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_int
0.00/0.00	% Ordering    : kbo
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 int \
0.00/0.00	  --ho-no-ext-pos \
0.00/0.00	  --ho-no-ext-neg \
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   : n111.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 14:48:09 CST 2018
248.50/248.78	% done 58304 iterations in 248.583s
248.50/248.78	% SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
248.50/248.78	% SZS output start Refutation
248.50/248.79	tff(conj_5, axiom,
248.50/248.79	  (member(event,
248.50/248.79	          says(s,aa,
248.50/248.79	               crypt(shrK(aa),
248.50/248.79	                     mPair(nonce(nAa),mPair(agent(ba),mPair(key(ka),xa))))),
248.50/248.79	          set(event,evs5)))).
248.50/248.79	tff('0', plain,
248.50/248.79	    member(event, 
248.50/248.79	      says(s, aa, 
248.50/248.79	        crypt(shrK(aa), 
248.50/248.79	          mPair(nonce(nAa), mPair(agent(ba), mPair(key(ka), xa))))), 
248.50/248.79	      set(event, evs5)),
248.50/248.79	    inference('cnf', [status(esa)], [conj_5])).
248.50/248.79	tff(conj_8, conjecture,
248.50/248.79	  (member(event,says(a,b,crypt(ka,mPair(nonce(nBa),nonce(nBa)))),
248.50/248.79	          set(event,evs5)) | 
248.50/248.79	   ((b = ba) & (a = aa)) | (nb != nBa) | (k != ka) | 
248.50/248.79	   (~
248.50/248.79	     member(msg,
248.50/248.79	            crypt(shrK(a),mPair(nonce(na),mPair(agent(b),mPair(key(k),x)))),
248.50/248.79	            parts(knows(spy,evs5)))))).
248.50/248.79	tff(zf_stmt_0, negated_conjecture,
248.50/248.79	  (~
248.50/248.79	    (member(event,says(a,b,crypt(ka,mPair(nonce(nBa),nonce(nBa)))),
248.50/248.79	            set(event,evs5)) | 
248.50/248.79	     ((b = ba) & (a = aa)) | (nb != nBa) | (k != ka) | 
248.50/248.79	     (~
248.50/248.79	       member(msg,
248.50/248.79	              crypt(shrK(a),mPair(nonce(na),mPair(agent(b),mPair(key(k),x)))),
248.50/248.79	              parts(knows(spy,evs5))))))).
248.50/248.79	tff('1', plain, k = ka, inference('cnf', [status(esa)], [zf_stmt_0])).
248.50/248.79	tff('2', plain,
248.50/248.79	    member(event, 
248.50/248.79	      says(s, aa, 
248.50/248.79	        crypt(shrK(aa), 
248.50/248.79	          mPair(nonce(nAa), mPair(agent(ba), mPair(key(k), xa))))), 
248.50/248.79	      set(event, evs5)),
248.50/248.79	    inference('demod', [status(thm)], ['0', '1'])).
248.50/248.79	tff(fact_10_Says__imp__parts__knows__Spy, axiom,
248.50/248.79	  (![Evsa:list(event),Xa:msg,Ba:agent1,Aa:agent1]:
248.50/248.79	     (member(event,says(Aa,Ba,Xa),set(event,Evsa)) =>
248.50/248.79	      member(msg,Xa,parts(knows(spy,Evsa)))))).
248.50/248.79	tff('3', plain,
248.50/248.79	    ![X32 : msg, X33 : list(event), X34 : agent1, X35 : agent1]:
248.50/248.79	      (member(msg, X32, parts(knows(spy, X33)))
248.50/248.79	       | ~ member(event, says(X34, X35, X32), set(event, X33))),
248.50/248.79	    inference('cnf', [status(esa)], [fact_10_Says__imp__parts__knows__Spy])).
248.50/248.79	tff('4', plain,
248.50/248.79	    (~ $true
248.50/248.79	     | member(msg, 
248.50/248.79	         crypt(shrK(aa), 
248.50/248.79	           mPair(nonce(nAa), mPair(agent(ba), mPair(key(k), xa)))), 
248.50/248.79	         parts(knows(spy, evs5)))),
248.50/248.79	    inference('sup-', [status(thm)], ['2', '3'])).
248.50/248.79	tff('5', plain,
248.50/248.79	    member(msg, 
248.50/248.79	      crypt(shrK(aa), mPair(nonce(nAa), mPair(agent(ba), mPair(key(k), xa)))), 
248.50/248.79	      parts(knows(spy, evs5))),
248.50/248.79	    inference('simplify', [status(thm)], ['4'])).
248.50/248.79	tff('6', plain,
248.50/248.79	    member(msg, 
248.50/248.79	      crypt(shrK(a), mPair(nonce(na), mPair(agent(b), mPair(key(k), x)))), 
248.50/248.79	      parts(knows(spy, evs5))),
248.50/248.79	    inference('cnf', [status(esa)], [zf_stmt_0])).
248.50/248.79	tff(fact_67_A__trusts__NS2, axiom,
248.50/248.79	  (![Evsa:list(event),Xa:msg,Ka:nat,Ba:agent1,NAa:msg,Aa:agent1]:
248.50/248.79	     (member(msg,
248.50/248.79	             crypt(shrK(Aa),mPair(NAa,mPair(agent(Ba),mPair(key(Ka),Xa)))),
248.50/248.79	             parts(knows(spy,Evsa))) =>
248.50/248.79	      ((~member(agent1,Aa,bad)) =>
248.50/248.79	       (member(list(event),Evsa,nS_Sha254967238shared) =>
248.50/248.79	        member(event,
248.50/248.79	               says(server,Aa,
248.50/248.79	                    crypt(shrK(Aa),
248.50/248.79	                          mPair(NAa,mPair(agent(Ba),mPair(key(Ka),Xa))))),
248.50/248.79	               set(event,Evsa))))))).
