0.00/0.00	% File    : /export/starexec/sandbox/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 $2  \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --ho-purify ext \
0.00/0.00	  --ho-ext-axiom \
0.00/0.00	  --restrict-hidden-sup-at-vars \
0.00/0.00	  --ho-prim-enum none \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --dont-select-ho-var-lits \
0.00/0.00	  --no-fool
0.00/0.20	% Computer   : n114.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 15:00:55 CST 2018
191.60/191.85	% done 21545 iterations in 191.642s
191.60/191.85	% SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
191.60/191.85	% SZS output start Refutation
191.60/191.86	tff(conj_5, axiom,
191.60/191.86	  (ord_less_eq(fun(nat,bool),kk,
191.60/191.86	               uminus_uminus(fun(nat,bool),
191.60/191.86	                             image(agent,nat,shrK,top_top(fun(agent,bool))))))).
191.60/191.86	tff('0', plain,
191.60/191.86	    ord_less_eq(fun(nat, bool), kk, 
191.60/191.86	      uminus_uminus(fun(nat, bool), 
191.60/191.86	        image(agent, nat, shrK, top_top(fun(agent, bool))))),
191.60/191.86	    inference('cnf', [status(esa)], [conj_5])).
191.60/191.86	tff(fact_98_sup__absorb1, axiom,
191.60/191.86	  (![A:$tType]:
191.60/191.86	     (semilattice_sup(A) =>
191.60/191.86	      (![X:A,Y:A]: (ord_less_eq(A,Y,X) => (sup_sup(A,X,Y) = X)))))).
191.60/191.86	tff('1', plain,
191.60/191.86	    ![X329 : $tType, X330 : X329, X331 : X329]:
191.60/191.86	      (~ ord_less_eq(X329, X330, X331)
191.60/191.86	       | sup_sup(X329, X331, X330) = X331
191.60/191.86	       | ~ semilattice_sup(X329)),
191.60/191.86	    inference('cnf', [status(esa)], [fact_98_sup__absorb1])).
191.60/191.86	tff('2', plain,
191.60/191.86	    (~ $true
191.60/191.86	     | ~ semilattice_sup(fun(nat, bool))
191.60/191.86	     | sup_sup(fun(nat, bool), 
191.60/191.86	         uminus_uminus(fun(nat, bool), 
191.60/191.86	           image(agent, nat, shrK, top_top(fun(agent, bool)))), kk)
191.60/191.86	        = uminus_uminus(fun(nat, bool), 
191.60/191.86	            image(agent, nat, shrK, top_top(fun(agent, bool))))),
191.60/191.86	    inference('sup-', [status(thm)], ['0', '1'])).
191.60/191.86	tff(arity_HOL_Obool___Lattices_Olattice, axiom, (lattice(bool))).
191.60/191.86	tff('3', plain, lattice(bool),
191.60/191.86	    inference('cnf', [status(esa)], [arity_HOL_Obool___Lattices_Olattice])).
191.60/191.86	tff(arity_fun___Lattices_Osemilattice__sup, axiom,
191.60/191.86	  (![T_1:$tType,T_2:$tType]: (lattice(T_2) => semilattice_sup(fun(T_1,T_2))))).
191.60/191.86	tff('4', plain,
191.60/191.86	    ![X339 : $tType, X340 : $tType]:
191.60/191.86	      (semilattice_sup(fun(X339, X340)) | ~ lattice(X340)),
191.60/191.86	    inference('cnf', [status(esa)], [arity_fun___Lattices_Osemilattice__sup])).
191.60/191.86	tff('5', plain, ![X0 : $tType]: (~ $true | semilattice_sup(fun(X0, bool))),
191.60/191.86	    inference('sup-', [status(thm)], ['3', '4'])).
191.60/191.86	tff('6', plain, ![X0 : $tType]: semilattice_sup(fun(X0, bool)),
191.60/191.86	    inference('simplify', [status(thm)], ['5'])).
191.60/191.86	tff(fact_81_Un__commute, axiom,
191.60/191.86	  (![A:$tType,B2:fun(A,bool),A2:fun(A,bool)]:
191.60/191.86	     (sup_sup(fun(A,bool),A2,B2) = sup_sup(fun(A,bool),B2,A2)))).
191.60/191.86	tff('7', plain,
191.60/191.86	    ![X277 : $tType, X278 : fun(X277, bool), X279 : fun(X277, bool)]:
191.60/191.86	      sup_sup(fun(X277, bool), X279, X278)
191.60/191.86	       = sup_sup(fun(X277, bool), X278, X279),
191.60/191.86	    inference('cnf', [status(esa)], [fact_81_Un__commute])).
191.60/191.86	tff('8', plain,
191.60/191.86	    (~ $true
191.60/191.86	     | ~ $true
191.60/191.86	     | sup_sup(fun(nat, bool), kk, 
191.60/191.86	         uminus_uminus(fun(nat, bool), 
191.60/191.86	           image(agent, nat, shrK, top_top(fun(agent, bool)))))
191.60/191.86	        = uminus_uminus(fun(nat, bool), 
191.60/191.86	            image(agent, nat, shrK, top_top(fun(agent, bool))))),
191.60/191.86	    inference('demod', [status(thm)], ['2', '6', '7'])).
191.60/191.86	tff('9', plain,
191.60/191.86	    sup_sup(fun(nat, bool), kk, 
191.60/191.86	      uminus_uminus(fun(nat, bool), 
191.60/191.86	        image(agent, nat, shrK, top_top(fun(agent, bool)))))
191.60/191.86	     = uminus_uminus(fun(nat, bool), 
191.60/191.86	         image(agent, nat, shrK, top_top(fun(agent, bool)))),
191.60/191.86	    inference('simplify', [status(thm)], ['8'])).
191.60/191.86	tff(conj_6, conjecture,
191.60/191.86	  ((pp(aa(fun(msg,bool),bool,
191.60/191.86	          aa(msg,fun(fun(msg,bool),bool),member(msg),aa(nat,msg,key,k)),
191.60/191.86	          analz(knows(spy,evs2)))) | 
191.60/191.86	    pp(aa(fun(nat,bool),bool,aa(nat,fun(fun(nat,bool),bool),member(nat),k),kk)) | 
191.60/191.86	    ((~
191.60/191.86	       pp(aa(fun(msg,bool),bool,
191.60/191.86	             aa(msg,fun(fun(msg,bool),bool),member(msg),aa(nat,msg,key,k)),
191.60/191.86	             analz(knows(spy,evs2))))) & 
191.60/191.86	     (~
191.60/191.86	       pp(aa(fun(nat,bool),bool,
191.60/191.86	             aa(nat,fun(fun(nat,bool),bool),member(nat),k),kk))) & 
191.60/191.86	     (k != kab)) | 
191.60/191.86	    (~
191.60/191.86	      pp(aa(fun(nat,bool),bool,
191.60/191.86	            aa(nat,fun(fun(nat,bool),bool),member(nat),aa(agent,nat,shrK,a)),
191.60/191.86	            kk))) | 
191.60/191.86	    pp(aa(fun(msg,bool),bool,
191.60/191.86	          aa(msg,fun(fun(msg,bool),bool),member(msg),
191.60/191.86	             aa(nat,msg,key,aa(agent,nat,shrK,a))),
191.60/191.86	          analz(knows(spy,evs2)))) | 
191.60/191.86	    pp(aa(fun(msg,bool),bool,
191.60/191.86	          aa(msg,fun(fun(msg,bool),bool),member(msg),
191.60/191.86	             aa(nat,msg,key,aa(agent,nat,shrK,b))),
191.60/191.86	          analz(knows(spy,evs2)))) | 
191.60/191.86	    (aa(agent,nat,shrK,b) = kab)) & 
191.60/191.86	   (((pp(aa(fun(msg,bool),bool,
191.60/191.86	            aa(msg,fun(fun(msg,bool),bool),member(msg),aa(nat,msg,key,k)),
191.60/191.86	            analz(knows(spy,evs2)))) | 
191.60/191.86	      pp(aa(fun(nat,bool),bool,aa(nat,fun(fun(nat,bool),bool),member(nat),k),
191.60/191.86	            kk)) | 
191.60/191.86	      ((~
191.60/191.86	         pp(aa(fun(msg,bool),bool,
191.60/191.86	               aa(msg,fun(fun(msg,bool),bool),member(msg),aa(nat,msg,key,k)),
191.60/191.86	               analz(knows(spy,evs2))))) & 
191.60/191.86	       (~
191.60/191.86	         pp(aa(fun(nat,bool),bool,
191.60/191.86	               aa(nat,fun(fun(nat,bool),bool),member(nat),k),kk))) & 
191.60/191.86	       (k != kab)) | 
191.60/191.86	      (~
191.60/191.86	        pp(aa(fun(nat,bool),bool,
191.60/191.86	              aa(nat,fun(fun(nat,bool),bool),member(nat),aa(agent,nat,shrK,a)),
191.60/191.86	              kk))) | 
191.60/191.86	      pp(aa(fun(msg,bool),bool,
191.60/191.86	            aa(msg,fun(fun(msg,bool),bool),member(msg),
191.60/191.86	               aa(nat,msg,key,aa(agent,nat,shrK,b))),
191.60/191.86	            analz(knows(spy,evs2)))) | 
191.60/191.86	      pp(aa(fun(nat,bool),bool,
191.60/191.86	            aa(nat,fun(fun(nat,bool),bool),member(nat),aa(agent,nat,shrK,b)),
191.60/191.86	            kk)) | 
