TSTP Solution File: REL031-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : REL031-1 : 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 : n002.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 13:44:15 EDT 2023
% Result : Unsatisfiable 3.60s 0.83s
% Output : Proof 3.60s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : REL031-1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 19:46:02 EDT 2023
% 0.13/0.34 % CPUTime :
% 3.60/0.83 Command-line arguments: --flatten
% 3.60/0.83
% 3.60/0.83 % SZS status Unsatisfiable
% 3.60/0.83
% 3.60/0.83 % SZS output start Proof
% 3.60/0.83 Axiom 1 (converse_idempotence_8): converse(converse(X)) = X.
% 3.60/0.83 Axiom 2 (maddux1_join_commutativity_1): join(X, Y) = join(Y, X).
% 3.60/0.83 Axiom 3 (composition_identity_6): composition(X, one) = X.
% 3.60/0.83 Axiom 4 (converse_additivity_9): converse(join(X, Y)) = join(converse(X), converse(Y)).
% 3.60/0.83 Axiom 5 (maddux2_join_associativity_2): join(X, join(Y, Z)) = join(join(X, Y), Z).
% 3.60/0.83 Axiom 6 (converse_multiplicativity_10): converse(composition(X, Y)) = composition(converse(Y), converse(X)).
% 3.60/0.83 Axiom 7 (composition_associativity_5): composition(X, composition(Y, Z)) = composition(composition(X, Y), Z).
% 3.60/0.83 Axiom 8 (goals_14): join(composition(converse(sk1), sk1), one) = one.
% 3.60/0.83 Axiom 9 (goals_15): join(composition(converse(sk2), sk2), one) = one.
% 3.60/0.83 Axiom 10 (composition_distributivity_7): composition(join(X, Y), Z) = join(composition(X, Z), composition(Y, Z)).
% 3.60/0.83
% 3.60/0.83 Lemma 11: converse(composition(converse(X), Y)) = composition(converse(Y), X).
% 3.60/0.83 Proof:
% 3.60/0.83 converse(composition(converse(X), Y))
% 3.60/0.83 = { by axiom 6 (converse_multiplicativity_10) }
% 3.60/0.83 composition(converse(Y), converse(converse(X)))
% 3.60/0.83 = { by axiom 1 (converse_idempotence_8) }
% 3.60/0.83 composition(converse(Y), X)
% 3.60/0.83
% 3.60/0.83 Lemma 12: join(composition(converse(sk2), sk2), one) = join(composition(converse(sk1), sk1), one).
% 3.60/0.83 Proof:
% 3.60/0.83 join(composition(converse(sk2), sk2), one)
% 3.60/0.83 = { by axiom 9 (goals_15) }
% 3.60/0.83 one
% 3.60/0.83 = { by axiom 8 (goals_14) R->L }
% 3.60/0.83 join(composition(converse(sk1), sk1), one)
% 3.60/0.83
% 3.60/0.83 Lemma 13: join(join(composition(converse(sk1), sk1), one), X) = join(X, one).
% 3.60/0.83 Proof:
% 3.60/0.83 join(join(composition(converse(sk1), sk1), one), X)
% 3.60/0.83 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 3.60/0.83 join(X, join(composition(converse(sk1), sk1), one))
% 3.60/0.83 = { by axiom 8 (goals_14) }
% 3.60/0.83 join(X, one)
% 3.60/0.83
% 3.60/0.83 Lemma 14: composition(converse(join(composition(converse(sk1), sk1), one)), X) = X.
% 3.60/0.83 Proof:
% 3.60/0.83 composition(converse(join(composition(converse(sk1), sk1), one)), X)
% 3.60/0.83 = { by axiom 8 (goals_14) }
% 3.60/0.83 composition(converse(one), X)
% 3.60/0.83 = { by lemma 11 R->L }
% 3.60/0.83 converse(composition(converse(X), one))
% 3.60/0.83 = { by axiom 3 (composition_identity_6) }
% 3.60/0.83 converse(converse(X))
% 3.60/0.83 = { by axiom 1 (converse_idempotence_8) }
% 3.60/0.84 X
% 3.60/0.84
% 3.60/0.84 Lemma 15: composition(join(composition(converse(sk1), sk1), one), X) = X.
