TSTP Solution File: GRP175-2 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP175-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n021.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 10:37:19 EDT 2022
% Result : Unsatisfiable 0.60s 0.82s
% Output : CNFRefutation 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 21
% Syntax : Number of clauses : 65 ( 36 unt; 0 nHn; 48 RR)
% Number of literals : 108 ( 107 equ; 46 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 : 59 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
multiply(identity,X) = X ).
cnf(left_inverse,axiom,
multiply(inverse(X),X) = identity ).
cnf(symmetry_of_glb,axiom,
greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ).
cnf(monotony_glb1,axiom,
multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_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(p06b_1,hypothesis,
greatest_lower_bound(identity,b) = identity ).
cnf(prove_p06b,negated_conjecture,
greatest_lower_bound(identity,multiply(inverse(a),multiply(b,a))) != identity ).
cnf(refute_0_0,plain,
multiply(inverse(X_117),greatest_lower_bound(X_117,X_118)) = greatest_lower_bound(multiply(inverse(X_117),X_117),multiply(inverse(X_117),X_118)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(inverse(X_117))),bind(Y,$fot(X_117)),bind(Z,$fot(X_118))]]) ).
cnf(refute_0_1,plain,
multiply(inverse(X_117),X_117) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_117))]]) ).
cnf(refute_0_2,plain,
( multiply(inverse(X_117),X_117) != identity
| multiply(inverse(X_117),greatest_lower_bound(X_117,X_118)) != greatest_lower_bound(multiply(inverse(X_117),X_117),multiply(inverse(X_117),X_118))
| multiply(inverse(X_117),greatest_lower_bound(X_117,X_118)) = greatest_lower_bound(identity,multiply(inverse(X_117),X_118)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_117),greatest_lower_bound(X_117,X_118)),greatest_lower_bound(multiply(inverse(X_117),X_117),multiply(inverse(X_117),X_118))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_3,plain,
( multiply(inverse(X_117),greatest_lower_bound(X_117,X_118)) != greatest_lower_bound(multiply(inverse(X_117),X_117),multiply(inverse(X_117),X_118))
| multiply(inverse(X_117),greatest_lower_bound(X_117,X_118)) = greatest_lower_bound(identity,multiply(inverse(X_117),X_118)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_117),X_117),identity) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
multiply(inverse(X_117),greatest_lower_bound(X_117,X_118)) = greatest_lower_bound(identity,multiply(inverse(X_117),X_118)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_117),greatest_lower_bound(X_117,X_118)),greatest_lower_bound(multiply(inverse(X_117),X_117),multiply(inverse(X_117),X_118))) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_6,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_7,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( multiply(inverse(X_117),greatest_lower_bound(X_117,X_118)) != greatest_lower_bound(identity,multiply(inverse(X_117),X_118))
| greatest_lower_bound(identity,multiply(inverse(X_117),X_118)) = multiply(inverse(X_117),greatest_lower_bound(X_117,X_118)) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(multiply(inverse(X_117),greatest_lower_bound(X_117,X_118)))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(inverse(X_117),X_118))))]]) ).
cnf(refute_0_9,plain,
greatest_lower_bound(identity,multiply(inverse(X_117),X_118)) = multiply(inverse(X_117),greatest_lower_bound(X_117,X_118)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_117),greatest_lower_bound(X_117,X_118)),greatest_lower_bound(identity,multiply(inverse(X_117),X_118))) )],[refute_0_4,refute_0_8]) ).
cnf(refute_0_10,plain,
greatest_lower_bound(identity,multiply(inverse(a),multiply(b,a))) = multiply(inverse(a),greatest_lower_bound(a,multiply(b,a))),
inference(subst,[],[refute_0_9:[bind(X_117,$fot(a)),bind(X_118,$fot(multiply(b,a)))]]) ).
cnf(refute_0_11,plain,
( multiply(inverse(a),greatest_lower_bound(a,multiply(b,a))) != identity
| greatest_lower_bound(identity,multiply(inverse(a),multiply(b,a))) != multiply(inverse(a),greatest_lower_bound(a,multiply(b,a)))
| greatest_lower_bound(identity,multiply(inverse(a),multiply(b,a))) = identity ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(a),multiply(b,a))),multiply(inverse(a),greatest_lower_bound(a,multiply(b,a)))) ),[1],$fot(identity)]]) ).
