%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : COL070-1 : TPTP v8.1.0. Released v1.2.0. % 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 : Fri Jul 15 00:37:28 EDT 2022 % Result : Unsatisfiable 37.24s 37.48s % Output : Proof 37.24s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : COL070-1 : TPTP v8.1.0. Released v1.2.0. % 0.07/0.13 % Command : moca.sh %s % 0.13/0.34 % Computer : n020.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Tue May 31 12:45:53 EDT 2022 % 0.13/0.34 % CPUTime : % 37.24/37.48 % SZS status Unsatisfiable % 37.24/37.48 % SZS output start Proof % 37.24/37.48 The input problem is unsatisfiable because % 37.24/37.48 % 37.24/37.48 [1] the following set of Horn clauses is unsatisfiable: % 37.24/37.48 % 37.24/37.48 apply(apply(apply(n1, X), Y), Z) = apply(apply(apply(X, Y), Y), Z) % 37.24/37.48 apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z)) % 37.24/37.48 Y = apply(combinator, Y) ==> \bottom % 37.24/37.48 % 37.24/37.48 This holds because % 37.24/37.48 % 37.24/37.48 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 37.24/37.48 % 37.24/37.48 E: % 37.24/37.48 apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z)) % 37.24/37.48 apply(apply(apply(n1, X), Y), Z) = apply(apply(apply(X, Y), Y), Z) % 37.24/37.48 f1(Y, Y) = true__ % 37.24/37.48 f1(apply(combinator, Y), Y) = false__ % 37.24/37.48 G: % 37.24/37.48 true__ = false__ % 37.24/37.48 % 37.24/37.48 This holds because % 37.24/37.48 % 37.24/37.48 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 37.24/37.48 % 37.24/37.48 apply(X0, apply(apply(Y1, Y1), Y2)) = apply(apply(apply(n1, apply(b, apply(b, X0))), Y1), Y2) % 37.24/37.48 apply(apply(X0, apply(Y1, Y1)), Y2) = apply(apply(apply(n1, apply(b, X0)), Y1), Y2) % 37.24/37.48 apply(apply(Y1, apply(Y1, Y1)), Y2) = apply(apply(apply(n1, apply(n1, b)), Y1), Y2) % 37.24/37.48 apply(apply(apply(Y1, Y1), Y1), Y2) = apply(apply(apply(n1, n1), Y1), Y2) % 37.24/37.48 apply(apply(apply(n1, X), Y), Z) = apply(apply(apply(X, Y), Y), Z) % 37.24/37.48 apply(apply(apply(n1, apply(n1, X0)), Y1), Y2) = apply(apply(apply(n1, apply(X0, Y1)), Y1), Y2) % 37.24/37.48 apply(apply(apply(n1, apply(n1, apply(b, b))), Y1), Y2) = apply(apply(Y1, Y1), apply(Y1, Y2)) % 37.24/37.48 apply(apply(apply(n1, apply(n1, n1)), Y1), Y2) = apply(apply(apply(n1, apply(Y1, Y1)), Y1), Y2) % 37.24/37.48 apply(apply(apply(apply(X0, Y1), Y1), Y1), Y2) -> apply(apply(apply(n1, apply(n1, X0)), Y1), Y2) % 37.24/37.48 apply(apply(apply(apply(n1, apply(b, b)), X1), Y1), Y2) -> apply(apply(X1, X1), apply(Y1, Y2)) % 37.24/37.48 apply(apply(apply(b, X), Y), Z) -> apply(X, apply(Y, Z)) % 37.24/37.48 apply(apply(apply(n1, b), Y1), Y2) -> apply(Y1, apply(Y1, Y2)) % 37.24/37.48 f1(Y, Y) -> true__ % 37.24/37.48 f1(apply(apply(apply(n1, apply(b, apply(b, combinator))), X1), X2), apply(apply(X1, X1), X2)) -> false__ % 37.24/37.48 f1(apply(combinator, Y), Y) -> false__ % 37.24/37.48 false__ -> true__ % 37.24/37.48 with the LPO induced by % 37.24/37.48 apply > n1 > b > combinator > f1 > false__ > true__ % 37.24/37.48 % 37.24/37.48 % SZS output end Proof % 37.24/37.48 %------------------------------------------------------------------------------