TSTP Solution File: GRP159-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP159-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n017.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 10:37:06 EDT 2022
% Result : Unsatisfiable 0.19s 0.37s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 16
% Syntax : Number of clauses : 41 ( 24 unt; 0 nHn; 30 RR)
% Number of literals : 65 ( 64 equ; 27 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 38 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(symmetry_of_glb,axiom,
greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ).
cnf(symmetry_of_lub,axiom,
least_upper_bound(X,Y) = least_upper_bound(Y,X) ).
cnf(lub_absorbtion,axiom,
least_upper_bound(X,greatest_lower_bound(X,Y)) = X ).
cnf(monotony_lub1,axiom,
multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ).
cnf(ax_mono2c_1,hypothesis,
greatest_lower_bound(a,b) = a ).
cnf(prove_ax_mono2c,negated_conjecture,
least_upper_bound(multiply(c,a),multiply(c,b)) != multiply(c,b) ).
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( $equal(X0,X0) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( multiply(X,least_upper_bound(Y,Z)) != least_upper_bound(multiply(X,Y),multiply(X,Z))
| least_upper_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X,least_upper_bound(Y,Z)))),bind(Y0,$fot(least_upper_bound(multiply(X,Y),multiply(X,Z))))]]) ).
cnf(refute_0_4,plain,
least_upper_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Y),multiply(X,Z))) )],[monotony_lub1,refute_0_3]) ).
cnf(refute_0_5,plain,
least_upper_bound(multiply(c,a),multiply(c,b)) = multiply(c,least_upper_bound(a,b)),
inference(subst,[],[refute_0_4:[bind(X,$fot(c)),bind(Y,$fot(a)),bind(Z,$fot(b))]]) ).
cnf(refute_0_6,plain,
( multiply(c,least_upper_bound(a,b)) != multiply(c,b)
| least_upper_bound(multiply(c,a),multiply(c,b)) != multiply(c,least_upper_bound(a,b))
| least_upper_bound(multiply(c,a),multiply(c,b)) = multiply(c,b) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(c,a),multiply(c,b)),multiply(c,least_upper_bound(a,b))) ),[1],$fot(multiply(c,b))]]) ).
cnf(refute_0_7,plain,
( multiply(c,least_upper_bound(a,b)) != multiply(c,b)
| least_upper_bound(multiply(c,a),multiply(c,b)) = multiply(c,b) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(c,a),multiply(c,b)),multiply(c,least_upper_bound(a,b))) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
multiply(c,least_upper_bound(a,b)) != multiply(c,b),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(c,a),multiply(c,b)),multiply(c,b)) )],[refute_0_7,prove_ax_mono2c]) ).
cnf(refute_0_9,plain,
least_upper_bound(X_8,greatest_lower_bound(X_8,X_9)) = X_8,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_8)),bind(Y,$fot(X_9))]]) ).
cnf(refute_0_10,plain,
greatest_lower_bound(X_9,X_8) = greatest_lower_bound(X_8,X_9),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_9)),bind(Y,$fot(X_8))]]) ).
cnf(refute_0_11,plain,
( greatest_lower_bound(X_9,X_8) != greatest_lower_bound(X_8,X_9)
| greatest_lower_bound(X_8,X_9) = greatest_lower_bound(X_9,X_8) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X_9,X_8))),bind(Y0,$fot(greatest_lower_bound(X_8,X_9)))]]) ).
cnf(refute_0_12,plain,
greatest_lower_bound(X_8,X_9) = greatest_lower_bound(X_9,X_8),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_9,X_8),greatest_lower_bound(X_8,X_9)) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( greatest_lower_bound(X_8,X_9) != greatest_lower_bound(X_9,X_8)
| least_upper_bound(X_8,greatest_lower_bound(X_8,X_9)) != X_8
| least_upper_bound(X_8,greatest_lower_bound(X_9,X_8)) = X_8 ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_8,greatest_lower_bound(X_8,X_9)),X_8) ),[0,1],$fot(greatest_lower_bound(X_9,X_8))]]) ).
cnf(refute_0_14,plain,
( least_upper_bound(X_8,greatest_lower_bound(X_8,X_9)) != X_8
| least_upper_bound(X_8,greatest_lower_bound(X_9,X_8)) = X_8 ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_8,X_9),greatest_lower_bound(X_9,X_8)) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
least_upper_bound(X_8,greatest_lower_bound(X_9,X_8)) = X_8,
inference(resolve,[$cnf( $equal(least_upper_bound(X_8,greatest_lower_bound(X_8,X_9)),X_8) )],[refute_0_9,refute_0_14]) ).
