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_int
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 $2  \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --ho-purify int \
0.00/0.00	  --ho-no-ext-pos \
0.00/0.00	  --ho-no-ext-neg \
0.00/0.00	  --ho-prim-enum none \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --dont-select-ho-var-lits \
0.00/0.00	  --no-fool
0.00/0.20	% Computer   : n059.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 15:00:55 CST 2018
136.02/136.31	% done 20982 iterations in 136.102s
136.02/136.31	% SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
136.02/136.31	% SZS output start Refutation
136.11/136.31	tff(conj_5, axiom,
136.11/136.31	  (ord_less_eq(fun(nat,bool),kk,
136.11/136.31	               uminus_uminus(fun(nat,bool),
136.11/136.31	                             image(agent,nat,shrK,top_top(fun(agent,bool))))))).
136.11/136.31	tff('0', plain,
136.11/136.31	    ord_less_eq(fun(nat, bool), kk, 
136.11/136.31	      uminus_uminus(fun(nat, bool), 
136.11/136.31	        image(agent, nat, shrK, top_top(fun(agent, bool))))),
136.11/136.31	    inference('cnf', [status(esa)], [conj_5])).
136.11/136.31	tff(fact_98_sup__absorb1, axiom,
136.11/136.31	  (![A:$tType]:
136.11/136.31	     (semilattice_sup(A) =>
136.11/136.31	      (![X:A,Y:A]: (ord_less_eq(A,Y,X) => (sup_sup(A,X,Y) = X)))))).
136.11/136.31	tff('1', plain,
136.11/136.31	    ![X329 : $tType, X330 : X329, X331 : X329]:
136.11/136.31	      (~ ord_less_eq(X329, X330, X331)
136.11/136.31	       | sup_sup(X329, X331, X330) = X331
136.11/136.31	       | ~ semilattice_sup(X329)),
136.11/136.31	    inference('cnf', [status(esa)], [fact_98_sup__absorb1])).
136.11/136.31	tff('2', plain,
136.11/136.31	    (~ $true
136.11/136.31	     | ~ semilattice_sup(fun(nat, bool))
136.11/136.31	     | sup_sup(fun(nat, bool), 
136.11/136.31	         uminus_uminus(fun(nat, bool), 
136.11/136.31	           image(agent, nat, shrK, top_top(fun(agent, bool)))), kk)
136.11/136.31	        = uminus_uminus(fun(nat, bool), 
136.11/136.31	            image(agent, nat, shrK, top_top(fun(agent, bool))))),
136.11/136.31	    inference('sup-', [status(thm)], ['0', '1'])).
136.11/136.31	tff(arity_HOL_Obool___Lattices_Olattice, axiom, (lattice(bool))).
136.11/136.31	tff('3', plain, lattice(bool),
136.11/136.31	    inference('cnf', [status(esa)], [arity_HOL_Obool___Lattices_Olattice])).
136.11/136.31	tff(arity_fun___Lattices_Osemilattice__sup, axiom,
136.11/136.31	  (![T_1:$tType,T_2:$tType]: (lattice(T_2) => semilattice_sup(fun(T_1,T_2))))).
136.11/136.31	tff('4', plain,
136.11/136.31	    ![X339 : $tType, X340 : $tType]:
136.11/136.31	      (semilattice_sup(fun(X339, X340)) | ~ lattice(X340)),
136.11/136.31	    inference('cnf', [status(esa)], [arity_fun___Lattices_Osemilattice__sup])).
136.11/136.31	tff('5', plain, ![X0 : $tType]: (~ $true | semilattice_sup(fun(X0, bool))),
136.11/136.31	    inference('sup-', [status(thm)], ['3', '4'])).
136.11/136.31	tff('6', plain, ![X0 : $tType]: semilattice_sup(fun(X0, bool)),
136.11/136.31	    inference('simplify', [status(thm)], ['5'])).
136.11/136.31	tff(fact_81_Un__commute, axiom,
136.11/136.31	  (![A:$tType,B2:fun(A,bool),A2:fun(A,bool)]:
136.11/136.31	     (sup_sup(fun(A,bool),A2,B2) = sup_sup(fun(A,bool),B2,A2)))).
136.11/136.31	tff('7', plain,
136.11/136.31	    ![X277 : $tType, X278 : fun(X277, bool), X279 : fun(X277, bool)]:
136.11/136.31	      sup_sup(fun(X277, bool), X279, X278)
136.11/136.31	       = sup_sup(fun(X277, bool), X278, X279),
136.11/136.31	    inference('cnf', [status(esa)], [fact_81_Un__commute])).
136.11/136.31	tff('8', plain,
136.11/136.31	    (~ $true
136.11/136.31	     | ~ $true
136.11/136.31	     | sup_sup(fun(nat, bool), kk, 
136.11/136.31	         uminus_uminus(fun(nat, bool), 
136.11/136.31	           image(agent, nat, shrK, top_top(fun(agent, bool)))))
136.11/136.31	        = uminus_uminus(fun(nat, bool), 
136.11/136.31	            image(agent, nat, shrK, top_top(fun(agent, bool))))),
136.11/136.31	    inference('demod', [status(thm)], ['2', '6', '7'])).
136.11/136.31	tff('9', plain,
136.11/136.31	    sup_sup(fun(nat, bool), kk, 
136.11/136.31	      uminus_uminus(fun(nat, bool), 
136.11/136.31	        image(agent, nat, shrK, top_top(fun(agent, bool)))))
136.11/136.31	     = uminus_uminus(fun(nat, bool), 
136.11/136.31	         image(agent, nat, shrK, top_top(fun(agent, bool)))),
136.11/136.31	    inference('simplify', [status(thm)], ['8'])).
136.11/136.31	tff(conj_6, conjecture,
136.11/136.31	  ((pp(aa(fun(msg,bool),bool,
136.11/136.31	          aa(msg,fun(fun(msg,bool),bool),member(msg),aa(nat,msg,key,k)),
136.11/136.31	          analz(knows(spy,evs2)))) | 
136.11/136.31	    pp(aa(fun(nat,bool),bool,aa(nat,fun(fun(nat,bool),bool),member(nat),k),kk)) | 
136.11/136.31	    ((~
136.11/136.31	       pp(aa(fun(msg,bool),bool,
136.11/136.31	             aa(msg,fun(fun(msg,bool),bool),member(msg),aa(nat,msg,key,k)),
136.11/136.31	             analz(knows(spy,evs2))))) & 
136.11/136.31	     (~
136.11/136.31	       pp(aa(fun(nat,bool),bool,
136.11/136.31	             aa(nat,fun(fun(nat,bool),bool),member(nat),k),kk))) & 
136.11/136.31	     (k != kab)) | 
136.11/136.31	    (~
136.11/136.31	      pp(aa(fun(nat,bool),bool,
136.11/136.31	            aa(nat,fun(fun(nat,bool),bool),member(nat),aa(agent,nat,shrK,a)),
136.11/136.31	            kk))) | 
136.11/136.31	    pp(aa(fun(msg,bool),bool,
136.11/136.31	          aa(msg,fun(fun(msg,bool),bool),member(msg),
136.11/136.31	             aa(nat,msg,key,aa(agent,nat,shrK,a))),
136.11/136.31	          analz(knows(spy,evs2)))) | 
136.11/136.31	    pp(aa(fun(msg,bool),bool,
136.11/136.31	          aa(msg,fun(fun(msg,bool),bool),member(msg),
136.11/136.31	             aa(nat,msg,key,aa(agent,nat,shrK,b))),
136.11/136.31	          analz(knows(spy,evs2)))) | 
136.11/136.31	    (aa(agent,nat,shrK,b) = kab)) & 
136.11/136.31	   (((pp(aa(fun(msg,bool),bool,
136.11/136.31	            aa(msg,fun(fun(msg,bool),bool),member(msg),aa(nat,msg,key,k)),
136.11/136.31	            analz(knows(spy,evs2)))) | 
136.11/136.31	      pp(aa(fun(nat,bool),bool,aa(nat,fun(fun(nat,bool),bool),member(nat),k),
136.11/136.31	            kk)) | 
136.11/136.31	      ((~
136.11/136.31	         pp(aa(fun(msg,bool),bool,
136.11/136.31	               aa(msg,fun(fun(msg,bool),bool),member(msg),aa(nat,msg,key,k)),
136.11/136.31	               analz(knows(spy,evs2))))) & 
136.11/136.31	       (~
136.11/136.31	         pp(aa(fun(nat,bool),bool,
136.11/136.31	               aa(nat,fun(fun(nat,bool),bool),member(nat),k),kk))) & 
136.11/136.31	       (k != kab)) | 
136.11/136.31	      (~
136.11/136.31	        pp(aa(fun(nat,bool),bool,
136.11/136.31	              aa(nat,fun(fun(nat,bool),bool),member(nat),aa(agent,nat,shrK,a)),
136.11/136.31	              kk))) | 
136.11/136.31	      pp(aa(fun(msg,bool),bool,
136.11/136.31	            aa(msg,fun(fun(msg,bool),bool),member(msg),
136.11/136.31	               aa(nat,msg,key,aa(agent,nat,shrK,b))),
136.11/136.31	            analz(knows(spy,evs2)))) | 
136.11/136.31	      pp(aa(fun(nat,bool),bool,
136.11/136.31	            aa(nat,fun(fun(nat,bool),bool),member(nat),aa(agent,nat,shrK,b)),
136.11/136.31	            kk)) | 
136.11/136.31	      (aa(agent,nat,shrK,b) = kab)) & 
