TSTP Solution File: SET849-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SET849-2 : 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 : n025.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 15:33:31 EDT 2023
% Result : Unsatisfiable 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET849-2 : 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
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 12:53:22 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.38 Command-line arguments: --no-flatten-goal
% 0.19/0.38
% 0.19/0.38 % SZS status Unsatisfiable
% 0.19/0.38
% 0.19/0.38 % SZS output start Proof
% 0.19/0.38 Take the following subset of the input axioms:
% 0.19/0.39 fof(cls_Set_Osubset__refl_0, axiom, ![V_A, T_a]: c_lessequals(V_A, V_A, tc_set(T_a))).
% 0.19/0.39 fof(cls_Zorn_OTFin__UnionI_0, axiom, ![V_Y, V_S, 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))))).
% 0.19/0.39 fof(cls_Zorn_Oequal__succ__Union_1, axiom, ![T_a2, V_S2]: (~c_in(c_Union(c_Zorn_OTFin(V_S2, T_a2), tc_set(T_a2)), c_Zorn_OTFin(V_S2, T_a2), tc_set(tc_set(T_a2))) | c_Union(c_Zorn_OTFin(V_S2, T_a2), tc_set(T_a2))=c_Zorn_Osucc(V_S2, c_Union(c_Zorn_OTFin(V_S2, T_a2), tc_set(T_a2)), T_a2))).
% 0.19/0.39 fof(cls_conjecture_1, negated_conjecture, 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))).
% 0.19/0.39
% 0.19/0.39 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.39 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.39 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.39 fresh(y, y, x1...xn) = u
% 0.19/0.39 C => fresh(s, t, x1...xn) = v
% 0.19/0.39 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.39 variables of u and v.
% 0.19/0.39 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.39 input problem has no model of domain size 1).
% 0.19/0.39
% 0.19/0.39 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.39
% 0.19/0.39 Axiom 1 (cls_Set_Osubset__refl_0): c_lessequals(X, X, tc_set(Y)) = true.
% 0.19/0.39 Axiom 2 (cls_Zorn_OTFin__UnionI_0): fresh(X, X, Y, Z, W) = true.
% 0.19/0.39 Axiom 3 (cls_Zorn_Oequal__succ__Union_1): fresh2(X, X, Y, Z) = c_Union(c_Zorn_OTFin(Y, Z), tc_set(Z)).
% 0.19/0.39 Axiom 4 (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))).
% 0.19/0.39 Axiom 5 (cls_Zorn_Oequal__succ__Union_1): fresh2(c_in(c_Union(c_Zorn_OTFin(X, Y), tc_set(Y)), c_Zorn_OTFin(X, Y), tc_set(tc_set(Y))), true, X, Y) = c_Zorn_Osucc(X, c_Union(c_Zorn_OTFin(X, Y), tc_set(Y)), Y).
% 0.19/0.39
% 0.19/0.39 Goal 1 (cls_conjecture_1): 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)).
% 0.19/0.39 Proof:
% 0.19/0.39 c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a)
% 0.19/0.39 = { by axiom 5 (cls_Zorn_Oequal__succ__Union_1) R->L }
% 0.19/0.39 fresh2(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, v_S, t_a)
% 0.19/0.39 = { by axiom 4 (cls_Zorn_OTFin__UnionI_0) R->L }
% 0.19/0.39 fresh2(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, v_S, t_a)
% 0.19/0.39 = { by axiom 1 (cls_Set_Osubset__refl_0) }
% 0.19/0.39 fresh2(fresh(true, true, c_Zorn_OTFin(v_S, t_a), v_S, t_a), true, v_S, t_a)
% 0.19/0.39 = { by axiom 2 (cls_Zorn_OTFin__UnionI_0) }
% 0.19/0.39 fresh2(true, true, v_S, t_a)
% 0.19/0.39 = { by axiom 3 (cls_Zorn_Oequal__succ__Union_1) }
% 0.19/0.39 c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a))
% 0.19/0.39 % SZS output end Proof
% 0.19/0.39
% 0.19/0.39 RESULT: Unsatisfiable (the axioms are contradictory).
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