%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP511-1 : TPTP v8.1.0. Released v2.6.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n017.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 10:55:55 EDT 2022 % Result : Unsatisfiable 12.74s 12.87s % Output : Proof 12.74s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : GRP511-1 : TPTP v8.1.0. Released v2.6.0. % 0.06/0.13 % Command : moca.sh %s % 0.12/0.33 % Computer : n017.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 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Tue Jun 14 00:57:23 EDT 2022 % 0.12/0.34 % CPUTime : % 12.74/12.87 % SZS status Unsatisfiable % 12.74/12.87 % SZS output start Proof % 12.74/12.87 The input problem is unsatisfiable because % 12.74/12.87 % 12.74/12.87 [1] the following set of Horn clauses is unsatisfiable: % 12.74/12.87 % 12.74/12.87 multiply(multiply(multiply(A, B), C), inverse(multiply(A, C))) = B % 12.74/12.87 multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)) ==> \bottom % 12.74/12.87 % 12.74/12.87 This holds because % 12.74/12.87 % 12.74/12.87 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 12.74/12.87 % 12.74/12.87 E: % 12.74/12.87 f1(multiply(a3, multiply(b3, c3))) = false__ % 12.74/12.87 f1(multiply(multiply(a3, b3), c3)) = true__ % 12.74/12.87 multiply(multiply(multiply(A, B), C), inverse(multiply(A, C))) = B % 12.74/12.87 G: % 12.74/12.87 true__ = false__ % 12.74/12.87 % 12.74/12.87 This holds because % 12.74/12.87 % 12.74/12.87 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 12.74/12.87 % 12.74/12.87 multiply(X0, multiply(X2, multiply(inverse(X1), inverse(X0)))) = multiply(inverse(X1), X2) % 12.74/12.87 multiply(X1, X0) = multiply(X0, X1) % 12.74/12.87 multiply(X1, inverse(Y0)) = multiply(inverse(Y0), X1) % 12.74/12.87 multiply(X1, inverse(inverse(X0))) = multiply(inverse(inverse(X0)), inverse(inverse(X1))) % 12.74/12.87 multiply(X1, multiply(X0, Y2)) = multiply(Y2, multiply(X0, X1)) % 12.74/12.87 multiply(X1, multiply(multiply(inverse(X1), Y0), Y2)) = multiply(Y2, Y0) % 12.74/12.87 multiply(Y0, X1) = multiply(Y1, multiply(X1, multiply(inverse(Y1), Y0))) % 12.74/12.87 multiply(Y0, inverse(Y0)) = multiply(X1, inverse(X1)) % 12.74/12.87 multiply(Y0, multiply(X2, multiply(X1, inverse(Y0)))) = multiply(X1, X2) % 12.74/12.87 multiply(Y0, multiply(Y2, Y1)) = multiply(Y2, multiply(Y1, Y0)) % 12.74/12.87 multiply(Y2, multiply(Y1, Y0)) = multiply(Y1, multiply(Y2, Y0)) % 12.74/12.87 multiply(false__, inverse(false__)) = multiply(X1, inverse(X1)) % 12.74/12.87 multiply(false__, multiply(X1, multiply(inverse(false__), multiply(Y0, multiply(inverse(X1), inverse(X0)))))) = multiply(inverse(X0), Y0) % 12.74/12.87 multiply(inverse(X0), X0) = multiply(false__, inverse(false__)) % 12.74/12.87 multiply(inverse(X0), inverse(inverse(X0))) = inverse(multiply(X1, inverse(X1))) % 12.74/12.87 multiply(inverse(X0), inverse(inverse(X0))) = multiply(inverse(X1), inverse(inverse(X1))) % 12.74/12.87 multiply(inverse(Y0), Y0) = multiply(X1, inverse(X1)) % 12.74/12.87 multiply(inverse(false__), inverse(inverse(false__))) = multiply(X1, inverse(X1)) % 12.74/12.87 