TSTP Solution File: SET849-2 by Moca---0.1
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% File : Moca---0.1
% Problem : SET849-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n008.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 03:45:11 EDT 2022
% Result : Unsatisfiable 0.13s 0.40s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET849-2 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % Command : moca.sh %s
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jul 10 14:46:23 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.40 % SZS status Unsatisfiable
% 0.13/0.40 % SZS output start Proof
% 0.13/0.40 The input problem is unsatisfiable because
% 0.13/0.40
% 0.13/0.40 [1] the following set of Horn clauses is unsatisfiable:
% 0.13/0.40
% 0.13/0.40 c_lessequals(V_A, V_A, tc_set(T_a))
% 0.13/0.40 c_lessequals(V_Y, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(tc_set(T_a)))) ==> c_in(c_Union(V_Y, tc_set(T_a)), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))
% 0.13/0.40 c_in(c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))) ==> c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)) = c_Zorn_Osucc(V_S, c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)), T_a)
% 0.13/0.40 c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a) = c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)) ==> \bottom
% 0.13/0.40
% 0.13/0.40 This holds because
% 0.13/0.40
% 0.13/0.40 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 0.13/0.40
% 0.13/0.40 E:
% 0.13/0.40 c_lessequals(V_A, V_A, tc_set(T_a)) = true__
% 0.13/0.40 f1(c_lessequals(V_Y, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(tc_set(T_a)))), V_Y, T_a, V_S) = true__
% 0.13/0.40 f1(true__, V_Y, T_a, V_S) = c_in(c_Union(V_Y, tc_set(T_a)), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))
% 0.13/0.40 f2(c_in(c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))), V_S, T_a) = c_Zorn_Osucc(V_S, c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)), T_a)
% 0.13/0.40 f2(true__, V_S, T_a) = c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a))
% 0.13/0.40 f3(c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a))) = false__
% 0.13/0.40 f3(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a)) = true__
% 0.13/0.40 G:
% 0.13/0.40 true__ = false__
% 0.13/0.40
% 0.13/0.40 This holds because
% 0.13/0.40
% 0.13/0.40 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 0.13/0.40
% 0.13/0.40 f2(c_in(c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))), V_S, T_a) = c_Zorn_Osucc(V_S, c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)), T_a)
% 0.13/0.40 c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)) -> f2(true__, V_S, T_a)
% 0.13/0.40 c_Zorn_Osucc(Y0, f2(true__, Y0, Y1), Y1) -> f2(true__, Y0, Y1)
% 0.13/0.40 c_in(c_Union(V_Y, tc_set(T_a)), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))) -> f1(true__, V_Y, T_a, V_S)
% 0.13/0.40 c_in(f2(true__, X0, Y1), c_Zorn_OTFin(Y2, Y1), tc_set(tc_set(Y1))) -> f1(true__, c_Zorn_OTFin(X0, Y1), Y1, Y2)
% 0.13/0.40 c_lessequals(V_A, V_A, tc_set(T_a)) -> true__
% 0.13/0.40 f1(c_lessequals(V_Y, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(tc_set(T_a)))), V_Y, T_a, V_S) -> true__
% 0.13/0.40 f1(true__, c_Zorn_OTFin(Y1, Y2), Y2, Y1) -> true__
% 0.13/0.40 f3(c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a))) -> false__
% 0.13/0.40 f3(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a)) -> true__
% 0.13/0.40 f3(c_Zorn_Osucc(v_S, f2(true__, v_S, t_a), t_a)) -> true__
% 0.13/0.40 f3(f2(f1(true__, c_Zorn_OTFin(v_S, t_a), t_a, v_S), v_S, t_a)) -> true__
% 0.13/0.40 f3(f2(true__, v_S, t_a)) -> false__
% 0.13/0.40 false__ -> true__
% 0.13/0.40 with the LPO induced by
% 0.13/0.40 t_a > v_S > f3 > tc_set > c_Zorn_Osucc > c_Union > f2 > c_Zorn_OTFin > c_in > f1 > c_lessequals > false__ > true__
% 0.13/0.40
% 0.13/0.40 % SZS output end Proof
% 0.13/0.40
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