0.00/0.00	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : app
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : kbo
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-ho \
0.00/0.00	  --no-avatar \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n058.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 07:53:39 CST 2018
119.62/119.86	% done 10669 iterations in 119.657s
119.62/119.86	% SZS status Theorem for 'stdin'
119.62/119.86	% SZS output start Refutation
119.62/119.86	tff(zf_stmt_126, axiom,
119.62/119.86	  (![K:int]: (app_encode_app(int,int,number_number_of(int),K) = K))).
119.62/119.86	tff('0', plain,
119.62/119.86	    ![X196 : int]:
119.62/119.86	      app_encode_app(int, int, number_number_of(int), X196) = X196,
119.62/119.86	    inference('cnf', [status(esa)], [zf_stmt_126])).
119.62/119.86	tff(zf_stmt_46, axiom,
119.62/119.86	  (![A:$tType]:
119.62/119.86	     (number_ring(A) =>
119.62/119.86	      (app_encode_app(int,A,number_number_of(A),
119.62/119.86	                      app_encode_app(int,int,bit1,pls)) =
119.62/119.86	       one_one(A))))).
119.62/119.86	tff('1', plain,
119.62/119.86	    ![X13 : $tType]:
119.62/119.86	      (app_encode_app(int, X13, number_number_of(X13), 
119.62/119.86	         app_encode_app(int, int, bit1, pls))
119.62/119.86	        = one_one(X13)
119.62/119.86	       | ~ number_ring(X13)),
119.62/119.86	    inference('cnf', [status(esa)], [zf_stmt_46])).
119.62/119.86	tff('2', plain,
119.62/119.86	    (app_encode_app(int, int, bit1, pls) = one_one(int) | ~ number_ring(int)),
119.62/119.86	    inference('sup+', [status(thm)], ['0', '1'])).
119.62/119.86	tff(zf_stmt_139, axiom, (number_ring(int))).
119.62/119.86	tff('3', plain, number_ring(int),
119.62/119.86	    inference('cnf', [status(esa)], [zf_stmt_139])).
119.62/119.86	tff('4', plain,
119.62/119.86	    (app_encode_app(int, int, bit1, pls) = one_one(int) | ~ $true),
119.62/119.86	    inference('demod', [status(thm)], ['2', '3'])).
119.62/119.86	tff('5', plain, app_encode_app(int, int, bit1, pls) = one_one(int),
119.62/119.86	    inference('simplify', [status(thm)], ['4'])).
119.62/119.86	tff(zf_stmt_51, axiom,
119.62/119.86	  (![L1:int,K:int]:
119.62/119.86	     (app_encode_app(int,int,
119.62/119.86	                     app_encode_app(int,app_encode_fun(int,int),
119.62/119.86	                                    minus_minus(int),
119.62/119.86	                                    app_encode_app(int,int,bit1,K)),
119.62/119.86	                     app_encode_app(int,int,bit1,L1)) =
119.62/119.86	      app_encode_app(int,int,bit0,
119.62/119.86	                     app_encode_app(int,int,
119.62/119.86	                                    app_encode_app(int,
119.62/119.86	                                                   app_encode_fun(int,int),
119.62/119.86	                                                   minus_minus(int),K),
119.62/119.86	                                    L1))))).
119.62/119.86	tff('6', plain,
119.62/119.86	    ![X17 : int, X18 : int]:
119.62/119.86	      app_encode_app(int, int, 
119.62/119.86	        app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
119.62/119.86	          app_encode_app(int, int, bit1, X17)), 
119.62/119.86	        app_encode_app(int, int, bit1, X18))
119.62/119.86	       = app_encode_app(int, int, bit0, 
119.62/119.86	           app_encode_app(int, int, 
119.62/119.86	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
119.62/119.86	               X17), X18)),
119.62/119.86	    inference('cnf', [status(esa)], [zf_stmt_51])).
119.62/119.86	tff('7', plain,
119.62/119.86	    ![X0 : int]:
119.62/119.86	      app_encode_app(int, int, 
119.62/119.86	        app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
119.62/119.86	          app_encode_app(int, int, bit1, X0)), one_one(int))
119.62/119.86	       = app_encode_app(int, int, bit0, 
119.62/119.86	           app_encode_app(int, int, 
119.62/119.86	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
119.62/119.86	               X0), pls)),
119.62/119.86	    inference('sup+', [status(thm)], ['5', '6'])).
119.62/119.86	tff(zf_stmt_99, axiom,
119.62/119.86	  (![Z1:int,W1:int]:
119.62/119.86	     (app_encode_app(int,$o,
119.62/119.86	                     app_encode_app(int,app_encode_fun(int,$o),
119.62/119.86	                                    ord_less_eq(int),W1),
119.62/119.86	                     app_encode_app(int,int,
119.62/119.86	                                    app_encode_app(int,
119.62/119.86	                                                   app_encode_fun(int,int),
119.62/119.86	                                                   minus_minus(int),Z1),
119.62/119.86	                                    one_one(int))) <=>
119.62/119.86	      app_encode_app(int,$o,
119.62/119.86	                     app_encode_app(int,app_encode_fun(int,$o),ord_less(int),
119.62/119.86	                                    W1),
119.62/119.86	                     Z1)))).
119.62/119.86	tff('8', plain,
119.62/119.86	    ![X136 : int, X137 : int]:
119.62/119.86	      (app_encode_app(int, $o, 
119.62/119.86	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), X137), 
119.62/119.86	         app_encode_app(int, int, 
119.62/119.86	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
119.62/119.86	             X136), one_one(int)))
119.62/119.86	       | ~ app_encode_app(int, $o, 
119.62/119.86	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
119.62/119.86	               X137), X136)),
119.62/119.86	    inference('cnf', [status(esa)], [zf_stmt_99])).
119.62/119.86	tff('9', plain,
119.62/119.86	    ![X0 : int, X1 : int]:
119.62/119.86	      (app_encode_app(int, $o, 
119.62/119.86	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), X1), 
119.62/119.86	         app_encode_app(int, int, bit0, 
119.62/119.86	           app_encode_app(int, int, 
119.62/119.86	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
119.62/119.86	               X0), pls)))
119.62/119.86	       | ~ app_encode_app(int, $o, 
119.62/119.86	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), X1), 
119.62/119.86	             app_encode_app(int, int, bit1, X0))),
119.62/119.86	    inference('sup+', [status(thm)], ['7', '8'])).
119.62/119.86	tff(zf_stmt_69, axiom,
119.62/119.86	  (![W:int]:
119.62/119.86	     (app_encode_app(int,int,
119.62/119.86	                     app_encode_app(int,app_encode_fun(int,int),
119.62/119.86	                                    times_times(int),pls),
119.62/119.86	                     W) =
119.62/119.86	      pls))).
119.62/119.86	tff('10', plain,
119.62/119.86	    ![X54 : int]:
119.62/119.86	      app_encode_app(int, int, 
119.62/119.86	        app_encode_app(int, app_encode_fun(int, int), times_times(int), pls), 
119.62/119.86	        X54)
119.62/119.86	       = pls,
119.62/119.86	    inference('cnf', [status(esa)], [zf_stmt_69])).
119.62/119.86	tff(zf_stmt_45, axiom,
119.62/119.86	  (![L1:int,K:int]:
119.62/119.86	     (app_encode_app(int,int,
119.62/119.86	                     app_encode_app(int,app_encode_fun(int,int),
119.62/119.86	                                    times_times(int),
119.62/119.86	                                    app_encode_app(int,int,bit1,K)),
119.62/119.86	                     L1) =
119.62/119.86	      app_encode_app(int,int,
119.62/119.86	                     app_encode_app(int,app_encode_fun(int,int),
119.62/119.86	                                    plus_plus(int),
119.62/119.86	                                    app_encode_app(int,int,bit0,
119.62/119.86	                                                   app_encode_app(int,int,
119.62/119.86	                                                                  app_encode_app(
119.62/119.86	                                                                  int,
119.62/119.86	                                                                  app_encode_fun(
119.62/119.86	                                                                  int,int),
119.62/119.86	                                                                  times_times(
119.62/119.86	                                                                  int),K),L1))),
119.62/119.86	                     L1)))).
119.62/119.86	tff('11', plain,
119.62/119.86	    ![X11 : int, X12 : int]:
119.62/119.86	      app_encode_app(int, int, 
119.62/119.86	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
119.62/119.86	          app_encode_app(int, int, bit1, X11)), X12)
119.62/119.86	       = app_encode_app(int, int, 
119.62/119.86	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
119.62/119.86	             app_encode_app(int, int, bit0, 
119.62/119.86	               app_encode_app(int, int, 
119.62/119.86	                 app_encode_app(int, app_encode_fun(int, int), 
119.62/119.86	                   times_times(int), X11), X12))), X12),
119.62/119.86	    inference('cnf', [status(esa)], [zf_stmt_45])).
119.62/119.86	tff('12', plain,
119.62/119.86	    ![X0 : int]:
119.62/119.86	      app_encode_app(int, int, 
119.62/119.86	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
119.62/119.86	          app_encode_app(int, int, bit1, pls)), X0)
119.62/119.86	       = app_encode_app(int, int, 
119.62/119.86	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
119.62/119.86	             app_encode_app(int, int, bit0, pls)), X0),
119.62/119.86	    inference('sup+', [status(thm)], ['10', '11'])).
119.62/119.86	tff(zf_stmt_62, axiom, (app_encode_app(int,int,bit0,pls) = pls)).
119.62/119.86	tff('13', plain, app_encode_app(int, int, bit0, pls) = pls,
119.62/119.86	    inference('cnf', [status(esa)], [zf_stmt_62])).
119.62/119.86	tff('14', plain,
119.62/119.86	    ![X0 : int]:
119.62/119.86	      app_encode_app(int, int, 
119.62/119.86	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
119.62/119.86	          one_one(int)), X0)
119.62/119.86	       = app_encode_app(int, int, 
119.62/119.86	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
119.62/119.86	           X0),
119.62/119.86	    inference('demod', [status(thm)], ['12', '5', '13'])).
