%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP543-1 : TPTP v8.1.0. Released v2.6.0. % 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 : Sat Jul 16 10:56:09 EDT 2022 % Result : Unsatisfiable 43.65s 43.63s % Output : Proof 43.65s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : GRP543-1 : TPTP v8.1.0. Released v2.6.0. % 0.08/0.13 % Command : moca.sh %s % 0.12/0.34 % Computer : n021.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Mon Jun 13 16:54:27 EDT 2022 % 0.12/0.34 % CPUTime : % 43.65/43.63 % SZS status Unsatisfiable % 43.65/43.63 % SZS output start Proof % 43.65/43.63 The input problem is unsatisfiable because % 43.65/43.63 % 43.65/43.63 [1] the following set of Horn clauses is unsatisfiable: % 43.65/43.63 % 43.65/43.63 divide(divide(identity, divide(divide(divide(A, B), C), A)), C) = B % 43.65/43.63 multiply(A, B) = divide(A, divide(identity, B)) % 43.65/43.63 inverse(A) = divide(identity, A) % 43.65/43.63 identity = divide(A, A) % 43.65/43.63 multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)) ==> \bottom % 43.65/43.63 % 43.65/43.63 This holds because % 43.65/43.63 % 43.65/43.63 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 43.65/43.63 % 43.65/43.63 E: % 43.65/43.63 divide(divide(identity, divide(divide(divide(A, B), C), A)), C) = B % 43.65/43.63 f1(multiply(a3, multiply(b3, c3))) = false__ % 43.65/43.63 f1(multiply(multiply(a3, b3), c3)) = true__ % 43.65/43.63 identity = divide(A, A) % 43.65/43.63 inverse(A) = divide(identity, A) % 43.65/43.63 multiply(A, B) = divide(A, divide(identity, B)) % 43.65/43.63 G: % 43.65/43.63 true__ = false__ % 43.65/43.63 % 43.65/43.63 This holds because % 43.65/43.63 % 43.65/43.63 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 43.65/43.63 % 43.65/43.63 divide(X0, divide(X1, Y1)) = divide(Y1, inverse(divide(X0, X1))) % 43.65/43.63 divide(X0, divide(X1, inverse(Y1))) = inverse(divide(X1, divide(X0, Y1))) % 43.65/43.63 divide(X0, inverse(Y1)) = divide(Y1, inverse(X0)) % 43.65/43.63 divide(X0, inverse(divide(X1, Y1))) = inverse(divide(Y1, divide(X0, inverse(X1)))) % 43.65/43.63 divide(X0, inverse(divide(X1, inverse(Y1)))) = divide(Y1, inverse(divide(X0, inverse(X1)))) % 43.65/43.63 divide(X1, Y2) = divide(divide(Y0, Y2), divide(Y0, X1)) % 43.65/43.63 divide(X1, Y2) = divide(divide(Y0, Y2), inverse(divide(X1, Y0))) % 43.65/43.63 divide(Y0, X0) = inverse(divide(X0, Y0)) % 43.65/43.63 divide(Y0, X1) = divide(X0, divide(X1, inverse(divide(X0, Y0)))) % 43.65/43.63 divide(Y0, X1) = inverse(divide(X0, inverse(divide(X1, divide(X0, inverse(Y0)))))) % 43.65/43.63 divide(Y0, divide(X1, divide(Y1, Y0))) = divide(Y1, X1) % 43.65/43.63 divide(Y0, divide(X1, inverse(X0))) = inverse(divide(X1, inverse(divide(X0, Y0)))) % 43.65/43.63 