) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
inverse(X) = multiply(inverse(inverse(Y)),inverse(multiply(X,Y))),
inference(resolve,[$cnf( $equal(inverse(X),multiply(inverse(inverse(Y)),multiply(inverse(Y),inverse(X)))) )],[refute_0_10,refute_0_17]) ).
cnf(refute_0_19,plain,
inverse(multiply(X_14,inverse(X))) = multiply(inverse(inverse(X)),inverse(X_14)),
inference(subst,[],[p12x_3:[bind(X,$fot(X_14)),bind(Y,$fot(inverse(X)))]]) ).
cnf(refute_0_20,plain,
( inverse(multiply(X_14,inverse(X))) != multiply(inverse(inverse(X)),inverse(X_14))
| inverse(inverse(X)) != X
| inverse(multiply(X_14,inverse(X))) = multiply(X,inverse(X_14)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_14,inverse(X))),multiply(inverse(inverse(X)),inverse(X_14))) ),[1,0],$fot(X)]]) ).
cnf(refute_0_21,plain,
( inverse(multiply(X_14,inverse(X))) != multiply(inverse(inverse(X)),inverse(X_14))
| inverse(multiply(X_14,inverse(X))) = multiply(X,inverse(X_14)) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p12x_2,refute_0_20]) ).
cnf(refute_0_22,plain,
inverse(multiply(X_14,inverse(X))) = multiply(X,inverse(X_14)),
inference(resolve,[$cnf( $equal(inverse(multiply(X_14,inverse(X))),multiply(inverse(inverse(X)),inverse(X_14))) )],[refute_0_19,refute_0_21]) ).
cnf(refute_0_23,plain,
inverse(multiply(multiply(X,Y),inverse(Y))) = multiply(Y,inverse(multiply(X,Y))),
inference(subst,[],[refute_0_22:[bind(X,$fot(Y)),bind(X_14,$fot(multiply(X,Y)))]]) ).
cnf(refute_0_24,plain,
multiply(inverse(inverse(Y)),inverse(multiply(X,Y))) = inverse(multiply(multiply(X,Y),inverse(Y))),
inference(subst,[],[refute_0_15:[bind(X,$fot(multiply(X,Y))),bind(Y,$fot(inverse(Y)))]]) ).
cnf(refute_0_25,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_26,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_13,refute_0_25]) ).
cnf(refute_0_27,plain,
( multiply(inverse(inverse(Y)),inverse(multiply(X,Y))) != inverse(multiply(multiply(X,Y),inverse(Y)))
| inverse(multiply(multiply(X,Y),inverse(Y))) != multiply(Y,inverse(multiply(X,Y)))
| multiply(inverse(inverse(Y)),inverse(multiply(X,Y))) = multiply(Y,inverse(multiply(X,Y))) ),
inference(subst,[],[refute_0_26:[bind(X0,$fot(multiply(inverse(inverse(Y)),inverse(multiply(X,Y))))),bind(Y0,$fot(inverse(multiply(multiply(X,Y),inverse(Y))))),bind(Z0,$fot(multiply(Y,inverse(multiply(X,Y)))))]]) ).
cnf(refute_0_28,plain,
( inverse(multiply(multiply(X,Y),inverse(Y))) != multiply(Y,inverse(multiply(X,Y)))
| multiply(inverse(inverse(Y)),inverse(multiply(X,Y))) = multiply(Y,inverse(multiply(X,Y))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(Y)),inverse(multiply(X,Y))),inverse(multiply(multiply(X,Y),inverse(Y)))) )],[refute_0_24,refute_0_27]) ).
cnf(refute_0_29,plain,
multiply(inverse(inverse(Y)),inverse(multiply(X,Y))) = multiply(Y,inverse(multiply(X,Y))),
inference(resolve,[$cnf( $equal(inverse(multiply(multiply(X,Y),inverse(Y))),multiply(Y,inverse(multiply(X,Y)))) )],[refute_0_23,refute_0_28]) ).
cnf(refute_0_30,plain,
( multiply(inverse(inverse(Y)),inverse(multiply(X,Y))) != multiply(Y,inverse(multiply(X,Y)))
| inverse(X) != multiply(inverse(inverse(Y)),inverse(multiply(X,Y)))
| inverse(X) = multiply(Y,inverse(multiply(X,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(X),multiply(inverse(inverse(Y)),inverse(multiply(X,Y)))) ),[1],$fot(multiply(Y,inverse(multiply(X,Y))))]]) ).
cnf(refute_0_31,plain,
( inverse(X) != multiply(inverse(inverse(Y)),inverse(multiply(X,Y)))
| inverse(X) = multiply(Y,inverse(multiply(X,Y))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(Y)),inverse(multiply(X,Y))),multiply(Y,inverse(multiply(X,Y)))) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
inverse(X) = multiply(Y,inverse(multiply(X,Y))),
inference(resolve,[$cnf( $equal(inverse(X),multiply(inverse(inverse(Y)),inverse(multiply(X,Y)))) )],[refute_0_18,refute_0_31]) ).
cnf(refute_0_33,plain,
inverse(b) = multiply(inverse(greatest_lower_bound(a,c)),inverse(multiply(b,inverse(greatest_lower_bound(a,c))))),
inference(subst,[],[refute_0_32:[bind(X,$fot(b)),bind(Y,$fot(inverse(greatest_lower_bound(a,c))))]]) ).
cnf(refute_0_34,plain,
multiply(least_upper_bound(X_92,inverse(X_91)),X_91) = least_upper_bound(multiply(X_92,X_91),multiply(inverse(X_91),X_91)),
inference(subst,[],[monotony_lub2:[bind(X,$fot(X_91)),bind(Y,$fot(X_92)),bind(Z,$fot(inverse(X_91)))]]) ).
cnf(refute_0_35,plain,
multiply(inverse(X_91),X_91) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_91))]]) ).
cnf(refute_0_36,plain,
( multiply(inverse(X_91),X_91) != identity
| multiply(least_upper_bound(X_92,inverse(X_91)),X_91) != least_upper_bound(multiply(X_92,X_91),multiply(inverse(X_91),X_91))
| multiply(least_upper_bound(X_92,inverse(X_91)),X_91) = least_upper_bound(multiply(X_92,X_91),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_92,inverse(X_91)),X_91),least_upper_bound(multiply(X_92,X_91),multiply(inverse(X_91),X_91))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_37,plain,
( multiply(least_upper_bound(X_92,inverse(X_91)),X_91) != least_upper_bound(multiply(X_92,X_91),multiply(inverse(X_91),X_91))
| multiply(least_upper_bound(X_92,inverse(X_91)),X_91) = least_upper_bound(multiply(X_92,X_91),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_91),X_91),identity) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
multiply(least_upper_bound(X_92,inverse(X_91)),X_91) = least_upper_bound(multiply(X_92,X_91),identity),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_92,inverse(X_91)),X_91),least_upper_bound(multiply(X_92,X_91),multiply(inverse(X_91),X_91))) )],[refute_0_34,refute_0_37]) ).
cnf(refute_0_39,plain,
( least_upper_bound(X,Y) != least_upper_bound(Y,X)
| least_upper_bound(Y,X) = least_upper_bound(X,Y) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(least_upper_bound(X,Y))),bind(Y0,$fot(least_upper_bound(Y,X)))]]) ).
cnf(refute_0_40,plain,
least_upper_bound(Y,X) = least_upper_bound(X,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(X,Y),least_upper_bound(Y,X)) )],[symmetry_of_lub,refute_0_39]) ).
cnf(refute_0_41,plain,
least_upper_bound(multiply(X_92,X_91),identity) = least_upper_bound(identity,multiply(X_92,X_91)),
inference(subst,[],[refute_0_40:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_92,X_91)))]]) ).
cnf(refute_0_42,plain,
( multiply(least_upper_bound(X_92,inverse(X_91)),X_91) != least_upper_bound(multiply(X_92,X_91),identity)
| least_upper_bound(multiply(X_92,X_91),identity) != least_upper_bound(identity,multiply(X_92,X_91))
| multiply(least_upper_bound(X_92,inverse(X_91)),X_91) = least_upper_bound(identity,multiply(X_92,X_91)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_92,inverse(X_91)),X_91),least_upper_bound(identity,multiply(X_92,X_91))) ),[0],$fot(least_upper_bound(multiply(X_92,X_91),identity))]]) ).
cnf(refute_0_43,plain,
( multiply(least_upper_bound(X_92,inverse(X_91)),X_91) != least_upper_bound(multiply(X_92,X_91),identity)
| multiply(least_upper_bound(X_92,inverse(X_91)),X_91) = least_upper_bound(identity,multiply(X_92,X_91)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_92,X_91),identity),least_upper_bound(identity,multiply(X_92,X_91))) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
multiply(least_upper_bound(X_92,inverse(X_91)),X_91) = least_upper_bound(identity,multiply(X_92,X_91)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_92,inverse(X_91)),X_91),least_upper_bound(multiply(X_92,X_91),identity)) )],[refute_0_38,refute_0_43]) ).
cnf(refute_0_45,plain,
multiply(least_upper_bound(X_95,inverse(inverse(X))),inverse(X)) = least_upper_bound(identity,multiply(X_95,inverse(X))),
inference(subst,[],[refute_0_44:[bind(X_91,$fot(inverse(X))),bind(X_92,$fot(X_95))]]) ).
cnf(refute_0_46,plain,
( multiply(least_upper_bound(X_95,inverse(inverse(X))),inverse(X)) != least_upper_bound(identity,multiply(X_95,inverse(X)))
| inverse(inverse(X)) != X
| multiply(least_upper_bound(X_95,X),inverse(X)) = least_upper_bound(identity,multiply(X_95,inverse(X))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_95,inverse(inverse(X))),inverse(X)),least_upper_bound(identity,multiply(X_95,inverse(X)))) ),[0,0,1],$fot(X)]]) ).
cnf(refute_0_47,plain,
( multiply(least_upper_bound(X_95,inverse(inverse(X))),inverse(X)) != least_upper_bound(identity,multiply(X_95,inverse(X)))
| multiply(least_upper_bound(X_95,X),inverse(X)) = least_upper_bound(identity,multiply(X_95,inverse(X))) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p12x_2,refute_0_46]) ).
cnf(refute_0_48,plain,
multiply(least_upper_bound(X_95,X),inverse(X)) = least_upper_bound(identity,multiply(X_95,inverse(X))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_95,inverse(inverse(X))),inverse(X)),least_upper_bound(identity,multiply(X_95,inverse(X)))) )],[refute_0_45,refute_0_47]) ).
cnf(refute_0_49,plain,
multiply(least_upper_bound(b,c),inverse(c)) = least_upper_bound(identity,multiply(b,inverse(c))),
inference(subst,[],[refute_0_48:[bind(X,$fot(c)),bind(X_95,$fot(b))]]) ).
cnf(refute_0_50,plain,
( least_upper_bound(a,c) != least_upper_bound(b,c)
| least_upper_bound(b,c) = least_upper_bound(a,c) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(least_upper_bound(a,c))),bind(Y0,$fot(least_upper_bound(b,c)))]]) ).
cnf(refute_0_51,plain,
least_upper_bound(b,c) = least_upper_bound(a,c),
inference(resolve,[$cnf( $equal(least_upper_bound(a,c),least_upper_bound(b,c)) )],[p12x_5,refute_0_50]) ).
cnf(refute_0_52,plain,
( multiply(least_upper_bound(b,c),inverse(c)) != least_upper_bound(identity,multiply(b,inverse(c)))
| least_upper_bound(b,c) != least_upper_bound(a,c)
| multiply(least_upper_bound(a,c),inverse(c)) = least_upper_bound(identity,multiply(b,inverse(c))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(b,c),inverse(c)),least_upper_bound(identity,multiply(b,inverse(c)))) ),[0,0],$fot(least_upper_bound(a,c))]]) ).