cnf(refute_0_12,plain,
( multiply(inverse(a),greatest_lower_bound(a,multiply(b,a))) != identity
| greatest_lower_bound(identity,multiply(inverse(a),multiply(b,a))) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(a),multiply(b,a))),multiply(inverse(a),greatest_lower_bound(a,multiply(b,a)))) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
multiply(inverse(a),greatest_lower_bound(a,multiply(b,a))) != identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(a),multiply(b,a))),identity) )],[refute_0_12,prove_p06b]) ).
cnf(refute_0_14,plain,
multiply(inverse(a),a) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(a))]]) ).
cnf(refute_0_15,plain,
multiply(identity,a) = a,
inference(subst,[],[left_identity:[bind(X,$fot(a))]]) ).
cnf(refute_0_16,plain,
( greatest_lower_bound(X,Y) != greatest_lower_bound(Y,X)
| greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(greatest_lower_bound(X,Y))),bind(Y0,$fot(greatest_lower_bound(Y,X)))]]) ).
cnf(refute_0_17,plain,
greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X)) )],[symmetry_of_glb,refute_0_16]) ).
cnf(refute_0_18,plain,
greatest_lower_bound(identity,b) = greatest_lower_bound(b,identity),
inference(subst,[],[refute_0_17:[bind(X,$fot(b)),bind(Y,$fot(identity))]]) ).
cnf(refute_0_19,plain,
( greatest_lower_bound(identity,b) != greatest_lower_bound(b,identity)
| greatest_lower_bound(identity,b) != identity
| greatest_lower_bound(b,identity) = identity ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,b),identity) ),[0],$fot(greatest_lower_bound(b,identity))]]) ).
cnf(refute_0_20,plain,
( greatest_lower_bound(identity,b) != identity
| greatest_lower_bound(b,identity) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,b),greatest_lower_bound(b,identity)) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
greatest_lower_bound(b,identity) = identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,b),identity) )],[p06b_1,refute_0_20]) ).
cnf(refute_0_22,plain,
multiply(greatest_lower_bound(b,identity),a) = multiply(greatest_lower_bound(b,identity),a),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(b,identity),a))]]) ).
cnf(refute_0_23,plain,
( multiply(greatest_lower_bound(b,identity),a) != multiply(greatest_lower_bound(b,identity),a)
| greatest_lower_bound(b,identity) != identity
| multiply(greatest_lower_bound(b,identity),a) = multiply(identity,a) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(b,identity),a),multiply(greatest_lower_bound(b,identity),a)) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_24,plain,
( greatest_lower_bound(b,identity) != identity
| multiply(greatest_lower_bound(b,identity),a) = multiply(identity,a) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(b,identity),a),multiply(greatest_lower_bound(b,identity),a)) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
multiply(greatest_lower_bound(b,identity),a) = multiply(identity,a),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,identity),identity) )],[refute_0_21,refute_0_24]) ).
cnf(refute_0_26,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_27,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_7,refute_0_26]) ).
cnf(refute_0_28,plain,
( multiply(greatest_lower_bound(b,identity),a) != multiply(identity,a)
| multiply(identity,a) != a
| multiply(greatest_lower_bound(b,identity),a) = a ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(multiply(greatest_lower_bound(b,identity),a))),bind(Y0,$fot(multiply(identity,a))),bind(Z0,$fot(a))]]) ).
cnf(refute_0_29,plain,
( multiply(identity,a) != a
| multiply(greatest_lower_bound(b,identity),a) = a ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(b,identity),a),multiply(identity,a)) )],[refute_0_25,refute_0_28]) ).
cnf(refute_0_30,plain,
multiply(greatest_lower_bound(b,identity),a) = a,
inference(resolve,[$cnf( $equal(multiply(identity,a),a) )],[refute_0_15,refute_0_29]) ).
cnf(refute_0_31,plain,
multiply(greatest_lower_bound(X_132,identity),X_131) = greatest_lower_bound(multiply(X_132,X_131),multiply(identity,X_131)),
inference(subst,[],[monotony_glb2:[bind(X,$fot(X_131)),bind(Y,$fot(X_132)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_32,plain,
multiply(identity,X_131) = X_131,
inference(subst,[],[left_identity:[bind(X,$fot(X_131))]]) ).
