TSTP Solution File: SWW275+1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWW275+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 : n020.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 00:54:34 EDT 2023
% Result : Theorem 196.32s 25.55s
% Output : Proof 196.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW275+1 : TPTP v8.1.2. Released v5.2.0.
% 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 : n020.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 18:26:44 EDT 2023
% 0.13/0.35 % CPUTime :
% 196.32/25.55 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 196.32/25.55
% 196.32/25.55 % SZS status Theorem
% 196.32/25.55
% 196.32/25.55 % SZS output start Proof
% 196.32/25.55 Take the following subset of the input axioms:
% 196.32/25.55 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__1, axiom, class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)).
% 196.32/25.55 fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__1, axiom, ![T_1]: (class_Rings_Ocomm__semiring__1(T_1) => class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1)))).
% 196.32/25.55 fof(conj_0, conjecture, (v_r____=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) & c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), v_na____)) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))), v_na____)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))), c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____))), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_na____, c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____))))).
% 196.32/25.55 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J, axiom, ![T_a, V_x, V_p, V_q]: (class_Rings_Ocomm__semiring__1(T_a) => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), V_p)), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), V_q))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_p, V_q)))).
% 196.32/25.55 fof(fact_le__add__diff__inverse2, axiom, ![V_n, V_m]: (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_n, V_m) => c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_m, V_n), V_n)=V_m)).
% 196.32/25.55 fof(fact_nat__add__commute, axiom, ![V_n2, V_m2]: c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_m2, V_n2)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_n2, V_m2)).
% 196.32/25.55 fof(fact_oop, axiom, ![V_a]: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Oorder(tc_Complex_Ocomplex, V_a, v_pa____), v_na____)).
% 196.32/25.55
% 196.32/25.55 Now clausify the problem and encode Horn clauses using encoding 3 of
% 196.32/25.55 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 196.32/25.55 We repeatedly replace C & s=t => u=v by the two clauses:
% 196.32/25.55 fresh(y, y, x1...xn) = u
% 196.32/25.55 C => fresh(s, t, x1...xn) = v
% 196.32/25.55 where fresh is a fresh function symbol and x1..xn are the free
% 196.32/25.55 variables of u and v.
% 196.32/25.55 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 196.32/25.55 input problem has no model of domain size 1).
% 196.32/25.55
% 196.32/25.55 The encoding turns the above axioms into the following unit equations and goals:
% 196.32/25.55
% 196.32/25.55 Axiom 1 (arity_Complex__Ocomplex__Rings_Ocomm__semiring__1): class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) = true2.
% 196.32/25.55 Axiom 2 (fact_nat__add__commute): c_Groups_Oplus__class_Oplus(tc_Nat_Onat, X, Y) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, Y, X).
% 196.32/25.55 Axiom 3 (arity_Polynomial__Opoly__Rings_Ocomm__semiring__1): fresh1163(X, X, Y) = true2.
% 196.32/25.55 Axiom 4 (arity_Polynomial__Opoly__Rings_Ocomm__semiring__1): fresh1163(class_Rings_Ocomm__semiring__1(X), true2, X) = class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X)).
% 196.32/25.55 Axiom 5 (fact_le__add__diff__inverse2): fresh20(X, X, Y, Z) = Y.
% 196.32/25.55 Axiom 6 (fact_oop): c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Oorder(tc_Complex_Ocomplex, X, v_pa____), v_na____) = true2.
% 196.32/25.55 Axiom 7 (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J): fresh988(X, X, Y, Z, W, V) = hAPP(hAPP(c_Power_Opower__class_Opower(V), W), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, Z, Y)).
% 196.32/25.55 Axiom 8 (fact_le__add__diff__inverse2): fresh20(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, X, Y), true2, Y, X) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, Y, X), X).
% 196.32/25.55 Axiom 9 (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J): fresh988(class_Rings_Ocomm__semiring__1(X), true2, Y, Z, W, X) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X), hAPP(hAPP(c_Power_Opower__class_Opower(X), W), Z)), hAPP(hAPP(c_Power_Opower__class_Opower(X), W), Y)).
% 196.32/25.55
% 196.32/25.55 Goal 1 (conj_0): hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))), v_na____) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))), c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____))), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_na____, c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____)))).
% 196.32/25.55 Proof:
% 196.32/25.55 hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))), v_na____)
% 196.32/25.56 = { by axiom 5 (fact_le__add__diff__inverse2) R->L }
% 196.32/25.56 hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))), fresh20(true2, true2, v_na____, c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____)))
% 196.32/25.56 = { by axiom 6 (fact_oop) R->L }
% 196.32/25.56 hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))), fresh20(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____), v_na____), true2, v_na____, c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____)))
% 196.32/25.56 = { by axiom 8 (fact_le__add__diff__inverse2) }
% 196.32/25.56 hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_na____, c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____)), c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____)))
% 196.32/25.56 = { by axiom 2 (fact_nat__add__commute) }
% 196.32/25.56 hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_na____, c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____))))
% 196.32/25.56 = { by axiom 7 (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) R->L }
% 196.32/25.56 fresh988(true2, true2, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_na____, c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____)), c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), tc_Polynomial_Opoly(tc_Complex_Ocomplex))
% 196.32/25.56 = { by axiom 3 (arity_Polynomial__Opoly__Rings_Ocomm__semiring__1) R->L }
% 196.32/25.56 fresh988(fresh1163(true2, true2, tc_Complex_Ocomplex), true2, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_na____, c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____)), c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), tc_Polynomial_Opoly(tc_Complex_Ocomplex))
% 196.32/25.56 = { by axiom 1 (arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) R->L }
% 196.32/25.56 fresh988(fresh1163(class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex), true2, tc_Complex_Ocomplex), true2, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_na____, c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____)), c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), tc_Polynomial_Opoly(tc_Complex_Ocomplex))
% 196.32/25.56 = { by axiom 4 (arity_Polynomial__Opoly__Rings_Ocomm__semiring__1) }
% 196.32/25.56 fresh988(class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), true2, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_na____, c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____)), c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), tc_Polynomial_Opoly(tc_Complex_Ocomplex))
% 196.32/25.56 = { by axiom 9 (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) }
% 196.32/25.56 hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))), c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____))), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_na____, c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____))))
% 196.32/25.56 % SZS output end Proof
% 196.32/25.56
% 196.32/25.56 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------