0.11/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.11/0.13	% Command    : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
0.12/0.34	% Computer   : n002.cluster.edu
0.12/0.34	% Model      : x86_64 x86_64
0.12/0.34	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.34	% Memory     : 8042.1875MB
0.12/0.34	% OS         : Linux 3.10.0-693.el7.x86_64
0.12/0.34	% CPULimit   : 1200
0.12/0.34	% WCLimit    : 120
0.12/0.34	% DateTime   : Wed Jul 14 16:57:17 EDT 2021
0.12/0.34	% CPUTime    : 
31.35/4.33	% SZS status Theorem
31.35/4.33	
31.35/4.34	% SZS output start Proof
31.35/4.34	Take the following subset of the input axioms:
31.35/4.34	  fof(conj_0, hypothesis, hBOOL(hoare_165779456gleton)).
31.35/4.34	  fof(conj_1, hypothesis, hBOOL(wT_bodies)).
31.35/4.34	  fof(conj_5, hypothesis, some_com(y)=hAPP_p799580910on_com(body, pn)).
31.35/4.34	  fof(conj_7, conjecture, hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT, body_1), dom_pname_com(body))), insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT, y), bot_bo620288102e_bool)))).
31.35/4.34	  fof(fact_0_empty, axiom, ![G]: hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G), bot_bo620288102e_bool))).
31.35/4.34	  fof(fact_103_MGF, axiom, ![C_1]: (hBOOL(hoare_165779456gleton) => (hBOOL(wT_bodies) => (hBOOL(wt(C_1)) => hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(bot_bo620288102e_bool), insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT, C_1), bot_bo620288102e_bool))))))).
31.35/4.34	  fof(fact_288_WT__bodiesD, axiom, ![Pn, B_2]: (hBOOL(wT_bodies) => (some_com(B_2)=hAPP_p799580910on_com(body, Pn) => hBOOL(wt(B_2))))).
31.35/4.34	  fof(fact_4_cut, axiom, ![G, G_1, Ts]: ((hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G), Ts)) <= hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G), G_1))) <= hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G_1), Ts)))).
31.35/4.34	
31.35/4.34	Now clausify the problem and encode Horn clauses using encoding 3 of
31.35/4.34	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
31.35/4.34	We repeatedly replace C & s=t => u=v by the two clauses:
31.35/4.34	  fresh(y, y, x1...xn) = u
31.35/4.34	  C => fresh(s, t, x1...xn) = v
31.35/4.34	where fresh is a fresh function symbol and x1..xn are the free
31.35/4.34	variables of u and v.
31.35/4.34	A predicate p(X) is encoded as p(X)=true (this is sound, because the
31.35/4.34	input problem has no model of domain size 1).
31.35/4.34	
31.35/4.34	The encoding turns the above axioms into the following unit equations and goals:
31.35/4.34	
31.35/4.34	Axiom 1 (conj_1): hBOOL(wT_bodies) = true2.
31.35/4.34	Axiom 2 (conj_0): hBOOL(hoare_165779456gleton) = true2.
31.35/4.34	Axiom 3 (conj_5): some_com(y) = hAPP_p799580910on_com(body, pn).
31.35/4.34	Axiom 4 (fact_103_MGF): fresh396(X, X, Y) = true2.
31.35/4.34	Axiom 5 (fact_288_WT__bodiesD): fresh203(X, X, Y) = true2.
31.35/4.34	Axiom 6 (fact_0_empty): hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(X), bot_bo620288102e_bool)) = true2.
31.35/4.34	Axiom 7 (fact_103_MGF): fresh394(X, X, Y) = fresh395(hBOOL(wT_bodies), true2, Y).
31.35/4.34	Axiom 8 (fact_288_WT__bodiesD): fresh204(X, X, Y, Z) = hBOOL(wt(Z)).
31.35/4.34	Axiom 9 (fact_4_cut): fresh167(X, X, Y, Z) = true2.
31.35/4.34	Axiom 10 (fact_103_MGF): fresh395(X, X, Y) = fresh396(hBOOL(wt(Y)), true2, Y).
31.35/4.34	Axiom 11 (fact_4_cut): fresh168(X, X, Y, Z, W) = hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(Y), W)).
31.35/4.34	Axiom 12 (fact_288_WT__bodiesD): fresh204(hBOOL(wT_bodies), true2, X, Y) = fresh203(some_com(Y), hAPP_p799580910on_com(body, X), Y).
31.35/4.34	Axiom 13 (fact_103_MGF): fresh394(hBOOL(hoare_165779456gleton), true2, X) = hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(bot_bo620288102e_bool), insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT, X), bot_bo620288102e_bool))).
31.35/4.34	Axiom 14 (fact_4_cut): fresh168(hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(X), Y)), true2, Z, X, Y) = fresh167(hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(Z), X)), true2, Z, Y).
