%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : REL009+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 12:33:02 PM UTC 2026
% Result : Theorem 6.85s 1.33s
% Output : Proof 6.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL009+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n017.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 27 22:45:35 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.85/1.33 Command-line arguments: --no-flatten-goal
% 6.85/1.33
% 6.85/1.33 % SZS status Theorem
% 6.85/1.33
% 6.85/1.34 % SZS output start Proof
% 6.85/1.34 Axiom 1 (converse_idempotence): converse(converse(X)) = X.
% 6.85/1.34 Axiom 2 (maddux1_join_commutativity): join(X, Y) = join(Y, X).
% 6.85/1.34 Axiom 3 (goals): join(x0, x1) = x1.
% 6.85/1.34 Axiom 4 (converse_multiplicativity): converse(composition(X, Y)) = composition(converse(Y), converse(X)).
% 6.85/1.34 Axiom 5 (converse_additivity): converse(join(X, Y)) = join(converse(X), converse(Y)).
% 6.85/1.34 Axiom 6 (composition_distributivity): composition(join(X, Y), Z) = join(composition(X, Z), composition(Y, Z)).
% 6.85/1.34
% 6.85/1.34 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)).
% 6.85/1.34 Proof:
% 6.85/1.34 tuple(join(composition(x0, x2), composition(x1, x2)), join(composition(x2, x0), composition(x2, x1)))
% 6.85/1.34 = { by axiom 6 (composition_distributivity) R->L }
% 6.85/1.34 tuple(composition(join(x0, x1), x2), join(composition(x2, x0), composition(x2, x1)))
% 6.85/1.34 = { by axiom 3 (goals) }
% 6.85/1.34 tuple(composition(x1, x2), join(composition(x2, x0), composition(x2, x1)))
% 6.85/1.34 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 6.85/1.34 tuple(composition(x1, x2), join(composition(x2, x1), composition(x2, x0)))
% 6.85/1.34 = { by axiom 1 (converse_idempotence) R->L }
% 6.85/1.34 tuple(composition(x1, x2), join(composition(x2, x1), composition(x2, converse(converse(x0)))))
% 6.85/1.34 = { by axiom 1 (converse_idempotence) R->L }
% 6.85/1.34 tuple(composition(x1, x2), converse(converse(join(composition(x2, x1), composition(x2, converse(converse(x0)))))))
% 6.85/1.34 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 6.85/1.34 tuple(composition(x1, x2), converse(converse(join(composition(x2, converse(converse(x0))), composition(x2, x1)))))
% 6.85/1.34 = { by axiom 5 (converse_additivity) }
% 6.85/1.34 tuple(composition(x1, x2), converse(join(converse(composition(x2, converse(converse(x0)))), converse(composition(x2, x1)))))
% 6.85/1.34 = { by axiom 4 (converse_multiplicativity) }
% 6.85/1.34 tuple(composition(x1, x2), converse(join(composition(converse(converse(converse(x0))), converse(x2)), converse(composition(x2, x1)))))
% 6.85/1.34 = { by axiom 1 (converse_idempotence) }
% 6.85/1.34 tuple(composition(x1, x2), converse(join(composition(converse(x0), converse(x2)), converse(composition(x2, x1)))))
% 6.85/1.34 = { by axiom 2 (maddux1_join_commutativity) }
% 6.85/1.34 tuple(composition(x1, x2), converse(join(converse(composition(x2, x1)), composition(converse(x0), converse(x2)))))
% 6.85/1.34 = { by axiom 4 (converse_multiplicativity) }
% 6.85/1.34 tuple(composition(x1, x2), converse(join(composition(converse(x1), converse(x2)), composition(converse(x0), converse(x2)))))
% 6.85/1.34 = { by axiom 6 (composition_distributivity) R->L }
% 6.85/1.34 tuple(composition(x1, x2), converse(composition(join(converse(x1), converse(x0)), converse(x2))))
% 6.85/1.34 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 6.85/1.34 tuple(composition(x1, x2), converse(composition(join(converse(x0), converse(x1)), converse(x2))))
% 6.85/1.34 = { by axiom 1 (converse_idempotence) R->L }
% 6.85/1.34 tuple(composition(x1, x2), converse(composition(join(converse(converse(converse(x0))), converse(x1)), converse(x2))))
% 6.85/1.34 = { by axiom 5 (converse_additivity) R->L }
% 6.85/1.34 tuple(composition(x1, x2), converse(composition(converse(join(converse(converse(x0)), x1)), converse(x2))))
% 6.85/1.34 = { by axiom 2 (maddux1_join_commutativity) }
% 6.85/1.34 tuple(composition(x1, x2), converse(composition(converse(join(x1, converse(converse(x0)))), converse(x2))))
% 6.85/1.35 = { by axiom 4 (converse_multiplicativity) R->L }
% 6.85/1.35 tuple(composition(x1, x2), converse(converse(composition(x2, join(x1, converse(converse(x0)))))))
% 6.85/1.35 = { by axiom 1 (converse_idempotence) }
% 6.85/1.35 tuple(composition(x1, x2), composition(x2, join(x1, converse(converse(x0)))))
% 6.85/1.35 = { by axiom 1 (converse_idempotence) }
% 6.85/1.35 tuple(composition(x1, x2), composition(x2, join(x1, x0)))
% 6.85/1.35 = { by axiom 2 (maddux1_join_commutativity) }
% 6.85/1.35 tuple(composition(x1, x2), composition(x2, join(x0, x1)))
% 6.85/1.35 = { by axiom 3 (goals) }
% 6.85/1.35 tuple(composition(x1, x2), composition(x2, x1))
% 6.85/1.35 % SZS output end Proof
% 6.85/1.35
% 6.85/1.35 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------