0.11/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.11/0.12	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.12/0.33	% Computer   : n024.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 11:59:20 EDT 2019
0.12/0.33	% CPUTime    : 
1.82/2.06	% SZS status Unsatisfiable
1.82/2.06	
1.82/2.06	% SZS output start Proof
1.82/2.06	Take the following subset of the input axioms:
1.97/2.16	  fof(composition_associativity_5, axiom, ![A, C, B]: composition(composition(A, B), C)=composition(A, composition(B, C))).
1.97/2.16	  fof(composition_identity_6, axiom, ![A]: A=composition(A, one)).
1.97/2.16	  fof(converse_additivity_9, axiom, ![A, B]: join(converse(A), converse(B))=converse(join(A, B))).
1.97/2.16	  fof(converse_cancellativity_11, axiom, ![A, B]: join(composition(converse(A), complement(composition(A, B))), complement(B))=complement(B)).
1.97/2.16	  fof(converse_idempotence_8, axiom, ![A]: converse(converse(A))=A).
1.97/2.16	  fof(converse_multiplicativity_10, axiom, ![A, B]: converse(composition(A, B))=composition(converse(B), converse(A))).
1.97/2.16	  fof(def_top_12, axiom, ![A]: join(A, complement(A))=top).
1.97/2.16	  fof(def_zero_13, axiom, ![A]: zero=meet(A, complement(A))).
1.97/2.16	  fof(goals_17, negated_conjecture, meet(converse(sk1), converse(sk2))!=converse(meet(sk1, sk2))).
1.97/2.16	  fof(maddux1_join_commutativity_1, axiom, ![A, B]: join(B, A)=join(A, B)).
1.97/2.16	  fof(maddux2_join_associativity_2, axiom, ![A, C, B]: join(join(A, B), C)=join(A, join(B, C))).
1.97/2.16	  fof(maddux3_a_kind_of_de_Morgan_3, axiom, ![A, B]: join(complement(join(complement(A), complement(B))), complement(join(complement(A), B)))=A).
1.97/2.16	  fof(maddux4_definiton_of_meet_4, axiom, ![A, B]: complement(join(complement(A), complement(B)))=meet(A, B)).
1.97/2.16	
1.97/2.16	Now clausify the problem and encode Horn clauses using encoding 3 of
1.97/2.16	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
1.97/2.16	We repeatedly replace C & s=t => u=v by the two clauses:
1.97/2.16	  fresh(y, y, x1...xn) = u
1.97/2.16	  C => fresh(s, t, x1...xn) = v
1.97/2.16	where fresh is a fresh function symbol and x1..xn are the free
1.97/2.16	variables of u and v.
1.97/2.16	A predicate p(X) is encoded as p(X)=true (this is sound, because the
1.97/2.16	input problem has no model of domain size 1).
1.97/2.16	
1.97/2.16	The encoding turns the above axioms into the following unit equations and goals:
1.97/2.16	
1.97/2.16	Axiom 1 (maddux1_join_commutativity_1): join(X, Y) = join(Y, X).
1.97/2.16	Axiom 2 (maddux4_definiton_of_meet_4): complement(join(complement(X), complement(Y))) = meet(X, Y).
1.97/2.16	Axiom 3 (composition_identity_6): X = composition(X, one).
1.97/2.16	Axiom 4 (maddux3_a_kind_of_de_Morgan_3): join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y))) = X.
1.97/2.16	Axiom 5 (converse_idempotence_8): converse(converse(X)) = X.
1.97/2.16	Axiom 6 (maddux2_join_associativity_2): join(join(X, Y), Z) = join(X, join(Y, Z)).
1.97/2.16	Axiom 7 (converse_cancellativity_11): join(composition(converse(X), complement(composition(X, Y))), complement(Y)) = complement(Y).
1.97/2.16	Axiom 8 (def_zero_13): zero = meet(X, complement(X)).
1.97/2.16	Axiom 9 (def_top_12): join(X, complement(X)) = top.
1.97/2.16	Axiom 10 (converse_multiplicativity_10): converse(composition(X, Y)) = composition(converse(Y), converse(X)).
1.97/2.16	Axiom 11 (converse_additivity_9): join(converse(X), converse(Y)) = converse(join(X, Y)).
1.97/2.17	Axiom 12 (composition_associativity_5): composition(composition(X, Y), Z) = composition(X, composition(Y, Z)).
1.97/2.17	
1.97/2.17	Lemma 13: meet(X, Y) = meet(Y, X).
1.97/2.17	Proof:
1.97/2.17	  meet(X, Y)
1.97/2.17	= { by axiom 2 (maddux4_definiton_of_meet_4) }
1.97/2.17	  complement(join(complement(X), complement(Y)))
1.97/2.17	= { by axiom 1 (maddux1_join_commutativity_1) }
1.97/2.17	  complement(join(complement(Y), complement(X)))
1.97/2.17	= { by axiom 2 (maddux4_definiton_of_meet_4) }
1.97/2.17	  meet(Y, X)
1.97/2.17	
1.97/2.17	Lemma 14: join(meet(X, Y), complement(join(complement(X), Y))) = X.
1.97/2.17	Proof:
1.97/2.17	  join(meet(X, Y), complement(join(complement(X), Y)))
1.97/2.17	= { by axiom 2 (maddux4_definiton_of_meet_4) }
1.97/2.17	  join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y)))
1.97/2.17	= { by axiom 4 (maddux3_a_kind_of_de_Morgan_3) }
1.97/2.17	  X
1.97/2.17	
1.97/2.17	Lemma 15: complement(top) = zero.
1.97/2.17	Proof:
1.97/2.17	  complement(top)
1.97/2.17	= { by axiom 9 (def_top_12) }
1.97/2.17	  complement(join(complement(?), complement(complement(?))))
1.97/2.17	= { by axiom 2 (maddux4_definiton_of_meet_4) }
1.97/2.17	  meet(?, complement(?))
