0.07/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.07/0.12	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.13/0.33	% Computer   : n003.cluster.edu
0.13/0.33	% Model      : x86_64 x86_64
0.13/0.33	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.33	% Memory     : 8042.1875MB
0.13/0.33	% OS         : Linux 3.10.0-693.el7.x86_64
0.13/0.33	% CPULimit   : 180
0.13/0.33	% DateTime   : Thu Aug 29 09:59:17 EDT 2019
0.13/0.33	% CPUTime    : 
0.19/0.41	% SZS status Unsatisfiable
0.19/0.41	
0.19/0.41	% SZS output start Proof
0.19/0.41	Take the following subset of the input axioms:
0.19/0.41	  fof(prove_normal_axioms_4, negated_conjecture, join(a, b)!=join(b, a)).
0.19/0.41	  fof(wal_absorbtion_1, axiom, ![A, B]: A=join(meet(A, B), meet(A, join(A, B)))).
0.19/0.41	  fof(wal_absorbtion_2, axiom, ![A, B]: A=join(meet(A, A), meet(B, join(A, A)))).
0.19/0.41	  fof(wal_absorbtion_3, axiom, ![A, B]: join(meet(A, B), meet(B, join(A, B)))=B).
0.19/0.41	  fof(wal_absorbtion_4, axiom, ![A, B, C]: A=meet(meet(join(A, B), join(C, A)), A)).
0.19/0.41	  fof(wal_absorbtion_5, axiom, ![A, B, C]: join(join(meet(A, B), meet(C, A)), A)=A).
0.19/0.41	
0.19/0.41	Now clausify the problem and encode Horn clauses using encoding 3 of
0.19/0.41	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
0.19/0.41	We repeatedly replace C & s=t => u=v by the two clauses:
0.19/0.41	  fresh(y, y, x1...xn) = u
0.19/0.41	  C => fresh(s, t, x1...xn) = v
0.19/0.41	where fresh is a fresh function symbol and x1..xn are the free
0.19/0.41	variables of u and v.
0.19/0.41	A predicate p(X) is encoded as p(X)=true (this is sound, because the
0.19/0.41	input problem has no model of domain size 1).
0.19/0.41	
0.19/0.41	The encoding turns the above axioms into the following unit equations and goals:
0.19/0.41	
0.19/0.41	Axiom 1 (wal_absorbtion_5): join(join(meet(X, Y), meet(Z, X)), X) = X.
0.19/0.41	Axiom 2 (wal_absorbtion_4): X = meet(meet(join(X, Y), join(Z, X)), X).
0.19/0.41	Axiom 3 (wal_absorbtion_3): join(meet(X, Y), meet(Y, join(X, Y))) = Y.
0.19/0.41	Axiom 4 (wal_absorbtion_1): X = join(meet(X, Y), meet(X, join(X, Y))).
0.19/0.41	Axiom 5 (wal_absorbtion_2): X = join(meet(X, X), meet(Y, join(X, X))).
0.19/0.41	
0.19/0.41	Lemma 6: meet(meet(join(X, Y), X), X) = X.
0.19/0.41	Proof:
0.19/0.41	  meet(meet(join(X, Y), X), X)
0.19/0.41	= { by axiom 1 (wal_absorbtion_5) }
0.19/0.41	  meet(meet(join(X, Y), join(join(meet(X, ?), meet(?, X)), X)), X)
0.19/0.41	= { by axiom 2 (wal_absorbtion_4) }
0.19/0.42	  X
0.19/0.42	
0.19/0.42	Lemma 7: meet(X, X) = X.
0.19/0.42	Proof:
0.19/0.42	  meet(X, X)
0.19/0.42	= { by axiom 2 (wal_absorbtion_4) }
0.19/0.42	  meet(meet(meet(join(X, ?), join(?, X)), X), X)
0.19/0.42	= { by axiom 4 (wal_absorbtion_1) }
0.19/0.42	  meet(meet(join(meet(meet(join(X, ?), join(?, X)), X), meet(meet(join(X, ?), join(?, X)), join(meet(join(X, ?), join(?, X)), X))), X), X)
0.19/0.42	= { by axiom 2 (wal_absorbtion_4) }
0.19/0.42	  meet(meet(join(meet(meet(join(X, ?), join(?, X)), X), meet(meet(join(X, ?), join(?, X)), join(meet(join(X, ?), join(?, X)), X))), meet(meet(join(X, ?), join(?, X)), X)), X)
0.19/0.42	= { by axiom 2 (wal_absorbtion_4) }
0.19/0.42	  meet(meet(join(meet(meet(join(X, ?), join(?, X)), X), meet(meet(join(X, ?), join(?, X)), join(meet(join(X, ?), join(?, X)), X))), meet(meet(join(X, ?), join(?, X)), X)), meet(meet(join(X, ?), join(?, X)), X))
0.19/0.42	= { by lemma 6 }
0.19/0.42	  meet(meet(join(X, ?), join(?, X)), X)
0.19/0.42	= { by axiom 2 (wal_absorbtion_4) }
0.19/0.42	  X
0.19/0.42	
0.19/0.42	Lemma 8: meet(join(X, X), X) = X.
