TSTP Solution File: SET845-2 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : SET845-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n006.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 : Tue Jul 19 03:45:08 EDT 2022
% Result : Unsatisfiable 1.36s 1.46s
% Output : Proof 1.36s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET845-2 : TPTP v8.1.0. Released v3.2.0.
% 0.08/0.14 % Command : moca.sh %s
% 0.14/0.35 % Computer : n006.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Mon Jul 11 08:24:50 EDT 2022
% 0.14/0.35 % CPUTime :
% 1.36/1.46 % SZS status Unsatisfiable
% 1.36/1.46 % SZS output start Proof
% 1.36/1.46 The input problem is unsatisfiable because
% 1.36/1.46
% 1.36/1.46 [1] the following set of Horn clauses is unsatisfiable:
% 1.36/1.46
% 1.36/1.46 c_in(V_B, V_A, tc_set(T_a)) ==> c_lessequals(V_B, c_Union(V_A, T_a), tc_set(T_a))
% 1.36/1.46 c_lessequals(V_B, V_A, tc_set(T_a)) & c_lessequals(V_A, V_B, tc_set(T_a)) ==> V_A = V_B
% 1.36/1.46 c_lessequals(V_x, c_Zorn_Osucc(V_S, V_x, T_a), tc_set(tc_set(T_a)))
% 1.36/1.46 c_in(V_x, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))) ==> c_in(c_Zorn_Osucc(V_S, V_x, T_a), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))
% 1.36/1.46 c_in(v_m, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))
% 1.36/1.46 v_m = c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a))
% 1.36/1.46 v_m = c_Zorn_Osucc(v_S, v_m, t_a) ==> \bottom
% 1.36/1.46
% 1.36/1.46 This holds because
% 1.36/1.46
% 1.36/1.46 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 1.36/1.46
% 1.36/1.46 E:
% 1.36/1.46 c_in(v_m, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a))) = true__
% 1.36/1.46 c_lessequals(V_x, c_Zorn_Osucc(V_S, V_x, T_a), tc_set(tc_set(T_a))) = true__
% 1.36/1.46 f1(c_in(V_B, V_A, tc_set(T_a)), V_B, V_A, T_a) = true__
% 1.36/1.46 f1(true__, V_B, V_A, T_a) = c_lessequals(V_B, c_Union(V_A, T_a), tc_set(T_a))
% 1.36/1.46 f2(true__, V_A, V_B) = V_A
% 1.36/1.46 f3(c_lessequals(V_A, V_B, tc_set(T_a)), V_B, V_A, T_a) = V_B
% 1.36/1.46 f3(true__, V_B, V_A, T_a) = f2(c_lessequals(V_B, V_A, tc_set(T_a)), V_A, V_B)
% 1.36/1.46 f4(c_in(V_x, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))), V_S, V_x, T_a) = true__
% 1.36/1.46 f4(true__, V_S, V_x, T_a) = c_in(c_Zorn_Osucc(V_S, V_x, T_a), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))
% 1.36/1.46 f5(c_Zorn_Osucc(v_S, v_m, t_a)) = false__
% 1.36/1.46 f5(v_m) = true__
% 1.36/1.46 v_m = c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a))
% 1.36/1.46 G:
% 1.36/1.46 true__ = false__
% 1.36/1.46
% 1.36/1.46 This holds because
% 1.36/1.46
% 1.36/1.46 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 1.36/1.46
% 1.36/1.46 c_lessequals(Y0, v_m, tc_set(tc_set(t_a))) = f1(true__, Y0, c_Zorn_OTFin(v_S, t_a), tc_set(t_a))
% 1.36/1.46 c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)) -> v_m
% 1.36/1.46 c_Zorn_Osucc(v_S, v_m, t_a) -> v_m
% 1.36/1.46 c_in(c_Zorn_Osucc(V_S, V_x, T_a), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))) -> f4(true__, V_S, V_x, T_a)
% 1.36/1.46 c_in(v_m, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a))) -> true__
% 1.36/1.46 c_lessequals(V_B, c_Union(V_A, T_a), tc_set(T_a)) -> f1(true__, V_B, V_A, T_a)
% 1.36/1.47 c_lessequals(V_x, c_Zorn_Osucc(V_S, V_x, T_a), tc_set(tc_set(T_a))) -> true__
% 1.36/1.47 c_lessequals(v_m, v_m, tc_set(tc_set(t_a))) -> true__
% 1.36/1.47 f1(c_in(V_B, V_A, tc_set(T_a)), V_B, V_A, T_a) -> true__
% 1.36/1.47 f1(f4(true__, X0, X1, X2), c_Zorn_Osucc(X0, X1, X2), c_Zorn_OTFin(X0, X2), tc_set(X2)) -> true__
% 1.36/1.47 f1(true__, c_Zorn_Osucc(v_S, v_m, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(t_a)) -> true__
% 1.36/1.47 f1(true__, v_m, c_Zorn_OTFin(v_S, t_a), tc_set(t_a)) -> true__
% 1.36/1.47 f2(c_lessequals(V_B, V_A, tc_set(T_a)), V_A, V_B) -> f3(true__, V_B, V_A, T_a)
% 1.36/1.47 f2(f1(true__, Y0, X1, Y2), c_Union(X1, Y2), Y0) -> f3(true__, Y0, c_Union(X1, Y2), Y2)
% 1.36/1.47 f2(f1(true__, Y0, c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), v_m, Y0) -> f3(true__, Y0, v_m, tc_set(t_a))
% 1.36/1.47 f2(true__, V_A, V_B) -> V_A
% 1.36/1.47 f3(c_lessequals(V_A, V_B, tc_set(T_a)), V_B, V_A, T_a) -> V_B
% 1.36/1.47 f3(f1(true__, Y0, X1, Y2), c_Union(X1, Y2), Y0, Y2) -> c_Union(X1, Y2)
% 1.36/1.47 f3(f1(true__, Y0, c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), v_m, Y0, tc_set(t_a)) -> v_m
% 1.36/1.47 f3(true__, Y0, c_Zorn_Osucc(X1, Y0, X2), tc_set(X2)) -> c_Zorn_Osucc(X1, Y0, X2)
% 1.36/1.47 f3(true__, c_Zorn_Osucc(X1, Y0, X2), Y0, tc_set(X2)) -> c_Zorn_Osucc(X1, Y0, X2)
% 1.36/1.47 f3(true__, v_m, v_m, tc_set(t_a)) -> v_m
% 1.36/1.47 f4(c_in(V_x, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))), V_S, V_x, T_a) -> true__
% 1.36/1.47 f4(f4(true__, Y1, X1, Y2), Y1, c_Zorn_Osucc(Y1, X1, Y2), Y2) -> true__
% 1.36/1.47 f4(true__, v_S, c_Zorn_Osucc(v_S, v_m, t_a), t_a) -> true__
% 1.36/1.47 f4(true__, v_S, v_m, t_a) -> true__
% 1.36/1.47 f5(c_Zorn_Osucc(v_S, v_m, t_a)) -> false__
% 1.36/1.47 f5(v_m) -> true__
% 1.36/1.47 false__ -> true__
% 1.36/1.47 with the LPO induced by
% 1.36/1.47 f5 > c_in > f4 > c_Zorn_Osucc > v_S > c_Zorn_OTFin > v_m > f2 > f3 > c_lessequals > f1 > c_Union > t_a > tc_set > false__ > true__
% 1.36/1.47
% 1.36/1.47 % SZS output end Proof
% 1.36/1.47
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