TSTP Solution File: SET855-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SET855-1 : 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 : n002.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 15:33:32 EDT 2023
% Result : Unsatisfiable 41.20s 5.66s
% Output : Proof 41.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET855-1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.14 % 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 : n002.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 12:50:33 EDT 2023
% 0.14/0.35 % CPUTime :
% 41.20/5.66 Command-line arguments: --no-flatten-goal
% 41.20/5.66
% 41.20/5.66 % SZS status Unsatisfiable
% 41.20/5.66
% 41.20/5.66 % SZS output start Proof
% 41.20/5.66 Take the following subset of the input axioms:
% 41.20/5.66 fof(cls_Set_Osubset__antisym_0, axiom, ![T_a, V_A, V_B]: (~c_lessequals(V_B, V_A, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a)) | V_A=V_B))).
% 41.20/5.66 fof(cls_conjecture_2, negated_conjecture, c_lessequals(v_n, c_Union(v_Y, tc_set(t_a)), tc_set(tc_set(t_a)))).
% 41.20/5.66 fof(cls_conjecture_3, negated_conjecture, c_lessequals(c_Union(v_Y, tc_set(t_a)), v_n, tc_set(tc_set(t_a)))).
% 41.20/5.66 fof(cls_conjecture_4, negated_conjecture, v_n!=c_Union(v_Y, tc_set(t_a))).
% 41.20/5.66
% 41.20/5.66 Now clausify the problem and encode Horn clauses using encoding 3 of
% 41.20/5.66 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 41.20/5.66 We repeatedly replace C & s=t => u=v by the two clauses:
% 41.20/5.66 fresh(y, y, x1...xn) = u
% 41.20/5.66 C => fresh(s, t, x1...xn) = v
% 41.20/5.66 where fresh is a fresh function symbol and x1..xn are the free
% 41.20/5.66 variables of u and v.
% 41.20/5.66 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 41.20/5.66 input problem has no model of domain size 1).
% 41.20/5.66
% 41.20/5.66 The encoding turns the above axioms into the following unit equations and goals:
% 41.20/5.66
% 41.20/5.66 Axiom 1 (cls_Set_Osubset__antisym_0): fresh30(X, X, Y, Z) = Y.
% 41.20/5.66 Axiom 2 (cls_Set_Osubset__antisym_0): fresh31(X, X, Y, Z, W) = Z.
% 41.20/5.66 Axiom 3 (cls_conjecture_2): c_lessequals(v_n, c_Union(v_Y, tc_set(t_a)), tc_set(tc_set(t_a))) = true2.
% 41.20/5.66 Axiom 4 (cls_conjecture_3): c_lessequals(c_Union(v_Y, tc_set(t_a)), v_n, tc_set(tc_set(t_a))) = true2.
% 41.20/5.66 Axiom 5 (cls_Set_Osubset__antisym_0): fresh31(c_lessequals(X, Y, tc_set(Z)), true2, Y, X, Z) = fresh30(c_lessequals(Y, X, tc_set(Z)), true2, Y, X).
% 41.20/5.66
% 41.20/5.66 Goal 1 (cls_conjecture_4): v_n = c_Union(v_Y, tc_set(t_a)).
% 41.20/5.66 Proof:
% 41.20/5.66 v_n
% 41.20/5.66 = { by axiom 2 (cls_Set_Osubset__antisym_0) R->L }
% 41.20/5.66 fresh31(true2, true2, c_Union(v_Y, tc_set(t_a)), v_n, tc_set(t_a))
% 41.20/5.66 = { by axiom 3 (cls_conjecture_2) R->L }
% 41.20/5.66 fresh31(c_lessequals(v_n, c_Union(v_Y, tc_set(t_a)), tc_set(tc_set(t_a))), true2, c_Union(v_Y, tc_set(t_a)), v_n, tc_set(t_a))
% 41.20/5.66 = { by axiom 5 (cls_Set_Osubset__antisym_0) }
% 41.20/5.66 fresh30(c_lessequals(c_Union(v_Y, tc_set(t_a)), v_n, tc_set(tc_set(t_a))), true2, c_Union(v_Y, tc_set(t_a)), v_n)
% 41.20/5.66 = { by axiom 4 (cls_conjecture_3) }
% 41.20/5.66 fresh30(true2, true2, c_Union(v_Y, tc_set(t_a)), v_n)
% 41.20/5.66 = { by axiom 1 (cls_Set_Osubset__antisym_0) }
% 41.20/5.66 c_Union(v_Y, tc_set(t_a))
% 41.20/5.66 % SZS output end Proof
% 41.20/5.66
% 41.20/5.66 RESULT: Unsatisfiable (the axioms are contradictory).
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