TSTP Solution File: LAT029-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT029-1 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 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 : 300s
% DateTime : Thu Aug 31 06:27:11 EDT 2023
% Result : Unsatisfiable 0.14s 0.38s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : LAT029-1 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.10 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.10/0.30 % Computer : n032.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Thu Aug 24 07:58:56 EDT 2023
% 0.14/0.30 % CPUTime :
% 0.14/0.38 Command-line arguments: --no-flatten-goal
% 0.14/0.38
% 0.14/0.38 % SZS status Unsatisfiable
% 0.14/0.38
% 0.14/0.40 % SZS output start Proof
% 0.14/0.40 Take the following subset of the input axioms:
% 0.14/0.40 fof(prove_normal_axioms, negated_conjecture, meet(a, a)!=a | (meet(b, a)!=meet(a, b) | (join(a, a)!=a | join(b, a)!=join(a, b)))).
% 0.14/0.40 fof(wal_absorbtion_1, axiom, ![X, Y]: join(meet(X, Y), meet(X, join(X, Y)))=X).
% 0.14/0.40 fof(wal_absorbtion_2, axiom, ![X2, Y2]: join(meet(X2, X2), meet(Y2, join(X2, X2)))=X2).
% 0.14/0.40 fof(wal_absorbtion_3, axiom, ![X2, Y2]: join(meet(X2, Y2), meet(Y2, join(X2, Y2)))=Y2).
% 0.14/0.40 fof(wal_absorbtion_4, axiom, ![Z, X2, Y2]: meet(meet(join(X2, Y2), join(Z, X2)), X2)=X2).
% 0.14/0.40 fof(wal_absorbtion_5, axiom, ![X2, Y2, Z2]: join(join(meet(X2, Y2), meet(Z2, X2)), X2)=X2).
% 0.14/0.40
% 0.14/0.40 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.14/0.40 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.14/0.40 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.14/0.40 fresh(y, y, x1...xn) = u
% 0.14/0.40 C => fresh(s, t, x1...xn) = v
% 0.14/0.40 where fresh is a fresh function symbol and x1..xn are the free
% 0.14/0.40 variables of u and v.
% 0.14/0.40 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.14/0.40 input problem has no model of domain size 1).
% 0.14/0.40
% 0.14/0.40 The encoding turns the above axioms into the following unit equations and goals:
% 0.14/0.40
% 0.14/0.40 Axiom 1 (wal_absorbtion_2): join(meet(X, X), meet(Y, join(X, X))) = X.
% 0.14/0.40 Axiom 2 (wal_absorbtion_1): join(meet(X, Y), meet(X, join(X, Y))) = X.
% 0.14/0.40 Axiom 3 (wal_absorbtion_3): join(meet(X, Y), meet(Y, join(X, Y))) = Y.
% 0.14/0.40 Axiom 4 (wal_absorbtion_5): join(join(meet(X, Y), meet(Z, X)), X) = X.
% 0.14/0.40 Axiom 5 (wal_absorbtion_4): meet(meet(join(X, Y), join(Z, X)), X) = X.
% 0.14/0.40
% 0.14/0.40 Lemma 6: meet(meet(join(X, Y), X), X) = X.
% 0.14/0.40 Proof:
% 0.14/0.40 meet(meet(join(X, Y), X), X)
% 0.14/0.40 = { by axiom 4 (wal_absorbtion_5) R->L }
% 0.14/0.40 meet(meet(join(X, Y), join(join(meet(X, Z), meet(W, X)), X)), X)
% 0.14/0.40 = { by axiom 5 (wal_absorbtion_4) }
% 0.14/0.40 X
% 0.14/0.40
% 0.14/0.40 Lemma 7: meet(X, X) = X.