191.60/191.86	      (aa(agent,nat,shrK,b) = kab)) & 
191.60/191.86	     (pp(aa(fun(msg,bool),bool,
191.60/191.86	            aa(msg,fun(fun(msg,bool),bool),member(msg),aa(nat,msg,key,k)),
191.60/191.86	            analz(knows(spy,evs2)))) | 
191.60/191.86	      pp(aa(fun(nat,bool),bool,aa(nat,fun(fun(nat,bool),bool),member(nat),k),
191.60/191.86	            kk)) | 
191.60/191.86	      ((~
191.60/191.86	         pp(aa(fun(msg,bool),bool,
191.60/191.86	               aa(msg,fun(fun(msg,bool),bool),member(msg),aa(nat,msg,key,k)),
191.60/191.86	               analz(knows(spy,evs2))))) & 
191.60/191.86	       (~
191.60/191.86	         pp(aa(fun(nat,bool),bool,
191.60/191.86	               aa(nat,fun(fun(nat,bool),bool),member(nat),k),kk))) & 
191.60/191.86	       (k != kab)) | 
191.60/191.86	      (~
191.60/191.86	        pp(aa(fun(nat,bool),bool,
191.60/191.86	              aa(nat,fun(fun(nat,bool),bool),member(nat),aa(agent,nat,shrK,a)),
191.60/191.86	              kk))) | 
191.60/191.86	      ((~
191.60/191.86	         pp(aa(fun(msg,bool),bool,
191.60/191.86	               aa(msg,fun(fun(msg,bool),bool),member(msg),
191.60/191.86	                  aa(nat,msg,key,aa(agent,nat,shrK,b))),
191.60/191.86	               analz(knows(spy,evs2))))) & 
191.60/191.86	       (~
191.60/191.86	         pp(aa(fun(nat,bool),bool,
191.60/191.86	               aa(nat,fun(fun(nat,bool),bool),member(nat),
191.60/191.86	                  aa(agent,nat,shrK,b)),
191.60/191.86	               kk))) & 
191.60/191.86	       (aa(agent,nat,shrK,b) != kab)))) | 
191.60/191.86	    pp(aa(fun(msg,bool),bool,
191.60/191.86	          aa(msg,fun(fun(msg,bool),bool),member(msg),
191.60/191.86	             aa(nat,msg,key,aa(agent,nat,shrK,a))),
191.60/191.86	          analz(knows(spy,evs2)))) | 
191.60/191.86	    ((~
191.60/191.86	       pp(aa(fun(msg,bool),bool,
191.60/191.86	             aa(msg,fun(fun(msg,bool),bool),member(msg),
191.60/191.86	                aa(nat,msg,key,aa(agent,nat,shrK,b))),
191.60/191.86	             analz(knows(spy,evs2))))) & 
191.60/191.86	     (aa(agent,nat,shrK,b) != kab))))).
191.60/191.86	tff(zf_stmt_0, negated_conjecture,
191.60/191.86	  (~
191.60/191.86	    ((pp(aa(fun(msg,bool),bool,
191.60/191.86	            aa(msg,fun(fun(msg,bool),bool),member(msg),aa(nat,msg,key,k)),
191.60/191.86	            analz(knows(spy,evs2)))) | 
191.60/191.86	      pp(aa(fun(nat,bool),bool,aa(nat,fun(fun(nat,bool),bool),member(nat),k),
191.60/191.86	            kk)) | 
191.60/191.86	      ((~
191.60/191.86	         pp(aa(fun(msg,bool),bool,
191.60/191.86	               aa(msg,fun(fun(msg,bool),bool),member(msg),aa(nat,msg,key,k)),
191.60/191.86	               analz(knows(spy,evs2))))) & 
191.60/191.86	       (~
191.60/191.86	         pp(aa(fun(nat,bool),bool,
191.60/191.86	               aa(nat,fun(fun(nat,bool),bool),member(nat),k),kk))) & 
191.60/191.86	       (k != kab)) | 
191.60/191.86	      (~
191.60/191.86	        pp(aa(fun(nat,bool),bool,
191.60/191.86	              aa(nat,fun(fun(nat,bool),bool),member(nat),aa(agent,nat,shrK,a)),
191.60/191.86	              kk))) | 
191.60/191.86	      pp(aa(fun(msg,bool),bool,
191.60/191.86	            aa(msg,fun(fun(msg,bool),bool),member(msg),
191.60/191.86	               aa(nat,msg,key,aa(agent,nat,shrK,a))),
191.60/191.86	            analz(knows(spy,evs2)))) | 
191.60/191.86	      pp(aa(fun(msg,bool),bool,
191.60/191.86	            aa(msg,fun(fun(msg,bool),bool),member(msg),
191.60/191.86	               aa(nat,msg,key,aa(agent,nat,shrK,b))),
191.60/191.86	            analz(knows(spy,evs2)))) | 
191.60/191.86	      (aa(agent,nat,shrK,b) = kab)) & 
191.60/191.86	     (((pp(aa(fun(msg,bool),bool,
191.60/191.86	              aa(msg,fun(fun(msg,bool),bool),member(msg),aa(nat,msg,key,k)),
191.60/191.86	              analz(knows(spy,evs2)))) | 
191.60/191.86	        pp(aa(fun(nat,bool),bool,
191.60/191.86	              aa(nat,fun(fun(nat,bool),bool),member(nat),k),kk)) | 
191.60/191.86	        ((~
191.60/191.86	           pp(aa(fun(msg,bool),bool,
191.60/191.86	                 aa(msg,fun(fun(msg,bool),bool),member(msg),aa(nat,msg,key,k)),
191.60/191.86	                 analz(knows(spy,evs2))))) & 
191.60/191.86	         (~
191.60/191.86	           pp(aa(fun(nat,bool),bool,
191.60/191.86	                 aa(nat,fun(fun(nat,bool),bool),member(nat),k),kk))) & 
191.60/191.86	         (k != kab)) | 
191.60/191.86	        (~
191.60/191.86	          pp(aa(fun(nat,bool),bool,
191.60/191.86	                aa(nat,fun(fun(nat,bool),bool),member(nat),
191.60/191.86	                   aa(agent,nat,shrK,a)),
191.60/191.86	                kk))) | 
191.60/191.86	        pp(aa(fun(msg,bool),bool,
191.60/191.86	              aa(msg,fun(fun(msg,bool),bool),member(msg),
191.60/191.86	                 aa(nat,msg,key,aa(agent,nat,shrK,b))),
191.60/191.86	              analz(knows(spy,evs2)))) | 
191.60/191.86	        pp(aa(fun(nat,bool),bool,
191.60/191.86	              aa(nat,fun(fun(nat,bool),bool),member(nat),aa(agent,nat,shrK,b)),
191.60/191.86	              kk)) | 
191.60/191.86	        (aa(agent,nat,shrK,b) = kab)) & 
191.60/191.86	       (pp(aa(fun(msg,bool),bool,
191.60/191.86	              aa(msg,fun(fun(msg,bool),bool),member(msg),aa(nat,msg,key,k)),
191.60/191.86	              analz(knows(spy,evs2)))) | 
191.60/191.86	        pp(aa(fun(nat,bool),bool,
191.60/191.86	              aa(nat,fun(fun(nat,bool),bool),member(nat),k),kk)) | 
191.60/191.86	        ((~
191.60/191.86	           pp(aa(fun(msg,bool),bool,
191.60/191.86	                 aa(msg,fun(fun(msg,bool),bool),member(msg),aa(nat,msg,key,k)),
191.60/191.86	                 analz(knows(spy,evs2))))) & 
191.60/191.86	         (~
191.60/191.86	           pp(aa(fun(nat,bool),bool,
191.60/191.86	                 aa(nat,fun(fun(nat,bool),bool),member(nat),k),kk))) & 
191.60/191.86	         (k != kab)) | 
191.60/191.86	        (~
191.60/191.86	          pp(aa(fun(nat,bool),bool,
191.60/191.86	                aa(nat,fun(fun(nat,bool),bool),member(nat),
191.60/191.86	                   aa(agent,nat,shrK,a)),
191.60/191.86	                kk))) | 
191.60/191.86	        ((~
191.60/191.86	           pp(aa(fun(msg,bool),bool,
191.60/191.86	                 aa(msg,fun(fun(msg,bool),bool),member(msg),
191.60/191.86	                    aa(nat,msg,key,aa(agent,nat,shrK,b))),
191.60/191.86	                 analz(knows(spy,evs2))))) & 
191.60/191.86	         (~
191.60/191.86	           pp(aa(fun(nat,bool),bool,
191.60/191.86	                 aa(nat,fun(fun(nat,bool),bool),member(nat),
191.60/191.86	                    aa(agent,nat,shrK,b)),
191.60/191.86	                 kk))) & 
191.60/191.86	         (aa(agent,nat,shrK,b) != kab)))) | 
191.60/191.86	      pp(aa(fun(msg,bool),bool,
191.60/191.86	            aa(msg,fun(fun(msg,bool),bool),member(msg),
191.60/191.86	               aa(nat,msg,key,aa(agent,nat,shrK,a))),
191.60/191.86	            analz(knows(spy,evs2)))) | 
191.60/191.86	      ((~
191.60/191.86	         pp(aa(fun(msg,bool),bool,
191.60/191.86	               aa(msg,fun(fun(msg,bool),bool),member(msg),
191.60/191.86	                  aa(nat,msg,key,aa(agent,nat,shrK,b))),
191.60/191.86	               analz(knows(spy,evs2))))) & 
191.60/191.86	       (aa(agent,nat,shrK,b) != kab)))))).
