0.00/0.01	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.01	% app-encoded or not : original
0.00/0.01	% Variant    : purification_ext
0.00/0.01	% Ordering    : rpo6
0.00/0.01	% Command    : 
0.00/0.01	#!/bin/sh
0.00/0.01	
0.00/0.01	./zipperposition.native ${1:+"$1"} \
0.00/0.01	  -i tptp \
0.00/0.01	  -o tptp \
0.00/0.01	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.01	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.01	  --no-avatar \
0.00/0.01	  --ho \
0.00/0.01	  --force-ho \
0.00/0.01	  --no-ho-elim-pred-var \
0.00/0.01	  --ho-general-ext-pos \
0.00/0.01	  --no-ho-unif \
0.00/0.01	  --no-induction \
0.00/0.01	  --no-unif-pattern \
0.00/0.01	  --ord $2  \
0.00/0.01	  --simultaneous-sup false \
0.00/0.01	  --ho-purify ext \
0.00/0.01	  --ho-ext-axiom \
0.00/0.01	  --restrict-hidden-sup-at-vars \
0.00/0.01	  --ho-prim-enum none \
0.00/0.01	  --no-max-vars \
0.00/0.01	  --dont-select-ho-var-lits \
0.00/0.01	  --no-fool
0.00/0.20	% Computer   : n078.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 14:48:39 CST 2018
2.89/3.11	% done 3224 iterations in 2.902s
2.89/3.11	% SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
2.89/3.11	% SZS output start Refutation
2.89/3.11	tff(conj_5, axiom,
2.89/3.11	  (member(event,
2.89/3.11	          says(s,aa,
2.89/3.11	               crypt(shrK(aa),
2.89/3.11	                     mPair(nonce(nAa),mPair(agent(ba),mPair(key(ka),xa))))),
2.89/3.11	          set(event,evs5)))).
2.89/3.11	tff('0', plain,
2.89/3.11	    member(event, 
2.89/3.11	      says(s, aa, 
2.89/3.11	        crypt(shrK(aa), 
2.89/3.11	          mPair(nonce(nAa), mPair(agent(ba), mPair(key(ka), xa))))), 
2.89/3.11	      set(event, evs5)),
2.89/3.11	    inference('cnf', [status(esa)], [conj_5])).
2.89/3.11	tff(conj_8, conjecture,
2.89/3.11	  (member(event,says(a,b,crypt(ka,mPair(nonce(nBa),nonce(nBa)))),
2.89/3.11	          set(event,evs5)) | 
2.89/3.11	   ((b = ba) & (a = aa)) | (nb != nBa) | (k != ka) | 
2.89/3.11	   (~
2.89/3.11	     member(msg,
2.89/3.11	            crypt(shrK(a),mPair(nonce(na),mPair(agent(b),mPair(key(k),x)))),
2.89/3.11	            parts(knows(spy,evs5)))))).
2.89/3.11	tff(zf_stmt_0, negated_conjecture,
2.89/3.11	  (~
2.89/3.11	    (member(event,says(a,b,crypt(ka,mPair(nonce(nBa),nonce(nBa)))),
2.89/3.11	            set(event,evs5)) | 
2.89/3.11	     ((b = ba) & (a = aa)) | (nb != nBa) | (k != ka) | 
2.89/3.11	     (~
2.89/3.11	       member(msg,
2.89/3.11	              crypt(shrK(a),mPair(nonce(na),mPair(agent(b),mPair(key(k),x)))),
2.89/3.11	              parts(knows(spy,evs5))))))).
2.89/3.11	tff('1', plain, k = ka, inference('cnf', [status(esa)], [zf_stmt_0])).
2.89/3.11	tff('2', plain,
2.89/3.11	    member(event, 
2.89/3.11	      says(s, aa, 
2.89/3.11	        crypt(shrK(aa), 
2.89/3.11	          mPair(nonce(nAa), mPair(agent(ba), mPair(key(k), xa))))), 
2.89/3.11	      set(event, evs5)),
2.89/3.11	    inference('demod', [status(thm)], ['0', '1'])).
