%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP665-11 : TPTP v8.1.0. Released v8.1.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n026.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 10:57:36 EDT 2022 % Result : Unsatisfiable 10.55s 10.60s % Output : Proof 10.55s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : GRP665-11 : TPTP v8.1.0. Released v8.1.0. % 0.03/0.13 % Command : moca.sh %s % 0.14/0.34 % Computer : n026.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 04:15:50 EDT 2022 % 0.14/0.35 % CPUTime : % 10.55/10.60 % SZS status Unsatisfiable % 10.55/10.60 % SZS output start Proof % 10.55/10.60 The input problem is unsatisfiable because % 10.55/10.60 % 10.55/10.60 [1] the following set of Horn clauses is unsatisfiable: % 10.55/10.60 % 10.55/10.60 mult(A, ld(A, B)) = B % 10.55/10.60 ld(A, mult(A, B)) = B % 10.55/10.60 mult(rd(A, B), B) = A % 10.55/10.60 rd(mult(A, B), B) = A % 10.55/10.60 mult(A, unit) = A % 10.55/10.60 mult(unit, A) = A % 10.55/10.60 mult(A, mult(B, C)) = mult(rd(mult(A, B), A), mult(A, C)) % 10.55/10.60 mult(mult(A, B), C) = mult(mult(A, C), ld(C, mult(B, C))) % 10.55/10.60 mult(op_c, A) = mult(A, op_c) % 10.55/10.60 mult(mult(x0, op_c), x1) = mult(x0, mult(op_c, x1)) ==> \bottom % 10.55/10.60 % 10.55/10.60 This holds because % 10.55/10.60 % 10.55/10.60 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 10.55/10.60 % 10.55/10.60 E: % 10.55/10.60 f1(mult(mult(x0, op_c), x1)) = true__ % 10.55/10.60 f1(mult(x0, mult(op_c, x1))) = false__ % 10.55/10.60 ld(A, mult(A, B)) = B % 10.55/10.60 mult(A, ld(A, B)) = B % 10.55/10.60 mult(A, mult(B, C)) = mult(rd(mult(A, B), A), mult(A, C)) % 10.55/10.60 mult(A, unit) = A % 10.55/10.60 mult(mult(A, B), C) = mult(mult(A, C), ld(C, mult(B, C))) % 10.55/10.60 mult(op_c, A) = mult(A, op_c) % 10.55/10.60 mult(rd(A, B), B) = A % 10.55/10.60 mult(unit, A) = A % 10.55/10.60 rd(mult(A, B), B) = A % 10.55/10.60 G: % 10.55/10.60 true__ = false__ % 10.55/10.60 % 10.55/10.60 This holds because % 10.55/10.60 % 10.55/10.60 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 10.55/10.60 % 10.55/10.60 ld(X0, X0) = ld(Y0, Y0) % 10.55/10.60 ld(X0, X0) = rd(Y0, Y0) % 10.55/10.60 ld(Y0, Y0) = unit % 10.55/10.60 ld(Y0, ld(op_c, Y0)) = ld(false__, ld(op_c, false__)) % 10.55/10.60 ld(Y0, mult(ld(op_c, Y0), X1)) = ld(op_c, X1) % 