TSTP Solution File: SWW182+1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWW182+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 : 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 : Fri Sep 1 00:54:21 EDT 2023
% Result : Timeout 294.25s 38.01s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWW182+1 : TPTP v8.1.2. Released v5.2.0.
% 0.11/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n011.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Aug 27 21:24:40 EDT 2023
% 0.12/0.34 % CPUTime :
% 294.25/38.01 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 294.25/38.01
% 294.25/38.01 % SZS status Theorem
% 294.25/38.01
% 294.25/38.02 % SZS output start Proof
% 294.25/38.02 Take the following subset of the input axioms:
% 294.25/38.02 fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__0, axiom, ![T_1]: (class_Rings_Ocomm__semiring__0(T_1) => class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(T_1)))).
% 294.25/38.02 fof(clrel_Rings_Ocomm__semiring__0__Groups_Ocomm__monoid__add, axiom, ![T]: (class_Rings_Ocomm__semiring__0(T) => class_Groups_Ocomm__monoid__add(T))).
% 294.25/38.02 fof(conj_0, conjecture, c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a, c_Polynomial_OpCons(t_a, v_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))), v_h)=c_Polynomial_OpCons(t_a, v_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))).
% 294.25/38.02 fof(fact_add__0, axiom, ![T_a, V_a]: (class_Groups_Ocomm__monoid__add(T_a) => c_Groups_Oplus__class_Oplus(T_a, c_Groups_Ozero__class_Ozero(T_a), V_a)=V_a)).
% 294.25/38.02 fof(fact_offset__poly__0, axiom, ![V_h, T_a2]: (class_Rings_Ocomm__semiring__0(T_a2) => c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a2, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a2)), V_h)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a2)))).
% 294.25/38.02 fof(fact_offset__poly__pCons, axiom, ![V_p, T_a2, V_a2, V_h2]: (class_Rings_Ocomm__semiring__0(T_a2) => c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a2, c_Polynomial_OpCons(T_a2, V_a2, V_p), V_h2)=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a2), c_Polynomial_Osmult(T_a2, V_h2, c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a2, V_p, V_h2)), c_Polynomial_OpCons(T_a2, V_a2, c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a2, V_p, V_h2))))).
% 294.25/38.02 fof(fact_smult__0__right, axiom, ![T_a2, V_a2]: (class_Rings_Ocomm__semiring__0(T_a2) => c_Polynomial_Osmult(T_a2, V_a2, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a2)))=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a2)))).
% 294.25/38.02 fof(tfree_0, hypothesis, class_Rings_Ocomm__semiring__0(t_a)).
% 294.25/38.02
% 294.25/38.02 Now clausify the problem and encode Horn clauses using encoding 3 of
% 294.25/38.02 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 294.25/38.02 We repeatedly replace C & s=t => u=v by the two clauses:
% 294.25/38.02 fresh(y, y, x1...xn) = u
% 294.25/38.02 C => fresh(s, t, x1...xn) = v
% 294.25/38.02 where fresh is a fresh function symbol and x1..xn are the free
% 294.25/38.02 variables of u and v.
% 294.25/38.02 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 294.25/38.02 input problem has no model of domain size 1).
% 294.25/38.02
% 294.25/38.02 The encoding turns the above axioms into the following unit equations and goals:
% 294.25/38.02
% 294.25/38.02 Axiom 1 (tfree_0): class_Rings_Ocomm__semiring__0(t_a) = true2.
% 294.25/38.02 Axiom 2 (arity_Polynomial__Opoly__Rings_Ocomm__semiring__0): fresh1146(X, X, Y) = true2.
% 294.25/38.02 Axiom 3 (clrel_Rings_Ocomm__semiring__0__Groups_Ocomm__monoid__add): fresh1108(X, X, Y) = true2.
% 294.25/38.02 Axiom 4 (arity_Polynomial__Opoly__Rings_Ocomm__semiring__0): fresh1146(class_Rings_Ocomm__semiring__0(X), true2, X) = class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X)).
% 294.25/38.02 Axiom 5 (clrel_Rings_Ocomm__semiring__0__Groups_Ocomm__monoid__add): fresh1108(class_Rings_Ocomm__semiring__0(X), true2, X) = class_Groups_Ocomm__monoid__add(X).
% 294.25/38.02 Axiom 6 (fact_offset__poly__0): fresh468(X, X, Y, Z) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(Z)).
% 294.25/38.02 Axiom 7 (fact_smult__0__right): fresh326(X, X, Y, Z) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(Z)).
% 294.25/38.02 Axiom 8 (fact_add__0): fresh164(X, X, Y, Z) = Y.
% 294.25/38.02 Axiom 9 (fact_offset__poly__0): fresh468(class_Rings_Ocomm__semiring__0(X), true2, Y, X) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X)), Y).
% 294.58/38.02 Axiom 10 (fact_smult__0__right): fresh326(class_Rings_Ocomm__semiring__0(X), true2, Y, X) = c_Polynomial_Osmult(X, Y, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X))).
% 294.58/38.02 Axiom 11 (fact_add__0): fresh164(class_Groups_Ocomm__monoid__add(X), true2, Y, X) = c_Groups_Oplus__class_Oplus(X, c_Groups_Ozero__class_Ozero(X), Y).
% 294.58/38.02 Axiom 12 (fact_offset__poly__pCons): fresh467(X, X, Y, Z, W, V) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V, c_Polynomial_OpCons(V, W, Z), Y).