119.62/119.86	tff(zf_stmt_76, axiom,
119.62/119.86	  (![B:$tType]:
119.62/119.86	     ((number(B) & ring(B)) =>
119.62/119.86	      (![V1:int,B1:B,A2:B]:
119.62/119.86	         (app_encode_app(B,B,
119.62/119.86	                         app_encode_app(B,app_encode_fun(B,B),times_times(B),
119.62/119.86	                                        app_encode_app(B,B,
119.62/119.86	                                                       app_encode_app(
119.62/119.86	                                                       B,app_encode_fun(B,B),
119.62/119.86	                                                       minus_minus(B),A2),B1)),
119.62/119.86	                         app_encode_app(int,B,number_number_of(B),V1)) =
119.62/119.86	          app_encode_app(B,B,
119.62/119.86	                         app_encode_app(B,app_encode_fun(B,B),minus_minus(B),
119.62/119.86	                                        app_encode_app(B,B,
119.62/119.86	                                                       app_encode_app(
119.62/119.86	                                                       B,app_encode_fun(B,B),
119.62/119.86	                                                       times_times(B),A2),
119.62/119.86	                                                       app_encode_app(
119.62/119.86	                                                       int,B,
119.62/119.86	                                                       number_number_of(B),V1))),
119.62/119.86	                         app_encode_app(B,B,
119.62/119.86	                                        app_encode_app(B,app_encode_fun(B,B),
119.62/119.86	                                                       times_times(B),B1),
119.62/119.86	                                        app_encode_app(int,B,
119.62/119.86	                                                       number_number_of(B),V1)))))))).
119.62/119.86	tff('15', plain,
119.62/119.86	    ![X70 : $tType, X71 : X70, X72 : int, X73 : X70]:
119.62/119.86	      (app_encode_app(X70, X70, 
119.62/119.86	         app_encode_app(X70, app_encode_fun(X70, X70), times_times(X70), 
119.62/119.86	           app_encode_app(X70, X70, 
119.62/119.86	             app_encode_app(X70, app_encode_fun(X70, X70), minus_minus(X70), 
119.62/119.86	               X71), X73)), 
119.62/119.86	         app_encode_app(int, X70, number_number_of(X70), X72))
119.62/119.86	        = app_encode_app(X70, X70, 
119.62/119.86	            app_encode_app(X70, app_encode_fun(X70, X70), minus_minus(X70), 
119.62/119.86	              app_encode_app(X70, X70, 
119.62/119.86	                app_encode_app(X70, app_encode_fun(X70, X70), 
119.62/119.86	                  times_times(X70), X71), 
119.62/119.86	                app_encode_app(int, X70, number_number_of(X70), X72))), 
119.62/119.86	            app_encode_app(X70, X70, 
119.62/119.86	              app_encode_app(X70, app_encode_fun(X70, X70), 
119.62/119.86	                times_times(X70), X73), 
119.62/119.86	              app_encode_app(int, X70, number_number_of(X70), X72)))
119.62/119.86	       | ~ ring(X70)
119.62/119.86	       | ~ number(X70)),
119.62/119.86	    inference('cnf', [status(esa)], [zf_stmt_76])).
119.62/119.86	tff('16', plain,
119.62/119.86	    ![X0 : int, X1 : int]:
119.62/119.86	      (app_encode_app(int, int, 
119.62/119.86	         app_encode_app(int, app_encode_fun(int, int), times_times(int), 
119.62/119.86	           app_encode_app(int, int, 
119.62/119.86	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
119.62/119.86	               X1), pls)), 
119.62/119.86	         app_encode_app(int, int, number_number_of(int), X0))
119.62/119.86	        = app_encode_app(int, int, 
119.62/119.86	            app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
119.62/119.86	              app_encode_app(int, int, 
119.62/119.86	                app_encode_app(int, app_encode_fun(int, int), 
119.62/119.86	                  times_times(int), X1), 
119.62/119.86	                app_encode_app(int, int, number_number_of(int), X0))), pls)
119.62/119.86	       | ~ number(int)
119.62/119.86	       | ~ ring(int)),
119.62/119.86	    inference('sup+', [status(thm)], ['10', '15'])).
119.62/119.86	tff(zf_stmt_142, axiom, (number(int))).
119.62/119.86	tff('17', plain, number(int), inference('cnf', [status(esa)], [zf_stmt_142])).
119.62/119.86	tff(zf_stmt_141, axiom, (ring(int))).
119.62/119.86	tff('18', plain, ring(int), inference('cnf', [status(esa)], [zf_stmt_141])).
119.62/119.86	tff('19', plain,
119.62/119.86	    ![X0 : int, X1 : int]:
119.62/119.86	      (app_encode_app(int, int, 
119.62/119.86	         app_encode_app(int, app_encode_fun(int, int), times_times(int), 
119.62/119.86	           app_encode_app(int, int, 
119.62/119.86	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
119.62/119.86	               X1), pls)), X0)
119.62/119.86	        = app_encode_app(int, int, 
119.62/119.86	            app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
119.62/119.86	              app_encode_app(int, int, 
119.62/119.86	                app_encode_app(int, app_encode_fun(int, int), 
119.62/119.86	                  times_times(int), X1), X0)), pls)
119.62/119.86	       | ~ $true
119.62/119.86	       | ~ $true),
119.62/119.86	    inference('demod', [status(thm)], ['16', '0', '0', '17', '18'])).
119.62/119.86	tff('20', plain,
119.62/119.86	    ![X0 : int, X1 : int]:
119.62/119.86	      app_encode_app(int, int, 
119.62/119.86	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
119.62/119.86	          app_encode_app(int, int, 
119.62/119.86	            app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
119.62/119.86	              X1), pls)), X0)
119.62/119.86	       = app_encode_app(int, int, 
119.62/119.86	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
119.62/119.86	             app_encode_app(int, int, 
119.62/119.86	               app_encode_app(int, app_encode_fun(int, int), 
119.62/119.86	                 times_times(int), X1), X0)), pls),
119.62/119.86	    inference('simplify', [status(thm)], ['19'])).
119.62/119.86	tff('21', plain,
119.62/119.86	    ![X0 : int]:
119.62/119.86	      app_encode_app(int, int, 
119.62/119.86	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
119.62/119.86	          app_encode_app(int, int, 
119.62/119.86	            app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
119.62/119.86	              one_one(int)), pls)), X0)
119.62/119.86	       = app_encode_app(int, int, 
119.62/119.86	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
119.62/119.86	             app_encode_app(int, int, 
119.62/119.86	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
119.62/119.86	                 pls), X0)), pls),
119.62/119.86	    inference('sup+', [status(thm)], ['14', '20'])).
119.62/119.86	tff(zf_stmt_50, axiom,
119.62/119.86	  (![L1:int,K:int]:
119.62/119.86	     (app_encode_app(int,int,
119.62/119.86	                     app_encode_app(int,app_encode_fun(int,int),
119.62/119.86	                                    minus_minus(int),
119.62/119.86	                                    app_encode_app(int,int,bit1,K)),
119.62/119.86	                     app_encode_app(int,int,bit0,L1)) =
119.62/119.86	      app_encode_app(int,int,bit1,
119.62/119.86	                     app_encode_app(int,int,
119.62/119.86	                                    app_encode_app(int,
119.62/119.86	                                                   app_encode_fun(int,int),
119.62/119.86	                                                   minus_minus(int),K),
119.62/119.86	                                    L1))))).
119.62/119.86	tff('22', plain,
119.62/119.86	    ![X15 : int, X16 : int]:
119.62/119.86	      app_encode_app(int, int, 
119.62/119.86	        app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
119.62/119.86	          app_encode_app(int, int, bit1, X15)), 
119.62/119.86	        app_encode_app(int, int, bit0, X16))
119.62/119.86	       = app_encode_app(int, int, bit1, 
119.62/119.86	           app_encode_app(int, int, 
119.62/119.86	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
119.62/119.86	               X15), X16)),
119.62/119.86	    inference('cnf', [status(esa)], [zf_stmt_50])).
119.62/119.86	tff('23', plain,
119.62/119.86	    ![X0 : int]:
119.62/119.86	      app_encode_app(int, int, 
119.62/119.86	        app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
119.62/119.86	          app_encode_app(int, int, bit1, X0)), pls)
119.62/119.86	       = app_encode_app(int, int, bit1, 
119.62/119.86	           app_encode_app(int, int, 
119.62/119.86	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
119.62/119.86	               X0), pls)),
119.62/119.86	    inference('sup+', [status(thm)], ['13', '22'])).
119.62/119.86	tff('24', plain,
119.62/119.86	    app_encode_app(int, int, 
119.62/119.86	      app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
119.62/119.86	        one_one(int)), pls)
119.62/119.86	     = app_encode_app(int, int, bit1, 
119.62/119.86	         app_encode_app(int, int, 
119.62/119.86	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
119.62/119.86	             pls), pls)),
119.62/119.86	    inference('sup+', [status(thm)], ['5', '23'])).
119.62/119.86	tff('25', plain,
119.62/119.86	    ![X0 : int, X1 : int, X2 : int]:
119.62/119.86	      (app_encode_app(int, int, 
119.62/119.86	         app_encode_app(int, app_encode_fun(int, int), times_times(int), 
119.62/119.86	           app_encode_app(int, int, 
119.62/119.86	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
119.62/119.86	               X2), X1)), 
119.62/119.86	         app_encode_app(int, int, number_number_of(int), X0))
119.62/119.86	        = app_encode_app(int, int, 
119.62/119.86	            app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
119.62/119.87	              app_encode_app(int, int, 
119.62/119.87	                app_encode_app(int, app_encode_fun(int, int), 
119.62/119.87	                  times_times(int), X2), X0)), 
119.62/119.87	            app_encode_app(int, int, 
119.62/119.87	              app_encode_app(int, app_encode_fun(int, int), 
119.62/119.87	                times_times(int), X1), 
119.62/119.87	              app_encode_app(int, int, number_number_of(int), X0)))
119.62/119.87	       | ~ number(int)
119.62/119.87	       | ~ ring(int)),
119.62/119.87	    inference('sup+', [status(thm)], ['0', '15'])).
119.62/119.87	tff('26', plain,
119.62/119.87	    ![X0 : int, X1 : int, X2 : int]:
119.62/119.87	      (app_encode_app(int, int, 
119.62/119.87	         app_encode_app(int, app_encode_fun(int, int), times_times(int), 
119.62/119.87	           app_encode_app(int, int, 
119.62/119.87	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
119.62/119.87	               X2), X1)), X0)
119.62/119.87	        = app_encode_app(int, int, 
119.62/119.87	            app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
119.62/119.87	              app_encode_app(int, int, 
119.62/119.87	                app_encode_app(int, app_encode_fun(int, int), 
119.62/119.87	                  times_times(int), X2), X0)), 
119.62/119.87	            app_encode_app(int, int, 
119.62/119.87	              app_encode_app(int, app_encode_fun(int, int), 
119.62/119.87	                times_times(int), X1), X0))
119.62/119.87	       | ~ $true
119.62/119.87	       | ~ $true),
119.62/119.87	    inference('demod', [status(thm)], ['25', '0', '0', '17', '18'])).
