%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : REL027+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:33:16 PM UTC 2026
% Result : Theorem 7.59s 1.44s
% Output : Proof 7.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL027+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n011.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 22:53:15 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.59/1.44 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 7.59/1.44
% 7.59/1.44 % SZS status Theorem
% 7.59/1.44
% 7.59/1.47 % SZS output start Proof
% 7.59/1.47 Axiom 1 (maddux1_join_commutativity): join(X, Y) = join(Y, X).
% 7.59/1.47 Axiom 2 (def_top): top = join(X, complement(X)).
% 7.59/1.47 Axiom 3 (goals): join(x0, one) = one.
% 7.59/1.47 Axiom 4 (composition_identity): composition(X, one) = X.
% 7.59/1.47 Axiom 5 (def_zero): zero = meet(X, complement(X)).
% 7.59/1.47 Axiom 6 (converse_idempotence): converse(converse(X)) = X.
% 7.59/1.47 Axiom 7 (maddux4_definiton_of_meet): meet(X, Y) = complement(join(complement(X), complement(Y))).
% 7.59/1.47 Axiom 8 (converse_additivity): converse(join(X, Y)) = join(converse(X), converse(Y)).
% 7.59/1.47 Axiom 9 (maddux2_join_associativity): join(X, join(Y, Z)) = join(join(X, Y), Z).
% 7.59/1.47 Axiom 10 (converse_multiplicativity): converse(composition(X, Y)) = composition(converse(Y), converse(X)).
% 7.59/1.47 Axiom 11 (composition_associativity): composition(X, composition(Y, Z)) = composition(composition(X, Y), Z).
% 7.59/1.47 Axiom 12 (composition_distributivity): composition(join(X, Y), Z) = join(composition(X, Z), composition(Y, Z)).
% 7.59/1.47 Axiom 13 (maddux3_a_kind_of_de_Morgan): X = join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y))).
% 7.59/1.47 Axiom 14 (converse_cancellativity): join(composition(converse(X), complement(composition(X, Y))), complement(Y)) = complement(Y).
% 7.59/1.47
% 7.59/1.47 Lemma 15: complement(top) = zero.
% 7.59/1.47 Proof:
% 7.59/1.47 complement(top)
% 7.59/1.47 = { by axiom 2 (def_top) }
% 7.59/1.47 complement(join(complement(X), complement(complement(X))))
% 7.59/1.47 = { by axiom 7 (maddux4_definiton_of_meet) R->L }
% 7.59/1.47 meet(X, complement(X))
% 7.59/1.47 = { by axiom 5 (def_zero) R->L }
% 7.59/1.47 zero
% 7.59/1.47
% 7.59/1.47 Lemma 16: join(X, join(Y, complement(X))) = join(Y, top).
% 7.59/1.47 Proof:
% 7.59/1.47 join(X, join(Y, complement(X)))
% 7.59/1.47 = { by axiom 1 (maddux1_join_commutativity) R->L }
% 7.59/1.47 join(X, join(complement(X), Y))
% 7.59/1.47 = { by axiom 9 (maddux2_join_associativity) }
% 7.59/1.47 join(join(X, complement(X)), Y)
% 7.59/1.47 = { by axiom 2 (def_top) R->L }
% 7.59/1.47 join(top, Y)
% 7.59/1.47 = { by axiom 1 (maddux1_join_commutativity) }
% 7.59/1.47 join(Y, top)
% 7.59/1.47
% 7.59/1.47 Lemma 17: composition(converse(one), X) = X.
% 7.59/1.47 Proof:
% 7.59/1.47 composition(converse(one), X)
% 7.59/1.47 = { by axiom 6 (converse_idempotence) R->L }
% 7.59/1.47 composition(converse(one), converse(converse(X)))
% 7.59/1.47 = { by axiom 10 (converse_multiplicativity) R->L }
% 7.59/1.47 converse(composition(converse(X), one))
% 7.59/1.47 = { by axiom 4 (composition_identity) }
% 7.59/1.47 converse(converse(X))
% 7.59/1.47 = { by axiom 6 (converse_idempotence) }
% 7.59/1.47 X
% 7.59/1.47
% 7.59/1.47 Lemma 18: composition(one, X) = X.
% 7.59/1.47 Proof:
% 7.59/1.47 composition(one, X)
% 7.59/1.47 = { by lemma 17 R->L }
% 7.59/1.47 composition(converse(one), composition(one, X))
% 7.59/1.47 = { by axiom 11 (composition_associativity) }
% 7.59/1.47 composition(composition(converse(one), one), X)
% 7.59/1.47 = { by axiom 4 (composition_identity) }
% 7.59/1.47 composition(converse(one), X)
% 7.59/1.47 = { by lemma 17 }
% 7.59/1.47 X
% 7.59/1.47
% 7.59/1.47 Lemma 19: join(complement(X), complement(X)) = complement(X).