31.35/4.34	
31.35/4.34	Goal 1 (conj_7): hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT, body_1), dom_pname_com(body))), insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT, y), bot_bo620288102e_bool))) = true2.
31.35/4.34	Proof:
31.35/4.34	  hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT, body_1), dom_pname_com(body))), insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT, y), bot_bo620288102e_bool)))
31.35/4.34	= { by axiom 11 (fact_4_cut) R->L }
31.35/4.34	  fresh168(true2, true2, image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT, body_1), dom_pname_com(body)), bot_bo620288102e_bool, insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT, y), bot_bo620288102e_bool))
31.35/4.34	= { by axiom 4 (fact_103_MGF) R->L }
31.35/4.34	  fresh168(fresh396(true2, true2, y), true2, image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT, body_1), dom_pname_com(body)), bot_bo620288102e_bool, insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT, y), bot_bo620288102e_bool))
31.35/4.34	= { by axiom 5 (fact_288_WT__bodiesD) R->L }
31.35/4.34	  fresh168(fresh396(fresh203(some_com(y), some_com(y), y), true2, y), true2, image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT, body_1), dom_pname_com(body)), bot_bo620288102e_bool, insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT, y), bot_bo620288102e_bool))
31.35/4.34	= { by axiom 3 (conj_5) }
31.35/4.34	  fresh168(fresh396(fresh203(some_com(y), hAPP_p799580910on_com(body, pn), y), true2, y), true2, image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT, body_1), dom_pname_com(body)), bot_bo620288102e_bool, insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT, y), bot_bo620288102e_bool))
31.35/4.34	= { by axiom 12 (fact_288_WT__bodiesD) R->L }
31.35/4.34	  fresh168(fresh396(fresh204(hBOOL(wT_bodies), true2, pn, y), true2, y), true2, image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT, body_1), dom_pname_com(body)), bot_bo620288102e_bool, insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT, y), bot_bo620288102e_bool))
31.35/4.34	= { by axiom 1 (conj_1) }
31.35/4.34	  fresh168(fresh396(fresh204(true2, true2, pn, y), true2, y), true2, image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT, body_1), dom_pname_com(body)), bot_bo620288102e_bool, insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT, y), bot_bo620288102e_bool))
31.35/4.34	= { by axiom 8 (fact_288_WT__bodiesD) }
31.35/4.34	  fresh168(fresh396(hBOOL(wt(y)), true2, y), true2, image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT, body_1), dom_pname_com(body)), bot_bo620288102e_bool, insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT, y), bot_bo620288102e_bool))
31.35/4.34	= { by axiom 10 (fact_103_MGF) R->L }
31.35/4.34	  fresh168(fresh395(true2, true2, y), true2, image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT, body_1), dom_pname_com(body)), bot_bo620288102e_bool, insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT, y), bot_bo620288102e_bool))
31.35/4.34	= { by axiom 1 (conj_1) R->L }
31.35/4.34	  fresh168(fresh395(hBOOL(wT_bodies), true2, y), true2, image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT, body_1), dom_pname_com(body)), bot_bo620288102e_bool, insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT, y), bot_bo620288102e_bool))
31.35/4.34	= { by axiom 7 (fact_103_MGF) R->L }
31.35/4.34	  fresh168(fresh394(true2, true2, y), true2, image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT, body_1), dom_pname_com(body)), bot_bo620288102e_bool, insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT, y), bot_bo620288102e_bool))
31.35/4.34	= { by axiom 2 (conj_0) R->L }
31.35/4.34	  fresh168(fresh394(hBOOL(hoare_165779456gleton), true2, y), true2, image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT, body_1), dom_pname_com(body)), bot_bo620288102e_bool, insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT, y), bot_bo620288102e_bool))
31.35/4.34	= { by axiom 13 (fact_103_MGF) }
31.35/4.34	  fresh168(hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(bot_bo620288102e_bool), insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT, y), bot_bo620288102e_bool))), true2, image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT, body_1), dom_pname_com(body)), bot_bo620288102e_bool, insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT, y), bot_bo620288102e_bool))
31.35/4.34	= { by axiom 14 (fact_4_cut) }
31.35/4.34	  fresh167(hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT, body_1), dom_pname_com(body))), bot_bo620288102e_bool)), true2, image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT, body_1), dom_pname_com(body)), insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT, y), bot_bo620288102e_bool))
31.35/4.34	= { by axiom 6 (fact_0_empty) }
31.35/4.34	  fresh167(true2, true2, image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT, body_1), dom_pname_com(body)), insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT, y), bot_bo620288102e_bool))
31.35/4.34	= { by axiom 9 (fact_4_cut) }
31.35/4.34	  true2
31.35/4.34	% SZS output end Proof
31.35/4.34	
31.35/4.34	RESULT: Theorem (the conjecture is true).
31.35/4.36	EOF