0.00/0.00	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : app
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : rpo6
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-ho \
0.00/0.00	  --no-avatar \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n078.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 08:22:38 CST 2018
0.00/0.24	% done 76 iterations in 0.043s
0.00/0.24	% SZS status Theorem for 'stdin'
0.00/0.24	% SZS output start Refutation
0.00/0.25	tff(zf_stmt_18, conjecture,
0.00/0.25	  (~
0.00/0.25	    (?[X1:algorithm]:
0.00/0.25	       (![Y1:program,Z1:input]:
0.00/0.25	          app_encode_app(input,$o,
0.00/0.25	                         app_encode_app(program,app_encode_fun(input,$o),
0.00/0.25	                                        app_encode_app(algorithm,
0.00/0.25	                                                       app_encode_fun(
0.00/0.25	                                                       program,
0.00/0.25	                                                       app_encode_fun(
0.00/0.25	                                                       input,$o)),decides,X1),
0.00/0.25	                                        Y1),
0.00/0.25	                         Z1))))).
0.00/0.25	tff(zf_stmt_0, negated_conjecture,
0.00/0.25	  (?[X1:algorithm]:
0.00/0.25	     (![Y1:program,Z1:input]:
0.00/0.25	        app_encode_app(input,$o,
0.00/0.25	                       app_encode_app(program,app_encode_fun(input,$o),
0.00/0.25	                                      app_encode_app(algorithm,
0.00/0.25	                                                     app_encode_fun(program,
0.00/0.25	                                                                    app_encode_fun(
0.00/0.25	                                                                    input,$o)),
0.00/0.25	                                                     decides,X1),
0.00/0.25	                                      Y1),
0.00/0.25	                       Z1)))).
0.00/0.25	tff('0', plain,
0.00/0.25	    ![X21 : program, X22 : input]:
0.00/0.25	      app_encode_app(input, $o, 
0.00/0.25	        app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.25	          app_encode_app(algorithm, 
0.00/0.25	            app_encode_fun(program, app_encode_fun(input, $o)), decides, 
0.00/0.25	            sk_X1), X21), X22),
0.00/0.25	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.25	tff(zf_stmt_14, axiom,
0.00/0.25	  ((?[X:algorithm]:
0.00/0.25	      (![Y:program,Z:input]:
0.00/0.25	         app_encode_app(input,$o,
0.00/0.25	                        app_encode_app(program,app_encode_fun(input,$o),
0.00/0.25	                                       app_encode_app(algorithm,
0.00/0.25	                                                      app_encode_fun(
0.00/0.25	                                                      program,
0.00/0.25	                                                      app_encode_fun(
0.00/0.25	                                                      input,$o)),decides,X),
0.00/0.25	                                       Y),
0.00/0.25	                        Z))) =>
0.00/0.25	   (?[W:program]:
0.00/0.25	      (![Y:program,Z:input]:
0.00/0.25	         app_encode_app(input,$o,
0.00/0.25	                        app_encode_app(program,app_encode_fun(input,$o),
0.00/0.25	                                       app_encode_app(algorithm,
0.00/0.25	                                                      app_encode_fun(
0.00/0.25	                                                      program,
0.00/0.25	                                                      app_encode_fun(
0.00/0.25	                                                      input,$o)),decides,
0.00/0.25	                                                      app_encode_app(
0.00/0.25	                                                      program,algorithm,
0.00/0.25	                                                      algorithm_of,W)),
0.00/0.25	                                       Y),
0.00/0.25	                        Z))))).
0.00/0.25	tff('1', plain,
0.00/0.25	    ![X0 : program, X1 : input, X2 : algorithm]:
0.00/0.25	      (app_encode_app(input, $o, 
0.00/0.25	         app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.25	           app_encode_app(algorithm, 
0.00/0.25	             app_encode_fun(program, app_encode_fun(input, $o)), decides, 
0.00/0.25	             app_encode_app(program, algorithm, algorithm_of, sk_W)), X0), 
0.00/0.25	         X1)
0.00/0.25	       | ~ app_encode_app(input, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.25	               app_encode_app(algorithm, 
0.00/0.25	                 app_encode_fun(program, app_encode_fun(input, $o)), 
0.00/0.25	                 decides, X2), sk_Y(X2)), sk_Z(X2))),
0.00/0.25	    inference('cnf', [status(esa)], [zf_stmt_14])).
0.00/0.25	tff('2', plain,
0.00/0.25	    ![X0 : input, X1 : program]:
0.00/0.25	      (~ $true
0.00/0.25	       | app_encode_app(input, $o, 
0.00/0.25	           app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.25	             app_encode_app(algorithm, 
0.00/0.25	               app_encode_fun(program, app_encode_fun(input, $o)), decides, 
0.00/0.25	               app_encode_app(program, algorithm, algorithm_of, sk_W)), X1), 
0.00/0.25	           X0)),
0.00/0.25	    inference('sup-', [status(thm)], ['0', '1'])).
0.00/0.25	tff('3', plain,
0.00/0.25	    ![X0 : input, X1 : program]:
0.00/0.25	      app_encode_app(input, $o, 
0.00/0.25	        app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.25	          app_encode_app(algorithm, 
0.00/0.25	            app_encode_fun(program, app_encode_fun(input, $o)), decides, 
0.00/0.25	            app_encode_app(program, algorithm, algorithm_of, sk_W)), X1), X0),
0.00/0.25	    inference('simplify', [status(thm)], ['2'])).
0.00/0.25	tff(zf_stmt_15, axiom,
0.00/0.25	  (![W:program,Y:program,Z:input]:
0.00/0.25	     (app_encode_app(input,$o,
0.00/0.25	                     app_encode_app(program,app_encode_fun(input,$o),
0.00/0.25	                                    app_encode_app(algorithm,
0.00/0.25	                                                   app_encode_fun(program,
0.00/0.25	                                                                  app_encode_fun(
0.00/0.25	                                                                  input,$o)),
0.00/0.25	                                                   decides,
0.00/0.25	                                                   app_encode_app(program,
0.00/0.25	                                                                  algorithm,
0.00/0.25	                                                                  algorithm_of,
0.00/0.25	                                                                  W)),
0.00/0.25	                                    Y),
0.00/0.25	                     Z) =>
0.00/0.25	      (![Y:program,Z:input]:
0.00/0.25	         ((app_encode_app(input,$o,
0.00/0.25	                          app_encode_app(program,app_encode_fun(input,$o),
0.00/0.25	                                         halts2,Y),
0.00/0.25	                          Z) =>
0.00/0.25	           (app_encode_app(input,$o,
0.00/0.25	                           app_encode_app(program,app_encode_fun(input,$o),
0.00/0.25	                                          app_encode_app(program,
0.00/0.25	                                                         app_encode_fun(
0.00/0.25	                                                         program,
0.00/0.25	                                                         app_encode_fun(
0.00/0.25	                                                         input,$o)),halts3,W),
0.00/0.25	                                          Y),
0.00/0.25	                           Z) & 
0.00/0.25	            app_encode_app(output,$o,
0.00/0.25	                           app_encode_app(program,app_encode_fun(output,$o),
0.00/0.25	                                          outputs,W),
0.00/0.25	                           good))) & 
0.00/0.25	          ((~
0.00/0.25	             app_encode_app(input,$o,
0.00/0.25	                            app_encode_app(program,app_encode_fun(input,$o),
0.00/0.25	                                           halts2,Y),
0.00/0.25	                            Z)) =>
0.00/0.25	           (app_encode_app(input,$o,
0.00/0.25	                           app_encode_app(program,app_encode_fun(input,$o),
0.00/0.25	                                          app_encode_app(program,
0.00/0.25	                                                         app_encode_fun(
0.00/0.25	                                                         program,
0.00/0.25	                                                         app_encode_fun(
0.00/0.25	                                                         input,$o)),halts3,W),
0.00/0.25	                                          Y),
0.00/0.25	                           Z) & 
0.00/0.25	            app_encode_app(output,$o,
0.00/0.25	                           app_encode_app(program,app_encode_fun(output,$o),
0.00/0.25	                                          outputs,W),
0.00/0.25	                           bad)))))))).
0.00/0.25	tff('4', plain,
0.00/0.25	    ![X3 : program, X5 : program, X6 : program, X7 : input, X8 : input]:
0.00/0.25	      (app_encode_app(input, $o, 
0.00/0.25	         app_encode_app(program, app_encode_fun(input, $o), halts2, X3), X8)
0.00/0.25	       | app_encode_app(input, $o, 
0.00/0.25	           app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.25	             app_encode_app(program, 
0.00/0.25	               app_encode_fun(program, app_encode_fun(input, $o)), halts3, 
0.00/0.25	               X5), X3), X8)
0.00/0.25	       | ~ app_encode_app(input, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.25	               app_encode_app(algorithm, 
0.00/0.25	                 app_encode_fun(program, app_encode_fun(input, $o)), 
0.00/0.25	                 decides, 
0.00/0.25	                 app_encode_app(program, algorithm, algorithm_of, X5)), X6), 
0.00/0.25	             X7)),
0.00/0.25	    inference('cnf', [status(esa)], [zf_stmt_15])).
0.00/0.25	tff('5', plain,
0.00/0.25	    ![X3 : program, X4 : input, X5 : program, X6 : program, X7 : input]:
0.00/0.25	      (~ app_encode_app(input, $o, 
0.00/0.25	           app_encode_app(program, app_encode_fun(input, $o), halts2, X3), 
0.00/0.25	           X4)
0.00/0.25	       | app_encode_app(input, $o, 
0.00/0.25	           app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.25	             app_encode_app(program, 
0.00/0.25	               app_encode_fun(program, app_encode_fun(input, $o)), halts3, 
0.00/0.25	               X5), X3), X4)
0.00/0.25	       | ~ app_encode_app(input, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.25	               app_encode_app(algorithm, 
0.00/0.25	                 app_encode_fun(program, app_encode_fun(input, $o)), 
0.00/0.25	                 decides, 
0.00/0.25	                 app_encode_app(program, algorithm, algorithm_of, X5)), X6), 
0.00/0.25	             X7)),
0.00/0.25	    inference('cnf', [status(esa)], [zf_stmt_15])).