% 7.59/1.47 Proof:
% 7.59/1.47 join(complement(X), complement(X))
% 7.59/1.47 = { by lemma 17 R->L }
% 7.59/1.47 join(complement(X), composition(converse(one), complement(X)))
% 7.59/1.47 = { by lemma 18 R->L }
% 7.59/1.47 join(complement(X), composition(converse(one), complement(composition(one, X))))
% 7.59/1.47 = { by axiom 1 (maddux1_join_commutativity) R->L }
% 7.59/1.47 join(composition(converse(one), complement(composition(one, X))), complement(X))
% 7.59/1.47 = { by axiom 14 (converse_cancellativity) }
% 7.59/1.47 complement(X)
% 7.59/1.47
% 7.59/1.47 Lemma 20: join(top, complement(X)) = top.
% 7.59/1.47 Proof:
% 7.59/1.47 join(top, complement(X))
% 7.59/1.47 = { by axiom 1 (maddux1_join_commutativity) R->L }
% 7.59/1.47 join(complement(X), top)
% 7.59/1.47 = { by lemma 16 R->L }
% 7.59/1.47 join(X, join(complement(X), complement(X)))
% 7.59/1.47 = { by lemma 19 }
% 7.59/1.47 join(X, complement(X))
% 7.59/1.47 = { by axiom 2 (def_top) R->L }
% 7.59/1.47 top
% 7.59/1.47
% 7.59/1.47 Lemma 21: join(X, top) = top.
% 7.59/1.47 Proof:
% 7.59/1.47 join(X, top)
% 7.59/1.47 = { by lemma 20 R->L }
% 7.59/1.47 join(X, join(top, complement(X)))
% 7.59/1.47 = { by lemma 16 }
% 7.59/1.47 join(top, top)
% 7.59/1.47 = { by lemma 16 R->L }
% 7.59/1.47 join(x0, join(top, complement(x0)))
% 7.59/1.47 = { by lemma 20 }
% 7.59/1.47 join(x0, top)
% 7.59/1.47 = { by axiom 2 (def_top) }
% 7.59/1.47 join(x0, join(one, complement(one)))
% 7.59/1.47 = { by axiom 9 (maddux2_join_associativity) }
% 7.59/1.47 join(join(x0, one), complement(one))
% 7.59/1.47 = { by axiom 3 (goals) }
% 7.59/1.47 join(one, complement(one))
% 7.59/1.47 = { by axiom 2 (def_top) R->L }
% 7.59/1.47 top
% 7.59/1.47
% 7.59/1.47 Lemma 22: join(meet(X, Y), complement(join(complement(X), Y))) = X.
% 7.59/1.47 Proof:
% 7.59/1.47 join(meet(X, Y), complement(join(complement(X), Y)))
% 7.59/1.47 = { by axiom 7 (maddux4_definiton_of_meet) }
% 7.59/1.47 join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y)))
% 7.59/1.47 = { by axiom 13 (maddux3_a_kind_of_de_Morgan) R->L }
% 7.59/1.47 X
% 7.59/1.47
% 7.59/1.47 Lemma 23: join(zero, complement(complement(X))) = X.
% 7.59/1.47 Proof:
% 7.59/1.47 join(zero, complement(complement(X)))
% 7.59/1.47 = { by axiom 5 (def_zero) }
% 7.59/1.47 join(meet(X, complement(X)), complement(complement(X)))
% 7.59/1.47 = { by lemma 19 R->L }
% 7.59/1.47 join(meet(X, complement(X)), complement(join(complement(X), complement(X))))
% 7.59/1.47 = { by lemma 22 }
% 7.59/1.47 X
% 7.59/1.47
% 7.59/1.47 Lemma 24: join(X, zero) = X.
% 7.59/1.47 Proof:
% 7.59/1.47 join(X, zero)
% 7.59/1.47 = { by axiom 1 (maddux1_join_commutativity) R->L }
% 7.59/1.47 join(zero, X)
% 7.59/1.47 = { by lemma 22 R->L }
% 7.59/1.47 join(zero, join(meet(X, complement(X)), complement(join(complement(X), complement(X)))))
% 7.59/1.47 = { by axiom 5 (def_zero) R->L }
% 7.59/1.47 join(zero, join(zero, complement(join(complement(X), complement(X)))))
% 7.59/1.47 = { by axiom 7 (maddux4_definiton_of_meet) R->L }
% 7.59/1.47 join(zero, join(zero, meet(X, X)))
% 7.59/1.47 = { by axiom 9 (maddux2_join_associativity) }
% 7.59/1.47 join(join(zero, zero), meet(X, X))
% 7.59/1.47 = { by lemma 15 R->L }
% 7.59/1.47 join(join(zero, complement(top)), meet(X, X))
% 7.59/1.47 = { by lemma 15 R->L }
% 7.59/1.47 join(join(complement(top), complement(top)), meet(X, X))
% 7.59/1.47 = { by lemma 19 }
% 7.59/1.47 join(complement(top), meet(X, X))
% 7.59/1.47 = { by lemma 15 }
% 7.59/1.47 join(zero, meet(X, X))
% 7.59/1.47 = { by axiom 1 (maddux1_join_commutativity) }
% 7.59/1.47 join(meet(X, X), zero)
% 7.59/1.47 = { by axiom 7 (maddux4_definiton_of_meet) }
% 7.59/1.47 join(complement(join(complement(X), complement(X))), zero)
% 7.59/1.47 = { by lemma 19 }
% 7.59/1.47 join(complement(complement(X)), zero)
% 7.59/1.47 = { by axiom 1 (maddux1_join_commutativity) }
% 7.59/1.47 join(zero, complement(complement(X)))
% 7.59/1.47 = { by lemma 23 }
% 7.59/1.47 X
% 7.59/1.47
% 7.59/1.47 Lemma 25: join(zero, X) = X.