cnf(refute_0_33,plain,
( multiply(greatest_lower_bound(X_132,identity),X_131) != greatest_lower_bound(multiply(X_132,X_131),multiply(identity,X_131))
| multiply(identity,X_131) != X_131
| multiply(greatest_lower_bound(X_132,identity),X_131) = greatest_lower_bound(multiply(X_132,X_131),X_131) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_132,identity),X_131),greatest_lower_bound(multiply(X_132,X_131),multiply(identity,X_131))) ),[1,1],$fot(X_131)]]) ).
cnf(refute_0_34,plain,
( multiply(greatest_lower_bound(X_132,identity),X_131) != greatest_lower_bound(multiply(X_132,X_131),multiply(identity,X_131))
| multiply(greatest_lower_bound(X_132,identity),X_131) = greatest_lower_bound(multiply(X_132,X_131),X_131) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_131),X_131) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
multiply(greatest_lower_bound(X_132,identity),X_131) = greatest_lower_bound(multiply(X_132,X_131),X_131),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_132,identity),X_131),greatest_lower_bound(multiply(X_132,X_131),multiply(identity,X_131))) )],[refute_0_31,refute_0_34]) ).
cnf(refute_0_36,plain,
greatest_lower_bound(multiply(X_132,X_131),X_131) = greatest_lower_bound(X_131,multiply(X_132,X_131)),
inference(subst,[],[refute_0_17:[bind(X,$fot(X_131)),bind(Y,$fot(multiply(X_132,X_131)))]]) ).
cnf(refute_0_37,plain,
( multiply(greatest_lower_bound(X_132,identity),X_131) != greatest_lower_bound(multiply(X_132,X_131),X_131)
| greatest_lower_bound(multiply(X_132,X_131),X_131) != greatest_lower_bound(X_131,multiply(X_132,X_131))
| multiply(greatest_lower_bound(X_132,identity),X_131) = greatest_lower_bound(X_131,multiply(X_132,X_131)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_132,identity),X_131),greatest_lower_bound(X_131,multiply(X_132,X_131))) ),[0],$fot(greatest_lower_bound(multiply(X_132,X_131),X_131))]]) ).
cnf(refute_0_38,plain,
( multiply(greatest_lower_bound(X_132,identity),X_131) != greatest_lower_bound(multiply(X_132,X_131),X_131)
| multiply(greatest_lower_bound(X_132,identity),X_131) = greatest_lower_bound(X_131,multiply(X_132,X_131)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_132,X_131),X_131),greatest_lower_bound(X_131,multiply(X_132,X_131))) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
multiply(greatest_lower_bound(X_132,identity),X_131) = greatest_lower_bound(X_131,multiply(X_132,X_131)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_132,identity),X_131),greatest_lower_bound(multiply(X_132,X_131),X_131)) )],[refute_0_35,refute_0_38]) ).
cnf(refute_0_40,plain,
( multiply(greatest_lower_bound(X_132,identity),X_131) != greatest_lower_bound(X_131,multiply(X_132,X_131))
| greatest_lower_bound(X_131,multiply(X_132,X_131)) = multiply(greatest_lower_bound(X_132,identity),X_131) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(multiply(greatest_lower_bound(X_132,identity),X_131))),bind(Y0,$fot(greatest_lower_bound(X_131,multiply(X_132,X_131))))]]) ).
cnf(refute_0_41,plain,
greatest_lower_bound(X_131,multiply(X_132,X_131)) = multiply(greatest_lower_bound(X_132,identity),X_131),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_132,identity),X_131),greatest_lower_bound(X_131,multiply(X_132,X_131))) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
greatest_lower_bound(a,multiply(b,a)) = multiply(greatest_lower_bound(b,identity),a),
inference(subst,[],[refute_0_41:[bind(X_131,$fot(a)),bind(X_132,$fot(b))]]) ).
cnf(refute_0_43,plain,
( multiply(greatest_lower_bound(b,identity),a) != a
| greatest_lower_bound(a,multiply(b,a)) != multiply(greatest_lower_bound(b,identity),a)
| greatest_lower_bound(a,multiply(b,a)) = a ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(greatest_lower_bound(a,multiply(b,a)))),bind(Y0,$fot(multiply(greatest_lower_bound(b,identity),a))),bind(Z0,$fot(a))]]) ).
