TSTP Solution File: SWV242-2 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : SWV242-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n022.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 20:42:14 EDT 2022
% Result : Unsatisfiable 13.24s 13.23s
% Output : Proof 13.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV242-2 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % Command : moca.sh %s
% 0.12/0.33 % Computer : n022.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jun 15 22:02:47 EDT 2022
% 0.12/0.34 % CPUTime :
% 13.24/13.23 % SZS status Unsatisfiable
% 13.24/13.23 % SZS output start Proof
% 13.24/13.23 The input problem is unsatisfiable because
% 13.24/13.23
% 13.24/13.23 [1] the following set of Horn clauses is unsatisfiable:
% 13.24/13.23
% 13.24/13.23 c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg))
% 13.24/13.23 c_lessequals(v_H, c_Message_Oanalz(v_H_H), tc_set(tc_Message_Omsg))
% 13.24/13.23 c_lessequals(v_H, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) & c_lessequals(v_G, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) ==> \bottom
% 13.24/13.23 c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg)) ==> c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_H), tc_set(tc_Message_Omsg))
% 13.24/13.23 c_lessequals(V_A, c_union(V_A, V_B, T_a), tc_set(T_a))
% 13.24/13.23 c_lessequals(V_B, c_union(V_A, V_B, T_a), tc_set(T_a))
% 13.24/13.23 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))
% 13.24/13.23
% 13.24/13.23 This holds because
% 13.24/13.23
% 13.24/13.23 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 13.24/13.23
% 13.24/13.23 E:
% 13.24/13.23 c_lessequals(V_A, c_union(V_A, V_B, T_a), tc_set(T_a)) = true__
% 13.24/13.23 c_lessequals(V_B, c_union(V_A, V_B, T_a), tc_set(T_a)) = true__
% 13.24/13.23 c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg)) = true__
% 13.24/13.23 c_lessequals(v_H, c_Message_Oanalz(v_H_H), tc_set(tc_Message_Omsg)) = true__
% 13.24/13.23 f1(true__) = false__
% 13.24/13.23 f2(c_lessequals(v_G, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) = true__
% 13.24/13.23 f2(true__) = f1(c_lessequals(v_H, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))
% 13.24/13.23 f3(c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg)), V_G, V_H) = true__
% 13.24/13.23 f3(true__, V_G, V_H) = c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_H), tc_set(tc_Message_Omsg))
% 13.24/13.23 f4(true__, V_A, V_C, T_a) = c_lessequals(V_A, V_C, tc_set(T_a))
% 13.24/13.23 f5(c_lessequals(V_A, V_B, tc_set(T_a)), V_B, V_C, T_a, V_A) = true__
% 13.24/13.23 f5(true__, V_B, V_C, T_a, V_A) = f4(c_lessequals(V_B, V_C, tc_set(T_a)), V_A, V_C, T_a)
% 13.24/13.23 G:
% 13.24/13.23 true__ = false__
% 13.24/13.23