248.50/248.79	tff('7', plain,
248.50/248.79	    ![X203 : list(event), X204 : agent1, X205 : msg, X206 : agent1, 
248.50/248.79	      X207 : nat, X208 : msg]:
248.50/248.79	      (~ member(list(event), X203, nS_Sha254967238shared)
248.50/248.79	       | ~ member(msg, 
248.50/248.79	             crypt(shrK(X204), 
248.50/248.79	               mPair(X205, mPair(agent(X206), mPair(key(X207), X208)))), 
248.50/248.79	             parts(knows(spy, X203)))
248.50/248.79	       | member(event, 
248.50/248.79	           says(server, X204, 
248.50/248.79	             crypt(shrK(X204), 
248.50/248.79	               mPair(X205, mPair(agent(X206), mPair(key(X207), X208))))), 
248.50/248.79	           set(event, X203))
248.50/248.79	       | member(agent1, X204, bad)),
248.50/248.79	    inference('cnf', [status(esa)], [fact_67_A__trusts__NS2])).
248.50/248.79	tff(fact_88_unique__session__keys, axiom,
248.50/248.79	  (![X1:msg,B:agent1,NA:msg,A:agent1,Evsa:list(event),Xa:msg,Ka:nat,
248.50/248.79	     Ba:agent1,NAa:msg,Aa:agent1]:
248.50/248.79	     (member(event,
248.50/248.79	             says(server,Aa,
248.50/248.79	                  crypt(shrK(Aa),
248.50/248.79	                        mPair(NAa,mPair(agent(Ba),mPair(key(Ka),Xa))))),
248.50/248.79	             set(event,Evsa)) =>
248.50/248.79	      (member(event,
248.50/248.79	              says(server,A,
248.50/248.79	                   crypt(shrK(A),mPair(NA,mPair(agent(B),mPair(key(Ka),X1))))),
248.50/248.79	              set(event,Evsa)) =>
248.50/248.79	       (member(list(event),Evsa,nS_Sha254967238shared) =>
248.50/248.79	        ((Xa = X1) & (Ba = B) & (NAa = NA) & (Aa = A))))))).
248.50/248.79	tff('8', plain,
248.50/248.79	    ![X299 : agent1, X300 : msg, X301 : agent1, X302 : nat, X303 : msg, 
248.50/248.79	      X304 : list(event), X305 : agent1, X306 : msg, X307 : agent1, 
248.50/248.79	      X308 : msg]:
248.50/248.79	      (~ member(event, 
248.50/248.79	           says(server, X299, 
248.50/248.79	             crypt(shrK(X299), 
248.50/248.79	               mPair(X300, mPair(agent(X301), mPair(key(X302), X303))))), 
248.50/248.79	           set(event, X304))
248.50/248.79	       | ~ member(list(event), X304, nS_Sha254967238shared)
248.50/248.79	       | ~ member(event, 
248.50/248.79	             says(server, X305, 
248.50/248.79	               crypt(shrK(X305), 
248.50/248.79	                 mPair(X306, mPair(agent(X307), mPair(key(X302), X308))))), 
248.50/248.79	             set(event, X304))
248.50/248.79	       | X308 = X303),
248.50/248.79	    inference('cnf', [status(esa)], [fact_88_unique__session__keys])).
248.50/248.79	tff('9', plain,
248.50/248.79	    ![X0 : list(event), X1 : msg, X2 : nat, X3 : agent1, X4 : msg, 
248.50/248.79	      X5 : agent1, X6 : msg, X7 : agent1, X8 : msg, X9 : agent1]:
248.50/248.79	      (~ $true
248.50/248.79	       | member(agent1, X5, bad)
248.50/248.79	       | ~ member(msg, 
248.50/248.79	             crypt(shrK(X5), mPair(X4, mPair(agent(X3), mPair(key(X2), X1)))), 
248.50/248.79	             parts(knows(spy, X0)))
248.50/248.79	       | ~ member(list(event), X0, nS_Sha254967238shared)
248.50/248.79	       | X6 = X1
248.50/248.79	       | ~ member(event, 
248.50/248.79	             says(server, X9, 
248.50/248.79	               crypt(shrK(X9), 
248.50/248.79	                 mPair(X8, mPair(agent(X7), mPair(key(X2), X6))))), 
248.50/248.79	             set(event, X0))
248.50/248.79	       | ~ member(list(event), X0, nS_Sha254967238shared)),
248.50/248.79	    inference('sup-', [status(thm)], ['7', '8'])).
