%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : REL001-1 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n021.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 19:46:31 EDT 2022 % Result : Unsatisfiable 9.67s 9.66s % Output : Proof 9.67s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : REL001-1 : TPTP v8.1.0. Released v4.0.0. % 0.10/0.13 % Command : moca.sh %s % 0.13/0.34 % Computer : n021.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Fri Jul 8 08:53:20 EDT 2022 % 0.13/0.34 % CPUTime : % 9.67/9.66 % SZS status Unsatisfiable % 9.67/9.66 % SZS output start Proof % 9.67/9.66 The input problem is unsatisfiable because % 9.67/9.66 % 9.67/9.66 [1] the following set of Horn clauses is unsatisfiable: % 9.67/9.66 % 9.67/9.66 join(A, B) = join(B, A) % 9.67/9.66 join(A, join(B, C)) = join(join(A, B), C) % 9.67/9.66 A = join(complement(join(complement(A), complement(B))), complement(join(complement(A), B))) % 9.67/9.66 meet(A, B) = complement(join(complement(A), complement(B))) % 9.67/9.66 composition(A, composition(B, C)) = composition(composition(A, B), C) % 9.67/9.66 composition(A, one) = A % 9.67/9.66 composition(join(A, B), C) = join(composition(A, C), composition(B, C)) % 9.67/9.66 converse(converse(A)) = A % 9.67/9.66 converse(join(A, B)) = join(converse(A), converse(B)) % 9.67/9.66 converse(composition(A, B)) = composition(converse(B), converse(A)) % 9.67/9.66 join(composition(converse(A), complement(composition(A, B))), complement(B)) = complement(B) % 9.67/9.66 top = join(A, complement(A)) % 9.67/9.66 zero = meet(A, complement(A)) % 9.67/9.66 join(zero, sk1) = sk1 ==> \bottom % 9.67/9.66 % 9.67/9.66 This holds because % 9.67/9.66 % 9.67/9.66 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 9.67/9.66 % 9.67/9.66 E: % 9.67/9.66 A = join(complement(join(complement(A), complement(B))), complement(join(complement(A), B))) % 9.67/9.66 composition(A, composition(B, C)) = composition(composition(A, B), C) % 9.67/9.66 composition(A, one) = A % 9.67/9.66 composition(join(A, B), C) = join(composition(A, C), composition(B, C)) % 9.67/9.66 converse(composition(A, B)) = composition(converse(B), converse(A)) % 9.67/9.66 converse(converse(A)) = A % 9.67/9.66 converse(join(A, B)) = join(converse(A), converse(B)) % 9.67/9.66 f1(join(zero, sk1)) = true__ % 9.67/9.66 f1(sk1) = false__ % 9.67/9.66 join(A, B) = join(B, A) % 9.67/9.66 join(A, join(B, C)) = join(join(A, B), C) % 9.67/9.66 join(composition(converse(A), complement(composition(A, B))), complement(B)) = complement(B) % 9.67/9.66 meet(A, B) = complement(join(complement(A), complement(B))) % 9.67/9.66 top = join(A, complement(A)) % 9.67/9.66 zero = meet(A, complement(A)) % 9.67/9.66 G: % 9.67/9.66 true__ = false__ % 9.67/9.66 % 9.67/9.66 This holds because % 9.67/9.66 % 9.67/9.66 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 9.67/9.66 % 9.67/9.66 join(A, B) = join(B, A) % 9.67/9.66 join(Y0, complement(one)) = join(complement(one), join(complement(one), Y0)) % 9.67/9.66 join(Y0, join(Y1, complement(Y0))) = join(top, Y1) % 9.67/9.66 join(Y0, top) = join(top, complement(complement(Y0))) % 9.67/9.66 join(Y0, top) = join(top, top) % 9.67/9.66 