TSTP Solution File: GRP162-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP162-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n032.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 0.13s 0.32s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 18
% Syntax : Number of clauses : 50 ( 29 unt; 0 nHn; 37 RR)
% Number of literals : 80 ( 79 equ; 31 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 38 ( 4 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(associativity_of_glb,axiom,
greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) ).
cnf(lub_absorbtion,axiom,
least_upper_bound(X,greatest_lower_bound(X,Y)) = X ).
cnf(glb_absorbtion,axiom,
greatest_lower_bound(X,least_upper_bound(X,Y)) = X ).
cnf(ax_transa_1,hypothesis,
least_upper_bound(a,b) = b ).
cnf(ax_transa_2,hypothesis,
least_upper_bound(b,c) = c ).
cnf(prove_ax_transa,negated_conjecture,
least_upper_bound(a,c) != c ).
cnf(refute_0_0,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_1,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_2,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_3,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_4,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( greatest_lower_bound(X_9,X_8) != greatest_lower_bound(X_8,X_9)
| greatest_lower_bound(X_8,X_9) = greatest_lower_bound(X_9,X_8) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(greatest_lower_bound(X_9,X_8))),bind(Y0,$fot(greatest_lower_bound(X_8,X_9)))]]) ).
cnf(refute_0_6,plain,
greatest_lower_bound(X_8,X_9) = greatest_lower_bound(X_9,X_8),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_9,X_8),greatest_lower_bound(X_8,X_9)) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
( greatest_lower_bound(X_8,X_9) != greatest_lower_bound(X_9,X_8)
| least_upper_bound(X_8,greatest_lower_bound(X_8,X_9)) != X_8
| least_upper_bound(X_8,greatest_lower_bound(X_9,X_8)) = X_8 ),
introduced(tautology,[equality,[$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_8,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( $equal(greatest_lower_bound(X_8,X_9),greatest_lower_bound(X_9,X_8)) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
least_upper_bound(X_8,greatest_lower_bound(X_9,X_8)) = X_8,
inference(resolve,[$cnf( $equal(least_upper_bound(X_8,greatest_lower_bound(X_8,X_9)),X_8) )],[refute_0_0,refute_0_8]) ).
cnf(refute_0_10,plain,
least_upper_bound(c,greatest_lower_bound(a,c)) = c,
inference(subst,[],[refute_0_9:[bind(X_8,$fot(c)),bind(X_9,$fot(a))]]) ).
cnf(refute_0_11,plain,
greatest_lower_bound(a,greatest_lower_bound(b,X_18)) = greatest_lower_bound(greatest_lower_bound(a,b),X_18),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(a)),bind(Y,$fot(b)),bind(Z,$fot(X_18))]]) ).
cnf(refute_0_12,plain,
greatest_lower_bound(a,least_upper_bound(a,b)) = a,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(a)),bind(Y,$fot(b))]]) ).
cnf(refute_0_13,plain,
( greatest_lower_bound(a,least_upper_bound(a,b)) != a
| least_upper_bound(a,b) != b
| greatest_lower_bound(a,b) = a ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,least_upper_bound(a,b)),a) ),[0,1],$fot(b)]]) ).
cnf(refute_0_14,plain,
( greatest_lower_bound(a,least_upper_bound(a,b)) != a
| greatest_lower_bound(a,b) = a ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,b),b) )],[ax_transa_1,refute_0_13]) ).
cnf(refute_0_15,plain,
greatest_lower_bound(a,b) = a,
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,least_upper_bound(a,b)),a) )],[refute_0_12,refute_0_14]) ).
cnf(refute_0_16,plain,
( greatest_lower_bound(a,b) != a
| greatest_lower_bound(a,greatest_lower_bound(b,X_18)) != greatest_lower_bound(greatest_lower_bound(a,b),X_18)
| greatest_lower_bound(a,greatest_lower_bound(b,X_18)) = greatest_lower_bound(a,X_18) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(b,X_18)),greatest_lower_bound(greatest_lower_bound(a,b),X_18)) ),[1,0],$fot(a)]]) ).
cnf(refute_0_17,plain,
( greatest_lower_bound(a,greatest_lower_bound(b,X_18)) != greatest_lower_bound(greatest_lower_bound(a,b),X_18)
| greatest_lower_bound(a,greatest_lower_bound(b,X_18)) = greatest_lower_bound(a,X_18) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,b),a) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
greatest_lower_bound(a,greatest_lower_bound(b,X_18)) = greatest_lower_bound(a,X_18),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(b,X_18)),greatest_lower_bound(greatest_lower_bound(a,b),X_18)) )],[refute_0_11,refute_0_17]) ).
cnf(refute_0_19,plain,
greatest_lower_bound(a,greatest_lower_bound(b,c)) = greatest_lower_bound(a,c),
inference(subst,[],[refute_0_18:[bind(X_18,$fot(c))]]) ).
cnf(refute_0_20,plain,
greatest_lower_bound(b,least_upper_bound(b,c)) = b,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(b)),bind(Y,$fot(c))]]) ).