2.89/3.11	tff(fact_10_Says__imp__parts__knows__Spy, axiom,
2.89/3.11	  (![Evsa:list(event),Xa:msg,Ba:agent1,Aa:agent1]:
2.89/3.11	     (member(event,says(Aa,Ba,Xa),set(event,Evsa)) =>
2.89/3.11	      member(msg,Xa,parts(knows(spy,Evsa)))))).
2.89/3.11	tff('3', plain,
2.89/3.11	    ![X32 : msg, X33 : list(event), X34 : agent1, X35 : agent1]:
2.89/3.11	      (member(msg, X32, parts(knows(spy, X33)))
2.89/3.11	       | ~ member(event, says(X34, X35, X32), set(event, X33))),
2.89/3.11	    inference('cnf', [status(esa)], [fact_10_Says__imp__parts__knows__Spy])).
2.89/3.11	tff('4', plain,
2.89/3.11	    (~ $true
2.89/3.11	     | member(msg, 
2.89/3.11	         crypt(shrK(aa), 
2.89/3.11	           mPair(nonce(nAa), mPair(agent(ba), mPair(key(k), xa)))), 
2.89/3.11	         parts(knows(spy, evs5)))),
2.89/3.11	    inference('sup-', [status(thm)], ['2', '3'])).
2.89/3.11	tff('5', plain,
2.89/3.11	    member(msg, 
2.89/3.11	      crypt(shrK(aa), mPair(nonce(nAa), mPair(agent(ba), mPair(key(k), xa)))), 
2.89/3.11	      parts(knows(spy, evs5))),
2.89/3.11	    inference('simplify', [status(thm)], ['4'])).
2.89/3.11	tff(conj_2, axiom, (member(list(event),evs5,nS_Sha254967238shared))).
2.89/3.11	tff('6', plain, member(list(event), evs5, nS_Sha254967238shared),
2.89/3.11	    inference('cnf', [status(esa)], [conj_2])).
2.89/3.11	tff(fact_67_A__trusts__NS2, axiom,
2.89/3.11	  (![Evsa:list(event),Xa:msg,Ka:nat,Ba:agent1,NAa:msg,Aa:agent1]:
2.89/3.11	     (member(msg,
2.89/3.11	             crypt(shrK(Aa),mPair(NAa,mPair(agent(Ba),mPair(key(Ka),Xa)))),
2.89/3.11	             parts(knows(spy,Evsa))) =>
2.89/3.11	      ((~member(agent1,Aa,bad)) =>
2.89/3.11	       (member(list(event),Evsa,nS_Sha254967238shared) =>
2.89/3.11	        member(event,
2.89/3.11	               says(server,Aa,
2.89/3.11	                    crypt(shrK(Aa),
2.89/3.11	                          mPair(NAa,mPair(agent(Ba),mPair(key(Ka),Xa))))),
2.89/3.11	               set(event,Evsa))))))).
2.89/3.11	tff('7', plain,
2.89/3.11	    ![X203 : list(event), X204 : agent1, X205 : msg, X206 : agent1, 
2.89/3.11	      X207 : nat, X208 : msg]:
2.89/3.11	      (~ member(list(event), X203, nS_Sha254967238shared)
2.89/3.11	       | ~ member(msg, 
2.89/3.11	             crypt(shrK(X204), 
2.89/3.11	               mPair(X205, mPair(agent(X206), mPair(key(X207), X208)))), 
2.89/3.11	             parts(knows(spy, X203)))
2.89/3.11	       | member(event, 
2.89/3.11	           says(server, X204, 
2.89/3.11	             crypt(shrK(X204), 
2.89/3.11	               mPair(X205, mPair(agent(X206), mPair(key(X207), X208))))), 
2.89/3.11	           set(event, X203))
2.89/3.11	       | member(agent1, X204, bad)),
2.89/3.11	    inference('cnf', [status(esa)], [fact_67_A__trusts__NS2])).
