0.09/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.09/0.12	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.13/0.33	% Computer   : n006.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 10:09:39 EDT 2019
0.13/0.33	% CPUTime    : 
0.79/1.01	% SZS status Unsatisfiable
0.79/1.01	
0.79/1.01	% SZS output start Proof
0.79/1.01	Take the following subset of the input axioms:
0.88/1.03	  fof(absorption1, axiom, ![X, Y]: meet(X, join(X, Y))=X).
0.88/1.03	  fof(absorption2, axiom, ![X, Y]: X=join(X, meet(X, Y))).
0.88/1.03	  fof(associativity_of_join, axiom, ![Z, X, Y]: join(X, join(Y, Z))=join(join(X, Y), Z)).
0.88/1.03	  fof(associativity_of_meet, axiom, ![Z, X, Y]: meet(meet(X, Y), Z)=meet(X, meet(Y, Z))).
0.88/1.03	  fof(commutativity_of_join, axiom, ![X, Y]: join(X, Y)=join(Y, X)).
0.88/1.03	  fof(commutativity_of_meet, axiom, ![X, Y]: meet(Y, X)=meet(X, Y)).
0.88/1.03	  fof(idempotence_of_meet, axiom, ![X]: meet(X, X)=X).
0.88/1.03	  fof(nr_3, hypothesis, ![Z, X, Y]: join(meet(Z, join(X, meet(Y, Z))), meet(X, join(Y, Z)))=meet(join(X, meet(Y, Z)), join(Z, meet(X, Y)))).
0.88/1.03	  fof(prove_this, negated_conjecture, meet(meet(a, meet(join(b, c), join(b, d))), join(meet(a, join(b, meet(c, d))), join(meet(a, c), meet(a, d))))!=meet(a, meet(join(b, c), join(b, d)))).
0.88/1.03	
0.88/1.03	Now clausify the problem and encode Horn clauses using encoding 3 of
0.88/1.03	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
0.88/1.03	We repeatedly replace C & s=t => u=v by the two clauses:
0.88/1.03	  fresh(y, y, x1...xn) = u
0.88/1.03	  C => fresh(s, t, x1...xn) = v
0.88/1.03	where fresh is a fresh function symbol and x1..xn are the free
0.88/1.03	variables of u and v.
0.88/1.03	A predicate p(X) is encoded as p(X)=true (this is sound, because the
0.88/1.03	input problem has no model of domain size 1).
0.88/1.03	
0.88/1.03	The encoding turns the above axioms into the following unit equations and goals:
0.88/1.03	
0.88/1.03	Axiom 1 (commutativity_of_join): join(X, Y) = join(Y, X).
0.88/1.03	Axiom 2 (idempotence_of_meet): meet(X, X) = X.
0.88/1.03	Axiom 3 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
0.88/1.03	Axiom 4 (absorption2): X = join(X, meet(X, Y)).
0.88/1.03	Axiom 5 (absorption1): meet(X, join(X, Y)) = X.
0.88/1.03	Axiom 6 (associativity_of_join): join(X, join(Y, Z)) = join(join(X, Y), Z).
0.88/1.03	Axiom 7 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
0.88/1.03	Axiom 8 (nr_3): join(meet(X, join(Y, meet(Z, X))), meet(Y, join(Z, X))) = meet(join(Y, meet(Z, X)), join(X, meet(Y, Z))).
0.88/1.03	
0.88/1.03	Lemma 9: join(X, meet(Y, X)) = X.
0.88/1.03	Proof:
0.88/1.03	  join(X, meet(Y, X))
0.88/1.03	= { by axiom 3 (commutativity_of_meet) }
0.88/1.03	  join(X, meet(X, Y))
0.88/1.03	= { by axiom 4 (absorption2) }
0.88/1.03	  X
0.88/1.03	
0.88/1.03	Lemma 10: join(X, meet(Y, meet(Z, X))) = X.