cnf(refute_0_53,plain,
( multiply(least_upper_bound(b,c),inverse(c)) != least_upper_bound(identity,multiply(b,inverse(c)))
| multiply(least_upper_bound(a,c),inverse(c)) = least_upper_bound(identity,multiply(b,inverse(c))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,c),least_upper_bound(a,c)) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
multiply(least_upper_bound(a,c),inverse(c)) = least_upper_bound(identity,multiply(b,inverse(c))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,c),inverse(c)),least_upper_bound(identity,multiply(b,inverse(c)))) )],[refute_0_49,refute_0_53]) ).
cnf(refute_0_55,plain,
multiply(X_76,least_upper_bound(inverse(X_76),X_78)) = least_upper_bound(multiply(X_76,inverse(X_76)),multiply(X_76,X_78)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(X_76)),bind(Y,$fot(inverse(X_76))),bind(Z,$fot(X_78))]]) ).
cnf(refute_0_56,plain,
multiply(inverse(inverse(X_1)),inverse(X_1)) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(inverse(X_1)))]]) ).
cnf(refute_0_57,plain,
inverse(inverse(X_1)) = X_1,
inference(subst,[],[p12x_2:[bind(X,$fot(X_1))]]) ).
cnf(refute_0_58,plain,
( multiply(inverse(inverse(X_1)),inverse(X_1)) != identity
| inverse(inverse(X_1)) != X_1
| multiply(X_1,inverse(X_1)) = identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X_1)),inverse(X_1)),identity) ),[0,0],$fot(X_1)]]) ).
cnf(refute_0_59,plain,
( multiply(inverse(inverse(X_1)),inverse(X_1)) != identity
| multiply(X_1,inverse(X_1)) = identity ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_1)),X_1) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
multiply(X_1,inverse(X_1)) = identity,
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_1)),inverse(X_1)),identity) )],[refute_0_56,refute_0_59]) ).
cnf(refute_0_61,plain,
multiply(X_76,inverse(X_76)) = identity,
inference(subst,[],[refute_0_60:[bind(X_1,$fot(X_76))]]) ).
cnf(refute_0_62,plain,
( multiply(X_76,inverse(X_76)) != identity
| multiply(X_76,least_upper_bound(inverse(X_76),X_78)) != least_upper_bound(multiply(X_76,inverse(X_76)),multiply(X_76,X_78))
| multiply(X_76,least_upper_bound(inverse(X_76),X_78)) = least_upper_bound(identity,multiply(X_76,X_78)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_76,least_upper_bound(inverse(X_76),X_78)),least_upper_bound(multiply(X_76,inverse(X_76)),multiply(X_76,X_78))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_63,plain,
( multiply(X_76,least_upper_bound(inverse(X_76),X_78)) != least_upper_bound(multiply(X_76,inverse(X_76)),multiply(X_76,X_78))
| multiply(X_76,least_upper_bound(inverse(X_76),X_78)) = least_upper_bound(identity,multiply(X_76,X_78)) ),
inference(resolve,[$cnf( $equal(multiply(X_76,inverse(X_76)),identity) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
multiply(X_76,least_upper_bound(inverse(X_76),X_78)) = least_upper_bound(identity,multiply(X_76,X_78)),
inference(resolve,[$cnf( $equal(multiply(X_76,least_upper_bound(inverse(X_76),X_78)),least_upper_bound(multiply(X_76,inverse(X_76)),multiply(X_76,X_78))) )],[refute_0_55,refute_0_63]) ).
cnf(refute_0_65,plain,
multiply(X_82,least_upper_bound(inverse(X_82),inverse(Y))) = least_upper_bound(identity,multiply(X_82,inverse(Y))),
inference(subst,[],[refute_0_64:[bind(X_76,$fot(X_82)),bind(X_78,$fot(inverse(Y)))]]) ).
cnf(refute_0_66,plain,
inverse(greatest_lower_bound(X_82,Y)) = least_upper_bound(inverse(X_82),inverse(Y)),
inference(subst,[],[p12x_6:[bind(X,$fot(X_82))]]) ).
cnf(refute_0_67,plain,
( inverse(greatest_lower_bound(X_82,Y)) != least_upper_bound(inverse(X_82),inverse(Y))
| least_upper_bound(inverse(X_82),inverse(Y)) = inverse(greatest_lower_bound(X_82,Y)) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(inverse(greatest_lower_bound(X_82,Y)))),bind(Y0,$fot(least_upper_bound(inverse(X_82),inverse(Y))))]]) ).
cnf(refute_0_68,plain,
least_upper_bound(inverse(X_82),inverse(Y)) = inverse(greatest_lower_bound(X_82,Y)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_82,Y)),least_upper_bound(inverse(X_82),inverse(Y))) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
( multiply(X_82,least_upper_bound(inverse(X_82),inverse(Y))) != least_upper_bound(identity,multiply(X_82,inverse(Y)))
| least_upper_bound(inverse(X_82),inverse(Y)) != inverse(greatest_lower_bound(X_82,Y))
| multiply(X_82,inverse(greatest_lower_bound(X_82,Y))) = least_upper_bound(identity,multiply(X_82,inverse(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_82,least_upper_bound(inverse(X_82),inverse(Y))),least_upper_bound(identity,multiply(X_82,inverse(Y)))) ),[0,1],$fot(inverse(greatest_lower_bound(X_82,Y)))]]) ).
cnf(refute_0_70,plain,
( multiply(X_82,least_upper_bound(inverse(X_82),inverse(Y))) != least_upper_bound(identity,multiply(X_82,inverse(Y)))
| multiply(X_82,inverse(greatest_lower_bound(X_82,Y))) = least_upper_bound(identity,multiply(X_82,inverse(Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_82),inverse(Y)),inverse(greatest_lower_bound(X_82,Y))) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
multiply(X_82,inverse(greatest_lower_bound(X_82,Y))) = least_upper_bound(identity,multiply(X_82,inverse(Y))),
inference(resolve,[$cnf( $equal(multiply(X_82,least_upper_bound(inverse(X_82),inverse(Y))),least_upper_bound(identity,multiply(X_82,inverse(Y)))) )],[refute_0_65,refute_0_70]) ).
cnf(refute_0_72,plain,
multiply(least_upper_bound(X_82,Y),inverse(Y)) = least_upper_bound(identity,multiply(X_82,inverse(Y))),
inference(subst,[],[refute_0_48:[bind(X,$fot(Y)),bind(X_95,$fot(X_82))]]) ).
cnf(refute_0_73,plain,
( multiply(least_upper_bound(X_82,Y),inverse(Y)) != least_upper_bound(identity,multiply(X_82,inverse(Y)))
| least_upper_bound(identity,multiply(X_82,inverse(Y))) = multiply(least_upper_bound(X_82,Y),inverse(Y)) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(multiply(least_upper_bound(X_82,Y),inverse(Y)))),bind(Y0,$fot(least_upper_bound(identity,multiply(X_82,inverse(Y)))))]]) ).
cnf(refute_0_74,plain,
least_upper_bound(identity,multiply(X_82,inverse(Y))) = multiply(least_upper_bound(X_82,Y),inverse(Y)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_82,Y),inverse(Y)),least_upper_bound(identity,multiply(X_82,inverse(Y)))) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
( multiply(X_82,inverse(greatest_lower_bound(X_82,Y))) != least_upper_bound(identity,multiply(X_82,inverse(Y)))
| least_upper_bound(identity,multiply(X_82,inverse(Y))) != multiply(least_upper_bound(X_82,Y),inverse(Y))
| multiply(X_82,inverse(greatest_lower_bound(X_82,Y))) = multiply(least_upper_bound(X_82,Y),inverse(Y)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_82,inverse(greatest_lower_bound(X_82,Y))),multiply(least_upper_bound(X_82,Y),inverse(Y))) ),[0],$fot(least_upper_bound(identity,multiply(X_82,inverse(Y))))]]) ).
cnf(refute_0_76,plain,
( multiply(X_82,inverse(greatest_lower_bound(X_82,Y))) != least_upper_bound(identity,multiply(X_82,inverse(Y)))
| multiply(X_82,inverse(greatest_lower_bound(X_82,Y))) = multiply(least_upper_bound(X_82,Y),inverse(Y)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_82,inverse(Y))),multiply(least_upper_bound(X_82,Y),inverse(Y))) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
multiply(X_82,inverse(greatest_lower_bound(X_82,Y))) = multiply(least_upper_bound(X_82,Y),inverse(Y)),
inference(resolve,[$cnf( $equal(multiply(X_82,inverse(greatest_lower_bound(X_82,Y))),least_upper_bound(identity,multiply(X_82,inverse(Y)))) )],[refute_0_71,refute_0_76]) ).
cnf(refute_0_78,plain,
( multiply(X_82,inverse(greatest_lower_bound(X_82,Y))) != multiply(least_upper_bound(X_82,Y),inverse(Y))
| multiply(least_upper_bound(X_82,Y),inverse(Y)) = multiply(X_82,inverse(greatest_lower_bound(X_82,Y))) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(multiply(X_82,inverse(greatest_lower_bound(X_82,Y))))),bind(Y0,$fot(multiply(least_upper_bound(X_82,Y),inverse(Y))))]]) ).
cnf(refute_0_79,plain,
multiply(least_upper_bound(X_82,Y),inverse(Y)) = multiply(X_82,inverse(greatest_lower_bound(X_82,Y))),
inference(resolve,[$cnf( $equal(multiply(X_82,inverse(greatest_lower_bound(X_82,Y))),multiply(least_upper_bound(X_82,Y),inverse(Y))) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
multiply(least_upper_bound(a,c),inverse(c)) = multiply(a,inverse(greatest_lower_bound(a,c))),
inference(subst,[],[refute_0_79:[bind(Y,$fot(c)),bind(X_82,$fot(a))]]) ).
cnf(refute_0_81,plain,
( multiply(least_upper_bound(a,c),inverse(c)) != multiply(a,inverse(greatest_lower_bound(a,c)))
| multiply(least_upper_bound(a,c),inverse(c)) != least_upper_bound(identity,multiply(b,inverse(c)))
| multiply(a,inverse(greatest_lower_bound(a,c))) = least_upper_bound(identity,multiply(b,inverse(c))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(a,c),inverse(c)),least_upper_bound(identity,multiply(b,inverse(c)))) ),[0],$fot(multiply(a,inverse(greatest_lower_bound(a,c))))]]) ).
cnf(refute_0_82,plain,
( multiply(least_upper_bound(a,c),inverse(c)) != least_upper_bound(identity,multiply(b,inverse(c)))
| multiply(a,inverse(greatest_lower_bound(a,c))) = least_upper_bound(identity,multiply(b,inverse(c))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,c),inverse(c)),multiply(a,inverse(greatest_lower_bound(a,c)))) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
( greatest_lower_bound(a,c) != greatest_lower_bound(b,c)
| greatest_lower_bound(b,c) = greatest_lower_bound(a,c) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(greatest_lower_bound(a,c))),bind(Y0,$fot(greatest_lower_bound(b,c)))]]) ).
cnf(refute_0_84,plain,
greatest_lower_bound(b,c) = greatest_lower_bound(a,c),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,c),greatest_lower_bound(b,c)) )],[p12x_4,refute_0_83]) ).
cnf(refute_0_85,plain,
inverse(greatest_lower_bound(b,c)) = inverse(greatest_lower_bound(b,c)),
introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(b,c)))]]) ).
cnf(refute_0_86,plain,
( greatest_lower_bound(b,c) != greatest_lower_bound(a,c)
| inverse(greatest_lower_bound(b,c)) != inverse(greatest_lower_bound(b,c))
| inverse(greatest_lower_bound(b,c)) = inverse(greatest_lower_bound(a,c)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(b,c)),inverse(greatest_lower_bound(b,c))) ),[1,0],$fot(greatest_lower_bound(a,c))]]) ).
cnf(refute_0_87,plain,
( greatest_lower_bound(b,c) != greatest_lower_bound(a,c)
| inverse(greatest_lower_bound(b,c)) = inverse(greatest_lower_bound(a,c)) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(b,c)),inverse(greatest_lower_bound(b,c))) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
inverse(greatest_lower_bound(b,c)) = inverse(greatest_lower_bound(a,c)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,c),greatest_lower_bound(a,c)) )],[refute_0_84,refute_0_87]) ).
