%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP679-1 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n022.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 10:57:46 EDT 2022 % Result : Unsatisfiable 29.87s 29.98s % Output : Proof 29.87s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GRP679-1 : TPTP v8.1.0. Released v4.0.0. % 0.07/0.13 % Command : moca.sh %s % 0.14/0.34 % Computer : n022.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 600 % 0.14/0.34 % DateTime : Mon Jun 13 21:50:03 EDT 2022 % 0.14/0.34 % CPUTime : % 29.87/29.98 % SZS status Unsatisfiable % 29.87/29.98 % SZS output start Proof % 29.87/29.98 The input problem is unsatisfiable because % 29.87/29.98 % 29.87/29.98 [1] the following set of Horn clauses is unsatisfiable: % 29.87/29.98 % 29.87/29.98 mult(A, ld(A, B)) = B % 29.87/29.98 ld(A, mult(A, B)) = B % 29.87/29.98 mult(rd(A, B), B) = A % 29.87/29.98 rd(mult(A, B), B) = A % 29.87/29.98 mult(A, unit) = A % 29.87/29.98 mult(unit, A) = A % 29.87/29.98 mult(A, mult(B, mult(A, C))) = mult(mult(A, mult(B, A)), C) % 29.87/29.98 mult(op_c, A) = mult(A, op_c) % 29.87/29.98 mult(mult(op_c, op_c), a) = mult(a, mult(op_c, op_c)) ==> \bottom % 29.87/29.98 % 29.87/29.98 This holds because % 29.87/29.98 % 29.87/29.98 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 29.87/29.98 % 29.87/29.98 E: % 29.87/29.98 f1(mult(a, mult(op_c, op_c))) = false__ % 29.87/29.98 f1(mult(mult(op_c, op_c), a)) = true__ % 29.87/29.98 ld(A, mult(A, B)) = B % 29.87/29.98 mult(A, ld(A, B)) = B % 29.87/29.98 mult(A, mult(B, mult(A, C))) = mult(mult(A, mult(B, A)), C) % 29.87/29.98 mult(A, unit) = A % 29.87/29.98 mult(op_c, A) = mult(A, op_c) % 29.87/29.98 mult(rd(A, B), B) = A % 29.87/29.98 mult(unit, A) = A % 29.87/29.98 rd(mult(A, B), B) = A % 29.87/29.98 G: % 29.87/29.98 true__ = false__ % 29.87/29.98 % 29.87/29.98 This holds because % 29.87/29.98 % 29.87/29.98 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 29.87/29.98 % 29.87/29.98 ld(X0, X0) = ld(Y0, Y0) % 29.87/29.98 ld(X0, X0) = rd(Y0, Y0) % 29.87/29.98 ld(Y0, Y0) = rd(false__, false__) % 29.87/29.98 ld(Y0, Y0) = unit % 29.87/29.98 ld(Y0, mult(X1, Y2)) = mult(rd(ld(Y0, X1), Y0), mult(Y0, Y2)) % 29.87/29.98 ld(Y0, mult(mult(Y0, X1), X2)) = mult(rd(X1, Y0), mult(Y0, X2)) % 29.87/29.98 ld(Y0, mult(mult(Y0, X1), ld(Y0, X2))) = mult(rd(X1, Y0), X2) % 29.87/29.98 ld(Y0, mult(mult(op_c, Y0), Y2)) = mult(rd(op_c, Y0), mult(Y0, Y2)) % 29.87/29.98 ld(Y0, mult(op_c, mult(Y0, Y1))) = mult(rd(Y1, Y0), mult(Y0, op_c)) % 29.87/29.98 ld(mult(Y0, mult(Y1, Y0)), mult(Y0, mult(Y1, Y0))) = rd(false__, false__) % 29.87/29.98 ld(mult(op_c, mult(Y0, op_c)), mult(op_c, Y0)) = ld(op_c, ld(X1, X1)) % 29.87/29.98 ld(mult(op_c, mult(Y1, op_c)), mult(op_c, mult(Y1, X0))) = rd(X0, op_c) % 29.87/29.98 