0.88/1.03	Proof:
0.88/1.03	  join(X, meet(Y, meet(Z, X)))
0.88/1.03	= { by axiom 7 (associativity_of_meet) }
0.88/1.03	  join(X, meet(meet(Y, Z), X))
0.88/1.03	= { by lemma 9 }
0.88/1.03	  X
0.88/1.03	
0.88/1.03	Lemma 11: join(meet(Y, join(Z, X)), meet(X, join(Y, meet(Z, X)))) = meet(join(Y, meet(Z, X)), join(X, meet(Y, Z))).
0.88/1.03	Proof:
0.88/1.03	  join(meet(Y, join(Z, X)), meet(X, join(Y, meet(Z, X))))
0.88/1.03	= { by axiom 1 (commutativity_of_join) }
0.88/1.03	  join(meet(X, join(Y, meet(Z, X))), meet(Y, join(Z, X)))
0.88/1.03	= { by axiom 8 (nr_3) }
0.88/1.03	  meet(join(Y, meet(Z, X)), join(X, meet(Y, Z)))
0.88/1.03	
0.88/1.03	Lemma 12: meet(X, meet(Y, join(Z, meet(X, Y)))) = meet(X, Y).
0.88/1.03	Proof:
0.88/1.03	  meet(X, meet(Y, join(Z, meet(X, Y))))
0.88/1.03	= { by axiom 1 (commutativity_of_join) }
0.88/1.03	  meet(X, meet(Y, join(meet(X, Y), Z)))
0.88/1.03	= { by axiom 7 (associativity_of_meet) }
0.88/1.03	  meet(meet(X, Y), join(meet(X, Y), Z))
0.88/1.03	= { by axiom 5 (absorption1) }
0.88/1.03	  meet(X, Y)
0.88/1.03	
0.88/1.03	Lemma 13: join(meet(X, Z), meet(X, join(Y, meet(X, Z)))) = meet(X, join(Y, meet(X, Z))).
0.88/1.03	Proof:
0.88/1.03	  join(meet(X, Z), meet(X, join(Y, meet(X, Z))))
0.88/1.03	= { by axiom 3 (commutativity_of_meet) }
0.88/1.03	  join(meet(Z, X), meet(X, join(Y, meet(X, Z))))
0.88/1.03	= { by axiom 3 (commutativity_of_meet) }
0.88/1.03	  join(meet(Z, X), meet(X, join(Y, meet(Z, X))))
0.88/1.03	= { by axiom 1 (commutativity_of_join) }
0.88/1.03	  join(meet(X, join(Y, meet(Z, X))), meet(Z, X))
0.88/1.03	= { by lemma 12 }
0.88/1.03	  join(meet(X, join(Y, meet(Z, X))), meet(Z, meet(X, join(Y, meet(Z, X)))))
0.88/1.03	= { by lemma 9 }
0.88/1.03	  meet(X, join(Y, meet(Z, X)))
0.88/1.03	= { by axiom 3 (commutativity_of_meet) }
0.88/1.03	  meet(X, join(Y, meet(X, Z)))
0.88/1.03	
0.88/1.03	Lemma 14: meet(X, join(meet(X, Y), meet(X, Z))) = meet(X, join(Y, meet(X, Z))).
0.88/1.03	Proof:
0.88/1.03	  meet(X, join(meet(X, Y), meet(X, Z)))
0.88/1.03	= { by lemma 10 }
0.88/1.03	  meet(join(X, meet(Y, meet(Z, X))), join(meet(X, Y), meet(X, Z)))
0.88/1.03	= { by axiom 3 (commutativity_of_meet) }
0.88/1.03	  meet(join(X, meet(Y, meet(Z, X))), join(meet(X, Y), meet(Z, X)))
0.88/1.03	= { by axiom 1 (commutativity_of_join) }
0.88/1.03	  meet(join(X, meet(Y, meet(Z, X))), join(meet(Z, X), meet(X, Y)))
0.88/1.03	= { by lemma 11 }
0.88/1.03	  join(meet(X, join(Y, meet(Z, X))), meet(meet(Z, X), join(X, meet(Y, meet(Z, X)))))
0.88/1.03	= { by lemma 10 }
0.88/1.03	  join(meet(X, join(Y, meet(Z, X))), meet(meet(Z, X), X))
0.88/1.03	= { by axiom 7 (associativity_of_meet) }
0.88/1.03	  join(meet(X, join(Y, meet(Z, X))), meet(Z, meet(X, X)))
0.88/1.03	= { by axiom 2 (idempotence_of_meet) }
0.88/1.03	  join(meet(X, join(Y, meet(Z, X))), meet(Z, X))
0.88/1.03	= { by axiom 1 (commutativity_of_join) }
0.88/1.03	  join(meet(Z, X), meet(X, join(Y, meet(Z, X))))
0.88/1.03	= { by axiom 3 (commutativity_of_meet) }
0.88/1.03	  join(meet(X, Z), meet(X, join(Y, meet(Z, X))))
0.88/1.03	= { by axiom 3 (commutativity_of_meet) }
0.88/1.03	  join(meet(X, Z), meet(X, join(Y, meet(X, Z))))
0.88/1.03	= { by lemma 13 }
0.88/1.03	  meet(X, join(Y, meet(X, Z)))
0.88/1.03	
0.88/1.03	Lemma 15: join(meet(X, Y), meet(X, Z)) = meet(X, join(Y, meet(X, Z))).