cnf(refute_0_89,plain,
multiply(b,inverse(greatest_lower_bound(b,c))) = multiply(b,inverse(greatest_lower_bound(b,c))),
introduced(tautology,[refl,[$fot(multiply(b,inverse(greatest_lower_bound(b,c))))]]) ).
cnf(refute_0_90,plain,
( multiply(b,inverse(greatest_lower_bound(b,c))) != multiply(b,inverse(greatest_lower_bound(b,c)))
| inverse(greatest_lower_bound(b,c)) != inverse(greatest_lower_bound(a,c))
| multiply(b,inverse(greatest_lower_bound(b,c))) = multiply(b,inverse(greatest_lower_bound(a,c))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(b,inverse(greatest_lower_bound(b,c))),multiply(b,inverse(greatest_lower_bound(b,c)))) ),[1,1],$fot(inverse(greatest_lower_bound(a,c)))]]) ).
cnf(refute_0_91,plain,
( inverse(greatest_lower_bound(b,c)) != inverse(greatest_lower_bound(a,c))
| multiply(b,inverse(greatest_lower_bound(b,c))) = multiply(b,inverse(greatest_lower_bound(a,c))) ),
inference(resolve,[$cnf( $equal(multiply(b,inverse(greatest_lower_bound(b,c))),multiply(b,inverse(greatest_lower_bound(b,c)))) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
multiply(b,inverse(greatest_lower_bound(b,c))) = multiply(b,inverse(greatest_lower_bound(a,c))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(b,c)),inverse(greatest_lower_bound(a,c))) )],[refute_0_88,refute_0_91]) ).
cnf(refute_0_93,plain,
multiply(least_upper_bound(b,c),inverse(c)) = multiply(b,inverse(greatest_lower_bound(b,c))),
inference(subst,[],[refute_0_79:[bind(Y,$fot(c)),bind(X_82,$fot(b))]]) ).
cnf(refute_0_94,plain,
multiply(least_upper_bound(X_92,X_93),inverse(X_92)) = least_upper_bound(multiply(X_92,inverse(X_92)),multiply(X_93,inverse(X_92))),
inference(subst,[],[monotony_lub2:[bind(X,$fot(inverse(X_92))),bind(Y,$fot(X_92)),bind(Z,$fot(X_93))]]) ).
cnf(refute_0_95,plain,
multiply(X_92,inverse(X_92)) = identity,
inference(subst,[],[refute_0_60:[bind(X_1,$fot(X_92))]]) ).
cnf(refute_0_96,plain,
( multiply(X_92,inverse(X_92)) != identity
| multiply(least_upper_bound(X_92,X_93),inverse(X_92)) != least_upper_bound(multiply(X_92,inverse(X_92)),multiply(X_93,inverse(X_92)))
| multiply(least_upper_bound(X_92,X_93),inverse(X_92)) = least_upper_bound(identity,multiply(X_93,inverse(X_92))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_92,X_93),inverse(X_92)),least_upper_bound(multiply(X_92,inverse(X_92)),multiply(X_93,inverse(X_92)))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_97,plain,
( multiply(least_upper_bound(X_92,X_93),inverse(X_92)) != least_upper_bound(multiply(X_92,inverse(X_92)),multiply(X_93,inverse(X_92)))
| multiply(least_upper_bound(X_92,X_93),inverse(X_92)) = least_upper_bound(identity,multiply(X_93,inverse(X_92))) ),
inference(resolve,[$cnf( $equal(multiply(X_92,inverse(X_92)),identity) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
multiply(least_upper_bound(X_92,X_93),inverse(X_92)) = least_upper_bound(identity,multiply(X_93,inverse(X_92))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_92,X_93),inverse(X_92)),least_upper_bound(multiply(X_92,inverse(X_92)),multiply(X_93,inverse(X_92)))) )],[refute_0_94,refute_0_97]) ).
cnf(refute_0_99,plain,
multiply(least_upper_bound(X_92,identity),inverse(X_92)) = least_upper_bound(identity,multiply(identity,inverse(X_92))),
inference(subst,[],[refute_0_98:[bind(X_93,$fot(identity))]]) ).
cnf(refute_0_100,plain,
inverse(multiply(X_48,inverse(least_upper_bound(identity,X_29)))) = multiply(least_upper_bound(identity,X_29),inverse(X_48)),
inference(subst,[],[refute_0_22:[bind(X,$fot(least_upper_bound(identity,X_29))),bind(X_14,$fot(X_48))]]) ).
cnf(refute_0_101,plain,
inverse(least_upper_bound(X_27,identity)) = greatest_lower_bound(inverse(X_27),inverse(identity)),
inference(subst,[],[p12x_7:[bind(X,$fot(X_27)),bind(Y,$fot(identity))]]) ).
cnf(refute_0_102,plain,
( inverse(identity) != identity
| inverse(least_upper_bound(X_27,identity)) != greatest_lower_bound(inverse(X_27),inverse(identity))
| inverse(least_upper_bound(X_27,identity)) = greatest_lower_bound(inverse(X_27),identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_27,identity)),greatest_lower_bound(inverse(X_27),inverse(identity))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_103,plain,
( inverse(least_upper_bound(X_27,identity)) != greatest_lower_bound(inverse(X_27),inverse(identity))
| inverse(least_upper_bound(X_27,identity)) = greatest_lower_bound(inverse(X_27),identity) ),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[p12x_1,refute_0_102]) ).
cnf(refute_0_104,plain,
inverse(least_upper_bound(X_27,identity)) = greatest_lower_bound(inverse(X_27),identity),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_27,identity)),greatest_lower_bound(inverse(X_27),inverse(identity))) )],[refute_0_101,refute_0_103]) ).
cnf(refute_0_105,plain,
( greatest_lower_bound(X,Y) != greatest_lower_bound(Y,X)
| greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(greatest_lower_bound(X,Y))),bind(Y0,$fot(greatest_lower_bound(Y,X)))]]) ).
cnf(refute_0_106,plain,
greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X)) )],[symmetry_of_glb,refute_0_105]) ).
cnf(refute_0_107,plain,
greatest_lower_bound(inverse(X_27),identity) = greatest_lower_bound(identity,inverse(X_27)),
inference(subst,[],[refute_0_106:[bind(X,$fot(identity)),bind(Y,$fot(inverse(X_27)))]]) ).
cnf(refute_0_108,plain,
( greatest_lower_bound(inverse(X_27),identity) != greatest_lower_bound(identity,inverse(X_27))
| inverse(least_upper_bound(X_27,identity)) != greatest_lower_bound(inverse(X_27),identity)
| inverse(least_upper_bound(X_27,identity)) = greatest_lower_bound(identity,inverse(X_27)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_27,identity)),greatest_lower_bound(inverse(X_27),identity)) ),[1],$fot(greatest_lower_bound(identity,inverse(X_27)))]]) ).
cnf(refute_0_109,plain,
( inverse(least_upper_bound(X_27,identity)) != greatest_lower_bound(inverse(X_27),identity)
| inverse(least_upper_bound(X_27,identity)) = greatest_lower_bound(identity,inverse(X_27)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_27),identity),greatest_lower_bound(identity,inverse(X_27))) )],[refute_0_107,refute_0_108]) ).
cnf(refute_0_110,plain,
inverse(least_upper_bound(X_27,identity)) = greatest_lower_bound(identity,inverse(X_27)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_27,identity)),greatest_lower_bound(inverse(X_27),identity)) )],[refute_0_104,refute_0_109]) ).
cnf(refute_0_111,plain,
inverse(least_upper_bound(X_29,identity)) = greatest_lower_bound(identity,inverse(X_29)),
inference(subst,[],[refute_0_110:[bind(X_27,$fot(X_29))]]) ).
cnf(refute_0_112,plain,
least_upper_bound(identity,X_29) = least_upper_bound(X_29,identity),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(identity)),bind(Y,$fot(X_29))]]) ).
cnf(refute_0_113,plain,
( least_upper_bound(identity,X_29) != least_upper_bound(X_29,identity)
| least_upper_bound(X_29,identity) = least_upper_bound(identity,X_29) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(least_upper_bound(identity,X_29))),bind(Y0,$fot(least_upper_bound(X_29,identity)))]]) ).
cnf(refute_0_114,plain,
least_upper_bound(X_29,identity) = least_upper_bound(identity,X_29),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,X_29),least_upper_bound(X_29,identity)) )],[refute_0_112,refute_0_113]) ).
cnf(refute_0_115,plain,
( inverse(least_upper_bound(X_29,identity)) != greatest_lower_bound(identity,inverse(X_29))
| least_upper_bound(X_29,identity) != least_upper_bound(identity,X_29)
| inverse(least_upper_bound(identity,X_29)) = greatest_lower_bound(identity,inverse(X_29)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_29,identity)),greatest_lower_bound(identity,inverse(X_29))) ),[0,0],$fot(least_upper_bound(identity,X_29))]]) ).
cnf(refute_0_116,plain,
( inverse(least_upper_bound(X_29,identity)) != greatest_lower_bound(identity,inverse(X_29))
| inverse(least_upper_bound(identity,X_29)) = greatest_lower_bound(identity,inverse(X_29)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_29,identity),least_upper_bound(identity,X_29)) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
inverse(least_upper_bound(identity,X_29)) = greatest_lower_bound(identity,inverse(X_29)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_29,identity)),greatest_lower_bound(identity,inverse(X_29))) )],[refute_0_111,refute_0_116]) ).
cnf(refute_0_118,plain,
( inverse(least_upper_bound(X_27,identity)) != greatest_lower_bound(identity,inverse(X_27))
| greatest_lower_bound(identity,inverse(X_27)) = inverse(least_upper_bound(X_27,identity)) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(inverse(least_upper_bound(X_27,identity)))),bind(Y0,$fot(greatest_lower_bound(identity,inverse(X_27))))]]) ).
cnf(refute_0_119,plain,
greatest_lower_bound(identity,inverse(X_27)) = inverse(least_upper_bound(X_27,identity)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_27,identity)),greatest_lower_bound(identity,inverse(X_27))) )],[refute_0_110,refute_0_118]) ).
cnf(refute_0_120,plain,
greatest_lower_bound(identity,inverse(X_29)) = inverse(least_upper_bound(X_29,identity)),
inference(subst,[],[refute_0_119:[bind(X_27,$fot(X_29))]]) ).
cnf(refute_0_121,plain,
( greatest_lower_bound(identity,inverse(X_29)) != inverse(least_upper_bound(X_29,identity))
| inverse(least_upper_bound(identity,X_29)) != greatest_lower_bound(identity,inverse(X_29))
| inverse(least_upper_bound(identity,X_29)) = inverse(least_upper_bound(X_29,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,X_29)),greatest_lower_bound(identity,inverse(X_29))) ),[1],$fot(inverse(least_upper_bound(X_29,identity)))]]) ).
cnf(refute_0_122,plain,
( inverse(least_upper_bound(identity,X_29)) != greatest_lower_bound(identity,inverse(X_29))
| inverse(least_upper_bound(identity,X_29)) = inverse(least_upper_bound(X_29,identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(X_29)),inverse(least_upper_bound(X_29,identity))) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
inverse(least_upper_bound(identity,X_29)) = inverse(least_upper_bound(X_29,identity)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,X_29)),greatest_lower_bound(identity,inverse(X_29))) )],[refute_0_117,refute_0_122]) ).
cnf(refute_0_124,plain,
( inverse(multiply(X_48,inverse(least_upper_bound(identity,X_29)))) != multiply(least_upper_bound(identity,X_29),inverse(X_48))
| inverse(least_upper_bound(identity,X_29)) != inverse(least_upper_bound(X_29,identity))
| inverse(multiply(X_48,inverse(least_upper_bound(X_29,identity)))) = multiply(least_upper_bound(identity,X_29),inverse(X_48)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_48,inverse(least_upper_bound(identity,X_29)))),multiply(least_upper_bound(identity,X_29),inverse(X_48))) ),[0,0,1],$fot(inverse(least_upper_bound(X_29,identity)))]]) ).