% 13.24/13.23 This holds because
% 13.24/13.23
% 13.24/13.23 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 13.24/13.23
% 13.24/13.23
% 13.24/13.23 c_lessequals(V_A, V_C, tc_set(T_a)) -> f4(true__, V_A, V_C, T_a)
% 13.24/13.23 c_lessequals(V_A, c_union(V_A, V_B, T_a), tc_set(T_a)) -> true__
% 13.24/13.23 c_lessequals(V_B, c_union(V_A, V_B, T_a), tc_set(T_a)) -> true__
% 13.24/13.23 c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg)) -> true__
% 13.24/13.23 c_lessequals(v_H, c_Message_Oanalz(v_H_H), tc_set(tc_Message_Omsg)) -> true__
% 13.24/13.23 f1(f4(true__, v_H, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_Message_Omsg)) -> true__
% 13.24/13.23 f1(true__) -> false__
% 13.24/13.23 f2(c_lessequals(v_G, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) -> true__
% 13.24/13.23 f2(f4(true__, v_G, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_Message_Omsg)) -> true__
% 13.24/13.23 f2(true__) -> f1(c_lessequals(v_H, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))
% 13.24/13.23 f3(c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg)), V_G, V_H) -> true__
% 13.24/13.23 f3(f4(true__, Y0, Y1, tc_Message_Omsg), Y0, Y1) -> true__
% 13.24/13.23 f3(true__, V_G, V_H) -> c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_H), tc_set(tc_Message_Omsg))
% 13.24/13.23 f4(f4(true__, c_Message_Oanalz(c_Message_Oanalz(c_Message_Oanalz(v_G_H))), Y3, tc_Message_Omsg), c_Message_Oanalz(c_Message_Oanalz(v_G)), Y3, tc_Message_Omsg) -> true__
% 13.24/13.23 f4(f4(true__, c_Message_Oanalz(c_Message_Oanalz(v_G_H)), Y3, tc_Message_Omsg), c_Message_Oanalz(v_G), Y3, tc_Message_Omsg) -> true__
% 13.24/13.23 f4(f4(true__, c_Message_Oanalz(c_Message_Oanalz(v_H_H)), Y3, tc_Message_Omsg), c_Message_Oanalz(v_H), Y3, tc_Message_Omsg) -> true__
% 13.24/13.23 f4(f4(true__, c_Message_Oanalz(c_union(X0, X1, tc_Message_Omsg)), Y3, tc_Message_Omsg), c_Message_Oanalz(X0), Y3, tc_Message_Omsg) -> true__
% 13.24/13.23 f4(f4(true__, c_Message_Oanalz(c_union(X0, v_G_H, tc_Message_Omsg)), Y3, tc_Message_Omsg), v_G, Y3, tc_Message_Omsg) -> true__
% 13.24/13.23 f4(f4(true__, c_Message_Oanalz(c_union(X0, v_H_H, tc_Message_Omsg)), Y3, tc_Message_Omsg), v_H, Y3, tc_Message_Omsg) -> true__
% 13.24/13.23 f4(f4(true__, c_Message_Oanalz(c_union(X1, X0, tc_Message_Omsg)), Y3, tc_Message_Omsg), c_Message_Oanalz(X0), Y3, tc_Message_Omsg) -> true__
% 13.24/13.23 f4(f4(true__, c_Message_Oanalz(c_union(v_G_H, X0, tc_Message_Omsg)), Y3, tc_Message_Omsg), v_G, Y3, tc_Message_Omsg) -> true__
% 13.24/13.23 f4(f4(true__, c_Message_Oanalz(c_union(v_H_H, X0, tc_Message_Omsg)), Y3, tc_Message_Omsg), v_H, Y3, tc_Message_Omsg) -> true__
% 13.24/13.23 f4(f4(true__, c_Message_Oanalz(v_G_H), Y3, tc_Message_Omsg), v_G, Y3, tc_Message_Omsg) -> true__
