0.00/0.03	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.04	% Command  : prover9 -casc 180 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
0.11/0.37	% Computer : n029.cluster.edu
0.11/0.37	% Model    : x86_64 x86_64
0.11/0.37	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.11/0.37	% Memory   : 8046.5625MB
0.11/0.37	% OS       : Linux 6.8.0-71-generic
0.11/0.37	% CPULimit : 1440
0.11/0.37	% WCLimit  : 180
0.11/0.37	% DateTime : Mon Jul 27 09:26:31 UTC 2026
0.11/0.37	% CPUTime  : 
0.11/0.37	% Prover9 (64) version 2026-6A, July 2026, CASC-J13.
0.11/0.37	% Process 2668467 was started by sandbox2 on n029,
0.11/0.37	% Mon Jul 27 09:26:31 2026
0.11/0.37	% The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 180 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
0.11/0.38	
0.11/0.38	% From the command line: assign(max_seconds, 180).
2.33/0.80	
2.33/0.80	% SZS status Theorem for theBenchmark
2.33/0.80	
2.33/0.80	% Proof 1 at 0.25 (+ 0.11) seconds.
2.33/0.80	% Length of proof is 47.
2.33/0.80	% Level of proof is 11.
2.33/0.80	% Maximum clause weight is 39.000.
2.33/0.80	% Given clauses 43.
2.33/0.80	
2.33/0.80	% SZS output start CNFRefutation for theBenchmark
2.33/0.80	fof(intruder_can_record, axiom, ! [U,V,W] : (message(sent(U,V,W)) => intruder_message(W)), file('theBenchmark.p',intruder_can_record)).
2.33/0.80	fof(intruder_decomposes_pairs, axiom, ! [U,V] : (intruder_message(pair(U,V)) => (intruder_message(U) & intruder_message(V))), file('theBenchmark.p',intruder_decomposes_pairs)).
2.33/0.80	fof(intruder_message_sent, axiom, ! [U,V,W] : ((intruder_message(U) & party_of_protocol(W) & party_of_protocol(V)) => message(sent(V,W,U))), file('theBenchmark.p',intruder_message_sent)).
2.33/0.80	fof(intruder_holds_key, axiom, ! [V,W] : ((intruder_message(V) & party_of_protocol(W)) => intruder_holds(key(V,W))), file('theBenchmark.p',intruder_holds_key)).
2.33/0.80	fof(b_accepts_secure_session_key, axiom, ! [V,X,Y] : ((message(sent(X,b,pair(encrypt(triple(X,V,generate_expiration_time(Y)),bt),encrypt(generate_b_nonce(Y),V)))) & b_stored(pair(X,Y))) => b_holds(key(V,X))), file('theBenchmark.p',b_accepts_secure_session_key)).
2.33/0.80	fof(b_creates_freash_nonces_in_time, axiom, ! [U,V] : ((fresh_to_b(V) & message(sent(U,b,pair(U,V)))) => (b_stored(pair(U,V)) & message(sent(b,t,triple(b,generate_b_nonce(V),encrypt(triple(U,V,generate_expiration_time(V)),bt)))))), file('theBenchmark.p',b_creates_freash_nonces_in_time)).
2.33/0.80	fof(intruder_composes_pairs, axiom, ! [U,V] : ((intruder_message(U) & intruder_message(V)) => intruder_message(pair(U,V))), file('theBenchmark.p',intruder_composes_pairs)).
2.33/0.80	fof(intruder_key_encrypts, axiom, ! [U,V,W] : ((party_of_protocol(W) & intruder_holds(key(V,W)) & intruder_message(U)) => intruder_message(encrypt(U,V))), file('theBenchmark.p',intruder_key_encrypts)).
2.33/0.80	fof(intruder_decomposes_triples, axiom, ! [U,V,W] : (intruder_message(triple(U,V,W)) => (intruder_message(U) & intruder_message(W) & intruder_message(V))), file('theBenchmark.p',intruder_decomposes_triples)).
2.33/0.80	fof(co1, conjecture, ? [U] : (intruder_holds(key(U,b)) & b_holds(key(U,a))), file('theBenchmark.p',co1)).
2.33/0.80	fof(co1_neg, negated_conjecture, ~(? [U] : (intruder_holds(key(U,b)) & b_holds(key(U,a)))), inference(assume_negation, [status(cth)], [co1])).
2.33/0.80	cnf(c_19, plain, ~fresh_to_b(A) | ~message(sent(B,b,pair(B,A))) | b_stored(pair(B,A)), inference(clausify, [status(thm)], [b_creates_freash_nonces_in_time])).
2.33/0.80	fof(nonce_a_is_fresh_to_b, axiom, (fresh_to_b(an_a_nonce)), file('theBenchmark.p',nonce_a_is_fresh_to_b)).
2.33/0.80	cnf(c_20, plain, fresh_to_b(an_a_nonce), inference(clausify, [status(thm)], [nonce_a_is_fresh_to_b])).