join(Y1, join(Y0, Y2)) = join(Y0, join(Y1, Y2)) % 9.67/9.66 join(Y2, join(Y0, Y1)) = join(Y0, join(Y1, Y2)) % 9.67/9.66 join(converse(top), converse(top)) = join(converse(Y0), converse(top)) % 9.67/9.66 complement(complement(Y0)) -> Y0 % 9.67/9.66 complement(top) -> zero % 9.67/9.66 complement(zero) -> top % 9.67/9.66 composition(A, one) -> A % 9.67/9.66 composition(Y0, composition(one, Y2)) -> composition(Y0, Y2) % 9.67/9.66 composition(composition(A, B), C) -> composition(A, composition(B, C)) % 9.67/9.66 composition(converse(one), X0) -> X0 % 9.67/9.66 composition(converse(one), converse(Y0)) -> converse(Y0) % 9.67/9.66 composition(join(A, B), C) -> join(composition(A, C), composition(B, C)) % 9.67/9.66 composition(one, Y1) -> Y1 % 9.67/9.66 composition(top, complement(composition(top, top))) -> zero % 9.67/9.66 converse(complement(converse(zero))) -> top % 9.67/9.66 converse(composition(A, B)) -> composition(converse(B), converse(A)) % 9.67/9.66 converse(converse(A)) -> A % 9.67/9.66 converse(join(A, B)) -> join(converse(A), converse(B)) % 9.67/9.66 converse(one) -> one % 9.67/9.66 converse(top) -> top % 9.67/9.66 f1(join(zero, sk1)) -> true__ % 9.67/9.66 f1(sk1) -> false__ % 9.67/9.66 join(A, complement(A)) -> top % 9.67/9.66 join(X0, complement(complement(join(zero, complement(X0))))) -> top % 9.67/9.66 join(X0, converse(complement(converse(X0)))) -> converse(top) % 9.67/9.66 join(Y0, complement(join(Y0, zero))) -> top % 9.67/9.66 join(Y0, join(Y1, complement(join(Y0, Y1)))) -> top % 9.67/9.66 join(Y0, join(Y1, complement(join(Y1, Y0)))) -> top % 9.67/9.66 join(Y0, join(complement(Y0), Y2)) -> join(top, Y2) % 9.67/9.66 join(Y0, top) -> top % 9.67/9.66 join(Y1, join(Y0, complement(Y1))) -> join(Y0, top) % 9.67/9.66 join(Y1, zero) -> Y1 % 9.67/9.66 join(complement(Y0), composition(converse(X0), complement(composition(X0, Y0)))) -> complement(Y0) % 9.67/9.66 join(complement(Y0), join(zero, Y0)) -> top % 9.67/9.66 join(complement(Y1), complement(Y1)) -> complement(Y1) % 9.67/9.66 join(complement(Y1), composition(X0, complement(composition(converse(X0), Y1)))) -> complement(Y1) % 9.67/9.66 join(complement(Y1), composition(top, complement(composition(top, Y1)))) -> complement(Y1) % 9.67/9.66 join(complement(Y1), join(Y1, zero)) -> top % 9.67/9.66 join(complement(join(X0, zero)), join(zero, X0)) -> top % 9.67/9.66 join(complement(join(complement(A), complement(B))), complement(join(complement(A), B))) -> A % 9.67/9.66 join(complement(join(top, complement(Y0))), complement(join(zero, complement(Y0)))) -> Y0 % 9.67/9.66 join(complement(join(zero, Y1)), complement(join(zero, complement(Y1)))) -> top % 9.67/9.66 join(complement(one), complement(one)) -> complement(one) % 9.67/9.66 join(complement(one), composition(X0, complement(converse(X0)))) -> complement(one) % 9.67/9.66 join(complement(one), composition(converse(Y0), complement(Y0))) -> complement(one) % 9.67/9.66 join(complement(one), composition(converse(top), zero)) -> complement(one) % 9.67/9.66 join(complement(one), composition(top, zero)) -> complement(one) % 9.67/9.66 join(composition(Y0, Y2), composition(top, Y2)) -> composition(top, Y2) % 9.67/9.66 join(composition(converse(A), complement(composition(A, B))), complement(B)) -> complement(B) % 