% 7.59/1.47 Proof:
% 7.59/1.47 join(zero, X)
% 7.59/1.47 = { by axiom 1 (maddux1_join_commutativity) R->L }
% 7.59/1.47 join(X, zero)
% 7.59/1.47 = { by lemma 24 }
% 7.59/1.47 X
% 7.59/1.47
% 7.59/1.47 Lemma 26: complement(complement(X)) = X.
% 7.59/1.47 Proof:
% 7.59/1.47 complement(complement(X))
% 7.59/1.47 = { by lemma 25 R->L }
% 7.59/1.47 join(zero, complement(complement(X)))
% 7.59/1.47 = { by lemma 23 }
% 7.59/1.47 X
% 7.59/1.47
% 7.59/1.47 Lemma 27: meet(Y, X) = meet(X, Y).
% 7.59/1.48 Proof:
% 7.59/1.48 meet(Y, X)
% 7.59/1.48 = { by axiom 7 (maddux4_definiton_of_meet) }
% 7.59/1.48 complement(join(complement(Y), complement(X)))
% 7.59/1.48 = { by axiom 1 (maddux1_join_commutativity) R->L }
% 7.59/1.48 complement(join(complement(X), complement(Y)))
% 7.59/1.48 = { by axiom 7 (maddux4_definiton_of_meet) R->L }
% 7.59/1.48 meet(X, Y)
% 7.59/1.48
% 7.59/1.48 Lemma 28: complement(join(zero, complement(X))) = meet(X, top).
% 7.59/1.48 Proof:
% 7.59/1.48 complement(join(zero, complement(X)))
% 7.59/1.48 = { by lemma 15 R->L }
% 7.59/1.48 complement(join(complement(top), complement(X)))
% 7.59/1.48 = { by axiom 7 (maddux4_definiton_of_meet) R->L }
% 7.59/1.48 meet(top, X)
% 7.59/1.48 = { by lemma 27 R->L }
% 7.59/1.48 meet(X, top)
% 7.59/1.48
% 7.59/1.48 Lemma 29: meet(X, top) = X.
% 7.59/1.48 Proof:
% 7.59/1.48 meet(X, top)
% 7.59/1.48 = { by lemma 28 R->L }
% 7.59/1.48 complement(join(zero, complement(X)))
% 7.59/1.48 = { by lemma 25 }
% 7.59/1.48 complement(complement(X))
% 7.59/1.48 = { by lemma 26 }
% 7.59/1.48 X
% 7.59/1.48
% 7.59/1.48 Lemma 30: converse(join(X, converse(Y))) = join(Y, converse(X)).
% 7.59/1.48 Proof:
% 7.59/1.48 converse(join(X, converse(Y)))
% 7.59/1.48 = { by axiom 1 (maddux1_join_commutativity) R->L }
% 7.59/1.48 converse(join(converse(Y), X))
% 7.59/1.48 = { by axiom 8 (converse_additivity) }
% 7.59/1.48 join(converse(converse(Y)), converse(X))
% 7.59/1.48 = { by axiom 6 (converse_idempotence) }
% 7.59/1.48 join(Y, converse(X))
% 7.59/1.48
% 7.59/1.48 Lemma 31: join(X, converse(top)) = converse(top).
% 7.59/1.48 Proof:
% 7.59/1.48 join(X, converse(top))
% 7.59/1.48 = { by lemma 30 R->L }
% 7.59/1.48 converse(join(top, converse(X)))
% 7.59/1.48 = { by axiom 1 (maddux1_join_commutativity) R->L }
% 7.59/1.48 converse(join(converse(X), top))
% 7.59/1.48 = { by lemma 21 }
% 7.59/1.48 converse(top)
% 7.59/1.48
% 7.59/1.48 Lemma 32: join(X, join(complement(X), Y)) = join(Y, top).
% 7.59/1.48 Proof:
% 7.59/1.48 join(X, join(complement(X), Y))
% 7.59/1.48 = { by axiom 1 (maddux1_join_commutativity) R->L }
% 7.59/1.48 join(X, join(Y, complement(X)))
% 7.59/1.48 = { by lemma 16 }
% 7.59/1.48 join(Y, top)
% 7.59/1.48
% 7.59/1.48 Lemma 33: converse(composition(top, X)) = composition(converse(X), top).