119.62/119.87	tff('27', plain,
119.62/119.87	    ![X0 : int, X1 : int, X2 : int]:
119.62/119.87	      app_encode_app(int, int, 
119.62/119.87	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
119.62/119.87	          app_encode_app(int, int, 
119.62/119.87	            app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
119.62/119.87	              X2), X1)), X0)
119.62/119.87	       = app_encode_app(int, int, 
119.62/119.87	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
119.62/119.87	             app_encode_app(int, int, 
119.62/119.87	               app_encode_app(int, app_encode_fun(int, int), 
119.62/119.87	                 times_times(int), X2), X0)), 
119.62/119.87	           app_encode_app(int, int, 
119.62/119.87	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
119.62/119.87	               X1), X0)),
119.62/119.87	    inference('simplify', [status(thm)], ['26'])).
119.62/119.87	tff(zf_stmt_75, axiom,
119.62/119.87	  (![A:$tType]:
119.62/119.87	     (number_ring(A) =>
119.62/119.87	      (app_encode_app(int,A,number_number_of(A),pls) = zero_zero(A))))).
119.62/119.87	tff('28', plain,
119.62/119.87	    ![X69 : $tType]:
119.62/119.87	      (app_encode_app(int, X69, number_number_of(X69), pls) = zero_zero(X69)
119.62/119.87	       | ~ number_ring(X69)),
119.62/119.87	    inference('cnf', [status(esa)], [zf_stmt_75])).
119.62/119.87	tff(zf_stmt_77, axiom,
119.62/119.87	  (![B:$tType]:
119.62/119.87	     ((number(B) & ring(B)) =>
119.62/119.87	      (![C:B,B1:B,V1:int]:
119.62/119.87	         (app_encode_app(B,B,
119.62/119.87	                         app_encode_app(B,app_encode_fun(B,B),times_times(B),
119.62/119.87	                                        app_encode_app(int,B,
119.62/119.87	                                                       number_number_of(B),V1)),
119.62/119.87	                         app_encode_app(B,B,
119.62/119.87	                                        app_encode_app(B,app_encode_fun(B,B),
119.62/119.87	                                                       minus_minus(B),B1),
119.62/119.87	                                        C)) =
119.62/119.87	          app_encode_app(B,B,
119.62/119.87	                         app_encode_app(B,app_encode_fun(B,B),minus_minus(B),
119.62/119.87	                                        app_encode_app(B,B,
119.62/119.87	                                                       app_encode_app(
119.62/119.87	                                                       B,app_encode_fun(B,B),
119.62/119.87	                                                       times_times(B),
119.62/119.87	                                                       app_encode_app(
119.62/119.87	                                                       int,B,
119.62/119.87	                                                       number_number_of(B),V1)),
119.62/119.87	                                                       B1)),
119.62/119.87	                         app_encode_app(B,B,
119.62/119.87	                                        app_encode_app(B,app_encode_fun(B,B),
119.62/119.87	                                                       times_times(B),
119.62/119.87	                                                       app_encode_app(
119.62/119.87	                                                       int,B,
119.62/119.87	                                                       number_number_of(B),V1)),
119.62/119.87	                                        C))))))).
119.62/119.87	tff('29', plain,
119.62/119.87	    ![X74 : $tType, X75 : int, X76 : X74, X77 : X74]:
119.62/119.87	      (app_encode_app(X74, X74, 
119.62/119.87	         app_encode_app(X74, app_encode_fun(X74, X74), times_times(X74), 
119.62/119.87	           app_encode_app(int, X74, number_number_of(X74), X75)), 
119.62/119.87	         app_encode_app(X74, X74, 
119.62/119.87	           app_encode_app(X74, app_encode_fun(X74, X74), minus_minus(X74), 
119.62/119.87	             X76), X77))
119.62/119.87	        = app_encode_app(X74, X74, 
119.62/119.87	            app_encode_app(X74, app_encode_fun(X74, X74), minus_minus(X74), 
119.62/119.87	              app_encode_app(X74, X74, 
119.62/119.87	                app_encode_app(X74, app_encode_fun(X74, X74), 
119.62/119.87	                  times_times(X74), 
119.62/119.87	                  app_encode_app(int, X74, number_number_of(X74), X75)), X76)), 
119.62/119.87	            app_encode_app(X74, X74, 
119.62/119.87	              app_encode_app(X74, app_encode_fun(X74, X74), 
119.62/119.87	                times_times(X74), 
119.62/119.87	                app_encode_app(int, X74, number_number_of(X74), X75)), X77))
119.62/119.87	       | ~ ring(X74)
119.62/119.87	       | ~ number(X74)),
119.62/119.87	    inference('cnf', [status(esa)], [zf_stmt_77])).
119.62/119.87	tff('30', plain,
119.62/119.87	    ![X0 : $tType, X1 : X0, X2 : X0]:
119.62/119.87	      (app_encode_app(X0, X0, 
119.62/119.87	         app_encode_app(X0, app_encode_fun(X0, X0), times_times(X0), 
119.62/119.87	           app_encode_app(int, X0, number_number_of(X0), pls)), 
119.62/119.87	         app_encode_app(X0, X0, 
119.62/119.87	           app_encode_app(X0, app_encode_fun(X0, X0), minus_minus(X0), X2), 
119.62/119.87	           X1))
119.62/119.87	        = app_encode_app(X0, X0, 
119.62/119.87	            app_encode_app(X0, app_encode_fun(X0, X0), minus_minus(X0), 
119.62/119.87	              app_encode_app(X0, X0, 
119.62/119.87	                app_encode_app(X0, app_encode_fun(X0, X0), times_times(X0), 
119.62/119.87	                  zero_zero(X0)), X2)), 
119.62/119.87	            app_encode_app(X0, X0, 
119.62/119.87	              app_encode_app(X0, app_encode_fun(X0, X0), times_times(X0), 
119.62/119.87	                app_encode_app(int, X0, number_number_of(X0), pls)), X1))
119.62/119.87	       | ~ number_ring(X0)
119.62/119.87	       | ~ number(X0)
119.62/119.87	       | ~ ring(X0)),
119.62/119.87	    inference('sup+', [status(thm)], ['28', '29'])).
119.62/119.87	tff('31', plain,
119.62/119.87	    ![X0 : int]:
119.62/119.87	      (app_encode_app(int, int, 
119.62/119.87	         app_encode_app(int, app_encode_fun(int, int), times_times(int), 
119.62/119.87	           app_encode_app(int, int, number_number_of(int), pls)), 
119.62/119.87	         app_encode_app(int, int, 
119.62/119.87	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
119.62/119.87	             X0), X0))
119.62/119.87	        = app_encode_app(int, int, 
119.62/119.87	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
119.62/119.87	              app_encode_app(int, int, 
119.62/119.87	                app_encode_app(int, app_encode_fun(int, int), 
119.62/119.87	                  minus_minus(int), zero_zero(int)), 
119.62/119.87	                app_encode_app(int, int, number_number_of(int), pls))), X0)
119.62/119.87	       | ~ ring(int)
119.62/119.87	       | ~ number(int)
119.62/119.87	       | ~ number_ring(int)),
119.62/119.87	    inference('sup+', [status(thm)], ['27', '30'])).
119.62/119.87	tff(zf_stmt_119, axiom, (pls = zero_zero(int))).
119.62/119.87	tff('32', plain, pls = zero_zero(int),
119.62/119.87	    inference('cnf', [status(esa)], [zf_stmt_119])).
119.62/119.87	tff('33', plain,
119.62/119.87	    ![X0 : int, X1 : int]:
119.62/119.87	      (app_encode_app(int, int, 
119.62/119.87	         app_encode_app(int, app_encode_fun(int, int), times_times(int), 
119.62/119.87	           app_encode_app(int, int, 
119.62/119.87	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
119.62/119.87	               pls), X1)), 
119.62/119.87	         app_encode_app(int, int, number_number_of(int), X0))
119.62/119.87	        = app_encode_app(int, int, 
119.62/119.87	            app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
119.62/119.87	              pls), 
119.62/119.87	            app_encode_app(int, int, 
119.62/119.87	              app_encode_app(int, app_encode_fun(int, int), 
119.62/119.87	                times_times(int), X1), 
119.62/119.87	              app_encode_app(int, int, number_number_of(int), X0)))
119.62/119.87	       | ~ number(int)
119.62/119.87	       | ~ ring(int)),
119.62/119.87	    inference('sup+', [status(thm)], ['10', '15'])).
119.62/119.87	tff('34', plain,
119.62/119.87	    ![X0 : int, X1 : int]:
119.62/119.87	      (app_encode_app(int, int, 
119.62/119.87	         app_encode_app(int, app_encode_fun(int, int), times_times(int), 
119.62/119.87	           app_encode_app(int, int, 
119.62/119.87	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
119.62/119.87	               pls), X1)), X0)
119.62/119.87	        = app_encode_app(int, int, 
119.62/119.87	            app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
119.62/119.87	              pls), 
119.62/119.87	            app_encode_app(int, int, 
119.62/119.87	              app_encode_app(int, app_encode_fun(int, int), 
119.62/119.87	                times_times(int), X1), X0))
119.62/119.87	       | ~ $true
119.62/119.87	       | ~ $true),
119.62/119.87	    inference('demod', [status(thm)], ['33', '0', '0', '17', '18'])).
119.62/119.87	tff('35', plain,
119.62/119.87	    ![X0 : int, X1 : int]:
119.62/119.87	      app_encode_app(int, int, 
119.62/119.87	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
119.62/119.87	          app_encode_app(int, int, 
119.62/119.87	            app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
119.62/119.87	              pls), X1)), X0)
119.62/119.87	       = app_encode_app(int, int, 
119.62/119.87	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
119.62/119.87	             pls), 
119.62/119.87	           app_encode_app(int, int, 
119.62/119.87	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
119.62/119.87	               X1), X0)),
119.62/119.87	    inference('simplify', [status(thm)], ['34'])).
119.62/119.87	tff('36', plain,
119.62/119.87	    (pls
119.62/119.87	      = app_encode_app(int, int, 
119.62/119.87	          app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
119.62/119.87	            pls), pls)
119.62/119.87	     | ~ $true
119.62/119.87	     | ~ $true
119.62/119.87	     | ~ $true),
119.62/119.87	    inference('demod', [status(thm)],
119.62/119.87	              ['31', '0', '10', '32', '0', '35', '10', '18', '17', '3'])).
119.62/119.87	tff('37', plain,
119.62/119.87	    pls
119.62/119.87	     = app_encode_app(int, int, 
119.62/119.87	         app_encode_app(int, app_encode_fun(int, int), minus_minus(int), pls), 
119.62/119.87	         pls),
119.62/119.87	    inference('simplify', [status(thm)], ['36'])).
