TSTP Solution File: REL023+2 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : REL023+2 : TPTP v8.1.2. Released v4.0.0.
% 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 : n002.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 13:44:04 EDT 2023
% Result : Theorem 0.20s 0.45s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : REL023+2 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n002.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Aug 25 20:44:02 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.45 Command-line arguments: --no-flatten-goal
% 0.20/0.45
% 0.20/0.45 % SZS status Theorem
% 0.20/0.45
% 0.20/0.48 % SZS output start Proof
% 0.20/0.48 Axiom 1 (converse_idempotence): converse(converse(X)) = X.
% 0.20/0.48 Axiom 2 (maddux1_join_commutativity): join(X, Y) = join(Y, X).
% 0.20/0.48 Axiom 3 (composition_identity): composition(X, one) = X.
% 0.20/0.48 Axiom 4 (def_top): top = join(X, complement(X)).
% 0.20/0.48 Axiom 5 (def_zero): zero = meet(X, complement(X)).
% 0.20/0.48 Axiom 6 (maddux2_join_associativity): join(X, join(Y, Z)) = join(join(X, Y), Z).
% 0.20/0.48 Axiom 7 (converse_multiplicativity): converse(composition(X, Y)) = composition(converse(Y), converse(X)).
% 0.20/0.48 Axiom 8 (composition_associativity): composition(X, composition(Y, Z)) = composition(composition(X, Y), Z).
% 0.20/0.48 Axiom 9 (maddux4_definiton_of_meet): meet(X, Y) = complement(join(complement(X), complement(Y))).
% 0.20/0.48 Axiom 10 (composition_distributivity): composition(join(X, Y), Z) = join(composition(X, Z), composition(Y, Z)).
% 0.20/0.48 Axiom 11 (converse_cancellativity): join(composition(converse(X), complement(composition(X, Y))), complement(Y)) = complement(Y).
% 0.20/0.48 Axiom 12 (maddux3_a_kind_of_de_Morgan): X = join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y))).
% 0.20/0.48
% 0.20/0.48 Lemma 13: complement(top) = zero.
% 0.20/0.48 Proof:
% 0.20/0.48 complement(top)
% 0.20/0.48 = { by axiom 4 (def_top) }
% 0.20/0.48 complement(join(complement(X), complement(complement(X))))
% 0.20/0.48 = { by axiom 9 (maddux4_definiton_of_meet) R->L }
% 0.20/0.48 meet(X, complement(X))
% 0.20/0.48 = { by axiom 5 (def_zero) R->L }
% 0.20/0.48 zero
% 0.20/0.48
% 0.20/0.48 Lemma 14: join(X, join(Y, complement(X))) = join(Y, top).
% 0.20/0.48 Proof:
% 0.20/0.48 join(X, join(Y, complement(X)))
% 0.20/0.48 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 0.20/0.48 join(X, join(complement(X), Y))
% 0.20/0.48 = { by axiom 6 (maddux2_join_associativity) }
% 0.20/0.48 join(join(X, complement(X)), Y)
% 0.20/0.48 = { by axiom 4 (def_top) R->L }
% 0.20/0.48 join(top, Y)
% 0.20/0.48 = { by axiom 2 (maddux1_join_commutativity) }
% 0.20/0.49 join(Y, top)
% 0.20/0.49
% 0.20/0.49 Lemma 15: composition(converse(one), X) = X.
% 0.20/0.49 Proof:
% 0.20/0.49 composition(converse(one), X)
% 0.20/0.49 = { by axiom 1 (converse_idempotence) R->L }
% 0.20/0.49 composition(converse(one), converse(converse(X)))
% 0.20/0.49 = { by axiom 7 (converse_multiplicativity) R->L }
% 0.20/0.49 converse(composition(converse(X), one))
% 0.20/0.49 = { by axiom 3 (composition_identity) }
% 0.20/0.49 converse(converse(X))
% 0.20/0.49 = { by axiom 1 (converse_idempotence) }
% 0.20/0.49 X
% 0.20/0.49
% 0.20/0.49 Lemma 16: join(complement(X), complement(X)) = complement(X).