248.50/248.79	tff('10', plain,
248.50/248.79	    ![X0 : list(event), X1 : msg, X2 : nat, X3 : agent1, X4 : msg, 
248.50/248.79	      X5 : agent1, X6 : msg, X7 : agent1, X8 : msg, X9 : agent1]:
248.50/248.79	      (~ member(event, 
248.50/248.79	           says(server, X9, 
248.50/248.79	             crypt(shrK(X9), mPair(X8, mPair(agent(X7), mPair(key(X2), X6))))), 
248.50/248.79	           set(event, X0))
248.50/248.79	       | X6 = X1
248.50/248.79	       | ~ member(list(event), X0, nS_Sha254967238shared)
248.50/248.79	       | ~ member(msg, 
248.50/248.79	             crypt(shrK(X5), mPair(X4, mPair(agent(X3), mPair(key(X2), X1)))), 
248.50/248.79	             parts(knows(spy, X0)))
248.50/248.79	       | member(agent1, X5, bad)),
248.50/248.79	    inference('simplify', [status(thm)], ['9'])).
248.50/248.79	tff('11', plain,
248.50/248.79	    ![X0 : list(event), X1 : msg, X2 : nat, X3 : agent1, X4 : msg, 
248.50/248.79	      X5 : agent1, X6 : agent1, X7 : msg, X8 : agent1, X9 : msg]:
248.50/248.79	      (~ $true
248.50/248.79	       | member(agent1, X5, bad)
248.50/248.79	       | ~ member(msg, 
248.50/248.79	             crypt(shrK(X5), mPair(X4, mPair(agent(X3), mPair(key(X2), X1)))), 
248.50/248.79	             parts(knows(spy, X0)))
248.50/248.79	       | ~ member(list(event), X0, nS_Sha254967238shared)
248.50/248.79	       | member(agent1, X6, bad)
248.50/248.79	       | ~ member(msg, 
248.50/248.79	             crypt(shrK(X6), mPair(X9, mPair(agent(X8), mPair(key(X2), X7)))), 
248.50/248.79	             parts(knows(spy, X0)))
248.50/248.79	       | ~ member(list(event), X0, nS_Sha254967238shared)
248.50/248.79	       | X1 = X7),
248.50/248.79	    inference('sup-', [status(thm)], ['7', '10'])).
248.50/248.79	tff('12', plain,
248.50/248.79	    ![X0 : list(event), X1 : msg, X2 : nat, X3 : agent1, X4 : msg, 
248.50/248.79	      X5 : agent1, X6 : agent1, X7 : msg, X8 : agent1, X9 : msg]:
248.50/248.79	      (X1 = X7
248.50/248.79	       | ~ member(msg, 
248.50/248.79	             crypt(shrK(X6), mPair(X9, mPair(agent(X8), mPair(key(X2), X7)))), 
248.50/248.79	             parts(knows(spy, X0)))
248.50/248.79	       | member(agent1, X6, bad)
248.50/248.79	       | ~ member(list(event), X0, nS_Sha254967238shared)
248.50/248.79	       | ~ member(msg, 
248.50/248.79	             crypt(shrK(X5), mPair(X4, mPair(agent(X3), mPair(key(X2), X1)))), 
248.50/248.79	             parts(knows(spy, X0)))
248.50/248.79	       | member(agent1, X5, bad)),
248.50/248.79	    inference('simplify', [status(thm)], ['11'])).
248.50/248.79	tff('13', plain,
248.50/248.79	    ![X0 : agent1, X1 : msg, X2 : agent1, X3 : msg]:
248.50/248.79	      (~ $true
248.50/248.79	       | member(agent1, X0, bad)
248.50/248.79	       | ~ member(msg, 
248.50/248.79	             crypt(shrK(X0), mPair(X3, mPair(agent(X2), mPair(key(k), X1)))), 
248.50/248.79	             parts(knows(spy, evs5)))
248.50/248.79	       | ~ member(list(event), evs5, nS_Sha254967238shared)
248.50/248.79	       | member(agent1, a, bad)
248.50/248.79	       | X1 = x),
248.50/248.79	    inference('sup-', [status(thm)], ['6', '12'])).
248.50/248.79	tff(conj_2, axiom, (member(list(event),evs5,nS_Sha254967238shared))).
248.50/248.79	tff('14', plain, member(list(event), evs5, nS_Sha254967238shared),
248.50/248.79	    inference('cnf', [status(esa)], [conj_2])).
248.50/248.79	tff('15', plain,
248.50/248.79	    ![X0 : agent1, X1 : msg, X2 : agent1, X3 : msg]:
248.50/248.79	      (~ $true
248.50/248.79	       | member(agent1, X0, bad)
248.50/248.79	       | ~ member(msg, 
248.50/248.79	             crypt(shrK(X0), mPair(X3, mPair(agent(X2), mPair(key(k), X1)))), 
248.50/248.79	             parts(knows(spy, evs5)))
248.50/248.79	       | ~ $true
248.50/248.79	       | member(agent1, a, bad)
248.50/248.79	       | X1 = x),
248.50/248.79	    inference('demod', [status(thm)], ['13', '14'])).
248.50/248.79	tff('16', plain,
248.50/248.79	    ![X0 : agent1, X1 : msg, X2 : agent1, X3 : msg]:
248.50/248.79	      (X1 = x
248.50/248.79	       | member(agent1, a, bad)
248.50/248.79	       | ~ member(msg, 
248.50/248.79	             crypt(shrK(X0), mPair(X3, mPair(agent(X2), mPair(key(k), X1)))), 
248.50/248.79	             parts(knows(spy, evs5)))
248.50/248.79	       | member(agent1, X0, bad)),
248.50/248.79	    inference('simplify', [status(thm)], ['15'])).
248.50/248.79	tff(conj_0, axiom, (~member(agent1,a,bad))).
248.50/248.79	tff('17', plain, ~ member(agent1, a, bad),
248.50/248.79	    inference('cnf', [status(esa)], [conj_0])).