191.60/191.86	tff('10', plain,
191.60/191.86	    (pp(
191.60/191.86	       aa(fun(nat, bool), bool, 
191.60/191.86	         aa(nat, fun(fun(nat, bool), bool), member(nat), 
191.60/191.86	           aa(agent, nat, shrK, a)), kk))
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(nat, bool), bool, 
191.60/191.86	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
191.60/191.86	             aa(agent, nat, shrK, a)), kk))
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(msg, bool), bool, 
191.60/191.86	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
191.60/191.86	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
191.60/191.86	           analz(knows(spy, evs2))))
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(nat, bool), bool, 
191.60/191.86	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
191.60/191.86	             aa(agent, nat, shrK, b)), kk))
191.60/191.86	     | aa(agent, nat, shrK, b) = kab),
191.60/191.86	    inference('cnf', [status(esa)], [zf_stmt_0])).
191.60/191.86	tff('11', plain,
191.60/191.86	    (aa(agent, nat, shrK, b) = kab
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(nat, bool), bool, 
191.60/191.86	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
191.60/191.86	             aa(agent, nat, shrK, b)), kk))
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(msg, bool), bool, 
191.60/191.86	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
191.60/191.86	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
191.60/191.86	           analz(knows(spy, evs2))))
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(nat, bool), bool, 
191.60/191.86	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
191.60/191.86	             aa(agent, nat, shrK, a)), kk))),
191.60/191.86	    inference('simplify', [status(thm)], ['10'])).
191.60/191.86	tff('12', plain,
191.60/191.86	    (k = kab
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(nat, bool), bool, 
191.60/191.86	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(msg, bool), bool, 
191.60/191.86	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
191.60/191.86	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
191.60/191.86	     | k = kab
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(nat, bool), bool, 
191.60/191.86	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(msg, bool), bool, 
191.60/191.86	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
191.60/191.86	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(msg, bool), bool, 
191.60/191.86	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
191.60/191.86	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
191.60/191.86	           analz(knows(spy, evs2))))
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(nat, bool), bool, 
191.60/191.86	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
191.60/191.86	             aa(agent, nat, shrK, b)), kk))
191.60/191.86	     | aa(agent, nat, shrK, b) = kab),
191.60/191.86	    inference('cnf', [status(esa)], [zf_stmt_0])).
191.60/191.86	tff('13', plain,
191.60/191.86	    (aa(agent, nat, shrK, b) = kab
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(nat, bool), bool, 
191.60/191.86	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
191.60/191.86	             aa(agent, nat, shrK, b)), kk))
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(msg, bool), bool, 
191.60/191.86	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
191.60/191.86	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
191.60/191.86	           analz(knows(spy, evs2))))
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(msg, bool), bool, 
191.60/191.86	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
191.60/191.86	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(nat, bool), bool, 
191.60/191.86	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
191.60/191.86	     | k = kab),
191.60/191.86	    inference('simplify', [status(thm)], ['12'])).
191.60/191.86	tff('14', plain,
191.60/191.86	    (k = kab
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(nat, bool), bool, 
191.60/191.86	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(msg, bool), bool, 
191.60/191.86	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
191.60/191.86	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
191.60/191.86	     | aa(agent, nat, shrK, b) != kab
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(msg, bool), bool, 
191.60/191.86	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
191.60/191.86	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(nat, bool), bool, 
191.60/191.86	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
191.60/191.86	     | k = kab),
191.60/191.86	    inference('cnf', [status(esa)], [zf_stmt_0])).
191.60/191.86	tff('15', plain,
191.60/191.86	    (aa(agent, nat, shrK, b) != kab
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(msg, bool), bool, 
191.60/191.86	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
191.60/191.86	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(nat, bool), bool, 
191.60/191.86	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
191.60/191.86	     | k = kab),
191.60/191.86	    inference('simplify', [status(thm)], ['14'])).
191.60/191.86	tff('16', plain,
191.60/191.86	    (~ pp(
191.60/191.86	         aa(fun(msg, bool), bool, 
191.60/191.86	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
191.60/191.86	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
191.60/191.86	     | ~ pp(
191.60/191.86	           aa(fun(msg, bool), bool, 
191.60/191.86	             aa(msg, fun(fun(msg, bool), bool), member(msg), 
191.60/191.86	               aa(nat, msg, key, k)), analz(knows(spy, evs2))))
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(msg, bool), bool, 
191.60/191.86	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
191.60/191.86	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
191.60/191.86	           analz(knows(spy, evs2))))
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(nat, bool), bool, 
191.60/191.86	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
191.60/191.86	             aa(agent, nat, shrK, b)), kk))
191.60/191.86	     | aa(agent, nat, shrK, b) = kab),
191.60/191.86	    inference('cnf', [status(esa)], [zf_stmt_0])).
191.60/191.86	tff('17', plain,
191.60/191.86	    (aa(agent, nat, shrK, b) = kab
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(nat, bool), bool, 
191.60/191.86	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
191.60/191.86	             aa(agent, nat, shrK, b)), kk))
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(msg, bool), bool, 
191.60/191.86	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
191.60/191.86	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
191.60/191.86	           analz(knows(spy, evs2))))
191.60/191.86	     | ~ pp(
191.60/191.86	           aa(fun(msg, bool), bool, 
191.60/191.86	             aa(msg, fun(fun(msg, bool), bool), member(msg), 
191.60/191.86	               aa(nat, msg, key, k)), analz(knows(spy, evs2))))),
191.60/191.86	    inference('simplify', [status(thm)], ['16'])).
191.60/191.86	tff('18', plain,
191.60/191.86	    (~ pp(
191.60/191.86	         aa(fun(msg, bool), bool, 
191.60/191.86	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
191.60/191.86	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
191.60/191.86	     | aa(agent, nat, shrK, b) != kab
191.60/191.86	     | ~ pp(
191.60/191.86	           aa(fun(msg, bool), bool, 
191.60/191.86	             aa(msg, fun(fun(msg, bool), bool), member(msg), 
191.60/191.86	               aa(nat, msg, key, k)), analz(knows(spy, evs2))))),
191.60/191.86	    inference('cnf', [status(esa)], [zf_stmt_0])).
