TSTP Solution File: SET845-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SET845-2 : 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 : n023.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 0.15s 0.34s
% Output : Proof 0.15s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : SET845-2 : TPTP v8.1.2. Released v3.2.0.
% 0.02/0.11 % 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 : n023.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 16:24:56 EDT 2023
% 0.10/0.31 % CPUTime :
% 0.15/0.34 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.15/0.34
% 0.15/0.34 % SZS status Unsatisfiable
% 0.15/0.34
% 0.15/0.35 % SZS output start Proof
% 0.15/0.35 Take the following subset of the input axioms:
% 0.15/0.35 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)))).
% 0.15/0.35 fof(cls_Set_Osubset__antisym_0, axiom, ![T_a2, V_B2, V_A2]: (~c_lessequals(V_B2, V_A2, tc_set(T_a2)) | (~c_lessequals(V_A2, V_B2, tc_set(T_a2)) | V_A2=V_B2))).
% 0.15/0.35 fof(cls_Zorn_OAbrial__axiom1_0, axiom, ![V_x, V_S, T_a2]: c_lessequals(V_x, c_Zorn_Osucc(V_S, V_x, T_a2), tc_set(tc_set(T_a2)))).
% 0.15/0.35 fof(cls_Zorn_OTFin_OsuccI_0, axiom, ![T_a2, V_x2, V_S2]: (~c_in(V_x2, c_Zorn_OTFin(V_S2, T_a2), tc_set(tc_set(T_a2))) | c_in(c_Zorn_Osucc(V_S2, V_x2, T_a2), c_Zorn_OTFin(V_S2, T_a2), tc_set(tc_set(T_a2))))).
% 0.15/0.35 fof(cls_conjecture_0, negated_conjecture, c_in(v_m, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))).
% 0.15/0.35 fof(cls_conjecture_1, negated_conjecture, v_m=c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a))).
% 0.15/0.35 fof(cls_conjecture_2, negated_conjecture, v_m!=c_Zorn_Osucc(v_S, v_m, t_a)).
% 0.15/0.35
% 0.15/0.35 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.15/0.35 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.15/0.35 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.15/0.35 fresh(y, y, x1...xn) = u
% 0.15/0.35 C => fresh(s, t, x1...xn) = v
% 0.15/0.35 where fresh is a fresh function symbol and x1..xn are the free
% 0.15/0.35 variables of u and v.
% 0.15/0.35 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.15/0.35 input problem has no model of domain size 1).
% 0.15/0.35
% 0.15/0.35 The encoding turns the above axioms into the following unit equations and goals:
% 0.15/0.35
% 0.15/0.35 Axiom 1 (cls_Set_Osubset__antisym_0): fresh(X, X, Y, Z) = Y.
% 0.15/0.35 Axiom 2 (cls_conjecture_1): v_m = c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)).
% 0.15/0.35 Axiom 3 (cls_Zorn_OTFin_OsuccI_0): fresh4(X, X, Y, Z, W) = true.
% 0.15/0.35 Axiom 4 (cls_Set_OUnion__upper_0): fresh3(X, X, Y, Z, W) = true.
% 0.15/0.35 Axiom 5 (cls_Set_Osubset__antisym_0): fresh2(X, X, Y, Z, W) = Z.
% 0.15/0.35 Axiom 6 (cls_conjecture_0): c_in(v_m, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a))) = true.
% 0.15/0.35 Axiom 7 (cls_Zorn_OAbrial__axiom1_0): c_lessequals(X, c_Zorn_Osucc(Y, X, Z), tc_set(tc_set(Z))) = true.
% 0.15/0.35 Axiom 8 (cls_Set_OUnion__upper_0): fresh3(c_in(X, Y, tc_set(Z)), true, X, Y, Z) = c_lessequals(X, c_Union(Y, Z), tc_set(Z)).