% 3.60/0.84 Proof:
% 3.60/0.84 composition(join(composition(converse(sk1), sk1), one), X)
% 3.60/0.84 = { by lemma 14 R->L }
% 3.60/0.84 composition(converse(join(composition(converse(sk1), sk1), one)), composition(join(composition(converse(sk1), sk1), one), X))
% 3.60/0.84 = { by axiom 8 (goals_14) }
% 3.60/0.84 composition(converse(join(composition(converse(sk1), sk1), one)), composition(one, X))
% 3.60/0.84 = { by axiom 7 (composition_associativity_5) }
% 3.60/0.84 composition(composition(converse(join(composition(converse(sk1), sk1), one)), one), X)
% 3.60/0.84 = { by axiom 3 (composition_identity_6) }
% 3.60/0.84 composition(converse(join(composition(converse(sk1), sk1), one)), X)
% 3.60/0.84 = { by lemma 14 }
% 3.60/0.84 X
% 3.60/0.84
% 3.60/0.84 Goal 1 (goals_16): join(composition(converse(composition(sk1, sk2)), composition(sk1, sk2)), one) = one.
% 3.60/0.84 Proof:
% 3.60/0.84 join(composition(converse(composition(sk1, sk2)), composition(sk1, sk2)), one)
% 3.60/0.84 = { by lemma 13 R->L }
% 3.60/0.84 join(join(composition(converse(sk1), sk1), one), composition(converse(composition(sk1, sk2)), composition(sk1, sk2)))
% 3.60/0.84 = { by lemma 12 R->L }
% 3.60/0.84 join(join(composition(converse(sk2), sk2), one), composition(converse(composition(sk1, sk2)), composition(sk1, sk2)))
% 3.60/0.84 = { by lemma 13 R->L }
% 3.60/0.84 join(join(join(composition(converse(sk1), sk1), one), composition(converse(sk2), sk2)), composition(converse(composition(sk1, sk2)), composition(sk1, sk2)))
% 3.60/0.84 = { by axiom 5 (maddux2_join_associativity_2) R->L }
% 3.60/0.84 join(join(composition(converse(sk1), sk1), one), join(composition(converse(sk2), sk2), composition(converse(composition(sk1, sk2)), composition(sk1, sk2))))
% 3.60/0.84 = { by lemma 11 R->L }
% 3.60/0.84 join(join(composition(converse(sk1), sk1), one), join(composition(converse(sk2), sk2), converse(composition(converse(composition(sk1, sk2)), composition(sk1, sk2)))))
% 3.60/0.84 = { by axiom 7 (composition_associativity_5) }
% 3.60/0.84 join(join(composition(converse(sk1), sk1), one), join(composition(converse(sk2), sk2), converse(composition(composition(converse(composition(sk1, sk2)), sk1), sk2))))
% 3.60/0.84 = { by axiom 6 (converse_multiplicativity_10) }
% 3.60/0.84 join(join(composition(converse(sk1), sk1), one), join(composition(converse(sk2), sk2), composition(converse(sk2), converse(composition(converse(composition(sk1, sk2)), sk1)))))
% 3.60/0.84 = { by lemma 11 }
% 3.60/0.84 join(join(composition(converse(sk1), sk1), one), join(composition(converse(sk2), sk2), composition(converse(sk2), composition(converse(sk1), composition(sk1, sk2)))))
% 3.60/0.84 = { by axiom 7 (composition_associativity_5) }
% 3.60/0.84 join(join(composition(converse(sk1), sk1), one), join(composition(converse(sk2), sk2), composition(converse(sk2), composition(composition(converse(sk1), sk1), sk2))))
% 3.60/0.84 = { by axiom 7 (composition_associativity_5) }