cnf(refute_0_16,plain,
least_upper_bound(b,greatest_lower_bound(a,b)) = b,
inference(subst,[],[refute_0_15:[bind(X_8,$fot(b)),bind(X_9,$fot(a))]]) ).
cnf(refute_0_17,plain,
( greatest_lower_bound(a,b) != a
| least_upper_bound(b,greatest_lower_bound(a,b)) != b
| least_upper_bound(b,a) = b ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(a,b)),b) ),[0,1],$fot(a)]]) ).
cnf(refute_0_18,plain,
( least_upper_bound(b,greatest_lower_bound(a,b)) != b
| least_upper_bound(b,a) = b ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,b),a) )],[ax_mono2c_1,refute_0_17]) ).
cnf(refute_0_19,plain,
least_upper_bound(b,a) = b,
inference(resolve,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(a,b)),b) )],[refute_0_16,refute_0_18]) ).
cnf(refute_0_20,plain,
( least_upper_bound(X,Y) != least_upper_bound(Y,X)
| least_upper_bound(Y,X) = least_upper_bound(X,Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X,Y))),bind(Y0,$fot(least_upper_bound(Y,X)))]]) ).
cnf(refute_0_21,plain,
least_upper_bound(Y,X) = least_upper_bound(X,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(X,Y),least_upper_bound(Y,X)) )],[symmetry_of_lub,refute_0_20]) ).
cnf(refute_0_22,plain,
least_upper_bound(b,a) = least_upper_bound(a,b),
inference(subst,[],[refute_0_21:[bind(X,$fot(a)),bind(Y,$fot(b))]]) ).
cnf(refute_0_23,plain,
( least_upper_bound(b,a) != b
| least_upper_bound(b,a) != least_upper_bound(a,b)
| least_upper_bound(a,b) = b ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,a),b) ),[0],$fot(least_upper_bound(a,b))]]) ).
cnf(refute_0_24,plain,
( least_upper_bound(b,a) != b
| least_upper_bound(a,b) = b ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,a),least_upper_bound(a,b)) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
least_upper_bound(a,b) = b,
inference(resolve,[$cnf( $equal(least_upper_bound(b,a),b) )],[refute_0_19,refute_0_24]) ).
cnf(refute_0_26,plain,
multiply(c,least_upper_bound(a,b)) = multiply(c,least_upper_bound(a,b)),
introduced(tautology,[refl,[$fot(multiply(c,least_upper_bound(a,b)))]]) ).
cnf(refute_0_27,plain,
( multiply(c,least_upper_bound(a,b)) != multiply(c,least_upper_bound(a,b))
| least_upper_bound(a,b) != b
| multiply(c,least_upper_bound(a,b)) = multiply(c,b) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(c,least_upper_bound(a,b)),multiply(c,least_upper_bound(a,b))) ),[1,1],$fot(b)]]) ).
cnf(refute_0_28,plain,
( least_upper_bound(a,b) != b
| multiply(c,least_upper_bound(a,b)) = multiply(c,b) ),
inference(resolve,[$cnf( $equal(multiply(c,least_upper_bound(a,b)),multiply(c,least_upper_bound(a,b))) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
multiply(c,least_upper_bound(a,b)) = multiply(c,b),
inference(resolve,[$cnf( $equal(least_upper_bound(a,b),b) )],[refute_0_25,refute_0_28]) ).
cnf(refute_0_30,plain,
( multiply(c,b) != multiply(c,b)
| multiply(c,least_upper_bound(a,b)) != multiply(c,b)
| multiply(c,least_upper_bound(a,b)) = multiply(c,b) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(c,least_upper_bound(a,b)),multiply(c,b)) ),[1],$fot(multiply(c,b))]]) ).
cnf(refute_0_31,plain,
( multiply(c,b) != multiply(c,b)
| multiply(c,least_upper_bound(a,b)) = multiply(c,b) ),
inference(resolve,[$cnf( $equal(multiply(c,least_upper_bound(a,b)),multiply(c,b)) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
multiply(c,b) != multiply(c,b),
inference(resolve,[$cnf( $equal(multiply(c,least_upper_bound(a,b)),multiply(c,b)) )],[refute_0_31,refute_0_8]) ).
cnf(refute_0_33,plain,
multiply(c,b) = multiply(c,b),
introduced(tautology,[refl,[$fot(multiply(c,b))]]) ).
cnf(refute_0_34,plain,
$false,
inference(resolve,[$cnf( $equal(multiply(c,b),multiply(c,b)) )],[refute_0_33,refute_0_32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP159-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n017.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 13 21:37:23 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.37 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.37
% 0.19/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.19/0.37
%------------------------------------------------------------------------------