0.00/0.01	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.01	% app-encoded or not : appext
0.00/0.01	% Variant    : fo
0.00/0.01	% Ordering    : rpo6
0.00/0.01	% Command    : 
0.00/0.01	#!/bin/sh
0.00/0.01	
0.00/0.01	./zipperposition.native ${1:+"$1"} \
0.00/0.01	  -i tptp \
0.00/0.01	  -o tptp \
0.00/0.01	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.01	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.01	  --no-ho \
0.00/0.01	  --no-avatar \
0.00/0.01	  --no-induction \
0.00/0.01	  --no-unif-pattern \
0.00/0.01	  --ord $2 \
0.00/0.01	  --simultaneous-sup false \
0.00/0.01	  --no-max-vars \
0.00/0.01	  --no-fool
0.00/0.20	% Computer   : n106.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 08:22:40 CST 2018
0.00/0.50	% done 573 iterations in 0.288s
0.00/0.50	% SZS status Theorem for 'stdin'
0.00/0.50	% SZS output start Refutation
0.00/0.50	tff(zf_stmt_19, conjecture,
0.00/0.50	  (~
0.00/0.50	    (?[X1:algorithm]:
0.00/0.50	       (![Y1:program,Z1:input]:
0.00/0.50	          app_encode_app(input,$o,
0.00/0.50	                         app_encode_app(program,app_encode_fun(input,$o),
0.00/0.50	                                        app_encode_app(algorithm,
0.00/0.50	                                                       app_encode_fun(
0.00/0.50	                                                       program,
0.00/0.50	                                                       app_encode_fun(
0.00/0.50	                                                       input,$o)),decides,X1),
0.00/0.50	                                        Y1),
0.00/0.50	                         Z1))))).
0.00/0.50	tff(zf_stmt_0, negated_conjecture,
0.00/0.50	  (?[X1:algorithm]:
0.00/0.50	     (![Y1:program,Z1:input]:
0.00/0.50	        app_encode_app(input,$o,
0.00/0.50	                       app_encode_app(program,app_encode_fun(input,$o),
0.00/0.50	                                      app_encode_app(algorithm,
0.00/0.50	                                                     app_encode_fun(program,
0.00/0.50	                                                                    app_encode_fun(
0.00/0.50	                                                                    input,$o)),
0.00/0.50	                                                     decides,X1),
0.00/0.50	                                      Y1),
0.00/0.50	                       Z1)))).
0.00/0.50	tff('0', plain,
0.00/0.50	    ![X25 : program, X26 : input]:
0.00/0.50	      app_encode_app(input, $o, 
0.00/0.50	        app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.50	          app_encode_app(algorithm, 
0.00/0.50	            app_encode_fun(program, app_encode_fun(input, $o)), decides, 
0.00/0.50	            sk_X1), X25), X26),
0.00/0.50	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.50	tff(zf_stmt_15, axiom,
0.00/0.50	  ((?[X:algorithm]:
0.00/0.50	      (![Y:program,Z:input]:
0.00/0.50	         app_encode_app(input,$o,
0.00/0.50	                        app_encode_app(program,app_encode_fun(input,$o),
0.00/0.50	                                       app_encode_app(algorithm,
0.00/0.50	                                                      app_encode_fun(
0.00/0.50	                                                      program,
0.00/0.50	                                                      app_encode_fun(
0.00/0.50	                                                      input,$o)),decides,X),
0.00/0.50	                                       Y),
0.00/0.50	                        Z))) =>
0.00/0.50	   (?[W:program]:
0.00/0.50	      (![Y:program,Z:input]:
0.00/0.50	         app_encode_app(input,$o,
0.00/0.50	                        app_encode_app(program,app_encode_fun(input,$o),
0.00/0.50	                                       app_encode_app(algorithm,
0.00/0.50	                                                      app_encode_fun(
0.00/0.50	                                                      program,
0.00/0.50	                                                      app_encode_fun(
0.00/0.50	                                                      input,$o)),decides,
0.00/0.50	                                                      app_encode_app(
0.00/0.50	                                                      program,algorithm,
0.00/0.50	                                                      algorithm_of,W)),
0.00/0.50	                                       Y),
0.00/0.50	                        Z))))).
0.00/0.50	tff('1', plain,
0.00/0.50	    ![X4 : program, X5 : input, X6 : algorithm]:
0.00/0.50	      (app_encode_app(input, $o, 
0.00/0.50	         app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.50	           app_encode_app(algorithm, 
0.00/0.50	             app_encode_fun(program, app_encode_fun(input, $o)), decides, 
0.00/0.50	             app_encode_app(program, algorithm, algorithm_of, sk_W)), X4), 
0.00/0.50	         X5)
0.00/0.50	       | ~ app_encode_app(input, $o, 
0.00/0.50	             app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.50	               app_encode_app(algorithm, 
0.00/0.50	                 app_encode_fun(program, app_encode_fun(input, $o)), 
0.00/0.50	                 decides, X6), sk_Y(X6)), sk_Z1(X6))),
0.00/0.50	    inference('cnf', [status(esa)], [zf_stmt_15])).
0.00/0.50	tff('2', plain,
0.00/0.50	    ![X0 : input, X1 : program]:
0.00/0.50	      (~ $true
0.00/0.50	       | app_encode_app(input, $o, 
0.00/0.50	           app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.50	             app_encode_app(algorithm, 
0.00/0.50	               app_encode_fun(program, app_encode_fun(input, $o)), decides, 
0.00/0.50	               app_encode_app(program, algorithm, algorithm_of, sk_W)), X1), 
0.00/0.50	           X0)),
0.00/0.50	    inference('sup-', [status(thm)], ['0', '1'])).
0.00/0.50	tff('3', plain,
0.00/0.50	    ![X0 : input, X1 : program]:
0.00/0.50	      app_encode_app(input, $o, 
0.00/0.50	        app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.50	          app_encode_app(algorithm, 
0.00/0.50	            app_encode_fun(program, app_encode_fun(input, $o)), decides, 
0.00/0.50	            app_encode_app(program, algorithm, algorithm_of, sk_W)), X1), X0),
0.00/0.50	    inference('simplify', [status(thm)], ['2'])).
0.00/0.50	tff(zf_stmt_2, axiom,
0.00/0.50	  (![X:app_encode_fun(Alpha,Beta),Y:app_encode_fun(Alpha,Beta)]:
0.00/0.50	     ((![Z:Alpha]:
0.00/0.50	         (app_encode_app(Alpha,Beta,X,Z) = app_encode_app(Alpha,Beta,Y,Z))) =>
0.00/0.50	      (X = Y)))).
0.00/0.50	tff('4', plain,
0.00/0.50	    ![X0 : $tType, X1 : $tType, X2 : app_encode_fun(X0, X1), 
0.00/0.50	      X3 : app_encode_fun(X0, X1)]:
0.00/0.50	      (X3 = X2
0.00/0.50	       | app_encode_app(X0, X1, X3, sk_Z(X1, X0, X2, X3))
0.00/0.50	          != app_encode_app(X0, X1, X2, sk_Z(X1, X0, X2, X3))),
0.00/0.50	    inference('cnf', [status(esa)], [zf_stmt_2])).
0.00/0.50	tff('5', plain,
0.00/0.50	    ![X0 : program, X1 : app_encode_fun(input, $o)]:
0.00/0.50	      ($true
0.00/0.50	        != app_encode_app(input, $o, X1, 
0.00/0.50	             sk_Z($o, input, X1, 
0.00/0.50	               app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.50	                 app_encode_app(algorithm, 
0.00/0.50	                   app_encode_fun(program, app_encode_fun(input, $o)), 
0.00/0.50	                   decides, sk_X1), X0)))
0.00/0.50	       | app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.50	           app_encode_app(algorithm, 
0.00/0.50	             app_encode_fun(program, app_encode_fun(input, $o)), decides, 
0.00/0.50	             sk_X1), X0)
0.00/0.50	          = X1),
0.00/0.50	    inference('sup-', [status(thm)], ['0', '4'])).
0.00/0.50	tff('6', plain,
0.00/0.50	    ![X0 : program, X1 : program]:
0.00/0.50	      ($true != $true
0.00/0.50	       | app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.50	           app_encode_app(algorithm, 
0.00/0.50	             app_encode_fun(program, app_encode_fun(input, $o)), decides, 
0.00/0.50	             sk_X1), X0)
0.00/0.50	          = app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.50	              app_encode_app(algorithm, 
0.00/0.50	                app_encode_fun(program, app_encode_fun(input, $o)), decides, 
0.00/0.50	                app_encode_app(program, algorithm, algorithm_of, sk_W)), X1)),
0.00/0.50	    inference('sup-', [status(thm)], ['3', '5'])).
0.00/0.50	tff('7', plain,
0.00/0.50	    ![X0 : program, X1 : program]:
0.00/0.50	      app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.50	        app_encode_app(algorithm, 
0.00/0.50	          app_encode_fun(program, app_encode_fun(input, $o)), decides, sk_X1), 
0.00/0.50	        X0)
0.00/0.50	       = app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.50	           app_encode_app(algorithm, 
0.00/0.50	             app_encode_fun(program, app_encode_fun(input, $o)), decides, 
0.00/0.50	             app_encode_app(program, algorithm, algorithm_of, sk_W)), X1),
0.00/0.50	    inference('simplify', [status(thm)], ['6'])).
0.00/0.50	tff('8', plain,
0.00/0.50	    ![X0 : program, X1 : program]:
0.00/0.50	      ($true != $true
0.00/0.50	       | app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.50	           app_encode_app(algorithm, 
0.00/0.50	             app_encode_fun(program, app_encode_fun(input, $o)), decides, 
0.00/0.50	             sk_X1), X0)
0.00/0.50	          = app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.50	              app_encode_app(algorithm, 
0.00/0.50	                app_encode_fun(program, app_encode_fun(input, $o)), decides, 
0.00/0.50	                sk_X1), X1)),
0.00/0.50	    inference('sup-', [status(thm)], ['0', '5'])).
0.00/0.50	tff('9', plain,
0.00/0.50	    ![X0 : program, X1 : program]:
0.00/0.50	      app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.50	        app_encode_app(algorithm, 
0.00/0.50	          app_encode_fun(program, app_encode_fun(input, $o)), decides, sk_X1), 
0.00/0.50	        X0)
0.00/0.50	       = app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.50	           app_encode_app(algorithm, 
0.00/0.50	             app_encode_fun(program, app_encode_fun(input, $o)), decides, 
0.00/0.50	             sk_X1), X1),
0.00/0.50	    inference('simplify', [status(thm)], ['8'])).
0.00/0.50	tff('10', plain,
0.00/0.50	    ![X0 : program, X1 : app_encode_fun(program, app_encode_fun(input, $o))]:
0.00/0.50	      (app_encode_app(program, app_encode_fun(input, $o), X1, 
0.00/0.50	         sk_Z(app_encode_fun(input, $o), program, 
0.00/0.50	           app_encode_app(algorithm, 
0.00/0.50	             app_encode_fun(program, app_encode_fun(input, $o)), decides, 
0.00/0.50	             sk_X1), X1))
0.00/0.50	        != app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.50	             app_encode_app(algorithm, 
0.00/0.50	               app_encode_fun(program, app_encode_fun(input, $o)), decides, 
0.00/0.50	               sk_X1), X0)
0.00/0.50	       | X1
0.00/0.50	          = app_encode_app(algorithm, 
0.00/0.50	              app_encode_fun(program, app_encode_fun(input, $o)), decides, 
0.00/0.50	              sk_X1)),
0.00/0.50	    inference('sup-', [status(thm)], ['9', '4'])).
0.00/0.50	tff('11', plain,
0.00/0.50	    ![X0 : program, X1 : program]:
0.00/0.50	      (app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.50	         app_encode_app(algorithm, 
0.00/0.50	           app_encode_fun(program, app_encode_fun(input, $o)), decides, 
0.00/0.50	           sk_X1), X0)
0.00/0.50	        != app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.50	             app_encode_app(algorithm, 
0.00/0.50	               app_encode_fun(program, app_encode_fun(input, $o)), decides, 
0.00/0.50	               sk_X1), X1)
0.00/0.50	       | app_encode_app(algorithm, 
0.00/0.50	           app_encode_fun(program, app_encode_fun(input, $o)), decides, 
0.00/0.50	           app_encode_app(program, algorithm, algorithm_of, sk_W))
0.00/0.50	          = app_encode_app(algorithm, 
0.00/0.50	              app_encode_fun(program, app_encode_fun(input, $o)), decides, 
0.00/0.50	              sk_X1)),
0.00/0.50	    inference('sup-', [status(thm)], ['7', '10'])).
