TSTP Solution File: SWW246+1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWW246+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 : n028.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 00:54:30 EDT 2023
% Result : Theorem 107.16s 14.19s
% Output : Proof 107.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWW246+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
% 0.14/0.35 % Computer : n028.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Aug 27 21:52:09 EDT 2023
% 0.14/0.36 % CPUTime :
% 107.16/14.19 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 107.16/14.19
% 107.16/14.19 % SZS status Theorem
% 107.16/14.19
% 107.16/14.19 % SZS output start Proof
% 107.16/14.19 Take the following subset of the input axioms:
% 107.16/14.19 fof(clrel_Rings_Oidom__Rings_Ocomm__semiring__0, axiom, ![T]: (class_Rings_Oidom(T) => class_Rings_Ocomm__semiring__0(T))).
% 107.16/14.19 fof(fact__C0_C, axiom, class_Rings_Oidom(t_a) => ~c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a, t_a, c_Polynomial_Opoly(t_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))).
% 107.16/14.19 fof(fact_constant__def, axiom, ![V_f_2, T_b, T_c]: (c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b, T_c, V_f_2) <=> ![B_x, B_y]: hAPP(V_f_2, B_x)=hAPP(V_f_2, B_y))).
% 107.16/14.19 fof(fact_poly__0, axiom, ![V_x, T_a]: (class_Rings_Ocomm__semiring__0(T_a) => hAPP(c_Polynomial_Opoly(T_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))), V_x)=c_Groups_Ozero__class_Ozero(T_a))).
% 107.16/14.19 fof(tfree_0, hypothesis, class_Rings_Oidom(t_a)).
% 107.16/14.19
% 107.16/14.19 Now clausify the problem and encode Horn clauses using encoding 3 of
% 107.16/14.19 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 107.16/14.19 We repeatedly replace C & s=t => u=v by the two clauses:
% 107.16/14.19 fresh(y, y, x1...xn) = u
% 107.16/14.19 C => fresh(s, t, x1...xn) = v
% 107.16/14.19 where fresh is a fresh function symbol and x1..xn are the free
% 107.16/14.19 variables of u and v.
% 107.16/14.19 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 107.16/14.19 input problem has no model of domain size 1).
% 107.16/14.19
% 107.16/14.19 The encoding turns the above axioms into the following unit equations and goals:
% 107.16/14.20
% 107.16/14.20 Axiom 1 (tfree_0): class_Rings_Oidom(t_a) = true2.
% 107.16/14.20 Axiom 2 (clrel_Rings_Oidom__Rings_Ocomm__semiring__0): fresh1007(X, X, Y) = true2.
% 107.16/14.20 Axiom 3 (clrel_Rings_Oidom__Rings_Ocomm__semiring__0): fresh1007(class_Rings_Oidom(X), true2, X) = class_Rings_Ocomm__semiring__0(X).
% 107.16/14.20 Axiom 4 (fact_poly__0): fresh403(X, X, Y, Z) = c_Groups_Ozero__class_Ozero(Z).
% 107.16/14.20 Axiom 5 (fact_constant__def): fresh895(X, X, Y, Z, W) = true2.
% 107.16/14.20 Axiom 6 (fact_poly__0): fresh403(class_Rings_Ocomm__semiring__0(X), true2, Y, X) = hAPP(c_Polynomial_Opoly(X, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X))), Y).
% 107.16/14.20 Axiom 7 (fact_constant__def): fresh895(hAPP(X, b_x3(X)), hAPP(X, b_y(X)), X, Y, Z) = c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(Z, Y, X).
% 107.16/14.20
% 107.16/14.20 Lemma 8: class_Rings_Ocomm__semiring__0(t_a) = true2.
