TSTP Solution File: SET859-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SET859-1 : 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 : n028.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 15:33:34 EDT 2023
% Result : Unsatisfiable 91.85s 12.19s
% Output : Proof 91.85s
% 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 : SET859-1 : 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 : n028.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 16:48:22 EDT 2023
% 0.13/0.34 % CPUTime :
% 91.85/12.19 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 91.85/12.19
% 91.85/12.19 % SZS status Unsatisfiable
% 91.85/12.19
% 91.85/12.19 % SZS output start Proof
% 91.85/12.19 Take the following subset of the input axioms:
% 91.85/12.20 fof(cls_Set_Osubset__trans_0, axiom, ![T_a, V_A, V_B, V_C]: (~c_lessequals(V_B, V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a)) | c_lessequals(V_A, V_C, tc_set(T_a))))).
% 91.85/12.20 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)))).
% 91.85/12.20 fof(cls_conjecture_2, negated_conjecture, c_lessequals(c_Zorn_Osucc(v_S, v_n, t_a), v_m, tc_set(tc_set(t_a)))).
% 91.85/12.20 fof(cls_conjecture_3, negated_conjecture, ~c_lessequals(v_n, v_m, tc_set(tc_set(t_a)))).
% 91.85/12.20
% 91.85/12.20 Now clausify the problem and encode Horn clauses using encoding 3 of
% 91.85/12.20 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 91.85/12.20 We repeatedly replace C & s=t => u=v by the two clauses:
% 91.85/12.20 fresh(y, y, x1...xn) = u
% 91.85/12.20 C => fresh(s, t, x1...xn) = v
% 91.85/12.20 where fresh is a fresh function symbol and x1..xn are the free
% 91.85/12.20 variables of u and v.
% 91.85/12.20 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 91.85/12.20 input problem has no model of domain size 1).
% 91.85/12.20
% 91.85/12.20 The encoding turns the above axioms into the following unit equations and goals:
% 91.85/12.20
% 91.85/12.20 Axiom 1 (cls_Set_Osubset__trans_0): fresh984(X, X, Y, Z, W) = true2.
% 91.85/12.20 Axiom 2 (cls_Set_Osubset__trans_0): fresh985(X, X, Y, Z, W, V) = c_lessequals(V, Z, tc_set(W)).
% 91.85/12.20 Axiom 3 (cls_Zorn_OAbrial__axiom1_0): c_lessequals(X, c_Zorn_Osucc(Y, X, Z), tc_set(tc_set(Z))) = true2.
% 91.85/12.20 Axiom 4 (cls_conjecture_2): c_lessequals(c_Zorn_Osucc(v_S, v_n, t_a), v_m, tc_set(tc_set(t_a))) = true2.
% 91.85/12.20 Axiom 5 (cls_Set_Osubset__trans_0): fresh985(c_lessequals(X, Y, tc_set(Z)), true2, Y, W, Z, X) = fresh984(c_lessequals(Y, W, tc_set(Z)), true2, W, Z, X).
% 91.85/12.20
% 91.85/12.20 Goal 1 (cls_conjecture_3): c_lessequals(v_n, v_m, tc_set(tc_set(t_a))) = true2.
% 91.85/12.20 Proof:
% 91.85/12.20 c_lessequals(v_n, v_m, tc_set(tc_set(t_a)))
% 91.85/12.20 = { by axiom 2 (cls_Set_Osubset__trans_0) R->L }
% 91.85/12.20 fresh985(true2, true2, c_Zorn_Osucc(v_S, v_n, t_a), v_m, tc_set(t_a), v_n)
% 91.85/12.20 = { by axiom 3 (cls_Zorn_OAbrial__axiom1_0) R->L }
% 91.85/12.20 fresh985(c_lessequals(v_n, c_Zorn_Osucc(v_S, v_n, t_a), tc_set(tc_set(t_a))), true2, c_Zorn_Osucc(v_S, v_n, t_a), v_m, tc_set(t_a), v_n)
% 91.85/12.20 = { by axiom 5 (cls_Set_Osubset__trans_0) }
% 91.85/12.20 fresh984(c_lessequals(c_Zorn_Osucc(v_S, v_n, t_a), v_m, tc_set(tc_set(t_a))), true2, v_m, tc_set(t_a), v_n)
% 91.85/12.20 = { by axiom 4 (cls_conjecture_2) }
% 91.85/12.20 fresh984(true2, true2, v_m, tc_set(t_a), v_n)
% 91.85/12.20 = { by axiom 1 (cls_Set_Osubset__trans_0) }
% 91.85/12.20 true2
% 91.85/12.20 % SZS output end Proof
% 91.85/12.20
% 91.85/12.20 RESULT: Unsatisfiable (the axioms are contradictory).
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