0.03/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.03/0.13	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.13/0.34	% Computer   : n026.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   : 180
0.13/0.34	% DateTime   : Thu Aug 29 12:05:35 EDT 2019
0.13/0.35	% CPUTime    : 
163.26/163.55	% SZS status Theorem
163.26/163.55	
163.26/163.55	% SZS output start Proof
163.26/163.55	Take the following subset of the input axioms:
163.26/163.56	  fof(conj_1, conjecture, ![B_Z, B_s]: (![B_s_H]: (v_P(B_Z, B_s_H) <= c_Natural_Oevaln(c_Com_Ocom_OSKIP, B_s, v_n, B_s_H)) <= v_P(B_Z, B_s))).
163.26/163.56	  fof(fact_evaln__elim__cases_I1_J, axiom, ![V_n, V_t, V_s]: (c_Natural_Oevaln(c_Com_Ocom_OSKIP, V_s, V_n, V_t) => V_s=V_t)).
163.26/163.56	
163.26/163.56	Now clausify the problem and encode Horn clauses using encoding 3 of
163.26/163.56	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
163.26/163.56	We repeatedly replace C & s=t => u=v by the two clauses:
163.26/163.56	  fresh(y, y, x1...xn) = u
163.26/163.56	  C => fresh(s, t, x1...xn) = v
163.26/163.56	where fresh is a fresh function symbol and x1..xn are the free
163.26/163.56	variables of u and v.
163.26/163.56	A predicate p(X) is encoded as p(X)=true (this is sound, because the
163.26/163.56	input problem has no model of domain size 1).
163.26/163.56	
163.26/163.56	The encoding turns the above axioms into the following unit equations and goals:
163.26/163.56	
163.26/163.56	Axiom 1 (fact_evaln__elim__cases_I1_J): fresh42(X, X, Y, Z) = Y.
163.26/163.56	Axiom 2 (fact_evaln__elim__cases_I1_J): fresh42(c_Natural_Oevaln(c_Com_Ocom_OSKIP, X, Y, Z), true2, Z, X) = X.
163.26/163.56	Axiom 3 (conj_1): c_Natural_Oevaln(c_Com_Ocom_OSKIP, sK174_conj_1_B_s, v_n, sK173_conj_1_B_s_H) = true2.
163.26/163.56	Axiom 4 (conj_1_1): v_P(sK175_conj_1_B_Z, sK174_conj_1_B_s) = true2.
163.26/163.56	
163.26/163.56	Goal 1 (conj_1_2): v_P(sK175_conj_1_B_Z, sK173_conj_1_B_s_H) = true2.
163.26/163.56	Proof:
163.26/163.56	  v_P(sK175_conj_1_B_Z, sK173_conj_1_B_s_H)
163.26/163.56	= { by axiom 1 (fact_evaln__elim__cases_I1_J) }
163.26/163.56	  v_P(sK175_conj_1_B_Z, fresh42(true2, true2, sK173_conj_1_B_s_H, sK174_conj_1_B_s))
163.26/163.56	= { by axiom 3 (conj_1) }
163.26/163.56	  v_P(sK175_conj_1_B_Z, fresh42(c_Natural_Oevaln(c_Com_Ocom_OSKIP, sK174_conj_1_B_s, v_n, sK173_conj_1_B_s_H), true2, sK173_conj_1_B_s_H, sK174_conj_1_B_s))
163.26/163.56	= { by axiom 2 (fact_evaln__elim__cases_I1_J) }
163.26/163.56	  v_P(sK175_conj_1_B_Z, sK174_conj_1_B_s)
163.26/163.56	= { by axiom 4 (conj_1_1) }
163.26/163.56	  true2
163.26/163.56	% SZS output end Proof
163.26/163.56	
163.26/163.56	RESULT: Theorem (the conjecture is true).
163.39/163.71	EOF