TSTP Solution File: REL001+1 by Twee---2.4.2
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- Process Solution
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% File : Twee---2.4.2
% Problem : REL001+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 : n004.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 13:43:42 EDT 2023
% Result : Theorem 0.20s 0.43s
% 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 : REL001+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
% 0.13/0.35 % Computer : n004.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Aug 25 20:00:08 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.43 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.20/0.43
% 0.20/0.43 % SZS status Theorem
% 0.20/0.43
% 0.20/0.44 % SZS output start Proof
% 0.20/0.44 Axiom 1 (maddux1_join_commutativity): join(X, Y) = join(Y, X).
% 0.20/0.44 Axiom 2 (composition_identity): composition(X, one) = X.
% 0.20/0.44 Axiom 3 (converse_idempotence): converse(converse(X)) = X.
% 0.20/0.44 Axiom 4 (def_top): top = join(X, complement(X)).
% 0.20/0.44 Axiom 5 (def_zero): zero = meet(X, complement(X)).
% 0.20/0.44 Axiom 6 (maddux2_join_associativity): join(X, join(Y, Z)) = join(join(X, Y), Z).
% 0.20/0.44 Axiom 7 (converse_multiplicativity): converse(composition(X, Y)) = composition(converse(Y), converse(X)).
% 0.20/0.44 Axiom 8 (composition_associativity): composition(X, composition(Y, Z)) = composition(composition(X, Y), Z).
% 0.20/0.44 Axiom 9 (maddux4_definiton_of_meet): meet(X, Y) = complement(join(complement(X), complement(Y))).
% 0.20/0.44 Axiom 10 (converse_cancellativity): join(composition(converse(X), complement(composition(X, Y))), complement(Y)) = complement(Y).
% 0.20/0.44 Axiom 11 (maddux3_a_kind_of_de_Morgan): X = join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y))).
% 0.20/0.44
% 0.20/0.44 Lemma 12: complement(top) = zero.
% 0.20/0.44 Proof:
% 0.20/0.44 complement(top)
% 0.20/0.44 = { by axiom 4 (def_top) }
% 0.20/0.44 complement(join(complement(X), complement(complement(X))))
% 0.20/0.44 = { by axiom 9 (maddux4_definiton_of_meet) R->L }
% 0.20/0.44 meet(X, complement(X))
% 0.20/0.44 = { by axiom 5 (def_zero) R->L }
% 0.20/0.44 zero
% 0.20/0.44
% 0.20/0.44 Lemma 13: composition(converse(one), X) = X.
% 0.20/0.44 Proof:
% 0.20/0.44 composition(converse(one), X)
% 0.20/0.44 = { by axiom 3 (converse_idempotence) R->L }
% 0.20/0.44 composition(converse(one), converse(converse(X)))
% 0.20/0.44 = { by axiom 7 (converse_multiplicativity) R->L }
% 0.20/0.44 converse(composition(converse(X), one))
% 0.20/0.44 = { by axiom 2 (composition_identity) }
% 0.20/0.44 converse(converse(X))
% 0.20/0.44 = { by axiom 3 (converse_idempotence) }
% 0.20/0.44 X
% 0.20/0.44
% 0.20/0.44 Lemma 14: join(complement(X), complement(X)) = complement(X).
% 0.20/0.44 Proof:
% 0.20/0.44 join(complement(X), complement(X))
% 0.20/0.44 = { by lemma 13 R->L }
% 0.20/0.44 join(complement(X), composition(converse(one), complement(X)))
% 0.20/0.44 = { by lemma 13 R->L }
% 0.20/0.44 join(complement(X), composition(converse(one), complement(composition(converse(one), X))))
% 0.20/0.44 = { by axiom 2 (composition_identity) R->L }
% 0.20/0.44 join(complement(X), composition(converse(one), complement(composition(composition(converse(one), one), X))))
% 0.20/0.44 = { by axiom 8 (composition_associativity) R->L }
% 0.20/0.44 join(complement(X), composition(converse(one), complement(composition(converse(one), composition(one, X)))))
% 0.20/0.44 = { by lemma 13 }
% 0.20/0.44 join(complement(X), composition(converse(one), complement(composition(one, X))))
% 0.20/0.44 = { by axiom 1 (maddux1_join_commutativity) R->L }
% 0.20/0.44 join(composition(converse(one), complement(composition(one, X))), complement(X))
% 0.20/0.44 = { by axiom 10 (converse_cancellativity) }
% 0.20/0.44 complement(X)
% 0.20/0.44
% 0.20/0.44 Lemma 15: join(meet(X, Y), complement(join(complement(X), Y))) = X.
% 0.20/0.44 Proof:
% 0.20/0.44 join(meet(X, Y), complement(join(complement(X), Y)))
% 0.20/0.44 = { by axiom 9 (maddux4_definiton_of_meet) }
% 0.20/0.44 join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y)))
% 0.20/0.44 = { by axiom 11 (maddux3_a_kind_of_de_Morgan) R->L }
% 0.20/0.44 X
% 0.20/0.44
% 0.20/0.44 Goal 1 (goals): join(zero, x0) = x0.
% 0.20/0.44 Proof:
% 0.20/0.44 join(zero, x0)
% 0.20/0.44 = { by lemma 15 R->L }
% 0.20/0.44 join(zero, join(meet(x0, complement(x0)), complement(join(complement(x0), complement(x0)))))
% 0.20/0.44 = { by axiom 5 (def_zero) R->L }
% 0.20/0.44 join(zero, join(zero, complement(join(complement(x0), complement(x0)))))
% 0.20/0.44 = { by axiom 9 (maddux4_definiton_of_meet) R->L }
% 0.20/0.44 join(zero, join(zero, meet(x0, x0)))
% 0.20/0.44 = { by axiom 6 (maddux2_join_associativity) }
% 0.20/0.44 join(join(zero, zero), meet(x0, x0))
% 0.20/0.44 = { by lemma 12 R->L }
% 0.20/0.44 join(join(zero, complement(top)), meet(x0, x0))
% 0.20/0.44 = { by lemma 12 R->L }
% 0.20/0.44 join(join(complement(top), complement(top)), meet(x0, x0))
% 0.20/0.44 = { by lemma 14 }
% 0.20/0.44 join(complement(top), meet(x0, x0))
% 0.20/0.44 = { by lemma 12 }
% 0.20/0.44 join(zero, meet(x0, x0))
% 0.20/0.44 = { by axiom 1 (maddux1_join_commutativity) }
% 0.20/0.44 join(meet(x0, x0), zero)
% 0.20/0.44 = { by axiom 9 (maddux4_definiton_of_meet) }
% 0.20/0.44 join(complement(join(complement(x0), complement(x0))), zero)
% 0.20/0.44 = { by lemma 14 }
% 0.20/0.44 join(complement(complement(x0)), zero)
% 0.20/0.44 = { by axiom 1 (maddux1_join_commutativity) }
% 0.20/0.44 join(zero, complement(complement(x0)))
% 0.20/0.44 = { by axiom 5 (def_zero) }
% 0.20/0.44 join(meet(x0, complement(x0)), complement(complement(x0)))
% 0.20/0.44 = { by lemma 14 R->L }
% 0.20/0.44 join(meet(x0, complement(x0)), complement(join(complement(x0), complement(x0))))
% 0.20/0.44 = { by lemma 15 }
% 0.20/0.44 x0
% 0.20/0.44 % SZS output end Proof
% 0.20/0.44
% 0.20/0.44 RESULT: Theorem (the conjecture is true).
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