TSTP Solution File: REL050+3 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : REL050+3 : 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 : n016.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 13:44:34 EDT 2023
% Result : Theorem 0.17s 0.45s
% Output : Proof 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : REL050+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.32 % Computer : n016.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Aug 25 19:35:56 EDT 2023
% 0.12/0.32 % CPUTime :
% 0.17/0.45 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.17/0.45
% 0.17/0.45 % SZS status Theorem
% 0.17/0.45
% 0.17/0.47 % SZS output start Proof
% 0.17/0.47 Axiom 1 (composition_identity): composition(X, one) = X.
% 0.17/0.47 Axiom 2 (maddux1_join_commutativity): join(X, Y) = join(Y, X).
% 0.17/0.47 Axiom 3 (converse_idempotence): converse(converse(X)) = X.
% 0.17/0.47 Axiom 4 (def_top): top = join(X, complement(X)).
% 0.17/0.47 Axiom 5 (def_zero): zero = meet(X, complement(X)).
% 0.17/0.47 Axiom 6 (converse_multiplicativity): converse(composition(X, Y)) = composition(converse(Y), converse(X)).
% 0.17/0.47 Axiom 7 (composition_associativity): composition(X, composition(Y, Z)) = composition(composition(X, Y), Z).
% 0.17/0.47 Axiom 8 (converse_additivity): converse(join(X, Y)) = join(converse(X), converse(Y)).
% 0.17/0.47 Axiom 9 (maddux2_join_associativity): join(X, join(Y, Z)) = join(join(X, Y), Z).
% 0.17/0.47 Axiom 10 (maddux4_definiton_of_meet): meet(X, Y) = complement(join(complement(X), complement(Y))).
% 0.17/0.47 Axiom 11 (composition_distributivity): composition(join(X, Y), Z) = join(composition(X, Z), composition(Y, Z)).
% 0.17/0.47 Axiom 12 (converse_cancellativity): join(composition(converse(X), complement(composition(X, Y))), complement(Y)) = complement(Y).
% 0.17/0.47 Axiom 13 (maddux3_a_kind_of_de_Morgan): X = join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y))).
% 0.17/0.47
% 0.17/0.47 Lemma 14: complement(top) = zero.
% 0.17/0.47 Proof:
% 0.17/0.47 complement(top)
% 0.17/0.47 = { by axiom 4 (def_top) }
% 0.17/0.47 complement(join(complement(X), complement(complement(X))))
% 0.17/0.47 = { by axiom 10 (maddux4_definiton_of_meet) R->L }
% 0.17/0.47 meet(X, complement(X))
% 0.17/0.47 = { by axiom 5 (def_zero) R->L }
% 0.17/0.47 zero
% 0.17/0.47
% 0.17/0.47 Lemma 15: converse(join(X, converse(Y))) = join(Y, converse(X)).
% 0.17/0.47 Proof:
% 0.17/0.47 converse(join(X, converse(Y)))
% 0.17/0.47 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 0.17/0.47 converse(join(converse(Y), X))
% 0.17/0.47 = { by axiom 8 (converse_additivity) }
% 0.17/0.47 join(converse(converse(Y)), converse(X))
% 0.17/0.47 = { by axiom 3 (converse_idempotence) }
% 0.17/0.47 join(Y, converse(X))
% 0.17/0.47
% 0.17/0.47 Lemma 16: join(X, join(Y, complement(X))) = join(Y, top).
% 0.17/0.47 Proof:
% 0.17/0.47 join(X, join(Y, complement(X)))
% 0.17/0.47 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 0.17/0.47 join(X, join(complement(X), Y))
% 0.17/0.47 = { by axiom 9 (maddux2_join_associativity) }
% 0.17/0.47 join(join(X, complement(X)), Y)
% 0.17/0.47 = { by axiom 4 (def_top) R->L }
% 0.17/0.47 join(top, Y)
% 0.17/0.47 = { by axiom 2 (maddux1_join_commutativity) }
% 0.17/0.48 join(Y, top)
% 0.17/0.48
% 0.17/0.48 Lemma 17: converse(composition(converse(X), Y)) = composition(converse(Y), X).
