0.10/0.11	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.10/0.12	% Command    : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
0.11/0.32	% Computer   : n002.cluster.edu
0.11/0.32	% Model      : x86_64 x86_64
0.11/0.32	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.11/0.32	% Memory     : 8042.1875MB
0.11/0.32	% OS         : Linux 3.10.0-693.el7.x86_64
0.11/0.32	% CPULimit   : 1200
0.11/0.32	% WCLimit    : 120
0.11/0.32	% DateTime   : Wed Jul 14 15:39:02 EDT 2021
0.11/0.32	% CPUTime    : 
279.37/35.45	% SZS status Theorem
279.37/35.45	
279.37/35.45	% SZS output start Proof
279.37/35.45	Take the following subset of the input axioms:
279.37/35.45	  fof(arity_Complex__Ocomplex__Int_Oring__char__0, axiom, class_Int_Oring__char__0(tc_Complex_Ocomplex)).
279.37/35.45	  fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__0, axiom, class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)).
279.37/35.45	  fof(arity_Complex__Ocomplex__Rings_Oidom, axiom, class_Rings_Oidom(tc_Complex_Ocomplex)).
279.37/35.45	  fof(conj_0, hypothesis, ![B_x]: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)=hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q), B_x)).
279.37/35.45	  fof(conj_1, conjecture, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))=v_q).
279.37/35.45	  fof(fact_ext, axiom, ![V_f_2, V_g_2]: (![B_x]: hAPP(V_g_2, B_x)=hAPP(V_f_2, B_x) => V_f_2=V_g_2)).
279.37/35.45	  fof(fact_pe, axiom, v_p=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))).
279.37/35.45	  fof(fact_poly__0, axiom, ![V_x, T_a]: (c_Groups_Ozero__class_Ozero(T_a)=hAPP(c_Polynomial_Opoly(T_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))), V_x) <= class_Rings_Ocomm__semiring__0(T_a))).
279.37/35.45	  fof(fact_poly__zero, axiom, ![T_a, V_pa_2]: ((class_Rings_Oidom(T_a) & class_Int_Oring__char__0(T_a)) => (c_Polynomial_Opoly(T_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))=c_Polynomial_Opoly(T_a, V_pa_2) <=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))=V_pa_2))).
279.37/35.45	
279.37/35.45	Now clausify the problem and encode Horn clauses using encoding 3 of
279.37/35.45	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
279.37/35.45	We repeatedly replace C & s=t => u=v by the two clauses:
279.37/35.45	  fresh(y, y, x1...xn) = u
279.37/35.45	  C => fresh(s, t, x1...xn) = v
279.37/35.45	where fresh is a fresh function symbol and x1..xn are the free
279.37/35.45	variables of u and v.
279.37/35.45	A predicate p(X) is encoded as p(X)=true (this is sound, because the
279.37/35.45	input problem has no model of domain size 1).
279.37/35.45	
279.37/35.45	The encoding turns the above axioms into the following unit equations and goals:
279.37/35.45	
279.37/35.45	Axiom 1 (arity_Complex__Ocomplex__Rings_Ocomm__semiring__0): class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) = true2.
279.37/35.45	Axiom 2 (arity_Complex__Ocomplex__Rings_Oidom): class_Rings_Oidom(tc_Complex_Ocomplex) = true2.
279.37/35.46	Axiom 3 (arity_Complex__Ocomplex__Int_Oring__char__0): class_Int_Oring__char__0(tc_Complex_Ocomplex) = true2.
279.37/35.46	Axiom 4 (fact_pe): v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)).
279.37/35.46	Axiom 5 (conj_0): c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q), X).
279.37/35.46	Axiom 6 (fact_poly__zero_1): fresh1709(X, X, Y, Z) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(Z)).
279.37/35.46	Axiom 7 (fact_poly__0): fresh441(X, X, Y, Z) = c_Groups_Ozero__class_Ozero(Z).
279.37/35.46	Axiom 8 (fact_poly__zero_1): fresh173(X, X, Y, Z) = Y.
279.37/35.46	Axiom 9 (fact_ext): fresh5(X, X, Y, Z) = Y.