1.97/2.17	= { by axiom 8 (def_zero_13) }
1.97/2.17	  zero
1.97/2.17	
1.97/2.17	Lemma 16: complement(join(zero, complement(X))) = meet(X, top).
1.97/2.17	Proof:
1.97/2.17	  complement(join(zero, complement(X)))
1.97/2.17	= { by lemma 15 }
1.97/2.17	  complement(join(complement(top), complement(X)))
1.97/2.17	= { by axiom 2 (maddux4_definiton_of_meet_4) }
1.97/2.17	  meet(top, X)
1.97/2.17	= { by lemma 13 }
1.97/2.17	  meet(X, top)
1.97/2.17	
1.97/2.17	Lemma 17: composition(converse(one), X) = X.
1.97/2.17	Proof:
1.97/2.17	  composition(converse(one), X)
1.97/2.17	= { by axiom 5 (converse_idempotence_8) }
1.97/2.17	  composition(converse(one), converse(converse(X)))
1.97/2.17	= { by axiom 10 (converse_multiplicativity_10) }
1.97/2.17	  converse(composition(converse(X), one))
1.97/2.17	= { by axiom 3 (composition_identity_6) }
1.97/2.17	  converse(converse(X))
1.97/2.17	= { by axiom 5 (converse_idempotence_8) }
1.97/2.17	  X
1.97/2.17	
1.97/2.17	Lemma 18: join(complement(X), complement(X)) = complement(X).
1.97/2.17	Proof:
1.97/2.17	  join(complement(X), complement(X))
1.97/2.17	= { by lemma 17 }
1.97/2.17	  join(complement(X), composition(converse(one), complement(X)))
1.97/2.17	= { by lemma 17 }
1.97/2.17	  join(complement(X), composition(converse(one), complement(composition(converse(one), X))))
1.97/2.17	= { by axiom 3 (composition_identity_6) }
1.97/2.17	  join(complement(X), composition(converse(one), complement(composition(composition(converse(one), one), X))))
1.97/2.17	= { by axiom 12 (composition_associativity_5) }
1.97/2.17	  join(complement(X), composition(converse(one), complement(composition(converse(one), composition(one, X)))))
1.97/2.17	= { by lemma 17 }
1.97/2.17	  join(complement(X), composition(converse(one), complement(composition(one, X))))
1.97/2.17	= { by axiom 1 (maddux1_join_commutativity_1) }
1.97/2.17	  join(composition(converse(one), complement(composition(one, X))), complement(X))
1.97/2.17	= { by axiom 7 (converse_cancellativity_11) }
1.97/2.17	  complement(X)
1.97/2.17	
1.97/2.17	Lemma 19: join(X, join(Y, Z)) = join(Z, join(X, Y)).
1.97/2.17	Proof:
1.97/2.17	  join(X, join(Y, Z))
1.97/2.17	= { by axiom 6 (maddux2_join_associativity_2) }
1.97/2.17	  join(join(X, Y), Z)
1.97/2.17	= { by axiom 1 (maddux1_join_commutativity_1) }
1.97/2.17	  join(Z, join(X, Y))
1.97/2.17	
1.97/2.17	Lemma 20: join(X, join(complement(X), Y)) = join(Y, top).
1.97/2.17	Proof:
1.97/2.17	  join(X, join(complement(X), Y))
1.97/2.17	= { by lemma 19 }
1.97/2.17	  join(complement(X), join(Y, X))
1.97/2.17	= { by lemma 19 }
1.97/2.17	  join(Y, join(X, complement(X)))
1.97/2.17	= { by axiom 9 (def_top_12) }
1.97/2.17	  join(Y, top)
1.97/2.17	
1.97/2.17	Lemma 21: join(top, complement(X)) = top.
1.97/2.17	Proof:
1.97/2.17	  join(top, complement(X))
1.97/2.17	= { by axiom 1 (maddux1_join_commutativity_1) }
1.97/2.17	  join(complement(X), top)
1.97/2.17	= { by axiom 1 (maddux1_join_commutativity_1) }
1.97/2.17	  join(top, complement(X))
1.97/2.17	= { by axiom 9 (def_top_12) }
1.97/2.17	  join(join(X, complement(X)), complement(X))
1.97/2.17	= { by axiom 6 (maddux2_join_associativity_2) }
1.97/2.17	  join(X, join(complement(X), complement(X)))
1.97/2.17	= { by lemma 18 }
1.97/2.17	  join(X, complement(X))
1.97/2.17	= { by axiom 9 (def_top_12) }
1.97/2.17	  top
1.97/2.17	
1.97/2.17	Lemma 22: join(X, top) = top.
1.97/2.17	Proof:
1.97/2.17	  join(X, top)
1.97/2.17	= { by axiom 9 (def_top_12) }
1.97/2.17	  join(X, join(complement(X), complement(complement(X))))
1.97/2.17	= { by lemma 20 }
1.97/2.17	  join(complement(complement(X)), top)
1.97/2.17	= { by axiom 1 (maddux1_join_commutativity_1) }
1.97/2.17	  join(top, complement(complement(X)))
1.97/2.17	= { by lemma 21 }
1.97/2.17	  top
1.97/2.17	
1.97/2.17	Lemma 23: join(zero, meet(X, top)) = X.
1.97/2.17	Proof:
1.97/2.17	  join(zero, meet(X, top))
1.97/2.17	= { by axiom 1 (maddux1_join_commutativity_1) }
1.97/2.17	  join(meet(X, top), zero)
1.97/2.17	= { by lemma 15 }
1.97/2.17	  join(meet(X, top), complement(top))
1.97/2.17	= { by lemma 22 }
1.97/2.17	  join(meet(X, top), complement(join(complement(X), top)))
1.97/2.17	= { by lemma 14 }
1.97/2.17	  X
1.97/2.17	
1.97/2.17	Lemma 24: join(meet(X, Y), meet(X, complement(Y))) = X.