119.62/119.87	tff('38', plain,
119.62/119.87	    app_encode_app(int, int, 
119.62/119.87	      app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
119.62/119.87	        one_one(int)), pls)
119.62/119.87	     = app_encode_app(int, int, bit1, pls),
119.62/119.87	    inference('demod', [status(thm)], ['24', '37'])).
119.62/119.87	tff('39', plain,
119.62/119.87	    app_encode_app(int, int, 
119.62/119.87	      app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
119.62/119.87	        one_one(int)), pls)
119.62/119.87	     = one_one(int),
119.62/119.87	    inference('demod', [status(thm)], ['38', '5'])).
119.62/119.87	tff('40', plain,
119.62/119.87	    ![X0 : int]:
119.62/119.87	      app_encode_app(int, int, 
119.62/119.87	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
119.62/119.87	          one_one(int)), X0)
119.62/119.87	       = app_encode_app(int, int, 
119.62/119.87	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
119.62/119.87	             app_encode_app(int, int, 
119.62/119.87	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
119.62/119.87	                 pls), X0)), pls),
119.62/119.87	    inference('demod', [status(thm)], ['21', '39'])).
119.62/119.87	tff('41', plain,
119.62/119.87	    ![X0 : int]:
119.62/119.87	      app_encode_app(int, int, 
119.62/119.87	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
119.62/119.87	        X0)
119.62/119.87	       = app_encode_app(int, int, 
119.62/119.87	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
119.62/119.87	             app_encode_app(int, int, 
119.62/119.87	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
119.62/119.87	                 pls), X0)), pls),
119.62/119.87	    inference('demod', [status(thm)], ['40', '14'])).
119.62/119.87	tff(zf_stmt_82, axiom,
119.62/119.87	  (![A:$tType]:
119.62/119.87	     (number_ring(A) =>
119.62/119.87	      (![Z:A,W:int,V1:int]:
119.62/119.87	         (app_encode_app(A,A,
119.62/119.87	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
119.62/119.87	                                        app_encode_app(int,A,
119.62/119.87	                                                       number_number_of(A),V1)),
119.62/119.87	                         app_encode_app(A,A,
119.62/119.87	                                        app_encode_app(A,app_encode_fun(A,A),
119.62/119.87	                                                       plus_plus(A),
119.62/119.87	                                                       app_encode_app(
119.62/119.87	                                                       int,A,
119.62/119.87	                                                       number_number_of(A),W)),
119.62/119.87	                                        Z)) =
119.62/119.87	          app_encode_app(A,A,
119.62/119.87	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
119.62/119.87	                                        app_encode_app(int,A,
119.62/119.87	                                                       number_number_of(A),
119.62/119.87	                                                       app_encode_app(
119.62/119.87	                                                       int,int,
119.62/119.87	                                                       app_encode_app(
119.62/119.87	                                                       int,
119.62/119.87	                                                       app_encode_fun(
119.62/119.87	                                                       int,int),
119.62/119.87	                                                       plus_plus(int),V1),W))),
119.62/119.87	                         Z)))))).
119.62/119.87	tff('42', plain,
119.62/119.87	    ![X93 : $tType, X94 : int, X95 : int, X96 : X93]:
119.62/119.87	      (app_encode_app(X93, X93, 
119.62/119.87	         app_encode_app(X93, app_encode_fun(X93, X93), plus_plus(X93), 
119.62/119.87	           app_encode_app(int, X93, number_number_of(X93), X94)), 
119.62/119.87	         app_encode_app(X93, X93, 
119.62/119.87	           app_encode_app(X93, app_encode_fun(X93, X93), plus_plus(X93), 
119.62/119.87	             app_encode_app(int, X93, number_number_of(X93), X95)), X96))
119.62/119.87	        = app_encode_app(X93, X93, 
119.62/119.87	            app_encode_app(X93, app_encode_fun(X93, X93), plus_plus(X93), 
119.62/119.87	              app_encode_app(int, X93, number_number_of(X93), 
119.62/119.87	                app_encode_app(int, int, 
119.62/119.87	                  app_encode_app(int, app_encode_fun(int, int), 
119.62/119.87	                    plus_plus(int), X94), X95))), X96)
119.62/119.87	       | ~ number_ring(X93)),
119.62/119.87	    inference('cnf', [status(esa)], [zf_stmt_82])).
119.62/119.87	tff('43', plain,
119.62/119.87	    ![X0 : int, X1 : int, X2 : int]:
119.62/119.87	      (app_encode_app(int, int, 
119.62/119.87	         app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
119.62/119.87	         app_encode_app(int, int, 
119.62/119.87	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
119.62/119.87	             app_encode_app(int, int, number_number_of(int), X2)), X1))
119.62/119.87	        = app_encode_app(int, int, 
119.62/119.87	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
119.62/119.87	              app_encode_app(int, int, number_number_of(int), 
119.62/119.87	                app_encode_app(int, int, 
119.62/119.87	                  app_encode_app(int, app_encode_fun(int, int), 
119.62/119.87	                    plus_plus(int), X0), X2))), X1)
119.62/119.87	       | ~ number_ring(int)),
119.62/119.87	    inference('sup+', [status(thm)], ['0', '42'])).
119.62/119.87	tff('44', plain,
119.62/119.87	    ![X0 : int, X1 : int, X2 : int]:
119.62/119.87	      (app_encode_app(int, int, 
119.62/119.87	         app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
119.62/119.87	         app_encode_app(int, int, 
119.62/119.87	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X2), 
119.62/119.87	           X1))
119.62/119.87	        = app_encode_app(int, int, 
119.62/119.87	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
119.62/119.87	              app_encode_app(int, int, 
119.62/119.87	                app_encode_app(int, app_encode_fun(int, int), 
119.62/119.87	                  plus_plus(int), X0), X2)), X1)
119.62/119.87	       | ~ $true),
119.62/119.87	    inference('demod', [status(thm)], ['43', '0', '0', '3'])).
119.62/119.87	tff('45', plain,
119.62/119.87	    ![X0 : int, X1 : int, X2 : int]:
119.62/119.87	      app_encode_app(int, int, 
119.62/119.87	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
119.62/119.87	        app_encode_app(int, int, 
119.62/119.87	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X2), 
119.62/119.87	          X1))
119.62/119.87	       = app_encode_app(int, int, 
119.62/119.87	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
119.62/119.87	             app_encode_app(int, int, 
119.62/119.87	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
119.62/119.87	                 X0), X2)), X1),
119.62/119.87	    inference('simplify', [status(thm)], ['44'])).
119.62/119.87	tff(zf_stmt_133, axiom,
119.62/119.87	  (![A:$tType]:
119.62/119.87	     (number_ring(A) =>
119.62/119.87	      (![W:int]:
119.62/119.87	         (app_encode_app(int,A,number_number_of(A),
119.62/119.87	                         app_encode_app(int,int,bit0,W)) =
119.62/119.87	          app_encode_app(A,A,
119.62/119.87	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
119.62/119.87	                                        app_encode_app(A,A,
119.62/119.87	                                                       app_encode_app(
119.62/119.87	                                                       A,app_encode_fun(A,A),
119.62/119.87	                                                       plus_plus(A),
119.62/119.87	                                                       zero_zero(A)),
119.62/119.87	                                                       app_encode_app(
119.62/119.87	                                                       int,A,
119.62/119.87	                                                       number_number_of(A),W))),
119.62/119.87	                         app_encode_app(int,A,number_number_of(A),W))))))).
119.62/119.87	tff('46', plain,
119.62/119.87	    ![X206 : $tType, X207 : int]:
119.62/119.87	      (app_encode_app(int, X206, number_number_of(X206), 
119.62/119.87	         app_encode_app(int, int, bit0, X207))
119.62/119.87	        = app_encode_app(X206, X206, 
119.62/119.87	            app_encode_app(X206, app_encode_fun(X206, X206), 
119.62/119.87	              plus_plus(X206), 
119.62/119.87	              app_encode_app(X206, X206, 
119.62/119.87	                app_encode_app(X206, app_encode_fun(X206, X206), 
119.62/119.87	                  plus_plus(X206), zero_zero(X206)), 
119.62/119.87	                app_encode_app(int, X206, number_number_of(X206), X207))), 
119.62/119.87	            app_encode_app(int, X206, number_number_of(X206), X207))
119.62/119.87	       | ~ number_ring(X206)),
119.62/119.87	    inference('cnf', [status(esa)], [zf_stmt_133])).
119.62/119.87	tff('47', plain,
119.62/119.87	    ![X0 : int]:
119.62/119.87	      (app_encode_app(int, int, number_number_of(int), 
119.62/119.87	         app_encode_app(int, int, bit0, X0))
119.62/119.87	        = app_encode_app(int, int, 
119.62/119.87	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
119.62/119.87	              zero_zero(int)), 
119.62/119.87	            app_encode_app(int, int, 
119.62/119.87	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
119.62/119.87	                app_encode_app(int, int, number_number_of(int), X0)), 
119.62/119.87	              app_encode_app(int, int, number_number_of(int), X0)))
119.62/119.87	       | ~ number_ring(int)),
119.62/119.87	    inference('sup+', [status(thm)], ['45', '46'])).
119.62/119.87	tff('48', plain,
119.62/119.87	    ![X0 : int]:
119.62/119.87	      (app_encode_app(int, int, bit0, X0)
119.62/119.87	        = app_encode_app(int, int, 
119.62/119.87	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
119.62/119.87	              pls), 
119.62/119.87	            app_encode_app(int, int, 
119.62/119.87	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
119.62/119.87	                X0), X0))
119.62/119.87	       | ~ $true),
119.62/119.87	    inference('demod', [status(thm)], ['47', '0', '32', '0', '0', '3'])).
119.62/119.87	tff('49', plain,
119.62/119.87	    ![X0 : int]:
119.62/119.87	      app_encode_app(int, int, bit0, X0)
119.62/119.87	       = app_encode_app(int, int, 
119.62/119.87	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
119.62/119.87	           app_encode_app(int, int, 
119.62/119.87	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
119.62/119.87	               X0), X0)),
119.62/119.87	    inference('simplify', [status(thm)], ['48'])).
119.62/119.87	tff(zf_stmt_93, axiom,
119.62/119.87	  (![L1:int,K:int]:
119.62/119.87	     (app_encode_app(int,int,
119.62/119.87	                     app_encode_app(int,app_encode_fun(int,int),
119.62/119.87	                                    plus_plus(int),
119.62/119.87	                                    app_encode_app(int,int,bit0,K)),
119.62/119.87	                     app_encode_app(int,int,bit1,L1)) =
119.62/119.87	      app_encode_app(int,int,bit1,
119.62/119.87	                     app_encode_app(int,int,
119.62/119.87	                                    app_encode_app(int,
119.62/119.87	                                                   app_encode_fun(int,int),
119.62/119.87	                                                   plus_plus(int),K),
119.62/119.87	                                    L1))))).
