0.03/0.11	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.03/0.12	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.12/0.33	% Computer   : n015.cluster.edu
0.12/0.33	% Model      : x86_64 x86_64
0.12/0.33	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.33	% Memory     : 8042.1875MB
0.12/0.33	% OS         : Linux 3.10.0-693.el7.x86_64
0.12/0.33	% CPULimit   : 180
0.12/0.33	% DateTime   : Thu Aug 29 12:20:52 EDT 2019
0.12/0.33	% CPUTime    : 
0.56/0.77	% SZS status Unsatisfiable
0.56/0.77	
0.56/0.77	% SZS output start Proof
0.56/0.77	Take the following subset of the input axioms:
0.56/0.77	  fof(absorption, axiom, ![X, Y]: X=meet(X, join(X, Y))).
0.56/0.77	  fof(distribution, axiom, ![X, Y, Z]: meet(X, join(Y, Z))=join(meet(Z, X), meet(Y, X))).
0.56/0.77	  fof(prove_associativity_of_join, negated_conjecture, join(join(a, b), c)!=join(a, join(b, c))).
0.56/0.77	
0.56/0.77	Now clausify the problem and encode Horn clauses using encoding 3 of
0.56/0.77	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
0.56/0.77	We repeatedly replace C & s=t => u=v by the two clauses:
0.56/0.77	  fresh(y, y, x1...xn) = u
0.56/0.77	  C => fresh(s, t, x1...xn) = v
0.56/0.77	where fresh is a fresh function symbol and x1..xn are the free
0.56/0.77	variables of u and v.
0.56/0.77	A predicate p(X) is encoded as p(X)=true (this is sound, because the
0.56/0.77	input problem has no model of domain size 1).
0.56/0.77	
0.56/0.77	The encoding turns the above axioms into the following unit equations and goals:
0.56/0.77	
0.56/0.77	Axiom 1 (distribution): meet(X, join(Y, Z)) = join(meet(Z, X), meet(Y, X)).
0.60/0.78	Axiom 2 (absorption): X = meet(X, join(X, Y)).
0.60/0.78	
0.60/0.78	Lemma 3: meet(meet(X, Y), meet(Y, join(Z, X))) = meet(X, Y).
0.60/0.78	Proof:
0.60/0.78	  meet(meet(X, Y), meet(Y, join(Z, X)))
0.60/0.78	= { by axiom 1 (distribution) }
0.60/0.78	  meet(meet(X, Y), join(meet(X, Y), meet(Z, Y)))
0.60/0.78	= { by axiom 2 (absorption) }
0.60/0.78	  meet(X, Y)
0.60/0.78	
0.60/0.78	Lemma 4: meet(meet(X, Y), Y) = meet(X, Y).
0.60/0.78	Proof:
0.60/0.78	  meet(meet(X, Y), Y)
0.60/0.78	= { by axiom 2 (absorption) }
0.60/0.78	  meet(meet(X, Y), meet(Y, join(Y, X)))
0.60/0.78	= { by lemma 3 }
0.60/0.78	  meet(X, Y)
0.60/0.78	
0.60/0.78	Lemma 5: meet(X, join(meet(Y, X), Z)) = meet(X, join(Y, Z)).
0.60/0.78	Proof:
0.60/0.78	  meet(X, join(meet(Y, X), Z))
0.60/0.78	= { by axiom 1 (distribution) }
0.60/0.78	  join(meet(Z, X), meet(meet(Y, X), X))
0.60/0.78	= { by lemma 4 }
0.60/0.78	  join(meet(Z, X), meet(Y, X))
0.60/0.78	= { by axiom 1 (distribution) }
0.60/0.78	  meet(X, join(Y, Z))
0.60/0.78	
0.60/0.78	Lemma 6: meet(X, join(Y, meet(Z, X))) = meet(X, join(Y, Z)).
0.60/0.78	Proof:
0.60/0.78	  meet(X, join(Y, meet(Z, X)))
0.60/0.78	= { by axiom 1 (distribution) }
0.60/0.78	  join(meet(meet(Z, X), X), meet(Y, X))
0.60/0.78	= { by lemma 4 }
0.60/0.78	  join(meet(Z, X), meet(Y, X))
0.60/0.78	= { by axiom 1 (distribution) }
0.60/0.78	  meet(X, join(Y, Z))
0.60/0.78	
0.60/0.78	Lemma 7: meet(X, meet(X, join(Z, Y))) = meet(X, join(Y, Z)).