ld(op_c, mult(X0, Y2)) = mult(ld(op_c, ld(op_c, X0)), mult(op_c, Y2)) % 29.87/29.98 ld(rd(X0, Y1), mult(X0, Y2)) = mult(rd(Y1, rd(X0, Y1)), mult(rd(X0, Y1), Y2)) % 29.87/29.98 mult(X0, ld(rd(X0, Y1), Y2)) = mult(rd(X0, Y1), mult(rd(Y1, rd(X0, Y1)), Y2)) % 29.87/29.98 mult(X0, mult(op_c, op_c)) = mult(op_c, mult(op_c, X0)) % 29.87/29.98 mult(X1, ld(Y0, Y2)) = mult(Y0, mult(rd(ld(Y0, X1), Y0), Y2)) % 29.87/29.98 mult(Y0, mult(Y1, mult(op_c, Y0))) = mult(op_c, mult(Y0, mult(Y1, Y0))) % 29.87/29.98 mult(Y0, mult(op_c, Y0)) = mult(op_c, mult(Y0, Y0)) % 29.87/29.98 mult(Y0, mult(op_c, rd(Y1, Y0))) = mult(mult(Y0, Y1), ld(Y0, op_c)) % 29.87/29.98 mult(Y0, mult(rd(Y1, Y0), X1)) = mult(mult(Y0, Y1), ld(Y0, X1)) % 29.87/29.98 mult(Y0, rd(Y1, Y0)) = mult(mult(Y0, Y1), ld(Y0, ld(X1, X1))) % 29.87/29.98 mult(mult(Y1, op_c), ld(op_c, Y2)) = mult(op_c, mult(ld(op_c, Y1), Y2)) % 29.87/29.98 mult(mult(op_c, Y0), ld(Y0, Y2)) = mult(Y0, mult(rd(op_c, Y0), Y2)) % 29.87/29.98 mult(op_c, A) = mult(A, op_c) % 29.87/29.98 mult(op_c, mult(X0, mult(X0, mult(Y1, mult(X0, X0))))) = mult(X0, mult(X0, mult(Y1, mult(X0, mult(X0, op_c))))) % 29.87/29.98 mult(op_c, mult(X0, mult(X0, op_c))) = mult(X0, mult(X0, mult(op_c, op_c))) % 29.87/29.98 mult(op_c, mult(X1, op_c)) = mult(X1, mult(op_c, op_c)) % 29.87/29.98 mult(op_c, mult(Y0, Y0)) = mult(Y0, mult(Y0, op_c)) % 29.87/29.98 mult(op_c, mult(Y0, mult(X0, mult(X0, Y0)))) = mult(Y0, mult(X0, mult(X0, mult(Y0, op_c)))) % 29.87/29.98 mult(op_c, mult(Y0, mult(Y0, op_c))) = mult(Y0, mult(op_c, mult(Y0, op_c))) % 29.87/29.98 mult(op_c, mult(Y0, mult(Y0, op_c))) = mult(Y0, mult(op_c, mult(op_c, Y0))) % 29.87/29.98 mult(op_c, mult(Y0, mult(Y1, Y0))) = mult(Y0, mult(Y1, mult(Y0, op_c))) % 29.87/29.98 mult(op_c, mult(Y0, mult(Y1, mult(Y0, mult(Y2, mult(Y0, mult(Y1, Y0))))))) = mult(Y0, mult(Y1, mult(Y0, mult(Y2, mult(Y0, mult(Y1, mult(Y0, op_c))))))) % 29.87/29.98 mult(op_c, mult(Y0, mult(Y1, mult(Y2, mult(Y1, Y0))))) = mult(Y0, mult(Y1, mult(Y2, mult(Y1, mult(Y0, op_c))))) % 29.87/29.98 mult(op_c, mult(ld(Y1, X1), X1)) = mult(ld(Y1, X1), mult(Y1, mult(ld(Y1, X1), op_c))) % 29.87/29.98 mult(op_c, mult(ld(Y1, X1), X1)) = mult(ld(Y1, X1), mult(Y1, mult(op_c, ld(Y1, X1)))) % 29.87/29.98 mult(op_c, mult(op_c, mult(X0, mult(rd(X1, mult(X0, X1)), X0)))) = mult(op_c, mult(X0, op_c)) % 29.87/29.98 mult(op_c, mult(op_c, mult(op_c, Y1))) = mult(op_c, mult(Y1, mult(op_c, op_c))) % 29.87/29.98 mult(rd(Y0, Y1), mult(op_c, Y1)) = ld(Y1, mult(mult(Y1, Y0), op_c)) % 29.87/29.98 rd(X0, X0) = rd(Y0, Y0) % 29.87/29.98 rd(X2, op_c) = mult(X1, mult(op_c, ld(mult(op_c, mult(X1, op_c)), X2))) % 29.87/29.98 rd(Y1, Y1) = rd(false__, false__) % 29.87/29.98 rd(Y1, Y1) = unit % 29.87/29.98 f1(mult(a, mult(op_c, op_c))) -> false__ % 29.87/29.98 