%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : REL050+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 12:33:35 PM UTC 2026
% Result : Theorem 1.53s 0.62s
% Output : Proof 1.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL050+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n002.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 27 22:59:51 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.53/0.62 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 1.53/0.62
% 1.53/0.62 % SZS status Theorem
% 1.53/0.62
% 1.78/0.66 % SZS output start Proof
% 1.78/0.66 Axiom 1 (composition_identity): composition(X, one) = X.
% 1.78/0.66 Axiom 2 (maddux1_join_commutativity): join(X, Y) = join(Y, X).
% 1.78/0.66 Axiom 3 (def_top): top = join(X, complement(X)).
% 1.78/0.66 Axiom 4 (converse_idempotence): converse(converse(X)) = X.
% 1.78/0.66 Axiom 5 (def_zero): zero = meet(X, complement(X)).
% 1.78/0.66 Axiom 6 (maddux4_definiton_of_meet): meet(X, Y) = complement(join(complement(X), complement(Y))).
% 1.78/0.66 Axiom 7 (converse_multiplicativity): converse(composition(X, Y)) = composition(converse(Y), converse(X)).
% 1.78/0.66 Axiom 8 (composition_associativity): composition(X, composition(Y, Z)) = composition(composition(X, Y), Z).
% 1.78/0.66 Axiom 9 (converse_additivity): converse(join(X, Y)) = join(converse(X), converse(Y)).
% 1.78/0.66 Axiom 10 (maddux2_join_associativity): join(X, join(Y, Z)) = join(join(X, Y), Z).
% 1.78/0.66 Axiom 11 (composition_distributivity): composition(join(X, Y), Z) = join(composition(X, Z), composition(Y, Z)).
% 1.78/0.66 Axiom 12 (maddux3_a_kind_of_de_Morgan): X = join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y))).
% 1.78/0.66 Axiom 13 (converse_cancellativity): join(composition(converse(X), complement(composition(X, Y))), complement(Y)) = complement(Y).
% 1.78/0.66
% 1.78/0.66 Lemma 14: complement(top) = zero.
% 1.78/0.66 Proof:
% 1.78/0.66 complement(top)
% 1.78/0.66 = { by axiom 3 (def_top) }
% 1.78/0.66 complement(join(complement(X), complement(complement(X))))
% 1.78/0.66 = { by axiom 6 (maddux4_definiton_of_meet) R->L }
% 1.78/0.66 meet(X, complement(X))
% 1.78/0.66 = { by axiom 5 (def_zero) R->L }
% 1.78/0.66 zero
% 1.78/0.66
% 1.78/0.66 Lemma 15: join(X, join(Y, complement(X))) = join(Y, top).
% 1.78/0.66 Proof:
% 1.78/0.66 join(X, join(Y, complement(X)))
% 1.78/0.66 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 1.78/0.66 join(X, join(complement(X), Y))
% 1.78/0.66 = { by axiom 10 (maddux2_join_associativity) }
% 1.78/0.66 join(join(X, complement(X)), Y)
% 1.78/0.66 = { by axiom 3 (def_top) R->L }
% 1.78/0.66 join(top, Y)
% 1.78/0.66 = { by axiom 2 (maddux1_join_commutativity) }
% 1.78/0.66 join(Y, top)
% 1.78/0.66
% 1.78/0.66 Lemma 16: converse(composition(converse(X), Y)) = composition(converse(Y), X).
% 1.78/0.66 Proof:
% 1.78/0.66 converse(composition(converse(X), Y))
% 1.78/0.66 = { by axiom 7 (converse_multiplicativity) }
% 1.78/0.66 composition(converse(Y), converse(converse(X)))
% 1.78/0.66 = { by axiom 4 (converse_idempotence) }
% 1.78/0.66 composition(converse(Y), X)
% 1.78/0.66
% 1.78/0.66 Lemma 17: composition(converse(one), X) = X.
