TSTP Solution File: GRP166-3 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP166-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n004.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 0.93s 1.17s
% Output : CNFRefutation 0.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of clauses : 36 ( 20 unt; 0 nHn; 25 RR)
% Number of literals : 60 ( 59 equ; 26 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_lub,axiom,
least_upper_bound(X,Y) = least_upper_bound(Y,X) ).
cnf(monotony_lub2,axiom,
multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) ).
cnf(lat3a_2,hypothesis,
least_upper_bound(b,identity) = b ).
cnf(prove_lat3a,negated_conjecture,
least_upper_bound(a,multiply(b,a)) != multiply(b,a) ).
cnf(refute_0_0,plain,
multiply(least_upper_bound(b,identity),a) = multiply(least_upper_bound(b,identity),a),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(b,identity),a))]]) ).
cnf(refute_0_1,plain,
( multiply(least_upper_bound(b,identity),a) != multiply(least_upper_bound(b,identity),a)
| least_upper_bound(b,identity) != b
| multiply(least_upper_bound(b,identity),a) = multiply(b,a) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(b,identity),a),multiply(least_upper_bound(b,identity),a)) ),[1,0],$fot(b)]]) ).
cnf(refute_0_2,plain,
( least_upper_bound(b,identity) != b
| multiply(least_upper_bound(b,identity),a) = multiply(b,a) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,identity),a),multiply(least_upper_bound(b,identity),a)) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
multiply(least_upper_bound(b,identity),a) = multiply(b,a),
inference(resolve,[$cnf( $equal(least_upper_bound(b,identity),b) )],[lat3a_2,refute_0_2]) ).
cnf(refute_0_4,plain,
multiply(least_upper_bound(X_116,identity),X_115) = least_upper_bound(multiply(X_116,X_115),multiply(identity,X_115)),
inference(subst,[],[monotony_lub2:[bind(X,$fot(X_115)),bind(Y,$fot(X_116)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_5,plain,
multiply(identity,X_115) = X_115,
inference(subst,[],[left_identity:[bind(X,$fot(X_115))]]) ).
cnf(refute_0_6,plain,
( multiply(identity,X_115) != X_115
| multiply(least_upper_bound(X_116,identity),X_115) != least_upper_bound(multiply(X_116,X_115),multiply(identity,X_115))
| multiply(least_upper_bound(X_116,identity),X_115) = least_upper_bound(multiply(X_116,X_115),X_115) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_116,identity),X_115),least_upper_bound(multiply(X_116,X_115),multiply(identity,X_115))) ),[1,1],$fot(X_115)]]) ).
cnf(refute_0_7,plain,
( multiply(least_upper_bound(X_116,identity),X_115) != least_upper_bound(multiply(X_116,X_115),multiply(identity,X_115))
| multiply(least_upper_bound(X_116,identity),X_115) = least_upper_bound(multiply(X_116,X_115),X_115) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_115),X_115) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
multiply(least_upper_bound(X_116,identity),X_115) = least_upper_bound(multiply(X_116,X_115),X_115),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_116,identity),X_115),least_upper_bound(multiply(X_116,X_115),multiply(identity,X_115))) )],[refute_0_4,refute_0_7]) ).
cnf(refute_0_9,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_10,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_11,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
( least_upper_bound(X,Y) != least_upper_bound(Y,X)
| least_upper_bound(Y,X) = least_upper_bound(X,Y) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(least_upper_bound(X,Y))),bind(Y0,$fot(least_upper_bound(Y,X)))]]) ).
cnf(refute_0_13,plain,
least_upper_bound(Y,X) = least_upper_bound(X,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(X,Y),least_upper_bound(Y,X)) )],[symmetry_of_lub,refute_0_12]) ).
cnf(refute_0_14,plain,
least_upper_bound(multiply(X_116,X_115),X_115) = least_upper_bound(X_115,multiply(X_116,X_115)),
inference(subst,[],[refute_0_13:[bind(X,$fot(X_115)),bind(Y,$fot(multiply(X_116,X_115)))]]) ).
cnf(refute_0_15,plain,
( multiply(least_upper_bound(X_116,identity),X_115) != least_upper_bound(multiply(X_116,X_115),X_115)
| least_upper_bound(multiply(X_116,X_115),X_115) != least_upper_bound(X_115,multiply(X_116,X_115))
| multiply(least_upper_bound(X_116,identity),X_115) = least_upper_bound(X_115,multiply(X_116,X_115)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_116,identity),X_115),least_upper_bound(X_115,multiply(X_116,X_115))) ),[0],$fot(least_upper_bound(multiply(X_116,X_115),X_115))]]) ).
