TSTP Solution File: GRP186-3 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP186-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n007.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 10:37:52 EDT 2022
% Result : Unsatisfiable 0.99s 1.21s
% Output : CNFRefutation 0.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 40
% Syntax : Number of clauses : 128 ( 70 unt; 0 nHn; 67 RR)
% Number of literals : 213 ( 212 equ; 88 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 171 ( 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_lub,axiom,
least_upper_bound(X,Y) = least_upper_bound(Y,X) ).
cnf(idempotence_of_gld,axiom,
greatest_lower_bound(X,X) = X ).
cnf(monotony_lub1,axiom,
multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ).
cnf(monotony_glb2,axiom,
multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) ).
cnf(prove_p23x,negated_conjecture,
least_upper_bound(multiply(a,b),identity) != multiply(a,least_upper_bound(inverse(a),b)) ).
cnf(refute_0_0,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_1,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_2,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( least_upper_bound(X,Y) != least_upper_bound(Y,X)
| least_upper_bound(Y,X) = least_upper_bound(X,Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X,Y))),bind(Y0,$fot(least_upper_bound(Y,X)))]]) ).
cnf(refute_0_4,plain,
least_upper_bound(Y,X) = least_upper_bound(X,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(X,Y),least_upper_bound(Y,X)) )],[symmetry_of_lub,refute_0_3]) ).
cnf(refute_0_5,plain,
least_upper_bound(multiply(a,b),identity) = least_upper_bound(identity,multiply(a,b)),
inference(subst,[],[refute_0_4:[bind(X,$fot(identity)),bind(Y,$fot(multiply(a,b)))]]) ).
cnf(refute_0_6,plain,
( least_upper_bound(multiply(a,b),identity) != least_upper_bound(identity,multiply(a,b))
| least_upper_bound(identity,multiply(a,b)) != multiply(a,least_upper_bound(inverse(a),b))
| least_upper_bound(multiply(a,b),identity) = multiply(a,least_upper_bound(inverse(a),b)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(multiply(a,b),identity),multiply(a,least_upper_bound(inverse(a),b))) ),[0],$fot(least_upper_bound(identity,multiply(a,b)))]]) ).
cnf(refute_0_7,plain,
( least_upper_bound(identity,multiply(a,b)) != multiply(a,least_upper_bound(inverse(a),b))
| least_upper_bound(multiply(a,b),identity) = multiply(a,least_upper_bound(inverse(a),b)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(a,b),identity),least_upper_bound(identity,multiply(a,b))) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
least_upper_bound(inverse(a),b) = least_upper_bound(b,inverse(a)),
inference(subst,[],[refute_0_4:[bind(X,$fot(b)),bind(Y,$fot(inverse(a)))]]) ).
cnf(refute_0_9,plain,
multiply(a,least_upper_bound(inverse(a),b)) = multiply(a,least_upper_bound(inverse(a),b)),
introduced(tautology,[refl,[$fot(multiply(a,least_upper_bound(inverse(a),b)))]]) ).
cnf(refute_0_10,plain,
( multiply(a,least_upper_bound(inverse(a),b)) != multiply(a,least_upper_bound(inverse(a),b))
| least_upper_bound(inverse(a),b) != least_upper_bound(b,inverse(a))
| multiply(a,least_upper_bound(inverse(a),b)) = multiply(a,least_upper_bound(b,inverse(a))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(a,least_upper_bound(inverse(a),b)),multiply(a,least_upper_bound(inverse(a),b))) ),[1,1],$fot(least_upper_bound(b,inverse(a)))]]) ).
cnf(refute_0_11,plain,
( least_upper_bound(inverse(a),b) != least_upper_bound(b,inverse(a))
| multiply(a,least_upper_bound(inverse(a),b)) = multiply(a,least_upper_bound(b,inverse(a))) ),
inference(resolve,[$cnf( $equal(multiply(a,least_upper_bound(inverse(a),b)),multiply(a,least_upper_bound(inverse(a),b))) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
multiply(a,least_upper_bound(inverse(a),b)) = multiply(a,least_upper_bound(b,inverse(a))),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(a),b),least_upper_bound(b,inverse(a))) )],[refute_0_8,refute_0_11]) ).
cnf(refute_0_13,plain,
( multiply(a,least_upper_bound(inverse(a),b)) != multiply(a,least_upper_bound(b,inverse(a)))
| least_upper_bound(identity,multiply(a,b)) != multiply(a,least_upper_bound(b,inverse(a)))
| least_upper_bound(identity,multiply(a,b)) = multiply(a,least_upper_bound(inverse(a),b)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(identity,multiply(a,b)),multiply(a,least_upper_bound(inverse(a),b))) ),[1],$fot(multiply(a,least_upper_bound(b,inverse(a))))]]) ).
cnf(refute_0_14,plain,
( least_upper_bound(identity,multiply(a,b)) != multiply(a,least_upper_bound(b,inverse(a)))
| least_upper_bound(identity,multiply(a,b)) = multiply(a,least_upper_bound(inverse(a),b)) ),
inference(resolve,[$cnf( $equal(multiply(a,least_upper_bound(inverse(a),b)),multiply(a,least_upper_bound(b,inverse(a)))) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
( least_upper_bound(identity,multiply(a,b)) != multiply(a,least_upper_bound(b,inverse(a)))
| least_upper_bound(multiply(a,b),identity) = multiply(a,least_upper_bound(inverse(a),b)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(a,b)),multiply(a,least_upper_bound(inverse(a),b))) )],[refute_0_14,refute_0_7]) ).
