TSTP Solution File: SET855-2 by Moca---0.1
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% File : Moca---0.1
% Problem : SET855-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n003.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 03:45:15 EDT 2022
% Result : Unsatisfiable 0.19s 0.63s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SET855-2 : TPTP v8.1.0. Released v3.2.0.
% 0.10/0.12 % Command : moca.sh %s
% 0.13/0.33 % Computer : n003.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jul 10 10:45:59 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.19/0.63 % SZS status Unsatisfiable
% 0.19/0.63 % SZS output start Proof
% 0.19/0.63 The input problem is unsatisfiable because
% 0.19/0.63
% 0.19/0.63 [1] the following set of Horn clauses is unsatisfiable:
% 0.19/0.63
% 0.19/0.63 c_lessequals(V_B, V_A, tc_set(T_a)) & c_lessequals(V_A, V_B, tc_set(T_a)) ==> V_A = V_B
% 0.19/0.63 c_lessequals(v_n, c_Union(v_Y, tc_set(t_a)), tc_set(tc_set(t_a)))
% 0.19/0.63 c_lessequals(c_Union(v_Y, tc_set(t_a)), v_n, tc_set(tc_set(t_a)))
% 0.19/0.63 v_n = c_Union(v_Y, tc_set(t_a)) ==> \bottom
% 0.19/0.63
% 0.19/0.63 This holds because
% 0.19/0.63
% 0.19/0.63 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 0.19/0.63
% 0.19/0.63 E:
% 0.19/0.63 c_lessequals(c_Union(v_Y, tc_set(t_a)), v_n, tc_set(tc_set(t_a))) = true__
% 0.19/0.63 c_lessequals(v_n, c_Union(v_Y, tc_set(t_a)), tc_set(tc_set(t_a))) = true__
% 0.19/0.63 f1(true__, V_A, V_B) = V_A
% 0.19/0.63 f2(c_lessequals(V_A, V_B, tc_set(T_a)), V_B, V_A, T_a) = V_B
% 0.19/0.63 f2(true__, V_B, V_A, T_a) = f1(c_lessequals(V_B, V_A, tc_set(T_a)), V_A, V_B)
% 0.19/0.63 f3(c_Union(v_Y, tc_set(t_a))) = false__
% 0.19/0.63 f3(v_n) = true__
% 0.19/0.63 G:
% 0.19/0.63 true__ = false__
% 0.19/0.63
% 0.19/0.63 This holds because
% 0.19/0.63
% 0.19/0.63 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 0.19/0.63
% 0.19/0.63
% 0.19/0.63 c_Union(v_Y, tc_set(t_a)) -> v_n
% 0.19/0.63 c_lessequals(c_Union(v_Y, tc_set(t_a)), v_n, tc_set(tc_set(t_a))) -> true__
% 0.19/0.63 c_lessequals(v_n, c_Union(v_Y, tc_set(t_a)), tc_set(tc_set(t_a))) -> true__
% 0.19/0.63 c_lessequals(v_n, v_n, tc_set(tc_set(t_a))) -> true__
% 0.19/0.63 f1(c_lessequals(V_B, V_A, tc_set(T_a)), V_A, V_B) -> f2(true__, V_B, V_A, T_a)
% 0.19/0.63 f1(true__, V_A, V_B) -> V_A
% 0.19/0.63 f2(c_lessequals(V_A, V_B, tc_set(T_a)), V_B, V_A, T_a) -> V_B
% 0.19/0.63 f2(true__, c_Union(v_Y, tc_set(t_a)), v_n, tc_set(t_a)) -> c_Union(v_Y, tc_set(t_a))
% 0.19/0.63 f2(true__, c_Union(v_Y, tc_set(t_a)), v_n, tc_set(t_a)) -> v_n
% 0.19/0.63 f2(true__, v_n, c_Union(v_Y, tc_set(t_a)), tc_set(t_a)) -> c_Union(v_Y, tc_set(t_a))
% 0.19/0.63 f2(true__, v_n, c_Union(v_Y, tc_set(t_a)), tc_set(t_a)) -> v_n
% 0.19/0.63 f2(true__, v_n, v_n, tc_set(t_a)) -> v_n
% 0.19/0.63 f3(c_Union(v_Y, tc_set(t_a))) -> false__
% 0.19/0.63 f3(v_n) -> true__
% 0.19/0.63 false__ -> true__
% 0.19/0.63 with the LPO induced by
% 0.19/0.63 f3 > t_a > v_Y > c_Union > v_n > f1 > f2 > tc_set > c_lessequals > false__ > true__
% 0.19/0.63
% 0.19/0.63 % SZS output end Proof
% 0.19/0.63
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