191.60/191.86	tff('19', plain,
191.60/191.86	    (aa(agent, nat, shrK, b) != kab
191.60/191.86	     | ~ pp(
191.60/191.86	           aa(fun(msg, bool), bool, 
191.60/191.86	             aa(msg, fun(fun(msg, bool), bool), member(msg), 
191.60/191.86	               aa(nat, msg, key, k)), analz(knows(spy, evs2))))),
191.60/191.86	    inference('simplify', [status(thm)], ['18'])).
191.60/191.86	tff('20', plain,
191.60/191.86	    (~ pp(
191.60/191.86	         aa(fun(msg, bool), bool, 
191.60/191.86	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
191.60/191.86	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(msg, bool), bool, 
191.60/191.86	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
191.60/191.86	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
191.60/191.86	           analz(knows(spy, evs2))))
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(nat, bool), bool, 
191.60/191.86	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
191.60/191.86	             aa(agent, nat, shrK, b)), kk))),
191.60/191.86	    inference('clc', [status(thm)], ['17', '19'])).
191.60/191.86	tff('21', plain,
191.60/191.86	    (~ pp(
191.60/191.86	         aa(fun(msg, bool), bool, 
191.60/191.86	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
191.60/191.86	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
191.60/191.86	     | ~ pp(
191.60/191.86	           aa(fun(msg, bool), bool, 
191.60/191.86	             aa(msg, fun(fun(msg, bool), bool), member(msg), 
191.60/191.86	               aa(nat, msg, key, aa(agent, nat, shrK, b))), 
191.60/191.86	             analz(knows(spy, evs2))))
191.60/191.86	     | ~ pp(
191.60/191.86	           aa(fun(msg, bool), bool, 
191.60/191.86	             aa(msg, fun(fun(msg, bool), bool), member(msg), 
191.60/191.86	               aa(nat, msg, key, k)), analz(knows(spy, evs2))))),
191.60/191.86	    inference('cnf', [status(esa)], [zf_stmt_0])).
191.60/191.86	tff('22', plain,
191.60/191.86	    (~ pp(
191.60/191.86	         aa(fun(msg, bool), bool, 
191.60/191.86	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
191.60/191.86	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
191.60/191.86	           analz(knows(spy, evs2))))
191.60/191.86	     | ~ pp(
191.60/191.86	           aa(fun(msg, bool), bool, 
191.60/191.86	             aa(msg, fun(fun(msg, bool), bool), member(msg), 
191.60/191.86	               aa(nat, msg, key, k)), analz(knows(spy, evs2))))),
191.60/191.86	    inference('simplify', [status(thm)], ['21'])).
191.60/191.86	tff('23', plain,
191.60/191.86	    (pp(
191.60/191.86	       aa(fun(nat, bool), bool, 
191.60/191.86	         aa(nat, fun(fun(nat, bool), bool), member(nat), 
191.60/191.86	           aa(agent, nat, shrK, b)), kk))
191.60/191.86	     | ~ pp(
191.60/191.86	           aa(fun(msg, bool), bool, 
191.60/191.86	             aa(msg, fun(fun(msg, bool), bool), member(msg), 
191.60/191.86	               aa(nat, msg, key, k)), analz(knows(spy, evs2))))),
191.60/191.86	    inference('clc', [status(thm)], ['20', '22'])).
191.60/191.86	tff('24', plain,
191.60/191.86	    (~ pp(
191.60/191.86	         aa(fun(msg, bool), bool, 
191.60/191.86	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
191.60/191.86	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
191.60/191.86	     | ~ pp(
191.60/191.86	           aa(fun(nat, bool), bool, 
191.60/191.86	             aa(nat, fun(fun(nat, bool), bool), member(nat), 
191.60/191.86	               aa(agent, nat, shrK, b)), kk))
191.60/191.86	     | ~ pp(
191.60/191.86	           aa(fun(msg, bool), bool, 
191.60/191.86	             aa(msg, fun(fun(msg, bool), bool), member(msg), 
191.60/191.86	               aa(nat, msg, key, k)), analz(knows(spy, evs2))))),
191.60/191.86	    inference('cnf', [status(esa)], [zf_stmt_0])).
191.60/191.86	tff('25', plain,
191.60/191.86	    (~ pp(
191.60/191.86	         aa(fun(nat, bool), bool, 
191.60/191.86	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
191.60/191.86	             aa(agent, nat, shrK, b)), kk))
191.60/191.86	     | ~ pp(
191.60/191.86	           aa(fun(msg, bool), bool, 
191.60/191.86	             aa(msg, fun(fun(msg, bool), bool), member(msg), 
191.60/191.86	               aa(nat, msg, key, k)), analz(knows(spy, evs2))))),
191.60/191.86	    inference('simplify', [status(thm)], ['24'])).
191.60/191.86	tff('26', plain,
191.60/191.86	    ~ pp(
191.60/191.86	        aa(fun(msg, bool), bool, 
191.60/191.86	          aa(msg, fun(fun(msg, bool), bool), member(msg), 
191.60/191.86	            aa(nat, msg, key, k)), analz(knows(spy, evs2)))),
191.60/191.86	    inference('clc', [status(thm)], ['23', '25'])).
191.60/191.86	tff('27', plain,
191.60/191.86	    (k = kab
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(nat, bool), bool, 
191.60/191.86	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
191.60/191.86	     | aa(agent, nat, shrK, b) != kab),
191.60/191.86	    inference('clc', [status(thm)], ['15', '26'])).
191.60/191.86	tff('28', plain,
191.60/191.86	    (~ pp(
191.60/191.86	         aa(fun(nat, bool), bool, 
191.60/191.86	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
191.60/191.86	     | ~ pp(
191.60/191.86	           aa(fun(nat, bool), bool, 
191.60/191.86	             aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(msg, bool), bool, 
191.60/191.86	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
191.60/191.86	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
191.60/191.86	           analz(knows(spy, evs2))))
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(nat, bool), bool, 
191.60/191.86	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
191.60/191.86	             aa(agent, nat, shrK, b)), kk))
191.60/191.86	     | aa(agent, nat, shrK, b) = kab),
191.60/191.86	    inference('cnf', [status(esa)], [zf_stmt_0])).
191.60/191.86	tff('29', plain,
191.60/191.86	    (aa(agent, nat, shrK, b) = kab
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(nat, bool), bool, 
191.60/191.86	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
191.60/191.86	             aa(agent, nat, shrK, b)), kk))
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(msg, bool), bool, 
191.60/191.86	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
191.60/191.86	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
191.60/191.86	           analz(knows(spy, evs2))))
191.60/191.86	     | ~ pp(
191.60/191.86	           aa(fun(nat, bool), bool, 
191.60/191.86	             aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))),
191.60/191.86	    inference('simplify', [status(thm)], ['28'])).
191.60/191.86	tff('30', plain,
191.60/191.86	    (~ pp(
191.60/191.86	         aa(fun(nat, bool), bool, 
191.60/191.86	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
191.60/191.86	     | aa(agent, nat, shrK, b) != kab
191.60/191.86	     | ~ pp(
191.60/191.86	           aa(fun(nat, bool), bool, 
191.60/191.86	             aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))),
191.60/191.86	    inference('cnf', [status(esa)], [zf_stmt_0])).
191.60/191.86	tff('31', plain,
191.60/191.86	    (aa(agent, nat, shrK, b) != kab
191.60/191.86	     | ~ pp(
191.60/191.86	           aa(fun(nat, bool), bool, 
191.60/191.86	             aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))),
191.60/191.86	    inference('simplify', [status(thm)], ['30'])).
191.60/191.86	tff('32', plain,
191.60/191.86	    (~ pp(
191.60/191.86	         aa(fun(nat, bool), bool, 
191.60/191.86	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(msg, bool), bool, 
191.60/191.86	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
191.60/191.86	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
191.60/191.86	           analz(knows(spy, evs2))))
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(nat, bool), bool, 
191.60/191.86	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
191.60/191.86	             aa(agent, nat, shrK, b)), kk))),
191.60/191.86	    inference('clc', [status(thm)], ['29', '31'])).