cnf(refute_0_16,plain,
least_upper_bound(identity,multiply(a,b)) != multiply(a,least_upper_bound(b,inverse(a))),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(a,b),identity),multiply(a,least_upper_bound(inverse(a),b))) )],[refute_0_15,prove_p23x]) ).
cnf(refute_0_17,plain,
multiply(inverse(X_36),least_upper_bound(X_35,X_36)) = least_upper_bound(multiply(inverse(X_36),X_35),multiply(inverse(X_36),X_36)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(inverse(X_36))),bind(Y,$fot(X_35)),bind(Z,$fot(X_36))]]) ).
cnf(refute_0_18,plain,
multiply(inverse(X_36),X_36) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_36))]]) ).
cnf(refute_0_19,plain,
( multiply(inverse(X_36),X_36) != identity
| multiply(inverse(X_36),least_upper_bound(X_35,X_36)) != least_upper_bound(multiply(inverse(X_36),X_35),multiply(inverse(X_36),X_36))
| multiply(inverse(X_36),least_upper_bound(X_35,X_36)) = least_upper_bound(multiply(inverse(X_36),X_35),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_36),least_upper_bound(X_35,X_36)),least_upper_bound(multiply(inverse(X_36),X_35),multiply(inverse(X_36),X_36))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_20,plain,
( multiply(inverse(X_36),least_upper_bound(X_35,X_36)) != least_upper_bound(multiply(inverse(X_36),X_35),multiply(inverse(X_36),X_36))
| multiply(inverse(X_36),least_upper_bound(X_35,X_36)) = least_upper_bound(multiply(inverse(X_36),X_35),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_36),X_36),identity) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
multiply(inverse(X_36),least_upper_bound(X_35,X_36)) = least_upper_bound(multiply(inverse(X_36),X_35),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_36),least_upper_bound(X_35,X_36)),least_upper_bound(multiply(inverse(X_36),X_35),multiply(inverse(X_36),X_36))) )],[refute_0_17,refute_0_20]) ).
cnf(refute_0_22,plain,
least_upper_bound(multiply(inverse(X_36),X_35),identity) = least_upper_bound(identity,multiply(inverse(X_36),X_35)),
inference(subst,[],[refute_0_4:[bind(X,$fot(identity)),bind(Y,$fot(multiply(inverse(X_36),X_35)))]]) ).
cnf(refute_0_23,plain,
( multiply(inverse(X_36),least_upper_bound(X_35,X_36)) != least_upper_bound(multiply(inverse(X_36),X_35),identity)
| least_upper_bound(multiply(inverse(X_36),X_35),identity) != least_upper_bound(identity,multiply(inverse(X_36),X_35))
| multiply(inverse(X_36),least_upper_bound(X_35,X_36)) = least_upper_bound(identity,multiply(inverse(X_36),X_35)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_36),least_upper_bound(X_35,X_36)),least_upper_bound(identity,multiply(inverse(X_36),X_35))) ),[0],$fot(least_upper_bound(multiply(inverse(X_36),X_35),identity))]]) ).
cnf(refute_0_24,plain,
( multiply(inverse(X_36),least_upper_bound(X_35,X_36)) != least_upper_bound(multiply(inverse(X_36),X_35),identity)
| multiply(inverse(X_36),least_upper_bound(X_35,X_36)) = least_upper_bound(identity,multiply(inverse(X_36),X_35)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(X_36),X_35),identity),least_upper_bound(identity,multiply(inverse(X_36),X_35))) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
multiply(inverse(X_36),least_upper_bound(X_35,X_36)) = least_upper_bound(identity,multiply(inverse(X_36),X_35)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_36),least_upper_bound(X_35,X_36)),least_upper_bound(multiply(inverse(X_36),X_35),identity)) )],[refute_0_21,refute_0_24]) ).
cnf(refute_0_26,plain,
multiply(inverse(inverse(X_119)),least_upper_bound(X_35,inverse(X_119))) = least_upper_bound(identity,multiply(inverse(inverse(X_119)),X_35)),
inference(subst,[],[refute_0_25:[bind(X_36,$fot(inverse(X_119)))]]) ).
cnf(refute_0_27,plain,
multiply(multiply(inverse(X_67),X_67),X_68) = multiply(inverse(X_67),multiply(X_67,X_68)),
inference(subst,[],[associativity:[bind(X,$fot(inverse(X_67))),bind(Y,$fot(X_67)),bind(Z,$fot(X_68))]]) ).
cnf(refute_0_28,plain,
multiply(inverse(X_67),X_67) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_67))]]) ).
cnf(refute_0_29,plain,
( multiply(multiply(inverse(X_67),X_67),X_68) != multiply(inverse(X_67),multiply(X_67,X_68))
| multiply(inverse(X_67),X_67) != identity
| multiply(identity,X_68) = multiply(inverse(X_67),multiply(X_67,X_68)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_67),X_67),X_68),multiply(inverse(X_67),multiply(X_67,X_68))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_30,plain,
( multiply(multiply(inverse(X_67),X_67),X_68) != multiply(inverse(X_67),multiply(X_67,X_68))
| multiply(identity,X_68) = multiply(inverse(X_67),multiply(X_67,X_68)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_67),X_67),identity) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
multiply(identity,X_68) = multiply(inverse(X_67),multiply(X_67,X_68)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_67),X_67),X_68),multiply(inverse(X_67),multiply(X_67,X_68))) )],[refute_0_27,refute_0_30]) ).
