TSTP Solution File: SWW209+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWW209+1 : TPTP v8.1.2. Released v5.2.0.
% 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 : n013.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 : Fri Sep 1 00:54:25 EDT 2023
% Result : Theorem 110.20s 14.50s
% Output : Proof 110.72s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SWW209+1 : TPTP v8.1.2. Released v5.2.0.
% 0.15/0.15 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.36 % Computer : n013.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sun Aug 27 17:35:47 EDT 2023
% 0.15/0.36 % CPUTime :
% 110.20/14.50 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 110.20/14.50
% 110.20/14.50 % SZS status Theorem
% 110.20/14.50
% 110.72/14.51 % SZS output start Proof
% 110.72/14.51 Take the following subset of the input axioms:
% 110.72/14.51 fof(conj_0, conjecture, ![B_m, B_n]: (c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m, B_n) => c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), B_m), hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), B_n)))).
% 110.72/14.51 fof(fact__096ALL_Am_An_O_Am_A_060_An_A_N_N_062_Af_Am_A_060_Af_An_096, axiom, ![B_m2, B_n2]: (c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m2, B_n2) => c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_f____, B_m2), hAPP(v_f____, B_n2)))).
% 110.72/14.51 fof(fact__096ALL_Am_An_O_Am_A_060_An_A_N_N_062_Ag_Am_A_060_Ag_An_096, axiom, ![B_m2, B_n2]: (c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m2, B_n2) => c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_ga____, B_m2), hAPP(v_ga____, B_n2)))).
% 110.72/14.51 fof(fact_o__apply, axiom, ![V_gb_2, V_fa_2, T_a, T_b, T_c, V_xa_2]: hAPP(hAPP(c_Fun_Ocomp(T_b, T_a, T_c, V_fa_2), V_gb_2), V_xa_2)=hAPP(V_fa_2, hAPP(V_gb_2, V_xa_2))).
% 110.72/14.51
% 110.72/14.51 Now clausify the problem and encode Horn clauses using encoding 3 of
% 110.72/14.51 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 110.72/14.51 We repeatedly replace C & s=t => u=v by the two clauses:
% 110.72/14.51 fresh(y, y, x1...xn) = u
% 110.72/14.51 C => fresh(s, t, x1...xn) = v
% 110.72/14.51 where fresh is a fresh function symbol and x1..xn are the free
% 110.72/14.51 variables of u and v.
% 110.72/14.51 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 110.72/14.51 input problem has no model of domain size 1).
% 110.72/14.51
% 110.72/14.51 The encoding turns the above axioms into the following unit equations and goals:
% 110.72/14.51
% 110.72/14.51 Axiom 1 (conj_0): c_Orderings_Oord__class_Oless(tc_Nat_Onat, b_m, b_n) = true2.
% 110.72/14.51 Axiom 2 (fact__096ALL_Am_An_O_Am_A_060_An_A_N_N_062_Af_Am_A_060_Af_An_096): fresh1128(X, X, Y, Z) = true2.
% 110.72/14.51 Axiom 3 (fact__096ALL_Am_An_O_Am_A_060_An_A_N_N_062_Ag_Am_A_060_Ag_An_096): fresh1127(X, X, Y, Z) = true2.
% 110.72/14.51 Axiom 4 (fact_o__apply): hAPP(hAPP(c_Fun_Ocomp(X, Y, Z, W), V), U) = hAPP(W, hAPP(V, U)).
% 110.72/14.51 Axiom 5 (fact__096ALL_Am_An_O_Am_A_060_An_A_N_N_062_Af_Am_A_060_Af_An_096): fresh1128(c_Orderings_Oord__class_Oless(tc_Nat_Onat, X, Y), true2, X, Y) = c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_f____, X), hAPP(v_f____, Y)).
% 110.72/14.51 Axiom 6 (fact__096ALL_Am_An_O_Am_A_060_An_A_N_N_062_Ag_Am_A_060_Ag_An_096): fresh1127(c_Orderings_Oord__class_Oless(tc_Nat_Onat, X, Y), true2, X, Y) = c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_ga____, X), hAPP(v_ga____, Y)).
% 110.72/14.51
% 110.72/14.51 Goal 1 (conj_0_1): c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), b_m), hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), b_n)) = true2.
% 110.72/14.51 Proof:
% 110.72/14.51 c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), b_m), hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), b_n))
% 110.72/14.51 = { by axiom 4 (fact_o__apply) }
% 110.72/14.51 c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), b_m), hAPP(v_f____, hAPP(v_ga____, b_n)))
% 110.72/14.51 = { by axiom 4 (fact_o__apply) }
% 110.72/14.51 c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_f____, hAPP(v_ga____, b_m)), hAPP(v_f____, hAPP(v_ga____, b_n)))
% 110.72/14.51 = { by axiom 5 (fact__096ALL_Am_An_O_Am_A_060_An_A_N_N_062_Af_Am_A_060_Af_An_096) R->L }
% 110.72/14.51 fresh1128(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_ga____, b_m), hAPP(v_ga____, b_n)), true2, hAPP(v_ga____, b_m), hAPP(v_ga____, b_n))
% 110.72/14.51 = { by axiom 6 (fact__096ALL_Am_An_O_Am_A_060_An_A_N_N_062_Ag_Am_A_060_Ag_An_096) R->L }
% 110.72/14.51 fresh1128(fresh1127(c_Orderings_Oord__class_Oless(tc_Nat_Onat, b_m, b_n), true2, b_m, b_n), true2, hAPP(v_ga____, b_m), hAPP(v_ga____, b_n))
% 110.72/14.51 = { by axiom 1 (conj_0) }
% 110.72/14.51 fresh1128(fresh1127(true2, true2, b_m, b_n), true2, hAPP(v_ga____, b_m), hAPP(v_ga____, b_n))
% 110.72/14.51 = { by axiom 3 (fact__096ALL_Am_An_O_Am_A_060_An_A_N_N_062_Ag_Am_A_060_Ag_An_096) }
% 110.72/14.51 fresh1128(true2, true2, hAPP(v_ga____, b_m), hAPP(v_ga____, b_n))
% 110.72/14.51 = { by axiom 2 (fact__096ALL_Am_An_O_Am_A_060_An_A_N_N_062_Af_Am_A_060_Af_An_096) }
% 110.72/14.51 true2
% 110.72/14.51 % SZS output end Proof
% 110.72/14.51
% 110.72/14.51 RESULT: Theorem (the conjecture is true).
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