1.97/2.17	Proof:
1.97/2.17	  join(meet(X, Y), meet(X, complement(Y)))
1.97/2.17	= { by axiom 1 (maddux1_join_commutativity_1) }
1.97/2.17	  join(meet(X, complement(Y)), meet(X, Y))
1.97/2.17	= { by axiom 2 (maddux4_definiton_of_meet_4) }
1.97/2.17	  join(meet(X, complement(Y)), complement(join(complement(X), complement(Y))))
1.97/2.17	= { by lemma 14 }
1.97/2.17	  X
1.97/2.17	
1.97/2.17	Lemma 25: join(zero, meet(X, X)) = X.
1.97/2.17	Proof:
1.97/2.17	  join(zero, meet(X, X))
1.97/2.17	= { by axiom 8 (def_zero_13) }
1.97/2.17	  join(meet(X, complement(X)), meet(X, X))
1.97/2.17	= { by axiom 2 (maddux4_definiton_of_meet_4) }
1.97/2.17	  join(meet(X, complement(X)), complement(join(complement(X), complement(X))))
1.97/2.17	= { by lemma 14 }
1.97/2.17	  X
1.97/2.17	
1.97/2.17	Lemma 26: join(X, meet(Y, Y)) = join(Y, meet(X, X)).
1.97/2.17	Proof:
1.97/2.17	  join(X, meet(Y, Y))
1.97/2.17	= { by axiom 1 (maddux1_join_commutativity_1) }
1.97/2.17	  join(meet(Y, Y), X)
1.97/2.17	= { by lemma 25 }
1.97/2.17	  join(meet(Y, Y), join(zero, meet(X, X)))
1.97/2.17	= { by axiom 6 (maddux2_join_associativity_2) }
1.97/2.17	  join(join(meet(Y, Y), zero), meet(X, X))
1.97/2.17	= { by axiom 1 (maddux1_join_commutativity_1) }
1.97/2.17	  join(join(zero, meet(Y, Y)), meet(X, X))
1.97/2.17	= { by lemma 25 }
1.97/2.17	  join(Y, meet(X, X))
1.97/2.17	
1.97/2.17	Lemma 27: join(X, zero) = X.
1.97/2.17	Proof:
1.97/2.17	  join(X, zero)
1.97/2.17	= { by lemma 15 }
1.97/2.17	  join(X, complement(top))
1.97/2.17	= { by lemma 21 }
1.97/2.17	  join(X, complement(join(top, complement(zero))))
1.97/2.17	= { by lemma 24 }
1.97/2.17	  join(X, complement(join(join(meet(top, complement(top)), meet(top, complement(complement(top)))), complement(zero))))
1.97/2.17	= { by axiom 8 (def_zero_13) }
1.97/2.17	  join(X, complement(join(join(zero, meet(top, complement(complement(top)))), complement(zero))))
1.97/2.17	= { by lemma 18 }
1.97/2.17	  join(X, complement(join(join(zero, meet(top, complement(join(complement(top), complement(top))))), complement(zero))))
1.97/2.17	= { by axiom 2 (maddux4_definiton_of_meet_4) }
1.97/2.17	  join(X, complement(join(join(zero, meet(top, meet(top, top))), complement(zero))))
1.97/2.17	= { by lemma 13 }
1.97/2.17	  join(X, complement(join(join(zero, meet(meet(top, top), top)), complement(zero))))
1.97/2.17	= { by lemma 23 }
1.97/2.17	  join(X, complement(join(meet(top, top), complement(zero))))
1.97/2.17	= { by lemma 16 }
1.97/2.17	  join(X, complement(join(complement(join(zero, complement(top))), complement(zero))))
1.97/2.17	= { by lemma 15 }
1.97/2.17	  join(X, complement(join(complement(join(complement(top), complement(top))), complement(zero))))
1.97/2.17	= { by lemma 18 }
1.97/2.17	  join(X, complement(join(complement(complement(top)), complement(zero))))
1.97/2.17	= { by lemma 15 }
1.97/2.17	  join(X, complement(join(complement(zero), complement(zero))))
1.97/2.17	= { by axiom 2 (maddux4_definiton_of_meet_4) }
1.97/2.17	  join(X, meet(zero, zero))
1.97/2.17	= { by lemma 26 }
1.97/2.17	  join(zero, meet(X, X))
1.97/2.17	= { by lemma 25 }
1.97/2.17	  X
1.97/2.17	
1.97/2.17	Lemma 28: join(complement(converse(X)), converse(join(X, Y))) = top.
1.97/2.17	Proof:
1.97/2.17	  join(complement(converse(X)), converse(join(X, Y)))
1.97/2.17	= { by axiom 1 (maddux1_join_commutativity_1) }
1.97/2.17	  join(complement(converse(X)), converse(join(Y, X)))
1.97/2.17	= { by axiom 1 (maddux1_join_commutativity_1) }
1.97/2.17	  join(converse(join(Y, X)), complement(converse(X)))
1.97/2.17	= { by axiom 11 (converse_additivity_9) }
1.97/2.17	  join(join(converse(Y), converse(X)), complement(converse(X)))
1.97/2.17	= { by axiom 6 (maddux2_join_associativity_2) }
1.97/2.17	  join(converse(Y), join(converse(X), complement(converse(X))))
1.97/2.17	= { by axiom 9 (def_top_12) }
1.97/2.17	  join(converse(Y), top)
1.97/2.17	= { by lemma 22 }
1.97/2.17	  top
1.97/2.17	
1.97/2.17	Lemma 29: meet(converse(X), converse(join(X, Y))) = converse(X).