191.60/191.86	tff('33', plain,
191.60/191.86	    (~ pp(
191.60/191.86	         aa(fun(nat, bool), bool, 
191.60/191.86	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
191.60/191.86	     | ~ pp(
191.60/191.86	           aa(fun(msg, bool), bool, 
191.60/191.86	             aa(msg, fun(fun(msg, bool), bool), member(msg), 
191.60/191.86	               aa(nat, msg, key, aa(agent, nat, shrK, b))), 
191.60/191.86	             analz(knows(spy, evs2))))
191.60/191.86	     | ~ pp(
191.60/191.86	           aa(fun(nat, bool), bool, 
191.60/191.86	             aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))),
191.60/191.86	    inference('cnf', [status(esa)], [zf_stmt_0])).
191.60/191.86	tff('34', plain,
191.60/191.86	    (~ pp(
191.60/191.86	         aa(fun(msg, bool), bool, 
191.60/191.86	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
191.60/191.86	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
191.60/191.86	           analz(knows(spy, evs2))))
191.60/191.86	     | ~ pp(
191.60/191.86	           aa(fun(nat, bool), bool, 
191.60/191.86	             aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))),
191.60/191.86	    inference('simplify', [status(thm)], ['33'])).
191.60/191.86	tff('35', plain,
191.60/191.86	    (pp(
191.60/191.86	       aa(fun(nat, bool), bool, 
191.60/191.86	         aa(nat, fun(fun(nat, bool), bool), member(nat), 
191.60/191.86	           aa(agent, nat, shrK, b)), kk))
191.60/191.86	     | ~ pp(
191.60/191.86	           aa(fun(nat, bool), bool, 
191.60/191.86	             aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))),
191.60/191.86	    inference('clc', [status(thm)], ['32', '34'])).
191.60/191.86	tff('36', plain,
191.60/191.86	    (~ pp(
191.60/191.86	         aa(fun(nat, bool), bool, 
191.60/191.86	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
191.60/191.86	     | ~ pp(
191.60/191.86	           aa(fun(nat, bool), bool, 
191.60/191.86	             aa(nat, fun(fun(nat, bool), bool), member(nat), 
191.60/191.86	               aa(agent, nat, shrK, b)), kk))
191.60/191.86	     | ~ pp(
191.60/191.86	           aa(fun(nat, bool), bool, 
191.60/191.86	             aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))),
191.60/191.86	    inference('cnf', [status(esa)], [zf_stmt_0])).
191.60/191.86	tff('37', plain,
191.60/191.86	    (~ pp(
191.60/191.86	         aa(fun(nat, bool), bool, 
191.60/191.86	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
191.60/191.86	             aa(agent, nat, shrK, b)), kk))
191.60/191.86	     | ~ pp(
191.60/191.86	           aa(fun(nat, bool), bool, 
191.60/191.86	             aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))),
191.60/191.86	    inference('simplify', [status(thm)], ['36'])).
191.60/191.86	tff('38', plain,
191.60/191.86	    ~ pp(
191.60/191.86	        aa(fun(nat, bool), bool, 
191.60/191.86	          aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk)),
191.60/191.86	    inference('clc', [status(thm)], ['35', '37'])).
191.60/191.86	tff('39', plain, (aa(agent, nat, shrK, b) != kab | k = kab),
191.60/191.86	    inference('clc', [status(thm)], ['27', '38'])).
191.60/191.86	tff('40', plain,
191.60/191.86	    (k = kab
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(nat, bool), bool, 
191.60/191.86	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(msg, bool), bool, 
191.60/191.86	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
191.60/191.86	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(msg, bool), bool, 
191.60/191.86	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
191.60/191.86	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
191.60/191.86	           analz(knows(spy, evs2))))
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(nat, bool), bool, 
191.60/191.86	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
191.60/191.86	             aa(agent, nat, shrK, b)), kk))),
191.60/191.86	    inference('clc', [status(thm)], ['13', '39'])).
191.60/191.86	tff('41', plain,
191.60/191.86	    (pp(
191.60/191.86	       aa(fun(nat, bool), bool, 
191.60/191.86	         aa(nat, fun(fun(nat, bool), bool), member(nat), 
191.60/191.86	           aa(agent, nat, shrK, b)), kk))
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(msg, bool), bool, 
191.60/191.86	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
191.60/191.86	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
191.60/191.86	           analz(knows(spy, evs2))))
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(msg, bool), bool, 
191.60/191.86	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
191.60/191.86	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
191.60/191.86	     | k = kab),
191.60/191.86	    inference('clc', [status(thm)], ['40', '38'])).
191.60/191.86	tff('42', plain,
191.60/191.86	    (k = kab
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(nat, bool), bool, 
191.60/191.86	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(msg, bool), bool, 
191.60/191.86	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
191.60/191.86	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
191.60/191.86	     | ~ pp(
191.60/191.86	           aa(fun(nat, bool), bool, 
191.60/191.86	             aa(nat, fun(fun(nat, bool), bool), member(nat), 
191.60/191.86	               aa(agent, nat, shrK, b)), kk))
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(msg, bool), bool, 
191.60/191.86	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
191.60/191.86	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(nat, bool), bool, 
191.60/191.86	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
191.60/191.86	     | k = kab),
191.60/191.86	    inference('cnf', [status(esa)], [zf_stmt_0])).
191.60/191.86	tff('43', plain,
191.60/191.86	    (~ pp(
191.60/191.86	         aa(fun(nat, bool), bool, 
191.60/191.86	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
191.60/191.86	             aa(agent, nat, shrK, b)), kk))
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(msg, bool), bool, 
191.60/191.86	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
191.60/191.86	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(nat, bool), bool, 
191.60/191.86	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
191.60/191.86	     | k = kab),
191.60/191.86	    inference('simplify', [status(thm)], ['42'])).
191.60/191.86	tff('44', plain,
191.60/191.86	    (k = kab
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(nat, bool), bool, 
191.60/191.86	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
191.60/191.86	     | ~ pp(
191.60/191.86	           aa(fun(nat, bool), bool, 
191.60/191.86	             aa(nat, fun(fun(nat, bool), bool), member(nat), 
191.60/191.86	               aa(agent, nat, shrK, b)), kk))),
191.60/191.86	    inference('clc', [status(thm)], ['43', '26'])).
191.60/191.86	tff('45', plain,
191.60/191.86	    (~ pp(
191.60/191.86	         aa(fun(nat, bool), bool, 
191.60/191.86	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
191.60/191.86	             aa(agent, nat, shrK, b)), kk))
191.60/191.86	     | k = kab),
191.60/191.86	    inference('clc', [status(thm)], ['44', '38'])).
191.60/191.86	tff('46', plain,
191.60/191.86	    (k = kab
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(msg, bool), bool, 
191.60/191.86	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
191.60/191.86	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(msg, bool), bool, 
191.60/191.86	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
191.60/191.86	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
191.60/191.86	           analz(knows(spy, evs2))))),
191.60/191.86	    inference('clc', [status(thm)], ['41', '45'])).
191.60/191.86	tff('47', plain,
191.60/191.86	    (pp(
191.60/191.86	       aa(fun(msg, bool), bool, 
191.60/191.86	         aa(msg, fun(fun(msg, bool), bool), member(msg), 
191.60/191.86	           aa(nat, msg, key, aa(agent, nat, shrK, b))), 
191.60/191.86	         analz(knows(spy, evs2))))
191.60/191.86	     | k = kab),
191.60/191.86	    inference('clc', [status(thm)], ['46', '26'])).
191.60/191.86	tff('48', plain,
191.60/191.86	    (k = kab
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(nat, bool), bool, 
191.60/191.86	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(msg, bool), bool, 
191.60/191.86	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
191.60/191.86	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
191.60/191.86	     | ~ pp(
191.60/191.86	           aa(fun(msg, bool), bool, 
191.60/191.86	             aa(msg, fun(fun(msg, bool), bool), member(msg), 
191.60/191.86	               aa(nat, msg, key, aa(agent, nat, shrK, b))), 
191.60/191.86	             analz(knows(spy, evs2))))
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(msg, bool), bool, 
191.60/191.86	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
191.60/191.86	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(nat, bool), bool, 
191.60/191.86	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
191.60/191.86	     | k = kab),
191.60/191.86	    inference('cnf', [status(esa)], [zf_stmt_0])).