% 0.15/0.35 Axiom 9 (cls_Set_Osubset__antisym_0): fresh2(c_lessequals(X, Y, tc_set(Z)), true, Y, X, Z) = fresh(c_lessequals(Y, X, tc_set(Z)), true, Y, X).
% 0.15/0.35 Axiom 10 (cls_Zorn_OTFin_OsuccI_0): fresh4(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))).
% 0.15/0.35
% 0.15/0.35 Goal 1 (cls_conjecture_2): v_m = c_Zorn_Osucc(v_S, v_m, t_a).
% 0.15/0.35 Proof:
% 0.15/0.35 v_m
% 0.15/0.35 = { by axiom 1 (cls_Set_Osubset__antisym_0) R->L }
% 0.15/0.35 fresh(true, true, v_m, c_Zorn_Osucc(v_S, v_m, t_a))
% 0.15/0.35 = { by axiom 7 (cls_Zorn_OAbrial__axiom1_0) R->L }
% 0.15/0.35 fresh(c_lessequals(v_m, c_Zorn_Osucc(v_S, v_m, t_a), tc_set(tc_set(t_a))), true, v_m, c_Zorn_Osucc(v_S, v_m, t_a))
% 0.15/0.35 = { by axiom 9 (cls_Set_Osubset__antisym_0) R->L }
% 0.15/0.35 fresh2(c_lessequals(c_Zorn_Osucc(v_S, v_m, t_a), v_m, tc_set(tc_set(t_a))), true, v_m, c_Zorn_Osucc(v_S, v_m, t_a), tc_set(t_a))
% 0.15/0.35 = { by axiom 2 (cls_conjecture_1) }
% 0.15/0.35 fresh2(c_lessequals(c_Zorn_Osucc(v_S, v_m, t_a), c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), tc_set(tc_set(t_a))), true, v_m, c_Zorn_Osucc(v_S, v_m, t_a), tc_set(t_a))
% 0.15/0.35 = { by axiom 8 (cls_Set_OUnion__upper_0) R->L }
% 0.15/0.35 fresh2(fresh3(c_in(c_Zorn_Osucc(v_S, v_m, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a))), true, c_Zorn_Osucc(v_S, v_m, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), true, v_m, c_Zorn_Osucc(v_S, v_m, t_a), tc_set(t_a))
% 0.15/0.35 = { by axiom 10 (cls_Zorn_OTFin_OsuccI_0) R->L }
% 0.15/0.35 fresh2(fresh3(fresh4(c_in(v_m, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a))), true, v_m, v_S, t_a), true, c_Zorn_Osucc(v_S, v_m, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), true, v_m, c_Zorn_Osucc(v_S, v_m, t_a), tc_set(t_a))
% 0.15/0.35 = { by axiom 6 (cls_conjecture_0) }
% 0.15/0.35 fresh2(fresh3(fresh4(true, true, v_m, v_S, t_a), true, c_Zorn_Osucc(v_S, v_m, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), true, v_m, c_Zorn_Osucc(v_S, v_m, t_a), tc_set(t_a))
% 0.15/0.35 = { by axiom 3 (cls_Zorn_OTFin_OsuccI_0) }
% 0.15/0.35 fresh2(fresh3(true, true, c_Zorn_Osucc(v_S, v_m, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), true, v_m, c_Zorn_Osucc(v_S, v_m, t_a), tc_set(t_a))
% 0.15/0.35 = { by axiom 4 (cls_Set_OUnion__upper_0) }
% 0.15/0.35 fresh2(true, true, v_m, c_Zorn_Osucc(v_S, v_m, t_a), tc_set(t_a))
% 0.15/0.35 = { by axiom 5 (cls_Set_Osubset__antisym_0) }
% 0.15/0.35 c_Zorn_Osucc(v_S, v_m, t_a)
% 0.15/0.35 % SZS output end Proof
% 0.15/0.35
% 0.15/0.35 RESULT: Unsatisfiable (the axioms are contradictory).
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