% 13.24/13.23 f4(f4(true__, c_Message_Oanalz(v_H_H), Y3, tc_Message_Omsg), v_H, Y3, tc_Message_Omsg) -> true__
% 13.24/13.23 f4(f4(true__, c_union(X0, c_Message_Oanalz(v_G_H), tc_Message_Omsg), Y3, tc_Message_Omsg), v_G, Y3, tc_Message_Omsg) -> true__
% 13.24/13.23 f4(f4(true__, c_union(X0, c_Message_Oanalz(v_H_H), tc_Message_Omsg), Y3, tc_Message_Omsg), v_H, Y3, tc_Message_Omsg) -> true__
% 13.24/13.23 f4(f4(true__, c_union(X1, Y0, Y2), Y3, Y2), Y0, Y3, Y2) -> true__
% 13.24/13.23 f4(f4(true__, c_union(Y0, X1, Y2), Y3, Y2), Y0, Y3, Y2) -> true__
% 13.24/13.23 f4(f4(true__, c_union(c_Message_Oanalz(v_G_H), X0, tc_Message_Omsg), Y3, tc_Message_Omsg), v_G, Y3, tc_Message_Omsg) -> true__
% 13.24/13.23 f4(f4(true__, c_union(c_Message_Oanalz(v_H_H), X0, tc_Message_Omsg), Y3, tc_Message_Omsg), v_H, Y3, tc_Message_Omsg) -> true__
% 13.24/13.23 f4(true__, Y0, c_union(X1, Y0, Y2), Y2) -> true__
% 13.24/13.23 f4(true__, Y0, c_union(X1, c_union(Y0, Y1, Y2), Y2), Y2) -> true__
% 13.24/13.23 f4(true__, Y0, c_union(Y0, X1, Y2), Y2) -> true__
% 13.24/13.23 f4(true__, Y0, c_union(c_union(Y0, Y1, Y2), X1, Y2), Y2) -> true__
% 13.24/13.23 f4(true__, Y1, c_union(X1, c_union(Y0, Y1, Y2), Y2), Y2) -> true__
% 13.24/13.23 f4(true__, Y1, c_union(c_union(Y0, Y1, Y2), X1, Y2), Y2) -> true__
% 13.24/13.23 f4(true__, c_Message_Oanalz(Y0), c_Message_Oanalz(c_union(X1, Y0, tc_Message_Omsg)), tc_Message_Omsg) -> true__
% 13.24/13.23 f4(true__, c_Message_Oanalz(Y0), c_Message_Oanalz(c_union(X1, c_union(X2, Y0, tc_Message_Omsg), tc_Message_Omsg)), tc_Message_Omsg) -> true__
% 13.24/13.23 f4(true__, c_Message_Oanalz(Y0), c_Message_Oanalz(c_union(X1, c_union(Y0, X2, tc_Message_Omsg), tc_Message_Omsg)), tc_Message_Omsg) -> true__
% 13.24/13.23 f4(true__, c_Message_Oanalz(Y0), c_Message_Oanalz(c_union(Y0, X1, tc_Message_Omsg)), tc_Message_Omsg) -> true__
% 13.24/13.23 f4(true__, c_Message_Oanalz(Y0), c_Message_Oanalz(c_union(c_union(X1, Y0, tc_Message_Omsg), X3, tc_Message_Omsg)), tc_Message_Omsg) -> true__
% 13.24/13.23 f4(true__, c_Message_Oanalz(Y0), c_Message_Oanalz(c_union(c_union(Y0, X1, tc_Message_Omsg), X3, tc_Message_Omsg)), tc_Message_Omsg) -> true__
% 13.24/13.23 f4(true__, c_Message_Oanalz(c_Message_Oanalz(X0)), c_Message_Oanalz(c_Message_Oanalz(c_union(X0, X1, tc_Message_Omsg))), tc_Message_Omsg) -> true__
% 13.24/13.23 f4(true__, c_Message_Oanalz(c_Message_Oanalz(X0)), c_Message_Oanalz(c_Message_Oanalz(c_union(X1, X0, tc_Message_Omsg))), tc_Message_Omsg) -> true__
% 13.24/13.23 f4(true__, c_Message_Oanalz(c_Message_Oanalz(c_Message_Oanalz(X0))), c_Message_Oanalz(c_Message_Oanalz(c_Message_Oanalz(c_union(X0, X1, tc_Message_Omsg)))), tc_Message_Omsg) -> true__
