TSTP Solution File: REL031-2 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : REL031-2 : 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 : n007.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 13:44:16 EDT 2023
% Result : Unsatisfiable 0.20s 0.50s
% Output : Proof 0.20s
% 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 : REL031-2 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.13 % 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 : n007.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 19:47:41 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.50 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.20/0.50
% 0.20/0.50 % SZS status Unsatisfiable
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% 0.20/0.51 % SZS output start Proof
% 0.20/0.51 Axiom 1 (converse_idempotence_8): converse(converse(X)) = X.
% 0.20/0.51 Axiom 2 (maddux1_join_commutativity_1): join(X, Y) = join(Y, X).
% 0.20/0.51 Axiom 3 (composition_identity_6): composition(X, one) = X.
% 0.20/0.51 Axiom 4 (converse_additivity_9): converse(join(X, Y)) = join(converse(X), converse(Y)).
% 0.20/0.51 Axiom 5 (maddux2_join_associativity_2): join(X, join(Y, Z)) = join(join(X, Y), Z).
% 0.20/0.51 Axiom 6 (converse_multiplicativity_10): converse(composition(X, Y)) = composition(converse(Y), converse(X)).
% 0.20/0.51 Axiom 7 (composition_associativity_5): composition(X, composition(Y, Z)) = composition(composition(X, Y), Z).
% 0.20/0.51 Axiom 8 (goals_17): join(composition(converse(sk1), sk1), one) = one.
% 0.20/0.51 Axiom 9 (goals_18): join(composition(converse(sk2), sk2), one) = one.
% 0.20/0.51 Axiom 10 (composition_distributivity_7): composition(join(X, Y), Z) = join(composition(X, Z), composition(Y, Z)).
% 0.20/0.51
% 0.20/0.51 Lemma 11: converse(composition(converse(X), Y)) = composition(converse(Y), X).
% 0.20/0.51 Proof:
% 0.20/0.51 converse(composition(converse(X), Y))
% 0.20/0.51 = { by axiom 6 (converse_multiplicativity_10) }
% 0.20/0.51 composition(converse(Y), converse(converse(X)))
% 0.20/0.51 = { by axiom 1 (converse_idempotence_8) }
% 0.20/0.51 composition(converse(Y), X)
% 0.20/0.51
% 0.20/0.51 Lemma 12: composition(converse(one), X) = X.
% 0.20/0.51 Proof:
% 0.20/0.51 composition(converse(one), X)
% 0.20/0.51 = { by lemma 11 R->L }
% 0.20/0.51 converse(composition(converse(X), one))
% 0.20/0.51 = { by axiom 3 (composition_identity_6) }
% 0.20/0.51 converse(converse(X))
% 0.20/0.51 = { by axiom 1 (converse_idempotence_8) }
% 0.20/0.51 X
% 0.20/0.51
% 0.20/0.51 Lemma 13: converse(one) = one.
% 0.20/0.51 Proof:
% 0.20/0.51 converse(one)
% 0.20/0.51 = { by axiom 3 (composition_identity_6) R->L }
% 0.20/0.51 composition(converse(one), one)
% 0.20/0.51 = { by lemma 12 }
% 0.20/0.51 one
% 0.20/0.51
% 0.20/0.51 Lemma 14: join(one, composition(converse(sk2), sk2)) = one.
% 0.20/0.51 Proof:
% 0.20/0.51 join(one, composition(converse(sk2), sk2))
% 0.20/0.51 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 0.20/0.51 join(composition(converse(sk2), sk2), one)
% 0.20/0.51 = { by axiom 9 (goals_18) }
% 0.20/0.51 one
% 0.20/0.51
% 0.20/0.51 Goal 1 (goals_19): join(composition(converse(composition(sk1, sk2)), composition(sk1, sk2)), one) = one.