0.00/0.50	tff(zf_stmt_16, axiom,
0.00/0.50	  (![W:program,Y:program,Z:input]:
0.00/0.50	     (app_encode_app(input,$o,
0.00/0.50	                     app_encode_app(program,app_encode_fun(input,$o),
0.00/0.50	                                    app_encode_app(algorithm,
0.00/0.50	                                                   app_encode_fun(program,
0.00/0.50	                                                                  app_encode_fun(
0.00/0.50	                                                                  input,$o)),
0.00/0.50	                                                   decides,
0.00/0.50	                                                   app_encode_app(program,
0.00/0.50	                                                                  algorithm,
0.00/0.50	                                                                  algorithm_of,
0.00/0.50	                                                                  W)),
0.00/0.50	                                    Y),
0.00/0.50	                     Z) =>
0.00/0.50	      (![Y:program,Z:input]:
0.00/0.50	         ((app_encode_app(input,$o,
0.00/0.50	                          app_encode_app(program,app_encode_fun(input,$o),
0.00/0.50	                                         halts2,Y),
0.00/0.50	                          Z) =>
0.00/0.50	           (app_encode_app(input,$o,
0.00/0.50	                           app_encode_app(program,app_encode_fun(input,$o),
0.00/0.50	                                          app_encode_app(program,
0.00/0.50	                                                         app_encode_fun(
0.00/0.50	                                                         program,
0.00/0.50	                                                         app_encode_fun(
0.00/0.50	                                                         input,$o)),halts3,W),
0.00/0.50	                                          Y),
0.00/0.50	                           Z) & 
0.00/0.50	            app_encode_app(output,$o,
0.00/0.50	                           app_encode_app(program,app_encode_fun(output,$o),
0.00/0.50	                                          outputs,W),
0.00/0.50	                           good))) & 
0.00/0.50	          ((~
0.00/0.50	             app_encode_app(input,$o,
0.00/0.50	                            app_encode_app(program,app_encode_fun(input,$o),
0.00/0.50	                                           halts2,Y),
0.00/0.50	                            Z)) =>
0.00/0.50	           (app_encode_app(input,$o,
0.00/0.50	                           app_encode_app(program,app_encode_fun(input,$o),
0.00/0.50	                                          app_encode_app(program,
0.00/0.50	                                                         app_encode_fun(
0.00/0.50	                                                         program,
0.00/0.50	                                                         app_encode_fun(
0.00/0.50	                                                         input,$o)),halts3,W),
0.00/0.50	                                          Y),
0.00/0.50	                           Z) & 
0.00/0.50	            app_encode_app(output,$o,
0.00/0.50	                           app_encode_app(program,app_encode_fun(output,$o),
0.00/0.50	                                          outputs,W),
0.00/0.50	                           bad)))))))).
0.00/0.50	tff('12', plain,
0.00/0.50	    ![X7 : program, X9 : program, X10 : program, X11 : input, X12 : input]:
0.00/0.50	      (app_encode_app(input, $o, 
0.00/0.50	         app_encode_app(program, app_encode_fun(input, $o), halts2, X7), X12)
0.00/0.50	       | app_encode_app(input, $o, 
0.00/0.50	           app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.50	             app_encode_app(program, 
0.00/0.50	               app_encode_fun(program, app_encode_fun(input, $o)), halts3, 
0.00/0.50	               X9), X7), X12)
0.00/0.50	       | ~ app_encode_app(input, $o, 
0.00/0.50	             app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.50	               app_encode_app(algorithm, 
0.00/0.50	                 app_encode_fun(program, app_encode_fun(input, $o)), 
0.00/0.50	                 decides, 
0.00/0.50	                 app_encode_app(program, algorithm, algorithm_of, X9)), X10), 
0.00/0.50	             X11)),
0.00/0.50	    inference('cnf', [status(esa)], [zf_stmt_16])).
0.00/0.50	tff('13', plain,
0.00/0.50	    ![X7 : program, X8 : input, X9 : program, X10 : program, X11 : input]:
0.00/0.50	      (~ app_encode_app(input, $o, 
0.00/0.50	           app_encode_app(program, app_encode_fun(input, $o), halts2, X7), 
0.00/0.50	           X8)
0.00/0.50	       | app_encode_app(input, $o, 
0.00/0.50	           app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.50	             app_encode_app(program, 
0.00/0.50	               app_encode_fun(program, app_encode_fun(input, $o)), halts3, 
0.00/0.50	               X9), X7), X8)
0.00/0.50	       | ~ app_encode_app(input, $o, 
0.00/0.50	             app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.50	               app_encode_app(algorithm, 
0.00/0.50	                 app_encode_fun(program, app_encode_fun(input, $o)), 
0.00/0.50	                 decides, 
0.00/0.50	                 app_encode_app(program, algorithm, algorithm_of, X9)), X10), 
0.00/0.50	             X11)),
0.00/0.50	    inference('cnf', [status(esa)], [zf_stmt_16])).
0.00/0.50	tff('14', plain,
0.00/0.50	    ![X7 : program, X9 : program, X10 : program, X11 : input, X12 : input]:
0.00/0.50	      (~ app_encode_app(input, $o, 
0.00/0.50	           app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.50	             app_encode_app(algorithm, 
0.00/0.50	               app_encode_fun(program, app_encode_fun(input, $o)), decides, 
0.00/0.50	               app_encode_app(program, algorithm, algorithm_of, X9)), X10), 
0.00/0.50	           X11)
0.00/0.50	       | app_encode_app(input, $o, 
0.00/0.50	           app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.50	             app_encode_app(program, 
0.00/0.50	               app_encode_fun(program, app_encode_fun(input, $o)), halts3, 
0.00/0.50	               X9), X7), X12)),
0.00/0.50	    inference('clc', [status(thm)], ['12', '13'])).
0.00/0.50	tff('15', plain,
0.00/0.50	    ![X0 : program, X1 : input, X3 : input, X4 : program]:
0.00/0.50	      (~ app_encode_app(input, $o, 
0.00/0.50	           app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.50	             app_encode_app(algorithm, 
0.00/0.50	               app_encode_fun(program, app_encode_fun(input, $o)), decides, 
0.00/0.50	               sk_X1), X0), X1)
0.00/0.50	       | app_encode_app(input, $o, 
0.00/0.50	           app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.50	             app_encode_app(program, 
0.00/0.50	               app_encode_fun(program, app_encode_fun(input, $o)), halts3, 
0.00/0.50	               sk_W), X4), X3)),
0.00/0.50	    inference('sup-', [status(thm)], ['7', '14'])).
0.00/0.50	tff('16', plain,
0.00/0.50	    ![X3 : input, X4 : program]:
0.00/0.50	      (~ $true
0.00/0.50	       | app_encode_app(input, $o, 
0.00/0.50	           app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.50	             app_encode_app(program, 
0.00/0.50	               app_encode_fun(program, app_encode_fun(input, $o)), halts3, 
0.00/0.50	               sk_W), X4), X3)),
0.00/0.50	    inference('demod', [status(thm)], ['15', '0'])).
0.00/0.50	tff('17', plain,
0.00/0.50	    ![X3 : input, X4 : program]:
0.00/0.50	      app_encode_app(input, $o, 
0.00/0.50	        app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.50	          app_encode_app(program, 
0.00/0.50	            app_encode_fun(program, app_encode_fun(input, $o)), halts3, sk_W), 
0.00/0.50	          X4), X3),
0.00/0.50	    inference('simplify', [status(thm)], ['16'])).
0.00/0.50	tff('18', plain,
0.00/0.50	    ![X0 : program, X1 : program]:
0.00/0.50	      ($true != $true
0.00/0.50	       | app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.50	           app_encode_app(algorithm, 
0.00/0.50	             app_encode_fun(program, app_encode_fun(input, $o)), decides, 
0.00/0.50	             sk_X1), X0)
0.00/0.50	          = app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.50	              app_encode_app(program, 
0.00/0.50	                app_encode_fun(program, app_encode_fun(input, $o)), halts3, 
0.00/0.50	                sk_W), X1)),
0.00/0.50	    inference('sup-', [status(thm)], ['17', '5'])).
0.00/0.50	tff('19', plain,
0.00/0.50	    ![X0 : program, X1 : program]:
0.00/0.50	      app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.50	        app_encode_app(algorithm, 
0.00/0.50	          app_encode_fun(program, app_encode_fun(input, $o)), decides, sk_X1), 
0.00/0.50	        X0)
0.00/0.50	       = app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.50	           app_encode_app(program, 
0.00/0.50	             app_encode_fun(program, app_encode_fun(input, $o)), halts3, 
0.00/0.50	             sk_W), X1),
0.00/0.50	    inference('simplify', [status(thm)], ['18'])).
0.00/0.50	tff('20', plain,
0.00/0.50	    ![X0 : program, X1 : program]:
0.00/0.50	      (app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.50	         app_encode_app(algorithm, 
0.00/0.50	           app_encode_fun(program, app_encode_fun(input, $o)), decides, 
0.00/0.50	           sk_X1), X0)
0.00/0.50	        != app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.50	             app_encode_app(program, 
0.00/0.50	               app_encode_fun(program, app_encode_fun(input, $o)), halts3, 
0.00/0.50	               sk_W), X1)
0.00/0.50	       | app_encode_app(algorithm, 
0.00/0.50	           app_encode_fun(program, app_encode_fun(input, $o)), decides, 
0.00/0.50	           app_encode_app(program, algorithm, algorithm_of, sk_W))
0.00/0.50	          = app_encode_app(algorithm, 
0.00/0.50	              app_encode_fun(program, app_encode_fun(input, $o)), decides, 
0.00/0.50	              sk_X1)),
0.00/0.50	    inference('demod', [status(thm)], ['11', '19'])).
0.00/0.50	tff('21', plain,
0.00/0.50	    ![X0 : program, X1 : app_encode_fun(program, app_encode_fun(input, $o))]:
0.00/0.50	      (app_encode_app(program, app_encode_fun(input, $o), X1, 
0.00/0.50	         sk_Z(app_encode_fun(input, $o), program, 
0.00/0.50	           app_encode_app(program, 
0.00/0.50	             app_encode_fun(program, app_encode_fun(input, $o)), halts3, 
0.00/0.50	             sk_W), X1))
0.00/0.50	        != app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.50	             app_encode_app(algorithm, 
0.00/0.50	               app_encode_fun(program, app_encode_fun(input, $o)), decides, 
0.00/0.50	               sk_X1), X0)
0.00/0.50	       | X1
0.00/0.50	          = app_encode_app(program, 
0.00/0.50	              app_encode_fun(program, app_encode_fun(input, $o)), halts3, 
0.00/0.50	              sk_W)),
0.00/0.50	    inference('sup-', [status(thm)], ['19', '4'])).
0.00/0.50	tff('22', plain,
0.00/0.50	    app_encode_app(algorithm, 
0.00/0.50	      app_encode_fun(program, app_encode_fun(input, $o)), decides, sk_X1)
0.00/0.50	     = app_encode_app(program, 
0.00/0.50	         app_encode_fun(program, app_encode_fun(input, $o)), halts3, sk_W),
0.00/0.50	    inference('eq_res', [status(thm)], ['21'])).
0.00/0.50	tff('23', plain,
0.00/0.50	    ![X0 : program, X1 : program]:
0.00/0.50	      (app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.50	         app_encode_app(program, 
0.00/0.50	           app_encode_fun(program, app_encode_fun(input, $o)), halts3, sk_W), 
0.00/0.50	         X0)
0.00/0.50	        != app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.50	             app_encode_app(program, 
0.00/0.50	               app_encode_fun(program, app_encode_fun(input, $o)), halts3, 
0.00/0.50	               sk_W), X1)
0.00/0.50	       | app_encode_app(algorithm, 
0.00/0.50	           app_encode_fun(program, app_encode_fun(input, $o)), decides, 
0.00/0.50	           app_encode_app(program, algorithm, algorithm_of, sk_W))
0.00/0.50	          = app_encode_app(program, 
0.00/0.50	              app_encode_fun(program, app_encode_fun(input, $o)), halts3, 
0.00/0.50	              sk_W)),
0.00/0.50	    inference('demod', [status(thm)], ['20', '22', '22'])).
0.00/0.50	tff('24', plain,
0.00/0.50	    ![X0 : program, X1 : program]:
0.00/0.50	      app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.50	        app_encode_app(program, 
0.00/0.50	          app_encode_fun(program, app_encode_fun(input, $o)), halts3, sk_W), 
0.00/0.50	        X0)
0.00/0.50	       = app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.50	           app_encode_app(algorithm, 
0.00/0.50	             app_encode_fun(program, app_encode_fun(input, $o)), decides, 
0.00/0.50	             sk_X1), X1),
0.00/0.50	    inference('sup+', [status(thm)], ['19', '9'])).
0.00/0.50	tff('25', plain,
0.00/0.50	    ![X0 : program, X1 : program]:
0.00/0.50	      app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.50	        app_encode_app(program, 
0.00/0.50	          app_encode_fun(program, app_encode_fun(input, $o)), halts3, sk_W), 
0.00/0.50	        X0)
0.00/0.50	       = app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.50	           app_encode_app(program, 
0.00/0.50	             app_encode_fun(program, app_encode_fun(input, $o)), halts3, 
0.00/0.50	             sk_W), X1),
0.00/0.50	    inference('demod', [status(thm)], ['24', '19'])).
0.00/0.50	tff('26', plain,
0.00/0.50	    app_encode_app(algorithm, 
0.00/0.50	      app_encode_fun(program, app_encode_fun(input, $o)), decides, 
0.00/0.50	      app_encode_app(program, algorithm, algorithm_of, sk_W))
0.00/0.50	     = app_encode_app(program, 
0.00/0.50	         app_encode_fun(program, app_encode_fun(input, $o)), halts3, sk_W),
0.00/0.50	    inference('clc', [status(thm)], ['23', '25'])).