% 13.24/13.23 f4(true__, c_Message_Oanalz(c_Message_Oanalz(c_Message_Oanalz(X0))), c_Message_Oanalz(c_Message_Oanalz(c_Message_Oanalz(c_union(X1, X0, tc_Message_Omsg)))), tc_Message_Omsg) -> true__
% 13.24/13.23 f4(true__, c_Message_Oanalz(c_Message_Oanalz(c_Message_Oanalz(c_Message_Oanalz(v_G)))), c_Message_Oanalz(c_Message_Oanalz(c_Message_Oanalz(c_Message_Oanalz(c_Message_Oanalz(v_G_H))))), tc_Message_Omsg) -> true__
% 13.24/13.23 f4(true__, c_Message_Oanalz(c_Message_Oanalz(c_Message_Oanalz(v_G))), c_Message_Oanalz(c_Message_Oanalz(c_Message_Oanalz(c_Message_Oanalz(v_G_H)))), tc_Message_Omsg) -> true__
% 13.24/13.23 f4(true__, c_Message_Oanalz(c_Message_Oanalz(c_Message_Oanalz(v_H))), c_Message_Oanalz(c_Message_Oanalz(c_Message_Oanalz(c_Message_Oanalz(v_H_H)))), tc_Message_Omsg) -> true__
% 13.24/13.23 f4(true__, c_Message_Oanalz(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_Message_Oanalz(c_Message_Oanalz(c_union(X0, v_G_H, tc_Message_Omsg)))), tc_Message_Omsg) -> true__
% 13.24/13.23 f4(true__, c_Message_Oanalz(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_Message_Oanalz(c_Message_Oanalz(c_union(v_G_H, X0, tc_Message_Omsg)))), tc_Message_Omsg) -> true__
% 13.24/13.23 f4(true__, c_Message_Oanalz(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_Message_Oanalz(c_Message_Oanalz(v_G_H))), tc_Message_Omsg) -> true__
% 13.24/13.23 f4(true__, c_Message_Oanalz(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_Message_Oanalz(c_union(X0, c_Message_Oanalz(v_G_H), tc_Message_Omsg))), tc_Message_Omsg) -> true__
% 13.24/13.24 f4(true__, c_Message_Oanalz(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G_H), X0, tc_Message_Omsg))), tc_Message_Omsg) -> true__
% 13.24/13.24 f4(true__, c_Message_Oanalz(c_Message_Oanalz(v_H)), c_Message_Oanalz(c_Message_Oanalz(c_Message_Oanalz(c_union(v_H_H, X0, tc_Message_Omsg)))), tc_Message_Omsg) -> true__
% 13.24/13.24 f4(true__, c_Message_Oanalz(c_Message_Oanalz(v_H)), c_Message_Oanalz(c_Message_Oanalz(c_Message_Oanalz(v_H_H))), tc_Message_Omsg) -> true__
% 13.24/13.24 f4(true__, c_Message_Oanalz(c_Message_Oanalz(v_H)), c_Message_Oanalz(c_Message_Oanalz(c_union(X0, c_Message_Oanalz(v_H_H), tc_Message_Omsg))), tc_Message_Omsg) -> true__
% 13.24/13.24 f4(true__, c_Message_Oanalz(c_Message_Oanalz(v_H)), c_Message_Oanalz(c_Message_Oanalz(c_union(c_Message_Oanalz(v_H_H), X0, tc_Message_Omsg))), tc_Message_Omsg) -> true__
% 13.24/13.24 f4(true__, c_Message_Oanalz(v_G), c_Message_Oanalz(c_Message_Oanalz(c_union(X0, v_G_H, tc_Message_Omsg))), tc_Message_Omsg) -> true__
% 13.24/13.24 f4(true__, c_Message_Oanalz(v_G), c_Message_Oanalz(c_Message_Oanalz(c_union(v_G_H, X0, tc_Message_Omsg))), tc_Message_Omsg) -> true__
% 13.24/13.24 f4(true__, c_Message_Oanalz(v_G), c_Message_Oanalz(c_Message_Oanalz(v_G_H)), tc_Message_Omsg) -> true__