cnf(refute_0_32,plain,
multiply(identity,X_68) = X_68,
inference(subst,[],[left_identity:[bind(X,$fot(X_68))]]) ).
cnf(refute_0_33,plain,
( multiply(identity,X_68) != X_68
| multiply(identity,X_68) != multiply(inverse(X_67),multiply(X_67,X_68))
| X_68 = multiply(inverse(X_67),multiply(X_67,X_68)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_68),multiply(inverse(X_67),multiply(X_67,X_68))) ),[0],$fot(X_68)]]) ).
cnf(refute_0_34,plain,
( multiply(identity,X_68) != multiply(inverse(X_67),multiply(X_67,X_68))
| X_68 = multiply(inverse(X_67),multiply(X_67,X_68)) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_68),X_68) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
X_68 = multiply(inverse(X_67),multiply(X_67,X_68)),
inference(resolve,[$cnf( $equal(multiply(identity,X_68),multiply(inverse(X_67),multiply(X_67,X_68))) )],[refute_0_31,refute_0_34]) ).
cnf(refute_0_36,plain,
X_70 = multiply(inverse(greatest_lower_bound(inverse(X_70),X_55)),multiply(greatest_lower_bound(inverse(X_70),X_55),X_70)),
inference(subst,[],[refute_0_35:[bind(X_67,$fot(greatest_lower_bound(inverse(X_70),X_55))),bind(X_68,$fot(X_70))]]) ).
cnf(refute_0_37,plain,
multiply(greatest_lower_bound(inverse(X_53),X_55),X_53) = greatest_lower_bound(multiply(inverse(X_53),X_53),multiply(X_55,X_53)),
inference(subst,[],[monotony_glb2:[bind(X,$fot(X_53)),bind(Y,$fot(inverse(X_53))),bind(Z,$fot(X_55))]]) ).
cnf(refute_0_38,plain,
multiply(inverse(X_53),X_53) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_53))]]) ).
cnf(refute_0_39,plain,
( multiply(greatest_lower_bound(inverse(X_53),X_55),X_53) != greatest_lower_bound(multiply(inverse(X_53),X_53),multiply(X_55,X_53))
| multiply(inverse(X_53),X_53) != identity
| multiply(greatest_lower_bound(inverse(X_53),X_55),X_53) = greatest_lower_bound(identity,multiply(X_55,X_53)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_53),X_55),X_53),greatest_lower_bound(multiply(inverse(X_53),X_53),multiply(X_55,X_53))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_40,plain,
( multiply(greatest_lower_bound(inverse(X_53),X_55),X_53) != greatest_lower_bound(multiply(inverse(X_53),X_53),multiply(X_55,X_53))
| multiply(greatest_lower_bound(inverse(X_53),X_55),X_53) = greatest_lower_bound(identity,multiply(X_55,X_53)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_53),X_53),identity) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
multiply(greatest_lower_bound(inverse(X_53),X_55),X_53) = greatest_lower_bound(identity,multiply(X_55,X_53)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_53),X_55),X_53),greatest_lower_bound(multiply(inverse(X_53),X_53),multiply(X_55,X_53))) )],[refute_0_37,refute_0_40]) ).
cnf(refute_0_42,plain,
multiply(greatest_lower_bound(inverse(X_70),X_55),X_70) = greatest_lower_bound(identity,multiply(X_55,X_70)),
inference(subst,[],[refute_0_41:[bind(X_53,$fot(X_70))]]) ).
cnf(refute_0_43,plain,
( X_70 != multiply(inverse(greatest_lower_bound(inverse(X_70),X_55)),multiply(greatest_lower_bound(inverse(X_70),X_55),X_70))
| multiply(greatest_lower_bound(inverse(X_70),X_55),X_70) != greatest_lower_bound(identity,multiply(X_55,X_70))
| X_70 = multiply(inverse(greatest_lower_bound(inverse(X_70),X_55)),greatest_lower_bound(identity,multiply(X_55,X_70))) ),
introduced(tautology,[equality,[$cnf( $equal(X_70,multiply(inverse(greatest_lower_bound(inverse(X_70),X_55)),multiply(greatest_lower_bound(inverse(X_70),X_55),X_70))) ),[1,1],$fot(greatest_lower_bound(identity,multiply(X_55,X_70)))]]) ).
cnf(refute_0_44,plain,
( X_70 != multiply(inverse(greatest_lower_bound(inverse(X_70),X_55)),multiply(greatest_lower_bound(inverse(X_70),X_55),X_70))
| X_70 = multiply(inverse(greatest_lower_bound(inverse(X_70),X_55)),greatest_lower_bound(identity,multiply(X_55,X_70))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_70),X_55),X_70),greatest_lower_bound(identity,multiply(X_55,X_70))) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
X_70 = multiply(inverse(greatest_lower_bound(inverse(X_70),X_55)),greatest_lower_bound(identity,multiply(X_55,X_70))),
inference(resolve,[$cnf( $equal(X_70,multiply(inverse(greatest_lower_bound(inverse(X_70),X_55)),multiply(greatest_lower_bound(inverse(X_70),X_55),X_70))) )],[refute_0_36,refute_0_44]) ).