0.00/0.25	tff('6', plain,
0.00/0.25	    ![X3 : program, X5 : program, X6 : program, X7 : input, X8 : input]:
0.00/0.25	      (~ app_encode_app(input, $o, 
0.00/0.25	           app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.25	             app_encode_app(algorithm, 
0.00/0.25	               app_encode_fun(program, app_encode_fun(input, $o)), decides, 
0.00/0.25	               app_encode_app(program, algorithm, algorithm_of, X5)), X6), 
0.00/0.25	           X7)
0.00/0.25	       | app_encode_app(input, $o, 
0.00/0.25	           app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.25	             app_encode_app(program, 
0.00/0.25	               app_encode_fun(program, app_encode_fun(input, $o)), halts3, 
0.00/0.25	               X5), X3), X8)),
0.00/0.25	    inference('clc', [status(thm)], ['4', '5'])).
0.00/0.25	tff('7', plain,
0.00/0.25	    ![X2 : input, X3 : program]:
0.00/0.25	      (~ $true
0.00/0.25	       | app_encode_app(input, $o, 
0.00/0.25	           app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.25	             app_encode_app(program, 
0.00/0.25	               app_encode_fun(program, app_encode_fun(input, $o)), halts3, 
0.00/0.25	               sk_W), X3), X2)),
0.00/0.25	    inference('sup-', [status(thm)], ['3', '6'])).
0.00/0.25	tff('8', plain,
0.00/0.25	    ![X2 : input, X3 : program]:
0.00/0.25	      app_encode_app(input, $o, 
0.00/0.25	        app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.25	          app_encode_app(program, 
0.00/0.25	            app_encode_fun(program, app_encode_fun(input, $o)), halts3, sk_W), 
0.00/0.25	          X3), X2),
0.00/0.25	    inference('simplify', [status(thm)], ['7'])).
0.00/0.25	tff(zf_stmt_16, axiom,
0.00/0.25	  ((?[W:program]:
0.00/0.25	      (![Y:program]:
0.00/0.25	         (((~
0.00/0.25	             app_encode_app(input,$o,
0.00/0.25	                            app_encode_app(program,app_encode_fun(input,$o),
0.00/0.25	                                           halts2,Y),
0.00/0.25	                            app_encode_app(program,input,as_input,Y))) =>
0.00/0.25	           (app_encode_app(output,$o,
0.00/0.25	                           app_encode_app(program,app_encode_fun(output,$o),
0.00/0.25	                                          outputs,W),
0.00/0.25	                           bad) & 
0.00/0.25	            app_encode_app(input,$o,
0.00/0.25	                           app_encode_app(program,app_encode_fun(input,$o),
0.00/0.25	                                          app_encode_app(program,
0.00/0.25	                                                         app_encode_fun(
0.00/0.25	                                                         program,
0.00/0.25	                                                         app_encode_fun(
0.00/0.25	                                                         input,$o)),halts3,W),
0.00/0.25	                                          Y),
0.00/0.25	                           app_encode_app(program,input,as_input,Y)))) & 
0.00/0.25	          (app_encode_app(input,$o,
0.00/0.25	                          app_encode_app(program,app_encode_fun(input,$o),
0.00/0.25	                                         halts2,Y),
0.00/0.25	                          app_encode_app(program,input,as_input,Y)) =>
0.00/0.25	           (app_encode_app(output,$o,
0.00/0.25	                           app_encode_app(program,app_encode_fun(output,$o),
0.00/0.25	                                          outputs,W),
0.00/0.25	                           good) & 
0.00/0.25	            app_encode_app(input,$o,
0.00/0.25	                           app_encode_app(program,app_encode_fun(input,$o),
0.00/0.25	                                          app_encode_app(program,
0.00/0.25	                                                         app_encode_fun(
0.00/0.25	                                                         program,
0.00/0.25	                                                         app_encode_fun(
0.00/0.25	                                                         input,$o)),halts3,W),
0.00/0.25	                                          Y),
0.00/0.25	                           app_encode_app(program,input,as_input,Y))))))) =>
0.00/0.25	   (?[V:program]:
0.00/0.25	      (![Y:program]:
0.00/0.25	         (((~
0.00/0.25	             app_encode_app(input,$o,
0.00/0.25	                            app_encode_app(program,app_encode_fun(input,$o),
0.00/0.25	                                           halts2,Y),
0.00/0.25	                            app_encode_app(program,input,as_input,Y))) =>
0.00/0.25	           (app_encode_app(output,$o,
0.00/0.25	                           app_encode_app(program,app_encode_fun(output,$o),
0.00/0.25	                                          outputs,V),
0.00/0.25	                           bad) & 
0.00/0.25	            app_encode_app(input,$o,
0.00/0.25	                           app_encode_app(program,app_encode_fun(input,$o),
0.00/0.25	                                          halts2,V),
0.00/0.25	                           app_encode_app(program,input,as_input,Y)))) & 
0.00/0.25	          (app_encode_app(input,$o,
0.00/0.25	                          app_encode_app(program,app_encode_fun(input,$o),
0.00/0.25	                                         halts2,Y),
0.00/0.25	                          app_encode_app(program,input,as_input,Y)) =>
0.00/0.25	           (app_encode_app(output,$o,
0.00/0.25	                           app_encode_app(program,app_encode_fun(output,$o),
0.00/0.25	                                          outputs,V),
0.00/0.25	                           good) & 
0.00/0.25	            app_encode_app(input,$o,
0.00/0.25	                           app_encode_app(program,app_encode_fun(input,$o),
0.00/0.25	                                          halts2,V),
0.00/0.25	                           app_encode_app(program,input,as_input,Y))))))))).
0.00/0.25	tff(zf_stmt_1, axiom,
0.00/0.25	  (((~
0.00/0.25	      app_encode_app(input,$o,
0.00/0.25	                     app_encode_app(program,app_encode_fun(input,$o),halts2,Y),
0.00/0.25	                     app_encode_app(program,input,as_input,Y))) =>
0.00/0.25	    (app_encode_app(input,$o,
0.00/0.25	                    app_encode_app(program,app_encode_fun(input,$o),
0.00/0.25	                                   app_encode_app(program,
0.00/0.25	                                                  app_encode_fun(program,
0.00/0.25	                                                                 app_encode_fun(
0.00/0.25	                                                                 input,$o)),
0.00/0.25	                                                  halts3,W),
0.00/0.25	                                   Y),
0.00/0.25	                    app_encode_app(program,input,as_input,Y)) & 
0.00/0.25	     app_encode_app(output,$o,
0.00/0.25	                    app_encode_app(program,app_encode_fun(output,$o),outputs,
0.00/0.25	                                   W),
0.00/0.25	                    bad))) =>
0.00/0.25	   zip_tseitin0(Y,W))).
0.00/0.25	tff('9', plain,
0.00/0.25	    ![X9 : program, X10 : program]:
0.00/0.25	      (zip_tseitin0(X9, X10)
0.00/0.25	       | ~ app_encode_app(input, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.25	               app_encode_app(program, 
0.00/0.25	                 app_encode_fun(program, app_encode_fun(input, $o)), halts3, 
0.00/0.25	                 X10), X9), app_encode_app(program, input, as_input, X9))
0.00/0.25	       | ~ app_encode_app(output, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(output, $o), outputs, 
0.00/0.25	               X10), bad)),
0.00/0.25	    inference('cnf', [status(esa)], [zf_stmt_1])).
0.00/0.25	tff(zf_stmt_2, axiom,
0.00/0.25	  ((app_encode_app(input,$o,
0.00/0.25	                   app_encode_app(program,app_encode_fun(input,$o),halts2,Y),
0.00/0.25	                   app_encode_app(program,input,as_input,Y)) =>
0.00/0.25	    (app_encode_app(input,$o,
0.00/0.25	                    app_encode_app(program,app_encode_fun(input,$o),
0.00/0.25	                                   app_encode_app(program,
0.00/0.25	                                                  app_encode_fun(program,
0.00/0.25	                                                                 app_encode_fun(
0.00/0.25	                                                                 input,$o)),
0.00/0.25	                                                  halts3,W),
0.00/0.25	                                   Y),
0.00/0.25	                    app_encode_app(program,input,as_input,Y)) & 
0.00/0.25	     app_encode_app(output,$o,
0.00/0.25	                    app_encode_app(program,app_encode_fun(output,$o),outputs,
0.00/0.25	                                   W),
0.00/0.25	                    good))) =>
0.00/0.25	   zip_tseitin1(Y,W))).
0.00/0.25	tff('10', plain,
0.00/0.25	    ![X9 : program, X10 : program]:
0.00/0.25	      (zip_tseitin1(X9, X10)
0.00/0.25	       | app_encode_app(input, $o, 
0.00/0.25	           app_encode_app(program, app_encode_fun(input, $o), halts2, X9), 
0.00/0.25	           app_encode_app(program, input, as_input, X9))),
0.00/0.25	    inference('cnf', [status(esa)], [zf_stmt_2])).
0.00/0.25	tff(zf_stmt_3, type, zip_tseitin4 : (program * program) > $o).
0.00/0.25	tff(zf_stmt_4, axiom,
0.00/0.25	  (zip_tseitin4(Y,V) =>
0.00/0.25	   ((app_encode_app(input,$o,
0.00/0.25	                    app_encode_app(program,app_encode_fun(input,$o),halts2,Y),
0.00/0.25	                    app_encode_app(program,input,as_input,Y)) =>
0.00/0.25	     zip_tseitin3(Y,V)) & 
0.00/0.25	    ((~
0.00/0.25	       app_encode_app(input,$o,
0.00/0.25	                      app_encode_app(program,app_encode_fun(input,$o),halts2,
0.00/0.25	                                     Y),
0.00/0.25	                      app_encode_app(program,input,as_input,Y))) =>
0.00/0.25	     zip_tseitin2(Y,V))))).
0.00/0.25	tff(zf_stmt_5, type, zip_tseitin3 : (program * program) > $o).
0.00/0.25	tff(zf_stmt_6, axiom,
0.00/0.25	  (zip_tseitin3(Y,V) =>
0.00/0.25	   (app_encode_app(input,$o,
0.00/0.25	                   app_encode_app(program,app_encode_fun(input,$o),halts2,V),
0.00/0.25	                   app_encode_app(program,input,as_input,Y)) & 
0.00/0.25	    app_encode_app(output,$o,
0.00/0.25	                   app_encode_app(program,app_encode_fun(output,$o),outputs,V),
0.00/0.25	                   good)))).
0.00/0.25	tff(zf_stmt_7, type, zip_tseitin2 : (program * program) > $o).