2.89/3.11	tff('8', plain,
2.89/3.11	    ![X0 : agent1, X1 : msg, X2 : nat, X3 : agent1, X4 : msg]:
2.89/3.11	      (~ $true
2.89/3.11	       | member(agent1, X0, bad)
2.89/3.11	       | member(event, 
2.89/3.11	           says(server, X0, 
2.89/3.11	             crypt(shrK(X0), mPair(X4, mPair(agent(X3), mPair(key(X2), X1))))), 
2.89/3.11	           set(event, evs5))
2.89/3.11	       | ~ member(msg, 
2.89/3.11	             crypt(shrK(X0), mPair(X4, mPair(agent(X3), mPair(key(X2), X1)))), 
2.89/3.11	             parts(knows(spy, evs5)))),
2.89/3.11	    inference('sup-', [status(thm)], ['6', '7'])).
2.89/3.11	tff('9', plain,
2.89/3.11	    ![X0 : agent1, X1 : msg, X2 : nat, X3 : agent1, X4 : msg]:
2.89/3.11	      (~ member(msg, 
2.89/3.11	           crypt(shrK(X0), mPair(X4, mPair(agent(X3), mPair(key(X2), X1)))), 
2.89/3.11	           parts(knows(spy, evs5)))
2.89/3.11	       | member(event, 
2.89/3.11	           says(server, X0, 
2.89/3.11	             crypt(shrK(X0), mPair(X4, mPair(agent(X3), mPair(key(X2), X1))))), 
2.89/3.11	           set(event, evs5))
2.89/3.11	       | member(agent1, X0, bad)),
2.89/3.11	    inference('simplify', [status(thm)], ['8'])).
2.89/3.11	tff('10', plain,
2.89/3.11	    (~ $true
2.89/3.11	     | member(agent1, aa, bad)
2.89/3.11	     | member(event, 
2.89/3.11	         says(server, aa, 
2.89/3.11	           crypt(shrK(aa), 
2.89/3.11	             mPair(nonce(nAa), mPair(agent(ba), mPair(key(k), xa))))), 
2.89/3.11	         set(event, evs5))),
2.89/3.11	    inference('sup-', [status(thm)], ['5', '9'])).
2.89/3.11	tff('11', plain,
2.89/3.11	    (member(event, 
2.89/3.11	       says(server, aa, 
2.89/3.11	         crypt(shrK(aa), 
2.89/3.11	           mPair(nonce(nAa), mPair(agent(ba), mPair(key(k), xa))))), 
2.89/3.11	       set(event, evs5))
2.89/3.11	     | member(agent1, aa, bad)),
2.89/3.11	    inference('simplify', [status(thm)], ['10'])).
2.89/3.11	tff(fact_11_Says__imp__analz__Spy, axiom,
2.89/3.11	  (![Evsa:list(event),Xa:msg,Ba:agent1,Aa:agent1]:
2.89/3.11	     (member(event,says(Aa,Ba,Xa),set(event,Evsa)) =>
2.89/3.11	      member(msg,Xa,analz(knows(spy,Evsa)))))).
2.89/3.11	tff('12', plain,
2.89/3.11	    ![X36 : msg, X37 : list(event), X38 : agent1, X39 : agent1]:
2.89/3.11	      (member(msg, X36, analz(knows(spy, X37)))
2.89/3.11	       | ~ member(event, says(X38, X39, X36), set(event, X37))),
2.89/3.11	    inference('cnf', [status(esa)], [fact_11_Says__imp__analz__Spy])).
2.89/3.11	tff('13', plain,
2.89/3.11	    (~ $true
2.89/3.11	     | member(msg, 
2.89/3.11	         crypt(shrK(aa), 
2.89/3.11	           mPair(nonce(nAa), mPair(agent(ba), mPair(key(k), xa)))), 
2.89/3.11	         analz(knows(spy, evs5)))),
2.89/3.11	    inference('sup-', [status(thm)], ['2', '12'])).
