TSTP Solution File: SET865-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SET865-2 : 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 : n021.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 15:33:36 EDT 2023
% Result : Unsatisfiable 0.21s 0.41s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET865-2 : 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
% 0.14/0.35 % Computer : n021.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 08:35:41 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.41 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.21/0.41
% 0.21/0.41 % SZS status Unsatisfiable
% 0.21/0.41
% 0.21/0.42 % SZS output start Proof
% 0.21/0.42 Take the following subset of the input axioms:
% 0.21/0.42 fof(cls_Set_OsubsetD_0, axiom, ![V_c, V_A, T_a, V_B]: (~c_in(V_c, V_A, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a)) | c_in(V_c, V_B, T_a)))).
% 0.21/0.42 fof(cls_Zorn_OHausdorff_0, axiom, ![V_S, T_a2]: c_in(c_Zorn_OHausdorff__1(V_S, T_a2), c_Zorn_Omaxchain(V_S, T_a2), tc_set(tc_set(T_a2)))).
% 0.21/0.42 fof(cls_Zorn_Omaxchain__Zorn_0, axiom, ![V_u, T_a2, V_S2, V_c2]: (~c_in(V_u, V_S2, tc_set(T_a2)) | (~c_in(V_c2, c_Zorn_Omaxchain(V_S2, T_a2), tc_set(tc_set(T_a2))) | (~c_lessequals(c_Union(V_c2, T_a2), V_u, tc_set(T_a2)) | c_Union(V_c2, T_a2)=V_u)))).
% 0.21/0.42 fof(cls_Zorn_Omaxchain__subset__chain_0, axiom, ![T_a2, V_S2]: c_lessequals(c_Zorn_Omaxchain(V_S2, T_a2), c_Zorn_Ochain(V_S2, T_a2), tc_set(tc_set(tc_set(T_a2))))).
% 0.21/0.42 fof(cls_conjecture_0, negated_conjecture, ![V_U]: (c_in(c_Union(V_U, t_a), v_S, tc_set(t_a)) | ~c_in(V_U, c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a))))).
% 0.21/0.42 fof(cls_conjecture_1, negated_conjecture, ![V_U2]: (c_in(v_x(V_U2), v_S, tc_set(t_a)) | ~c_in(V_U2, v_S, tc_set(t_a)))).
% 0.21/0.42 fof(cls_conjecture_2, negated_conjecture, ![V_U2]: (c_lessequals(V_U2, v_x(V_U2), tc_set(t_a)) | ~c_in(V_U2, v_S, tc_set(t_a)))).
% 0.21/0.42 fof(cls_conjecture_3, negated_conjecture, ![V_U2]: (V_U2!=v_x(V_U2) | ~c_in(V_U2, v_S, tc_set(t_a)))).
% 0.21/0.42
% 0.21/0.42 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.42 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.42 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.42 fresh(y, y, x1...xn) = u
% 0.21/0.42 C => fresh(s, t, x1...xn) = v
% 0.21/0.42 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.42 variables of u and v.
% 0.21/0.42 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.42 input problem has no model of domain size 1).
% 0.21/0.42
% 0.21/0.42 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.42
% 0.21/0.42 Axiom 1 (cls_conjecture_2): fresh(X, X, Y) = true2.
% 0.21/0.42 Axiom 2 (cls_conjecture_0): fresh3(X, X, Y) = true2.
% 0.21/0.42 Axiom 3 (cls_conjecture_1): fresh2(X, X, Y) = true2.
% 0.21/0.42 Axiom 4 (cls_Zorn_Omaxchain__Zorn_0): fresh8(X, X, Y, Z, W) = Y.
% 0.21/0.42 Axiom 5 (cls_Set_OsubsetD_0): fresh6(X, X, Y, Z, W) = true2.
% 0.21/0.42 Axiom 6 (cls_Set_OsubsetD_0): fresh5(X, X, Y, Z, W, V) = c_in(Y, V, W).
