%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP467-1 : TPTP v8.1.0. Released v2.6.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n006.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 10:55:39 EDT 2022 % Result : Unsatisfiable 2.01s 2.15s % Output : Proof 2.01s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : GRP467-1 : TPTP v8.1.0. Released v2.6.0. % 0.11/0.12 % Command : moca.sh %s % 0.13/0.33 % Computer : n006.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 600 % 0.13/0.33 % DateTime : Tue Jun 14 02:05:26 EDT 2022 % 0.13/0.33 % CPUTime : % 2.01/2.15 % SZS status Unsatisfiable % 2.01/2.15 % SZS output start Proof % 2.01/2.15 The input problem is unsatisfiable because % 2.01/2.15 % 2.01/2.15 [1] the following set of Horn clauses is unsatisfiable: % 2.01/2.15 % 2.01/2.15 divide(divide(A, A), divide(B, divide(divide(C, divide(D, B)), inverse(D)))) = C % 2.01/2.15 multiply(A, B) = divide(A, inverse(B)) % 2.01/2.15 multiply(multiply(inverse(b2), b2), a2) = a2 ==> \bottom % 2.01/2.15 % 2.01/2.15 This holds because % 2.01/2.15 % 2.01/2.15 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 2.01/2.15 % 2.01/2.15 E: % 2.01/2.15 divide(divide(A, A), divide(B, divide(divide(C, divide(D, B)), inverse(D)))) = C % 2.01/2.15 f1(a2) = false__ % 2.01/2.15 f1(multiply(multiply(inverse(b2), b2), a2)) = true__ % 2.01/2.15 multiply(A, B) = divide(A, inverse(B)) % 2.01/2.15 G: % 2.01/2.15 true__ = false__ % 2.01/2.15 % 2.01/2.15 This holds because % 2.01/2.15 % 2.01/2.15 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 2.01/2.15 % 2.01/2.15 divide(g1, divide(Y1, Y3)) = divide(Y3, Y1) % 2.01/2.15 divide(g1, divide(inverse(Y1), Y3)) = divide(Y3, inverse(Y1)) % 2.01/2.15 divide(X0, X0) -> g1 % 2.01/2.15 divide(divide(Y0, Y0), divide(divide(X1, divide(divide(X2, divide(X3, X1)), inverse(X3))), divide(divide(Y2, X2), inverse(divide(X0, X0))))) -> Y2 % 2.01/2.15 divide(g1, divide(Y0, divide(divide(Y0, Y1), inverse(Y1)))) -> g1 % 2.01/2.15 divide(g1, divide(Y1, divide(divide(Y2, divide(Y3, Y1)), inverse(Y3)))) -> Y2 % 2.01/2.15 divide(g1, divide(Y1, divide(divide(Y2, g1), inverse(Y1)))) -> Y2 % 2.01/2.15 divide(g1, divide(divide(X0, divide(g1, inverse(X1))), divide(divide(Y1, divide(X1, X0)), inverse(g1)))) -> Y1 % 2.01/2.15 divide(g1, divide(divide(divide(Y0, g1), inverse(Y2)), divide(Y0, inverse(Y2)))) -> g1 % 2.01/2.15 divide(g1, divide(divide(divide(Y1, divide(Y2, Y3)), inverse(Y2)), divide(Y1, inverse(Y3)))) -> g1 % 2.01/2.15 divide(g1, divide(divide(divide(Y1, divide(Y2, inverse(X1))), inverse(Y2)), divide(Y1, inverse(inverse(X1))))) -> g1 % 2.01/2.15 divide(g1, divide(divide(divide(inverse(Y2), divide(Y1, Y2)), inverse(Y1)), g1)) -> g1 % 2.01/2.15 divide(g1, divide(divide(divide(inverse(false__), g1), inverse(false__)), g1)) -> g1 % 2.01/2.15 divide(g1, divide(divide(g1, Y1), inverse(Y1))) -> g1 % 2.01/2.15 divide(g1, divide(divide(g1, inverse(Y1)), divide(divide(Y1, Y2), inverse(Y2)))) -> g1 % 2.01/2.15 divide(g1, divide(g1, divide(Y1, Y0))) -> divide(Y1, Y0) % 2.01/2.15 divide(g1, divide(g1, divide(Y1, inverse(Y0)))) -> divide(Y1, inverse(Y0)) % 2.01/2.15 divide(g1, divide(g1, divide(inverse(X1), Y0))) -> divide(inverse(X1), Y0) % 2.01/2.15 divide(g1, divide(inverse(X0), divide(divide(Y1, X0), inverse(g1)))) -> Y1 % 2.01/2.15 divide(g1, inverse(Y1)) -> Y1 % 2.01/2.15 f1(a2) -> false__ % 2.01/2.15 f1(divide(g1, inverse(a2))) -> true__ % 2.01/2.15 multiply(A, B) -> divide(A, inverse(B)) % 2.01/2.15 true__ -> false__ % 2.01/2.15 with the LPO induced by % 2.01/2.15 b2 > multiply > inverse > divide > g1 > a2 > f1 > true__ > false__ % 2.01/2.15 % 2.01/2.15 % SZS output end Proof % 2.01/2.15 %------------------------------------------------------------------------------