0.60/0.78	Proof:
0.60/0.78	  meet(X, meet(X, join(Z, Y)))
0.60/0.78	= { by axiom 1 (distribution) }
0.60/0.78	  meet(X, join(meet(Y, X), meet(Z, X)))
0.60/0.78	= { by lemma 5 }
0.60/0.78	  meet(X, join(Y, meet(Z, X)))
0.60/0.78	= { by lemma 6 }
0.60/0.78	  meet(X, join(Y, Z))
0.60/0.78	
0.60/0.78	Lemma 8: meet(X, join(Y, X)) = meet(X, X).
0.60/0.78	Proof:
0.60/0.78	  meet(X, join(Y, X))
0.60/0.78	= { by lemma 7 }
0.60/0.78	  meet(X, meet(X, join(X, Y)))
0.60/0.78	= { by axiom 2 (absorption) }
0.60/0.78	  meet(X, X)
0.60/0.78	
0.60/0.78	Lemma 9: meet(X, X) = X.
0.60/0.78	Proof:
0.60/0.78	  meet(X, X)
0.60/0.78	= { by lemma 8 }
0.60/0.78	  meet(X, join(X, X))
0.60/0.78	= { by axiom 2 (absorption) }
0.60/0.78	  X
0.60/0.78	
0.60/0.78	Lemma 10: meet(join(X, Y), join(X, Z)) = join(meet(Z, join(X, Y)), X).
0.60/0.78	Proof:
0.60/0.78	  meet(join(X, Y), join(X, Z))
0.60/0.78	= { by axiom 1 (distribution) }
0.60/0.78	  join(meet(Z, join(X, Y)), meet(X, join(X, Y)))
0.60/0.78	= { by axiom 2 (absorption) }
0.60/0.78	  join(meet(Z, join(X, Y)), X)
0.60/0.78	
0.60/0.78	Lemma 11: join(X, Y) = join(Y, X).
0.60/0.78	Proof:
0.60/0.78	  join(X, Y)
0.60/0.78	= { by lemma 9 }
0.60/0.78	  meet(join(X, Y), join(X, Y))
0.60/0.78	= { by lemma 10 }
0.60/0.78	  join(meet(Y, join(X, Y)), X)
0.60/0.78	= { by lemma 8 }
0.60/0.78	  join(meet(Y, Y), X)
0.60/0.78	= { by lemma 9 }
0.60/0.78	  join(Y, X)
0.60/0.78	
0.60/0.78	Lemma 12: meet(join(X, Y), join(Z, X)) = join(X, meet(Z, join(X, Y))).
0.60/0.78	Proof:
0.60/0.78	  meet(join(X, Y), join(Z, X))
0.60/0.78	= { by axiom 1 (distribution) }
0.60/0.78	  join(meet(X, join(X, Y)), meet(Z, join(X, Y)))
0.60/0.78	= { by axiom 2 (absorption) }
0.60/0.78	  join(X, meet(Z, join(X, Y)))
0.60/0.78	
0.60/0.78	Lemma 13: join(X, meet(Y, X)) = X.
0.60/0.78	Proof:
0.60/0.78	  join(X, meet(Y, X))
0.60/0.78	= { by lemma 9 }
0.60/0.78	  join(meet(X, X), meet(Y, X))
0.60/0.78	= { by axiom 1 (distribution) }
0.60/0.78	  meet(X, join(Y, X))
0.60/0.78	= { by lemma 8 }
0.60/0.78	  meet(X, X)
0.60/0.78	= { by lemma 9 }
0.60/0.78	  X
0.60/0.78	
0.60/0.78	Lemma 14: join(X, meet(join(X, Y), join(X, Y))) = join(X, Y).
0.60/0.78	Proof:
0.60/0.78	  join(X, meet(join(X, Y), join(X, Y)))
0.60/0.78	= { by lemma 12 }
0.60/0.78	  meet(join(X, Y), join(join(X, Y), X))
0.60/0.78	= { by axiom 2 (absorption) }
0.60/0.78	  join(X, Y)
0.60/0.78	
0.60/0.78	Lemma 15: join(X, X) = X.
0.60/0.78	Proof:
0.60/0.78	  join(X, X)
0.60/0.78	= { by axiom 2 (absorption) }
0.60/0.78	  join(X, meet(X, join(X, ?)))
0.60/0.78	= { by lemma 6 }
0.60/0.78	  join(X, meet(X, join(X, meet(?, X))))
0.60/0.78	= { by lemma 13 }
0.60/0.78	  join(X, meet(join(X, meet(?, X)), join(X, meet(?, X))))
0.60/0.78	= { by lemma 14 }
0.60/0.78	  join(X, meet(?, X))
0.60/0.78	= { by lemma 13 }
0.60/0.78	  X
0.60/0.78	
0.60/0.78	Lemma 16: meet(X, Y) = meet(Y, X).