0.00/0.25	tff(zf_stmt_8, axiom,
0.00/0.25	  (zip_tseitin2(Y,V) =>
0.00/0.25	   (app_encode_app(input,$o,
0.00/0.25	                   app_encode_app(program,app_encode_fun(input,$o),halts2,V),
0.00/0.25	                   app_encode_app(program,input,as_input,Y)) & 
0.00/0.25	    app_encode_app(output,$o,
0.00/0.25	                   app_encode_app(program,app_encode_fun(output,$o),outputs,V),
0.00/0.25	                   bad)))).
0.00/0.25	tff(zf_stmt_9, type, zip_tseitin1 : (program * program) > $o).
0.00/0.25	tff(zf_stmt_10, type, zip_tseitin0 : (program * program) > $o).
0.00/0.25	tff(zf_stmt_11, axiom,
0.00/0.25	  ((?[W:program]: (![Y:program]: (zip_tseitin1(Y,W) & zip_tseitin0(Y,W)))) =>
0.00/0.25	   (?[V:program]: (![Y:program]: zip_tseitin4(Y,V))))).
0.00/0.25	tff('11', plain,
0.00/0.25	    ![X13 : program, X14 : program]:
0.00/0.25	      (zip_tseitin4(X13, sk_V)
0.00/0.25	       | ~ zip_tseitin0(sk_Y1(X14), X14)
0.00/0.25	       | ~ zip_tseitin1(sk_Y1(X14), X14)),
0.00/0.25	    inference('cnf', [status(esa)], [zf_stmt_11])).
0.00/0.25	tff('12', plain,
0.00/0.25	    ![X0 : program, X1 : program]:
0.00/0.25	      (~ $true
0.00/0.25	       | app_encode_app(input, $o, 
0.00/0.25	           app_encode_app(program, app_encode_fun(input, $o), halts2, 
0.00/0.25	             sk_Y1(X0)), app_encode_app(program, input, as_input, sk_Y1(X0)))
0.00/0.25	       | ~ zip_tseitin0(sk_Y1(X0), X0)
0.00/0.25	       | zip_tseitin4(X1, sk_V)),
0.00/0.25	    inference('sup-', [status(thm)], ['10', '11'])).
0.00/0.25	tff('13', plain,
0.00/0.25	    ![X0 : program, X1 : program]:
0.00/0.25	      (zip_tseitin4(X1, sk_V)
0.00/0.25	       | ~ zip_tseitin0(sk_Y1(X0), X0)
0.00/0.25	       | app_encode_app(input, $o, 
0.00/0.25	           app_encode_app(program, app_encode_fun(input, $o), halts2, 
0.00/0.25	             sk_Y1(X0)), app_encode_app(program, input, as_input, sk_Y1(X0)))),
0.00/0.25	    inference('simplify', [status(thm)], ['12'])).
0.00/0.25	tff('14', plain,
0.00/0.25	    ![X0 : program, X1 : program]:
0.00/0.25	      (~ $true
0.00/0.25	       | ~ app_encode_app(output, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(output, $o), outputs, X0), 
0.00/0.25	             bad)
0.00/0.25	       | ~ app_encode_app(input, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.25	               app_encode_app(program, 
0.00/0.25	                 app_encode_fun(program, app_encode_fun(input, $o)), halts3, 
0.00/0.25	                 X0), sk_Y1(X0)), 
0.00/0.25	             app_encode_app(program, input, as_input, sk_Y1(X0)))
0.00/0.25	       | app_encode_app(input, $o, 
0.00/0.25	           app_encode_app(program, app_encode_fun(input, $o), halts2, 
0.00/0.25	             sk_Y1(X0)), app_encode_app(program, input, as_input, sk_Y1(X0)))
0.00/0.25	       | zip_tseitin4(X1, sk_V)),
0.00/0.25	    inference('sup-', [status(thm)], ['9', '13'])).
0.00/0.25	tff('15', plain,
0.00/0.25	    ![X0 : program, X1 : program]:
0.00/0.25	      (zip_tseitin4(X1, sk_V)
0.00/0.25	       | app_encode_app(input, $o, 
0.00/0.25	           app_encode_app(program, app_encode_fun(input, $o), halts2, 
0.00/0.25	             sk_Y1(X0)), app_encode_app(program, input, as_input, sk_Y1(X0)))
0.00/0.25	       | ~ app_encode_app(input, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.25	               app_encode_app(program, 
0.00/0.25	                 app_encode_fun(program, app_encode_fun(input, $o)), halts3, 
0.00/0.25	                 X0), sk_Y1(X0)), 
0.00/0.25	             app_encode_app(program, input, as_input, sk_Y1(X0)))
0.00/0.25	       | ~ app_encode_app(output, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(output, $o), outputs, X0), 
0.00/0.25	             bad)),
0.00/0.25	    inference('simplify', [status(thm)], ['14'])).
0.00/0.25	tff('16', plain,
0.00/0.25	    ![X0 : program]:
0.00/0.25	      (~ $true
0.00/0.25	       | ~ app_encode_app(output, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(output, $o), outputs, 
0.00/0.25	               sk_W), bad)
0.00/0.25	       | app_encode_app(input, $o, 
0.00/0.25	           app_encode_app(program, app_encode_fun(input, $o), halts2, 
0.00/0.25	             sk_Y1(sk_W)), 
0.00/0.25	           app_encode_app(program, input, as_input, sk_Y1(sk_W)))
0.00/0.25	       | zip_tseitin4(X0, sk_V)),
0.00/0.25	    inference('sup-', [status(thm)], ['8', '15'])).
0.00/0.25	tff('17', plain,
0.00/0.25	    ![X3 : program, X5 : program, X6 : program, X7 : input, X8 : input]:
0.00/0.25	      (app_encode_app(input, $o, 
0.00/0.25	         app_encode_app(program, app_encode_fun(input, $o), halts2, X3), X8)
0.00/0.25	       | app_encode_app(output, $o, 
0.00/0.25	           app_encode_app(program, app_encode_fun(output, $o), outputs, X5), 
0.00/0.25	           bad)
0.00/0.25	       | ~ app_encode_app(input, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.25	               app_encode_app(algorithm, 
0.00/0.25	                 app_encode_fun(program, app_encode_fun(input, $o)), 
0.00/0.25	                 decides, 
0.00/0.25	                 app_encode_app(program, algorithm, algorithm_of, X5)), X6), 
0.00/0.25	             X7)),
0.00/0.25	    inference('cnf', [status(esa)], [zf_stmt_15])).
0.00/0.25	tff('18', plain,
0.00/0.25	    ![X2 : input, X3 : program]:
0.00/0.25	      (~ $true
0.00/0.25	       | app_encode_app(output, $o, 
0.00/0.25	           app_encode_app(program, app_encode_fun(output, $o), outputs, sk_W), 
0.00/0.25	           bad)
0.00/0.25	       | app_encode_app(input, $o, 
0.00/0.25	           app_encode_app(program, app_encode_fun(input, $o), halts2, X3), 
0.00/0.25	           X2)),
0.00/0.25	    inference('sup-', [status(thm)], ['3', '17'])).
0.00/0.25	tff('19', plain,
0.00/0.25	    ![X2 : input, X3 : program]:
0.00/0.25	      (app_encode_app(input, $o, 
0.00/0.25	         app_encode_app(program, app_encode_fun(input, $o), halts2, X3), X2)
0.00/0.25	       | app_encode_app(output, $o, 
0.00/0.25	           app_encode_app(program, app_encode_fun(output, $o), outputs, sk_W), 
0.00/0.25	           bad)),
0.00/0.25	    inference('simplify', [status(thm)], ['18'])).
0.00/0.25	tff('20', plain,
0.00/0.25	    ![X3 : program, X4 : input, X5 : program, X6 : program, X7 : input]:
0.00/0.25	      (~ app_encode_app(input, $o, 
0.00/0.25	           app_encode_app(program, app_encode_fun(input, $o), halts2, X3), 
0.00/0.25	           X4)
0.00/0.25	       | app_encode_app(output, $o, 
0.00/0.25	           app_encode_app(program, app_encode_fun(output, $o), outputs, X5), 
0.00/0.25	           good)
0.00/0.25	       | ~ app_encode_app(input, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.25	               app_encode_app(algorithm, 
0.00/0.25	                 app_encode_fun(program, app_encode_fun(input, $o)), 
0.00/0.25	                 decides, 
0.00/0.25	                 app_encode_app(program, algorithm, algorithm_of, X5)), X6), 
0.00/0.25	             X7)),
0.00/0.25	    inference('cnf', [status(esa)], [zf_stmt_15])).
0.00/0.25	tff('21', plain,
0.00/0.25	    ![X2 : input, X3 : program, X4 : program]:
0.00/0.25	      (~ $true
0.00/0.25	       | app_encode_app(output, $o, 
0.00/0.25	           app_encode_app(program, app_encode_fun(output, $o), outputs, sk_W), 
0.00/0.25	           bad)
0.00/0.25	       | ~ app_encode_app(input, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.25	               app_encode_app(algorithm, 
0.00/0.25	                 app_encode_fun(program, app_encode_fun(input, $o)), 
0.00/0.25	                 decides, 
0.00/0.25	                 app_encode_app(program, algorithm, algorithm_of, X4)), X3), 
0.00/0.25	             X2)
0.00/0.25	       | app_encode_app(output, $o, 
0.00/0.25	           app_encode_app(program, app_encode_fun(output, $o), outputs, X4), 
0.00/0.25	           good)),
0.00/0.25	    inference('sup-', [status(thm)], ['19', '20'])).
0.00/0.25	tff('22', plain,
0.00/0.25	    ![X2 : input, X3 : program, X4 : program]:
0.00/0.25	      (app_encode_app(output, $o, 
0.00/0.25	         app_encode_app(program, app_encode_fun(output, $o), outputs, X4), 
0.00/0.25	         good)
0.00/0.25	       | ~ app_encode_app(input, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.25	               app_encode_app(algorithm, 
0.00/0.25	                 app_encode_fun(program, app_encode_fun(input, $o)), 
0.00/0.25	                 decides, 
0.00/0.25	                 app_encode_app(program, algorithm, algorithm_of, X4)), X3), 
0.00/0.25	             X2)
0.00/0.25	       | app_encode_app(output, $o, 
0.00/0.25	           app_encode_app(program, app_encode_fun(output, $o), outputs, sk_W), 
0.00/0.25	           bad)),
0.00/0.25	    inference('simplify', [status(thm)], ['21'])).
