TSTP Solution File: GRP186-4 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP186-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n010.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 10:37:53 EDT 2022
% Result : Unsatisfiable 0.21s 0.55s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 16
% Syntax : Number of clauses : 42 ( 24 unt; 0 nHn; 28 RR)
% Number of literals : 68 ( 67 equ; 29 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 : 38 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_inverse,axiom,
multiply(inverse(X),X) = identity ).
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(p23x_2,hypothesis,
inverse(inverse(X)) = 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( $equal(least_upper_bound(multiply(a,b),identity),multiply(a,least_upper_bound(inverse(a),b))) )],[refute_0_15,prove_p23x]) ).
cnf(refute_0_17,plain,
multiply(X_67,least_upper_bound(X_68,inverse(X_67))) = least_upper_bound(multiply(X_67,X_68),multiply(X_67,inverse(X_67))),
inference(subst,[],[monotony_lub1:[bind(X,$fot(X_67)),bind(Y,$fot(X_68)),bind(Z,$fot(inverse(X_67)))]]) ).
cnf(refute_0_18,plain,
multiply(inverse(inverse(X_1)),inverse(X_1)) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(inverse(X_1)))]]) ).
cnf(refute_0_19,plain,
inverse(inverse(X_1)) = X_1,
inference(subst,[],[p23x_2:[bind(X,$fot(X_1))]]) ).
cnf(refute_0_20,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_21,plain,
( multiply(inverse(inverse(X_1)),inverse(X_1)) != identity
| multiply(X_1,inverse(X_1)) = identity ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_1)),X_1) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
multiply(X_1,inverse(X_1)) = identity,
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_1)),inverse(X_1)),identity) )],[refute_0_18,refute_0_21]) ).
cnf(refute_0_23,plain,
multiply(X_67,inverse(X_67)) = identity,
inference(subst,[],[refute_0_22:[bind(X_1,$fot(X_67))]]) ).
cnf(refute_0_24,plain,
( multiply(X_67,inverse(X_67)) != identity
| multiply(X_67,least_upper_bound(X_68,inverse(X_67))) != least_upper_bound(multiply(X_67,X_68),multiply(X_67,inverse(X_67)))
| multiply(X_67,least_upper_bound(X_68,inverse(X_67))) = least_upper_bound(multiply(X_67,X_68),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_67,least_upper_bound(X_68,inverse(X_67))),least_upper_bound(multiply(X_67,X_68),multiply(X_67,inverse(X_67)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_25,plain,
( multiply(X_67,least_upper_bound(X_68,inverse(X_67))) != least_upper_bound(multiply(X_67,X_68),multiply(X_67,inverse(X_67)))
| multiply(X_67,least_upper_bound(X_68,inverse(X_67))) = least_upper_bound(multiply(X_67,X_68),identity) ),
inference(resolve,[$cnf( $equal(multiply(X_67,inverse(X_67)),identity) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
multiply(X_67,least_upper_bound(X_68,inverse(X_67))) = least_upper_bound(multiply(X_67,X_68),identity),
inference(resolve,[$cnf( $equal(multiply(X_67,least_upper_bound(X_68,inverse(X_67))),least_upper_bound(multiply(X_67,X_68),multiply(X_67,inverse(X_67)))) )],[refute_0_17,refute_0_25]) ).
cnf(refute_0_27,plain,
least_upper_bound(multiply(X_67,X_68),identity) = least_upper_bound(identity,multiply(X_67,X_68)),
inference(subst,[],[refute_0_4:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_67,X_68)))]]) ).
cnf(refute_0_28,plain,
( multiply(X_67,least_upper_bound(X_68,inverse(X_67))) != least_upper_bound(multiply(X_67,X_68),identity)
| least_upper_bound(multiply(X_67,X_68),identity) != least_upper_bound(identity,multiply(X_67,X_68))
| multiply(X_67,least_upper_bound(X_68,inverse(X_67))) = least_upper_bound(identity,multiply(X_67,X_68)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_67,least_upper_bound(X_68,inverse(X_67))),least_upper_bound(identity,multiply(X_67,X_68))) ),[0],$fot(least_upper_bound(multiply(X_67,X_68),identity))]]) ).
cnf(refute_0_29,plain,
( multiply(X_67,least_upper_bound(X_68,inverse(X_67))) != least_upper_bound(multiply(X_67,X_68),identity)
| multiply(X_67,least_upper_bound(X_68,inverse(X_67))) = least_upper_bound(identity,multiply(X_67,X_68)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_67,X_68),identity),least_upper_bound(identity,multiply(X_67,X_68))) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
multiply(X_67,least_upper_bound(X_68,inverse(X_67))) = least_upper_bound(identity,multiply(X_67,X_68)),
inference(resolve,[$cnf( $equal(multiply(X_67,least_upper_bound(X_68,inverse(X_67))),least_upper_bound(multiply(X_67,X_68),identity)) )],[refute_0_26,refute_0_29]) ).
cnf(refute_0_31,plain,
multiply(a,least_upper_bound(b,inverse(a))) = least_upper_bound(identity,multiply(a,b)),
inference(subst,[],[refute_0_30:[bind(X_67,$fot(a)),bind(X_68,$fot(b))]]) ).
cnf(refute_0_32,plain,
( multiply(a,least_upper_bound(b,inverse(a))) != least_upper_bound(identity,multiply(a,b))
| least_upper_bound(identity,multiply(a,b)) != least_upper_bound(identity,multiply(a,b))
| least_upper_bound(identity,multiply(a,b)) = multiply(a,least_upper_bound(b,inverse(a))) ),
introduced(tautology,[equality,[$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_33,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( $equal(multiply(a,least_upper_bound(b,inverse(a))),least_upper_bound(identity,multiply(a,b))) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
least_upper_bound(identity,multiply(a,b)) != least_upper_bound(identity,multiply(a,b)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(a,b)),multiply(a,least_upper_bound(b,inverse(a)))) )],[refute_0_33,refute_0_16]) ).
cnf(refute_0_35,plain,
least_upper_bound(identity,multiply(a,b)) = least_upper_bound(identity,multiply(a,b)),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,multiply(a,b)))]]) ).
cnf(refute_0_36,plain,
$false,
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(a,b)),least_upper_bound(identity,multiply(a,b))) )],[refute_0_35,refute_0_34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP186-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n010.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 10:38:24 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.21/0.55 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.55
% 0.21/0.55 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.21/0.55
%------------------------------------------------------------------------------