% 3.60/0.84 join(join(composition(converse(sk1), sk1), one), join(composition(converse(sk2), sk2), composition(composition(converse(sk2), composition(converse(sk1), sk1)), sk2)))
% 3.60/0.84 = { by axiom 10 (composition_distributivity_7) R->L }
% 3.60/0.84 join(join(composition(converse(sk1), sk1), one), composition(join(converse(sk2), composition(converse(sk2), composition(converse(sk1), sk1))), sk2))
% 3.60/0.84 = { by lemma 11 R->L }
% 3.60/0.84 join(join(composition(converse(sk1), sk1), one), composition(join(converse(sk2), composition(converse(sk2), converse(composition(converse(sk1), sk1)))), sk2))
% 3.60/0.84 = { by axiom 1 (converse_idempotence_8) R->L }
% 3.60/0.84 join(join(composition(converse(sk1), sk1), one), composition(join(converse(sk2), composition(converse(converse(converse(sk2))), converse(composition(converse(sk1), sk1)))), sk2))
% 3.60/0.84 = { by axiom 6 (converse_multiplicativity_10) R->L }
% 3.60/0.84 join(join(composition(converse(sk1), sk1), one), composition(join(converse(sk2), converse(composition(composition(converse(sk1), sk1), converse(converse(sk2))))), sk2))
% 3.60/0.84 = { by axiom 1 (converse_idempotence_8) R->L }
% 3.60/0.84 join(join(composition(converse(sk1), sk1), one), composition(join(converse(converse(converse(sk2))), converse(composition(composition(converse(sk1), sk1), converse(converse(sk2))))), sk2))
% 3.60/0.84 = { by axiom 4 (converse_additivity_9) R->L }
% 3.60/0.84 join(join(composition(converse(sk1), sk1), one), composition(converse(join(converse(converse(sk2)), composition(composition(converse(sk1), sk1), converse(converse(sk2))))), sk2))
% 3.60/0.84 = { by lemma 15 R->L }
% 3.60/0.84 join(join(composition(converse(sk1), sk1), one), composition(converse(join(composition(join(composition(converse(sk1), sk1), one), converse(converse(sk2))), composition(composition(converse(sk1), sk1), converse(converse(sk2))))), sk2))
% 3.60/0.84 = { by axiom 10 (composition_distributivity_7) R->L }
% 3.60/0.84 join(join(composition(converse(sk1), sk1), one), composition(converse(composition(join(join(composition(converse(sk1), sk1), one), composition(converse(sk1), sk1)), converse(converse(sk2)))), sk2))
% 3.60/0.84 = { by lemma 13 }
% 3.60/0.84 join(join(composition(converse(sk1), sk1), one), composition(converse(composition(join(composition(converse(sk1), sk1), one), converse(converse(sk2)))), sk2))
% 3.60/0.84 = { by lemma 15 }
% 3.60/0.84 join(join(composition(converse(sk1), sk1), one), composition(converse(converse(converse(sk2))), sk2))
% 3.60/0.84 = { by axiom 1 (converse_idempotence_8) }
% 3.60/0.84 join(join(composition(converse(sk1), sk1), one), composition(converse(sk2), sk2))
% 3.60/0.84 = { by lemma 13 }
% 3.60/0.84 join(composition(converse(sk2), sk2), one)
% 3.60/0.84 = { by lemma 12 }
% 3.60/0.84 join(composition(converse(sk1), sk1), one)
% 3.60/0.84 = { by axiom 8 (goals_14) }
% 3.60/0.84 one
% 3.60/0.84 % SZS output end Proof
% 3.60/0.84
% 3.60/0.84 RESULT: Unsatisfiable (the axioms are contradictory).
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