0.00/0.25	tff('23', plain,
0.00/0.25	    (~ $true
0.00/0.25	     | app_encode_app(output, $o, 
0.00/0.25	         app_encode_app(program, app_encode_fun(output, $o), outputs, sk_W), 
0.00/0.25	         bad)
0.00/0.25	     | app_encode_app(output, $o, 
0.00/0.25	         app_encode_app(program, app_encode_fun(output, $o), outputs, sk_W), 
0.00/0.25	         good)),
0.00/0.25	    inference('sup-', [status(thm)], ['3', '22'])).
0.00/0.25	tff('24', plain,
0.00/0.25	    (app_encode_app(output, $o, 
0.00/0.25	       app_encode_app(program, app_encode_fun(output, $o), outputs, sk_W), 
0.00/0.25	       good)
0.00/0.25	     | app_encode_app(output, $o, 
0.00/0.25	         app_encode_app(program, app_encode_fun(output, $o), outputs, sk_W), 
0.00/0.25	         bad)),
0.00/0.25	    inference('simplify', [status(thm)], ['23'])).
0.00/0.25	tff(zf_stmt_17, axiom,
0.00/0.25	  ((?[V:program]:
0.00/0.25	      (![Y:program]:
0.00/0.25	         (((~
0.00/0.25	             app_encode_app(input,$o,
0.00/0.25	                            app_encode_app(program,app_encode_fun(input,$o),
0.00/0.25	                                           halts2,Y),
0.00/0.25	                            app_encode_app(program,input,as_input,Y))) =>
0.00/0.25	           (app_encode_app(output,$o,
0.00/0.25	                           app_encode_app(program,app_encode_fun(output,$o),
0.00/0.25	                                          outputs,V),
0.00/0.25	                           bad) & 
0.00/0.25	            app_encode_app(input,$o,
0.00/0.25	                           app_encode_app(program,app_encode_fun(input,$o),
0.00/0.25	                                          halts2,V),
0.00/0.25	                           app_encode_app(program,input,as_input,Y)))) & 
0.00/0.25	          (app_encode_app(input,$o,
0.00/0.25	                          app_encode_app(program,app_encode_fun(input,$o),
0.00/0.25	                                         halts2,Y),
0.00/0.25	                          app_encode_app(program,input,as_input,Y)) =>
0.00/0.25	           (app_encode_app(output,$o,
0.00/0.25	                           app_encode_app(program,app_encode_fun(output,$o),
0.00/0.25	                                          outputs,V),
0.00/0.25	                           good) & 
0.00/0.25	            app_encode_app(input,$o,
0.00/0.25	                           app_encode_app(program,app_encode_fun(input,$o),
0.00/0.25	                                          halts2,V),
0.00/0.25	                           app_encode_app(program,input,as_input,Y))))))) =>
0.00/0.25	   (?[U:program]:
0.00/0.25	      (![Y:program]:
0.00/0.25	         (((~
0.00/0.25	             app_encode_app(input,$o,
0.00/0.25	                            app_encode_app(program,app_encode_fun(input,$o),
0.00/0.25	                                           halts2,Y),
0.00/0.25	                            app_encode_app(program,input,as_input,Y))) =>
0.00/0.25	           (app_encode_app(output,$o,
0.00/0.25	                           app_encode_app(program,app_encode_fun(output,$o),
0.00/0.25	                                          outputs,U),
0.00/0.25	                           bad) & 
0.00/0.25	            app_encode_app(input,$o,
0.00/0.25	                           app_encode_app(program,app_encode_fun(input,$o),
0.00/0.25	                                          halts2,U),
0.00/0.25	                           app_encode_app(program,input,as_input,Y)))) & 
0.00/0.25	          (app_encode_app(input,$o,
0.00/0.25	                          app_encode_app(program,app_encode_fun(input,$o),
0.00/0.25	                                         halts2,Y),
0.00/0.25	                          app_encode_app(program,input,as_input,Y)) =>
0.00/0.25	           (~
0.00/0.25	             app_encode_app(input,$o,
0.00/0.25	                            app_encode_app(program,app_encode_fun(input,$o),
0.00/0.25	                                           halts2,U),
0.00/0.25	                            app_encode_app(program,input,as_input,Y))))))))).
0.00/0.25	tff(zf_stmt_12, axiom,
0.00/0.25	  (((~
0.00/0.25	      app_encode_app(input,$o,
0.00/0.25	                     app_encode_app(program,app_encode_fun(input,$o),halts2,Y),
0.00/0.25	                     app_encode_app(program,input,as_input,Y))) =>
0.00/0.25	    (app_encode_app(input,$o,
0.00/0.25	                    app_encode_app(program,app_encode_fun(input,$o),halts2,V),
0.00/0.25	                    app_encode_app(program,input,as_input,Y)) & 
0.00/0.25	     app_encode_app(output,$o,
0.00/0.25	                    app_encode_app(program,app_encode_fun(output,$o),outputs,
0.00/0.25	                                   V),
0.00/0.25	                    bad))) =>
0.00/0.25	   zip_tseitin5(Y,V))).
0.00/0.25	tff('25', plain,
0.00/0.25	    ![X15 : program, X16 : program]:
0.00/0.25	      (zip_tseitin5(X15, X16)
0.00/0.25	       | ~ app_encode_app(input, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(input, $o), halts2, X15), 
0.00/0.25	             app_encode_app(program, input, as_input, X15))),
0.00/0.25	    inference('cnf', [status(esa)], [zf_stmt_12])).
0.00/0.25	tff(zf_stmt_13, axiom,
0.00/0.25	  ((app_encode_app(input,$o,
0.00/0.25	                   app_encode_app(program,app_encode_fun(input,$o),halts2,Y),
0.00/0.25	                   app_encode_app(program,input,as_input,Y)) =>
0.00/0.25	    (app_encode_app(input,$o,
0.00/0.25	                    app_encode_app(program,app_encode_fun(input,$o),halts2,V),
0.00/0.25	                    app_encode_app(program,input,as_input,Y)) & 
0.00/0.25	     app_encode_app(output,$o,
0.00/0.25	                    app_encode_app(program,app_encode_fun(output,$o),outputs,
0.00/0.25	                                   V),
0.00/0.25	                    good))) =>
0.00/0.25	   zip_tseitin6(Y,V))).
0.00/0.25	tff('26', plain,
0.00/0.25	    ![X15 : program, X16 : program]:
0.00/0.25	      (zip_tseitin6(X15, X16)
0.00/0.25	       | ~ app_encode_app(input, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(input, $o), halts2, X16), 
0.00/0.25	             app_encode_app(program, input, as_input, X15))
0.00/0.25	       | ~ app_encode_app(output, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(output, $o), outputs, 
0.00/0.25	               X16), good)),
0.00/0.25	    inference('cnf', [status(esa)], [zf_stmt_13])).
0.00/0.25	tff(zf_stmt_14, type, zip_tseitin8 : (program * program) > $o).
0.00/0.25	tff(zf_stmt_15, axiom,
0.00/0.25	  (zip_tseitin8(Y,U) =>
0.00/0.25	   ((app_encode_app(input,$o,
0.00/0.25	                    app_encode_app(program,app_encode_fun(input,$o),halts2,Y),
0.00/0.25	                    app_encode_app(program,input,as_input,Y)) =>
0.00/0.25	     (~
0.00/0.25	       app_encode_app(input,$o,
0.00/0.25	                      app_encode_app(program,app_encode_fun(input,$o),halts2,
0.00/0.25	                                     U),
0.00/0.25	                      app_encode_app(program,input,as_input,Y)))) & 
0.00/0.25	    ((~
0.00/0.25	       app_encode_app(input,$o,
0.00/0.25	                      app_encode_app(program,app_encode_fun(input,$o),halts2,
0.00/0.25	                                     Y),
0.00/0.25	                      app_encode_app(program,input,as_input,Y))) =>
0.00/0.25	     zip_tseitin7(Y,U))))).
0.00/0.25	tff(zf_stmt_16, type, zip_tseitin7 : (program * program) > $o).
0.00/0.25	tff(zf_stmt_17, axiom,
0.00/0.25	  (zip_tseitin7(Y,U) =>
0.00/0.25	   (app_encode_app(input,$o,
0.00/0.25	                   app_encode_app(program,app_encode_fun(input,$o),halts2,U),
0.00/0.25	                   app_encode_app(program,input,as_input,Y)) & 
0.00/0.25	    app_encode_app(output,$o,
0.00/0.25	                   app_encode_app(program,app_encode_fun(output,$o),outputs,U),
0.00/0.25	                   bad)))).
0.00/0.25	tff(zf_stmt_18, type, zip_tseitin6 : (program * program) > $o).
0.00/0.25	tff(zf_stmt_19, type, zip_tseitin5 : (program * program) > $o).
0.00/0.25	tff(zf_stmt_20, axiom,
0.00/0.25	  ((?[V:program]: (![Y:program]: (zip_tseitin6(Y,V) & zip_tseitin5(Y,V)))) =>
0.00/0.25	   (?[U:program]: (![Y:program]: zip_tseitin8(Y,U))))).
0.00/0.25	tff('27', plain,
0.00/0.25	    ![X19 : program, X20 : program]:
0.00/0.25	      (zip_tseitin8(X19, sk_U)
0.00/0.25	       | ~ zip_tseitin5(sk_Y2(X20), X20)
0.00/0.25	       | ~ zip_tseitin6(sk_Y2(X20), X20)),
0.00/0.25	    inference('cnf', [status(esa)], [zf_stmt_20])).
0.00/0.25	tff('28', plain,
0.00/0.25	    ![X0 : program, X1 : program]:
0.00/0.25	      (~ $true
0.00/0.25	       | ~ app_encode_app(output, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(output, $o), outputs, X0), 
0.00/0.25	             good)
0.00/0.25	       | ~ app_encode_app(input, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.25	             app_encode_app(program, input, as_input, sk_Y2(X0)))
0.00/0.25	       | ~ zip_tseitin5(sk_Y2(X0), X0)
0.00/0.25	       | zip_tseitin8(X1, sk_U)),
0.00/0.25	    inference('sup-', [status(thm)], ['26', '27'])).
