%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP703-10 : TPTP v8.1.0. Released v8.1.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n020.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 10:57:59 EDT 2022 % Result : Unsatisfiable 4.69s 4.74s % Output : Proof 4.69s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : GRP703-10 : TPTP v8.1.0. Released v8.1.0. % 0.11/0.12 % Command : moca.sh %s % 0.12/0.33 % Computer : n020.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 10:58:19 EDT 2022 % 0.12/0.33 % CPUTime : % 4.69/4.74 % SZS status Unsatisfiable % 4.69/4.74 % SZS output start Proof % 4.69/4.74 The input problem is unsatisfiable because % 4.69/4.74 % 4.69/4.74 [1] the following set of Horn clauses is unsatisfiable: % 4.69/4.74 % 4.69/4.74 mult(A, ld(A, B)) = B % 4.69/4.74 ld(A, mult(A, B)) = B % 4.69/4.74 mult(rd(A, B), B) = A % 4.69/4.74 rd(mult(A, B), B) = A % 4.69/4.74 mult(A, unit) = A % 4.69/4.74 mult(unit, A) = A % 4.69/4.74 mult(A, mult(B, mult(B, C))) = mult(mult(mult(A, B), B), C) % 4.69/4.74 mult(op_c, mult(A, B)) = mult(mult(op_c, A), B) % 4.69/4.74 mult(A, mult(B, op_c)) = mult(mult(A, B), op_c) % 4.69/4.74 mult(A, mult(op_c, B)) = mult(mult(A, op_c), B) % 4.69/4.74 op_d = ld(A, mult(op_c, A)) % 4.69/4.74 op_e = mult(mult(rd(op_c, mult(A, B)), B), A) % 4.69/4.74 op_f = mult(A, mult(B, ld(mult(A, B), op_c))) % 4.69/4.74 mult(op_e, mult(x2, x3)) = mult(mult(op_e, x2), x3) ==> \bottom % 4.69/4.74 % 4.69/4.74 This holds because % 4.69/4.74 % 4.69/4.74 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 4.69/4.74 % 4.69/4.74 E: % 4.69/4.74 f1(mult(mult(op_e, x2), x3)) = false__ % 4.69/4.74 f1(mult(op_e, mult(x2, x3))) = true__ % 4.69/4.74 ld(A, mult(A, B)) = B % 4.69/4.74 mult(A, ld(A, B)) = B % 4.69/4.74 mult(A, mult(B, mult(B, C))) = mult(mult(mult(A, B), B), C) % 4.69/4.74 mult(A, mult(B, op_c)) = mult(mult(A, B), op_c) % 4.69/4.74 mult(A, mult(op_c, B)) = mult(mult(A, op_c), B) % 4.69/4.74 mult(A, unit) = A % 4.69/4.74 mult(op_c, mult(A, B)) = mult(mult(op_c, A), B) % 4.69/4.74 mult(rd(A, B), B) = A % 4.69/4.74 mult(unit, A) = A % 4.69/4.74 op_d = ld(A, mult(op_c, A)) % 4.69/4.74 op_e = mult(mult(rd(op_c, mult(A, B)), B), A) % 4.69/4.74 op_f = mult(A, mult(B, ld(mult(A, B), op_c))) % 4.69/4.74 rd(mult(A, B), B) = A % 4.69/4.74 G: % 4.69/4.74 true__ = false__ % 4.69/4.74 % 4.69/4.74 This holds because % 4.69/4.74 % 4.69/4.74 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 4.69/4.74 % 4.69/4.74 mult(Y0, mult(op_c, Y1)) = mult(op_c, mult(Y0, Y1)) % 4.69/4.74 mult(Y0, op_c) = mult(op_c, Y0) % 4.69/4.74 mult(op_c, X0) = mult(rd(X0, Y1), mult(Y1, op_c)) % 4.69/4.74 mult(op_c, X1) = mult(Y0, mult(ld(Y0, X1), op_c)) % 4.69/4.74 mult(op_c, mult(Y0, Y1)) = mult(Y0, mult(Y1, op_c)) % 4.69/4.74 mult(op_c, mult(op_c, Y0)) = mult(Y0, mult(op_c, op_c)) % 4.69/4.74 rd(mult(X0, mult(op_c, op_c)), op_c) = mult(op_c, X0) % 4.69/4.74 f1(mult(op_c, mult(x2, x3))) -> false__ % 4.69/4.74 f1(mult(op_e, mult(x2, x3))) -> true__ % 4.69/4.74 f1(mult(op_f, mult(x2, x3))) -> true__ % 4.69/4.74 ld(A, mult(A, B)) -> B % 4.69/4.74 ld(A, mult(op_c, A)) -> op_c % 4.69/4.74 ld(Y0, Y0) -> unit % 4.69/4.74 ld(op_c, Y0) -> rd(Y0, op_c) % 4.69/4.74 ld(rd(X0, Y1), X0) -> Y1 % 4.69/4.74 ld(unit, Y1) -> Y1 % 4.69/4.74 mult(A, ld(A, B)) -> B % 4.69/4.74 mult(A, mult(B, ld(mult(A, B), op_c))) -> op_c % 4.69/4.74 mult(A, unit) -> A % 4.69/4.74 mult(mult(A, B), op_c) -> mult(A, mult(B, op_c)) % 4.69/4.74 mult(mult(A, op_c), B) -> mult(A, mult(op_c, B)) % 4.69/4.74 mult(mult(Y0, Y1), Y1) -> mult(Y0, mult(Y1, Y1)) % 4.69/4.74 mult(mult(Y1, Y1), Y2) -> mult(Y1, mult(Y1, Y2)) % 4.69/4.74 mult(mult(mult(A, B), B), C) -> mult(A, mult(B, mult(B, C))) % 4.69/4.74 mult(mult(op_c, A), B) -> mult(op_c, mult(A, B)) % 4.69/4.74 mult(mult(rd(op_c, mult(A, B)), B), A) -> op_c % 4.69/4.74 mult(op_c, mult(Y0, ld(mult(op_c, Y0), X1))) -> X1 % 4.69/4.74 mult(op_c, mult(Y0, rd(X1, op_c))) -> mult(Y0, X1) % 4.69/4.74 mult(op_c, rd(Y0, op_c)) -> Y0 % 4.69/4.74 mult(rd(A, B), B) -> A % 4.69/4.74 mult(unit, A) -> A % 4.69/4.74 op_d -> op_c % 4.69/4.74 op_e -> op_c % 4.69/4.74 op_f -> op_c % 4.69/4.74 rd(X1, ld(Y0, X1)) -> Y0 % 4.69/4.74 rd(Y0, rd(Y0, op_c)) -> op_c % 4.69/4.74 rd(Y0, unit) -> Y0 % 4.69/4.74 rd(Y1, Y1) -> unit % 4.69/4.74 rd(mult(A, B), B) -> A % 4.69/4.74 rd(mult(X0, mult(X1, op_c)), mult(X0, X1)) -> op_c % 4.69/4.74 rd(mult(X0, mult(X1, op_c)), op_c) -> mult(X0, X1) % 4.69/4.74 rd(mult(Y0, op_c), Y0) -> op_c % 4.69/4.74 rd(mult(op_c, Y0), op_c) -> Y0 % 4.69/4.74 true__ -> false__ % 4.69/4.74 with the LPO induced by % 4.69/4.74 x3 > x2 > f1 > mult > op_d > op_f > op_e > op_c > ld > rd > unit > true__ > false__ % 4.69/4.74 % 4.69/4.74 % SZS output end Proof % 4.69/4.74 %------------------------------------------------------------------------------