2.89/3.11	tff('14', plain,
2.89/3.11	    member(msg, 
2.89/3.11	      crypt(shrK(aa), mPair(nonce(nAa), mPair(agent(ba), mPair(key(k), xa)))), 
2.89/3.11	      analz(knows(spy, evs5))),
2.89/3.11	    inference('simplify', [status(thm)], ['13'])).
2.89/3.11	tff(fact_7_Crypt__Spy__analz__bad, axiom,
2.89/3.11	  (![Evsa:list(event),Xa:msg,Aa:agent1]:
2.89/3.11	     (member(msg,crypt(shrK(Aa),Xa),analz(knows(spy,Evsa))) =>
2.89/3.11	      (member(agent1,Aa,bad) => member(msg,Xa,analz(knows(spy,Evsa))))))).
2.89/3.11	tff('15', plain,
2.89/3.11	    ![X28 : msg, X29 : list(event), X30 : agent1]:
2.89/3.11	      (member(msg, X28, analz(knows(spy, X29)))
2.89/3.11	       | ~ member(msg, crypt(shrK(X30), X28), analz(knows(spy, X29)))
2.89/3.11	       | ~ member(agent1, X30, bad)),
2.89/3.11	    inference('cnf', [status(esa)], [fact_7_Crypt__Spy__analz__bad])).
2.89/3.11	tff('16', plain,
2.89/3.11	    (~ $true
2.89/3.11	     | ~ member(agent1, aa, bad)
2.89/3.11	     | member(msg, mPair(nonce(nAa), mPair(agent(ba), mPair(key(k), xa))), 
2.89/3.11	         analz(knows(spy, evs5)))),
2.89/3.11	    inference('sup-', [status(thm)], ['14', '15'])).
2.89/3.11	tff('17', plain,
2.89/3.11	    (member(msg, mPair(nonce(nAa), mPair(agent(ba), mPair(key(k), xa))), 
2.89/3.11	       analz(knows(spy, evs5)))
2.89/3.11	     | ~ member(agent1, aa, bad)),
2.89/3.11	    inference('simplify', [status(thm)], ['16'])).
2.89/3.11	tff(fact_26_MPair__analz, axiom,
2.89/3.11	  (![H:fun(msg,bool),Y:msg,Xa:msg]:
2.89/3.11	     (member(msg,mPair(Xa,Y),analz(H)) =>
2.89/3.11	      (~(member(msg,Xa,analz(H)) => (~member(msg,Y,analz(H)))))))).
2.89/3.11	tff('18', plain,
2.89/3.11	    ![X80 : msg, X81 : fun(msg, bool), X82 : msg]:
2.89/3.11	      (member(msg, X80, analz(X81))
2.89/3.11	       | ~ member(msg, mPair(X82, X80), analz(X81))),
2.89/3.11	    inference('cnf', [status(esa)], [fact_26_MPair__analz])).
2.89/3.11	tff('19', plain,
2.89/3.11	    (~ $true
2.89/3.11	     | ~ member(agent1, aa, bad)
2.89/3.11	     | member(msg, mPair(agent(ba), mPair(key(k), xa)), 
2.89/3.11	         analz(knows(spy, evs5)))),
2.89/3.11	    inference('sup-', [status(thm)], ['17', '18'])).
2.89/3.11	tff('20', plain,
2.89/3.11	    (member(msg, mPair(agent(ba), mPair(key(k), xa)), 
2.89/3.11	       analz(knows(spy, evs5)))
2.89/3.11	     | ~ member(agent1, aa, bad)),
2.89/3.11	    inference('simplify', [status(thm)], ['19'])).
2.89/3.11	tff('21', plain,
2.89/3.11	    (~ $true
2.89/3.11	     | ~ member(agent1, aa, bad)
2.89/3.11	     | member(msg, mPair(key(k), xa), analz(knows(spy, evs5)))),
2.89/3.11	    inference('sup-', [status(thm)], ['20', '18'])).
2.89/3.11	tff('22', plain,
2.89/3.11	    (member(msg, mPair(key(k), xa), analz(knows(spy, evs5)))
2.89/3.11	     | ~ member(agent1, aa, bad)),
2.89/3.11	    inference('simplify', [status(thm)], ['21'])).
