%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP166-4 : 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 10:37:09 EDT 2022
% Result : Unsatisfiable 0.38s 0.57s
% Output : CNFRefutation 0.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of clauses : 40 ( 22 unt; 0 nHn; 29 RR)
% Number of literals : 67 ( 66 equ; 29 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 42 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
multiply(identity,X) = X ).
cnf(symmetry_of_glb,axiom,
greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ).
cnf(monotony_glb2,axiom,
multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) ).
cnf(lat3b_2,hypothesis,
greatest_lower_bound(b,identity) = identity ).
cnf(prove_lat3b,negated_conjecture,
greatest_lower_bound(a,multiply(b,a)) != a ).
cnf(refute_0_0,plain,
multiply(identity,a) = a,
inference(subst,[],[left_identity:[bind(X,$fot(a))]]) ).
cnf(refute_0_1,plain,
multiply(greatest_lower_bound(b,identity),a) = multiply(greatest_lower_bound(b,identity),a),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(b,identity),a))]]) ).
cnf(refute_0_2,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_3,plain,
( greatest_lower_bound(b,identity) != identity
| multiply(greatest_lower_bound(b,identity),a) = multiply(identity,a) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(b,identity),a),multiply(greatest_lower_bound(b,identity),a)) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
multiply(greatest_lower_bound(b,identity),a) = multiply(identity,a),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,identity),identity) )],[lat3b_2,refute_0_3]) ).
cnf(refute_0_5,plain,
X0 = X0,
introduced(tautology,[refl,[$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( $equal(X0,X0) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_9,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
( multiply(greatest_lower_bound(b,identity),a) != multiply(identity,a)
| multiply(identity,a) != a
| multiply(greatest_lower_bound(b,identity),a) = a ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(multiply(greatest_lower_bound(b,identity),a))),bind(Y0,$fot(multiply(identity,a))),bind(Z0,$fot(a))]]) ).
cnf(refute_0_11,plain,
( multiply(identity,a) != a
| multiply(greatest_lower_bound(b,identity),a) = a ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(b,identity),a),multiply(identity,a)) )],[refute_0_4,refute_0_10]) ).
cnf(refute_0_12,plain,
multiply(greatest_lower_bound(b,identity),a) = a,
inference(resolve,[$cnf( $equal(multiply(identity,a),a) )],[refute_0_0,refute_0_11]) ).
cnf(refute_0_13,plain,
multiply(greatest_lower_bound(X_70,identity),X_69) = greatest_lower_bound(multiply(X_70,X_69),multiply(identity,X_69)),
inference(subst,[],[monotony_glb2:[bind(X,$fot(X_69)),bind(Y,$fot(X_70)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_14,plain,
multiply(identity,X_69) = X_69,
inference(subst,[],[left_identity:[bind(X,$fot(X_69))]]) ).
cnf(refute_0_15,plain,
( multiply(greatest_lower_bound(X_70,identity),X_69) != greatest_lower_bound(multiply(X_70,X_69),multiply(identity,X_69))
| multiply(identity,X_69) != X_69
| multiply(greatest_lower_bound(X_70,identity),X_69) = greatest_lower_bound(multiply(X_70,X_69),X_69) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_70,identity),X_69),greatest_lower_bound(multiply(X_70,X_69),multiply(identity,X_69))) ),[1,1],$fot(X_69)]]) ).
cnf(refute_0_16,plain,
( multiply(greatest_lower_bound(X_70,identity),X_69) != greatest_lower_bound(multiply(X_70,X_69),multiply(identity,X_69))
| multiply(greatest_lower_bound(X_70,identity),X_69) = greatest_lower_bound(multiply(X_70,X_69),X_69) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_69),X_69) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
multiply(greatest_lower_bound(X_70,identity),X_69) = greatest_lower_bound(multiply(X_70,X_69),X_69),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_70,identity),X_69),greatest_lower_bound(multiply(X_70,X_69),multiply(identity,X_69))) )],[refute_0_13,refute_0_16]) ).
cnf(refute_0_18,plain,
( greatest_lower_bound(X,Y) != greatest_lower_bound(Y,X)
| greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(greatest_lower_bound(X,Y))),bind(Y0,$fot(greatest_lower_bound(Y,X)))]]) ).
cnf(refute_0_19,plain,
greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X)) )],[symmetry_of_glb,refute_0_18]) ).