f1(mult(mult(op_c, op_c), a)) -> true__ % 29.87/29.98 f1(mult(op_c, mult(op_c, a))) -> true__ % 29.87/29.98 ld(A, mult(A, B)) -> B % 29.87/29.98 ld(Y0, mult(op_c, Y0)) -> op_c % 29.87/29.98 ld(Y0, mult(op_c, mult(Y0, Y0))) -> mult(Y0, op_c) % 29.87/29.98 ld(Y0, mult(op_c, mult(Y0, mult(X1, Y0)))) -> mult(X1, mult(Y0, op_c)) % 29.87/29.98 ld(Y0, mult(op_c, mult(Y0, mult(Y0, op_c)))) -> mult(op_c, mult(Y0, op_c)) % 29.87/29.98 ld(Y0, mult(op_c, mult(Y0, op_c))) -> mult(op_c, op_c) % 29.87/29.98 ld(Y0, mult(op_c, mult(op_c, Y0))) -> mult(op_c, op_c) % 29.87/29.98 ld(ld(X0, X0), Y0) -> Y0 % 29.87/29.98 ld(ld(op_c, X1), X1) -> op_c % 29.87/29.98 ld(mult(X0, X0), mult(X0, mult(X0, Y1))) -> Y1 % 29.87/29.98 ld(mult(X0, X1), mult(X0, mult(rd(X1, X0), X2))) -> ld(X0, X2) % 29.87/29.98 ld(mult(X0, mult(X1, X0)), mult(X0, mult(X1, mult(X0, Y1)))) -> Y1 % 29.87/29.98 ld(mult(X0, mult(X1, mult(X0, mult(X2, mult(X0, mult(X1, X0)))))), mult(X0, mult(X1, mult(X0, mult(X2, mult(X0, mult(X1, mult(X0, Y1)))))))) -> Y1 % 29.87/29.98 ld(mult(X0, mult(X1, mult(X2, mult(X1, X0)))), mult(X0, mult(X1, mult(X2, mult(X1, mult(X0, Y1)))))) -> Y1 % 29.87/29.98 ld(mult(X0, mult(op_c, op_c)), mult(op_c, mult(op_c, mult(op_c, X0)))) -> op_c % 29.87/29.98 ld(mult(X0, op_c), mult(X0, mult(op_c, op_c))) -> op_c % 29.87/29.98 ld(mult(X1, mult(op_c, ld(mult(op_c, mult(X1, op_c)), X2))), X2) -> op_c % 29.87/29.98 ld(mult(X1, mult(op_c, op_c)), mult(op_c, mult(op_c, mult(X1, op_c)))) -> op_c % 29.87/29.98 ld(mult(Y0, Y0), mult(Y0, X1)) -> ld(Y0, X1) % 29.87/29.98 ld(mult(Y0, Y0), mult(Y0, mult(op_c, Y0))) -> op_c % 29.87/29.98 ld(mult(Y0, mult(Y0, op_c)), mult(Y0, mult(op_c, Y0))) -> ld(false__, false__) % 29.87/29.98 ld(mult(Y0, mult(Y0, op_c)), mult(Y0, mult(op_c, mult(Y0, Y2)))) -> Y2 % 29.87/29.98 ld(mult(Y0, mult(Y1, Y0)), mult(Y0, mult(Y1, X1))) -> ld(Y0, X1) % 29.87/29.98 ld(mult(Y0, mult(Y1, Y0)), mult(Y0, mult(Y1, mult(op_c, Y0)))) -> op_c % 29.87/29.98 ld(mult(Y0, mult(op_c, Y0)), mult(Y0, mult(Y0, op_c))) -> ld(false__, false__) % 29.87/29.98 ld(mult(Y0, mult(op_c, Y0)), mult(Y0, mult(mult(Y0, Y2), op_c))) -> Y2 % 29.87/29.98 ld(mult(Y0, mult(rd(X0, mult(Y0, Y2)), Y0)), mult(Y0, X0)) -> Y2 % 29.87/29.98 ld(mult(ld(Y1, X1), X1), mult(ld(Y1, X1), mult(Y1, mult(ld(Y1, X1), Y2)))) -> Y2 % 29.87/29.98 ld(mult(ld(op_c, X1), X2), mult(mult(op_c, X1), ld(op_c, X2))) -> op_c % 29.87/29.98 ld(mult(op_c, X0), mult(X0, mult(op_c, op_c))) -> op_c % 29.87/29.98 ld(mult(op_c, X0), mult(op_c, mult(ld(op_c, X0), Y1))) -> ld(op_c, Y1) % 29.87/29.98 ld(mult(op_c, ld(mult(op_c, op_c), X1)), X1) -> op_c % 29.87/29.98 ld(mult(op_c, mult(Y0, op_c)), mult(mult(Y0, Y1), op_c)) -> ld(op_c, Y1) % 29.87/29.98 ld(mult(op_c, mult(Y0, op_c)), mult(op_c, Y0)) -> ld(op_c, ld(false__, false__)) % 29.87/29.98 