TSTP Solution File: SWV242-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV242-2 : 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 : 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 : 300s
% DateTime : Thu Aug 31 23:03:09 EDT 2023
% Result : Unsatisfiable 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWV242-2 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.33 % Computer : n008.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 : 300
% 0.13/0.33 % DateTime : Tue Aug 29 09:08:32 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.19/0.39 Command-line arguments: --flatten
% 0.19/0.39
% 0.19/0.39 % SZS status Unsatisfiable
% 0.19/0.39
% 0.19/0.40 % SZS output start Proof
% 0.19/0.40 Take the following subset of the input axioms:
% 0.19/0.40 fof(cls_Message_Oanalz__mono_0, axiom, ![V_G, V_H]: (~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)))).
% 0.19/0.40 fof(cls_Set_OUn__upper1_0, axiom, ![V_A, V_B, T_a]: c_lessequals(V_A, c_union(V_A, V_B, T_a), tc_set(T_a))).
% 0.19/0.40 fof(cls_Set_OUn__upper2_0, axiom, ![V_A2, V_B2, T_a2]: c_lessequals(V_B2, c_union(V_A2, V_B2, T_a2), tc_set(T_a2))).
% 0.19/0.40 fof(cls_Set_Osubset__trans_0, axiom, ![V_C, V_A2, V_B2, T_a2]: (~c_lessequals(V_B2, V_C, tc_set(T_a2)) | (~c_lessequals(V_A2, V_B2, tc_set(T_a2)) | c_lessequals(V_A2, V_C, tc_set(T_a2))))).
% 0.19/0.40 fof(cls_conjecture_0, negated_conjecture, c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg))).
% 0.19/0.40 fof(cls_conjecture_1, negated_conjecture, c_lessequals(v_H, c_Message_Oanalz(v_H_H), tc_set(tc_Message_Omsg))).
% 0.19/0.40 fof(cls_conjecture_2, negated_conjecture, ~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))).
% 0.19/0.40
% 0.19/0.40 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.40 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.40 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.40 fresh(y, y, x1...xn) = u
% 0.19/0.40 C => fresh(s, t, x1...xn) = v
% 0.19/0.40 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.40 variables of u and v.
% 0.19/0.40 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.40 input problem has no model of domain size 1).
% 0.19/0.40
% 0.19/0.40 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.40
% 0.19/0.40 Axiom 1 (cls_Message_Oanalz__mono_0): fresh2(X, X, Y, Z) = true.
% 0.19/0.40 Axiom 2 (cls_Set_Osubset__trans_0): fresh(X, X, Y, Z, W) = true.
% 0.19/0.40 Axiom 3 (cls_conjecture_0): c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg)) = true.
% 0.19/0.40 Axiom 4 (cls_conjecture_1): c_lessequals(v_H, c_Message_Oanalz(v_H_H), tc_set(tc_Message_Omsg)) = true.
% 0.19/0.40 Axiom 5 (cls_Set_Osubset__trans_0): fresh3(X, X, Y, Z, W, V) = c_lessequals(V, Z, tc_set(W)).
% 0.19/0.40 Axiom 6 (cls_Set_OUn__upper1_0): c_lessequals(X, c_union(X, Y, Z), tc_set(Z)) = true.
% 0.19/0.40 Axiom 7 (cls_Set_OUn__upper2_0): c_lessequals(X, c_union(Y, X, Z), tc_set(Z)) = true.
% 0.19/0.40 Axiom 8 (cls_Message_Oanalz__mono_0): fresh2(c_lessequals(X, Y, tc_set(tc_Message_Omsg)), true, X, Y) = c_lessequals(c_Message_Oanalz(X), c_Message_Oanalz(Y), tc_set(tc_Message_Omsg)).
% 0.19/0.40 Axiom 9 (cls_Set_Osubset__trans_0): fresh3(c_lessequals(X, Y, tc_set(Z)), true, Y, W, Z, X) = fresh(c_lessequals(Y, W, tc_set(Z)), true, W, Z, X).
