0.03/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.03/0.13	% Command    : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
0.13/0.34	% Computer   : n019.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   : 1200
0.13/0.34	% WCLimit    : 120
0.13/0.34	% DateTime   : Wed Jul 14 16:53:14 EDT 2021
0.13/0.34	% CPUTime    : 
61.60/8.08	% SZS status Theorem
61.60/8.08	
61.60/8.09	% SZS output start Proof
61.60/8.09	Take the following subset of the input axioms:
61.60/8.09	  fof(conj_1, hypothesis, hBOOL(hAPP(fun(x_a, bool), bool, hAPP(fun(x_a, bool), fun(fun(x_a, bool), bool), ord_less_eq(fun(x_a, bool)), g), hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u)))).
61.60/8.09	  fof(conj_4, hypothesis, hBOOL(hAPP(fun(pname, bool), bool, hAPP(pname, fun(fun(pname, bool), bool), member(pname), pn), u))).
61.60/8.09	  fof(conj_6, conjecture, hBOOL(hAPP(fun(x_a, bool), bool, hAPP(fun(x_a, bool), fun(fun(x_a, bool), bool), ord_less_eq(fun(x_a, bool)), hAPP(fun(x_a, bool), fun(x_a, bool), hAPP(x_a, fun(fun(x_a, bool), fun(x_a, bool)), insert(x_a), hAPP(pname, x_a, mgt_call, pn)), g)), hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u)))).
61.60/8.09	  fof(fact_55_insertI1, axiom, ![X_b, A_2, B]: hBOOL(hAPP(fun(X_b, bool), bool, hAPP(X_b, fun(fun(X_b, bool), bool), member(X_b), A_2), hAPP(fun(X_b, bool), fun(X_b, bool), hAPP(X_b, fun(fun(X_b, bool), fun(X_b, bool)), insert(X_b), A_2), B)))).
61.60/8.09	  fof(fact_84_insert__subset, axiom, ![X_b, A_1, B, X_2]: ((hBOOL(hAPP(fun(X_b, bool), bool, hAPP(fun(X_b, bool), fun(fun(X_b, bool), bool), ord_less_eq(fun(X_b, bool)), A_1), B)) & hBOOL(hAPP(fun(X_b, bool), bool, hAPP(X_b, fun(fun(X_b, bool), bool), member(X_b), X_2), B))) <=> hBOOL(hAPP(fun(X_b, bool), bool, hAPP(fun(X_b, bool), fun(fun(X_b, bool), bool), ord_less_eq(fun(X_b, bool)), hAPP(fun(X_b, bool), fun(X_b, bool), hAPP(X_b, fun(fun(X_b, bool), fun(X_b, bool)), insert(X_b), X_2), A_1)), B)))).
61.60/8.09	  fof(fact_89_insert__image, axiom, ![X_c, X_b, F, A_1, X_2]: (hBOOL(hAPP(fun(X_b, bool), bool, hAPP(X_b, fun(fun(X_b, bool), bool), member(X_b), X_2), A_1)) => hAPP(fun(X_c, bool), fun(X_c, bool), hAPP(X_c, fun(fun(X_c, bool), fun(X_c, bool)), insert(X_c), hAPP(X_b, X_c, F, X_2)), hAPP(fun(X_b, bool), fun(X_c, bool), hAPP(fun(X_b, X_c), fun(fun(X_b, bool), fun(X_c, bool)), image(X_b, X_c), F), A_1))=hAPP(fun(X_b, bool), fun(X_c, bool), hAPP(fun(X_b, X_c), fun(fun(X_b, bool), fun(X_c, bool)), image(X_b, X_c), F), A_1))).
61.60/8.09	
61.60/8.09	Now clausify the problem and encode Horn clauses using encoding 3 of
61.60/8.09	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
61.60/8.09	We repeatedly replace C & s=t => u=v by the two clauses:
61.60/8.09	  fresh(y, y, x1...xn) = u
61.60/8.09	  C => fresh(s, t, x1...xn) = v
61.60/8.09	where fresh is a fresh function symbol and x1..xn are the free
61.60/8.09	variables of u and v.