136.11/136.31	     (pp(aa(fun(msg,bool),bool,
136.11/136.31	            aa(msg,fun(fun(msg,bool),bool),member(msg),aa(nat,msg,key,k)),
136.11/136.31	            analz(knows(spy,evs2)))) | 
136.11/136.31	      pp(aa(fun(nat,bool),bool,aa(nat,fun(fun(nat,bool),bool),member(nat),k),
136.11/136.31	            kk)) | 
136.11/136.31	      ((~
136.11/136.31	         pp(aa(fun(msg,bool),bool,
136.11/136.31	               aa(msg,fun(fun(msg,bool),bool),member(msg),aa(nat,msg,key,k)),
136.11/136.31	               analz(knows(spy,evs2))))) & 
136.11/136.31	       (~
136.11/136.31	         pp(aa(fun(nat,bool),bool,
136.11/136.31	               aa(nat,fun(fun(nat,bool),bool),member(nat),k),kk))) & 
136.11/136.31	       (k != kab)) | 
136.11/136.31	      (~
136.11/136.31	        pp(aa(fun(nat,bool),bool,
136.11/136.31	              aa(nat,fun(fun(nat,bool),bool),member(nat),aa(agent,nat,shrK,a)),
136.11/136.31	              kk))) | 
136.11/136.31	      ((~
136.11/136.31	         pp(aa(fun(msg,bool),bool,
136.11/136.31	               aa(msg,fun(fun(msg,bool),bool),member(msg),
136.11/136.31	                  aa(nat,msg,key,aa(agent,nat,shrK,b))),
136.11/136.31	               analz(knows(spy,evs2))))) & 
136.11/136.31	       (~
136.11/136.31	         pp(aa(fun(nat,bool),bool,
136.11/136.31	               aa(nat,fun(fun(nat,bool),bool),member(nat),
136.11/136.31	                  aa(agent,nat,shrK,b)),
136.11/136.31	               kk))) & 
136.11/136.31	       (aa(agent,nat,shrK,b) != kab)))) | 
136.11/136.31	    pp(aa(fun(msg,bool),bool,
136.11/136.31	          aa(msg,fun(fun(msg,bool),bool),member(msg),
136.11/136.31	             aa(nat,msg,key,aa(agent,nat,shrK,a))),
136.11/136.31	          analz(knows(spy,evs2)))) | 
136.11/136.31	    ((~
136.11/136.31	       pp(aa(fun(msg,bool),bool,
136.11/136.31	             aa(msg,fun(fun(msg,bool),bool),member(msg),
136.11/136.31	                aa(nat,msg,key,aa(agent,nat,shrK,b))),
136.11/136.31	             analz(knows(spy,evs2))))) & 
136.11/136.31	     (aa(agent,nat,shrK,b) != kab))))).
136.11/136.31	tff(zf_stmt_0, negated_conjecture,
136.11/136.31	  (~
136.11/136.31	    ((pp(aa(fun(msg,bool),bool,
136.11/136.31	            aa(msg,fun(fun(msg,bool),bool),member(msg),aa(nat,msg,key,k)),
136.11/136.31	            analz(knows(spy,evs2)))) | 
136.11/136.31	      pp(aa(fun(nat,bool),bool,aa(nat,fun(fun(nat,bool),bool),member(nat),k),
136.11/136.31	            kk)) | 
136.11/136.31	      ((~
136.11/136.31	         pp(aa(fun(msg,bool),bool,
136.11/136.31	               aa(msg,fun(fun(msg,bool),bool),member(msg),aa(nat,msg,key,k)),
136.11/136.31	               analz(knows(spy,evs2))))) & 
136.11/136.31	       (~
136.11/136.31	         pp(aa(fun(nat,bool),bool,
136.11/136.31	               aa(nat,fun(fun(nat,bool),bool),member(nat),k),kk))) & 
136.11/136.31	       (k != kab)) | 
136.11/136.31	      (~
136.11/136.31	        pp(aa(fun(nat,bool),bool,
136.11/136.31	              aa(nat,fun(fun(nat,bool),bool),member(nat),aa(agent,nat,shrK,a)),
136.11/136.31	              kk))) | 
136.11/136.31	      pp(aa(fun(msg,bool),bool,
136.11/136.31	            aa(msg,fun(fun(msg,bool),bool),member(msg),
136.11/136.31	               aa(nat,msg,key,aa(agent,nat,shrK,a))),
136.11/136.31	            analz(knows(spy,evs2)))) | 
136.11/136.31	      pp(aa(fun(msg,bool),bool,
136.11/136.31	            aa(msg,fun(fun(msg,bool),bool),member(msg),
136.11/136.31	               aa(nat,msg,key,aa(agent,nat,shrK,b))),
136.11/136.31	            analz(knows(spy,evs2)))) | 
136.11/136.31	      (aa(agent,nat,shrK,b) = kab)) & 
136.11/136.31	     (((pp(aa(fun(msg,bool),bool,
136.11/136.31	              aa(msg,fun(fun(msg,bool),bool),member(msg),aa(nat,msg,key,k)),
136.11/136.31	              analz(knows(spy,evs2)))) | 
136.11/136.31	        pp(aa(fun(nat,bool),bool,
136.11/136.31	              aa(nat,fun(fun(nat,bool),bool),member(nat),k),kk)) | 
136.11/136.31	        ((~
136.11/136.31	           pp(aa(fun(msg,bool),bool,
136.11/136.31	                 aa(msg,fun(fun(msg,bool),bool),member(msg),aa(nat,msg,key,k)),
136.11/136.31	                 analz(knows(spy,evs2))))) & 
136.11/136.31	         (~
136.11/136.31	           pp(aa(fun(nat,bool),bool,
136.11/136.31	                 aa(nat,fun(fun(nat,bool),bool),member(nat),k),kk))) & 
136.11/136.31	         (k != kab)) | 
136.11/136.31	        (~
136.11/136.31	          pp(aa(fun(nat,bool),bool,
136.11/136.31	                aa(nat,fun(fun(nat,bool),bool),member(nat),
136.11/136.31	                   aa(agent,nat,shrK,a)),
136.11/136.31	                kk))) | 
136.11/136.31	        pp(aa(fun(msg,bool),bool,
136.11/136.31	              aa(msg,fun(fun(msg,bool),bool),member(msg),
136.11/136.31	                 aa(nat,msg,key,aa(agent,nat,shrK,b))),
136.11/136.31	              analz(knows(spy,evs2)))) | 
136.11/136.31	        pp(aa(fun(nat,bool),bool,
136.11/136.31	              aa(nat,fun(fun(nat,bool),bool),member(nat),aa(agent,nat,shrK,b)),
136.11/136.31	              kk)) | 
136.11/136.31	        (aa(agent,nat,shrK,b) = kab)) & 
136.11/136.31	       (pp(aa(fun(msg,bool),bool,
136.11/136.31	              aa(msg,fun(fun(msg,bool),bool),member(msg),aa(nat,msg,key,k)),
136.11/136.31	              analz(knows(spy,evs2)))) | 
136.11/136.31	        pp(aa(fun(nat,bool),bool,
136.11/136.31	              aa(nat,fun(fun(nat,bool),bool),member(nat),k),kk)) | 
136.11/136.31	        ((~
136.11/136.31	           pp(aa(fun(msg,bool),bool,
136.11/136.31	                 aa(msg,fun(fun(msg,bool),bool),member(msg),aa(nat,msg,key,k)),
136.11/136.31	                 analz(knows(spy,evs2))))) & 
136.11/136.31	         (~
136.11/136.31	           pp(aa(fun(nat,bool),bool,
136.11/136.31	                 aa(nat,fun(fun(nat,bool),bool),member(nat),k),kk))) & 
136.11/136.31	         (k != kab)) | 
136.11/136.31	        (~
136.11/136.31	          pp(aa(fun(nat,bool),bool,
136.11/136.31	                aa(nat,fun(fun(nat,bool),bool),member(nat),
136.11/136.31	                   aa(agent,nat,shrK,a)),
136.11/136.31	                kk))) | 
136.11/136.31	        ((~
136.11/136.31	           pp(aa(fun(msg,bool),bool,
136.11/136.31	                 aa(msg,fun(fun(msg,bool),bool),member(msg),
136.11/136.31	                    aa(nat,msg,key,aa(agent,nat,shrK,b))),
136.11/136.31	                 analz(knows(spy,evs2))))) & 
136.11/136.31	         (~
136.11/136.31	           pp(aa(fun(nat,bool),bool,
136.11/136.31	                 aa(nat,fun(fun(nat,bool),bool),member(nat),
136.11/136.31	                    aa(agent,nat,shrK,b)),
136.11/136.31	                 kk))) & 
136.11/136.31	         (aa(agent,nat,shrK,b) != kab)))) | 
136.11/136.31	      pp(aa(fun(msg,bool),bool,
136.11/136.31	            aa(msg,fun(fun(msg,bool),bool),member(msg),
136.11/136.31	               aa(nat,msg,key,aa(agent,nat,shrK,a))),
136.11/136.31	            analz(knows(spy,evs2)))) | 
136.11/136.31	      ((~
136.11/136.31	         pp(aa(fun(msg,bool),bool,
136.11/136.31	               aa(msg,fun(fun(msg,bool),bool),member(msg),
136.11/136.31	                  aa(nat,msg,key,aa(agent,nat,shrK,b))),
136.11/136.31	               analz(knows(spy,evs2))))) & 
136.11/136.31	       (aa(agent,nat,shrK,b) != kab)))))).
