%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : REL015-1 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n003.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 19:46:49 EDT 2022 % Result : Unsatisfiable 11.50s 11.43s % Output : Proof 11.50s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.14 % Problem : REL015-1 : TPTP v8.1.0. Released v4.0.0. % 0.08/0.15 % Command : moca.sh %s % 0.14/0.36 % Computer : n003.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 600 % 0.14/0.36 % DateTime : Fri Jul 8 10:39:43 EDT 2022 % 0.14/0.37 % CPUTime : % 11.50/11.43 % SZS status Unsatisfiable % 11.50/11.43 % SZS output start Proof % 11.50/11.43 The input problem is unsatisfiable because % 11.50/11.43 % 11.50/11.43 [1] the following set of Horn clauses is unsatisfiable: % 11.50/11.43 % 11.50/11.43 join(A, B) = join(B, A) % 11.50/11.43 join(A, join(B, C)) = join(join(A, B), C) % 11.50/11.43 A = join(complement(join(complement(A), complement(B))), complement(join(complement(A), B))) % 11.50/11.43 meet(A, B) = complement(join(complement(A), complement(B))) % 11.50/11.43 composition(A, composition(B, C)) = composition(composition(A, B), C) % 11.50/11.43 composition(A, one) = A % 11.50/11.43 composition(join(A, B), C) = join(composition(A, C), composition(B, C)) % 11.50/11.43 converse(converse(A)) = A % 11.50/11.43 converse(join(A, B)) = join(converse(A), converse(B)) % 11.50/11.43 converse(composition(A, B)) = composition(converse(B), converse(A)) % 11.50/11.43 join(composition(converse(A), complement(composition(A, B))), complement(B)) = complement(B) % 11.50/11.43 top = join(A, complement(A)) % 11.50/11.43 zero = meet(A, complement(A)) % 11.50/11.43 composition(top, top) = top ==> \bottom % 11.50/11.43 % 11.50/11.43 This holds because % 11.50/11.43 % 11.50/11.43 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 11.50/11.43 % 11.50/11.43 E: % 11.50/11.43 A = join(complement(join(complement(A), complement(B))), complement(join(complement(A), B))) % 11.50/11.43 composition(A, composition(B, C)) = composition(composition(A, B), C) % 11.50/11.43 composition(A, one) = A % 11.50/11.43 composition(join(A, B), C) = join(composition(A, C), composition(B, C)) % 11.50/11.43 converse(composition(A, B)) = composition(converse(B), converse(A)) % 11.50/11.43 converse(converse(A)) = A % 11.50/11.43 converse(join(A, B)) = join(converse(A), converse(B)) % 11.50/11.43 f1(composition(top, top)) = true__ % 11.50/11.43 f1(top) = false__ % 11.50/11.43 join(A, B) = join(B, A) % 11.50/11.43 join(A, join(B, C)) = join(join(A, B), C) % 11.50/11.43 join(composition(converse(A), complement(composition(A, B))), complement(B)) = complement(B) % 11.50/11.43 meet(A, B) = complement(join(complement(A), complement(B))) % 11.50/11.43 top = join(A, complement(A)) % 11.50/11.43 zero = meet(A, complement(A)) % 11.50/11.43 G: % 11.50/11.43 true__ = false__ % 11.50/11.43 % 11.50/11.43 This holds because % 11.50/11.43 % 11.50/11.43 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 11.50/11.43 % 11.50/11.43 join(A, B) = join(B, A) % 11.50/11.43 join(Y0, join(Y1, complement(Y0))) = join(top, Y1) % 11.50/11.43 join(Y0, join(Y2, Y1)) = join(Y1, join(Y2, Y0)) % 11.50/11.43 join(Y0, top) = join(complement(Y1), join(Y1, Y0)) % 11.50/11.43 join(Y0, top) = join(top, join(complement(one), Y0)) % 11.50/11.43 join(Y0, top) = join(top, top) % 11.50/11.43 join(Y1, join(Y2, Y0)) = join(Y2, join(Y1, Y0)) % 11.50/11.43 