%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP704-10 : TPTP v8.1.0. Released v8.1.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n010.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 10:58:00 EDT 2022 % Result : Unsatisfiable 5.29s 5.43s % Output : Proof 5.29s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : GRP704-10 : TPTP v8.1.0. Released v8.1.0. % 0.03/0.13 % Command : moca.sh %s % 0.12/0.34 % Computer : n010.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % 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 : Mon Jun 13 13:54:09 EDT 2022 % 0.12/0.34 % CPUTime : % 5.29/5.43 % SZS status Unsatisfiable % 5.29/5.43 % SZS output start Proof % 5.29/5.43 The input problem is unsatisfiable because % 5.29/5.43 % 5.29/5.43 [1] the following set of Horn clauses is unsatisfiable: % 5.29/5.43 % 5.29/5.43 mult(A, ld(A, B)) = B % 5.29/5.43 ld(A, mult(A, B)) = B % 5.29/5.43 mult(rd(A, B), B) = A % 5.29/5.43 rd(mult(A, B), B) = A % 5.29/5.43 mult(A, unit) = A % 5.29/5.43 mult(unit, A) = A % 5.29/5.43 mult(A, mult(B, mult(B, C))) = mult(mult(mult(A, B), B), C) % 5.29/5.43 mult(op_c, mult(A, B)) = mult(mult(op_c, A), B) % 5.29/5.43 mult(A, mult(B, op_c)) = mult(mult(A, B), op_c) % 5.29/5.43 mult(A, mult(op_c, B)) = mult(mult(A, op_c), B) % 5.29/5.43 op_d = ld(A, mult(op_c, A)) % 5.29/5.43 op_e = mult(mult(rd(op_c, mult(A, B)), B), A) % 5.29/5.43 op_f = mult(A, mult(B, ld(mult(A, B), op_c))) % 5.29/5.43 mult(op_f, mult(x4, x5)) = mult(mult(op_f, x4), x5) ==> \bottom % 5.29/5.43 % 5.29/5.43 This holds because % 5.29/5.43 % 5.29/5.43 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 5.29/5.43 % 5.29/5.43 E: % 5.29/5.43 f1(mult(mult(op_f, x4), x5)) = false__ % 5.29/5.43 f1(mult(op_f, mult(x4, x5))) = true__ % 5.29/5.43 ld(A, mult(A, B)) = B % 5.29/5.43 mult(A, ld(A, B)) = B % 5.29/5.43 mult(A, mult(B, mult(B, C))) = mult(mult(mult(A, B), B), C) % 5.29/5.43 mult(A, mult(B, op_c)) = mult(mult(A, B), op_c) % 5.29/5.43 mult(A, mult(op_c, B)) = mult(mult(A, op_c), B) % 5.29/5.43 mult(A, unit) = A % 5.29/5.43 mult(op_c, mult(A, B)) = mult(mult(op_c, A), B) % 5.29/5.43 mult(rd(A, B), B) = A % 5.29/5.43 mult(unit, A) = A % 5.29/5.43 op_d = ld(A, mult(op_c, A)) % 5.29/5.43 op_e = mult(mult(rd(op_c, mult(A, B)), B), A) % 5.29/5.43 op_f = mult(A, mult(B, ld(mult(A, B), op_c))) % 5.29/5.43 rd(mult(A, B), B) = A % 5.29/5.43 G: % 5.29/5.43 true__ = false__ % 5.29/5.43 % 5.29/5.43 This holds because % 5.29/5.43 % 5.29/5.43 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 5.29/5.43 % 5.29/5.43 ld(op_e, mult(X0, mult(op_e, op_e))) = mult(op_e, X0) % 5.29/5.43 mult(Y0, mult(op_e, Y1)) = mult(op_e, mult(Y0, Y1)) % 