%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : REL002-1 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n011.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 : 600s % DateTime : Mon Jul 18 19:46:32 EDT 2022 % Result : Unsatisfiable 9.25s 9.25s % Output : Proof 9.25s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : REL002-1 : TPTP v8.1.0. Released v4.0.0. % 0.12/0.12 % Command : moca.sh %s % 0.12/0.33 % Computer : n011.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Fri Jul 8 11:24:24 EDT 2022 % 0.12/0.34 % CPUTime : % 9.25/9.25 % SZS status Unsatisfiable % 9.25/9.25 % SZS output start Proof % 9.25/9.25 The input problem is unsatisfiable because % 9.25/9.25 % 9.25/9.25 [1] the following set of Horn clauses is unsatisfiable: % 9.25/9.25 % 9.25/9.25 join(A, B) = join(B, A) % 9.25/9.25 join(A, join(B, C)) = join(join(A, B), C) % 9.25/9.25 A = join(complement(join(complement(A), complement(B))), complement(join(complement(A), B))) % 9.25/9.25 meet(A, B) = complement(join(complement(A), complement(B))) % 9.25/9.25 composition(A, composition(B, C)) = composition(composition(A, B), C) % 9.25/9.25 composition(A, one) = A % 9.25/9.25 composition(join(A, B), C) = join(composition(A, C), composition(B, C)) % 9.25/9.25 converse(converse(A)) = A % 9.25/9.25 converse(join(A, B)) = join(converse(A), converse(B)) % 9.25/9.25 converse(composition(A, B)) = composition(converse(B), converse(A)) % 9.25/9.25 join(composition(converse(A), complement(composition(A, B))), complement(B)) = complement(B) % 9.25/9.25 top = join(A, complement(A)) % 9.25/9.25 zero = meet(A, complement(A)) % 9.25/9.25 join(sk1, top) = top ==> \bottom % 9.25/9.25 % 9.25/9.25 This holds because % 9.25/9.25 % 9.25/9.25 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 9.25/9.25 % 9.25/9.25 E: % 9.25/9.25 A = join(complement(join(complement(A), complement(B))), complement(join(complement(A), B))) % 9.25/9.25 composition(A, composition(B, C)) = composition(composition(A, B), C) % 9.25/9.25 composition(A, one) = A % 9.25/9.25 composition(join(A, B), C) = join(composition(A, C), composition(B, C)) % 9.25/9.25 converse(composition(A, B)) = composition(converse(B), converse(A)) % 9.25/9.25 converse(converse(A)) = A % 9.25/9.25 converse(join(A, B)) = join(converse(A), converse(B)) % 9.25/9.25 f1(join(sk1, top)) = true__ % 9.25/9.25 f1(top) = false__ % 9.25/9.25 join(A, B) = join(B, A) % 9.25/9.25 join(A, join(B, C)) = join(join(A, B), C) % 9.25/9.25 join(composition(converse(A), complement(composition(A, B))), complement(B)) = complement(B) % 9.25/9.25 meet(A, B) = complement(join(complement(A), complement(B))) % 9.25/9.25 top = join(A, complement(A)) % 9.25/9.25 zero = meet(A, complement(A)) % 9.25/9.25 G: % 9.25/9.25 true__ = false__ % 9.25/9.25 % 9.25/9.25 This holds because % 9.25/9.25 % 9.25/9.25 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 9.25/9.25 % 9.25/9.25 join(A, B) = join(B, A) % 9.25/9.25 join(Y0, join(Y1, complement(Y0))) = join(top, Y1) % 9.25/9.25 join(Y0, top) = join(one, top) % 9.25/9.25 join(Y0, top) = join(top, complement(complement(Y0))) % 9.25/9.25 join(Y0, top) = join(top, join(complement(one), Y0)) % 9.25/9.25 join(Y1, join(Y0, Y2)) = join(Y0, join(Y1, Y2)) % 9.25/9.25 join(Y2, join(Y0, Y1)) = join(Y0, join(Y1, Y2)) % 9.25/9.25 join(zero, join(Y0, top)) = join(top, Y0) % 9.25/9.25 complement(top) -> zero % 9.25/9.25 composition(A, one) -> A % 9.25/9.25 composition(Y0, composition(one, Y2)) -> composition(Y0, Y2) % 9.25/9.25 composition(composition(A, B), C) -> composition(A, composition(B, C)) % 9.25/9.25 composition(converse(one), X0) -> X0 % 9.25/9.25 composition(converse(one), converse(Y0)) -> converse(Y0) % 9.25/9.25 composition(join(A, B), C) -> join(composition(A, C), composition(B, C)) % 9.25/9.25 composition(one, Y1) -> Y1 % 9.25/9.25 converse(composition(A, B)) -> composition(converse(B), converse(A)) % 9.25/9.25 converse(converse(A)) -> A % 9.25/9.25 converse(join(A, B)) -> join(converse(A), converse(B)) % 9.25/9.25 converse(one) -> one % 9.25/9.25 f1(join(sk1, top)) -> true__ % 9.25/9.25 f1(join(top, complement(complement(sk1)))) -> true__ % 9.25/9.25 f1(join(top, join(complement(one), sk1))) -> true__ % 9.25/9.25 f1(join(top, sk1)) -> true__ % 9.25/9.25 f1(top) -> false__ % 9.25/9.25 join(A, complement(A)) -> top % 9.25/9.25 join(X0, converse(complement(converse(X0)))) -> converse(top) % 9.25/9.25 join(X0, join(converse(zero), converse(complement(converse(X0))))) -> converse(top) % 9.25/9.25 join(Y0, join(Y1, complement(join(Y0, Y1)))) -> top % 9.25/9.25 join(Y0, join(Y1, complement(join(Y1, Y0)))) -> top % 9.25/9.25 join(Y0, join(complement(Y0), Y2)) -> join(top, Y2) % 9.25/9.25 join(Y0, join(zero, complement(Y0))) -> top % 9.25/9.25 join(Y0, top) -> top % 9.25/9.25 join(Y1, join(Y0, complement(Y1))) -> join(Y0, top) % 9.25/9.25 join(complement(Y0), join(zero, Y0)) -> top % 9.25/9.25 join(complement(Y1), complement(Y1)) -> complement(Y1) % 9.25/9.25 join(complement(Y1), composition(X0, complement(composition(converse(X0), Y1)))) -> complement(Y1) % 9.25/9.25 join(complement(Y1), join(Y1, zero)) -> top % 9.25/9.25 join(complement(join(complement(A), complement(B))), complement(join(complement(A), B))) -> A % 9.25/9.25 join(complement(join(zero, Y1)), complement(join(zero, complement(Y1)))) -> top % 9.25/9.25 join(complement(join(zero, complement(Y0))), complement(join(top, complement(Y0)))) -> Y0 % 9.25/9.25 join(complement(one), complement(one)) -> complement(one) % 9.25/9.25 join(complement(one), composition(X0, complement(converse(X0)))) -> complement(one) % 9.25/9.25 join(complement(one), composition(converse(Y0), complement(Y0))) -> complement(one) % 9.25/9.25 join(complement(one), composition(converse(top), zero)) -> complement(one) % 9.25/9.25 join(composition(converse(A), complement(composition(A, B))), complement(B)) -> complement(B) % 9.25/9.25 join(composition(zero, Y2), composition(top, Y2)) -> composition(top, Y2) % 9.25/9.25 join(converse(Y0), converse(complement(Y0))) -> converse(top) % 9.25/9.25 join(converse(Y0), join(converse(zero), converse(complement(Y0)))) -> converse(top) % 9.25/9.25 join(converse(top), complement(converse(complement(converse(zero))))) -> top % 9.25/9.25 join(converse(top), converse(complement(X0))) -> converse(top) % 9.25/9.25 join(converse(top), converse(complement(one))) -> converse(top) % 9.25/9.25 join(converse(top), converse(complement(zero))) -> join(converse(top), converse(top)) % 9.25/9.25 join(converse(top), converse(top)) -> join(one, converse(top)) % 9.25/9.25 join(converse(zero), converse(top)) -> converse(top) % 9.25/9.25 join(converse(zero), converse(zero)) -> converse(zero) % 9.25/9.25 join(join(A, B), C) -> join(A, join(B, C)) % 9.25/9.25 join(one, converse(complement(one))) -> converse(top) % 9.25/9.25 join(one, join(converse(zero), converse(complement(one)))) -> converse(top) % 9.25/9.25 join(one, top) -> top % 9.25/9.25 join(top, Y0) -> top % 9.25/9.25 join(top, complement(Y0)) -> top % 9.25/9.25 join(top, complement(complement(Y0))) -> join(top, Y0) % 9.25/9.25 join(top, complement(converse(zero))) -> join(top, top) % 9.25/9.25 join(top, complement(one)) -> top % 9.25/9.25 join(top, complement(zero)) -> join(top, top) % 9.25/9.25 join(top, converse(complement(converse(zero)))) -> join(top, converse(top)) % 9.25/9.25 join(top, converse(zero)) -> top % 9.25/9.25 join(top, join(Y0, complement(one))) -> join(Y0, top) % 9.25/9.25 join(top, join(Y0, converse(zero))) -> join(Y0, top) % 9.25/9.25 join(top, join(Y0, converse(zero))) -> join(top, Y0) % 9.25/9.25 join(top, join(Y0, zero)) -> join(top, Y0) % 9.25/9.25 join(top, join(complement(one), Y0)) -> join(top, Y0) % 9.25/9.25 join(top, join(complement(one), complement(complement(zero)))) -> top % 9.25/9.25 join(top, join(complement(zero), complement(join(top, top)))) -> top % 9.25/9.25 join(top, join(converse(zero), Y2)) -> join(top, Y2) % 9.25/9.25 join(top, join(top, complement(join(one, top)))) -> top % 9.25/9.25 join(top, join(zero, Y1)) -> join(top, Y1) % 9.25/9.25 join(top, join(zero, zero)) -> top % 9.25/9.25 join(top, top) -> join(one, top) % 9.25/9.25 join(zero, composition(X0, complement(composition(converse(X0), top)))) -> zero % 9.25/9.25 join(zero, composition(converse(Y0), complement(composition(Y0, top)))) -> zero % 9.25/9.25 join(zero, converse(top)) -> converse(top) % 9.25/9.25 join(zero, join(Y0, top)) -> join(Y0, top) % 9.25/9.25 join(zero, join(Y0, zero)) -> join(zero, Y0) % 9.25/9.25 join(zero, join(top, Y2)) -> join(top, Y2) % 9.25/9.25 join(zero, join(zero, Y2)) -> join(zero, Y2) % 9.25/9.25 join(zero, top) -> top % 9.25/9.25 join(zero, zero) -> zero % 9.25/9.25 meet(A, B) -> complement(join(complement(A), complement(B))) % 9.25/9.25 meet(A, complement(A)) -> zero % 9.25/9.25 true__ -> false__ % 9.25/9.25 with the LPO induced by % 9.25/9.25 sk1 > converse > composition > meet > join > complement > top > f1 > zero > one > true__ > false__ % 9.25/9.25 % 9.25/9.25 % SZS output end Proof % 9.25/9.25 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