cnf(refute_0_46,plain,
X_118 = multiply(inverse(greatest_lower_bound(inverse(X_118),inverse(X_118))),greatest_lower_bound(identity,multiply(inverse(X_118),X_118))),
inference(subst,[],[refute_0_45:[bind(X_55,$fot(inverse(X_118))),bind(X_70,$fot(X_118))]]) ).
cnf(refute_0_47,plain,
multiply(inverse(X_118),X_118) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_118))]]) ).
cnf(refute_0_48,plain,
( X_118 != multiply(inverse(greatest_lower_bound(inverse(X_118),inverse(X_118))),greatest_lower_bound(identity,multiply(inverse(X_118),X_118)))
| multiply(inverse(X_118),X_118) != identity
| X_118 = multiply(inverse(greatest_lower_bound(inverse(X_118),inverse(X_118))),greatest_lower_bound(identity,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(X_118,multiply(inverse(greatest_lower_bound(inverse(X_118),inverse(X_118))),greatest_lower_bound(identity,multiply(inverse(X_118),X_118)))) ),[1,1,1],$fot(identity)]]) ).
cnf(refute_0_49,plain,
( X_118 != multiply(inverse(greatest_lower_bound(inverse(X_118),inverse(X_118))),greatest_lower_bound(identity,multiply(inverse(X_118),X_118)))
| X_118 = multiply(inverse(greatest_lower_bound(inverse(X_118),inverse(X_118))),greatest_lower_bound(identity,identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_118),X_118),identity) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
X_118 = multiply(inverse(greatest_lower_bound(inverse(X_118),inverse(X_118))),greatest_lower_bound(identity,identity)),
inference(resolve,[$cnf( $equal(X_118,multiply(inverse(greatest_lower_bound(inverse(X_118),inverse(X_118))),greatest_lower_bound(identity,multiply(inverse(X_118),X_118)))) )],[refute_0_46,refute_0_49]) ).
cnf(refute_0_51,plain,
X_70 = multiply(inverse(inverse(X_70)),multiply(inverse(X_70),X_70)),
inference(subst,[],[refute_0_35:[bind(X_67,$fot(inverse(X_70))),bind(X_68,$fot(X_70))]]) ).
cnf(refute_0_52,plain,
multiply(inverse(X_70),X_70) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_70))]]) ).
cnf(refute_0_53,plain,
( X_70 != multiply(inverse(inverse(X_70)),multiply(inverse(X_70),X_70))
| multiply(inverse(X_70),X_70) != identity
| X_70 = multiply(inverse(inverse(X_70)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(X_70,multiply(inverse(inverse(X_70)),multiply(inverse(X_70),X_70))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_54,plain,
( X_70 != multiply(inverse(inverse(X_70)),multiply(inverse(X_70),X_70))
| X_70 = multiply(inverse(inverse(X_70)),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_70),X_70),identity) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
X_70 = multiply(inverse(inverse(X_70)),identity),
inference(resolve,[$cnf( $equal(X_70,multiply(inverse(inverse(X_70)),multiply(inverse(X_70),X_70))) )],[refute_0_51,refute_0_54]) ).
cnf(refute_0_56,plain,
multiply(X_69,X_70) = multiply(inverse(inverse(X_69)),multiply(inverse(X_69),multiply(X_69,X_70))),
inference(subst,[],[refute_0_35:[bind(X_67,$fot(inverse(X_69))),bind(X_68,$fot(multiply(X_69,X_70)))]]) ).
cnf(refute_0_57,plain,
X_70 = multiply(inverse(X_69),multiply(X_69,X_70)),
inference(subst,[],[refute_0_35:[bind(X_67,$fot(X_69)),bind(X_68,$fot(X_70))]]) ).
cnf(refute_0_58,plain,
( X_70 != multiply(inverse(X_69),multiply(X_69,X_70))
| multiply(inverse(X_69),multiply(X_69,X_70)) = X_70 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_70)),bind(Y0,$fot(multiply(inverse(X_69),multiply(X_69,X_70))))]]) ).
cnf(refute_0_59,plain,
multiply(inverse(X_69),multiply(X_69,X_70)) = X_70,
inference(resolve,[$cnf( $equal(X_70,multiply(inverse(X_69),multiply(X_69,X_70))) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
( multiply(X_69,X_70) != multiply(inverse(inverse(X_69)),multiply(inverse(X_69),multiply(X_69,X_70)))
| multiply(inverse(X_69),multiply(X_69,X_70)) != X_70
| multiply(X_69,X_70) = multiply(inverse(inverse(X_69)),X_70) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_69,X_70),multiply(inverse(inverse(X_69)),multiply(inverse(X_69),multiply(X_69,X_70)))) ),[1,1],$fot(X_70)]]) ).