119.62/119.87	tff('50', plain,
119.62/119.87	    ![X120 : int, X121 : int]:
119.62/119.87	      app_encode_app(int, int, 
119.62/119.87	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
119.62/119.87	          app_encode_app(int, int, bit0, X120)), 
119.62/119.87	        app_encode_app(int, int, bit1, X121))
119.62/119.87	       = app_encode_app(int, int, bit1, 
119.62/119.87	           app_encode_app(int, int, 
119.62/119.87	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
119.62/119.87	               X120), X121)),
119.62/119.87	    inference('cnf', [status(esa)], [zf_stmt_93])).
119.62/119.87	tff('51', plain,
119.62/119.87	    ![X0 : int]:
119.62/119.87	      app_encode_app(int, int, 
119.62/119.87	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
119.62/119.87	        app_encode_app(int, int, bit1, X0))
119.62/119.87	       = app_encode_app(int, int, bit1, 
119.62/119.87	           app_encode_app(int, int, 
119.62/119.87	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
119.62/119.87	               pls), X0)),
119.62/119.87	    inference('sup+', [status(thm)], ['13', '50'])).
119.62/119.87	tff('52', plain,
119.62/119.87	    app_encode_app(int, int, 
119.62/119.87	      app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
119.62/119.87	      one_one(int))
119.62/119.87	     = app_encode_app(int, int, bit1, 
119.62/119.87	         app_encode_app(int, int, 
119.62/119.87	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
119.62/119.87	           pls)),
119.62/119.87	    inference('sup+', [status(thm)], ['5', '51'])).
119.62/119.87	tff(zf_stmt_55, axiom,
119.62/119.87	  (![A:$tType]:
119.62/119.87	     (linord219039673up_add(A) =>
119.62/119.87	      (![A1:A]:
119.62/119.87	         ((app_encode_app(A,A,
119.62/119.87	                          app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
119.62/119.87	                                         A1),
119.62/119.87	                          A1) =
119.62/119.87	           zero_zero(A)) <=>
119.62/119.87	          (A1 = zero_zero(A))))))).
119.62/119.87	tff('53', plain,
119.62/119.87	    ![X29 : $tType, X30 : X29]:
119.62/119.87	      (X30 != zero_zero(X29)
119.62/119.87	       | app_encode_app(X29, X29, 
119.62/119.87	           app_encode_app(X29, app_encode_fun(X29, X29), plus_plus(X29), X30), 
119.62/119.87	           X30)
119.62/119.87	          = zero_zero(X29)
119.62/119.87	       | ~ linord219039673up_add(X29)),
119.62/119.87	    inference('cnf', [status(esa)], [zf_stmt_55])).
119.62/119.87	tff('54', plain,
119.62/119.87	    ![X29 : $tType]:
119.62/119.87	      (~ linord219039673up_add(X29)
119.62/119.87	       | app_encode_app(X29, X29, 
119.62/119.87	           app_encode_app(X29, app_encode_fun(X29, X29), plus_plus(X29), 
119.62/119.87	             zero_zero(X29)), zero_zero(X29))
119.62/119.87	          = zero_zero(X29)),
119.62/119.87	    inference('simplify', [status(thm)], ['53'])).
119.62/119.87	tff('55', plain,
119.62/119.87	    (app_encode_app(int, int, 
119.62/119.87	       app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
119.62/119.87	       zero_zero(int))
119.62/119.87	      = zero_zero(int)
119.62/119.87	     | ~ linord219039673up_add(int)),
119.62/119.87	    inference('sup+', [status(thm)], ['32', '54'])).
119.62/119.87	tff(zf_stmt_134, axiom, (linord219039673up_add(int))).
119.62/119.87	tff('56', plain, linord219039673up_add(int),
119.62/119.87	    inference('cnf', [status(esa)], [zf_stmt_134])).
119.62/119.87	tff('57', plain,
119.62/119.87	    (app_encode_app(int, int, 
119.62/119.87	       app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
119.62/119.87	       pls)
119.62/119.87	      = pls
119.62/119.87	     | ~ $true),
119.62/119.87	    inference('demod', [status(thm)], ['55', '32', '32', '56'])).
119.62/119.87	tff('58', plain,
119.62/119.87	    app_encode_app(int, int, 
119.62/119.87	      app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
119.62/119.87	      pls)
119.62/119.87	     = pls,
119.62/119.87	    inference('simplify', [status(thm)], ['57'])).
119.62/119.87	tff('59', plain,
119.62/119.87	    app_encode_app(int, int, 
119.62/119.87	      app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
119.62/119.87	      one_one(int))
119.62/119.87	     = app_encode_app(int, int, bit1, pls),
119.62/119.87	    inference('demod', [status(thm)], ['52', '58'])).
119.62/119.87	tff('60', plain,
119.62/119.87	    app_encode_app(int, int, 
119.62/119.87	      app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
119.62/119.87	      one_one(int))
119.62/119.87	     = one_one(int),
119.62/119.87	    inference('demod', [status(thm)], ['59', '5'])).
119.62/119.87	tff(zf_stmt_73, axiom,
119.62/119.87	  (![B:$tType]:
119.62/119.87	     ((number(B) & semiring(B)) =>
119.62/119.87	      (![V1:int,B1:B,A2:B]:
119.62/119.87	         (app_encode_app(B,B,
119.62/119.87	                         app_encode_app(B,app_encode_fun(B,B),times_times(B),
119.62/119.87	                                        app_encode_app(B,B,
119.62/119.87	                                                       app_encode_app(
119.62/119.87	                                                       B,app_encode_fun(B,B),
119.62/119.87	                                                       plus_plus(B),A2),B1)),
119.62/119.87	                         app_encode_app(int,B,number_number_of(B),V1)) =
119.62/119.87	          app_encode_app(B,B,
119.62/119.87	                         app_encode_app(B,app_encode_fun(B,B),plus_plus(B),
119.62/119.87	                                        app_encode_app(B,B,
119.62/119.87	                                                       app_encode_app(
119.62/119.87	                                                       B,app_encode_fun(B,B),
119.62/119.87	                                                       times_times(B),A2),
119.62/119.87	                                                       app_encode_app(
119.62/119.87	                                                       int,B,
119.62/119.87	                                                       number_number_of(B),V1))),
119.62/119.87	                         app_encode_app(B,B,
119.62/119.87	                                        app_encode_app(B,app_encode_fun(B,B),
119.62/119.87	                                                       times_times(B),B1),
119.62/119.87	                                        app_encode_app(int,B,
119.62/119.87	                                                       number_number_of(B),V1)))))))).
119.62/119.87	tff('61', plain,
119.62/119.87	    ![X61 : $tType, X62 : X61, X63 : int, X64 : X61]:
119.62/119.87	      (app_encode_app(X61, X61, 
119.62/119.87	         app_encode_app(X61, app_encode_fun(X61, X61), times_times(X61), 
119.62/119.87	           app_encode_app(X61, X61, 
119.62/119.87	             app_encode_app(X61, app_encode_fun(X61, X61), plus_plus(X61), 
119.62/119.87	               X62), X64)), 
119.62/119.87	         app_encode_app(int, X61, number_number_of(X61), X63))
119.62/119.87	        = app_encode_app(X61, X61, 
119.62/119.87	            app_encode_app(X61, app_encode_fun(X61, X61), plus_plus(X61), 
119.62/119.87	              app_encode_app(X61, X61, 
119.62/119.87	                app_encode_app(X61, app_encode_fun(X61, X61), 
119.62/119.87	                  times_times(X61), X62), 
119.62/119.87	                app_encode_app(int, X61, number_number_of(X61), X63))), 
119.62/119.87	            app_encode_app(X61, X61, 
119.62/119.87	              app_encode_app(X61, app_encode_fun(X61, X61), 
119.62/119.87	                times_times(X61), X64), 
119.62/119.87	              app_encode_app(int, X61, number_number_of(X61), X63)))
119.62/119.87	       | ~ semiring(X61)
119.62/119.87	       | ~ number(X61)),
119.62/119.87	    inference('cnf', [status(esa)], [zf_stmt_73])).
119.62/119.87	tff('62', plain,
119.62/119.87	    ![X0 : int, X1 : int]:
119.62/119.87	      (app_encode_app(int, int, 
119.62/119.87	         app_encode_app(int, app_encode_fun(int, int), times_times(int), 
119.62/119.87	           app_encode_app(int, int, 
119.62/119.87	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
119.62/119.87	               pls), X1)), 
119.62/119.87	         app_encode_app(int, int, number_number_of(int), X0))
119.62/119.87	        = app_encode_app(int, int, 
119.62/119.87	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
119.62/119.87	              pls), 
119.62/119.87	            app_encode_app(int, int, 
119.62/119.87	              app_encode_app(int, app_encode_fun(int, int), 
119.62/119.87	                times_times(int), X1), 
119.62/119.87	              app_encode_app(int, int, number_number_of(int), X0)))
119.62/119.87	       | ~ number(int)
119.62/119.87	       | ~ semiring(int)),
119.62/119.87	    inference('sup+', [status(thm)], ['10', '61'])).
119.62/119.87	tff(zf_stmt_140, axiom, (semiring(int))).
119.62/119.87	tff('63', plain, semiring(int),
119.62/119.87	    inference('cnf', [status(esa)], [zf_stmt_140])).
119.62/119.87	tff('64', plain,
119.62/119.87	    ![X0 : int, X1 : int]:
119.62/119.87	      (app_encode_app(int, int, 
119.62/119.87	         app_encode_app(int, app_encode_fun(int, int), times_times(int), 
119.62/119.87	           app_encode_app(int, int, 
119.62/119.87	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
119.62/119.87	               pls), X1)), X0)
119.62/119.87	        = app_encode_app(int, int, 
119.62/119.87	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
119.62/119.87	              pls), 
119.62/119.87	            app_encode_app(int, int, 
119.62/119.87	              app_encode_app(int, app_encode_fun(int, int), 
119.62/119.87	                times_times(int), X1), X0))
119.62/119.87	       | ~ $true
119.62/119.87	       | ~ $true),
119.62/119.87	    inference('demod', [status(thm)], ['62', '0', '0', '17', '63'])).
119.62/119.87	tff('65', plain,
119.62/119.87	    ![X0 : int, X1 : int]:
119.62/119.87	      app_encode_app(int, int, 
119.62/119.87	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
119.62/119.87	          app_encode_app(int, int, 
119.62/119.87	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
119.62/119.87	              pls), X1)), X0)
119.62/119.87	       = app_encode_app(int, int, 
119.62/119.87	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
119.62/119.87	           app_encode_app(int, int, 
119.62/119.87	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
119.62/119.87	               X1), X0)),
119.62/119.87	    inference('simplify', [status(thm)], ['64'])).