% 107.16/14.20 Proof:
% 107.16/14.20 class_Rings_Ocomm__semiring__0(t_a)
% 107.16/14.20 = { by axiom 3 (clrel_Rings_Oidom__Rings_Ocomm__semiring__0) R->L }
% 107.16/14.20 fresh1007(class_Rings_Oidom(t_a), true2, t_a)
% 107.16/14.20 = { by axiom 1 (tfree_0) }
% 107.16/14.20 fresh1007(true2, true2, t_a)
% 107.16/14.20 = { by axiom 2 (clrel_Rings_Oidom__Rings_Ocomm__semiring__0) }
% 107.16/14.20 true2
% 107.16/14.20
% 107.16/14.20 Goal 1 (fact__C0_C): tuple2(class_Rings_Oidom(t_a), c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a, t_a, c_Polynomial_Opoly(t_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))) = tuple2(true2, true2).
% 107.16/14.20 Proof:
% 107.16/14.20 tuple2(class_Rings_Oidom(t_a), c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a, t_a, c_Polynomial_Opoly(t_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))))
% 107.16/14.20 = { by axiom 1 (tfree_0) }
% 107.16/14.20 tuple2(true2, c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a, t_a, c_Polynomial_Opoly(t_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))))
% 107.16/14.20 = { by axiom 7 (fact_constant__def) R->L }
% 107.16/14.20 tuple2(true2, fresh895(hAPP(c_Polynomial_Opoly(t_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))), b_x3(c_Polynomial_Opoly(t_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))), hAPP(c_Polynomial_Opoly(t_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))), b_y(c_Polynomial_Opoly(t_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))), c_Polynomial_Opoly(t_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))), t_a, t_a))
% 107.16/14.20 = { by axiom 6 (fact_poly__0) R->L }
% 107.16/14.20 tuple2(true2, fresh895(hAPP(c_Polynomial_Opoly(t_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))), b_x3(c_Polynomial_Opoly(t_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))), fresh403(class_Rings_Ocomm__semiring__0(t_a), true2, b_y(c_Polynomial_Opoly(t_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))), t_a), c_Polynomial_Opoly(t_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))), t_a, t_a))
% 107.16/14.20 = { by lemma 8 }
% 107.16/14.20 tuple2(true2, fresh895(hAPP(c_Polynomial_Opoly(t_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))), b_x3(c_Polynomial_Opoly(t_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))), fresh403(true2, true2, b_y(c_Polynomial_Opoly(t_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))), t_a), c_Polynomial_Opoly(t_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))), t_a, t_a))
% 107.16/14.20 = { by axiom 4 (fact_poly__0) }
% 107.16/14.20 tuple2(true2, fresh895(hAPP(c_Polynomial_Opoly(t_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))), b_x3(c_Polynomial_Opoly(t_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))), c_Groups_Ozero__class_Ozero(t_a), c_Polynomial_Opoly(t_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))), t_a, t_a))
% 107.16/14.20 = { by axiom 4 (fact_poly__0) R->L }
% 107.16/14.20 tuple2(true2, fresh895(hAPP(c_Polynomial_Opoly(t_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))), b_x3(c_Polynomial_Opoly(t_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))), fresh403(true2, true2, b_x3(c_Polynomial_Opoly(t_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))), t_a), c_Polynomial_Opoly(t_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))), t_a, t_a))
% 107.16/14.20 = { by lemma 8 R->L }
% 107.16/14.20 tuple2(true2, fresh895(hAPP(c_Polynomial_Opoly(t_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))), b_x3(c_Polynomial_Opoly(t_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))), fresh403(class_Rings_Ocomm__semiring__0(t_a), true2, b_x3(c_Polynomial_Opoly(t_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))), t_a), c_Polynomial_Opoly(t_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))), t_a, t_a))
% 107.16/14.20 = { by axiom 6 (fact_poly__0) }
% 107.16/14.20 tuple2(true2, fresh895(hAPP(c_Polynomial_Opoly(t_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))), b_x3(c_Polynomial_Opoly(t_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))), hAPP(c_Polynomial_Opoly(t_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))), b_x3(c_Polynomial_Opoly(t_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))), c_Polynomial_Opoly(t_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))), t_a, t_a))
% 107.16/14.20 = { by axiom 5 (fact_constant__def) }
% 107.16/14.20 tuple2(true2, true2)
% 107.16/14.20 % SZS output end Proof
% 107.16/14.20
% 107.16/14.20 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------