136.11/136.31	tff('10', plain,
136.11/136.31	    (pp(
136.11/136.31	       aa(fun(nat, bool), bool, 
136.11/136.31	         aa(nat, fun(fun(nat, bool), bool), member(nat), 
136.11/136.31	           aa(agent, nat, shrK, a)), kk))
136.11/136.31	     | pp(
136.11/136.31	         aa(fun(nat, bool), bool, 
136.11/136.31	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
136.11/136.31	             aa(agent, nat, shrK, a)), kk))
136.11/136.31	     | pp(
136.11/136.31	         aa(fun(msg, bool), bool, 
136.11/136.31	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
136.11/136.31	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
136.11/136.31	           analz(knows(spy, evs2))))
136.11/136.31	     | pp(
136.11/136.31	         aa(fun(nat, bool), bool, 
136.11/136.31	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
136.11/136.31	             aa(agent, nat, shrK, b)), kk))
136.11/136.31	     | aa(agent, nat, shrK, b) = kab),
136.11/136.31	    inference('cnf', [status(esa)], [zf_stmt_0])).
136.11/136.31	tff('11', plain,
136.11/136.31	    (aa(agent, nat, shrK, b) = kab
136.11/136.31	     | pp(
136.11/136.31	         aa(fun(nat, bool), bool, 
136.11/136.31	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
136.11/136.31	             aa(agent, nat, shrK, b)), kk))
136.11/136.31	     | pp(
136.11/136.31	         aa(fun(msg, bool), bool, 
136.11/136.31	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
136.11/136.31	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
136.11/136.31	           analz(knows(spy, evs2))))
136.11/136.31	     | pp(
136.11/136.31	         aa(fun(nat, bool), bool, 
136.11/136.31	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
136.11/136.31	             aa(agent, nat, shrK, a)), kk))),
136.11/136.31	    inference('simplify', [status(thm)], ['10'])).
136.11/136.31	tff('12', plain,
136.11/136.31	    (k = kab
136.11/136.31	     | pp(
136.11/136.31	         aa(fun(nat, bool), bool, 
136.11/136.31	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
136.11/136.31	     | pp(
136.11/136.31	         aa(fun(msg, bool), bool, 
136.11/136.31	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
136.11/136.31	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
136.11/136.31	     | k = kab
136.11/136.31	     | pp(
136.11/136.31	         aa(fun(nat, bool), bool, 
136.11/136.31	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
136.11/136.31	     | pp(
136.11/136.31	         aa(fun(msg, bool), bool, 
136.11/136.31	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
136.11/136.31	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
136.11/136.31	     | pp(
136.11/136.31	         aa(fun(msg, bool), bool, 
136.11/136.31	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
136.11/136.31	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
136.11/136.31	           analz(knows(spy, evs2))))
136.11/136.31	     | pp(
136.11/136.31	         aa(fun(nat, bool), bool, 
136.11/136.31	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
136.11/136.31	             aa(agent, nat, shrK, b)), kk))
136.11/136.31	     | aa(agent, nat, shrK, b) = kab),
136.11/136.31	    inference('cnf', [status(esa)], [zf_stmt_0])).
136.11/136.31	tff('13', plain,
136.11/136.31	    (aa(agent, nat, shrK, b) = kab
136.11/136.31	     | pp(
136.11/136.31	         aa(fun(nat, bool), bool, 
136.11/136.31	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
136.11/136.31	             aa(agent, nat, shrK, b)), kk))
136.11/136.31	     | pp(
136.11/136.31	         aa(fun(msg, bool), bool, 
136.11/136.31	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
136.11/136.31	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
136.11/136.31	           analz(knows(spy, evs2))))
136.11/136.31	     | pp(
136.11/136.31	         aa(fun(msg, bool), bool, 
136.11/136.31	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
136.11/136.31	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
136.11/136.31	     | pp(
136.11/136.31	         aa(fun(nat, bool), bool, 
136.11/136.31	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
136.11/136.31	     | k = kab),
136.11/136.31	    inference('simplify', [status(thm)], ['12'])).
136.11/136.31	tff('14', plain,
136.11/136.31	    (k = kab
136.11/136.31	     | pp(
136.11/136.31	         aa(fun(nat, bool), bool, 
136.11/136.31	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
136.11/136.31	     | pp(
136.11/136.31	         aa(fun(msg, bool), bool, 
136.11/136.31	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
136.11/136.31	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
136.11/136.31	     | aa(agent, nat, shrK, b) != kab
136.11/136.31	     | pp(
136.11/136.31	         aa(fun(msg, bool), bool, 
136.11/136.31	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
136.11/136.31	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
136.11/136.31	     | pp(
136.11/136.31	         aa(fun(nat, bool), bool, 
136.11/136.31	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
136.11/136.31	     | k = kab),
136.11/136.31	    inference('cnf', [status(esa)], [zf_stmt_0])).
136.11/136.31	tff('15', plain,
136.11/136.31	    (aa(agent, nat, shrK, b) != kab
136.11/136.31	     | pp(
136.11/136.31	         aa(fun(msg, bool), bool, 
136.11/136.31	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
136.11/136.31	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
136.11/136.31	     | pp(
136.11/136.31	         aa(fun(nat, bool), bool, 
136.11/136.31	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
136.11/136.31	     | k = kab),
136.11/136.31	    inference('simplify', [status(thm)], ['14'])).
136.11/136.31	tff('16', plain,
136.11/136.31	    (~ pp(
136.11/136.31	         aa(fun(msg, bool), bool, 
136.11/136.31	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
136.11/136.31	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
136.11/136.31	     | ~ pp(
136.11/136.31	           aa(fun(msg, bool), bool, 
136.11/136.31	             aa(msg, fun(fun(msg, bool), bool), member(msg), 
136.11/136.31	               aa(nat, msg, key, k)), analz(knows(spy, evs2))))
136.11/136.31	     | pp(
136.11/136.31	         aa(fun(msg, bool), bool, 
136.11/136.31	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
136.11/136.31	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
136.11/136.31	           analz(knows(spy, evs2))))
136.11/136.31	     | pp(
136.11/136.31	         aa(fun(nat, bool), bool, 
136.11/136.31	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
136.11/136.31	             aa(agent, nat, shrK, b)), kk))
136.11/136.31	     | aa(agent, nat, shrK, b) = kab),
136.11/136.31	    inference('cnf', [status(esa)], [zf_stmt_0])).
136.11/136.31	tff('17', plain,
136.11/136.31	    (aa(agent, nat, shrK, b) = kab
136.11/136.31	     | pp(
136.11/136.31	         aa(fun(nat, bool), bool, 
136.11/136.31	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
136.11/136.31	             aa(agent, nat, shrK, b)), kk))
136.11/136.31	     | pp(
136.11/136.31	         aa(fun(msg, bool), bool, 
136.11/136.31	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
136.11/136.31	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
136.11/136.31	           analz(knows(spy, evs2))))
136.11/136.31	     | ~ pp(
136.11/136.31	           aa(fun(msg, bool), bool, 
136.11/136.31	             aa(msg, fun(fun(msg, bool), bool), member(msg), 
136.11/136.31	               aa(nat, msg, key, k)), analz(knows(spy, evs2))))),
136.11/136.31	    inference('simplify', [status(thm)], ['16'])).
136.11/136.31	tff('18', plain,
136.11/136.31	    (~ pp(
136.11/136.31	         aa(fun(msg, bool), bool, 
136.11/136.31	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
136.11/136.31	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
136.11/136.31	     | aa(agent, nat, shrK, b) != kab
136.11/136.31	     | ~ pp(
136.11/136.31	           aa(fun(msg, bool), bool, 
136.11/136.31	             aa(msg, fun(fun(msg, bool), bool), member(msg), 
136.11/136.31	               aa(nat, msg, key, k)), analz(knows(spy, evs2))))),
136.11/136.31	    inference('cnf', [status(esa)], [zf_stmt_0])).