0.19/0.42	Proof:
0.19/0.42	  meet(join(X, X), X)
0.19/0.42	= { by lemma 7 }
0.19/0.42	  meet(meet(join(X, X), join(X, X)), X)
0.19/0.42	= { by axiom 2 (wal_absorbtion_4) }
0.19/0.42	  X
0.19/0.42	
0.19/0.42	Lemma 9: join(join(meet(X, Y), X), X) = X.
0.19/0.42	Proof:
0.19/0.42	  join(join(meet(X, Y), X), X)
0.19/0.42	= { by axiom 2 (wal_absorbtion_4) }
0.19/0.42	  join(join(meet(X, Y), meet(meet(join(X, ?), join(?, X)), X)), X)
0.19/0.42	= { by axiom 1 (wal_absorbtion_5) }
0.19/0.42	  X
0.19/0.42	
0.19/0.42	Lemma 10: join(X, X) = X.
0.19/0.42	Proof:
0.19/0.42	  join(X, X)
0.19/0.42	= { by lemma 8 }
0.19/0.42	  join(meet(join(X, X), X), X)
0.19/0.42	= { by lemma 7 }
0.19/0.42	  join(meet(join(X, X), X), meet(X, X))
0.19/0.42	= { by lemma 9 }
0.19/0.42	  join(meet(join(X, X), X), meet(X, join(join(meet(X, X), X), X)))
0.19/0.42	= { by lemma 7 }
0.19/0.42	  join(meet(join(X, X), X), meet(X, join(join(X, X), X)))
0.19/0.42	= { by axiom 3 (wal_absorbtion_3) }
0.19/0.42	  X
0.19/0.42	
0.19/0.42	Lemma 11: meet(meet(Y, join(Z, meet(X, Y))), meet(X, Y)) = meet(X, Y).
0.19/0.42	Proof:
0.19/0.42	  meet(meet(Y, join(Z, meet(X, Y))), meet(X, Y))
0.19/0.42	= { by axiom 3 (wal_absorbtion_3) }
0.19/0.42	  meet(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, meet(X, Y))), meet(X, Y))
0.19/0.42	= { by axiom 2 (wal_absorbtion_4) }
0.19/0.42	  meet(X, Y)
0.19/0.42	
0.19/0.42	Lemma 12: meet(Y, meet(X, Y)) = meet(X, Y).
0.19/0.42	Proof:
0.19/0.42	  meet(Y, meet(X, Y))
0.19/0.42	= { by lemma 8 }
0.19/0.42	  meet(meet(join(Y, Y), Y), meet(X, Y))
0.19/0.42	= { by axiom 5 (wal_absorbtion_2) }
0.19/0.42	  meet(meet(join(Y, Y), join(meet(Y, Y), meet(X, join(Y, Y)))), meet(X, Y))
0.19/0.42	= { by lemma 10 }
0.19/0.42	  meet(meet(join(Y, Y), join(meet(Y, Y), meet(X, join(Y, Y)))), meet(X, join(Y, Y)))
0.19/0.42	= { by lemma 11 }
0.19/0.42	  meet(X, join(Y, Y))
0.19/0.42	= { by lemma 10 }
0.19/0.42	  meet(X, Y)
0.19/0.42	
0.19/0.42	Lemma 13: meet(meet(X, Y), Y) = meet(X, Y).