248.50/248.79	tff('18', plain,
248.50/248.79	    ![X0 : agent1, X1 : msg, X2 : agent1, X3 : msg]:
248.50/248.79	      (member(agent1, X0, bad)
248.50/248.79	       | ~ member(msg, 
248.50/248.79	             crypt(shrK(X0), mPair(X3, mPair(agent(X2), mPair(key(k), X1)))), 
248.50/248.79	             parts(knows(spy, evs5)))
248.50/248.79	       | X1 = x),
248.50/248.79	    inference('clc', [status(thm)], ['16', '17'])).
248.50/248.79	tff('19', plain, (~ $true | xa = x | member(agent1, aa, bad)),
248.50/248.79	    inference('sup-', [status(thm)], ['5', '18'])).
248.50/248.79	tff('20', plain, (member(agent1, aa, bad) | xa = x),
248.50/248.79	    inference('simplify', [status(thm)], ['19'])).
248.50/248.79	tff(fact_11_Says__imp__analz__Spy, axiom,
248.50/248.79	  (![Evsa:list(event),Xa:msg,Ba:agent1,Aa:agent1]:
248.50/248.79	     (member(event,says(Aa,Ba,Xa),set(event,Evsa)) =>
248.50/248.79	      member(msg,Xa,analz(knows(spy,Evsa)))))).
248.50/248.79	tff('21', plain,
248.50/248.79	    ![X36 : msg, X37 : list(event), X38 : agent1, X39 : agent1]:
248.50/248.79	      (member(msg, X36, analz(knows(spy, X37)))
248.50/248.79	       | ~ member(event, says(X38, X39, X36), set(event, X37))),
248.50/248.79	    inference('cnf', [status(esa)], [fact_11_Says__imp__analz__Spy])).
248.50/248.79	tff('22', plain,
248.50/248.79	    (~ $true
248.50/248.79	     | member(msg, 
248.50/248.79	         crypt(shrK(aa), 
248.50/248.79	           mPair(nonce(nAa), mPair(agent(ba), mPair(key(k), xa)))), 
248.50/248.79	         analz(knows(spy, evs5)))),
248.50/248.79	    inference('sup-', [status(thm)], ['2', '21'])).
248.50/248.79	tff('23', plain,
248.50/248.79	    member(msg, 
248.50/248.79	      crypt(shrK(aa), mPair(nonce(nAa), mPair(agent(ba), mPair(key(k), xa)))), 
248.50/248.79	      analz(knows(spy, evs5))),
248.50/248.79	    inference('simplify', [status(thm)], ['22'])).
248.50/248.79	tff(fact_7_Crypt__Spy__analz__bad, axiom,
248.50/248.79	  (![Evsa:list(event),Xa:msg,Aa:agent1]:
248.50/248.79	     (member(msg,crypt(shrK(Aa),Xa),analz(knows(spy,Evsa))) =>
248.50/248.79	      (member(agent1,Aa,bad) => member(msg,Xa,analz(knows(spy,Evsa))))))).
248.50/248.79	tff('24', plain,
248.50/248.79	    ![X28 : msg, X29 : list(event), X30 : agent1]:
248.50/248.79	      (member(msg, X28, analz(knows(spy, X29)))
248.50/248.79	       | ~ member(msg, crypt(shrK(X30), X28), analz(knows(spy, X29)))
248.50/248.79	       | ~ member(agent1, X30, bad)),
248.50/248.79	    inference('cnf', [status(esa)], [fact_7_Crypt__Spy__analz__bad])).
248.50/248.79	tff('25', plain,
248.50/248.79	    (~ $true
248.50/248.79	     | ~ member(agent1, aa, bad)
248.50/248.79	     | member(msg, mPair(nonce(nAa), mPair(agent(ba), mPair(key(k), xa))), 
248.50/248.79	         analz(knows(spy, evs5)))),
248.50/248.79	    inference('sup-', [status(thm)], ['23', '24'])).
248.50/248.79	tff('26', plain,
248.50/248.79	    (member(msg, mPair(nonce(nAa), mPair(agent(ba), mPair(key(k), xa))), 
248.50/248.79	       analz(knows(spy, evs5)))
248.50/248.79	     | ~ member(agent1, aa, bad)),
248.50/248.79	    inference('simplify', [status(thm)], ['25'])).
248.50/248.79	tff(fact_26_MPair__analz, axiom,
248.50/248.79	  (![H:fun(msg,bool),Y:msg,Xa:msg]:
248.50/248.79	     (member(msg,mPair(Xa,Y),analz(H)) =>
248.50/248.79	      (~(member(msg,Xa,analz(H)) => (~member(msg,Y,analz(H)))))))).
248.50/248.79	tff('27', plain,
248.50/248.79	    ![X80 : msg, X81 : fun(msg, bool), X82 : msg]:
248.50/248.79	      (member(msg, X80, analz(X81))
248.50/248.79	       | ~ member(msg, mPair(X82, X80), analz(X81))),
248.50/248.79	    inference('cnf', [status(esa)], [fact_26_MPair__analz])).
248.50/248.79	tff('28', plain,
248.50/248.79	    (~ $true
248.50/248.79	     | ~ member(agent1, aa, bad)
248.50/248.79	     | member(msg, mPair(agent(ba), mPair(key(k), xa)), 
248.50/248.79	         analz(knows(spy, evs5)))),
248.50/248.79	    inference('sup-', [status(thm)], ['26', '27'])).