% 0.21/0.42 Axiom 7 (cls_Zorn_Omaxchain__Zorn_0): fresh4(X, X, Y, Z, W, V) = c_Union(V, W).
% 0.21/0.42 Axiom 8 (cls_conjecture_2): fresh(c_in(X, v_S, tc_set(t_a)), true2, X) = c_lessequals(X, v_x(X), tc_set(t_a)).
% 0.21/0.42 Axiom 9 (cls_conjecture_1): fresh2(c_in(X, v_S, tc_set(t_a)), true2, X) = c_in(v_x(X), v_S, tc_set(t_a)).
% 0.21/0.42 Axiom 10 (cls_Zorn_Omaxchain__Zorn_0): fresh7(X, X, Y, Z, W, V) = fresh8(c_in(Y, Z, tc_set(W)), true2, Y, W, V).
% 0.21/0.42 Axiom 11 (cls_Zorn_OHausdorff_0): c_in(c_Zorn_OHausdorff__1(X, Y), c_Zorn_Omaxchain(X, Y), tc_set(tc_set(Y))) = true2.
% 0.21/0.42 Axiom 12 (cls_Set_OsubsetD_0): fresh5(c_lessequals(X, Y, tc_set(Z)), true2, W, X, Z, Y) = fresh6(c_in(W, X, Z), true2, W, Z, Y).
% 0.21/0.42 Axiom 13 (cls_conjecture_0): fresh3(c_in(X, c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a))), true2, X) = c_in(c_Union(X, t_a), v_S, tc_set(t_a)).
% 0.21/0.42 Axiom 14 (cls_Zorn_Omaxchain__subset__chain_0): c_lessequals(c_Zorn_Omaxchain(X, Y), c_Zorn_Ochain(X, Y), tc_set(tc_set(tc_set(Y)))) = true2.
% 0.21/0.42 Axiom 15 (cls_Zorn_Omaxchain__Zorn_0): fresh7(c_lessequals(c_Union(X, Y), Z, tc_set(Y)), true2, Z, W, Y, X) = fresh4(c_in(X, c_Zorn_Omaxchain(W, Y), tc_set(tc_set(Y))), true2, Z, W, Y, X).
% 0.21/0.42
% 0.21/0.42 Lemma 16: c_in(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_S, tc_set(t_a)) = true2.
% 0.21/0.42 Proof:
% 0.21/0.42 c_in(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_S, tc_set(t_a))
% 0.21/0.42 = { by axiom 13 (cls_conjecture_0) R->L }
% 0.21/0.42 fresh3(c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a))), true2, c_Zorn_OHausdorff__1(v_S, t_a))
% 0.21/0.42 = { by axiom 6 (cls_Set_OsubsetD_0) R->L }
% 0.21/0.42 fresh3(fresh5(true2, true2, c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a)), c_Zorn_Ochain(v_S, t_a)), true2, c_Zorn_OHausdorff__1(v_S, t_a))
% 0.21/0.42 = { by axiom 14 (cls_Zorn_Omaxchain__subset__chain_0) R->L }
% 0.21/0.42 fresh3(fresh5(c_lessequals(c_Zorn_Omaxchain(v_S, t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(tc_set(t_a)))), true2, c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a)), c_Zorn_Ochain(v_S, t_a)), true2, c_Zorn_OHausdorff__1(v_S, t_a))
% 0.21/0.42 = { by axiom 12 (cls_Set_OsubsetD_0) }
% 0.21/0.42 fresh3(fresh6(c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a))), true2, c_Zorn_OHausdorff__1(v_S, t_a), tc_set(tc_set(t_a)), c_Zorn_Ochain(v_S, t_a)), true2, c_Zorn_OHausdorff__1(v_S, t_a))
% 0.21/0.42 = { by axiom 11 (cls_Zorn_OHausdorff_0) }
% 0.21/0.42 fresh3(fresh6(true2, true2, c_Zorn_OHausdorff__1(v_S, t_a), tc_set(tc_set(t_a)), c_Zorn_Ochain(v_S, t_a)), true2, c_Zorn_OHausdorff__1(v_S, t_a))
% 0.21/0.42 = { by axiom 5 (cls_Set_OsubsetD_0) }
% 0.21/0.42 fresh3(true2, true2, c_Zorn_OHausdorff__1(v_S, t_a))
% 0.21/0.42 = { by axiom 2 (cls_conjecture_0) }
% 0.21/0.42 true2
% 0.21/0.42
% 0.21/0.42 Goal 1 (cls_conjecture_3): tuple(X, c_in(X, v_S, tc_set(t_a))) = tuple(v_x(X), true2).