ld(mult(op_c, mult(Y1, op_c)), mult(op_c, mult(Y1, mult(Y2, op_c)))) -> Y2 % 29.87/29.98 ld(mult(op_c, mult(Y1, op_c)), mult(op_c, mult(op_c, Y1))) -> ld(false__, false__) % 29.87/29.98 ld(mult(op_c, mult(op_c, Y0)), mult(op_c, mult(Y0, Y1))) -> ld(op_c, Y1) % 29.87/29.98 ld(mult(op_c, mult(op_c, Y1)), mult(op_c, mult(Y1, mult(op_c, Y2)))) -> Y2 % 29.87/29.98 ld(mult(op_c, mult(op_c, Y1)), mult(op_c, mult(Y1, op_c))) -> ld(false__, false__) % 29.87/29.98 ld(mult(op_c, mult(rd(X0, Y1), op_c)), mult(op_c, X0)) -> ld(op_c, Y1) % 29.87/29.98 ld(mult(op_c, op_c), mult(op_c, X0)) -> ld(op_c, X0) % 29.87/29.98 ld(mult(op_c, op_c), mult(op_c, mult(Y1, op_c))) -> Y1 % 29.87/29.98 ld(mult(rd(X0, Y1), rd(X0, Y1)), mult(rd(X0, Y1), X0)) -> Y1 % 29.87/29.98 ld(mult(rd(X0, Y2), mult(Y1, rd(X0, Y2))), mult(rd(X0, Y2), mult(Y1, X0))) -> Y2 % 29.87/29.98 ld(mult(rd(X0, op_c), X0), mult(rd(X0, op_c), mult(op_c, mult(rd(X0, op_c), Y2)))) -> Y2 % 29.87/29.98 ld(mult(rd(X1, op_c), mult(op_c, X2)), mult(mult(op_c, X1), X2)) -> op_c % 29.87/29.98 ld(op_c, mult(X0, mult(X0, op_c))) -> mult(X0, X0) % 29.87/29.98 ld(op_c, mult(X0, mult(X1, mult(X0, op_c)))) -> mult(X0, mult(X1, X0)) % 29.87/29.98 ld(op_c, mult(X0, mult(X1, mult(op_c, X0)))) -> mult(X0, mult(X1, X0)) % 29.87/29.98 ld(op_c, mult(X0, mult(op_c, mult(X0, op_c)))) -> mult(X0, mult(X0, op_c)) % 29.87/29.98 ld(op_c, mult(X0, mult(op_c, op_c))) -> mult(X0, op_c) % 29.87/29.98 ld(op_c, mult(X0, mult(op_c, op_c))) -> mult(op_c, X0) % 29.87/29.98 ld(op_c, mult(Y0, mult(op_c, Y0))) -> mult(Y0, Y0) % 29.87/29.98 ld(op_c, mult(Y1, op_c)) -> Y1 % 29.87/29.98 ld(op_c, mult(ld(X0, X1), mult(X0, mult(ld(X0, X1), op_c)))) -> mult(ld(X0, X1), X1) % 29.87/29.98 ld(op_c, mult(ld(op_c, X0), X0)) -> mult(ld(op_c, X0), ld(op_c, X0)) % 29.87/29.98 ld(op_c, mult(mult(Y1, op_c), Y2)) -> mult(ld(op_c, Y1), mult(op_c, Y2)) % 29.87/29.98 ld(op_c, mult(mult(op_c, X0), X0)) -> mult(mult(op_c, X0), ld(op_c, X0)) % 29.87/29.98 ld(op_c, mult(mult(op_c, Y0), Y2)) -> mult(ld(op_c, Y0), mult(Y2, op_c)) % 29.87/29.98 ld(rd(X0, X0), Y0) -> Y0 % 29.87/29.98 ld(rd(X0, X1), ld(X1, mult(mult(X1, X0), X2))) -> mult(X1, X2) % 29.87/29.98 ld(rd(X0, Y1), X0) -> Y1 % 29.87/29.98 ld(unit, Y1) -> Y1 % 29.87/29.98 mult(A, ld(A, B)) -> B % 29.87/29.98 mult(A, unit) -> A % 29.87/29.98 mult(X0, mult(X0, mult(rd(op_c, mult(X0, mult(X0, mult(X0, X0)))), mult(X0, X0)))) -> op_c % 29.87/29.98 mult(X0, mult(X1, mult(X0, mult(rd(op_c, mult(X0, mult(X1, mult(X0, mult(X0, mult(X1, X0)))))), mult(X0, mult(X1, X0)))))) -> op_c % 29.87/29.98 mult(X0, mult(X1, mult(X0, mult(rd(op_c, mult(X0, mult(X1, mult(X0, op_c)))), mult(X0, mult(X1, X0)))))) -> mult(X0, mult(X1, X0)) % 29.87/29.98 mult(X0, mult(X1, mult(op_c, mult(rd(X0, mult(op_c, mult(X1, mult(X0, mult(X0, mult(X1, X0)))))), mult(op_c, mult(X1, X0)))))) -> op_c % 29.87/29.98 mult(X0, mult(op_c, mult(X0, mult(rd(op_c, mult(X0, mult(op_c, mult(X0, mult(X0, mult(X0, op_c)))))), mult(X0, mult(op_c, X0)))))) -> op_c % 29.87/29.98 mult(X0, mult(op_c, mult(X0, mult(rd(op_c, mult(X0, mult(op_c, mult(X0, op_c)))), mult(X0, mult(op_c, X0)))))) -> mult(X0, mult(X0, op_c)) % 29.87/29.98 mult(X0, mult(op_c, mult(rd(op_c, mult(op_c, mult(X0, mult(X0, op_c)))), mult(op_c, X0)))) -> op_c % 29.87/29.98 mult(X0, mult(op_c, mult(rd(op_c, mult(op_c, mult(X0, mult(op_c, X0)))), mult(op_c, X0)))) -> op_c % 29.87/29.98 mult(X0, mult(op_c, mult(rd(op_c, mult(op_c, mult(X0, op_c))), mult(op_c, X0)))) -> mult(X0, op_c) % 29.87/29.98 mult(X0, mult(op_c, mult(rd(op_c, mult(op_c, mult(X0, op_c))), mult(op_c, X0)))) -> mult(op_c, X0) % 29.87/29.98 mult(X0, mult(rd(X1, X0), mult(rd(X2, mult(rd(X1, X0), X2)), X1))) -> mult(X0, X1) % 29.87/29.98 mult(X1, mult(Y0, ld(mult(Y0, mult(X1, Y0)), X2))) -> ld(Y0, X2) % 29.87/29.98 mult(Y0, ld(X0, X0)) -> Y0 % 29.87/29.98 mult(Y0, ld(mult(Y0, Y0), X1)) -> ld(Y0, X1) % 29.87/29.98 mult(Y0, mult(Y0, ld(mult(Y0, Y0), X1))) -> X1 % 29.87/29.98 mult(Y0, mult(Y1, mult(Y0, ld(mult(Y0, mult(Y1, Y0)), X1)))) -> X1 % 29.87/29.98 mult(Y0, mult(Y1, mult(Y0, mult(Y2, mult(Y0, mult(Y1, mult(Y0, ld(mult(Y0, mult(Y1, mult(Y0, mult(Y2, mult(Y0, mult(Y1, Y0)))))), X1)))))))) -> X1 % 29.87/29.98 mult(Y0, mult(Y1, mult(Y0, mult(rd(X0, mult(Y0, mult(Y1, Y0))), mult(Y0, mult(Y1, mult(Y0, Y3))))))) -> mult(mult(Y0, mult(Y1, mult(Y0, X0))), Y3) % 29.87/29.98 mult(Y0, mult(Y1, mult(Y2, mult(Y1, mult(Y0, ld(mult(Y0, mult(Y1, mult(Y2, mult(Y1, Y0)))), X1)))))) -> X1 % 29.87/29.98 mult(Y0, mult(Y1, mult(rd(X0, mult(Y1, Y0)), mult(Y1, mult(Y0, Y3))))) -> mult(mult(Y0, mult(Y1, X0)), Y3) % 29.87/29.98 mult(Y0, mult(mult(Y0, Y2), mult(rd(op_c, mult(mult(Y0, Y2), mult(Y0, Y2))), mult(mult(Y0, Y2), Y0)))) -> mult(Y0, mult(op_c, Y0)) % 29.87/29.98 mult(Y0, mult(op_c, ld(mult(op_c, mult(op_c, Y0)), Y1))) -> ld(op_c, Y1) % 29.87/29.98 mult(Y0, mult(op_c, mult(Y0, ld(mult(Y0, mult(Y0, op_c)), Y2)))) -> Y2 % 29.87/29.98 mult(Y0, mult(op_c, mult(rd(Y0, mult(op_c, mult(Y0, mult(Y0, Y0)))), mult(op_c, Y0)))) -> op_c % 29.87/29.98 mult(Y0, mult(op_c, mult(rd(Y0, mult(op_c, mult(Y0, op_c))), mult(op_c, Y0)))) -> mult(Y0, Y0) % 29.87/29.98 mult(Y0, mult(rd(X0, Y0), mult(Y0, Y2))) -> mult(mult(Y0, X0), Y2) % 29.87/29.98 mult(Y0, mult(rd(Y1, Y0), mult(op_c, Y0))) -> mult(mult(Y0, Y1), op_c) % 29.87/29.98 mult(Y0, mult(rd(ld(false__, false__), Y0), Y2)) -> Y2 % 29.87/29.98 mult(Y0, mult(rd(op_c, mult(Y0, op_c)), Y0)) -> Y0 % 29.87/29.98 mult(Y0, rd(X0, X0)) -> Y0 % 29.87/29.98 mult(Y0, rd(Y1, Y0)) -> mult(mult(Y0, Y1), ld(Y0, ld(false__, false__))) % 29.87/29.98 