191.60/191.86	tff('49', plain,
191.60/191.86	    (~ pp(
191.60/191.86	         aa(fun(msg, bool), bool, 
191.60/191.86	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
191.60/191.86	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
191.60/191.86	           analz(knows(spy, evs2))))
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(msg, bool), bool, 
191.60/191.86	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
191.60/191.86	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(nat, bool), bool, 
191.60/191.86	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
191.60/191.86	     | k = kab),
191.60/191.86	    inference('simplify', [status(thm)], ['48'])).
191.60/191.86	tff('50', plain,
191.60/191.86	    (k = kab
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(nat, bool), bool, 
191.60/191.86	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
191.60/191.86	     | ~ pp(
191.60/191.86	           aa(fun(msg, bool), bool, 
191.60/191.86	             aa(msg, fun(fun(msg, bool), bool), member(msg), 
191.60/191.86	               aa(nat, msg, key, aa(agent, nat, shrK, b))), 
191.60/191.86	             analz(knows(spy, evs2))))),
191.60/191.86	    inference('clc', [status(thm)], ['49', '26'])).
191.60/191.86	tff('51', plain,
191.60/191.86	    (~ pp(
191.60/191.86	         aa(fun(msg, bool), bool, 
191.60/191.86	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
191.60/191.86	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
191.60/191.86	           analz(knows(spy, evs2))))
191.60/191.86	     | k = kab),
191.60/191.86	    inference('clc', [status(thm)], ['50', '38'])).
191.60/191.86	tff('52', plain, k = kab, inference('clc', [status(thm)], ['47', '51'])).
191.60/191.86	tff('53', plain,
191.60/191.86	    (aa(agent, nat, shrK, b) = k
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(nat, bool), bool, 
191.60/191.86	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
191.60/191.86	             aa(agent, nat, shrK, b)), kk))
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(msg, bool), bool, 
191.60/191.86	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
191.60/191.86	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
191.60/191.86	           analz(knows(spy, evs2))))
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(nat, bool), bool, 
191.60/191.86	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
191.60/191.86	             aa(agent, nat, shrK, a)), kk))),
191.60/191.86	    inference('demod', [status(thm)], ['11', '52'])).
191.60/191.86	tff('54', plain,
191.60/191.86	    (pp(
191.60/191.86	       aa(fun(nat, bool), bool, 
191.60/191.86	         aa(nat, fun(fun(nat, bool), bool), member(nat), 
191.60/191.86	           aa(agent, nat, shrK, a)), kk))
191.60/191.86	     | aa(agent, nat, shrK, b) != kab
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(nat, bool), bool, 
191.60/191.86	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
191.60/191.86	             aa(agent, nat, shrK, a)), kk))),
191.60/191.86	    inference('cnf', [status(esa)], [zf_stmt_0])).
191.60/191.86	tff('55', plain,
191.60/191.86	    (aa(agent, nat, shrK, b) != kab
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(nat, bool), bool, 
191.60/191.86	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
191.60/191.86	             aa(agent, nat, shrK, a)), kk))),
191.60/191.86	    inference('simplify', [status(thm)], ['54'])).
191.60/191.86	tff('56', plain,
191.60/191.86	    (aa(agent, nat, shrK, b) != k
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(nat, bool), bool, 
191.60/191.86	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
191.60/191.86	             aa(agent, nat, shrK, a)), kk))),
191.60/191.86	    inference('demod', [status(thm)], ['55', '52'])).
191.60/191.86	tff('57', plain,
191.60/191.86	    (pp(
191.60/191.86	       aa(fun(nat, bool), bool, 
191.60/191.86	         aa(nat, fun(fun(nat, bool), bool), member(nat), 
191.60/191.86	           aa(agent, nat, shrK, a)), kk))
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(msg, bool), bool, 
191.60/191.86	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
191.60/191.86	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
191.60/191.86	           analz(knows(spy, evs2))))
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(nat, bool), bool, 
191.60/191.86	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
191.60/191.86	             aa(agent, nat, shrK, b)), kk))),
191.60/191.86	    inference('clc', [status(thm)], ['53', '56'])).
191.60/191.86	tff('58', plain,
191.60/191.86	    (pp(
191.60/191.86	       aa(fun(nat, bool), bool, 
191.60/191.86	         aa(nat, fun(fun(nat, bool), bool), member(nat), 
191.60/191.86	           aa(agent, nat, shrK, a)), kk))
191.60/191.86	     | ~ pp(
191.60/191.86	           aa(fun(msg, bool), bool, 
191.60/191.86	             aa(msg, fun(fun(msg, bool), bool), member(msg), 
191.60/191.86	               aa(nat, msg, key, aa(agent, nat, shrK, b))), 
191.60/191.86	             analz(knows(spy, evs2))))
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(nat, bool), bool, 
191.60/191.86	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
191.60/191.86	             aa(agent, nat, shrK, a)), kk))),
191.60/191.86	    inference('cnf', [status(esa)], [zf_stmt_0])).
191.60/191.86	tff('59', plain,
191.60/191.86	    (~ pp(
191.60/191.86	         aa(fun(msg, bool), bool, 
191.60/191.86	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
191.60/191.86	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
191.60/191.86	           analz(knows(spy, evs2))))
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(nat, bool), bool, 
191.60/191.86	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
191.60/191.86	             aa(agent, nat, shrK, a)), kk))),
191.60/191.86	    inference('simplify', [status(thm)], ['58'])).
191.60/191.86	tff('60', plain,
191.60/191.86	    (pp(
191.60/191.86	       aa(fun(nat, bool), bool, 
191.60/191.86	         aa(nat, fun(fun(nat, bool), bool), member(nat), 
191.60/191.86	           aa(agent, nat, shrK, b)), kk))
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(nat, bool), bool, 
191.60/191.86	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
191.60/191.86	             aa(agent, nat, shrK, a)), kk))),
191.60/191.86	    inference('clc', [status(thm)], ['57', '59'])).
191.60/191.86	tff('61', plain,
191.60/191.86	    (pp(
191.60/191.86	       aa(fun(nat, bool), bool, 
191.60/191.86	         aa(nat, fun(fun(nat, bool), bool), member(nat), 
191.60/191.86	           aa(agent, nat, shrK, a)), kk))
191.60/191.86	     | ~ pp(
191.60/191.86	           aa(fun(nat, bool), bool, 
191.60/191.86	             aa(nat, fun(fun(nat, bool), bool), member(nat), 
191.60/191.86	               aa(agent, nat, shrK, b)), kk))
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(nat, bool), bool, 
191.60/191.86	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
191.60/191.86	             aa(agent, nat, shrK, a)), kk))),
191.60/191.86	    inference('cnf', [status(esa)], [zf_stmt_0])).
191.60/191.86	tff('62', plain,
191.60/191.86	    (~ pp(
191.60/191.86	         aa(fun(nat, bool), bool, 
191.60/191.86	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
191.60/191.86	             aa(agent, nat, shrK, b)), kk))
191.60/191.86	     | pp(
191.60/191.86	         aa(fun(nat, bool), bool, 
191.60/191.86	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
191.60/191.86	             aa(agent, nat, shrK, a)), kk))),
191.60/191.86	    inference('simplify', [status(thm)], ['61'])).
191.60/191.86	tff('63', plain,
191.60/191.86	    pp(
191.60/191.86	      aa(fun(nat, bool), bool, 
191.60/191.86	        aa(nat, fun(fun(nat, bool), bool), member(nat), 
191.60/191.86	          aa(agent, nat, shrK, a)), kk)),
191.60/191.86	    inference('clc', [status(thm)], ['60', '62'])).
191.60/191.86	tff(fact_19_UnCI, axiom,
191.60/191.86	  (![A:$tType,A2:fun(A,bool),B2:fun(A,bool),C2:A]:
191.60/191.86	     (((~pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),C2),B2))) =>
191.60/191.86	       pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),C2),A2))) =>
191.60/191.86	      pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),C2),
191.60/191.86	            sup_sup(fun(A,bool),A2,B2)))))).
191.60/191.86	tff('64', plain,
191.60/191.86	    ![X54 : $tType, X55 : X54, X56 : fun(X54, bool), X57 : fun(X54, bool)]:
191.60/191.86	      (pp(
191.60/191.86	         aa(fun(X54, bool), bool, 
191.60/191.86	           aa(X54, fun(fun(X54, bool), bool), member(X54), X55), 
191.60/191.86	           sup_sup(fun(X54, bool), X56, X57)))
191.60/191.86	       | ~ pp(
191.60/191.86	             aa(fun(X54, bool), bool, 
191.60/191.86	               aa(X54, fun(fun(X54, bool), bool), member(X54), X55), X56))),
191.60/191.86	    inference('cnf', [status(esa)], [fact_19_UnCI])).