136.11/136.31	tff('19', plain,
136.11/136.31	    (aa(agent, nat, shrK, b) != kab
136.11/136.31	     | ~ pp(
136.11/136.31	           aa(fun(msg, bool), bool, 
136.11/136.31	             aa(msg, fun(fun(msg, bool), bool), member(msg), 
136.11/136.31	               aa(nat, msg, key, k)), analz(knows(spy, evs2))))),
136.11/136.31	    inference('simplify', [status(thm)], ['18'])).
136.11/136.31	tff('20', plain,
136.11/136.31	    (~ pp(
136.11/136.31	         aa(fun(msg, bool), bool, 
136.11/136.31	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
136.11/136.31	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
136.11/136.31	     | pp(
136.11/136.31	         aa(fun(msg, bool), bool, 
136.11/136.31	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
136.11/136.31	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
136.11/136.31	           analz(knows(spy, evs2))))
136.11/136.31	     | pp(
136.11/136.31	         aa(fun(nat, bool), bool, 
136.11/136.31	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
136.11/136.31	             aa(agent, nat, shrK, b)), kk))),
136.11/136.31	    inference('clc', [status(thm)], ['17', '19'])).
136.11/136.31	tff('21', plain,
136.11/136.31	    (~ pp(
136.11/136.31	         aa(fun(msg, bool), bool, 
136.11/136.31	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
136.11/136.31	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
136.11/136.31	     | ~ pp(
136.11/136.31	           aa(fun(msg, bool), bool, 
136.11/136.31	             aa(msg, fun(fun(msg, bool), bool), member(msg), 
136.11/136.31	               aa(nat, msg, key, aa(agent, nat, shrK, b))), 
136.11/136.31	             analz(knows(spy, evs2))))
136.11/136.31	     | ~ pp(
136.11/136.31	           aa(fun(msg, bool), bool, 
136.11/136.31	             aa(msg, fun(fun(msg, bool), bool), member(msg), 
136.11/136.31	               aa(nat, msg, key, k)), analz(knows(spy, evs2))))),
136.11/136.31	    inference('cnf', [status(esa)], [zf_stmt_0])).
136.11/136.31	tff('22', plain,
136.11/136.31	    (~ pp(
136.11/136.31	         aa(fun(msg, bool), bool, 
136.11/136.31	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
136.11/136.31	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
136.11/136.31	           analz(knows(spy, evs2))))
136.11/136.31	     | ~ pp(
136.11/136.31	           aa(fun(msg, bool), bool, 
136.11/136.31	             aa(msg, fun(fun(msg, bool), bool), member(msg), 
136.11/136.31	               aa(nat, msg, key, k)), analz(knows(spy, evs2))))),
136.11/136.31	    inference('simplify', [status(thm)], ['21'])).
136.11/136.31	tff('23', plain,
136.11/136.31	    (pp(
136.11/136.31	       aa(fun(nat, bool), bool, 
136.11/136.31	         aa(nat, fun(fun(nat, bool), bool), member(nat), 
136.11/136.31	           aa(agent, nat, shrK, b)), kk))
136.11/136.31	     | ~ pp(
136.11/136.31	           aa(fun(msg, bool), bool, 
136.11/136.31	             aa(msg, fun(fun(msg, bool), bool), member(msg), 
136.11/136.31	               aa(nat, msg, key, k)), analz(knows(spy, evs2))))),
136.11/136.31	    inference('clc', [status(thm)], ['20', '22'])).
136.11/136.31	tff('24', plain,
136.11/136.31	    (~ pp(
136.11/136.31	         aa(fun(msg, bool), bool, 
136.11/136.31	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
136.11/136.31	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
136.11/136.31	     | ~ pp(
136.11/136.31	           aa(fun(nat, bool), bool, 
136.11/136.31	             aa(nat, fun(fun(nat, bool), bool), member(nat), 
136.11/136.31	               aa(agent, nat, shrK, b)), kk))
136.11/136.31	     | ~ pp(
136.11/136.31	           aa(fun(msg, bool), bool, 
136.11/136.31	             aa(msg, fun(fun(msg, bool), bool), member(msg), 
136.11/136.31	               aa(nat, msg, key, k)), analz(knows(spy, evs2))))),
136.11/136.31	    inference('cnf', [status(esa)], [zf_stmt_0])).
136.11/136.31	tff('25', plain,
136.11/136.31	    (~ pp(
136.11/136.31	         aa(fun(nat, bool), bool, 
136.11/136.31	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
136.11/136.31	             aa(agent, nat, shrK, b)), kk))
136.11/136.31	     | ~ pp(
136.11/136.31	           aa(fun(msg, bool), bool, 
136.11/136.31	             aa(msg, fun(fun(msg, bool), bool), member(msg), 
136.11/136.31	               aa(nat, msg, key, k)), analz(knows(spy, evs2))))),
136.11/136.31	    inference('simplify', [status(thm)], ['24'])).
136.11/136.31	tff('26', plain,
136.11/136.31	    ~ pp(
136.11/136.31	        aa(fun(msg, bool), bool, 
136.11/136.31	          aa(msg, fun(fun(msg, bool), bool), member(msg), 
136.11/136.31	            aa(nat, msg, key, k)), analz(knows(spy, evs2)))),
136.11/136.31	    inference('clc', [status(thm)], ['23', '25'])).
136.11/136.31	tff('27', plain,
136.11/136.31	    (k = kab
136.11/136.31	     | pp(
136.11/136.31	         aa(fun(nat, bool), bool, 
136.11/136.31	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
136.11/136.31	     | aa(agent, nat, shrK, b) != kab),
136.11/136.31	    inference('clc', [status(thm)], ['15', '26'])).
136.11/136.31	tff('28', plain,
136.11/136.31	    (~ pp(
136.11/136.31	         aa(fun(nat, bool), bool, 
136.11/136.31	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
136.11/136.31	     | ~ pp(
136.11/136.31	           aa(fun(nat, bool), bool, 
136.11/136.31	             aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
136.11/136.31	     | pp(
136.11/136.31	         aa(fun(msg, bool), bool, 
136.11/136.31	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
136.11/136.31	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
136.11/136.31	           analz(knows(spy, evs2))))
136.11/136.31	     | pp(
136.11/136.31	         aa(fun(nat, bool), bool, 
136.11/136.31	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
136.11/136.31	             aa(agent, nat, shrK, b)), kk))
136.11/136.31	     | aa(agent, nat, shrK, b) = kab),
136.11/136.31	    inference('cnf', [status(esa)], [zf_stmt_0])).
136.11/136.31	tff('29', plain,
136.11/136.31	    (aa(agent, nat, shrK, b) = kab
136.11/136.31	     | pp(
136.11/136.31	         aa(fun(nat, bool), bool, 
136.11/136.31	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
136.11/136.31	             aa(agent, nat, shrK, b)), kk))
136.11/136.31	     | pp(
136.11/136.31	         aa(fun(msg, bool), bool, 
136.11/136.31	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
136.11/136.31	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
136.11/136.31	           analz(knows(spy, evs2))))
136.11/136.31	     | ~ pp(
136.11/136.31	           aa(fun(nat, bool), bool, 
136.11/136.31	             aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))),
136.11/136.31	    inference('simplify', [status(thm)], ['28'])).
136.11/136.31	tff('30', plain,
136.11/136.31	    (~ pp(
136.11/136.31	         aa(fun(nat, bool), bool, 
136.11/136.31	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
136.11/136.31	     | aa(agent, nat, shrK, b) != kab
136.11/136.31	     | ~ pp(
136.11/136.31	           aa(fun(nat, bool), bool, 
136.11/136.31	             aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))),
136.11/136.31	    inference('cnf', [status(esa)], [zf_stmt_0])).
136.11/136.31	tff('31', plain,
136.11/136.31	    (aa(agent, nat, shrK, b) != kab
136.11/136.31	     | ~ pp(
136.11/136.31	           aa(fun(nat, bool), bool, 
136.11/136.31	             aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))),
136.11/136.31	    inference('simplify', [status(thm)], ['30'])).
136.11/136.31	tff('32', plain,
136.11/136.31	    (~ pp(
136.11/136.31	         aa(fun(nat, bool), bool, 
136.11/136.31	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
136.11/136.31	     | pp(
136.11/136.31	         aa(fun(msg, bool), bool, 
136.11/136.31	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
136.11/136.31	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
136.11/136.31	           analz(knows(spy, evs2))))
136.11/136.31	     | pp(
136.11/136.31	         aa(fun(nat, bool), bool, 
136.11/136.31	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
136.11/136.31	             aa(agent, nat, shrK, b)), kk))),
136.11/136.31	    inference('clc', [status(thm)], ['29', '31'])).