% 7.59/1.48 Proof:
% 7.59/1.48 converse(composition(top, X))
% 7.59/1.48 = { by axiom 10 (converse_multiplicativity) }
% 7.59/1.48 composition(converse(X), converse(top))
% 7.59/1.48 = { by lemma 31 R->L }
% 7.59/1.48 composition(converse(X), join(Y, converse(top)))
% 7.59/1.48 = { by lemma 31 R->L }
% 7.59/1.48 composition(converse(X), join(Y, join(complement(Y), converse(top))))
% 7.59/1.48 = { by lemma 32 }
% 7.59/1.48 composition(converse(X), join(converse(top), top))
% 7.59/1.48 = { by lemma 21 }
% 7.59/1.48 composition(converse(X), top)
% 7.59/1.48
% 7.59/1.48 Lemma 34: complement(join(meet(X, Y), complement(Z))) = meet(Z, join(complement(X), complement(Y))).
% 7.59/1.48 Proof:
% 7.59/1.48 complement(join(meet(X, Y), complement(Z)))
% 7.59/1.48 = { by axiom 7 (maddux4_definiton_of_meet) }
% 7.59/1.48 complement(join(complement(join(complement(X), complement(Y))), complement(Z)))
% 7.59/1.48 = { by axiom 7 (maddux4_definiton_of_meet) R->L }
% 7.59/1.48 meet(join(complement(X), complement(Y)), Z)
% 7.59/1.48 = { by lemma 27 R->L }
% 7.59/1.48 meet(Z, join(complement(X), complement(Y)))
% 7.59/1.48
% 7.59/1.48 Lemma 35: complement(meet(complement(X), Y)) = join(X, complement(Y)).
% 7.59/1.48 Proof:
% 7.59/1.48 complement(meet(complement(X), Y))
% 7.59/1.48 = { by lemma 27 }
% 7.59/1.48 complement(meet(Y, complement(X)))
% 7.59/1.48 = { by lemma 24 R->L }
% 7.59/1.48 complement(join(meet(Y, complement(X)), zero))
% 7.59/1.48 = { by lemma 15 R->L }
% 7.59/1.48 complement(join(meet(Y, complement(X)), complement(top)))
% 7.59/1.48 = { by lemma 34 }
% 7.59/1.48 meet(top, join(complement(Y), complement(complement(X))))
% 7.59/1.48 = { by lemma 26 R->L }
% 7.59/1.48 meet(top, complement(complement(join(complement(Y), complement(complement(X))))))
% 7.59/1.48 = { by lemma 27 }
% 7.59/1.48 meet(complement(complement(join(complement(Y), complement(complement(X))))), top)
% 7.59/1.48 = { by lemma 28 R->L }
% 7.59/1.48 complement(join(zero, complement(complement(complement(join(complement(Y), complement(complement(X))))))))
% 7.59/1.48 = { by lemma 23 }
% 7.59/1.48 complement(complement(join(complement(Y), complement(complement(X)))))
% 7.59/1.48 = { by lemma 26 }
% 7.59/1.48 join(complement(Y), complement(complement(X)))
% 7.59/1.48 = { by axiom 1 (maddux1_join_commutativity) }
% 7.59/1.48 join(complement(complement(X)), complement(Y))
% 7.59/1.48 = { by lemma 26 }
% 7.59/1.48 join(X, complement(Y))
% 7.59/1.48
% 7.59/1.48 Lemma 36: composition(join(X, one), Y) = join(Y, composition(X, Y)).
% 7.59/1.48 Proof:
% 7.59/1.48 composition(join(X, one), Y)
% 7.59/1.48 = { by axiom 1 (maddux1_join_commutativity) R->L }
% 7.59/1.48 composition(join(one, X), Y)
% 7.59/1.48 = { by axiom 12 (composition_distributivity) }
% 7.59/1.48 join(composition(one, Y), composition(X, Y))
% 7.59/1.48 = { by lemma 18 }
% 7.59/1.48 join(Y, composition(X, Y))
% 7.59/1.48
% 7.59/1.48 Lemma 37: converse(join(converse(X), Y)) = join(X, converse(Y)).
% 7.59/1.48 Proof:
% 7.59/1.48 converse(join(converse(X), Y))
% 7.59/1.48 = { by axiom 1 (maddux1_join_commutativity) R->L }
% 7.59/1.48 converse(join(Y, converse(X)))
% 7.59/1.48 = { by lemma 30 }
% 7.59/1.48 join(X, converse(Y))
% 7.59/1.48
% 7.59/1.48 Lemma 38: converse(composition(X, converse(Y))) = composition(Y, converse(X)).
% 7.59/1.48 Proof:
% 7.59/1.48 converse(composition(X, converse(Y)))
% 7.59/1.48 = { by axiom 10 (converse_multiplicativity) }
% 7.59/1.48 composition(converse(converse(Y)), converse(X))
% 7.59/1.48 = { by axiom 6 (converse_idempotence) }
% 7.59/1.48 composition(Y, converse(X))
% 7.59/1.48
% 7.59/1.48 Lemma 39: join(meet(complement(composition(x0, top)), one), meet(complement(x0), one)) = meet(complement(x0), one).