% 0.21/0.42 The goal is true when:
% 0.21/0.42 X = c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)
% 0.21/0.42
% 0.21/0.42 Proof:
% 0.21/0.42 tuple(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), c_in(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_S, tc_set(t_a)))
% 0.21/0.42 = { by lemma 16 }
% 0.21/0.42 tuple(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), true2)
% 0.21/0.42 = { by axiom 7 (cls_Zorn_Omaxchain__Zorn_0) R->L }
% 0.21/0.42 tuple(fresh4(true2, true2, v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), v_S, t_a, c_Zorn_OHausdorff__1(v_S, t_a)), true2)
% 0.21/0.42 = { by axiom 11 (cls_Zorn_OHausdorff_0) R->L }
% 0.21/0.42 tuple(fresh4(c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a))), true2, v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), v_S, t_a, c_Zorn_OHausdorff__1(v_S, t_a)), true2)
% 0.21/0.42 = { by axiom 15 (cls_Zorn_Omaxchain__Zorn_0) R->L }
% 0.21/0.42 tuple(fresh7(c_lessequals(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), tc_set(t_a)), true2, v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), v_S, t_a, c_Zorn_OHausdorff__1(v_S, t_a)), true2)
% 0.21/0.42 = { by axiom 8 (cls_conjecture_2) R->L }
% 0.21/0.42 tuple(fresh7(fresh(c_in(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_S, tc_set(t_a)), true2, c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), true2, v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), v_S, t_a, c_Zorn_OHausdorff__1(v_S, t_a)), true2)
% 0.21/0.42 = { by lemma 16 }
% 0.21/0.42 tuple(fresh7(fresh(true2, true2, c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), true2, v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), v_S, t_a, c_Zorn_OHausdorff__1(v_S, t_a)), true2)
% 0.21/0.42 = { by axiom 1 (cls_conjecture_2) }
% 0.21/0.42 tuple(fresh7(true2, true2, v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), v_S, t_a, c_Zorn_OHausdorff__1(v_S, t_a)), true2)
% 0.21/0.42 = { by axiom 10 (cls_Zorn_Omaxchain__Zorn_0) }
% 0.21/0.42 tuple(fresh8(c_in(v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), v_S, tc_set(t_a)), true2, v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), t_a, c_Zorn_OHausdorff__1(v_S, t_a)), true2)
% 0.21/0.42 = { by axiom 9 (cls_conjecture_1) R->L }
% 0.21/0.42 tuple(fresh8(fresh2(c_in(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_S, tc_set(t_a)), true2, c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), true2, v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), t_a, c_Zorn_OHausdorff__1(v_S, t_a)), true2)
% 0.21/0.42 = { by lemma 16 }
% 0.21/0.42 tuple(fresh8(fresh2(true2, true2, c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), true2, v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), t_a, c_Zorn_OHausdorff__1(v_S, t_a)), true2)
% 0.21/0.42 = { by axiom 3 (cls_conjecture_1) }
% 0.21/0.42 tuple(fresh8(true2, true2, v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), t_a, c_Zorn_OHausdorff__1(v_S, t_a)), true2)
% 0.21/0.42 = { by axiom 4 (cls_Zorn_Omaxchain__Zorn_0) }
% 0.21/0.42 tuple(v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), true2)
% 0.21/0.42 % SZS output end Proof
% 0.21/0.42
% 0.21/0.42 RESULT: Unsatisfiable (the axioms are contradictory).
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