0.00/0.50	tff(zf_stmt_17, axiom,
0.00/0.50	  ((?[W:program]:
0.00/0.50	      (![Y:program]:
0.00/0.50	         (((~
0.00/0.50	             app_encode_app(input,$o,
0.00/0.50	                            app_encode_app(program,app_encode_fun(input,$o),
0.00/0.50	                                           halts2,Y),
0.00/0.50	                            app_encode_app(program,input,as_input,Y))) =>
0.00/0.50	           (app_encode_app(output,$o,
0.00/0.50	                           app_encode_app(program,app_encode_fun(output,$o),
0.00/0.50	                                          outputs,W),
0.00/0.50	                           bad) & 
0.00/0.50	            app_encode_app(input,$o,
0.00/0.50	                           app_encode_app(program,app_encode_fun(input,$o),
0.00/0.50	                                          app_encode_app(program,
0.00/0.50	                                                         app_encode_fun(
0.00/0.50	                                                         program,
0.00/0.50	                                                         app_encode_fun(
0.00/0.50	                                                         input,$o)),halts3,W),
0.00/0.50	                                          Y),
0.00/0.50	                           app_encode_app(program,input,as_input,Y)))) & 
0.00/0.50	          (app_encode_app(input,$o,
0.00/0.50	                          app_encode_app(program,app_encode_fun(input,$o),
0.00/0.50	                                         halts2,Y),
0.00/0.50	                          app_encode_app(program,input,as_input,Y)) =>
0.00/0.50	           (app_encode_app(output,$o,
0.00/0.50	                           app_encode_app(program,app_encode_fun(output,$o),
0.00/0.50	                                          outputs,W),
0.00/0.50	                           good) & 
0.00/0.50	            app_encode_app(input,$o,
0.00/0.50	                           app_encode_app(program,app_encode_fun(input,$o),
0.00/0.50	                                          app_encode_app(program,
0.00/0.50	                                                         app_encode_fun(
0.00/0.50	                                                         program,
0.00/0.50	                                                         app_encode_fun(
0.00/0.50	                                                         input,$o)),halts3,W),
0.00/0.50	                                          Y),
0.00/0.50	                           app_encode_app(program,input,as_input,Y))))))) =>
0.00/0.50	   (?[V:program]:
0.00/0.50	      (![Y:program]:
0.00/0.50	         (((~
0.00/0.50	             app_encode_app(input,$o,
0.00/0.50	                            app_encode_app(program,app_encode_fun(input,$o),
0.00/0.50	                                           halts2,Y),
0.00/0.50	                            app_encode_app(program,input,as_input,Y))) =>
0.00/0.50	           (app_encode_app(output,$o,
0.00/0.50	                           app_encode_app(program,app_encode_fun(output,$o),
0.00/0.50	                                          outputs,V),
0.00/0.50	                           bad) & 
0.00/0.50	            app_encode_app(input,$o,
0.00/0.50	                           app_encode_app(program,app_encode_fun(input,$o),
0.00/0.50	                                          halts2,V),
0.00/0.50	                           app_encode_app(program,input,as_input,Y)))) & 
0.00/0.50	          (app_encode_app(input,$o,
0.00/0.50	                          app_encode_app(program,app_encode_fun(input,$o),
0.00/0.50	                                         halts2,Y),
0.00/0.50	                          app_encode_app(program,input,as_input,Y)) =>
0.00/0.50	           (app_encode_app(output,$o,
0.00/0.50	                           app_encode_app(program,app_encode_fun(output,$o),
0.00/0.50	                                          outputs,V),
0.00/0.50	                           good) & 
0.00/0.50	            app_encode_app(input,$o,
0.00/0.50	                           app_encode_app(program,app_encode_fun(input,$o),
0.00/0.50	                                          halts2,V),
0.00/0.50	                           app_encode_app(program,input,as_input,Y))))))))).
0.00/0.50	tff(zf_stmt_1, axiom,
0.00/0.50	  (((~
0.00/0.50	      app_encode_app(input,$o,
0.00/0.50	                     app_encode_app(program,app_encode_fun(input,$o),halts2,Y),
0.00/0.50	                     app_encode_app(program,input,as_input,Y))) =>
0.00/0.50	    (app_encode_app(input,$o,
0.00/0.50	                    app_encode_app(program,app_encode_fun(input,$o),
0.00/0.50	                                   app_encode_app(program,
0.00/0.50	                                                  app_encode_fun(program,
0.00/0.50	                                                                 app_encode_fun(
0.00/0.50	                                                                 input,$o)),
0.00/0.50	                                                  halts3,W),
0.00/0.50	                                   Y),
0.00/0.50	                    app_encode_app(program,input,as_input,Y)) & 
0.00/0.50	     app_encode_app(output,$o,
0.00/0.50	                    app_encode_app(program,app_encode_fun(output,$o),outputs,
0.00/0.50	                                   W),
0.00/0.50	                    bad))) =>
0.00/0.50	   zip_tseitin0(Y,W))).
0.00/0.50	tff('27', plain,
0.00/0.50	    ![X13 : program, X14 : program]:
0.00/0.50	      (zip_tseitin0(X13, X14)
0.00/0.50	       | ~ app_encode_app(input, $o, 
0.00/0.50	             app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.50	               app_encode_app(program, 
0.00/0.50	                 app_encode_fun(program, app_encode_fun(input, $o)), halts3, 
0.00/0.50	                 X14), X13), app_encode_app(program, input, as_input, X13))
0.00/0.50	       | ~ app_encode_app(output, $o, 
0.00/0.50	             app_encode_app(program, app_encode_fun(output, $o), outputs, 
0.00/0.50	               X14), bad)),
0.00/0.50	    inference('cnf', [status(esa)], [zf_stmt_1])).
0.00/0.50	tff(zf_stmt_2, axiom,
0.00/0.50	  ((app_encode_app(input,$o,
0.00/0.50	                   app_encode_app(program,app_encode_fun(input,$o),halts2,Y),
0.00/0.50	                   app_encode_app(program,input,as_input,Y)) =>
0.00/0.50	    (app_encode_app(input,$o,
0.00/0.50	                    app_encode_app(program,app_encode_fun(input,$o),
0.00/0.50	                                   app_encode_app(program,
0.00/0.50	                                                  app_encode_fun(program,
0.00/0.50	                                                                 app_encode_fun(
0.00/0.50	                                                                 input,$o)),
0.00/0.50	                                                  halts3,W),
0.00/0.50	                                   Y),
0.00/0.50	                    app_encode_app(program,input,as_input,Y)) & 
0.00/0.50	     app_encode_app(output,$o,
0.00/0.50	                    app_encode_app(program,app_encode_fun(output,$o),outputs,
0.00/0.50	                                   W),
0.00/0.50	                    good))) =>
0.00/0.50	   zip_tseitin1(Y,W))).
0.00/0.50	tff('28', plain,
0.00/0.50	    ![X13 : program, X14 : program]:
0.00/0.50	      (zip_tseitin1(X13, X14)
0.00/0.50	       | app_encode_app(input, $o, 
0.00/0.50	           app_encode_app(program, app_encode_fun(input, $o), halts2, X13), 
0.00/0.50	           app_encode_app(program, input, as_input, X13))),
0.00/0.50	    inference('cnf', [status(esa)], [zf_stmt_2])).
0.00/0.50	tff(zf_stmt_3, type, zip_tseitin4 : (program * program) > $o).
0.00/0.50	tff(zf_stmt_4, axiom,
0.00/0.50	  (zip_tseitin4(Y,V) =>
0.00/0.50	   ((app_encode_app(input,$o,
0.00/0.50	                    app_encode_app(program,app_encode_fun(input,$o),halts2,Y),
0.00/0.50	                    app_encode_app(program,input,as_input,Y)) =>
0.00/0.50	     zip_tseitin3(Y,V)) & 
0.00/0.50	    ((~
0.00/0.50	       app_encode_app(input,$o,
0.00/0.50	                      app_encode_app(program,app_encode_fun(input,$o),halts2,
0.00/0.50	                                     Y),
0.00/0.50	                      app_encode_app(program,input,as_input,Y))) =>
0.00/0.50	     zip_tseitin2(Y,V))))).
0.00/0.50	tff(zf_stmt_5, type, zip_tseitin3 : (program * program) > $o).
0.00/0.50	tff(zf_stmt_6, axiom,
0.00/0.50	  (zip_tseitin3(Y,V) =>
0.00/0.50	   (app_encode_app(input,$o,
0.00/0.50	                   app_encode_app(program,app_encode_fun(input,$o),halts2,V),
0.00/0.50	                   app_encode_app(program,input,as_input,Y)) & 
0.00/0.50	    app_encode_app(output,$o,
0.00/0.50	                   app_encode_app(program,app_encode_fun(output,$o),outputs,V),
0.00/0.50	                   good)))).
0.00/0.50	tff(zf_stmt_7, type, zip_tseitin2 : (program * program) > $o).
0.00/0.50	tff(zf_stmt_8, axiom,
0.00/0.50	  (zip_tseitin2(Y,V) =>
0.00/0.50	   (app_encode_app(input,$o,
0.00/0.50	                   app_encode_app(program,app_encode_fun(input,$o),halts2,V),
0.00/0.50	                   app_encode_app(program,input,as_input,Y)) & 
0.00/0.50	    app_encode_app(output,$o,
0.00/0.50	                   app_encode_app(program,app_encode_fun(output,$o),outputs,V),
0.00/0.50	                   bad)))).
0.00/0.50	tff(zf_stmt_9, type, zip_tseitin1 : (program * program) > $o).
0.00/0.50	tff(zf_stmt_10, type, zip_tseitin0 : (program * program) > $o).
0.00/0.50	tff(zf_stmt_11, axiom,
0.00/0.50	  ((?[W:program]: (![Y:program]: (zip_tseitin1(Y,W) & zip_tseitin0(Y,W)))) =>
0.00/0.50	   (?[V:program]: (![Y:program]: zip_tseitin4(Y,V))))).
0.00/0.50	tff('29', plain,
0.00/0.50	    ![X17 : program, X18 : program]:
0.00/0.50	      (zip_tseitin4(X17, sk_V)
0.00/0.50	       | ~ zip_tseitin0(sk_Y1(X18), X18)
0.00/0.50	       | ~ zip_tseitin1(sk_Y1(X18), X18)),
0.00/0.50	    inference('cnf', [status(esa)], [zf_stmt_11])).
0.00/0.50	tff('30', plain,
0.00/0.50	    ![X0 : program, X1 : program]:
0.00/0.50	      (~ $true
0.00/0.50	       | app_encode_app(input, $o, 
0.00/0.50	           app_encode_app(program, app_encode_fun(input, $o), halts2, 
0.00/0.50	             sk_Y1(X0)), app_encode_app(program, input, as_input, sk_Y1(X0)))
0.00/0.50	       | ~ zip_tseitin0(sk_Y1(X0), X0)
0.00/0.50	       | zip_tseitin4(X1, sk_V)),
0.00/0.50	    inference('sup-', [status(thm)], ['28', '29'])).
0.00/0.50	tff('31', plain,
0.00/0.50	    ![X0 : program, X1 : program]:
0.00/0.50	      (zip_tseitin4(X1, sk_V)
0.00/0.50	       | ~ zip_tseitin0(sk_Y1(X0), X0)
0.00/0.50	       | app_encode_app(input, $o, 
0.00/0.50	           app_encode_app(program, app_encode_fun(input, $o), halts2, 
0.00/0.50	             sk_Y1(X0)), app_encode_app(program, input, as_input, sk_Y1(X0)))),
0.00/0.50	    inference('simplify', [status(thm)], ['30'])).
0.00/0.50	tff('32', plain,
0.00/0.50	    ![X0 : program, X1 : program]:
0.00/0.50	      (~ $true
0.00/0.50	       | ~ app_encode_app(output, $o, 
0.00/0.50	             app_encode_app(program, app_encode_fun(output, $o), outputs, X0), 
0.00/0.50	             bad)
0.00/0.50	       | ~ app_encode_app(input, $o, 
0.00/0.50	             app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.50	               app_encode_app(program, 
0.00/0.50	                 app_encode_fun(program, app_encode_fun(input, $o)), halts3, 
0.00/0.50	                 X0), sk_Y1(X0)), 
0.00/0.50	             app_encode_app(program, input, as_input, sk_Y1(X0)))
0.00/0.50	       | app_encode_app(input, $o, 
0.00/0.50	           app_encode_app(program, app_encode_fun(input, $o), halts2, 
0.00/0.50	             sk_Y1(X0)), app_encode_app(program, input, as_input, sk_Y1(X0)))
0.00/0.50	       | zip_tseitin4(X1, sk_V)),
0.00/0.50	    inference('sup-', [status(thm)], ['27', '31'])).
0.00/0.50	tff('33', plain,
0.00/0.50	    ![X0 : program, X1 : program]:
0.00/0.50	      (zip_tseitin4(X1, sk_V)
0.00/0.50	       | app_encode_app(input, $o, 
0.00/0.50	           app_encode_app(program, app_encode_fun(input, $o), halts2, 
0.00/0.50	             sk_Y1(X0)), app_encode_app(program, input, as_input, sk_Y1(X0)))
0.00/0.50	       | ~ app_encode_app(input, $o, 
0.00/0.50	             app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.50	               app_encode_app(program, 
0.00/0.50	                 app_encode_fun(program, app_encode_fun(input, $o)), halts3, 
0.00/0.50	                 X0), sk_Y1(X0)), 
0.00/0.50	             app_encode_app(program, input, as_input, sk_Y1(X0)))
0.00/0.50	       | ~ app_encode_app(output, $o, 
0.00/0.50	             app_encode_app(program, app_encode_fun(output, $o), outputs, X0), 
0.00/0.50	             bad)),
0.00/0.50	    inference('simplify', [status(thm)], ['32'])).
