TSTP Solution File: COL124-2 by Moca---0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% 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
%------------------------------------------------------------------------------