% 1.78/0.66 Proof:
% 1.78/0.66 composition(converse(one), X)
% 1.78/0.66 = { by lemma 16 R->L }
% 1.78/0.66 converse(composition(converse(X), one))
% 1.78/0.66 = { by axiom 1 (composition_identity) }
% 1.78/0.66 converse(converse(X))
% 1.78/0.66 = { by axiom 4 (converse_idempotence) }
% 1.78/0.66 X
% 1.78/0.66
% 1.78/0.66 Lemma 18: composition(one, X) = X.
% 1.78/0.66 Proof:
% 1.78/0.66 composition(one, X)
% 1.78/0.66 = { by lemma 17 R->L }
% 1.78/0.66 composition(converse(one), composition(one, X))
% 1.78/0.66 = { by axiom 8 (composition_associativity) }
% 1.78/0.66 composition(composition(converse(one), one), X)
% 1.78/0.66 = { by axiom 1 (composition_identity) }
% 1.78/0.66 composition(converse(one), X)
% 1.78/0.66 = { by lemma 17 }
% 1.78/0.66 X
% 1.78/0.66
% 1.78/0.66 Lemma 19: join(complement(X), composition(converse(Y), complement(composition(Y, X)))) = complement(X).
% 1.78/0.66 Proof:
% 1.78/0.66 join(complement(X), composition(converse(Y), complement(composition(Y, X))))
% 1.78/0.66 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 1.78/0.66 join(composition(converse(Y), complement(composition(Y, X))), complement(X))
% 1.78/0.66 = { by axiom 13 (converse_cancellativity) }
% 1.78/0.66 complement(X)
% 1.78/0.66
% 1.78/0.66 Lemma 20: join(complement(X), complement(X)) = complement(X).
% 1.78/0.66 Proof:
% 1.78/0.66 join(complement(X), complement(X))
% 1.78/0.66 = { by lemma 17 R->L }
% 1.78/0.66 join(complement(X), composition(converse(one), complement(X)))
% 1.78/0.66 = { by lemma 18 R->L }
% 1.78/0.66 join(complement(X), composition(converse(one), complement(composition(one, X))))
% 1.78/0.66 = { by lemma 19 }
% 1.78/0.66 complement(X)
% 1.78/0.66
% 1.78/0.66 Lemma 21: join(top, complement(X)) = top.
% 1.78/0.66 Proof:
% 1.78/0.66 join(top, complement(X))
% 1.78/0.66 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 1.78/0.66 join(complement(X), top)
% 1.78/0.66 = { by lemma 15 R->L }
% 1.78/0.66 join(X, join(complement(X), complement(X)))
% 1.78/0.66 = { by lemma 20 }
% 1.78/0.66 join(X, complement(X))
% 1.78/0.66 = { by axiom 3 (def_top) R->L }
% 1.78/0.66 top
% 1.78/0.66
% 1.78/0.66 Lemma 22: join(X, top) = top.
% 1.78/0.66 Proof:
% 1.78/0.66 join(X, top)
% 1.78/0.66 = { by lemma 21 R->L }
% 1.78/0.66 join(X, join(top, complement(X)))
% 1.78/0.66 = { by lemma 15 }
% 1.78/0.66 join(top, top)
% 1.78/0.66 = { by axiom 3 (def_top) }
% 1.78/0.66 join(top, join(zero, complement(zero)))
% 1.78/0.66 = { by axiom 10 (maddux2_join_associativity) }
% 1.78/0.66 join(join(top, zero), complement(zero))
% 1.78/0.66 = { by lemma 14 R->L }
% 1.78/0.66 join(join(top, complement(top)), complement(zero))
% 1.78/0.66 = { by axiom 3 (def_top) R->L }
% 1.78/0.66 join(top, complement(zero))
% 1.78/0.66 = { by lemma 21 }
% 1.78/0.66 top
% 1.78/0.66
% 1.78/0.66 Lemma 23: join(meet(X, Y), complement(join(complement(X), Y))) = X.
