0.08/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.08/0.13	% Command    : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
0.14/0.34	% Computer   : n011.cluster.edu
0.14/0.34	% Model      : x86_64 x86_64
0.14/0.34	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.14/0.34	% Memory     : 8042.1875MB
0.14/0.34	% OS         : Linux 3.10.0-693.el7.x86_64
0.14/0.34	% CPULimit   : 1200
0.14/0.34	% WCLimit    : 120
0.14/0.34	% DateTime   : Wed Jul 14 16:45:40 EDT 2021
0.14/0.34	% CPUTime    : 
123.76/15.95	% SZS status Theorem
123.76/15.95	
123.76/15.95	% SZS output start Proof
123.76/15.95	Take the following subset of the input axioms:
123.76/15.95	  fof(conj_1, hypothesis, hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool, g), image_pname_a(mgt_call, u)))).
123.76/15.95	  fof(conj_4, hypothesis, hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname, pn), u))).
123.76/15.95	  fof(conj_6, conjecture, hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool, insert_a(hAPP_pname_a(mgt_call, pn), g)), image_pname_a(mgt_call, u)))).
123.76/15.95	  fof(fact_261_imageI, axiom, ![F, A, X_2]: (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a, hAPP_pname_a(F, X_2)), image_pname_a(F, A))) <= hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname, X_2), A)))).
123.76/15.95	  fof(fact_274_insert__subset, axiom, ![A, B, X_2]: (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool, insert_a(X_2, A)), B)) <=> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool, A), B)) & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a, X_2), B))))).
123.76/15.95	
123.76/15.95	Now clausify the problem and encode Horn clauses using encoding 3 of
123.76/15.95	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
123.76/15.95	We repeatedly replace C & s=t => u=v by the two clauses:
123.76/15.95	  fresh(y, y, x1...xn) = u
123.76/15.95	  C => fresh(s, t, x1...xn) = v
123.76/15.95	where fresh is a fresh function symbol and x1..xn are the free
123.76/15.95	variables of u and v.
123.76/15.95	A predicate p(X) is encoded as p(X)=true (this is sound, because the
123.76/15.95	input problem has no model of domain size 1).
123.76/15.95	
123.76/15.95	The encoding turns the above axioms into the following unit equations and goals:
123.76/15.95	
123.76/15.95	Axiom 1 (conj_4): hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname, pn), u)) = true2.
123.76/15.95	Axiom 2 (fact_261_imageI): fresh219(X, X, Y, Z, W) = true2.
123.76/15.95	Axiom 3 (fact_274_insert__subset): fresh206(X, X, Y, Z, W) = true2.
123.76/15.95	Axiom 4 (conj_1): hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool, g), image_pname_a(mgt_call, u))) = true2.
123.76/15.95	Axiom 5 (fact_274_insert__subset): fresh207(X, X, Y, Z, W) = hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool, insert_a(Y, Z)), W)).
123.76/15.95	Axiom 6 (fact_261_imageI): fresh219(hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname, X), Y)), true2, Z, X, Y) = hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a, hAPP_pname_a(Z, X)), image_pname_a(Z, Y))).
123.76/15.95	Axiom 7 (fact_274_insert__subset): fresh207(hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool, X), Y)), true2, Z, X, Y) = fresh206(hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a, Z), Y)), true2, Z, X, Y).
123.76/15.95	
123.76/15.95	Goal 1 (conj_6): hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool, insert_a(hAPP_pname_a(mgt_call, pn), g)), image_pname_a(mgt_call, u))) = true2.
123.76/15.95	Proof:
123.76/15.95	  hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool, insert_a(hAPP_pname_a(mgt_call, pn), g)), image_pname_a(mgt_call, u)))
123.76/15.95	= { by axiom 5 (fact_274_insert__subset) R->L }
123.76/15.95	  fresh207(true2, true2, hAPP_pname_a(mgt_call, pn), g, image_pname_a(mgt_call, u))
123.76/15.95	= { by axiom 4 (conj_1) R->L }
123.76/15.95	  fresh207(hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool, g), image_pname_a(mgt_call, u))), true2, hAPP_pname_a(mgt_call, pn), g, image_pname_a(mgt_call, u))
123.76/15.95	= { by axiom 7 (fact_274_insert__subset) }
123.76/15.95	  fresh206(hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a, hAPP_pname_a(mgt_call, pn)), image_pname_a(mgt_call, u))), true2, hAPP_pname_a(mgt_call, pn), g, image_pname_a(mgt_call, u))
123.76/15.95	= { by axiom 6 (fact_261_imageI) R->L }
123.76/15.95	  fresh206(fresh219(hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname, pn), u)), true2, mgt_call, pn, u), true2, hAPP_pname_a(mgt_call, pn), g, image_pname_a(mgt_call, u))
123.76/15.95	= { by axiom 1 (conj_4) }
123.76/15.95	  fresh206(fresh219(true2, true2, mgt_call, pn, u), true2, hAPP_pname_a(mgt_call, pn), g, image_pname_a(mgt_call, u))
123.76/15.95	= { by axiom 2 (fact_261_imageI) }
123.76/15.95	  fresh206(true2, true2, hAPP_pname_a(mgt_call, pn), g, image_pname_a(mgt_call, u))
123.76/15.95	= { by axiom 3 (fact_274_insert__subset) }
123.76/15.95	  true2
123.76/15.95	% SZS output end Proof
123.76/15.95	
123.76/15.95	RESULT: Theorem (the conjecture is true).
123.76/15.99	EOF