multiply(inverse(inverse(X0)), inverse(X0)) = multiply(inverse(Y1), inverse(inverse(Y1))) % 12.74/12.87 multiply(inverse(inverse(X0)), inverse(inverse(inverse(X1)))) = inverse(multiply(X1, inverse(X0))) % 12.74/12.87 multiply(inverse(inverse(X0)), inverse(inverse(inverse(X1)))) = multiply(inverse(X1), inverse(inverse(X0))) % 12.74/12.87 multiply(inverse(inverse(X1)), inverse(inverse(X0))) = multiply(inverse(inverse(X0)), inverse(inverse(X1))) % 12.74/12.87 multiply(multiply(X0, X1), multiply(inverse(X1), inverse(X0))) = multiply(Y1, inverse(Y1)) % 12.74/12.87 multiply(multiply(X1, Y2), multiply(inverse(Y2), X0)) = multiply(X0, X1) % 12.74/12.87 multiply(multiply(X1, Y2), multiply(inverse(Y2), inverse(Y0))) = multiply(inverse(Y0), X1) % 12.74/12.87 multiply(multiply(X2, Y2), inverse(multiply(Y0, Y2))) = inverse(multiply(multiply(X1, Y0), inverse(multiply(X1, X2)))) % 12.74/12.87 multiply(multiply(X2, Y2), inverse(multiply(Y0, Y2))) = multiply(multiply(X2, false__), inverse(multiply(Y0, false__))) % 12.74/12.87 multiply(multiply(Y0, Y1), multiply(Y2, inverse(Y1))) = multiply(Y2, Y0) % 12.74/12.87 multiply(multiply(Y0, inverse(X0)), multiply(X0, Y2)) = multiply(Y2, Y0) % 12.74/12.87 multiply(multiply(Y0, inverse(Y1)), multiply(Y2, Y1)) = multiply(Y2, Y0) % 12.74/12.87 multiply(multiply(Y0, multiply(X1, inverse(inverse(X0)))), inverse(Y0)) = multiply(inverse(inverse(X0)), inverse(inverse(X1))) % 12.74/12.87 multiply(multiply(Y1, Y0), multiply(inverse(Y1), Y2)) = multiply(Y2, Y0) % 12.74/12.87 multiply(multiply(false__, multiply(false__, false__)), multiply(inverse(false__), multiply(inverse(false__), inverse(false__)))) = multiply(Y1, inverse(Y1)) % 12.74/12.87 multiply(multiply(inverse(X1), inverse(X0)), multiply(X0, X1)) = multiply(Y1, inverse(Y1)) % 12.74/12.87 multiply(multiply(inverse(X1), inverse(X0)), multiply(X0, X1)) = multiply(false__, inverse(false__)) % 12.74/12.87 multiply(multiply(inverse(Y1), Y0), multiply(Y1, Y2)) = multiply(Y2, Y0) % 12.74/12.87 multiply(multiply(inverse(false__), X1), multiply(false__, multiply(Y0, multiply(inverse(X1), inverse(X0))))) = multiply(inverse(X0), Y0) % 12.74/12.87 f1(multiply(a3, multiply(b3, c3))) -> false__ % 12.74/12.87 f1(multiply(multiply(a3, b3), c3)) -> true__ % 12.74/12.87 inverse(inverse(Y1)) -> Y1 % 12.74/12.87 inverse(inverse(inverse(X1))) -> inverse(X1) % 12.74/12.87 inverse(inverse(multiply(X0, X1))) -> multiply(X1, inverse(inverse(X0))) % 12.74/12.87 inverse(inverse(multiply(X0, X1))) -> multiply(inverse(inverse(X0)), inverse(inverse(X1))) % 12.74/12.87 inverse(multiply(X0, X1)) -> multiply(inverse(X1), inverse(X0)) % 12.74/12.87 inverse(multiply(Y0, inverse(X1))) -> multiply(inverse(Y0), inverse(inverse(X1))) % 12.74/12.87 multiply(X0, multiply(X1, multiply(inverse(X0), multiply(inverse(X1), Y1)))) -> Y1 % 12.74/12.87 multiply(X0, multiply(Y1, inverse(Y1))) -> X0 % 12.74/12.87 multiply(X0, multiply(inverse(X0), Y1)) -> Y1 % 12.74/12.87 multiply(X1, inverse(multiply(multiply(X0, X1), inverse(multiply(X0, Y1))))) -> Y1 % 12.74/12.87 multiply(X1, inverse(multiply(multiply(Y1, X1), Y2))) -> inverse(multiply(Y1, Y2)) % 