% 0.17/0.48 Proof:
% 0.17/0.48 converse(composition(converse(X), Y))
% 0.17/0.48 = { by axiom 6 (converse_multiplicativity) }
% 0.17/0.48 composition(converse(Y), converse(converse(X)))
% 0.17/0.48 = { by axiom 3 (converse_idempotence) }
% 0.17/0.48 composition(converse(Y), X)
% 0.17/0.48
% 0.17/0.48 Lemma 18: composition(converse(one), X) = X.
% 0.17/0.48 Proof:
% 0.17/0.48 composition(converse(one), X)
% 0.17/0.48 = { by lemma 17 R->L }
% 0.17/0.48 converse(composition(converse(X), one))
% 0.17/0.48 = { by axiom 1 (composition_identity) }
% 0.17/0.48 converse(converse(X))
% 0.17/0.48 = { by axiom 3 (converse_idempotence) }
% 0.17/0.48 X
% 0.17/0.48
% 0.17/0.48 Lemma 19: composition(one, X) = X.
% 0.17/0.48 Proof:
% 0.17/0.48 composition(one, X)
% 0.17/0.48 = { by lemma 18 R->L }
% 0.17/0.48 composition(converse(one), composition(one, X))
% 0.17/0.48 = { by axiom 7 (composition_associativity) }
% 0.17/0.48 composition(composition(converse(one), one), X)
% 0.17/0.48 = { by axiom 1 (composition_identity) }
% 0.17/0.48 composition(converse(one), X)
% 0.17/0.48 = { by lemma 18 }
% 0.17/0.48 X
% 0.17/0.48
% 0.17/0.48 Lemma 20: join(complement(X), composition(converse(Y), complement(composition(Y, X)))) = complement(X).
% 0.17/0.48 Proof:
% 0.17/0.48 join(complement(X), composition(converse(Y), complement(composition(Y, X))))
% 0.17/0.48 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 0.17/0.48 join(composition(converse(Y), complement(composition(Y, X))), complement(X))
% 0.17/0.48 = { by axiom 12 (converse_cancellativity) }
% 0.17/0.48 complement(X)
% 0.17/0.48
% 0.17/0.48 Lemma 21: join(complement(X), complement(X)) = complement(X).
% 0.17/0.48 Proof:
% 0.17/0.48 join(complement(X), complement(X))
% 0.17/0.48 = { by lemma 18 R->L }
% 0.17/0.48 join(complement(X), composition(converse(one), complement(X)))
% 0.17/0.48 = { by lemma 19 R->L }
% 0.17/0.48 join(complement(X), composition(converse(one), complement(composition(one, X))))
% 0.17/0.48 = { by lemma 20 }
% 0.17/0.48 complement(X)
% 0.17/0.48
% 0.17/0.48 Lemma 22: join(top, complement(X)) = top.
% 0.17/0.48 Proof:
% 0.17/0.48 join(top, complement(X))
% 0.17/0.48 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 0.17/0.48 join(complement(X), top)
% 0.17/0.48 = { by lemma 16 R->L }
% 0.17/0.48 join(X, join(complement(X), complement(X)))
% 0.17/0.48 = { by lemma 21 }
% 0.17/0.48 join(X, complement(X))
% 0.17/0.48 = { by axiom 4 (def_top) R->L }
% 0.17/0.48 top
% 0.17/0.48
% 0.17/0.48 Lemma 23: join(Y, top) = join(X, top).