191.60/191.86	tff(fact_76_mem__def, axiom,
191.60/191.86	  (![A:$tType,A2:fun(A,bool),X2:A]:
191.60/191.86	     (pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),X2),A2)) <=>
191.60/191.86	      pp(aa(A,bool,A2,X2))))).
191.60/191.86	tff('65', plain,
191.60/191.86	    ![X260 : $tType, X261 : fun(X260, bool), X262 : X260]:
191.60/191.86	      (pp(aa(X260, bool, X261, X262))
191.60/191.86	       | ~ pp(
191.60/191.86	             aa(fun(X260, bool), bool, 
191.60/191.86	               aa(X260, fun(fun(X260, bool), bool), member(X260), X262), 
191.60/191.86	               X261))),
191.60/191.86	    inference('cnf', [status(esa)], [fact_76_mem__def])).
191.60/191.86	tff('66', plain,
191.60/191.86	    ![X0 : $tType, X1 : fun(X0, bool), X2 : fun(X0, bool), X3 : X0]:
191.60/191.86	      (~ $true
191.60/191.86	       | ~ pp(
191.60/191.86	             aa(fun(X0, bool), bool, 
191.60/191.86	               aa(X0, fun(fun(X0, bool), bool), member(X0), X3), X2))
191.60/191.86	       | pp(aa(X0, bool, sup_sup(fun(X0, bool), X2, X1), X3))),
191.60/191.86	    inference('sup-', [status(thm)], ['64', '65'])).
191.60/191.86	tff('67', plain,
191.60/191.86	    ![X0 : $tType, X1 : fun(X0, bool), X2 : fun(X0, bool), X3 : X0]:
191.60/191.86	      (pp(aa(X0, bool, sup_sup(fun(X0, bool), X2, X1), X3))
191.60/191.86	       | ~ pp(
191.60/191.86	             aa(fun(X0, bool), bool, 
191.60/191.86	               aa(X0, fun(fun(X0, bool), bool), member(X0), X3), X2))),
191.60/191.86	    inference('simplify', [status(thm)], ['66'])).
191.60/191.86	tff('68', plain,
191.60/191.86	    ![X0 : fun(nat, bool)]:
191.60/191.86	      (~ $true
191.60/191.86	       | pp(
191.60/191.86	           aa(nat, bool, sup_sup(fun(nat, bool), kk, X0), 
191.60/191.86	             aa(agent, nat, shrK, a)))),
191.60/191.86	    inference('sup-', [status(thm)], ['63', '67'])).
191.60/191.86	tff('69', plain,
191.60/191.86	    ![X0 : fun(nat, bool)]:
191.60/191.86	      pp(
191.60/191.86	        aa(nat, bool, sup_sup(fun(nat, bool), kk, X0), 
191.60/191.86	          aa(agent, nat, shrK, a))),
191.60/191.86	    inference('simplify', [status(thm)], ['68'])).
191.60/191.86	tff('70', plain,
191.60/191.86	    pp(
191.60/191.86	      aa(nat, bool, 
191.60/191.86	        uminus_uminus(fun(nat, bool), 
191.60/191.86	          image(agent, nat, shrK, top_top(fun(agent, bool)))), 
191.60/191.86	        aa(agent, nat, shrK, a))),
191.60/191.86	    inference('sup+', [status(thm)], ['9', '69'])).
191.60/191.86	tff(help_COMBB_1_1_U, axiom,
191.60/191.86	  (![C:$tType,B:$tType,A:$tType,R:A,Q:fun(A,B),P:fun(B,C)]:
191.60/191.86	     (aa(A,C,combb(B,C,A,P,Q),R) = aa(B,C,P,aa(A,B,Q,R))))).
191.60/191.86	tff('71', plain,
191.60/191.86	    ![X347 : $tType, X348 : $tType, X349 : fun(X347, X348), X350 : $tType, 
191.60/191.86	      X351 : fun(X350, X347), X352 : X350]:
191.60/191.86	      aa(X350, X348, combb(X347, X348, X350, X349, X351), X352)
191.60/191.86	       = aa(X347, X348, X349, aa(X350, X347, X351, X352)),
191.60/191.86	    inference('cnf', [status(esa)], [help_COMBB_1_1_U])).
191.60/191.86	tff(help_fNot_1_1_U, axiom,
191.60/191.86	  (![P:bool]: ((~pp(P)) | (~pp(aa(bool,bool,fNot,P)))))).
191.60/191.86	tff('72', plain,
191.60/191.86	    ![X345 : bool]: (~ pp(X345) | ~ pp(aa(bool, bool, fNot, X345))),
191.60/191.86	    inference('cnf', [status(esa)], [help_fNot_1_1_U])).
191.60/191.86	tff('73', plain,
191.60/191.86	    ![X0 : $tType, X1 : X0, X2 : fun(X0, bool)]:
191.60/191.86	      (~ pp(aa(X0, bool, combb(bool, bool, X0, fNot, X2), X1))
191.60/191.86	       | ~ pp(aa(X0, bool, X2, X1))),
191.60/191.86	    inference('sup-', [status(thm)], ['71', '72'])).
191.60/191.86	tff(fact_93_Collect__neg__eq, axiom,
191.60/191.86	  (![A:$tType,P1:fun(A,bool)]:
191.60/191.86	     (collect(A,combb(bool,bool,A,fNot,P1)) =
191.60/191.86	      uminus_uminus(fun(A,bool),collect(A,P1))))).
191.60/191.86	tff('74', plain,
191.60/191.86	    ![X310 : $tType, X311 : fun(X310, bool)]:
191.60/191.86	      collect(X310, combb(bool, bool, X310, fNot, X311))
191.60/191.86	       = uminus_uminus(fun(X310, bool), collect(X310, X311)),
191.60/191.86	    inference('cnf', [status(esa)], [fact_93_Collect__neg__eq])).
191.60/191.86	tff(fact_77_Collect__def, axiom,
191.60/191.86	  (![A:$tType,P1:fun(A,bool)]: (collect(A,P1) = P1))).
191.60/191.86	tff('75', plain,
191.60/191.86	    ![X264 : $tType, X265 : fun(X264, bool)]: collect(X264, X265) = X265,
191.60/191.86	    inference('cnf', [status(esa)], [fact_77_Collect__def])).
191.60/191.86	tff('76', plain,
191.60/191.86	    ![X310 : $tType, X311 : fun(X310, bool)]:
191.60/191.86	      combb(bool, bool, X310, fNot, X311)
191.60/191.86	       = uminus_uminus(fun(X310, bool), X311),
191.60/191.86	    inference('demod', [status(thm)], ['74', '75', '75'])).
191.60/191.86	tff('77', plain,
191.60/191.86	    ![X0 : $tType, X1 : X0, X2 : fun(X0, bool)]:
191.60/191.86	      (~ pp(aa(X0, bool, uminus_uminus(fun(X0, bool), X2), X1))
191.60/191.86	       | ~ pp(aa(X0, bool, X2, X1))),
191.60/191.86	    inference('demod', [status(thm)], ['73', '76'])).
191.60/191.86	tff('78', plain,
191.60/191.86	    (~ $true
191.60/191.86	     | ~ pp(
191.60/191.86	           aa(nat, bool, image(agent, nat, shrK, top_top(fun(agent, bool))), 
191.60/191.86	             aa(agent, nat, shrK, a)))),
191.60/191.86	    inference('sup-', [status(thm)], ['70', '77'])).
191.60/191.86	tff(help_COMBC_1_1_U, axiom,
191.60/191.86	  (![A:$tType,C:$tType,B:$tType,R:A,Q:B,P:fun(A,fun(B,C))]:
191.60/191.86	     (aa(A,C,combc(A,B,C,P,Q),R) = aa(B,C,aa(A,fun(B,C),P,R),Q)))).
