0.00/0.00	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : original
0.00/0.00	% Variant    : purification_ext
0.00/0.00	% Ordering    : rpo6
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-avatar \
0.00/0.00	  --ho \
0.00/0.00	  --force-ho \
0.00/0.00	  --no-ho-elim-pred-var \
0.00/0.00	  --ho-general-ext-pos \
0.00/0.00	  --no-ho-unif \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2  \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --ho-purify ext \
0.00/0.00	  --ho-ext-axiom \
0.00/0.00	  --restrict-hidden-sup-at-vars \
0.00/0.00	  --ho-prim-enum none \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --dont-select-ho-var-lits \
0.00/0.00	  --no-fool
0.00/0.20	% Computer   : n184.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 14:31:54 CST 2018
0.83/1.05	% done 922 iterations in 0.846s
0.83/1.05	% SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
0.83/1.05	% SZS output start Refutation
0.83/1.05	tff(conj_0, axiom,
0.83/1.05	  (member(event,
0.83/1.05	          says(server,a,crypt(k1,mPair(na,mPair(agent1(b),mPair(key(k),x))))),
0.83/1.05	          set(event,evs)))).
0.83/1.05	tff('0', plain,
0.83/1.05	    member(event, 
0.83/1.05	      says(server, a, 
0.83/1.05	        crypt(k1, mPair(na, mPair(agent1(b), mPair(key(k), x))))), 
0.83/1.05	      set(event, evs)),
0.83/1.05	    inference('cnf', [status(esa)], [conj_0])).
0.83/1.05	tff(conj_4, axiom, (member(list(event),evs,nS_Sha254967238shared))).
0.83/1.05	tff('1', plain, member(list(event), evs, nS_Sha254967238shared),
0.83/1.05	    inference('cnf', [status(esa)], [conj_4])).
0.83/1.05	tff(fact_91_Says__Server__message__form, axiom,
0.83/1.05	  (![Evsa:list(event),Xa:msg,Ka:nat,Ba:agent,N:msg,K_a:nat,Aa:agent]:
0.83/1.05	     (member(event,
0.83/1.05	             says(server,Aa,
0.83/1.05	                  crypt(K_a,mPair(N,mPair(agent1(Ba),mPair(key(Ka),Xa))))),
0.83/1.05	             set(event,Evsa)) =>
0.83/1.05	      (member(list(event),Evsa,nS_Sha254967238shared) =>
0.83/1.05	       ((K_a = aa(agent,nat,shrK,Aa)) & 
0.83/1.05	        (Xa = crypt(aa(agent,nat,shrK,Ba),mPair(key(Ka),agent1(Aa)))) & 
0.83/1.05	        (~member(nat,Ka,image(agent,nat,shrK,top_top(fun(agent,bool)))))))))).
0.83/1.05	tff('2', plain,
0.83/1.05	    ![X300 : list(event), X301 : agent, X302 : nat, X303 : msg, 
0.83/1.05	      X304 : agent, X305 : nat, X306 : msg]:
0.83/1.05	      (~ member(list(event), X300, nS_Sha254967238shared)
0.83/1.05	       | ~ member(event, 
0.83/1.05	             says(server, X301, 
0.83/1.05	               crypt(X302, 
0.83/1.05	                 mPair(X303, mPair(agent1(X304), mPair(key(X305), X306))))), 
0.83/1.05	             set(event, X300))
0.83/1.05	       | X302 = aa(agent, nat, shrK, X301)),
0.83/1.05	    inference('cnf', [status(esa)], [fact_91_Says__Server__message__form])).
0.83/1.05	tff('3', plain,
0.83/1.05	    ![X0 : nat, X1 : agent, X2 : msg, X3 : nat, X4 : agent, X5 : msg]:
0.83/1.05	      (~ $true
0.83/1.05	       | X0 = aa(agent, nat, shrK, X1)
0.83/1.05	       | ~ member(event, 
0.83/1.05	             says(server, X1, 
0.83/1.05	               crypt(X0, mPair(X5, mPair(agent1(X4), mPair(key(X3), X2))))), 
0.83/1.05	             set(event, evs))),
0.83/1.05	    inference('sup-', [status(thm)], ['1', '2'])).