% 0.14/0.40 Proof:
% 0.14/0.40 meet(X, X)
% 0.14/0.40 = { by axiom 5 (wal_absorbtion_4) R->L }
% 0.14/0.40 meet(meet(meet(join(X, Y), join(Z, X)), X), X)
% 0.14/0.40 = { by axiom 5 (wal_absorbtion_4) R->L }
% 0.14/0.40 meet(meet(meet(join(X, Y), join(Z, X)), X), meet(meet(join(X, Y), join(Z, X)), X))
% 0.14/0.40 = { by axiom 5 (wal_absorbtion_4) R->L }
% 0.14/0.40 meet(meet(meet(join(X, Y), join(Z, X)), meet(meet(join(X, Y), join(Z, X)), X)), meet(meet(join(X, Y), join(Z, X)), X))
% 0.14/0.40 = { by axiom 2 (wal_absorbtion_1) R->L }
% 0.14/0.40 meet(meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(meet(join(X, Y), join(Z, X)), join(meet(join(X, Y), join(Z, X)), X))), meet(meet(join(X, Y), join(Z, X)), X)), meet(meet(join(X, Y), join(Z, X)), X))
% 0.14/0.40 = { by lemma 6 }
% 0.14/0.40 meet(meet(join(X, Y), join(Z, X)), X)
% 0.14/0.40 = { by axiom 5 (wal_absorbtion_4) }
% 0.14/0.40 X
% 0.14/0.40
% 0.14/0.40 Lemma 8: join(join(meet(X, Y), X), X) = X.
% 0.14/0.40 Proof:
% 0.14/0.40 join(join(meet(X, Y), X), X)
% 0.14/0.40 = { by axiom 5 (wal_absorbtion_4) R->L }
% 0.14/0.40 join(join(meet(X, Y), meet(meet(join(X, Z), join(W, X)), X)), X)
% 0.14/0.40 = { by axiom 4 (wal_absorbtion_5) }
% 0.14/0.41 X
% 0.14/0.41
% 0.14/0.41 Lemma 9: join(X, X) = X.
% 0.14/0.41 Proof:
% 0.14/0.41 join(X, X)
% 0.14/0.41 = { by lemma 7 R->L }
% 0.14/0.41 join(X, meet(X, X))
% 0.14/0.41 = { by axiom 5 (wal_absorbtion_4) R->L }
% 0.14/0.41 join(meet(meet(join(X, X), join(X, X)), X), meet(X, X))
% 0.14/0.41 = { by lemma 7 }
% 0.14/0.41 join(meet(join(X, X), X), meet(X, X))
% 0.14/0.41 = { by lemma 8 R->L }
% 0.14/0.41 join(meet(join(X, X), X), meet(X, join(join(meet(X, X), X), X)))
% 0.14/0.41 = { by lemma 7 }
% 0.14/0.41 join(meet(join(X, X), X), meet(X, join(join(X, X), X)))
% 0.14/0.41 = { by axiom 3 (wal_absorbtion_3) }
% 0.14/0.41 X
% 0.14/0.41
% 0.14/0.41 Lemma 10: meet(meet(X, join(Y, X)), X) = X.
% 0.14/0.41 Proof:
% 0.14/0.41 meet(meet(X, join(Y, X)), X)
% 0.14/0.41 = { by axiom 1 (wal_absorbtion_2) R->L }
% 0.14/0.41 meet(meet(join(meet(X, X), meet(meet(join(join(X, X), Z), join(W, join(X, X))), join(X, X))), join(Y, X)), X)
% 0.14/0.41 = { by axiom 5 (wal_absorbtion_4) }
% 0.14/0.41 meet(meet(join(meet(X, X), join(X, X)), join(Y, X)), X)
% 0.14/0.41 = { by lemma 7 }
% 0.14/0.41 meet(meet(join(X, join(X, X)), join(Y, X)), X)
% 0.14/0.41 = { by axiom 5 (wal_absorbtion_4) }
% 0.14/0.41 X
% 0.14/0.41
% 0.14/0.41 Lemma 11: meet(meet(X, meet(Y, X)), meet(Y, X)) = meet(Y, X).
% 0.14/0.41 Proof:
% 0.14/0.41 meet(meet(X, meet(Y, X)), meet(Y, X))
% 0.14/0.41 = { by axiom 3 (wal_absorbtion_3) R->L }
% 0.14/0.41 meet(meet(join(meet(Y, X), meet(X, join(Y, X))), meet(Y, X)), meet(Y, X))
% 0.14/0.41 = { by lemma 6 }
% 0.14/0.41 meet(Y, X)
% 0.14/0.41
% 0.14/0.41 Lemma 12: join(X, meet(Y, X)) = X.
