TSTP Solution File: SWV254-2 by Moca---0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : SWV254-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n015.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 : Wed Jul 20 20:42:22 EDT 2022
% Result : Unsatisfiable 1.07s 1.20s
% Output : Proof 1.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SWV254-2 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % Command : moca.sh %s
% 0.15/0.35 % Computer : n015.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 600
% 0.15/0.35 % DateTime : Wed Jun 15 20:02:10 EDT 2022
% 0.21/0.35 % CPUTime :
% 1.07/1.20 % SZS status Unsatisfiable
% 1.07/1.20 % SZS output start Proof
% 1.07/1.20 The input problem is unsatisfiable because
% 1.07/1.20
% 1.07/1.20 [1] the following set of Horn clauses is unsatisfiable:
% 1.07/1.20
% 1.07/1.20 class_Orderings_Oorder(T_a) & c_lessequals(V_n, V_m, T_a) ==> c_SetInterval_OatLeastLessThan(V_m, V_n, T_a) = c_emptyset
% 1.07/1.20 c_SetInterval_OatLeastLessThan(V_m, c_Suc(V_m), tc_nat) = c_insert(V_m, c_emptyset, tc_nat)
% 1.07/1.20 c_emptyset = c_insert(V_a, V_A, T_a) ==> \bottom
% 1.07/1.20 c_lessequals(V_U, v_x(V_U), tc_nat)
% 1.07/1.20 v_x(V_U) = v_nat
% 1.07/1.20 class_Orderings_Oorder(tc_nat)
% 1.07/1.20
% 1.07/1.20 This holds because
% 1.07/1.20
% 1.07/1.20 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 1.07/1.20
% 1.07/1.20 E:
% 1.07/1.20 c_SetInterval_OatLeastLessThan(V_m, c_Suc(V_m), tc_nat) = c_insert(V_m, c_emptyset, tc_nat)
% 1.07/1.20 c_lessequals(V_U, v_x(V_U), tc_nat) = true__
% 1.07/1.20 class_Orderings_Oorder(tc_nat) = true__
% 1.07/1.20 f1(true__, V_m, V_n, T_a) = c_SetInterval_OatLeastLessThan(V_m, V_n, T_a)
% 1.07/1.20 f2(c_lessequals(V_n, V_m, T_a), T_a, V_m, V_n) = c_emptyset
% 1.07/1.20 f2(true__, T_a, V_m, V_n) = f1(class_Orderings_Oorder(T_a), V_m, V_n, T_a)
% 1.07/1.20 f3(c_emptyset) = false__
% 1.07/1.20 f3(c_insert(V_a, V_A, T_a)) = true__
% 1.07/1.20 v_x(V_U) = v_nat
% 1.07/1.20 G:
% 1.07/1.20 true__ = false__
% 1.07/1.20
% 1.07/1.20 This holds because
% 1.07/1.20
% 1.07/1.20 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 1.07/1.20
% 1.07/1.20
% 1.07/1.20 c_SetInterval_OatLeastLessThan(V_m, V_n, T_a) -> f1(true__, V_m, V_n, T_a)
% 1.07/1.20 c_insert(V_m, c_emptyset, tc_nat) -> c_SetInterval_OatLeastLessThan(V_m, c_Suc(V_m), tc_nat)
% 1.07/1.20 c_lessequals(V_U, v_x(V_U), tc_nat) -> true__
% 1.07/1.20 c_lessequals(Y0, v_nat, tc_nat) -> true__
% 1.07/1.20 class_Orderings_Oorder(tc_nat) -> true__
% 1.07/1.20 f1(class_Orderings_Oorder(T_a), V_m, V_n, T_a) -> f2(true__, T_a, V_m, V_n)
% 1.07/1.20 f1(true__, Y1, Y2, tc_nat) -> f2(true__, tc_nat, Y1, Y2)
% 1.07/1.20 f2(c_lessequals(V_n, V_m, T_a), T_a, V_m, V_n) -> c_emptyset
% 1.07/1.20 f2(true__, tc_nat, v_nat, Y0) -> c_emptyset
% 1.07/1.20 f3(c_emptyset) -> false__
% 1.07/1.20 f3(c_insert(V_a, V_A, T_a)) -> true__
% 1.07/1.20 f3(f1(true__, Y0, c_Suc(Y0), tc_nat)) -> true__
% 1.07/1.20 f3(f2(true__, tc_nat, Y0, c_Suc(Y0))) -> true__
% 1.07/1.20 false__ -> true__
% 1.07/1.20 v_x(V_U) -> v_nat
% 1.07/1.20 with the LPO induced by
% 1.07/1.20 v_x > v_nat > f3 > c_lessequals > c_emptyset > c_insert > c_Suc > c_SetInterval_OatLeastLessThan > f1 > tc_nat > f2 > class_Orderings_Oorder > false__ > true__
% 1.07/1.20
% 1.07/1.20 % SZS output end Proof
% 1.07/1.20
%------------------------------------------------------------------------------