10.55/10.60 ld(Y0, mult(ld(op_c, Y0), mult(ld(false__, ld(op_c, false__)), X1))) = ld(false__, mult(ld(op_c, false__), ld(op_c, X1))) % 10.55/10.60 ld(Y0, mult(ld(op_c, Y0), mult(ld(false__, ld(op_c, false__)), X1))) = mult(ld(op_c, X1), ld(false__, ld(op_c, false__))) % 10.55/10.60 ld(Y0, mult(mult(Y0, ld(false__, ld(op_c, false__))), Y1)) = ld(op_c, Y1) % 10.55/10.60 ld(Y0, mult(mult(ld(false__, ld(op_c, false__)), Y0), Y1)) = ld(op_c, Y1) % 10.55/10.60 ld(Y0, mult(mult(ld(op_c, Y0), ld(false__, ld(op_c, false__))), X1)) = mult(ld(op_c, X1), ld(false__, ld(op_c, false__))) % 10.55/10.60 ld(op_c, Y0) = mult(Y0, ld(false__, ld(op_c, false__))) % 10.55/10.60 ld(op_c, Y0) = mult(Y0, ld(op_c, ld(false__, false__))) % 10.55/10.60 ld(op_c, Y1) = mult(ld(false__, ld(op_c, false__)), Y1) % 10.55/10.60 ld(op_c, Y1) = mult(ld(op_c, ld(X0, X0)), Y1) % 10.55/10.60 ld(op_c, Y1) = mult(ld(op_c, ld(false__, false__)), Y1) % 10.55/10.60 mult(X0, ld(op_c, X1)) = mult(ld(op_c, X0), X1) % 10.55/10.60 mult(X0, mult(Y1, mult(op_c, op_c))) = mult(op_c, mult(X0, mult(op_c, Y1))) % 10.55/10.60 mult(X0, mult(Y1, mult(op_c, op_c))) = mult(op_c, mult(op_c, mult(X0, Y1))) % 10.55/10.60 mult(X0, mult(op_c, mult(X1, op_c))) = mult(op_c, mult(op_c, mult(X0, X1))) % 10.55/10.60 mult(X1, mult(op_c, mult(ld(X1, Y0), op_c))) = mult(Y0, mult(op_c, op_c)) % 10.55/10.60 mult(X1, mult(op_c, mult(op_c, ld(X1, Y0)))) = mult(Y0, mult(op_c, op_c)) % 10.55/10.60 mult(X1, op_c) = mult(Y0, mult(op_c, ld(Y0, X1))) % 10.55/10.60 mult(X1, op_c) = mult(mult(Y0, op_c), ld(Y0, X1)) % 10.55/10.60 mult(Y0, mult(X0, mult(X1, op_c))) = mult(op_c, mult(Y0, mult(X0, X1))) % 10.55/10.60 mult(Y0, mult(X0, mult(op_c, X1))) = mult(op_c, mult(Y0, mult(X0, X1))) % 10.55/10.60 mult(Y0, mult(Y1, ld(false__, ld(op_c, false__)))) = mult(ld(op_c, Y0), Y1) % 10.55/10.60 mult(Y0, mult(ld(false__, ld(op_c, false__)), Y1)) = mult(ld(op_c, Y0), Y1) % 10.55/10.60 mult(Y0, mult(op_c, mult(op_c, X1))) = mult(op_c, mult(Y0, mult(X1, op_c))) % 10.55/10.60 mult(Y1, mult(Y2, op_c)) = mult(op_c, mult(Y1, Y2)) % 10.55/10.60 mult(Y1, mult(op_c, Y2)) = mult(op_c, mult(Y1, Y2)) % 10.55/10.60 mult(Y1, mult(op_c, op_c)) = mult(op_c, mult(op_c, Y1)) % 10.55/10.60 mult(false__, ld(X0, ld(op_c, X0))) = ld(op_c, false__) % 10.55/10.60 