%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : COL124-2 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n028.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 00:38:05 EDT 2022 % Result : Unsatisfiable 0.79s 0.94s % Output : Proof 0.79s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.11 % Problem : COL124-2 : TPTP v8.1.0. Released v3.2.0. % 0.06/0.12 % Command : moca.sh %s % 0.12/0.33 % Computer : n028.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 : Tue May 31 13:15:51 EDT 2022 % 0.12/0.33 % CPUTime : % 0.79/0.94 % SZS status Unsatisfiable % 0.79/0.94 % SZS output start Proof % 0.79/0.94 The input problem is unsatisfiable because % 0.79/0.94 % 0.79/0.94 [1] the following set of Horn clauses is unsatisfiable: % 0.79/0.94 % 0.79/0.94 c_in(c_Pair(V_U, V_W, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) & c_in(c_Pair(V_U, V_V, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) ==> c_in(c_Pair(V_V, v_x(V_U, V_V, V_W), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) % 0.79/0.94 c_in(c_Pair(c_Comb_OI, V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) ==> \bottom % 0.79/0.94 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_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) % 0.79/0.94 % 0.79/0.94 This holds because % 0.79/0.94 % 0.79/0.94 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.79/0.94 % 0.79/0.94 E: % 0.79/0.94 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_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) = true__ % 0.79/0.94 f1(true__, V_V, V_U, V_W) = c_in(c_Pair(V_V, v_x(V_U, V_V, V_W), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) % 0.79/0.94 f2(c_in(c_Pair(V_U, V_V, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), V_U, V_W, V_V) = true__ % 0.79/0.94 f2(true__, V_U, V_W, V_V) = f1(c_in(c_Pair(V_U, V_W, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), V_V, V_U, V_W) % 0.79/0.94 f3(c_in(c_Pair(c_Comb_OI, V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) = true__ % 0.79/0.94 f3(true__) = false__ % 0.79/0.94 G: % 0.79/0.94 true__ = false__ % 0.79/0.94 % 0.79/0.94 This holds because % 0.79/0.94 % 0.79/0.94 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.79/0.94 % 0.79/0.94 % 0.79/0.94 c_in(c_Pair(Y2, v_x(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, Y2), Y1), Y2, Y2), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) -> true__ % 0.79/0.94 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_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) -> true__ % 0.79/0.94 f1(c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, Y1), X1), Y2, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), Y1, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, Y1), X1), Y2) -> true__ % 0.79/0.94 f1(true__, V_V, V_U, V_W) -> c_in(c_Pair(V_V, v_x(V_U, V_V, V_W), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) % 0.79/0.94 f2(c_in(c_Pair(V_U, V_V, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), V_U, V_W, V_V) -> true__ % 0.79/0.94 f2(true__, V_U, V_W, V_V) -> f1(c_in(c_Pair(V_U, V_W, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), V_V, V_U, V_W) % 0.79/0.94 f3(c_in(c_Pair(c_Comb_OI, V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) -> true__ % 0.79/0.94 f3(true__) -> false__ % 0.79/0.94 true__ -> false__ % 0.79/0.94 with the LPO induced by % 0.79/0.94 f2 > f1 > v_x > f3 > tc_prod > c_Comb_Ocontract > c_in > c_Comb_OI > tc_Comb_Ocomb > c_Pair > c_Comb_Ocomb_OK > c_Comb_Ocomb_Oop_A_D_D > true__ > false__ % 0.79/0.94 % 0.79/0.94 % SZS output end Proof % 0.79/0.94 %------------------------------------------------------------------------------