% 0.20/0.49 Proof:
% 0.20/0.49 join(complement(X), complement(X))
% 0.20/0.49 = { by lemma 15 R->L }
% 0.20/0.49 join(complement(X), composition(converse(one), complement(X)))
% 0.20/0.49 = { by lemma 15 R->L }
% 0.20/0.49 join(complement(X), composition(converse(one), complement(composition(converse(one), X))))
% 0.20/0.49 = { by axiom 3 (composition_identity) R->L }
% 0.20/0.49 join(complement(X), composition(converse(one), complement(composition(composition(converse(one), one), X))))
% 0.20/0.49 = { by axiom 8 (composition_associativity) R->L }
% 0.20/0.49 join(complement(X), composition(converse(one), complement(composition(converse(one), composition(one, X)))))
% 0.20/0.49 = { by lemma 15 }
% 0.20/0.49 join(complement(X), composition(converse(one), complement(composition(one, X))))
% 0.20/0.49 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 0.20/0.49 join(composition(converse(one), complement(composition(one, X))), complement(X))
% 0.20/0.49 = { by axiom 11 (converse_cancellativity) }
% 0.20/0.49 complement(X)
% 0.20/0.49
% 0.20/0.49 Lemma 17: join(top, complement(X)) = top.
% 0.20/0.49 Proof:
% 0.20/0.49 join(top, complement(X))
% 0.20/0.49 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 0.20/0.49 join(complement(X), top)
% 0.20/0.49 = { by lemma 14 R->L }
% 0.20/0.49 join(X, join(complement(X), complement(X)))
% 0.20/0.49 = { by lemma 16 }
% 0.20/0.49 join(X, complement(X))
% 0.20/0.49 = { by axiom 4 (def_top) R->L }
% 0.20/0.49 top
% 0.20/0.49
% 0.20/0.49 Lemma 18: join(meet(X, Y), complement(join(complement(X), Y))) = X.
% 0.20/0.49 Proof:
% 0.20/0.49 join(meet(X, Y), complement(join(complement(X), Y)))
% 0.20/0.49 = { by axiom 9 (maddux4_definiton_of_meet) }
% 0.20/0.49 join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y)))
% 0.20/0.49 = { by axiom 12 (maddux3_a_kind_of_de_Morgan) R->L }
% 0.20/0.49 X
% 0.20/0.49
% 0.20/0.49 Lemma 19: join(zero, meet(X, X)) = X.
% 0.20/0.49 Proof:
% 0.20/0.49 join(zero, meet(X, X))
% 0.20/0.49 = { by axiom 9 (maddux4_definiton_of_meet) }
% 0.20/0.49 join(zero, complement(join(complement(X), complement(X))))
% 0.20/0.49 = { by axiom 5 (def_zero) }
% 0.20/0.49 join(meet(X, complement(X)), complement(join(complement(X), complement(X))))
% 0.20/0.49 = { by lemma 18 }
% 0.20/0.49 X
% 0.20/0.49
% 0.20/0.49 Lemma 20: join(zero, join(X, complement(complement(Y)))) = join(X, Y).
% 0.20/0.49 Proof:
% 0.20/0.49 join(zero, join(X, complement(complement(Y))))
% 0.20/0.49 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 0.20/0.49 join(zero, join(complement(complement(Y)), X))
% 0.20/0.49 = { by lemma 16 R->L }
% 0.20/0.49 join(zero, join(complement(join(complement(Y), complement(Y))), X))
% 0.20/0.49 = { by axiom 9 (maddux4_definiton_of_meet) R->L }
% 0.20/0.49 join(zero, join(meet(Y, Y), X))
% 0.20/0.49 = { by axiom 6 (maddux2_join_associativity) }
% 0.20/0.49 join(join(zero, meet(Y, Y)), X)
% 0.20/0.49 = { by lemma 19 }
% 0.20/0.49 join(Y, X)
% 0.20/0.49 = { by axiom 2 (maddux1_join_commutativity) }
% 0.20/0.49 join(X, Y)
% 0.20/0.49
% 0.20/0.49 Lemma 21: join(zero, complement(complement(X))) = X.