1.97/2.17	Proof:
1.97/2.17	  meet(converse(X), converse(join(X, Y)))
1.97/2.17	= { by lemma 27 }
1.97/2.17	  join(meet(converse(X), converse(join(X, Y))), zero)
1.97/2.17	= { by lemma 15 }
1.97/2.17	  join(meet(converse(X), converse(join(X, Y))), complement(top))
1.97/2.17	= { by lemma 28 }
1.97/2.17	  join(meet(converse(X), converse(join(X, Y))), complement(join(complement(converse(X)), converse(join(X, Y)))))
1.97/2.17	= { by lemma 14 }
1.97/2.17	  converse(X)
1.97/2.17	
1.97/2.17	Lemma 30: join(zero, X) = X.
1.97/2.17	Proof:
1.97/2.17	  join(zero, X)
1.97/2.17	= { by axiom 1 (maddux1_join_commutativity_1) }
1.97/2.17	  join(X, zero)
1.97/2.17	= { by lemma 27 }
1.97/2.17	  X
1.97/2.17	
1.97/2.17	Lemma 31: meet(X, top) = X.
1.97/2.17	Proof:
1.97/2.17	  meet(X, top)
1.97/2.17	= { by lemma 30 }
1.97/2.17	  join(zero, meet(X, top))
1.97/2.17	= { by lemma 23 }
1.97/2.17	  X
1.97/2.17	
1.97/2.17	Lemma 32: complement(complement(X)) = X.
1.97/2.17	Proof:
1.97/2.17	  complement(complement(X))
1.97/2.17	= { by lemma 30 }
1.97/2.17	  complement(join(zero, complement(X)))
1.97/2.17	= { by lemma 16 }
1.97/2.17	  meet(X, top)
1.97/2.17	= { by lemma 31 }
1.97/2.17	  X
1.97/2.17	
1.97/2.17	Lemma 33: meet(X, X) = X.
1.97/2.17	Proof:
1.97/2.17	  meet(X, X)
1.97/2.17	= { by lemma 30 }
1.97/2.17	  join(zero, meet(X, X))
1.97/2.17	= { by lemma 25 }
1.97/2.17	  X
1.97/2.17	
1.97/2.17	Lemma 34: complement(join(complement(X), meet(Y, Z))) = meet(X, join(complement(Y), complement(Z))).
1.97/2.17	Proof:
1.97/2.17	  complement(join(complement(X), meet(Y, Z)))
1.97/2.17	= { by lemma 13 }
1.97/2.17	  complement(join(complement(X), meet(Z, Y)))
1.97/2.17	= { by axiom 1 (maddux1_join_commutativity_1) }
1.97/2.17	  complement(join(meet(Z, Y), complement(X)))
1.97/2.17	= { by axiom 2 (maddux4_definiton_of_meet_4) }
1.97/2.17	  complement(join(complement(join(complement(Z), complement(Y))), complement(X)))
1.97/2.17	= { by axiom 2 (maddux4_definiton_of_meet_4) }
1.97/2.17	  meet(join(complement(Z), complement(Y)), X)
1.97/2.17	= { by lemma 13 }
1.97/2.17	  meet(X, join(complement(Z), complement(Y)))
1.97/2.17	= { by axiom 1 (maddux1_join_commutativity_1) }
1.97/2.17	  meet(X, join(complement(Y), complement(Z)))
1.97/2.17	
1.97/2.17	Lemma 35: meet(top, X) = X.
1.97/2.17	Proof:
1.97/2.17	  meet(top, X)
1.97/2.17	= { by lemma 13 }
1.97/2.17	  meet(X, top)
1.97/2.17	= { by lemma 31 }
1.97/2.17	  X
1.97/2.17	
1.97/2.17	Lemma 36: join(complement(X), complement(Y)) = complement(meet(X, Y)).
1.97/2.17	Proof:
1.97/2.17	  join(complement(X), complement(Y))
1.97/2.17	= { by lemma 35 }
1.97/2.17	  meet(top, join(complement(X), complement(Y)))
1.97/2.17	= { by lemma 34 }
1.97/2.17	  complement(join(complement(top), meet(X, Y)))
1.97/2.17	= { by lemma 15 }
1.97/2.17	  complement(join(zero, meet(X, Y)))
1.97/2.17	= { by lemma 30 }
1.97/2.17	  complement(meet(X, Y))
1.97/2.17	
1.97/2.17	Lemma 37: complement(join(Y, complement(X))) = meet(X, complement(Y)).
1.97/2.17	Proof:
1.97/2.17	  complement(join(Y, complement(X)))
1.97/2.17	= { by lemma 33 }
1.97/2.17	  complement(join(Y, meet(complement(X), complement(X))))
1.97/2.17	= { by lemma 26 }
1.97/2.17	  complement(join(complement(X), meet(Y, Y)))
1.97/2.17	= { by lemma 34 }
1.97/2.17	  meet(X, join(complement(Y), complement(Y)))
1.97/2.17	= { by lemma 36 }
1.97/2.17	  meet(X, complement(meet(Y, Y)))
1.97/2.17	= { by lemma 33 }
1.97/2.17	  meet(X, complement(Y))
1.97/2.17	
1.97/2.17	Lemma 38: complement(meet(X, complement(Y))) = join(Y, complement(X)).
1.97/2.17	Proof:
1.97/2.17	  complement(meet(X, complement(Y)))
1.97/2.17	= { by lemma 13 }
1.97/2.17	  complement(meet(complement(Y), X))
1.97/2.17	= { by lemma 30 }
1.97/2.17	  complement(meet(join(zero, complement(Y)), X))
1.97/2.17	= { by lemma 36 }
1.97/2.17	  join(complement(join(zero, complement(Y))), complement(X))
1.97/2.17	= { by lemma 16 }
1.97/2.17	  join(meet(Y, top), complement(X))
1.97/2.17	= { by lemma 31 }
1.97/2.18	  join(Y, complement(X))
1.97/2.18	
1.97/2.18	Lemma 39: join(meet(Y, complement(X)), complement(join(X, Y))) = complement(X).