0.60/0.78	Proof:
0.60/0.78	  meet(X, Y)
0.60/0.78	= { by lemma 15 }
0.60/0.78	  join(meet(X, Y), meet(X, Y))
0.60/0.78	= { by axiom 1 (distribution) }
0.60/0.78	  meet(Y, join(X, X))
0.60/0.78	= { by lemma 15 }
0.60/0.78	  meet(Y, X)
0.60/0.79	
0.60/0.79	Lemma 17: meet(join(Z, X), join(Y, X)) = join(X, meet(Y, join(X, Z))).
0.60/0.79	Proof:
0.60/0.79	  meet(join(Z, X), join(Y, X))
0.60/0.79	= { by lemma 11 }
0.60/0.79	  meet(join(X, Z), join(Y, X))
0.60/0.79	= { by lemma 12 }
0.60/0.79	  join(X, meet(Y, join(X, Z)))
0.60/0.79	
0.60/0.79	Lemma 18: meet(X, join(Y, join(X, Z))) = X.
0.60/0.79	Proof:
0.60/0.79	  meet(X, join(Y, join(X, Z)))
0.60/0.79	= { by lemma 11 }
0.60/0.79	  meet(X, join(join(X, Z), Y))
0.60/0.79	= { by lemma 7 }
0.60/0.79	  meet(X, meet(X, join(Y, join(X, Z))))
0.60/0.79	= { by lemma 9 }
0.60/0.79	  meet(meet(X, X), meet(X, join(Y, join(X, Z))))
0.60/0.79	= { by lemma 11 }
0.60/0.79	  meet(meet(X, X), meet(X, join(Y, join(Z, X))))
0.60/0.79	= { by lemma 15 }
0.60/0.79	  meet(meet(X, X), join(meet(X, join(Y, join(Z, X))), meet(X, join(Y, join(Z, X)))))
0.60/0.79	= { by lemma 5 }
0.60/0.79	  meet(meet(X, X), join(meet(meet(X, join(Y, join(Z, X))), meet(X, X)), meet(X, join(Y, join(Z, X)))))
0.60/0.79	= { by lemma 6 }
0.60/0.79	  meet(meet(X, X), join(meet(meet(X, join(Y, join(Z, X))), meet(X, X)), meet(meet(X, join(Y, join(Z, X))), meet(X, X))))
0.60/0.79	= { by lemma 3 }
0.60/0.79	  meet(meet(meet(X, X), meet(X, join(Z, X))), join(meet(meet(X, join(Y, join(Z, X))), meet(X, X)), meet(meet(X, join(Y, join(Z, X))), meet(X, X))))
0.60/0.79	= { by lemma 16 }
0.60/0.79	  meet(meet(meet(X, X), meet(join(Z, X), X)), join(meet(meet(X, join(Y, join(Z, X))), meet(X, X)), meet(meet(X, join(Y, join(Z, X))), meet(X, X))))
0.60/0.79	= { by lemma 16 }
0.60/0.79	  meet(meet(meet(join(Z, X), X), meet(X, X)), join(meet(meet(X, join(Y, join(Z, X))), meet(X, X)), meet(meet(X, join(Y, join(Z, X))), meet(X, X))))
0.60/0.79	= { by lemma 15 }
0.60/0.79	  meet(meet(meet(join(Z, X), X), meet(X, X)), meet(meet(X, join(Y, join(Z, X))), meet(X, X)))
0.60/0.79	= { by lemma 16 }
0.60/0.79	  meet(meet(meet(join(Z, X), X), meet(X, X)), meet(meet(X, X), meet(X, join(Y, join(Z, X)))))
0.60/0.79	= { by lemma 11 }
0.60/0.79	  meet(meet(meet(join(Z, X), X), meet(X, X)), meet(meet(X, X), meet(X, join(join(Z, X), Y))))
0.60/0.79	= { by axiom 1 (distribution) }
0.60/0.79	  meet(meet(meet(join(Z, X), X), meet(X, X)), meet(meet(X, X), join(meet(Y, X), meet(join(Z, X), X))))
0.60/0.79	= { by lemma 3 }
0.60/0.79	  meet(meet(join(Z, X), X), meet(X, X))
0.60/0.79	= { by lemma 16 }
0.60/0.79	  meet(meet(X, X), meet(join(Z, X), X))
0.60/0.79	= { by lemma 16 }
0.60/0.79	  meet(meet(X, X), meet(X, join(Z, X)))
0.60/0.79	= { by lemma 3 }
0.60/0.79	  meet(X, X)
0.60/0.79	= { by lemma 9 }
0.60/0.80	  X
0.60/0.80	
0.60/0.80	Lemma 19: join(X, join(Y, meet(X, join(Y, Z)))) = join(X, Y).
