TSTP Solution File: SET850-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SET850-1 : 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 : n011.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 56.62s 7.62s
% Output : Proof 56.62s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET850-1 : TPTP v8.1.2. Released v3.2.0.
% 0.08/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n011.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 12:55:54 EDT 2023
% 0.13/0.35 % CPUTime :
% 56.62/7.62 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 56.62/7.62
% 56.62/7.62 % SZS status Unsatisfiable
% 56.62/7.62
% 56.62/7.63 % SZS output start Proof
% 56.62/7.63 Take the following subset of the input axioms:
% 56.62/7.63 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))))).
% 56.62/7.63 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)))).
% 56.62/7.63 fof(cls_conjecture_0, negated_conjecture, c_lessequals(v_x, v_y, tc_set(tc_set(t_a)))).
% 56.62/7.63 fof(cls_conjecture_1, negated_conjecture, ~c_lessequals(v_x, c_Zorn_Osucc(v_S, v_y, t_a), tc_set(tc_set(t_a)))).
% 56.62/7.63
% 56.62/7.63 Now clausify the problem and encode Horn clauses using encoding 3 of
% 56.62/7.63 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 56.62/7.63 We repeatedly replace C & s=t => u=v by the two clauses:
% 56.62/7.63 fresh(y, y, x1...xn) = u
% 56.62/7.63 C => fresh(s, t, x1...xn) = v
% 56.62/7.63 where fresh is a fresh function symbol and x1..xn are the free
% 56.62/7.63 variables of u and v.
% 56.62/7.63 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 56.62/7.63 input problem has no model of domain size 1).
% 56.62/7.63
% 56.62/7.63 The encoding turns the above axioms into the following unit equations and goals:
% 56.62/7.63
% 56.62/7.63 Axiom 1 (cls_conjecture_0): c_lessequals(v_x, v_y, tc_set(tc_set(t_a))) = true2.
% 56.62/7.63 Axiom 2 (cls_Set_Osubset__trans_0): fresh984(X, X, Y, Z, W) = true2.
% 56.62/7.63 Axiom 3 (cls_Set_Osubset__trans_0): fresh985(X, X, Y, Z, W, V) = c_lessequals(V, Z, tc_set(W)).
% 56.62/7.63 Axiom 4 (cls_Zorn_OAbrial__axiom1_0): c_lessequals(X, c_Zorn_Osucc(Y, X, Z), tc_set(tc_set(Z))) = true2.
% 56.62/7.63 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).
% 56.62/7.63
% 56.62/7.63 Goal 1 (cls_conjecture_1): c_lessequals(v_x, c_Zorn_Osucc(v_S, v_y, t_a), tc_set(tc_set(t_a))) = true2.
% 56.62/7.63 Proof:
% 56.62/7.63 c_lessequals(v_x, c_Zorn_Osucc(v_S, v_y, t_a), tc_set(tc_set(t_a)))
% 56.62/7.63 = { by axiom 3 (cls_Set_Osubset__trans_0) R->L }
% 56.62/7.63 fresh985(true2, true2, v_y, c_Zorn_Osucc(v_S, v_y, t_a), tc_set(t_a), v_x)
% 56.62/7.63 = { by axiom 1 (cls_conjecture_0) R->L }
% 56.62/7.63 fresh985(c_lessequals(v_x, v_y, tc_set(tc_set(t_a))), true2, v_y, c_Zorn_Osucc(v_S, v_y, t_a), tc_set(t_a), v_x)
% 56.62/7.63 = { by axiom 5 (cls_Set_Osubset__trans_0) }
% 56.62/7.63 fresh984(c_lessequals(v_y, c_Zorn_Osucc(v_S, v_y, t_a), tc_set(tc_set(t_a))), true2, c_Zorn_Osucc(v_S, v_y, t_a), tc_set(t_a), v_x)
% 56.62/7.63 = { by axiom 4 (cls_Zorn_OAbrial__axiom1_0) }
% 56.62/7.63 fresh984(true2, true2, c_Zorn_Osucc(v_S, v_y, t_a), tc_set(t_a), v_x)
% 56.62/7.63 = { by axiom 2 (cls_Set_Osubset__trans_0) }
% 56.62/7.63 true2
% 56.62/7.63 % SZS output end Proof
% 56.62/7.63
% 56.62/7.63 RESULT: Unsatisfiable (the axioms are contradictory).
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