%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : SYN058-1 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n022.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 09:13:28 EDT 2022 % Result : Unsatisfiable 1.38s 1.52s % Output : Proof 1.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.14 % Problem : SYN058-1 : TPTP v8.1.0. Released v1.0.0. % 0.04/0.14 % Command : moca.sh %s % 0.14/0.36 % Computer : n022.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 600 % 0.14/0.36 % DateTime : Mon Jul 11 13:50:25 EDT 2022 % 0.14/0.36 % CPUTime : % 1.38/1.52 % SZS status Unsatisfiable % 1.38/1.52 % SZS output start Proof % 1.38/1.52 The input problem is unsatisfiable because % 1.38/1.52 % 1.38/1.52 [1] the following set of Horn clauses is unsatisfiable: % 1.38/1.52 % 1.38/1.52 big_p(X) ==> big_q(Y) % 1.38/1.52 big_q(b) ==> big_q(c) % 1.38/1.52 big_q(b) ==> big_s(c) % 1.38/1.52 big_r(b) ==> big_q(c) % 1.38/1.52 big_r(b) ==> big_s(c) % 1.38/1.52 big_s(Y) & big_f(X) ==> big_g(X) % 1.38/1.52 big_p(d) % 1.38/1.52 big_f(d) % 1.38/1.52 big_g(d) ==> \bottom % 1.38/1.52 % 1.38/1.52 This holds because % 1.38/1.52 % 1.38/1.52 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 1.38/1.52 % 1.38/1.52 E: % 1.38/1.52 big_f(d) = true__ % 1.38/1.52 big_p(d) = true__ % 1.38/1.52 f1(big_p(X), Y) = true__ % 1.38/1.52 f1(true__, Y) = big_q(Y) % 1.38/1.52 f2(big_q(b)) = true__ % 1.38/1.52 f2(true__) = big_q(c) % 1.38/1.52 f3(big_q(b)) = true__ % 1.38/1.52 f3(true__) = big_s(c) % 1.38/1.52 f4(big_r(b)) = true__ % 1.38/1.52 f4(true__) = big_q(c) % 1.38/1.52 f5(big_r(b)) = true__ % 1.38/1.52 f5(true__) = big_s(c) % 1.38/1.52 f6(true__, X) = big_g(X) % 1.38/1.52 f7(big_f(X), Y, X) = true__ % 1.38/1.52 f7(true__, Y, X) = f6(big_s(Y), X) % 1.38/1.52 f8(big_g(d)) = true__ % 1.38/1.52 f8(true__) = false__ % 1.38/1.52 G: % 1.38/1.52 true__ = false__ % 1.38/1.52 % 1.38/1.52 This holds because % 1.38/1.52 % 1.38/1.52 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 1.38/1.52 % 1.38/1.52 f6(f3(true__), Y1) = f7(true__, c, Y1) % 1.38/1.52 f6(true__, Y0) = f7(true__, c, Y0) % 1.38/1.52 big_f(d) -> true__ % 1.38/1.52 big_g(X) -> f6(true__, X) % 1.38/1.52 big_p(d) -> true__ % 1.38/1.52 big_q(Y) -> f1(true__, Y) % 1.38/1.52 big_s(c) -> f3(true__) % 1.38/1.52 f1(big_p(X), Y) -> true__ % 1.38/1.52 f1(true__, Y1) -> true__ % 1.38/1.52 f2(big_q(b)) -> true__ % 1.38/1.52 f2(f1(true__, b)) -> true__ % 1.38/1.52 f2(true__) -> big_q(c) % 1.38/1.52 f3(big_q(b)) -> true__ % 1.38/1.52 f3(f1(true__, b)) -> true__ % 1.38/1.52 f3(true__) -> true__ % 1.38/1.52 f4(big_r(b)) -> true__ % 1.38/1.52 f4(true__) -> big_q(c) % 1.38/1.52 f5(big_r(b)) -> true__ % 1.38/1.52 f5(true__) -> big_s(c) % 1.38/1.52 f6(big_s(Y), X) -> f7(true__, Y, X) % 1.38/1.52 f7(big_f(X), Y, X) -> true__ % 1.38/1.52 f7(true__, Y1, d) -> true__ % 1.38/1.52 f8(big_g(d)) -> true__ % 1.38/1.52 f8(f6(true__, d)) -> true__ % 1.38/1.52 f8(true__) -> false__ % 1.38/1.52 false__ -> true__ % 1.38/1.52 with the LPO induced by % 1.38/1.52 d > f4 > f2 > f5 > c > f3 > big_f > f8 > big_g > f6 > f7 > big_s > big_q > f1 > big_r > b > big_p > false__ > true__ % 1.38/1.52 % 1.38/1.52 % SZS output end Proof % 1.38/1.52 %------------------------------------------------------------------------------