119.62/119.87	tff('66', plain,
119.62/119.87	    ![X0 : int]:
119.62/119.87	      app_encode_app(int, int, 
119.62/119.87	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
119.62/119.87	          one_one(int)), X0)
119.62/119.87	       = app_encode_app(int, int, 
119.62/119.87	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
119.62/119.87	           app_encode_app(int, int, 
119.62/119.87	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
119.62/119.87	               one_one(int)), X0)),
119.62/119.87	    inference('sup+', [status(thm)], ['60', '65'])).
119.62/119.87	tff('67', plain,
119.62/119.87	    ![X0 : int]:
119.62/119.87	      app_encode_app(int, int, 
119.62/119.87	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
119.62/119.87	        X0)
119.62/119.87	       = app_encode_app(int, int, 
119.62/119.87	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
119.62/119.87	           app_encode_app(int, int, 
119.62/119.87	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
119.62/119.87	               pls), X0)),
119.62/119.87	    inference('demod', [status(thm)], ['66', '14', '14'])).
119.62/119.87	tff('68', plain,
119.62/119.87	    ![X0 : int]:
119.62/119.87	      app_encode_app(int, int, 
119.62/119.87	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
119.62/119.87	        app_encode_app(int, int, 
119.62/119.87	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
119.62/119.87	          X0))
119.62/119.87	       = app_encode_app(int, int, 
119.62/119.87	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
119.62/119.87	           app_encode_app(int, int, bit0, X0)),
119.62/119.87	    inference('sup+', [status(thm)], ['49', '67'])).
119.62/119.87	tff(zf_stmt_71, axiom,
119.62/119.87	  (![L1:int,K:int]:
119.62/119.87	     (app_encode_app(int,int,
119.62/119.87	                     app_encode_app(int,app_encode_fun(int,int),
119.62/119.87	                                    plus_plus(int),
119.62/119.87	                                    app_encode_app(int,int,bit0,K)),
119.62/119.87	                     app_encode_app(int,int,bit0,L1)) =
119.62/119.87	      app_encode_app(int,int,bit0,
119.62/119.87	                     app_encode_app(int,int,
119.62/119.87	                                    app_encode_app(int,
119.62/119.87	                                                   app_encode_fun(int,int),
119.62/119.87	                                                   plus_plus(int),K),
119.62/119.87	                                    L1))))).
119.62/119.87	tff('69', plain,
119.62/119.87	    ![X57 : int, X58 : int]:
119.62/119.87	      app_encode_app(int, int, 
119.62/119.87	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
119.62/119.87	          app_encode_app(int, int, bit0, X57)), 
119.62/119.87	        app_encode_app(int, int, bit0, X58))
119.62/119.87	       = app_encode_app(int, int, bit0, 
119.62/119.87	           app_encode_app(int, int, 
119.62/119.87	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
119.62/119.87	               X57), X58)),
119.62/119.87	    inference('cnf', [status(esa)], [zf_stmt_71])).
119.62/119.87	tff('70', plain,
119.62/119.87	    ![X0 : int]:
119.62/119.87	      app_encode_app(int, int, 
119.62/119.87	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
119.62/119.87	        app_encode_app(int, int, bit0, X0))
119.62/119.87	       = app_encode_app(int, int, bit0, 
119.62/119.87	           app_encode_app(int, int, 
119.62/119.87	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
119.62/119.87	               pls), X0)),
119.62/119.87	    inference('sup+', [status(thm)], ['13', '69'])).
119.62/119.87	tff('71', plain,
119.62/119.87	    ![X0 : int]:
119.62/119.87	      app_encode_app(int, int, 
119.62/119.87	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
119.62/119.87	        app_encode_app(int, int, 
119.62/119.87	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
119.62/119.87	          X0))
119.62/119.87	       = app_encode_app(int, int, bit0, 
119.62/119.87	           app_encode_app(int, int, 
119.62/119.87	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
119.62/119.87	               pls), X0)),
119.62/119.87	    inference('demod', [status(thm)], ['68', '70'])).
119.62/119.87	tff('72', plain,
119.62/119.87	    ![X0 : int]:
119.62/119.87	      app_encode_app(int, int, bit0, X0)
119.62/119.87	       = app_encode_app(int, int, bit0, 
119.62/119.87	           app_encode_app(int, int, 
119.62/119.87	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
119.62/119.87	               pls), X0)),
119.62/119.87	    inference('sup+', [status(thm)], ['71', '49'])).
119.62/119.87	tff(zf_stmt_72, axiom,
119.62/119.87	  (![L1:int,K:int]:
119.62/119.87	     (app_encode_app(int,int,
119.62/119.87	                     app_encode_app(int,app_encode_fun(int,int),
119.62/119.87	                                    minus_minus(int),
119.62/119.87	                                    app_encode_app(int,int,bit0,K)),
119.62/119.87	                     app_encode_app(int,int,bit0,L1)) =
119.62/119.87	      app_encode_app(int,int,bit0,
119.62/119.87	                     app_encode_app(int,int,
119.62/119.87	                                    app_encode_app(int,
119.62/119.87	                                                   app_encode_fun(int,int),
119.62/119.87	                                                   minus_minus(int),K),
119.62/119.87	                                    L1))))).
119.62/119.87	tff('73', plain,
119.62/119.87	    ![X59 : int, X60 : int]:
119.62/119.87	      app_encode_app(int, int, 
119.62/119.87	        app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
119.62/119.87	          app_encode_app(int, int, bit0, X59)), 
119.62/119.87	        app_encode_app(int, int, bit0, X60))
119.62/119.87	       = app_encode_app(int, int, bit0, 
119.62/119.87	           app_encode_app(int, int, 
119.62/119.87	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
119.62/119.87	               X59), X60)),
119.62/119.87	    inference('cnf', [status(esa)], [zf_stmt_72])).
119.62/119.87	tff('74', plain,
119.62/119.87	    ![X0 : int, X1 : int]:
119.62/119.87	      app_encode_app(int, int, 
119.62/119.87	        app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
119.62/119.87	          app_encode_app(int, int, bit0, X0)), 
119.62/119.87	        app_encode_app(int, int, bit0, X1))
119.62/119.87	       = app_encode_app(int, int, bit0, 
119.62/119.87	           app_encode_app(int, int, 
119.62/119.87	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
119.62/119.87	               app_encode_app(int, int, 
119.62/119.87	                 app_encode_app(int, app_encode_fun(int, int), 
119.62/119.87	                   plus_plus(int), pls), X0)), X1)),
119.62/119.87	    inference('sup+', [status(thm)], ['72', '73'])).
119.62/119.87	tff('75', plain,
119.62/119.87	    ![X0 : int, X1 : int]:
119.62/119.87	      app_encode_app(int, int, bit0, 
119.62/119.87	        app_encode_app(int, int, 
119.62/119.87	          app_encode_app(int, app_encode_fun(int, int), minus_minus(int), X0), 
119.62/119.87	          X1))
119.62/119.87	       = app_encode_app(int, int, bit0, 
119.62/119.87	           app_encode_app(int, int, 
119.62/119.87	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
119.62/119.87	               app_encode_app(int, int, 
119.62/119.87	                 app_encode_app(int, app_encode_fun(int, int), 
119.62/119.87	                   plus_plus(int), pls), X0)), X1)),
119.62/119.87	    inference('demod', [status(thm)], ['74', '73'])).
119.62/119.87	tff('76', plain,
119.62/119.87	    ![X0 : int]:
119.62/119.87	      app_encode_app(int, int, bit0, 
119.62/119.87	        app_encode_app(int, int, 
119.62/119.87	          app_encode_app(int, app_encode_fun(int, int), minus_minus(int), X0), 
119.62/119.87	          pls))
119.62/119.87	       = app_encode_app(int, int, bit0, 
119.62/119.87	           app_encode_app(int, int, 
119.62/119.87	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
119.62/119.87	               pls), X0)),
119.62/119.87	    inference('sup+', [status(thm)], ['41', '75'])).
119.62/119.87	tff('77', plain,
119.62/119.87	    ![X0 : int]:
119.62/119.87	      app_encode_app(int, int, bit0, 
119.62/119.87	        app_encode_app(int, int, 
119.62/119.87	          app_encode_app(int, app_encode_fun(int, int), minus_minus(int), X0), 
119.62/119.87	          pls))
119.62/119.87	       = app_encode_app(int, int, bit0, X0),
119.62/119.87	    inference('demod', [status(thm)], ['76', '72'])).
119.62/119.87	tff('78', plain,
119.62/119.87	    ![X0 : int, X1 : int]:
119.62/119.87	      (app_encode_app(int, $o, 
119.62/119.87	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), X1), 
119.62/119.87	         app_encode_app(int, int, bit0, X0))
119.62/119.87	       | ~ app_encode_app(int, $o, 
119.62/119.87	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), X1), 
119.62/119.87	             app_encode_app(int, int, bit1, X0))),
119.62/119.87	    inference('demod', [status(thm)], ['9', '77'])).
119.62/119.87	tff(zf_stmt_150, conjecture,
119.62/119.87	  (app_encode_app(int,$o,
119.62/119.87	                  app_encode_app(int,app_encode_fun(int,$o),ord_less_eq(int),
119.62/119.87	                                 s),
119.62/119.87	                  app_encode_app(int,int,
119.62/119.87	                                 app_encode_app(int,app_encode_fun(int,int),
119.62/119.87	                                                minus_minus(int),
119.62/119.87	                                                app_encode_app(int,int,
119.62/119.87	                                                               app_encode_app(
119.62/119.87	                                                               int,
119.62/119.87	                                                               app_encode_fun(
119.62/119.87	                                                               int,int),
119.62/119.87	                                                               plus_plus(int),
119.62/119.87	                                                               app_encode_app(
119.62/119.87	                                                               int,int,
119.62/119.87	                                                               app_encode_app(
119.62/119.87	                                                               int,
119.62/119.87	                                                               app_encode_fun(
119.62/119.87	                                                               int,int),
119.62/119.87	                                                               times_times(
119.62/119.87	                                                               int),
119.62/119.87	                                                               app_encode_app(
119.62/119.87	                                                               int,int,
119.62/119.87	                                                               number_number_of(
119.62/119.87	                                                               int),
119.62/119.87	                                                               app_encode_app(
119.62/119.87	                                                               int,int,bit0,
119.62/119.87	                                                               app_encode_app(
119.62/119.87	                                                               int,int,bit0,
119.62/119.87	                                                               app_encode_app(
119.62/119.87	                                                               int,int,bit1,
119.62/119.87	                                                               pls))))),m)),
119.62/119.87	                                                               one_one(int))),
119.62/119.87	                                 one_one(int))))).