mult(ld(false__, ld(op_c, false__)), Y0) = mult(Y0, ld(false__, ld(op_c, false__))) % 10.55/10.60 mult(mult(A, B), C) = mult(mult(A, C), ld(C, mult(B, C))) % 10.55/10.60 mult(mult(X0, mult(X1, op_c)), Y1) = mult(mult(X0, X1), mult(Y1, op_c)) % 10.55/10.60 mult(mult(X0, mult(X1, op_c)), ld(mult(X0, X1), Y1)) = mult(Y1, op_c) % 10.55/10.60 mult(mult(X0, mult(op_c, X1)), Y1) = mult(mult(X0, X1), mult(Y1, op_c)) % 10.55/10.60 mult(mult(X0, mult(op_c, X1)), ld(mult(X0, X1), Y1)) = mult(Y1, op_c) % 10.55/10.60 mult(mult(X0, mult(op_c, op_c)), Y1) = mult(X0, mult(op_c, mult(Y1, op_c))) % 10.55/10.60 mult(mult(Y0, X1), mult(op_c, op_c)) = mult(Y0, mult(op_c, mult(X1, op_c))) % 10.55/10.60 mult(mult(Y0, X1), mult(op_c, op_c)) = mult(Y0, mult(op_c, mult(op_c, X1))) % 10.55/10.60 mult(mult(Y0, X1), mult(op_c, op_c)) = mult(op_c, mult(Y0, mult(op_c, X1))) % 10.55/10.60 mult(mult(Y0, Y1), op_c) = mult(Y0, mult(op_c, Y1)) % 10.55/10.60 mult(mult(Y0, Y1), op_c) = mult(mult(Y0, op_c), Y1) % 10.55/10.60 mult(mult(Y1, op_c), Y2) = mult(mult(op_c, Y2), ld(Y2, mult(Y1, Y2))) % 10.55/10.60 mult(mult(Y1, op_c), ld(Y1, mult(Y2, Y1))) = mult(mult(op_c, Y2), Y1) % 10.55/10.60 mult(mult(op_c, Y0), Y1) = mult(Y0, mult(Y1, op_c)) % 10.55/10.60 mult(mult(op_c, Y0), ld(Y0, Y1)) = mult(Y1, op_c) % 10.55/10.60 mult(op_c, A) = mult(A, op_c) % 10.55/10.60 mult(op_c, X0) = mult(rd(X0, Y1), mult(Y1, op_c)) % 10.55/10.60 mult(op_c, X1) = mult(Y0, mult(ld(Y0, X1), op_c)) % 10.55/10.60 mult(op_c, mult(X0, mult(X1, op_c))) = mult(mult(X0, X1), mult(op_c, op_c)) % 10.55/10.60 mult(op_c, mult(X0, op_c)) = mult(rd(X0, X1), mult(op_c, mult(X1, op_c))) % 10.55/10.60 mult(op_c, mult(X1, op_c)) = mult(Y0, mult(op_c, mult(op_c, ld(Y0, X1)))) % 10.55/10.60 mult(op_c, mult(Y0, mult(op_c, X1))) = mult(Y0, mult(op_c, mult(X1, op_c))) % 10.55/10.60 mult(op_c, mult(Y1, op_c)) = mult(mult(op_c, op_c), Y1) % 10.55/10.60 mult(op_c, mult(op_c, X0)) = mult(rd(X0, X1), mult(op_c, mult(X1, op_c))) % 10.55/10.60 mult(op_c, mult(op_c, mult(Y0, X1))) = mult(Y0, mult(op_c, mult(op_c, X1))) % 10.55/10.60 mult(op_c, mult(op_c, mult(op_c, Y0))) = mult(Y0, mult(op_c, mult(op_c, op_c))) % 10.55/10.60 mult(rd(Y0, mult(X0, X1)), mult(X0, mult(op_c, X1))) = mult(op_c, Y0) % 10.55/10.60 mult(rd(Y1, X1), mult(X1, mult(op_c, op_c))) = mult(op_c, mult(op_c, Y1)) % 10.55/10.60 rd(X0, X0) = rd(Y0, Y0) % 