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 $2 \
0.00/0.01	  --simultaneous-sup false \
0.00/0.01	  --no-max-vars \
0.00/0.01	  --no-fool
0.00/0.20	% Computer   : n119.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 07:27:38 CST 2018
276.63/276.83	% done 10415 iterations in 276.621s
276.63/276.83	% SZS status Theorem for 'stdin'
276.63/276.83	% SZS output start Refutation
276.63/276.84	tff(zf_stmt_166, axiom, (![P:bool]: ((P = fTrue) | (P = fFalse)))).
276.63/276.84	tff('0', plain, ![X380 : bool]: (X380 = fTrue | X380 = fFalse),
276.63/276.84	    inference('cnf', [status(esa)], [zf_stmt_166])).
276.63/276.84	tff(zf_stmt_158, axiom, (app_encode_app(bool,$o,pp,fTrue))).
276.63/276.84	tff('1', plain, app_encode_app(bool, $o, pp, fTrue),
276.63/276.84	    inference('cnf', [status(esa)], [zf_stmt_158])).
276.63/276.84	tff('2', plain,
276.63/276.84	    ![X0 : bool]: (app_encode_app(bool, $o, pp, X0) | X0 = fFalse),
276.63/276.84	    inference('sup+', [status(thm)], ['0', '1'])).
276.63/276.84	tff(zf_stmt_167, conjecture,
276.63/276.84	  (app_encode_app(bool,$o,pp,
276.63/276.84	                  app_encode_app(type,bool,
276.63/276.84	                                 app_encode_app(fun(type,bool),
276.63/276.84	                                                app_encode_fun(type,bool),
276.63/276.84	                                                aa(type,bool),
276.63/276.84	                                                app_encode_app(dB,
276.63/276.84	                                                               fun(type,bool),
276.63/276.84	                                                               app_encode_app(
276.63/276.84	                                                               fun(nat,type),
276.63/276.84	                                                               app_encode_fun(
276.63/276.84	                                                               dB,
276.63/276.84	                                                               fun(type,bool)),
276.63/276.84	                                                               typing,
276.63/276.84	                                                               app_encode_app(
276.63/276.84	                                                               type,
276.63/276.84	                                                               fun(nat,type),
276.63/276.84	                                                               app_encode_app(
276.63/276.84	                                                               nat,
276.63/276.84	                                                               app_encode_fun(
276.63/276.84	                                                               type,
276.63/276.84	                                                               fun(nat,type)),
276.63/276.84	                                                               app_encode_app(
276.63/276.84	                                                               fun(nat,type),
276.63/276.84	                                                               app_encode_fun(
276.63/276.84	                                                               nat,
276.63/276.84	                                                               app_encode_fun(
276.63/276.84	                                                               type,
276.63/276.84	                                                               fun(nat,type))),
276.63/276.84	                                                               shift(type),e),
276.63/276.84	                                                               i),t1)),
276.63/276.84	                                                               app_encode_app(
276.63/276.84	                                                               list(dB),dB,
276.63/276.84	                                                               app_encode_app(
276.63/276.84	                                                               dB,
276.63/276.84	                                                               app_encode_fun(
276.63/276.84	                                                               list(dB),dB),
276.63/276.84	                                                               app_encode_app(
276.63/276.84	                                                               fun(dB,
276.63/276.84	                                                                   fun(dB,dB)),
276.63/276.84	                                                               app_encode_fun(
276.63/276.84	                                                               dB,
276.63/276.84	                                                               app_encode_fun(
276.63/276.84	                                                               list(dB),dB)),
276.63/276.84	                                                               foldl(dB,dB),
276.63/276.84	                                                               app),
276.63/276.84	                                                               app_encode_app(
276.63/276.84	                                                               nat,dB,
276.63/276.84	                                                               app_encode_app(
276.63/276.84	                                                               dB,
276.63/276.84	                                                               app_encode_fun(
276.63/276.84	                                                               nat,dB),
276.63/276.84	                                                               app_encode_app(
276.63/276.84	                                                               dB,
276.63/276.84	                                                               app_encode_fun(
276.63/276.84	                                                               dB,
276.63/276.84	                                                               app_encode_fun(
276.63/276.84	                                                               nat,dB)),
276.63/276.84	                                                               subst,r),a),
276.63/276.84	                                                               zero_zero(nat))),
276.63/276.84	                                                               as))),
276.63/276.84	                                 t)))).