248.50/248.79	tff('29', plain,
248.50/248.79	    (member(msg, mPair(agent(ba), mPair(key(k), xa)), 
248.50/248.79	       analz(knows(spy, evs5)))
248.50/248.79	     | ~ member(agent1, aa, bad)),
248.50/248.79	    inference('simplify', [status(thm)], ['28'])).
248.50/248.79	tff('30', plain,
248.50/248.79	    (~ $true
248.50/248.79	     | ~ member(agent1, aa, bad)
248.50/248.79	     | member(msg, mPair(key(k), xa), analz(knows(spy, evs5)))),
248.50/248.79	    inference('sup-', [status(thm)], ['29', '27'])).
248.50/248.79	tff('31', plain,
248.50/248.79	    (member(msg, mPair(key(k), xa), analz(knows(spy, evs5)))
248.50/248.79	     | ~ member(agent1, aa, bad)),
248.50/248.79	    inference('simplify', [status(thm)], ['30'])).
248.50/248.79	tff('32', plain,
248.50/248.79	    ![X80 : msg, X81 : fun(msg, bool), X82 : msg]:
248.50/248.79	      (member(msg, X82, analz(X81))
248.50/248.79	       | ~ member(msg, mPair(X82, X80), analz(X81))),
248.50/248.79	    inference('cnf', [status(esa)], [fact_26_MPair__analz])).
248.50/248.79	tff('33', plain,
248.50/248.79	    (~ $true
248.50/248.79	     | ~ member(agent1, aa, bad)
248.50/248.79	     | member(msg, key(k), analz(knows(spy, evs5)))),
248.50/248.79	    inference('sup-', [status(thm)], ['31', '32'])).
248.50/248.79	tff('34', plain,
248.50/248.79	    (member(msg, key(k), analz(knows(spy, evs5))) | ~ member(agent1, aa, bad)),
248.50/248.79	    inference('simplify', [status(thm)], ['33'])).
248.50/248.79	tff(conj_6, axiom, (~member(msg,key(k),analz(knows(spy,evs5))))).
248.50/248.79	tff('35', plain, ~ member(msg, key(k), analz(knows(spy, evs5))),
248.50/248.79	    inference('cnf', [status(esa)], [conj_6])).
248.50/248.79	tff('36', plain, ~ member(agent1, aa, bad),
248.50/248.79	    inference('clc', [status(thm)], ['34', '35'])).
248.50/248.79	tff('37', plain, xa = x, inference('clc', [status(thm)], ['20', '36'])).
248.50/248.79	tff('38', plain,
248.50/248.79	    member(msg, 
248.50/248.79	      crypt(shrK(aa), mPair(nonce(nAa), mPair(agent(ba), mPair(key(k), x)))), 
248.50/248.79	      parts(knows(spy, evs5))),
248.50/248.79	    inference('demod', [status(thm)], ['5', '37'])).
248.50/248.79	tff('39', plain,
248.50/248.79	    ![X299 : agent1, X300 : msg, X301 : agent1, X302 : nat, X303 : msg, 
248.50/248.79	      X304 : list(event), X305 : agent1, X306 : msg, X307 : agent1, 
248.50/248.79	      X308 : msg]:
248.50/248.79	      (~ member(event, 
248.50/248.79	           says(server, X299, 
248.50/248.79	             crypt(shrK(X299), 
248.50/248.79	               mPair(X300, mPair(agent(X301), mPair(key(X302), X303))))), 
248.50/248.79	           set(event, X304))
248.50/248.79	       | ~ member(list(event), X304, nS_Sha254967238shared)
248.50/248.79	       | ~ member(event, 
248.50/248.79	             says(server, X305, 
248.50/248.79	               crypt(shrK(X305), 
248.50/248.79	                 mPair(X306, mPair(agent(X307), mPair(key(X302), X308))))), 
248.50/248.79	             set(event, X304))
248.50/248.79	       | X307 = X301),
248.50/248.79	    inference('cnf', [status(esa)], [fact_88_unique__session__keys])).
248.50/248.79	tff('40', plain,
248.50/248.79	    ![X0 : list(event), X1 : msg, X2 : nat, X3 : agent1, X4 : msg, 
248.50/248.79	      X5 : agent1, X6 : agent1, X7 : msg, X8 : msg, X9 : agent1]:
248.50/248.79	      (~ $true
248.50/248.79	       | member(agent1, X5, bad)
248.50/248.79	       | ~ member(msg, 
248.50/248.79	             crypt(shrK(X5), mPair(X4, mPair(agent(X3), mPair(key(X2), X1)))), 
248.50/248.79	             parts(knows(spy, X0)))
248.50/248.79	       | ~ member(list(event), X0, nS_Sha254967238shared)
248.50/248.79	       | X6 = X3
248.50/248.79	       | ~ member(event, 
248.50/248.79	             says(server, X9, 
248.50/248.79	               crypt(shrK(X9), 
248.50/248.79	                 mPair(X8, mPair(agent(X6), mPair(key(X2), X7))))), 
248.50/248.79	             set(event, X0))
248.50/248.79	       | ~ member(list(event), X0, nS_Sha254967238shared)),
248.50/248.79	    inference('sup-', [status(thm)], ['7', '39'])).