% 0.14/0.41 Proof:
% 0.14/0.41 join(X, meet(Y, X))
% 0.14/0.41 = { by lemma 7 R->L }
% 0.14/0.41 join(meet(X, X), meet(Y, X))
% 0.14/0.41 = { by lemma 9 R->L }
% 0.14/0.41 join(meet(X, X), meet(Y, join(X, X)))
% 0.14/0.41 = { by axiom 1 (wal_absorbtion_2) }
% 0.14/0.41 X
% 0.14/0.41
% 0.14/0.41 Lemma 13: meet(X, meet(Y, X)) = meet(Y, X).
% 0.14/0.41 Proof:
% 0.14/0.41 meet(X, meet(Y, X))
% 0.14/0.41 = { by lemma 8 R->L }
% 0.14/0.41 join(join(meet(meet(X, meet(Y, X)), meet(Y, X)), meet(X, meet(Y, X))), meet(X, meet(Y, X)))
% 0.14/0.41 = { by lemma 11 }
% 0.14/0.41 join(join(meet(Y, X), meet(X, meet(Y, X))), meet(X, meet(Y, X)))
% 0.14/0.41 = { by lemma 12 }
% 0.14/0.41 join(meet(Y, X), meet(X, meet(Y, X)))
% 0.14/0.41 = { by lemma 12 }
% 0.14/0.41 meet(Y, X)
% 0.14/0.41
% 0.14/0.41 Lemma 14: meet(meet(X, Y), Y) = meet(X, Y).
% 0.14/0.41 Proof:
% 0.14/0.41 meet(meet(X, Y), Y)
% 0.14/0.41 = { by lemma 9 R->L }
% 0.14/0.41 join(meet(meet(X, Y), Y), meet(meet(X, Y), Y))
% 0.14/0.41 = { by axiom 2 (wal_absorbtion_1) R->L }
% 0.14/0.41 join(meet(meet(X, Y), Y), meet(meet(X, Y), join(meet(Y, meet(X, Y)), meet(Y, join(Y, meet(X, Y))))))
% 0.14/0.41 = { by lemma 13 }
% 0.14/0.41 join(meet(meet(X, Y), Y), meet(meet(X, Y), join(meet(X, Y), meet(Y, join(Y, meet(X, Y))))))
% 0.14/0.41 = { by lemma 12 }
% 0.14/0.41 join(meet(meet(X, Y), Y), meet(meet(X, Y), join(meet(X, Y), meet(Y, Y))))
% 0.14/0.41 = { by lemma 7 }
% 0.14/0.41 join(meet(meet(X, Y), Y), meet(meet(X, Y), join(meet(X, Y), Y)))
% 0.14/0.41 = { by axiom 2 (wal_absorbtion_1) }
% 0.14/0.41 meet(X, Y)
% 0.14/0.41
% 0.14/0.41 Lemma 15: meet(join(meet(X, Y), X), X) = join(meet(X, Y), X).
% 0.14/0.41 Proof:
% 0.14/0.41 meet(join(meet(X, Y), X), X)
% 0.14/0.41 = { by lemma 9 R->L }
% 0.14/0.41 join(meet(join(meet(X, Y), X), X), meet(join(meet(X, Y), X), X))
% 0.14/0.41 = { by lemma 8 R->L }
% 0.14/0.41 join(meet(join(meet(X, Y), X), X), meet(join(meet(X, Y), X), join(join(meet(X, Y), X), X)))
% 0.14/0.41 = { by axiom 2 (wal_absorbtion_1) }
% 0.14/0.41 join(meet(X, Y), X)
% 0.14/0.41
% 0.14/0.41 Lemma 16: meet(meet(X, Y), X) = meet(X, Y).