2.89/3.11	tff('23', plain,
2.89/3.11	    ![X80 : msg, X81 : fun(msg, bool), X82 : msg]:
2.89/3.11	      (member(msg, X82, analz(X81))
2.89/3.11	       | ~ member(msg, mPair(X82, X80), analz(X81))),
2.89/3.11	    inference('cnf', [status(esa)], [fact_26_MPair__analz])).
2.89/3.11	tff('24', plain,
2.89/3.11	    (~ $true
2.89/3.11	     | ~ member(agent1, aa, bad)
2.89/3.11	     | member(msg, key(k), analz(knows(spy, evs5)))),
2.89/3.11	    inference('sup-', [status(thm)], ['22', '23'])).
2.89/3.11	tff('25', plain,
2.89/3.11	    (member(msg, key(k), analz(knows(spy, evs5))) | ~ member(agent1, aa, bad)),
2.89/3.11	    inference('simplify', [status(thm)], ['24'])).
2.89/3.11	tff(conj_6, axiom, (~member(msg,key(k),analz(knows(spy,evs5))))).
2.89/3.11	tff('26', plain, ~ member(msg, key(k), analz(knows(spy, evs5))),
2.89/3.11	    inference('cnf', [status(esa)], [conj_6])).
2.89/3.11	tff('27', plain, ~ member(agent1, aa, bad),
2.89/3.11	    inference('clc', [status(thm)], ['25', '26'])).
2.89/3.11	tff('28', plain,
2.89/3.11	    member(event, 
2.89/3.11	      says(server, aa, 
2.89/3.11	        crypt(shrK(aa), 
2.89/3.11	          mPair(nonce(nAa), mPair(agent(ba), mPair(key(k), xa))))), 
2.89/3.11	      set(event, evs5)),
2.89/3.11	    inference('clc', [status(thm)], ['11', '27'])).
2.89/3.11	tff('29', plain,
2.89/3.11	    member(msg, 
2.89/3.11	      crypt(shrK(a), mPair(nonce(na), mPair(agent(b), mPair(key(k), x)))), 
2.89/3.11	      parts(knows(spy, evs5))),
2.89/3.11	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.89/3.11	tff('30', plain,
2.89/3.11	    (~ $true
2.89/3.11	     | member(agent1, a, bad)
2.89/3.11	     | member(event, 
2.89/3.11	         says(server, a, 
2.89/3.11	           crypt(shrK(a), 
2.89/3.11	             mPair(nonce(na), mPair(agent(b), mPair(key(k), x))))), 
2.89/3.11	         set(event, evs5))),
2.89/3.11	    inference('sup-', [status(thm)], ['29', '9'])).
2.89/3.11	tff('31', plain,
2.89/3.11	    (member(event, 
2.89/3.11	       says(server, a, 
2.89/3.11	         crypt(shrK(a), mPair(nonce(na), mPair(agent(b), mPair(key(k), x))))), 
2.89/3.11	       set(event, evs5))
2.89/3.11	     | member(agent1, a, bad)),
2.89/3.11	    inference('simplify', [status(thm)], ['30'])).
2.89/3.11	tff(conj_0, axiom, (~member(agent1,a,bad))).
2.89/3.11	tff('32', plain, ~ member(agent1, a, bad),
2.89/3.11	    inference('cnf', [status(esa)], [conj_0])).
2.89/3.11	tff('33', plain,
2.89/3.11	    member(event, 
2.89/3.11	      says(server, a, 
2.89/3.11	        crypt(shrK(a), mPair(nonce(na), mPair(agent(b), mPair(key(k), x))))), 
2.89/3.11	      set(event, evs5)),
2.89/3.11	    inference('clc', [status(thm)], ['31', '32'])).