9.67/9.66 join(composition(top, Y2), composition(top, Y2)) -> composition(top, Y2) % 9.67/9.66 join(composition(top, Y2), composition(zero, Y2)) -> composition(top, Y2) % 9.67/9.66 join(composition(zero, Y2), composition(zero, Y2)) -> composition(zero, Y2) % 9.67/9.66 join(converse(X0), join(converse(zero), converse(complement(X0)))) -> top % 9.67/9.66 join(converse(Y0), converse(complement(Y0))) -> converse(top) % 9.67/9.66 join(converse(Y0), converse(top)) -> converse(top) % 9.67/9.66 join(converse(complement(X0)), converse(complement(X0))) -> converse(complement(X0)) % 9.67/9.66 join(converse(complement(one)), converse(complement(one))) -> converse(complement(one)) % 9.67/9.66 join(converse(top), converse(Y1)) -> converse(top) % 9.67/9.66 join(converse(top), converse(complement(X0))) -> converse(top) % 9.67/9.66 join(converse(top), converse(complement(one))) -> converse(top) % 9.67/9.66 join(converse(top), converse(complement(zero))) -> join(converse(top), converse(top)) % 9.67/9.66 join(converse(top), converse(top)) -> converse(top) % 9.67/9.66 join(converse(top), converse(zero)) -> converse(top) % 9.67/9.66 join(converse(zero), converse(Y1)) -> converse(Y1) % 9.67/9.66 join(converse(zero), converse(zero)) -> converse(zero) % 9.67/9.66 join(join(A, B), C) -> join(A, join(B, C)) % 9.67/9.66 join(one, converse(complement(one))) -> converse(top) % 9.67/9.66 join(one, join(Y0, converse(complement(one)))) -> top % 9.67/9.66 join(one, join(converse(complement(one)), Y0)) -> top % 9.67/9.66 join(one, join(zero, converse(complement(one)))) -> top % 9.67/9.66 join(top, Y0) -> top % 9.67/9.66 join(top, complement(Y0)) -> top % 9.67/9.66 join(top, complement(complement(Y0))) -> join(top, Y0) % 9.67/9.66 join(top, complement(one)) -> top % 9.67/9.66 join(top, complement(zero)) -> join(top, top) % 9.67/9.66 join(top, converse(zero)) -> top % 9.67/9.66 join(top, join(Y0, zero)) -> join(top, Y0) % 9.67/9.66 join(top, join(zero, Y1)) -> join(top, Y1) % 9.67/9.66 join(top, one) -> join(top, top) % 9.67/9.66 join(top, top) -> top % 9.67/9.66 join(top, zero) -> top % 9.67/9.66 join(zero, X0) -> X0 % 9.67/9.66 join(zero, complement(join(zero, complement(Y0)))) -> Y0 % 9.67/9.66 join(zero, composition(X0, complement(composition(converse(X0), top)))) -> zero % 9.67/9.66 join(zero, composition(converse(Y0), complement(composition(Y0, top)))) -> zero % 9.67/9.66 join(zero, composition(top, complement(composition(top, top)))) -> zero % 9.67/9.66 join(zero, converse(top)) -> converse(top) % 9.67/9.66 join(zero, join(Y0, zero)) -> join(zero, Y0) % 9.67/9.66 join(zero, join(top, top)) -> join(top, top) % 9.67/9.66 join(zero, join(zero, Y2)) -> join(zero, Y2) % 9.67/9.66 join(zero, zero) -> zero % 9.67/9.66 meet(A, B) -> complement(join(complement(A), complement(B))) % 9.67/9.66 meet(A, complement(A)) -> zero % 9.67/9.66 true__ -> false__ % 9.67/9.66 with the LPO induced by % 9.67/9.66 sk1 > f1 > converse > composition > one > meet > join > complement > zero > top > true__ > false__ % 9.67/9.66 % 9.67/9.66 % SZS output end Proof % 9.67/9.66 %------------------------------------------------------------------------------