%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP166-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n027.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 10:37:08 EDT 2022
% Result : Unsatisfiable 0.55s 0.76s
% Output : CNFRefutation 0.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 21
% Syntax : Number of clauses : 67 ( 38 unt; 0 nHn; 38 RR)
% Number of literals : 109 ( 108 equ; 44 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 91 ( 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(monotony_lub1,axiom,
multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ).
cnf(lat2a_2,hypothesis,
least_upper_bound(b,identity) = b ).
cnf(prove_lat2a,negated_conjecture,
least_upper_bound(a,multiply(a,b)) != multiply(a,b) ).
cnf(refute_0_0,plain,
multiply(a,least_upper_bound(b,identity)) = multiply(a,least_upper_bound(b,identity)),
introduced(tautology,[refl,[$fot(multiply(a,least_upper_bound(b,identity)))]]) ).
cnf(refute_0_1,plain,
( multiply(a,least_upper_bound(b,identity)) != multiply(a,least_upper_bound(b,identity))
| least_upper_bound(b,identity) != b
| multiply(a,least_upper_bound(b,identity)) = multiply(a,b) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(a,least_upper_bound(b,identity)),multiply(a,least_upper_bound(b,identity))) ),[1,1],$fot(b)]]) ).
cnf(refute_0_2,plain,
( least_upper_bound(b,identity) != b
| multiply(a,least_upper_bound(b,identity)) = multiply(a,b) ),
inference(resolve,[$cnf( $equal(multiply(a,least_upper_bound(b,identity)),multiply(a,least_upper_bound(b,identity))) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
multiply(a,least_upper_bound(b,identity)) = multiply(a,b),
inference(resolve,[$cnf( $equal(least_upper_bound(b,identity),b) )],[lat2a_2,refute_0_2]) ).
cnf(refute_0_4,plain,
multiply(X_87,least_upper_bound(X_88,identity)) = least_upper_bound(multiply(X_87,X_88),multiply(X_87,identity)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(X_87)),bind(Y,$fot(X_88)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_5,plain,
multiply(multiply(inverse(X_66),X_66),X_67) = multiply(inverse(X_66),multiply(X_66,X_67)),
inference(subst,[],[associativity:[bind(X,$fot(inverse(X_66))),bind(Y,$fot(X_66)),bind(Z,$fot(X_67))]]) ).
cnf(refute_0_6,plain,
multiply(inverse(X_66),X_66) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_66))]]) ).
cnf(refute_0_7,plain,
( multiply(multiply(inverse(X_66),X_66),X_67) != multiply(inverse(X_66),multiply(X_66,X_67))
| multiply(inverse(X_66),X_66) != identity
| multiply(identity,X_67) = multiply(inverse(X_66),multiply(X_66,X_67)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_66),X_66),X_67),multiply(inverse(X_66),multiply(X_66,X_67))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_8,plain,
( multiply(multiply(inverse(X_66),X_66),X_67) != multiply(inverse(X_66),multiply(X_66,X_67))
| multiply(identity,X_67) = multiply(inverse(X_66),multiply(X_66,X_67)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_66),X_66),identity) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
multiply(identity,X_67) = multiply(inverse(X_66),multiply(X_66,X_67)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_66),X_66),X_67),multiply(inverse(X_66),multiply(X_66,X_67))) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
multiply(identity,X_67) = X_67,
inference(subst,[],[left_identity:[bind(X,$fot(X_67))]]) ).
cnf(refute_0_11,plain,
( multiply(identity,X_67) != X_67
| multiply(identity,X_67) != multiply(inverse(X_66),multiply(X_66,X_67))
| X_67 = multiply(inverse(X_66),multiply(X_66,X_67)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_67),multiply(inverse(X_66),multiply(X_66,X_67))) ),[0],$fot(X_67)]]) ).
cnf(refute_0_12,plain,
( multiply(identity,X_67) != multiply(inverse(X_66),multiply(X_66,X_67))
| X_67 = multiply(inverse(X_66),multiply(X_66,X_67)) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_67),X_67) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
X_67 = multiply(inverse(X_66),multiply(X_66,X_67)),
inference(resolve,[$cnf( $equal(multiply(identity,X_67),multiply(inverse(X_66),multiply(X_66,X_67))) )],[refute_0_9,refute_0_12]) ).