% 1.78/0.66 Proof:
% 1.78/0.66 join(meet(X, Y), complement(join(complement(X), Y)))
% 1.78/0.66 = { by axiom 6 (maddux4_definiton_of_meet) }
% 1.78/0.66 join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y)))
% 1.78/0.66 = { by axiom 12 (maddux3_a_kind_of_de_Morgan) R->L }
% 1.78/0.66 X
% 1.78/0.66
% 1.78/0.66 Lemma 24: join(zero, meet(X, top)) = X.
% 1.78/0.66 Proof:
% 1.78/0.66 join(zero, meet(X, top))
% 1.78/0.66 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 1.78/0.66 join(meet(X, top), zero)
% 1.78/0.66 = { by lemma 14 R->L }
% 1.78/0.66 join(meet(X, top), complement(top))
% 1.78/0.66 = { by lemma 22 R->L }
% 1.78/0.66 join(meet(X, top), complement(join(complement(X), top)))
% 1.78/0.66 = { by lemma 23 }
% 1.78/0.66 X
% 1.78/0.66
% 1.78/0.66 Lemma 25: complement(join(zero, complement(X))) = meet(X, top).
% 1.78/0.66 Proof:
% 1.78/0.66 complement(join(zero, complement(X)))
% 1.78/0.66 = { by lemma 14 R->L }
% 1.78/0.66 complement(join(complement(top), complement(X)))
% 1.78/0.66 = { by axiom 2 (maddux1_join_commutativity) }
% 1.78/0.66 complement(join(complement(X), complement(top)))
% 1.78/0.66 = { by axiom 6 (maddux4_definiton_of_meet) R->L }
% 1.78/0.66 meet(X, top)
% 1.78/0.66
% 1.78/0.66 Lemma 26: join(zero, complement(complement(X))) = X.
% 1.78/0.66 Proof:
% 1.78/0.66 join(zero, complement(complement(X)))
% 1.78/0.66 = { by axiom 5 (def_zero) }
% 1.78/0.66 join(meet(X, complement(X)), complement(complement(X)))
% 1.78/0.66 = { by lemma 20 R->L }
% 1.78/0.66 join(meet(X, complement(X)), complement(join(complement(X), complement(X))))
% 1.78/0.66 = { by lemma 23 }
% 1.78/0.66 X
% 1.78/0.66
% 1.78/0.66 Lemma 27: join(zero, complement(X)) = complement(X).
% 1.78/0.66 Proof:
% 1.78/0.66 join(zero, complement(X))
% 1.78/0.66 = { by lemma 26 R->L }
% 1.78/0.66 join(zero, complement(join(zero, complement(complement(X)))))
% 1.78/0.66 = { by lemma 25 }
% 1.78/0.66 join(zero, meet(complement(X), top))
% 1.78/0.66 = { by lemma 24 }
% 1.78/0.66 complement(X)
% 1.78/0.66
% 1.78/0.66 Lemma 28: join(X, zero) = X.
% 1.78/0.66 Proof:
% 1.78/0.67 join(X, zero)
% 1.78/0.67 = { by lemma 14 R->L }
% 1.78/0.67 join(X, complement(top))
% 1.78/0.67 = { by lemma 22 R->L }
% 1.78/0.67 join(X, complement(join(complement(X), top)))
% 1.78/0.67 = { by lemma 24 R->L }
% 1.78/0.67 join(join(zero, meet(X, top)), complement(join(complement(X), top)))
% 1.78/0.67 = { by lemma 25 R->L }
% 1.78/0.67 join(join(zero, complement(join(zero, complement(X)))), complement(join(complement(X), top)))
% 1.78/0.67 = { by lemma 27 }
% 1.78/0.67 join(complement(join(zero, complement(X))), complement(join(complement(X), top)))
% 1.78/0.67 = { by lemma 25 }
% 1.78/0.67 join(meet(X, top), complement(join(complement(X), top)))
% 1.78/0.67 = { by lemma 23 }
% 1.78/0.67 X
% 1.78/0.67
% 1.78/0.67 Lemma 29: join(top, X) = top.
% 1.78/0.67 Proof:
% 1.78/0.67 join(top, X)
% 1.78/0.67 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 1.78/0.67 join(X, top)
% 1.78/0.67 = { by lemma 22 }
% 1.78/0.67 top
% 1.78/0.67
% 1.78/0.67 Lemma 30: join(zero, X) = X.