0.88/1.03	Proof:
0.88/1.03	  join(meet(X, Y), meet(X, Z))
0.88/1.03	= { by lemma 9 }
0.88/1.03	  join(join(meet(X, Y), meet(X, Z)), meet(X, join(meet(X, Y), meet(X, Z))))
0.88/1.03	= { by lemma 14 }
0.88/1.03	  join(join(meet(X, Y), meet(X, Z)), meet(X, join(Y, meet(X, Z))))
0.88/1.03	= { by axiom 6 (associativity_of_join) }
0.88/1.03	  join(meet(X, Y), join(meet(X, Z), meet(X, join(Y, meet(X, Z)))))
0.88/1.03	= { by axiom 3 (commutativity_of_meet) }
0.88/1.03	  join(meet(Y, X), join(meet(X, Z), meet(X, join(Y, meet(X, Z)))))
0.88/1.03	= { by lemma 13 }
0.88/1.03	  join(meet(Y, X), meet(X, join(Y, meet(X, Z))))
0.88/1.03	= { by axiom 1 (commutativity_of_join) }
0.88/1.03	  join(meet(X, join(Y, meet(X, Z))), meet(Y, X))
0.88/1.03	= { by axiom 5 (absorption1) }
0.88/1.03	  join(meet(X, join(Y, meet(X, Z))), meet(meet(Y, join(Y, meet(X, Z))), X))
0.88/1.03	= { by axiom 7 (associativity_of_meet) }
0.88/1.03	  join(meet(X, join(Y, meet(X, Z))), meet(Y, meet(join(Y, meet(X, Z)), X)))
0.88/1.03	= { by axiom 3 (commutativity_of_meet) }
0.88/1.03	  join(meet(X, join(Y, meet(X, Z))), meet(Y, meet(X, join(Y, meet(X, Z)))))
0.88/1.03	= { by lemma 9 }
0.88/1.03	  meet(X, join(Y, meet(X, Z)))
0.88/1.03	
0.88/1.03	Lemma 16: meet(X, meet(Y, Z)) = meet(Y, meet(X, Z)).
0.88/1.03	Proof:
0.88/1.03	  meet(X, meet(Y, Z))
0.88/1.03	= { by axiom 7 (associativity_of_meet) }
0.88/1.03	  meet(meet(X, Y), Z)
0.88/1.03	= { by axiom 3 (commutativity_of_meet) }
0.88/1.03	  meet(meet(Y, X), Z)
0.88/1.03	= { by axiom 7 (associativity_of_meet) }
0.88/1.03	  meet(Y, meet(X, Z))
0.88/1.03	
0.88/1.03	Lemma 17: meet(X, join(Y, meet(X, Z))) = meet(X, join(Z, meet(X, Y))).