0.19/0.42	Proof:
0.19/0.42	  meet(meet(X, Y), Y)
0.19/0.42	= { by lemma 10 }
0.19/0.42	  join(meet(meet(X, Y), Y), meet(meet(X, Y), Y))
0.19/0.42	= { by axiom 4 (wal_absorbtion_1) }
0.19/0.42	  join(meet(meet(X, Y), Y), meet(meet(X, Y), join(meet(Y, meet(X, Y)), meet(Y, join(Y, meet(X, Y))))))
0.19/0.42	= { by lemma 12 }
0.19/0.42	  join(meet(meet(X, Y), Y), meet(meet(X, Y), join(meet(X, Y), meet(Y, join(Y, meet(X, Y))))))
0.19/0.42	= { by lemma 7 }
0.19/0.42	  join(meet(meet(X, Y), Y), meet(meet(X, Y), join(meet(X, Y), meet(Y, join(meet(Y, Y), meet(X, Y))))))
0.19/0.42	= { by lemma 10 }
0.19/0.42	  join(meet(meet(X, Y), Y), meet(meet(X, Y), join(meet(X, Y), meet(Y, join(meet(Y, Y), meet(X, join(Y, Y)))))))
0.19/0.42	= { by axiom 5 (wal_absorbtion_2) }
0.19/0.42	  join(meet(meet(X, Y), Y), meet(meet(X, Y), join(meet(X, Y), meet(Y, Y))))
0.19/0.42	= { by lemma 7 }
0.19/0.42	  join(meet(meet(X, Y), Y), meet(meet(X, Y), join(meet(X, Y), Y)))
0.19/0.42	= { by axiom 4 (wal_absorbtion_1) }
0.19/0.42	  meet(X, Y)
0.19/0.42	
0.19/0.42	Lemma 14: meet(join(X, Y), X) = X.
0.19/0.42	Proof:
0.19/0.42	  meet(join(X, Y), X)
0.19/0.42	= { by lemma 13 }
0.19/0.42	  meet(meet(join(X, Y), X), X)
0.19/0.42	= { by lemma 6 }
0.19/0.42	  X
0.19/0.42	
0.19/0.42	Lemma 15: meet(join(meet(X, Y), X), X) = join(meet(X, Y), X).
0.19/0.42	Proof:
0.19/0.42	  meet(join(meet(X, Y), X), X)
0.19/0.42	= { by lemma 10 }
0.19/0.42	  join(meet(join(meet(X, Y), X), X), meet(join(meet(X, Y), X), X))
0.19/0.42	= { by lemma 9 }
0.19/0.42	  join(meet(join(meet(X, Y), X), X), meet(join(meet(X, Y), X), join(join(meet(X, Y), X), X)))
0.19/0.42	= { by axiom 4 (wal_absorbtion_1) }
0.19/0.42	  join(meet(X, Y), X)
0.19/0.42	
0.19/0.42	Lemma 16: meet(meet(X, join(W, X)), X) = X.
0.19/0.42	Proof:
0.19/0.42	  meet(meet(X, join(W, X)), X)
0.19/0.42	= { by axiom 2 (wal_absorbtion_4) }
0.19/0.42	  meet(meet(X, join(W, meet(meet(join(X, ?), join(?, X)), X))), X)
0.19/0.42	= { by axiom 2 (wal_absorbtion_4) }
0.19/0.42	  meet(meet(X, join(W, meet(meet(join(X, ?), join(?, X)), X))), meet(meet(join(X, ?), join(?, X)), X))
0.19/0.42	= { by lemma 11 }
0.19/0.42	  meet(meet(join(X, ?), join(?, X)), X)
0.19/0.42	= { by axiom 2 (wal_absorbtion_4) }
0.19/0.43	  X
0.19/0.43	
0.19/0.43	Lemma 17: meet(meet(X, Y), X) = meet(X, Y).