0.60/0.80	Proof:
0.60/0.80	  join(X, join(Y, meet(X, join(Y, Z))))
0.60/0.80	= { by axiom 2 (absorption) }
0.60/0.80	  join(meet(X, join(X, Y)), join(Y, meet(X, join(Y, Z))))
0.60/0.80	= { by lemma 12 }
0.60/0.80	  join(meet(X, join(X, Y)), meet(join(Y, Z), join(X, Y)))
0.60/0.80	= { by lemma 11 }
0.60/0.80	  join(meet(X, join(X, Y)), meet(join(Y, Z), join(Y, X)))
0.60/0.80	= { by lemma 9 }
0.60/0.80	  join(meet(X, join(X, Y)), meet(join(Y, Z), join(Y, meet(X, X))))
0.60/0.80	= { by lemma 8 }
0.60/0.80	  join(meet(X, join(X, Y)), meet(join(Y, Z), join(Y, meet(X, join(Y, X)))))
0.60/0.80	= { by lemma 17 }
0.60/0.80	  join(meet(X, join(X, Y)), meet(join(Y, Z), meet(join(X, Y), join(X, Y))))
0.60/0.80	= { by lemma 11 }
0.60/0.80	  join(meet(X, join(X, Y)), meet(join(Y, Z), meet(join(X, Y), join(Y, X))))
0.60/0.80	= { by axiom 1 (distribution) }
0.60/0.80	  join(meet(X, join(X, Y)), meet(join(Y, Z), join(meet(X, join(X, Y)), meet(Y, join(X, Y)))))
0.60/0.80	= { by lemma 12 }
0.60/0.80	  meet(join(meet(X, join(X, Y)), meet(Y, join(X, Y))), join(join(Y, Z), meet(X, join(X, Y))))
0.60/0.80	= { by axiom 1 (distribution) }
0.60/0.80	  meet(meet(join(X, Y), join(Y, X)), join(join(Y, Z), meet(X, join(X, Y))))
0.60/0.80	= { by lemma 16 }
0.60/0.80	  meet(join(join(Y, Z), meet(X, join(X, Y))), meet(join(X, Y), join(Y, X)))
0.60/0.80	= { by axiom 2 (absorption) }
0.60/0.80	  meet(join(join(Y, Z), X), meet(join(X, Y), join(Y, X)))
0.60/0.80	= { by lemma 11 }
0.60/0.80	  meet(join(X, join(Y, Z)), meet(join(X, Y), join(Y, X)))
0.60/0.80	= { by lemma 11 }
0.60/0.80	  meet(join(X, join(Y, Z)), meet(join(X, Y), join(X, Y)))
0.60/0.80	= { by lemma 9 }
0.60/0.80	  meet(join(X, join(Y, Z)), join(X, Y))
0.60/0.80	= { by lemma 10 }
0.60/0.80	  join(meet(Y, join(X, join(Y, Z))), X)
0.60/0.80	= { by lemma 11 }
0.60/0.80	  join(X, meet(Y, join(X, join(Y, Z))))
0.60/0.80	= { by lemma 12 }
0.60/0.80	  meet(join(X, join(Y, Z)), join(Y, X))
0.60/0.80	= { by lemma 9 }
0.60/0.80	  meet(meet(join(X, join(Y, Z)), join(Y, X)), meet(join(X, join(Y, Z)), join(Y, X)))
0.60/0.80	= { by lemma 8 }
0.60/0.80	  meet(meet(join(X, join(Y, Z)), join(Y, X)), join(Y, meet(join(X, join(Y, Z)), join(Y, X))))
0.60/0.80	= { by lemma 11 }
0.60/0.80	  meet(meet(join(X, join(Y, Z)), join(Y, X)), join(meet(join(X, join(Y, Z)), join(Y, X)), Y))
0.60/0.80	= { by lemma 10 }
0.60/0.80	  meet(meet(join(X, join(Y, Z)), join(Y, X)), meet(join(Y, X), join(Y, join(X, join(Y, Z)))))
0.60/0.80	= { by lemma 4 }
0.60/0.80	  meet(meet(join(X, join(Y, Z)), join(Y, X)), meet(meet(join(Y, X), join(Y, join(X, join(Y, Z)))), join(Y, join(X, join(Y, Z)))))
0.60/0.80	= { by lemma 10 }
0.60/0.80	  meet(meet(join(X, join(Y, Z)), join(Y, X)), meet(join(meet(join(X, join(Y, Z)), join(Y, X)), Y), join(Y, join(X, join(Y, Z)))))