61.60/8.09	A predicate p(X) is encoded as p(X)=true (this is sound, because the
61.60/8.09	input problem has no model of domain size 1).
61.60/8.09	
61.60/8.09	The encoding turns the above axioms into the following unit equations and goals:
61.60/8.09	
61.60/8.09	Axiom 1 (fact_84_insert__subset): fresh132(X, X, Y, Z, W, V) = true2.
61.60/8.09	Axiom 2 (fact_52_subsetD): fresh69(X, X, Y, Z, W, V) = hBOOL(hAPP(fun(Y, bool), bool, hAPP(Y, fun(fun(Y, bool), bool), member(Y), Z), V)).
61.60/8.09	Axiom 3 (conj_4): hBOOL(hAPP(fun(pname, bool), bool, hAPP(pname, fun(fun(pname, bool), bool), member(pname), pn), u)) = true2.
61.60/8.09	Axiom 4 (fact_72_subset__trans): fresh46(X, X, Y, Z, W, V) = hBOOL(hAPP(fun(Y, bool), bool, hAPP(fun(Y, bool), fun(fun(Y, bool), bool), ord_less_eq(fun(Y, bool)), W), Z)).
61.60/8.09	Axiom 5 (fact_89_insert__image): fresh31(X, X, Y, Z, W, V, U) = hAPP(fun(Z, bool), fun(Y, bool), hAPP(fun(Z, Y), fun(fun(Z, bool), fun(Y, bool)), image(Z, Y), W), U).
61.60/8.09	Axiom 6 (fact_84_insert__subset): fresh131(X, X, Y, Z, W, V) = fresh132(hBOOL(hAPP(fun(Y, bool), bool, hAPP(Y, fun(fun(Y, bool), bool), member(Y), Z), V)), true2, Y, Z, W, V).
61.60/8.09	Axiom 7 (fact_55_insertI1): hBOOL(hAPP(fun(X, bool), bool, hAPP(X, fun(fun(X, bool), bool), member(X), Y), hAPP(fun(X, bool), fun(X, bool), hAPP(X, fun(fun(X, bool), fun(X, bool)), insert(X), Y), Z))) = true2.
61.60/8.09	Axiom 8 (fact_84_insert__subset): fresh131(hBOOL(hAPP(fun(X, bool), bool, hAPP(fun(X, bool), fun(fun(X, bool), bool), ord_less_eq(fun(X, bool)), Y), Z)), true2, X, W, Y, Z) = hBOOL(hAPP(fun(X, bool), bool, hAPP(fun(X, bool), fun(fun(X, bool), bool), ord_less_eq(fun(X, bool)), hAPP(fun(X, bool), fun(X, bool), hAPP(X, fun(fun(X, bool), fun(X, bool)), insert(X), W), Y)), Z)).
61.60/8.09	Axiom 9 (conj_1): hBOOL(hAPP(fun(x_a, bool), bool, hAPP(fun(x_a, bool), fun(fun(x_a, bool), bool), ord_less_eq(fun(x_a, bool)), g), hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u))) = true2.
61.60/8.10	Axiom 10 (fact_89_insert__image): fresh31(hBOOL(hAPP(fun(X, bool), bool, hAPP(X, fun(fun(X, bool), bool), member(X), Y), Z)), true2, W, X, V, Y, Z) = hAPP(fun(W, bool), fun(W, bool), hAPP(W, fun(fun(W, bool), fun(W, bool)), insert(W), hAPP(X, W, V, Y)), hAPP(fun(X, bool), fun(W, bool), hAPP(fun(X, W), fun(fun(X, bool), fun(W, bool)), image(X, W), V), Z)).
61.60/8.10	
61.60/8.10	Goal 1 (conj_6): hBOOL(hAPP(fun(x_a, bool), bool, hAPP(fun(x_a, bool), fun(fun(x_a, bool), bool), ord_less_eq(fun(x_a, bool)), hAPP(fun(x_a, bool), fun(x_a, bool), hAPP(x_a, fun(fun(x_a, bool), fun(x_a, bool)), insert(x_a), hAPP(pname, x_a, mgt_call, pn)), g)), hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u))) = true2.