12.74/12.87 multiply(X1, inverse(multiply(multiply(multiply(Y2, multiply(multiply(X0, X1), X2)), Y3), inverse(multiply(X0, X2))))) -> inverse(multiply(Y2, Y3)) % 12.74/12.87 multiply(X1, multiply(inverse(Y0), multiply(inverse(X1), multiply(Y0, Y1)))) -> Y1 % 12.74/12.87 multiply(X2, inverse(multiply(Y0, inverse(multiply(multiply(X1, multiply(Y0, Y1)), inverse(multiply(X1, X2))))))) -> Y1 % 12.74/12.87 multiply(Y0, inverse(multiply(multiply(Y1, Y0), inverse(X2)))) -> multiply(multiply(X2, false__), inverse(multiply(Y1, false__))) % 12.74/12.87 multiply(Y0, inverse(multiply(multiply(multiply(multiply(X0, X1), X2), Y0), inverse(X1)))) -> inverse(multiply(X0, X2)) % 12.74/12.87 multiply(Y0, multiply(X1, multiply(X2, inverse(Y0)))) -> multiply(X1, X2) % 12.74/12.87 multiply(Y0, multiply(Y1, inverse(Y0))) -> Y1 % 12.74/12.87 multiply(Y0, multiply(inverse(X0), X0)) -> Y0 % 12.74/12.87 multiply(Y0, multiply(inverse(X1), inverse(Y0))) -> inverse(X1) % 12.74/12.87 multiply(Y0, multiply(multiply(X0, X1), multiply(inverse(X1), inverse(X0)))) -> Y0 % 12.74/12.87 multiply(Y0, multiply(multiply(X1, X0), multiply(inverse(X1), inverse(X0)))) -> Y0 % 12.74/12.87 multiply(Y0, multiply(multiply(inverse(X1), inverse(X0)), multiply(X0, X1))) -> Y0 % 12.74/12.87 multiply(Y1, multiply(Y0, multiply(inverse(Y1), X1))) -> multiply(Y0, X1) % 12.74/12.87 multiply(false__, multiply(X0, multiply(inverse(false__), multiply(inverse(X1), inverse(X0))))) -> inverse(X1) % 12.74/12.87 multiply(false__, multiply(X1, multiply(inverse(false__), multiply(inverse(X1), Y1)))) -> Y1 % 12.74/12.87 multiply(false__, multiply(X1, multiply(inverse(false__), multiply(inverse(X1), inverse(X0))))) -> inverse(X0) % 12.74/12.87 multiply(false__, multiply(inverse(X0), multiply(inverse(false__), multiply(Y0, X0)))) -> Y0 % 12.74/12.87 multiply(false__, multiply(inverse(X1), multiply(inverse(false__), multiply(inverse(X0), X1)))) -> inverse(X0) % 12.74/12.87 multiply(false__, multiply(multiply(inverse(false__), X0), multiply(inverse(X1), inverse(X0)))) -> inverse(X1) % 12.74/12.87 multiply(false__, multiply(multiply(inverse(false__), X1), multiply(inverse(X1), Y1))) -> Y1 % 12.74/12.87 multiply(false__, multiply(multiply(inverse(false__), X1), multiply(inverse(X1), inverse(X0)))) -> inverse(X0) % 12.74/12.87 multiply(false__, multiply(multiply(inverse(false__), inverse(X0)), multiply(X0, Y1))) -> Y1 % 12.74/12.87 multiply(false__, multiply(multiply(inverse(false__), inverse(X0)), multiply(X0, inverse(Y1)))) -> inverse(Y1) % 12.74/12.87 multiply(inverse(X0), inverse(inverse(multiply(X0, Y2)))) -> Y2 % 12.74/12.87 multiply(inverse(X0), multiply(inverse(Y1), inverse(inverse(X0)))) -> inverse(Y1) % 12.74/12.87 multiply(inverse(X0), multiply(inverse(inverse(X0)), inverse(inverse(Y1)))) -> Y1 % 12.74/12.87 multiply(inverse(X1), inverse(multiply(Y0, inverse(Y0)))) -> inverse(X1) % 12.74/12.87 multiply(inverse(X1), inverse(multiply(Y1, inverse(X1)))) -> inverse(Y1) % 12.74/12.87 multiply(inverse(Y0), multiply(X0, inverse(X0))) -> inverse(Y0) % 12.74/12.87 multiply(inverse(Y0), multiply(Y0, Y1)) -> Y1 % 12.74/12.87 