119.62/119.87	tff(zf_stmt_0, negated_conjecture,
119.62/119.87	  (~
119.62/119.87	    app_encode_app(int,$o,
119.62/119.87	                   app_encode_app(int,app_encode_fun(int,$o),
119.62/119.87	                                  ord_less_eq(int),s),
119.62/119.87	                   app_encode_app(int,int,
119.62/119.87	                                  app_encode_app(int,app_encode_fun(int,int),
119.62/119.87	                                                 minus_minus(int),
119.62/119.87	                                                 app_encode_app(int,int,
119.62/119.87	                                                                app_encode_app(
119.62/119.87	                                                                int,
119.62/119.87	                                                                app_encode_fun(
119.62/119.87	                                                                int,int),
119.62/119.87	                                                                plus_plus(
119.62/119.87	                                                                int),
119.62/119.87	                                                                app_encode_app(
119.62/119.87	                                                                int,int,
119.62/119.87	                                                                app_encode_app(
119.62/119.87	                                                                int,
119.62/119.87	                                                                app_encode_fun(
119.62/119.87	                                                                int,int),
119.62/119.87	                                                                times_times(
119.62/119.87	                                                                int),
119.62/119.87	                                                                app_encode_app(
119.62/119.87	                                                                int,int,
119.62/119.87	                                                                number_number_of(
119.62/119.87	                                                                int),
119.62/119.87	                                                                app_encode_app(
119.62/119.87	                                                                int,int,bit0,
119.62/119.87	                                                                app_encode_app(
119.62/119.87	                                                                int,int,bit0,
119.62/119.87	                                                                app_encode_app(
119.62/119.87	                                                                int,int,bit1,
119.62/119.87	                                                                pls))))),m)),
119.62/119.87	                                                                one_one(int))),
119.62/119.87	                                  one_one(int))))).
119.62/119.87	tff('79', plain,
119.62/119.87	    ~ app_encode_app(int, $o, 
119.62/119.87	        app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), s), 
119.62/119.87	        app_encode_app(int, int, 
119.62/119.87	          app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
119.62/119.87	            app_encode_app(int, int, 
119.62/119.87	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
119.62/119.87	                app_encode_app(int, int, 
119.62/119.87	                  app_encode_app(int, app_encode_fun(int, int), 
119.62/119.87	                    times_times(int), 
119.62/119.87	                    app_encode_app(int, int, number_number_of(int), 
119.62/119.87	                      app_encode_app(int, int, bit0, 
119.62/119.87	                        app_encode_app(int, int, bit0, 
119.62/119.87	                          app_encode_app(int, int, bit1, pls))))), m)), 
119.62/119.87	              one_one(int))), one_one(int))),
119.62/119.87	    inference('cnf', [status(esa)], [zf_stmt_0])).
119.62/119.87	tff(zf_stmt_70, axiom,
119.62/119.87	  (![L1:int,K:int]:
119.62/119.87	     (app_encode_app(int,int,
119.62/119.87	                     app_encode_app(int,app_encode_fun(int,int),
119.62/119.87	                                    times_times(int),
119.62/119.87	                                    app_encode_app(int,int,bit0,K)),
119.62/119.87	                     L1) =
119.62/119.87	      app_encode_app(int,int,bit0,
119.62/119.87	                     app_encode_app(int,int,
119.62/119.87	                                    app_encode_app(int,
119.62/119.87	                                                   app_encode_fun(int,int),
119.62/119.87	                                                   times_times(int),K),
119.62/119.87	                                    L1))))).
119.62/119.87	tff('80', plain,
119.62/119.87	    ![X55 : int, X56 : int]:
119.62/119.87	      app_encode_app(int, int, 
119.62/119.87	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
119.62/119.87	          app_encode_app(int, int, bit0, X55)), X56)
119.62/119.87	       = app_encode_app(int, int, bit0, 
119.62/119.87	           app_encode_app(int, int, 
119.62/119.87	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
119.62/119.87	               X55), X56)),
119.62/119.87	    inference('cnf', [status(esa)], [zf_stmt_70])).
119.62/119.87	tff('81', plain,
119.62/119.87	    ![X0 : int]:
119.62/119.87	      app_encode_app(int, int, 
119.62/119.87	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
119.62/119.87	          app_encode_app(int, int, bit0, X0)), one_one(int))
119.62/119.87	       = app_encode_app(int, int, bit1, 
119.62/119.87	           app_encode_app(int, int, 
119.62/119.87	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
119.62/119.87	               X0), pls)),
119.62/119.87	    inference('sup+', [status(thm)], ['5', '50'])).
119.62/119.87	tff('82', plain,
119.62/119.87	    ![X0 : int]:
119.62/119.87	      app_encode_app(int, int, 
119.62/119.87	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
119.62/119.87	          app_encode_app(int, int, bit0, X0)), pls)
119.62/119.87	       = app_encode_app(int, int, bit0, 
119.62/119.87	           app_encode_app(int, int, 
119.62/119.87	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
119.62/119.87	               X0), pls)),
119.62/119.87	    inference('sup+', [status(thm)], ['13', '69'])).
119.62/119.87	tff(zf_stmt_92, axiom,
119.62/119.87	  (![L1:int,K:int]:
119.62/119.87	     (app_encode_app(int,int,
119.62/119.87	                     app_encode_app(int,app_encode_fun(int,int),
119.62/119.87	                                    plus_plus(int),
119.62/119.87	                                    app_encode_app(int,int,bit1,K)),
119.62/119.87	                     app_encode_app(int,int,bit0,L1)) =
119.62/119.87	      app_encode_app(int,int,bit1,
119.62/119.87	                     app_encode_app(int,int,
119.62/119.87	                                    app_encode_app(int,
119.62/119.87	                                                   app_encode_fun(int,int),
119.62/119.87	                                                   plus_plus(int),K),
119.62/119.87	                                    L1))))).
119.62/119.87	tff('83', plain,
119.62/119.87	    ![X118 : int, X119 : int]:
119.62/119.87	      app_encode_app(int, int, 
119.62/119.87	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
119.62/119.87	          app_encode_app(int, int, bit1, X118)), 
119.62/119.87	        app_encode_app(int, int, bit0, X119))
119.62/119.87	       = app_encode_app(int, int, bit1, 
119.62/119.87	           app_encode_app(int, int, 
119.62/119.87	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
119.62/119.87	               X118), X119)),
119.62/119.87	    inference('cnf', [status(esa)], [zf_stmt_92])).
119.62/119.87	tff('84', plain,
119.62/119.87	    ![X0 : int]:
119.62/119.87	      app_encode_app(int, int, 
119.62/119.87	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
119.62/119.87	          app_encode_app(int, int, bit1, X0)), pls)
119.62/119.87	       = app_encode_app(int, int, bit1, 
119.62/119.87	           app_encode_app(int, int, 
119.62/119.87	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
119.62/119.87	               X0), pls)),
119.62/119.87	    inference('sup+', [status(thm)], ['13', '83'])).
119.62/119.87	tff('85', plain,
119.62/119.87	    app_encode_app(int, int, 
119.62/119.87	      app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
119.62/119.87	        one_one(int)), pls)
119.62/119.87	     = app_encode_app(int, int, bit1, 
119.62/119.87	         app_encode_app(int, int, 
119.62/119.87	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
119.62/119.87	           pls)),
119.62/119.87	    inference('sup+', [status(thm)], ['5', '84'])).
119.62/119.87	tff('86', plain,
119.62/119.87	    app_encode_app(int, int, 
119.62/119.87	      app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
119.62/119.87	        one_one(int)), pls)
119.62/119.87	     = app_encode_app(int, int, 
119.62/119.87	         app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
119.62/119.87	         one_one(int)),
119.62/119.87	    inference('sup+', [status(thm)], ['52', '85'])).
119.62/119.87	tff('87', plain,
119.62/119.87	    app_encode_app(int, int, 
119.62/119.87	      app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
119.62/119.87	        one_one(int)), pls)
119.62/119.87	     = one_one(int),
119.62/119.87	    inference('demod', [status(thm)], ['86', '60'])).
119.62/119.87	tff('88', plain,
119.62/119.87	    ![X0 : int, X1 : int]:
119.62/119.87	      (app_encode_app(int, int, 
119.62/119.87	         app_encode_app(int, app_encode_fun(int, int), times_times(int), 
119.62/119.87	           app_encode_app(int, int, 
119.62/119.87	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
119.62/119.87	               X1), pls)), 
119.62/119.87	         app_encode_app(int, int, number_number_of(int), X0))
119.62/119.87	        = app_encode_app(int, int, 
119.62/119.87	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
119.62/119.87	              app_encode_app(int, int, 
119.62/119.87	                app_encode_app(int, app_encode_fun(int, int), 
119.62/119.87	                  times_times(int), X1), 
119.62/119.87	                app_encode_app(int, int, number_number_of(int), X0))), pls)
119.62/119.87	       | ~ number(int)
119.62/119.87	       | ~ semiring(int)),
119.62/119.87	    inference('sup+', [status(thm)], ['10', '61'])).
119.62/119.87	tff('89', plain,
119.62/119.87	    ![X0 : int, X1 : int]:
119.62/119.87	      (app_encode_app(int, int, 
119.62/119.87	         app_encode_app(int, app_encode_fun(int, int), times_times(int), 
119.62/119.87	           app_encode_app(int, int, 
119.62/119.87	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
119.62/119.87	               X1), pls)), X0)
119.62/119.87	        = app_encode_app(int, int, 
119.62/119.87	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
119.62/119.87	              app_encode_app(int, int, 
119.62/119.87	                app_encode_app(int, app_encode_fun(int, int), 
119.62/119.87	                  times_times(int), X1), X0)), pls)
119.62/119.87	       | ~ $true
119.62/119.87	       | ~ $true),
119.62/119.87	    inference('demod', [status(thm)], ['88', '0', '0', '17', '63'])).
119.62/119.87	tff('90', plain,
119.62/119.87	    ![X0 : int, X1 : int]:
119.62/119.87	      app_encode_app(int, int, 
119.62/119.87	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
119.62/119.87	          app_encode_app(int, int, 
119.62/119.87	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X1), 
119.62/119.87	            pls)), X0)
119.62/119.87	       = app_encode_app(int, int, 
119.62/119.87	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
119.62/119.87	             app_encode_app(int, int, 
119.62/119.87	               app_encode_app(int, app_encode_fun(int, int), 
119.62/119.87	                 times_times(int), X1), X0)), pls),
119.62/119.87	    inference('simplify', [status(thm)], ['89'])).
