TSTP Solution File: LAT088-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LAT088-1 : TPTP v8.1.0. Released v2.6.0.
% 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 : Sun Jul 17 05:59:50 EDT 2022
% Result : Unsatisfiable 0.18s 0.43s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 18
% Syntax : Number of clauses : 46 ( 23 unt; 0 nHn; 28 RR)
% Number of literals : 81 ( 80 equ; 37 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 108 ( 16 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(wal_absorbtion_1,axiom,
join(meet(A,B),meet(A,join(A,B))) = A ).
cnf(wal_absorbtion_4,axiom,
meet(meet(join(A,B),join(C,A)),A) = A ).
cnf(wal_absorbtion_5,axiom,
join(join(meet(A,B),meet(C,A)),A) = A ).
cnf(prove_normal_axioms_1,negated_conjecture,
meet(a,a) != a ).
cnf(refute_0_0,plain,
meet(meet(join(A,B),join(join(meet(A,X_13),meet(X_14,A)),A)),A) = A,
inference(subst,[],[wal_absorbtion_4:[bind(C,$fot(join(meet(A,X_13),meet(X_14,A))))]]) ).
cnf(refute_0_1,plain,
join(join(meet(A,X_13),meet(X_14,A)),A) = A,
inference(subst,[],[wal_absorbtion_5:[bind(B,$fot(X_13)),bind(C,$fot(X_14))]]) ).
cnf(refute_0_2,plain,
( join(join(meet(A,X_13),meet(X_14,A)),A) != A
| meet(meet(join(A,B),join(join(meet(A,X_13),meet(X_14,A)),A)),A) != A
| meet(meet(join(A,B),A),A) = A ),
introduced(tautology,[equality,[$cnf( $equal(meet(meet(join(A,B),join(join(meet(A,X_13),meet(X_14,A)),A)),A),A) ),[0,0,1],$fot(A)]]) ).
cnf(refute_0_3,plain,
( meet(meet(join(A,B),join(join(meet(A,X_13),meet(X_14,A)),A)),A) != A
| meet(meet(join(A,B),A),A) = A ),
inference(resolve,[$cnf( $equal(join(join(meet(A,X_13),meet(X_14,A)),A),A) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
meet(meet(join(A,B),A),A) = A,
inference(resolve,[$cnf( $equal(meet(meet(join(A,B),join(join(meet(A,X_13),meet(X_14,A)),A)),A),A) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
meet(meet(join(meet(A,B),meet(A,join(A,B))),meet(A,B)),meet(A,B)) = meet(A,B),
inference(subst,[],[refute_0_4:[bind(A,$fot(meet(A,B))),bind(B,$fot(meet(A,join(A,B))))]]) ).
cnf(refute_0_6,plain,
( join(meet(A,B),meet(A,join(A,B))) != A
| meet(meet(join(meet(A,B),meet(A,join(A,B))),meet(A,B)),meet(A,B)) != meet(A,B)
| meet(meet(A,meet(A,B)),meet(A,B)) = meet(A,B) ),
introduced(tautology,[equality,[$cnf( $equal(meet(meet(join(meet(A,B),meet(A,join(A,B))),meet(A,B)),meet(A,B)),meet(A,B)) ),[0,0,0],$fot(A)]]) ).
cnf(refute_0_7,plain,
( meet(meet(join(meet(A,B),meet(A,join(A,B))),meet(A,B)),meet(A,B)) != meet(A,B)
| meet(meet(A,meet(A,B)),meet(A,B)) = meet(A,B) ),
inference(resolve,[$cnf( $equal(join(meet(A,B),meet(A,join(A,B))),A) )],[wal_absorbtion_1,refute_0_6]) ).
cnf(refute_0_8,plain,
meet(meet(A,meet(A,B)),meet(A,B)) = meet(A,B),
inference(resolve,[$cnf( $equal(meet(meet(join(meet(A,B),meet(A,join(A,B))),meet(A,B)),meet(A,B)),meet(A,B)) )],[refute_0_5,refute_0_7]) ).
cnf(refute_0_9,plain,
meet(meet(meet(join(X_33,B),join(C,X_33)),meet(meet(join(X_33,B),join(C,X_33)),X_33)),meet(meet(join(X_33,B),join(C,X_33)),X_33)) = meet(meet(join(X_33,B),join(C,X_33)),X_33),
inference(subst,[],[refute_0_8:[bind(A,$fot(meet(join(X_33,B),join(C,X_33)))),bind(B,$fot(X_33))]]) ).