% 294.58/38.02 Axiom 13 (fact_offset__poly__pCons): fresh467(class_Rings_Ocomm__semiring__0(X), true2, Y, Z, W, X) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X), c_Polynomial_Osmult(X, Y, c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X, Z, Y)), c_Polynomial_OpCons(X, W, c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X, Z, Y))).
% 294.58/38.02
% 294.58/38.02 Lemma 14: c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)), X) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)).
% 294.58/38.02 Proof:
% 294.58/38.02 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)), X)
% 294.58/38.02 = { by axiom 9 (fact_offset__poly__0) R->L }
% 294.58/38.02 fresh468(class_Rings_Ocomm__semiring__0(t_a), true2, X, t_a)
% 294.58/38.02 = { by axiom 1 (tfree_0) }
% 294.58/38.02 fresh468(true2, true2, X, t_a)
% 294.58/38.02 = { by axiom 6 (fact_offset__poly__0) }
% 294.58/38.02 c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
% 294.58/38.02
% 294.58/38.02 Goal 1 (conj_0): c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a, c_Polynomial_OpCons(t_a, v_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))), v_h) = c_Polynomial_OpCons(t_a, v_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))).
% 294.58/38.02 Proof:
% 294.58/38.02 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a, c_Polynomial_OpCons(t_a, v_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))), v_h)
% 294.58/38.02 = { by axiom 12 (fact_offset__poly__pCons) R->L }
% 294.58/38.02 fresh467(true2, true2, v_h, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)), v_a, t_a)
% 294.58/38.02 = { by axiom 1 (tfree_0) R->L }
% 294.58/38.02 fresh467(class_Rings_Ocomm__semiring__0(t_a), true2, v_h, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)), v_a, t_a)
% 294.58/38.02 = { by axiom 13 (fact_offset__poly__pCons) }
% 294.58/38.02 c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a), c_Polynomial_Osmult(t_a, v_h, c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)), v_h)), c_Polynomial_OpCons(t_a, v_a, c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)), v_h)))
% 294.58/38.02 = { by lemma 14 }
% 294.58/38.02 c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a), c_Polynomial_Osmult(t_a, v_h, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))), c_Polynomial_OpCons(t_a, v_a, c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)), v_h)))
% 294.58/38.02 = { by axiom 10 (fact_smult__0__right) R->L }
% 294.58/38.02 c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a), fresh326(class_Rings_Ocomm__semiring__0(t_a), true2, v_h, t_a), c_Polynomial_OpCons(t_a, v_a, c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)), v_h)))
% 294.58/38.02 = { by axiom 1 (tfree_0) }
% 294.58/38.02 c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a), fresh326(true2, true2, v_h, t_a), c_Polynomial_OpCons(t_a, v_a, c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)), v_h)))
% 294.58/38.02 = { by axiom 7 (fact_smult__0__right) }
% 294.58/38.02 c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)), c_Polynomial_OpCons(t_a, v_a, c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)), v_h)))
% 294.58/38.02 = { by axiom 11 (fact_add__0) R->L }
% 294.58/38.02 fresh164(class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(t_a)), true2, c_Polynomial_OpCons(t_a, v_a, c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)), v_h)), tc_Polynomial_Opoly(t_a))
% 294.58/38.02 = { by axiom 5 (clrel_Rings_Ocomm__semiring__0__Groups_Ocomm__monoid__add) R->L }
% 294.58/38.02 fresh164(fresh1108(class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(t_a)), true2, tc_Polynomial_Opoly(t_a)), true2, c_Polynomial_OpCons(t_a, v_a, c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)), v_h)), tc_Polynomial_Opoly(t_a))
% 294.58/38.02 = { by axiom 4 (arity_Polynomial__Opoly__Rings_Ocomm__semiring__0) R->L }
% 294.58/38.02 fresh164(fresh1108(fresh1146(class_Rings_Ocomm__semiring__0(t_a), true2, t_a), true2, tc_Polynomial_Opoly(t_a)), true2, c_Polynomial_OpCons(t_a, v_a, c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)), v_h)), tc_Polynomial_Opoly(t_a))
% 294.58/38.02 = { by axiom 1 (tfree_0) }
% 294.58/38.02 fresh164(fresh1108(fresh1146(true2, true2, t_a), true2, tc_Polynomial_Opoly(t_a)), true2, c_Polynomial_OpCons(t_a, v_a, c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)), v_h)), tc_Polynomial_Opoly(t_a))
% 294.58/38.02 = { by axiom 2 (arity_Polynomial__Opoly__Rings_Ocomm__semiring__0) }
% 294.58/38.02 fresh164(fresh1108(true2, true2, tc_Polynomial_Opoly(t_a)), true2, c_Polynomial_OpCons(t_a, v_a, c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)), v_h)), tc_Polynomial_Opoly(t_a))
% 294.58/38.02 = { by axiom 3 (clrel_Rings_Ocomm__semiring__0__Groups_Ocomm__monoid__add) }
% 294.58/38.02 fresh164(true2, true2, c_Polynomial_OpCons(t_a, v_a, c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)), v_h)), tc_Polynomial_Opoly(t_a))
% 294.58/38.02 = { by axiom 8 (fact_add__0) }
% 294.58/38.02 c_Polynomial_OpCons(t_a, v_a, c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)), v_h))
% 294.58/38.02 = { by lemma 14 }
% 294.58/38.02 c_Polynomial_OpCons(t_a, v_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))
% 294.58/38.02 % SZS output end Proof
% 294.58/38.02
% 294.58/38.02 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------