cnf(refute_0_61,plain,
( multiply(X_69,X_70) != multiply(inverse(inverse(X_69)),multiply(inverse(X_69),multiply(X_69,X_70)))
| multiply(X_69,X_70) = multiply(inverse(inverse(X_69)),X_70) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_69),multiply(X_69,X_70)),X_70) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
multiply(X_69,X_70) = multiply(inverse(inverse(X_69)),X_70),
inference(resolve,[$cnf( $equal(multiply(X_69,X_70),multiply(inverse(inverse(X_69)),multiply(inverse(X_69),multiply(X_69,X_70)))) )],[refute_0_56,refute_0_61]) ).
cnf(refute_0_63,plain,
( multiply(X_69,X_70) != multiply(inverse(inverse(X_69)),X_70)
| multiply(inverse(inverse(X_69)),X_70) = multiply(X_69,X_70) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X_69,X_70))),bind(Y0,$fot(multiply(inverse(inverse(X_69)),X_70)))]]) ).
cnf(refute_0_64,plain,
multiply(inverse(inverse(X_69)),X_70) = multiply(X_69,X_70),
inference(resolve,[$cnf( $equal(multiply(X_69,X_70),multiply(inverse(inverse(X_69)),X_70)) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
multiply(inverse(inverse(X_70)),identity) = multiply(X_70,identity),
inference(subst,[],[refute_0_64:[bind(X_69,$fot(X_70)),bind(X_70,$fot(identity))]]) ).
cnf(refute_0_66,plain,
( X_70 != multiply(inverse(inverse(X_70)),identity)
| multiply(inverse(inverse(X_70)),identity) != multiply(X_70,identity)
| X_70 = multiply(X_70,identity) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_70,multiply(X_70,identity)) ),[0],$fot(multiply(inverse(inverse(X_70)),identity))]]) ).
cnf(refute_0_67,plain,
( X_70 != multiply(inverse(inverse(X_70)),identity)
| X_70 = multiply(X_70,identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_70)),identity),multiply(X_70,identity)) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
X_70 = multiply(X_70,identity),
inference(resolve,[$cnf( $equal(X_70,multiply(inverse(inverse(X_70)),identity)) )],[refute_0_55,refute_0_67]) ).
cnf(refute_0_69,plain,
( X_70 != multiply(X_70,identity)
| multiply(X_70,identity) = X_70 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_70)),bind(Y0,$fot(multiply(X_70,identity)))]]) ).
cnf(refute_0_70,plain,
multiply(X_70,identity) = X_70,
inference(resolve,[$cnf( $equal(X_70,multiply(X_70,identity)) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
multiply(inverse(inverse(X_118)),identity) = inverse(inverse(X_118)),
inference(subst,[],[refute_0_70:[bind(X_70,$fot(inverse(inverse(X_118))))]]) ).
cnf(refute_0_72,plain,
greatest_lower_bound(identity,identity) = identity,
inference(subst,[],[idempotence_of_gld:[bind(X,$fot(identity))]]) ).
cnf(refute_0_73,plain,
multiply(inverse(inverse(X_118)),greatest_lower_bound(identity,identity)) = multiply(inverse(inverse(X_118)),greatest_lower_bound(identity,identity)),
introduced(tautology,[refl,[$fot(multiply(inverse(inverse(X_118)),greatest_lower_bound(identity,identity)))]]) ).
cnf(refute_0_74,plain,
( multiply(inverse(inverse(X_118)),greatest_lower_bound(identity,identity)) != multiply(inverse(inverse(X_118)),greatest_lower_bound(identity,identity))
| greatest_lower_bound(identity,identity) != identity
| multiply(inverse(inverse(X_118)),greatest_lower_bound(identity,identity)) = multiply(inverse(inverse(X_118)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X_118)),greatest_lower_bound(identity,identity)),multiply(inverse(inverse(X_118)),greatest_lower_bound(identity,identity))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_75,plain,
( greatest_lower_bound(identity,identity) != identity
| multiply(inverse(inverse(X_118)),greatest_lower_bound(identity,identity)) = multiply(inverse(inverse(X_118)),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_118)),greatest_lower_bound(identity,identity)),multiply(inverse(inverse(X_118)),greatest_lower_bound(identity,identity))) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
multiply(inverse(inverse(X_118)),greatest_lower_bound(identity,identity)) = multiply(inverse(inverse(X_118)),identity),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,identity),identity) )],[refute_0_72,refute_0_75]) ).
cnf(refute_0_77,plain,
greatest_lower_bound(inverse(X_118),inverse(X_118)) = inverse(X_118),
inference(subst,[],[idempotence_of_gld:[bind(X,$fot(inverse(X_118)))]]) ).
cnf(refute_0_78,plain,
inverse(greatest_lower_bound(inverse(X_118),inverse(X_118))) = inverse(greatest_lower_bound(inverse(X_118),inverse(X_118))),
introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(inverse(X_118),inverse(X_118))))]]) ).
cnf(refute_0_79,plain,
( greatest_lower_bound(inverse(X_118),inverse(X_118)) != inverse(X_118)
| inverse(greatest_lower_bound(inverse(X_118),inverse(X_118))) != inverse(greatest_lower_bound(inverse(X_118),inverse(X_118)))
| inverse(greatest_lower_bound(inverse(X_118),inverse(X_118))) = inverse(inverse(X_118)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(inverse(X_118),inverse(X_118))),inverse(greatest_lower_bound(inverse(X_118),inverse(X_118)))) ),[1,0],$fot(inverse(X_118))]]) ).