0.00/0.50	tff('34', plain,
0.00/0.50	    ![X0 : program, X1 : program]:
0.00/0.50	      (~ app_encode_app(input, $o, 
0.00/0.50	           app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.50	             app_encode_app(program, 
0.00/0.50	               app_encode_fun(program, app_encode_fun(input, $o)), halts3, 
0.00/0.50	               sk_W), X0), 
0.00/0.50	           app_encode_app(program, input, as_input, sk_Y1(sk_W)))
0.00/0.50	       | ~ app_encode_app(output, $o, 
0.00/0.50	             app_encode_app(program, app_encode_fun(output, $o), outputs, 
0.00/0.50	               sk_W), bad)
0.00/0.50	       | app_encode_app(input, $o, 
0.00/0.50	           app_encode_app(program, app_encode_fun(input, $o), halts2, 
0.00/0.50	             sk_Y1(sk_W)), 
0.00/0.50	           app_encode_app(program, input, as_input, sk_Y1(sk_W)))
0.00/0.50	       | zip_tseitin4(X1, sk_V)),
0.00/0.50	    inference('sup-', [status(thm)], ['25', '33'])).
0.00/0.50	tff('35', plain,
0.00/0.50	    ![X7 : program, X9 : program, X10 : program, X11 : input, X12 : input]:
0.00/0.50	      (app_encode_app(input, $o, 
0.00/0.50	         app_encode_app(program, app_encode_fun(input, $o), halts2, X7), X12)
0.00/0.50	       | app_encode_app(output, $o, 
0.00/0.50	           app_encode_app(program, app_encode_fun(output, $o), outputs, X9), 
0.00/0.50	           bad)
0.00/0.50	       | ~ app_encode_app(input, $o, 
0.00/0.50	             app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.50	               app_encode_app(algorithm, 
0.00/0.50	                 app_encode_fun(program, app_encode_fun(input, $o)), 
0.00/0.50	                 decides, 
0.00/0.50	                 app_encode_app(program, algorithm, algorithm_of, X9)), X10), 
0.00/0.50	             X11)),
0.00/0.50	    inference('cnf', [status(esa)], [zf_stmt_16])).
0.00/0.50	tff('36', plain,
0.00/0.50	    ![X0 : program, X1 : input, X3 : input, X4 : program]:
0.00/0.50	      (~ app_encode_app(input, $o, 
0.00/0.50	           app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.50	             app_encode_app(algorithm, 
0.00/0.50	               app_encode_fun(program, app_encode_fun(input, $o)), decides, 
0.00/0.50	               sk_X1), X0), X1)
0.00/0.50	       | app_encode_app(output, $o, 
0.00/0.50	           app_encode_app(program, app_encode_fun(output, $o), outputs, sk_W), 
0.00/0.50	           bad)
0.00/0.50	       | app_encode_app(input, $o, 
0.00/0.50	           app_encode_app(program, app_encode_fun(input, $o), halts2, X4), 
0.00/0.50	           X3)),
0.00/0.50	    inference('sup-', [status(thm)], ['7', '35'])).
0.00/0.50	tff('37', plain,
0.00/0.50	    ![X3 : input, X4 : program]:
0.00/0.50	      (~ $true
0.00/0.50	       | app_encode_app(output, $o, 
0.00/0.50	           app_encode_app(program, app_encode_fun(output, $o), outputs, sk_W), 
0.00/0.50	           bad)
0.00/0.50	       | app_encode_app(input, $o, 
0.00/0.50	           app_encode_app(program, app_encode_fun(input, $o), halts2, X4), 
0.00/0.50	           X3)),
0.00/0.50	    inference('demod', [status(thm)], ['36', '0'])).
0.00/0.50	tff('38', plain,
0.00/0.50	    ![X3 : input, X4 : program]:
0.00/0.50	      (app_encode_app(input, $o, 
0.00/0.50	         app_encode_app(program, app_encode_fun(input, $o), halts2, X4), X3)
0.00/0.50	       | app_encode_app(output, $o, 
0.00/0.50	           app_encode_app(program, app_encode_fun(output, $o), outputs, sk_W), 
0.00/0.50	           bad)),
0.00/0.50	    inference('simplify', [status(thm)], ['37'])).
0.00/0.50	tff('39', plain,
0.00/0.50	    ![X0 : program, X1 : program]:
0.00/0.50	      ($true != $true
0.00/0.50	       | app_encode_app(output, $o, 
0.00/0.50	           app_encode_app(program, app_encode_fun(output, $o), outputs, sk_W), 
0.00/0.50	           bad)
0.00/0.50	       | app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.50	           app_encode_app(algorithm, 
0.00/0.50	             app_encode_fun(program, app_encode_fun(input, $o)), decides, 
0.00/0.50	             sk_X1), X0)
0.00/0.50	          = app_encode_app(program, app_encode_fun(input, $o), halts2, X1)),
0.00/0.50	    inference('sup-', [status(thm)], ['38', '5'])).
0.00/0.50	tff('40', plain,
0.00/0.50	    ![X0 : program, X1 : program]:
0.00/0.50	      (app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.50	         app_encode_app(algorithm, 
0.00/0.50	           app_encode_fun(program, app_encode_fun(input, $o)), decides, 
0.00/0.50	           sk_X1), X0)
0.00/0.50	        = app_encode_app(program, app_encode_fun(input, $o), halts2, X1)
0.00/0.50	       | app_encode_app(output, $o, 
0.00/0.50	           app_encode_app(program, app_encode_fun(output, $o), outputs, sk_W), 
0.00/0.50	           bad)),
0.00/0.50	    inference('simplify', [status(thm)], ['39'])).
0.00/0.50	tff('41', plain,
0.00/0.50	    ![X7 : program, X8 : input, X9 : program, X10 : program, X11 : input]:
0.00/0.50	      (~ app_encode_app(input, $o, 
0.00/0.50	           app_encode_app(program, app_encode_fun(input, $o), halts2, X7), 
0.00/0.50	           X8)
0.00/0.50	       | app_encode_app(output, $o, 
0.00/0.50	           app_encode_app(program, app_encode_fun(output, $o), outputs, X9), 
0.00/0.50	           good)
0.00/0.50	       | ~ app_encode_app(input, $o, 
0.00/0.50	             app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.50	               app_encode_app(algorithm, 
0.00/0.50	                 app_encode_fun(program, app_encode_fun(input, $o)), 
0.00/0.50	                 decides, 
0.00/0.50	                 app_encode_app(program, algorithm, algorithm_of, X9)), X10), 
0.00/0.50	             X11)),
0.00/0.50	    inference('cnf', [status(esa)], [zf_stmt_16])).
0.00/0.50	tff('42', plain,
0.00/0.50	    ![X0 : program, X1 : input, X3 : input, X4 : program, X5 : program]:
0.00/0.50	      (~ app_encode_app(input, $o, 
0.00/0.50	           app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.50	             app_encode_app(algorithm, 
0.00/0.50	               app_encode_fun(program, app_encode_fun(input, $o)), decides, 
0.00/0.50	               sk_X1), X0), X1)
0.00/0.50	       | app_encode_app(output, $o, 
0.00/0.50	           app_encode_app(program, app_encode_fun(output, $o), outputs, sk_W), 
0.00/0.50	           bad)
0.00/0.50	       | ~ app_encode_app(input, $o, 
0.00/0.50	             app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.50	               app_encode_app(algorithm, 
0.00/0.50	                 app_encode_fun(program, app_encode_fun(input, $o)), 
0.00/0.50	                 decides, 
0.00/0.50	                 app_encode_app(program, algorithm, algorithm_of, X5)), X4), 
0.00/0.50	             X3)
0.00/0.50	       | app_encode_app(output, $o, 
0.00/0.50	           app_encode_app(program, app_encode_fun(output, $o), outputs, X5), 
0.00/0.50	           good)),
0.00/0.50	    inference('sup-', [status(thm)], ['40', '41'])).
0.00/0.50	tff('43', plain,
0.00/0.50	    ![X3 : input, X4 : program, X5 : program]:
0.00/0.50	      (~ $true
0.00/0.50	       | app_encode_app(output, $o, 
0.00/0.50	           app_encode_app(program, app_encode_fun(output, $o), outputs, sk_W), 
0.00/0.50	           bad)
0.00/0.50	       | ~ app_encode_app(input, $o, 
0.00/0.50	             app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.50	               app_encode_app(algorithm, 
0.00/0.50	                 app_encode_fun(program, app_encode_fun(input, $o)), 
0.00/0.50	                 decides, 
0.00/0.50	                 app_encode_app(program, algorithm, algorithm_of, X5)), X4), 
0.00/0.50	             X3)
0.00/0.50	       | app_encode_app(output, $o, 
0.00/0.50	           app_encode_app(program, app_encode_fun(output, $o), outputs, X5), 
0.00/0.50	           good)),
0.00/0.50	    inference('demod', [status(thm)], ['42', '0'])).
0.00/0.50	tff('44', plain,
0.00/0.50	    ![X3 : input, X4 : program, X5 : program]:
0.00/0.50	      (app_encode_app(output, $o, 
0.00/0.50	         app_encode_app(program, app_encode_fun(output, $o), outputs, X5), 
0.00/0.50	         good)
0.00/0.50	       | ~ app_encode_app(input, $o, 
0.00/0.50	             app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.50	               app_encode_app(algorithm, 
0.00/0.50	                 app_encode_fun(program, app_encode_fun(input, $o)), 
0.00/0.50	                 decides, 
0.00/0.50	                 app_encode_app(program, algorithm, algorithm_of, X5)), X4), 
0.00/0.50	             X3)
0.00/0.50	       | app_encode_app(output, $o, 
0.00/0.50	           app_encode_app(program, app_encode_fun(output, $o), outputs, sk_W), 
0.00/0.50	           bad)),
0.00/0.50	    inference('simplify', [status(thm)], ['43'])).
0.00/0.50	tff('45', plain,
0.00/0.50	    ![X0 : input, X1 : program]:
0.00/0.50	      (~ app_encode_app(input, $o, 
0.00/0.50	           app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.50	             app_encode_app(program, 
0.00/0.50	               app_encode_fun(program, app_encode_fun(input, $o)), halts3, 
0.00/0.50	               sk_W), X1), X0)
0.00/0.50	       | app_encode_app(output, $o, 
0.00/0.50	           app_encode_app(program, app_encode_fun(output, $o), outputs, sk_W), 
0.00/0.50	           bad)
0.00/0.50	       | app_encode_app(output, $o, 
0.00/0.50	           app_encode_app(program, app_encode_fun(output, $o), outputs, sk_W), 
0.00/0.50	           good)),
0.00/0.50	    inference('sup-', [status(thm)], ['26', '44'])).
0.00/0.50	tff('46', plain,
0.00/0.50	    (~ $true
0.00/0.50	     | app_encode_app(output, $o, 
0.00/0.50	         app_encode_app(program, app_encode_fun(output, $o), outputs, sk_W), 
0.00/0.50	         bad)
0.00/0.50	     | app_encode_app(output, $o, 
0.00/0.50	         app_encode_app(program, app_encode_fun(output, $o), outputs, sk_W), 
0.00/0.50	         good)),
0.00/0.50	    inference('demod', [status(thm)], ['45', '17'])).
0.00/0.50	tff('47', plain,
0.00/0.50	    (app_encode_app(output, $o, 
0.00/0.50	       app_encode_app(program, app_encode_fun(output, $o), outputs, sk_W), 
0.00/0.50	       good)
0.00/0.50	     | app_encode_app(output, $o, 
0.00/0.50	         app_encode_app(program, app_encode_fun(output, $o), outputs, sk_W), 
0.00/0.50	         bad)),
0.00/0.50	    inference('simplify', [status(thm)], ['46'])).
0.00/0.50	tff('48', plain,
0.00/0.50	    ![X0 : program, X1 : program]:
0.00/0.50	      (app_encode_app(program, app_encode_fun(input, $o), halts2, X0)
0.00/0.50	        = app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.50	            app_encode_app(algorithm, 
0.00/0.50	              app_encode_fun(program, app_encode_fun(input, $o)), decides, 
0.00/0.50	              sk_X1), X1)
0.00/0.50	       | app_encode_app(output, $o, 
0.00/0.50	           app_encode_app(program, app_encode_fun(output, $o), outputs, sk_W), 
0.00/0.50	           bad)),
0.00/0.50	    inference('sup+', [status(thm)], ['40', '9'])).
0.00/0.50	tff('49', plain,
0.00/0.50	    ![X0 : program, X1 : program]:
0.00/0.50	      (app_encode_app(program, app_encode_fun(input, $o), halts2, X0)
0.00/0.50	        = app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.50	            app_encode_app(program, 
0.00/0.50	              app_encode_fun(program, app_encode_fun(input, $o)), halts3, 
0.00/0.50	              sk_W), X1)
0.00/0.50	       | app_encode_app(output, $o, 
0.00/0.50	           app_encode_app(program, app_encode_fun(output, $o), outputs, sk_W), 
0.00/0.50	           bad)),
0.00/0.50	    inference('demod', [status(thm)], ['48', '19'])).