cnf(refute_0_125,plain,
( inverse(multiply(X_48,inverse(least_upper_bound(identity,X_29)))) != multiply(least_upper_bound(identity,X_29),inverse(X_48))
| inverse(multiply(X_48,inverse(least_upper_bound(X_29,identity)))) = multiply(least_upper_bound(identity,X_29),inverse(X_48)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,X_29)),inverse(least_upper_bound(X_29,identity))) )],[refute_0_123,refute_0_124]) ).
cnf(refute_0_126,plain,
inverse(multiply(X_48,inverse(least_upper_bound(X_29,identity)))) = multiply(least_upper_bound(identity,X_29),inverse(X_48)),
inference(resolve,[$cnf( $equal(inverse(multiply(X_48,inverse(least_upper_bound(identity,X_29)))),multiply(least_upper_bound(identity,X_29),inverse(X_48))) )],[refute_0_100,refute_0_125]) ).
cnf(refute_0_127,plain,
inverse(multiply(X_48,inverse(least_upper_bound(X_29,identity)))) = multiply(least_upper_bound(X_29,identity),inverse(X_48)),
inference(subst,[],[refute_0_22:[bind(X,$fot(least_upper_bound(X_29,identity))),bind(X_14,$fot(X_48))]]) ).
cnf(refute_0_128,plain,
( inverse(multiply(X_48,inverse(least_upper_bound(X_29,identity)))) != multiply(least_upper_bound(X_29,identity),inverse(X_48))
| inverse(multiply(X_48,inverse(least_upper_bound(X_29,identity)))) != multiply(least_upper_bound(identity,X_29),inverse(X_48))
| multiply(least_upper_bound(X_29,identity),inverse(X_48)) = multiply(least_upper_bound(identity,X_29),inverse(X_48)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_48,inverse(least_upper_bound(X_29,identity)))),multiply(least_upper_bound(identity,X_29),inverse(X_48))) ),[0],$fot(multiply(least_upper_bound(X_29,identity),inverse(X_48)))]]) ).
cnf(refute_0_129,plain,
( inverse(multiply(X_48,inverse(least_upper_bound(X_29,identity)))) != multiply(least_upper_bound(identity,X_29),inverse(X_48))
| multiply(least_upper_bound(X_29,identity),inverse(X_48)) = multiply(least_upper_bound(identity,X_29),inverse(X_48)) ),
inference(resolve,[$cnf( $equal(inverse(multiply(X_48,inverse(least_upper_bound(X_29,identity)))),multiply(least_upper_bound(X_29,identity),inverse(X_48))) )],[refute_0_127,refute_0_128]) ).
cnf(refute_0_130,plain,
multiply(least_upper_bound(X_29,identity),inverse(X_48)) = multiply(least_upper_bound(identity,X_29),inverse(X_48)),
inference(resolve,[$cnf( $equal(inverse(multiply(X_48,inverse(least_upper_bound(X_29,identity)))),multiply(least_upper_bound(identity,X_29),inverse(X_48))) )],[refute_0_126,refute_0_129]) ).
cnf(refute_0_131,plain,
multiply(least_upper_bound(X_92,identity),inverse(X_92)) = multiply(least_upper_bound(identity,X_92),inverse(X_92)),
inference(subst,[],[refute_0_130:[bind(X_29,$fot(X_92)),bind(X_48,$fot(X_92))]]) ).
cnf(refute_0_132,plain,
( multiply(least_upper_bound(X_92,identity),inverse(X_92)) != multiply(least_upper_bound(identity,X_92),inverse(X_92))
| multiply(least_upper_bound(X_92,identity),inverse(X_92)) != least_upper_bound(identity,multiply(identity,inverse(X_92)))
| multiply(least_upper_bound(identity,X_92),inverse(X_92)) = least_upper_bound(identity,multiply(identity,inverse(X_92))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_92,identity),inverse(X_92)),least_upper_bound(identity,multiply(identity,inverse(X_92)))) ),[0],$fot(multiply(least_upper_bound(identity,X_92),inverse(X_92)))]]) ).
cnf(refute_0_133,plain,
( multiply(least_upper_bound(X_92,identity),inverse(X_92)) != least_upper_bound(identity,multiply(identity,inverse(X_92)))
| multiply(least_upper_bound(identity,X_92),inverse(X_92)) = least_upper_bound(identity,multiply(identity,inverse(X_92))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_92,identity),inverse(X_92)),multiply(least_upper_bound(identity,X_92),inverse(X_92))) )],[refute_0_131,refute_0_132]) ).
cnf(refute_0_134,plain,
multiply(least_upper_bound(identity,X_92),inverse(X_92)) = least_upper_bound(identity,multiply(identity,inverse(X_92))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_92,identity),inverse(X_92)),least_upper_bound(identity,multiply(identity,inverse(X_92)))) )],[refute_0_99,refute_0_133]) ).
cnf(refute_0_135,plain,
multiply(identity,inverse(greatest_lower_bound(identity,X_92))) = inverse(greatest_lower_bound(identity,X_92)),
inference(subst,[],[left_identity:[bind(X,$fot(inverse(greatest_lower_bound(identity,X_92))))]]) ).
cnf(refute_0_136,plain,
inverse(multiply(greatest_lower_bound(inverse(inverse(X)),X_108),inverse(X))) = multiply(X,inverse(greatest_lower_bound(inverse(inverse(X)),X_108))),
inference(subst,[],[refute_0_22:[bind(X_14,$fot(greatest_lower_bound(inverse(inverse(X)),X_108)))]]) ).
cnf(refute_0_137,plain,
multiply(greatest_lower_bound(inverse(X_97),X_99),X_97) = greatest_lower_bound(multiply(inverse(X_97),X_97),multiply(X_99,X_97)),
inference(subst,[],[monotony_glb2:[bind(X,$fot(X_97)),bind(Y,$fot(inverse(X_97))),bind(Z,$fot(X_99))]]) ).
cnf(refute_0_138,plain,
multiply(inverse(X_97),X_97) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_97))]]) ).
cnf(refute_0_139,plain,
( multiply(greatest_lower_bound(inverse(X_97),X_99),X_97) != greatest_lower_bound(multiply(inverse(X_97),X_97),multiply(X_99,X_97))
| multiply(inverse(X_97),X_97) != identity
| multiply(greatest_lower_bound(inverse(X_97),X_99),X_97) = greatest_lower_bound(identity,multiply(X_99,X_97)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_97),X_99),X_97),greatest_lower_bound(multiply(inverse(X_97),X_97),multiply(X_99,X_97))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_140,plain,
( multiply(greatest_lower_bound(inverse(X_97),X_99),X_97) != greatest_lower_bound(multiply(inverse(X_97),X_97),multiply(X_99,X_97))
| multiply(greatest_lower_bound(inverse(X_97),X_99),X_97) = greatest_lower_bound(identity,multiply(X_99,X_97)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_97),X_97),identity) )],[refute_0_138,refute_0_139]) ).
cnf(refute_0_141,plain,
multiply(greatest_lower_bound(inverse(X_97),X_99),X_97) = greatest_lower_bound(identity,multiply(X_99,X_97)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_97),X_99),X_97),greatest_lower_bound(multiply(inverse(X_97),X_97),multiply(X_99,X_97))) )],[refute_0_137,refute_0_140]) ).
cnf(refute_0_142,plain,
multiply(greatest_lower_bound(inverse(inverse(X)),X_108),inverse(X)) = greatest_lower_bound(identity,multiply(X_108,inverse(X))),
inference(subst,[],[refute_0_141:[bind(X_97,$fot(inverse(X))),bind(X_99,$fot(X_108))]]) ).
cnf(refute_0_143,plain,
( multiply(greatest_lower_bound(inverse(inverse(X)),X_108),inverse(X)) != greatest_lower_bound(identity,multiply(X_108,inverse(X)))
| inverse(multiply(greatest_lower_bound(inverse(inverse(X)),X_108),inverse(X))) != multiply(X,inverse(greatest_lower_bound(inverse(inverse(X)),X_108)))
| inverse(greatest_lower_bound(identity,multiply(X_108,inverse(X)))) = multiply(X,inverse(greatest_lower_bound(inverse(inverse(X)),X_108))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(greatest_lower_bound(inverse(inverse(X)),X_108),inverse(X))),multiply(X,inverse(greatest_lower_bound(inverse(inverse(X)),X_108)))) ),[0,0],$fot(greatest_lower_bound(identity,multiply(X_108,inverse(X))))]]) ).
cnf(refute_0_144,plain,
( inverse(multiply(greatest_lower_bound(inverse(inverse(X)),X_108),inverse(X))) != multiply(X,inverse(greatest_lower_bound(inverse(inverse(X)),X_108)))
| inverse(greatest_lower_bound(identity,multiply(X_108,inverse(X)))) = multiply(X,inverse(greatest_lower_bound(inverse(inverse(X)),X_108))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(inverse(X)),X_108),inverse(X)),greatest_lower_bound(identity,multiply(X_108,inverse(X)))) )],[refute_0_142,refute_0_143]) ).
cnf(refute_0_145,plain,
inverse(greatest_lower_bound(identity,multiply(X_108,inverse(X)))) = multiply(X,inverse(greatest_lower_bound(inverse(inverse(X)),X_108))),
inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(inverse(inverse(X)),X_108),inverse(X))),multiply(X,inverse(greatest_lower_bound(inverse(inverse(X)),X_108)))) )],[refute_0_136,refute_0_144]) ).
cnf(refute_0_146,plain,
inverse(greatest_lower_bound(X_20,identity)) = least_upper_bound(inverse(X_20),inverse(identity)),
inference(subst,[],[p12x_6:[bind(X,$fot(X_20)),bind(Y,$fot(identity))]]) ).
cnf(refute_0_147,plain,
( inverse(greatest_lower_bound(X_20,identity)) != least_upper_bound(inverse(X_20),inverse(identity))
| inverse(identity) != identity
| inverse(greatest_lower_bound(X_20,identity)) = least_upper_bound(inverse(X_20),identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X_20,identity)),least_upper_bound(inverse(X_20),inverse(identity))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_148,plain,
( inverse(greatest_lower_bound(X_20,identity)) != least_upper_bound(inverse(X_20),inverse(identity))
| inverse(greatest_lower_bound(X_20,identity)) = least_upper_bound(inverse(X_20),identity) ),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[p12x_1,refute_0_147]) ).
cnf(refute_0_149,plain,
inverse(greatest_lower_bound(X_20,identity)) = least_upper_bound(inverse(X_20),identity),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_20,identity)),least_upper_bound(inverse(X_20),inverse(identity))) )],[refute_0_146,refute_0_148]) ).
cnf(refute_0_150,plain,
least_upper_bound(inverse(X_20),identity) = least_upper_bound(identity,inverse(X_20)),
inference(subst,[],[refute_0_40:[bind(X,$fot(identity)),bind(Y,$fot(inverse(X_20)))]]) ).
cnf(refute_0_151,plain,
( inverse(greatest_lower_bound(X_20,identity)) != least_upper_bound(inverse(X_20),identity)
| least_upper_bound(inverse(X_20),identity) != least_upper_bound(identity,inverse(X_20))
| inverse(greatest_lower_bound(X_20,identity)) = least_upper_bound(identity,inverse(X_20)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(inverse(greatest_lower_bound(X_20,identity)),least_upper_bound(identity,inverse(X_20))) ),[0],$fot(least_upper_bound(inverse(X_20),identity))]]) ).
cnf(refute_0_152,plain,
( inverse(greatest_lower_bound(X_20,identity)) != least_upper_bound(inverse(X_20),identity)
| inverse(greatest_lower_bound(X_20,identity)) = least_upper_bound(identity,inverse(X_20)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_20),identity),least_upper_bound(identity,inverse(X_20))) )],[refute_0_150,refute_0_151]) ).
cnf(refute_0_153,plain,
inverse(greatest_lower_bound(X_20,identity)) = least_upper_bound(identity,inverse(X_20)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_20,identity)),least_upper_bound(inverse(X_20),identity)) )],[refute_0_149,refute_0_152]) ).