0.83/1.05	tff('4', plain,
0.83/1.05	    ![X0 : nat, X1 : agent, X2 : msg, X3 : nat, X4 : agent, X5 : msg]:
0.83/1.05	      (~ member(event, 
0.83/1.05	           says(server, X1, 
0.83/1.05	             crypt(X0, mPair(X5, mPair(agent1(X4), mPair(key(X3), X2))))), 
0.83/1.05	           set(event, evs))
0.83/1.05	       | X0 = aa(agent, nat, shrK, X1)),
0.83/1.05	    inference('simplify', [status(thm)], ['3'])).
0.83/1.05	tff('5', plain, (~ $true | k1 = aa(agent, nat, shrK, a)),
0.83/1.05	    inference('sup-', [status(thm)], ['0', '4'])).
0.83/1.05	tff('6', plain, k1 = aa(agent, nat, shrK, a),
0.83/1.05	    inference('simplify', [status(thm)], ['5'])).
0.83/1.05	tff('7', plain,
0.83/1.05	    member(event, 
0.83/1.05	      says(server, a, 
0.83/1.05	        crypt(aa(agent, nat, shrK, a), 
0.83/1.05	          mPair(na, mPair(agent1(b), mPair(key(k), x))))), set(event, evs)),
0.83/1.05	    inference('demod', [status(thm)], ['0', '6'])).
0.83/1.05	tff(fact_4_Says__imp__spies, axiom,
0.83/1.05	  (![Evsa:list(event),Xa:msg,Ba:agent,Aa:agent]:
0.83/1.05	     (member(event,says(Aa,Ba,Xa),set(event,Evsa)) =>
0.83/1.05	      member(msg,Xa,knows(spy,Evsa))))).
0.83/1.05	tff('8', plain,
0.83/1.05	    ![X10 : msg, X11 : list(event), X12 : agent, X13 : agent]:
0.83/1.05	      (member(msg, X10, knows(spy, X11))
0.83/1.05	       | ~ member(event, says(X12, X13, X10), set(event, X11))),
0.83/1.05	    inference('cnf', [status(esa)], [fact_4_Says__imp__spies])).
0.83/1.05	tff('9', plain,
0.83/1.05	    (~ $true
0.83/1.05	     | member(msg, crypt(k1, mPair(na, mPair(agent1(b), mPair(key(k), x)))), 
0.83/1.05	         knows(spy, evs))),
0.83/1.05	    inference('sup-', [status(thm)], ['0', '8'])).
0.83/1.05	tff('10', plain,
0.83/1.05	    member(msg, crypt(k1, mPair(na, mPair(agent1(b), mPair(key(k), x)))), 
0.83/1.05	      knows(spy, evs)),
0.83/1.05	    inference('simplify', [status(thm)], ['9'])).
0.83/1.05	tff('11', plain,
0.83/1.05	    member(msg, 
0.83/1.05	      crypt(aa(agent, nat, shrK, a), 
0.83/1.05	        mPair(na, mPair(agent1(b), mPair(key(k), x)))), knows(spy, evs)),
0.83/1.05	    inference('demod', [status(thm)], ['10', '6'])).
0.83/1.05	tff(fact_49_parts_OInj, axiom,
0.83/1.05	  (![H:fun(msg,bool),Xa:msg]: (member(msg,Xa,H) => member(msg,Xa,parts(H))))).
0.83/1.05	tff('12', plain,
0.83/1.05	    ![X162 : msg, X163 : fun(msg, bool)]:
0.83/1.05	      (member(msg, X162, parts(X163)) | ~ member(msg, X162, X163)),
0.83/1.05	    inference('cnf', [status(esa)], [fact_49_parts_OInj])).