cnf(refute_0_16,plain,
( multiply(least_upper_bound(X_116,identity),X_115) != least_upper_bound(multiply(X_116,X_115),X_115)
| multiply(least_upper_bound(X_116,identity),X_115) = least_upper_bound(X_115,multiply(X_116,X_115)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_116,X_115),X_115),least_upper_bound(X_115,multiply(X_116,X_115))) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
multiply(least_upper_bound(X_116,identity),X_115) = least_upper_bound(X_115,multiply(X_116,X_115)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_116,identity),X_115),least_upper_bound(multiply(X_116,X_115),X_115)) )],[refute_0_8,refute_0_16]) ).
cnf(refute_0_18,plain,
( multiply(least_upper_bound(X_116,identity),X_115) != least_upper_bound(X_115,multiply(X_116,X_115))
| least_upper_bound(X_115,multiply(X_116,X_115)) = multiply(least_upper_bound(X_116,identity),X_115) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(multiply(least_upper_bound(X_116,identity),X_115))),bind(Y0,$fot(least_upper_bound(X_115,multiply(X_116,X_115))))]]) ).
cnf(refute_0_19,plain,
least_upper_bound(X_115,multiply(X_116,X_115)) = multiply(least_upper_bound(X_116,identity),X_115),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_116,identity),X_115),least_upper_bound(X_115,multiply(X_116,X_115))) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
least_upper_bound(a,multiply(b,a)) = multiply(least_upper_bound(b,identity),a),
inference(subst,[],[refute_0_19:[bind(X_115,$fot(a)),bind(X_116,$fot(b))]]) ).
cnf(refute_0_21,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_22,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_11,refute_0_21]) ).
cnf(refute_0_23,plain,
( multiply(least_upper_bound(b,identity),a) != multiply(b,a)
| least_upper_bound(a,multiply(b,a)) != multiply(least_upper_bound(b,identity),a)
| least_upper_bound(a,multiply(b,a)) = multiply(b,a) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(least_upper_bound(a,multiply(b,a)))),bind(Y0,$fot(multiply(least_upper_bound(b,identity),a))),bind(Z0,$fot(multiply(b,a)))]]) ).
cnf(refute_0_24,plain,
( multiply(least_upper_bound(b,identity),a) != multiply(b,a)
| least_upper_bound(a,multiply(b,a)) = multiply(b,a) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,multiply(b,a)),multiply(least_upper_bound(b,identity),a)) )],[refute_0_20,refute_0_23]) ).
cnf(refute_0_25,plain,
least_upper_bound(a,multiply(b,a)) = multiply(b,a),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,identity),a),multiply(b,a)) )],[refute_0_3,refute_0_24]) ).
cnf(refute_0_26,plain,
( multiply(b,a) != multiply(b,a)
| least_upper_bound(a,multiply(b,a)) != multiply(b,a)
| least_upper_bound(a,multiply(b,a)) = multiply(b,a) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(a,multiply(b,a)),multiply(b,a)) ),[0,1],$fot(multiply(b,a))]]) ).
cnf(refute_0_27,plain,
( multiply(b,a) != multiply(b,a)
| least_upper_bound(a,multiply(b,a)) = multiply(b,a) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,multiply(b,a)),multiply(b,a)) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
multiply(b,a) != multiply(b,a),
inference(resolve,[$cnf( $equal(least_upper_bound(a,multiply(b,a)),multiply(b,a)) )],[refute_0_27,prove_lat3a]) ).
cnf(refute_0_29,plain,
multiply(b,a) = multiply(b,a),
introduced(tautology,[refl,[$fot(multiply(b,a))]]) ).
cnf(refute_0_30,plain,
$false,
inference(resolve,[$cnf( $equal(multiply(b,a),multiply(b,a)) )],[refute_0_29,refute_0_28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP166-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.14 % Command : metis --show proof --show saturation %s
% 0.14/0.35 % Computer : n004.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Tue Jun 14 01:49:24 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.93/1.17 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.93/1.17
% 0.93/1.17 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.93/1.17
%------------------------------------------------------------------------------