% 0.20/0.49 Proof:
% 0.20/0.49 join(zero, complement(complement(X)))
% 0.20/0.49 = { by axiom 5 (def_zero) }
% 0.20/0.49 join(meet(X, complement(X)), complement(complement(X)))
% 0.20/0.49 = { by lemma 16 R->L }
% 0.20/0.49 join(meet(X, complement(X)), complement(join(complement(X), complement(X))))
% 0.20/0.49 = { by lemma 18 }
% 0.20/0.49 X
% 0.20/0.49
% 0.20/0.49 Lemma 22: join(zero, complement(X)) = complement(X).
% 0.20/0.49 Proof:
% 0.20/0.49 join(zero, complement(X))
% 0.20/0.49 = { by lemma 21 R->L }
% 0.20/0.49 join(zero, join(zero, complement(complement(complement(X)))))
% 0.20/0.49 = { by lemma 16 R->L }
% 0.20/0.49 join(zero, join(zero, join(complement(complement(complement(X))), complement(complement(complement(X))))))
% 0.20/0.49 = { by lemma 20 }
% 0.20/0.49 join(zero, join(complement(complement(complement(X))), complement(X)))
% 0.20/0.49 = { by axiom 2 (maddux1_join_commutativity) }
% 0.20/0.49 join(zero, join(complement(X), complement(complement(complement(X)))))
% 0.20/0.49 = { by lemma 20 }
% 0.20/0.49 join(complement(X), complement(X))
% 0.20/0.49 = { by lemma 16 }
% 0.20/0.49 complement(X)
% 0.20/0.49
% 0.20/0.49 Lemma 23: join(X, zero) = X.
% 0.20/0.49 Proof:
% 0.20/0.49 join(X, zero)
% 0.20/0.49 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 0.20/0.49 join(zero, X)
% 0.20/0.49 = { by lemma 20 R->L }
% 0.20/0.49 join(zero, join(zero, complement(complement(X))))
% 0.20/0.49 = { by lemma 22 }
% 0.20/0.49 join(zero, complement(complement(X)))
% 0.20/0.49 = { by lemma 21 }
% 0.20/0.49 X
% 0.20/0.49
% 0.20/0.49 Lemma 24: join(X, top) = top.
% 0.20/0.49 Proof:
% 0.20/0.49 join(X, top)
% 0.20/0.49 = { by lemma 17 R->L }
% 0.20/0.49 join(X, join(top, complement(X)))
% 0.20/0.49 = { by lemma 14 }
% 0.20/0.49 join(top, top)
% 0.20/0.49 = { by lemma 14 R->L }
% 0.20/0.49 join(join(zero, zero), join(top, complement(join(zero, zero))))
% 0.20/0.49 = { by lemma 17 }
% 0.20/0.49 join(join(zero, zero), top)
% 0.20/0.49 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 0.20/0.49 join(top, join(zero, zero))
% 0.20/0.49 = { by lemma 23 }
% 0.20/0.49 join(top, zero)
% 0.20/0.49 = { by lemma 23 }
% 0.20/0.49 top
% 0.20/0.49
% 0.20/0.49 Lemma 25: meet(Y, X) = meet(X, Y).