1.97/2.18	Proof:
1.97/2.18	  join(meet(Y, complement(X)), complement(join(X, Y)))
1.97/2.18	= { by lemma 13 }
1.97/2.18	  join(meet(complement(X), Y), complement(join(X, Y)))
1.97/2.18	= { by lemma 30 }
1.97/2.18	  join(meet(join(zero, complement(X)), Y), complement(join(X, Y)))
1.97/2.18	= { by axiom 1 (maddux1_join_commutativity_1) }
1.97/2.18	  join(meet(join(zero, complement(X)), Y), complement(join(Y, X)))
1.97/2.18	= { by lemma 31 }
1.97/2.18	  join(meet(join(zero, complement(X)), Y), complement(join(Y, meet(X, top))))
1.97/2.18	= { by lemma 16 }
1.97/2.18	  join(meet(join(zero, complement(X)), Y), complement(join(Y, complement(join(zero, complement(X))))))
1.97/2.18	= { by axiom 1 (maddux1_join_commutativity_1) }
1.97/2.18	  join(meet(join(zero, complement(X)), Y), complement(join(complement(join(zero, complement(X))), Y)))
1.97/2.18	= { by lemma 14 }
1.97/2.18	  join(zero, complement(X))
1.97/2.18	= { by lemma 30 }
1.97/2.18	  complement(X)
1.97/2.18	
1.97/2.18	Lemma 40: join(X, complement(join(X, Y))) = join(X, complement(Y)).
1.97/2.18	Proof:
1.97/2.18	  join(X, complement(join(X, Y)))
1.97/2.18	= { by axiom 1 (maddux1_join_commutativity_1) }
1.97/2.18	  join(complement(join(X, Y)), X)
1.97/2.18	= { by lemma 32 }
1.97/2.18	  join(complement(join(X, complement(complement(Y)))), X)
1.97/2.18	= { by axiom 5 (converse_idempotence_8) }
1.97/2.18	  join(complement(join(X, complement(converse(converse(complement(Y)))))), X)
1.97/2.18	= { by lemma 29 }
1.97/2.18	  join(complement(join(X, complement(meet(converse(converse(complement(Y))), converse(join(converse(complement(Y)), converse(X))))))), X)
1.97/2.18	= { by axiom 5 (converse_idempotence_8) }
1.97/2.18	  join(complement(join(X, complement(meet(complement(Y), converse(join(converse(complement(Y)), converse(X))))))), X)
1.97/2.18	= { by axiom 11 (converse_additivity_9) }
1.97/2.18	  join(complement(join(X, complement(meet(complement(Y), converse(converse(join(complement(Y), X))))))), X)
1.97/2.18	= { by axiom 5 (converse_idempotence_8) }
1.97/2.18	  join(complement(join(X, complement(meet(complement(Y), join(complement(Y), X))))), X)
1.97/2.18	= { by axiom 1 (maddux1_join_commutativity_1) }
1.97/2.18	  join(complement(join(X, complement(meet(complement(Y), join(X, complement(Y)))))), X)
1.97/2.18	= { by lemma 13 }
1.97/2.18	  join(complement(join(X, complement(meet(join(X, complement(Y)), complement(Y))))), X)
1.97/2.18	= { by lemma 38 }
1.97/2.18	  join(complement(join(X, join(Y, complement(join(X, complement(Y)))))), X)
1.97/2.18	= { by lemma 37 }
1.97/2.18	  join(complement(join(X, join(Y, meet(Y, complement(X))))), X)
1.97/2.18	= { by axiom 6 (maddux2_join_associativity_2) }
1.97/2.18	  join(complement(join(join(X, Y), meet(Y, complement(X)))), X)
1.97/2.18	= { by axiom 1 (maddux1_join_commutativity_1) }
1.97/2.18	  join(complement(join(meet(Y, complement(X)), join(X, Y))), X)
1.97/2.18	= { by lemma 31 }
1.97/2.18	  join(complement(join(meet(Y, complement(X)), meet(join(X, Y), top))), X)
1.97/2.18	= { by lemma 16 }
1.97/2.18	  join(complement(join(meet(Y, complement(X)), complement(join(zero, complement(join(X, Y)))))), X)
1.97/2.18	= { by lemma 37 }
1.97/2.18	  join(meet(join(zero, complement(join(X, Y))), complement(meet(Y, complement(X)))), X)
1.97/2.18	= { by lemma 30 }
1.97/2.18	  join(meet(complement(join(X, Y)), complement(meet(Y, complement(X)))), X)
1.97/2.18	= { by lemma 32 }
1.97/2.18	  join(meet(complement(join(X, Y)), complement(meet(Y, complement(X)))), complement(complement(X)))
1.97/2.18	= { by lemma 39 }
1.97/2.18	  join(meet(complement(join(X, Y)), complement(meet(Y, complement(X)))), complement(join(meet(Y, complement(X)), complement(join(X, Y)))))
1.97/2.18	= { by lemma 39 }
1.97/2.18	  complement(meet(Y, complement(X)))
1.97/2.18	= { by lemma 38 }
1.97/2.18	  join(X, complement(Y))
1.97/2.18	
1.97/2.18	Lemma 41: meet(X, join(complement(X), Y)) = meet(X, Y).
1.97/2.18	Proof:
1.97/2.18	  meet(X, join(complement(X), Y))
1.97/2.18	= { by axiom 1 (maddux1_join_commutativity_1) }
1.97/2.18	  meet(X, join(Y, complement(X)))
1.97/2.18	= { by axiom 1 (maddux1_join_commutativity_1) }
1.97/2.18	  meet(X, join(complement(X), Y))
1.97/2.18	= { by axiom 2 (maddux4_definiton_of_meet_4) }
1.97/2.18	  complement(join(complement(X), complement(join(complement(X), Y))))
1.97/2.18	= { by lemma 40 }
1.97/2.18	  complement(join(complement(X), complement(Y)))
1.97/2.18	= { by axiom 2 (maddux4_definiton_of_meet_4) }
1.97/2.18	  meet(X, Y)
1.97/2.18	
1.97/2.18	Lemma 42: converse(join(converse(X), Y)) = join(X, converse(Y)).
