TSTP Solution File: SWW272+1 by Twee---2.5.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.5.0
% Problem : SWW272+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee /export/starexec/sandbox2/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% 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 : Mon Jun 24 18:26:41 EDT 2024
% Result : Theorem 209.03s 26.69s
% Output : Proof 209.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWW272+1 : TPTP v8.2.0. Released v5.2.0.
% 0.12/0.12 % Command : parallel-twee /export/starexec/sandbox2/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jun 19 09:28:54 EDT 2024
% 0.12/0.34 % CPUTime :
% 209.03/26.69 Command-line arguments: --no-flatten-goal
% 209.03/26.69
% 209.03/26.69 % SZS status Theorem
% 209.03/26.69
% 209.03/26.69 % SZS output start Proof
% 209.03/26.69 Take the following subset of the input axioms:
% 209.03/26.69 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__1, axiom, class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)).
% 209.03/26.69 fof(arity_Complex__Ocomplex__Rings_Oidom, axiom, class_Rings_Oidom(tc_Complex_Ocomplex)).
% 209.03/26.69 fof(arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors, axiom, ![T_1]: (class_Rings_Oidom(T_1) => class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1)))).
% 209.03/26.69 fof(conj_0, conjecture, v_s____!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))).
% 209.03/26.69 fof(fact_mult__eq__0__iff, axiom, ![T_a, V_aa_2, V_b_2]: (class_Rings_Oring__no__zero__divisors(T_a) => (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_aa_2), V_b_2)=c_Groups_Ozero__class_Ozero(T_a) <=> (V_aa_2=c_Groups_Ozero__class_Ozero(T_a) | V_b_2=c_Groups_Ozero__class_Ozero(T_a))))).
% 209.03/26.70 fof(fact_one__poly__def, axiom, ![T_a2]: (class_Rings_Ocomm__semiring__1(T_a2) => c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a2))=c_Polynomial_OpCons(T_a2, c_Groups_Oone__class_Oone(T_a2), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a2))))).
% 209.03/26.70 fof(fact_pne, axiom, v_pa____!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))).
% 209.03/26.70 fof(fact_s, axiom, v_pa____=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____))), v_s____)).
% 209.03/26.70
% 209.03/26.70 Now clausify the problem and encode Horn clauses using encoding 3 of
% 209.03/26.70 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 209.03/26.70 We repeatedly replace C & s=t => u=v by the two clauses:
% 209.03/26.70 fresh(y, y, x1...xn) = u
% 209.03/26.70 C => fresh(s, t, x1...xn) = v
% 209.03/26.70 where fresh is a fresh function symbol and x1..xn are the free
% 209.03/26.70 variables of u and v.
% 209.03/26.70 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 209.03/26.70 input problem has no model of domain size 1).
% 209.03/26.70
% 209.03/26.70 The encoding turns the above axioms into the following unit equations and goals:
% 209.03/26.70
% 209.03/26.70 Axiom 1 (arity_Complex__Ocomplex__Rings_Oidom): class_Rings_Oidom(tc_Complex_Ocomplex) = true2.
% 209.03/26.70 Axiom 2 (arity_Complex__Ocomplex__Rings_Ocomm__semiring__1): class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) = true2.
% 209.03/26.70 Axiom 3 (conj_0): v_s____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)).
% 209.03/26.70 Axiom 4 (arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors): fresh1130(X, X, Y) = true2.
% 209.03/26.70 Axiom 5 (fact_one__poly__def): fresh440(X, X, Y) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(Y)).
% 209.03/26.70 Axiom 6 (arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors): fresh1130(class_Rings_Oidom(X), true2, X) = class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X)).
% 209.03/26.70 Axiom 7 (fact_mult__eq__0__iff): fresh604(X, X, Y, Z, W) = c_Groups_Ozero__class_Ozero(W).
% 209.03/26.70 Axiom 8 (fact_realpow__minus__mult): fresh1222(X, X, Y, Z, W) = hAPP(hAPP(c_Power_Opower__class_Opower(W), Y), Z).
% 209.03/26.70 Axiom 9 (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J): fresh976(X, X, Y, Z, W) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(W), Y), Z).
% 209.03/26.70 Axiom 10 (fact_mult__eq__0__iff): fresh605(X, X, Y, Z, W) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(W), Z), Y).