0.88/1.03	Proof:
0.88/1.03	  meet(X, join(Y, meet(X, Z)))
0.88/1.03	= { by lemma 14 }
0.88/1.03	  meet(X, join(meet(X, Y), meet(X, Z)))
0.88/1.03	= { by axiom 1 (commutativity_of_join) }
0.88/1.03	  meet(X, join(meet(X, Z), meet(X, Y)))
0.88/1.03	= { by lemma 14 }
0.88/1.03	  meet(X, join(Z, meet(X, Y)))
0.88/1.03	
0.88/1.03	Lemma 18: meet(X, meet(Y, Z)) = meet(Z, meet(X, Y)).
0.88/1.03	Proof:
0.88/1.03	  meet(X, meet(Y, Z))
0.88/1.03	= { by axiom 7 (associativity_of_meet) }
0.88/1.03	  meet(meet(X, Y), Z)
0.88/1.03	= { by axiom 3 (commutativity_of_meet) }
0.88/1.05	  meet(Z, meet(X, Y))
0.88/1.05	
0.88/1.05	Goal 1 (prove_this): meet(meet(a, meet(join(b, c), join(b, d))), join(meet(a, join(b, meet(c, d))), join(meet(a, c), meet(a, d)))) = meet(a, meet(join(b, c), join(b, d))).
0.88/1.05	Proof:
0.88/1.05	  meet(meet(a, meet(join(b, c), join(b, d))), join(meet(a, join(b, meet(c, d))), join(meet(a, c), meet(a, d))))
0.88/1.05	= { by axiom 7 (associativity_of_meet) }
0.88/1.05	  meet(a, meet(meet(join(b, c), join(b, d)), join(meet(a, join(b, meet(c, d))), join(meet(a, c), meet(a, d)))))
0.88/1.05	= { by axiom 7 (associativity_of_meet) }
0.88/1.05	  meet(a, meet(join(b, c), meet(join(b, d), join(meet(a, join(b, meet(c, d))), join(meet(a, c), meet(a, d))))))
0.88/1.05	= { by axiom 1 (commutativity_of_join) }
0.88/1.05	  meet(a, meet(join(b, c), meet(join(b, d), join(join(meet(a, c), meet(a, d)), meet(a, join(b, meet(c, d)))))))
0.88/1.05	= { by axiom 6 (associativity_of_join) }
0.88/1.05	  meet(a, meet(join(b, c), meet(join(b, d), join(meet(a, c), join(meet(a, d), meet(a, join(b, meet(c, d))))))))
0.88/1.05	= { by lemma 15 }
0.88/1.05	  meet(a, meet(join(b, c), meet(join(b, d), join(meet(a, c), meet(a, join(d, meet(a, join(b, meet(c, d)))))))))
0.88/1.05	= { by lemma 15 }
0.88/1.05	  meet(a, meet(join(b, c), meet(join(b, d), meet(a, join(c, meet(a, join(d, meet(a, join(b, meet(c, d))))))))))
0.88/1.05	= { by lemma 16 }
0.88/1.05	  meet(a, meet(join(b, c), meet(a, meet(join(b, d), join(c, meet(a, join(d, meet(a, join(b, meet(c, d))))))))))
0.88/1.05	= { by lemma 16 }
0.88/1.05	  meet(a, meet(a, meet(join(b, c), meet(join(b, d), join(c, meet(a, join(d, meet(a, join(b, meet(c, d))))))))))
0.88/1.05	= { by axiom 7 (associativity_of_meet) }
0.88/1.05	  meet(meet(a, a), meet(join(b, c), meet(join(b, d), join(c, meet(a, join(d, meet(a, join(b, meet(c, d)))))))))
0.88/1.05	= { by axiom 2 (idempotence_of_meet) }
0.88/1.05	  meet(a, meet(join(b, c), meet(join(b, d), join(c, meet(a, join(d, meet(a, join(b, meet(c, d)))))))))
0.88/1.05	= { by lemma 17 }
0.88/1.05	  meet(a, meet(join(b, c), meet(join(b, d), join(c, meet(a, join(join(b, meet(c, d)), meet(a, d)))))))
0.88/1.05	= { by axiom 3 (commutativity_of_meet) }
0.88/1.05	  meet(a, meet(join(b, c), meet(join(b, d), join(c, meet(join(join(b, meet(c, d)), meet(a, d)), a)))))