0.00/0.50	tff(zf_stmt_18, axiom,
0.00/0.50	  ((?[V:program]:
0.00/0.50	      (![Y:program]:
0.00/0.50	         (((~
0.00/0.50	             app_encode_app(input,$o,
0.00/0.50	                            app_encode_app(program,app_encode_fun(input,$o),
0.00/0.50	                                           halts2,Y),
0.00/0.50	                            app_encode_app(program,input,as_input,Y))) =>
0.00/0.50	           (app_encode_app(output,$o,
0.00/0.50	                           app_encode_app(program,app_encode_fun(output,$o),
0.00/0.50	                                          outputs,V),
0.00/0.50	                           bad) & 
0.00/0.50	            app_encode_app(input,$o,
0.00/0.50	                           app_encode_app(program,app_encode_fun(input,$o),
0.00/0.50	                                          halts2,V),
0.00/0.50	                           app_encode_app(program,input,as_input,Y)))) & 
0.00/0.50	          (app_encode_app(input,$o,
0.00/0.50	                          app_encode_app(program,app_encode_fun(input,$o),
0.00/0.50	                                         halts2,Y),
0.00/0.50	                          app_encode_app(program,input,as_input,Y)) =>
0.00/0.50	           (app_encode_app(output,$o,
0.00/0.50	                           app_encode_app(program,app_encode_fun(output,$o),
0.00/0.50	                                          outputs,V),
0.00/0.50	                           good) & 
0.00/0.50	            app_encode_app(input,$o,
0.00/0.50	                           app_encode_app(program,app_encode_fun(input,$o),
0.00/0.50	                                          halts2,V),
0.00/0.50	                           app_encode_app(program,input,as_input,Y))))))) =>
0.00/0.50	   (?[U:program]:
0.00/0.50	      (![Y:program]:
0.00/0.50	         (((~
0.00/0.50	             app_encode_app(input,$o,
0.00/0.50	                            app_encode_app(program,app_encode_fun(input,$o),
0.00/0.50	                                           halts2,Y),
0.00/0.50	                            app_encode_app(program,input,as_input,Y))) =>
0.00/0.50	           (app_encode_app(output,$o,
0.00/0.50	                           app_encode_app(program,app_encode_fun(output,$o),
0.00/0.50	                                          outputs,U),
0.00/0.50	                           bad) & 
0.00/0.50	            app_encode_app(input,$o,
0.00/0.50	                           app_encode_app(program,app_encode_fun(input,$o),
0.00/0.50	                                          halts2,U),
0.00/0.50	                           app_encode_app(program,input,as_input,Y)))) & 
0.00/0.50	          (app_encode_app(input,$o,
0.00/0.50	                          app_encode_app(program,app_encode_fun(input,$o),
0.00/0.50	                                         halts2,Y),
0.00/0.50	                          app_encode_app(program,input,as_input,Y)) =>
0.00/0.50	           (~
0.00/0.50	             app_encode_app(input,$o,
0.00/0.50	                            app_encode_app(program,app_encode_fun(input,$o),
0.00/0.50	                                           halts2,U),
0.00/0.50	                            app_encode_app(program,input,as_input,Y))))))))).
0.00/0.50	tff(zf_stmt_12, axiom,
0.00/0.50	  (((~
0.00/0.50	      app_encode_app(input,$o,
0.00/0.50	                     app_encode_app(program,app_encode_fun(input,$o),halts2,Y),
0.00/0.50	                     app_encode_app(program,input,as_input,Y))) =>
0.00/0.50	    (app_encode_app(input,$o,
0.00/0.50	                    app_encode_app(program,app_encode_fun(input,$o),halts2,V),
0.00/0.50	                    app_encode_app(program,input,as_input,Y)) & 
0.00/0.50	     app_encode_app(output,$o,
0.00/0.50	                    app_encode_app(program,app_encode_fun(output,$o),outputs,
0.00/0.50	                                   V),
0.00/0.50	                    bad))) =>
0.00/0.50	   zip_tseitin5(Y,V))).
0.00/0.50	tff('50', plain,
0.00/0.50	    ![X19 : program, X20 : program]:
0.00/0.50	      (zip_tseitin5(X19, X20)
0.00/0.50	       | ~ app_encode_app(input, $o, 
0.00/0.50	             app_encode_app(program, app_encode_fun(input, $o), halts2, X19), 
0.00/0.50	             app_encode_app(program, input, as_input, X19))),
0.00/0.50	    inference('cnf', [status(esa)], [zf_stmt_12])).
0.00/0.50	tff(zf_stmt_13, axiom,
0.00/0.50	  ((app_encode_app(input,$o,
0.00/0.50	                   app_encode_app(program,app_encode_fun(input,$o),halts2,Y),
0.00/0.50	                   app_encode_app(program,input,as_input,Y)) =>
0.00/0.50	    (app_encode_app(input,$o,
0.00/0.50	                    app_encode_app(program,app_encode_fun(input,$o),halts2,V),
0.00/0.50	                    app_encode_app(program,input,as_input,Y)) & 
0.00/0.50	     app_encode_app(output,$o,
0.00/0.50	                    app_encode_app(program,app_encode_fun(output,$o),outputs,
0.00/0.50	                                   V),
0.00/0.50	                    good))) =>
0.00/0.50	   zip_tseitin6(Y,V))).
0.00/0.50	tff('51', plain,
0.00/0.50	    ![X19 : program, X20 : program]:
0.00/0.50	      (zip_tseitin6(X19, X20)
0.00/0.50	       | ~ app_encode_app(input, $o, 
0.00/0.50	             app_encode_app(program, app_encode_fun(input, $o), halts2, X20), 
0.00/0.50	             app_encode_app(program, input, as_input, X19))
0.00/0.50	       | ~ app_encode_app(output, $o, 
0.00/0.50	             app_encode_app(program, app_encode_fun(output, $o), outputs, 
0.00/0.50	               X20), good)),
0.00/0.50	    inference('cnf', [status(esa)], [zf_stmt_13])).
0.00/0.50	tff(zf_stmt_14, type, zip_tseitin8 : (program * program) > $o).
0.00/0.50	tff(zf_stmt_15, axiom,
0.00/0.50	  (zip_tseitin8(Y,U) =>
0.00/0.50	   ((app_encode_app(input,$o,
0.00/0.50	                    app_encode_app(program,app_encode_fun(input,$o),halts2,Y),
0.00/0.50	                    app_encode_app(program,input,as_input,Y)) =>
0.00/0.50	     (~
0.00/0.50	       app_encode_app(input,$o,
0.00/0.50	                      app_encode_app(program,app_encode_fun(input,$o),halts2,
0.00/0.50	                                     U),
0.00/0.50	                      app_encode_app(program,input,as_input,Y)))) & 
0.00/0.50	    ((~
0.00/0.50	       app_encode_app(input,$o,
0.00/0.50	                      app_encode_app(program,app_encode_fun(input,$o),halts2,
0.00/0.51	                                     Y),
0.00/0.51	                      app_encode_app(program,input,as_input,Y))) =>
0.00/0.51	     zip_tseitin7(Y,U))))).
0.00/0.51	tff(zf_stmt_16, type, zip_tseitin7 : (program * program) > $o).
0.00/0.51	tff(zf_stmt_17, axiom,
0.00/0.51	  (zip_tseitin7(Y,U) =>
0.00/0.51	   (app_encode_app(input,$o,
0.00/0.51	                   app_encode_app(program,app_encode_fun(input,$o),halts2,U),
0.00/0.51	                   app_encode_app(program,input,as_input,Y)) & 
0.00/0.51	    app_encode_app(output,$o,
0.00/0.51	                   app_encode_app(program,app_encode_fun(output,$o),outputs,U),
0.00/0.51	                   bad)))).
0.00/0.51	tff(zf_stmt_18, type, zip_tseitin6 : (program * program) > $o).
0.00/0.51	tff(zf_stmt_19, type, zip_tseitin5 : (program * program) > $o).
0.00/0.51	tff(zf_stmt_20, axiom,
0.00/0.51	  ((?[V:program]: (![Y:program]: (zip_tseitin6(Y,V) & zip_tseitin5(Y,V)))) =>
0.00/0.51	   (?[U:program]: (![Y:program]: zip_tseitin8(Y,U))))).
0.00/0.51	tff('52', plain,
0.00/0.51	    ![X23 : program, X24 : program]:
0.00/0.51	      (zip_tseitin8(X23, sk_U)
0.00/0.51	       | ~ zip_tseitin5(sk_Y2(X24), X24)
0.00/0.51	       | ~ zip_tseitin6(sk_Y2(X24), X24)),
0.00/0.51	    inference('cnf', [status(esa)], [zf_stmt_20])).
0.00/0.51	tff('53', plain,
0.00/0.51	    ![X0 : program, X1 : program]:
0.00/0.51	      (~ $true
0.00/0.51	       | ~ app_encode_app(output, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(output, $o), outputs, X0), 
0.00/0.51	             good)
0.00/0.51	       | ~ app_encode_app(input, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.51	             app_encode_app(program, input, as_input, sk_Y2(X0)))
0.00/0.51	       | ~ zip_tseitin5(sk_Y2(X0), X0)
0.00/0.51	       | zip_tseitin8(X1, sk_U)),
0.00/0.51	    inference('sup-', [status(thm)], ['51', '52'])).
0.00/0.51	tff('54', plain,
0.00/0.51	    ![X0 : program, X1 : program]:
0.00/0.51	      (zip_tseitin8(X1, sk_U)
0.00/0.51	       | ~ zip_tseitin5(sk_Y2(X0), X0)
0.00/0.51	       | ~ app_encode_app(input, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.51	             app_encode_app(program, input, as_input, sk_Y2(X0)))
0.00/0.51	       | ~ app_encode_app(output, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(output, $o), outputs, X0), 
0.00/0.51	             good)),
0.00/0.51	    inference('simplify', [status(thm)], ['53'])).
0.00/0.51	tff('55', plain,
0.00/0.51	    ![X0 : program, X1 : program]:
0.00/0.51	      (~ $true
0.00/0.51	       | ~ app_encode_app(input, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(input, $o), halts2, 
0.00/0.51	               sk_Y2(X0)), 
0.00/0.51	             app_encode_app(program, input, as_input, sk_Y2(X0)))
0.00/0.51	       | ~ app_encode_app(output, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(output, $o), outputs, X0), 
0.00/0.51	             good)
0.00/0.51	       | ~ app_encode_app(input, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.51	             app_encode_app(program, input, as_input, sk_Y2(X0)))
0.00/0.51	       | zip_tseitin8(X1, sk_U)),
0.00/0.51	    inference('sup-', [status(thm)], ['50', '54'])).
0.00/0.51	tff('56', plain,
0.00/0.51	    ![X0 : program, X1 : program]:
0.00/0.51	      (zip_tseitin8(X1, sk_U)
0.00/0.51	       | ~ app_encode_app(input, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.51	             app_encode_app(program, input, as_input, sk_Y2(X0)))
0.00/0.51	       | ~ app_encode_app(output, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(output, $o), outputs, X0), 
0.00/0.51	             good)
0.00/0.51	       | ~ app_encode_app(input, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(input, $o), halts2, 
0.00/0.51	               sk_Y2(X0)), 
0.00/0.51	             app_encode_app(program, input, as_input, sk_Y2(X0)))),
0.00/0.51	    inference('simplify', [status(thm)], ['55'])).
0.00/0.51	tff('57', plain,
0.00/0.51	    ![X0 : program, X1 : program, X2 : program]:
0.00/0.51	      (~ app_encode_app(input, $o, 
0.00/0.51	           app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.51	             app_encode_app(program, 
0.00/0.51	               app_encode_fun(program, app_encode_fun(input, $o)), halts3, 
0.00/0.51	               sk_W), X0), 
0.00/0.51	           app_encode_app(program, input, as_input, sk_Y2(X1)))
0.00/0.51	       | app_encode_app(output, $o, 
0.00/0.51	           app_encode_app(program, app_encode_fun(output, $o), outputs, sk_W), 
0.00/0.51	           bad)
0.00/0.51	       | ~ app_encode_app(output, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(output, $o), outputs, X1), 
0.00/0.51	             good)
0.00/0.51	       | ~ app_encode_app(input, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(input, $o), halts2, X1), 
0.00/0.51	             app_encode_app(program, input, as_input, sk_Y2(X1)))
0.00/0.51	       | zip_tseitin8(X2, sk_U)),
0.00/0.51	    inference('sup-', [status(thm)], ['49', '56'])).
0.00/0.51	tff('58', plain,
0.00/0.51	    ![X1 : program, X2 : program]:
0.00/0.51	      (~ $true
0.00/0.51	       | app_encode_app(output, $o, 
0.00/0.51	           app_encode_app(program, app_encode_fun(output, $o), outputs, sk_W), 
0.00/0.51	           bad)
0.00/0.51	       | ~ app_encode_app(output, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(output, $o), outputs, X1), 
0.00/0.51	             good)
0.00/0.51	       | ~ app_encode_app(input, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(input, $o), halts2, X1), 
0.00/0.51	             app_encode_app(program, input, as_input, sk_Y2(X1)))
0.00/0.51	       | zip_tseitin8(X2, sk_U)),
0.00/0.51	    inference('demod', [status(thm)], ['57', '17'])).