% 7.59/1.48 Proof:
% 7.59/1.48 join(meet(complement(composition(x0, top)), one), meet(complement(x0), one))
% 7.59/1.48 = { by axiom 1 (maddux1_join_commutativity) R->L }
% 7.59/1.48 join(meet(complement(x0), one), meet(complement(composition(x0, top)), one))
% 7.59/1.48 = { by lemma 22 R->L }
% 7.59/1.48 join(meet(complement(x0), one), join(meet(meet(complement(composition(x0, top)), one), complement(meet(complement(x0), one))), complement(join(complement(meet(complement(composition(x0, top)), one)), complement(meet(complement(x0), one))))))
% 7.59/1.48 = { by lemma 35 }
% 7.59/1.48 join(meet(complement(x0), one), join(meet(meet(complement(composition(x0, top)), one), join(x0, complement(one))), complement(join(complement(meet(complement(composition(x0, top)), one)), complement(meet(complement(x0), one))))))
% 7.59/1.48 = { by lemma 26 R->L }
% 7.59/1.48 join(meet(complement(x0), one), join(meet(meet(complement(composition(x0, top)), one), join(complement(complement(x0)), complement(one))), complement(join(complement(meet(complement(composition(x0, top)), one)), complement(meet(complement(x0), one))))))
% 7.59/1.48 = { by lemma 34 R->L }
% 7.59/1.48 join(meet(complement(x0), one), join(complement(join(meet(complement(x0), one), complement(meet(complement(composition(x0, top)), one)))), complement(join(complement(meet(complement(composition(x0, top)), one)), complement(meet(complement(x0), one))))))
% 7.59/1.48 = { by lemma 35 }
% 7.59/1.48 join(meet(complement(x0), one), join(complement(join(meet(complement(x0), one), join(composition(x0, top), complement(one)))), complement(join(complement(meet(complement(composition(x0, top)), one)), complement(meet(complement(x0), one))))))
% 7.59/1.48 = { by axiom 1 (maddux1_join_commutativity) R->L }
% 7.59/1.48 join(meet(complement(x0), one), join(complement(join(meet(complement(x0), one), join(complement(one), composition(x0, top)))), complement(join(complement(meet(complement(composition(x0, top)), one)), complement(meet(complement(x0), one))))))
% 7.59/1.48 = { by axiom 9 (maddux2_join_associativity) }
% 7.59/1.48 join(meet(complement(x0), one), join(complement(join(join(meet(complement(x0), one), complement(one)), composition(x0, top))), complement(join(complement(meet(complement(composition(x0, top)), one)), complement(meet(complement(x0), one))))))
% 7.59/1.48 = { by axiom 3 (goals) R->L }
% 7.59/1.48 join(meet(complement(x0), one), join(complement(join(join(meet(complement(x0), one), complement(join(x0, one))), composition(x0, top))), complement(join(complement(meet(complement(composition(x0, top)), one)), complement(meet(complement(x0), one))))))
% 7.59/1.48 = { by lemma 26 R->L }
% 7.59/1.48 join(meet(complement(x0), one), join(complement(join(join(meet(complement(x0), one), complement(join(complement(complement(x0)), one))), composition(x0, top))), complement(join(complement(meet(complement(composition(x0, top)), one)), complement(meet(complement(x0), one))))))
% 7.59/1.48 = { by lemma 22 }
% 7.59/1.48 join(meet(complement(x0), one), join(complement(join(complement(x0), composition(x0, top))), complement(join(complement(meet(complement(composition(x0, top)), one)), complement(meet(complement(x0), one))))))
% 7.59/1.48 = { by axiom 1 (maddux1_join_commutativity) }
% 7.59/1.48 join(meet(complement(x0), one), join(complement(join(composition(x0, top), complement(x0))), complement(join(complement(meet(complement(composition(x0, top)), one)), complement(meet(complement(x0), one))))))
% 7.59/1.48 = { by axiom 6 (converse_idempotence) R->L }
% 7.59/1.48 join(meet(complement(x0), one), join(complement(join(composition(converse(converse(x0)), top), complement(x0))), complement(join(complement(meet(complement(composition(x0, top)), one)), complement(meet(complement(x0), one))))))
% 7.59/1.48 = { by lemma 33 R->L }
% 7.59/1.48 join(meet(complement(x0), one), join(complement(join(converse(composition(top, converse(x0))), complement(x0))), complement(join(complement(meet(complement(composition(x0, top)), one)), complement(meet(complement(x0), one))))))
% 7.59/1.48 = { by lemma 21 R->L }