10.55/10.60 rd(Y1, Y1) = unit % 10.55/10.60 f1(mult(mult(op_c, x0), x1)) -> true__ % 10.55/10.60 f1(mult(mult(x0, op_c), x1)) -> true__ % 10.55/10.60 f1(mult(op_c, mult(x0, x1))) -> false__ % 10.55/10.60 f1(mult(x0, mult(op_c, x1))) -> false__ % 10.55/10.60 ld(A, mult(A, B)) -> B % 10.55/10.60 ld(Y0, mult(X1, op_c)) -> mult(op_c, ld(Y0, X1)) % 10.55/10.60 ld(Y0, mult(ld(false__, ld(op_c, false__)), Y0)) -> ld(false__, ld(op_c, false__)) % 10.55/10.60 ld(Y0, mult(op_c, X1)) -> mult(ld(Y0, X1), op_c) % 10.55/10.60 ld(Y0, mult(op_c, Y0)) -> op_c % 10.55/10.60 ld(Y0, mult(op_c, mult(Y0, X1))) -> mult(X1, op_c) % 10.55/10.60 ld(Y0, mult(op_c, mult(Y0, X1))) -> mult(op_c, X1) % 10.55/10.60 ld(Y0, mult(op_c, mult(op_c, Y0))) -> mult(op_c, op_c) % 10.55/10.60 ld(Y0, mult(rd(Y0, X1), mult(X1, op_c))) -> op_c % 10.55/10.60 ld(false__, mult(ld(op_c, false__), ld(ld(op_c, Y0), X1))) -> ld(Y0, X1) % 10.55/10.60 ld(ld(X0, X0), Y0) -> Y0 % 10.55/10.60 ld(ld(X1, mult(ld(op_c, X1), Y0)), Y0) -> op_c % 10.55/10.60 ld(ld(false__, ld(op_c, false__)), Y1) -> mult(Y1, op_c) % 10.55/10.60 ld(ld(false__, ld(op_c, false__)), ld(op_c, Y1)) -> Y1 % 10.55/10.60 ld(ld(op_c, X0), mult(X0, ld(op_c, Y1))) -> Y1 % 10.55/10.60 ld(ld(op_c, X1), X1) -> op_c % 10.55/10.60 ld(ld(op_c, ld(false__, false__)), Y1) -> mult(Y1, op_c) % 10.55/10.60 ld(mult(X0, X1), mult(X0, mult(X1, op_c))) -> op_c % 10.55/10.60 ld(mult(X0, X1), mult(X0, mult(op_c, X1))) -> op_c % 10.55/10.60 ld(mult(X0, ld(op_c, X1)), mult(X0, X1)) -> op_c % 10.55/10.60 ld(mult(X0, op_c), X0) -> ld(false__, ld(op_c, false__)) % 10.55/10.60 ld(mult(X0, op_c), mult(X0, Y1)) -> ld(op_c, Y1) % 10.55/10.60 ld(mult(X0, op_c), mult(X0, mult(Y1, op_c))) -> Y1 % 10.55/10.60 ld(mult(X0, op_c), mult(X1, op_c)) -> ld(X0, X1) % 10.55/10.60 ld(mult(X1, op_c), mult(op_c, mult(op_c, X1))) -> op_c % 10.55/10.60 ld(mult(Y0, ld(false__, ld(op_c, false__))), Y0) -> op_c % 10.55/10.60 ld(mult(false__, ld(X0, ld(op_c, X0))), false__) -> op_c % 10.55/10.60 ld(mult(ld(false__, ld(op_c, false__)), Y0), Y0) -> op_c % 10.55/10.60 ld(mult(ld(op_c, X0), X1), mult(X0, X1)) -> op_c % 10.55/10.60 ld(mult(op_c, X0), mult(X0, mult(Y1, op_c))) -> Y1 % 10.55/10.60 ld(mult(op_c, X0), mult(X1, op_c)) -> ld(X0, X1) % 10.55/10.60 ld(mult(op_c, X1), X1) -> ld(false__, ld(op_c, false__)) % 10.55/10.60 