0.00/0.51	tff('59', plain,
0.00/0.51	    ![X1 : program, X2 : program]:
0.00/0.51	      (zip_tseitin8(X2, sk_U)
0.00/0.51	       | ~ app_encode_app(input, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(input, $o), halts2, X1), 
0.00/0.51	             app_encode_app(program, input, as_input, sk_Y2(X1)))
0.00/0.51	       | ~ app_encode_app(output, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(output, $o), outputs, X1), 
0.00/0.51	             good)
0.00/0.51	       | app_encode_app(output, $o, 
0.00/0.51	           app_encode_app(program, app_encode_fun(output, $o), outputs, sk_W), 
0.00/0.51	           bad)),
0.00/0.51	    inference('simplify', [status(thm)], ['58'])).
0.00/0.51	tff('60', plain,
0.00/0.51	    ![X1 : program, X2 : program]:
0.00/0.51	      (app_encode_app(output, $o, 
0.00/0.51	         app_encode_app(program, app_encode_fun(output, $o), outputs, sk_W), 
0.00/0.51	         bad)
0.00/0.51	       | ~ app_encode_app(output, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(output, $o), outputs, X1), 
0.00/0.51	             good)
0.00/0.51	       | zip_tseitin8(X2, sk_U)),
0.00/0.51	    inference('clc', [status(thm)], ['59', '38'])).
0.00/0.51	tff('61', plain,
0.00/0.51	    ![X0 : program]:
0.00/0.51	      (~ $true
0.00/0.51	       | app_encode_app(output, $o, 
0.00/0.51	           app_encode_app(program, app_encode_fun(output, $o), outputs, sk_W), 
0.00/0.51	           bad)
0.00/0.51	       | zip_tseitin8(X0, sk_U)
0.00/0.51	       | app_encode_app(output, $o, 
0.00/0.51	           app_encode_app(program, app_encode_fun(output, $o), outputs, sk_W), 
0.00/0.51	           bad)),
0.00/0.51	    inference('sup-', [status(thm)], ['47', '60'])).
0.00/0.51	tff('62', plain,
0.00/0.51	    ![X0 : program]:
0.00/0.51	      (zip_tseitin8(X0, sk_U)
0.00/0.51	       | app_encode_app(output, $o, 
0.00/0.51	           app_encode_app(program, app_encode_fun(output, $o), outputs, sk_W), 
0.00/0.51	           bad)),
0.00/0.51	    inference('simplify', [status(thm)], ['61'])).
0.00/0.51	tff('63', plain,
0.00/0.51	    ![X21 : program, X22 : program]:
0.00/0.51	      (~ app_encode_app(input, $o, 
0.00/0.51	           app_encode_app(program, app_encode_fun(input, $o), halts2, X22), 
0.00/0.51	           app_encode_app(program, input, as_input, X22))
0.00/0.51	       | ~ app_encode_app(input, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(input, $o), halts2, X21), 
0.00/0.51	             app_encode_app(program, input, as_input, X22))
0.00/0.51	       | ~ zip_tseitin8(X22, X21)),
0.00/0.51	    inference('cnf', [status(esa)], [zf_stmt_15])).
0.00/0.51	tff('64', plain,
0.00/0.51	    ![X0 : program]:
0.00/0.51	      (~ $true
0.00/0.51	       | app_encode_app(output, $o, 
0.00/0.51	           app_encode_app(program, app_encode_fun(output, $o), outputs, sk_W), 
0.00/0.51	           bad)
0.00/0.51	       | ~ app_encode_app(input, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(input, $o), halts2, sk_U), 
0.00/0.51	             app_encode_app(program, input, as_input, X0))
0.00/0.51	       | ~ app_encode_app(input, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.51	             app_encode_app(program, input, as_input, X0))),
0.00/0.51	    inference('sup-', [status(thm)], ['62', '63'])).
0.00/0.51	tff('65', plain,
0.00/0.51	    ![X0 : program]:
0.00/0.51	      (~ app_encode_app(input, $o, 
0.00/0.51	           app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.51	           app_encode_app(program, input, as_input, X0))
0.00/0.51	       | ~ app_encode_app(input, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(input, $o), halts2, sk_U), 
0.00/0.51	             app_encode_app(program, input, as_input, X0))
0.00/0.51	       | app_encode_app(output, $o, 
0.00/0.51	           app_encode_app(program, app_encode_fun(output, $o), outputs, sk_W), 
0.00/0.51	           bad)),
0.00/0.51	    inference('simplify', [status(thm)], ['64'])).
0.00/0.51	tff('66', plain,
0.00/0.51	    ![X0 : program]:
0.00/0.51	      (app_encode_app(output, $o, 
0.00/0.51	         app_encode_app(program, app_encode_fun(output, $o), outputs, sk_W), 
0.00/0.51	         bad)
0.00/0.51	       | ~ app_encode_app(input, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(input, $o), halts2, sk_U), 
0.00/0.51	             app_encode_app(program, input, as_input, X0))),
0.00/0.51	    inference('clc', [status(thm)], ['65', '38'])).
0.00/0.51	tff('67', plain,
0.00/0.51	    app_encode_app(output, $o, 
0.00/0.51	      app_encode_app(program, app_encode_fun(output, $o), outputs, sk_W), 
0.00/0.51	      bad),
0.00/0.51	    inference('clc', [status(thm)], ['66', '38'])).
0.00/0.51	tff('68', plain,
0.00/0.51	    ![X1 : program]:
0.00/0.51	      (~ $true
0.00/0.51	       | ~ $true
0.00/0.51	       | app_encode_app(input, $o, 
0.00/0.51	           app_encode_app(program, app_encode_fun(input, $o), halts2, 
0.00/0.51	             sk_Y1(sk_W)), 
0.00/0.51	           app_encode_app(program, input, as_input, sk_Y1(sk_W)))
0.00/0.51	       | zip_tseitin4(X1, sk_V)),
0.00/0.51	    inference('demod', [status(thm)], ['34', '17', '67'])).
0.00/0.51	tff('69', plain,
0.00/0.51	    ![X1 : program]:
0.00/0.51	      (zip_tseitin4(X1, sk_V)
0.00/0.51	       | app_encode_app(input, $o, 
0.00/0.51	           app_encode_app(program, app_encode_fun(input, $o), halts2, 
0.00/0.51	             sk_Y1(sk_W)), 
0.00/0.51	           app_encode_app(program, input, as_input, sk_Y1(sk_W)))),
0.00/0.51	    inference('simplify', [status(thm)], ['68'])).
0.00/0.51	tff('70', plain,
0.00/0.51	    ![X0 : input, X1 : program, X2 : program, X3 : program]:
0.00/0.51	      (~ $true
0.00/0.51	       | zip_tseitin4(X3, sk_V)
0.00/0.51	       | ~ app_encode_app(input, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.51	               app_encode_app(algorithm, 
0.00/0.51	                 app_encode_fun(program, app_encode_fun(input, $o)), 
0.00/0.51	                 decides, 
0.00/0.51	                 app_encode_app(program, algorithm, algorithm_of, X2)), X1), 
0.00/0.51	             X0)
0.00/0.51	       | app_encode_app(output, $o, 
0.00/0.51	           app_encode_app(program, app_encode_fun(output, $o), outputs, X2), 
0.00/0.51	           good)),
0.00/0.51	    inference('sup-', [status(thm)], ['69', '41'])).
0.00/0.51	tff('71', plain,
0.00/0.51	    ![X0 : input, X1 : program, X2 : program, X3 : program]:
0.00/0.51	      (app_encode_app(output, $o, 
0.00/0.51	         app_encode_app(program, app_encode_fun(output, $o), outputs, X2), 
0.00/0.51	         good)
0.00/0.51	       | ~ app_encode_app(input, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.51	               app_encode_app(algorithm, 
0.00/0.51	                 app_encode_fun(program, app_encode_fun(input, $o)), 
0.00/0.51	                 decides, 
0.00/0.51	                 app_encode_app(program, algorithm, algorithm_of, X2)), X1), 
0.00/0.51	             X0)
0.00/0.51	       | zip_tseitin4(X3, sk_V)),
0.00/0.51	    inference('simplify', [status(thm)], ['70'])).
0.00/0.51	tff('72', plain,
0.00/0.51	    ![X0 : input, X1 : program, X2 : program]:
0.00/0.51	      (~ app_encode_app(input, $o, 
0.00/0.51	           app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.51	             app_encode_app(program, 
0.00/0.51	               app_encode_fun(program, app_encode_fun(input, $o)), halts3, 
0.00/0.51	               sk_W), X1), X0)
0.00/0.51	       | zip_tseitin4(X2, sk_V)
0.00/0.51	       | app_encode_app(output, $o, 
0.00/0.51	           app_encode_app(program, app_encode_fun(output, $o), outputs, sk_W), 
0.00/0.51	           good)),
0.00/0.51	    inference('sup-', [status(thm)], ['26', '71'])).
0.00/0.51	tff('73', plain,
0.00/0.51	    ![X2 : program]:
0.00/0.51	      (~ $true
0.00/0.51	       | zip_tseitin4(X2, sk_V)
0.00/0.51	       | app_encode_app(output, $o, 
0.00/0.51	           app_encode_app(program, app_encode_fun(output, $o), outputs, sk_W), 
0.00/0.51	           good)),
0.00/0.51	    inference('demod', [status(thm)], ['72', '17'])).
0.00/0.51	tff('74', plain,
0.00/0.51	    ![X2 : program]:
0.00/0.51	      (app_encode_app(output, $o, 
0.00/0.51	         app_encode_app(program, app_encode_fun(output, $o), outputs, sk_W), 
0.00/0.51	         good)
0.00/0.51	       | zip_tseitin4(X2, sk_V)),
0.00/0.51	    inference('simplify', [status(thm)], ['73'])).
0.00/0.51	tff('75', plain,
0.00/0.51	    ![X13 : program, X14 : program]:
0.00/0.51	      (zip_tseitin1(X13, X14)
0.00/0.51	       | ~ app_encode_app(input, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.51	               app_encode_app(program, 
0.00/0.51	                 app_encode_fun(program, app_encode_fun(input, $o)), halts3, 
0.00/0.51	                 X14), X13), app_encode_app(program, input, as_input, X13))
0.00/0.51	       | ~ app_encode_app(output, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(output, $o), outputs, 
0.00/0.51	               X14), good)),
0.00/0.51	    inference('cnf', [status(esa)], [zf_stmt_2])).
0.00/0.51	tff('76', plain,
0.00/0.51	    ![X0 : program, X1 : program]:
0.00/0.51	      (~ $true
0.00/0.51	       | ~ app_encode_app(output, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(output, $o), outputs, X0), 
0.00/0.51	             good)
0.00/0.51	       | ~ app_encode_app(input, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.51	               app_encode_app(program, 
0.00/0.51	                 app_encode_fun(program, app_encode_fun(input, $o)), halts3, 
0.00/0.51	                 X0), sk_Y1(X0)), 
0.00/0.51	             app_encode_app(program, input, as_input, sk_Y1(X0)))
0.00/0.51	       | ~ zip_tseitin0(sk_Y1(X0), X0)
0.00/0.51	       | zip_tseitin4(X1, sk_V)),
0.00/0.51	    inference('sup-', [status(thm)], ['75', '29'])).
0.00/0.51	tff('77', plain,
0.00/0.51	    ![X0 : program, X1 : program]:
0.00/0.51	      (zip_tseitin4(X1, sk_V)
0.00/0.51	       | ~ zip_tseitin0(sk_Y1(X0), X0)
0.00/0.51	       | ~ app_encode_app(input, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.51	               app_encode_app(program, 
0.00/0.51	                 app_encode_fun(program, app_encode_fun(input, $o)), halts3, 
0.00/0.51	                 X0), sk_Y1(X0)), 
0.00/0.51	             app_encode_app(program, input, as_input, sk_Y1(X0)))
0.00/0.51	       | ~ app_encode_app(output, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(output, $o), outputs, X0), 
0.00/0.51	             good)),
0.00/0.51	    inference('simplify', [status(thm)], ['76'])).
0.00/0.51	tff('78', plain,
0.00/0.51	    ![X0 : program, X1 : program]:
0.00/0.51	      (~ $true
0.00/0.51	       | ~ app_encode_app(output, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(output, $o), outputs, X0), 
0.00/0.51	             bad)
0.00/0.51	       | ~ app_encode_app(input, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.51	               app_encode_app(program, 
0.00/0.51	                 app_encode_fun(program, app_encode_fun(input, $o)), halts3, 
0.00/0.51	                 X0), sk_Y1(X0)), 
0.00/0.51	             app_encode_app(program, input, as_input, sk_Y1(X0)))
0.00/0.51	       | ~ app_encode_app(output, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(output, $o), outputs, X0), 
0.00/0.51	             good)
0.00/0.51	       | ~ app_encode_app(input, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.51	               app_encode_app(program, 
0.00/0.51	                 app_encode_fun(program, app_encode_fun(input, $o)), halts3, 
0.00/0.51	                 X0), sk_Y1(X0)), 
0.00/0.51	             app_encode_app(program, input, as_input, sk_Y1(X0)))
0.00/0.51	       | zip_tseitin4(X1, sk_V)),
0.00/0.51	    inference('sup-', [status(thm)], ['27', '77'])).
