TSTP Solution File: REL015+1 by Twee---2.4.2
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- Process Solution
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% File : Twee---2.4.2
% Problem : REL015+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 : n025.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 13:43:54 EDT 2023
% Result : Theorem 0.21s 0.41s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : REL015+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.18/0.35 % Computer : n025.cluster.edu
% 0.18/0.35 % Model : x86_64 x86_64
% 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35 % Memory : 8042.1875MB
% 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35 % CPULimit : 300
% 0.18/0.35 % WCLimit : 300
% 0.18/0.35 % DateTime : Fri Aug 25 19:28:52 EDT 2023
% 0.18/0.35 % CPUTime :
% 0.21/0.41 Command-line arguments: --flatten
% 0.21/0.41
% 0.21/0.41 % SZS status Theorem
% 0.21/0.41
% 0.21/0.42 % SZS output start Proof
% 0.21/0.42 Axiom 1 (converse_idempotence): converse(converse(X)) = X.
% 0.21/0.42 Axiom 2 (composition_identity): composition(X, one) = X.
% 0.21/0.42 Axiom 3 (maddux1_join_commutativity): join(X, Y) = join(Y, X).
% 0.21/0.42 Axiom 4 (def_zero): zero = meet(X, complement(X)).
% 0.21/0.42 Axiom 5 (def_top): top = join(X, complement(X)).
% 0.21/0.42 Axiom 6 (converse_multiplicativity): converse(composition(X, Y)) = composition(converse(Y), converse(X)).
% 0.21/0.42 Axiom 7 (composition_associativity): composition(X, composition(Y, Z)) = composition(composition(X, Y), Z).
% 0.21/0.42 Axiom 8 (maddux2_join_associativity): join(X, join(Y, Z)) = join(join(X, Y), Z).
% 0.21/0.42 Axiom 9 (maddux4_definiton_of_meet): meet(X, Y) = complement(join(complement(X), complement(Y))).
% 0.21/0.42 Axiom 10 (composition_distributivity): composition(join(X, Y), Z) = join(composition(X, Z), composition(Y, Z)).
% 0.21/0.42 Axiom 11 (converse_cancellativity): join(composition(converse(X), complement(composition(X, Y))), complement(Y)) = complement(Y).
% 0.21/0.42
% 0.21/0.42 Lemma 12: join(X, join(Y, complement(X))) = join(Y, top).
% 0.21/0.42 Proof:
% 0.21/0.42 join(X, join(Y, complement(X)))
% 0.21/0.42 = { by axiom 3 (maddux1_join_commutativity) R->L }
% 0.21/0.42 join(X, join(complement(X), Y))
% 0.21/0.42 = { by axiom 8 (maddux2_join_associativity) }
% 0.21/0.42 join(join(X, complement(X)), Y)
% 0.21/0.42 = { by axiom 5 (def_top) R->L }
% 0.21/0.42 join(top, Y)
% 0.21/0.42 = { by axiom 3 (maddux1_join_commutativity) }
% 0.21/0.42 join(Y, top)
% 0.21/0.42
% 0.21/0.42 Lemma 13: composition(converse(one), X) = X.
% 0.21/0.42 Proof:
% 0.21/0.42 composition(converse(one), X)
% 0.21/0.42 = { by axiom 1 (converse_idempotence) R->L }
% 0.21/0.42 composition(converse(one), converse(converse(X)))
% 0.21/0.42 = { by axiom 6 (converse_multiplicativity) R->L }
% 0.21/0.42 converse(composition(converse(X), one))
% 0.21/0.42 = { by axiom 2 (composition_identity) }
% 0.21/0.42 converse(converse(X))
% 0.21/0.42 = { by axiom 1 (converse_idempotence) }
% 0.21/0.42 X
% 0.21/0.42
% 0.21/0.42 Lemma 14: join(top, complement(X)) = top.