% 0.20/0.51 Proof:
% 0.20/0.51 join(composition(converse(composition(sk1, sk2)), composition(sk1, sk2)), one)
% 0.20/0.51 = { by axiom 2 (maddux1_join_commutativity_1) }
% 0.20/0.51 join(one, composition(converse(composition(sk1, sk2)), composition(sk1, sk2)))
% 0.20/0.51 = { by axiom 7 (composition_associativity_5) }
% 0.20/0.51 join(one, composition(composition(converse(composition(sk1, sk2)), sk1), sk2))
% 0.20/0.51 = { by lemma 14 R->L }
% 0.20/0.51 join(join(one, composition(converse(sk2), sk2)), composition(composition(converse(composition(sk1, sk2)), sk1), sk2))
% 0.20/0.51 = { by axiom 5 (maddux2_join_associativity_2) R->L }
% 0.20/0.51 join(one, join(composition(converse(sk2), sk2), composition(composition(converse(composition(sk1, sk2)), sk1), sk2)))
% 0.20/0.51 = { by axiom 2 (maddux1_join_commutativity_1) }
% 0.20/0.51 join(one, join(composition(composition(converse(composition(sk1, sk2)), sk1), sk2), composition(converse(sk2), sk2)))
% 0.20/0.51 = { by axiom 10 (composition_distributivity_7) R->L }
% 0.20/0.51 join(one, composition(join(composition(converse(composition(sk1, sk2)), sk1), converse(sk2)), sk2))
% 0.20/0.51 = { by axiom 2 (maddux1_join_commutativity_1) }
% 0.20/0.51 join(one, composition(join(converse(sk2), composition(converse(composition(sk1, sk2)), sk1)), sk2))
% 0.20/0.51 = { by axiom 6 (converse_multiplicativity_10) }
% 0.20/0.51 join(one, composition(join(converse(sk2), composition(composition(converse(sk2), converse(sk1)), sk1)), sk2))
% 0.20/0.51 = { by axiom 1 (converse_idempotence_8) R->L }
% 0.20/0.51 join(one, composition(join(converse(sk2), composition(composition(converse(converse(converse(sk2))), converse(sk1)), sk1)), sk2))
% 0.20/0.51 = { by axiom 6 (converse_multiplicativity_10) R->L }
% 0.20/0.51 join(one, composition(join(converse(sk2), composition(converse(composition(sk1, converse(converse(sk2)))), sk1)), sk2))
% 0.20/0.51 = { by lemma 11 R->L }
% 0.20/0.51 join(one, composition(join(converse(sk2), converse(composition(converse(sk1), composition(sk1, converse(converse(sk2)))))), sk2))
% 0.20/0.51 = { by axiom 1 (converse_idempotence_8) R->L }
% 0.20/0.51 join(one, composition(join(converse(converse(converse(sk2))), converse(composition(converse(sk1), composition(sk1, converse(converse(sk2)))))), sk2))
% 0.20/0.51 = { by axiom 4 (converse_additivity_9) R->L }
% 0.20/0.51 join(one, composition(converse(join(converse(converse(sk2)), composition(converse(sk1), composition(sk1, converse(converse(sk2)))))), sk2))
% 0.20/0.51 = { by axiom 7 (composition_associativity_5) }
% 0.20/0.51 join(one, composition(converse(join(converse(converse(sk2)), composition(composition(converse(sk1), sk1), converse(converse(sk2))))), sk2))
% 0.20/0.51 = { by lemma 12 R->L }
% 0.20/0.51 join(one, composition(converse(join(composition(converse(one), converse(converse(sk2))), composition(composition(converse(sk1), sk1), converse(converse(sk2))))), sk2))
% 0.20/0.51 = { by axiom 10 (composition_distributivity_7) R->L }
% 0.20/0.51 join(one, composition(converse(composition(join(converse(one), composition(converse(sk1), sk1)), converse(converse(sk2)))), sk2))
% 0.20/0.51 = { by lemma 13 }
% 0.20/0.51 join(one, composition(converse(composition(join(one, composition(converse(sk1), sk1)), converse(converse(sk2)))), sk2))
% 0.20/0.51 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 0.20/0.51 join(one, composition(converse(composition(join(composition(converse(sk1), sk1), one), converse(converse(sk2)))), sk2))
% 0.20/0.51 = { by axiom 8 (goals_17) }
% 0.20/0.51 join(one, composition(converse(composition(one, converse(converse(sk2)))), sk2))
% 0.20/0.51 = { by lemma 13 R->L }
% 0.20/0.51 join(one, composition(converse(composition(converse(one), converse(converse(sk2)))), sk2))
% 0.20/0.51 = { by lemma 12 }
% 0.20/0.51 join(one, composition(converse(converse(converse(sk2))), sk2))
% 0.20/0.51 = { by axiom 1 (converse_idempotence_8) }
% 0.20/0.51 join(one, composition(converse(sk2), sk2))
% 0.20/0.51 = { by lemma 14 }
% 0.20/0.51 one
% 0.20/0.51 % SZS output end Proof
% 0.20/0.51
% 0.20/0.51 RESULT: Unsatisfiable (the axioms are contradictory).
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