cnf(refute_0_44,plain,
( multiply(greatest_lower_bound(b,identity),a) != a
| greatest_lower_bound(a,multiply(b,a)) = a ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,multiply(b,a)),multiply(greatest_lower_bound(b,identity),a)) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
greatest_lower_bound(a,multiply(b,a)) = a,
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(b,identity),a),a) )],[refute_0_30,refute_0_44]) ).
cnf(refute_0_46,plain,
multiply(inverse(a),greatest_lower_bound(a,multiply(b,a))) = multiply(inverse(a),greatest_lower_bound(a,multiply(b,a))),
introduced(tautology,[refl,[$fot(multiply(inverse(a),greatest_lower_bound(a,multiply(b,a))))]]) ).
cnf(refute_0_47,plain,
( multiply(inverse(a),greatest_lower_bound(a,multiply(b,a))) != multiply(inverse(a),greatest_lower_bound(a,multiply(b,a)))
| greatest_lower_bound(a,multiply(b,a)) != a
| multiply(inverse(a),greatest_lower_bound(a,multiply(b,a))) = multiply(inverse(a),a) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(a),greatest_lower_bound(a,multiply(b,a))),multiply(inverse(a),greatest_lower_bound(a,multiply(b,a)))) ),[1,1],$fot(a)]]) ).
cnf(refute_0_48,plain,
( greatest_lower_bound(a,multiply(b,a)) != a
| multiply(inverse(a),greatest_lower_bound(a,multiply(b,a))) = multiply(inverse(a),a) ),
inference(resolve,[$cnf( $equal(multiply(inverse(a),greatest_lower_bound(a,multiply(b,a))),multiply(inverse(a),greatest_lower_bound(a,multiply(b,a)))) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
multiply(inverse(a),greatest_lower_bound(a,multiply(b,a))) = multiply(inverse(a),a),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,multiply(b,a)),a) )],[refute_0_45,refute_0_48]) ).
cnf(refute_0_50,plain,
( multiply(inverse(a),a) != identity
| multiply(inverse(a),greatest_lower_bound(a,multiply(b,a))) != multiply(inverse(a),a)
| multiply(inverse(a),greatest_lower_bound(a,multiply(b,a))) = identity ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(multiply(inverse(a),greatest_lower_bound(a,multiply(b,a))))),bind(Y0,$fot(multiply(inverse(a),a))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_51,plain,
( multiply(inverse(a),a) != identity
| multiply(inverse(a),greatest_lower_bound(a,multiply(b,a))) = identity ),
inference(resolve,[$cnf( $equal(multiply(inverse(a),greatest_lower_bound(a,multiply(b,a))),multiply(inverse(a),a)) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
multiply(inverse(a),greatest_lower_bound(a,multiply(b,a))) = identity,
inference(resolve,[$cnf( $equal(multiply(inverse(a),a),identity) )],[refute_0_14,refute_0_51]) ).
cnf(refute_0_53,plain,
( multiply(inverse(a),greatest_lower_bound(a,multiply(b,a))) != identity
| identity != identity
| multiply(inverse(a),greatest_lower_bound(a,multiply(b,a))) = identity ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(a),greatest_lower_bound(a,multiply(b,a))),identity) ),[0],$fot(identity)]]) ).
cnf(refute_0_54,plain,
( identity != identity
| multiply(inverse(a),greatest_lower_bound(a,multiply(b,a))) = identity ),
inference(resolve,[$cnf( $equal(multiply(inverse(a),greatest_lower_bound(a,multiply(b,a))),identity) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
identity != identity,
inference(resolve,[$cnf( $equal(multiply(inverse(a),greatest_lower_bound(a,multiply(b,a))),identity) )],[refute_0_54,refute_0_13]) ).
cnf(refute_0_56,plain,
identity = identity,
introduced(tautology,[refl,[$fot(identity)]]) ).
cnf(refute_0_57,plain,
$false,
inference(resolve,[$cnf( $equal(identity,identity) )],[refute_0_56,refute_0_55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : GRP175-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.00/0.08 % Command : metis --show proof --show saturation %s
% 0.07/0.26 % Computer : n021.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 600
% 0.07/0.26 % DateTime : Mon Jun 13 14:12:27 EDT 2022
% 0.07/0.26 % CPUTime :
% 0.07/0.27 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.60/0.82 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.60/0.82
% 0.60/0.82 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.60/0.82
%------------------------------------------------------------------------------