mult(Y1, mult(rd(X1, mult(Y1, X1)), Y1)) -> Y1 % 29.87/29.98 mult(Y1, mult(rd(op_c, mult(Y1, Y1)), Y1)) -> op_c % 29.87/29.98 mult(ld(X0, X0), Y0) -> Y0 % 29.87/29.98 mult(ld(Y0, rd(false__, false__)), mult(Y0, mult(ld(Y0, rd(false__, false__)), Y2))) -> mult(ld(Y0, rd(false__, false__)), Y2) % 29.87/29.98 mult(ld(Y1, X1), mult(Y1, mult(ld(Y1, X1), ld(mult(ld(Y1, X1), X1), Y2)))) -> Y2 % 29.87/29.98 mult(ld(Y1, Y1), mult(Y1, mult(ld(Y1, Y1), Y2))) -> mult(Y1, Y2) % 29.87/29.98 mult(ld(op_c, X0), mult(rd(X0, mult(ld(op_c, X0), mult(ld(op_c, X0), ld(op_c, X0)))), ld(op_c, X0))) -> op_c % 29.87/29.98 mult(mult(A, mult(B, A)), C) -> mult(A, mult(B, mult(A, C))) % 29.87/29.98 mult(mult(X0, mult(X0, mult(X0, X0))), Y1) -> mult(X0, mult(X0, mult(X0, mult(X0, Y1)))) % 29.87/29.98 mult(mult(X0, mult(X1, mult(X0, mult(Y1, mult(X0, mult(X1, X0)))))), Y2) -> mult(X0, mult(X1, mult(X0, mult(Y1, mult(X0, mult(X1, mult(X0, Y2))))))) % 29.87/29.98 mult(mult(Y0, X1), mult(rd(ld(Y0, X2), mult(mult(Y0, X1), mult(rd(X1, Y0), X2))), mult(Y0, X1))) -> Y0 % 29.87/29.98 mult(mult(Y0, Y0), Y2) -> mult(Y0, mult(Y0, Y2)) % 29.87/29.98 mult(mult(Y0, mult(X0, mult(X1, mult(X0, Y0)))), Y2) -> mult(Y0, mult(X0, mult(X1, mult(X0, mult(Y0, Y2))))) % 29.87/29.98 mult(mult(Y0, mult(Y0, op_c)), Y2) -> mult(Y0, mult(op_c, mult(Y0, Y2))) % 29.87/29.98 mult(mult(Y0, mult(Y1, mult(Y0, mult(Y0, mult(Y1, Y0))))), Y3) -> mult(Y0, mult(Y1, mult(Y0, mult(Y0, mult(Y1, mult(Y0, Y3)))))) % 29.87/29.98 mult(mult(Y0, mult(Y1, mult(Y0, mult(Y0, mult(Y1, mult(Y0, op_c)))))), Y3) -> mult(Y0, mult(Y1, mult(Y0, mult(op_c, mult(Y0, mult(Y1, mult(Y0, Y3))))))) % 29.87/29.98 mult(mult(Y0, mult(Y1, mult(Y1, Y0))), Y3) -> mult(Y0, mult(Y1, mult(Y1, mult(Y0, Y3)))) % 29.87/29.98 mult(mult(Y0, mult(Y1, mult(mult(Y1, Y0), op_c))), Y3) -> mult(Y0, mult(Y1, mult(op_c, mult(Y1, mult(Y0, Y3))))) % 29.87/29.98 mult(mult(Y0, mult(op_c, mult(Y0, mult(Y2, mult(Y0, mult(Y0, op_c)))))), Y3) -> mult(Y0, mult(op_c, mult(Y0, mult(Y2, mult(Y0, mult(op_c, mult(Y0, Y3))))))) % 29.87/29.98 mult(mult(Y0, mult(op_c, mult(Y2, mult(Y0, op_c)))), Y3) -> mult(Y0, mult(op_c, mult(Y2, mult(op_c, mult(Y0, Y3))))) % 29.87/29.98 mult(mult(Y0, mult(rd(X0, Y0), mult(Y2, X0))), Y3) -> mult(Y0, mult(rd(X0, Y0), mult(Y2, mult(rd(X0, Y0), mult(Y0, Y3))))) % 29.87/29.98 mult(mult(ld(Y1, X1), X1), Y2) -> mult(ld(Y1, X1), mult(Y1, mult(ld(Y1, X1), Y2))) % 29.87/29.98 mult(mult(ld(Y1, X1), mult(Y1, mult(Y2, X1))), Y3) -> mult(ld(Y1, X1), mult(Y1, mult(Y2, mult(Y1, mult(ld(Y1, X1), Y3))))) % 29.87/29.98 mult(mult(ld(Y1, X1), mult(Y1, mult(ld(Y1, X1), mult(Y2, mult(ld(Y1, X1), X1))))), Y3) -> mult(ld(Y1, X1), mult(Y1, mult(ld(Y1, X1), mult(Y2, mult(ld(Y1, X1), mult(Y1, mult(ld(Y1, X1), Y3))))))) % 29.87/29.98 