cnf(refute_0_10,plain,
meet(meet(join(X_33,B),join(C,X_33)),X_33) = X_33,
inference(subst,[],[wal_absorbtion_4:[bind(A,$fot(X_33))]]) ).
cnf(refute_0_11,plain,
( meet(meet(join(X_33,B),join(C,X_33)),X_33) != X_33
| meet(meet(meet(join(X_33,B),join(C,X_33)),meet(meet(join(X_33,B),join(C,X_33)),X_33)),meet(meet(join(X_33,B),join(C,X_33)),X_33)) != meet(meet(join(X_33,B),join(C,X_33)),X_33)
| meet(meet(meet(join(X_33,B),join(C,X_33)),meet(meet(join(X_33,B),join(C,X_33)),X_33)),X_33) = meet(meet(join(X_33,B),join(C,X_33)),X_33) ),
introduced(tautology,[equality,[$cnf( $equal(meet(meet(meet(join(X_33,B),join(C,X_33)),meet(meet(join(X_33,B),join(C,X_33)),X_33)),meet(meet(join(X_33,B),join(C,X_33)),X_33)),meet(meet(join(X_33,B),join(C,X_33)),X_33)) ),[0,1],$fot(X_33)]]) ).
cnf(refute_0_12,plain,
( meet(meet(meet(join(X_33,B),join(C,X_33)),meet(meet(join(X_33,B),join(C,X_33)),X_33)),meet(meet(join(X_33,B),join(C,X_33)),X_33)) != meet(meet(join(X_33,B),join(C,X_33)),X_33)
| meet(meet(meet(join(X_33,B),join(C,X_33)),meet(meet(join(X_33,B),join(C,X_33)),X_33)),X_33) = meet(meet(join(X_33,B),join(C,X_33)),X_33) ),
inference(resolve,[$cnf( $equal(meet(meet(join(X_33,B),join(C,X_33)),X_33),X_33) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
meet(meet(meet(join(X_33,B),join(C,X_33)),meet(meet(join(X_33,B),join(C,X_33)),X_33)),X_33) = meet(meet(join(X_33,B),join(C,X_33)),X_33),
inference(resolve,[$cnf( $equal(meet(meet(meet(join(X_33,B),join(C,X_33)),meet(meet(join(X_33,B),join(C,X_33)),X_33)),meet(meet(join(X_33,B),join(C,X_33)),X_33)),meet(meet(join(X_33,B),join(C,X_33)),X_33)) )],[refute_0_9,refute_0_12]) ).
cnf(refute_0_14,plain,
meet(meet(join(X_33,B),join(C,X_33)),meet(meet(join(X_33,B),join(C,X_33)),X_33)) = meet(meet(join(X_33,B),join(C,X_33)),meet(meet(join(X_33,B),join(C,X_33)),X_33)),
introduced(tautology,[refl,[$fot(meet(meet(join(X_33,B),join(C,X_33)),meet(meet(join(X_33,B),join(C,X_33)),X_33)))]]) ).
cnf(refute_0_15,plain,
( meet(meet(join(X_33,B),join(C,X_33)),X_33) != X_33
| meet(meet(join(X_33,B),join(C,X_33)),meet(meet(join(X_33,B),join(C,X_33)),X_33)) != meet(meet(join(X_33,B),join(C,X_33)),meet(meet(join(X_33,B),join(C,X_33)),X_33))
| meet(meet(join(X_33,B),join(C,X_33)),meet(meet(join(X_33,B),join(C,X_33)),X_33)) = meet(meet(join(X_33,B),join(C,X_33)),X_33) ),
introduced(tautology,[equality,[$cnf( $equal(meet(meet(join(X_33,B),join(C,X_33)),meet(meet(join(X_33,B),join(C,X_33)),X_33)),meet(meet(join(X_33,B),join(C,X_33)),meet(meet(join(X_33,B),join(C,X_33)),X_33))) ),[1,1],$fot(X_33)]]) ).
cnf(refute_0_16,plain,
( meet(meet(join(X_33,B),join(C,X_33)),X_33) != X_33
| meet(meet(join(X_33,B),join(C,X_33)),meet(meet(join(X_33,B),join(C,X_33)),X_33)) = meet(meet(join(X_33,B),join(C,X_33)),X_33) ),
inference(resolve,[$cnf( $equal(meet(meet(join(X_33,B),join(C,X_33)),meet(meet(join(X_33,B),join(C,X_33)),X_33)),meet(meet(join(X_33,B),join(C,X_33)),meet(meet(join(X_33,B),join(C,X_33)),X_33))) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
meet(meet(join(X_33,B),join(C,X_33)),meet(meet(join(X_33,B),join(C,X_33)),X_33)) = meet(meet(join(X_33,B),join(C,X_33)),X_33),
inference(resolve,[$cnf( $equal(meet(meet(join(X_33,B),join(C,X_33)),X_33),X_33) )],[refute_0_10,refute_0_16]) ).