279.37/35.46	Axiom 10 (fact_poly__zero_1): fresh1708(X, X, Y, Z) = fresh1709(class_Rings_Oidom(Z), true2, Y, Z).
279.37/35.46	Axiom 11 (fact_poly__0): fresh441(class_Rings_Ocomm__semiring__0(X), true2, Y, X) = hAPP(c_Polynomial_Opoly(X, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X))), Y).
279.37/35.46	Axiom 12 (fact_poly__zero_1): fresh1708(class_Int_Oring__char__0(X), true2, Y, X) = fresh173(c_Polynomial_Opoly(X, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X))), c_Polynomial_Opoly(X, Y), Y, X).
279.37/35.46	Axiom 13 (fact_ext): fresh5(hAPP(X, b_x2(X, Y)), hAPP(Y, b_x2(X, Y)), X, Y) = Y.
279.37/35.46	
279.37/35.46	Goal 1 (conj_1): c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_q.
279.37/35.46	Proof:
279.37/35.46	  c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
279.37/35.46	= { by axiom 6 (fact_poly__zero_1) R->L }
279.37/35.46	  fresh1709(true2, true2, v_q, tc_Complex_Ocomplex)
279.37/35.46	= { by axiom 2 (arity_Complex__Ocomplex__Rings_Oidom) R->L }
279.37/35.46	  fresh1709(class_Rings_Oidom(tc_Complex_Ocomplex), true2, v_q, tc_Complex_Ocomplex)
279.37/35.46	= { by axiom 10 (fact_poly__zero_1) R->L }
279.37/35.46	  fresh1708(true2, true2, v_q, tc_Complex_Ocomplex)
279.37/35.46	= { by axiom 3 (arity_Complex__Ocomplex__Int_Oring__char__0) R->L }
279.37/35.46	  fresh1708(class_Int_Oring__char__0(tc_Complex_Ocomplex), true2, v_q, tc_Complex_Ocomplex)
279.37/35.46	= { by axiom 12 (fact_poly__zero_1) }
279.37/35.46	  fresh173(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q), v_q, tc_Complex_Ocomplex)
279.37/35.46	= { by axiom 4 (fact_pe) R->L }
279.37/35.46	  fresh173(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p), c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q), v_q, tc_Complex_Ocomplex)
279.37/35.46	= { by axiom 13 (fact_ext) R->L }
279.37/35.46	  fresh173(fresh5(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q), b_x2(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q), c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p), b_x2(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q), c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p))), c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q), c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p)), c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q), v_q, tc_Complex_Ocomplex)
279.37/35.46	= { by axiom 5 (conj_0) R->L }
279.37/35.46	  fresh173(fresh5(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p), b_x2(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q), c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p))), c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q), c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p)), c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q), v_q, tc_Complex_Ocomplex)
279.37/35.46	= { by axiom 4 (fact_pe) }
279.37/35.46	  fresh173(fresh5(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), b_x2(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q), c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p))), c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q), c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p)), c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q), v_q, tc_Complex_Ocomplex)
279.37/35.46	= { by axiom 11 (fact_poly__0) R->L }
279.37/35.46	  fresh173(fresh5(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex), fresh441(class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex), true2, b_x2(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q), c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p)), tc_Complex_Ocomplex), c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q), c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p)), c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q), v_q, tc_Complex_Ocomplex)
279.37/35.46	= { by axiom 1 (arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) }
279.37/35.46	  fresh173(fresh5(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex), fresh441(true2, true2, b_x2(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q), c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p)), tc_Complex_Ocomplex), c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q), c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p)), c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q), v_q, tc_Complex_Ocomplex)
279.37/35.46	= { by axiom 7 (fact_poly__0) }
279.37/35.46	  fresh173(fresh5(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex), c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q), c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p)), c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q), v_q, tc_Complex_Ocomplex)
279.37/35.46	= { by axiom 9 (fact_ext) }
279.37/35.46	  fresh173(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q), c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q), v_q, tc_Complex_Ocomplex)
279.37/35.46	= { by axiom 8 (fact_poly__zero_1) }
279.37/35.46	  v_q
279.37/35.46	% SZS output end Proof
279.37/35.46	
279.37/35.46	RESULT: Theorem (the conjecture is true).
279.37/35.51	EOF