%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP168-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n016.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 10:37:14 EDT 2022
% Result : Unsatisfiable 0.12s 0.35s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of clauses : 34 ( 18 unt; 0 nHn; 29 RR)
% Number of literals : 58 ( 57 equ; 26 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 : 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(p01a_1,hypothesis,
least_upper_bound(a,b) = b ).
cnf(prove_p01a,negated_conjecture,
least_upper_bound(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c))) != multiply(inverse(c),multiply(b,c)) ).
cnf(refute_0_0,plain,
multiply(least_upper_bound(a,b),c) = multiply(least_upper_bound(a,b),c),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(a,b),c))]]) ).
cnf(refute_0_1,plain,
( multiply(least_upper_bound(a,b),c) != multiply(least_upper_bound(a,b),c)
| least_upper_bound(a,b) != b
| multiply(least_upper_bound(a,b),c) = multiply(b,c) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(a,b),c),multiply(least_upper_bound(a,b),c)) ),[1,0],$fot(b)]]) ).
cnf(refute_0_2,plain,
( least_upper_bound(a,b) != b
| multiply(least_upper_bound(a,b),c) = multiply(b,c) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,b),c),multiply(least_upper_bound(a,b),c)) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
multiply(least_upper_bound(a,b),c) = multiply(b,c),
inference(resolve,[$cnf( $equal(least_upper_bound(a,b),b) )],[p01a_1,refute_0_2]) ).
cnf(refute_0_4,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_5,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_6,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
( multiply(least_upper_bound(Y,Z),X) != least_upper_bound(multiply(Y,X),multiply(Z,X))
| least_upper_bound(multiply(Y,X),multiply(Z,X)) = multiply(least_upper_bound(Y,Z),X) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(multiply(least_upper_bound(Y,Z),X))),bind(Y0,$fot(least_upper_bound(multiply(Y,X),multiply(Z,X))))]]) ).
cnf(refute_0_8,plain,
least_upper_bound(multiply(Y,X),multiply(Z,X)) = multiply(least_upper_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Y,X),multiply(Z,X))) )],[monotony_lub2,refute_0_7]) ).
cnf(refute_0_9,plain,
least_upper_bound(multiply(a,c),multiply(b,c)) = multiply(least_upper_bound(a,b),c),
inference(subst,[],[refute_0_8:[bind(X,$fot(c)),bind(Y,$fot(a)),bind(Z,$fot(b))]]) ).
cnf(refute_0_10,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_11,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_6,refute_0_10]) ).
cnf(refute_0_12,plain,
( multiply(least_upper_bound(a,b),c) != multiply(b,c)
| least_upper_bound(multiply(a,c),multiply(b,c)) != multiply(least_upper_bound(a,b),c)
| least_upper_bound(multiply(a,c),multiply(b,c)) = multiply(b,c) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(least_upper_bound(multiply(a,c),multiply(b,c)))),bind(Y0,$fot(multiply(least_upper_bound(a,b),c))),bind(Z0,$fot(multiply(b,c)))]]) ).
cnf(refute_0_13,plain,
( multiply(least_upper_bound(a,b),c) != multiply(b,c)
| least_upper_bound(multiply(a,c),multiply(b,c)) = multiply(b,c) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(a,c),multiply(b,c)),multiply(least_upper_bound(a,b),c)) )],[refute_0_9,refute_0_12]) ).
cnf(refute_0_14,plain,
least_upper_bound(multiply(a,c),multiply(b,c)) = multiply(b,c),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,b),c),multiply(b,c)) )],[refute_0_3,refute_0_13]) ).
cnf(refute_0_15,plain,
multiply(inverse(c),least_upper_bound(multiply(a,c),multiply(b,c))) = multiply(inverse(c),least_upper_bound(multiply(a,c),multiply(b,c))),
introduced(tautology,[refl,[$fot(multiply(inverse(c),least_upper_bound(multiply(a,c),multiply(b,c))))]]) ).
cnf(refute_0_16,plain,
( multiply(inverse(c),least_upper_bound(multiply(a,c),multiply(b,c))) != multiply(inverse(c),least_upper_bound(multiply(a,c),multiply(b,c)))
| least_upper_bound(multiply(a,c),multiply(b,c)) != multiply(b,c)
| multiply(inverse(c),least_upper_bound(multiply(a,c),multiply(b,c))) = multiply(inverse(c),multiply(b,c)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(c),least_upper_bound(multiply(a,c),multiply(b,c))),multiply(inverse(c),least_upper_bound(multiply(a,c),multiply(b,c)))) ),[1,1],$fot(multiply(b,c))]]) ).