cnf(refute_0_18,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_19,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_20,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_22,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
( meet(meet(join(X_33,B),join(C,X_33)),X_33) != X_33
| meet(meet(join(X_33,B),join(C,X_33)),meet(meet(join(X_33,B),join(C,X_33)),X_33)) != meet(meet(join(X_33,B),join(C,X_33)),X_33)
| meet(meet(join(X_33,B),join(C,X_33)),meet(meet(join(X_33,B),join(C,X_33)),X_33)) = X_33 ),
inference(subst,[],[refute_0_22:[bind(X,$fot(meet(meet(join(X_33,B),join(C,X_33)),meet(meet(join(X_33,B),join(C,X_33)),X_33)))),bind(Y,$fot(meet(meet(join(X_33,B),join(C,X_33)),X_33))),bind(Z,$fot(X_33))]]) ).
cnf(refute_0_24,plain,
( meet(meet(join(X_33,B),join(C,X_33)),X_33) != X_33
| meet(meet(join(X_33,B),join(C,X_33)),meet(meet(join(X_33,B),join(C,X_33)),X_33)) = X_33 ),
inference(resolve,[$cnf( $equal(meet(meet(join(X_33,B),join(C,X_33)),meet(meet(join(X_33,B),join(C,X_33)),X_33)),meet(meet(join(X_33,B),join(C,X_33)),X_33)) )],[refute_0_17,refute_0_23]) ).
cnf(refute_0_25,plain,
meet(meet(join(X_33,B),join(C,X_33)),meet(meet(join(X_33,B),join(C,X_33)),X_33)) = X_33,
inference(resolve,[$cnf( $equal(meet(meet(join(X_33,B),join(C,X_33)),X_33),X_33) )],[refute_0_10,refute_0_24]) ).
cnf(refute_0_26,plain,
meet(meet(meet(join(X_33,B),join(C,X_33)),meet(meet(join(X_33,B),join(C,X_33)),X_33)),X_33) = meet(meet(meet(join(X_33,B),join(C,X_33)),meet(meet(join(X_33,B),join(C,X_33)),X_33)),X_33),
introduced(tautology,[refl,[$fot(meet(meet(meet(join(X_33,B),join(C,X_33)),meet(meet(join(X_33,B),join(C,X_33)),X_33)),X_33))]]) ).
cnf(refute_0_27,plain,
( meet(meet(join(X_33,B),join(C,X_33)),meet(meet(join(X_33,B),join(C,X_33)),X_33)) != X_33
| meet(meet(meet(join(X_33,B),join(C,X_33)),meet(meet(join(X_33,B),join(C,X_33)),X_33)),X_33) != meet(meet(meet(join(X_33,B),join(C,X_33)),meet(meet(join(X_33,B),join(C,X_33)),X_33)),X_33)
| meet(meet(meet(join(X_33,B),join(C,X_33)),meet(meet(join(X_33,B),join(C,X_33)),X_33)),X_33) = meet(X_33,X_33) ),
introduced(tautology,[equality,[$cnf( $equal(meet(meet(meet(join(X_33,B),join(C,X_33)),meet(meet(join(X_33,B),join(C,X_33)),X_33)),X_33),meet(meet(meet(join(X_33,B),join(C,X_33)),meet(meet(join(X_33,B),join(C,X_33)),X_33)),X_33)) ),[1,0],$fot(X_33)]]) ).
cnf(refute_0_28,plain,
( meet(meet(join(X_33,B),join(C,X_33)),meet(meet(join(X_33,B),join(C,X_33)),X_33)) != X_33
| meet(meet(meet(join(X_33,B),join(C,X_33)),meet(meet(join(X_33,B),join(C,X_33)),X_33)),X_33) = meet(X_33,X_33) ),
inference(resolve,[$cnf( $equal(meet(meet(meet(join(X_33,B),join(C,X_33)),meet(meet(join(X_33,B),join(C,X_33)),X_33)),X_33),meet(meet(meet(join(X_33,B),join(C,X_33)),meet(meet(join(X_33,B),join(C,X_33)),X_33)),X_33)) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
meet(meet(meet(join(X_33,B),join(C,X_33)),meet(meet(join(X_33,B),join(C,X_33)),X_33)),X_33) = meet(X_33,X_33),
inference(resolve,[$cnf( $equal(meet(meet(join(X_33,B),join(C,X_33)),meet(meet(join(X_33,B),join(C,X_33)),X_33)),X_33) )],[refute_0_25,refute_0_28]) ).
