%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP702-12 : TPTP v8.1.0. Released v8.1.0. % 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 10:57:58 EDT 2022 % Result : Unsatisfiable 3.18s 3.29s % Output : Proof 3.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GRP702-12 : TPTP v8.1.0. Released v8.1.0. % 0.07/0.12 % 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 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Tue Jun 14 07:47:53 EDT 2022 % 0.12/0.33 % CPUTime : % 3.18/3.29 % SZS status Unsatisfiable % 3.18/3.29 % SZS output start Proof % 3.18/3.29 The input problem is unsatisfiable because % 3.18/3.29 % 3.18/3.29 [1] the following set of Horn clauses is unsatisfiable: % 3.18/3.29 % 3.18/3.29 mult(A, ld(A, B)) = B % 3.18/3.29 ld(A, mult(A, B)) = B % 3.18/3.29 mult(rd(A, B), B) = A % 3.18/3.29 rd(mult(A, B), B) = A % 3.18/3.29 mult(A, unit) = A % 3.18/3.29 mult(unit, A) = A % 3.18/3.29 mult(A, mult(B, mult(B, C))) = mult(mult(mult(A, B), B), C) % 3.18/3.29 mult(op_c, mult(A, B)) = mult(mult(op_c, A), B) % 3.18/3.29 mult(A, mult(B, op_c)) = mult(mult(A, B), op_c) % 3.18/3.29 mult(A, mult(op_c, B)) = mult(mult(A, op_c), B) % 3.18/3.29 op_d = ld(A, mult(op_c, A)) % 3.18/3.29 op_e = mult(mult(rd(op_c, mult(A, B)), B), A) % 3.18/3.29 op_f = mult(A, mult(B, ld(mult(A, B), op_c))) % 3.18/3.29 mult(x0, mult(op_d, x1)) = mult(mult(x0, op_d), x1) ==> \bottom % 3.18/3.29 % 3.18/3.29 This holds because % 3.18/3.29 % 3.18/3.29 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 3.18/3.29 % 3.18/3.29 E: % 3.18/3.29 f1(mult(mult(x0, op_d), x1)) = false__ % 3.18/3.29 f1(mult(x0, mult(op_d, x1))) = true__ % 3.18/3.29 ld(A, mult(A, B)) = B % 3.18/3.29 mult(A, ld(A, B)) = B % 3.18/3.29 mult(A, mult(B, mult(B, C))) = mult(mult(mult(A, B), B), C) % 3.18/3.29 mult(A, mult(B, op_c)) = mult(mult(A, B), op_c) % 3.18/3.29 mult(A, mult(op_c, B)) = mult(mult(A, op_c), B) % 3.18/3.29 mult(A, unit) = A % 3.18/3.29 mult(op_c, mult(A, B)) = mult(mult(op_c, A), B) % 3.18/3.29 mult(rd(A, B), B) = A % 3.18/3.29 mult(unit, A) = A % 3.18/3.29 op_d = ld(A, mult(op_c, A)) % 3.18/3.29 op_e = mult(mult(rd(op_c, mult(A, B)), B), A) % 3.18/3.29 op_f = mult(A, mult(B, ld(mult(A, B), op_c))) % 3.18/3.29 rd(mult(A, B), B) = A % 3.18/3.29 G: % 3.18/3.29 true__ = false__ % 3.18/3.29 % 3.18/3.29 This holds because % 3.18/3.29 % 3.18/3.29 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 3.18/3.29 % 3.18/3.29 mult(Y0, op_f) = mult(op_f, Y0) % 3.18/3.29 mult(op_f, mult(Y0, Y1)) = mult(Y0, mult(Y1, op_f)) % 3.18/3.29 f1(mult(mult(op_f, x0), x1)) -> false__ % 3.18/3.29 f1(mult(mult(x0, op_d), x1)) -> false__ % 3.18/3.29 f1(mult(x0, mult(op_c, x1))) -> false__ % 3.18/3.29 f1(mult(x0, mult(op_c, x1))) -> true__ % 3.18/3.29 f1(mult(x0, mult(op_d, x1))) -> true__ % 3.18/3.29 f1(mult(x0, mult(op_f, x1))) -> false__ % 3.18/3.29 f1(mult(x0, mult(op_f, x1))) -> true__ % 3.18/3.29 ld(A, mult(A, B)) -> B % 3.18/3.29 ld(Y0, Y0) -> unit % 3.18/3.29 ld(Y0, mult(op_f, Y0)) -> op_f % 3.18/3.29 ld(ld(op_f, Y0), Y0) -> op_f % 3.18/3.29 ld(op_f, mult(Y1, op_f)) -> Y1 % 3.18/3.29 ld(rd(X0, Y1), X0) -> Y1 % 3.18/3.29 ld(unit, Y1) -> Y1 % 3.18/3.29 mult(A, ld(A, B)) -> B % 3.18/3.29 mult(A, mult(B, ld(mult(A, B), op_c))) -> op_f % 3.18/3.29 mult(A, unit) -> A % 3.18/3.29 mult(mult(A, B), op_c) -> mult(A, mult(B, op_f)) % 3.18/3.29 mult(mult(A, op_c), B) -> mult(A, mult(op_f, B)) % 3.18/3.29 mult(mult(Y0, Y1), Y1) -> mult(Y0, mult(Y1, Y1)) % 3.18/3.29 mult(mult(Y0, op_f), Y1) -> mult(Y0, mult(op_f, Y1)) % 3.18/3.29 mult(mult(mult(A, B), B), C) -> mult(A, mult(B, mult(B, C))) % 3.18/3.29 mult(mult(op_c, A), B) -> mult(op_f, mult(A, B)) % 3.18/3.29 mult(mult(op_f, Y0), Y1) -> mult(op_f, mult(Y0, Y1)) % 3.18/3.29 mult(mult(rd(op_c, mult(A, B)), B), A) -> op_f % 3.18/3.29 mult(op_f, rd(Y0, op_f)) -> Y0 % 3.18/3.29 mult(rd(A, B), B) -> A % 3.18/3.29 mult(unit, A) -> A % 3.18/3.29 op_c -> op_f % 3.18/3.29 op_d -> op_f % 3.18/3.29 op_e -> op_f % 3.18/3.29 rd(X0, op_f) -> ld(op_f, X0) % 3.18/3.29 rd(X1, ld(Y0, X1)) -> Y0 % 3.18/3.29 rd(Y0, unit) -> Y0 % 3.18/3.29 rd(Y1, Y1) -> unit % 3.18/3.29 rd(mult(A, B), B) -> A % 3.18/3.29 rd(mult(Y0, op_f), Y0) -> op_f % 3.18/3.29 rd(mult(Y1, op_e), Y1) -> op_f % 3.18/3.29 rd(mult(op_e, Y0), op_e) -> Y0 % 3.18/3.29 rd(mult(op_f, Y0), op_f) -> Y0 % 3.18/3.29 true__ -> false__ % 3.18/3.29 with the LPO induced by % 3.18/3.29 x1 > x0 > f1 > mult > op_d > op_e > op_c > op_f > rd > ld > unit > true__ > false__ % 3.18/3.29 % 3.18/3.29 % SZS output end Proof % 3.18/3.29 %------------------------------------------------------------------------------