2.89/3.11	tff(fact_88_unique__session__keys, axiom,
2.89/3.11	  (![X1:msg,B:agent1,NA:msg,A:agent1,Evsa:list(event),Xa:msg,Ka:nat,
2.89/3.11	     Ba:agent1,NAa:msg,Aa:agent1]:
2.89/3.11	     (member(event,
2.89/3.11	             says(server,Aa,
2.89/3.11	                  crypt(shrK(Aa),
2.89/3.11	                        mPair(NAa,mPair(agent(Ba),mPair(key(Ka),Xa))))),
2.89/3.11	             set(event,Evsa)) =>
2.89/3.11	      (member(event,
2.89/3.11	              says(server,A,
2.89/3.11	                   crypt(shrK(A),mPair(NA,mPair(agent(B),mPair(key(Ka),X1))))),
2.89/3.11	              set(event,Evsa)) =>
2.89/3.11	       (member(list(event),Evsa,nS_Sha254967238shared) =>
2.89/3.11	        ((Xa = X1) & (Ba = B) & (NAa = NA) & (Aa = A))))))).
2.89/3.11	tff('34', plain,
2.89/3.11	    ![X299 : agent1, X300 : msg, X301 : agent1, X302 : nat, X303 : msg, 
2.89/3.11	      X304 : list(event), X305 : agent1, X306 : msg, X307 : agent1, 
2.89/3.11	      X308 : msg]:
2.89/3.11	      (~ member(event, 
2.89/3.11	           says(server, X299, 
2.89/3.11	             crypt(shrK(X299), 
2.89/3.11	               mPair(X300, mPair(agent(X301), mPair(key(X302), X303))))), 
2.89/3.11	           set(event, X304))
2.89/3.11	       | ~ member(list(event), X304, nS_Sha254967238shared)
2.89/3.11	       | ~ member(event, 
2.89/3.11	             says(server, X305, 
2.89/3.11	               crypt(shrK(X305), 
2.89/3.11	                 mPair(X306, mPair(agent(X307), mPair(key(X302), X308))))), 
2.89/3.11	             set(event, X304))
2.89/3.11	       | X308 = X303),
2.89/3.11	    inference('cnf', [status(esa)], [fact_88_unique__session__keys])).
2.89/3.11	tff('35', plain,
2.89/3.11	    ![X0 : msg, X1 : agent1, X2 : msg, X3 : agent1]:
2.89/3.11	      (~ $true
2.89/3.11	       | X0 = x
2.89/3.11	       | ~ member(event, 
2.89/3.11	             says(server, X3, 
2.89/3.11	               crypt(shrK(X3), 
2.89/3.11	                 mPair(X2, mPair(agent(X1), mPair(key(k), X0))))), 
2.89/3.11	             set(event, evs5))
2.89/3.11	       | ~ member(list(event), evs5, nS_Sha254967238shared)),
2.89/3.11	    inference('sup-', [status(thm)], ['33', '34'])).
2.89/3.11	tff('36', plain,
2.89/3.11	    ![X0 : msg, X1 : agent1, X2 : msg, X3 : agent1]:
2.89/3.11	      (~ $true
2.89/3.11	       | X0 = x
2.89/3.11	       | ~ member(event, 
2.89/3.11	             says(server, X3, 
2.89/3.11	               crypt(shrK(X3), 
2.89/3.11	                 mPair(X2, mPair(agent(X1), mPair(key(k), X0))))), 
2.89/3.11	             set(event, evs5))
2.89/3.11	       | ~ $true),
2.89/3.11	    inference('demod', [status(thm)], ['35', '6'])).
2.89/3.11	tff('37', plain,
2.89/3.11	    ![X0 : msg, X1 : agent1, X2 : msg, X3 : agent1]:
2.89/3.11	      (~ member(event, 
2.89/3.11	           says(server, X3, 
2.89/3.11	             crypt(shrK(X3), mPair(X2, mPair(agent(X1), mPair(key(k), X0))))), 
2.89/3.11	           set(event, evs5))
2.89/3.11	       | X0 = x),
2.89/3.11	    inference('simplify', [status(thm)], ['36'])).
2.89/3.11	tff('38', plain, (~ $true | xa = x),
2.89/3.11	    inference('sup-', [status(thm)], ['28', '37'])).
