TSTP Solution File: SET844-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SET844-1 : 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 : n032.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 15:33:28 EDT 2023
% Result : Unsatisfiable 67.98s 9.16s
% Output : Proof 67.98s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SET844-1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.11 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.10/0.31 % Computer : n032.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Sat Aug 26 16:08:43 EDT 2023
% 0.10/0.31 % CPUTime :
% 67.98/9.16 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 67.98/9.16
% 67.98/9.16 % SZS status Unsatisfiable
% 67.98/9.16
% 67.98/9.17 % SZS output start Proof
% 67.98/9.17 Take the following subset of the input axioms:
% 67.98/9.17 fof(cls_Set_Osubset__refl_0, axiom, ![T_a, V_A]: c_lessequals(V_A, V_A, tc_set(T_a))).
% 67.98/9.17 fof(cls_Zorn_OTFin__UnionI_0, axiom, ![V_S, V_Y, T_a2]: (~c_lessequals(V_Y, c_Zorn_OTFin(V_S, T_a2), tc_set(tc_set(tc_set(T_a2)))) | c_in(c_Union(V_Y, tc_set(T_a2)), c_Zorn_OTFin(V_S, T_a2), tc_set(tc_set(T_a2))))).
% 67.98/9.17 fof(cls_Zorn_Oeq__succ__upper_0, axiom, ![V_m, V_n, T_a2, V_S2]: (~c_in(V_m, c_Zorn_OTFin(V_S2, T_a2), tc_set(tc_set(T_a2))) | (~c_in(V_n, c_Zorn_OTFin(V_S2, T_a2), tc_set(tc_set(T_a2))) | (V_m!=c_Zorn_Osucc(V_S2, V_m, T_a2) | c_lessequals(V_n, V_m, tc_set(tc_set(T_a2))))))).
% 67.98/9.17 fof(cls_conjecture_0, negated_conjecture, c_in(v_m, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))).
% 67.98/9.17 fof(cls_conjecture_1, negated_conjecture, v_m=c_Zorn_Osucc(v_S, v_m, t_a)).
% 67.98/9.17 fof(cls_conjecture_2, negated_conjecture, ~c_lessequals(c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), v_m, tc_set(tc_set(t_a)))).
% 67.98/9.17
% 67.98/9.17 Now clausify the problem and encode Horn clauses using encoding 3 of
% 67.98/9.17 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 67.98/9.17 We repeatedly replace C & s=t => u=v by the two clauses:
% 67.98/9.17 fresh(y, y, x1...xn) = u
% 67.98/9.17 C => fresh(s, t, x1...xn) = v
% 67.98/9.17 where fresh is a fresh function symbol and x1..xn are the free
% 67.98/9.17 variables of u and v.
% 67.98/9.17 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 67.98/9.17 input problem has no model of domain size 1).
% 67.98/9.17
% 67.98/9.17 The encoding turns the above axioms into the following unit equations and goals:
% 67.98/9.17
% 67.98/9.17 Axiom 1 (cls_conjecture_1): v_m = c_Zorn_Osucc(v_S, v_m, t_a).
% 67.98/9.17 Axiom 2 (cls_Set_Osubset__refl_0): c_lessequals(X, X, tc_set(Y)) = true2.
% 67.98/9.17 Axiom 3 (cls_Zorn_Oeq__succ__upper_0): fresh1152(X, X, Y, Z, W) = true2.
% 67.98/9.17 Axiom 4 (cls_Zorn_OTFin__UnionI_0): fresh970(X, X, Y, Z, W) = true2.
% 67.98/9.17 Axiom 5 (cls_Zorn_Oeq__succ__upper_0): fresh969(X, X, Y, Z, W, V) = c_lessequals(V, Y, tc_set(tc_set(W))).
% 67.98/9.17 Axiom 6 (cls_conjecture_0): c_in(v_m, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a))) = true2.
% 67.98/9.17 Axiom 7 (cls_Zorn_Oeq__succ__upper_0): fresh1151(X, X, Y, Z, W, V) = fresh1152(Y, c_Zorn_Osucc(Z, Y, W), Y, W, V).
% 67.98/9.17 Axiom 8 (cls_Zorn_OTFin__UnionI_0): fresh970(c_lessequals(X, c_Zorn_OTFin(Y, Z), tc_set(tc_set(tc_set(Z)))), true2, X, Y, Z) = c_in(c_Union(X, tc_set(Z)), c_Zorn_OTFin(Y, Z), tc_set(tc_set(Z))).
% 67.98/9.17 Axiom 9 (cls_Zorn_Oeq__succ__upper_0): fresh1151(c_in(X, c_Zorn_OTFin(Y, Z), tc_set(tc_set(Z))), true2, W, Y, Z, X) = fresh969(c_in(W, c_Zorn_OTFin(Y, Z), tc_set(tc_set(Z))), true2, W, Y, Z, X).
% 67.98/9.17
% 67.98/9.17 Goal 1 (cls_conjecture_2): c_lessequals(c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), v_m, tc_set(tc_set(t_a))) = true2.
% 67.98/9.17 Proof:
% 67.98/9.17 c_lessequals(c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), v_m, tc_set(tc_set(t_a)))
% 67.98/9.17 = { by axiom 5 (cls_Zorn_Oeq__succ__upper_0) R->L }
% 67.98/9.17 fresh969(true2, true2, v_m, v_S, t_a, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)))
% 67.98/9.17 = { by axiom 6 (cls_conjecture_0) R->L }
% 67.98/9.17 fresh969(c_in(v_m, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a))), true2, v_m, v_S, t_a, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)))
% 67.98/9.17 = { by axiom 9 (cls_Zorn_Oeq__succ__upper_0) R->L }
% 67.98/9.17 fresh1151(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))), true2, v_m, v_S, t_a, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)))
% 67.98/9.17 = { by axiom 8 (cls_Zorn_OTFin__UnionI_0) R->L }
% 67.98/9.17 fresh1151(fresh970(c_lessequals(c_Zorn_OTFin(v_S, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(tc_set(t_a)))), true2, c_Zorn_OTFin(v_S, t_a), v_S, t_a), true2, v_m, v_S, t_a, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)))
% 67.98/9.17 = { by axiom 2 (cls_Set_Osubset__refl_0) }
% 67.98/9.17 fresh1151(fresh970(true2, true2, c_Zorn_OTFin(v_S, t_a), v_S, t_a), true2, v_m, v_S, t_a, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)))
% 67.98/9.17 = { by axiom 4 (cls_Zorn_OTFin__UnionI_0) }
% 67.98/9.17 fresh1151(true2, true2, v_m, v_S, t_a, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)))
% 67.98/9.17 = { by axiom 7 (cls_Zorn_Oeq__succ__upper_0) }
% 67.98/9.17 fresh1152(v_m, c_Zorn_Osucc(v_S, v_m, t_a), v_m, t_a, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)))
% 67.98/9.17 = { by axiom 1 (cls_conjecture_1) R->L }
% 67.98/9.17 fresh1152(v_m, v_m, v_m, t_a, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)))
% 67.98/9.17 = { by axiom 3 (cls_Zorn_Oeq__succ__upper_0) }
% 67.98/9.17 true2
% 67.98/9.17 % SZS output end Proof
% 67.98/9.17
% 67.98/9.17 RESULT: Unsatisfiable (the axioms are contradictory).
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