191.60/191.86	tff('79', plain,
191.60/191.86	    ![X353 : $tType, X354 : $tType, X355 : $tType, 
191.60/191.86	      X356 : fun(X355, fun(X353, X354)), X357 : X355, X358 : X353]:
191.60/191.86	      aa(X355, X354, combc(X355, X353, X354, X356, X358), X357)
191.60/191.86	       = aa(X353, X354, aa(X355, fun(X353, X354), X356, X357), X358),
191.60/191.86	    inference('cnf', [status(esa)], [help_COMBC_1_1_U])).
191.60/191.86	tff(fact_17_UNIV__I, axiom,
191.60/191.86	  (![A:$tType,X2:A]:
191.60/191.86	     pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),X2),
191.60/191.86	           top_top(fun(A,bool)))))).
191.60/191.86	tff('80', plain,
191.60/191.86	    ![X48 : $tType, X49 : X48]:
191.60/191.86	      pp(
191.60/191.86	        aa(fun(X48, bool), bool, 
191.60/191.86	          aa(X48, fun(fun(X48, bool), bool), member(X48), X49), 
191.60/191.86	          top_top(fun(X48, bool)))),
191.60/191.86	    inference('cnf', [status(esa)], [fact_17_UNIV__I])).
191.60/191.86	tff(fact_16_image__eqI, axiom,
191.60/191.86	  (![A:$tType,B:$tType,A2:fun(B,bool),X2:B,F:fun(B,A),B3:A]:
191.60/191.86	     ((B3 = aa(B,A,F,X2)) =>
191.60/191.86	      (pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),X2),A2)) =>
191.60/191.86	       pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),B3),
191.60/191.86	             image(B,A,F,A2))))))).
191.60/191.86	tff('81', plain,
191.60/191.86	    ![X42 : $tType, X43 : X42, X44 : fun(X42, bool), X45 : $tType, 
191.60/191.86	      X46 : fun(X42, X45), X47 : X45]:
191.60/191.86	      (~ pp(
191.60/191.86	           aa(fun(X42, bool), bool, 
191.60/191.86	             aa(X42, fun(fun(X42, bool), bool), member(X42), X43), X44))
191.60/191.86	       | X47 != aa(X42, X45, X46, X43)
191.60/191.86	       | pp(
191.60/191.86	           aa(fun(X45, bool), bool, 
191.60/191.86	             aa(X45, fun(fun(X45, bool), bool), member(X45), X47), 
191.60/191.86	             image(X42, X45, X46, X44)))),
191.60/191.86	    inference('cnf', [status(esa)], [fact_16_image__eqI])).
191.60/191.86	tff('82', plain,
191.60/191.86	    ![X42 : $tType, X43 : X42, X44 : fun(X42, bool), X45 : $tType, 
191.60/191.86	      X46 : fun(X42, X45)]:
191.60/191.86	      (pp(
191.60/191.86	         aa(fun(X45, bool), bool, 
191.60/191.86	           aa(X45, fun(fun(X45, bool), bool), member(X45), 
191.60/191.86	             aa(X42, X45, X46, X43)), image(X42, X45, X46, X44)))
191.60/191.86	       | ~ pp(
191.60/191.86	             aa(fun(X42, bool), bool, 
191.60/191.86	               aa(X42, fun(fun(X42, bool), bool), member(X42), X43), X44))),
191.60/191.86	    inference('simplify', [status(thm)], ['81'])).
191.60/191.86	tff('83', plain,
191.60/191.86	    ![X0 : $tType, X1 : X0, X2 : $tType, X3 : fun(X0, X2)]:
191.60/191.86	      (~ $true
191.60/191.86	       | pp(
191.60/191.86	           aa(fun(X2, bool), bool, 
191.60/191.86	             aa(X2, fun(fun(X2, bool), bool), member(X2), aa(X0, X2, X3, X1)), 
191.60/191.86	             image(X0, X2, X3, top_top(fun(X0, bool)))))),
191.60/191.86	    inference('sup-', [status(thm)], ['80', '82'])).
191.60/191.86	tff('84', plain,
191.60/191.86	    ![X0 : $tType, X1 : X0, X2 : $tType, X3 : fun(X0, X2)]:
191.60/191.86	      pp(
191.60/191.86	        aa(fun(X2, bool), bool, 
191.60/191.86	          aa(X2, fun(fun(X2, bool), bool), member(X2), aa(X0, X2, X3, X1)), 
191.60/191.86	          image(X0, X2, X3, top_top(fun(X0, bool))))),
191.60/191.86	    inference('simplify', [status(thm)], ['83'])).
191.60/191.86	tff('85', plain,
191.60/191.86	    ![X0 : $tType, X1 : $tType, X2 : X1, X3 : fun(X1, X0)]:
191.60/191.86	      pp(
191.60/191.86	        aa(X0, bool, 
191.60/191.86	          combc(X0, fun(X0, bool), bool, member(X0), 
191.60/191.86	            image(X1, X0, X3, top_top(fun(X1, bool)))), aa(X1, X0, X3, X2))),
191.60/191.86	    inference('sup+', [status(thm)], ['79', '84'])).
191.60/191.86	tff(fact_88_Compl__eq, axiom,
191.60/191.86	  (![A:$tType,A2:fun(A,bool)]:
191.60/191.86	     (uminus_uminus(fun(A,bool),A2) =
191.60/191.86	      collect(A,
191.60/191.86	              combb(bool,bool,A,fNot,combc(A,fun(A,bool),bool,member(A),A2)))))).
191.60/191.86	tff('86', plain,
191.60/191.86	    ![X295 : $tType, X296 : fun(X295, bool)]:
191.60/191.86	      uminus_uminus(fun(X295, bool), X296)
191.60/191.86	       = collect(X295, 
191.60/191.86	           combb(bool, bool, X295, fNot, 
191.60/191.86	             combc(X295, fun(X295, bool), bool, member(X295), X296))),
191.60/191.86	    inference('cnf', [status(esa)], [fact_88_Compl__eq])).
191.60/191.86	tff('87', plain,
191.60/191.86	    ![X295 : $tType, X296 : fun(X295, bool)]:
191.60/191.86	      uminus_uminus(fun(X295, bool), X296)
191.60/191.86	       = uminus_uminus(fun(X295, bool), 
191.60/191.86	           combc(X295, fun(X295, bool), bool, member(X295), X296)),
191.60/191.86	    inference('demod', [status(thm)], ['86', '76', '75'])).
191.60/191.86	tff(fact_87_double__complement, axiom,
191.60/191.86	  (![A:$tType,A2:fun(A,bool)]:
191.60/191.86	     (uminus_uminus(fun(A,bool),uminus_uminus(fun(A,bool),A2)) = A2))).
191.60/191.86	tff('88', plain,
191.60/191.86	    ![X293 : $tType, X294 : fun(X293, bool)]:
191.60/191.86	      uminus_uminus(fun(X293, bool), uminus_uminus(fun(X293, bool), X294))
191.60/191.86	       = X294,
191.60/191.86	    inference('cnf', [status(esa)], [fact_87_double__complement])).
191.60/191.86	tff('89', plain,
191.60/191.86	    ![X0 : $tType, X1 : fun(X0, bool)]:
191.60/191.86	      uminus_uminus(fun(X0, bool), uminus_uminus(fun(X0, bool), X1))
191.60/191.86	       = combc(X0, fun(X0, bool), bool, member(X0), X1),
191.60/191.86	    inference('sup+', [status(thm)], ['87', '88'])).
191.60/191.86	tff('90', plain,
191.60/191.86	    ![X0 : $tType, X1 : fun(X0, bool)]:
191.60/191.86	      X1 = combc(X0, fun(X0, bool), bool, member(X0), X1),
191.60/191.86	    inference('demod', [status(thm)], ['89', '88'])).
191.60/191.86	tff('91', plain,
191.60/191.86	    ![X0 : $tType, X1 : $tType, X2 : X1, X3 : fun(X1, X0)]:
191.60/191.86	      pp(
191.60/191.86	        aa(X0, bool, image(X1, X0, X3, top_top(fun(X1, bool))), 
191.60/191.86	          aa(X1, X0, X3, X2))),
191.60/191.86	    inference('demod', [status(thm)], ['85', '90'])).
191.60/191.86	tff('92', plain, (~ $true | ~ $true),
191.60/191.86	    inference('demod', [status(thm)], ['78', '91'])).
191.60/191.86	tff('93', plain, $false, inference('simplify', [status(thm)], ['92'])).
191.60/191.86	
191.60/191.86	% SZS output end Refutation
191.60/191.87	EOF