2.89/3.11	tff('39', plain, xa = x, inference('simplify', [status(thm)], ['38'])).
2.89/3.11	tff('40', plain,
2.89/3.11	    member(event, 
2.89/3.11	      says(server, aa, 
2.89/3.11	        crypt(shrK(aa), 
2.89/3.11	          mPair(nonce(nAa), mPair(agent(ba), mPair(key(k), x))))), 
2.89/3.11	      set(event, evs5)),
2.89/3.11	    inference('demod', [status(thm)], ['28', '39'])).
2.89/3.11	tff('41', plain,
2.89/3.11	    ![X299 : agent1, X300 : msg, X301 : agent1, X302 : nat, X303 : msg, 
2.89/3.11	      X304 : list(event), X305 : agent1, X306 : msg, X307 : agent1, 
2.89/3.11	      X308 : msg]:
2.89/3.11	      (~ member(event, 
2.89/3.11	           says(server, X299, 
2.89/3.11	             crypt(shrK(X299), 
2.89/3.11	               mPair(X300, mPair(agent(X301), mPair(key(X302), X303))))), 
2.89/3.11	           set(event, X304))
2.89/3.11	       | ~ member(list(event), X304, nS_Sha254967238shared)
2.89/3.11	       | ~ member(event, 
2.89/3.11	             says(server, X305, 
2.89/3.11	               crypt(shrK(X305), 
2.89/3.11	                 mPair(X306, mPair(agent(X307), mPair(key(X302), X308))))), 
2.89/3.11	             set(event, X304))
2.89/3.11	       | X307 = X301),
2.89/3.11	    inference('cnf', [status(esa)], [fact_88_unique__session__keys])).
2.89/3.11	tff('42', plain,
2.89/3.11	    ![X0 : agent1, X1 : msg, X2 : msg, X3 : agent1]:
2.89/3.11	      (~ $true
2.89/3.11	       | X0 = b
2.89/3.11	       | ~ member(event, 
2.89/3.11	             says(server, X3, 
2.89/3.11	               crypt(shrK(X3), 
2.89/3.11	                 mPair(X2, mPair(agent(X0), mPair(key(k), X1))))), 
2.89/3.11	             set(event, evs5))
2.89/3.11	       | ~ member(list(event), evs5, nS_Sha254967238shared)),
2.89/3.11	    inference('sup-', [status(thm)], ['33', '41'])).
2.89/3.11	tff('43', plain,
2.89/3.11	    ![X0 : agent1, X1 : msg, X2 : msg, X3 : agent1]:
2.89/3.11	      (~ $true
2.89/3.11	       | X0 = b
2.89/3.11	       | ~ member(event, 
2.89/3.11	             says(server, X3, 
2.89/3.11	               crypt(shrK(X3), 
2.89/3.11	                 mPair(X2, mPair(agent(X0), mPair(key(k), X1))))), 
2.89/3.11	             set(event, evs5))
2.89/3.11	       | ~ $true),
2.89/3.11	    inference('demod', [status(thm)], ['42', '6'])).
2.89/3.11	tff('44', plain,
2.89/3.11	    ![X0 : agent1, X1 : msg, X2 : msg, X3 : agent1]:
2.89/3.11	      (~ member(event, 
2.89/3.11	           says(server, X3, 
2.89/3.11	             crypt(shrK(X3), mPair(X2, mPair(agent(X0), mPair(key(k), X1))))), 
2.89/3.11	           set(event, evs5))
2.89/3.11	       | X0 = b),
2.89/3.11	    inference('simplify', [status(thm)], ['43'])).
2.89/3.11	tff('45', plain, (~ $true | ba = b),
2.89/3.11	    inference('sup-', [status(thm)], ['40', '44'])).
2.89/3.11	tff('46', plain, ba = b, inference('simplify', [status(thm)], ['45'])).
2.89/3.11	tff('47', plain,
2.89/3.11	    member(event, 
2.89/3.11	      says(server, aa, 
2.89/3.11	        crypt(shrK(aa), mPair(nonce(nAa), mPair(agent(b), mPair(key(k), x))))), 
2.89/3.11	      set(event, evs5)),
2.89/3.11	    inference('demod', [status(thm)], ['40', '46'])).
