TSTP Solution File: REL001-1 by Twee---2.4.2
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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 : n032.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 : Unsatisfiable 0.16s 0.38s
% Output : Proof 0.16s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : REL001-1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.11 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.11/0.31 % Computer : n032.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Fri Aug 25 19:19:58 EDT 2023
% 0.11/0.31 % CPUTime :
% 0.16/0.38 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.16/0.38
% 0.16/0.38 % SZS status Unsatisfiable
% 0.16/0.38
% 0.16/0.38 % SZS output start Proof
% 0.16/0.38 Axiom 1 (maddux1_join_commutativity_1): join(X, Y) = join(Y, X).
% 0.16/0.38 Axiom 2 (composition_identity_6): composition(X, one) = X.
% 0.16/0.38 Axiom 3 (converse_idempotence_8): converse(converse(X)) = X.
% 0.16/0.38 Axiom 4 (def_top_12): top = join(X, complement(X)).
% 0.16/0.38 Axiom 5 (def_zero_13): zero = meet(X, complement(X)).
% 0.16/0.38 Axiom 6 (maddux2_join_associativity_2): join(X, join(Y, Z)) = join(join(X, Y), Z).
% 0.16/0.38 Axiom 7 (converse_multiplicativity_10): converse(composition(X, Y)) = composition(converse(Y), converse(X)).
% 0.16/0.38 Axiom 8 (composition_associativity_5): composition(X, composition(Y, Z)) = composition(composition(X, Y), Z).
% 0.16/0.38 Axiom 9 (maddux4_definiton_of_meet_4): meet(X, Y) = complement(join(complement(X), complement(Y))).
% 0.16/0.38 Axiom 10 (converse_cancellativity_11): join(composition(converse(X), complement(composition(X, Y))), complement(Y)) = complement(Y).
% 0.16/0.38 Axiom 11 (maddux3_a_kind_of_de_Morgan_3): X = join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y))).
% 0.16/0.38
% 0.16/0.38 Lemma 12: complement(top) = zero.
% 0.16/0.38 Proof:
% 0.16/0.38 complement(top)
% 0.16/0.38 = { by axiom 4 (def_top_12) }
% 0.16/0.38 complement(join(complement(X), complement(complement(X))))
% 0.16/0.38 = { by axiom 9 (maddux4_definiton_of_meet_4) R->L }
% 0.16/0.38 meet(X, complement(X))
% 0.16/0.38 = { by axiom 5 (def_zero_13) R->L }
% 0.16/0.38 zero
% 0.16/0.38
% 0.16/0.38 Lemma 13: composition(converse(one), X) = X.
% 0.16/0.38 Proof:
% 0.16/0.38 composition(converse(one), X)
% 0.16/0.38 = { by axiom 3 (converse_idempotence_8) R->L }
% 0.16/0.38 composition(converse(one), converse(converse(X)))
% 0.16/0.38 = { by axiom 7 (converse_multiplicativity_10) R->L }
% 0.16/0.38 converse(composition(converse(X), one))
% 0.16/0.38 = { by axiom 2 (composition_identity_6) }
% 0.16/0.38 converse(converse(X))
% 0.16/0.38 = { by axiom 3 (converse_idempotence_8) }
% 0.16/0.38 X
% 0.16/0.38
% 0.16/0.38 Lemma 14: join(complement(X), complement(X)) = complement(X).