cnf(refute_0_21,plain,
( greatest_lower_bound(b,least_upper_bound(b,c)) != b
| least_upper_bound(b,c) != c
| greatest_lower_bound(b,c) = b ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(b,c)),b) ),[0,1],$fot(c)]]) ).
cnf(refute_0_22,plain,
( greatest_lower_bound(b,least_upper_bound(b,c)) != b
| greatest_lower_bound(b,c) = b ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,c),c) )],[ax_transa_2,refute_0_21]) ).
cnf(refute_0_23,plain,
greatest_lower_bound(b,c) = b,
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(b,c)),b) )],[refute_0_20,refute_0_22]) ).
cnf(refute_0_24,plain,
( greatest_lower_bound(a,greatest_lower_bound(b,c)) != greatest_lower_bound(a,c)
| greatest_lower_bound(b,c) != b
| greatest_lower_bound(a,b) = greatest_lower_bound(a,c) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(b,c)),greatest_lower_bound(a,c)) ),[0,1],$fot(b)]]) ).
cnf(refute_0_25,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( $equal(greatest_lower_bound(b,c),b) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
greatest_lower_bound(a,b) = greatest_lower_bound(a,c),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(b,c)),greatest_lower_bound(a,c)) )],[refute_0_19,refute_0_25]) ).
cnf(refute_0_27,plain,
( greatest_lower_bound(a,b) != a
| greatest_lower_bound(a,b) != greatest_lower_bound(a,c)
| a = greatest_lower_bound(a,c) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,b),greatest_lower_bound(a,c)) ),[0],$fot(a)]]) ).
cnf(refute_0_28,plain,
( greatest_lower_bound(a,b) != greatest_lower_bound(a,c)
| a = greatest_lower_bound(a,c) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,b),a) )],[refute_0_15,refute_0_27]) ).
cnf(refute_0_29,plain,
a = greatest_lower_bound(a,c),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,b),greatest_lower_bound(a,c)) )],[refute_0_26,refute_0_28]) ).
cnf(refute_0_30,plain,
( a != greatest_lower_bound(a,c)
| greatest_lower_bound(a,c) = a ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(a)),bind(Y0,$fot(greatest_lower_bound(a,c)))]]) ).
cnf(refute_0_31,plain,
greatest_lower_bound(a,c) = a,
inference(resolve,[$cnf( $equal(a,greatest_lower_bound(a,c)) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
( greatest_lower_bound(a,c) != a
| least_upper_bound(c,greatest_lower_bound(a,c)) != c
| least_upper_bound(c,a) = c ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(c,greatest_lower_bound(a,c)),c) ),[0,1],$fot(a)]]) ).
cnf(refute_0_33,plain,
( least_upper_bound(c,greatest_lower_bound(a,c)) != c
| least_upper_bound(c,a) = c ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,c),a) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
least_upper_bound(c,a) = c,
inference(resolve,[$cnf( $equal(least_upper_bound(c,greatest_lower_bound(a,c)),c) )],[refute_0_10,refute_0_33]) ).
cnf(refute_0_35,plain,
( least_upper_bound(X,Y) != least_upper_bound(Y,X)
| least_upper_bound(Y,X) = least_upper_bound(X,Y) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(least_upper_bound(X,Y))),bind(Y0,$fot(least_upper_bound(Y,X)))]]) ).
cnf(refute_0_36,plain,
least_upper_bound(Y,X) = least_upper_bound(X,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(X,Y),least_upper_bound(Y,X)) )],[symmetry_of_lub,refute_0_35]) ).
cnf(refute_0_37,plain,
least_upper_bound(c,a) = least_upper_bound(a,c),
inference(subst,[],[refute_0_36:[bind(X,$fot(a)),bind(Y,$fot(c))]]) ).
cnf(refute_0_38,plain,
( least_upper_bound(c,a) != c
| least_upper_bound(c,a) != least_upper_bound(a,c)
| least_upper_bound(a,c) = c ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(c,a),c) ),[0],$fot(least_upper_bound(a,c))]]) ).
cnf(refute_0_39,plain,
( least_upper_bound(c,a) != c
| least_upper_bound(a,c) = c ),
inference(resolve,[$cnf( $equal(least_upper_bound(c,a),least_upper_bound(a,c)) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
least_upper_bound(a,c) = c,
inference(resolve,[$cnf( $equal(least_upper_bound(c,a),c) )],[refute_0_34,refute_0_39]) ).
cnf(refute_0_41,plain,
$false,
inference(resolve,[$cnf( $equal(least_upper_bound(a,c),c) )],[refute_0_40,prove_ax_transa]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : GRP162-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.00/0.09 % Command : metis --show proof --show saturation %s
% 0.08/0.28 % Computer : n032.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 600
% 0.08/0.28 % DateTime : Mon Jun 13 05:07:11 EDT 2022
% 0.08/0.28 % CPUTime :
% 0.08/0.28 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.32 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.32
% 0.13/0.32 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.32
%------------------------------------------------------------------------------