2.89/3.11	tff('48', plain,
2.89/3.11	    ![X299 : agent1, X300 : msg, X301 : agent1, X302 : nat, X303 : msg, 
2.89/3.11	      X304 : list(event), X305 : agent1, X306 : msg, X307 : agent1, 
2.89/3.11	      X308 : msg]:
2.89/3.11	      (~ member(event, 
2.89/3.11	           says(server, X299, 
2.89/3.11	             crypt(shrK(X299), 
2.89/3.11	               mPair(X300, mPair(agent(X301), mPair(key(X302), X303))))), 
2.89/3.11	           set(event, X304))
2.89/3.11	       | ~ member(list(event), X304, nS_Sha254967238shared)
2.89/3.11	       | ~ member(event, 
2.89/3.11	             says(server, X305, 
2.89/3.11	               crypt(shrK(X305), 
2.89/3.11	                 mPair(X306, mPair(agent(X307), mPair(key(X302), X308))))), 
2.89/3.11	             set(event, X304))
2.89/3.11	       | X305 = X299),
2.89/3.11	    inference('cnf', [status(esa)], [fact_88_unique__session__keys])).
2.89/3.11	tff('49', plain,
2.89/3.11	    ![X0 : agent1, X1 : msg, X2 : agent1, X3 : msg]:
2.89/3.11	      (~ $true
2.89/3.11	       | X0 = a
2.89/3.11	       | ~ member(event, 
2.89/3.11	             says(server, X0, 
2.89/3.11	               crypt(shrK(X0), 
2.89/3.11	                 mPair(X3, mPair(agent(X2), mPair(key(k), X1))))), 
2.89/3.11	             set(event, evs5))
2.89/3.11	       | ~ member(list(event), evs5, nS_Sha254967238shared)),
2.89/3.11	    inference('sup-', [status(thm)], ['33', '48'])).
2.89/3.11	tff('50', plain,
2.89/3.11	    ![X0 : agent1, X1 : msg, X2 : agent1, X3 : msg]:
2.89/3.11	      (~ $true
2.89/3.11	       | X0 = a
2.89/3.11	       | ~ member(event, 
2.89/3.11	             says(server, X0, 
2.89/3.11	               crypt(shrK(X0), 
2.89/3.11	                 mPair(X3, mPair(agent(X2), mPair(key(k), X1))))), 
2.89/3.11	             set(event, evs5))
2.89/3.11	       | ~ $true),
2.89/3.11	    inference('demod', [status(thm)], ['49', '6'])).
2.89/3.11	tff('51', plain,
2.89/3.11	    ![X0 : agent1, X1 : msg, X2 : agent1, X3 : msg]:
2.89/3.11	      (~ member(event, 
2.89/3.11	           says(server, X0, 
2.89/3.11	             crypt(shrK(X0), mPair(X3, mPair(agent(X2), mPair(key(k), X1))))), 
2.89/3.11	           set(event, evs5))
2.89/3.11	       | X0 = a),
2.89/3.11	    inference('simplify', [status(thm)], ['50'])).
2.89/3.11	tff('52', plain, (~ $true | aa = a),
2.89/3.11	    inference('sup-', [status(thm)], ['47', '51'])).
2.89/3.11	tff('53', plain, aa = a, inference('simplify', [status(thm)], ['52'])).
2.89/3.11	tff('54', plain, (b != ba | a != aa),
2.89/3.11	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.89/3.11	tff('55', plain, (b != b | a != aa),
2.89/3.11	    inference('demod', [status(thm)], ['54', '46'])).
2.89/3.11	tff('56', plain, a != aa, inference('simplify', [status(thm)], ['55'])).
2.89/3.11	tff('57', plain, $false,
2.89/3.11	    inference('simplify_reflect-', [status(thm)], ['53', '56'])).
2.89/3.11	
2.89/3.11	% SZS output end Refutation
2.89/3.12	EOF