136.11/136.31	tff('33', plain,
136.11/136.31	    (~ pp(
136.11/136.31	         aa(fun(nat, bool), bool, 
136.11/136.31	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
136.11/136.31	     | ~ pp(
136.11/136.31	           aa(fun(msg, bool), bool, 
136.11/136.31	             aa(msg, fun(fun(msg, bool), bool), member(msg), 
136.11/136.31	               aa(nat, msg, key, aa(agent, nat, shrK, b))), 
136.11/136.31	             analz(knows(spy, evs2))))
136.11/136.31	     | ~ pp(
136.11/136.31	           aa(fun(nat, bool), bool, 
136.11/136.31	             aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))),
136.11/136.31	    inference('cnf', [status(esa)], [zf_stmt_0])).
136.11/136.31	tff('34', plain,
136.11/136.31	    (~ pp(
136.11/136.31	         aa(fun(msg, bool), bool, 
136.11/136.31	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
136.11/136.31	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
136.11/136.31	           analz(knows(spy, evs2))))
136.11/136.31	     | ~ pp(
136.11/136.31	           aa(fun(nat, bool), bool, 
136.11/136.31	             aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))),
136.11/136.31	    inference('simplify', [status(thm)], ['33'])).
136.11/136.31	tff('35', plain,
136.11/136.31	    (pp(
136.11/136.31	       aa(fun(nat, bool), bool, 
136.11/136.31	         aa(nat, fun(fun(nat, bool), bool), member(nat), 
136.11/136.31	           aa(agent, nat, shrK, b)), kk))
136.11/136.31	     | ~ pp(
136.11/136.31	           aa(fun(nat, bool), bool, 
136.11/136.31	             aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))),
136.11/136.31	    inference('clc', [status(thm)], ['32', '34'])).
136.11/136.31	tff('36', plain,
136.11/136.31	    (~ pp(
136.11/136.31	         aa(fun(nat, bool), bool, 
136.11/136.31	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
136.11/136.31	     | ~ pp(
136.11/136.31	           aa(fun(nat, bool), bool, 
136.11/136.31	             aa(nat, fun(fun(nat, bool), bool), member(nat), 
136.11/136.31	               aa(agent, nat, shrK, b)), kk))
136.11/136.31	     | ~ pp(
136.11/136.31	           aa(fun(nat, bool), bool, 
136.11/136.31	             aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))),
136.11/136.31	    inference('cnf', [status(esa)], [zf_stmt_0])).
136.11/136.31	tff('37', plain,
136.11/136.31	    (~ pp(
136.11/136.31	         aa(fun(nat, bool), bool, 
136.11/136.31	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
136.11/136.31	             aa(agent, nat, shrK, b)), kk))
136.11/136.31	     | ~ pp(
136.11/136.31	           aa(fun(nat, bool), bool, 
136.11/136.31	             aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))),
136.11/136.31	    inference('simplify', [status(thm)], ['36'])).
136.11/136.31	tff('38', plain,
136.11/136.31	    ~ pp(
136.11/136.31	        aa(fun(nat, bool), bool, 
136.11/136.31	          aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk)),
136.11/136.31	    inference('clc', [status(thm)], ['35', '37'])).
136.11/136.31	tff('39', plain, (aa(agent, nat, shrK, b) != kab | k = kab),
136.11/136.31	    inference('clc', [status(thm)], ['27', '38'])).
136.11/136.31	tff('40', plain,
136.11/136.31	    (k = kab
136.11/136.31	     | pp(
136.11/136.31	         aa(fun(nat, bool), bool, 
136.11/136.31	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
136.11/136.31	     | pp(
136.11/136.31	         aa(fun(msg, bool), bool, 
136.11/136.31	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
136.11/136.31	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
136.11/136.31	     | pp(
136.11/136.31	         aa(fun(msg, bool), bool, 
136.11/136.31	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
136.11/136.31	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
136.11/136.31	           analz(knows(spy, evs2))))
136.11/136.31	     | pp(
136.11/136.31	         aa(fun(nat, bool), bool, 
136.11/136.31	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
136.11/136.31	             aa(agent, nat, shrK, b)), kk))),
136.11/136.31	    inference('clc', [status(thm)], ['13', '39'])).
136.11/136.31	tff('41', plain,
136.11/136.31	    (pp(
136.11/136.31	       aa(fun(nat, bool), bool, 
136.11/136.31	         aa(nat, fun(fun(nat, bool), bool), member(nat), 
136.11/136.31	           aa(agent, nat, shrK, b)), kk))
136.11/136.31	     | pp(
136.11/136.31	         aa(fun(msg, bool), bool, 
136.11/136.31	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
136.11/136.31	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
136.11/136.31	           analz(knows(spy, evs2))))
136.11/136.31	     | pp(
136.11/136.31	         aa(fun(msg, bool), bool, 
136.11/136.31	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
136.11/136.31	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
136.11/136.31	     | k = kab),
136.11/136.31	    inference('clc', [status(thm)], ['40', '38'])).
136.11/136.31	tff('42', plain,
136.11/136.31	    (k = kab
136.11/136.31	     | pp(
136.11/136.31	         aa(fun(nat, bool), bool, 
136.11/136.31	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
136.11/136.31	     | pp(
136.11/136.31	         aa(fun(msg, bool), bool, 
136.11/136.31	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
136.11/136.31	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
136.11/136.32	     | ~ pp(
136.11/136.32	           aa(fun(nat, bool), bool, 
136.11/136.32	             aa(nat, fun(fun(nat, bool), bool), member(nat), 
136.11/136.32	               aa(agent, nat, shrK, b)), kk))
136.11/136.32	     | pp(
136.11/136.32	         aa(fun(msg, bool), bool, 
136.11/136.32	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
136.11/136.32	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
136.11/136.32	     | pp(
136.11/136.32	         aa(fun(nat, bool), bool, 
136.11/136.32	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
136.11/136.32	     | k = kab),
136.11/136.32	    inference('cnf', [status(esa)], [zf_stmt_0])).
136.11/136.32	tff('43', plain,
136.11/136.32	    (~ pp(
136.11/136.32	         aa(fun(nat, bool), bool, 
136.11/136.32	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
136.11/136.32	             aa(agent, nat, shrK, b)), kk))
136.11/136.32	     | pp(
136.11/136.32	         aa(fun(msg, bool), bool, 
136.11/136.32	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
136.11/136.32	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
136.11/136.32	     | pp(
136.11/136.32	         aa(fun(nat, bool), bool, 
136.11/136.32	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
136.11/136.32	     | k = kab),
136.11/136.32	    inference('simplify', [status(thm)], ['42'])).
136.11/136.32	tff('44', plain,
136.11/136.32	    (k = kab
136.11/136.32	     | pp(
136.11/136.32	         aa(fun(nat, bool), bool, 
136.11/136.32	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
136.11/136.32	     | ~ pp(
136.11/136.32	           aa(fun(nat, bool), bool, 
136.11/136.32	             aa(nat, fun(fun(nat, bool), bool), member(nat), 
136.11/136.32	               aa(agent, nat, shrK, b)), kk))),
136.11/136.32	    inference('clc', [status(thm)], ['43', '26'])).
136.11/136.32	tff('45', plain,
136.11/136.32	    (~ pp(
136.11/136.32	         aa(fun(nat, bool), bool, 
136.11/136.32	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
136.11/136.32	             aa(agent, nat, shrK, b)), kk))
136.11/136.32	     | k = kab),
136.11/136.32	    inference('clc', [status(thm)], ['44', '38'])).
136.11/136.32	tff('46', plain,
136.11/136.32	    (k = kab
136.11/136.32	     | pp(
136.11/136.32	         aa(fun(msg, bool), bool, 
136.11/136.32	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
136.11/136.32	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
136.11/136.32	     | pp(
136.11/136.32	         aa(fun(msg, bool), bool, 
136.11/136.32	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
136.11/136.32	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
136.11/136.32	           analz(knows(spy, evs2))))),
136.11/136.32	    inference('clc', [status(thm)], ['41', '45'])).
136.11/136.32	tff('47', plain,
136.11/136.32	    (pp(
136.11/136.32	       aa(fun(msg, bool), bool, 
136.11/136.32	         aa(msg, fun(fun(msg, bool), bool), member(msg), 
136.11/136.32	           aa(nat, msg, key, aa(agent, nat, shrK, b))), 
136.11/136.32	         analz(knows(spy, evs2))))
136.11/136.32	     | k = kab),
136.11/136.32	    inference('clc', [status(thm)], ['46', '26'])).