ld(mult(op_c, X1), mult(X1, Y1)) -> ld(op_c, Y1) % 10.55/10.60 ld(mult(op_c, Y0), op_c) -> ld(Y0, ld(false__, false__)) % 10.55/10.60 ld(mult(op_c, op_c), op_c) -> ld(false__, ld(op_c, false__)) % 10.55/10.60 ld(mult(op_c, rd(X0, mult(Y1, op_c))), X0) -> Y1 % 10.55/10.60 ld(mult(rd(X0, mult(X1, op_c)), X1), X0) -> op_c % 10.55/10.60 ld(op_c, mult(X0, X1)) -> mult(X0, ld(op_c, X1)) % 10.55/10.60 ld(op_c, mult(X0, mult(X1, op_c))) -> mult(X0, X1) % 10.55/10.60 ld(op_c, mult(X0, mult(op_c, X1))) -> mult(X0, X1) % 10.55/10.60 ld(op_c, mult(Y1, op_c)) -> Y1 % 10.55/10.60 ld(rd(X0, Y1), X0) -> Y1 % 10.55/10.60 ld(unit, Y1) -> Y1 % 10.55/10.60 mult(A, ld(A, B)) -> B % 10.55/10.60 mult(A, unit) -> A % 10.55/10.60 mult(X1, ld(ld(op_c, X1), Y1)) -> mult(Y1, op_c) % 10.55/10.60 mult(Y0, ld(X0, X0)) -> Y0 % 10.55/10.60 mult(Y0, mult(ld(Y0, Y1), op_c)) -> mult(Y1, op_c) % 10.55/10.60 mult(Y0, mult(op_c, mult(ld(Y0, X1), op_c))) -> mult(op_c, mult(X1, op_c)) % 10.55/10.60 mult(Y0, rd(X0, X0)) -> Y0 % 10.55/10.60 mult(Y1, mult(op_c, ld(Y1, Y0))) -> mult(op_c, Y0) % 10.55/10.60 mult(ld(X0, X0), Y0) -> Y0 % 10.55/10.60 mult(ld(false__, ld(op_c, false__)), ld(ld(op_c, Y0), X1)) -> ld(Y0, X1) % 10.55/10.60 mult(ld(ld(op_c, Y0), X1), ld(false__, ld(op_c, false__))) -> ld(Y0, X1) % 10.55/10.60 mult(mult(X0, X1), mult(op_c, op_c)) -> mult(X0, mult(X1, mult(op_c, op_c))) % 10.55/10.60 mult(mult(X0, mult(op_c, op_c)), Y1) -> mult(op_c, mult(X0, mult(op_c, Y1))) % 10.55/10.60 mult(mult(X0, mult(op_c, op_c)), ld(mult(op_c, X0), Y1)) -> mult(Y1, op_c) % 10.55/10.60 mult(mult(Y0, Y1), op_c) -> mult(Y0, mult(Y1, op_c)) % 10.55/10.60 mult(mult(Y0, op_c), Y1) -> mult(op_c, mult(Y0, Y1)) % 10.55/10.60 mult(mult(op_c, Y0), Y1) -> mult(Y0, mult(op_c, Y1)) % 10.55/10.60 mult(mult(op_c, op_c), Y1) -> mult(op_c, mult(op_c, Y1)) % 10.55/10.60 mult(op_c, ld(X1, mult(ld(op_c, X1), Y1))) -> Y1 % 10.55/10.60 mult(op_c, ld(Y0, ld(op_c, Y0))) -> ld(false__, false__) % 10.55/10.60 mult(op_c, ld(mult(X0, op_c), X1)) -> ld(X0, X1) % 10.55/10.60 mult(op_c, ld(mult(X0, op_c), mult(X0, Y1))) -> Y1 % 10.55/10.60 mult(op_c, ld(mult(op_c, X0), X1)) -> ld(X0, X1) % 10.55/10.60 mult(op_c, mult(Y0, ld(mult(Y0, op_c), X1))) -> X1 % 10.55/10.60 mult(op_c, mult(Y0, ld(op_c, X1))) -> mult(Y0, X1) % 10.55/10.60 mult(op_c, mult(Y1, ld(false__, ld(op_c, false__)))) -> Y1 % 10.55/10.60 mult(op_c, mult(ld(X1, ld(op_c, X1)), Y1)) -> Y1 % 10.55/10.60 mult(op_c, mult(ld(false__, ld(op_c, false__)), Y1)) -> Y1 % 10.55/10.60 mult(op_c, mult(ld(op_c, X1), Y1)) -> mult(X1, Y1) % 10.55/10.60 mult(op_c, mult(op_c, ld(mult(X1, op_c), X1))) -> op_c % 10.55/10.60 mult(op_c, mult(op_c, ld(mult(op_c, op_c), Y1))) -> Y1 % 10.55/10.60 mult(op_c, mult(op_c, rd(X0, mult(op_c, op_c)))) -> X0 % 10.55/10.60 mult(op_c, mult(rd(X0, mult(Y1, op_c)), Y1)) -> X0 % 10.55/10.60 mult(op_c, mult(rd(X0, mult(op_c, Y1)), Y1)) -> X0 % 10.55/10.60 mult(op_c, rd(X0, mult(Y1, op_c))) -> rd(X0, Y1) % 10.55/10.60 mult(op_c, rd(X0, mult(op_c, op_c))) -> ld(op_c, X0) % 10.55/10.60 mult(op_c, rd(Y0, op_c)) -> Y0 % 10.55/10.60 mult(rd(A, B), B) -> A % 10.55/10.60 mult(rd(X0, Y1), mult(op_c, Y1)) -> mult(X0, op_c) % 10.55/10.60 mult(rd(X0, mult(X1, op_c)), X1) -> ld(op_c, X0) % 10.55/10.60 mult(rd(X0, mult(op_c, X1)), X1) -> ld(op_c, X0) % 10.55/10.60 mult(rd(Y0, Y1), mult(Y1, op_c)) -> mult(Y0, op_c) % 10.55/10.60 mult(rd(Y0, ld(op_c, X0)), X0) -> mult(op_c, Y0) % 10.55/10.60 mult(rd(ld(X1, X1), Y1), mult(Y1, op_c)) -> op_c % 10.55/10.60 mult(rd(ld(false__, false__), Y1), mult(Y1, op_c)) -> op_c % 10.55/10.60 mult(rd(ld(false__, false__), false__), mult(false__, mult(op_c, op_c))) -> mult(op_c, op_c) % 10.55/10.60 mult(rd(mult(A, B), A), mult(A, C)) -> mult(A, mult(B, C)) % 10.55/10.60 mult(unit, A) -> A % 10.55/10.60 rd(X0, mult(rd(X0, mult(X1, op_c)), X1)) -> op_c % 10.55/10.60 rd(X0, op_c) -> ld(op_c, X0) % 10.55/10.60 rd(X0, rd(X0, op_c)) -> op_c % 10.55/10.60 rd(X1, ld(Y0, X1)) -> Y0 % 10.55/10.60 rd(Y0, ld(X0, X0)) -> Y0 % 10.55/10.60 rd(Y0, ld(X1, mult(ld(op_c, X1), Y0))) -> op_c % 10.55/10.60 rd(Y0, ld(false__, false__)) -> Y0 % 10.55/10.60 rd(Y0, mult(Y0, ld(false__, ld(op_c, false__)))) -> op_c % 10.55/10.60 rd(Y0, mult(ld(false__, ld(op_c, false__)), Y0)) -> op_c % 10.55/10.60 rd(Y0, unit) -> Y0 % 10.55/10.60 rd(false__, mult(false__, ld(X0, ld(op_c, X0)))) -> op_c % 10.55/10.60 rd(ld(false__, false__), ld(false__, ld(op_c, false__))) -> op_c % 10.55/10.60 rd(ld(op_c, Y1), Y1) -> ld(false__, ld(op_c, false__)) % 10.55/10.60 rd(ld(op_c, Y1), ld(false__, ld(op_c, false__))) -> Y1 % 10.55/10.60 rd(ld(op_c, false__), ld(X0, ld(op_c, X0))) -> false__ % 10.55/10.60 rd(mult(A, B), B) -> A % 10.55/10.60 rd(mult(X0, X1), mult(X0, ld(op_c, X1))) -> op_c % 10.55/10.60 rd(mult(X0, X1), mult(ld(op_c, X0), X1)) -> op_c % 10.55/10.60 rd(mult(X0, ld(op_c, Y1)), Y1) -> ld(op_c, X0) % 10.55/10.60 rd(mult(X0, mult(X1, op_c)), mult(X0, X1)) -> op_c % 10.55/10.60 rd(mult(X0, mult(Y1, op_c)), Y1) -> mult(X0, op_c) % 10.55/10.60 rd(mult(X0, mult(Y1, op_c)), Y1) -> mult(op_c, X0) % 10.55/10.60 rd(mult(X0, mult(op_c, X1)), mult(X0, X1)) -> op_c % 10.55/10.60 rd(mult(X0, mult(op_c, op_c)), mult(op_c, X0)) -> op_c % 10.55/10.60 rd(mult(X0, op_c), mult(op_c, X1)) -> rd(X0, X1) % 10.55/10.60 rd(mult(X1, op_c), ld(X0, X1)) -> mult(op_c, X0) % 10.55/10.60 rd(mult(X1, op_c), mult(op_c, ld(Y0, X1))) -> Y0 % 10.55/10.60 rd(mult(Y0, X0), ld(op_c, X0)) -> mult(op_c, Y0) % 10.55/10.60 rd(mult(Y0, mult(X1, op_c)), mult(op_c, X1)) -> Y0 % 10.55/10.60 rd(mult(Y0, mult(op_c, X1)), mult(X1, op_c)) -> Y0 % 10.55/10.60 rd(mult(Y0, mult(op_c, Y1)), Y1) -> mult(Y0, op_c) % 10.55/10.60 rd(mult(Y0, mult(op_c, Y1)), Y1) -> mult(op_c, Y0) % 10.55/10.60 rd(mult(Y1, op_c), Y1) -> op_c % 10.55/10.60 rd(mult(ld(op_c, Y0), X1), ld(op_c, X1)) -> Y0 % 10.55/10.60 rd(mult(op_c, X0), mult(X1, op_c)) -> rd(X0, X1) % 10.55/10.60 rd(mult(op_c, X0), mult(op_c, Y1)) -> rd(X0, Y1) % 10.55/10.60 rd(mult(op_c, X1), mult(ld(Y0, X1), op_c)) -> Y0 % 10.55/10.60 rd(mult(op_c, X1), mult(op_c, ld(Y0, X1))) -> Y0 % 10.55/10.60 rd(mult(op_c, Y0), op_c) -> Y0 % 10.55/10.60 rd(mult(op_c, Y1), mult(Y1, op_c)) -> ld(false__, false__) % 10.55/10.60 rd(mult(op_c, mult(X0, Y1)), Y1) -> mult(X0, op_c) % 10.55/10.60 rd(mult(op_c, mult(Y0, X1)), mult(X1, op_c)) -> Y0 % 10.55/10.60 rd(mult(op_c, mult(Y0, X1)), mult(op_c, X1)) -> Y0 % 10.55/10.60 rd(mult(op_c, mult(op_c, X0)), mult(X0, op_c)) -> op_c % 10.55/10.60 rd(mult(op_c, mult(op_c, Y0)), mult(op_c, op_c)) -> Y0 % 10.55/10.60 rd(mult(op_c, mult(op_c, Y1)), Y1) -> mult(op_c, op_c) % 10.55/10.60 rd(mult(rd(Y1, X1), mult(X1, op_c)), Y1) -> op_c % 10.55/10.60 rd(op_c, ld(Y1, ld(false__, false__))) -> mult(op_c, Y1) % 10.55/10.60 true__ -> false__ % 10.55/10.60 with the LPO induced by % 10.55/10.60 x1 > x0 > f1 > op_c > unit > rd > ld > mult > true__ > false__ % 10.55/10.60 % 10.55/10.60 % SZS output end Proof % 10.55/10.60 %------------------------------------------------------------------------------