1.97/2.18	Proof:
1.97/2.18	  converse(join(converse(X), Y))
1.97/2.18	= { by axiom 1 (maddux1_join_commutativity_1) }
1.97/2.18	  converse(join(Y, converse(X)))
1.97/2.18	= { by axiom 1 (maddux1_join_commutativity_1) }
1.97/2.18	  converse(join(converse(X), Y))
1.97/2.18	= { by axiom 11 (converse_additivity_9) }
1.97/2.18	  join(converse(converse(X)), converse(Y))
1.97/2.18	= { by axiom 5 (converse_idempotence_8) }
1.97/2.18	  join(X, converse(Y))
1.97/2.18	
1.97/2.18	Lemma 43: join(X, converse(top)) = converse(top).
1.97/2.18	Proof:
1.97/2.18	  join(X, converse(top))
1.97/2.18	= { by lemma 42 }
1.97/2.18	  converse(join(converse(X), top))
1.97/2.18	= { by lemma 22 }
1.97/2.18	  converse(top)
1.97/2.18	
1.97/2.18	Lemma 44: meet(complement(X), converse(complement(converse(X)))) = complement(X).
1.97/2.18	Proof:
1.97/2.18	  meet(complement(X), converse(complement(converse(X))))
1.97/2.18	= { by lemma 13 }
1.97/2.18	  meet(converse(complement(converse(X))), complement(X))
1.97/2.18	= { by lemma 27 }
1.97/2.18	  join(meet(converse(complement(converse(X))), complement(X)), zero)
1.97/2.18	= { by lemma 15 }
1.97/2.18	  join(meet(converse(complement(converse(X))), complement(X)), complement(top))
1.97/2.18	= { by lemma 22 }
1.97/2.18	  join(meet(converse(complement(converse(X))), complement(X)), complement(join(converse(top), top)))
1.97/2.18	= { by lemma 20 }
1.97/2.18	  join(meet(converse(complement(converse(X))), complement(X)), complement(join(?, join(complement(?), converse(top)))))
1.97/2.18	= { by lemma 43 }
1.97/2.18	  join(meet(converse(complement(converse(X))), complement(X)), complement(join(?, converse(top))))
1.97/2.18	= { by lemma 43 }
1.97/2.18	  join(meet(converse(complement(converse(X))), complement(X)), complement(converse(top)))
1.97/2.18	= { by axiom 9 (def_top_12) }
1.97/2.18	  join(meet(converse(complement(converse(X))), complement(X)), complement(converse(join(converse(X), complement(converse(X))))))
1.97/2.18	= { by lemma 42 }
1.97/2.18	  join(meet(converse(complement(converse(X))), complement(X)), complement(join(X, converse(complement(converse(X))))))
1.97/2.18	= { by lemma 39 }
2.05/2.28	  complement(X)
2.05/2.28	
2.05/2.28	Goal 1 (goals_17): meet(converse(sk1), converse(sk2)) = converse(meet(sk1, sk2)).
2.05/2.28	Proof:
2.05/2.28	  meet(converse(sk1), converse(sk2))
2.05/2.28	= { by lemma 41 }
2.05/2.28	  meet(converse(sk1), join(complement(converse(sk1)), converse(sk2)))
2.05/2.28	= { by lemma 42 }
2.05/2.28	  meet(converse(sk1), converse(join(converse(complement(converse(sk1))), sk2)))
2.05/2.28	= { by lemma 32 }
2.05/2.28	  meet(converse(sk1), converse(join(converse(complement(converse(sk1))), complement(complement(sk2)))))
2.05/2.28	= { by lemma 40 }
2.05/2.28	  meet(converse(sk1), converse(join(converse(complement(converse(sk1))), complement(join(converse(complement(converse(sk1))), complement(sk2))))))
2.05/2.28	= { by lemma 37 }
2.05/2.28	  meet(converse(sk1), converse(join(converse(complement(converse(sk1))), meet(sk2, complement(converse(complement(converse(sk1))))))))
2.05/2.28	= { by lemma 42 }
2.05/2.28	  meet(converse(sk1), join(complement(converse(sk1)), converse(meet(sk2, complement(converse(complement(converse(sk1))))))))
2.05/2.28	= { by axiom 5 (converse_idempotence_8) }
2.05/2.28	  meet(converse(sk1), join(complement(converse(sk1)), converse(meet(sk2, converse(converse(complement(converse(complement(converse(sk1))))))))))
2.05/2.28	= { by lemma 24 }
2.05/2.28	  meet(converse(sk1), join(complement(converse(sk1)), converse(meet(sk2, converse(join(meet(converse(complement(converse(complement(converse(sk1))))), complement(converse(sk1))), meet(converse(complement(converse(complement(converse(sk1))))), complement(complement(converse(sk1))))))))))
2.05/2.28	= { by lemma 13 }
2.05/2.28	  meet(converse(sk1), join(complement(converse(sk1)), converse(meet(sk2, converse(join(meet(complement(converse(sk1)), converse(complement(converse(complement(converse(sk1)))))), meet(converse(complement(converse(complement(converse(sk1))))), complement(complement(converse(sk1))))))))))
2.05/2.28	= { by axiom 5 (converse_idempotence_8) }
2.05/2.28	  meet(converse(sk1), join(complement(converse(sk1)), converse(meet(sk2, converse(join(meet(converse(converse(complement(converse(sk1)))), converse(complement(converse(complement(converse(sk1)))))), meet(converse(complement(converse(complement(converse(sk1))))), complement(complement(converse(sk1))))))))))
2.05/2.28	= { by lemma 13 }
2.05/2.28	  meet(converse(sk1), join(complement(converse(sk1)), converse(meet(sk2, converse(join(meet(converse(complement(converse(complement(converse(sk1))))), converse(converse(complement(converse(sk1))))), meet(converse(complement(converse(complement(converse(sk1))))), complement(complement(converse(sk1))))))))))
2.05/2.28	= { by lemma 35 }
2.05/2.28	  meet(converse(sk1), join(complement(converse(sk1)), converse(meet(sk2, converse(join(meet(converse(complement(converse(complement(converse(sk1))))), meet(top, converse(converse(complement(converse(sk1)))))), meet(converse(complement(converse(complement(converse(sk1))))), complement(complement(converse(sk1))))))))))
