TSTP Solution File: SET859-2 by Moca---0.1
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% File : Moca---0.1
% Problem : SET859-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n027.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 03:45:18 EDT 2022
% Result : Unsatisfiable 0.80s 0.94s
% Output : Proof 0.80s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET859-2 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % Command : moca.sh %s
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jul 11 10:54:33 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.80/0.94 % SZS status Unsatisfiable
% 0.80/0.94 % SZS output start Proof
% 0.80/0.94 The input problem is unsatisfiable because
% 0.80/0.94
% 0.80/0.94 [1] the following set of Horn clauses is unsatisfiable:
% 0.80/0.94
% 0.80/0.94 c_lessequals(V_B, V_C, tc_set(T_a)) & c_lessequals(V_A, V_B, tc_set(T_a)) ==> c_lessequals(V_A, V_C, tc_set(T_a))
% 0.80/0.94 c_lessequals(V_x, c_Zorn_Osucc(V_S, V_x, T_a), tc_set(tc_set(T_a)))
% 0.80/0.94 c_lessequals(c_Zorn_Osucc(v_S, v_n, t_a), v_m, tc_set(tc_set(t_a)))
% 0.80/0.94 c_lessequals(v_n, v_m, tc_set(tc_set(t_a))) ==> \bottom
% 0.80/0.94
% 0.80/0.94 This holds because
% 0.80/0.94
% 0.80/0.94 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 0.80/0.94
% 0.80/0.94 E:
% 0.80/0.94 c_lessequals(V_x, c_Zorn_Osucc(V_S, V_x, T_a), tc_set(tc_set(T_a))) = true__
% 0.80/0.94 c_lessequals(c_Zorn_Osucc(v_S, v_n, t_a), v_m, tc_set(tc_set(t_a))) = true__
% 0.80/0.94 f1(true__, V_A, V_C, T_a) = c_lessequals(V_A, V_C, tc_set(T_a))
% 0.80/0.94 f2(c_lessequals(V_A, V_B, tc_set(T_a)), V_B, V_C, T_a, V_A) = true__
% 0.80/0.94 f2(true__, V_B, V_C, T_a, V_A) = f1(c_lessequals(V_B, V_C, tc_set(T_a)), V_A, V_C, T_a)
% 0.80/0.94 f3(c_lessequals(v_n, v_m, tc_set(tc_set(t_a)))) = true__
% 0.80/0.94 f3(true__) = false__
% 0.80/0.94 G:
% 0.80/0.94 true__ = false__
% 0.80/0.94
% 0.80/0.94 This holds because
% 0.80/0.94
% 0.80/0.94 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 0.80/0.94
% 0.80/0.94
% 0.80/0.94 c_lessequals(V_A, V_C, tc_set(T_a)) -> f1(true__, V_A, V_C, T_a)
% 0.80/0.94 c_lessequals(V_x, c_Zorn_Osucc(V_S, V_x, T_a), tc_set(tc_set(T_a))) -> true__
% 0.80/0.94 c_lessequals(c_Zorn_Osucc(v_S, v_n, t_a), v_m, tc_set(tc_set(t_a))) -> true__
% 0.80/0.94 f1(f1(true__, c_Zorn_Osucc(X0, v_m, t_a), Y3, tc_set(t_a)), c_Zorn_Osucc(v_S, v_n, t_a), Y3, tc_set(t_a)) -> true__
% 0.80/0.94 f1(f1(true__, c_Zorn_Osucc(X1, Y0, X2), Y3, tc_set(X2)), Y0, Y3, tc_set(X2)) -> true__
% 0.80/0.94 f1(f1(true__, c_Zorn_Osucc(X1, c_Zorn_Osucc(X2, Y0, X3), X3), Y3, tc_set(X3)), Y0, Y3, tc_set(X3)) -> true__
% 0.80/0.94 f1(f1(true__, v_m, Y3, tc_set(t_a)), c_Zorn_Osucc(v_S, v_n, t_a), Y3, tc_set(t_a)) -> true__
% 0.80/0.94 f1(f1(true__, v_m, Y3, tc_set(t_a)), v_n, Y3, tc_set(t_a)) -> true__
% 0.80/0.94 f1(true__, Y0, c_Zorn_Osucc(X1, Y0, X2), tc_set(X2)) -> true__
% 0.80/0.94 f1(true__, Y1, c_Zorn_Osucc(X1, c_Zorn_Osucc(X2, c_Zorn_Osucc(Y0, Y1, Y2), Y2), Y2), tc_set(Y2)) -> true__
% 0.80/0.94 f1(true__, Y1, c_Zorn_Osucc(X1, c_Zorn_Osucc(Y0, Y1, Y2), Y2), tc_set(Y2)) -> true__
% 0.80/0.94 f1(true__, c_Zorn_Osucc(v_S, v_n, t_a), c_Zorn_Osucc(X1, c_Zorn_Osucc(X2, v_m, t_a), t_a), tc_set(t_a)) -> true__
% 0.80/0.94 f1(true__, c_Zorn_Osucc(v_S, v_n, t_a), c_Zorn_Osucc(X1, v_m, t_a), tc_set(t_a)) -> true__
% 0.80/0.94 f1(true__, c_Zorn_Osucc(v_S, v_n, t_a), v_m, tc_set(t_a)) -> true__
% 0.80/0.94 f1(true__, v_n, c_Zorn_Osucc(X0, v_m, t_a), tc_set(t_a)) -> true__
% 0.80/0.94 f1(true__, v_n, v_m, tc_set(t_a)) -> true__
% 0.80/0.94 f2(c_lessequals(V_A, V_B, tc_set(T_a)), V_B, V_C, T_a, V_A) -> true__
% 0.80/0.94 f2(f1(true__, Y0, Y1, Y2), Y1, Y3, Y2, Y0) -> true__
% 0.80/0.94 f2(true__, V_B, V_C, T_a, V_A) -> f1(c_lessequals(V_B, V_C, tc_set(T_a)), V_A, V_C, T_a)
% 0.80/0.94 f3(c_lessequals(v_n, v_m, tc_set(tc_set(t_a)))) -> true__
% 0.80/0.94 f3(f1(true__, v_n, v_m, tc_set(t_a))) -> true__
% 0.80/0.94 f3(true__) -> false__
% 0.80/0.94 false__ -> true__
% 0.80/0.94 with the LPO induced by
% 0.80/0.94 f3 > v_m > t_a > v_n > v_S > c_Zorn_Osucc > f2 > c_lessequals > f1 > tc_set > false__ > true__
% 0.80/0.94
% 0.80/0.94 % SZS output end Proof
% 0.80/0.94
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