%------------------------------------------------------------------------------
% 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 : n016.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 : Unsatisfiable 3.74s 0.93s
% Output : Proof 3.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL009-2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n016.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Sun Sep 27 22:55:33 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.74/0.93 Command-line arguments: --flatten --complete-subsets
% 3.74/0.93
% 3.74/0.93 % SZS status Unsatisfiable
% 3.74/0.93
% 3.74/0.93 % SZS output start Proof
% 3.74/0.93 Axiom 1 (converse_idempotence_8): converse(converse(X)) = X.
% 3.74/0.93 Axiom 2 (goals_17): join(sk1, sk2) = sk2.
% 3.74/0.93 Axiom 3 (converse_additivity_9): converse(join(X, Y)) = join(converse(X), converse(Y)).
% 3.74/0.93 Axiom 4 (converse_multiplicativity_10): converse(composition(X, Y)) = composition(converse(Y), converse(X)).
% 3.74/0.93 Axiom 5 (composition_distributivity_7): composition(join(X, Y), Z) = join(composition(X, Z), composition(Y, Z)).
% 3.74/0.93
% 3.74/0.93 Lemma 6: composition(converse(join(sk1, sk2)), converse(X)) = converse(composition(X, sk2)).
% 3.74/0.93 Proof:
% 3.74/0.93 composition(converse(join(sk1, sk2)), converse(X))
% 3.74/0.93 = { by axiom 4 (converse_multiplicativity_10) R->L }
% 3.74/0.93 converse(composition(X, join(sk1, sk2)))
% 3.74/0.93 = { by axiom 2 (goals_17) }
% 3.74/0.93 converse(composition(X, sk2))
% 3.74/0.93
% 3.74/0.93 Goal 1 (goals_18): tuple(join(composition(sk1, sk3), composition(sk2, sk3)), join(composition(sk3, sk1), composition(sk3, sk2))) = tuple(composition(sk2, sk3), composition(sk3, sk2)).
% 3.74/0.93 Proof:
% 3.74/0.93 tuple(join(composition(sk1, sk3), composition(sk2, sk3)), join(composition(sk3, sk1), composition(sk3, sk2)))
% 3.74/0.93 = { by axiom 5 (composition_distributivity_7) R->L }
% 3.74/0.93 tuple(composition(join(sk1, sk2), sk3), join(composition(sk3, sk1), composition(sk3, sk2)))
% 3.74/0.93 = { by axiom 2 (goals_17) }
% 3.74/0.93 tuple(composition(sk2, sk3), join(composition(sk3, sk1), composition(sk3, sk2)))
% 3.74/0.93 = { by axiom 1 (converse_idempotence_8) R->L }
% 3.74/0.93 tuple(composition(sk2, sk3), converse(converse(join(composition(sk3, sk1), composition(sk3, sk2)))))
% 3.74/0.93 = { by axiom 3 (converse_additivity_9) }
% 3.74/0.93 tuple(composition(sk2, sk3), converse(join(converse(composition(sk3, sk1)), converse(composition(sk3, sk2)))))
% 3.74/0.93 = { by lemma 6 R->L }
% 3.74/0.93 tuple(composition(sk2, sk3), converse(join(converse(composition(sk3, sk1)), composition(converse(join(sk1, sk2)), converse(sk3)))))
% 3.74/0.93 = { by axiom 4 (converse_multiplicativity_10) }
% 3.74/0.93 tuple(composition(sk2, sk3), converse(join(composition(converse(sk1), converse(sk3)), composition(converse(join(sk1, sk2)), converse(sk3)))))
% 3.74/0.93 = { by axiom 5 (composition_distributivity_7) R->L }
% 3.74/0.93 tuple(composition(sk2, sk3), converse(composition(join(converse(sk1), converse(join(sk1, sk2))), converse(sk3))))
% 3.74/0.93 = { by axiom 2 (goals_17) }
% 3.74/0.93 tuple(composition(sk2, sk3), converse(composition(join(converse(sk1), converse(sk2)), converse(sk3))))
% 3.74/0.93 = { by axiom 3 (converse_additivity_9) R->L }
% 3.74/0.93 tuple(composition(sk2, sk3), converse(composition(converse(join(sk1, sk2)), converse(sk3))))
% 3.74/0.93 = { by lemma 6 }
% 3.74/0.93 tuple(composition(sk2, sk3), converse(converse(composition(sk3, sk2))))
% 3.74/0.93 = { by axiom 1 (converse_idempotence_8) }
% 3.74/0.93 tuple(composition(sk2, sk3), composition(sk3, sk2))
% 3.74/0.93 % SZS output end Proof
% 3.74/0.93
% 3.74/0.93 RESULT: Unsatisfiable (the axioms are contradictory).
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