% 0.14/0.41 Proof:
% 0.14/0.41 meet(meet(X, Y), X)
% 0.14/0.41 = { by lemma 9 R->L }
% 0.14/0.41 join(meet(meet(X, Y), X), meet(meet(X, Y), X))
% 0.14/0.41 = { by lemma 10 R->L }
% 0.14/0.41 join(meet(meet(X, Y), X), meet(meet(X, Y), meet(meet(X, join(meet(X, Y), X)), X)))
% 0.14/0.41 = { by lemma 14 R->L }
% 0.14/0.41 join(meet(meet(X, Y), X), meet(meet(X, Y), meet(meet(meet(X, join(meet(X, Y), X)), join(meet(X, Y), X)), X)))
% 0.14/0.41 = { by lemma 15 R->L }
% 0.14/0.41 join(meet(meet(X, Y), X), meet(meet(X, Y), meet(meet(meet(X, join(meet(X, Y), X)), meet(join(meet(X, Y), X), X)), X)))
% 0.14/0.41 = { by lemma 15 R->L }
% 0.14/0.41 join(meet(meet(X, Y), X), meet(meet(X, Y), meet(meet(meet(X, meet(join(meet(X, Y), X), X)), meet(join(meet(X, Y), X), X)), X)))
% 0.14/0.41 = { by lemma 11 }
% 0.14/0.41 join(meet(meet(X, Y), X), meet(meet(X, Y), meet(meet(join(meet(X, Y), X), X), X)))
% 0.14/0.41 = { by lemma 15 }
% 0.14/0.41 join(meet(meet(X, Y), X), meet(meet(X, Y), meet(join(meet(X, Y), X), X)))
% 0.14/0.41 = { by lemma 15 }
% 0.14/0.41 join(meet(meet(X, Y), X), meet(meet(X, Y), join(meet(X, Y), X)))
% 0.14/0.41 = { by axiom 2 (wal_absorbtion_1) }
% 0.14/0.41 meet(X, Y)
% 0.14/0.41
% 0.14/0.41 Lemma 17: meet(meet(X, Y), meet(Y, X)) = meet(Y, X).
% 0.14/0.41 Proof:
% 0.14/0.41 meet(meet(X, Y), meet(Y, X))
% 0.14/0.41 = { by axiom 1 (wal_absorbtion_2) R->L }
% 0.14/0.41 meet(meet(X, join(meet(Y, Y), meet(meet(join(Y, Y), X), join(Y, Y)))), meet(Y, X))
% 0.14/0.41 = { by lemma 16 }
% 0.14/0.41 meet(meet(X, join(meet(Y, Y), meet(join(Y, Y), X))), meet(Y, X))
% 0.14/0.41 = { by lemma 7 }
% 0.14/0.41 meet(meet(X, join(Y, meet(join(Y, Y), X))), meet(Y, X))
% 0.14/0.41 = { by lemma 9 }
% 0.14/0.41 meet(meet(X, join(Y, meet(Y, X))), meet(Y, X))
% 0.14/0.41 = { by axiom 3 (wal_absorbtion_3) R->L }
% 0.14/0.41 meet(meet(join(meet(Y, X), meet(X, join(Y, X))), join(Y, meet(Y, X))), meet(Y, X))
% 0.14/0.41 = { by axiom 5 (wal_absorbtion_4) }
% 0.14/0.41 meet(Y, X)
% 0.14/0.41
% 0.14/0.41 Lemma 18: meet(X, Y) = meet(Y, X).
% 0.14/0.41 Proof:
% 0.14/0.41 meet(X, Y)
% 0.14/0.41 = { by lemma 17 R->L }
% 0.14/0.41 meet(meet(Y, X), meet(X, Y))
% 0.14/0.41 = { by lemma 16 R->L }
% 0.14/0.41 meet(meet(meet(Y, X), meet(X, Y)), meet(Y, X))
% 0.14/0.41 = { by lemma 17 }
% 0.14/0.41 meet(meet(X, Y), meet(Y, X))
% 0.14/0.41 = { by lemma 17 }
% 0.14/0.41 meet(Y, X)
% 0.14/0.41
% 0.14/0.41 Lemma 19: meet(X, join(Y, X)) = X.
% 0.14/0.41 Proof:
% 0.14/0.41 meet(X, join(Y, X))
% 0.14/0.41 = { by lemma 16 R->L }
% 0.14/0.41 meet(meet(X, join(Y, X)), X)
% 0.14/0.41 = { by lemma 10 }
% 0.14/0.41 X
% 0.14/0.41
% 0.14/0.41 Lemma 20: meet(join(X, Y), X) = X.