248.50/248.79	tff('41', plain,
248.50/248.79	    ![X0 : list(event), X1 : msg, X2 : nat, X3 : agent1, X4 : msg, 
248.50/248.79	      X5 : agent1, X6 : agent1, X7 : msg, X8 : msg, X9 : agent1]:
248.50/248.79	      (~ member(event, 
248.50/248.79	           says(server, X9, 
248.50/248.79	             crypt(shrK(X9), mPair(X8, mPair(agent(X6), mPair(key(X2), X7))))), 
248.50/248.79	           set(event, X0))
248.50/248.79	       | X6 = X3
248.50/248.79	       | ~ member(list(event), X0, nS_Sha254967238shared)
248.50/248.79	       | ~ member(msg, 
248.50/248.79	             crypt(shrK(X5), mPair(X4, mPair(agent(X3), mPair(key(X2), X1)))), 
248.50/248.79	             parts(knows(spy, X0)))
248.50/248.79	       | member(agent1, X5, bad)),
248.50/248.79	    inference('simplify', [status(thm)], ['40'])).
248.50/248.79	tff('42', plain,
248.50/248.79	    ![X0 : list(event), X1 : msg, X2 : nat, X3 : agent1, X4 : msg, 
248.50/248.79	      X5 : agent1, X6 : agent1, X7 : msg, X8 : agent1, X9 : msg]:
248.50/248.79	      (~ $true
248.50/248.79	       | member(agent1, X5, bad)
248.50/248.79	       | ~ member(msg, 
248.50/248.79	             crypt(shrK(X5), mPair(X4, mPair(agent(X3), mPair(key(X2), X1)))), 
248.50/248.79	             parts(knows(spy, X0)))
248.50/248.79	       | ~ member(list(event), X0, nS_Sha254967238shared)
248.50/248.79	       | member(agent1, X6, bad)
248.50/248.79	       | ~ member(msg, 
248.50/248.79	             crypt(shrK(X6), mPair(X9, mPair(agent(X8), mPair(key(X2), X7)))), 
248.50/248.79	             parts(knows(spy, X0)))
248.50/248.79	       | ~ member(list(event), X0, nS_Sha254967238shared)
248.50/248.79	       | X3 = X8),
248.50/248.79	    inference('sup-', [status(thm)], ['7', '41'])).
248.50/248.79	tff('43', plain,
248.50/248.79	    ![X0 : list(event), X1 : msg, X2 : nat, X3 : agent1, X4 : msg, 
248.50/248.79	      X5 : agent1, X6 : agent1, X7 : msg, X8 : agent1, X9 : msg]:
248.50/248.79	      (X3 = X8
248.50/248.79	       | ~ member(msg, 
248.50/248.79	             crypt(shrK(X6), mPair(X9, mPair(agent(X8), mPair(key(X2), X7)))), 
248.50/248.79	             parts(knows(spy, X0)))
248.50/248.79	       | member(agent1, X6, bad)
248.50/248.79	       | ~ member(list(event), X0, nS_Sha254967238shared)
248.50/248.79	       | ~ member(msg, 
248.50/248.79	             crypt(shrK(X5), mPair(X4, mPair(agent(X3), mPair(key(X2), X1)))), 
248.50/248.79	             parts(knows(spy, X0)))
248.50/248.79	       | member(agent1, X5, bad)),
248.50/248.79	    inference('simplify', [status(thm)], ['42'])).
248.50/248.79	tff('44', plain,
248.50/248.79	    ![X0 : agent1, X1 : msg, X2 : agent1, X3 : msg]:
248.50/248.79	      (~ $true
248.50/248.79	       | member(agent1, X0, bad)
248.50/248.79	       | ~ member(msg, 
248.50/248.79	             crypt(shrK(X0), mPair(X3, mPair(agent(X2), mPair(key(k), X1)))), 
248.50/248.79	             parts(knows(spy, evs5)))
248.50/248.79	       | ~ member(list(event), evs5, nS_Sha254967238shared)
248.50/248.79	       | member(agent1, a, bad)
248.50/248.79	       | X2 = b),
248.50/248.79	    inference('sup-', [status(thm)], ['6', '43'])).
248.50/248.79	tff('45', plain,
248.50/248.79	    ![X0 : agent1, X1 : msg, X2 : agent1, X3 : msg]:
248.50/248.79	      (~ $true
248.50/248.79	       | member(agent1, X0, bad)
248.50/248.79	       | ~ member(msg, 
248.50/248.79	             crypt(shrK(X0), mPair(X3, mPair(agent(X2), mPair(key(k), X1)))), 
248.50/248.79	             parts(knows(spy, evs5)))
248.50/248.79	       | ~ $true
248.50/248.79	       | member(agent1, a, bad)
248.50/248.79	       | X2 = b),
248.50/248.79	    inference('demod', [status(thm)], ['44', '14'])).
248.50/248.79	tff('46', plain,
248.50/248.79	    ![X0 : agent1, X1 : msg, X2 : agent1, X3 : msg]:
248.50/248.79	      (X2 = b
248.50/248.79	       | member(agent1, a, bad)
248.50/248.79	       | ~ member(msg, 
248.50/248.79	             crypt(shrK(X0), mPair(X3, mPair(agent(X2), mPair(key(k), X1)))), 
248.50/248.79	             parts(knows(spy, evs5)))
248.50/248.79	       | member(agent1, X0, bad)),
248.50/248.79	    inference('simplify', [status(thm)], ['45'])).