% 0.20/0.49 Proof:
% 0.20/0.49 meet(Y, X)
% 0.20/0.49 = { by axiom 9 (maddux4_definiton_of_meet) }
% 0.20/0.49 complement(join(complement(Y), complement(X)))
% 0.20/0.49 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 0.20/0.49 complement(join(complement(X), complement(Y)))
% 0.20/0.49 = { by axiom 9 (maddux4_definiton_of_meet) R->L }
% 0.20/0.49 meet(X, Y)
% 0.20/0.49
% 0.20/0.49 Lemma 26: complement(join(zero, complement(X))) = meet(X, top).
% 0.20/0.49 Proof:
% 0.20/0.49 complement(join(zero, complement(X)))
% 0.20/0.49 = { by lemma 13 R->L }
% 0.20/0.49 complement(join(complement(top), complement(X)))
% 0.20/0.49 = { by axiom 9 (maddux4_definiton_of_meet) R->L }
% 0.20/0.49 meet(top, X)
% 0.20/0.49 = { by lemma 25 R->L }
% 0.20/0.49 meet(X, top)
% 0.20/0.49
% 0.20/0.49 Lemma 27: join(X, complement(zero)) = top.
% 0.20/0.49 Proof:
% 0.20/0.49 join(X, complement(zero))
% 0.20/0.49 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 0.20/0.49 join(complement(zero), X)
% 0.20/0.49 = { by lemma 20 R->L }
% 0.20/0.49 join(zero, join(complement(zero), complement(complement(X))))
% 0.20/0.49 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 0.20/0.49 join(zero, join(complement(complement(X)), complement(zero)))
% 0.20/0.49 = { by lemma 14 }
% 0.20/0.49 join(complement(complement(X)), top)
% 0.20/0.49 = { by lemma 24 }
% 0.20/0.49 top
% 0.20/0.49
% 0.20/0.49 Lemma 28: meet(X, top) = X.
% 0.20/0.49 Proof:
% 0.20/0.49 meet(X, top)
% 0.20/0.49 = { by lemma 26 R->L }
% 0.20/0.49 complement(join(zero, complement(X)))
% 0.20/0.49 = { by lemma 22 R->L }
% 0.20/0.49 join(zero, complement(join(zero, complement(X))))
% 0.20/0.49 = { by lemma 26 }
% 0.20/0.49 join(zero, meet(X, top))
% 0.20/0.49 = { by lemma 27 R->L }
% 0.20/0.49 join(zero, meet(X, join(complement(zero), complement(zero))))
% 0.20/0.49 = { by lemma 16 }
% 0.20/0.49 join(zero, meet(X, complement(zero)))
% 0.20/0.49 = { by lemma 13 R->L }
% 0.20/0.49 join(complement(top), meet(X, complement(zero)))
% 0.20/0.49 = { by lemma 27 R->L }
% 0.20/0.49 join(complement(join(complement(X), complement(zero))), meet(X, complement(zero)))
% 0.20/0.49 = { by axiom 9 (maddux4_definiton_of_meet) R->L }
% 0.20/0.49 join(meet(X, zero), meet(X, complement(zero)))
% 0.20/0.49 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 0.20/0.49 join(meet(X, complement(zero)), meet(X, zero))
% 0.20/0.49 = { by axiom 9 (maddux4_definiton_of_meet) }
% 0.20/0.49 join(meet(X, complement(zero)), complement(join(complement(X), complement(zero))))
% 0.20/0.49 = { by lemma 18 }
% 0.20/0.49 X
% 0.20/0.49
% 0.20/0.49 Lemma 29: meet(X, join(complement(Y), complement(Z))) = complement(join(complement(X), meet(Y, Z))).
