TSTP Solution File: REL009-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : REL009-1 : 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 : n027.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 13:43:49 EDT 2023
% Result : Unsatisfiable 0.19s 0.62s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : REL009-1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.17/0.34 % Computer : n027.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Fri Aug 25 19:49:34 EDT 2023
% 0.17/0.35 % CPUTime :
% 0.19/0.62 Command-line arguments: --no-flatten-goal
% 0.19/0.62
% 0.19/0.62 % SZS status Unsatisfiable
% 0.19/0.62
% 0.19/0.63 % SZS output start Proof
% 0.19/0.63 Take the following subset of the input axioms:
% 0.19/0.63 fof(composition_distributivity_7, axiom, ![A, B, C]: composition(join(A, B), C)=join(composition(A, C), composition(B, C))).
% 0.19/0.63 fof(converse_additivity_9, axiom, ![A2, B2]: converse(join(A2, B2))=join(converse(A2), converse(B2))).
% 0.19/0.63 fof(converse_idempotence_8, axiom, ![A2]: converse(converse(A2))=A2).
% 0.19/0.63 fof(converse_multiplicativity_10, axiom, ![A2, B2]: converse(composition(A2, B2))=composition(converse(B2), converse(A2))).
% 0.19/0.63 fof(goals_14, negated_conjecture, join(sk1, sk2)=sk2).
% 0.19/0.63 fof(goals_15, negated_conjecture, join(composition(sk1, sk3), composition(sk2, sk3))!=composition(sk2, sk3) | join(composition(sk3, sk1), composition(sk3, sk2))!=composition(sk3, sk2)).
% 0.19/0.63 fof(maddux1_join_commutativity_1, axiom, ![A2, B2]: join(A2, B2)=join(B2, A2)).
% 0.19/0.63
% 0.19/0.63 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.63 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.63 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.63 fresh(y, y, x1...xn) = u
% 0.19/0.63 C => fresh(s, t, x1...xn) = v
% 0.19/0.63 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.63 variables of u and v.
% 0.19/0.63 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.63 input problem has no model of domain size 1).
% 0.19/0.63
% 0.19/0.63 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.63
% 0.19/0.63 Axiom 1 (converse_idempotence_8): converse(converse(X)) = X.
% 0.19/0.63 Axiom 2 (maddux1_join_commutativity_1): join(X, Y) = join(Y, X).
% 0.19/0.63 Axiom 3 (goals_14): join(sk1, sk2) = sk2.
% 0.19/0.63 Axiom 4 (converse_multiplicativity_10): converse(composition(X, Y)) = composition(converse(Y), converse(X)).
% 0.19/0.63 Axiom 5 (converse_additivity_9): converse(join(X, Y)) = join(converse(X), converse(Y)).
% 0.19/0.63 Axiom 6 (composition_distributivity_7): composition(join(X, Y), Z) = join(composition(X, Z), composition(Y, Z)).
% 0.19/0.63
% 0.19/0.63 Goal 1 (goals_15): tuple(join(composition(sk1, sk3), composition(sk2, sk3)), join(composition(sk3, sk1), composition(sk3, sk2))) = tuple(composition(sk2, sk3), composition(sk3, sk2)).