cnf(refute_0_154,plain,
inverse(greatest_lower_bound(multiply(X_48,inverse(X_47)),identity)) = least_upper_bound(identity,inverse(multiply(X_48,inverse(X_47)))),
inference(subst,[],[refute_0_153:[bind(X_20,$fot(multiply(X_48,inverse(X_47))))]]) ).
cnf(refute_0_155,plain,
inverse(multiply(X_48,inverse(X_47))) = multiply(X_47,inverse(X_48)),
inference(subst,[],[refute_0_22:[bind(X,$fot(X_47)),bind(X_14,$fot(X_48))]]) ).
cnf(refute_0_156,plain,
( inverse(multiply(X_48,inverse(X_47))) != multiply(X_47,inverse(X_48))
| inverse(greatest_lower_bound(multiply(X_48,inverse(X_47)),identity)) != least_upper_bound(identity,inverse(multiply(X_48,inverse(X_47))))
| inverse(greatest_lower_bound(multiply(X_48,inverse(X_47)),identity)) = least_upper_bound(identity,multiply(X_47,inverse(X_48))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(multiply(X_48,inverse(X_47)),identity)),least_upper_bound(identity,inverse(multiply(X_48,inverse(X_47))))) ),[1,1],$fot(multiply(X_47,inverse(X_48)))]]) ).
cnf(refute_0_157,plain,
( inverse(greatest_lower_bound(multiply(X_48,inverse(X_47)),identity)) != least_upper_bound(identity,inverse(multiply(X_48,inverse(X_47))))
| inverse(greatest_lower_bound(multiply(X_48,inverse(X_47)),identity)) = least_upper_bound(identity,multiply(X_47,inverse(X_48))) ),
inference(resolve,[$cnf( $equal(inverse(multiply(X_48,inverse(X_47))),multiply(X_47,inverse(X_48))) )],[refute_0_155,refute_0_156]) ).
cnf(refute_0_158,plain,
inverse(greatest_lower_bound(multiply(X_48,inverse(X_47)),identity)) = least_upper_bound(identity,multiply(X_47,inverse(X_48))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(multiply(X_48,inverse(X_47)),identity)),least_upper_bound(identity,inverse(multiply(X_48,inverse(X_47))))) )],[refute_0_154,refute_0_157]) ).
cnf(refute_0_159,plain,
inverse(greatest_lower_bound(X_22,identity)) = least_upper_bound(identity,inverse(X_22)),
inference(subst,[],[refute_0_153:[bind(X_20,$fot(X_22))]]) ).
cnf(refute_0_160,plain,
greatest_lower_bound(identity,X_22) = greatest_lower_bound(X_22,identity),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(identity)),bind(Y,$fot(X_22))]]) ).
cnf(refute_0_161,plain,
( greatest_lower_bound(identity,X_22) != greatest_lower_bound(X_22,identity)
| greatest_lower_bound(X_22,identity) = greatest_lower_bound(identity,X_22) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(greatest_lower_bound(identity,X_22))),bind(Y0,$fot(greatest_lower_bound(X_22,identity)))]]) ).
cnf(refute_0_162,plain,
greatest_lower_bound(X_22,identity) = greatest_lower_bound(identity,X_22),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,X_22),greatest_lower_bound(X_22,identity)) )],[refute_0_160,refute_0_161]) ).
cnf(refute_0_163,plain,
( greatest_lower_bound(X_22,identity) != greatest_lower_bound(identity,X_22)
| inverse(greatest_lower_bound(X_22,identity)) != least_upper_bound(identity,inverse(X_22))
| inverse(greatest_lower_bound(identity,X_22)) = least_upper_bound(identity,inverse(X_22)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X_22,identity)),least_upper_bound(identity,inverse(X_22))) ),[0,0],$fot(greatest_lower_bound(identity,X_22))]]) ).
cnf(refute_0_164,plain,
( inverse(greatest_lower_bound(X_22,identity)) != least_upper_bound(identity,inverse(X_22))
| inverse(greatest_lower_bound(identity,X_22)) = least_upper_bound(identity,inverse(X_22)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_22,identity),greatest_lower_bound(identity,X_22)) )],[refute_0_162,refute_0_163]) ).
cnf(refute_0_165,plain,
inverse(greatest_lower_bound(identity,X_22)) = least_upper_bound(identity,inverse(X_22)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_22,identity)),least_upper_bound(identity,inverse(X_22))) )],[refute_0_159,refute_0_164]) ).
cnf(refute_0_166,plain,
( inverse(greatest_lower_bound(X_20,identity)) != least_upper_bound(identity,inverse(X_20))
| least_upper_bound(identity,inverse(X_20)) = inverse(greatest_lower_bound(X_20,identity)) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(inverse(greatest_lower_bound(X_20,identity)))),bind(Y0,$fot(least_upper_bound(identity,inverse(X_20))))]]) ).
cnf(refute_0_167,plain,
least_upper_bound(identity,inverse(X_20)) = inverse(greatest_lower_bound(X_20,identity)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_20,identity)),least_upper_bound(identity,inverse(X_20))) )],[refute_0_153,refute_0_166]) ).
cnf(refute_0_168,plain,
least_upper_bound(identity,inverse(X_22)) = inverse(greatest_lower_bound(X_22,identity)),
inference(subst,[],[refute_0_167:[bind(X_20,$fot(X_22))]]) ).
cnf(refute_0_169,plain,
( inverse(greatest_lower_bound(identity,X_22)) != least_upper_bound(identity,inverse(X_22))
| least_upper_bound(identity,inverse(X_22)) != inverse(greatest_lower_bound(X_22,identity))
| inverse(greatest_lower_bound(identity,X_22)) = inverse(greatest_lower_bound(X_22,identity)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(inverse(greatest_lower_bound(identity,X_22)),inverse(greatest_lower_bound(X_22,identity))) ),[0],$fot(least_upper_bound(identity,inverse(X_22)))]]) ).
cnf(refute_0_170,plain,
( inverse(greatest_lower_bound(identity,X_22)) != least_upper_bound(identity,inverse(X_22))
| inverse(greatest_lower_bound(identity,X_22)) = inverse(greatest_lower_bound(X_22,identity)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(X_22)),inverse(greatest_lower_bound(X_22,identity))) )],[refute_0_168,refute_0_169]) ).
cnf(refute_0_171,plain,
inverse(greatest_lower_bound(identity,X_22)) = inverse(greatest_lower_bound(X_22,identity)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,X_22)),least_upper_bound(identity,inverse(X_22))) )],[refute_0_165,refute_0_170]) ).
cnf(refute_0_172,plain,
( inverse(greatest_lower_bound(identity,X_22)) != inverse(greatest_lower_bound(X_22,identity))
| inverse(greatest_lower_bound(X_22,identity)) = inverse(greatest_lower_bound(identity,X_22)) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(inverse(greatest_lower_bound(identity,X_22)))),bind(Y0,$fot(inverse(greatest_lower_bound(X_22,identity))))]]) ).
cnf(refute_0_173,plain,
inverse(greatest_lower_bound(X_22,identity)) = inverse(greatest_lower_bound(identity,X_22)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,X_22)),inverse(greatest_lower_bound(X_22,identity))) )],[refute_0_171,refute_0_172]) ).
cnf(refute_0_174,plain,
inverse(greatest_lower_bound(multiply(X_48,inverse(X_47)),identity)) = inverse(greatest_lower_bound(identity,multiply(X_48,inverse(X_47)))),
inference(subst,[],[refute_0_173:[bind(X_22,$fot(multiply(X_48,inverse(X_47))))]]) ).
cnf(refute_0_175,plain,
( inverse(greatest_lower_bound(multiply(X_48,inverse(X_47)),identity)) != inverse(greatest_lower_bound(identity,multiply(X_48,inverse(X_47))))
| inverse(greatest_lower_bound(multiply(X_48,inverse(X_47)),identity)) != least_upper_bound(identity,multiply(X_47,inverse(X_48)))
| inverse(greatest_lower_bound(identity,multiply(X_48,inverse(X_47)))) = least_upper_bound(identity,multiply(X_47,inverse(X_48))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(multiply(X_48,inverse(X_47)),identity)),least_upper_bound(identity,multiply(X_47,inverse(X_48)))) ),[0],$fot(inverse(greatest_lower_bound(identity,multiply(X_48,inverse(X_47)))))]]) ).
cnf(refute_0_176,plain,
( inverse(greatest_lower_bound(multiply(X_48,inverse(X_47)),identity)) != least_upper_bound(identity,multiply(X_47,inverse(X_48)))
| inverse(greatest_lower_bound(identity,multiply(X_48,inverse(X_47)))) = least_upper_bound(identity,multiply(X_47,inverse(X_48))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(multiply(X_48,inverse(X_47)),identity)),inverse(greatest_lower_bound(identity,multiply(X_48,inverse(X_47))))) )],[refute_0_174,refute_0_175]) ).
cnf(refute_0_177,plain,
inverse(greatest_lower_bound(identity,multiply(X_48,inverse(X_47)))) = least_upper_bound(identity,multiply(X_47,inverse(X_48))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(multiply(X_48,inverse(X_47)),identity)),least_upper_bound(identity,multiply(X_47,inverse(X_48)))) )],[refute_0_158,refute_0_176]) ).
cnf(refute_0_178,plain,
inverse(greatest_lower_bound(identity,multiply(X_108,inverse(X)))) = least_upper_bound(identity,multiply(X,inverse(X_108))),
inference(subst,[],[refute_0_177:[bind(X_47,$fot(X)),bind(X_48,$fot(X_108))]]) ).
cnf(refute_0_179,plain,
( inverse(greatest_lower_bound(identity,multiply(X_108,inverse(X)))) != multiply(X,inverse(greatest_lower_bound(inverse(inverse(X)),X_108)))
| inverse(greatest_lower_bound(identity,multiply(X_108,inverse(X)))) != least_upper_bound(identity,multiply(X,inverse(X_108)))
| least_upper_bound(identity,multiply(X,inverse(X_108))) = multiply(X,inverse(greatest_lower_bound(inverse(inverse(X)),X_108))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(X_108,inverse(X)))),multiply(X,inverse(greatest_lower_bound(inverse(inverse(X)),X_108)))) ),[0],$fot(least_upper_bound(identity,multiply(X,inverse(X_108))))]]) ).
cnf(refute_0_180,plain,
( inverse(greatest_lower_bound(identity,multiply(X_108,inverse(X)))) != multiply(X,inverse(greatest_lower_bound(inverse(inverse(X)),X_108)))
| least_upper_bound(identity,multiply(X,inverse(X_108))) = multiply(X,inverse(greatest_lower_bound(inverse(inverse(X)),X_108))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(X_108,inverse(X)))),least_upper_bound(identity,multiply(X,inverse(X_108)))) )],[refute_0_178,refute_0_179]) ).
cnf(refute_0_181,plain,
( inverse(greatest_lower_bound(X,Y)) != least_upper_bound(inverse(X),inverse(Y))
| least_upper_bound(inverse(X),inverse(Y)) = inverse(greatest_lower_bound(X,Y)) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(inverse(greatest_lower_bound(X,Y)))),bind(Y0,$fot(least_upper_bound(inverse(X),inverse(Y))))]]) ).
cnf(refute_0_182,plain,
least_upper_bound(inverse(X),inverse(Y)) = inverse(greatest_lower_bound(X,Y)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X,Y)),least_upper_bound(inverse(X),inverse(Y))) )],[p12x_6,refute_0_181]) ).
cnf(refute_0_183,plain,
least_upper_bound(inverse(X),inverse(X_108)) = inverse(greatest_lower_bound(X,X_108)),
inference(subst,[],[refute_0_182:[bind(Y,$fot(X_108))]]) ).
cnf(refute_0_184,plain,
inverse(greatest_lower_bound(inverse(X),X_21)) = least_upper_bound(inverse(inverse(X)),inverse(X_21)),
inference(subst,[],[p12x_6:[bind(X,$fot(inverse(X))),bind(Y,$fot(X_21))]]) ).