0.19/0.43	Proof:
0.19/0.43	  meet(meet(X, Y), X)
0.19/0.43	= { by lemma 10 }
0.19/0.43	  join(meet(meet(X, Y), X), meet(meet(X, Y), X))
0.19/0.43	= { by lemma 16 }
0.19/0.43	  join(meet(meet(X, Y), X), meet(meet(X, Y), meet(meet(X, join(meet(X, Y), X)), X)))
0.19/0.43	= { by lemma 13 }
0.19/0.43	  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)))
0.19/0.43	= { by axiom 3 (wal_absorbtion_3) }
0.19/0.43	  join(meet(meet(X, Y), X), meet(meet(X, Y), meet(meet(meet(join(meet(join(meet(X, Y), X), X), meet(X, join(join(meet(X, Y), X), X))), join(meet(X, Y), X)), join(meet(X, Y), X)), X)))
0.19/0.43	= { by lemma 15 }
0.19/0.43	  join(meet(meet(X, Y), X), meet(meet(X, Y), meet(meet(meet(join(meet(join(meet(X, Y), X), X), meet(X, join(join(meet(X, Y), X), X))), meet(join(meet(X, Y), X), X)), join(meet(X, Y), X)), X)))
0.19/0.43	= { by lemma 15 }
0.19/0.43	  join(meet(meet(X, Y), X), meet(meet(X, Y), meet(meet(meet(join(meet(join(meet(X, Y), X), X), meet(X, join(join(meet(X, Y), X), X))), meet(join(meet(X, Y), X), X)), meet(join(meet(X, Y), X), X)), X)))
0.19/0.43	= { by lemma 6 }
0.19/0.43	  join(meet(meet(X, Y), X), meet(meet(X, Y), meet(meet(join(meet(X, Y), X), X), X)))
0.19/0.43	= { by lemma 15 }
0.19/0.43	  join(meet(meet(X, Y), X), meet(meet(X, Y), meet(join(meet(X, Y), X), X)))
0.19/0.43	= { by lemma 15 }
0.19/0.43	  join(meet(meet(X, Y), X), meet(meet(X, Y), join(meet(X, Y), X)))
0.19/0.43	= { by axiom 4 (wal_absorbtion_1) }
0.19/0.43	  meet(X, Y)
0.19/0.43	
0.19/0.43	Lemma 18: join(join(Y, X), join(X, Y)) = join(X, Y).
0.19/0.43	Proof:
0.19/0.43	  join(join(Y, X), join(X, Y))
0.19/0.43	= { by lemma 16 }
0.19/0.43	  join(join(meet(meet(Y, join(X, Y)), Y), X), join(X, Y))
0.19/0.43	= { by lemma 17 }
0.19/0.43	  join(join(meet(Y, join(X, Y)), X), join(X, Y))
0.19/0.43	= { by lemma 12 }
0.19/0.43	  join(join(meet(join(X, Y), meet(Y, join(X, Y))), X), join(X, Y))
0.19/0.43	= { by lemma 14 }
0.19/0.43	  join(join(meet(join(X, Y), meet(Y, join(X, Y))), meet(join(X, Y), X)), join(X, Y))
0.19/0.43	= { by lemma 17 }
0.19/0.43	  join(join(meet(join(X, Y), meet(Y, join(X, Y))), meet(meet(join(X, Y), X), join(X, Y))), join(X, Y))
0.19/0.43	= { by lemma 14 }
0.19/0.43	  join(join(meet(join(X, Y), meet(Y, join(X, Y))), meet(X, join(X, Y))), join(X, Y))
0.19/0.43	= { by axiom 1 (wal_absorbtion_5) }
0.19/0.43	  join(X, Y)
0.19/0.43	
0.19/0.43	Goal 1 (prove_normal_axioms_4): join(a, b) = join(b, a).
0.19/0.43	Proof:
0.19/0.43	  join(a, b)
0.19/0.43	= { by lemma 18 }
0.19/0.43	  join(join(b, a), join(a, b))
0.19/0.43	= { by lemma 18 }
0.19/0.43	  join(join(join(a, b), join(b, a)), join(a, b))
0.19/0.43	= { by lemma 7 }
0.19/0.43	  join(meet(join(join(a, b), join(b, a)), join(join(a, b), join(b, a))), join(a, b))
0.19/0.43	= { by lemma 14 }
0.19/0.43	  join(meet(join(join(a, b), join(b, a)), join(join(a, b), join(b, a))), meet(join(join(a, b), join(b, a)), join(a, b)))
0.19/0.43	= { by lemma 10 }
0.19/0.43	  join(meet(join(join(a, b), join(b, a)), join(join(a, b), join(b, a))), meet(join(join(join(a, b), join(b, a)), join(join(a, b), join(b, a))), join(a, b)))
0.19/0.43	= { by lemma 17 }
0.19/0.43	  join(meet(join(join(a, b), join(b, a)), join(join(a, b), join(b, a))), meet(meet(join(join(join(a, b), join(b, a)), join(join(a, b), join(b, a))), join(a, b)), join(join(join(a, b), join(b, a)), join(join(a, b), join(b, a)))))
0.19/0.43	= { by axiom 5 (wal_absorbtion_2) }
0.19/0.43	  join(join(a, b), join(b, a))
0.19/0.43	= { by lemma 18 }
0.19/0.43	  join(b, a)
0.19/0.43	% SZS output end Proof
0.19/0.43	
0.19/0.43	RESULT: Unsatisfiable (the axioms are contradictory).
0.19/0.43	EOF