cnf(refute_0_14,plain,
X_69 = multiply(inverse(inverse(X_69)),multiply(inverse(X_69),X_69)),
inference(subst,[],[refute_0_13:[bind(X_66,$fot(inverse(X_69))),bind(X_67,$fot(X_69))]]) ).
cnf(refute_0_15,plain,
multiply(inverse(X_69),X_69) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_69))]]) ).
cnf(refute_0_16,plain,
( X_69 != multiply(inverse(inverse(X_69)),multiply(inverse(X_69),X_69))
| multiply(inverse(X_69),X_69) != identity
| X_69 = multiply(inverse(inverse(X_69)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(X_69,multiply(inverse(inverse(X_69)),multiply(inverse(X_69),X_69))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_17,plain,
( X_69 != multiply(inverse(inverse(X_69)),multiply(inverse(X_69),X_69))
| X_69 = multiply(inverse(inverse(X_69)),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_69),X_69),identity) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
X_69 = multiply(inverse(inverse(X_69)),identity),
inference(resolve,[$cnf( $equal(X_69,multiply(inverse(inverse(X_69)),multiply(inverse(X_69),X_69))) )],[refute_0_14,refute_0_17]) ).
cnf(refute_0_19,plain,
multiply(X_68,X_69) = multiply(inverse(inverse(X_68)),multiply(inverse(X_68),multiply(X_68,X_69))),
inference(subst,[],[refute_0_13:[bind(X_66,$fot(inverse(X_68))),bind(X_67,$fot(multiply(X_68,X_69)))]]) ).
cnf(refute_0_20,plain,
X_69 = multiply(inverse(X_68),multiply(X_68,X_69)),
inference(subst,[],[refute_0_13:[bind(X_66,$fot(X_68)),bind(X_67,$fot(X_69))]]) ).
cnf(refute_0_21,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_22,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_23,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
( X_69 != multiply(inverse(X_68),multiply(X_68,X_69))
| multiply(inverse(X_68),multiply(X_68,X_69)) = X_69 ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(X_69)),bind(Y0,$fot(multiply(inverse(X_68),multiply(X_68,X_69))))]]) ).
cnf(refute_0_25,plain,
multiply(inverse(X_68),multiply(X_68,X_69)) = X_69,
inference(resolve,[$cnf( $equal(X_69,multiply(inverse(X_68),multiply(X_68,X_69))) )],[refute_0_20,refute_0_24]) ).
cnf(refute_0_26,plain,
( multiply(X_68,X_69) != multiply(inverse(inverse(X_68)),multiply(inverse(X_68),multiply(X_68,X_69)))
| multiply(inverse(X_68),multiply(X_68,X_69)) != X_69
| multiply(X_68,X_69) = multiply(inverse(inverse(X_68)),X_69) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_68,X_69),multiply(inverse(inverse(X_68)),multiply(inverse(X_68),multiply(X_68,X_69)))) ),[1,1],$fot(X_69)]]) ).
cnf(refute_0_27,plain,
( multiply(X_68,X_69) != multiply(inverse(inverse(X_68)),multiply(inverse(X_68),multiply(X_68,X_69)))
| multiply(X_68,X_69) = multiply(inverse(inverse(X_68)),X_69) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_68),multiply(X_68,X_69)),X_69) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
multiply(X_68,X_69) = multiply(inverse(inverse(X_68)),X_69),
inference(resolve,[$cnf( $equal(multiply(X_68,X_69),multiply(inverse(inverse(X_68)),multiply(inverse(X_68),multiply(X_68,X_69)))) )],[refute_0_19,refute_0_27]) ).
cnf(refute_0_29,plain,
( multiply(X_68,X_69) != multiply(inverse(inverse(X_68)),X_69)
| multiply(inverse(inverse(X_68)),X_69) = multiply(X_68,X_69) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(multiply(X_68,X_69))),bind(Y0,$fot(multiply(inverse(inverse(X_68)),X_69)))]]) ).
cnf(refute_0_30,plain,
multiply(inverse(inverse(X_68)),X_69) = multiply(X_68,X_69),
inference(resolve,[$cnf( $equal(multiply(X_68,X_69),multiply(inverse(inverse(X_68)),X_69)) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
multiply(inverse(inverse(X_69)),identity) = multiply(X_69,identity),
inference(subst,[],[refute_0_30:[bind(X_68,$fot(X_69)),bind(X_69,$fot(identity))]]) ).