61.60/8.10	Proof:
61.60/8.10	  hBOOL(hAPP(fun(x_a, bool), bool, hAPP(fun(x_a, bool), fun(fun(x_a, bool), bool), ord_less_eq(fun(x_a, bool)), hAPP(fun(x_a, bool), fun(x_a, bool), hAPP(x_a, fun(fun(x_a, bool), fun(x_a, bool)), insert(x_a), hAPP(pname, x_a, mgt_call, pn)), g)), hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u)))
61.60/8.10	= { by axiom 5 (fact_89_insert__image) R->L }
61.60/8.10	  hBOOL(hAPP(fun(x_a, bool), bool, hAPP(fun(x_a, bool), fun(fun(x_a, bool), bool), ord_less_eq(fun(x_a, bool)), hAPP(fun(x_a, bool), fun(x_a, bool), hAPP(x_a, fun(fun(x_a, bool), fun(x_a, bool)), insert(x_a), hAPP(pname, x_a, mgt_call, pn)), g)), fresh31(X, X, x_a, pname, mgt_call, Y, u)))
61.60/8.10	= { by axiom 8 (fact_84_insert__subset) R->L }
61.60/8.10	  fresh131(hBOOL(hAPP(fun(x_a, bool), bool, hAPP(fun(x_a, bool), fun(fun(x_a, bool), bool), ord_less_eq(fun(x_a, bool)), g), fresh31(X, X, x_a, pname, mgt_call, Y, u))), true2, x_a, hAPP(pname, x_a, mgt_call, pn), g, fresh31(X, X, x_a, pname, mgt_call, Y, u))
61.60/8.10	= { by axiom 4 (fact_72_subset__trans) R->L }
61.60/8.10	  fresh131(fresh46(Z, Z, x_a, fresh31(X, X, x_a, pname, mgt_call, Y, u), g, W), true2, x_a, hAPP(pname, x_a, mgt_call, pn), g, fresh31(X, X, x_a, pname, mgt_call, Y, u))
61.60/8.10	= { by axiom 5 (fact_89_insert__image) }
61.60/8.10	  fresh131(fresh46(Z, Z, x_a, hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u), g, W), true2, x_a, hAPP(pname, x_a, mgt_call, pn), g, fresh31(X, X, x_a, pname, mgt_call, Y, u))
61.60/8.10	= { by axiom 5 (fact_89_insert__image) }
61.60/8.10	  fresh131(fresh46(Z, Z, x_a, hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u), g, W), true2, x_a, hAPP(pname, x_a, mgt_call, pn), g, hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u))
61.60/8.10	= { by axiom 4 (fact_72_subset__trans) }
61.60/8.10	  fresh131(hBOOL(hAPP(fun(x_a, bool), bool, hAPP(fun(x_a, bool), fun(fun(x_a, bool), bool), ord_less_eq(fun(x_a, bool)), g), hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u))), true2, x_a, hAPP(pname, x_a, mgt_call, pn), g, hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u))
61.60/8.10	= { by axiom 9 (conj_1) }
61.60/8.10	  fresh131(true2, true2, x_a, hAPP(pname, x_a, mgt_call, pn), g, hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u))
61.60/8.10	= { by axiom 6 (fact_84_insert__subset) }
61.60/8.10	  fresh132(hBOOL(hAPP(fun(x_a, bool), bool, hAPP(x_a, fun(fun(x_a, bool), bool), member(x_a), hAPP(pname, x_a, mgt_call, pn)), hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u))), true2, x_a, hAPP(pname, x_a, mgt_call, pn), g, hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u))
61.60/8.10	= { by axiom 5 (fact_89_insert__image) R->L }
61.60/8.10	  fresh132(hBOOL(hAPP(fun(x_a, bool), bool, hAPP(x_a, fun(fun(x_a, bool), bool), member(x_a), hAPP(pname, x_a, mgt_call, pn)), fresh31(true2, true2, x_a, pname, mgt_call, pn, u))), true2, x_a, hAPP(pname, x_a, mgt_call, pn), g, hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u))
61.60/8.10	= { by axiom 3 (conj_4) R->L }