0.83/1.05	tff(fact_66_cert__A__form, axiom,
0.83/1.05	  (![Evsa:list(event),Xa:msg,Ka:nat,Ba:agent,NAa:msg,Aa:agent]:
0.83/1.05	     (member(msg,
0.83/1.05	             crypt(aa(agent,nat,shrK,Aa),
0.83/1.05	                   mPair(NAa,mPair(agent1(Ba),mPair(key(Ka),Xa)))),
0.83/1.05	             parts(knows(spy,Evsa))) =>
0.83/1.05	      ((~member(agent,Aa,bad)) =>
0.83/1.05	       (member(list(event),Evsa,nS_Sha254967238shared) =>
0.83/1.05	        ((Xa = crypt(aa(agent,nat,shrK,Ba),mPair(key(Ka),agent1(Aa)))) & 
0.83/1.05	         (~member(nat,Ka,image(agent,nat,shrK,top_top(fun(agent,bool))))))))))).
0.83/1.05	tff('13', plain,
0.83/1.05	    ![X208 : list(event), X209 : agent, X210 : msg, X211 : agent, 
0.83/1.05	      X212 : nat, X213 : msg]:
0.83/1.05	      (~ member(list(event), X208, nS_Sha254967238shared)
0.83/1.05	       | ~ member(msg, 
0.83/1.05	             crypt(aa(agent, nat, shrK, X209), 
0.83/1.05	               mPair(X210, mPair(agent1(X211), mPair(key(X212), X213)))), 
0.83/1.05	             parts(knows(spy, X208)))
0.83/1.05	       | X213
0.83/1.05	          = crypt(aa(agent, nat, shrK, X211), mPair(key(X212), agent1(X209)))
0.83/1.05	       | member(agent, X209, bad)),
0.83/1.05	    inference('cnf', [status(esa)], [fact_66_cert__A__form])).
0.83/1.05	tff('14', plain,
0.83/1.05	    ![X0 : agent, X1 : msg, X2 : nat, X3 : agent, X4 : msg]:
0.83/1.05	      (~ $true
0.83/1.05	       | member(agent, X0, bad)
0.83/1.05	       | X1 = crypt(aa(agent, nat, shrK, X3), mPair(key(X2), agent1(X0)))
0.83/1.05	       | ~ member(msg, 
0.83/1.05	             crypt(aa(agent, nat, shrK, X0), 
0.83/1.05	               mPair(X4, mPair(agent1(X3), mPair(key(X2), X1)))), 
0.83/1.05	             parts(knows(spy, evs)))),
0.83/1.05	    inference('sup-', [status(thm)], ['1', '13'])).
0.83/1.05	tff('15', plain,
0.83/1.05	    ![X0 : agent, X1 : msg, X2 : nat, X3 : agent, X4 : msg]:
0.83/1.05	      (~ member(msg, 
0.83/1.05	           crypt(aa(agent, nat, shrK, X0), 
0.83/1.05	             mPair(X4, mPair(agent1(X3), mPair(key(X2), X1)))), 
0.83/1.05	           parts(knows(spy, evs)))
0.83/1.05	       | X1 = crypt(aa(agent, nat, shrK, X3), mPair(key(X2), agent1(X0)))
0.83/1.05	       | member(agent, X0, bad)),
0.83/1.05	    inference('simplify', [status(thm)], ['14'])).
0.83/1.05	tff('16', plain,
0.83/1.05	    ![X0 : msg, X1 : nat, X2 : agent, X3 : msg, X4 : agent]:
0.83/1.05	      (~ $true
0.83/1.05	       | ~ member(msg, 
0.83/1.05	             crypt(aa(agent, nat, shrK, X4), 
0.83/1.05	               mPair(X3, mPair(agent1(X2), mPair(key(X1), X0)))), 
0.83/1.05	             knows(spy, evs))
0.83/1.05	       | member(agent, X4, bad)
0.83/1.05	       | X0 = crypt(aa(agent, nat, shrK, X2), mPair(key(X1), agent1(X4)))),
0.83/1.05	    inference('sup-', [status(thm)], ['12', '15'])).
