%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : COL112-2 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n021.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 00:37:56 EDT 2022 % Result : Unsatisfiable 0.14s 0.40s % Output : Proof 0.14s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : COL112-2 : TPTP v8.1.0. Released v3.2.0. % 0.06/0.13 % Command : moca.sh %s % 0.14/0.34 % Computer : n021.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 600 % 0.14/0.34 % DateTime : Tue May 31 07:59:29 EDT 2022 % 0.14/0.34 % CPUTime : % 0.14/0.40 % SZS status Unsatisfiable % 0.14/0.40 % SZS output start Proof % 0.14/0.40 The input problem is unsatisfiable because % 0.14/0.40 % 0.14/0.40 [1] the following set of Horn clauses is unsatisfiable: % 0.14/0.40 % 0.14/0.40 c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya), V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) & c_in(c_Pair(v_x, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) ==> \bottom % 0.14/0.40 c_in(c_Pair(V_x, V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) % 0.14/0.40 c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_y), V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) % 0.14/0.40 % 0.14/0.40 This holds because % 0.14/0.40 % 0.14/0.40 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.14/0.40 % 0.14/0.40 E: % 0.14/0.40 c_in(c_Pair(V_x, V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) = true__ % 0.14/0.40 c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_y), V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) = true__ % 0.14/0.40 f1(true__) = false__ % 0.14/0.40 f2(c_in(c_Pair(v_x, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), V_U) = true__ % 0.14/0.40 f2(true__, V_U) = f1(c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya), V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) % 0.14/0.40 G: % 0.14/0.40 true__ = false__ % 0.14/0.40 % 0.14/0.40 This holds because % 0.14/0.40 % 0.14/0.40 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.14/0.40 % 0.14/0.40 % 0.14/0.40 c_in(c_Pair(V_x, V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) -> true__ % 0.14/0.40 c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_y), V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) -> true__ % 0.14/0.40 f1(c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya), V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) -> f2(true__, V_U) % 0.14/0.40 f1(true__) -> false__ % 0.14/0.40 f2(c_in(c_Pair(v_x, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), V_U) -> true__ % 0.14/0.40 f2(true__, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya)) -> false__ % 0.14/0.40 f2(true__, v_x) -> false__ % 0.14/0.40 f2(true__, v_x) -> true__ % 0.14/0.40 false__ -> true__ % 0.14/0.40 with the LPO induced by % 0.14/0.40 f1 > f2 > tc_prod > c_Comb_Oparcontract > tc_Comb_Ocomb > v_ya > v_x > c_Comb_Ocomb_OK > c_Comb_Ocomb_Oop_A_D_D > c_Pair > c_in > false__ > true__ % 0.14/0.40 % 0.14/0.40 % SZS output end Proof % 0.14/0.40 %------------------------------------------------------------------------------