divide(Y0, divide(X1, inverse(X0))) = inverse(divide(divide(X0, inverse(X1)), Y0)) % 43.65/43.63 divide(divide(X0, X1), X2) = divide(divide(X0, X2), X1) % 43.65/43.63 divide(divide(X1, X0), Y2) = inverse(divide(divide(X0, inverse(Y2)), X1)) % 43.65/43.63 divide(divide(X1, X0), inverse(Y1)) = divide(Y1, divide(X0, X1)) % 43.65/43.63 divide(divide(X1, inverse(X0)), Y1) = inverse(divide(Y1, divide(X0, inverse(X1)))) % 43.65/43.63 divide(divide(X1, inverse(X0)), inverse(Y1)) = divide(Y1, inverse(divide(X0, inverse(X1)))) % 43.65/43.63 divide(divide(Y0, Y1), divide(X1, X0)) = divide(divide(X0, X1), divide(Y1, Y0)) % 43.65/43.63 divide(inverse(X1), inverse(X0)) = divide(X0, X1) % 43.65/43.63 divide(inverse(Y0), X0) = divide(inverse(X0), Y0) % 43.65/43.63 divide(inverse(Y0), X1) = inverse(divide(X1, inverse(Y0))) % 43.65/43.63 inverse(divide(X0, divide(X1, inverse(Y1)))) = divide(X1, divide(X0, Y1)) % 43.65/43.63 inverse(divide(X0, divide(X1, inverse(Y1)))) = divide(Y1, divide(X0, X1)) % 43.65/43.63 inverse(divide(Y0, divide(X1, X0))) = divide(X1, divide(X0, inverse(Y0))) % 43.65/43.63 inverse(divide(Y0, divide(X1, X0))) = inverse(divide(divide(X0, X1), inverse(Y0))) % 43.65/43.63 inverse(divide(Y0, inverse(X1))) = divide(X0, divide(X1, inverse(divide(X0, inverse(Y0))))) % 43.65/43.63 inverse(divide(Y0, inverse(X1))) = inverse(divide(X0, inverse(divide(X1, divide(X0, Y0))))) % 43.65/43.63 inverse(divide(Y0, inverse(divide(X1, X0)))) = divide(divide(X0, X1), Y0) % 43.65/43.63 inverse(divide(Y0, inverse(divide(X1, X0)))) = inverse(divide(X1, divide(X0, Y0))) % 43.65/43.63 inverse(divide(Y0, inverse(divide(X1, inverse(X0))))) = inverse(divide(X1, inverse(divide(X0, inverse(Y0))))) % 43.65/43.63 inverse(divide(Y0, inverse(divide(X1, inverse(X0))))) = inverse(divide(divide(X0, inverse(X1)), inverse(Y0))) % 43.65/43.63 inverse(divide(Y2, inverse(divide(divide(X1, Y2), Y0)))) = divide(Y0, X1) % 43.65/43.63 inverse(divide(divide(X0, X1), inverse(X2))) = divide(divide(X1, X2), X0) % 43.65/43.63 inverse(divide(divide(X1, X0), Y1)) = divide(Y1, inverse(divide(X0, X1))) % 43.65/43.63 inverse(divide(divide(X1, X0), inverse(Y1))) = divide(divide(X0, X1), Y1) % 43.65/43.63 inverse(divide(false__, inverse(divide(divide(Y2, false__), inverse(divide(divide(X1, Y2), Y0)))))) = divide(Y0, X1) % 43.65/43.63 inverse(divide(inverse(Y0), X1)) = divide(X1, inverse(Y0)) % 43.65/43.63 divide(A, A) -> identity % 43.65/43.63 divide(X0, divide(X1, divide(divide(X1, X0), X2))) -> inverse(X2) % 43.65/43.63 divide(X0, divide(Y1, inverse(divide(inverse(Y1), inverse(X0))))) -> identity % 43.65/43.63 divide(X0, divide(inverse(Y1), inverse(X0))) -> Y1 % 43.65/43.63 divide(X0, inverse(divide(X1, X0))) -> X1 % 43.65/43.63 divide(X0, inverse(divide(X1, divide(X0, inverse(divide(X1, Y1)))))) -> Y1 % 43.65/43.63 divide(X0, inverse(divide(inverse(X0), Y1))) -> inverse(Y1) % 43.65/43.63 divide(X1, divide(divide(Y0, Y2), divide(Y0, X1))) -> Y2 % 43.65/43.63 divide(X1, divide(divide(Y0, Y2), inverse(divide(X1, Y0)))) -> Y2 % 43.65/43.63 divide(Y0, divide(X1, inverse(Y0))) -> inverse(X1) % 43.65/43.63 divide(Y0, divide(Y0, Y1)) -> Y1 % 43.65/43.63 divide(Y0, identity) -> Y0 % 43.65/43.63 divide(Y0, inverse(divide(divide(X0, Y0), X1))) -> divide(X0, X1) % 43.65/43.63 divide(Y1, divide(X0, divide(divide(X0, X1), Y1))) -> inverse(X1) % 43.65/43.63 divide(divide(Y0, Y1), divide(X1, Y1)) -> divide(Y0, X1) % 43.65/43.63 divide(divide(Y0, Y1), inverse(divide(Y1, divide(Y0, Y2)))) -> Y2 % 43.65/43.63 divide(divide(Y0, Y1), inverse(divide(divide(Y2, Y0), inverse(Y1)))) -> Y2 % 43.65/43.63 divide(divide(Y0, Y2), Y1) -> inverse(divide(Y2, divide(Y0, Y1))) % 43.65/43.63 divide(divide(Y1, Y0), divide(divide(Y1, Y2), Y0)) -> Y2 % 43.65/43.63 divide(divide(identity, divide(divide(divide(A, B), C), A)), C) -> B % 43.65/43.63 divide(false__, inverse(divide(X0, divide(false__, inverse(divide(X0, Y1)))))) -> Y1 % 43.65/43.63 divide(identity, A) -> inverse(A) % 43.65/43.63 divide(inverse(X0), Y1) -> inverse(divide(X0, inverse(Y1))) % 43.65/43.63 divide(inverse(X0), divide(inverse(X0), Y1)) -> Y1 % 43.65/43.63 divide(inverse(X0), identity) -> inverse(X0) % 43.65/43.63 divide(inverse(X0), inverse(divide(X0, X1))) -> inverse(X1) % 43.65/43.63 divide(inverse(X1), divide(inverse(Y1), X1)) -> Y1 % 43.65/43.63 divide(inverse(Y0), divide(X0, Y0)) -> inverse(X0) % 43.65/43.63 divide(inverse(Y0), inverse(X1)) -> inverse(divide(Y0, X1)) % 43.65/43.63 divide(inverse(Y2), divide(X0, inverse(divide(inverse(X0), Y2)))) -> identity % 43.65/43.63 divide(inverse(Y2), divide(inverse(Y0), inverse(divide(Y0, Y2)))) -> identity % 43.65/43.63 divide(inverse(divide(X1, Y0)), divide(divide(Y0, Y1), X1)) -> Y1 % 43.65/43.63 divide(inverse(divide(X1, identity)), divide(X0, X1)) -> inverse(X0) % 43.65/43.63 divide(inverse(divide(Y0, Y1)), divide(Y1, Y0)) -> identity % 43.65/43.63 divide(inverse(divide(divide(divide(Y0, Y1), Y2), Y0)), Y2) -> Y1 % 43.65/43.63 divide(inverse(divide(divide(inverse(Y1), Y2), identity)), Y2) -> Y1 % 43.65/43.63 divide(inverse(divide(inverse(Y2), Y1)), Y2) -> Y1 % 43.65/43.63 divide(inverse(inverse(Y0)), divide(Y0, Y1)) -> Y1 % 43.65/43.63 divide(inverse(inverse(Y1)), identity) -> Y1 % 43.65/43.63 divide(inverse(inverse(inverse(divide(inverse(Y1), X1)))), X1) -> Y1 % 43.65/43.63 divide(inverse(inverse(inverse(inverse(X0)))), X1) -> divide(X0, X1) % 43.65/43.63 f1(divide(a3, inverse(divide(b3, inverse(c3))))) -> false__ % 43.65/43.63 f1(divide(b3, inverse(divide(a3, inverse(c3))))) -> true__ % 43.65/43.63 f1(divide(divide(a3, inverse(b3)), inverse(c3))) -> true__ % 43.65/43.63 f1(multiply(a3, multiply(b3, c3))) -> false__ % 43.65/43.63 f1(multiply(multiply(a3, b3), c3)) -> true__ % 43.65/43.63 inverse(divide(X0, divide(X1, divide(Y1, divide(X0, X1))))) -> inverse(Y1) % 43.65/43.63 inverse(divide(X0, divide(X1, inverse(divide(Y1, inverse(divide(X0, X1))))))) -> Y1 % 43.65/43.63 inverse(divide(X0, inverse(divide(X1, X0)))) -> inverse(X1) % 43.65/43.63 inverse(divide(X0, inverse(divide(inverse(X0), Y1)))) -> Y1 % 43.65/43.63 inverse(divide(X1, divide(X0, divide(divide(X0, X1), Y1)))) -> Y1 % 43.65/43.63 inverse(divide(Y2, divide(Y0, divide(divide(Y0, Y1), Y2)))) -> Y1 % 43.65/43.63 inverse(divide(Y2, divide(Y0, inverse(divide(divide(Y1, Y0), inverse(Y2)))))) -> Y1 % 43.65/43.63 inverse(divide(divide(X0, Y1), X1)) -> divide(Y1, divide(X0, X1)) % 43.65/43.63 inverse(divide(divide(Y0, Y1), divide(Y0, divide(Y1, Y2)))) -> Y2 % 43.65/43.63 inverse(divide(divide(Y0, Y1), inverse(divide(X1, Y0)))) -> divide(Y1, X1) % 43.65/43.63 inverse(divide(false__, divide(divide(false__, inverse(X1)), inverse(divide(Y0, X1))))) -> Y0 % 43.65/43.63 inverse(divide(false__, inverse(divide(X1, divide(false__, inverse(divide(Y1, inverse(X1)))))))) -> Y1 % 43.65/43.63 inverse(divide(false__, inverse(divide(divide(X1, false__), divide(X0, divide(divide(X0, X1), Y1)))))) -> Y1 % 43.65/43.63 inverse(divide(false__, inverse(divide(divide(X1, false__), divide(X1, Y1))))) -> inverse(Y1) % 43.65/43.63 inverse(divide(false__, inverse(divide(divide(X1, false__), divide(X1, inverse(Y1)))))) -> Y1 % 43.65/43.63 inverse(divide(false__, inverse(divide(divide(Y1, false__), inverse(divide(X0, Y1)))))) -> inverse(X0) % 43.65/43.63 inverse(divide(false__, inverse(divide(divide(Y1, false__), inverse(divide(divide(X1, X0), Y1)))))) -> divide(X0, X1) % 43.65/43.63 inverse(divide(false__, inverse(divide(divide(Y2, false__), divide(Y0, inverse(divide(Y2, divide(Y0, Y1)))))))) -> Y1 % 43.65/43.63 inverse(divide(false__, inverse(divide(divide(Y2, false__), divide(Y1, inverse(Y2)))))) -> Y1 % 43.65/43.63 inverse(divide(inverse(X1), Y0)) -> divide(X1, inverse(Y0)) % 43.65/43.63 inverse(divide(inverse(Y0), inverse(X1))) -> divide(Y0, X1) % 43.65/43.63 inverse(divide(inverse(Y0), inverse(divide(Y0, Y1)))) -> Y1 % 43.65/43.63 inverse(divide(inverse(Y1), identity)) -> Y1 % 43.65/43.63 inverse(identity) -> identity % 43.65/43.63 inverse(inverse(Y1)) -> Y1 % 43.65/43.63 multiply(A, B) -> divide(A, divide(identity, B)) % 43.65/43.63 true__ -> false__ % 43.65/43.63 with the LPO induced by % 43.65/43.63 c3 > b3 > a3 > f1 > multiply > divide > identity > inverse > true__ > false__ % 43.65/43.63 % 43.65/43.63 % SZS output end Proof % 43.65/43.63 %------------------------------------------------------------------------------