multiply(inverse(Y0), multiply(Y1, Y0)) -> Y1 % 12.74/12.87 multiply(inverse(Y0), multiply(inverse(X0), X0)) -> inverse(Y0) % 12.74/12.87 multiply(inverse(Y0), multiply(inverse(inverse(X0)), inverse(X0))) -> inverse(Y0) % 12.74/12.87 multiply(inverse(Y0), multiply(multiply(X0, X1), multiply(inverse(X1), inverse(X0)))) -> inverse(Y0) % 12.74/12.87 multiply(inverse(inverse(X0)), inverse(X0)) -> multiply(false__, inverse(false__)) % 12.74/12.87 multiply(inverse(inverse(X0)), multiply(inverse(X0), inverse(inverse(X1)))) -> inverse(inverse(X1)) % 12.74/12.87 multiply(inverse(inverse(multiply(X0, X1))), inverse(X1)) -> inverse(inverse(X0)) % 12.74/12.87 multiply(inverse(multiply(X0, X2)), inverse(multiply(X1, inverse(multiply(multiply(multiply(X0, X1), X2), Y2))))) -> Y2 % 12.74/12.87 multiply(inverse(multiply(X0, inverse(X1))), inverse(inverse(inverse(X1)))) -> inverse(X0) % 12.74/12.87 multiply(inverse(multiply(X1, X2)), inverse(multiply(Y0, inverse(Y0)))) -> inverse(multiply(X1, X2)) % 12.74/12.87 multiply(multiply(X0, X1), multiply(Y1, multiply(inverse(X1), inverse(X0)))) -> Y1 % 12.74/12.87 multiply(multiply(X0, X1), multiply(multiply(inverse(X1), inverse(X0)), Y1)) -> Y1 % 12.74/12.87 multiply(multiply(X0, false__), multiply(inverse(false__), multiply(inverse(X1), inverse(X0)))) -> inverse(X1) % 12.74/12.87 multiply(multiply(X0, inverse(X0)), inverse(false__)) -> inverse(false__) % 12.74/12.87 multiply(multiply(X0, inverse(X0)), inverse(inverse(false__))) -> inverse(inverse(false__)) % 12.74/12.87 multiply(multiply(X0, inverse(false__)), multiply(false__, inverse(X0))) -> multiply(false__, inverse(false__)) % 12.74/12.87 multiply(multiply(X0, inverse(false__)), multiply(false__, multiply(inverse(X1), inverse(X0)))) -> inverse(X1) % 12.74/12.87 multiply(multiply(X1, X0), multiply(Y0, multiply(inverse(X1), inverse(X0)))) -> Y0 % 12.74/12.87 multiply(multiply(X1, X0), multiply(multiply(inverse(X1), inverse(X0)), Y1)) -> Y1 % 12.74/12.87 multiply(multiply(X1, Y2), inverse(multiply(multiply(multiply(X0, X1), X2), Y2))) -> inverse(multiply(X0, X2)) % 12.74/12.87 multiply(multiply(X1, Y2), multiply(inverse(Y2), multiply(inverse(X1), inverse(X0)))) -> inverse(X0) % 12.74/12.87 multiply(multiply(X1, inverse(false__)), multiply(false__, multiply(inverse(X1), Y1))) -> Y1 % 12.74/12.87 multiply(multiply(X1, inverse(false__)), multiply(false__, multiply(inverse(X1), inverse(X0)))) -> inverse(X0) % 12.74/12.87 multiply(multiply(X2, false__), inverse(multiply(Y0, false__))) -> multiply(X2, inverse(Y0)) % 12.74/12.87 multiply(multiply(Y0, X0), inverse(Y0)) -> X0 % 12.74/12.87 multiply(multiply(Y0, Y2), multiply(inverse(Y0), Y1)) -> multiply(Y2, Y1) % 12.74/12.87 multiply(multiply(Y0, inverse(X1)), inverse(Y0)) -> inverse(X1) % 12.74/12.87 multiply(multiply(Y0, inverse(multiply(Y2, Y3))), inverse(Y0)) -> inverse(multiply(Y2, Y3)) % 12.74/12.87 multiply(multiply(Y0, multiply(X0, X1)), multiply(inverse(X1), inverse(X0))) -> Y0 % 12.74/12.87 multiply(multiply(Y0, multiply(inverse(X1), inverse(X0))), inverse(Y0)) -> multiply(inverse(X1), inverse(X0)) % 12.74/12.87 multiply(multiply(Y1, Y0), inverse(Y0)) -> Y1 % 12.74/12.87 multiply(multiply(Y1, Y2), Y0) -> multiply(Y2, multiply(Y1, Y0)) % 12.74/12.87 multiply(multiply(Y1, Y2), multiply(Y0, inverse(Y1))) -> multiply(Y2, Y0) % 12.74/12.87 multiply(multiply(Y1, inverse(Y1)), Y0) -> Y0 % 12.74/12.87 multiply(multiply(Y2, inverse(Y1)), multiply(Y0, Y1)) -> multiply(Y2, Y0) % 12.74/12.87 multiply(multiply(Y2, multiply(Y0, Y1)), multiply(inverse(Y2), inverse(Y0))) -> Y1 % 12.74/12.87 multiply(multiply(false__, inverse(X0)), multiply(inverse(false__), multiply(X0, Y1))) -> Y1 % 12.74/12.87 multiply(multiply(false__, inverse(X0)), multiply(inverse(false__), multiply(Y0, X0))) -> Y0 % 12.74/12.87 multiply(multiply(false__, inverse(X1)), multiply(inverse(false__), multiply(inverse(X0), X1))) -> inverse(X0) % 12.74/12.87 multiply(multiply(false__, inverse(false__)), Y1) -> Y1 % 12.74/12.87 multiply(multiply(false__, multiply(false__, false__)), multiply(inverse(false__), multiply(inverse(false__), inverse(false__)))) -> multiply(false__, inverse(false__)) % 12.74/12.87 multiply(multiply(false__, multiply(multiply(inverse(X1), inverse(X0)), inverse(inverse(X0)))), inverse(false__)) -> inverse(X1) % 12.74/12.87 multiply(multiply(inverse(X0), Y1), X0) -> Y1 % 12.74/12.87 multiply(multiply(inverse(X0), inverse(Y1)), X0) -> inverse(Y1) % 12.74/12.87 multiply(multiply(inverse(X0), inverse(false__)), multiply(false__, multiply(X0, Y1))) -> Y1 % 12.74/12.87 multiply(multiply(inverse(X0), inverse(false__)), multiply(false__, multiply(X0, inverse(Y1)))) -> inverse(Y1) % 12.74/12.87 multiply(multiply(inverse(X0), inverse(false__)), multiply(false__, multiply(Y0, X0))) -> Y0 % 12.74/12.87 multiply(multiply(inverse(X1), Y0), inverse(Y0)) -> inverse(X1) % 12.74/12.87 multiply(multiply(inverse(X1), Y2), inverse(multiply(multiply(X0, inverse(X1)), Y2))) -> inverse(X0) % 12.74/12.87 multiply(multiply(inverse(X1), false__), inverse(multiply(multiply(X0, inverse(X1)), false__))) -> inverse(X0) % 12.74/12.87 multiply(multiply(inverse(X1), inverse(X0)), inverse(inverse(X0))) -> inverse(X1) % 12.74/12.87 multiply(multiply(inverse(X1), inverse(X0)), multiply(Y1, inverse(Y1))) -> multiply(inverse(X1), inverse(X0)) % 12.74/12.87 multiply(multiply(inverse(X1), inverse(X0)), multiply(Y1, multiply(X0, X1))) -> Y1 % 12.74/12.87 multiply(multiply(inverse(X1), inverse(X0)), multiply(multiply(X0, X1), Y1)) -> Y1 % 12.74/12.87 multiply(multiply(inverse(X1), inverse(X0)), multiply(multiply(X1, X0), Y1)) -> Y1 % 12.74/12.87 multiply(multiply(inverse(X1), inverse(X0)), multiply(multiply(inverse(inverse(X0)), inverse(inverse(X1))), inverse(inverse(Y1)))) -> Y1 % 12.74/12.87 multiply(multiply(inverse(X1), inverse(false__)), multiply(false__, multiply(inverse(X0), X1))) -> inverse(X0) % 12.74/12.87 multiply(multiply(inverse(X1), inverse(inverse(X1))), inverse(inverse(X0))) -> inverse(inverse(X0)) % 12.74/12.87 multiply(multiply(inverse(Y0), Y2), multiply(Y0, Y1)) -> multiply(Y2, Y1) % 12.74/12.87 multiply(multiply(inverse(Y1), Y2), multiply(Y0, Y1)) -> multiply(Y2, Y0) % 12.74/12.87 multiply(multiply(inverse(Y2), inverse(Y0)), multiply(multiply(Y0, Y1), Y2)) -> Y1 % 