0.88/1.05	= { by axiom 5 (absorption1) }
0.88/1.05	  meet(a, meet(join(b, c), meet(join(b, d), join(c, meet(join(join(b, meet(c, d)), meet(a, d)), meet(a, join(a, meet(d, join(b, meet(c, d))))))))))
0.88/1.05	= { by lemma 18 }
0.88/1.05	  meet(a, meet(join(b, c), meet(join(b, d), join(c, meet(join(a, meet(d, join(b, meet(c, d)))), meet(join(join(b, meet(c, d)), meet(a, d)), a))))))
0.88/1.05	= { by lemma 18 }
0.88/1.05	  meet(a, meet(join(b, c), meet(join(b, d), join(c, meet(a, meet(join(a, meet(d, join(b, meet(c, d)))), join(join(b, meet(c, d)), meet(a, d))))))))
0.88/1.05	= { by lemma 11 }
0.88/1.05	  meet(a, meet(join(b, c), meet(join(b, d), join(c, meet(a, join(meet(a, join(d, join(b, meet(c, d)))), meet(join(b, meet(c, d)), join(a, meet(d, join(b, meet(c, d)))))))))))
0.88/1.05	= { by axiom 1 (commutativity_of_join) }
0.88/1.05	  meet(a, meet(join(b, c), meet(join(b, d), join(c, meet(a, join(meet(join(b, meet(c, d)), join(a, meet(d, join(b, meet(c, d))))), meet(a, join(d, join(b, meet(c, d))))))))))
0.88/1.05	= { by lemma 17 }
0.88/1.05	  meet(a, meet(join(b, c), meet(join(b, d), join(c, meet(a, join(join(d, join(b, meet(c, d))), meet(a, meet(join(b, meet(c, d)), join(a, meet(d, join(b, meet(c, d))))))))))))
0.88/1.05	= { by axiom 6 (associativity_of_join) }
0.88/1.05	  meet(a, meet(join(b, c), meet(join(b, d), join(c, meet(a, join(d, join(join(b, meet(c, d)), meet(a, meet(join(b, meet(c, d)), join(a, meet(d, join(b, meet(c, d)))))))))))))
0.88/1.05	= { by lemma 18 }
0.88/1.05	  meet(a, meet(join(b, c), meet(join(b, d), join(c, meet(a, join(d, join(join(b, meet(c, d)), meet(join(b, meet(c, d)), meet(join(a, meet(d, join(b, meet(c, d)))), a)))))))))
0.88/1.05	= { by axiom 4 (absorption2) }
0.88/1.05	  meet(a, meet(join(b, c), meet(join(b, d), join(c, meet(a, join(d, join(b, meet(c, d))))))))
0.88/1.05	= { by axiom 6 (associativity_of_join) }
0.88/1.05	  meet(a, meet(join(b, c), meet(join(b, d), join(c, meet(a, join(join(d, b), meet(c, d)))))))
0.88/1.05	= { by axiom 1 (commutativity_of_join) }
0.88/1.05	  meet(a, meet(join(b, c), meet(join(b, d), join(c, meet(a, join(join(b, d), meet(c, d)))))))
0.88/1.05	= { by axiom 6 (associativity_of_join) }
0.88/1.05	  meet(a, meet(join(b, c), meet(join(b, d), join(c, meet(a, join(b, join(d, meet(c, d))))))))
0.88/1.05	= { by lemma 9 }
0.88/1.05	  meet(a, meet(join(b, c), meet(join(b, d), join(c, meet(a, join(b, d))))))
0.88/1.05	= { by lemma 16 }
0.88/1.05	  meet(join(b, c), meet(a, meet(join(b, d), join(c, meet(a, join(b, d))))))
0.88/1.05	= { by lemma 12 }
0.88/1.05	  meet(join(b, c), meet(a, join(b, d)))
0.88/1.05	= { by lemma 16 }
0.88/1.05	  meet(a, meet(join(b, c), join(b, d)))
0.88/1.05	% SZS output end Proof
0.88/1.05	
0.88/1.05	RESULT: Unsatisfiable (the axioms are contradictory).
0.88/1.05	EOF