cnf(refute_0_80,plain,
( greatest_lower_bound(inverse(X_118),inverse(X_118)) != inverse(X_118)
| inverse(greatest_lower_bound(inverse(X_118),inverse(X_118))) = inverse(inverse(X_118)) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(X_118),inverse(X_118))),inverse(greatest_lower_bound(inverse(X_118),inverse(X_118)))) )],[refute_0_78,refute_0_79]) ).
cnf(refute_0_81,plain,
inverse(greatest_lower_bound(inverse(X_118),inverse(X_118))) = inverse(inverse(X_118)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_118),inverse(X_118)),inverse(X_118)) )],[refute_0_77,refute_0_80]) ).
cnf(refute_0_82,plain,
multiply(inverse(greatest_lower_bound(inverse(X_118),inverse(X_118))),greatest_lower_bound(identity,identity)) = multiply(inverse(greatest_lower_bound(inverse(X_118),inverse(X_118))),greatest_lower_bound(identity,identity)),
introduced(tautology,[refl,[$fot(multiply(inverse(greatest_lower_bound(inverse(X_118),inverse(X_118))),greatest_lower_bound(identity,identity)))]]) ).
cnf(refute_0_83,plain,
( multiply(inverse(greatest_lower_bound(inverse(X_118),inverse(X_118))),greatest_lower_bound(identity,identity)) != multiply(inverse(greatest_lower_bound(inverse(X_118),inverse(X_118))),greatest_lower_bound(identity,identity))
| inverse(greatest_lower_bound(inverse(X_118),inverse(X_118))) != inverse(inverse(X_118))
| multiply(inverse(greatest_lower_bound(inverse(X_118),inverse(X_118))),greatest_lower_bound(identity,identity)) = multiply(inverse(inverse(X_118)),greatest_lower_bound(identity,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(X_118),inverse(X_118))),greatest_lower_bound(identity,identity)),multiply(inverse(greatest_lower_bound(inverse(X_118),inverse(X_118))),greatest_lower_bound(identity,identity))) ),[1,0],$fot(inverse(inverse(X_118)))]]) ).
cnf(refute_0_84,plain,
( inverse(greatest_lower_bound(inverse(X_118),inverse(X_118))) != inverse(inverse(X_118))
| multiply(inverse(greatest_lower_bound(inverse(X_118),inverse(X_118))),greatest_lower_bound(identity,identity)) = multiply(inverse(inverse(X_118)),greatest_lower_bound(identity,identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(X_118),inverse(X_118))),greatest_lower_bound(identity,identity)),multiply(inverse(greatest_lower_bound(inverse(X_118),inverse(X_118))),greatest_lower_bound(identity,identity))) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
multiply(inverse(greatest_lower_bound(inverse(X_118),inverse(X_118))),greatest_lower_bound(identity,identity)) = multiply(inverse(inverse(X_118)),greatest_lower_bound(identity,identity)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(X_118),inverse(X_118))),inverse(inverse(X_118))) )],[refute_0_81,refute_0_84]) ).
cnf(refute_0_86,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_87,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_2,refute_0_86]) ).
cnf(refute_0_88,plain,
( multiply(inverse(greatest_lower_bound(inverse(X_118),inverse(X_118))),greatest_lower_bound(identity,identity)) != multiply(inverse(inverse(X_118)),greatest_lower_bound(identity,identity))
| multiply(inverse(inverse(X_118)),greatest_lower_bound(identity,identity)) != multiply(inverse(inverse(X_118)),identity)
| multiply(inverse(greatest_lower_bound(inverse(X_118),inverse(X_118))),greatest_lower_bound(identity,identity)) = multiply(inverse(inverse(X_118)),identity) ),
inference(subst,[],[refute_0_87:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(inverse(X_118),inverse(X_118))),greatest_lower_bound(identity,identity)))),bind(Y0,$fot(multiply(inverse(inverse(X_118)),greatest_lower_bound(identity,identity)))),bind(Z0,$fot(multiply(inverse(inverse(X_118)),identity)))]]) ).
cnf(refute_0_89,plain,
( multiply(inverse(inverse(X_118)),greatest_lower_bound(identity,identity)) != multiply(inverse(inverse(X_118)),identity)
| multiply(inverse(greatest_lower_bound(inverse(X_118),inverse(X_118))),greatest_lower_bound(identity,identity)) = multiply(inverse(inverse(X_118)),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(X_118),inverse(X_118))),greatest_lower_bound(identity,identity)),multiply(inverse(inverse(X_118)),greatest_lower_bound(identity,identity))) )],[refute_0_85,refute_0_88]) ).
cnf(refute_0_90,plain,
multiply(inverse(greatest_lower_bound(inverse(X_118),inverse(X_118))),greatest_lower_bound(identity,identity)) = multiply(inverse(inverse(X_118)),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_118)),greatest_lower_bound(identity,identity)),multiply(inverse(inverse(X_118)),identity)) )],[refute_0_76,refute_0_89]) ).
cnf(refute_0_91,plain,
( multiply(inverse(greatest_lower_bound(inverse(X_118),inverse(X_118))),greatest_lower_bound(identity,identity)) != multiply(inverse(inverse(X_118)),identity)
| multiply(inverse(inverse(X_118)),identity) != inverse(inverse(X_118))
| multiply(inverse(greatest_lower_bound(inverse(X_118),inverse(X_118))),greatest_lower_bound(identity,identity)) = inverse(inverse(X_118)) ),
inference(subst,[],[refute_0_87:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(inverse(X_118),inverse(X_118))),greatest_lower_bound(identity,identity)))),bind(Y0,$fot(multiply(inverse(inverse(X_118)),identity))),bind(Z0,$fot(inverse(inverse(X_118))))]]) ).