cnf(refute_0_185,plain,
( inverse(greatest_lower_bound(inverse(X),X_21)) != least_upper_bound(inverse(inverse(X)),inverse(X_21))
| inverse(inverse(X)) != X
| inverse(greatest_lower_bound(inverse(X),X_21)) = least_upper_bound(X,inverse(X_21)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(inverse(X),X_21)),least_upper_bound(inverse(inverse(X)),inverse(X_21))) ),[1,0],$fot(X)]]) ).
cnf(refute_0_186,plain,
( inverse(greatest_lower_bound(inverse(X),X_21)) != least_upper_bound(inverse(inverse(X)),inverse(X_21))
| inverse(greatest_lower_bound(inverse(X),X_21)) = least_upper_bound(X,inverse(X_21)) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p12x_2,refute_0_185]) ).
cnf(refute_0_187,plain,
inverse(greatest_lower_bound(inverse(X),X_21)) = least_upper_bound(X,inverse(X_21)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(X),X_21)),least_upper_bound(inverse(inverse(X)),inverse(X_21))) )],[refute_0_184,refute_0_186]) ).
cnf(refute_0_188,plain,
inverse(greatest_lower_bound(inverse(inverse(X)),X_108)) = least_upper_bound(inverse(X),inverse(X_108)),
inference(subst,[],[refute_0_187:[bind(X,$fot(inverse(X))),bind(X_21,$fot(X_108))]]) ).
cnf(refute_0_189,plain,
( inverse(greatest_lower_bound(inverse(inverse(X)),X_108)) != least_upper_bound(inverse(X),inverse(X_108))
| least_upper_bound(inverse(X),inverse(X_108)) != inverse(greatest_lower_bound(X,X_108))
| inverse(greatest_lower_bound(inverse(inverse(X)),X_108)) = inverse(greatest_lower_bound(X,X_108)) ),
inference(subst,[],[refute_0_26:[bind(X0,$fot(inverse(greatest_lower_bound(inverse(inverse(X)),X_108)))),bind(Y0,$fot(least_upper_bound(inverse(X),inverse(X_108)))),bind(Z0,$fot(inverse(greatest_lower_bound(X,X_108))))]]) ).
cnf(refute_0_190,plain,
( least_upper_bound(inverse(X),inverse(X_108)) != inverse(greatest_lower_bound(X,X_108))
| inverse(greatest_lower_bound(inverse(inverse(X)),X_108)) = inverse(greatest_lower_bound(X,X_108)) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(inverse(X)),X_108)),least_upper_bound(inverse(X),inverse(X_108))) )],[refute_0_188,refute_0_189]) ).
cnf(refute_0_191,plain,
inverse(greatest_lower_bound(inverse(inverse(X)),X_108)) = inverse(greatest_lower_bound(X,X_108)),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X),inverse(X_108)),inverse(greatest_lower_bound(X,X_108))) )],[refute_0_183,refute_0_190]) ).
cnf(refute_0_192,plain,
multiply(X,inverse(greatest_lower_bound(inverse(inverse(X)),X_108))) = multiply(X,inverse(greatest_lower_bound(inverse(inverse(X)),X_108))),
introduced(tautology,[refl,[$fot(multiply(X,inverse(greatest_lower_bound(inverse(inverse(X)),X_108))))]]) ).
cnf(refute_0_193,plain,
( multiply(X,inverse(greatest_lower_bound(inverse(inverse(X)),X_108))) != multiply(X,inverse(greatest_lower_bound(inverse(inverse(X)),X_108)))
| inverse(greatest_lower_bound(inverse(inverse(X)),X_108)) != inverse(greatest_lower_bound(X,X_108))
| multiply(X,inverse(greatest_lower_bound(inverse(inverse(X)),X_108))) = multiply(X,inverse(greatest_lower_bound(X,X_108))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X,inverse(greatest_lower_bound(inverse(inverse(X)),X_108))),multiply(X,inverse(greatest_lower_bound(inverse(inverse(X)),X_108)))) ),[1,1],$fot(inverse(greatest_lower_bound(X,X_108)))]]) ).
cnf(refute_0_194,plain,
( inverse(greatest_lower_bound(inverse(inverse(X)),X_108)) != inverse(greatest_lower_bound(X,X_108))
| multiply(X,inverse(greatest_lower_bound(inverse(inverse(X)),X_108))) = multiply(X,inverse(greatest_lower_bound(X,X_108))) ),
inference(resolve,[$cnf( $equal(multiply(X,inverse(greatest_lower_bound(inverse(inverse(X)),X_108))),multiply(X,inverse(greatest_lower_bound(inverse(inverse(X)),X_108)))) )],[refute_0_192,refute_0_193]) ).
cnf(refute_0_195,plain,
multiply(X,inverse(greatest_lower_bound(inverse(inverse(X)),X_108))) = multiply(X,inverse(greatest_lower_bound(X,X_108))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(inverse(X)),X_108)),inverse(greatest_lower_bound(X,X_108))) )],[refute_0_191,refute_0_194]) ).
cnf(refute_0_196,plain,
( multiply(X,inverse(greatest_lower_bound(inverse(inverse(X)),X_108))) != multiply(X,inverse(greatest_lower_bound(X,X_108)))
| least_upper_bound(identity,multiply(X,inverse(X_108))) != multiply(X,inverse(greatest_lower_bound(inverse(inverse(X)),X_108)))
| least_upper_bound(identity,multiply(X,inverse(X_108))) = multiply(X,inverse(greatest_lower_bound(X,X_108))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(X,inverse(X_108))),multiply(X,inverse(greatest_lower_bound(inverse(inverse(X)),X_108)))) ),[1],$fot(multiply(X,inverse(greatest_lower_bound(X,X_108))))]]) ).
cnf(refute_0_197,plain,
( least_upper_bound(identity,multiply(X,inverse(X_108))) != multiply(X,inverse(greatest_lower_bound(inverse(inverse(X)),X_108)))
| least_upper_bound(identity,multiply(X,inverse(X_108))) = multiply(X,inverse(greatest_lower_bound(X,X_108))) ),
inference(resolve,[$cnf( $equal(multiply(X,inverse(greatest_lower_bound(inverse(inverse(X)),X_108))),multiply(X,inverse(greatest_lower_bound(X,X_108)))) )],[refute_0_195,refute_0_196]) ).
cnf(refute_0_198,plain,
( inverse(greatest_lower_bound(identity,multiply(X_108,inverse(X)))) != multiply(X,inverse(greatest_lower_bound(inverse(inverse(X)),X_108)))
| least_upper_bound(identity,multiply(X,inverse(X_108))) = multiply(X,inverse(greatest_lower_bound(X,X_108))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X,inverse(X_108))),multiply(X,inverse(greatest_lower_bound(inverse(inverse(X)),X_108)))) )],[refute_0_180,refute_0_197]) ).
cnf(refute_0_199,plain,
least_upper_bound(identity,multiply(X,inverse(X_108))) = multiply(X,inverse(greatest_lower_bound(X,X_108))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(X_108,inverse(X)))),multiply(X,inverse(greatest_lower_bound(inverse(inverse(X)),X_108)))) )],[refute_0_145,refute_0_198]) ).
cnf(refute_0_200,plain,
least_upper_bound(identity,multiply(identity,inverse(X_92))) = multiply(identity,inverse(greatest_lower_bound(identity,X_92))),
inference(subst,[],[refute_0_199:[bind(X,$fot(identity)),bind(X_108,$fot(X_92))]]) ).
cnf(refute_0_201,plain,
( multiply(identity,inverse(greatest_lower_bound(identity,X_92))) != inverse(greatest_lower_bound(identity,X_92))
| least_upper_bound(identity,multiply(identity,inverse(X_92))) != multiply(identity,inverse(greatest_lower_bound(identity,X_92)))
| least_upper_bound(identity,multiply(identity,inverse(X_92))) = inverse(greatest_lower_bound(identity,X_92)) ),
inference(subst,[],[refute_0_26:[bind(X0,$fot(least_upper_bound(identity,multiply(identity,inverse(X_92))))),bind(Y0,$fot(multiply(identity,inverse(greatest_lower_bound(identity,X_92))))),bind(Z0,$fot(inverse(greatest_lower_bound(identity,X_92))))]]) ).
cnf(refute_0_202,plain,
( multiply(identity,inverse(greatest_lower_bound(identity,X_92))) != inverse(greatest_lower_bound(identity,X_92))
| least_upper_bound(identity,multiply(identity,inverse(X_92))) = inverse(greatest_lower_bound(identity,X_92)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(identity,inverse(X_92))),multiply(identity,inverse(greatest_lower_bound(identity,X_92)))) )],[refute_0_200,refute_0_201]) ).
cnf(refute_0_203,plain,
least_upper_bound(identity,multiply(identity,inverse(X_92))) = inverse(greatest_lower_bound(identity,X_92)),
inference(resolve,[$cnf( $equal(multiply(identity,inverse(greatest_lower_bound(identity,X_92))),inverse(greatest_lower_bound(identity,X_92))) )],[refute_0_135,refute_0_202]) ).
cnf(refute_0_204,plain,
( multiply(least_upper_bound(identity,X_92),inverse(X_92)) != least_upper_bound(identity,multiply(identity,inverse(X_92)))
| least_upper_bound(identity,multiply(identity,inverse(X_92))) != inverse(greatest_lower_bound(identity,X_92))
| multiply(least_upper_bound(identity,X_92),inverse(X_92)) = inverse(greatest_lower_bound(identity,X_92)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(identity,X_92),inverse(X_92)),inverse(greatest_lower_bound(identity,X_92))) ),[0],$fot(least_upper_bound(identity,multiply(identity,inverse(X_92))))]]) ).
cnf(refute_0_205,plain,
( multiply(least_upper_bound(identity,X_92),inverse(X_92)) != least_upper_bound(identity,multiply(identity,inverse(X_92)))
| multiply(least_upper_bound(identity,X_92),inverse(X_92)) = inverse(greatest_lower_bound(identity,X_92)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(identity,inverse(X_92))),inverse(greatest_lower_bound(identity,X_92))) )],[refute_0_203,refute_0_204]) ).
cnf(refute_0_206,plain,
multiply(least_upper_bound(identity,X_92),inverse(X_92)) = inverse(greatest_lower_bound(identity,X_92)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_92),inverse(X_92)),least_upper_bound(identity,multiply(identity,inverse(X_92)))) )],[refute_0_134,refute_0_205]) ).
cnf(refute_0_207,plain,
multiply(least_upper_bound(identity,multiply(X_93,inverse(X_92))),inverse(multiply(X_93,inverse(X_92)))) = inverse(greatest_lower_bound(identity,multiply(X_93,inverse(X_92)))),
inference(subst,[],[refute_0_206:[bind(X_92,$fot(multiply(X_93,inverse(X_92))))]]) ).
cnf(refute_0_208,plain,
( multiply(least_upper_bound(X_92,X_93),inverse(X_92)) != least_upper_bound(identity,multiply(X_93,inverse(X_92)))
| least_upper_bound(identity,multiply(X_93,inverse(X_92))) = multiply(least_upper_bound(X_92,X_93),inverse(X_92)) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(multiply(least_upper_bound(X_92,X_93),inverse(X_92)))),bind(Y0,$fot(least_upper_bound(identity,multiply(X_93,inverse(X_92)))))]]) ).
cnf(refute_0_209,plain,
least_upper_bound(identity,multiply(X_93,inverse(X_92))) = multiply(least_upper_bound(X_92,X_93),inverse(X_92)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_92,X_93),inverse(X_92)),least_upper_bound(identity,multiply(X_93,inverse(X_92)))) )],[refute_0_98,refute_0_208]) ).