0.00/0.25	tff('29', plain,
0.00/0.25	    ![X0 : program, X1 : program]:
0.00/0.25	      (zip_tseitin8(X1, sk_U)
0.00/0.25	       | ~ zip_tseitin5(sk_Y2(X0), X0)
0.00/0.25	       | ~ app_encode_app(input, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.25	             app_encode_app(program, input, as_input, sk_Y2(X0)))
0.00/0.25	       | ~ app_encode_app(output, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(output, $o), outputs, X0), 
0.00/0.25	             good)),
0.00/0.25	    inference('simplify', [status(thm)], ['28'])).
0.00/0.25	tff('30', plain,
0.00/0.25	    ![X0 : program, X1 : program]:
0.00/0.25	      (~ $true
0.00/0.25	       | ~ app_encode_app(input, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(input, $o), halts2, 
0.00/0.25	               sk_Y2(X0)), 
0.00/0.25	             app_encode_app(program, input, as_input, sk_Y2(X0)))
0.00/0.25	       | ~ app_encode_app(output, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(output, $o), outputs, X0), 
0.00/0.25	             good)
0.00/0.25	       | ~ app_encode_app(input, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.25	             app_encode_app(program, input, as_input, sk_Y2(X0)))
0.00/0.25	       | zip_tseitin8(X1, sk_U)),
0.00/0.25	    inference('sup-', [status(thm)], ['25', '29'])).
0.00/0.25	tff('31', plain,
0.00/0.25	    ![X0 : program, X1 : program]:
0.00/0.25	      (zip_tseitin8(X1, sk_U)
0.00/0.25	       | ~ app_encode_app(input, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.25	             app_encode_app(program, input, as_input, sk_Y2(X0)))
0.00/0.25	       | ~ app_encode_app(output, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(output, $o), outputs, X0), 
0.00/0.25	             good)
0.00/0.25	       | ~ app_encode_app(input, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(input, $o), halts2, 
0.00/0.25	               sk_Y2(X0)), 
0.00/0.25	             app_encode_app(program, input, as_input, sk_Y2(X0)))),
0.00/0.25	    inference('simplify', [status(thm)], ['30'])).
0.00/0.25	tff('32', plain,
0.00/0.25	    ![X0 : program, X1 : program]:
0.00/0.25	      (~ $true
0.00/0.25	       | app_encode_app(output, $o, 
0.00/0.25	           app_encode_app(program, app_encode_fun(output, $o), outputs, sk_W), 
0.00/0.25	           bad)
0.00/0.25	       | ~ app_encode_app(output, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(output, $o), outputs, X0), 
0.00/0.25	             good)
0.00/0.25	       | ~ app_encode_app(input, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.25	             app_encode_app(program, input, as_input, sk_Y2(X0)))
0.00/0.25	       | zip_tseitin8(X1, sk_U)),
0.00/0.25	    inference('sup-', [status(thm)], ['19', '31'])).
0.00/0.25	tff('33', plain,
0.00/0.25	    ![X0 : program, X1 : program]:
0.00/0.25	      (zip_tseitin8(X1, sk_U)
0.00/0.25	       | ~ app_encode_app(input, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.25	             app_encode_app(program, input, as_input, sk_Y2(X0)))
0.00/0.25	       | ~ app_encode_app(output, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(output, $o), outputs, X0), 
0.00/0.25	             good)
0.00/0.25	       | app_encode_app(output, $o, 
0.00/0.25	           app_encode_app(program, app_encode_fun(output, $o), outputs, sk_W), 
0.00/0.25	           bad)),
0.00/0.25	    inference('simplify', [status(thm)], ['32'])).
0.00/0.25	tff('34', plain,
0.00/0.25	    ![X0 : program, X1 : program]:
0.00/0.25	      (app_encode_app(output, $o, 
0.00/0.25	         app_encode_app(program, app_encode_fun(output, $o), outputs, sk_W), 
0.00/0.25	         bad)
0.00/0.25	       | ~ app_encode_app(output, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(output, $o), outputs, X0), 
0.00/0.25	             good)
0.00/0.25	       | zip_tseitin8(X1, sk_U)),
0.00/0.25	    inference('clc', [status(thm)], ['33', '19'])).
0.00/0.25	tff('35', plain,
0.00/0.25	    ![X0 : program]:
0.00/0.25	      (~ $true
0.00/0.25	       | app_encode_app(output, $o, 
0.00/0.25	           app_encode_app(program, app_encode_fun(output, $o), outputs, sk_W), 
0.00/0.25	           bad)
0.00/0.25	       | zip_tseitin8(X0, sk_U)
0.00/0.25	       | app_encode_app(output, $o, 
0.00/0.25	           app_encode_app(program, app_encode_fun(output, $o), outputs, sk_W), 
0.00/0.25	           bad)),
0.00/0.25	    inference('sup-', [status(thm)], ['24', '34'])).
0.00/0.25	tff('36', plain,
0.00/0.25	    ![X0 : program]:
0.00/0.25	      (zip_tseitin8(X0, sk_U)
0.00/0.25	       | app_encode_app(output, $o, 
0.00/0.25	           app_encode_app(program, app_encode_fun(output, $o), outputs, sk_W), 
0.00/0.25	           bad)),
0.00/0.25	    inference('simplify', [status(thm)], ['35'])).
0.00/0.25	tff('37', plain,
0.00/0.25	    ![X17 : program, X18 : program]:
0.00/0.25	      (~ app_encode_app(input, $o, 
0.00/0.25	           app_encode_app(program, app_encode_fun(input, $o), halts2, X18), 
0.00/0.25	           app_encode_app(program, input, as_input, X18))
0.00/0.25	       | ~ app_encode_app(input, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(input, $o), halts2, X17), 
0.00/0.25	             app_encode_app(program, input, as_input, X18))
0.00/0.25	       | ~ zip_tseitin8(X18, X17)),
0.00/0.25	    inference('cnf', [status(esa)], [zf_stmt_15])).
0.00/0.25	tff('38', plain,
0.00/0.25	    ![X0 : program]:
0.00/0.25	      (~ $true
0.00/0.25	       | app_encode_app(output, $o, 
0.00/0.25	           app_encode_app(program, app_encode_fun(output, $o), outputs, sk_W), 
0.00/0.25	           bad)
0.00/0.25	       | ~ app_encode_app(input, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(input, $o), halts2, sk_U), 
0.00/0.25	             app_encode_app(program, input, as_input, X0))
0.00/0.25	       | ~ app_encode_app(input, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.25	             app_encode_app(program, input, as_input, X0))),
0.00/0.25	    inference('sup-', [status(thm)], ['36', '37'])).
0.00/0.25	tff('39', plain,
0.00/0.25	    ![X0 : program]:
0.00/0.25	      (~ app_encode_app(input, $o, 
0.00/0.25	           app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.25	           app_encode_app(program, input, as_input, X0))
0.00/0.25	       | ~ app_encode_app(input, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(input, $o), halts2, sk_U), 
0.00/0.25	             app_encode_app(program, input, as_input, X0))
0.00/0.25	       | app_encode_app(output, $o, 
0.00/0.25	           app_encode_app(program, app_encode_fun(output, $o), outputs, sk_W), 
0.00/0.25	           bad)),
0.00/0.25	    inference('simplify', [status(thm)], ['38'])).
0.00/0.25	tff('40', plain,
0.00/0.25	    ![X0 : program]:
0.00/0.25	      (app_encode_app(output, $o, 
0.00/0.25	         app_encode_app(program, app_encode_fun(output, $o), outputs, sk_W), 
0.00/0.25	         bad)
0.00/0.25	       | ~ app_encode_app(input, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(input, $o), halts2, sk_U), 
0.00/0.25	             app_encode_app(program, input, as_input, X0))),
0.00/0.25	    inference('clc', [status(thm)], ['39', '19'])).
0.00/0.25	tff('41', plain,
0.00/0.25	    app_encode_app(output, $o, 
0.00/0.25	      app_encode_app(program, app_encode_fun(output, $o), outputs, sk_W), 
0.00/0.25	      bad),
0.00/0.25	    inference('clc', [status(thm)], ['40', '19'])).
0.00/0.25	tff('42', plain,
0.00/0.25	    ![X0 : program]:
0.00/0.25	      (~ $true
0.00/0.25	       | ~ $true
0.00/0.25	       | app_encode_app(input, $o, 
0.00/0.25	           app_encode_app(program, app_encode_fun(input, $o), halts2, 
0.00/0.25	             sk_Y1(sk_W)), 
0.00/0.25	           app_encode_app(program, input, as_input, sk_Y1(sk_W)))
0.00/0.25	       | zip_tseitin4(X0, sk_V)),
0.00/0.25	    inference('demod', [status(thm)], ['16', '41'])).
0.00/0.25	tff('43', plain,
0.00/0.25	    ![X0 : program]:
0.00/0.25	      (zip_tseitin4(X0, sk_V)
0.00/0.25	       | app_encode_app(input, $o, 
0.00/0.25	           app_encode_app(program, app_encode_fun(input, $o), halts2, 
0.00/0.25	             sk_Y1(sk_W)), 
0.00/0.25	           app_encode_app(program, input, as_input, sk_Y1(sk_W)))),
0.00/0.25	    inference('simplify', [status(thm)], ['42'])).
0.00/0.25	tff('44', plain,
0.00/0.25	    ![X0 : input, X1 : program, X2 : program, X3 : program]:
0.00/0.25	      (~ $true
0.00/0.25	       | zip_tseitin4(X3, sk_V)
0.00/0.25	       | ~ app_encode_app(input, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.25	               app_encode_app(algorithm, 
0.00/0.25	                 app_encode_fun(program, app_encode_fun(input, $o)), 
0.00/0.25	                 decides, 
0.00/0.25	                 app_encode_app(program, algorithm, algorithm_of, X2)), X1), 
0.00/0.25	             X0)
0.00/0.25	       | app_encode_app(output, $o, 
0.00/0.25	           app_encode_app(program, app_encode_fun(output, $o), outputs, X2), 
0.00/0.25	           good)),
0.00/0.25	    inference('sup-', [status(thm)], ['43', '20'])).