% 0.17/0.48 Proof:
% 0.17/0.48 join(Y, top)
% 0.17/0.48 = { by lemma 22 R->L }
% 0.17/0.48 join(Y, join(top, complement(Y)))
% 0.17/0.48 = { by lemma 16 }
% 0.17/0.48 join(top, top)
% 0.17/0.48 = { by lemma 16 R->L }
% 0.17/0.48 join(X, join(top, complement(X)))
% 0.17/0.48 = { by lemma 22 }
% 0.17/0.48 join(X, top)
% 0.17/0.48
% 0.17/0.48 Lemma 24: join(X, top) = top.
% 0.17/0.48 Proof:
% 0.17/0.48 join(X, top)
% 0.17/0.48 = { by lemma 23 }
% 0.17/0.48 join(complement(Y), top)
% 0.17/0.48 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 0.17/0.48 join(top, complement(Y))
% 0.17/0.48 = { by lemma 22 }
% 0.17/0.48 top
% 0.17/0.48
% 0.17/0.48 Lemma 25: join(top, X) = top.
% 0.17/0.48 Proof:
% 0.17/0.48 join(top, X)
% 0.17/0.48 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 0.17/0.48 join(X, top)
% 0.17/0.48 = { by lemma 23 R->L }
% 0.17/0.48 join(Y, top)
% 0.17/0.48 = { by lemma 24 }
% 0.17/0.48 top
% 0.17/0.48
% 0.17/0.48 Lemma 26: join(X, converse(top)) = converse(top).
% 0.17/0.48 Proof:
% 0.17/0.48 join(X, converse(top))
% 0.17/0.48 = { by lemma 15 R->L }
% 0.17/0.48 converse(join(top, converse(X)))
% 0.17/0.48 = { by lemma 25 }
% 0.17/0.48 converse(top)
% 0.17/0.48
% 0.17/0.48 Lemma 27: converse(top) = top.
% 0.17/0.48 Proof:
% 0.17/0.48 converse(top)
% 0.17/0.48 = { by lemma 26 R->L }
% 0.17/0.48 join(complement(X), converse(top))
% 0.17/0.48 = { by lemma 26 R->L }
% 0.17/0.48 join(complement(X), join(X, converse(top)))
% 0.17/0.48 = { by axiom 9 (maddux2_join_associativity) }
% 0.17/0.48 join(join(complement(X), X), converse(top))
% 0.17/0.48 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 0.17/0.48 join(join(X, complement(X)), converse(top))
% 0.17/0.48 = { by axiom 4 (def_top) R->L }
% 0.17/0.48 join(top, converse(top))
% 0.17/0.48 = { by axiom 2 (maddux1_join_commutativity) }
% 0.17/0.48 join(converse(top), top)
% 0.17/0.48 = { by lemma 24 }
% 0.17/0.48 top
% 0.17/0.48
% 0.17/0.48 Lemma 28: join(meet(X, Y), complement(join(complement(X), Y))) = X.
% 0.17/0.48 Proof:
% 0.17/0.48 join(meet(X, Y), complement(join(complement(X), Y)))
% 0.17/0.48 = { by axiom 10 (maddux4_definiton_of_meet) }
% 0.17/0.48 join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y)))
% 0.17/0.48 = { by axiom 13 (maddux3_a_kind_of_de_Morgan) R->L }
% 0.17/0.48 X
% 0.17/0.48
% 0.17/0.48 Lemma 29: join(zero, zero) = zero.
% 0.17/0.48 Proof:
% 0.17/0.48 join(zero, zero)
% 0.17/0.48 = { by lemma 14 R->L }
% 0.17/0.48 join(zero, complement(top))
% 0.17/0.48 = { by lemma 14 R->L }
% 0.17/0.48 join(complement(top), complement(top))
% 0.17/0.48 = { by lemma 21 }
% 0.17/0.48 complement(top)
% 0.17/0.48 = { by lemma 14 }
% 0.17/0.48 zero
% 0.17/0.48
% 0.17/0.48 Lemma 30: join(zero, join(zero, X)) = join(X, zero).