cnf(refute_0_92,plain,
( multiply(inverse(inverse(X_118)),identity) != inverse(inverse(X_118))
| multiply(inverse(greatest_lower_bound(inverse(X_118),inverse(X_118))),greatest_lower_bound(identity,identity)) = inverse(inverse(X_118)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(X_118),inverse(X_118))),greatest_lower_bound(identity,identity)),multiply(inverse(inverse(X_118)),identity)) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
multiply(inverse(greatest_lower_bound(inverse(X_118),inverse(X_118))),greatest_lower_bound(identity,identity)) = inverse(inverse(X_118)),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_118)),identity),inverse(inverse(X_118))) )],[refute_0_71,refute_0_92]) ).
cnf(refute_0_94,plain,
( X_118 != multiply(inverse(greatest_lower_bound(inverse(X_118),inverse(X_118))),greatest_lower_bound(identity,identity))
| multiply(inverse(greatest_lower_bound(inverse(X_118),inverse(X_118))),greatest_lower_bound(identity,identity)) != inverse(inverse(X_118))
| X_118 = inverse(inverse(X_118)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_118,inverse(inverse(X_118))) ),[0],$fot(multiply(inverse(greatest_lower_bound(inverse(X_118),inverse(X_118))),greatest_lower_bound(identity,identity)))]]) ).
cnf(refute_0_95,plain,
( X_118 != multiply(inverse(greatest_lower_bound(inverse(X_118),inverse(X_118))),greatest_lower_bound(identity,identity))
| X_118 = inverse(inverse(X_118)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(X_118),inverse(X_118))),greatest_lower_bound(identity,identity)),inverse(inverse(X_118))) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
X_118 = inverse(inverse(X_118)),
inference(resolve,[$cnf( $equal(X_118,multiply(inverse(greatest_lower_bound(inverse(X_118),inverse(X_118))),greatest_lower_bound(identity,identity))) )],[refute_0_50,refute_0_95]) ).
cnf(refute_0_97,plain,
X_119 = inverse(inverse(X_119)),
inference(subst,[],[refute_0_96:[bind(X_118,$fot(X_119))]]) ).
cnf(refute_0_98,plain,
( X_119 != inverse(inverse(X_119))
| inverse(inverse(X_119)) = X_119 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_119)),bind(Y0,$fot(inverse(inverse(X_119))))]]) ).
cnf(refute_0_99,plain,
inverse(inverse(X_119)) = X_119,
inference(resolve,[$cnf( $equal(X_119,inverse(inverse(X_119))) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
( multiply(inverse(inverse(X_119)),least_upper_bound(X_35,inverse(X_119))) != least_upper_bound(identity,multiply(inverse(inverse(X_119)),X_35))
| inverse(inverse(X_119)) != X_119
| multiply(X_119,least_upper_bound(X_35,inverse(X_119))) = least_upper_bound(identity,multiply(inverse(inverse(X_119)),X_35)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X_119)),least_upper_bound(X_35,inverse(X_119))),least_upper_bound(identity,multiply(inverse(inverse(X_119)),X_35))) ),[0,0],$fot(X_119)]]) ).
cnf(refute_0_101,plain,
( multiply(inverse(inverse(X_119)),least_upper_bound(X_35,inverse(X_119))) != least_upper_bound(identity,multiply(inverse(inverse(X_119)),X_35))
| multiply(X_119,least_upper_bound(X_35,inverse(X_119))) = least_upper_bound(identity,multiply(inverse(inverse(X_119)),X_35)) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_119)),X_119) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
multiply(X_119,least_upper_bound(X_35,inverse(X_119))) = least_upper_bound(identity,multiply(inverse(inverse(X_119)),X_35)),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_119)),least_upper_bound(X_35,inverse(X_119))),least_upper_bound(identity,multiply(inverse(inverse(X_119)),X_35))) )],[refute_0_26,refute_0_101]) ).
cnf(refute_0_103,plain,
multiply(inverse(inverse(X_119)),X_35) = multiply(inverse(inverse(X_119)),X_35),
introduced(tautology,[refl,[$fot(multiply(inverse(inverse(X_119)),X_35))]]) ).
cnf(refute_0_104,plain,
( multiply(inverse(inverse(X_119)),X_35) != multiply(inverse(inverse(X_119)),X_35)
| inverse(inverse(X_119)) != X_119
| multiply(inverse(inverse(X_119)),X_35) = multiply(X_119,X_35) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X_119)),X_35),multiply(inverse(inverse(X_119)),X_35)) ),[1,0],$fot(X_119)]]) ).
cnf(refute_0_105,plain,
( inverse(inverse(X_119)) != X_119
| multiply(inverse(inverse(X_119)),X_35) = multiply(X_119,X_35) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_119)),X_35),multiply(inverse(inverse(X_119)),X_35)) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
multiply(inverse(inverse(X_119)),X_35) = multiply(X_119,X_35),
inference(resolve,[$cnf( $equal(inverse(inverse(X_119)),X_119) )],[refute_0_99,refute_0_105]) ).