% 1.78/0.67 Proof:
% 1.78/0.67 join(zero, X)
% 1.78/0.67 = { by lemma 26 R->L }
% 1.78/0.67 join(zero, join(zero, complement(complement(X))))
% 1.78/0.67 = { by lemma 27 }
% 1.78/0.67 join(zero, complement(complement(X)))
% 1.78/0.67 = { by lemma 26 }
% 1.78/0.67 X
% 1.78/0.67
% 1.78/0.67 Lemma 31: converse(join(converse(X), Y)) = join(X, converse(Y)).
% 1.78/0.67 Proof:
% 1.78/0.67 converse(join(converse(X), Y))
% 1.78/0.67 = { by axiom 9 (converse_additivity) }
% 1.78/0.67 join(converse(converse(X)), converse(Y))
% 1.78/0.67 = { by axiom 4 (converse_idempotence) }
% 1.78/0.67 join(X, converse(Y))
% 1.78/0.67
% 1.78/0.67 Lemma 32: join(X, converse(top)) = converse(top).
% 1.78/0.67 Proof:
% 1.78/0.67 join(X, converse(top))
% 1.78/0.67 = { by lemma 31 R->L }
% 1.78/0.67 converse(join(converse(X), top))
% 1.78/0.67 = { by lemma 22 }
% 1.78/0.67 converse(top)
% 1.78/0.67
% 1.78/0.67 Lemma 33: converse(composition(X, top)) = composition(top, converse(X)).
% 1.78/0.67 Proof:
% 1.78/0.67 converse(composition(X, top))
% 1.78/0.67 = { by axiom 7 (converse_multiplicativity) }
% 1.78/0.67 composition(converse(top), converse(X))
% 1.78/0.67 = { by lemma 32 R->L }
% 1.78/0.67 composition(join(complement(Y), converse(top)), converse(X))
% 1.78/0.67 = { by lemma 32 R->L }
% 1.78/0.67 composition(join(complement(Y), join(Y, converse(top))), converse(X))
% 1.78/0.67 = { by axiom 10 (maddux2_join_associativity) }
% 1.78/0.67 composition(join(join(complement(Y), Y), converse(top)), converse(X))
% 1.78/0.67 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 1.78/0.67 composition(join(join(Y, complement(Y)), converse(top)), converse(X))
% 1.78/0.67 = { by axiom 3 (def_top) R->L }
% 1.78/0.67 composition(join(top, converse(top)), converse(X))
% 1.78/0.67 = { by axiom 2 (maddux1_join_commutativity) }
% 1.78/0.67 composition(join(converse(top), top), converse(X))
% 1.78/0.67 = { by lemma 22 }
% 1.78/0.67 composition(top, converse(X))
% 1.78/0.67
% 1.78/0.67 Lemma 34: join(X, composition(Y, X)) = composition(join(Y, one), X).
% 1.78/0.67 Proof:
% 1.78/0.67 join(X, composition(Y, X))
% 1.78/0.67 = { by lemma 18 R->L }
% 1.78/0.67 join(composition(one, X), composition(Y, X))
% 1.78/0.67 = { by axiom 11 (composition_distributivity) R->L }
% 1.78/0.67 composition(join(one, Y), X)
% 1.78/0.67 = { by axiom 2 (maddux1_join_commutativity) }
% 1.78/0.67 composition(join(Y, one), X)
% 1.78/0.67
% 1.78/0.67 Goal 1 (goals): tuple(join(complement(composition(x0_2, top)), composition(complement(composition(x0_2, top)), top)), join(composition(complement(composition(x0, top)), top), complement(composition(x0, top)))) = tuple(composition(complement(composition(x0_2, top)), top), complement(composition(x0, top))).