cnf(refute_0_32,plain,
( X_69 != multiply(inverse(inverse(X_69)),identity)
| multiply(inverse(inverse(X_69)),identity) != multiply(X_69,identity)
| X_69 = multiply(X_69,identity) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_69,multiply(X_69,identity)) ),[0],$fot(multiply(inverse(inverse(X_69)),identity))]]) ).
cnf(refute_0_33,plain,
( X_69 != multiply(inverse(inverse(X_69)),identity)
| X_69 = multiply(X_69,identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_69)),identity),multiply(X_69,identity)) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
X_69 = multiply(X_69,identity),
inference(resolve,[$cnf( $equal(X_69,multiply(inverse(inverse(X_69)),identity)) )],[refute_0_18,refute_0_33]) ).
cnf(refute_0_35,plain,
X_87 = multiply(X_87,identity),
inference(subst,[],[refute_0_34:[bind(X_69,$fot(X_87))]]) ).
cnf(refute_0_36,plain,
( X_87 != multiply(X_87,identity)
| multiply(X_87,identity) = X_87 ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(X_87)),bind(Y0,$fot(multiply(X_87,identity)))]]) ).
cnf(refute_0_37,plain,
multiply(X_87,identity) = X_87,
inference(resolve,[$cnf( $equal(X_87,multiply(X_87,identity)) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
( multiply(X_87,identity) != X_87
| multiply(X_87,least_upper_bound(X_88,identity)) != least_upper_bound(multiply(X_87,X_88),multiply(X_87,identity))
| multiply(X_87,least_upper_bound(X_88,identity)) = least_upper_bound(multiply(X_87,X_88),X_87) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_87,least_upper_bound(X_88,identity)),least_upper_bound(multiply(X_87,X_88),multiply(X_87,identity))) ),[1,1],$fot(X_87)]]) ).
cnf(refute_0_39,plain,
( multiply(X_87,least_upper_bound(X_88,identity)) != least_upper_bound(multiply(X_87,X_88),multiply(X_87,identity))
| multiply(X_87,least_upper_bound(X_88,identity)) = least_upper_bound(multiply(X_87,X_88),X_87) ),
inference(resolve,[$cnf( $equal(multiply(X_87,identity),X_87) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
multiply(X_87,least_upper_bound(X_88,identity)) = least_upper_bound(multiply(X_87,X_88),X_87),
inference(resolve,[$cnf( $equal(multiply(X_87,least_upper_bound(X_88,identity)),least_upper_bound(multiply(X_87,X_88),multiply(X_87,identity))) )],[refute_0_4,refute_0_39]) ).
cnf(refute_0_41,plain,
( least_upper_bound(X,Y) != least_upper_bound(Y,X)
| least_upper_bound(Y,X) = least_upper_bound(X,Y) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(least_upper_bound(X,Y))),bind(Y0,$fot(least_upper_bound(Y,X)))]]) ).
cnf(refute_0_42,plain,
least_upper_bound(Y,X) = least_upper_bound(X,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(X,Y),least_upper_bound(Y,X)) )],[symmetry_of_lub,refute_0_41]) ).
cnf(refute_0_43,plain,
least_upper_bound(multiply(X_87,X_88),X_87) = least_upper_bound(X_87,multiply(X_87,X_88)),
inference(subst,[],[refute_0_42:[bind(X,$fot(X_87)),bind(Y,$fot(multiply(X_87,X_88)))]]) ).
cnf(refute_0_44,plain,
( multiply(X_87,least_upper_bound(X_88,identity)) != least_upper_bound(multiply(X_87,X_88),X_87)
| least_upper_bound(multiply(X_87,X_88),X_87) != least_upper_bound(X_87,multiply(X_87,X_88))
| multiply(X_87,least_upper_bound(X_88,identity)) = least_upper_bound(X_87,multiply(X_87,X_88)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_87,least_upper_bound(X_88,identity)),least_upper_bound(X_87,multiply(X_87,X_88))) ),[0],$fot(least_upper_bound(multiply(X_87,X_88),X_87))]]) ).