5.29/5.43 mult(Y0, op_e) = mult(op_e, Y0) % 5.29/5.43 mult(Y1, mult(op_e, Y1)) = mult(op_e, mult(Y1, Y1)) % 5.29/5.43 mult(op_e, mult(Y0, Y1)) = mult(Y0, mult(Y1, op_e)) % 5.29/5.43 mult(op_e, mult(op_e, Y0)) = mult(Y0, mult(op_e, op_e)) % 5.29/5.43 f1(mult(mult(op_e, x4), x5)) -> false__ % 5.29/5.43 f1(mult(mult(op_f, x4), x5)) -> false__ % 5.29/5.43 f1(mult(op_c, mult(x4, x5))) -> false__ % 5.29/5.43 f1(mult(op_c, mult(x4, x5))) -> true__ % 5.29/5.43 f1(mult(op_e, mult(x4, x5))) -> true__ % 5.29/5.43 ld(A, mult(A, B)) -> B % 5.29/5.43 ld(Y0, Y0) -> unit % 5.29/5.43 ld(Y0, mult(op_e, Y0)) -> op_e % 5.29/5.43 ld(Y0, mult(op_e, mult(Y0, X1))) -> mult(op_e, X1) % 5.29/5.43 ld(ld(op_e, Y0), Y0) -> op_e % 5.29/5.43 ld(op_c, mult(X0, mult(X1, op_c))) -> mult(X0, X1) % 5.29/5.43 ld(op_e, mult(X0, mult(X1, op_e))) -> mult(X0, X1) % 5.29/5.43 ld(op_e, mult(Y0, op_e)) -> Y0 % 5.29/5.43 ld(rd(X0, Y1), X0) -> Y1 % 5.29/5.43 ld(unit, Y1) -> Y1 % 5.29/5.43 mult(A, ld(A, B)) -> B % 5.29/5.43 mult(A, unit) -> A % 5.29/5.43 mult(Y0, mult(Y1, ld(mult(Y0, Y1), op_e))) -> op_e % 5.29/5.43 mult(Y0, mult(ld(Y0, X1), op_c)) -> mult(op_e, X1) % 5.29/5.43 mult(mult(A, B), op_c) -> mult(A, mult(B, op_e)) % 5.29/5.43 mult(mult(Y0, Y1), Y1) -> mult(Y0, mult(Y1, Y1)) % 5.29/5.43 mult(mult(Y0, op_e), Y1) -> mult(Y0, mult(op_e, Y1)) % 5.29/5.43 mult(mult(Y1, Y1), Y2) -> mult(Y1, mult(Y1, Y2)) % 5.29/5.43 mult(mult(mult(A, B), B), C) -> mult(A, mult(B, mult(B, C))) % 5.29/5.43 mult(mult(op_e, Y0), Y1) -> mult(op_e, mult(Y0, Y1)) % 5.29/5.43 mult(mult(rd(op_e, mult(Y0, Y1)), Y1), Y0) -> op_e % 5.29/5.43 mult(op_c, mult(Y0, ld(mult(op_c, Y0), X1))) -> X1 % 5.29/5.43 mult(op_e, mult(Y0, ld(op_e, X1))) -> mult(Y0, X1) % 5.29/5.43 mult(op_e, mult(ld(op_e, X1), ld(op_e, X1))) -> mult(ld(op_e, X1), X1) % 5.29/5.43 mult(rd(A, B), B) -> A % 5.29/5.43 mult(rd(X0, Y1), mult(Y1, op_c)) -> mult(op_e, X0) % 5.29/5.43 mult(unit, A) -> A % 5.29/5.43 op_c -> op_e % 5.29/5.43 op_d -> op_e % 5.29/5.43 op_f -> op_e % 5.29/5.43 rd(X0, op_e) -> ld(op_e, X0) % 5.29/5.43 rd(X1, ld(Y0, X1)) -> Y0 % 5.29/5.43 rd(Y0, unit) -> Y0 % 5.29/5.43 rd(Y1, Y1) -> unit % 5.29/5.43 rd(mult(A, B), B) -> A % 5.29/5.43 rd(mult(X0, mult(X1, op_c)), mult(X0, X1)) -> op_e % 5.29/5.43 rd(mult(X0, mult(X1, op_e)), mult(X0, X1)) -> op_e % 5.29/5.43 rd(mult(Y1, op_e), Y1) -> op_e % 5.29/5.43 true__ -> false__ % 5.29/5.43 with the LPO induced by % 5.29/5.43 x5 > x4 > f1 > mult > op_d > rd > ld > op_f > op_c > op_e > unit > true__ > false__ % 5.29/5.43 % 5.29/5.43 % SZS output end Proof % 5.29/5.43 %------------------------------------------------------------------------------