TSTP Solution File: GRP163-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP163-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n024.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 10:37:07 EDT 2022
% Result : Unsatisfiable 0.21s 0.47s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of clauses : 21 ( 12 unt; 0 nHn; 17 RR)
% Number of literals : 34 ( 33 equ; 15 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 : 12 ( 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_transb_1,hypothesis,
greatest_lower_bound(a,b) = a ).
cnf(ax_transb_2,hypothesis,
greatest_lower_bound(b,c) = b ).
cnf(prove_ax_transb,negated_conjecture,
greatest_lower_bound(a,c) != a ).
cnf(refute_0_0,plain,
greatest_lower_bound(a,greatest_lower_bound(b,X_30)) = greatest_lower_bound(greatest_lower_bound(a,b),X_30),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(a)),bind(Y,$fot(b)),bind(Z,$fot(X_30))]]) ).
cnf(refute_0_1,plain,
( greatest_lower_bound(a,b) != a
| greatest_lower_bound(a,greatest_lower_bound(b,X_30)) != greatest_lower_bound(greatest_lower_bound(a,b),X_30)
| greatest_lower_bound(a,greatest_lower_bound(b,X_30)) = greatest_lower_bound(a,X_30) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(b,X_30)),greatest_lower_bound(greatest_lower_bound(a,b),X_30)) ),[1,0],$fot(a)]]) ).
cnf(refute_0_2,plain,
( greatest_lower_bound(a,greatest_lower_bound(b,X_30)) != greatest_lower_bound(greatest_lower_bound(a,b),X_30)
| greatest_lower_bound(a,greatest_lower_bound(b,X_30)) = greatest_lower_bound(a,X_30) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,b),a) )],[ax_transb_1,refute_0_1]) ).
cnf(refute_0_3,plain,
greatest_lower_bound(a,greatest_lower_bound(b,X_30)) = greatest_lower_bound(a,X_30),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(b,X_30)),greatest_lower_bound(greatest_lower_bound(a,b),X_30)) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
greatest_lower_bound(a,greatest_lower_bound(b,c)) = greatest_lower_bound(a,c),
inference(subst,[],[refute_0_3:[bind(X_30,$fot(c))]]) ).
cnf(refute_0_5,plain,
( greatest_lower_bound(a,greatest_lower_bound(b,c)) != greatest_lower_bound(a,c)
| greatest_lower_bound(b,c) != b
| greatest_lower_bound(a,b) = greatest_lower_bound(a,c) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(b,c)),greatest_lower_bound(a,c)) ),[0,1],$fot(b)]]) ).
cnf(refute_0_6,plain,
( greatest_lower_bound(a,greatest_lower_bound(b,c)) != greatest_lower_bound(a,c)
| greatest_lower_bound(a,b) = greatest_lower_bound(a,c) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,c),b) )],[ax_transb_2,refute_0_5]) ).
cnf(refute_0_7,plain,
greatest_lower_bound(a,b) = greatest_lower_bound(a,c),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(b,c)),greatest_lower_bound(a,c)) )],[refute_0_4,refute_0_6]) ).
cnf(refute_0_8,plain,
( greatest_lower_bound(a,b) != a
| greatest_lower_bound(a,b) != greatest_lower_bound(a,c)
| a = greatest_lower_bound(a,c) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,b),greatest_lower_bound(a,c)) ),[0],$fot(a)]]) ).
cnf(refute_0_9,plain,
( greatest_lower_bound(a,b) != greatest_lower_bound(a,c)
| a = greatest_lower_bound(a,c) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,b),a) )],[ax_transb_1,refute_0_8]) ).
cnf(refute_0_10,plain,
a = greatest_lower_bound(a,c),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,b),greatest_lower_bound(a,c)) )],[refute_0_7,refute_0_9]) ).
cnf(refute_0_11,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_12,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_13,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( a != greatest_lower_bound(a,c)
| greatest_lower_bound(a,c) = a ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(a)),bind(Y0,$fot(greatest_lower_bound(a,c)))]]) ).
cnf(refute_0_15,plain,
a != greatest_lower_bound(a,c),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,c),a) )],[refute_0_14,prove_ax_transb]) ).
cnf(refute_0_16,plain,
$false,
inference(resolve,[$cnf( $equal(a,greatest_lower_bound(a,c)) )],[refute_0_10,refute_0_15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : GRP163-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.14/0.14 % Command : metis --show proof --show saturation %s
% 0.14/0.35 % Computer : n024.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 10:13:03 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.21/0.47 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.47
% 0.21/0.47 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.21/0.47
%------------------------------------------------------------------------------