TSTP Solution File: GRP139-1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP139-1 : 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 10:37:00 EDT 2022
% Result : Unsatisfiable 0.12s 0.36s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of clauses : 27 ( 14 unt; 0 nHn; 24 RR)
% Number of literals : 47 ( 46 equ; 22 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 : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 20 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity_of_glb,axiom,
greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) ).
cnf(ax_glb1b_1_1,hypothesis,
greatest_lower_bound(a,c) = c ).
cnf(ax_glb1b_2_2,hypothesis,
greatest_lower_bound(b,c) = c ).
cnf(prove_ax_glb1b,negated_conjecture,
greatest_lower_bound(greatest_lower_bound(a,b),c) != c ).
cnf(refute_0_0,plain,
greatest_lower_bound(a,greatest_lower_bound(b,c)) = greatest_lower_bound(a,greatest_lower_bound(b,c)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(a,greatest_lower_bound(b,c)))]]) ).
cnf(refute_0_1,plain,
( greatest_lower_bound(a,greatest_lower_bound(b,c)) != greatest_lower_bound(a,greatest_lower_bound(b,c))
| greatest_lower_bound(b,c) != c
| greatest_lower_bound(a,greatest_lower_bound(b,c)) = greatest_lower_bound(a,c) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(b,c)),greatest_lower_bound(a,greatest_lower_bound(b,c))) ),[1,1],$fot(c)]]) ).
cnf(refute_0_2,plain,
( greatest_lower_bound(b,c) != c
| greatest_lower_bound(a,greatest_lower_bound(b,c)) = greatest_lower_bound(a,c) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(b,c)),greatest_lower_bound(a,greatest_lower_bound(b,c))) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
greatest_lower_bound(a,greatest_lower_bound(b,c)) = greatest_lower_bound(a,c),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,c),c) )],[ax_glb1b_2_2,refute_0_2]) ).
cnf(refute_0_4,plain,
X0 = X0,
introduced(tautology,[refl,[$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( $equal(X0,X0) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_8,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( greatest_lower_bound(a,c) != c
| greatest_lower_bound(a,greatest_lower_bound(b,c)) != greatest_lower_bound(a,c)
| greatest_lower_bound(a,greatest_lower_bound(b,c)) = c ),
inference(subst,[],[refute_0_8:[bind(X0,$fot(greatest_lower_bound(a,greatest_lower_bound(b,c)))),bind(Y0,$fot(greatest_lower_bound(a,c))),bind(Z0,$fot(c))]]) ).
cnf(refute_0_10,plain,
( greatest_lower_bound(a,c) != c
| greatest_lower_bound(a,greatest_lower_bound(b,c)) = c ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(b,c)),greatest_lower_bound(a,c)) )],[refute_0_3,refute_0_9]) ).
cnf(refute_0_11,plain,
greatest_lower_bound(a,greatest_lower_bound(b,c)) = c,
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,c),c) )],[ax_glb1b_1_1,refute_0_10]) ).
cnf(refute_0_12,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,Z)) != greatest_lower_bound(greatest_lower_bound(X,Y),Z)
| greatest_lower_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(Y,Z)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X,Y),Z)))]]) ).
cnf(refute_0_13,plain,
greatest_lower_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(greatest_lower_bound(X,Y),Z)) )],[associativity_of_glb,refute_0_12]) ).
cnf(refute_0_14,plain,
greatest_lower_bound(greatest_lower_bound(a,b),c) = greatest_lower_bound(a,greatest_lower_bound(b,c)),
inference(subst,[],[refute_0_13:[bind(X,$fot(a)),bind(Y,$fot(b)),bind(Z,$fot(c))]]) ).
cnf(refute_0_15,plain,
( greatest_lower_bound(a,greatest_lower_bound(b,c)) != c
| greatest_lower_bound(greatest_lower_bound(a,b),c) != greatest_lower_bound(a,greatest_lower_bound(b,c))
| greatest_lower_bound(greatest_lower_bound(a,b),c) = c ),
inference(subst,[],[refute_0_8:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(a,b),c))),bind(Y0,$fot(greatest_lower_bound(a,greatest_lower_bound(b,c)))),bind(Z0,$fot(c))]]) ).
cnf(refute_0_16,plain,
( greatest_lower_bound(a,greatest_lower_bound(b,c)) != c
| greatest_lower_bound(greatest_lower_bound(a,b),c) = c ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,b),c),greatest_lower_bound(a,greatest_lower_bound(b,c))) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
greatest_lower_bound(greatest_lower_bound(a,b),c) = c,
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(b,c)),c) )],[refute_0_11,refute_0_16]) ).
cnf(refute_0_18,plain,
( c != c
| greatest_lower_bound(greatest_lower_bound(a,b),c) != c
| greatest_lower_bound(greatest_lower_bound(a,b),c) = c ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,b),c),c) ),[0,1],$fot(c)]]) ).
cnf(refute_0_19,plain,
( c != c
| greatest_lower_bound(greatest_lower_bound(a,b),c) = c ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,b),c),c) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
c != c,
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,b),c),c) )],[refute_0_19,prove_ax_glb1b]) ).
cnf(refute_0_21,plain,
c = c,
introduced(tautology,[refl,[$fot(c)]]) ).
cnf(refute_0_22,plain,
$false,
inference(resolve,[$cnf( $equal(c,c) )],[refute_0_21,refute_0_20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP139-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.06/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n027.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 19:21:02 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.36 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.36
% 0.12/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.36
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