12.74/12.87 multiply(multiply(inverse(false__), X0), multiply(false__, multiply(inverse(X1), inverse(X0)))) -> inverse(X1) % 12.74/12.87 multiply(multiply(inverse(false__), X1), multiply(false__, multiply(inverse(X1), Y1))) -> Y1 % 12.74/12.87 multiply(multiply(inverse(false__), X1), multiply(false__, multiply(inverse(X1), inverse(X0)))) -> inverse(X0) % 12.74/12.87 multiply(multiply(inverse(false__), inverse(X0)), multiply(false__, multiply(X0, Y1))) -> Y1 % 12.74/12.87 multiply(multiply(inverse(false__), inverse(X0)), multiply(false__, multiply(X0, inverse(Y1)))) -> inverse(Y1) % 12.74/12.87 multiply(multiply(inverse(false__), inverse(X0)), multiply(false__, multiply(Y0, X0))) -> Y0 % 12.74/12.87 multiply(multiply(inverse(false__), inverse(X1)), multiply(false__, multiply(inverse(X0), X1))) -> inverse(X0) % 12.74/12.87 multiply(multiply(inverse(inverse(X0)), inverse(Y1)), inverse(X0)) -> inverse(Y1) % 12.74/12.87 multiply(multiply(inverse(multiply(X0, X1)), inverse(Y1)), multiply(X1, inverse(inverse(X0)))) -> inverse(Y1) % 12.74/12.87 multiply(multiply(inverse(multiply(X1, X2)), Y2), inverse(multiply(multiply(X0, inverse(multiply(X1, X2))), Y2))) -> inverse(X0) % 12.74/12.87 multiply(multiply(multiply(A, B), C), inverse(multiply(A, C))) -> B % 12.74/12.87 multiply(multiply(multiply(X0, X1), Y1), multiply(inverse(X1), inverse(X0))) -> Y1 % 12.74/12.87 multiply(multiply(multiply(X0, X1), inverse(Y1)), multiply(inverse(X1), inverse(X0))) -> inverse(Y1) % 12.74/12.87 multiply(multiply(multiply(X0, X1), multiply(inverse(X1), inverse(X0))), Y1) -> Y1 % 12.74/12.87 multiply(multiply(multiply(X1, X0), Y1), multiply(inverse(X1), inverse(X0))) -> Y1 % 12.74/12.87 multiply(multiply(multiply(X2, false__), inverse(multiply(Y1, false__))), inverse(multiply(X2, inverse(multiply(Y1, Y2))))) -> Y2 % 12.74/12.87 multiply(multiply(multiply(Y0, Y1), Y2), multiply(inverse(Y0), inverse(Y2))) -> Y1 % 12.74/12.87 multiply(multiply(multiply(Y0, Y1), inverse(multiply(multiply(X1, Y0), inverse(multiply(X1, X2))))), inverse(X2)) -> Y1 % 12.74/12.87 multiply(multiply(multiply(Y0, Y1), multiply(inverse(Y0), X1)), inverse(X1)) -> Y1 % 12.74/12.87 multiply(multiply(multiply(Y1, Y0), Y2), multiply(inverse(Y2), inverse(Y0))) -> Y1 % 12.74/12.87 multiply(multiply(multiply(inverse(X0), Y1), multiply(X0, X1)), inverse(X1)) -> Y1 % 12.74/12.87 multiply(multiply(multiply(inverse(false__), inverse(false__)), multiply(false__, X0)), multiply(false__, inverse(X0))) -> multiply(false__, inverse(false__)) % 12.74/12.87 multiply(multiply(multiply(multiply(X0, X1), Y1), inverse(X0)), inverse(X1)) -> Y1 % 12.74/12.87 multiply(multiply(multiply(multiply(X0, inverse(X1)), Y1), inverse(X0)), inverse(inverse(X1))) -> Y1 % 12.74/12.87 multiply(multiply(multiply(multiply(multiply(X0, X1), X2), Y1), inverse(multiply(X0, X2))), inverse(X1)) -> Y1 % 12.74/12.87 true__ -> false__ % 12.74/12.87 with the LPO induced by % 12.74/12.87 c3 > b3 > a3 > f1 > inverse > multiply > true__ > false__ % 12.74/12.87 % 12.74/12.87 % SZS output end Proof % 12.74/12.87 %------------------------------------------------------------------------------