136.11/136.32	tff('48', plain,
136.11/136.32	    (k = kab
136.11/136.32	     | pp(
136.11/136.32	         aa(fun(nat, bool), bool, 
136.11/136.32	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
136.11/136.32	     | pp(
136.11/136.32	         aa(fun(msg, bool), bool, 
136.11/136.32	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
136.11/136.32	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
136.11/136.32	     | ~ pp(
136.11/136.32	           aa(fun(msg, bool), bool, 
136.11/136.32	             aa(msg, fun(fun(msg, bool), bool), member(msg), 
136.11/136.32	               aa(nat, msg, key, aa(agent, nat, shrK, b))), 
136.11/136.32	             analz(knows(spy, evs2))))
136.11/136.32	     | pp(
136.11/136.32	         aa(fun(msg, bool), bool, 
136.11/136.32	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
136.11/136.32	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
136.11/136.32	     | pp(
136.11/136.32	         aa(fun(nat, bool), bool, 
136.11/136.32	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
136.11/136.32	     | k = kab),
136.11/136.32	    inference('cnf', [status(esa)], [zf_stmt_0])).
136.11/136.32	tff('49', plain,
136.11/136.32	    (~ pp(
136.11/136.32	         aa(fun(msg, bool), bool, 
136.11/136.32	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
136.11/136.32	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
136.11/136.32	           analz(knows(spy, evs2))))
136.11/136.32	     | pp(
136.11/136.32	         aa(fun(msg, bool), bool, 
136.11/136.32	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
136.11/136.32	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
136.11/136.32	     | pp(
136.11/136.32	         aa(fun(nat, bool), bool, 
136.11/136.32	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
136.11/136.32	     | k = kab),
136.11/136.32	    inference('simplify', [status(thm)], ['48'])).
136.11/136.32	tff('50', plain,
136.11/136.32	    (k = kab
136.11/136.32	     | pp(
136.11/136.32	         aa(fun(nat, bool), bool, 
136.11/136.32	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
136.11/136.32	     | ~ pp(
136.11/136.32	           aa(fun(msg, bool), bool, 
136.11/136.32	             aa(msg, fun(fun(msg, bool), bool), member(msg), 
136.11/136.32	               aa(nat, msg, key, aa(agent, nat, shrK, b))), 
136.11/136.32	             analz(knows(spy, evs2))))),
136.11/136.32	    inference('clc', [status(thm)], ['49', '26'])).
136.11/136.32	tff('51', plain,
136.11/136.32	    (~ pp(
136.11/136.32	         aa(fun(msg, bool), bool, 
136.11/136.32	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
136.11/136.32	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
136.11/136.32	           analz(knows(spy, evs2))))
136.11/136.32	     | k = kab),
136.11/136.32	    inference('clc', [status(thm)], ['50', '38'])).
136.11/136.32	tff('52', plain, k = kab, inference('clc', [status(thm)], ['47', '51'])).
136.11/136.32	tff('53', plain,
136.11/136.32	    (aa(agent, nat, shrK, b) = k
136.11/136.32	     | pp(
136.11/136.32	         aa(fun(nat, bool), bool, 
136.11/136.32	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
136.11/136.32	             aa(agent, nat, shrK, b)), kk))
136.11/136.32	     | pp(
136.11/136.32	         aa(fun(msg, bool), bool, 
136.11/136.32	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
136.11/136.32	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
136.11/136.32	           analz(knows(spy, evs2))))
136.11/136.32	     | pp(
136.11/136.32	         aa(fun(nat, bool), bool, 
136.11/136.32	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
136.11/136.32	             aa(agent, nat, shrK, a)), kk))),
136.11/136.32	    inference('demod', [status(thm)], ['11', '52'])).
136.11/136.32	tff('54', plain,
136.11/136.32	    (pp(
136.11/136.32	       aa(fun(nat, bool), bool, 
136.11/136.32	         aa(nat, fun(fun(nat, bool), bool), member(nat), 
136.11/136.32	           aa(agent, nat, shrK, a)), kk))
136.11/136.32	     | aa(agent, nat, shrK, b) != kab
136.11/136.32	     | pp(
136.11/136.32	         aa(fun(nat, bool), bool, 
136.11/136.32	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
136.11/136.32	             aa(agent, nat, shrK, a)), kk))),
136.11/136.32	    inference('cnf', [status(esa)], [zf_stmt_0])).
136.11/136.32	tff('55', plain,
136.11/136.32	    (aa(agent, nat, shrK, b) != kab
136.11/136.32	     | pp(
136.11/136.32	         aa(fun(nat, bool), bool, 
136.11/136.32	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
136.11/136.32	             aa(agent, nat, shrK, a)), kk))),
136.11/136.32	    inference('simplify', [status(thm)], ['54'])).
136.11/136.32	tff('56', plain,
136.11/136.32	    (aa(agent, nat, shrK, b) != k
136.11/136.32	     | pp(
136.11/136.32	         aa(fun(nat, bool), bool, 
136.11/136.32	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
136.11/136.32	             aa(agent, nat, shrK, a)), kk))),
136.11/136.32	    inference('demod', [status(thm)], ['55', '52'])).
136.11/136.32	tff('57', plain,
136.11/136.32	    (pp(
136.11/136.32	       aa(fun(nat, bool), bool, 
136.11/136.32	         aa(nat, fun(fun(nat, bool), bool), member(nat), 
136.11/136.32	           aa(agent, nat, shrK, a)), kk))
136.11/136.32	     | pp(
136.11/136.32	         aa(fun(msg, bool), bool, 
136.11/136.32	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
136.11/136.32	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
136.11/136.32	           analz(knows(spy, evs2))))
136.11/136.32	     | pp(
136.11/136.32	         aa(fun(nat, bool), bool, 
136.11/136.32	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
136.11/136.32	             aa(agent, nat, shrK, b)), kk))),
136.11/136.32	    inference('clc', [status(thm)], ['53', '56'])).
136.11/136.32	tff('58', plain,
136.11/136.32	    (pp(
136.11/136.32	       aa(fun(nat, bool), bool, 
136.11/136.32	         aa(nat, fun(fun(nat, bool), bool), member(nat), 
136.11/136.32	           aa(agent, nat, shrK, a)), kk))
136.11/136.32	     | ~ pp(
136.11/136.32	           aa(fun(msg, bool), bool, 
136.11/136.32	             aa(msg, fun(fun(msg, bool), bool), member(msg), 
136.11/136.32	               aa(nat, msg, key, aa(agent, nat, shrK, b))), 
136.11/136.32	             analz(knows(spy, evs2))))
136.11/136.32	     | pp(
136.11/136.32	         aa(fun(nat, bool), bool, 
136.11/136.32	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
136.11/136.32	             aa(agent, nat, shrK, a)), kk))),
136.11/136.32	    inference('cnf', [status(esa)], [zf_stmt_0])).
136.11/136.32	tff('59', plain,
136.11/136.32	    (~ pp(
136.11/136.32	         aa(fun(msg, bool), bool, 
136.11/136.32	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
136.11/136.32	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
136.11/136.32	           analz(knows(spy, evs2))))
136.11/136.32	     | pp(
136.11/136.32	         aa(fun(nat, bool), bool, 
136.11/136.32	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
136.11/136.32	             aa(agent, nat, shrK, a)), kk))),
136.11/136.32	    inference('simplify', [status(thm)], ['58'])).
136.11/136.32	tff('60', plain,
136.11/136.32	    (pp(
136.11/136.32	       aa(fun(nat, bool), bool, 
136.11/136.32	         aa(nat, fun(fun(nat, bool), bool), member(nat), 
136.11/136.32	           aa(agent, nat, shrK, b)), kk))
136.11/136.32	     | pp(
136.11/136.32	         aa(fun(nat, bool), bool, 
136.11/136.32	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
136.11/136.32	             aa(agent, nat, shrK, a)), kk))),
136.11/136.32	    inference('clc', [status(thm)], ['57', '59'])).
136.11/136.32	tff('61', plain,
136.11/136.32	    (pp(
136.11/136.32	       aa(fun(nat, bool), bool, 
136.11/136.32	         aa(nat, fun(fun(nat, bool), bool), member(nat), 
136.11/136.32	           aa(agent, nat, shrK, a)), kk))
136.11/136.32	     | ~ pp(
136.11/136.32	           aa(fun(nat, bool), bool, 
136.11/136.32	             aa(nat, fun(fun(nat, bool), bool), member(nat), 
136.11/136.32	               aa(agent, nat, shrK, b)), kk))
136.11/136.32	     | pp(
136.11/136.32	         aa(fun(nat, bool), bool, 
136.11/136.32	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
136.11/136.32	             aa(agent, nat, shrK, a)), kk))),
136.11/136.32	    inference('cnf', [status(esa)], [zf_stmt_0])).
136.11/136.32	tff('62', plain,
136.11/136.32	    (~ pp(
136.11/136.32	         aa(fun(nat, bool), bool, 
136.11/136.32	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
136.11/136.32	             aa(agent, nat, shrK, b)), kk))
136.11/136.32	     | pp(
136.11/136.32	         aa(fun(nat, bool), bool, 
136.11/136.32	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
136.11/136.32	             aa(agent, nat, shrK, a)), kk))),
136.11/136.32	    inference('simplify', [status(thm)], ['61'])).