61.60/8.10	  fresh132(hBOOL(hAPP(fun(x_a, bool), bool, hAPP(x_a, fun(fun(x_a, bool), bool), member(x_a), hAPP(pname, x_a, mgt_call, pn)), fresh31(hBOOL(hAPP(fun(pname, bool), bool, hAPP(pname, fun(fun(pname, bool), bool), member(pname), pn), u)), true2, x_a, pname, mgt_call, pn, u))), true2, x_a, hAPP(pname, x_a, mgt_call, pn), g, hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u))
61.60/8.10	= { by axiom 2 (fact_52_subsetD) R->L }
61.60/8.10	  fresh132(hBOOL(hAPP(fun(x_a, bool), bool, hAPP(x_a, fun(fun(x_a, bool), bool), member(x_a), hAPP(pname, x_a, mgt_call, pn)), fresh31(fresh69(V, V, pname, pn, U, u), true2, x_a, pname, mgt_call, pn, u))), true2, x_a, hAPP(pname, x_a, mgt_call, pn), g, hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u))
61.60/8.10	= { by axiom 2 (fact_52_subsetD) R->L }
61.60/8.10	  fresh132(fresh69(T, T, x_a, hAPP(pname, x_a, mgt_call, pn), S, fresh31(fresh69(V, V, pname, pn, U, u), true2, x_a, pname, mgt_call, pn, u)), true2, x_a, hAPP(pname, x_a, mgt_call, pn), g, hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u))
61.60/8.10	= { by axiom 2 (fact_52_subsetD) }
61.60/8.10	  fresh132(fresh69(T, T, x_a, hAPP(pname, x_a, mgt_call, pn), S, fresh31(hBOOL(hAPP(fun(pname, bool), bool, hAPP(pname, fun(fun(pname, bool), bool), member(pname), pn), u)), true2, x_a, pname, mgt_call, pn, u)), true2, x_a, hAPP(pname, x_a, mgt_call, pn), g, hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u))
61.60/8.10	= { by axiom 10 (fact_89_insert__image) }
61.60/8.10	  fresh132(fresh69(T, T, x_a, hAPP(pname, x_a, mgt_call, pn), S, hAPP(fun(x_a, bool), fun(x_a, bool), hAPP(x_a, fun(fun(x_a, bool), fun(x_a, bool)), insert(x_a), hAPP(pname, x_a, mgt_call, pn)), hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u))), true2, x_a, hAPP(pname, x_a, mgt_call, pn), g, hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u))
61.60/8.10	= { by axiom 5 (fact_89_insert__image) R->L }
61.60/8.10	  fresh132(fresh69(T, T, x_a, hAPP(pname, x_a, mgt_call, pn), S, hAPP(fun(x_a, bool), fun(x_a, bool), hAPP(x_a, fun(fun(x_a, bool), fun(x_a, bool)), insert(x_a), hAPP(pname, x_a, mgt_call, pn)), fresh31(X2, X2, x_a, pname, mgt_call, Y2, u))), true2, x_a, hAPP(pname, x_a, mgt_call, pn), g, hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u))
61.60/8.10	= { by axiom 2 (fact_52_subsetD) }
61.60/8.10	  fresh132(hBOOL(hAPP(fun(x_a, bool), bool, hAPP(x_a, fun(fun(x_a, bool), bool), member(x_a), hAPP(pname, x_a, mgt_call, pn)), hAPP(fun(x_a, bool), fun(x_a, bool), hAPP(x_a, fun(fun(x_a, bool), fun(x_a, bool)), insert(x_a), hAPP(pname, x_a, mgt_call, pn)), fresh31(X2, X2, x_a, pname, mgt_call, Y2, u)))), true2, x_a, hAPP(pname, x_a, mgt_call, pn), g, hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u))
61.60/8.10	= { by axiom 7 (fact_55_insertI1) }
61.60/8.10	  fresh132(true2, true2, x_a, hAPP(pname, x_a, mgt_call, pn), g, hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u))
61.60/8.10	= { by axiom 1 (fact_84_insert__subset) }
61.60/8.10	  true2
61.60/8.10	% SZS output end Proof
61.60/8.10	
61.60/8.10	RESULT: Theorem (the conjecture is true).
61.60/8.12	EOF