% 7.59/1.48 join(meet(complement(x0), one), join(complement(join(converse(composition(join(one, top), converse(x0))), complement(x0))), complement(join(complement(meet(complement(composition(x0, top)), one)), complement(meet(complement(x0), one))))))
% 7.59/1.48 = { by axiom 1 (maddux1_join_commutativity) R->L }
% 7.59/1.48 join(meet(complement(x0), one), join(complement(join(converse(composition(join(top, one), converse(x0))), complement(x0))), complement(join(complement(meet(complement(composition(x0, top)), one)), complement(meet(complement(x0), one))))))
% 7.59/1.48 = { by lemma 36 }
% 7.59/1.48 join(meet(complement(x0), one), join(complement(join(converse(join(converse(x0), composition(top, converse(x0)))), complement(x0))), complement(join(complement(meet(complement(composition(x0, top)), one)), complement(meet(complement(x0), one))))))
% 7.59/1.48 = { by lemma 37 }
% 7.59/1.48 join(meet(complement(x0), one), join(complement(join(join(x0, converse(composition(top, converse(x0)))), complement(x0))), complement(join(complement(meet(complement(composition(x0, top)), one)), complement(meet(complement(x0), one))))))
% 7.59/1.48 = { by lemma 33 }
% 7.59/1.48 join(meet(complement(x0), one), join(complement(join(join(x0, composition(converse(converse(x0)), top)), complement(x0))), complement(join(complement(meet(complement(composition(x0, top)), one)), complement(meet(complement(x0), one))))))
% 7.59/1.48 = { by axiom 6 (converse_idempotence) }
% 7.59/1.48 join(meet(complement(x0), one), join(complement(join(join(x0, composition(x0, top)), complement(x0))), complement(join(complement(meet(complement(composition(x0, top)), one)), complement(meet(complement(x0), one))))))
% 7.59/1.48 = { by axiom 9 (maddux2_join_associativity) R->L }
% 7.59/1.48 join(meet(complement(x0), one), join(complement(join(x0, join(composition(x0, top), complement(x0)))), complement(join(complement(meet(complement(composition(x0, top)), one)), complement(meet(complement(x0), one))))))
% 7.59/1.48 = { by axiom 1 (maddux1_join_commutativity) }
% 7.59/1.48 join(meet(complement(x0), one), join(complement(join(x0, join(complement(x0), composition(x0, top)))), complement(join(complement(meet(complement(composition(x0, top)), one)), complement(meet(complement(x0), one))))))
% 7.59/1.48 = { by lemma 32 }
% 7.59/1.48 join(meet(complement(x0), one), join(complement(join(composition(x0, top), top)), complement(join(complement(meet(complement(composition(x0, top)), one)), complement(meet(complement(x0), one))))))
% 7.59/1.48 = { by lemma 21 }
% 7.59/1.48 join(meet(complement(x0), one), join(complement(top), complement(join(complement(meet(complement(composition(x0, top)), one)), complement(meet(complement(x0), one))))))
% 7.59/1.48 = { by lemma 15 }
% 7.59/1.48 join(meet(complement(x0), one), join(zero, complement(join(complement(meet(complement(composition(x0, top)), one)), complement(meet(complement(x0), one))))))
% 7.59/1.48 = { by lemma 25 }
% 7.59/1.48 join(meet(complement(x0), one), complement(join(complement(meet(complement(composition(x0, top)), one)), complement(meet(complement(x0), one)))))
% 7.59/1.48 = { by axiom 7 (maddux4_definiton_of_meet) R->L }
% 7.59/1.48 join(meet(complement(x0), one), meet(meet(complement(composition(x0, top)), one), meet(complement(x0), one)))
% 7.59/1.48 = { by lemma 27 }
% 7.59/1.48 join(meet(complement(x0), one), meet(meet(complement(x0), one), meet(complement(composition(x0, top)), one)))
% 7.59/1.48 = { by axiom 1 (maddux1_join_commutativity) R->L }
% 7.59/1.48 join(meet(meet(complement(x0), one), meet(complement(composition(x0, top)), one)), meet(complement(x0), one))
% 7.59/1.48 = { by lemma 22 R->L }
% 7.59/1.48 join(meet(meet(complement(x0), one), meet(complement(composition(x0, top)), one)), join(meet(meet(complement(x0), one), meet(complement(composition(x0, top)), one)), complement(join(complement(meet(complement(x0), one)), meet(complement(composition(x0, top)), one)))))
% 7.59/1.48 = { by axiom 1 (maddux1_join_commutativity) R->L }
