TSTP Solution File: GRP176-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP176-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n008.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 10:37:20 EDT 2022
% Result : Unsatisfiable 0.12s 0.35s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of clauses : 26 ( 14 unt; 0 nHn; 21 RR)
% Number of literals : 44 ( 43 equ; 20 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; 4 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(monotony_lub1,axiom,
multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ).
cnf(monotony_lub2,axiom,
multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) ).
cnf(prove_p07,negated_conjecture,
multiply(c,multiply(least_upper_bound(a,b),d)) != least_upper_bound(multiply(c,multiply(a,d)),multiply(c,multiply(b,d))) ).
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( $equal(X0,X0) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( multiply(least_upper_bound(Y,Z),X) != least_upper_bound(multiply(Y,X),multiply(Z,X))
| least_upper_bound(multiply(Y,X),multiply(Z,X)) = multiply(least_upper_bound(Y,Z),X) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(Y,Z),X))),bind(Y0,$fot(least_upper_bound(multiply(Y,X),multiply(Z,X))))]]) ).
cnf(refute_0_4,plain,
least_upper_bound(multiply(Y,X),multiply(Z,X)) = multiply(least_upper_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Y,X),multiply(Z,X))) )],[monotony_lub2,refute_0_3]) ).
cnf(refute_0_5,plain,
least_upper_bound(multiply(a,d),multiply(b,d)) = multiply(least_upper_bound(a,b),d),
inference(subst,[],[refute_0_4:[bind(X,$fot(d)),bind(Y,$fot(a)),bind(Z,$fot(b))]]) ).
cnf(refute_0_6,plain,
multiply(c,least_upper_bound(multiply(a,d),multiply(b,d))) = multiply(c,least_upper_bound(multiply(a,d),multiply(b,d))),
introduced(tautology,[refl,[$fot(multiply(c,least_upper_bound(multiply(a,d),multiply(b,d))))]]) ).
cnf(refute_0_7,plain,
( multiply(c,least_upper_bound(multiply(a,d),multiply(b,d))) != multiply(c,least_upper_bound(multiply(a,d),multiply(b,d)))
| least_upper_bound(multiply(a,d),multiply(b,d)) != multiply(least_upper_bound(a,b),d)
| multiply(c,least_upper_bound(multiply(a,d),multiply(b,d))) = multiply(c,multiply(least_upper_bound(a,b),d)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(c,least_upper_bound(multiply(a,d),multiply(b,d))),multiply(c,least_upper_bound(multiply(a,d),multiply(b,d)))) ),[1,1],$fot(multiply(least_upper_bound(a,b),d))]]) ).
cnf(refute_0_8,plain,
( least_upper_bound(multiply(a,d),multiply(b,d)) != multiply(least_upper_bound(a,b),d)
| multiply(c,least_upper_bound(multiply(a,d),multiply(b,d))) = multiply(c,multiply(least_upper_bound(a,b),d)) ),
inference(resolve,[$cnf( $equal(multiply(c,least_upper_bound(multiply(a,d),multiply(b,d))),multiply(c,least_upper_bound(multiply(a,d),multiply(b,d)))) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
multiply(c,least_upper_bound(multiply(a,d),multiply(b,d))) = multiply(c,multiply(least_upper_bound(a,b),d)),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(a,d),multiply(b,d)),multiply(least_upper_bound(a,b),d)) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
( multiply(X,least_upper_bound(Y,Z)) != least_upper_bound(multiply(X,Y),multiply(X,Z))
| least_upper_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X,least_upper_bound(Y,Z)))),bind(Y0,$fot(least_upper_bound(multiply(X,Y),multiply(X,Z))))]]) ).
cnf(refute_0_11,plain,
least_upper_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Y),multiply(X,Z))) )],[monotony_lub1,refute_0_10]) ).
cnf(refute_0_12,plain,
least_upper_bound(multiply(c,multiply(a,d)),multiply(c,multiply(b,d))) = multiply(c,least_upper_bound(multiply(a,d),multiply(b,d))),
inference(subst,[],[refute_0_11:[bind(X,$fot(c)),bind(Y,$fot(multiply(a,d))),bind(Z,$fot(multiply(b,d)))]]) ).