% 0.16/0.38 Proof:
% 0.16/0.38 join(complement(X), complement(X))
% 0.16/0.38 = { by lemma 13 R->L }
% 0.16/0.38 join(complement(X), composition(converse(one), complement(X)))
% 0.16/0.38 = { by lemma 13 R->L }
% 0.16/0.38 join(complement(X), composition(converse(one), complement(composition(converse(one), X))))
% 0.16/0.38 = { by axiom 2 (composition_identity_6) R->L }
% 0.16/0.38 join(complement(X), composition(converse(one), complement(composition(composition(converse(one), one), X))))
% 0.16/0.38 = { by axiom 8 (composition_associativity_5) R->L }
% 0.16/0.38 join(complement(X), composition(converse(one), complement(composition(converse(one), composition(one, X)))))
% 0.16/0.38 = { by lemma 13 }
% 0.16/0.38 join(complement(X), composition(converse(one), complement(composition(one, X))))
% 0.16/0.38 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 0.16/0.38 join(composition(converse(one), complement(composition(one, X))), complement(X))
% 0.16/0.38 = { by axiom 10 (converse_cancellativity_11) }
% 0.16/0.38 complement(X)
% 0.16/0.38
% 0.16/0.38 Lemma 15: join(meet(X, Y), complement(join(complement(X), Y))) = X.
% 0.16/0.38 Proof:
% 0.16/0.38 join(meet(X, Y), complement(join(complement(X), Y)))
% 0.16/0.38 = { by axiom 9 (maddux4_definiton_of_meet_4) }
% 0.16/0.38 join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y)))
% 0.16/0.38 = { by axiom 11 (maddux3_a_kind_of_de_Morgan_3) R->L }
% 0.16/0.38 X
% 0.16/0.38
% 0.16/0.38 Goal 1 (goals_14): join(zero, sk1) = sk1.
% 0.16/0.38 Proof:
% 0.16/0.38 join(zero, sk1)
% 0.16/0.38 = { by lemma 15 R->L }
% 0.16/0.38 join(zero, join(meet(sk1, complement(sk1)), complement(join(complement(sk1), complement(sk1)))))
% 0.16/0.38 = { by axiom 5 (def_zero_13) R->L }
% 0.16/0.38 join(zero, join(zero, complement(join(complement(sk1), complement(sk1)))))
% 0.16/0.38 = { by axiom 9 (maddux4_definiton_of_meet_4) R->L }
% 0.16/0.38 join(zero, join(zero, meet(sk1, sk1)))
% 0.16/0.38 = { by axiom 6 (maddux2_join_associativity_2) }
% 0.16/0.38 join(join(zero, zero), meet(sk1, sk1))
% 0.16/0.38 = { by lemma 12 R->L }
% 0.16/0.38 join(join(zero, complement(top)), meet(sk1, sk1))
% 0.16/0.38 = { by lemma 12 R->L }
% 0.16/0.38 join(join(complement(top), complement(top)), meet(sk1, sk1))
% 0.16/0.38 = { by lemma 14 }
% 0.16/0.38 join(complement(top), meet(sk1, sk1))
% 0.16/0.38 = { by lemma 12 }
% 0.16/0.38 join(zero, meet(sk1, sk1))
% 0.16/0.38 = { by axiom 1 (maddux1_join_commutativity_1) }
% 0.16/0.38 join(meet(sk1, sk1), zero)
% 0.16/0.38 = { by axiom 9 (maddux4_definiton_of_meet_4) }
% 0.16/0.38 join(complement(join(complement(sk1), complement(sk1))), zero)
% 0.16/0.38 = { by lemma 14 }
% 0.16/0.38 join(complement(complement(sk1)), zero)
% 0.16/0.38 = { by axiom 1 (maddux1_join_commutativity_1) }
% 0.16/0.38 join(zero, complement(complement(sk1)))
% 0.16/0.38 = { by axiom 5 (def_zero_13) }
% 0.16/0.38 join(meet(sk1, complement(sk1)), complement(complement(sk1)))
% 0.16/0.38 = { by lemma 14 R->L }
% 0.16/0.38 join(meet(sk1, complement(sk1)), complement(join(complement(sk1), complement(sk1))))
% 0.16/0.38 = { by lemma 15 }
% 0.16/0.38 sk1
% 0.16/0.38 % SZS output end Proof
% 0.16/0.38
% 0.16/0.38 RESULT: Unsatisfiable (the axioms are contradictory).
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