join(Y2, join(Y0, Y1)) = join(Y0, join(Y1, Y2)) % 11.50/11.43 zero = meet(A, complement(A)) % 11.50/11.43 composition(A, one) -> A % 11.50/11.43 composition(Y0, composition(one, Y2)) -> composition(Y0, Y2) % 11.50/11.43 composition(composition(A, B), C) -> composition(A, composition(B, C)) % 11.50/11.43 composition(converse(one), X0) -> X0 % 11.50/11.43 composition(converse(one), composition(converse(X1), converse(X0))) -> composition(converse(X1), converse(X0)) % 11.50/11.43 composition(converse(one), converse(Y0)) -> converse(Y0) % 11.50/11.43 composition(converse(one), join(converse(X0), converse(X1))) -> join(converse(X0), converse(X1)) % 11.50/11.43 composition(join(A, B), C) -> join(composition(A, C), composition(B, C)) % 11.50/11.43 composition(one, Y1) -> Y1 % 11.50/11.43 composition(top, composition(top, Y2)) -> composition(top, Y2) % 11.50/11.43 composition(top, top) -> top % 11.50/11.43 converse(composition(A, B)) -> composition(converse(B), converse(A)) % 11.50/11.43 converse(converse(A)) -> A % 11.50/11.43 converse(join(A, B)) -> join(converse(A), converse(B)) % 11.50/11.43 converse(one) -> one % 11.50/11.43 converse(top) -> top % 11.50/11.43 f1(composition(top, top)) -> true__ % 11.50/11.43 f1(top) -> false__ % 11.50/11.43 join(A, complement(A)) -> top % 11.50/11.43 join(X0, converse(complement(converse(X0)))) -> converse(top) % 11.50/11.43 join(X0, converse(top)) -> converse(top) % 11.50/11.43 join(X0, join(X1, converse(complement(join(converse(X0), converse(X1)))))) -> converse(top) % 11.50/11.43 join(X0, join(X1, join(complement(X0), complement(top)))) -> top % 11.50/11.43 join(X0, join(converse(complement(converse(X0))), Y1)) -> top % 11.50/11.43 join(X0, join(converse(complement(converse(X0))), converse(Y1))) -> top % 11.50/11.43 join(Y0, composition(top, top)) -> top % 11.50/11.43 join(Y0, converse(top)) -> top % 11.50/11.43 join(Y0, join(Y1, complement(join(Y0, Y1)))) -> top % 11.50/11.43 join(Y0, join(Y1, complement(join(Y1, Y0)))) -> top % 11.50/11.43 join(Y0, join(complement(Y0), Y2)) -> join(top, Y2) % 11.50/11.43 join(Y0, join(one, converse(complement(join(one, converse(Y0)))))) -> top % 11.50/11.43 join(Y0, top) -> top % 11.50/11.43 join(Y1, composition(top, Y1)) -> composition(top, Y1) % 11.50/11.43 join(Y1, join(Y0, complement(Y1))) -> join(Y0, top) % 11.50/11.43 join(Y1, join(top, Y0)) -> top % 11.50/11.43 join(complement(Y0), composition(converse(X0), complement(composition(X0, Y0)))) -> complement(Y0) % 11.50/11.43 join(complement(Y0), join(complement(top), Y0)) -> top % 11.50/11.43 join(complement(Y1), complement(Y1)) -> complement(Y1) % 11.50/11.43 join(complement(Y1), composition(X0, complement(composition(converse(X0), Y1)))) -> complement(Y1) % 11.50/11.43 join(complement(Y1), composition(top, complement(composition(top, Y1)))) -> complement(Y1) % 11.50/11.43 join(complement(Y1), join(Y1, Y0)) -> join(top, Y0) % 11.50/11.43 join(complement(Y1), join(Y1, Y0)) -> top % 11.50/11.43 join(complement(Y1), join(Y1, complement(top))) -> top % 11.50/11.43 join(complement(converse(X0)), converse(top)) -> top % 11.50/11.43 join(complement(join(complement(A), complement(B))), complement(join(complement(A), B))) -> A % 11.50/11.43 join(complement(one), complement(one)) -> complement(one) % 11.50/11.43 join(complement(one), composition(X0, complement(converse(X0)))) -> complement(one) % 11.50/11.43 join(complement(one), composition(converse(Y0), complement(Y0))) -> complement(one) % 