0.00/0.25	tff('45', plain,
0.00/0.25	    ![X0 : input, X1 : program, X2 : program, X3 : program]:
0.00/0.25	      (app_encode_app(output, $o, 
0.00/0.25	         app_encode_app(program, app_encode_fun(output, $o), outputs, X2), 
0.00/0.25	         good)
0.00/0.25	       | ~ app_encode_app(input, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.25	               app_encode_app(algorithm, 
0.00/0.25	                 app_encode_fun(program, app_encode_fun(input, $o)), 
0.00/0.25	                 decides, 
0.00/0.25	                 app_encode_app(program, algorithm, algorithm_of, X2)), X1), 
0.00/0.25	             X0)
0.00/0.25	       | zip_tseitin4(X3, sk_V)),
0.00/0.25	    inference('simplify', [status(thm)], ['44'])).
0.00/0.25	tff('46', plain,
0.00/0.25	    ![X2 : program]:
0.00/0.25	      (~ $true
0.00/0.25	       | zip_tseitin4(X2, sk_V)
0.00/0.25	       | app_encode_app(output, $o, 
0.00/0.25	           app_encode_app(program, app_encode_fun(output, $o), outputs, sk_W), 
0.00/0.25	           good)),
0.00/0.25	    inference('sup-', [status(thm)], ['3', '45'])).
0.00/0.25	tff('47', plain,
0.00/0.25	    ![X2 : program]:
0.00/0.25	      (app_encode_app(output, $o, 
0.00/0.25	         app_encode_app(program, app_encode_fun(output, $o), outputs, sk_W), 
0.00/0.25	         good)
0.00/0.25	       | zip_tseitin4(X2, sk_V)),
0.00/0.25	    inference('simplify', [status(thm)], ['46'])).
0.00/0.25	tff('48', plain,
0.00/0.25	    ![X9 : program, X10 : program]:
0.00/0.25	      (zip_tseitin1(X9, X10)
0.00/0.25	       | ~ app_encode_app(input, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.25	               app_encode_app(program, 
0.00/0.25	                 app_encode_fun(program, app_encode_fun(input, $o)), halts3, 
0.00/0.25	                 X10), X9), app_encode_app(program, input, as_input, X9))
0.00/0.25	       | ~ app_encode_app(output, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(output, $o), outputs, 
0.00/0.25	               X10), good)),
0.00/0.25	    inference('cnf', [status(esa)], [zf_stmt_2])).
0.00/0.25	tff('49', plain,
0.00/0.25	    ![X0 : program, X1 : program]:
0.00/0.25	      (~ $true
0.00/0.25	       | ~ app_encode_app(output, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(output, $o), outputs, X0), 
0.00/0.25	             good)
0.00/0.25	       | ~ app_encode_app(input, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.25	               app_encode_app(program, 
0.00/0.25	                 app_encode_fun(program, app_encode_fun(input, $o)), halts3, 
0.00/0.25	                 X0), sk_Y1(X0)), 
0.00/0.25	             app_encode_app(program, input, as_input, sk_Y1(X0)))
0.00/0.25	       | ~ zip_tseitin0(sk_Y1(X0), X0)
0.00/0.25	       | zip_tseitin4(X1, sk_V)),
0.00/0.25	    inference('sup-', [status(thm)], ['48', '11'])).
0.00/0.25	tff('50', plain,
0.00/0.25	    ![X0 : program, X1 : program]:
0.00/0.25	      (zip_tseitin4(X1, sk_V)
0.00/0.25	       | ~ zip_tseitin0(sk_Y1(X0), X0)
0.00/0.25	       | ~ app_encode_app(input, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.25	               app_encode_app(program, 
0.00/0.25	                 app_encode_fun(program, app_encode_fun(input, $o)), halts3, 
0.00/0.25	                 X0), sk_Y1(X0)), 
0.00/0.25	             app_encode_app(program, input, as_input, sk_Y1(X0)))
0.00/0.25	       | ~ app_encode_app(output, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(output, $o), outputs, X0), 
0.00/0.25	             good)),
0.00/0.25	    inference('simplify', [status(thm)], ['49'])).
0.00/0.25	tff('51', plain,
0.00/0.25	    ![X0 : program, X1 : program]:
0.00/0.25	      (~ $true
0.00/0.25	       | ~ app_encode_app(output, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(output, $o), outputs, X0), 
0.00/0.25	             bad)
0.00/0.25	       | ~ app_encode_app(input, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.25	               app_encode_app(program, 
0.00/0.25	                 app_encode_fun(program, app_encode_fun(input, $o)), halts3, 
0.00/0.25	                 X0), sk_Y1(X0)), 
0.00/0.25	             app_encode_app(program, input, as_input, sk_Y1(X0)))
0.00/0.25	       | ~ app_encode_app(output, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(output, $o), outputs, X0), 
0.00/0.25	             good)
0.00/0.25	       | ~ app_encode_app(input, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.25	               app_encode_app(program, 
0.00/0.25	                 app_encode_fun(program, app_encode_fun(input, $o)), halts3, 
0.00/0.25	                 X0), sk_Y1(X0)), 
0.00/0.25	             app_encode_app(program, input, as_input, sk_Y1(X0)))
0.00/0.25	       | zip_tseitin4(X1, sk_V)),
0.00/0.25	    inference('sup-', [status(thm)], ['9', '50'])).
0.00/0.25	tff('52', plain,
0.00/0.25	    ![X0 : program, X1 : program]:
0.00/0.25	      (zip_tseitin4(X1, sk_V)
0.00/0.25	       | ~ app_encode_app(output, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(output, $o), outputs, X0), 
0.00/0.25	             good)
0.00/0.25	       | ~ app_encode_app(input, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(input, $o), 
0.00/0.25	               app_encode_app(program, 
0.00/0.25	                 app_encode_fun(program, app_encode_fun(input, $o)), halts3, 
0.00/0.25	                 X0), sk_Y1(X0)), 
0.00/0.25	             app_encode_app(program, input, as_input, sk_Y1(X0)))
0.00/0.25	       | ~ app_encode_app(output, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(output, $o), outputs, X0), 
0.00/0.25	             bad)),
0.00/0.25	    inference('simplify', [status(thm)], ['51'])).
0.00/0.25	tff('53', plain,
0.00/0.25	    ![X0 : program]:
0.00/0.25	      (~ $true
0.00/0.25	       | ~ app_encode_app(output, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(output, $o), outputs, 
0.00/0.25	               sk_W), bad)
0.00/0.25	       | ~ app_encode_app(output, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(output, $o), outputs, 
0.00/0.25	               sk_W), good)
0.00/0.25	       | zip_tseitin4(X0, sk_V)),
0.00/0.25	    inference('sup-', [status(thm)], ['8', '52'])).
0.00/0.25	tff('54', plain,
0.00/0.25	    ![X0 : program]:
0.00/0.25	      (~ $true
0.00/0.25	       | ~ $true
0.00/0.25	       | ~ app_encode_app(output, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(output, $o), outputs, 
0.00/0.25	               sk_W), good)
0.00/0.25	       | zip_tseitin4(X0, sk_V)),
0.00/0.25	    inference('demod', [status(thm)], ['53', '41'])).
0.00/0.25	tff('55', plain,
0.00/0.25	    ![X0 : program]:
0.00/0.25	      (zip_tseitin4(X0, sk_V)
0.00/0.25	       | ~ app_encode_app(output, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(output, $o), outputs, 
0.00/0.25	               sk_W), good)),
0.00/0.25	    inference('simplify', [status(thm)], ['54'])).
0.00/0.25	tff('56', plain, ![X2 : program]: zip_tseitin4(X2, sk_V),
0.00/0.25	    inference('clc', [status(thm)], ['47', '55'])).
0.00/0.25	tff('57', plain,
0.00/0.25	    ![X11 : program, X12 : program]:
0.00/0.25	      (app_encode_app(input, $o, 
0.00/0.25	         app_encode_app(program, app_encode_fun(input, $o), halts2, X12), 
0.00/0.25	         app_encode_app(program, input, as_input, X12))
0.00/0.25	       | zip_tseitin2(X12, X11)
0.00/0.25	       | ~ zip_tseitin4(X12, X11)),
0.00/0.25	    inference('cnf', [status(esa)], [zf_stmt_4])).
0.00/0.25	tff('58', plain,
0.00/0.25	    ![X0 : program]:
0.00/0.25	      (~ $true
0.00/0.25	       | zip_tseitin2(X0, sk_V)
0.00/0.25	       | app_encode_app(input, $o, 
0.00/0.25	           app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.25	           app_encode_app(program, input, as_input, X0))),
0.00/0.25	    inference('sup-', [status(thm)], ['56', '57'])).
0.00/0.25	tff('59', plain,
0.00/0.25	    ![X0 : program]:
0.00/0.25	      (app_encode_app(input, $o, 
0.00/0.25	         app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.25	         app_encode_app(program, input, as_input, X0))
0.00/0.25	       | zip_tseitin2(X0, sk_V)),
0.00/0.25	    inference('simplify', [status(thm)], ['58'])).
0.00/0.25	tff('60', plain,
0.00/0.25	    ![X11 : program, X12 : program]:
0.00/0.25	      (app_encode_app(output, $o, 
0.00/0.25	         app_encode_app(program, app_encode_fun(output, $o), outputs, X11), 
0.00/0.25	         bad)
0.00/0.25	       | ~ zip_tseitin2(X12, X11)),
0.00/0.25	    inference('cnf', [status(esa)], [zf_stmt_8])).
0.00/0.25	tff('61', plain,
0.00/0.25	    ![X0 : program]:
0.00/0.25	      (~ $true
0.00/0.25	       | app_encode_app(input, $o, 
0.00/0.25	           app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.25	           app_encode_app(program, input, as_input, X0))
0.00/0.25	       | app_encode_app(output, $o, 
0.00/0.25	           app_encode_app(program, app_encode_fun(output, $o), outputs, sk_V), 
0.00/0.25	           bad)),
0.00/0.25	    inference('sup-', [status(thm)], ['59', '60'])).
0.00/0.25	tff('62', plain,
0.00/0.25	    ![X0 : program]:
0.00/0.25	      (app_encode_app(output, $o, 
0.00/0.25	         app_encode_app(program, app_encode_fun(output, $o), outputs, sk_V), 
0.00/0.25	         bad)
0.00/0.25	       | app_encode_app(input, $o, 
0.00/0.25	           app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.25	           app_encode_app(program, input, as_input, X0))),
0.00/0.25	    inference('simplify', [status(thm)], ['61'])).