cnf(refute_0_13,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_14,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_2,refute_0_13]) ).
cnf(refute_0_15,plain,
( multiply(c,least_upper_bound(multiply(a,d),multiply(b,d))) != multiply(c,multiply(least_upper_bound(a,b),d))
| least_upper_bound(multiply(c,multiply(a,d)),multiply(c,multiply(b,d))) != multiply(c,least_upper_bound(multiply(a,d),multiply(b,d)))
| least_upper_bound(multiply(c,multiply(a,d)),multiply(c,multiply(b,d))) = multiply(c,multiply(least_upper_bound(a,b),d)) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(least_upper_bound(multiply(c,multiply(a,d)),multiply(c,multiply(b,d))))),bind(Y0,$fot(multiply(c,least_upper_bound(multiply(a,d),multiply(b,d))))),bind(Z0,$fot(multiply(c,multiply(least_upper_bound(a,b),d))))]]) ).
cnf(refute_0_16,plain,
( multiply(c,least_upper_bound(multiply(a,d),multiply(b,d))) != multiply(c,multiply(least_upper_bound(a,b),d))
| least_upper_bound(multiply(c,multiply(a,d)),multiply(c,multiply(b,d))) = multiply(c,multiply(least_upper_bound(a,b),d)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(c,multiply(a,d)),multiply(c,multiply(b,d))),multiply(c,least_upper_bound(multiply(a,d),multiply(b,d)))) )],[refute_0_12,refute_0_15]) ).
cnf(refute_0_17,plain,
least_upper_bound(multiply(c,multiply(a,d)),multiply(c,multiply(b,d))) = multiply(c,multiply(least_upper_bound(a,b),d)),
inference(resolve,[$cnf( $equal(multiply(c,least_upper_bound(multiply(a,d),multiply(b,d))),multiply(c,multiply(least_upper_bound(a,b),d))) )],[refute_0_9,refute_0_16]) ).
cnf(refute_0_18,plain,
( multiply(c,multiply(least_upper_bound(a,b),d)) != multiply(c,multiply(least_upper_bound(a,b),d))
| least_upper_bound(multiply(c,multiply(a,d)),multiply(c,multiply(b,d))) != multiply(c,multiply(least_upper_bound(a,b),d))
| multiply(c,multiply(least_upper_bound(a,b),d)) = least_upper_bound(multiply(c,multiply(a,d)),multiply(c,multiply(b,d))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(c,multiply(least_upper_bound(a,b),d)),least_upper_bound(multiply(c,multiply(a,d)),multiply(c,multiply(b,d)))) ),[1],$fot(multiply(c,multiply(least_upper_bound(a,b),d)))]]) ).
cnf(refute_0_19,plain,
( multiply(c,multiply(least_upper_bound(a,b),d)) != multiply(c,multiply(least_upper_bound(a,b),d))
| multiply(c,multiply(least_upper_bound(a,b),d)) = least_upper_bound(multiply(c,multiply(a,d)),multiply(c,multiply(b,d))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(c,multiply(a,d)),multiply(c,multiply(b,d))),multiply(c,multiply(least_upper_bound(a,b),d))) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
multiply(c,multiply(least_upper_bound(a,b),d)) != multiply(c,multiply(least_upper_bound(a,b),d)),
inference(resolve,[$cnf( $equal(multiply(c,multiply(least_upper_bound(a,b),d)),least_upper_bound(multiply(c,multiply(a,d)),multiply(c,multiply(b,d)))) )],[refute_0_19,prove_p07]) ).
cnf(refute_0_21,plain,
multiply(c,multiply(least_upper_bound(a,b),d)) = multiply(c,multiply(least_upper_bound(a,b),d)),
introduced(tautology,[refl,[$fot(multiply(c,multiply(least_upper_bound(a,b),d)))]]) ).
cnf(refute_0_22,plain,
$false,
inference(resolve,[$cnf( $equal(multiply(c,multiply(least_upper_bound(a,b),d)),multiply(c,multiply(least_upper_bound(a,b),d))) )],[refute_0_21,refute_0_20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.11 % Problem : GRP176-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.04/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n008.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 : Mon Jun 13 21:34:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.35 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.35
% 0.12/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.35
%------------------------------------------------------------------------------