0.10/0.11	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.10/0.11	% 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   : n029.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   : Tue Jul 13 17:01:40 EDT 2021
0.11/0.32	% CPUTime    : 
245.87/31.22	% SZS status Theorem
245.87/31.22	
245.87/31.22	% SZS output start Proof
245.87/31.22	Take the following subset of the input axioms:
245.87/31.23	  fof(conj_0, conjecture, hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(v_F, v_Q____)), c_Arrow__Order__Mirabelle_OLin))).
245.87/31.23	  fof(fact__096Q_A_058_AProf_096, axiom, hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), v_Q____), c_Arrow__Order__Mirabelle_OProf))).
245.87/31.23	  fof(fact_assms_I1_J, axiom, hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), v_F), c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Arrow__Order__Mirabelle_OProf, c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), c_Arrow__Order__Mirabelle_OLin))))).
245.87/31.23	  fof(fact_funcset__mem, axiom, ![V_x_2, V_f_2, T_b, T_a, V_B_2, V_A_2]: ((hBOOL(hAPP(hAPP(c_member(T_b), hAPP(V_f_2, V_x_2)), V_B_2)) <= hBOOL(hAPP(hAPP(c_member(T_a), V_x_2), V_A_2))) <= hBOOL(hAPP(hAPP(c_member(tc_fun(T_a, T_b)), V_f_2), c_FuncSet_OPi(T_a, T_b, V_A_2, c_COMBK(tc_fun(T_b, tc_HOL_Obool), T_a, V_B_2)))))).
245.87/31.23	  fof(fact_mem__def, axiom, ![V_x_2, T_a, V_A_2]: (hBOOL(hAPP(hAPP(c_member(T_a), V_x_2), V_A_2)) <=> hBOOL(hAPP(V_A_2, V_x_2)))).
245.87/31.23	
245.87/31.23	Now clausify the problem and encode Horn clauses using encoding 3 of
245.87/31.23	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
245.87/31.23	We repeatedly replace C & s=t => u=v by the two clauses:
245.87/31.23	  fresh(y, y, x1...xn) = u
245.87/31.23	  C => fresh(s, t, x1...xn) = v
245.87/31.23	where fresh is a fresh function symbol and x1..xn are the free
245.87/31.23	variables of u and v.
245.87/31.23	A predicate p(X) is encoded as p(X)=true (this is sound, because the
245.87/31.23	input problem has no model of domain size 1).
245.87/31.23	
245.87/31.23	The encoding turns the above axioms into the following unit equations and goals:
245.87/31.23	
245.87/31.23	Axiom 1 (fact_mem__def_1): fresh185(X, X, Y, Z) = true2.
245.87/31.23	Axiom 2 (fact_mem__def): fresh186(X, X, Y, Z, W) = true2.
245.87/31.23	Axiom 3 (fact_funcset__mem): fresh295(X, X, Y, Z, W, V) = true2.
245.87/31.23	Axiom 4 (fact_funcset__mem): fresh296(X, X, Y, Z, W, V, U, T) = hBOOL(hAPP(hAPP(c_member(U), hAPP(V, Y)), Z)).
245.87/31.23	Axiom 5 (fact_mem__def): fresh186(hBOOL(hAPP(X, Y)), true2, X, Y, Z) = hBOOL(hAPP(hAPP(c_member(Z), Y), X)).
245.87/31.23	Axiom 6 (fact_mem__def_1): fresh185(hBOOL(hAPP(hAPP(c_member(X), Y), Z)), true2, Z, Y) = hBOOL(hAPP(Z, Y)).
245.87/31.23	Axiom 7 (fact__096Q_A_058_AProf_096): hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), v_Q____), c_Arrow__Order__Mirabelle_OProf)) = true2.
245.87/31.23	Axiom 8 (fact_funcset__mem): fresh296(hBOOL(hAPP(hAPP(c_member(tc_fun(X, Y)), Z), c_FuncSet_OPi(X, Y, W, c_COMBK(tc_fun(Y, tc_HOL_Obool), X, V)))), true2, U, V, W, Z, Y, X) = fresh295(hBOOL(hAPP(hAPP(c_member(X), U), W)), true2, U, V, Z, Y).
245.87/31.23	Axiom 9 (fact_assms_I1_J): hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), v_F), c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Arrow__Order__Mirabelle_OProf, c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), c_Arrow__Order__Mirabelle_OLin)))) = true2.
245.87/31.23	
245.87/31.23	Goal 1 (conj_0): hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(v_F, v_Q____)), c_Arrow__Order__Mirabelle_OLin)) = true2.
245.87/31.23	Proof:
245.87/31.23	  hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(v_F, v_Q____)), c_Arrow__Order__Mirabelle_OLin))
245.87/31.23	= { by axiom 4 (fact_funcset__mem) R->L }
245.87/31.23	  fresh296(true2, true2, v_Q____, c_Arrow__Order__Mirabelle_OLin, c_Arrow__Order__Mirabelle_OProf, v_F, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)))
245.87/31.23	= { by axiom 9 (fact_assms_I1_J) R->L }
245.87/31.23	  fresh296(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), v_F), c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Arrow__Order__Mirabelle_OProf, c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), c_Arrow__Order__Mirabelle_OLin)))), true2, v_Q____, c_Arrow__Order__Mirabelle_OLin, c_Arrow__Order__Mirabelle_OProf, v_F, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)))
245.87/31.23	= { by axiom 8 (fact_funcset__mem) }
245.87/31.23	  fresh295(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), v_Q____), c_Arrow__Order__Mirabelle_OProf)), true2, v_Q____, c_Arrow__Order__Mirabelle_OLin, v_F, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))
245.87/31.23	= { by axiom 5 (fact_mem__def) R->L }
245.87/31.23	  fresh295(fresh186(hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf, v_Q____)), true2, c_Arrow__Order__Mirabelle_OProf, v_Q____, tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), true2, v_Q____, c_Arrow__Order__Mirabelle_OLin, v_F, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))
245.87/31.23	= { by axiom 6 (fact_mem__def_1) R->L }
245.87/31.23	  fresh295(fresh186(fresh185(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), v_Q____), c_Arrow__Order__Mirabelle_OProf)), true2, c_Arrow__Order__Mirabelle_OProf, v_Q____), true2, c_Arrow__Order__Mirabelle_OProf, v_Q____, tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), true2, v_Q____, c_Arrow__Order__Mirabelle_OLin, v_F, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))
245.87/31.23	= { by axiom 7 (fact__096Q_A_058_AProf_096) }
245.87/31.23	  fresh295(fresh186(fresh185(true2, true2, c_Arrow__Order__Mirabelle_OProf, v_Q____), true2, c_Arrow__Order__Mirabelle_OProf, v_Q____, tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), true2, v_Q____, c_Arrow__Order__Mirabelle_OLin, v_F, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))
245.87/31.23	= { by axiom 1 (fact_mem__def_1) }
245.87/31.23	  fresh295(fresh186(true2, true2, c_Arrow__Order__Mirabelle_OProf, v_Q____, tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), true2, v_Q____, c_Arrow__Order__Mirabelle_OLin, v_F, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))
245.87/31.23	= { by axiom 2 (fact_mem__def) }
245.87/31.23	  fresh295(true2, true2, v_Q____, c_Arrow__Order__Mirabelle_OLin, v_F, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))
245.87/31.23	= { by axiom 3 (fact_funcset__mem) }
245.87/31.23	  true2
245.87/31.23	% SZS output end Proof
245.87/31.23	
245.87/31.23	RESULT: Theorem (the conjecture is true).
245.87/31.31	EOF