cnf(refute_0_20,plain,
greatest_lower_bound(multiply(X_70,X_69),X_69) = greatest_lower_bound(X_69,multiply(X_70,X_69)),
inference(subst,[],[refute_0_19:[bind(X,$fot(X_69)),bind(Y,$fot(multiply(X_70,X_69)))]]) ).
cnf(refute_0_21,plain,
( multiply(greatest_lower_bound(X_70,identity),X_69) != greatest_lower_bound(multiply(X_70,X_69),X_69)
| greatest_lower_bound(multiply(X_70,X_69),X_69) != greatest_lower_bound(X_69,multiply(X_70,X_69))
| multiply(greatest_lower_bound(X_70,identity),X_69) = greatest_lower_bound(X_69,multiply(X_70,X_69)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_70,identity),X_69),greatest_lower_bound(X_69,multiply(X_70,X_69))) ),[0],$fot(greatest_lower_bound(multiply(X_70,X_69),X_69))]]) ).
cnf(refute_0_22,plain,
( multiply(greatest_lower_bound(X_70,identity),X_69) != greatest_lower_bound(multiply(X_70,X_69),X_69)
| multiply(greatest_lower_bound(X_70,identity),X_69) = greatest_lower_bound(X_69,multiply(X_70,X_69)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_70,X_69),X_69),greatest_lower_bound(X_69,multiply(X_70,X_69))) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
multiply(greatest_lower_bound(X_70,identity),X_69) = greatest_lower_bound(X_69,multiply(X_70,X_69)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_70,identity),X_69),greatest_lower_bound(multiply(X_70,X_69),X_69)) )],[refute_0_17,refute_0_22]) ).
cnf(refute_0_24,plain,
( multiply(greatest_lower_bound(X_70,identity),X_69) != greatest_lower_bound(X_69,multiply(X_70,X_69))
| greatest_lower_bound(X_69,multiply(X_70,X_69)) = multiply(greatest_lower_bound(X_70,identity),X_69) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(multiply(greatest_lower_bound(X_70,identity),X_69))),bind(Y0,$fot(greatest_lower_bound(X_69,multiply(X_70,X_69))))]]) ).
cnf(refute_0_25,plain,
greatest_lower_bound(X_69,multiply(X_70,X_69)) = multiply(greatest_lower_bound(X_70,identity),X_69),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_70,identity),X_69),greatest_lower_bound(X_69,multiply(X_70,X_69))) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
greatest_lower_bound(a,multiply(b,a)) = multiply(greatest_lower_bound(b,identity),a),
inference(subst,[],[refute_0_25:[bind(X_69,$fot(a)),bind(X_70,$fot(b))]]) ).
cnf(refute_0_27,plain,
( multiply(greatest_lower_bound(b,identity),a) != a
| greatest_lower_bound(a,multiply(b,a)) != multiply(greatest_lower_bound(b,identity),a)
| greatest_lower_bound(a,multiply(b,a)) = a ),
inference(subst,[],[refute_0_9:[bind(X0,$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_28,plain,
( multiply(greatest_lower_bound(b,identity),a) != a
| greatest_lower_bound(a,multiply(b,a)) = a ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,multiply(b,a)),multiply(greatest_lower_bound(b,identity),a)) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
greatest_lower_bound(a,multiply(b,a)) = a,
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(b,identity),a),a) )],[refute_0_12,refute_0_28]) ).
cnf(refute_0_30,plain,
( a != a
| greatest_lower_bound(a,multiply(b,a)) != a
| greatest_lower_bound(a,multiply(b,a)) = a ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,multiply(b,a)),a) ),[0,0],$fot(a)]]) ).
cnf(refute_0_31,plain,
( a != a
| greatest_lower_bound(a,multiply(b,a)) = a ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,multiply(b,a)),a) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
a != a,
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,multiply(b,a)),a) )],[refute_0_31,prove_lat3b]) ).
cnf(refute_0_33,plain,
a = a,
introduced(tautology,[refl,[$fot(a)]]) ).
cnf(refute_0_34,plain,
$false,
inference(resolve,[$cnf( $equal(a,a) )],[refute_0_33,refute_0_32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP166-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n027.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jun 13 04:18:01 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.38/0.57 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.38/0.57
% 0.38/0.57 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.38/0.58
%------------------------------------------------------------------------------