TSTP Solution File: SET846-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SET846-2 : 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 : n029.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 15:33:29 EDT 2023
% Result : Unsatisfiable 0.22s 0.40s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET846-2 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.36 % Computer : n029.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sat Aug 26 15:36:10 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.40 Command-line arguments: --no-flatten-goal
% 0.22/0.40
% 0.22/0.40 % SZS status Unsatisfiable
% 0.22/0.40
% 0.22/0.40 % SZS output start Proof
% 0.22/0.40 Take the following subset of the input axioms:
% 0.22/0.41 fof(cls_Set_OUnion__upper_0, axiom, ![V_B, V_A, T_a]: (~c_in(V_B, V_A, tc_set(T_a)) | c_lessequals(V_B, c_Union(V_A, T_a), tc_set(T_a)))).
% 0.22/0.41 fof(cls_Set_Osubset__refl_0, axiom, ![T_a2, V_A2]: c_lessequals(V_A2, V_A2, tc_set(T_a2))).
% 0.22/0.41 fof(cls_Zorn_OTFin_OsuccI_0, axiom, ![V_x, V_S, T_a2]: (~c_in(V_x, c_Zorn_OTFin(V_S, T_a2), tc_set(tc_set(T_a2))) | c_in(c_Zorn_Osucc(V_S, V_x, T_a2), c_Zorn_OTFin(V_S, T_a2), tc_set(tc_set(T_a2))))).
% 0.22/0.41 fof(cls_Zorn_OTFin__UnionI_0, axiom, ![V_Y, T_a2, V_S2]: (~c_lessequals(V_Y, c_Zorn_OTFin(V_S2, T_a2), tc_set(tc_set(tc_set(T_a2)))) | c_in(c_Union(V_Y, tc_set(T_a2)), c_Zorn_OTFin(V_S2, T_a2), tc_set(tc_set(T_a2))))).
% 0.22/0.41 fof(cls_conjecture_1, negated_conjecture, ~c_lessequals(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)), tc_set(tc_set(t_a)))).
% 0.22/0.41
% 0.22/0.41 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.22/0.41 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.22/0.41 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.22/0.41 fresh(y, y, x1...xn) = u
% 0.22/0.41 C => fresh(s, t, x1...xn) = v
% 0.22/0.41 where fresh is a fresh function symbol and x1..xn are the free
% 0.22/0.41 variables of u and v.
% 0.22/0.41 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.22/0.41 input problem has no model of domain size 1).
% 0.22/0.41
% 0.22/0.41 The encoding turns the above axioms into the following unit equations and goals:
% 0.22/0.41
% 0.22/0.41 Axiom 1 (cls_Set_Osubset__refl_0): c_lessequals(X, X, tc_set(Y)) = true.
% 0.22/0.41 Axiom 2 (cls_Zorn_OTFin__UnionI_0): fresh(X, X, Y, Z, W) = true.
% 0.22/0.41 Axiom 3 (cls_Zorn_OTFin_OsuccI_0): fresh3(X, X, Y, Z, W) = true.
% 0.22/0.41 Axiom 4 (cls_Set_OUnion__upper_0): fresh2(X, X, Y, Z, W) = true.
% 0.22/0.41 Axiom 5 (cls_Set_OUnion__upper_0): fresh2(c_in(X, Y, tc_set(Z)), true, X, Y, Z) = c_lessequals(X, c_Union(Y, Z), tc_set(Z)).
% 0.22/0.41 Axiom 6 (cls_Zorn_OTFin_OsuccI_0): fresh3(c_in(X, c_Zorn_OTFin(Y, Z), tc_set(tc_set(Z))), true, X, Y, Z) = c_in(c_Zorn_Osucc(Y, X, Z), c_Zorn_OTFin(Y, Z), tc_set(tc_set(Z))).
% 0.22/0.41 Axiom 7 (cls_Zorn_OTFin__UnionI_0): fresh(c_lessequals(X, c_Zorn_OTFin(Y, Z), tc_set(tc_set(tc_set(Z)))), true, X, Y, Z) = c_in(c_Union(X, tc_set(Z)), c_Zorn_OTFin(Y, Z), tc_set(tc_set(Z))).
% 0.22/0.41
% 0.22/0.41 Goal 1 (cls_conjecture_1): c_lessequals(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)), tc_set(tc_set(t_a))) = true.
% 0.22/0.41 Proof:
% 0.22/0.41 c_lessequals(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)), tc_set(tc_set(t_a)))
% 0.22/0.41 = { by axiom 5 (cls_Set_OUnion__upper_0) R->L }
% 0.22/0.41 fresh2(c_in(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a))), true, c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_Zorn_OTFin(v_S, t_a), tc_set(t_a))
% 0.22/0.41 = { by axiom 6 (cls_Zorn_OTFin_OsuccI_0) R->L }
% 0.22/0.41 fresh2(fresh3(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))), true, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), v_S, t_a), true, c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_Zorn_OTFin(v_S, t_a), tc_set(t_a))
% 0.22/0.41 = { by axiom 7 (cls_Zorn_OTFin__UnionI_0) R->L }
% 0.22/0.41 fresh2(fresh3(fresh(c_lessequals(c_Zorn_OTFin(v_S, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(tc_set(t_a)))), true, c_Zorn_OTFin(v_S, t_a), v_S, t_a), true, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), v_S, t_a), true, c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_Zorn_OTFin(v_S, t_a), tc_set(t_a))
% 0.22/0.41 = { by axiom 1 (cls_Set_Osubset__refl_0) }
% 0.22/0.41 fresh2(fresh3(fresh(true, true, c_Zorn_OTFin(v_S, t_a), v_S, t_a), true, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), v_S, t_a), true, c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_Zorn_OTFin(v_S, t_a), tc_set(t_a))
% 0.22/0.41 = { by axiom 2 (cls_Zorn_OTFin__UnionI_0) }
% 0.22/0.41 fresh2(fresh3(true, true, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), v_S, t_a), true, c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_Zorn_OTFin(v_S, t_a), tc_set(t_a))
% 0.22/0.41 = { by axiom 3 (cls_Zorn_OTFin_OsuccI_0) }
% 0.22/0.41 fresh2(true, true, c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_Zorn_OTFin(v_S, t_a), tc_set(t_a))
% 0.22/0.41 = { by axiom 4 (cls_Set_OUnion__upper_0) }
% 0.22/0.41 true
% 0.22/0.41 % SZS output end Proof
% 0.22/0.41
% 0.22/0.41 RESULT: Unsatisfiable (the axioms are contradictory).
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