% 0.17/0.48 Proof:
% 0.17/0.48 join(zero, join(zero, X))
% 0.17/0.48 = { by axiom 9 (maddux2_join_associativity) }
% 0.17/0.48 join(join(zero, zero), X)
% 0.17/0.48 = { by lemma 29 }
% 0.17/0.48 join(zero, X)
% 0.17/0.48 = { by axiom 2 (maddux1_join_commutativity) }
% 0.17/0.48 join(X, zero)
% 0.17/0.48
% 0.17/0.48 Lemma 31: join(X, zero) = X.
% 0.17/0.48 Proof:
% 0.17/0.48 join(X, zero)
% 0.17/0.48 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 0.17/0.48 join(zero, X)
% 0.17/0.48 = { by lemma 28 R->L }
% 0.17/0.48 join(zero, join(meet(X, complement(X)), complement(join(complement(X), complement(X)))))
% 0.17/0.48 = { by axiom 5 (def_zero) R->L }
% 0.17/0.48 join(zero, join(zero, complement(join(complement(X), complement(X)))))
% 0.17/0.48 = { by axiom 10 (maddux4_definiton_of_meet) R->L }
% 0.17/0.48 join(zero, join(zero, meet(X, X)))
% 0.17/0.48 = { by lemma 30 }
% 0.17/0.48 join(meet(X, X), zero)
% 0.17/0.48 = { by axiom 10 (maddux4_definiton_of_meet) }
% 0.17/0.48 join(complement(join(complement(X), complement(X))), zero)
% 0.17/0.48 = { by lemma 21 }
% 0.17/0.48 join(complement(complement(X)), zero)
% 0.17/0.48 = { by axiom 2 (maddux1_join_commutativity) }
% 0.17/0.48 join(zero, complement(complement(X)))
% 0.17/0.48 = { by axiom 5 (def_zero) }
% 0.17/0.48 join(meet(X, complement(X)), complement(complement(X)))
% 0.17/0.48 = { by lemma 21 R->L }
% 0.17/0.48 join(meet(X, complement(X)), complement(join(complement(X), complement(X))))
% 0.17/0.48 = { by lemma 28 }
% 0.17/0.48 X
% 0.17/0.48
% 0.17/0.48 Lemma 32: join(zero, X) = X.
% 0.17/0.48 Proof:
% 0.17/0.48 join(zero, X)
% 0.17/0.48 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 0.17/0.48 join(X, zero)
% 0.17/0.48 = { by lemma 31 }
% 0.17/0.48 X
% 0.17/0.48
% 0.17/0.48 Lemma 33: converse(composition(X, top)) = composition(top, converse(X)).
% 0.17/0.48 Proof:
% 0.17/0.48 converse(composition(X, top))
% 0.17/0.48 = { by axiom 6 (converse_multiplicativity) }
% 0.17/0.48 composition(converse(top), converse(X))
% 0.17/0.48 = { by lemma 27 }
% 0.17/0.48 composition(top, converse(X))
% 0.17/0.48
% 0.17/0.48 Lemma 34: join(X, composition(Y, X)) = composition(join(Y, one), X).
% 0.17/0.48 Proof:
% 0.17/0.48 join(X, composition(Y, X))
% 0.17/0.48 = { by lemma 19 R->L }
% 0.17/0.48 join(composition(one, X), composition(Y, X))
% 0.17/0.48 = { by axiom 11 (composition_distributivity) R->L }
% 0.17/0.48 composition(join(one, Y), X)
% 0.17/0.48 = { by axiom 2 (maddux1_join_commutativity) }
% 0.17/0.48 composition(join(Y, one), X)
% 0.17/0.48
% 0.17/0.48 Goal 1 (goals): complement(composition(x0, top)) = composition(complement(composition(x0, top)), top).
