TSTP Solution File: SWV258-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV258-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n016.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 : 300s
% DateTime : Thu Aug 31 23:03:15 EDT 2023
% Result : Unsatisfiable 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWV258-2 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n016.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 03:54:00 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.41 Command-line arguments: --no-flatten-goal
% 0.20/0.41
% 0.20/0.41 % SZS status Unsatisfiable
% 0.20/0.41
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 Take the following subset of the input axioms:
% 0.20/0.41 fof(cls_Message_Oparts__subset__iff_0, axiom, ![V_G, V_H]: (~c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)) | c_lessequals(V_G, c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)))).
% 0.20/0.41 fof(cls_Message_Oparts__subset__iff_1, axiom, ![V_G2, V_H2]: (~c_lessequals(V_G2, c_Message_Oparts(V_H2), tc_set(tc_Message_Omsg)) | c_lessequals(c_Message_Oparts(V_G2), c_Message_Oparts(V_H2), tc_set(tc_Message_Omsg)))).
% 0.20/0.41 fof(cls_Set_Oinsert__subset_2, axiom, ![V_x, V_B, T_a, V_A]: (~c_in(V_x, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a)) | c_lessequals(c_insert(V_x, V_A, T_a), V_B, tc_set(T_a))))).
% 0.20/0.41 fof(cls_Set_Osubset__refl_0, axiom, ![T_a2, V_A2]: c_lessequals(V_A2, V_A2, tc_set(T_a2))).
% 0.20/0.41 fof(cls_conjecture_0, negated_conjecture, c_in(v_X, c_Message_Oparts(v_H), tc_Message_Omsg)).
% 0.20/0.41 fof(cls_conjecture_1, negated_conjecture, ~c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oparts(v_H), tc_set(tc_Message_Omsg))).
% 0.20/0.41
% 0.20/0.41 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.41 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.41 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.41 fresh(y, y, x1...xn) = u
% 0.20/0.41 C => fresh(s, t, x1...xn) = v
% 0.20/0.41 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.41 variables of u and v.
% 0.20/0.41 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.41 input problem has no model of domain size 1).
% 0.20/0.41
% 0.20/0.41 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.41
% 0.20/0.41 Axiom 1 (cls_conjecture_0): c_in(v_X, c_Message_Oparts(v_H), tc_Message_Omsg) = true.
% 0.20/0.41 Axiom 2 (cls_Message_Oparts__subset__iff_1): fresh4(X, X, Y, Z) = true.
% 0.20/0.41 Axiom 3 (cls_Message_Oparts__subset__iff_0): fresh3(X, X, Y, Z) = true.
% 0.20/0.41 Axiom 4 (cls_Set_Osubset__refl_0): c_lessequals(X, X, tc_set(Y)) = true.
% 0.20/0.41 Axiom 5 (cls_Set_Oinsert__subset_2): fresh(X, X, Y, Z, W, V) = true.
% 0.20/0.41 Axiom 6 (cls_Set_Oinsert__subset_2): fresh2(X, X, Y, Z, W, V) = c_lessequals(c_insert(Y, V, W), Z, tc_set(W)).
% 0.20/0.41 Axiom 7 (cls_Message_Oparts__subset__iff_1): fresh4(c_lessequals(X, c_Message_Oparts(Y), tc_set(tc_Message_Omsg)), true, X, Y) = c_lessequals(c_Message_Oparts(X), c_Message_Oparts(Y), tc_set(tc_Message_Omsg)).
% 0.20/0.41 Axiom 8 (cls_Message_Oparts__subset__iff_0): fresh3(c_lessequals(c_Message_Oparts(X), c_Message_Oparts(Y), tc_set(tc_Message_Omsg)), true, X, Y) = c_lessequals(X, c_Message_Oparts(Y), tc_set(tc_Message_Omsg)).
% 0.20/0.41 Axiom 9 (cls_Set_Oinsert__subset_2): fresh2(c_lessequals(X, Y, tc_set(Z)), true, W, Y, Z, X) = fresh(c_in(W, Y, Z), true, W, Y, Z, X).
% 0.20/0.41
% 0.20/0.41 Goal 1 (cls_conjecture_1): c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oparts(v_H), tc_set(tc_Message_Omsg)) = true.
% 0.20/0.41 Proof:
% 0.20/0.41 c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oparts(v_H), tc_set(tc_Message_Omsg))
% 0.20/0.41 = { by axiom 7 (cls_Message_Oparts__subset__iff_1) R->L }
% 0.20/0.41 fresh4(c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Oparts(v_H), tc_set(tc_Message_Omsg)), true, c_insert(v_X, v_H, tc_Message_Omsg), v_H)
% 0.20/0.41 = { by axiom 6 (cls_Set_Oinsert__subset_2) R->L }
% 0.20/0.41 fresh4(fresh2(true, true, v_X, c_Message_Oparts(v_H), tc_Message_Omsg, v_H), true, c_insert(v_X, v_H, tc_Message_Omsg), v_H)
% 0.20/0.41 = { by axiom 3 (cls_Message_Oparts__subset__iff_0) R->L }
% 0.20/0.41 fresh4(fresh2(fresh3(true, true, v_H, v_H), true, v_X, c_Message_Oparts(v_H), tc_Message_Omsg, v_H), true, c_insert(v_X, v_H, tc_Message_Omsg), v_H)
% 0.20/0.41 = { by axiom 4 (cls_Set_Osubset__refl_0) R->L }
% 0.20/0.41 fresh4(fresh2(fresh3(c_lessequals(c_Message_Oparts(v_H), c_Message_Oparts(v_H), tc_set(tc_Message_Omsg)), true, v_H, v_H), true, v_X, c_Message_Oparts(v_H), tc_Message_Omsg, v_H), true, c_insert(v_X, v_H, tc_Message_Omsg), v_H)
% 0.20/0.41 = { by axiom 8 (cls_Message_Oparts__subset__iff_0) }
% 0.20/0.41 fresh4(fresh2(c_lessequals(v_H, c_Message_Oparts(v_H), tc_set(tc_Message_Omsg)), true, v_X, c_Message_Oparts(v_H), tc_Message_Omsg, v_H), true, c_insert(v_X, v_H, tc_Message_Omsg), v_H)
% 0.20/0.41 = { by axiom 9 (cls_Set_Oinsert__subset_2) }
% 0.20/0.41 fresh4(fresh(c_in(v_X, c_Message_Oparts(v_H), tc_Message_Omsg), true, v_X, c_Message_Oparts(v_H), tc_Message_Omsg, v_H), true, c_insert(v_X, v_H, tc_Message_Omsg), v_H)
% 0.20/0.41 = { by axiom 1 (cls_conjecture_0) }
% 0.20/0.41 fresh4(fresh(true, true, v_X, c_Message_Oparts(v_H), tc_Message_Omsg, v_H), true, c_insert(v_X, v_H, tc_Message_Omsg), v_H)
% 0.20/0.41 = { by axiom 5 (cls_Set_Oinsert__subset_2) }
% 0.20/0.41 fresh4(true, true, c_insert(v_X, v_H, tc_Message_Omsg), v_H)
% 0.20/0.41 = { by axiom 2 (cls_Message_Oparts__subset__iff_1) }
% 0.20/0.41 true
% 0.20/0.41 % SZS output end Proof
% 0.20/0.41
% 0.20/0.41 RESULT: Unsatisfiable (the axioms are contradictory).
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