248.50/248.79	tff('47', plain,
248.50/248.79	    ![X0 : agent1, X1 : msg, X2 : agent1, X3 : msg]:
248.50/248.79	      (member(agent1, X0, bad)
248.50/248.79	       | ~ member(msg, 
248.50/248.79	             crypt(shrK(X0), mPair(X3, mPair(agent(X2), mPair(key(k), X1)))), 
248.50/248.79	             parts(knows(spy, evs5)))
248.50/248.79	       | X2 = b),
248.50/248.79	    inference('clc', [status(thm)], ['46', '17'])).
248.50/248.79	tff('48', plain, (~ $true | ba = b | member(agent1, aa, bad)),
248.50/248.79	    inference('sup-', [status(thm)], ['38', '47'])).
248.50/248.79	tff('49', plain, (member(agent1, aa, bad) | ba = b),
248.50/248.79	    inference('simplify', [status(thm)], ['48'])).
248.50/248.79	tff('50', plain, ba = b, inference('clc', [status(thm)], ['49', '36'])).
248.50/248.79	tff('51', plain,
248.50/248.79	    member(msg, 
248.50/248.79	      crypt(shrK(aa), mPair(nonce(nAa), mPair(agent(b), mPair(key(k), x)))), 
248.50/248.79	      parts(knows(spy, evs5))),
248.50/248.79	    inference('demod', [status(thm)], ['38', '50'])).
248.50/248.79	tff('52', plain,
248.50/248.79	    ![X299 : agent1, X300 : msg, X301 : agent1, X302 : nat, X303 : msg, 
248.50/248.79	      X304 : list(event), X305 : agent1, X306 : msg, X307 : agent1, 
248.50/248.79	      X308 : msg]:
248.50/248.79	      (~ member(event, 
248.50/248.79	           says(server, X299, 
248.50/248.79	             crypt(shrK(X299), 
248.50/248.79	               mPair(X300, mPair(agent(X301), mPair(key(X302), X303))))), 
248.50/248.79	           set(event, X304))
248.50/248.79	       | ~ member(list(event), X304, nS_Sha254967238shared)
248.50/248.79	       | ~ member(event, 
248.50/248.79	             says(server, X305, 
248.50/248.79	               crypt(shrK(X305), 
248.50/248.79	                 mPair(X306, mPair(agent(X307), mPair(key(X302), X308))))), 
248.50/248.79	             set(event, X304))
248.50/248.79	       | X305 = X299),
248.50/248.79	    inference('cnf', [status(esa)], [fact_88_unique__session__keys])).
248.50/248.79	tff('53', plain,
248.50/248.79	    ![X0 : list(event), X1 : msg, X2 : nat, X3 : agent1, X4 : msg, 
248.50/248.79	      X5 : agent1, X6 : agent1, X7 : msg, X8 : agent1, X9 : msg]:
248.50/248.79	      (~ $true
248.50/248.79	       | member(agent1, X5, bad)
248.50/248.79	       | ~ member(msg, 
248.50/248.79	             crypt(shrK(X5), mPair(X4, mPair(agent(X3), mPair(key(X2), X1)))), 
248.50/248.79	             parts(knows(spy, X0)))
248.50/248.79	       | ~ member(list(event), X0, nS_Sha254967238shared)
248.50/248.79	       | X6 = X5
248.50/248.79	       | ~ member(event, 
248.50/248.79	             says(server, X6, 
248.50/248.79	               crypt(shrK(X6), 
248.50/248.79	                 mPair(X9, mPair(agent(X8), mPair(key(X2), X7))))), 
248.50/248.79	             set(event, X0))
248.50/248.79	       | ~ member(list(event), X0, nS_Sha254967238shared)),
248.50/248.79	    inference('sup-', [status(thm)], ['7', '52'])).
248.50/248.79	tff('54', plain,
248.50/248.79	    ![X0 : list(event), X1 : msg, X2 : nat, X3 : agent1, X4 : msg, 
248.50/248.79	      X5 : agent1, X6 : agent1, X7 : msg, X8 : agent1, X9 : msg]:
248.50/248.79	      (~ member(event, 
248.50/248.79	           says(server, X6, 
248.50/248.79	             crypt(shrK(X6), mPair(X9, mPair(agent(X8), mPair(key(X2), X7))))), 
248.50/248.79	           set(event, X0))
248.50/248.79	       | X6 = X5
248.50/248.79	       | ~ member(list(event), X0, nS_Sha254967238shared)
248.50/248.79	       | ~ member(msg, 
248.50/248.79	             crypt(shrK(X5), mPair(X4, mPair(agent(X3), mPair(key(X2), X1)))), 
248.50/248.79	             parts(knows(spy, X0)))
248.50/248.79	       | member(agent1, X5, bad)),
248.50/248.79	    inference('simplify', [status(thm)], ['53'])).
248.50/248.79	tff('55', plain,
248.50/248.79	    ![X0 : list(event), X1 : msg, X2 : nat, X3 : agent1, X4 : msg, 
248.50/248.79	      X5 : agent1, X6 : agent1, X7 : msg, X8 : agent1, X9 : msg]:
248.50/248.79	      (~ $true
248.50/248.79	       | member(agent1, X5, bad)
248.50/248.79	       | ~ member(msg, 
248.50/248.79	             crypt(shrK(X5), mPair(X4, mPair(agent(X3), mPair(key(X2), X1)))), 
248.50/248.79	             parts(knows(spy, X0)))
248.50/248.79	       | ~ member(list(event), X0, nS_Sha254967238shared)
248.50/248.79	       | member(agent1, X6, bad)
248.50/248.79	       | ~ member(msg, 
248.50/248.79	             crypt(shrK(X6), mPair(X9, mPair(agent(X8), mPair(key(X2), X7)))), 
248.50/248.79	             parts(knows(spy, X0)))
248.50/248.79	       | ~ member(list(event), X0, nS_Sha254967238shared)
248.50/248.79	       | X5 = X6),
248.50/248.79	    inference('sup-', [status(thm)], ['7', '54'])).
