TSTP Solution File: SWW225+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWW225+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 : n025.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 00:54:27 EDT 2023
% Result : Theorem 108.73s 14.36s
% Output : Proof 108.73s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWW225+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n025.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 : Sun Aug 27 19:20:09 EDT 2023
% 0.13/0.34 % CPUTime :
% 108.73/14.36 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 108.73/14.36
% 108.73/14.36 % SZS status Theorem
% 108.73/14.36
% 108.73/14.37 % SZS output start Proof
% 108.73/14.37 Take the following subset of the input axioms:
% 108.73/14.37 fof(conj_0, conjecture, c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____))), hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_Nat_OSuc(hAPP(v_f____, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____)))))).
% 108.73/14.37 fof(fact_Suc__le__mono, axiom, ![V_m_2, V_n_2]: (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(V_n_2), c_Nat_OSuc(V_m_2)) <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_n_2, V_m_2))).
% 108.73/14.38 fof(fact__096N1_A_L_AN2_A_060_061_Af_A_IN1_A_L_AN2_J_096, axiom, c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____), hAPP(v_f____, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____)))).
% 108.73/14.38 fof(fact_real__of__nat__le__iff, axiom, ![V_m_2_2, V_n_2_2]: (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), V_n_2_2), hAPP(c_RealDef_Oreal(tc_Nat_Onat), V_m_2_2)) <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_n_2_2, V_m_2_2))).
% 108.73/14.38
% 108.73/14.38 Now clausify the problem and encode Horn clauses using encoding 3 of
% 108.73/14.38 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 108.73/14.38 We repeatedly replace C & s=t => u=v by the two clauses:
% 108.73/14.38 fresh(y, y, x1...xn) = u
% 108.73/14.38 C => fresh(s, t, x1...xn) = v
% 108.73/14.38 where fresh is a fresh function symbol and x1..xn are the free
% 108.73/14.38 variables of u and v.
% 108.73/14.38 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 108.73/14.38 input problem has no model of domain size 1).
% 108.73/14.38
% 108.73/14.38 The encoding turns the above axioms into the following unit equations and goals:
% 108.73/14.38
% 108.73/14.38 Axiom 1 (fact_Suc__le__mono): fresh1006(X, X, Y, Z) = true2.
% 108.73/14.38 Axiom 2 (fact_real__of__nat__le__iff): fresh286(X, X, Y, Z) = true2.
% 108.73/14.38 Axiom 3 (fact_Suc__le__mono): fresh1006(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, X, Y), true2, Y, X) = c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(X), c_Nat_OSuc(Y)).
% 108.73/14.38 Axiom 4 (fact_real__of__nat__le__iff): fresh286(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, X, Y), true2, Y, X) = c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), X), hAPP(c_RealDef_Oreal(tc_Nat_Onat), Y)).
% 108.73/14.38 Axiom 5 (fact__096N1_A_L_AN2_A_060_061_Af_A_IN1_A_L_AN2_J_096): c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____), hAPP(v_f____, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____))) = true2.
% 108.73/14.38
% 108.73/14.38 Goal 1 (conj_0): c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____))), hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_Nat_OSuc(hAPP(v_f____, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____))))) = true2.
% 108.73/14.39 Proof:
% 108.73/14.39 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____))), hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_Nat_OSuc(hAPP(v_f____, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____)))))
% 108.73/14.39 = { by axiom 4 (fact_real__of__nat__le__iff) R->L }
% 108.73/14.39 fresh286(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____)), c_Nat_OSuc(hAPP(v_f____, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____)))), true2, c_Nat_OSuc(hAPP(v_f____, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____))), c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____)))
% 108.73/14.39 = { by axiom 3 (fact_Suc__le__mono) R->L }
% 108.73/14.39 fresh286(fresh1006(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____), hAPP(v_f____, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____))), true2, hAPP(v_f____, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____)), true2, c_Nat_OSuc(hAPP(v_f____, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____))), c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____)))
% 108.73/14.39 = { by axiom 5 (fact__096N1_A_L_AN2_A_060_061_Af_A_IN1_A_L_AN2_J_096) }
% 108.73/14.39 fresh286(fresh1006(true2, true2, hAPP(v_f____, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____)), true2, c_Nat_OSuc(hAPP(v_f____, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____))), c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____)))
% 108.73/14.39 = { by axiom 1 (fact_Suc__le__mono) }
% 108.73/14.39 fresh286(true2, true2, c_Nat_OSuc(hAPP(v_f____, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____))), c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____)))
% 108.73/14.39 = { by axiom 2 (fact_real__of__nat__le__iff) }
% 108.73/14.39 true2
% 108.73/14.39 % SZS output end Proof
% 108.73/14.39
% 108.73/14.39 RESULT: Theorem (the conjecture is true).
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