2.05/2.28	= { by lemma 31 }
2.05/2.28	  meet(converse(sk1), join(complement(converse(sk1)), converse(meet(sk2, converse(join(meet(meet(converse(complement(converse(complement(converse(sk1))))), meet(top, converse(converse(complement(converse(sk1)))))), top), meet(converse(complement(converse(complement(converse(sk1))))), complement(complement(converse(sk1))))))))))
2.05/2.28	= { by lemma 16 }
2.05/2.28	  meet(converse(sk1), join(complement(converse(sk1)), converse(meet(sk2, converse(join(complement(join(zero, complement(meet(converse(complement(converse(complement(converse(sk1))))), meet(top, converse(converse(complement(converse(sk1))))))))), meet(converse(complement(converse(complement(converse(sk1))))), complement(complement(converse(sk1))))))))))
2.05/2.28	= { by axiom 2 (maddux4_definiton_of_meet_4) }
2.05/2.29	  meet(converse(sk1), join(complement(converse(sk1)), converse(meet(sk2, converse(join(complement(join(zero, complement(meet(converse(complement(converse(complement(converse(sk1))))), complement(join(complement(top), complement(converse(converse(complement(converse(sk1))))))))))), meet(converse(complement(converse(complement(converse(sk1))))), complement(complement(converse(sk1))))))))))
2.05/2.29	= { by lemma 38 }
2.05/2.29	  meet(converse(sk1), join(complement(converse(sk1)), converse(meet(sk2, converse(join(complement(join(zero, join(join(complement(top), complement(converse(converse(complement(converse(sk1)))))), complement(converse(complement(converse(complement(converse(sk1))))))))), meet(converse(complement(converse(complement(converse(sk1))))), complement(complement(converse(sk1))))))))))
2.05/2.29	= { by axiom 6 (maddux2_join_associativity_2) }
2.05/2.29	  meet(converse(sk1), join(complement(converse(sk1)), converse(meet(sk2, converse(join(complement(join(zero, join(complement(top), join(complement(converse(converse(complement(converse(sk1))))), complement(converse(complement(converse(complement(converse(sk1)))))))))), meet(converse(complement(converse(complement(converse(sk1))))), complement(complement(converse(sk1))))))))))
2.05/2.29	= { by lemma 36 }
2.05/2.29	  meet(converse(sk1), join(complement(converse(sk1)), converse(meet(sk2, converse(join(complement(join(zero, join(complement(top), complement(meet(converse(converse(complement(converse(sk1)))), converse(complement(converse(complement(converse(sk1)))))))))), meet(converse(complement(converse(complement(converse(sk1))))), complement(complement(converse(sk1))))))))))
2.05/2.29	= { by lemma 36 }
2.05/2.29	  meet(converse(sk1), join(complement(converse(sk1)), converse(meet(sk2, converse(join(complement(join(zero, complement(meet(top, meet(converse(converse(complement(converse(sk1)))), converse(complement(converse(complement(converse(sk1)))))))))), meet(converse(complement(converse(complement(converse(sk1))))), complement(complement(converse(sk1))))))))))
2.05/2.29	= { by lemma 16 }
2.05/2.29	  meet(converse(sk1), join(complement(converse(sk1)), converse(meet(sk2, converse(join(meet(meet(top, meet(converse(converse(complement(converse(sk1)))), converse(complement(converse(complement(converse(sk1))))))), top), meet(converse(complement(converse(complement(converse(sk1))))), complement(complement(converse(sk1))))))))))
2.05/2.29	= { by lemma 31 }
2.05/2.29	  meet(converse(sk1), join(complement(converse(sk1)), converse(meet(sk2, converse(join(meet(top, meet(converse(converse(complement(converse(sk1)))), converse(complement(converse(complement(converse(sk1))))))), meet(converse(complement(converse(complement(converse(sk1))))), complement(complement(converse(sk1))))))))))
2.05/2.29	= { by lemma 13 }
2.05/2.29	  meet(converse(sk1), join(complement(converse(sk1)), converse(meet(sk2, converse(join(meet(meet(converse(converse(complement(converse(sk1)))), converse(complement(converse(complement(converse(sk1)))))), top), meet(converse(complement(converse(complement(converse(sk1))))), complement(complement(converse(sk1))))))))))
2.05/2.29	= { by lemma 28 }
2.05/2.29	  meet(converse(sk1), join(complement(converse(sk1)), converse(meet(sk2, converse(join(meet(meet(converse(converse(complement(converse(sk1)))), converse(complement(converse(complement(converse(sk1)))))), join(complement(converse(meet(converse(complement(converse(converse(complement(converse(sk1)))))), complement(converse(complement(converse(sk1))))))), converse(join(meet(converse(complement(converse(converse(complement(converse(sk1)))))), complement(converse(complement(converse(sk1))))), complement(join(complement(converse(complement(converse(converse(complement(converse(sk1))))))), complement(converse(complement(converse(sk1)))))))))), meet(converse(complement(converse(complement(converse(sk1))))), complement(complement(converse(sk1))))))))))
2.05/2.29	= { by lemma 14 }
2.05/2.29	  meet(converse(sk1), join(complement(converse(sk1)), converse(meet(sk2, converse(join(meet(meet(converse(converse(complement(converse(sk1)))), converse(complement(converse(complement(converse(sk1)))))), join(complement(converse(meet(converse(complement(converse(converse(complement(converse(sk1)))))), complement(converse(complement(converse(sk1))))))), converse(converse(complement(converse(converse(complement(converse(sk1))))))))), meet(converse(complement(converse(complement(converse(sk1))))), complement(complement(converse(sk1))))))))))