0.00/0.25	tff('63', plain,
0.00/0.25	    ![X11 : program, X12 : program]:
0.00/0.25	      (app_encode_app(input, $o, 
0.00/0.25	         app_encode_app(program, app_encode_fun(input, $o), halts2, X11), 
0.00/0.25	         app_encode_app(program, input, as_input, X12))
0.00/0.25	       | ~ zip_tseitin2(X12, X11)),
0.00/0.25	    inference('cnf', [status(esa)], [zf_stmt_8])).
0.00/0.25	tff('64', plain,
0.00/0.25	    ![X0 : program]:
0.00/0.25	      (~ $true
0.00/0.25	       | app_encode_app(input, $o, 
0.00/0.25	           app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.25	           app_encode_app(program, input, as_input, X0))
0.00/0.25	       | app_encode_app(input, $o, 
0.00/0.25	           app_encode_app(program, app_encode_fun(input, $o), halts2, sk_V), 
0.00/0.25	           app_encode_app(program, input, as_input, X0))),
0.00/0.25	    inference('sup-', [status(thm)], ['59', '63'])).
0.00/0.25	tff('65', plain,
0.00/0.25	    ![X0 : program]:
0.00/0.25	      (app_encode_app(input, $o, 
0.00/0.25	         app_encode_app(program, app_encode_fun(input, $o), halts2, sk_V), 
0.00/0.25	         app_encode_app(program, input, as_input, X0))
0.00/0.25	       | app_encode_app(input, $o, 
0.00/0.25	           app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.25	           app_encode_app(program, input, as_input, X0))),
0.00/0.25	    inference('simplify', [status(thm)], ['64'])).
0.00/0.25	tff('66', plain,
0.00/0.25	    ![X11 : program, X12 : program]:
0.00/0.25	      (~ app_encode_app(input, $o, 
0.00/0.25	           app_encode_app(program, app_encode_fun(input, $o), halts2, X12), 
0.00/0.25	           app_encode_app(program, input, as_input, X12))
0.00/0.25	       | zip_tseitin3(X12, X11)
0.00/0.25	       | ~ zip_tseitin4(X12, X11)),
0.00/0.25	    inference('cnf', [status(esa)], [zf_stmt_4])).
0.00/0.25	tff('67', plain,
0.00/0.25	    ![X0 : program]:
0.00/0.25	      (~ $true
0.00/0.25	       | zip_tseitin3(X0, sk_V)
0.00/0.25	       | ~ app_encode_app(input, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.25	             app_encode_app(program, input, as_input, X0))),
0.00/0.25	    inference('sup-', [status(thm)], ['56', '66'])).
0.00/0.25	tff('68', plain,
0.00/0.25	    ![X0 : program]:
0.00/0.25	      (~ app_encode_app(input, $o, 
0.00/0.25	           app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.25	           app_encode_app(program, input, as_input, X0))
0.00/0.25	       | zip_tseitin3(X0, sk_V)),
0.00/0.25	    inference('simplify', [status(thm)], ['67'])).
0.00/0.25	tff('69', plain,
0.00/0.25	    ![X11 : program, X12 : program]:
0.00/0.25	      (app_encode_app(input, $o, 
0.00/0.25	         app_encode_app(program, app_encode_fun(input, $o), halts2, X11), 
0.00/0.25	         app_encode_app(program, input, as_input, X12))
0.00/0.25	       | ~ zip_tseitin3(X12, X11)),
0.00/0.25	    inference('cnf', [status(esa)], [zf_stmt_6])).
0.00/0.25	tff('70', plain,
0.00/0.25	    ![X0 : program]:
0.00/0.25	      (~ $true
0.00/0.25	       | ~ app_encode_app(input, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.25	             app_encode_app(program, input, as_input, X0))
0.00/0.25	       | app_encode_app(input, $o, 
0.00/0.25	           app_encode_app(program, app_encode_fun(input, $o), halts2, sk_V), 
0.00/0.25	           app_encode_app(program, input, as_input, X0))),
0.00/0.25	    inference('sup-', [status(thm)], ['68', '69'])).
0.00/0.25	tff('71', plain,
0.00/0.25	    ![X0 : program]:
0.00/0.25	      (app_encode_app(input, $o, 
0.00/0.25	         app_encode_app(program, app_encode_fun(input, $o), halts2, sk_V), 
0.00/0.25	         app_encode_app(program, input, as_input, X0))
0.00/0.25	       | ~ app_encode_app(input, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.25	             app_encode_app(program, input, as_input, X0))),
0.00/0.25	    inference('simplify', [status(thm)], ['70'])).
0.00/0.25	tff('72', plain,
0.00/0.25	    ![X0 : program]:
0.00/0.25	      app_encode_app(input, $o, 
0.00/0.25	        app_encode_app(program, app_encode_fun(input, $o), halts2, sk_V), 
0.00/0.25	        app_encode_app(program, input, as_input, X0)),
0.00/0.25	    inference('clc', [status(thm)], ['65', '71'])).
0.00/0.25	tff('73', plain,
0.00/0.25	    ![X15 : program, X16 : program]:
0.00/0.25	      (zip_tseitin5(X15, X16)
0.00/0.25	       | ~ app_encode_app(input, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(input, $o), halts2, X16), 
0.00/0.25	             app_encode_app(program, input, as_input, X15))
0.00/0.25	       | ~ app_encode_app(output, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(output, $o), outputs, 
0.00/0.25	               X16), bad)),
0.00/0.25	    inference('cnf', [status(esa)], [zf_stmt_12])).
0.00/0.25	tff('74', plain,
0.00/0.25	    ![X0 : program, X1 : program]:
0.00/0.25	      (~ $true
0.00/0.25	       | ~ app_encode_app(output, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(output, $o), outputs, X0), 
0.00/0.25	             bad)
0.00/0.25	       | ~ app_encode_app(input, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.25	             app_encode_app(program, input, as_input, sk_Y2(X0)))
0.00/0.25	       | ~ app_encode_app(output, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(output, $o), outputs, X0), 
0.00/0.25	             good)
0.00/0.25	       | ~ app_encode_app(input, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.25	             app_encode_app(program, input, as_input, sk_Y2(X0)))
0.00/0.25	       | zip_tseitin8(X1, sk_U)),
0.00/0.25	    inference('sup-', [status(thm)], ['73', '29'])).
0.00/0.25	tff('75', plain,
0.00/0.25	    ![X0 : program, X1 : program]:
0.00/0.25	      (zip_tseitin8(X1, sk_U)
0.00/0.25	       | ~ app_encode_app(output, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(output, $o), outputs, X0), 
0.00/0.25	             good)
0.00/0.25	       | ~ app_encode_app(input, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.25	             app_encode_app(program, input, as_input, sk_Y2(X0)))
0.00/0.25	       | ~ app_encode_app(output, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(output, $o), outputs, X0), 
0.00/0.25	             bad)),
0.00/0.25	    inference('simplify', [status(thm)], ['74'])).
0.00/0.25	tff('76', plain,
0.00/0.25	    ![X0 : program]:
0.00/0.25	      (~ $true
0.00/0.25	       | ~ app_encode_app(output, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(output, $o), outputs, 
0.00/0.25	               sk_V), bad)
0.00/0.25	       | ~ app_encode_app(output, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(output, $o), outputs, 
0.00/0.25	               sk_V), good)
0.00/0.25	       | zip_tseitin8(X0, sk_U)),
0.00/0.25	    inference('sup-', [status(thm)], ['72', '75'])).
0.00/0.25	tff('77', plain,
0.00/0.25	    ![X0 : program]:
0.00/0.25	      (zip_tseitin8(X0, sk_U)
0.00/0.25	       | ~ app_encode_app(output, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(output, $o), outputs, 
0.00/0.25	               sk_V), good)
0.00/0.25	       | ~ app_encode_app(output, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(output, $o), outputs, 
0.00/0.25	               sk_V), bad)),
0.00/0.25	    inference('simplify', [status(thm)], ['76'])).
0.00/0.25	tff('78', plain,
0.00/0.25	    ![X11 : program, X12 : program]:
0.00/0.25	      (app_encode_app(output, $o, 
0.00/0.25	         app_encode_app(program, app_encode_fun(output, $o), outputs, X11), 
0.00/0.25	         good)
0.00/0.25	       | ~ zip_tseitin3(X12, X11)),
0.00/0.25	    inference('cnf', [status(esa)], [zf_stmt_6])).
0.00/0.25	tff('79', plain,
0.00/0.25	    ![X0 : program]:
0.00/0.25	      (~ $true
0.00/0.25	       | ~ app_encode_app(input, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.25	             app_encode_app(program, input, as_input, X0))
0.00/0.25	       | app_encode_app(output, $o, 
0.00/0.25	           app_encode_app(program, app_encode_fun(output, $o), outputs, sk_V), 
0.00/0.25	           good)),
0.00/0.25	    inference('sup-', [status(thm)], ['68', '78'])).
0.00/0.25	tff('80', plain,
0.00/0.25	    ![X0 : program]:
0.00/0.25	      (app_encode_app(output, $o, 
0.00/0.25	         app_encode_app(program, app_encode_fun(output, $o), outputs, sk_V), 
0.00/0.25	         good)
0.00/0.25	       | ~ app_encode_app(input, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.25	             app_encode_app(program, input, as_input, X0))),
0.00/0.25	    inference('simplify', [status(thm)], ['79'])).
0.00/0.25	tff('81', plain,
0.00/0.25	    (~ $true
0.00/0.25	     | app_encode_app(output, $o, 
0.00/0.25	         app_encode_app(program, app_encode_fun(output, $o), outputs, sk_V), 
0.00/0.25	         good)),
0.00/0.25	    inference('sup-', [status(thm)], ['72', '80'])).
0.00/0.25	tff('82', plain,
0.00/0.25	    app_encode_app(output, $o, 
0.00/0.25	      app_encode_app(program, app_encode_fun(output, $o), outputs, sk_V), 
0.00/0.25	      good),
0.00/0.25	    inference('simplify', [status(thm)], ['81'])).
0.00/0.25	tff('83', plain,
0.00/0.25	    ![X0 : program]:
0.00/0.25	      (zip_tseitin8(X0, sk_U)
0.00/0.25	       | ~ $true
0.00/0.25	       | ~ app_encode_app(output, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(output, $o), outputs, 
0.00/0.25	               sk_V), bad)),
0.00/0.25	    inference('demod', [status(thm)], ['77', '82'])).