0.00/0.51	tff('79', plain,
0.00/0.51	    ![X0 : program, X1 : program]:
0.00/0.51	      (zip_tseitin4(X1, sk_V)
0.00/0.51	       | ~ app_encode_app(output, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(output, $o), outputs, X0), 
0.00/0.51	             good)
0.00/0.51	       | ~ app_encode_app(input, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.51	               app_encode_app(program, 
0.00/0.51	                 app_encode_fun(program, app_encode_fun(input, $o)), halts3, 
0.00/0.51	                 X0), sk_Y1(X0)), 
0.00/0.51	             app_encode_app(program, input, as_input, sk_Y1(X0)))
0.00/0.51	       | ~ app_encode_app(output, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(output, $o), outputs, X0), 
0.00/0.51	             bad)),
0.00/0.51	    inference('simplify', [status(thm)], ['78'])).
0.00/0.51	tff('80', plain,
0.00/0.51	    ![X0 : program, X1 : program]:
0.00/0.51	      (~ app_encode_app(input, $o, 
0.00/0.51	           app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.51	             app_encode_app(program, 
0.00/0.51	               app_encode_fun(program, app_encode_fun(input, $o)), halts3, 
0.00/0.51	               sk_W), X0), 
0.00/0.51	           app_encode_app(program, input, as_input, sk_Y1(sk_W)))
0.00/0.51	       | ~ app_encode_app(output, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(output, $o), outputs, 
0.00/0.51	               sk_W), bad)
0.00/0.51	       | ~ app_encode_app(output, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(output, $o), outputs, 
0.00/0.51	               sk_W), good)
0.00/0.51	       | zip_tseitin4(X1, sk_V)),
0.00/0.51	    inference('sup-', [status(thm)], ['25', '79'])).
0.00/0.51	tff('81', plain,
0.00/0.51	    ![X1 : program]:
0.00/0.51	      (~ $true
0.00/0.51	       | ~ $true
0.00/0.51	       | ~ app_encode_app(output, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(output, $o), outputs, 
0.00/0.51	               sk_W), good)
0.00/0.51	       | zip_tseitin4(X1, sk_V)),
0.00/0.51	    inference('demod', [status(thm)], ['80', '17', '67'])).
0.00/0.51	tff('82', plain,
0.00/0.51	    ![X1 : program]:
0.00/0.51	      (zip_tseitin4(X1, sk_V)
0.00/0.51	       | ~ app_encode_app(output, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(output, $o), outputs, 
0.00/0.51	               sk_W), good)),
0.00/0.51	    inference('simplify', [status(thm)], ['81'])).
0.00/0.51	tff('83', plain, ![X2 : program]: zip_tseitin4(X2, sk_V),
0.00/0.51	    inference('clc', [status(thm)], ['74', '82'])).
0.00/0.51	tff('84', plain,
0.00/0.51	    ![X15 : program, X16 : program]:
0.00/0.51	      (app_encode_app(input, $o, 
0.00/0.51	         app_encode_app(program, app_encode_fun(input, $o), halts2, X16), 
0.00/0.51	         app_encode_app(program, input, as_input, X16))
0.00/0.51	       | zip_tseitin2(X16, X15)
0.00/0.51	       | ~ zip_tseitin4(X16, X15)),
0.00/0.51	    inference('cnf', [status(esa)], [zf_stmt_4])).
0.00/0.51	tff('85', plain,
0.00/0.51	    ![X0 : program]:
0.00/0.51	      (~ $true
0.00/0.51	       | zip_tseitin2(X0, sk_V)
0.00/0.51	       | app_encode_app(input, $o, 
0.00/0.51	           app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.51	           app_encode_app(program, input, as_input, X0))),
0.00/0.51	    inference('sup-', [status(thm)], ['83', '84'])).
0.00/0.51	tff('86', plain,
0.00/0.51	    ![X0 : program]:
0.00/0.51	      (app_encode_app(input, $o, 
0.00/0.51	         app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.51	         app_encode_app(program, input, as_input, X0))
0.00/0.51	       | zip_tseitin2(X0, sk_V)),
0.00/0.51	    inference('simplify', [status(thm)], ['85'])).
0.00/0.51	tff('87', plain,
0.00/0.51	    ![X15 : program, X16 : program]:
0.00/0.51	      (app_encode_app(output, $o, 
0.00/0.51	         app_encode_app(program, app_encode_fun(output, $o), outputs, X15), 
0.00/0.51	         bad)
0.00/0.51	       | ~ zip_tseitin2(X16, X15)),
0.00/0.51	    inference('cnf', [status(esa)], [zf_stmt_8])).
0.00/0.51	tff('88', plain,
0.00/0.51	    ![X0 : program]:
0.00/0.51	      (~ $true
0.00/0.51	       | app_encode_app(input, $o, 
0.00/0.51	           app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.51	           app_encode_app(program, input, as_input, X0))
0.00/0.51	       | app_encode_app(output, $o, 
0.00/0.51	           app_encode_app(program, app_encode_fun(output, $o), outputs, sk_V), 
0.00/0.51	           bad)),
0.00/0.51	    inference('sup-', [status(thm)], ['86', '87'])).
0.00/0.51	tff('89', plain,
0.00/0.51	    ![X0 : program]:
0.00/0.51	      (app_encode_app(output, $o, 
0.00/0.51	         app_encode_app(program, app_encode_fun(output, $o), outputs, sk_V), 
0.00/0.51	         bad)
0.00/0.51	       | app_encode_app(input, $o, 
0.00/0.51	           app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.51	           app_encode_app(program, input, as_input, X0))),
0.00/0.51	    inference('simplify', [status(thm)], ['88'])).
0.00/0.51	tff('90', plain,
0.00/0.51	    ![X15 : program, X16 : program]:
0.00/0.51	      (app_encode_app(input, $o, 
0.00/0.51	         app_encode_app(program, app_encode_fun(input, $o), halts2, X15), 
0.00/0.51	         app_encode_app(program, input, as_input, X16))
0.00/0.51	       | ~ zip_tseitin2(X16, X15)),
0.00/0.51	    inference('cnf', [status(esa)], [zf_stmt_8])).
0.00/0.51	tff('91', plain,
0.00/0.51	    ![X0 : program]:
0.00/0.51	      (~ $true
0.00/0.51	       | app_encode_app(input, $o, 
0.00/0.51	           app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.51	           app_encode_app(program, input, as_input, X0))
0.00/0.51	       | app_encode_app(input, $o, 
0.00/0.51	           app_encode_app(program, app_encode_fun(input, $o), halts2, sk_V), 
0.00/0.51	           app_encode_app(program, input, as_input, X0))),
0.00/0.51	    inference('sup-', [status(thm)], ['86', '90'])).
0.00/0.51	tff('92', plain,
0.00/0.51	    ![X0 : program]:
0.00/0.51	      (app_encode_app(input, $o, 
0.00/0.51	         app_encode_app(program, app_encode_fun(input, $o), halts2, sk_V), 
0.00/0.51	         app_encode_app(program, input, as_input, X0))
0.00/0.51	       | app_encode_app(input, $o, 
0.00/0.51	           app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.51	           app_encode_app(program, input, as_input, X0))),
0.00/0.51	    inference('simplify', [status(thm)], ['91'])).
0.00/0.51	tff('93', plain,
0.00/0.51	    ![X15 : program, X16 : program]:
0.00/0.51	      (~ app_encode_app(input, $o, 
0.00/0.51	           app_encode_app(program, app_encode_fun(input, $o), halts2, X16), 
0.00/0.51	           app_encode_app(program, input, as_input, X16))
0.00/0.51	       | zip_tseitin3(X16, X15)
0.00/0.51	       | ~ zip_tseitin4(X16, X15)),
0.00/0.51	    inference('cnf', [status(esa)], [zf_stmt_4])).
0.00/0.51	tff('94', plain,
0.00/0.51	    ![X0 : program]:
0.00/0.51	      (~ $true
0.00/0.51	       | zip_tseitin3(X0, sk_V)
0.00/0.51	       | ~ app_encode_app(input, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.51	             app_encode_app(program, input, as_input, X0))),
0.00/0.51	    inference('sup-', [status(thm)], ['83', '93'])).
0.00/0.51	tff('95', plain,
0.00/0.51	    ![X0 : program]:
0.00/0.51	      (~ app_encode_app(input, $o, 
0.00/0.51	           app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.51	           app_encode_app(program, input, as_input, X0))
0.00/0.51	       | zip_tseitin3(X0, sk_V)),
0.00/0.51	    inference('simplify', [status(thm)], ['94'])).
0.00/0.51	tff('96', plain,
0.00/0.51	    ![X15 : program, X16 : program]:
0.00/0.51	      (app_encode_app(input, $o, 
0.00/0.51	         app_encode_app(program, app_encode_fun(input, $o), halts2, X15), 
0.00/0.51	         app_encode_app(program, input, as_input, X16))
0.00/0.51	       | ~ zip_tseitin3(X16, X15)),
0.00/0.51	    inference('cnf', [status(esa)], [zf_stmt_6])).
0.00/0.51	tff('97', plain,
0.00/0.51	    ![X0 : program]:
0.00/0.51	      (~ $true
0.00/0.51	       | ~ app_encode_app(input, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.51	             app_encode_app(program, input, as_input, X0))
0.00/0.51	       | app_encode_app(input, $o, 
0.00/0.51	           app_encode_app(program, app_encode_fun(input, $o), halts2, sk_V), 
0.00/0.51	           app_encode_app(program, input, as_input, X0))),
0.00/0.51	    inference('sup-', [status(thm)], ['95', '96'])).
0.00/0.51	tff('98', plain,
0.00/0.51	    ![X0 : program]:
0.00/0.51	      (app_encode_app(input, $o, 
0.00/0.51	         app_encode_app(program, app_encode_fun(input, $o), halts2, sk_V), 
0.00/0.51	         app_encode_app(program, input, as_input, X0))
0.00/0.51	       | ~ app_encode_app(input, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.51	             app_encode_app(program, input, as_input, X0))),
0.00/0.51	    inference('simplify', [status(thm)], ['97'])).
0.00/0.51	tff('99', plain,
0.00/0.51	    ![X0 : program]:
0.00/0.51	      app_encode_app(input, $o, 
0.00/0.51	        app_encode_app(program, app_encode_fun(input, $o), halts2, sk_V), 
0.00/0.51	        app_encode_app(program, input, as_input, X0)),
0.00/0.51	    inference('clc', [status(thm)], ['92', '98'])).
0.00/0.51	tff('100', plain,
0.00/0.51	    ![X19 : program, X20 : program]:
0.00/0.51	      (zip_tseitin5(X19, X20)
0.00/0.51	       | ~ app_encode_app(input, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(input, $o), halts2, X20), 
0.00/0.51	             app_encode_app(program, input, as_input, X19))
0.00/0.51	       | ~ app_encode_app(output, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(output, $o), outputs, 
0.00/0.51	               X20), bad)),
0.00/0.51	    inference('cnf', [status(esa)], [zf_stmt_12])).
0.00/0.51	tff('101', plain,
0.00/0.51	    ![X0 : program, X1 : program]:
0.00/0.51	      (~ $true
0.00/0.51	       | ~ app_encode_app(output, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(output, $o), outputs, X0), 
0.00/0.51	             bad)
0.00/0.51	       | ~ app_encode_app(input, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.51	             app_encode_app(program, input, as_input, sk_Y2(X0)))
0.00/0.51	       | ~ app_encode_app(output, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(output, $o), outputs, X0), 
0.00/0.51	             good)
0.00/0.51	       | ~ app_encode_app(input, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.51	             app_encode_app(program, input, as_input, sk_Y2(X0)))
0.00/0.51	       | zip_tseitin8(X1, sk_U)),
0.00/0.51	    inference('sup-', [status(thm)], ['100', '54'])).
0.00/0.51	tff('102', plain,
0.00/0.51	    ![X0 : program, X1 : program]:
0.00/0.51	      (zip_tseitin8(X1, sk_U)
0.00/0.51	       | ~ app_encode_app(output, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(output, $o), outputs, X0), 
0.00/0.51	             good)
0.00/0.51	       | ~ app_encode_app(input, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.51	             app_encode_app(program, input, as_input, sk_Y2(X0)))
0.00/0.51	       | ~ app_encode_app(output, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(output, $o), outputs, X0), 
0.00/0.51	             bad)),
0.00/0.51	    inference('simplify', [status(thm)], ['101'])).
0.00/0.51	tff('103', plain,
0.00/0.51	    ![X0 : program]:
0.00/0.51	      (~ $true
0.00/0.51	       | ~ app_encode_app(output, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(output, $o), outputs, 
0.00/0.51	               sk_V), bad)
0.00/0.51	       | ~ app_encode_app(output, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(output, $o), outputs, 
0.00/0.51	               sk_V), good)
0.00/0.51	       | zip_tseitin8(X0, sk_U)),
0.00/0.51	    inference('sup-', [status(thm)], ['99', '102'])).