% 0.17/0.48 Proof:
% 0.17/0.48 complement(composition(x0, top))
% 0.17/0.48 = { by lemma 20 R->L }
% 0.17/0.48 join(complement(composition(x0, top)), composition(converse(converse(complement(composition(x0, top)))), complement(composition(converse(complement(composition(x0, top))), composition(x0, top)))))
% 0.17/0.48 = { by lemma 17 R->L }
% 0.17/0.48 join(complement(composition(x0, top)), composition(converse(converse(complement(composition(x0, top)))), complement(converse(composition(converse(composition(x0, top)), complement(composition(x0, top)))))))
% 0.17/0.48 = { by axiom 6 (converse_multiplicativity) }
% 0.17/0.48 join(complement(composition(x0, top)), composition(converse(converse(complement(composition(x0, top)))), complement(converse(composition(composition(converse(top), converse(x0)), complement(composition(x0, top)))))))
% 0.17/0.48 = { by axiom 7 (composition_associativity) R->L }
% 0.17/0.48 join(complement(composition(x0, top)), composition(converse(converse(complement(composition(x0, top)))), complement(converse(composition(converse(top), composition(converse(x0), complement(composition(x0, top))))))))
% 0.17/0.48 = { by lemma 32 R->L }
% 0.17/0.48 join(complement(composition(x0, top)), composition(converse(converse(complement(composition(x0, top)))), complement(converse(composition(converse(top), join(zero, composition(converse(x0), complement(composition(x0, top)))))))))
% 0.17/0.48 = { by lemma 14 R->L }
% 0.17/0.48 join(complement(composition(x0, top)), composition(converse(converse(complement(composition(x0, top)))), complement(converse(composition(converse(top), join(complement(top), composition(converse(x0), complement(composition(x0, top)))))))))
% 0.17/0.48 = { by lemma 20 }
% 0.17/0.48 join(complement(composition(x0, top)), composition(converse(converse(complement(composition(x0, top)))), complement(converse(composition(converse(top), complement(top))))))
% 0.17/0.48 = { by lemma 14 }
% 0.17/0.49 join(complement(composition(x0, top)), composition(converse(converse(complement(composition(x0, top)))), complement(converse(composition(converse(top), zero)))))
% 0.17/0.49 = { by lemma 27 }
% 0.17/0.49 join(complement(composition(x0, top)), composition(converse(converse(complement(composition(x0, top)))), complement(converse(composition(top, zero)))))
% 0.17/0.49 = { by lemma 14 R->L }
% 0.17/0.49 join(complement(composition(x0, top)), composition(converse(converse(complement(composition(x0, top)))), complement(converse(composition(top, complement(top))))))
% 0.17/0.49 = { by lemma 25 R->L }
% 0.17/0.49 join(complement(composition(x0, top)), composition(converse(converse(complement(composition(x0, top)))), complement(converse(composition(join(top, one), complement(top))))))
% 0.17/0.49 = { by lemma 27 R->L }
% 0.17/0.49 join(complement(composition(x0, top)), composition(converse(converse(complement(composition(x0, top)))), complement(converse(composition(join(converse(top), one), complement(top))))))
% 0.17/0.49 = { by lemma 34 R->L }
% 0.17/0.49 join(complement(composition(x0, top)), composition(converse(converse(complement(composition(x0, top)))), complement(converse(join(complement(top), composition(converse(top), complement(top)))))))
% 0.17/0.49 = { by lemma 25 R->L }
% 0.17/0.49 join(complement(composition(x0, top)), composition(converse(converse(complement(composition(x0, top)))), complement(converse(join(complement(top), composition(converse(top), complement(join(top, composition(top, top)))))))))
% 0.17/0.49 = { by lemma 34 }
% 0.17/0.49 join(complement(composition(x0, top)), composition(converse(converse(complement(composition(x0, top)))), complement(converse(join(complement(top), composition(converse(top), complement(composition(join(top, one), top))))))))