0.83/1.05	tff('17', plain,
0.83/1.05	    ![X0 : msg, X1 : nat, X2 : agent, X3 : msg, X4 : agent]:
0.83/1.05	      (X0 = crypt(aa(agent, nat, shrK, X2), mPair(key(X1), agent1(X4)))
0.83/1.05	       | member(agent, X4, bad)
0.83/1.05	       | ~ member(msg, 
0.83/1.05	             crypt(aa(agent, nat, shrK, X4), 
0.83/1.05	               mPair(X3, mPair(agent1(X2), mPair(key(X1), X0)))), 
0.83/1.05	             knows(spy, evs))),
0.83/1.05	    inference('simplify', [status(thm)], ['16'])).
0.83/1.05	tff('18', plain,
0.83/1.05	    (~ $true
0.83/1.05	     | member(agent, a, bad)
0.83/1.05	     | x = crypt(aa(agent, nat, shrK, b), mPair(key(k), agent1(a)))),
0.83/1.05	    inference('sup-', [status(thm)], ['11', '17'])).
0.83/1.05	tff('19', plain,
0.83/1.05	    (x = crypt(aa(agent, nat, shrK, b), mPair(key(k), agent1(a)))
0.83/1.05	     | member(agent, a, bad)),
0.83/1.05	    inference('simplify', [status(thm)], ['18'])).
0.83/1.05	tff(conj_2, axiom, (~member(agent,a,bad))).
0.83/1.05	tff('20', plain, ~ member(agent, a, bad),
0.83/1.05	    inference('cnf', [status(esa)], [conj_2])).
0.83/1.05	tff('21', plain,
0.83/1.05	    x = crypt(aa(agent, nat, shrK, b), mPair(key(k), agent1(a))),
0.83/1.05	    inference('clc', [status(thm)], ['19', '20'])).
0.83/1.05	tff('22', plain,
0.83/1.05	    member(event, 
0.83/1.05	      says(server, a, 
0.83/1.05	        crypt(aa(agent, nat, shrK, a), 
0.83/1.05	          mPair(na, 
0.83/1.05	            mPair(agent1(b), 
0.83/1.05	              mPair(key(k), 
0.83/1.05	                crypt(aa(agent, nat, shrK, b), mPair(key(k), agent1(a)))))))), 
0.83/1.05	      set(event, evs)),
0.83/1.05	    inference('demod', [status(thm)], ['7', '21'])).
0.83/1.05	tff(fact_7_secrecy__lemma, axiom,
0.83/1.05	  (![Evsa:list(event),Ka:nat,Ba:agent,NAa:msg,Aa:agent]:
0.83/1.05	     (member(event,
0.83/1.05	             says(server,Aa,
0.83/1.05	                  crypt(aa(agent,nat,shrK,Aa),
0.83/1.05	                        mPair(NAa,
0.83/1.05	                              mPair(agent1(Ba),
0.83/1.05	                                    mPair(key(Ka),
0.83/1.05	                                          crypt(aa(agent,nat,shrK,Ba),
0.83/1.05	                                                mPair(key(Ka),agent1(Aa)))))))),
0.83/1.05	             set(event,Evsa)) =>
0.83/1.05	      ((~member(agent,Aa,bad)) =>
0.83/1.05	       ((~member(agent,Ba,bad)) =>
0.83/1.05	        (member(list(event),Evsa,nS_Sha254967238shared) =>
0.83/1.05	         ((![NB2:msg]:
0.83/1.05	             (~
0.83/1.05	               member(event,notes(spy,mPair(NAa,mPair(NB2,key(Ka)))),
0.83/1.05	                      set(event,Evsa)))) =>
0.83/1.05	          (~member(msg,key(Ka),analz(knows(spy,Evsa))))))))))).