11.50/11.43 join(complement(one), composition(top, complement(top))) -> complement(one) % 11.50/11.43 join(complement(one), converse(top)) -> top % 11.50/11.43 join(composition(Y0, Y2), composition(top, Y2)) -> composition(top, Y2) % 11.50/11.43 join(composition(converse(A), complement(composition(A, B))), complement(B)) -> complement(B) % 11.50/11.43 join(composition(converse(X0), top), converse(complement(X0))) -> top % 11.50/11.43 join(composition(converse(X1), converse(X0)), converse(complement(composition(X0, X1)))) -> converse(top) % 11.50/11.43 join(composition(top, Y0), complement(Y0)) -> top % 11.50/11.43 join(composition(top, Y2), composition(Y1, Y2)) -> composition(top, Y2) % 11.50/11.43 join(converse(X0), join(converse(X1), converse(complement(join(X0, X1))))) -> converse(top) % 11.50/11.43 join(converse(X0), join(converse(complement(X0)), converse(X1))) -> top % 11.50/11.43 join(converse(Y0), converse(complement(Y0))) -> converse(top) % 11.50/11.43 join(converse(Y0), converse(top)) -> converse(top) % 11.50/11.43 join(converse(Y0), join(Y1, converse(complement(Y0)))) -> top % 11.50/11.43 join(converse(Y0), join(converse(complement(Y0)), X0)) -> top % 11.50/11.43 join(converse(complement(X0)), converse(complement(X0))) -> converse(complement(X0)) % 11.50/11.43 join(converse(complement(one)), converse(complement(one))) -> converse(complement(one)) % 11.50/11.43 join(converse(top), complement(converse(complement(converse(complement(top)))))) -> top % 11.50/11.43 join(converse(top), converse(Y0)) -> converse(top) % 11.50/11.43 join(converse(top), converse(complement(X0))) -> converse(top) % 11.50/11.43 join(converse(top), converse(complement(one))) -> converse(top) % 11.50/11.43 join(join(A, B), C) -> join(A, join(B, C)) % 11.50/11.43 join(one, converse(complement(one))) -> converse(top) % 11.50/11.43 join(one, converse(top)) -> converse(top) % 11.50/11.43 join(one, join(X0, converse(complement(join(one, converse(X0)))))) -> top % 11.50/11.43 join(one, join(Y0, converse(complement(one)))) -> top % 11.50/11.43 join(one, join(complement(converse(top)), converse(complement(one)))) -> top % 11.50/11.43 join(one, join(complement(top), converse(complement(one)))) -> top % 11.50/11.43 join(one, join(converse(Y0), converse(complement(join(Y0, one))))) -> top % 11.50/11.43 join(one, join(converse(Y0), converse(complement(one)))) -> top % 11.50/11.43 join(one, join(converse(Y1), converse(complement(join(one, Y1))))) -> top % 11.50/11.43 join(one, join(converse(complement(one)), Y0)) -> top % 11.50/11.43 join(one, join(converse(complement(one)), converse(Y1))) -> top % 11.50/11.43 join(one, join(one, converse(complement(join(one, one))))) -> top % 11.50/11.43 join(top, Y0) -> top % 11.50/11.43 join(top, complement(Y0)) -> top % 11.50/11.43 join(top, complement(complement(Y0))) -> join(Y0, top) % 11.50/11.43 join(top, complement(one)) -> top % 11.50/11.43 join(top, join(complement(one), Y0)) -> join(top, Y0) % 11.50/11.43 join(top, join(complement(one), Y0)) -> top % 11.50/11.43 join(top, top) -> join(one, top) % 11.50/11.43 meet(A, B) -> complement(join(complement(A), complement(B))) % 11.50/11.43 true__ -> false__ % 11.50/11.43 with the LPO induced by % 11.50/11.43 f1 > zero > converse > meet > complement > top > composition > one > join > true__ > false__ % 11.50/11.43 % 11.50/11.43 % SZS output end Proof % 11.50/11.43 %------------------------------------------------------------------------------