% 0.14/0.41 Proof:
% 0.14/0.41 meet(join(X, Y), X)
% 0.14/0.41 = { by lemma 14 R->L }
% 0.14/0.41 meet(meet(join(X, Y), X), X)
% 0.14/0.41 = { by lemma 6 }
% 0.14/0.41 X
% 0.14/0.41
% 0.14/0.41 Lemma 21: meet(join(X, Y), join(Y, X)) = join(X, Y).
% 0.14/0.41 Proof:
% 0.14/0.41 meet(join(X, Y), join(Y, X))
% 0.14/0.41 = { by lemma 18 R->L }
% 0.14/0.41 meet(join(Y, X), join(X, Y))
% 0.14/0.41 = { by lemma 19 R->L }
% 0.14/0.41 meet(join(Y, X), join(meet(X, join(Y, X)), Y))
% 0.14/0.41 = { by lemma 18 R->L }
% 0.14/0.41 meet(join(Y, X), join(meet(join(Y, X), X), Y))
% 0.14/0.41 = { by lemma 20 R->L }
% 0.14/0.41 meet(join(Y, X), join(meet(join(Y, X), X), meet(join(Y, X), Y)))
% 0.14/0.41 = { by lemma 18 R->L }
% 0.14/0.41 meet(join(Y, X), join(meet(join(Y, X), X), meet(Y, join(Y, X))))
% 0.14/0.41 = { by lemma 18 R->L }
% 0.14/0.41 meet(join(meet(join(Y, X), X), meet(Y, join(Y, X))), join(Y, X))
% 0.14/0.41 = { by lemma 9 R->L }
% 0.14/0.41 join(meet(join(meet(join(Y, X), X), meet(Y, join(Y, X))), join(Y, X)), meet(join(meet(join(Y, X), X), meet(Y, join(Y, X))), join(Y, X)))
% 0.14/0.41 = { by axiom 4 (wal_absorbtion_5) R->L }
% 0.14/0.41 join(meet(join(meet(join(Y, X), X), meet(Y, join(Y, X))), join(Y, X)), meet(join(meet(join(Y, X), X), meet(Y, join(Y, X))), join(join(meet(join(Y, X), X), meet(Y, join(Y, X))), join(Y, X))))
% 0.14/0.41 = { by axiom 2 (wal_absorbtion_1) }
% 0.14/0.41 join(meet(join(Y, X), X), meet(Y, join(Y, X)))
% 0.14/0.41 = { by lemma 18 }
% 0.14/0.41 join(meet(join(Y, X), X), meet(join(Y, X), Y))
% 0.14/0.41 = { by lemma 20 }
% 0.14/0.41 join(meet(join(Y, X), X), Y)
% 0.14/0.41 = { by lemma 18 }
% 0.14/0.41 join(meet(X, join(Y, X)), Y)
% 0.14/0.41 = { by lemma 19 }
% 0.14/0.41 join(X, Y)
% 0.14/0.41
% 0.14/0.41 Goal 1 (prove_normal_axioms): tuple(join(a, a), join(b, a), meet(a, a), meet(b, a)) = tuple(a, join(a, b), a, meet(a, b)).
% 0.14/0.41 Proof:
% 0.14/0.41 tuple(join(a, a), join(b, a), meet(a, a), meet(b, a))
% 0.14/0.41 = { by lemma 7 }
% 0.14/0.41 tuple(join(a, a), join(b, a), a, meet(b, a))
% 0.14/0.41 = { by lemma 9 }
% 0.14/0.41 tuple(a, join(b, a), a, meet(b, a))
% 0.14/0.41 = { by lemma 21 R->L }
% 0.14/0.41 tuple(a, meet(join(b, a), join(a, b)), a, meet(b, a))
% 0.14/0.41 = { by lemma 21 R->L }
% 0.14/0.41 tuple(a, meet(join(b, a), meet(join(a, b), join(b, a))), a, meet(b, a))
% 0.14/0.41 = { by lemma 13 }
% 0.14/0.41 tuple(a, meet(join(a, b), join(b, a)), a, meet(b, a))
% 0.14/0.41 = { by lemma 21 }
% 0.14/0.41 tuple(a, join(a, b), a, meet(b, a))
% 0.14/0.41 = { by lemma 18 R->L }
% 0.14/0.41 tuple(a, join(a, b), a, meet(a, b))
% 0.14/0.41 % SZS output end Proof
% 0.14/0.41
% 0.14/0.41 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------