2.33/0.80	cnf(c_21, plain, ~fresh_to_b(A) | ~message(sent(B,b,pair(B,A))) | message(sent(b,t,triple(b,generate_b_nonce(A),encrypt(triple(B,A,generate_expiration_time(A)),bt)))), inference(clausify, [status(thm)], [b_creates_freash_nonces_in_time])).
2.33/0.80	cnf(c_27, plain, ~party_of_protocol(A) | ~intruder_holds(key(B,A)) | ~intruder_message(C) | intruder_message(encrypt(C,B)), inference(clausify, [status(thm)], [intruder_key_encrypts])).
2.33/0.80	cnf(c_28, plain, ~intruder_message(A) | ~party_of_protocol(B) | intruder_holds(key(A,B)), inference(clausify, [status(thm)], [intruder_holds_key])).
2.33/0.80	cnf(c_30, negated_conjecture, ~intruder_holds(key(A,b)) | ~b_holds(key(A,a)), inference(clausify, [status(thm)], [co1_neg])).
2.33/0.80	cnf(c_31, plain, ~message(sent(A,b,pair(encrypt(triple(A,B,generate_expiration_time(C)),bt),encrypt(generate_b_nonce(C),B)))) | ~b_stored(pair(A,C)) | b_holds(key(B,A)), inference(clausify, [status(thm)], [b_accepts_secure_session_key])).
2.33/0.80	cnf(c_32, negated_conjecture, ~b_holds(key(A,a)) | ~intruder_message(A) | ~party_of_protocol(b),
2.33/0.80	    inference(resolve, [status(thm)], [c_30, c_28])).
2.33/0.80	cnf(c_34, plain, ~message(sent(A,b,pair(A,an_a_nonce))) | b_stored(pair(A,an_a_nonce)),
2.33/0.80	    inference(resolve, [status(thm)], [c_19, c_20])).
2.33/0.80	cnf(c_35, negated_conjecture, ~message(sent(a,b,pair(encrypt(triple(a,A,generate_expiration_time(B)),bt),encrypt(generate_b_nonce(B),A)))) | ~b_stored(pair(a,B)) | ~intruder_message(A) | ~party_of_protocol(b),
2.33/0.80	    inference(resolve, [status(thm)], [c_31, c_32])).
2.33/0.80	cnf(c_39, negated_conjecture, ~message(sent(a,b,pair(a,an_a_nonce))) | ~message(sent(a,b,pair(encrypt(triple(a,A,generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),A)))) | ~intruder_message(A) | ~party_of_protocol(b),
2.33/0.80	    inference(resolve, [status(thm)], [c_34, c_35])).
2.33/0.80	cnf(c_40, plain, ~party_of_protocol(A) | ~intruder_message(B) | intruder_message(encrypt(B,C)) | ~intruder_message(C) | ~party_of_protocol(A),
2.33/0.80	    inference(resolve, [status(thm)], [c_27, c_28])).
2.33/0.80	cnf(c_41, plain, ~party_of_protocol(A) | ~intruder_message(B) | intruder_message(encrypt(B,C)) | ~intruder_message(C),
2.33/0.80	    inference(copy, [status(thm)], [c_40])).
2.33/0.80	cnf(c_42, plain, ~message(sent(A,b,pair(A,an_a_nonce))) | message(sent(b,t,triple(b,generate_b_nonce(an_a_nonce),encrypt(triple(A,an_a_nonce,generate_expiration_time(an_a_nonce)),bt)))),
2.33/0.80	    inference(resolve, [status(thm)], [c_21, c_20])).
2.33/0.80	fof(a_is_party_of_protocol, axiom, (party_of_protocol(a)), file('theBenchmark.p',a_is_party_of_protocol)).
2.33/0.80	cnf(c_43, plain, party_of_protocol(a), inference(clausify, [status(thm)], [a_is_party_of_protocol])).
2.33/0.80	cnf(c_45, plain, ~intruder_message(triple(A,B,C)) | intruder_message(B), inference(clausify, [status(thm)], [intruder_decomposes_triples])).
2.33/0.80	cnf(c_46, plain, ~intruder_message(triple(A,B,C)) | intruder_message(C), inference(clausify, [status(thm)], [intruder_decomposes_triples])).
2.33/0.80	fof(a_sent_message_i_to_b, axiom, (message(sent(a,b,pair(a,an_a_nonce)))), file('theBenchmark.p',a_sent_message_i_to_b)).
2.33/0.80	cnf(c_48, plain, message(sent(a,b,pair(a,an_a_nonce))), inference(clausify, [status(thm)], [a_sent_message_i_to_b])).
2.33/0.80	fof(b_is_party_of_protocol, axiom, (party_of_protocol(b)), file('theBenchmark.p',b_is_party_of_protocol)).
2.33/0.80	cnf(c_49, plain, party_of_protocol(b), inference(clausify, [status(thm)], [b_is_party_of_protocol])).
2.33/0.80	cnf(c_50, plain, intruder_message(pair(A,B)) | ~intruder_message(A) | ~intruder_message(B), inference(clausify, [status(thm)], [intruder_composes_pairs])).
2.33/0.80	fof(t_is_party_of_protocol, axiom, (party_of_protocol(t)), file('theBenchmark.p',t_is_party_of_protocol)).