% 0.20/0.49 Proof:
% 0.20/0.49 meet(X, join(complement(Y), complement(Z)))
% 0.20/0.49 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 0.20/0.49 meet(X, join(complement(Z), complement(Y)))
% 0.20/0.49 = { by lemma 25 }
% 0.20/0.49 meet(join(complement(Z), complement(Y)), X)
% 0.20/0.49 = { by axiom 9 (maddux4_definiton_of_meet) }
% 0.20/0.49 complement(join(complement(join(complement(Z), complement(Y))), complement(X)))
% 0.20/0.49 = { by axiom 9 (maddux4_definiton_of_meet) R->L }
% 0.20/0.49 complement(join(meet(Z, Y), complement(X)))
% 0.20/0.49 = { by axiom 2 (maddux1_join_commutativity) }
% 0.20/0.49 complement(join(complement(X), meet(Z, Y)))
% 0.20/0.49 = { by lemma 25 R->L }
% 0.20/0.49 complement(join(complement(X), meet(Y, Z)))
% 0.20/0.49
% 0.20/0.49 Lemma 30: complement(join(X, complement(Y))) = meet(Y, complement(X)).
% 0.20/0.49 Proof:
% 0.20/0.49 complement(join(X, complement(Y)))
% 0.20/0.49 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 0.20/0.49 complement(join(complement(Y), X))
% 0.20/0.49 = { by lemma 28 R->L }
% 0.20/0.49 complement(join(complement(Y), meet(X, top)))
% 0.20/0.49 = { by lemma 25 R->L }
% 0.20/0.49 complement(join(complement(Y), meet(top, X)))
% 0.20/0.49 = { by lemma 29 R->L }
% 0.20/0.49 meet(Y, join(complement(top), complement(X)))
% 0.20/0.49 = { by lemma 13 }
% 0.20/0.49 meet(Y, join(zero, complement(X)))
% 0.20/0.49 = { by lemma 22 }
% 0.20/0.49 meet(Y, complement(X))
% 0.20/0.49
% 0.20/0.49 Lemma 31: complement(meet(X, complement(Y))) = join(Y, complement(X)).
% 0.20/0.49 Proof:
% 0.20/0.49 complement(meet(X, complement(Y)))
% 0.20/0.49 = { by lemma 23 R->L }
% 0.20/0.49 complement(join(meet(X, complement(Y)), zero))
% 0.20/0.49 = { by axiom 2 (maddux1_join_commutativity) }
% 0.20/0.49 complement(join(zero, meet(X, complement(Y))))
% 0.20/0.49 = { by lemma 30 R->L }
% 0.20/0.49 complement(join(zero, complement(join(Y, complement(X)))))
% 0.20/0.49 = { by lemma 26 }
% 0.20/0.49 meet(join(Y, complement(X)), top)
% 0.20/0.49 = { by lemma 28 }
% 0.20/0.49 join(Y, complement(X))
% 0.20/0.49
% 0.20/0.49 Goal 1 (goals): join(composition(meet(x0, converse(x1)), meet(x1, x2)), composition(x0, meet(x1, x2))) = composition(x0, meet(x1, x2)).
