0.03/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.03/0.12	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.12/0.33	% Computer   : n014.cluster.edu
0.12/0.33	% Model      : x86_64 x86_64
0.12/0.33	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.33	% Memory     : 8042.1875MB
0.12/0.33	% OS         : Linux 3.10.0-693.el7.x86_64
0.12/0.33	% CPULimit   : 180
0.12/0.33	% DateTime   : Thu Aug 29 09:25:39 EDT 2019
0.12/0.33	% CPUTime    : 
0.56/0.76	% SZS status Theorem
0.56/0.76	
0.56/0.76	% SZS output start Proof
0.56/0.76	Take the following subset of the input axioms:
0.56/0.76	  fof(co1, conjecture, p(enc(pp, a))).
0.56/0.76	  fof(enc_dec_cancel, axiom, ![U, V]: V=enc(i(U), enc(U, V))).
0.56/0.76	  fof(encrypt_a_stored_comms_key, axiom, ![W, U, V]: ((p(U) & (p(W) & p(V))) => p(enc(enc(i(tmk), V), enc(i(tc), U))))).
0.56/0.76	  fof(encrypt_clear_key_as_Tcomms_key, axiom, ![W, U, V]: (p(enc(tc, U)) <= (p(U) & (p(W) & p(V))))).
0.56/0.76	  fof(intruder_knows_1, axiom, p(enc(tmk, pp))).
0.56/0.76	  fof(intruder_knows_4, axiom, p(enc(lp, t2))).
0.56/0.76	  fof(intruder_knows_8, axiom, p(a)).
0.56/0.76	
0.56/0.76	Now clausify the problem and encode Horn clauses using encoding 3 of
0.56/0.76	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
0.56/0.76	We repeatedly replace C & s=t => u=v by the two clauses:
0.56/0.76	  fresh(y, y, x1...xn) = u
0.56/0.76	  C => fresh(s, t, x1...xn) = v
0.56/0.76	where fresh is a fresh function symbol and x1..xn are the free
0.56/0.76	variables of u and v.
0.56/0.76	A predicate p(X) is encoded as p(X)=true (this is sound, because the
0.56/0.76	input problem has no model of domain size 1).
0.56/0.76	
0.56/0.76	The encoding turns the above axioms into the following unit equations and goals:
0.56/0.76	
0.56/0.76	Axiom 1 (encrypt_a_stored_comms_key): fresh11(X, X, Y, Z) = true.
0.56/0.76	Axiom 2 (encrypt_a_stored_comms_key): fresh10(X, X, Y, Z) = fresh11(p(Y), true, Y, Z).
0.56/0.76	Axiom 3 (encrypt_a_stored_comms_key): fresh9(X, X, Y, Z) = fresh10(p(Z), true, Y, Z).
0.56/0.76	Axiom 4 (encrypt_clear_key_as_Tcomms_key): fresh2(X, X, Y) = p(enc(tc, Y)).
0.56/0.76	Axiom 5 (encrypt_clear_key_as_Tcomms_key): fresh34(X, X, Y) = true.
0.56/0.76	Axiom 6 (encrypt_clear_key_as_Tcomms_key): fresh33(X, X, Y, Z) = fresh34(p(Y), true, Y).
0.56/0.76	Axiom 7 (intruder_knows_4): p(enc(lp, t2)) = true.
0.56/0.76	Axiom 8 (encrypt_clear_key_as_Tcomms_key): fresh33(p(X), true, Y, Z) = fresh2(p(Z), true, Y).
0.56/0.76	Axiom 9 (intruder_knows_8): p(a) = true.
0.56/0.76	Axiom 10 (intruder_knows_1): p(enc(tmk, pp)) = true.
0.56/0.76	Axiom 11 (enc_dec_cancel): X = enc(i(Y), enc(Y, X)).
0.56/0.76	Axiom 12 (encrypt_a_stored_comms_key): fresh9(p(X), true, Y, Z) = p(enc(enc(i(tmk), Z), enc(i(tc), Y))).
0.56/0.76	
0.56/0.76	Goal 1 (co1): p(enc(pp, a)) = true.
0.56/0.76	Proof:
0.56/0.76	  p(enc(pp, a))
0.56/0.76	= { by axiom 11 (enc_dec_cancel) }
0.56/0.76	  p(enc(enc(i(tmk), enc(tmk, pp)), a))
0.56/0.76	= { by axiom 11 (enc_dec_cancel) }
0.56/0.76	  p(enc(enc(i(tmk), enc(tmk, pp)), enc(i(tc), enc(tc, a))))
0.56/0.76	= { by axiom 12 (encrypt_a_stored_comms_key) }
0.56/0.76	  fresh9(p(enc(lp, t2)), true, enc(tc, a), enc(tmk, pp))
0.56/0.76	= { by axiom 7 (intruder_knows_4) }
0.56/0.76	  fresh9(true, true, enc(tc, a), enc(tmk, pp))
0.56/0.76	= { by axiom 3 (encrypt_a_stored_comms_key) }
0.56/0.76	  fresh10(p(enc(tmk, pp)), true, enc(tc, a), enc(tmk, pp))
0.56/0.76	= { by axiom 10 (intruder_knows_1) }
0.56/0.76	  fresh10(true, true, enc(tc, a), enc(tmk, pp))
0.56/0.76	= { by axiom 2 (encrypt_a_stored_comms_key) }
0.56/0.76	  fresh11(p(enc(tc, a)), true, enc(tc, a), enc(tmk, pp))
0.56/0.76	= { by axiom 4 (encrypt_clear_key_as_Tcomms_key) }
0.56/0.76	  fresh11(fresh2(true, true, a), true, enc(tc, a), enc(tmk, pp))
0.56/0.76	= { by axiom 7 (intruder_knows_4) }
0.56/0.76	  fresh11(fresh2(p(enc(lp, t2)), true, a), true, enc(tc, a), enc(tmk, pp))
0.56/0.76	= { by axiom 8 (encrypt_clear_key_as_Tcomms_key) }
0.56/0.76	  fresh11(fresh33(p(enc(lp, t2)), true, a, enc(lp, t2)), true, enc(tc, a), enc(tmk, pp))
0.56/0.76	= { by axiom 7 (intruder_knows_4) }
0.56/0.76	  fresh11(fresh33(true, true, a, enc(lp, t2)), true, enc(tc, a), enc(tmk, pp))
0.56/0.76	= { by axiom 6 (encrypt_clear_key_as_Tcomms_key) }
0.56/0.76	  fresh11(fresh34(p(a), true, a), true, enc(tc, a), enc(tmk, pp))
0.56/0.76	= { by axiom 9 (intruder_knows_8) }
0.56/0.76	  fresh11(fresh34(true, true, a), true, enc(tc, a), enc(tmk, pp))
0.56/0.76	= { by axiom 5 (encrypt_clear_key_as_Tcomms_key) }
0.56/0.76	  fresh11(true, true, enc(tc, a), enc(tmk, pp))
0.56/0.76	= { by axiom 1 (encrypt_a_stored_comms_key) }
0.56/0.76	  true
0.56/0.76	% SZS output end Proof
0.56/0.76	
0.56/0.76	RESULT: Theorem (the conjecture is true).
0.61/0.77	EOF