136.11/136.32	tff('63', plain,
136.11/136.32	    pp(
136.11/136.32	      aa(fun(nat, bool), bool, 
136.11/136.32	        aa(nat, fun(fun(nat, bool), bool), member(nat), 
136.11/136.32	          aa(agent, nat, shrK, a)), kk)),
136.11/136.32	    inference('clc', [status(thm)], ['60', '62'])).
136.11/136.32	tff(fact_19_UnCI, axiom,
136.11/136.32	  (![A:$tType,A2:fun(A,bool),B2:fun(A,bool),C2:A]:
136.11/136.32	     (((~pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),C2),B2))) =>
136.11/136.32	       pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),C2),A2))) =>
136.11/136.32	      pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),C2),
136.11/136.32	            sup_sup(fun(A,bool),A2,B2)))))).
136.11/136.32	tff('64', plain,
136.11/136.32	    ![X54 : $tType, X55 : X54, X56 : fun(X54, bool), X57 : fun(X54, bool)]:
136.11/136.32	      (pp(
136.11/136.32	         aa(fun(X54, bool), bool, 
136.11/136.32	           aa(X54, fun(fun(X54, bool), bool), member(X54), X55), 
136.11/136.32	           sup_sup(fun(X54, bool), X56, X57)))
136.11/136.32	       | ~ pp(
136.11/136.32	             aa(fun(X54, bool), bool, 
136.11/136.32	               aa(X54, fun(fun(X54, bool), bool), member(X54), X55), X56))),
136.11/136.32	    inference('cnf', [status(esa)], [fact_19_UnCI])).
136.11/136.32	tff(fact_76_mem__def, axiom,
136.11/136.32	  (![A:$tType,A2:fun(A,bool),X2:A]:
136.11/136.32	     (pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),X2),A2)) <=>
136.11/136.32	      pp(aa(A,bool,A2,X2))))).
136.11/136.32	tff('65', plain,
136.11/136.32	    ![X260 : $tType, X261 : fun(X260, bool), X262 : X260]:
136.11/136.32	      (pp(aa(X260, bool, X261, X262))
136.11/136.32	       | ~ pp(
136.11/136.32	             aa(fun(X260, bool), bool, 
136.11/136.32	               aa(X260, fun(fun(X260, bool), bool), member(X260), X262), 
136.11/136.32	               X261))),
136.11/136.32	    inference('cnf', [status(esa)], [fact_76_mem__def])).
136.11/136.32	tff('66', plain,
136.11/136.32	    ![X0 : $tType, X1 : fun(X0, bool), X2 : fun(X0, bool), X3 : X0]:
136.11/136.32	      (~ $true
136.11/136.32	       | ~ pp(
136.11/136.32	             aa(fun(X0, bool), bool, 
136.11/136.32	               aa(X0, fun(fun(X0, bool), bool), member(X0), X3), X2))
136.11/136.32	       | pp(aa(X0, bool, sup_sup(fun(X0, bool), X2, X1), X3))),
136.11/136.32	    inference('sup-', [status(thm)], ['64', '65'])).
136.11/136.32	tff('67', plain,
136.11/136.32	    ![X0 : $tType, X1 : fun(X0, bool), X2 : fun(X0, bool), X3 : X0]:
136.11/136.32	      (pp(aa(X0, bool, sup_sup(fun(X0, bool), X2, X1), X3))
136.11/136.32	       | ~ pp(
136.11/136.32	             aa(fun(X0, bool), bool, 
136.11/136.32	               aa(X0, fun(fun(X0, bool), bool), member(X0), X3), X2))),
136.11/136.32	    inference('simplify', [status(thm)], ['66'])).
136.11/136.32	tff('68', plain,
136.11/136.32	    ![X0 : fun(nat, bool)]:
136.11/136.32	      (~ $true
136.11/136.32	       | pp(
136.11/136.32	           aa(nat, bool, sup_sup(fun(nat, bool), kk, X0), 
136.11/136.32	             aa(agent, nat, shrK, a)))),
136.11/136.32	    inference('sup-', [status(thm)], ['63', '67'])).
136.11/136.32	tff('69', plain,
136.11/136.32	    ![X0 : fun(nat, bool)]:
136.11/136.32	      pp(
136.11/136.32	        aa(nat, bool, sup_sup(fun(nat, bool), kk, X0), 
136.11/136.32	          aa(agent, nat, shrK, a))),
136.11/136.32	    inference('simplify', [status(thm)], ['68'])).
136.11/136.32	tff('70', plain,
136.11/136.32	    pp(
136.11/136.32	      aa(nat, bool, 
136.11/136.32	        uminus_uminus(fun(nat, bool), 
136.11/136.32	          image(agent, nat, shrK, top_top(fun(agent, bool)))), 
136.11/136.32	        aa(agent, nat, shrK, a))),
136.11/136.32	    inference('sup+', [status(thm)], ['9', '69'])).
136.11/136.32	tff(help_COMBB_1_1_U, axiom,
136.11/136.32	  (![C:$tType,B:$tType,A:$tType,R:A,Q:fun(A,B),P:fun(B,C)]:
136.11/136.32	     (aa(A,C,combb(B,C,A,P,Q),R) = aa(B,C,P,aa(A,B,Q,R))))).
136.11/136.32	tff('71', plain,
136.11/136.32	    ![X347 : $tType, X348 : $tType, X349 : fun(X347, X348), X350 : $tType, 
136.11/136.32	      X351 : fun(X350, X347), X352 : X350]:
136.11/136.32	      aa(X350, X348, combb(X347, X348, X350, X349, X351), X352)
136.11/136.32	       = aa(X347, X348, X349, aa(X350, X347, X351, X352)),
136.11/136.32	    inference('cnf', [status(esa)], [help_COMBB_1_1_U])).
136.11/136.32	tff(help_fNot_1_1_U, axiom,
136.11/136.32	  (![P:bool]: ((~pp(P)) | (~pp(aa(bool,bool,fNot,P)))))).
136.11/136.32	tff('72', plain,
136.11/136.32	    ![X345 : bool]: (~ pp(X345) | ~ pp(aa(bool, bool, fNot, X345))),
136.11/136.32	    inference('cnf', [status(esa)], [help_fNot_1_1_U])).
136.11/136.32	tff('73', plain,
136.11/136.32	    ![X0 : $tType, X1 : X0, X2 : fun(X0, bool)]:
136.11/136.32	      (~ pp(aa(X0, bool, combb(bool, bool, X0, fNot, X2), X1))
136.11/136.32	       | ~ pp(aa(X0, bool, X2, X1))),
136.11/136.32	    inference('sup-', [status(thm)], ['71', '72'])).
136.11/136.32	tff(fact_93_Collect__neg__eq, axiom,
136.11/136.32	  (![A:$tType,P1:fun(A,bool)]:
136.11/136.32	     (collect(A,combb(bool,bool,A,fNot,P1)) =
136.11/136.32	      uminus_uminus(fun(A,bool),collect(A,P1))))).
136.11/136.32	tff('74', plain,
136.11/136.32	    ![X310 : $tType, X311 : fun(X310, bool)]:
136.11/136.32	      collect(X310, combb(bool, bool, X310, fNot, X311))
136.11/136.32	       = uminus_uminus(fun(X310, bool), collect(X310, X311)),
136.11/136.32	    inference('cnf', [status(esa)], [fact_93_Collect__neg__eq])).
136.11/136.32	tff(fact_77_Collect__def, axiom,
136.11/136.32	  (![A:$tType,P1:fun(A,bool)]: (collect(A,P1) = P1))).
136.11/136.32	tff('75', plain,
136.11/136.32	    ![X264 : $tType, X265 : fun(X264, bool)]: collect(X264, X265) = X265,
136.11/136.32	    inference('cnf', [status(esa)], [fact_77_Collect__def])).
136.11/136.32	tff('76', plain,
136.11/136.32	    ![X310 : $tType, X311 : fun(X310, bool)]:
136.11/136.32	      combb(bool, bool, X310, fNot, X311)
136.11/136.32	       = uminus_uminus(fun(X310, bool), X311),
136.11/136.32	    inference('demod', [status(thm)], ['74', '75', '75'])).
136.11/136.32	tff('77', plain,
136.11/136.32	    ![X0 : $tType, X1 : X0, X2 : fun(X0, bool)]:
136.11/136.32	      (~ pp(aa(X0, bool, uminus_uminus(fun(X0, bool), X2), X1))
136.11/136.32	       | ~ pp(aa(X0, bool, X2, X1))),
136.11/136.32	    inference('demod', [status(thm)], ['73', '76'])).
136.11/136.32	tff('78', plain,
136.11/136.32	    (~ $true
136.11/136.32	     | ~ pp(
136.11/136.32	           aa(nat, bool, image(agent, nat, shrK, top_top(fun(agent, bool))), 
136.11/136.32	             aa(agent, nat, shrK, a)))),
136.11/136.32	    inference('sup-', [status(thm)], ['70', '77'])).