% 0.20/0.49 Proof:
% 0.20/0.49 join(composition(meet(x0, converse(x1)), meet(x1, x2)), composition(x0, meet(x1, x2)))
% 0.20/0.49 = { by axiom 2 (maddux1_join_commutativity) }
% 0.20/0.49 join(composition(x0, meet(x1, x2)), composition(meet(x0, converse(x1)), meet(x1, x2)))
% 0.20/0.49 = { by axiom 10 (composition_distributivity) R->L }
% 0.20/0.49 composition(join(x0, meet(x0, converse(x1))), meet(x1, x2))
% 0.20/0.50 = { by lemma 25 R->L }
% 0.20/0.50 composition(join(x0, meet(x0, converse(x1))), meet(x2, x1))
% 0.20/0.50 = { by axiom 9 (maddux4_definiton_of_meet) }
% 0.20/0.50 composition(join(x0, complement(join(complement(x0), complement(converse(x1))))), meet(x2, x1))
% 0.20/0.50 = { by lemma 31 R->L }
% 0.20/0.50 composition(complement(meet(join(complement(x0), complement(converse(x1))), complement(x0))), meet(x2, x1))
% 0.20/0.50 = { by lemma 25 R->L }
% 0.20/0.50 composition(complement(meet(complement(x0), join(complement(x0), complement(converse(x1))))), meet(x2, x1))
% 0.20/0.50 = { by lemma 31 R->L }
% 0.20/0.50 composition(complement(meet(complement(x0), complement(meet(converse(x1), complement(complement(x0)))))), meet(x2, x1))
% 0.20/0.50 = { by lemma 30 R->L }
% 0.20/0.50 composition(complement(complement(join(meet(converse(x1), complement(complement(x0))), complement(complement(x0))))), meet(x2, x1))
% 0.20/0.50 = { by axiom 2 (maddux1_join_commutativity) }
% 0.20/0.50 composition(complement(complement(join(complement(complement(x0)), meet(converse(x1), complement(complement(x0)))))), meet(x2, x1))
% 0.20/0.50 = { by lemma 22 R->L }
% 0.20/0.50 composition(complement(join(zero, complement(join(complement(complement(x0)), meet(converse(x1), complement(complement(x0))))))), meet(x2, x1))
% 0.20/0.50 = { by lemma 13 R->L }
% 0.20/0.50 composition(complement(join(complement(top), complement(join(complement(complement(x0)), meet(converse(x1), complement(complement(x0))))))), meet(x2, x1))
% 0.20/0.50 = { by lemma 24 R->L }
% 0.20/0.50 composition(complement(join(complement(join(complement(converse(x1)), top)), complement(join(complement(complement(x0)), meet(converse(x1), complement(complement(x0))))))), meet(x2, x1))
% 0.20/0.50 = { by lemma 14 R->L }
% 0.20/0.50 composition(complement(join(complement(join(complement(complement(x0)), join(complement(converse(x1)), complement(complement(complement(x0)))))), complement(join(complement(complement(x0)), meet(converse(x1), complement(complement(x0))))))), meet(x2, x1))
% 0.20/0.50 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 0.20/0.50 composition(complement(join(complement(join(complement(complement(x0)), join(complement(complement(complement(x0))), complement(converse(x1))))), complement(join(complement(complement(x0)), meet(converse(x1), complement(complement(x0))))))), meet(x2, x1))
% 0.20/0.50 = { by lemma 19 R->L }
% 0.20/0.50 composition(complement(join(complement(join(complement(complement(x0)), join(zero, meet(join(complement(complement(complement(x0))), complement(converse(x1))), join(complement(complement(complement(x0))), complement(converse(x1))))))), complement(join(complement(complement(x0)), meet(converse(x1), complement(complement(x0))))))), meet(x2, x1))
% 0.20/0.50 = { by lemma 29 }
% 0.20/0.50 composition(complement(join(complement(join(complement(complement(x0)), join(zero, complement(join(complement(join(complement(complement(complement(x0))), complement(converse(x1)))), meet(complement(complement(x0)), converse(x1))))))), complement(join(complement(complement(x0)), meet(converse(x1), complement(complement(x0))))))), meet(x2, x1))
% 0.20/0.50 = { by lemma 22 }
% 0.20/0.50 composition(complement(join(complement(join(complement(complement(x0)), complement(join(complement(join(complement(complement(complement(x0))), complement(converse(x1)))), meet(complement(complement(x0)), converse(x1)))))), complement(join(complement(complement(x0)), meet(converse(x1), complement(complement(x0))))))), meet(x2, x1))
