TSTP Solution File: REL008+1 by Twee---2.4.2
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- Process Solution
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% File : Twee---2.4.2
% Problem : REL008+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 : n028.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 13:43:47 EDT 2023
% Result : Theorem 0.20s 0.59s
% 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 : REL008+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
% 0.16/0.34 % Computer : n028.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Fri Aug 25 21:06:36 EDT 2023
% 0.16/0.34 % CPUTime :
% 0.20/0.59 Command-line arguments: --no-flatten-goal
% 0.20/0.59
% 0.20/0.59 % SZS status Theorem
% 0.20/0.59
% 0.20/0.60 % SZS output start Proof
% 0.20/0.60 Axiom 1 (converse_idempotence): converse(converse(X)) = X.
% 0.20/0.60 Axiom 2 (maddux1_join_commutativity): join(X, Y) = join(Y, X).
% 0.20/0.60 Axiom 3 (converse_multiplicativity): converse(composition(X, Y)) = composition(converse(Y), converse(X)).
% 0.20/0.60 Axiom 4 (converse_additivity): converse(join(X, Y)) = join(converse(X), converse(Y)).
% 0.20/0.60 Axiom 5 (composition_distributivity): composition(join(X, Y), Z) = join(composition(X, Z), composition(Y, Z)).
% 0.20/0.60
% 0.20/0.60 Goal 1 (goals): composition(x0, join(x1, x2)) = join(composition(x0, x1), composition(x0, x2)).
% 0.20/0.60 Proof:
% 0.20/0.60 composition(x0, join(x1, x2))
% 0.20/0.60 = { by axiom 1 (converse_idempotence) R->L }
% 0.20/0.60 composition(x0, join(x1, converse(converse(x2))))
% 0.20/0.60 = { by axiom 1 (converse_idempotence) R->L }
% 0.20/0.60 converse(converse(composition(x0, join(x1, converse(converse(x2))))))
% 0.20/0.60 = { by axiom 3 (converse_multiplicativity) }
% 0.20/0.60 converse(composition(converse(join(x1, converse(converse(x2)))), converse(x0)))
% 0.20/0.60 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 0.20/0.60 converse(composition(converse(join(converse(converse(x2)), x1)), converse(x0)))
% 0.20/0.60 = { by axiom 4 (converse_additivity) }
% 0.20/0.60 converse(composition(join(converse(converse(converse(x2))), converse(x1)), converse(x0)))
% 0.20/0.60 = { by axiom 1 (converse_idempotence) }
% 0.20/0.60 converse(composition(join(converse(x2), converse(x1)), converse(x0)))
% 0.20/0.60 = { by axiom 2 (maddux1_join_commutativity) }
% 0.20/0.60 converse(composition(join(converse(x1), converse(x2)), converse(x0)))
% 0.20/0.60 = { by axiom 5 (composition_distributivity) }
% 0.20/0.60 converse(join(composition(converse(x1), converse(x0)), composition(converse(x2), converse(x0))))
% 0.20/0.60 = { by axiom 3 (converse_multiplicativity) R->L }
% 0.20/0.60 converse(join(converse(composition(x0, x1)), composition(converse(x2), converse(x0))))
% 0.20/0.60 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 0.20/0.60 converse(join(composition(converse(x2), converse(x0)), converse(composition(x0, x1))))
% 0.20/0.60 = { by axiom 1 (converse_idempotence) R->L }
% 0.20/0.60 converse(join(composition(converse(converse(converse(x2))), converse(x0)), converse(composition(x0, x1))))
% 0.20/0.60 = { by axiom 3 (converse_multiplicativity) R->L }
% 0.20/0.60 converse(join(converse(composition(x0, converse(converse(x2)))), converse(composition(x0, x1))))
% 0.20/0.60 = { by axiom 4 (converse_additivity) R->L }
% 0.20/0.60 converse(converse(join(composition(x0, converse(converse(x2))), composition(x0, x1))))
% 0.20/0.60 = { by axiom 2 (maddux1_join_commutativity) }
% 0.20/0.60 converse(converse(join(composition(x0, x1), composition(x0, converse(converse(x2))))))
% 0.20/0.60 = { by axiom 1 (converse_idempotence) }
% 0.20/0.60 join(composition(x0, x1), composition(x0, converse(converse(x2))))
% 0.20/0.60 = { by axiom 1 (converse_idempotence) }
% 0.20/0.60 join(composition(x0, x1), composition(x0, x2))
% 0.20/0.60 % SZS output end Proof
% 0.20/0.60
% 0.20/0.60 RESULT: Theorem (the conjecture is true).
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