136.11/136.32	tff(help_COMBC_1_1_U, axiom,
136.11/136.32	  (![A:$tType,C:$tType,B:$tType,R:A,Q:B,P:fun(A,fun(B,C))]:
136.11/136.32	     (aa(A,C,combc(A,B,C,P,Q),R) = aa(B,C,aa(A,fun(B,C),P,R),Q)))).
136.11/136.32	tff('79', plain,
136.11/136.32	    ![X353 : $tType, X354 : $tType, X355 : $tType, 
136.11/136.32	      X356 : fun(X355, fun(X353, X354)), X357 : X355, X358 : X353]:
136.11/136.32	      aa(X355, X354, combc(X355, X353, X354, X356, X358), X357)
136.11/136.32	       = aa(X353, X354, aa(X355, fun(X353, X354), X356, X357), X358),
136.11/136.32	    inference('cnf', [status(esa)], [help_COMBC_1_1_U])).
136.11/136.32	tff(fact_17_UNIV__I, axiom,
136.11/136.32	  (![A:$tType,X2:A]:
136.11/136.32	     pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),X2),
136.11/136.32	           top_top(fun(A,bool)))))).
136.11/136.32	tff('80', plain,
136.11/136.32	    ![X48 : $tType, X49 : X48]:
136.11/136.32	      pp(
136.11/136.32	        aa(fun(X48, bool), bool, 
136.11/136.32	          aa(X48, fun(fun(X48, bool), bool), member(X48), X49), 
136.11/136.32	          top_top(fun(X48, bool)))),
136.11/136.32	    inference('cnf', [status(esa)], [fact_17_UNIV__I])).
136.11/136.32	tff(fact_16_image__eqI, axiom,
136.11/136.32	  (![A:$tType,B:$tType,A2:fun(B,bool),X2:B,F:fun(B,A),B3:A]:
136.11/136.32	     ((B3 = aa(B,A,F,X2)) =>
136.11/136.32	      (pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),X2),A2)) =>
136.11/136.32	       pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),B3),
136.11/136.32	             image(B,A,F,A2))))))).
136.11/136.32	tff('81', plain,
136.11/136.32	    ![X42 : $tType, X43 : X42, X44 : fun(X42, bool), X45 : $tType, 
136.11/136.32	      X46 : fun(X42, X45), X47 : X45]:
136.11/136.32	      (~ pp(
136.11/136.32	           aa(fun(X42, bool), bool, 
136.11/136.32	             aa(X42, fun(fun(X42, bool), bool), member(X42), X43), X44))
136.11/136.32	       | X47 != aa(X42, X45, X46, X43)
136.11/136.32	       | pp(
136.11/136.32	           aa(fun(X45, bool), bool, 
136.11/136.32	             aa(X45, fun(fun(X45, bool), bool), member(X45), X47), 
136.11/136.32	             image(X42, X45, X46, X44)))),
136.11/136.32	    inference('cnf', [status(esa)], [fact_16_image__eqI])).
136.11/136.32	tff('82', plain,
136.11/136.32	    ![X42 : $tType, X43 : X42, X44 : fun(X42, bool), X45 : $tType, 
136.11/136.32	      X46 : fun(X42, X45)]:
136.11/136.32	      (pp(
136.11/136.32	         aa(fun(X45, bool), bool, 
136.11/136.32	           aa(X45, fun(fun(X45, bool), bool), member(X45), 
136.11/136.32	             aa(X42, X45, X46, X43)), image(X42, X45, X46, X44)))
136.11/136.32	       | ~ pp(
136.11/136.32	             aa(fun(X42, bool), bool, 
136.11/136.32	               aa(X42, fun(fun(X42, bool), bool), member(X42), X43), X44))),
136.11/136.32	    inference('simplify', [status(thm)], ['81'])).
136.11/136.32	tff('83', plain,
136.11/136.32	    ![X0 : $tType, X1 : X0, X2 : $tType, X3 : fun(X0, X2)]:
136.11/136.32	      (~ $true
136.11/136.32	       | pp(
136.11/136.32	           aa(fun(X2, bool), bool, 
136.11/136.32	             aa(X2, fun(fun(X2, bool), bool), member(X2), aa(X0, X2, X3, X1)), 
136.11/136.32	             image(X0, X2, X3, top_top(fun(X0, bool)))))),
136.11/136.32	    inference('sup-', [status(thm)], ['80', '82'])).
136.11/136.32	tff('84', plain,
136.11/136.32	    ![X0 : $tType, X1 : X0, X2 : $tType, X3 : fun(X0, X2)]:
136.11/136.32	      pp(
136.11/136.32	        aa(fun(X2, bool), bool, 
136.11/136.32	          aa(X2, fun(fun(X2, bool), bool), member(X2), aa(X0, X2, X3, X1)), 
136.11/136.32	          image(X0, X2, X3, top_top(fun(X0, bool))))),
136.11/136.32	    inference('simplify', [status(thm)], ['83'])).
136.11/136.32	tff('85', plain,
136.11/136.32	    ![X0 : $tType, X1 : $tType, X2 : X1, X3 : fun(X1, X0)]:
136.11/136.32	      pp(
136.11/136.32	        aa(X0, bool, 
136.11/136.32	          combc(X0, fun(X0, bool), bool, member(X0), 
136.11/136.32	            image(X1, X0, X3, top_top(fun(X1, bool)))), aa(X1, X0, X3, X2))),
136.11/136.32	    inference('sup+', [status(thm)], ['79', '84'])).
136.11/136.32	tff(fact_88_Compl__eq, axiom,
136.11/136.32	  (![A:$tType,A2:fun(A,bool)]:
136.11/136.32	     (uminus_uminus(fun(A,bool),A2) =
136.11/136.32	      collect(A,
136.11/136.32	              combb(bool,bool,A,fNot,combc(A,fun(A,bool),bool,member(A),A2)))))).
136.11/136.32	tff('86', plain,
136.11/136.32	    ![X295 : $tType, X296 : fun(X295, bool)]:
136.11/136.32	      uminus_uminus(fun(X295, bool), X296)
136.11/136.32	       = collect(X295, 
136.11/136.32	           combb(bool, bool, X295, fNot, 
136.11/136.32	             combc(X295, fun(X295, bool), bool, member(X295), X296))),
136.11/136.32	    inference('cnf', [status(esa)], [fact_88_Compl__eq])).
136.11/136.32	tff('87', plain,
136.11/136.32	    ![X295 : $tType, X296 : fun(X295, bool)]:
136.11/136.32	      uminus_uminus(fun(X295, bool), X296)
136.11/136.32	       = uminus_uminus(fun(X295, bool), 
136.11/136.32	           combc(X295, fun(X295, bool), bool, member(X295), X296)),
136.11/136.32	    inference('demod', [status(thm)], ['86', '76', '75'])).
136.11/136.32	tff(fact_87_double__complement, axiom,
136.11/136.32	  (![A:$tType,A2:fun(A,bool)]:
136.11/136.32	     (uminus_uminus(fun(A,bool),uminus_uminus(fun(A,bool),A2)) = A2))).
136.11/136.32	tff('88', plain,
136.11/136.32	    ![X293 : $tType, X294 : fun(X293, bool)]:
136.11/136.32	      uminus_uminus(fun(X293, bool), uminus_uminus(fun(X293, bool), X294))
136.11/136.32	       = X294,
136.11/136.32	    inference('cnf', [status(esa)], [fact_87_double__complement])).
136.11/136.32	tff('89', plain,
136.11/136.32	    ![X0 : $tType, X1 : fun(X0, bool)]:
136.11/136.32	      uminus_uminus(fun(X0, bool), uminus_uminus(fun(X0, bool), X1))
136.11/136.32	       = combc(X0, fun(X0, bool), bool, member(X0), X1),
136.11/136.32	    inference('sup+', [status(thm)], ['87', '88'])).
136.11/136.32	tff('90', plain,
136.11/136.32	    ![X0 : $tType, X1 : fun(X0, bool)]:
136.11/136.32	      X1 = combc(X0, fun(X0, bool), bool, member(X0), X1),
136.11/136.32	    inference('demod', [status(thm)], ['89', '88'])).
136.11/136.32	tff('91', plain,
136.11/136.32	    ![X0 : $tType, X1 : $tType, X2 : X1, X3 : fun(X1, X0)]:
136.11/136.32	      pp(
136.11/136.32	        aa(X0, bool, image(X1, X0, X3, top_top(fun(X1, bool))), 
136.11/136.32	          aa(X1, X0, X3, X2))),
136.11/136.32	    inference('demod', [status(thm)], ['85', '90'])).
136.11/136.32	tff('92', plain, (~ $true | ~ $true),
136.11/136.32	    inference('demod', [status(thm)], ['78', '91'])).
136.11/136.32	tff('93', plain, $false, inference('simplify', [status(thm)], ['92'])).
136.11/136.32	
136.11/136.32	% SZS output end Refutation
136.11/136.32	EOF
