%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : SYN050-1 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n011.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 : Thu Jul 21 09:13:21 EDT 2022 % Result : Unsatisfiable 0.72s 0.87s % Output : Proof 0.72s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.11 % Problem : SYN050-1 : TPTP v8.1.0. Released v1.0.0. % 0.03/0.12 % Command : moca.sh %s % 0.12/0.33 % Computer : n011.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 : Mon Jul 11 13:15:42 EDT 2022 % 0.12/0.33 % CPUTime : % 0.72/0.87 % SZS status Unsatisfiable % 0.72/0.87 % SZS output start Proof % 0.72/0.87 The input problem is unsatisfiable because % 0.72/0.87 % 0.72/0.87 [1] the following set of Horn clauses is unsatisfiable: % 0.72/0.87 % 0.72/0.87 big_p(Y) & big_q(Z) ==> big_r(f(Y, Z)) % 0.72/0.87 big_p(Y) & big_q(Z) ==> big_s(X) % 0.72/0.87 big_p(a) % 0.72/0.87 big_q(b) % 0.72/0.87 big_r(W) ==> \bottom % 0.72/0.87 % 0.72/0.87 This holds because % 0.72/0.87 % 0.72/0.87 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.72/0.87 % 0.72/0.87 E: % 0.72/0.87 big_p(a) = true__ % 0.72/0.87 big_q(b) = true__ % 0.72/0.87 f1(true__, Y, Z) = big_r(f(Y, Z)) % 0.72/0.87 f2(big_q(Z), Y, Z) = true__ % 0.72/0.87 f2(true__, Y, Z) = f1(big_p(Y), Y, Z) % 0.72/0.87 f3(true__, X) = big_s(X) % 0.72/0.87 f4(big_q(Z), Y, X) = true__ % 0.72/0.87 f4(true__, Y, X) = f3(big_p(Y), X) % 0.72/0.87 f5(big_r(W)) = true__ % 0.72/0.87 f5(true__) = false__ % 0.72/0.87 G: % 0.72/0.87 true__ = false__ % 0.72/0.87 % 0.72/0.87 This holds because % 0.72/0.87 % 0.72/0.87 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.72/0.87 % 0.72/0.87 f3(true__, Y1) = f4(true__, a, Y1) % 0.72/0.87 big_p(a) -> true__ % 0.72/0.87 big_q(b) -> true__ % 0.72/0.87 big_r(f(Y, Z)) -> f1(true__, Y, Z) % 0.72/0.87 big_s(X) -> f3(true__, X) % 0.72/0.87 f1(big_p(Y), Y, Z) -> f2(true__, Y, Z) % 0.72/0.87 f1(true__, a, Y1) -> f2(true__, a, Y1) % 0.72/0.87 f2(big_q(Z), Y, Z) -> true__ % 0.72/0.87 f2(true__, Y1, b) -> true__ % 0.72/0.87 f3(big_p(Y), X) -> f4(true__, Y, X) % 0.72/0.87 f3(true__, Y1) -> true__ % 0.72/0.87 f4(big_q(Z), Y, X) -> true__ % 0.72/0.87 f4(true__, Y1, Y2) -> true__ % 0.72/0.87 f5(big_r(W)) -> true__ % 0.72/0.87 f5(f1(true__, X0, X1)) -> true__ % 0.72/0.87 f5(f2(true__, a, Y1)) -> true__ % 0.72/0.87 f5(true__) -> false__ % 0.72/0.87 false__ -> true__ % 0.72/0.87 with the LPO induced by % 0.72/0.87 f5 > b > a > big_s > f3 > f4 > big_p > big_q > big_r > f1 > f > f2 > false__ > true__ % 0.72/0.87 % 0.72/0.87 % SZS output end Proof % 0.72/0.87 %------------------------------------------------------------------------------