% 7.59/1.48 join(meet(meet(complement(x0), one), meet(complement(composition(x0, top)), one)), join(complement(join(complement(meet(complement(x0), one)), meet(complement(composition(x0, top)), one))), meet(meet(complement(x0), one), meet(complement(composition(x0, top)), one))))
% 7.59/1.48 = { by lemma 29 R->L }
% 7.59/1.48 join(meet(meet(complement(x0), one), meet(complement(composition(x0, top)), one)), join(complement(join(complement(meet(complement(x0), one)), meet(complement(composition(x0, top)), one))), meet(meet(meet(complement(x0), one), meet(complement(composition(x0, top)), one)), top)))
% 7.59/1.48 = { by lemma 28 R->L }
% 7.59/1.48 join(meet(meet(complement(x0), one), meet(complement(composition(x0, top)), one)), join(complement(join(complement(meet(complement(x0), one)), meet(complement(composition(x0, top)), one))), complement(join(zero, complement(meet(meet(complement(x0), one), meet(complement(composition(x0, top)), one)))))))
% 7.59/1.48 = { by lemma 29 R->L }
% 7.59/1.48 join(meet(meet(meet(complement(x0), one), meet(complement(composition(x0, top)), one)), top), join(complement(join(complement(meet(complement(x0), one)), meet(complement(composition(x0, top)), one))), complement(join(zero, complement(meet(meet(complement(x0), one), meet(complement(composition(x0, top)), one)))))))
% 7.59/1.48 = { by lemma 28 R->L }
% 7.59/1.48 join(complement(join(zero, complement(meet(meet(complement(x0), one), meet(complement(composition(x0, top)), one))))), join(complement(join(complement(meet(complement(x0), one)), meet(complement(composition(x0, top)), one))), complement(join(zero, complement(meet(meet(complement(x0), one), meet(complement(composition(x0, top)), one)))))))
% 7.59/1.48 = { by axiom 1 (maddux1_join_commutativity) R->L }
% 7.59/1.48 join(complement(join(zero, complement(meet(meet(complement(x0), one), meet(complement(composition(x0, top)), one))))), join(complement(join(zero, complement(meet(meet(complement(x0), one), meet(complement(composition(x0, top)), one))))), complement(join(complement(meet(complement(x0), one)), meet(complement(composition(x0, top)), one)))))
% 7.59/1.48 = { by axiom 9 (maddux2_join_associativity) }
% 7.59/1.48 join(join(complement(join(zero, complement(meet(meet(complement(x0), one), meet(complement(composition(x0, top)), one))))), complement(join(zero, complement(meet(meet(complement(x0), one), meet(complement(composition(x0, top)), one)))))), complement(join(complement(meet(complement(x0), one)), meet(complement(composition(x0, top)), one))))
% 7.59/1.48 = { by lemma 19 }
% 7.59/1.48 join(complement(join(zero, complement(meet(meet(complement(x0), one), meet(complement(composition(x0, top)), one))))), complement(join(complement(meet(complement(x0), one)), meet(complement(composition(x0, top)), one))))
% 7.59/1.48 = { by axiom 1 (maddux1_join_commutativity) }
% 7.59/1.48 join(complement(join(complement(meet(complement(x0), one)), meet(complement(composition(x0, top)), one))), complement(join(zero, complement(meet(meet(complement(x0), one), meet(complement(composition(x0, top)), one))))))
% 7.59/1.48 = { by lemma 28 }
% 7.59/1.48 join(complement(join(complement(meet(complement(x0), one)), meet(complement(composition(x0, top)), one))), meet(meet(meet(complement(x0), one), meet(complement(composition(x0, top)), one)), top))
% 7.59/1.48 = { by lemma 29 }
% 7.59/1.48 join(complement(join(complement(meet(complement(x0), one)), meet(complement(composition(x0, top)), one))), meet(meet(complement(x0), one), meet(complement(composition(x0, top)), one)))
% 7.59/1.48 = { by axiom 1 (maddux1_join_commutativity) }
% 7.59/1.48 join(meet(meet(complement(x0), one), meet(complement(composition(x0, top)), one)), complement(join(complement(meet(complement(x0), one)), meet(complement(composition(x0, top)), one))))
% 7.59/1.48 = { by lemma 22 }
% 7.59/1.48 meet(complement(x0), one)
% 7.59/1.48
% 7.59/1.48 Goal 1 (goals_1): tuple(join(meet(complement(composition(x0, top)), one), meet(complement(x0), one)), join(meet(complement(x0), one), meet(complement(composition(x0, top)), one))) = tuple(meet(complement(x0), one), meet(complement(composition(x0, top)), one)).