276.63/276.84	tff(zf_stmt_0, negated_conjecture,
276.63/276.84	  (~
276.63/276.84	    app_encode_app(bool,$o,pp,
276.63/276.84	                   app_encode_app(type,bool,
276.63/276.84	                                  app_encode_app(fun(type,bool),
276.63/276.84	                                                 app_encode_fun(type,bool),
276.63/276.84	                                                 aa(type,bool),
276.63/276.84	                                                 app_encode_app(dB,
276.63/276.84	                                                                fun(type,bool),
276.63/276.84	                                                                app_encode_app(
276.63/276.84	                                                                fun(nat,type),
276.63/276.84	                                                                app_encode_fun(
276.63/276.84	                                                                dB,
276.63/276.84	                                                                fun(type,bool)),
276.63/276.84	                                                                typing,
276.63/276.84	                                                                app_encode_app(
276.63/276.84	                                                                type,
276.63/276.84	                                                                fun(nat,type),
276.63/276.84	                                                                app_encode_app(
276.63/276.84	                                                                nat,
276.63/276.84	                                                                app_encode_fun(
276.63/276.84	                                                                type,
276.63/276.84	                                                                fun(nat,type)),
276.63/276.84	                                                                app_encode_app(
276.63/276.84	                                                                fun(nat,type),
276.63/276.84	                                                                app_encode_fun(
276.63/276.84	                                                                nat,
276.63/276.84	                                                                app_encode_fun(
276.63/276.84	                                                                type,
276.63/276.84	                                                                fun(nat,type))),
276.63/276.84	                                                                shift(type),e),
276.63/276.84	                                                                i),t1)),
276.63/276.84	                                                                app_encode_app(
276.63/276.84	                                                                list(dB),dB,
276.63/276.84	                                                                app_encode_app(
276.63/276.84	                                                                dB,
276.63/276.84	                                                                app_encode_fun(
276.63/276.84	                                                                list(dB),dB),
276.63/276.84	                                                                app_encode_app(
276.63/276.84	                                                                fun(dB,
276.63/276.84	                                                                    fun(
276.63/276.84	                                                                    dB,dB)),
276.63/276.84	                                                                app_encode_fun(
276.63/276.84	                                                                dB,
276.63/276.84	                                                                app_encode_fun(
276.63/276.84	                                                                list(dB),dB)),
276.63/276.84	                                                                foldl(dB,dB),
276.63/276.84	                                                                app),
276.63/276.84	                                                                app_encode_app(
276.63/276.84	                                                                nat,dB,
276.63/276.84	                                                                app_encode_app(
276.63/276.84	                                                                dB,
276.63/276.84	                                                                app_encode_fun(
276.63/276.84	                                                                nat,dB),
276.63/276.84	                                                                app_encode_app(
276.63/276.84	                                                                dB,
276.63/276.84	                                                                app_encode_fun(
276.63/276.84	                                                                dB,
276.63/276.84	                                                                app_encode_fun(
276.63/276.84	                                                                nat,dB)),
276.63/276.84	                                                                subst,r),a),
276.63/276.84	                                                                zero_zero(
276.63/276.84	                                                                nat))),as))),
276.63/276.84	                                  t)))).
276.63/276.84	tff('3', plain,
276.63/276.84	    ~ app_encode_app(bool, $o, pp, 
276.63/276.84	        app_encode_app(type, bool, 
276.63/276.84	          app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
276.63/276.84	            aa(type, bool), 
276.63/276.84	            app_encode_app(dB, fun(type, bool), 
276.63/276.84	              app_encode_app(fun(nat, type), 
276.63/276.84	                app_encode_fun(dB, fun(type, bool)), typing, 
276.63/276.84	                app_encode_app(type, fun(nat, type), 
276.63/276.84	                  app_encode_app(nat, app_encode_fun(type, fun(nat, type)), 
276.63/276.84	                    app_encode_app(fun(nat, type), 
276.63/276.84	                      app_encode_fun(nat, 
276.63/276.84	                        app_encode_fun(type, fun(nat, type))), shift(type), 
276.63/276.84	                      e), i), t1)), 
276.63/276.84	              app_encode_app(list(dB), dB, 
276.63/276.84	                app_encode_app(dB, app_encode_fun(list(dB), dB), 
276.63/276.84	                  app_encode_app(fun(dB, fun(dB, dB)), 
276.63/276.84	                    app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
276.63/276.84	                    foldl(dB, dB), app), 
276.63/276.84	                  app_encode_app(nat, dB, 
276.63/276.84	                    app_encode_app(dB, app_encode_fun(nat, dB), 
276.63/276.84	                      app_encode_app(dB, 
276.63/276.84	                        app_encode_fun(dB, app_encode_fun(nat, dB)), subst, 
276.63/276.84	                        r), a), zero_zero(nat))), as))), t)),
276.63/276.84	    inference('cnf', [status(esa)], [zf_stmt_0])).