% 0.19/0.40
% 0.19/0.40 Lemma 10: fresh2(c_lessequals(X, Y, tc_set(tc_Message_Omsg)), c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg)), X, Y) = c_lessequals(c_Message_Oanalz(X), c_Message_Oanalz(Y), tc_set(tc_Message_Omsg)).
% 0.19/0.40 Proof:
% 0.19/0.40 fresh2(c_lessequals(X, Y, tc_set(tc_Message_Omsg)), c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg)), X, Y)
% 0.19/0.40 = { by axiom 3 (cls_conjecture_0) }
% 0.19/0.40 fresh2(c_lessequals(X, Y, tc_set(tc_Message_Omsg)), true, X, Y)
% 0.19/0.40 = { by axiom 8 (cls_Message_Oanalz__mono_0) }
% 0.19/0.40 c_lessequals(c_Message_Oanalz(X), c_Message_Oanalz(Y), tc_set(tc_Message_Omsg))
% 0.19/0.40
% 0.19/0.40 Lemma 11: fresh3(c_lessequals(X, Y, tc_set(Z)), c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg)), Y, W, Z, X) = fresh(c_lessequals(Y, W, tc_set(Z)), c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg)), W, Z, X).
% 0.19/0.40 Proof:
% 0.19/0.40 fresh3(c_lessequals(X, Y, tc_set(Z)), c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg)), Y, W, Z, X)
% 0.19/0.40 = { by axiom 3 (cls_conjecture_0) }
% 0.19/0.40 fresh3(c_lessequals(X, Y, tc_set(Z)), true, Y, W, Z, X)
% 0.19/0.40 = { by axiom 9 (cls_Set_Osubset__trans_0) }
% 0.19/0.40 fresh(c_lessequals(Y, W, tc_set(Z)), true, W, Z, X)
% 0.19/0.40 = { by axiom 3 (cls_conjecture_0) R->L }
% 0.19/0.40 fresh(c_lessequals(Y, W, tc_set(Z)), c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg)), W, Z, X)
% 0.19/0.40
% 0.19/0.40 Goal 1 (cls_conjecture_2): tuple(c_lessequals(v_G, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)), c_lessequals(v_H, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) = tuple(true, true).
% 0.19/0.40 Proof:
% 0.19/0.40 tuple(c_lessequals(v_G, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)), c_lessequals(v_H, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))
% 0.19/0.40 = { by axiom 5 (cls_Set_Osubset__trans_0) R->L }
% 0.19/0.40 tuple(c_lessequals(v_G, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)), fresh3(c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg)), c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg)), c_Message_Oanalz(v_H_H), c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_Message_Omsg, v_H))
% 0.19/0.40 = { by axiom 3 (cls_conjecture_0) }
% 0.19/0.40 tuple(c_lessequals(v_G, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)), fresh3(true, c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg)), c_Message_Oanalz(v_H_H), c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_Message_Omsg, v_H))
% 0.19/0.40 = { by axiom 4 (cls_conjecture_1) R->L }
% 0.19/0.40 tuple(c_lessequals(v_G, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)), fresh3(c_lessequals(v_H, c_Message_Oanalz(v_H_H), tc_set(tc_Message_Omsg)), c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg)), c_Message_Oanalz(v_H_H), c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_Message_Omsg, v_H))
% 0.19/0.40 = { by lemma 11 }
% 0.19/0.40 tuple(c_lessequals(v_G, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)), fresh(c_lessequals(c_Message_Oanalz(v_H_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(v_G_H), tc_set(tc_Message_Omsg)), c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_Message_Omsg, v_H))
% 0.19/0.40 = { by lemma 10 R->L }
% 0.19/0.40 tuple(c_lessequals(v_G, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)), fresh(fresh2(c_lessequals(v_H_H, c_union(v_G_H, v_H_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)), c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg)), v_H_H, c_union(v_G_H, v_H_H, tc_Message_Omsg)), c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg)), c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_Message_Omsg, v_H))
% 0.19/0.40 = { by axiom 7 (cls_Set_OUn__upper2_0) }
% 0.19/0.41 tuple(c_lessequals(v_G, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)), fresh(fresh2(true, c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg)), v_H_H, c_union(v_G_H, v_H_H, tc_Message_Omsg)), c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg)), c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_Message_Omsg, v_H))
% 0.19/0.41 = { by axiom 3 (cls_conjecture_0) R->L }
% 0.19/0.41 tuple(c_lessequals(v_G, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)), fresh(fresh2(c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg)), c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg)), v_H_H, c_union(v_G_H, v_H_H, tc_Message_Omsg)), c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg)), c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_Message_Omsg, v_H))