cnf(refute_0_210,plain,
( multiply(least_upper_bound(identity,multiply(X_93,inverse(X_92))),inverse(multiply(X_93,inverse(X_92)))) != inverse(greatest_lower_bound(identity,multiply(X_93,inverse(X_92))))
| least_upper_bound(identity,multiply(X_93,inverse(X_92))) != multiply(least_upper_bound(X_92,X_93),inverse(X_92))
| multiply(multiply(least_upper_bound(X_92,X_93),inverse(X_92)),inverse(multiply(X_93,inverse(X_92)))) = inverse(greatest_lower_bound(identity,multiply(X_93,inverse(X_92)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(X_93,inverse(X_92))),inverse(multiply(X_93,inverse(X_92)))),inverse(greatest_lower_bound(identity,multiply(X_93,inverse(X_92))))) ),[0,0],$fot(multiply(least_upper_bound(X_92,X_93),inverse(X_92)))]]) ).
cnf(refute_0_211,plain,
( multiply(least_upper_bound(identity,multiply(X_93,inverse(X_92))),inverse(multiply(X_93,inverse(X_92)))) != inverse(greatest_lower_bound(identity,multiply(X_93,inverse(X_92))))
| multiply(multiply(least_upper_bound(X_92,X_93),inverse(X_92)),inverse(multiply(X_93,inverse(X_92)))) = inverse(greatest_lower_bound(identity,multiply(X_93,inverse(X_92)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_93,inverse(X_92))),multiply(least_upper_bound(X_92,X_93),inverse(X_92))) )],[refute_0_209,refute_0_210]) ).
cnf(refute_0_212,plain,
multiply(multiply(least_upper_bound(X_92,X_93),inverse(X_92)),inverse(multiply(X_93,inverse(X_92)))) = inverse(greatest_lower_bound(identity,multiply(X_93,inverse(X_92)))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(X_93,inverse(X_92))),inverse(multiply(X_93,inverse(X_92)))),inverse(greatest_lower_bound(identity,multiply(X_93,inverse(X_92))))) )],[refute_0_207,refute_0_211]) ).
cnf(refute_0_213,plain,
( inverse(X) != multiply(Y,inverse(multiply(X,Y)))
| multiply(Y,inverse(multiply(X,Y))) = inverse(X) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(inverse(X))),bind(Y0,$fot(multiply(Y,inverse(multiply(X,Y)))))]]) ).
cnf(refute_0_214,plain,
multiply(Y,inverse(multiply(X,Y))) = inverse(X),
inference(resolve,[$cnf( $equal(inverse(X),multiply(Y,inverse(multiply(X,Y)))) )],[refute_0_32,refute_0_213]) ).
cnf(refute_0_215,plain,
multiply(inverse(X_92),inverse(multiply(X_93,inverse(X_92)))) = inverse(X_93),
inference(subst,[],[refute_0_214:[bind(X,$fot(X_93)),bind(Y,$fot(inverse(X_92)))]]) ).
cnf(refute_0_216,plain,
multiply(least_upper_bound(X_92,X_93),multiply(inverse(X_92),inverse(multiply(X_93,inverse(X_92))))) = multiply(least_upper_bound(X_92,X_93),multiply(inverse(X_92),inverse(multiply(X_93,inverse(X_92))))),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(X_92,X_93),multiply(inverse(X_92),inverse(multiply(X_93,inverse(X_92))))))]]) ).
cnf(refute_0_217,plain,
( multiply(inverse(X_92),inverse(multiply(X_93,inverse(X_92)))) != inverse(X_93)
| multiply(least_upper_bound(X_92,X_93),multiply(inverse(X_92),inverse(multiply(X_93,inverse(X_92))))) != multiply(least_upper_bound(X_92,X_93),multiply(inverse(X_92),inverse(multiply(X_93,inverse(X_92)))))
| multiply(least_upper_bound(X_92,X_93),multiply(inverse(X_92),inverse(multiply(X_93,inverse(X_92))))) = multiply(least_upper_bound(X_92,X_93),inverse(X_93)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_92,X_93),multiply(inverse(X_92),inverse(multiply(X_93,inverse(X_92))))),multiply(least_upper_bound(X_92,X_93),multiply(inverse(X_92),inverse(multiply(X_93,inverse(X_92)))))) ),[1,1],$fot(inverse(X_93))]]) ).
cnf(refute_0_218,plain,
( multiply(inverse(X_92),inverse(multiply(X_93,inverse(X_92)))) != inverse(X_93)
| multiply(least_upper_bound(X_92,X_93),multiply(inverse(X_92),inverse(multiply(X_93,inverse(X_92))))) = multiply(least_upper_bound(X_92,X_93),inverse(X_93)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_92,X_93),multiply(inverse(X_92),inverse(multiply(X_93,inverse(X_92))))),multiply(least_upper_bound(X_92,X_93),multiply(inverse(X_92),inverse(multiply(X_93,inverse(X_92)))))) )],[refute_0_216,refute_0_217]) ).
cnf(refute_0_219,plain,
multiply(least_upper_bound(X_92,X_93),multiply(inverse(X_92),inverse(multiply(X_93,inverse(X_92))))) = multiply(least_upper_bound(X_92,X_93),inverse(X_93)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_92),inverse(multiply(X_93,inverse(X_92)))),inverse(X_93)) )],[refute_0_215,refute_0_218]) ).
cnf(refute_0_220,plain,
multiply(multiply(least_upper_bound(X_92,X_93),inverse(X_92)),inverse(multiply(X_93,inverse(X_92)))) = multiply(least_upper_bound(X_92,X_93),multiply(inverse(X_92),inverse(multiply(X_93,inverse(X_92))))),
inference(subst,[],[associativity:[bind(X,$fot(least_upper_bound(X_92,X_93))),bind(Y,$fot(inverse(X_92))),bind(Z,$fot(inverse(multiply(X_93,inverse(X_92)))))]]) ).
cnf(refute_0_221,plain,
( multiply(multiply(least_upper_bound(X_92,X_93),inverse(X_92)),inverse(multiply(X_93,inverse(X_92)))) != multiply(least_upper_bound(X_92,X_93),multiply(inverse(X_92),inverse(multiply(X_93,inverse(X_92)))))
| multiply(least_upper_bound(X_92,X_93),multiply(inverse(X_92),inverse(multiply(X_93,inverse(X_92))))) != multiply(least_upper_bound(X_92,X_93),inverse(X_93))
| multiply(multiply(least_upper_bound(X_92,X_93),inverse(X_92)),inverse(multiply(X_93,inverse(X_92)))) = multiply(least_upper_bound(X_92,X_93),inverse(X_93)) ),
inference(subst,[],[refute_0_26:[bind(X0,$fot(multiply(multiply(least_upper_bound(X_92,X_93),inverse(X_92)),inverse(multiply(X_93,inverse(X_92)))))),bind(Y0,$fot(multiply(least_upper_bound(X_92,X_93),multiply(inverse(X_92),inverse(multiply(X_93,inverse(X_92))))))),bind(Z0,$fot(multiply(least_upper_bound(X_92,X_93),inverse(X_93))))]]) ).
cnf(refute_0_222,plain,
( multiply(least_upper_bound(X_92,X_93),multiply(inverse(X_92),inverse(multiply(X_93,inverse(X_92))))) != multiply(least_upper_bound(X_92,X_93),inverse(X_93))
| multiply(multiply(least_upper_bound(X_92,X_93),inverse(X_92)),inverse(multiply(X_93,inverse(X_92)))) = multiply(least_upper_bound(X_92,X_93),inverse(X_93)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(least_upper_bound(X_92,X_93),inverse(X_92)),inverse(multiply(X_93,inverse(X_92)))),multiply(least_upper_bound(X_92,X_93),multiply(inverse(X_92),inverse(multiply(X_93,inverse(X_92)))))) )],[refute_0_220,refute_0_221]) ).
cnf(refute_0_223,plain,
multiply(multiply(least_upper_bound(X_92,X_93),inverse(X_92)),inverse(multiply(X_93,inverse(X_92)))) = multiply(least_upper_bound(X_92,X_93),inverse(X_93)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_92,X_93),multiply(inverse(X_92),inverse(multiply(X_93,inverse(X_92))))),multiply(least_upper_bound(X_92,X_93),inverse(X_93))) )],[refute_0_219,refute_0_222]) ).
cnf(refute_0_224,plain,
( multiply(multiply(least_upper_bound(X_92,X_93),inverse(X_92)),inverse(multiply(X_93,inverse(X_92)))) != multiply(least_upper_bound(X_92,X_93),inverse(X_93))
| multiply(multiply(least_upper_bound(X_92,X_93),inverse(X_92)),inverse(multiply(X_93,inverse(X_92)))) != inverse(greatest_lower_bound(identity,multiply(X_93,inverse(X_92))))
| multiply(least_upper_bound(X_92,X_93),inverse(X_93)) = inverse(greatest_lower_bound(identity,multiply(X_93,inverse(X_92)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(least_upper_bound(X_92,X_93),inverse(X_92)),inverse(multiply(X_93,inverse(X_92)))),inverse(greatest_lower_bound(identity,multiply(X_93,inverse(X_92))))) ),[0],$fot(multiply(least_upper_bound(X_92,X_93),inverse(X_93)))]]) ).
cnf(refute_0_225,plain,
( multiply(multiply(least_upper_bound(X_92,X_93),inverse(X_92)),inverse(multiply(X_93,inverse(X_92)))) != inverse(greatest_lower_bound(identity,multiply(X_93,inverse(X_92))))
| multiply(least_upper_bound(X_92,X_93),inverse(X_93)) = inverse(greatest_lower_bound(identity,multiply(X_93,inverse(X_92)))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(least_upper_bound(X_92,X_93),inverse(X_92)),inverse(multiply(X_93,inverse(X_92)))),multiply(least_upper_bound(X_92,X_93),inverse(X_93))) )],[refute_0_223,refute_0_224]) ).
cnf(refute_0_226,plain,
inverse(greatest_lower_bound(identity,multiply(X_93,inverse(X_92)))) = least_upper_bound(identity,multiply(X_92,inverse(X_93))),
inference(subst,[],[refute_0_177:[bind(X_47,$fot(X_92)),bind(X_48,$fot(X_93))]]) ).
cnf(refute_0_227,plain,
( multiply(least_upper_bound(X_92,X_93),inverse(X_93)) != inverse(greatest_lower_bound(identity,multiply(X_93,inverse(X_92))))
| inverse(greatest_lower_bound(identity,multiply(X_93,inverse(X_92)))) != least_upper_bound(identity,multiply(X_92,inverse(X_93)))
| multiply(least_upper_bound(X_92,X_93),inverse(X_93)) = least_upper_bound(identity,multiply(X_92,inverse(X_93))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_92,X_93),inverse(X_93)),least_upper_bound(identity,multiply(X_92,inverse(X_93)))) ),[0],$fot(inverse(greatest_lower_bound(identity,multiply(X_93,inverse(X_92)))))]]) ).
cnf(refute_0_228,plain,
( multiply(least_upper_bound(X_92,X_93),inverse(X_93)) != inverse(greatest_lower_bound(identity,multiply(X_93,inverse(X_92))))
| multiply(least_upper_bound(X_92,X_93),inverse(X_93)) = least_upper_bound(identity,multiply(X_92,inverse(X_93))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(X_93,inverse(X_92)))),least_upper_bound(identity,multiply(X_92,inverse(X_93)))) )],[refute_0_226,refute_0_227]) ).
cnf(refute_0_229,plain,
( multiply(multiply(least_upper_bound(X_92,X_93),inverse(X_92)),inverse(multiply(X_93,inverse(X_92)))) != inverse(greatest_lower_bound(identity,multiply(X_93,inverse(X_92))))
| multiply(least_upper_bound(X_92,X_93),inverse(X_93)) = least_upper_bound(identity,multiply(X_92,inverse(X_93))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_92,X_93),inverse(X_93)),inverse(greatest_lower_bound(identity,multiply(X_93,inverse(X_92))))) )],[refute_0_225,refute_0_228]) ).
cnf(refute_0_230,plain,
multiply(least_upper_bound(X_92,X_93),inverse(X_93)) = least_upper_bound(identity,multiply(X_92,inverse(X_93))),
inference(resolve,[$cnf( $equal(multiply(multiply(least_upper_bound(X_92,X_93),inverse(X_92)),inverse(multiply(X_93,inverse(X_92)))),inverse(greatest_lower_bound(identity,multiply(X_93,inverse(X_92))))) )],[refute_0_212,refute_0_229]) ).