276.63/276.84	tff('4', plain,
276.63/276.84	    (~ $true
276.63/276.84	     | app_encode_app(type, bool, 
276.63/276.84	         app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
276.63/276.84	           aa(type, bool), 
276.63/276.84	           app_encode_app(dB, fun(type, bool), 
276.63/276.84	             app_encode_app(fun(nat, type), 
276.63/276.84	               app_encode_fun(dB, fun(type, bool)), typing, 
276.63/276.84	               app_encode_app(type, fun(nat, type), 
276.63/276.84	                 app_encode_app(nat, app_encode_fun(type, fun(nat, type)), 
276.63/276.84	                   app_encode_app(fun(nat, type), 
276.63/276.84	                     app_encode_fun(nat, 
276.63/276.84	                       app_encode_fun(type, fun(nat, type))), shift(type), e), 
276.63/276.84	                   i), t1)), 
276.63/276.84	             app_encode_app(list(dB), dB, 
276.63/276.84	               app_encode_app(dB, app_encode_fun(list(dB), dB), 
276.63/276.84	                 app_encode_app(fun(dB, fun(dB, dB)), 
276.63/276.84	                   app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
276.63/276.84	                   foldl(dB, dB), app), 
276.63/276.84	                 app_encode_app(nat, dB, 
276.63/276.84	                   app_encode_app(dB, app_encode_fun(nat, dB), 
276.63/276.84	                     app_encode_app(dB, 
276.63/276.84	                       app_encode_fun(dB, app_encode_fun(nat, dB)), subst, r), 
276.63/276.84	                     a), zero_zero(nat))), as))), t)
276.63/276.84	        = fFalse),
276.63/276.84	    inference('sup-', [status(thm)], ['2', '3'])).
276.63/276.84	tff('5', plain,
276.63/276.84	    app_encode_app(type, bool, 
276.63/276.84	      app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
276.63/276.84	        aa(type, bool), 
276.63/276.84	        app_encode_app(dB, fun(type, bool), 
276.63/276.84	          app_encode_app(fun(nat, type), 
276.63/276.84	            app_encode_fun(dB, fun(type, bool)), typing, 
276.63/276.84	            app_encode_app(type, fun(nat, type), 
276.63/276.84	              app_encode_app(nat, app_encode_fun(type, fun(nat, type)), 
276.63/276.84	                app_encode_app(fun(nat, type), 
276.63/276.84	                  app_encode_fun(nat, app_encode_fun(type, fun(nat, type))), 
276.63/276.84	                  shift(type), e), i), t1)), 
276.63/276.84	          app_encode_app(list(dB), dB, 
276.63/276.84	            app_encode_app(dB, app_encode_fun(list(dB), dB), 
276.63/276.84	              app_encode_app(fun(dB, fun(dB, dB)), 
276.63/276.84	                app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
276.63/276.84	                foldl(dB, dB), app), 
276.63/276.84	              app_encode_app(nat, dB, 
276.63/276.84	                app_encode_app(dB, app_encode_fun(nat, dB), 
276.63/276.84	                  app_encode_app(dB, 
276.63/276.84	                    app_encode_fun(dB, app_encode_fun(nat, dB)), subst, r), 
276.63/276.84	                  a), zero_zero(nat))), as))), t)
276.63/276.84	     = fFalse,
276.63/276.84	    inference('simplify', [status(thm)], ['4'])).
276.63/276.84	tff(zf_stmt_60, axiom,
276.63/276.84	  (app_encode_app(bool,$o,pp,
276.63/276.84	                  app_encode_app(dB,bool,
276.63/276.84	                                 app_encode_app(fun(dB,bool),
276.63/276.84	                                                app_encode_fun(dB,bool),
276.63/276.84	                                                aa(dB,bool),
276.63/276.84	                                                app_encode_app(dB,
276.63/276.84	                                                               fun(dB,bool),
276.63/276.84	                                                               app_encode_app(
276.63/276.84	                                                               fun(dB,
276.63/276.84	                                                                   fun(
276.63/276.84	                                                                   dB,bool)),
276.63/276.84	                                                               app_encode_fun(
276.63/276.84	                                                               dB,
276.63/276.84	                                                               fun(dB,bool)),
276.63/276.84	                                                               aa(dB,
276.63/276.84	                                                                  fun(
276.63/276.84	                                                                  dB,bool)),
276.63/276.84	                                                               beta),
276.63/276.84	                                                               app_encode_app(
276.63/276.84	                                                               list(dB),dB,
276.63/276.84	                                                               app_encode_app(
276.63/276.84	                                                               dB,
276.63/276.84	                                                               app_encode_fun(
276.63/276.84	                                                               list(dB),dB),
276.63/276.84	                                                               app_encode_app(
276.63/276.84	                                                               fun(dB,
276.63/276.84	                                                                   fun(dB,dB)),
276.63/276.84	                                                               app_encode_fun(
276.63/276.84	                                                               dB,
276.63/276.84	                                                               app_encode_fun(
276.63/276.84	                                                               list(dB),dB)),
276.63/276.84	                                                               foldl(dB,dB),
276.63/276.84	                                                               app),