% 7.59/1.48 Proof:
% 7.59/1.48 tuple(join(meet(complement(composition(x0, top)), one), meet(complement(x0), one)), join(meet(complement(x0), one), meet(complement(composition(x0, top)), one)))
% 7.59/1.48 = { by axiom 1 (maddux1_join_commutativity) }
% 7.59/1.48 tuple(join(meet(complement(composition(x0, top)), one), meet(complement(x0), one)), join(meet(complement(composition(x0, top)), one), meet(complement(x0), one)))
% 7.59/1.48 = { by lemma 39 }
% 7.59/1.48 tuple(meet(complement(x0), one), join(meet(complement(composition(x0, top)), one), meet(complement(x0), one)))
% 7.59/1.48 = { by lemma 29 R->L }
% 7.59/1.48 tuple(meet(complement(x0), one), meet(join(meet(complement(composition(x0, top)), one), meet(complement(x0), one)), top))
% 7.59/1.48 = { by lemma 28 R->L }
% 7.59/1.48 tuple(meet(complement(x0), one), complement(join(zero, complement(join(meet(complement(composition(x0, top)), one), meet(complement(x0), one))))))
% 7.59/1.48 = { by lemma 39 }
% 7.59/1.48 tuple(meet(complement(x0), one), complement(join(zero, complement(meet(complement(x0), one)))))
% 7.59/1.48 = { by lemma 35 }
% 7.59/1.48 tuple(meet(complement(x0), one), complement(join(zero, join(x0, complement(one)))))
% 7.59/1.48 = { by axiom 1 (maddux1_join_commutativity) R->L }
% 7.59/1.48 tuple(meet(complement(x0), one), complement(join(zero, join(complement(one), x0))))
% 7.59/1.48 = { by lemma 18 R->L }
% 7.59/1.48 tuple(meet(complement(x0), one), complement(join(zero, join(composition(one, complement(one)), x0))))
% 7.59/1.48 = { by axiom 3 (goals) R->L }
% 7.59/1.48 tuple(meet(complement(x0), one), complement(join(zero, join(composition(join(x0, one), complement(one)), x0))))
% 7.59/1.48 = { by lemma 36 }
% 7.59/1.48 tuple(meet(complement(x0), one), complement(join(zero, join(join(complement(one), composition(x0, complement(one))), x0))))
% 7.59/1.48 = { by axiom 9 (maddux2_join_associativity) R->L }
% 7.59/1.49 tuple(meet(complement(x0), one), complement(join(zero, join(complement(one), join(composition(x0, complement(one)), x0)))))
% 7.59/1.49 = { by axiom 1 (maddux1_join_commutativity) }
% 7.59/1.49 tuple(meet(complement(x0), one), complement(join(zero, join(complement(one), join(x0, composition(x0, complement(one)))))))
% 7.59/1.49 = { by axiom 6 (converse_idempotence) R->L }
% 7.59/1.49 tuple(meet(complement(x0), one), complement(join(zero, join(complement(one), join(x0, composition(x0, converse(converse(complement(one)))))))))
% 7.59/1.49 = { by lemma 38 R->L }
% 7.59/1.49 tuple(meet(complement(x0), one), complement(join(zero, join(complement(one), join(x0, converse(composition(converse(complement(one)), converse(x0))))))))
% 7.59/1.49 = { by lemma 37 R->L }
% 7.59/1.49 tuple(meet(complement(x0), one), complement(join(zero, join(complement(one), converse(join(converse(x0), composition(converse(complement(one)), converse(x0))))))))
% 7.59/1.49 = { by lemma 36 R->L }
% 7.59/1.49 tuple(meet(complement(x0), one), complement(join(zero, join(complement(one), converse(composition(join(converse(complement(one)), one), converse(x0)))))))
% 7.59/1.49 = { by lemma 38 }
% 7.59/1.49 tuple(meet(complement(x0), one), complement(join(zero, join(complement(one), composition(x0, converse(join(converse(complement(one)), one)))))))
% 7.59/1.49 = { by axiom 1 (maddux1_join_commutativity) R->L }
% 7.59/1.49 tuple(meet(complement(x0), one), complement(join(zero, join(complement(one), composition(x0, converse(join(one, converse(complement(one)))))))))
% 7.59/1.49 = { by axiom 8 (converse_additivity) }
% 7.59/1.49 tuple(meet(complement(x0), one), complement(join(zero, join(complement(one), composition(x0, join(converse(one), converse(converse(complement(one)))))))))
% 7.59/1.49 = { by axiom 4 (composition_identity) R->L }
% 7.59/1.49 tuple(meet(complement(x0), one), complement(join(zero, join(complement(one), composition(x0, join(composition(converse(one), one), converse(converse(complement(one)))))))))
% 7.59/1.49 = { by lemma 17 }
% 7.59/1.49 tuple(meet(complement(x0), one), complement(join(zero, join(complement(one), composition(x0, join(one, converse(converse(complement(one)))))))))
% 7.59/1.49 = { by axiom 6 (converse_idempotence) }
% 7.59/1.49 tuple(meet(complement(x0), one), complement(join(zero, join(complement(one), composition(x0, join(one, complement(one)))))))
% 7.59/1.49 = { by axiom 2 (def_top) R->L }
% 7.59/1.49 tuple(meet(complement(x0), one), complement(join(zero, join(complement(one), composition(x0, top)))))
% 7.59/1.49 = { by axiom 1 (maddux1_join_commutativity) }
% 7.59/1.49 tuple(meet(complement(x0), one), complement(join(zero, join(composition(x0, top), complement(one)))))
% 7.59/1.49 = { by lemma 35 R->L }
% 7.59/1.49 tuple(meet(complement(x0), one), complement(join(zero, complement(meet(complement(composition(x0, top)), one)))))
% 7.59/1.49 = { by lemma 28 }
% 7.59/1.49 tuple(meet(complement(x0), one), meet(meet(complement(composition(x0, top)), one), top))
% 7.59/1.49 = { by lemma 29 }
% 7.59/1.49 tuple(meet(complement(x0), one), meet(complement(composition(x0, top)), one))
% 7.59/1.49 % SZS output end Proof
% 7.59/1.49
% 7.59/1.49 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------