0.00/0.51	tff('104', plain,
0.00/0.51	    ![X0 : program]:
0.00/0.51	      (zip_tseitin8(X0, sk_U)
0.00/0.51	       | ~ app_encode_app(output, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(output, $o), outputs, 
0.00/0.51	               sk_V), good)
0.00/0.51	       | ~ app_encode_app(output, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(output, $o), outputs, 
0.00/0.51	               sk_V), bad)),
0.00/0.51	    inference('simplify', [status(thm)], ['103'])).
0.00/0.51	tff('105', plain,
0.00/0.51	    ![X15 : program, X16 : program]:
0.00/0.51	      (app_encode_app(output, $o, 
0.00/0.51	         app_encode_app(program, app_encode_fun(output, $o), outputs, X15), 
0.00/0.51	         good)
0.00/0.51	       | ~ zip_tseitin3(X16, X15)),
0.00/0.51	    inference('cnf', [status(esa)], [zf_stmt_6])).
0.00/0.51	tff('106', plain,
0.00/0.51	    ![X0 : program]:
0.00/0.51	      (~ $true
0.00/0.51	       | ~ app_encode_app(input, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.51	             app_encode_app(program, input, as_input, X0))
0.00/0.51	       | app_encode_app(output, $o, 
0.00/0.51	           app_encode_app(program, app_encode_fun(output, $o), outputs, sk_V), 
0.00/0.51	           good)),
0.00/0.51	    inference('sup-', [status(thm)], ['95', '105'])).
0.00/0.51	tff('107', plain,
0.00/0.51	    ![X0 : program]:
0.00/0.51	      (app_encode_app(output, $o, 
0.00/0.51	         app_encode_app(program, app_encode_fun(output, $o), outputs, sk_V), 
0.00/0.51	         good)
0.00/0.51	       | ~ app_encode_app(input, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.51	             app_encode_app(program, input, as_input, X0))),
0.00/0.51	    inference('simplify', [status(thm)], ['106'])).
0.00/0.51	tff('108', plain,
0.00/0.51	    (~ $true
0.00/0.51	     | app_encode_app(output, $o, 
0.00/0.51	         app_encode_app(program, app_encode_fun(output, $o), outputs, sk_V), 
0.00/0.51	         good)),
0.00/0.51	    inference('sup-', [status(thm)], ['99', '107'])).
0.00/0.51	tff('109', plain,
0.00/0.51	    app_encode_app(output, $o, 
0.00/0.51	      app_encode_app(program, app_encode_fun(output, $o), outputs, sk_V), 
0.00/0.51	      good),
0.00/0.51	    inference('simplify', [status(thm)], ['108'])).
0.00/0.51	tff('110', plain,
0.00/0.51	    ![X0 : program]:
0.00/0.51	      (zip_tseitin8(X0, sk_U)
0.00/0.51	       | ~ $true
0.00/0.51	       | ~ app_encode_app(output, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(output, $o), outputs, 
0.00/0.51	               sk_V), bad)),
0.00/0.51	    inference('demod', [status(thm)], ['104', '109'])).
0.00/0.51	tff('111', plain,
0.00/0.51	    ![X0 : program]:
0.00/0.51	      (~ app_encode_app(output, $o, 
0.00/0.51	           app_encode_app(program, app_encode_fun(output, $o), outputs, sk_V), 
0.00/0.51	           bad)
0.00/0.51	       | zip_tseitin8(X0, sk_U)),
0.00/0.51	    inference('simplify', [status(thm)], ['110'])).
0.00/0.51	tff('112', plain,
0.00/0.51	    ![X0 : program, X1 : program]:
0.00/0.51	      (~ $true
0.00/0.51	       | app_encode_app(input, $o, 
0.00/0.51	           app_encode_app(program, app_encode_fun(input, $o), halts2, X1), 
0.00/0.51	           app_encode_app(program, input, as_input, X1))
0.00/0.51	       | zip_tseitin8(X0, sk_U)),
0.00/0.51	    inference('sup-', [status(thm)], ['89', '111'])).
0.00/0.51	tff('113', plain,
0.00/0.51	    ![X0 : program, X1 : program]:
0.00/0.51	      (zip_tseitin8(X0, sk_U)
0.00/0.51	       | app_encode_app(input, $o, 
0.00/0.51	           app_encode_app(program, app_encode_fun(input, $o), halts2, X1), 
0.00/0.51	           app_encode_app(program, input, as_input, X1))),
0.00/0.51	    inference('simplify', [status(thm)], ['112'])).
0.00/0.51	tff('114', plain,
0.00/0.51	    ![X21 : program, X22 : program]:
0.00/0.51	      (app_encode_app(input, $o, 
0.00/0.51	         app_encode_app(program, app_encode_fun(input, $o), halts2, X22), 
0.00/0.51	         app_encode_app(program, input, as_input, X22))
0.00/0.51	       | zip_tseitin7(X22, X21)
0.00/0.51	       | ~ zip_tseitin8(X22, X21)),
0.00/0.51	    inference('cnf', [status(esa)], [zf_stmt_15])).
0.00/0.51	tff('115', plain,
0.00/0.51	    ![X0 : program, X1 : program]:
0.00/0.51	      (~ $true
0.00/0.51	       | app_encode_app(input, $o, 
0.00/0.51	           app_encode_app(program, app_encode_fun(input, $o), halts2, X1), 
0.00/0.51	           app_encode_app(program, input, as_input, X1))
0.00/0.51	       | zip_tseitin7(X0, sk_U)
0.00/0.51	       | app_encode_app(input, $o, 
0.00/0.51	           app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.51	           app_encode_app(program, input, as_input, X0))),
0.00/0.51	    inference('sup-', [status(thm)], ['113', '114'])).
0.00/0.51	tff('116', plain,
0.00/0.51	    ![X0 : program, X1 : program]:
0.00/0.51	      (app_encode_app(input, $o, 
0.00/0.51	         app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.51	         app_encode_app(program, input, as_input, X0))
0.00/0.51	       | zip_tseitin7(X0, sk_U)
0.00/0.51	       | app_encode_app(input, $o, 
0.00/0.51	           app_encode_app(program, app_encode_fun(input, $o), halts2, X1), 
0.00/0.51	           app_encode_app(program, input, as_input, X1))),
0.00/0.51	    inference('simplify', [status(thm)], ['115'])).
0.00/0.51	tff('117', plain,
0.00/0.51	    ![X0 : program]:
0.00/0.51	      (app_encode_app(input, $o, 
0.00/0.51	         app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.51	         app_encode_app(program, input, as_input, X0))
0.00/0.51	       | zip_tseitin7(X0, sk_U)),
0.00/0.51	    inference('condensation', [status(thm)], ['116'])).
0.00/0.51	tff('118', plain,
0.00/0.51	    ![X21 : program, X22 : program]:
0.00/0.51	      (app_encode_app(input, $o, 
0.00/0.51	         app_encode_app(program, app_encode_fun(input, $o), halts2, X21), 
0.00/0.51	         app_encode_app(program, input, as_input, X22))
0.00/0.51	       | ~ zip_tseitin7(X22, X21)),
0.00/0.51	    inference('cnf', [status(esa)], [zf_stmt_17])).
0.00/0.51	tff('119', plain,
0.00/0.51	    ![X0 : program]:
0.00/0.51	      (~ $true
0.00/0.51	       | app_encode_app(input, $o, 
0.00/0.51	           app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.51	           app_encode_app(program, input, as_input, X0))
0.00/0.51	       | app_encode_app(input, $o, 
0.00/0.51	           app_encode_app(program, app_encode_fun(input, $o), halts2, sk_U), 
0.00/0.51	           app_encode_app(program, input, as_input, X0))),
0.00/0.51	    inference('sup-', [status(thm)], ['117', '118'])).
0.00/0.51	tff('120', plain,
0.00/0.51	    ![X0 : program]:
0.00/0.51	      (app_encode_app(input, $o, 
0.00/0.51	         app_encode_app(program, app_encode_fun(input, $o), halts2, sk_U), 
0.00/0.51	         app_encode_app(program, input, as_input, X0))
0.00/0.51	       | app_encode_app(input, $o, 
0.00/0.51	           app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.51	           app_encode_app(program, input, as_input, X0))),
0.00/0.51	    inference('simplify', [status(thm)], ['119'])).
0.00/0.51	tff('121', plain,
0.00/0.51	    (~ $true
0.00/0.51	     | app_encode_app(input, $o, 
0.00/0.51	         app_encode_app(program, app_encode_fun(input, $o), halts2, sk_U), 
0.00/0.51	         app_encode_app(program, input, as_input, sk_U))),
0.00/0.51	    inference('eq_fact', [status(thm)], ['120'])).
0.00/0.51	tff('122', plain,
0.00/0.51	    app_encode_app(input, $o, 
0.00/0.51	      app_encode_app(program, app_encode_fun(input, $o), halts2, sk_U), 
0.00/0.51	      app_encode_app(program, input, as_input, sk_U)),
0.00/0.51	    inference('simplify', [status(thm)], ['121'])).
0.00/0.51	tff('123', plain,
0.00/0.51	    ![X0 : program, X1 : program, X2 : program]:
0.00/0.51	      (~ $true
0.00/0.51	       | zip_tseitin8(X2, sk_U)
0.00/0.51	       | ~ app_encode_app(output, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(output, $o), outputs, X0), 
0.00/0.51	             good)
0.00/0.51	       | ~ app_encode_app(input, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.51	             app_encode_app(program, input, as_input, sk_Y2(X0)))
0.00/0.51	       | zip_tseitin8(X1, sk_U)),
0.00/0.51	    inference('sup-', [status(thm)], ['113', '56'])).
0.00/0.51	tff('124', plain,
0.00/0.51	    ![X0 : program, X1 : program, X2 : program]:
0.00/0.51	      (zip_tseitin8(X1, sk_U)
0.00/0.51	       | ~ app_encode_app(input, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.51	             app_encode_app(program, input, as_input, sk_Y2(X0)))
0.00/0.51	       | ~ app_encode_app(output, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(output, $o), outputs, X0), 
0.00/0.51	             good)
0.00/0.51	       | zip_tseitin8(X2, sk_U)),
0.00/0.51	    inference('simplify', [status(thm)], ['123'])).
0.00/0.51	tff('125', plain,
0.00/0.51	    ![X0 : program, X1 : program]:
0.00/0.51	      (zip_tseitin8(X0, sk_U)
0.00/0.51	       | ~ app_encode_app(input, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(input, $o), halts2, X1), 
0.00/0.51	             app_encode_app(program, input, as_input, sk_Y2(X1)))
0.00/0.51	       | ~ app_encode_app(output, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(output, $o), outputs, X1), 
0.00/0.51	             good)),
0.00/0.51	    inference('condensation', [status(thm)], ['124'])).
0.00/0.51	tff('126', plain,
0.00/0.51	    ![X0 : program]:
0.00/0.51	      (~ $true
0.00/0.51	       | ~ app_encode_app(output, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(output, $o), outputs, 
0.00/0.51	               sk_V), good)
0.00/0.51	       | zip_tseitin8(X0, sk_U)),
0.00/0.51	    inference('sup-', [status(thm)], ['99', '125'])).
0.00/0.51	tff('127', plain,
0.00/0.51	    ![X0 : program]: (~ $true | ~ $true | zip_tseitin8(X0, sk_U)),
0.00/0.51	    inference('demod', [status(thm)], ['126', '109'])).
0.00/0.51	tff('128', plain, ![X0 : program]: zip_tseitin8(X0, sk_U),
0.00/0.51	    inference('simplify', [status(thm)], ['127'])).
0.00/0.51	tff('129', plain,
0.00/0.51	    ![X0 : program]:
0.00/0.51	      (~ $true
0.00/0.51	       | ~ app_encode_app(input, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(input, $o), halts2, sk_U), 
0.00/0.51	             app_encode_app(program, input, as_input, X0))
0.00/0.51	       | ~ app_encode_app(input, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.51	             app_encode_app(program, input, as_input, X0))),
0.00/0.51	    inference('sup-', [status(thm)], ['128', '63'])).
0.00/0.51	tff('130', plain,
0.00/0.51	    ![X0 : program]:
0.00/0.51	      (~ app_encode_app(input, $o, 
0.00/0.51	           app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.51	           app_encode_app(program, input, as_input, X0))
0.00/0.51	       | ~ app_encode_app(input, $o, 
0.00/0.51	             app_encode_app(program, app_encode_fun(input, $o), halts2, sk_U), 
0.00/0.51	             app_encode_app(program, input, as_input, X0))),
0.00/0.51	    inference('simplify', [status(thm)], ['129'])).
0.00/0.51	tff('131', plain,
0.00/0.51	    (~ $true
0.00/0.51	     | ~ app_encode_app(input, $o, 
0.00/0.51	           app_encode_app(program, app_encode_fun(input, $o), halts2, sk_U), 
0.00/0.51	           app_encode_app(program, input, as_input, sk_U))),
0.00/0.51	    inference('sup-', [status(thm)], ['122', '130'])).
0.00/0.51	tff('132', plain, (~ $true | ~ $true),
0.00/0.51	    inference('demod', [status(thm)], ['131', '122'])).
0.00/0.51	tff('133', plain, $false, inference('simplify', [status(thm)], ['132'])).
0.00/0.51	
0.00/0.51	% SZS output end Refutation
0.00/0.51	EOF