2.33/0.80	cnf(c_51, plain, party_of_protocol(t), inference(clausify, [status(thm)], [t_is_party_of_protocol])).
2.33/0.80	cnf(c_53, plain, message(sent(A,B,C)) | ~intruder_message(C) | ~party_of_protocol(B) | ~party_of_protocol(A), inference(clausify, [status(thm)], [intruder_message_sent])).
2.33/0.80	cnf(c_55, plain, ~intruder_message(pair(A,B)) | intruder_message(B), inference(clausify, [status(thm)], [intruder_decomposes_pairs])).
2.33/0.80	cnf(c_58, plain, ~message(sent(A,B,C)) | intruder_message(C), inference(clausify, [status(thm)], [intruder_can_record])).
2.33/0.80	cnf(c_3000, negated_conjecture, ~message(sent(a,b,pair(encrypt(triple(a,A,generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),A)))) | ~intruder_message(A) | ~party_of_protocol(b),
2.33/0.80	    inference(resolve, [status(thm)], [c_48, c_39])).
2.33/0.80	cnf(c_67, negated_conjecture, ~message(sent(a,b,pair(encrypt(triple(a,A,generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),A)))) | ~intruder_message(A),
2.33/0.80	    inference(resolve, [status(thm)], [c_49, c_3000])).
2.33/0.80	cnf(c_68, plain, message(sent(b,t,triple(b,generate_b_nonce(an_a_nonce),encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt)))),
2.33/0.80	    inference(resolve, [status(thm)], [c_42, c_48])).
2.33/0.80	cnf(c_69, plain, intruder_message(pair(a,an_a_nonce)),
2.33/0.80	    inference(resolve, [status(thm)], [c_58, c_48])).
2.33/0.80	cnf(c_3001, negated_conjecture, ~intruder_message(A) | ~intruder_message(pair(encrypt(triple(a,A,generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),A))) | ~party_of_protocol(b) | ~party_of_protocol(a),
2.33/0.80	    inference(resolve, [status(thm)], [c_67, c_53])).
2.33/0.80	cnf(c_3002, negated_conjecture, ~intruder_message(A) | ~intruder_message(pair(encrypt(triple(a,A,generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),A))) | ~party_of_protocol(a),
2.33/0.80	    inference(resolve, [status(thm)], [c_49, c_3001])).
2.33/0.80	cnf(c_70, negated_conjecture, ~intruder_message(A) | ~intruder_message(pair(encrypt(triple(a,A,generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),A))),
2.33/0.80	    inference(resolve, [status(thm)], [c_43, c_3002])).
2.33/0.80	cnf(c_71, plain, intruder_message(triple(b,generate_b_nonce(an_a_nonce),encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt))),
2.33/0.80	    inference(resolve, [status(thm)], [c_58, c_68])).
2.33/0.80	cnf(c_74, plain, intruder_message(an_a_nonce),
2.33/0.80	    inference(resolve, [status(thm)], [c_55, c_69])).
2.33/0.80	cnf(c_100, plain, ~intruder_message(A) | ~intruder_message(encrypt(triple(a,A,generate_expiration_time(an_a_nonce)),bt)) | ~intruder_message(encrypt(generate_b_nonce(an_a_nonce),A)),
2.33/0.80	    inference(resolve, [status(thm)], [c_70, c_50])).
2.33/0.80	cnf(c_301, plain, ~intruder_message(encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt)) | ~intruder_message(encrypt(generate_b_nonce(an_a_nonce),an_a_nonce)),
2.33/0.80	    inference(resolve, [status(thm)], [c_74, c_100])).
2.33/0.80	cnf(c_2201, plain, intruder_message(encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt)),
2.33/0.80	    inference(resolve, [status(thm)], [c_46, c_71])).
2.33/0.80	cnf(c_2202, plain, intruder_message(generate_b_nonce(an_a_nonce)),
2.33/0.80	    inference(resolve, [status(thm)], [c_45, c_71])).
2.33/0.80	cnf(c_2215, plain, ~intruder_message(encrypt(generate_b_nonce(an_a_nonce),an_a_nonce)),
2.33/0.80	    inference(resolve, [status(thm)], [c_2201, c_301])).
2.33/0.80	cnf(c_3003, plain, ~party_of_protocol(A) | ~intruder_message(generate_b_nonce(an_a_nonce)) | ~intruder_message(an_a_nonce),
2.33/0.80	    inference(resolve, [status(thm)], [c_2215, c_41])).
2.33/0.80	cnf(c_3004, plain, ~party_of_protocol(A) | ~intruder_message(an_a_nonce),
2.33/0.80	    inference(resolve, [status(thm)], [c_2202, c_3003])).
2.33/0.80	cnf(c_2998, plain, ~party_of_protocol(A),
2.33/0.80	    inference(resolve, [status(thm)], [c_74, c_3004])).
2.33/0.80	cnf(c_2999, plain, $false,
2.33/0.80	    inference(resolve, [status(thm)], [c_2998, c_51])).
2.33/0.80	% SZS output end CNFRefutation for theBenchmark
2.33/0.80	EOF