% 0.21/0.42 Proof:
% 0.21/0.42 join(top, complement(X))
% 0.21/0.42 = { by axiom 3 (maddux1_join_commutativity) R->L }
% 0.21/0.42 join(complement(X), top)
% 0.21/0.42 = { by lemma 12 R->L }
% 0.21/0.42 join(X, join(complement(X), complement(X)))
% 0.21/0.42 = { by lemma 13 R->L }
% 0.21/0.42 join(X, join(complement(X), composition(converse(one), complement(X))))
% 0.21/0.42 = { by lemma 13 R->L }
% 0.21/0.42 join(X, join(complement(X), composition(converse(one), complement(composition(converse(one), X)))))
% 0.21/0.42 = { by axiom 2 (composition_identity) R->L }
% 0.21/0.42 join(X, join(complement(X), composition(converse(one), complement(composition(composition(converse(one), one), X)))))
% 0.21/0.42 = { by axiom 7 (composition_associativity) R->L }
% 0.21/0.42 join(X, join(complement(X), composition(converse(one), complement(composition(converse(one), composition(one, X))))))
% 0.21/0.42 = { by lemma 13 }
% 0.21/0.42 join(X, join(complement(X), composition(converse(one), complement(composition(one, X)))))
% 0.21/0.42 = { by axiom 3 (maddux1_join_commutativity) R->L }
% 0.21/0.42 join(X, join(composition(converse(one), complement(composition(one, X))), complement(X)))
% 0.21/0.43 = { by axiom 11 (converse_cancellativity) }
% 0.21/0.43 join(X, complement(X))
% 0.21/0.43 = { by axiom 5 (def_top) R->L }
% 0.21/0.43 top
% 0.21/0.43
% 0.21/0.43 Lemma 15: join(X, top) = top.
% 0.21/0.43 Proof:
% 0.21/0.43 join(X, top)
% 0.21/0.43 = { by lemma 14 R->L }
% 0.21/0.43 join(X, join(top, complement(X)))
% 0.21/0.43 = { by lemma 12 }
% 0.21/0.43 join(top, top)
% 0.21/0.43 = { by lemma 12 R->L }
% 0.21/0.43 join(zero, join(top, complement(zero)))
% 0.21/0.43 = { by lemma 14 }
% 0.21/0.43 join(zero, top)
% 0.21/0.43 = { by axiom 3 (maddux1_join_commutativity) R->L }
% 0.21/0.43 join(top, zero)
% 0.21/0.43 = { by axiom 4 (def_zero) }
% 0.21/0.43 join(top, meet(Y, complement(Y)))
% 0.21/0.43 = { by axiom 9 (maddux4_definiton_of_meet) }
% 0.21/0.43 join(top, complement(join(complement(Y), complement(complement(Y)))))
% 0.21/0.43 = { by axiom 5 (def_top) R->L }
% 0.21/0.43 join(top, complement(top))
% 0.21/0.43 = { by axiom 5 (def_top) R->L }
% 0.21/0.43 top
% 0.21/0.43
% 0.21/0.43 Goal 1 (goals): composition(top, top) = top.
% 0.21/0.43 Proof:
% 0.21/0.43 composition(top, top)
% 0.21/0.43 = { by lemma 15 R->L }
% 0.21/0.43 composition(join(converse(one), top), top)
% 0.21/0.43 = { by axiom 3 (maddux1_join_commutativity) R->L }
% 0.21/0.43 composition(join(top, converse(one)), top)
% 0.21/0.43 = { by axiom 10 (composition_distributivity) }
% 0.21/0.43 join(composition(top, top), composition(converse(one), top))
% 0.21/0.43 = { by lemma 13 }
% 0.21/0.43 join(composition(top, top), top)
% 0.21/0.43 = { by lemma 15 }
% 0.21/0.43 top
% 0.21/0.43 % SZS output end Proof
% 0.21/0.43
% 0.21/0.43 RESULT: Theorem (the conjecture is true).
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