mult(mult(op_c, X1), mult(rd(ld(op_c, X2), mult(op_c, mult(op_c, X1))), mult(op_c, X1))) -> mult(ld(op_c, X1), X2) % 29.87/29.98 mult(mult(op_c, Y1), ld(op_c, ld(false__, false__))) -> Y1 % 29.87/29.98 mult(mult(op_c, ld(Y0, op_c)), Y2) -> mult(ld(Y0, op_c), mult(Y0, mult(ld(Y0, op_c), Y2))) % 29.87/29.98 mult(mult(op_c, mult(Y1, mult(Y2, mult(op_c, Y1)))), Y3) -> mult(op_c, mult(Y1, mult(Y2, mult(Y1, mult(op_c, Y3))))) % 29.87/29.98 mult(mult(op_c, mult(Y1, mult(op_c, mult(Y2, mult(op_c, mult(op_c, Y1)))))), Y3) -> mult(op_c, mult(Y1, mult(op_c, mult(Y2, mult(op_c, mult(Y1, mult(op_c, Y3))))))) % 29.87/29.98 mult(mult(op_c, mult(op_c, Y1)), Y2) -> mult(op_c, mult(Y1, mult(op_c, Y2))) % 29.87/29.98 mult(mult(rd(X0, op_c), X0), Y1) -> mult(rd(X0, op_c), mult(op_c, mult(rd(X0, op_c), Y1))) % 29.87/29.98 mult(op_c, ld(mult(op_c, mult(Y0, op_c)), X1)) -> ld(Y0, ld(op_c, X1)) % 29.87/29.98 mult(op_c, ld(mult(op_c, op_c), X1)) -> ld(op_c, X1) % 29.87/29.98 mult(op_c, mult(Y0, mult(rd(X0, mult(Y0, op_c)), Y0))) -> mult(Y0, X0) % 29.87/29.98 mult(op_c, mult(Y0, mult(rd(X0, mult(op_c, Y0)), Y0))) -> mult(Y0, X0) % 29.87/29.98 mult(op_c, mult(Y1, mult(op_c, ld(mult(op_c, mult(op_c, Y1)), Y2)))) -> Y2 % 29.87/29.98 mult(op_c, mult(ld(op_c, X0), ld(op_c, X0))) -> mult(ld(op_c, X0), X0) % 29.87/29.98 mult(op_c, mult(ld(op_c, X1), mult(Y1, ld(op_c, X1)))) -> mult(ld(op_c, X1), mult(Y1, X1)) % 29.87/29.98 mult(op_c, mult(ld(op_c, X1), mult(op_c, Y1))) -> mult(mult(op_c, X1), Y1) % 29.87/29.98 mult(op_c, mult(op_c, mult(Y0, mult(X1, mult(rd(Y0, mult(X1, mult(Y0, mult(op_c, mult(X1, mult(op_c, Y0)))))), mult(X1, Y0)))))) -> Y0 % 29.87/29.98 mult(op_c, mult(op_c, mult(Y0, mult(Y0, mult(rd(op_c, mult(Y0, mult(Y0, mult(op_c, mult(op_c, mult(Y0, op_c)))))), mult(Y0, Y0)))))) -> Y0 % 29.87/29.98 mult(op_c, mult(op_c, mult(Y0, mult(rd(Y0, mult(Y0, mult(op_c, mult(Y0, op_c)))), Y0)))) -> Y0 % 29.87/29.98 mult(op_c, mult(op_c, mult(Y0, mult(rd(op_c, mult(Y0, mult(op_c, mult(op_c, op_c)))), Y0)))) -> Y0 % 29.87/29.98 mult(op_c, mult(op_c, mult(Y1, mult(rd(op_c, mult(Y1, mult(op_c, Y1))), Y1)))) -> mult(op_c, op_c) % 29.87/29.98 mult(op_c, mult(op_c, mult(op_c, mult(op_c, mult(op_c, mult(op_c, rd(X0, mult(op_c, mult(op_c, mult(op_c, mult(X0, mult(op_c, op_c)))))))))))) -> op_c % 29.87/29.98 mult(op_c, mult(op_c, mult(op_c, mult(op_c, rd(Y0, mult(op_c, mult(op_c, mult(op_c, op_c)))))))) -> Y0 % 29.87/29.98 mult(op_c, mult(op_c, mult(op_c, mult(op_c, rd(op_c, mult(op_c, mult(op_c, mult(op_c, op_c)))))))) -> op_c % 29.87/29.98 mult(op_c, mult(op_c, mult(op_c, rd(X0, mult(op_c, op_c))))) -> mult(op_c, X0) % 29.87/29.98 mult(op_c, mult(op_c, rd(X0, mult(op_c, op_c)))) -> X0 % 29.87/29.98 mult(op_c, mult(op_c, rd(Y0, mult(op_c, Y0)))) -> op_c % 29.87/29.98 mult(op_c, mult(rd(X0, op_c), mult(Y1, rd(X0, op_c)))) -> mult(rd(X0, op_c), mult(Y1, X0)) % 