TSTP Solution File: SET855-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SET855-2 : 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 : n005.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 15:33:33 EDT 2023
% Result : Unsatisfiable 0.20s 0.37s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET855-2 : TPTP v8.1.2. Released v3.2.0.
% 0.10/0.13 % 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 : n005.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 11:52:38 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.37 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.20/0.37
% 0.20/0.37 % SZS status Unsatisfiable
% 0.20/0.37
% 0.20/0.37 % SZS output start Proof
% 0.20/0.37 Take the following subset of the input axioms:
% 0.20/0.37 fof(cls_Set_Osubset__antisym_0, axiom, ![V_B, V_A, T_a]: (~c_lessequals(V_B, V_A, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a)) | V_A=V_B))).
% 0.20/0.38 fof(cls_conjecture_2, negated_conjecture, c_lessequals(v_n, c_Union(v_Y, tc_set(t_a)), tc_set(tc_set(t_a)))).
% 0.20/0.38 fof(cls_conjecture_3, negated_conjecture, c_lessequals(c_Union(v_Y, tc_set(t_a)), v_n, tc_set(tc_set(t_a)))).
% 0.20/0.38 fof(cls_conjecture_4, negated_conjecture, v_n!=c_Union(v_Y, tc_set(t_a))).
% 0.20/0.38
% 0.20/0.38 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.38 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.38 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.38 fresh(y, y, x1...xn) = u
% 0.20/0.38 C => fresh(s, t, x1...xn) = v
% 0.20/0.38 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.38 variables of u and v.
% 0.20/0.38 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.38 input problem has no model of domain size 1).
% 0.20/0.38
% 0.20/0.38 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.38
% 0.20/0.38 Axiom 1 (cls_Set_Osubset__antisym_0): fresh2(X, X, Y, Z) = Y.
% 0.20/0.38 Axiom 2 (cls_Set_Osubset__antisym_0): fresh(X, X, Y, Z, W) = Z.
% 0.20/0.38 Axiom 3 (cls_conjecture_2): c_lessequals(v_n, c_Union(v_Y, tc_set(t_a)), tc_set(tc_set(t_a))) = true.
% 0.20/0.38 Axiom 4 (cls_conjecture_3): c_lessequals(c_Union(v_Y, tc_set(t_a)), v_n, tc_set(tc_set(t_a))) = true.
% 0.20/0.38 Axiom 5 (cls_Set_Osubset__antisym_0): fresh(c_lessequals(X, Y, tc_set(Z)), true, Y, X, Z) = fresh2(c_lessequals(Y, X, tc_set(Z)), true, Y, X).
% 0.20/0.38
% 0.20/0.38 Goal 1 (cls_conjecture_4): v_n = c_Union(v_Y, tc_set(t_a)).
% 0.20/0.38 Proof:
% 0.20/0.38 v_n
% 0.20/0.38 = { by axiom 2 (cls_Set_Osubset__antisym_0) R->L }
% 0.20/0.38 fresh(true, true, c_Union(v_Y, tc_set(t_a)), v_n, tc_set(t_a))
% 0.20/0.38 = { by axiom 3 (cls_conjecture_2) R->L }
% 0.20/0.38 fresh(c_lessequals(v_n, c_Union(v_Y, tc_set(t_a)), tc_set(tc_set(t_a))), true, c_Union(v_Y, tc_set(t_a)), v_n, tc_set(t_a))
% 0.20/0.38 = { by axiom 5 (cls_Set_Osubset__antisym_0) }
% 0.20/0.38 fresh2(c_lessequals(c_Union(v_Y, tc_set(t_a)), v_n, tc_set(tc_set(t_a))), true, c_Union(v_Y, tc_set(t_a)), v_n)
% 0.20/0.38 = { by axiom 4 (cls_conjecture_3) }
% 0.20/0.38 fresh2(true, true, c_Union(v_Y, tc_set(t_a)), v_n)
% 0.20/0.38 = { by axiom 1 (cls_Set_Osubset__antisym_0) }
% 0.20/0.38 c_Union(v_Y, tc_set(t_a))
% 0.20/0.38 % SZS output end Proof
% 0.20/0.38
% 0.20/0.38 RESULT: Unsatisfiable (the axioms are contradictory).
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