% 1.78/0.67 Proof:
% 1.78/0.67 tuple(join(complement(composition(x0_2, top)), composition(complement(composition(x0_2, top)), top)), join(composition(complement(composition(x0, top)), top), complement(composition(x0, top))))
% 1.78/0.67 = { by axiom 4 (converse_idempotence) R->L }
% 1.78/0.67 tuple(converse(converse(join(complement(composition(x0_2, top)), composition(complement(composition(x0_2, top)), top)))), join(composition(complement(composition(x0, top)), top), complement(composition(x0, top))))
% 1.78/0.67 = { by axiom 9 (converse_additivity) }
% 1.78/0.67 tuple(converse(join(converse(complement(composition(x0_2, top))), converse(composition(complement(composition(x0_2, top)), top)))), join(composition(complement(composition(x0, top)), top), complement(composition(x0, top))))
% 1.78/0.67 = { by lemma 33 }
% 1.78/0.67 tuple(converse(join(converse(complement(composition(x0_2, top))), composition(top, converse(complement(composition(x0_2, top)))))), join(composition(complement(composition(x0, top)), top), complement(composition(x0, top))))
% 1.78/0.67 = { by lemma 34 }
% 1.78/0.67 tuple(converse(composition(join(top, one), converse(complement(composition(x0_2, top))))), join(composition(complement(composition(x0, top)), top), complement(composition(x0, top))))
% 1.78/0.67 = { by lemma 29 }
% 1.78/0.67 tuple(converse(composition(top, converse(complement(composition(x0_2, top))))), join(composition(complement(composition(x0, top)), top), complement(composition(x0, top))))
% 1.78/0.67 = { by lemma 33 R->L }
% 1.78/0.67 tuple(converse(converse(composition(complement(composition(x0_2, top)), top))), join(composition(complement(composition(x0, top)), top), complement(composition(x0, top))))
% 1.78/0.67 = { by axiom 4 (converse_idempotence) }
% 1.78/0.67 tuple(composition(complement(composition(x0_2, top)), top), join(composition(complement(composition(x0, top)), top), complement(composition(x0, top))))
% 1.78/0.67 = { by axiom 2 (maddux1_join_commutativity) }
% 1.78/0.67 tuple(composition(complement(composition(x0_2, top)), top), join(complement(composition(x0, top)), composition(complement(composition(x0, top)), top)))
% 1.78/0.67 = { by axiom 3 (def_top) }
% 1.78/0.67 tuple(composition(complement(composition(x0_2, top)), top), join(complement(composition(x0, top)), composition(complement(composition(x0, top)), join(zero, complement(zero)))))
% 1.78/0.67 = { by lemma 27 }
% 1.78/0.67 tuple(composition(complement(composition(x0_2, top)), top), join(complement(composition(x0, top)), composition(complement(composition(x0, top)), complement(zero))))
% 1.78/0.67 = { by axiom 4 (converse_idempotence) R->L }
% 1.78/0.67 tuple(composition(complement(composition(x0_2, top)), top), join(complement(composition(x0, top)), composition(converse(converse(complement(composition(x0, top)))), complement(zero))))
% 1.78/0.67 = { by lemma 28 R->L }
% 1.78/0.67 tuple(composition(complement(composition(x0_2, top)), top), join(complement(composition(x0, top)), composition(converse(converse(complement(composition(x0, top)))), complement(join(zero, zero)))))
% 1.78/0.67 = { by axiom 4 (converse_idempotence) R->L }
% 1.78/0.67 tuple(composition(complement(composition(x0_2, top)), top), join(complement(composition(x0, top)), composition(converse(converse(complement(composition(x0, top)))), complement(join(zero, converse(converse(zero)))))))
% 1.78/0.67 = { by lemma 28 R->L }
% 1.78/0.67 tuple(composition(complement(composition(x0_2, top)), top), join(complement(composition(x0, top)), composition(converse(converse(complement(composition(x0, top)))), complement(join(zero, converse(join(converse(zero), zero)))))))
% 1.78/0.67 = { by lemma 31 }
% 1.78/0.67 tuple(composition(complement(composition(x0_2, top)), top), join(complement(composition(x0, top)), composition(converse(converse(complement(composition(x0, top)))), complement(join(zero, join(zero, converse(zero)))))))
