%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP546-1 : TPTP v8.1.0. Released v2.6.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n008.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 : Sat Jul 16 10:56:10 EDT 2022 % Result : Unsatisfiable 0.76s 0.91s % Output : Proof 0.76s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.09/0.11 % Problem : GRP546-1 : TPTP v8.1.0. Released v2.6.0. % 0.09/0.12 % Command : moca.sh %s % 0.12/0.33 % Computer : n008.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 : Mon Jun 13 21:19:52 EDT 2022 % 0.12/0.33 % CPUTime : % 0.76/0.91 % SZS status Unsatisfiable % 0.76/0.91 % SZS output start Proof % 0.76/0.91 The input problem is unsatisfiable because % 0.76/0.91 % 0.76/0.91 [1] the following set of Horn clauses is unsatisfiable: % 0.76/0.91 % 0.76/0.91 divide(divide(identity, divide(A, B)), divide(divide(B, C), A)) = C % 0.76/0.91 multiply(A, B) = divide(A, divide(identity, B)) % 0.76/0.91 inverse(A) = divide(identity, A) % 0.76/0.91 identity = divide(A, A) % 0.76/0.91 multiply(multiply(inverse(b2), b2), a2) = a2 ==> \bottom % 0.76/0.91 % 0.76/0.91 This holds because % 0.76/0.91 % 0.76/0.91 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.76/0.91 % 0.76/0.91 E: % 0.76/0.91 divide(divide(identity, divide(A, B)), divide(divide(B, C), A)) = C % 0.76/0.91 f1(a2) = false__ % 0.76/0.91 f1(multiply(multiply(inverse(b2), b2), a2)) = true__ % 0.76/0.91 identity = divide(A, A) % 0.76/0.91 inverse(A) = divide(identity, A) % 0.76/0.91 multiply(A, B) = divide(A, divide(identity, B)) % 0.76/0.91 G: % 0.76/0.91 true__ = false__ % 0.76/0.91 % 0.76/0.91 This holds because % 0.76/0.91 % 0.76/0.91 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.76/0.91 % 0.76/0.91 % 0.76/0.91 divide(A, A) -> identity % 0.76/0.91 divide(Y0, identity) -> Y0 % 0.76/0.91 divide(divide(X0, X1), X0) -> inverse(X1) % 0.76/0.91 divide(divide(identity, divide(A, B)), divide(divide(B, C), A)) -> C % 0.76/0.91 divide(identity, A) -> inverse(A) % 0.76/0.91 divide(inverse(X0), identity) -> inverse(X0) % 0.76/0.91 divide(inverse(X0), identity) -> inverse(divide(X0, identity)) % 0.76/0.91 divide(inverse(X1), inverse(inverse(divide(X0, X1)))) -> inverse(X0) % 0.76/0.91 divide(inverse(divide(Y0, Y1)), divide(divide(Y1, Y2), Y0)) -> Y2 % 0.76/0.91 divide(inverse(divide(Y0, Y2)), inverse(Y0)) -> Y2 % 0.76/0.91 divide(inverse(divide(Y0, identity)), divide(inverse(Y2), Y0)) -> Y2 % 0.76/0.91 divide(inverse(divide(divide(Y1, Y2), Y1)), identity) -> Y2 % 0.76/0.91 divide(inverse(divide(inverse(X0), Y1)), X0) -> Y1 % 0.76/0.91 divide(inverse(divide(inverse(Y1), identity)), identity) -> Y1 % 0.76/0.91 divide(inverse(identity), divide(divide(Y1, Y2), Y1)) -> Y2 % 0.76/0.91 divide(inverse(inverse(Y1)), divide(divide(Y1, Y2), identity)) -> Y2 % 0.76/0.91 divide(inverse(inverse(Y1)), identity) -> Y1 % 0.76/0.91 f1(a2) -> false__ % 0.76/0.91 f1(inverse(inverse(a2))) -> true__ % 0.76/0.91 f1(multiply(multiply(inverse(b2), b2), a2)) -> true__ % 0.76/0.91 inverse(divide(X0, identity)) -> inverse(X0) % 0.76/0.91 inverse(divide(divide(Y0, Y1), Y0)) -> Y1 % 0.76/0.91 inverse(divide(inverse(Y1), identity)) -> Y1 % 0.76/0.91 inverse(identity) -> identity % 0.76/0.91 inverse(inverse(Y1)) -> Y1 % 0.76/0.91 multiply(A, B) -> divide(A, divide(identity, B)) % 0.76/0.91 true__ -> false__ % 0.76/0.91 with the LPO induced by % 0.76/0.91 b2 > a2 > f1 > multiply > divide > identity > inverse > true__ > false__ % 0.76/0.91 % 0.76/0.91 % SZS output end Proof % 0.76/0.91 %------------------------------------------------------------------------------