% 13.24/13.24 f4(true__, c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(X0, c_Message_Oanalz(v_G_H), tc_Message_Omsg)), tc_Message_Omsg) -> true__
% 13.24/13.24 f4(true__, c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(c_Message_Oanalz(v_G_H), X0, tc_Message_Omsg)), tc_Message_Omsg) -> true__
% 13.24/13.24 f4(true__, c_Message_Oanalz(v_H), c_Message_Oanalz(c_Message_Oanalz(c_union(X0, v_H_H, tc_Message_Omsg))), tc_Message_Omsg) -> true__
% 13.24/13.24 f4(true__, c_Message_Oanalz(v_H), c_Message_Oanalz(c_Message_Oanalz(c_union(v_H_H, X0, tc_Message_Omsg))), tc_Message_Omsg) -> true__
% 13.24/13.24 f4(true__, c_Message_Oanalz(v_H), c_Message_Oanalz(c_Message_Oanalz(v_H_H)), tc_Message_Omsg) -> true__
% 13.24/13.24 f4(true__, c_Message_Oanalz(v_H), c_Message_Oanalz(c_union(X0, c_Message_Oanalz(v_H_H), tc_Message_Omsg)), tc_Message_Omsg) -> true__
% 13.24/13.24 f4(true__, c_Message_Oanalz(v_H), c_Message_Oanalz(c_union(c_Message_Oanalz(v_H_H), X0, tc_Message_Omsg)), tc_Message_Omsg) -> true__
% 13.24/13.24 f4(true__, v_G, c_Message_Oanalz(c_union(X1, v_G_H, tc_Message_Omsg)), tc_Message_Omsg) -> true__
% 13.24/13.24 f4(true__, v_G, c_Message_Oanalz(c_union(v_G_H, X1, tc_Message_Omsg)), tc_Message_Omsg) -> true__
% 13.24/13.24 f4(true__, v_G, c_Message_Oanalz(v_G_H), tc_Message_Omsg) -> true__
% 13.24/13.24 f4(true__, v_G, c_union(X1, c_Message_Oanalz(v_G_H), tc_Message_Omsg), tc_Message_Omsg) -> true__
% 13.24/13.24 f4(true__, v_G, c_union(c_Message_Oanalz(v_G_H), X1, tc_Message_Omsg), tc_Message_Omsg) -> true__
% 13.24/13.24 f4(true__, v_H, c_Message_Oanalz(c_union(X1, v_H_H, tc_Message_Omsg)), tc_Message_Omsg) -> true__
% 13.24/13.24 f4(true__, v_H, c_Message_Oanalz(c_union(v_H_H, X1, tc_Message_Omsg)), tc_Message_Omsg) -> true__
% 13.24/13.24 f4(true__, v_H, c_Message_Oanalz(v_H_H), tc_Message_Omsg) -> true__
% 13.24/13.24 f4(true__, v_H, c_union(X1, c_Message_Oanalz(v_H_H), tc_Message_Omsg), tc_Message_Omsg) -> true__
% 13.24/13.24 f4(true__, v_H, c_union(c_Message_Oanalz(v_H_H), X1, tc_Message_Omsg), tc_Message_Omsg) -> true__
% 13.24/13.24 f5(c_lessequals(V_A, V_B, tc_set(T_a)), V_B, V_C, T_a, V_A) -> true__
% 13.24/13.24 f5(f4(true__, Y0, Y1, Y2), Y1, Y3, Y2, Y0) -> true__
% 13.24/13.24 f5(true__, V_B, V_C, T_a, V_A) -> f4(c_lessequals(V_B, V_C, tc_set(T_a)), V_A, V_C, T_a)
% 13.24/13.24 false__ -> true__
% 13.24/13.24 with the LPO induced by
% 13.24/13.24 f5 > v_G > f2 > c_union > f3 > c_lessequals > f4 > tc_set > v_G_H > c_Message_Oanalz > tc_Message_Omsg > f1 > v_H_H > v_H > false__ > true__
% 13.24/13.24
% 13.24/13.24 % SZS output end Proof
% 13.24/13.24
%------------------------------------------------------------------------------