248.50/248.79	tff('56', plain,
248.50/248.79	    ![X0 : list(event), X1 : msg, X2 : nat, X3 : agent1, X4 : msg, 
248.50/248.79	      X5 : agent1, X6 : agent1, X7 : msg, X8 : agent1, X9 : msg]:
248.50/248.79	      (X5 = X6
248.50/248.79	       | ~ member(msg, 
248.50/248.79	             crypt(shrK(X6), mPair(X9, mPair(agent(X8), mPair(key(X2), X7)))), 
248.50/248.79	             parts(knows(spy, X0)))
248.50/248.79	       | member(agent1, X6, bad)
248.50/248.79	       | ~ member(list(event), X0, nS_Sha254967238shared)
248.50/248.79	       | ~ member(msg, 
248.50/248.79	             crypt(shrK(X5), mPair(X4, mPair(agent(X3), mPair(key(X2), X1)))), 
248.50/248.79	             parts(knows(spy, X0)))
248.50/248.79	       | member(agent1, X5, bad)),
248.50/248.79	    inference('simplify', [status(thm)], ['55'])).
248.50/248.79	tff('57', plain,
248.50/248.79	    ![X0 : agent1, X1 : msg, X2 : agent1, X3 : msg]:
248.50/248.79	      (~ $true
248.50/248.79	       | member(agent1, X0, bad)
248.50/248.79	       | ~ member(msg, 
248.50/248.79	             crypt(shrK(X0), mPair(X3, mPair(agent(X2), mPair(key(k), X1)))), 
248.50/248.79	             parts(knows(spy, evs5)))
248.50/248.79	       | ~ member(list(event), evs5, nS_Sha254967238shared)
248.50/248.79	       | member(agent1, a, bad)
248.50/248.79	       | X0 = a),
248.50/248.79	    inference('sup-', [status(thm)], ['6', '56'])).
248.50/248.79	tff('58', plain,
248.50/248.79	    ![X0 : agent1, X1 : msg, X2 : agent1, X3 : msg]:
248.50/248.79	      (~ $true
248.50/248.79	       | member(agent1, X0, bad)
248.50/248.79	       | ~ member(msg, 
248.50/248.79	             crypt(shrK(X0), mPair(X3, mPair(agent(X2), mPair(key(k), X1)))), 
248.50/248.79	             parts(knows(spy, evs5)))
248.50/248.79	       | ~ $true
248.50/248.79	       | member(agent1, a, bad)
248.50/248.79	       | X0 = a),
248.50/248.79	    inference('demod', [status(thm)], ['57', '14'])).
248.50/248.79	tff('59', plain,
248.50/248.79	    ![X0 : agent1, X1 : msg, X2 : agent1, X3 : msg]:
248.50/248.79	      (X0 = a
248.50/248.79	       | member(agent1, a, bad)
248.50/248.79	       | ~ member(msg, 
248.50/248.79	             crypt(shrK(X0), mPair(X3, mPair(agent(X2), mPair(key(k), X1)))), 
248.50/248.79	             parts(knows(spy, evs5)))
248.50/248.79	       | member(agent1, X0, bad)),
248.50/248.79	    inference('simplify', [status(thm)], ['58'])).
248.50/248.79	tff('60', plain,
248.50/248.79	    ![X0 : agent1, X1 : msg, X2 : agent1, X3 : msg]:
248.50/248.79	      (member(agent1, X0, bad)
248.50/248.79	       | ~ member(msg, 
248.50/248.79	             crypt(shrK(X0), mPair(X3, mPair(agent(X2), mPair(key(k), X1)))), 
248.50/248.79	             parts(knows(spy, evs5)))
248.50/248.79	       | X0 = a),
248.50/248.79	    inference('clc', [status(thm)], ['59', '17'])).
248.50/248.79	tff('61', plain, (~ $true | aa = a | member(agent1, aa, bad)),
248.50/248.79	    inference('sup-', [status(thm)], ['51', '60'])).
248.50/248.79	tff('62', plain, (member(agent1, aa, bad) | aa = a),
248.50/248.79	    inference('simplify', [status(thm)], ['61'])).
248.50/248.79	tff('63', plain, (b != ba | a != aa),
248.50/248.79	    inference('cnf', [status(esa)], [zf_stmt_0])).
248.50/248.79	tff('64', plain, (b != b | a != aa),
248.50/248.79	    inference('demod', [status(thm)], ['63', '50'])).
248.50/248.79	tff('65', plain, a != aa, inference('simplify', [status(thm)], ['64'])).
248.50/248.79	tff('66', plain, member(agent1, aa, bad),
248.50/248.79	    inference('simplify_reflect-', [status(thm)], ['62', '65'])).
248.50/248.79	tff('67', plain, ~ $true, inference('sup-', [status(thm)], ['66', '36'])).
248.50/248.79	tff('68', plain, $false, inference('simplify', [status(thm)], ['67'])).
248.50/248.79	
248.50/248.79	% SZS output end Refutation
248.60/248.80	EOF