2.05/2.29	= { by axiom 1 (maddux1_join_commutativity_1) }
2.05/2.29	  meet(converse(sk1), join(complement(converse(sk1)), converse(meet(sk2, converse(join(meet(meet(converse(converse(complement(converse(sk1)))), converse(complement(converse(complement(converse(sk1)))))), join(converse(converse(complement(converse(converse(complement(converse(sk1))))))), complement(converse(meet(converse(complement(converse(converse(complement(converse(sk1)))))), complement(converse(complement(converse(sk1))))))))), meet(converse(complement(converse(complement(converse(sk1))))), complement(complement(converse(sk1))))))))))
2.05/2.29	= { by axiom 5 (converse_idempotence_8) }
2.05/2.29	  meet(converse(sk1), join(complement(converse(sk1)), converse(meet(sk2, converse(join(meet(meet(converse(converse(complement(converse(sk1)))), converse(complement(converse(complement(converse(sk1)))))), join(complement(converse(converse(complement(converse(sk1))))), complement(converse(meet(converse(complement(converse(converse(complement(converse(sk1)))))), complement(converse(complement(converse(sk1))))))))), meet(converse(complement(converse(complement(converse(sk1))))), complement(complement(converse(sk1))))))))))
2.05/2.29	= { by lemma 13 }
2.05/2.29	  meet(converse(sk1), join(complement(converse(sk1)), converse(meet(sk2, converse(join(meet(meet(converse(converse(complement(converse(sk1)))), converse(complement(converse(complement(converse(sk1)))))), join(complement(converse(converse(complement(converse(sk1))))), complement(converse(meet(complement(converse(complement(converse(sk1)))), converse(complement(converse(converse(complement(converse(sk1))))))))))), meet(converse(complement(converse(complement(converse(sk1))))), complement(complement(converse(sk1))))))))))
2.05/2.29	= { by lemma 44 }
2.05/2.29	  meet(converse(sk1), join(complement(converse(sk1)), converse(meet(sk2, converse(join(meet(meet(converse(converse(complement(converse(sk1)))), converse(complement(converse(complement(converse(sk1)))))), join(complement(converse(converse(complement(converse(sk1))))), complement(converse(complement(converse(complement(converse(sk1)))))))), meet(converse(complement(converse(complement(converse(sk1))))), complement(complement(converse(sk1))))))))))
2.05/2.29	= { by lemma 36 }
2.05/2.29	  meet(converse(sk1), join(complement(converse(sk1)), converse(meet(sk2, converse(join(meet(meet(converse(converse(complement(converse(sk1)))), converse(complement(converse(complement(converse(sk1)))))), complement(meet(converse(converse(complement(converse(sk1)))), converse(complement(converse(complement(converse(sk1)))))))), meet(converse(complement(converse(complement(converse(sk1))))), complement(complement(converse(sk1))))))))))
2.05/2.29	= { by axiom 8 (def_zero_13) }
2.05/2.29	  meet(converse(sk1), join(complement(converse(sk1)), converse(meet(sk2, converse(join(zero, meet(converse(complement(converse(complement(converse(sk1))))), complement(complement(converse(sk1))))))))))
2.05/2.29	= { by lemma 13 }
2.05/2.29	  meet(converse(sk1), join(complement(converse(sk1)), converse(meet(sk2, converse(join(zero, meet(complement(complement(converse(sk1))), converse(complement(converse(complement(converse(sk1))))))))))))
2.05/2.29	= { by lemma 30 }
2.05/2.29	  meet(converse(sk1), join(complement(converse(sk1)), converse(meet(sk2, converse(meet(complement(complement(converse(sk1))), converse(complement(converse(complement(converse(sk1)))))))))))
2.05/2.29	= { by lemma 44 }
2.05/2.29	  meet(converse(sk1), join(complement(converse(sk1)), converse(meet(sk2, converse(complement(complement(converse(sk1))))))))
2.05/2.29	= { by lemma 41 }
2.05/2.29	  meet(converse(sk1), converse(meet(sk2, converse(complement(complement(converse(sk1)))))))
2.05/2.29	= { by axiom 5 (converse_idempotence_8) }
2.05/2.29	  meet(converse(converse(converse(sk1))), converse(meet(sk2, converse(complement(complement(converse(sk1)))))))
2.05/2.29	= { by lemma 32 }
2.05/2.29	  meet(converse(converse(converse(sk1))), converse(meet(sk2, converse(converse(sk1)))))
2.05/2.29	= { by lemma 13 }
2.05/2.29	  meet(converse(converse(converse(sk1))), converse(meet(converse(converse(sk1)), sk2)))
2.05/2.29	= { by lemma 13 }
2.05/2.29	  meet(converse(meet(converse(converse(sk1)), sk2)), converse(converse(converse(sk1))))
2.05/2.29	= { by lemma 14 }
2.05/2.29	  meet(converse(meet(converse(converse(sk1)), sk2)), converse(join(meet(converse(converse(sk1)), sk2), complement(join(complement(converse(converse(sk1))), sk2)))))
2.05/2.29	= { by lemma 29 }
2.05/2.29	  converse(meet(converse(converse(sk1)), sk2))
2.05/2.29	= { by lemma 13 }
2.05/2.29	  converse(meet(sk2, converse(converse(sk1))))
2.05/2.29	= { by axiom 5 (converse_idempotence_8) }
2.05/2.29	  converse(meet(sk2, sk1))
2.05/2.29	= { by lemma 13 }
2.05/2.29	  converse(meet(sk1, sk2))
2.05/2.29	% SZS output end Proof
2.05/2.29	
2.05/2.29	RESULT: Unsatisfiable (the axioms are contradictory).
2.05/2.29	EOF