0.83/1.05	tff('23', plain,
0.83/1.05	    ![X21 : list(event), X22 : nat, X23 : msg, X24 : agent, X25 : agent]:
0.83/1.05	      (~ member(list(event), X21, nS_Sha254967238shared)
0.83/1.05	       | ~ member(msg, key(X22), analz(knows(spy, X21)))
0.83/1.05	       | member(event, 
0.83/1.05	           notes(spy, mPair(X23, mPair(sk_NB2(X23, X22, X21), key(X22)))), 
0.83/1.05	           set(event, X21))
0.83/1.05	       | member(agent, X24, bad)
0.83/1.05	       | ~ member(event, 
0.83/1.05	             says(server, X25, 
0.83/1.05	               crypt(aa(agent, nat, shrK, X25), 
0.83/1.05	                 mPair(X23, 
0.83/1.05	                   mPair(agent1(X24), 
0.83/1.05	                     mPair(key(X22), 
0.83/1.05	                       crypt(aa(agent, nat, shrK, X24), 
0.83/1.05	                         mPair(key(X22), agent1(X25)))))))), set(event, X21))
0.83/1.05	       | member(agent, X25, bad)),
0.83/1.05	    inference('cnf', [status(esa)], [fact_7_secrecy__lemma])).
0.83/1.05	tff('24', plain,
0.83/1.05	    (~ $true
0.83/1.05	     | member(agent, a, bad)
0.83/1.05	     | member(agent, b, bad)
0.83/1.05	     | member(event, 
0.83/1.05	         notes(spy, mPair(na, mPair(sk_NB2(na, k, evs), key(k)))), 
0.83/1.05	         set(event, evs))
0.83/1.05	     | ~ member(msg, key(k), analz(knows(spy, evs)))
0.83/1.05	     | ~ member(list(event), evs, nS_Sha254967238shared)),
0.83/1.05	    inference('sup-', [status(thm)], ['22', '23'])).
0.83/1.05	tff(conj_5, conjecture, (~member(msg,key(k),analz(knows(spy,evs))))).
0.83/1.05	tff(zf_stmt_0, negated_conjecture,
0.83/1.05	  (member(msg,key(k),analz(knows(spy,evs))))).
0.83/1.05	tff('25', plain, member(msg, key(k), analz(knows(spy, evs))),
0.83/1.05	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.83/1.05	tff('26', plain,
0.83/1.05	    (~ $true
0.83/1.05	     | member(agent, a, bad)
0.83/1.05	     | member(agent, b, bad)
0.83/1.05	     | member(event, 
0.83/1.05	         notes(spy, mPair(na, mPair(sk_NB2(na, k, evs), key(k)))), 
0.83/1.05	         set(event, evs))
0.83/1.05	     | ~ $true
0.83/1.05	     | ~ $true),
0.83/1.05	    inference('demod', [status(thm)], ['24', '25', '1'])).
0.83/1.05	tff('27', plain,
0.83/1.05	    (member(event, notes(spy, mPair(na, mPair(sk_NB2(na, k, evs), key(k)))), 
0.83/1.05	       set(event, evs))
0.83/1.05	     | member(agent, b, bad)
0.83/1.05	     | member(agent, a, bad)),
0.83/1.05	    inference('simplify', [status(thm)], ['26'])).
0.83/1.05	tff(conj_1, axiom,
0.83/1.05	  (![NB:msg]:
0.83/1.05	     (~member(event,notes(spy,mPair(na,mPair(NB,key(k)))),set(event,evs))))).
0.83/1.05	tff('28', plain,
0.83/1.05	    ![X340 : msg]:
0.83/1.05	      ~ member(event, notes(spy, mPair(na, mPair(X340, key(k)))), 
0.83/1.05	          set(event, evs)),
0.83/1.05	    inference('cnf', [status(esa)], [conj_1])).
0.83/1.05	tff('29', plain, (member(agent, a, bad) | member(agent, b, bad)),
0.83/1.05	    inference('clc', [status(thm)], ['27', '28'])).
0.83/1.05	tff('30', plain, member(agent, b, bad),
0.83/1.05	    inference('clc', [status(thm)], ['29', '20'])).
0.83/1.05	tff(conj_3, axiom, (~member(agent,b,bad))).
0.83/1.05	tff('31', plain, ~ member(agent, b, bad),
0.83/1.05	    inference('cnf', [status(esa)], [conj_3])).
0.83/1.05	tff('32', plain, ~ $true, inference('sup-', [status(thm)], ['30', '31'])).
0.83/1.05	tff('33', plain, $false, inference('simplify', [status(thm)], ['32'])).
0.83/1.05	
0.83/1.05	% SZS output end Refutation
0.83/1.05	EOF