% 209.03/26.70 Axiom 11 (fact_mult__eq__0__iff): fresh605(class_Rings_Oring__no__zero__divisors(X), true2, Y, Z, X) = fresh604(Y, c_Groups_Ozero__class_Ozero(X), Y, Z, X).
% 209.03/26.70 Axiom 12 (fact_one__poly__def): fresh440(class_Rings_Ocomm__semiring__1(X), true2, X) = c_Polynomial_OpCons(X, c_Groups_Oone__class_Oone(X), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X))).
% 209.03/26.70 Axiom 13 (fact_s): v_pa____ = 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____))), v_s____).
% 209.03/26.70
% 209.03/26.70 Goal 1 (fact_pne): v_pa____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)).
% 209.03/26.70 Proof:
% 209.03/26.70 v_pa____
% 209.03/26.70 = { by axiom 13 (fact_s) }
% 209.03/26.70 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____))), v_s____)
% 209.03/26.70 = { by axiom 9 (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) R->L }
% 209.03/26.70 fresh976(X, X, 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____)), v_s____, tc_Polynomial_Opoly(tc_Complex_Ocomplex))
% 209.03/26.70 = { by axiom 8 (fact_realpow__minus__mult) R->L }
% 209.03/26.70 fresh976(X, X, fresh1222(Y, Y, 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____), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_s____, tc_Polynomial_Opoly(tc_Complex_Ocomplex))
% 209.03/26.70 = { by axiom 12 (fact_one__poly__def) R->L }
% 209.03/26.70 fresh976(X, X, fresh1222(Y, Y, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), fresh440(class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex), true2, tc_Complex_Ocomplex)), c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_s____, tc_Polynomial_Opoly(tc_Complex_Ocomplex))
% 209.03/26.70 = { by axiom 2 (arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) }
% 209.03/26.70 fresh976(X, X, fresh1222(Y, Y, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), fresh440(true2, true2, tc_Complex_Ocomplex)), c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_s____, tc_Polynomial_Opoly(tc_Complex_Ocomplex))
% 209.03/26.70 = { by axiom 5 (fact_one__poly__def) }
% 209.03/26.70 fresh976(X, X, fresh1222(Y, Y, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_s____, tc_Polynomial_Opoly(tc_Complex_Ocomplex))
% 209.03/26.70 = { by axiom 9 (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) }
% 209.03/26.70 hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), fresh1222(Y, Y, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____), tc_Polynomial_Opoly(tc_Complex_Ocomplex))), v_s____)
% 209.03/26.70 = { by axiom 10 (fact_mult__eq__0__iff) R->L }
% 209.03/26.70 fresh605(true2, true2, v_s____, fresh1222(Y, Y, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), tc_Polynomial_Opoly(tc_Complex_Ocomplex))
% 209.03/26.70 = { by axiom 4 (arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors) R->L }
% 209.03/26.70 fresh605(fresh1130(true2, true2, tc_Complex_Ocomplex), true2, v_s____, fresh1222(Y, Y, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), tc_Polynomial_Opoly(tc_Complex_Ocomplex))
% 209.03/26.70 = { by axiom 1 (arity_Complex__Ocomplex__Rings_Oidom) R->L }
% 209.03/26.70 fresh605(fresh1130(class_Rings_Oidom(tc_Complex_Ocomplex), true2, tc_Complex_Ocomplex), true2, v_s____, fresh1222(Y, Y, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), tc_Polynomial_Opoly(tc_Complex_Ocomplex))
% 209.03/26.70 = { by axiom 6 (arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors) }
% 209.03/26.70 fresh605(class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), true2, v_s____, fresh1222(Y, Y, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), tc_Polynomial_Opoly(tc_Complex_Ocomplex))
% 209.03/26.70 = { by axiom 3 (conj_0) }
% 209.03/26.70 fresh605(class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), true2, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), fresh1222(Y, Y, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), tc_Polynomial_Opoly(tc_Complex_Ocomplex))
% 209.03/26.70 = { by axiom 11 (fact_mult__eq__0__iff) }
% 209.03/26.70 fresh604(c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), fresh1222(Y, Y, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), tc_Polynomial_Opoly(tc_Complex_Ocomplex))
% 209.03/26.70 = { by axiom 7 (fact_mult__eq__0__iff) }
% 209.03/26.70 c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
% 209.03/26.70 % SZS output end Proof
% 209.03/26.70
% 209.03/26.70 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------