% 0.19/0.63 Proof:
% 0.19/0.63 tuple(join(composition(sk1, sk3), composition(sk2, sk3)), join(composition(sk3, sk1), composition(sk3, sk2)))
% 0.19/0.63 = { by axiom 6 (composition_distributivity_7) R->L }
% 0.19/0.63 tuple(composition(join(sk1, sk2), sk3), join(composition(sk3, sk1), composition(sk3, sk2)))
% 0.19/0.63 = { by axiom 3 (goals_14) }
% 0.19/0.63 tuple(composition(sk2, sk3), join(composition(sk3, sk1), composition(sk3, sk2)))
% 0.19/0.63 = { by axiom 1 (converse_idempotence_8) R->L }
% 0.19/0.63 tuple(composition(sk2, sk3), join(composition(sk3, sk1), composition(sk3, converse(converse(sk2)))))
% 0.19/0.63 = { by axiom 1 (converse_idempotence_8) R->L }
% 0.19/0.63 tuple(composition(sk2, sk3), converse(converse(join(composition(sk3, sk1), composition(sk3, converse(converse(sk2)))))))
% 0.19/0.63 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 0.19/0.63 tuple(composition(sk2, sk3), converse(converse(join(composition(sk3, converse(converse(sk2))), composition(sk3, sk1)))))
% 0.19/0.63 = { by axiom 5 (converse_additivity_9) }
% 0.19/0.63 tuple(composition(sk2, sk3), converse(join(converse(composition(sk3, converse(converse(sk2)))), converse(composition(sk3, sk1)))))
% 0.19/0.63 = { by axiom 4 (converse_multiplicativity_10) }
% 0.19/0.63 tuple(composition(sk2, sk3), converse(join(composition(converse(converse(converse(sk2))), converse(sk3)), converse(composition(sk3, sk1)))))
% 0.19/0.63 = { by axiom 1 (converse_idempotence_8) }
% 0.19/0.63 tuple(composition(sk2, sk3), converse(join(composition(converse(sk2), converse(sk3)), converse(composition(sk3, sk1)))))
% 0.19/0.63 = { by axiom 2 (maddux1_join_commutativity_1) }
% 0.19/0.63 tuple(composition(sk2, sk3), converse(join(converse(composition(sk3, sk1)), composition(converse(sk2), converse(sk3)))))
% 0.19/0.63 = { by axiom 4 (converse_multiplicativity_10) }
% 0.19/0.63 tuple(composition(sk2, sk3), converse(join(composition(converse(sk1), converse(sk3)), composition(converse(sk2), converse(sk3)))))
% 0.19/0.63 = { by axiom 6 (composition_distributivity_7) R->L }
% 0.19/0.63 tuple(composition(sk2, sk3), converse(composition(join(converse(sk1), converse(sk2)), converse(sk3))))
% 0.19/0.63 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 0.19/0.63 tuple(composition(sk2, sk3), converse(composition(join(converse(sk2), converse(sk1)), converse(sk3))))
% 0.19/0.63 = { by axiom 1 (converse_idempotence_8) R->L }
% 0.19/0.63 tuple(composition(sk2, sk3), converse(composition(join(converse(converse(converse(sk2))), converse(sk1)), converse(sk3))))
% 0.19/0.63 = { by axiom 5 (converse_additivity_9) R->L }
% 0.19/0.63 tuple(composition(sk2, sk3), converse(composition(converse(join(converse(converse(sk2)), sk1)), converse(sk3))))
% 0.19/0.63 = { by axiom 2 (maddux1_join_commutativity_1) }
% 0.19/0.63 tuple(composition(sk2, sk3), converse(composition(converse(join(sk1, converse(converse(sk2)))), converse(sk3))))
% 0.19/0.63 = { by axiom 4 (converse_multiplicativity_10) R->L }
% 0.19/0.63 tuple(composition(sk2, sk3), converse(converse(composition(sk3, join(sk1, converse(converse(sk2)))))))
% 0.19/0.63 = { by axiom 1 (converse_idempotence_8) }
% 0.19/0.63 tuple(composition(sk2, sk3), composition(sk3, join(sk1, converse(converse(sk2)))))
% 0.19/0.63 = { by axiom 1 (converse_idempotence_8) }
% 0.19/0.63 tuple(composition(sk2, sk3), composition(sk3, join(sk1, sk2)))
% 0.19/0.63 = { by axiom 3 (goals_14) }
% 0.19/0.63 tuple(composition(sk2, sk3), composition(sk3, sk2))
% 0.19/0.63 % SZS output end Proof
% 0.19/0.63
% 0.19/0.63 RESULT: Unsatisfiable (the axioms are contradictory).
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