% 0.17/0.49 = { by lemma 25 }
% 0.17/0.49 join(complement(composition(x0, top)), composition(converse(converse(complement(composition(x0, top)))), complement(converse(join(complement(top), composition(converse(top), complement(composition(top, top))))))))
% 0.17/0.49 = { by lemma 20 }
% 0.17/0.49 join(complement(composition(x0, top)), composition(converse(converse(complement(composition(x0, top)))), complement(converse(complement(top)))))
% 0.17/0.49 = { by lemma 14 }
% 0.17/0.49 join(complement(composition(x0, top)), composition(converse(converse(complement(composition(x0, top)))), complement(converse(zero))))
% 0.17/0.49 = { by lemma 31 R->L }
% 0.17/0.49 join(complement(composition(x0, top)), composition(converse(converse(complement(composition(x0, top)))), complement(join(converse(zero), zero))))
% 0.17/0.49 = { by lemma 30 R->L }
% 0.17/0.49 join(complement(composition(x0, top)), composition(converse(converse(complement(composition(x0, top)))), complement(join(zero, join(zero, converse(zero))))))
% 0.17/0.49 = { by lemma 15 R->L }
% 0.17/0.49 join(complement(composition(x0, top)), composition(converse(converse(complement(composition(x0, top)))), complement(join(zero, converse(join(zero, converse(zero)))))))
% 0.17/0.49 = { by axiom 2 (maddux1_join_commutativity) }
% 0.17/0.49 join(complement(composition(x0, top)), composition(converse(converse(complement(composition(x0, top)))), complement(join(zero, converse(join(converse(zero), zero))))))
% 0.17/0.49 = { by lemma 31 }
% 0.17/0.49 join(complement(composition(x0, top)), composition(converse(converse(complement(composition(x0, top)))), complement(join(zero, converse(converse(zero))))))
% 0.17/0.49 = { by axiom 3 (converse_idempotence) }
% 0.17/0.49 join(complement(composition(x0, top)), composition(converse(converse(complement(composition(x0, top)))), complement(join(zero, zero))))
% 0.17/0.49 = { by lemma 29 }
% 0.17/0.49 join(complement(composition(x0, top)), composition(converse(converse(complement(composition(x0, top)))), complement(zero)))
% 0.17/0.49 = { by axiom 3 (converse_idempotence) }
% 0.17/0.49 join(complement(composition(x0, top)), composition(complement(composition(x0, top)), complement(zero)))
% 0.17/0.49 = { by lemma 32 R->L }
% 0.17/0.49 join(complement(composition(x0, top)), composition(complement(composition(x0, top)), join(zero, complement(zero))))
% 0.17/0.49 = { by axiom 4 (def_top) R->L }
% 0.17/0.49 join(complement(composition(x0, top)), composition(complement(composition(x0, top)), top))
% 0.17/0.49 = { by axiom 3 (converse_idempotence) R->L }
% 0.17/0.49 converse(converse(join(complement(composition(x0, top)), composition(complement(composition(x0, top)), top))))
% 0.17/0.49 = { by axiom 8 (converse_additivity) }
% 0.17/0.49 converse(join(converse(complement(composition(x0, top))), converse(composition(complement(composition(x0, top)), top))))
% 0.17/0.49 = { by lemma 33 }
% 0.17/0.49 converse(join(converse(complement(composition(x0, top))), composition(top, converse(complement(composition(x0, top))))))
% 0.17/0.49 = { by lemma 34 }
% 0.17/0.49 converse(composition(join(top, one), converse(complement(composition(x0, top)))))
% 0.17/0.49 = { by lemma 25 }
% 0.17/0.49 converse(composition(top, converse(complement(composition(x0, top)))))
% 0.17/0.49 = { by lemma 33 R->L }
% 0.17/0.49 converse(converse(composition(complement(composition(x0, top)), top)))
% 0.17/0.49 = { by axiom 3 (converse_idempotence) }
% 0.17/0.49 composition(complement(composition(x0, top)), top)
% 0.17/0.49 % SZS output end Proof
% 0.17/0.49
% 0.17/0.49 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------