119.62/119.87	tff('91', plain,
119.62/119.87	    ![X0 : int]:
119.62/119.87	      app_encode_app(int, int, 
119.62/119.87	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
119.62/119.87	          one_one(int)), X0)
119.62/119.87	       = app_encode_app(int, int, 
119.62/119.87	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
119.62/119.87	             app_encode_app(int, int, 
119.62/119.87	               app_encode_app(int, app_encode_fun(int, int), 
119.62/119.87	                 times_times(int), one_one(int)), X0)), pls),
119.62/119.87	    inference('sup+', [status(thm)], ['87', '90'])).
119.62/119.87	tff('92', plain,
119.62/119.87	    ![X0 : int]:
119.62/119.87	      app_encode_app(int, int, 
119.62/119.87	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
119.62/119.87	        X0)
119.62/119.87	       = app_encode_app(int, int, 
119.62/119.87	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
119.62/119.87	             app_encode_app(int, int, 
119.62/119.87	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
119.62/119.87	                 pls), X0)), pls),
119.62/119.87	    inference('demod', [status(thm)], ['91', '14', '14'])).
119.62/119.87	tff('93', plain,
119.62/119.87	    ![X0 : int]:
119.62/119.87	      app_encode_app(int, int, 
119.62/119.87	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
119.62/119.87	        X0)
119.62/119.87	       = app_encode_app(int, int, 
119.62/119.87	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
119.62/119.87	           app_encode_app(int, int, 
119.62/119.87	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
119.62/119.87	               X0), pls)),
119.62/119.87	    inference('demod', [status(thm)], ['92', '45'])).
119.62/119.87	tff('94', plain,
119.62/119.87	    ![X0 : int]:
119.62/119.87	      app_encode_app(int, int, 
119.62/119.87	        app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
119.62/119.87	          app_encode_app(int, int, bit0, X0)), pls)
119.62/119.87	       = app_encode_app(int, int, bit0, 
119.62/119.87	           app_encode_app(int, int, 
119.62/119.87	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
119.62/119.87	               X0), pls)),
119.62/119.87	    inference('sup+', [status(thm)], ['13', '73'])).
119.62/119.87	tff('95', plain,
119.62/119.87	    ~ app_encode_app(int, $o, 
119.62/119.87	        app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), s), 
119.62/119.87	        app_encode_app(int, int, bit0, 
119.62/119.87	          app_encode_app(int, int, bit0, 
119.62/119.87	            app_encode_app(int, int, 
119.62/119.87	              app_encode_app(int, app_encode_fun(int, int), 
119.62/119.87	                minus_minus(int), 
119.62/119.87	                app_encode_app(int, int, 
119.62/119.87	                  app_encode_app(int, app_encode_fun(int, int), 
119.62/119.87	                    plus_plus(int), pls), m)), pls)))),
119.62/119.87	    inference('demod', [status(thm)],
119.62/119.87	              ['79', '5', '0', '80', '80', '14', '81', '82', '45', '93', 
119.62/119.87	               '7', '94'])).
119.62/119.87	tff('96', plain,
119.62/119.87	    ~ app_encode_app(int, $o, 
119.62/119.87	        app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), s), 
119.62/119.87	        app_encode_app(int, int, bit0, 
119.62/119.87	          app_encode_app(int, int, bit0, 
119.62/119.87	            app_encode_app(int, int, 
119.62/119.87	              app_encode_app(int, app_encode_fun(int, int), 
119.62/119.87	                minus_minus(int), m), pls)))),
119.62/119.87	    inference('demod', [status(thm)], ['95', '75'])).
119.62/119.87	tff('97', plain,
119.62/119.87	    ~ app_encode_app(int, $o, 
119.62/119.87	        app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), s), 
119.62/119.87	        app_encode_app(int, int, bit0, app_encode_app(int, int, bit0, m))),
119.62/119.87	    inference('demod', [status(thm)], ['96', '77'])).
119.62/119.87	tff('98', plain,
119.62/119.87	    (~ $true
119.62/119.87	     | ~ app_encode_app(int, $o, 
119.62/119.87	           app_encode_app(int, app_encode_fun(int, $o), ord_less(int), s), 
119.62/119.87	           app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m)))),
119.62/119.87	    inference('sup-', [status(thm)], ['78', '97'])).
119.62/119.87	tff(zf_stmt_36, axiom,
119.62/119.87	  (app_encode_app(int,$o,
119.62/119.87	                  app_encode_app(int,app_encode_fun(int,$o),ord_less_eq(int),
119.62/119.87	                                 zero_zero(int)),
119.62/119.87	                  s) & 
119.62/119.87	   app_encode_app(int,$o,
119.62/119.87	                  app_encode_app(int,app_encode_fun(int,$o),ord_less(int),s),
119.62/119.87	                  app_encode_app(int,int,
119.62/119.87	                                 app_encode_app(int,app_encode_fun(int,int),
119.62/119.87	                                                plus_plus(int),
119.62/119.87	                                                app_encode_app(int,int,
119.62/119.87	                                                               app_encode_app(
119.62/119.87	                                                               int,
119.62/119.87	                                                               app_encode_fun(
119.62/119.87	                                                               int,int),
119.62/119.87	                                                               times_times(
119.62/119.87	                                                               int),
119.62/119.87	                                                               app_encode_app(
119.62/119.87	                                                               int,int,
119.62/119.87	                                                               number_number_of(
119.62/119.87	                                                               int),
119.62/119.87	                                                               app_encode_app(
119.62/119.87	                                                               int,int,bit0,
119.62/119.87	                                                               app_encode_app(
119.62/119.87	                                                               int,int,bit0,
119.62/119.87	                                                               app_encode_app(
119.62/119.87	                                                               int,int,bit1,
119.62/119.87	                                                               pls))))),m)),
119.62/119.87	                                 one_one(int))) & 
119.62/119.87	   app_encode_app(int,$o,
119.62/119.87	                  app_encode_app(int,app_encode_fun(int,$o),
119.62/119.87	                                 app_encode_app(int,
119.62/119.87	                                                app_encode_fun(int,
119.62/119.87	                                                               app_encode_fun(
119.62/119.87	                                                               int,$o)),
119.62/119.87	                                                zcong,s1),
119.62/119.87	                                 s),
119.62/119.87	                  app_encode_app(int,int,
119.62/119.87	                                 app_encode_app(int,app_encode_fun(int,int),
119.62/119.87	                                                plus_plus(int),
119.62/119.87	                                                app_encode_app(int,int,
119.62/119.87	                                                               app_encode_app(
119.62/119.87	                                                               int,
119.62/119.87	                                                               app_encode_fun(
119.62/119.87	                                                               int,int),
119.62/119.87	                                                               times_times(
119.62/119.87	                                                               int),
119.62/119.87	                                                               app_encode_app(
119.62/119.87	                                                               int,int,
119.62/119.87	                                                               number_number_of(
119.62/119.87	                                                               int),
119.62/119.87	                                                               app_encode_app(
119.62/119.87	                                                               int,int,bit0,
119.62/119.87	                                                               app_encode_app(
119.62/119.87	                                                               int,int,bit0,
119.62/119.87	                                                               app_encode_app(
119.62/119.87	                                                               int,int,bit1,
119.62/119.87	                                                               pls))))),m)),
119.62/119.87	                                 one_one(int))))).
119.62/119.87	tff('99', plain,
119.62/119.87	    app_encode_app(int, $o, 
119.62/119.87	      app_encode_app(int, app_encode_fun(int, $o), ord_less(int), s), 
119.62/119.87	      app_encode_app(int, int, 
119.62/119.87	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
119.62/119.87	          app_encode_app(int, int, 
119.62/119.87	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
119.62/119.87	              app_encode_app(int, int, number_number_of(int), 
119.62/119.87	                app_encode_app(int, int, bit0, 
119.62/119.87	                  app_encode_app(int, int, bit0, 
119.62/119.87	                    app_encode_app(int, int, bit1, pls))))), m)), 
119.62/119.87	        one_one(int))),
119.62/119.87	    inference('cnf', [status(esa)], [zf_stmt_36])).
119.62/119.87	tff('100', plain,
119.62/119.87	    app_encode_app(int, $o, 
119.62/119.87	      app_encode_app(int, app_encode_fun(int, $o), ord_less(int), s), 
119.62/119.87	      app_encode_app(int, int, 
119.62/119.87	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
119.62/119.87	          app_encode_app(int, int, 
119.62/119.87	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
119.62/119.87	              app_encode_app(int, int, bit0, 
119.62/119.87	                app_encode_app(int, int, bit0, 
119.62/119.87	                  app_encode_app(int, int, bit1, pls)))), m)), one_one(int))),
119.62/119.87	    inference('demod', [status(thm)], ['99', '0'])).
119.62/119.87	tff('101', plain,
119.62/119.87	    app_encode_app(int, $o, 
119.62/119.87	      app_encode_app(int, app_encode_fun(int, $o), ord_less(int), s), 
119.62/119.87	      app_encode_app(int, int, bit1, 
119.62/119.87	        app_encode_app(int, int, bit0, 
119.62/119.87	          app_encode_app(int, int, 
119.62/119.87	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
119.62/119.87	              app_encode_app(int, int, 
119.62/119.87	                app_encode_app(int, app_encode_fun(int, int), 
119.62/119.87	                  plus_plus(int), pls), m)), pls)))),
119.62/119.87	    inference('demod', [status(thm)],
119.62/119.87	              ['100', '5', '80', '80', '14', '81', '82'])).
119.62/119.87	tff('102', plain,
119.62/119.87	    app_encode_app(int, $o, 
119.62/119.87	      app_encode_app(int, app_encode_fun(int, $o), ord_less(int), s), 
119.62/119.87	      app_encode_app(int, int, bit1, 
119.62/119.87	        app_encode_app(int, int, bit0, 
119.62/119.87	          app_encode_app(int, int, 
119.62/119.87	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
119.62/119.87	              pls), m)))),
119.62/119.87	    inference('demod', [status(thm)], ['101', '92'])).
119.62/119.87	tff('103', plain,
119.62/119.87	    app_encode_app(int, $o, 
119.62/119.87	      app_encode_app(int, app_encode_fun(int, $o), ord_less(int), s), 
119.62/119.87	      app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m))),
119.62/119.87	    inference('demod', [status(thm)], ['102', '72'])).
119.62/119.87	tff('104', plain, (~ $true | ~ $true),
119.62/119.87	    inference('demod', [status(thm)], ['98', '103'])).
119.62/119.87	tff('105', plain, $false, inference('simplify', [status(thm)], ['104'])).
119.62/119.87	
119.62/119.87	% SZS output end Refutation
119.62/119.87	EOF