0.60/0.80	= { by lemma 16 }
0.60/0.80	  meet(meet(join(X, join(Y, Z)), join(Y, X)), meet(join(Y, join(X, join(Y, Z))), join(meet(join(X, join(Y, Z)), join(Y, X)), Y)))
0.60/0.80	= { by lemma 12 }
0.60/0.80	  meet(meet(join(X, join(Y, Z)), join(Y, X)), join(Y, meet(meet(join(X, join(Y, Z)), join(Y, X)), join(Y, join(X, join(Y, Z))))))
0.60/0.80	= { by lemma 16 }
0.60/0.80	  meet(meet(join(X, join(Y, Z)), join(Y, X)), join(Y, meet(join(Y, join(X, join(Y, Z))), meet(join(X, join(Y, Z)), join(Y, X)))))
0.60/0.80	= { by lemma 6 }
0.60/0.80	  meet(meet(join(X, join(Y, Z)), join(Y, X)), join(Y, join(Y, join(X, join(Y, Z)))))
0.60/0.80	= { by lemma 9 }
0.60/0.80	  meet(meet(join(X, join(Y, Z)), join(Y, X)), join(Y, meet(join(Y, join(X, join(Y, Z))), join(Y, join(X, join(Y, Z))))))
0.60/0.80	= { by lemma 14 }
0.60/0.80	  meet(meet(join(X, join(Y, Z)), join(Y, X)), join(Y, join(X, join(Y, Z))))
0.60/0.80	= { by lemma 16 }
0.60/0.80	  meet(join(Y, join(X, join(Y, Z))), meet(join(X, join(Y, Z)), join(Y, X)))
0.60/0.80	= { by lemma 11 }
0.60/0.80	  meet(join(join(X, join(Y, Z)), Y), meet(join(X, join(Y, Z)), join(Y, X)))
0.60/0.80	= { by lemma 12 }
0.60/0.80	  meet(join(join(X, join(Y, Z)), Y), join(X, meet(Y, join(X, join(Y, Z)))))
0.60/0.80	= { by lemma 18 }
0.60/0.80	  meet(join(join(X, join(Y, Z)), Y), join(X, Y))
0.60/0.80	= { by lemma 17 }
0.60/0.80	  join(Y, meet(X, join(Y, join(X, join(Y, Z)))))
0.60/0.80	= { by lemma 18 }
0.60/0.80	  join(Y, X)
0.60/0.80	= { by lemma 11 }
0.60/0.80	  join(X, Y)
0.60/0.80	
0.60/0.80	Lemma 20: join(join(X, Z), join(Y, Z)) = join(X, join(Y, Z)).
0.60/0.80	Proof:
0.60/0.80	  join(join(X, Z), join(Y, Z))
0.60/0.80	= { by lemma 11 }
0.60/0.80	  join(join(X, Z), join(Z, Y))
0.60/0.80	= { by lemma 11 }
0.60/0.80	  join(join(Z, Y), join(X, Z))
0.60/0.80	= { by lemma 19 }
0.60/0.80	  join(join(Z, Y), join(X, join(Z, meet(X, join(Z, Y)))))
0.60/0.80	= { by lemma 12 }
0.60/0.80	  join(join(Z, Y), join(X, meet(join(Z, Y), join(X, Z))))
0.60/0.80	= { by lemma 19 }
0.60/0.80	  join(join(Z, Y), X)
0.60/0.80	= { by lemma 11 }
0.60/0.80	  join(X, join(Z, Y))
0.60/0.80	= { by lemma 11 }
0.60/0.80	  join(X, join(Y, Z))
0.60/0.80	
0.60/0.80	Goal 1 (prove_associativity_of_join): join(join(a, b), c) = join(a, join(b, c)).
0.60/0.80	Proof:
0.60/0.80	  join(join(a, b), c)
0.60/0.80	= { by lemma 11 }
0.60/0.80	  join(c, join(a, b))
0.60/0.80	= { by lemma 20 }
0.60/0.80	  join(join(c, b), join(a, b))
0.60/0.80	= { by lemma 11 }
0.60/0.80	  join(join(a, b), join(c, b))
0.60/0.80	= { by lemma 20 }
0.60/0.80	  join(a, join(c, b))
0.60/0.80	= { by lemma 11 }
0.60/0.80	  join(a, join(b, c))
0.60/0.80	% SZS output end Proof
0.60/0.80	
0.60/0.80	RESULT: Unsatisfiable (the axioms are contradictory).
0.60/0.80	EOF