% 1.78/0.67 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 1.78/0.67 tuple(composition(complement(composition(x0_2, top)), top), join(complement(composition(x0, top)), composition(converse(converse(complement(composition(x0, top)))), complement(join(zero, join(converse(zero), zero))))))
% 1.78/0.67 = { by lemma 30 }
% 1.78/0.67 tuple(composition(complement(composition(x0_2, top)), top), join(complement(composition(x0, top)), composition(converse(converse(complement(composition(x0, top)))), complement(join(converse(zero), zero)))))
% 1.78/0.67 = { by lemma 28 }
% 1.78/0.67 tuple(composition(complement(composition(x0_2, top)), top), join(complement(composition(x0, top)), composition(converse(converse(complement(composition(x0, top)))), complement(converse(zero)))))
% 1.78/0.67 = { by lemma 14 R->L }
% 1.78/0.67 tuple(composition(complement(composition(x0_2, top)), top), join(complement(composition(x0, top)), composition(converse(converse(complement(composition(x0, top)))), complement(converse(complement(top))))))
% 1.78/0.67 = { by lemma 19 R->L }
% 1.78/0.67 tuple(composition(complement(composition(x0_2, top)), top), join(complement(composition(x0, top)), composition(converse(converse(complement(composition(x0, top)))), complement(converse(join(complement(top), composition(converse(composition(x0, top)), complement(composition(composition(x0, top), top)))))))))
% 1.78/0.67 = { by axiom 8 (composition_associativity) R->L }
% 1.78/0.67 tuple(composition(complement(composition(x0_2, top)), top), join(complement(composition(x0, top)), composition(converse(converse(complement(composition(x0, top)))), complement(converse(join(complement(top), composition(converse(composition(x0, top)), complement(composition(x0, composition(top, top))))))))))
% 1.78/0.67 = { by lemma 29 R->L }
% 1.78/0.68 tuple(composition(complement(composition(x0_2, top)), top), join(complement(composition(x0, top)), composition(converse(converse(complement(composition(x0, top)))), complement(converse(join(complement(top), composition(converse(composition(x0, top)), complement(composition(x0, composition(join(top, one), top))))))))))
% 1.78/0.68 = { by lemma 34 R->L }
% 1.78/0.68 tuple(composition(complement(composition(x0_2, top)), top), join(complement(composition(x0, top)), composition(converse(converse(complement(composition(x0, top)))), complement(converse(join(complement(top), composition(converse(composition(x0, top)), complement(composition(x0, join(top, composition(top, top)))))))))))
% 1.78/0.68 = { by lemma 29 }
% 1.78/0.68 tuple(composition(complement(composition(x0_2, top)), top), join(complement(composition(x0, top)), composition(converse(converse(complement(composition(x0, top)))), complement(converse(join(complement(top), composition(converse(composition(x0, top)), complement(composition(x0, top)))))))))
% 1.78/0.68 = { by lemma 14 }
% 1.78/0.68 tuple(composition(complement(composition(x0_2, top)), top), join(complement(composition(x0, top)), composition(converse(converse(complement(composition(x0, top)))), complement(converse(join(zero, composition(converse(composition(x0, top)), complement(composition(x0, top)))))))))
% 1.78/0.68 = { by lemma 30 }
% 1.78/0.68 tuple(composition(complement(composition(x0_2, top)), top), join(complement(composition(x0, top)), composition(converse(converse(complement(composition(x0, top)))), complement(converse(composition(converse(composition(x0, top)), complement(composition(x0, top))))))))
% 1.78/0.68 = { by lemma 16 }
% 1.78/0.68 tuple(composition(complement(composition(x0_2, top)), top), join(complement(composition(x0, top)), composition(converse(converse(complement(composition(x0, top)))), complement(composition(converse(complement(composition(x0, top))), composition(x0, top))))))
% 1.78/0.68 = { by lemma 19 }
% 1.78/0.68 tuple(composition(complement(composition(x0_2, top)), top), complement(composition(x0, top)))
% 1.78/0.68 % SZS output end Proof
% 1.78/0.68
% 1.78/0.68 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------