cnf(refute_0_107,plain,
least_upper_bound(identity,multiply(inverse(inverse(X_119)),X_35)) = least_upper_bound(identity,multiply(inverse(inverse(X_119)),X_35)),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,multiply(inverse(inverse(X_119)),X_35)))]]) ).
cnf(refute_0_108,plain,
( multiply(inverse(inverse(X_119)),X_35) != multiply(X_119,X_35)
| least_upper_bound(identity,multiply(inverse(inverse(X_119)),X_35)) != least_upper_bound(identity,multiply(inverse(inverse(X_119)),X_35))
| least_upper_bound(identity,multiply(inverse(inverse(X_119)),X_35)) = least_upper_bound(identity,multiply(X_119,X_35)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(inverse(X_119)),X_35)),least_upper_bound(identity,multiply(inverse(inverse(X_119)),X_35))) ),[1,1],$fot(multiply(X_119,X_35))]]) ).
cnf(refute_0_109,plain,
( multiply(inverse(inverse(X_119)),X_35) != multiply(X_119,X_35)
| least_upper_bound(identity,multiply(inverse(inverse(X_119)),X_35)) = least_upper_bound(identity,multiply(X_119,X_35)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(inverse(X_119)),X_35)),least_upper_bound(identity,multiply(inverse(inverse(X_119)),X_35))) )],[refute_0_107,refute_0_108]) ).
cnf(refute_0_110,plain,
least_upper_bound(identity,multiply(inverse(inverse(X_119)),X_35)) = least_upper_bound(identity,multiply(X_119,X_35)),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_119)),X_35),multiply(X_119,X_35)) )],[refute_0_106,refute_0_109]) ).
cnf(refute_0_111,plain,
( multiply(X_119,least_upper_bound(X_35,inverse(X_119))) != least_upper_bound(identity,multiply(inverse(inverse(X_119)),X_35))
| least_upper_bound(identity,multiply(inverse(inverse(X_119)),X_35)) != least_upper_bound(identity,multiply(X_119,X_35))
| multiply(X_119,least_upper_bound(X_35,inverse(X_119))) = least_upper_bound(identity,multiply(X_119,X_35)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_119,least_upper_bound(X_35,inverse(X_119))),least_upper_bound(identity,multiply(X_119,X_35))) ),[0],$fot(least_upper_bound(identity,multiply(inverse(inverse(X_119)),X_35)))]]) ).
cnf(refute_0_112,plain,
( multiply(X_119,least_upper_bound(X_35,inverse(X_119))) != least_upper_bound(identity,multiply(inverse(inverse(X_119)),X_35))
| multiply(X_119,least_upper_bound(X_35,inverse(X_119))) = least_upper_bound(identity,multiply(X_119,X_35)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(inverse(X_119)),X_35)),least_upper_bound(identity,multiply(X_119,X_35))) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
multiply(X_119,least_upper_bound(X_35,inverse(X_119))) = least_upper_bound(identity,multiply(X_119,X_35)),
inference(resolve,[$cnf( $equal(multiply(X_119,least_upper_bound(X_35,inverse(X_119))),least_upper_bound(identity,multiply(inverse(inverse(X_119)),X_35))) )],[refute_0_102,refute_0_112]) ).
cnf(refute_0_114,plain,
multiply(a,least_upper_bound(b,inverse(a))) = least_upper_bound(identity,multiply(a,b)),
inference(subst,[],[refute_0_113:[bind(X_119,$fot(a)),bind(X_35,$fot(b))]]) ).
cnf(refute_0_115,plain,
( multiply(a,least_upper_bound(b,inverse(a))) != least_upper_bound(identity,multiply(a,b))
| least_upper_bound(identity,multiply(a,b)) != least_upper_bound(identity,multiply(a,b))
| least_upper_bound(identity,multiply(a,b)) = multiply(a,least_upper_bound(b,inverse(a))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(identity,multiply(a,b)),multiply(a,least_upper_bound(b,inverse(a)))) ),[1],$fot(least_upper_bound(identity,multiply(a,b)))]]) ).
cnf(refute_0_116,plain,
( least_upper_bound(identity,multiply(a,b)) != least_upper_bound(identity,multiply(a,b))
| least_upper_bound(identity,multiply(a,b)) = multiply(a,least_upper_bound(b,inverse(a))) ),
inference(resolve,[$cnf( $equal(multiply(a,least_upper_bound(b,inverse(a))),least_upper_bound(identity,multiply(a,b))) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
least_upper_bound(identity,multiply(a,b)) != least_upper_bound(identity,multiply(a,b)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(a,b)),multiply(a,least_upper_bound(b,inverse(a)))) )],[refute_0_116,refute_0_16]) ).
cnf(refute_0_118,plain,
least_upper_bound(identity,multiply(a,b)) = least_upper_bound(identity,multiply(a,b)),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,multiply(a,b)))]]) ).
cnf(refute_0_119,plain,
$false,
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(a,b)),least_upper_bound(identity,multiply(a,b))) )],[refute_0_118,refute_0_117]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP186-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n007.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 13 03:49:38 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.99/1.21 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.99/1.21
% 0.99/1.21 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.99/1.22
%------------------------------------------------------------------------------