cnf(refute_0_30,plain,
( meet(meet(meet(join(X_33,B),join(C,X_33)),meet(meet(join(X_33,B),join(C,X_33)),X_33)),X_33) != meet(X_33,X_33)
| meet(meet(meet(join(X_33,B),join(C,X_33)),meet(meet(join(X_33,B),join(C,X_33)),X_33)),X_33) != meet(meet(join(X_33,B),join(C,X_33)),X_33)
| meet(X_33,X_33) = meet(meet(join(X_33,B),join(C,X_33)),X_33) ),
introduced(tautology,[equality,[$cnf( $equal(meet(meet(meet(join(X_33,B),join(C,X_33)),meet(meet(join(X_33,B),join(C,X_33)),X_33)),X_33),meet(meet(join(X_33,B),join(C,X_33)),X_33)) ),[0],$fot(meet(X_33,X_33))]]) ).
cnf(refute_0_31,plain,
( meet(meet(meet(join(X_33,B),join(C,X_33)),meet(meet(join(X_33,B),join(C,X_33)),X_33)),X_33) != meet(meet(join(X_33,B),join(C,X_33)),X_33)
| meet(X_33,X_33) = meet(meet(join(X_33,B),join(C,X_33)),X_33) ),
inference(resolve,[$cnf( $equal(meet(meet(meet(join(X_33,B),join(C,X_33)),meet(meet(join(X_33,B),join(C,X_33)),X_33)),X_33),meet(X_33,X_33)) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
( meet(X_33,X_33) != meet(meet(join(X_33,B),join(C,X_33)),X_33)
| meet(meet(join(X_33,B),join(C,X_33)),X_33) != X_33
| meet(X_33,X_33) = X_33 ),
introduced(tautology,[equality,[$cnf( ~ $equal(meet(X_33,X_33),X_33) ),[0],$fot(meet(meet(join(X_33,B),join(C,X_33)),X_33))]]) ).
cnf(refute_0_33,plain,
( meet(X_33,X_33) != meet(meet(join(X_33,B),join(C,X_33)),X_33)
| meet(X_33,X_33) = X_33 ),
inference(resolve,[$cnf( $equal(meet(meet(join(X_33,B),join(C,X_33)),X_33),X_33) )],[refute_0_10,refute_0_32]) ).
cnf(refute_0_34,plain,
( meet(meet(meet(join(X_33,B),join(C,X_33)),meet(meet(join(X_33,B),join(C,X_33)),X_33)),X_33) != meet(meet(join(X_33,B),join(C,X_33)),X_33)
| meet(X_33,X_33) = X_33 ),
inference(resolve,[$cnf( $equal(meet(X_33,X_33),meet(meet(join(X_33,B),join(C,X_33)),X_33)) )],[refute_0_31,refute_0_33]) ).
cnf(refute_0_35,plain,
meet(X_33,X_33) = X_33,
inference(resolve,[$cnf( $equal(meet(meet(meet(join(X_33,B),join(C,X_33)),meet(meet(join(X_33,B),join(C,X_33)),X_33)),X_33),meet(meet(join(X_33,B),join(C,X_33)),X_33)) )],[refute_0_13,refute_0_34]) ).
cnf(refute_0_36,plain,
meet(a,a) = a,
inference(subst,[],[refute_0_35:[bind(X_33,$fot(a))]]) ).
cnf(refute_0_37,plain,
( a != a
| meet(a,a) != a
| meet(a,a) = a ),
introduced(tautology,[equality,[$cnf( $equal(meet(a,a),a) ),[0,0],$fot(a)]]) ).
cnf(refute_0_38,plain,
( a != a
| meet(a,a) = a ),
inference(resolve,[$cnf( $equal(meet(a,a),a) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
a != a,
inference(resolve,[$cnf( $equal(meet(a,a),a) )],[refute_0_38,prove_normal_axioms_1]) ).
cnf(refute_0_40,plain,
a = a,
introduced(tautology,[refl,[$fot(a)]]) ).
cnf(refute_0_41,plain,
$false,
inference(resolve,[$cnf( $equal(a,a) )],[refute_0_40,refute_0_39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : LAT088-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.11/0.33 % Computer : n027.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Thu Jun 30 00:14:35 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.43 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.43
% 0.18/0.43 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.18/0.44
%------------------------------------------------------------------------------