29.87/29.98 mult(op_c, mult(rd(Y1, op_c), mult(Y2, op_c))) -> mult(mult(op_c, Y1), Y2) % 29.87/29.98 mult(op_c, rd(Y0, op_c)) -> Y0 % 29.87/29.98 mult(rd(A, B), B) -> A % 29.87/29.98 mult(rd(X0, X0), Y0) -> Y0 % 29.87/29.98 mult(rd(X0, Y2), mult(rd(Y1, rd(X0, Y2)), X0)) -> mult(mult(rd(X0, Y2), Y1), Y2) % 29.87/29.98 mult(rd(X0, op_c), mult(op_c, mult(rd(X0, op_c), ld(mult(rd(X0, op_c), X0), Y2)))) -> Y2 % 29.87/29.98 mult(rd(Y0, rd(X0, Y2)), X0) -> ld(rd(X0, Y2), mult(mult(rd(X0, Y2), Y0), Y2)) % 29.87/29.98 mult(rd(Y1, Y0), mult(Y0, ld(mult(Y0, Y1), X1))) -> ld(Y0, X1) % 29.87/29.98 mult(rd(ld(X1, X1), Y0), mult(Y0, Y2)) -> Y2 % 29.87/29.98 mult(rd(ld(false__, false__), Y0), mult(Y0, Y2)) -> Y2 % 29.87/29.98 mult(unit, A) -> A % 29.87/29.98 rd(X0, op_c) -> ld(op_c, X0) % 29.87/29.98 rd(X0, rd(X0, op_c)) -> op_c % 29.87/29.98 rd(X1, ld(Y0, X1)) -> Y0 % 29.87/29.98 rd(X1, mult(Y0, ld(mult(Y0, Y0), X1))) -> Y0 % 29.87/29.98 rd(X2, mult(X1, mult(Y0, ld(mult(Y0, mult(X1, Y0)), X2)))) -> Y0 % 29.87/29.98 rd(Y0, ld(X0, X0)) -> Y0 % 29.87/29.98 rd(Y0, rd(X0, X0)) -> Y0 % 29.87/29.98 rd(Y0, unit) -> Y0 % 29.87/29.98 rd(ld(X1, mult(mult(X1, X0), X2)), mult(X1, X2)) -> rd(X0, X1) % 29.87/29.98 rd(mult(A, B), B) -> A % 29.87/29.98 rd(mult(X0, mult(X0, Y1)), Y1) -> mult(X0, X0) % 29.87/29.98 rd(mult(X0, mult(X0, op_c)), mult(X0, X0)) -> op_c % 29.87/29.98 rd(mult(X0, mult(X1, mult(X0, Y1))), Y1) -> mult(X0, mult(X1, X0)) % 29.87/29.98 rd(mult(X0, mult(X1, mult(X0, op_c))), mult(X0, mult(X1, X0))) -> op_c % 29.87/29.98 rd(mult(X0, mult(op_c, mult(X0, op_c))), mult(X0, mult(X0, op_c))) -> op_c % 29.87/29.98 rd(mult(Y0, X0), Y2) -> mult(Y0, mult(rd(X0, mult(Y0, Y2)), Y0)) % 29.87/29.98 rd(mult(Y0, mult(Y1, X1)), ld(Y0, X1)) -> mult(Y0, mult(Y1, Y0)) % 29.87/29.98 rd(mult(Y0, mult(Y1, mult(op_c, Y0))), op_c) -> mult(Y0, mult(Y1, Y0)) % 29.87/29.98 rd(mult(Y0, mult(mult(Y0, Y2), op_c)), Y2) -> mult(Y0, mult(op_c, Y0)) % 29.87/29.98 rd(mult(Y1, op_c), Y1) -> op_c % 29.87/29.98 rd(mult(mult(Y0, X1), X2), mult(rd(X1, Y0), mult(Y0, X2))) -> Y0 % 29.87/29.98 rd(mult(op_c, Y0), op_c) -> Y0 % 29.87/29.98 rd(mult(op_c, mult(X0, mult(op_c, op_c))), mult(op_c, mult(op_c, X0))) -> op_c % 29.87/29.98 rd(mult(op_c, mult(Y0, mult(X1, Y0))), mult(X1, mult(Y0, op_c))) -> Y0 % 29.87/29.98 rd(mult(op_c, mult(Y1, mult(Y2, op_c))), Y2) -> mult(op_c, mult(Y1, op_c)) % 29.87/29.98 rd(mult(rd(X0, Y2), mult(Y1, X0)), Y2) -> mult(rd(X0, Y2), mult(Y1, rd(X0, Y2))) % 29.87/29.98 true__ -> false__ % 29.87/29.98 with the LPO induced by % 29.87/29.98 a > f1 > op_c > unit > rd > ld > mult > true__ > false__ % 29.87/29.98 % 29.87/29.98 % SZS output end Proof % 29.87/29.98 %------------------------------------------------------------------------------