cnf(refute_0_17,plain,
( least_upper_bound(multiply(a,c),multiply(b,c)) != multiply(b,c)
| multiply(inverse(c),least_upper_bound(multiply(a,c),multiply(b,c))) = multiply(inverse(c),multiply(b,c)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(c),least_upper_bound(multiply(a,c),multiply(b,c))),multiply(inverse(c),least_upper_bound(multiply(a,c),multiply(b,c)))) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
multiply(inverse(c),least_upper_bound(multiply(a,c),multiply(b,c))) = multiply(inverse(c),multiply(b,c)),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(a,c),multiply(b,c)),multiply(b,c)) )],[refute_0_14,refute_0_17]) ).
cnf(refute_0_19,plain,
( multiply(X,least_upper_bound(Y,Z)) != least_upper_bound(multiply(X,Y),multiply(X,Z))
| least_upper_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(multiply(X,least_upper_bound(Y,Z)))),bind(Y0,$fot(least_upper_bound(multiply(X,Y),multiply(X,Z))))]]) ).
cnf(refute_0_20,plain,
least_upper_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Y),multiply(X,Z))) )],[monotony_lub1,refute_0_19]) ).
cnf(refute_0_21,plain,
least_upper_bound(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c))) = multiply(inverse(c),least_upper_bound(multiply(a,c),multiply(b,c))),
inference(subst,[],[refute_0_20:[bind(X,$fot(inverse(c))),bind(Y,$fot(multiply(a,c))),bind(Z,$fot(multiply(b,c)))]]) ).
cnf(refute_0_22,plain,
( multiply(inverse(c),least_upper_bound(multiply(a,c),multiply(b,c))) != multiply(inverse(c),multiply(b,c))
| least_upper_bound(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c))) != multiply(inverse(c),least_upper_bound(multiply(a,c),multiply(b,c)))
| least_upper_bound(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c))) = multiply(inverse(c),multiply(b,c)) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(least_upper_bound(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c))))),bind(Y0,$fot(multiply(inverse(c),least_upper_bound(multiply(a,c),multiply(b,c))))),bind(Z0,$fot(multiply(inverse(c),multiply(b,c))))]]) ).
cnf(refute_0_23,plain,
( multiply(inverse(c),least_upper_bound(multiply(a,c),multiply(b,c))) != multiply(inverse(c),multiply(b,c))
| least_upper_bound(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c))) = multiply(inverse(c),multiply(b,c)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c))),multiply(inverse(c),least_upper_bound(multiply(a,c),multiply(b,c)))) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
least_upper_bound(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c))) = multiply(inverse(c),multiply(b,c)),
inference(resolve,[$cnf( $equal(multiply(inverse(c),least_upper_bound(multiply(a,c),multiply(b,c))),multiply(inverse(c),multiply(b,c))) )],[refute_0_18,refute_0_23]) ).
cnf(refute_0_25,plain,
( multiply(inverse(c),multiply(b,c)) != multiply(inverse(c),multiply(b,c))
| least_upper_bound(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c))) != multiply(inverse(c),multiply(b,c))
| least_upper_bound(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c))) = multiply(inverse(c),multiply(b,c)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c))),multiply(inverse(c),multiply(b,c))) ),[0,1],$fot(multiply(inverse(c),multiply(b,c)))]]) ).
cnf(refute_0_26,plain,
( multiply(inverse(c),multiply(b,c)) != multiply(inverse(c),multiply(b,c))
| least_upper_bound(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c))) = multiply(inverse(c),multiply(b,c)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c))),multiply(inverse(c),multiply(b,c))) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
multiply(inverse(c),multiply(b,c)) != multiply(inverse(c),multiply(b,c)),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c))),multiply(inverse(c),multiply(b,c))) )],[refute_0_26,prove_p01a]) ).
cnf(refute_0_28,plain,
multiply(inverse(c),multiply(b,c)) = multiply(inverse(c),multiply(b,c)),
introduced(tautology,[refl,[$fot(multiply(inverse(c),multiply(b,c)))]]) ).
cnf(refute_0_29,plain,
$false,
inference(resolve,[$cnf( $equal(multiply(inverse(c),multiply(b,c)),multiply(inverse(c),multiply(b,c))) )],[refute_0_28,refute_0_27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP168-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n016.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 : Tue Jun 14 00:19:30 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.35 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.35
% 0.12/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.36
%------------------------------------------------------------------------------