%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : REL009+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 12:33:03 PM UTC 2026
% Result : Theorem 1.84s 0.68s
% Output : Proof 1.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL009+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n020.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sun Sep 27 22:51:35 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.34 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.84/0.68 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 1.84/0.68
% 1.84/0.68 % SZS status Theorem
% 1.84/0.68
% 1.84/0.68 % SZS output start Proof
% 1.84/0.68 Axiom 1 (converse_idempotence): converse(converse(X)) = X.
% 1.84/0.68 Axiom 2 (maddux1_join_commutativity): join(X, Y) = join(Y, X).
% 1.84/0.68 Axiom 3 (goals): join(x0, x1) = x1.
% 1.84/0.68 Axiom 4 (converse_multiplicativity): converse(composition(X, Y)) = composition(converse(Y), converse(X)).
% 1.84/0.68 Axiom 5 (converse_additivity): converse(join(X, Y)) = join(converse(X), converse(Y)).
% 1.84/0.68 Axiom 6 (composition_distributivity): composition(join(X, Y), Z) = join(composition(X, Z), composition(Y, Z)).
% 1.84/0.68
% 1.84/0.68 Lemma 7: join(x1, x0) = x1.
% 1.84/0.68 Proof:
% 1.84/0.68 join(x1, x0)
% 1.84/0.68 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 1.84/0.68 join(x0, x1)
% 1.84/0.68 = { by axiom 3 (goals) }
% 1.84/0.68 x1
% 1.84/0.68
% 1.84/0.68 Goal 1 (goals_1): tuple(join(composition(x0, x2), composition(x1, x2)), join(composition(x2, x0), composition(x2, x1))) = tuple(composition(x1, x2), composition(x2, x1)).
% 1.84/0.68 Proof:
% 1.84/0.68 tuple(join(composition(x0, x2), composition(x1, x2)), join(composition(x2, x0), composition(x2, x1)))
% 1.84/0.68 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 1.84/0.68 tuple(join(composition(x0, x2), composition(x1, x2)), join(composition(x2, x1), composition(x2, x0)))
% 1.84/0.68 = { by axiom 1 (converse_idempotence) R->L }
% 1.84/0.68 tuple(join(composition(x0, x2), composition(x1, x2)), join(composition(x2, x1), composition(x2, converse(converse(x0)))))
% 1.84/0.68 = { by axiom 1 (converse_idempotence) R->L }
% 1.84/0.68 tuple(join(composition(x0, x2), composition(x1, x2)), join(composition(x2, x1), composition(converse(converse(x2)), converse(converse(x0)))))
% 1.84/0.68 = { by axiom 4 (converse_multiplicativity) R->L }
% 1.84/0.68 tuple(join(composition(x0, x2), composition(x1, x2)), join(composition(x2, x1), converse(composition(converse(x0), converse(x2)))))
% 1.84/0.68 = { by axiom 1 (converse_idempotence) R->L }
% 1.84/0.68 tuple(join(composition(x0, x2), composition(x1, x2)), join(converse(converse(composition(x2, x1))), converse(composition(converse(x0), converse(x2)))))
% 1.84/0.68 = { by axiom 5 (converse_additivity) R->L }
% 1.84/0.68 tuple(join(composition(x0, x2), composition(x1, x2)), converse(join(converse(composition(x2, x1)), composition(converse(x0), converse(x2)))))
% 1.84/0.68 = { by axiom 4 (converse_multiplicativity) }
% 1.84/0.68 tuple(join(composition(x0, x2), composition(x1, x2)), converse(join(composition(converse(x1), converse(x2)), composition(converse(x0), converse(x2)))))
% 1.84/0.68 = { by axiom 6 (composition_distributivity) R->L }
% 1.84/0.68 tuple(join(composition(x0, x2), composition(x1, x2)), converse(composition(join(converse(x1), converse(x0)), converse(x2))))
% 1.84/0.68 = { by axiom 2 (maddux1_join_commutativity) }
% 1.84/0.68 tuple(join(composition(x0, x2), composition(x1, x2)), converse(composition(join(converse(x0), converse(x1)), converse(x2))))
% 1.84/0.68 = { by axiom 4 (converse_multiplicativity) }
% 1.84/0.68 tuple(join(composition(x0, x2), composition(x1, x2)), composition(converse(converse(x2)), converse(join(converse(x0), converse(x1)))))
% 1.84/0.68 = { by axiom 1 (converse_idempotence) }
% 1.84/0.68 tuple(join(composition(x0, x2), composition(x1, x2)), composition(x2, converse(join(converse(x0), converse(x1)))))
% 1.84/0.68 = { by axiom 5 (converse_additivity) }
% 1.84/0.68 tuple(join(composition(x0, x2), composition(x1, x2)), composition(x2, join(converse(converse(x0)), converse(converse(x1)))))
% 1.84/0.68 = { by axiom 1 (converse_idempotence) }
% 1.84/0.68 tuple(join(composition(x0, x2), composition(x1, x2)), composition(x2, join(converse(converse(x0)), x1)))
% 1.84/0.68 = { by axiom 2 (maddux1_join_commutativity) }
% 1.84/0.68 tuple(join(composition(x0, x2), composition(x1, x2)), composition(x2, join(x1, converse(converse(x0)))))
% 1.84/0.68 = { by axiom 1 (converse_idempotence) }
% 1.84/0.68 tuple(join(composition(x0, x2), composition(x1, x2)), composition(x2, join(x1, x0)))
% 1.84/0.68 = { by lemma 7 }
% 1.84/0.68 tuple(join(composition(x0, x2), composition(x1, x2)), composition(x2, x1))
% 1.84/0.68 = { by axiom 6 (composition_distributivity) R->L }
% 1.84/0.68 tuple(composition(join(x0, x1), x2), composition(x2, x1))
% 1.84/0.68 = { by axiom 2 (maddux1_join_commutativity) }
% 1.84/0.68 tuple(composition(join(x1, x0), x2), composition(x2, x1))
% 1.84/0.68 = { by lemma 7 }
% 1.84/0.68 tuple(composition(x1, x2), composition(x2, x1))
% 1.84/0.68 % SZS output end Proof
% 1.84/0.69
% 1.84/0.69 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------