% 0.20/0.50 = { by axiom 9 (maddux4_definiton_of_meet) R->L }
% 0.20/0.50 composition(complement(join(complement(join(complement(complement(x0)), complement(join(meet(complement(complement(x0)), converse(x1)), meet(complement(complement(x0)), converse(x1)))))), complement(join(complement(complement(x0)), meet(converse(x1), complement(complement(x0))))))), meet(x2, x1))
% 0.20/0.50 = { by lemma 25 }
% 0.20/0.50 composition(complement(join(complement(join(complement(complement(x0)), complement(join(meet(converse(x1), complement(complement(x0))), meet(complement(complement(x0)), converse(x1)))))), complement(join(complement(complement(x0)), meet(converse(x1), complement(complement(x0))))))), meet(x2, x1))
% 0.20/0.50 = { by lemma 25 }
% 0.20/0.50 composition(complement(join(complement(join(complement(complement(x0)), complement(join(meet(converse(x1), complement(complement(x0))), meet(converse(x1), complement(complement(x0))))))), complement(join(complement(complement(x0)), meet(converse(x1), complement(complement(x0))))))), meet(x2, x1))
% 0.20/0.50 = { by axiom 9 (maddux4_definiton_of_meet) }
% 0.20/0.50 composition(complement(join(complement(join(complement(complement(x0)), complement(join(meet(converse(x1), complement(complement(x0))), complement(join(complement(converse(x1)), complement(complement(complement(x0))))))))), complement(join(complement(complement(x0)), meet(converse(x1), complement(complement(x0))))))), meet(x2, x1))
% 0.20/0.50 = { by axiom 9 (maddux4_definiton_of_meet) }
% 0.20/0.50 composition(complement(join(complement(join(complement(complement(x0)), complement(join(complement(join(complement(converse(x1)), complement(complement(complement(x0))))), complement(join(complement(converse(x1)), complement(complement(complement(x0))))))))), complement(join(complement(complement(x0)), meet(converse(x1), complement(complement(x0))))))), meet(x2, x1))
% 0.20/0.50 = { by lemma 16 }
% 0.20/0.50 composition(complement(join(complement(join(complement(complement(x0)), complement(complement(join(complement(converse(x1)), complement(complement(complement(x0)))))))), complement(join(complement(complement(x0)), meet(converse(x1), complement(complement(x0))))))), meet(x2, x1))
% 0.20/0.50 = { by axiom 9 (maddux4_definiton_of_meet) R->L }
% 0.20/0.50 composition(complement(join(complement(join(complement(complement(x0)), complement(meet(converse(x1), complement(complement(x0)))))), complement(join(complement(complement(x0)), meet(converse(x1), complement(complement(x0))))))), meet(x2, x1))
% 0.20/0.50 = { by lemma 25 R->L }
% 0.20/0.50 composition(complement(join(complement(join(complement(complement(x0)), complement(meet(complement(complement(x0)), converse(x1))))), complement(join(complement(complement(x0)), meet(converse(x1), complement(complement(x0))))))), meet(x2, x1))
% 0.20/0.50 = { by axiom 9 (maddux4_definiton_of_meet) R->L }
% 0.20/0.50 composition(complement(join(meet(complement(x0), meet(complement(complement(x0)), converse(x1))), complement(join(complement(complement(x0)), meet(converse(x1), complement(complement(x0))))))), meet(x2, x1))
% 0.20/0.50 = { by lemma 25 R->L }
% 0.20/0.50 composition(complement(join(meet(complement(x0), meet(converse(x1), complement(complement(x0)))), complement(join(complement(complement(x0)), meet(converse(x1), complement(complement(x0))))))), meet(x2, x1))
% 0.20/0.50 = { by lemma 18 }
% 0.20/0.50 composition(complement(complement(x0)), meet(x2, x1))
% 0.20/0.50 = { by lemma 22 R->L }
% 0.20/0.50 composition(join(zero, complement(complement(x0))), meet(x2, x1))
% 0.20/0.50 = { by lemma 21 }
% 0.20/0.50 composition(x0, meet(x2, x1))
% 0.20/0.50 = { by lemma 25 }
% 0.20/0.50 composition(x0, meet(x1, x2))
% 0.20/0.50 % SZS output end Proof
% 0.20/0.50
% 0.20/0.50 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------