cnf(refute_0_231,plain,
( multiply(least_upper_bound(X_92,X_93),inverse(X_93)) != least_upper_bound(identity,multiply(X_92,inverse(X_93)))
| least_upper_bound(identity,multiply(X_92,inverse(X_93))) = multiply(least_upper_bound(X_92,X_93),inverse(X_93)) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(multiply(least_upper_bound(X_92,X_93),inverse(X_93)))),bind(Y0,$fot(least_upper_bound(identity,multiply(X_92,inverse(X_93)))))]]) ).
cnf(refute_0_232,plain,
least_upper_bound(identity,multiply(X_92,inverse(X_93))) = multiply(least_upper_bound(X_92,X_93),inverse(X_93)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_92,X_93),inverse(X_93)),least_upper_bound(identity,multiply(X_92,inverse(X_93)))) )],[refute_0_230,refute_0_231]) ).
cnf(refute_0_233,plain,
least_upper_bound(identity,multiply(b,inverse(c))) = multiply(least_upper_bound(b,c),inverse(c)),
inference(subst,[],[refute_0_232:[bind(X_92,$fot(b)),bind(X_93,$fot(c))]]) ).
cnf(refute_0_234,plain,
( multiply(least_upper_bound(b,c),inverse(c)) != multiply(b,inverse(greatest_lower_bound(b,c)))
| least_upper_bound(identity,multiply(b,inverse(c))) != multiply(least_upper_bound(b,c),inverse(c))
| least_upper_bound(identity,multiply(b,inverse(c))) = multiply(b,inverse(greatest_lower_bound(b,c))) ),
inference(subst,[],[refute_0_26:[bind(X0,$fot(least_upper_bound(identity,multiply(b,inverse(c))))),bind(Y0,$fot(multiply(least_upper_bound(b,c),inverse(c)))),bind(Z0,$fot(multiply(b,inverse(greatest_lower_bound(b,c)))))]]) ).
cnf(refute_0_235,plain,
( multiply(least_upper_bound(b,c),inverse(c)) != multiply(b,inverse(greatest_lower_bound(b,c)))
| least_upper_bound(identity,multiply(b,inverse(c))) = multiply(b,inverse(greatest_lower_bound(b,c))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(b,inverse(c))),multiply(least_upper_bound(b,c),inverse(c))) )],[refute_0_233,refute_0_234]) ).
cnf(refute_0_236,plain,
least_upper_bound(identity,multiply(b,inverse(c))) = multiply(b,inverse(greatest_lower_bound(b,c))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,c),inverse(c)),multiply(b,inverse(greatest_lower_bound(b,c)))) )],[refute_0_93,refute_0_235]) ).
cnf(refute_0_237,plain,
( multiply(b,inverse(greatest_lower_bound(b,c))) != multiply(b,inverse(greatest_lower_bound(a,c)))
| least_upper_bound(identity,multiply(b,inverse(c))) != multiply(b,inverse(greatest_lower_bound(b,c)))
| least_upper_bound(identity,multiply(b,inverse(c))) = multiply(b,inverse(greatest_lower_bound(a,c))) ),
inference(subst,[],[refute_0_26:[bind(X0,$fot(least_upper_bound(identity,multiply(b,inverse(c))))),bind(Y0,$fot(multiply(b,inverse(greatest_lower_bound(b,c))))),bind(Z0,$fot(multiply(b,inverse(greatest_lower_bound(a,c)))))]]) ).
cnf(refute_0_238,plain,
( multiply(b,inverse(greatest_lower_bound(b,c))) != multiply(b,inverse(greatest_lower_bound(a,c)))
| least_upper_bound(identity,multiply(b,inverse(c))) = multiply(b,inverse(greatest_lower_bound(a,c))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(b,inverse(c))),multiply(b,inverse(greatest_lower_bound(b,c)))) )],[refute_0_236,refute_0_237]) ).
cnf(refute_0_239,plain,
least_upper_bound(identity,multiply(b,inverse(c))) = multiply(b,inverse(greatest_lower_bound(a,c))),
inference(resolve,[$cnf( $equal(multiply(b,inverse(greatest_lower_bound(b,c))),multiply(b,inverse(greatest_lower_bound(a,c)))) )],[refute_0_92,refute_0_238]) ).
cnf(refute_0_240,plain,
( multiply(a,inverse(greatest_lower_bound(a,c))) != least_upper_bound(identity,multiply(b,inverse(c)))
| least_upper_bound(identity,multiply(b,inverse(c))) != multiply(b,inverse(greatest_lower_bound(a,c)))
| multiply(a,inverse(greatest_lower_bound(a,c))) = multiply(b,inverse(greatest_lower_bound(a,c))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(a,inverse(greatest_lower_bound(a,c))),multiply(b,inverse(greatest_lower_bound(a,c)))) ),[0],$fot(least_upper_bound(identity,multiply(b,inverse(c))))]]) ).
cnf(refute_0_241,plain,
( multiply(a,inverse(greatest_lower_bound(a,c))) != least_upper_bound(identity,multiply(b,inverse(c)))
| multiply(a,inverse(greatest_lower_bound(a,c))) = multiply(b,inverse(greatest_lower_bound(a,c))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(b,inverse(c))),multiply(b,inverse(greatest_lower_bound(a,c)))) )],[refute_0_239,refute_0_240]) ).
cnf(refute_0_242,plain,
( multiply(least_upper_bound(a,c),inverse(c)) != least_upper_bound(identity,multiply(b,inverse(c)))
| multiply(a,inverse(greatest_lower_bound(a,c))) = multiply(b,inverse(greatest_lower_bound(a,c))) ),
inference(resolve,[$cnf( $equal(multiply(a,inverse(greatest_lower_bound(a,c))),least_upper_bound(identity,multiply(b,inverse(c)))) )],[refute_0_82,refute_0_241]) ).
cnf(refute_0_243,plain,
multiply(a,inverse(greatest_lower_bound(a,c))) = multiply(b,inverse(greatest_lower_bound(a,c))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,c),inverse(c)),least_upper_bound(identity,multiply(b,inverse(c)))) )],[refute_0_54,refute_0_242]) ).
cnf(refute_0_244,plain,
( multiply(a,inverse(greatest_lower_bound(a,c))) != multiply(b,inverse(greatest_lower_bound(a,c)))
| multiply(b,inverse(greatest_lower_bound(a,c))) = multiply(a,inverse(greatest_lower_bound(a,c))) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(multiply(a,inverse(greatest_lower_bound(a,c))))),bind(Y0,$fot(multiply(b,inverse(greatest_lower_bound(a,c)))))]]) ).
cnf(refute_0_245,plain,
multiply(b,inverse(greatest_lower_bound(a,c))) = multiply(a,inverse(greatest_lower_bound(a,c))),
inference(resolve,[$cnf( $equal(multiply(a,inverse(greatest_lower_bound(a,c))),multiply(b,inverse(greatest_lower_bound(a,c)))) )],[refute_0_243,refute_0_244]) ).
cnf(refute_0_246,plain,
( multiply(b,inverse(greatest_lower_bound(a,c))) != multiply(a,inverse(greatest_lower_bound(a,c)))
| inverse(b) != multiply(inverse(greatest_lower_bound(a,c)),inverse(multiply(b,inverse(greatest_lower_bound(a,c)))))
| inverse(b) = multiply(inverse(greatest_lower_bound(a,c)),inverse(multiply(a,inverse(greatest_lower_bound(a,c))))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(b),multiply(inverse(greatest_lower_bound(a,c)),inverse(multiply(b,inverse(greatest_lower_bound(a,c)))))) ),[1,1,0],$fot(multiply(a,inverse(greatest_lower_bound(a,c))))]]) ).
cnf(refute_0_247,plain,
( inverse(b) != multiply(inverse(greatest_lower_bound(a,c)),inverse(multiply(b,inverse(greatest_lower_bound(a,c)))))
| inverse(b) = multiply(inverse(greatest_lower_bound(a,c)),inverse(multiply(a,inverse(greatest_lower_bound(a,c))))) ),
inference(resolve,[$cnf( $equal(multiply(b,inverse(greatest_lower_bound(a,c))),multiply(a,inverse(greatest_lower_bound(a,c)))) )],[refute_0_245,refute_0_246]) ).
cnf(refute_0_248,plain,
inverse(b) = multiply(inverse(greatest_lower_bound(a,c)),inverse(multiply(a,inverse(greatest_lower_bound(a,c))))),
inference(resolve,[$cnf( $equal(inverse(b),multiply(inverse(greatest_lower_bound(a,c)),inverse(multiply(b,inverse(greatest_lower_bound(a,c)))))) )],[refute_0_33,refute_0_247]) ).
cnf(refute_0_249,plain,
multiply(inverse(greatest_lower_bound(a,c)),inverse(multiply(a,inverse(greatest_lower_bound(a,c))))) = inverse(a),
inference(subst,[],[refute_0_214:[bind(X,$fot(a)),bind(Y,$fot(inverse(greatest_lower_bound(a,c))))]]) ).
cnf(refute_0_250,plain,
( multiply(inverse(greatest_lower_bound(a,c)),inverse(multiply(a,inverse(greatest_lower_bound(a,c))))) != inverse(a)
| inverse(b) != multiply(inverse(greatest_lower_bound(a,c)),inverse(multiply(a,inverse(greatest_lower_bound(a,c)))))
| inverse(b) = inverse(a) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(b),multiply(inverse(greatest_lower_bound(a,c)),inverse(multiply(a,inverse(greatest_lower_bound(a,c)))))) ),[1],$fot(inverse(a))]]) ).
cnf(refute_0_251,plain,
( inverse(b) != multiply(inverse(greatest_lower_bound(a,c)),inverse(multiply(a,inverse(greatest_lower_bound(a,c)))))
| inverse(b) = inverse(a) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(a,c)),inverse(multiply(a,inverse(greatest_lower_bound(a,c))))),inverse(a)) )],[refute_0_249,refute_0_250]) ).
cnf(refute_0_252,plain,
inverse(b) = inverse(a),
inference(resolve,[$cnf( $equal(inverse(b),multiply(inverse(greatest_lower_bound(a,c)),inverse(multiply(a,inverse(greatest_lower_bound(a,c)))))) )],[refute_0_248,refute_0_251]) ).
cnf(refute_0_253,plain,
( inverse(b) != inverse(a)
| inverse(inverse(b)) != b
| inverse(inverse(a)) = b ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(b)),b) ),[0,0],$fot(inverse(a))]]) ).
cnf(refute_0_254,plain,
( inverse(inverse(b)) != b
| inverse(inverse(a)) = b ),
inference(resolve,[$cnf( $equal(inverse(b),inverse(a)) )],[refute_0_252,refute_0_253]) ).
cnf(refute_0_255,plain,
inverse(inverse(a)) = b,
inference(resolve,[$cnf( $equal(inverse(inverse(b)),b) )],[refute_0_0,refute_0_254]) ).
cnf(refute_0_256,plain,
inverse(inverse(a)) = a,
inference(subst,[],[p12x_2:[bind(X,$fot(a))]]) ).
cnf(refute_0_257,plain,
( inverse(inverse(a)) != a
| inverse(inverse(a)) != b
| a = b ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(a)),b) ),[0],$fot(a)]]) ).
cnf(refute_0_258,plain,
( inverse(inverse(a)) != b
| a = b ),
inference(resolve,[$cnf( $equal(inverse(inverse(a)),a) )],[refute_0_256,refute_0_257]) ).
cnf(refute_0_259,plain,
a = b,
inference(resolve,[$cnf( $equal(inverse(inverse(a)),b) )],[refute_0_255,refute_0_258]) ).
cnf(refute_0_260,plain,
$false,
inference(resolve,[$cnf( $equal(a,b) )],[refute_0_259,prove_p12x]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GRP181-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n020.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 08:31:50 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 19.04/19.30 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.04/19.30
% 19.04/19.30 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 19.15/19.32
%------------------------------------------------------------------------------