cnf(refute_0_45,plain,
( multiply(X_87,least_upper_bound(X_88,identity)) != least_upper_bound(multiply(X_87,X_88),X_87)
| multiply(X_87,least_upper_bound(X_88,identity)) = least_upper_bound(X_87,multiply(X_87,X_88)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_87,X_88),X_87),least_upper_bound(X_87,multiply(X_87,X_88))) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
multiply(X_87,least_upper_bound(X_88,identity)) = least_upper_bound(X_87,multiply(X_87,X_88)),
inference(resolve,[$cnf( $equal(multiply(X_87,least_upper_bound(X_88,identity)),least_upper_bound(multiply(X_87,X_88),X_87)) )],[refute_0_40,refute_0_45]) ).
cnf(refute_0_47,plain,
( multiply(X_87,least_upper_bound(X_88,identity)) != least_upper_bound(X_87,multiply(X_87,X_88))
| least_upper_bound(X_87,multiply(X_87,X_88)) = multiply(X_87,least_upper_bound(X_88,identity)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(multiply(X_87,least_upper_bound(X_88,identity)))),bind(Y0,$fot(least_upper_bound(X_87,multiply(X_87,X_88))))]]) ).
cnf(refute_0_48,plain,
least_upper_bound(X_87,multiply(X_87,X_88)) = multiply(X_87,least_upper_bound(X_88,identity)),
inference(resolve,[$cnf( $equal(multiply(X_87,least_upper_bound(X_88,identity)),least_upper_bound(X_87,multiply(X_87,X_88))) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
least_upper_bound(a,multiply(a,b)) = multiply(a,least_upper_bound(b,identity)),
inference(subst,[],[refute_0_48:[bind(X_87,$fot(a)),bind(X_88,$fot(b))]]) ).
cnf(refute_0_50,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_51,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_23,refute_0_50]) ).
cnf(refute_0_52,plain,
( multiply(a,least_upper_bound(b,identity)) != multiply(a,b)
| least_upper_bound(a,multiply(a,b)) != multiply(a,least_upper_bound(b,identity))
| least_upper_bound(a,multiply(a,b)) = multiply(a,b) ),
inference(subst,[],[refute_0_51:[bind(X0,$fot(least_upper_bound(a,multiply(a,b)))),bind(Y0,$fot(multiply(a,least_upper_bound(b,identity)))),bind(Z0,$fot(multiply(a,b)))]]) ).
cnf(refute_0_53,plain,
( multiply(a,least_upper_bound(b,identity)) != multiply(a,b)
| least_upper_bound(a,multiply(a,b)) = multiply(a,b) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,multiply(a,b)),multiply(a,least_upper_bound(b,identity))) )],[refute_0_49,refute_0_52]) ).
cnf(refute_0_54,plain,
least_upper_bound(a,multiply(a,b)) = multiply(a,b),
inference(resolve,[$cnf( $equal(multiply(a,least_upper_bound(b,identity)),multiply(a,b)) )],[refute_0_3,refute_0_53]) ).
cnf(refute_0_55,plain,
( multiply(a,b) != multiply(a,b)
| least_upper_bound(a,multiply(a,b)) != multiply(a,b)
| least_upper_bound(a,multiply(a,b)) = multiply(a,b) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(a,multiply(a,b)),multiply(a,b)) ),[0,1],$fot(multiply(a,b))]]) ).
cnf(refute_0_56,plain,
( multiply(a,b) != multiply(a,b)
| least_upper_bound(a,multiply(a,b)) = multiply(a,b) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,multiply(a,b)),multiply(a,b)) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
multiply(a,b) != multiply(a,b),
inference(resolve,[$cnf( $equal(least_upper_bound(a,multiply(a,b)),multiply(a,b)) )],[refute_0_56,prove_lat2a]) ).
cnf(refute_0_58,plain,
multiply(a,b) = multiply(a,b),
introduced(tautology,[refl,[$fot(multiply(a,b))]]) ).
cnf(refute_0_59,plain,
$false,
inference(resolve,[$cnf( $equal(multiply(a,b),multiply(a,b)) )],[refute_0_58,refute_0_57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP166-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n027.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 : Tue Jun 14 07:59:03 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.55/0.76 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.55/0.76
% 0.55/0.76 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.55/0.76
%------------------------------------------------------------------------------