0.00/0.25	tff('84', plain,
0.00/0.25	    ![X0 : program]:
0.00/0.25	      (~ app_encode_app(output, $o, 
0.00/0.25	           app_encode_app(program, app_encode_fun(output, $o), outputs, sk_V), 
0.00/0.25	           bad)
0.00/0.25	       | zip_tseitin8(X0, sk_U)),
0.00/0.25	    inference('simplify', [status(thm)], ['83'])).
0.00/0.25	tff('85', plain,
0.00/0.25	    ![X0 : program, X1 : program]:
0.00/0.25	      (~ $true
0.00/0.25	       | app_encode_app(input, $o, 
0.00/0.25	           app_encode_app(program, app_encode_fun(input, $o), halts2, X1), 
0.00/0.25	           app_encode_app(program, input, as_input, X1))
0.00/0.25	       | zip_tseitin8(X0, sk_U)),
0.00/0.25	    inference('sup-', [status(thm)], ['62', '84'])).
0.00/0.25	tff('86', plain,
0.00/0.25	    ![X0 : program, X1 : program]:
0.00/0.25	      (zip_tseitin8(X0, sk_U)
0.00/0.25	       | app_encode_app(input, $o, 
0.00/0.25	           app_encode_app(program, app_encode_fun(input, $o), halts2, X1), 
0.00/0.25	           app_encode_app(program, input, as_input, X1))),
0.00/0.25	    inference('simplify', [status(thm)], ['85'])).
0.00/0.25	tff('87', plain,
0.00/0.25	    ![X17 : program, X18 : program]:
0.00/0.25	      (app_encode_app(input, $o, 
0.00/0.25	         app_encode_app(program, app_encode_fun(input, $o), halts2, X18), 
0.00/0.25	         app_encode_app(program, input, as_input, X18))
0.00/0.25	       | zip_tseitin7(X18, X17)
0.00/0.25	       | ~ zip_tseitin8(X18, X17)),
0.00/0.25	    inference('cnf', [status(esa)], [zf_stmt_15])).
0.00/0.25	tff('88', plain,
0.00/0.25	    ![X0 : program, X1 : program]:
0.00/0.25	      (~ $true
0.00/0.25	       | app_encode_app(input, $o, 
0.00/0.25	           app_encode_app(program, app_encode_fun(input, $o), halts2, X1), 
0.00/0.25	           app_encode_app(program, input, as_input, X1))
0.00/0.25	       | zip_tseitin7(X0, sk_U)
0.00/0.25	       | app_encode_app(input, $o, 
0.00/0.25	           app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.25	           app_encode_app(program, input, as_input, X0))),
0.00/0.25	    inference('sup-', [status(thm)], ['86', '87'])).
0.00/0.25	tff('89', plain,
0.00/0.25	    ![X0 : program, X1 : program]:
0.00/0.25	      (app_encode_app(input, $o, 
0.00/0.25	         app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.25	         app_encode_app(program, input, as_input, X0))
0.00/0.25	       | zip_tseitin7(X0, sk_U)
0.00/0.25	       | app_encode_app(input, $o, 
0.00/0.25	           app_encode_app(program, app_encode_fun(input, $o), halts2, X1), 
0.00/0.25	           app_encode_app(program, input, as_input, X1))),
0.00/0.25	    inference('simplify', [status(thm)], ['88'])).
0.00/0.25	tff('90', plain,
0.00/0.25	    ![X0 : program]:
0.00/0.25	      (app_encode_app(input, $o, 
0.00/0.25	         app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.25	         app_encode_app(program, input, as_input, X0))
0.00/0.25	       | zip_tseitin7(X0, sk_U)),
0.00/0.25	    inference('condensation', [status(thm)], ['89'])).
0.00/0.25	tff('91', plain,
0.00/0.25	    ![X17 : program, X18 : program]:
0.00/0.25	      (app_encode_app(input, $o, 
0.00/0.25	         app_encode_app(program, app_encode_fun(input, $o), halts2, X17), 
0.00/0.25	         app_encode_app(program, input, as_input, X18))
0.00/0.25	       | ~ zip_tseitin7(X18, X17)),
0.00/0.25	    inference('cnf', [status(esa)], [zf_stmt_17])).
0.00/0.25	tff('92', plain,
0.00/0.25	    ![X0 : program]:
0.00/0.25	      (~ $true
0.00/0.25	       | app_encode_app(input, $o, 
0.00/0.25	           app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.25	           app_encode_app(program, input, as_input, X0))
0.00/0.25	       | app_encode_app(input, $o, 
0.00/0.25	           app_encode_app(program, app_encode_fun(input, $o), halts2, sk_U), 
0.00/0.25	           app_encode_app(program, input, as_input, X0))),
0.00/0.25	    inference('sup-', [status(thm)], ['90', '91'])).
0.00/0.25	tff('93', plain,
0.00/0.25	    ![X0 : program]:
0.00/0.25	      (app_encode_app(input, $o, 
0.00/0.25	         app_encode_app(program, app_encode_fun(input, $o), halts2, sk_U), 
0.00/0.25	         app_encode_app(program, input, as_input, X0))
0.00/0.25	       | app_encode_app(input, $o, 
0.00/0.25	           app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.25	           app_encode_app(program, input, as_input, X0))),
0.00/0.25	    inference('simplify', [status(thm)], ['92'])).
0.00/0.25	tff('94', plain,
0.00/0.25	    (~ $true
0.00/0.25	     | app_encode_app(input, $o, 
0.00/0.25	         app_encode_app(program, app_encode_fun(input, $o), halts2, sk_U), 
0.00/0.25	         app_encode_app(program, input, as_input, sk_U))),
0.00/0.25	    inference('eq_fact', [status(thm)], ['93'])).
0.00/0.25	tff('95', plain,
0.00/0.25	    app_encode_app(input, $o, 
0.00/0.25	      app_encode_app(program, app_encode_fun(input, $o), halts2, sk_U), 
0.00/0.25	      app_encode_app(program, input, as_input, sk_U)),
0.00/0.25	    inference('simplify', [status(thm)], ['94'])).
0.00/0.25	tff('96', plain,
0.00/0.25	    ![X0 : program, X1 : program, X2 : program]:
0.00/0.25	      (~ $true
0.00/0.25	       | zip_tseitin8(X2, sk_U)
0.00/0.25	       | ~ app_encode_app(output, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(output, $o), outputs, X0), 
0.00/0.25	             good)
0.00/0.25	       | ~ app_encode_app(input, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.25	             app_encode_app(program, input, as_input, sk_Y2(X0)))
0.00/0.25	       | zip_tseitin8(X1, sk_U)),
0.00/0.25	    inference('sup-', [status(thm)], ['86', '31'])).
0.00/0.25	tff('97', plain,
0.00/0.25	    ![X0 : program, X1 : program, X2 : program]:
0.00/0.25	      (zip_tseitin8(X1, sk_U)
0.00/0.25	       | ~ app_encode_app(input, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.25	             app_encode_app(program, input, as_input, sk_Y2(X0)))
0.00/0.25	       | ~ app_encode_app(output, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(output, $o), outputs, X0), 
0.00/0.25	             good)
0.00/0.25	       | zip_tseitin8(X2, sk_U)),
0.00/0.25	    inference('simplify', [status(thm)], ['96'])).
0.00/0.25	tff('98', plain,
0.00/0.25	    ![X0 : program, X1 : program]:
0.00/0.25	      (zip_tseitin8(X0, sk_U)
0.00/0.25	       | ~ app_encode_app(input, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(input, $o), halts2, X1), 
0.00/0.25	             app_encode_app(program, input, as_input, sk_Y2(X1)))
0.00/0.25	       | ~ app_encode_app(output, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(output, $o), outputs, X1), 
0.00/0.25	             good)),
0.00/0.25	    inference('condensation', [status(thm)], ['97'])).
0.00/0.25	tff('99', plain,
0.00/0.25	    ![X0 : program]:
0.00/0.25	      (~ $true
0.00/0.25	       | ~ app_encode_app(output, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(output, $o), outputs, 
0.00/0.25	               sk_V), good)
0.00/0.25	       | zip_tseitin8(X0, sk_U)),
0.00/0.25	    inference('sup-', [status(thm)], ['72', '98'])).
0.00/0.25	tff('100', plain,
0.00/0.25	    ![X0 : program]: (~ $true | ~ $true | zip_tseitin8(X0, sk_U)),
0.00/0.25	    inference('demod', [status(thm)], ['99', '82'])).
0.00/0.25	tff('101', plain, ![X0 : program]: zip_tseitin8(X0, sk_U),
0.00/0.25	    inference('simplify', [status(thm)], ['100'])).
0.00/0.25	tff('102', plain,
0.00/0.25	    ![X0 : program]:
0.00/0.25	      (~ $true
0.00/0.25	       | ~ app_encode_app(input, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(input, $o), halts2, sk_U), 
0.00/0.25	             app_encode_app(program, input, as_input, X0))
0.00/0.25	       | ~ app_encode_app(input, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.25	             app_encode_app(program, input, as_input, X0))),
0.00/0.25	    inference('sup-', [status(thm)], ['101', '37'])).
0.00/0.25	tff('103', plain,
0.00/0.25	    ![X0 : program]:
0.00/0.25	      (~ app_encode_app(input, $o, 
0.00/0.25	           app_encode_app(program, app_encode_fun(input, $o), halts2, X0), 
0.00/0.25	           app_encode_app(program, input, as_input, X0))
0.00/0.25	       | ~ app_encode_app(input, $o, 
0.00/0.25	             app_encode_app(program, app_encode_fun(input, $o), halts2, sk_U), 
0.00/0.25	             app_encode_app(program, input, as_input, X0))),
0.00/0.25	    inference('simplify', [status(thm)], ['102'])).
0.00/0.25	tff('104', plain,
0.00/0.25	    (~ $true
0.00/0.25	     | ~ app_encode_app(input, $o, 
0.00/0.25	           app_encode_app(program, app_encode_fun(input, $o), halts2, sk_U), 
0.00/0.25	           app_encode_app(program, input, as_input, sk_U))),
0.00/0.25	    inference('sup-', [status(thm)], ['95', '103'])).
0.00/0.25	tff('105', plain, (~ $true | ~ $true),
0.00/0.25	    inference('demod', [status(thm)], ['104', '95'])).
0.00/0.25	tff('106', plain, $false, inference('simplify', [status(thm)], ['105'])).
0.00/0.25	
0.00/0.25	% SZS output end Refutation
0.00/0.25	EOF