% 0.19/0.41 = { by axiom 1 (cls_Message_Oanalz__mono_0) }
% 0.19/0.41 tuple(c_lessequals(v_G, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)), fresh(true, c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg)), c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_Message_Omsg, v_H))
% 0.19/0.41 = { by axiom 3 (cls_conjecture_0) R->L }
% 0.19/0.41 tuple(c_lessequals(v_G, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)), fresh(c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg)), c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg)), c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_Message_Omsg, v_H))
% 0.19/0.41 = { by axiom 2 (cls_Set_Osubset__trans_0) }
% 0.19/0.41 tuple(c_lessequals(v_G, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true)
% 0.19/0.41 = { by axiom 3 (cls_conjecture_0) R->L }
% 0.19/0.41 tuple(c_lessequals(v_G, 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(v_G_H), tc_set(tc_Message_Omsg)))
% 0.19/0.41 = { by axiom 5 (cls_Set_Osubset__trans_0) R->L }
% 0.19/0.41 tuple(fresh3(c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg)), c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg)), c_Message_Oanalz(v_G_H), c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_Message_Omsg, v_G), c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg)))
% 0.19/0.41 = { by lemma 11 }
% 0.19/0.41 tuple(fresh(c_lessequals(c_Message_Oanalz(v_G_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(v_G_H), tc_set(tc_Message_Omsg)), c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_Message_Omsg, v_G), c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg)))
% 0.19/0.41 = { by lemma 10 R->L }
% 0.19/0.41 tuple(fresh(fresh2(c_lessequals(v_G_H, c_union(v_G_H, v_H_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)), c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg)), v_G_H, c_union(v_G_H, v_H_H, tc_Message_Omsg)), c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg)), c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_Message_Omsg, v_G), c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg)))
% 0.19/0.41 = { by axiom 6 (cls_Set_OUn__upper1_0) }
% 0.19/0.41 tuple(fresh(fresh2(true, c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg)), v_G_H, c_union(v_G_H, v_H_H, tc_Message_Omsg)), c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg)), c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_Message_Omsg, v_G), c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg)))
% 0.19/0.41 = { by axiom 3 (cls_conjecture_0) R->L }
% 0.19/0.41 tuple(fresh(fresh2(c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg)), c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg)), v_G_H, c_union(v_G_H, v_H_H, tc_Message_Omsg)), c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg)), c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_Message_Omsg, v_G), c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg)))
% 0.19/0.41 = { by axiom 1 (cls_Message_Oanalz__mono_0) }
% 0.19/0.41 tuple(fresh(true, c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg)), c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_Message_Omsg, v_G), c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg)))
% 0.19/0.41 = { by axiom 3 (cls_conjecture_0) R->L }
% 0.19/0.41 tuple(fresh(c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg)), c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg)), c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_Message_Omsg, v_G), c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg)))
% 0.19/0.41 = { by axiom 2 (cls_Set_Osubset__trans_0) }
% 0.19/0.41 tuple(true, c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg)))
% 0.19/0.41 = { by axiom 3 (cls_conjecture_0) R->L }
% 0.19/0.41 tuple(c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg)), c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg)))
% 0.19/0.41 = { by axiom 3 (cls_conjecture_0) }
% 0.19/0.41 tuple(c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg)), true)
% 0.19/0.41 = { by axiom 3 (cls_conjecture_0) }
% 0.19/0.41 tuple(true, true)
% 0.19/0.41 % SZS output end Proof
% 0.19/0.41
% 0.19/0.41 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------