276.63/276.84	                                                               app_encode_app(
276.63/276.84	                                                               dB,dB,
276.63/276.84	                                                               app_encode_app(
276.63/276.84	                                                               fun(dB,dB),
276.63/276.84	                                                               app_encode_fun(
276.63/276.84	                                                               dB,dB),
276.63/276.84	                                                               aa(dB,dB),
276.63/276.84	                                                               app_encode_app(
276.63/276.84	                                                               dB,fun(dB,dB),
276.63/276.84	                                                               app_encode_app(
276.63/276.84	                                                               fun(dB,
276.63/276.84	                                                                   fun(dB,dB)),
276.63/276.84	                                                               app_encode_fun(
276.63/276.84	                                                               dB,fun(dB,dB)),
276.63/276.84	                                                               aa(dB,
276.63/276.84	                                                                  fun(dB,dB)),
276.63/276.84	                                                               app),
276.63/276.84	                                                               app_encode_app(
276.63/276.84	                                                               dB,dB,abs,r))),
276.63/276.84	                                                               a)),as))),
276.63/276.84	                                 app_encode_app(list(dB),dB,
276.63/276.84	                                                app_encode_app(dB,
276.63/276.84	                                                               app_encode_fun(
276.63/276.84	                                                               list(dB),dB),
276.63/276.84	                                                               app_encode_app(
276.63/276.84	                                                               fun(dB,
276.63/276.84	                                                                   fun(dB,dB)),
276.63/276.84	                                                               app_encode_fun(
276.63/276.84	                                                               dB,
276.63/276.84	                                                               app_encode_fun(
276.63/276.84	                                                               list(dB),dB)),
276.63/276.84	                                                               foldl(dB,dB),
276.63/276.84	                                                               app),
276.63/276.84	                                                               app_encode_app(
276.63/276.84	                                                               nat,dB,
276.63/276.84	                                                               app_encode_app(
276.63/276.84	                                                               dB,
276.63/276.84	                                                               app_encode_fun(
276.63/276.84	                                                               nat,dB),
276.63/276.84	                                                               app_encode_app(
276.63/276.84	                                                               dB,
276.63/276.84	                                                               app_encode_fun(
276.63/276.84	                                                               dB,
276.63/276.84	                                                               app_encode_fun(
276.63/276.84	                                                               nat,dB)),
276.63/276.84	                                                               subst,r),a),
276.63/276.84	                                                               zero_zero(nat))),
276.63/276.84	                                                as))))).
276.63/276.84	tff('6', plain,
276.63/276.84	    app_encode_app(bool, $o, pp, 
276.63/276.84	      app_encode_app(dB, bool, 
276.63/276.84	        app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
276.63/276.84	          aa(dB, bool), 
276.63/276.84	          app_encode_app(dB, fun(dB, bool), 
276.63/276.84	            app_encode_app(fun(dB, fun(dB, bool)), 
276.63/276.84	              app_encode_fun(dB, fun(dB, bool)), aa(dB, fun(dB, bool)), beta), 
276.63/276.84	            app_encode_app(list(dB), dB, 
276.63/276.84	              app_encode_app(dB, app_encode_fun(list(dB), dB), 
276.63/276.84	                app_encode_app(fun(dB, fun(dB, dB)), 
276.63/276.84	                  app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
276.63/276.84	                  foldl(dB, dB), app), 
276.63/276.84	                app_encode_app(dB, dB, 
276.63/276.84	                  app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), 
276.63/276.84	                    aa(dB, dB), 
276.63/276.84	                    app_encode_app(dB, fun(dB, dB), 
276.63/276.84	                      app_encode_app(fun(dB, fun(dB, dB)), 
276.63/276.84	                        app_encode_fun(dB, fun(dB, dB)), 
276.63/276.84	                        aa(dB, fun(dB, dB)), app), 
276.63/276.84	                      app_encode_app(dB, dB, abs, r))), a)), as))), 
276.63/276.84	        app_encode_app(list(dB), dB, 
276.63/276.84	          app_encode_app(dB, app_encode_fun(list(dB), dB), 
276.63/276.84	            app_encode_app(fun(dB, fun(dB, dB)), 
276.63/276.84	              app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
276.63/276.84	              foldl(dB, dB), app), 
276.63/276.84	            app_encode_app(nat, dB, 
276.63/276.84	              app_encode_app(dB, app_encode_fun(nat, dB), 
276.63/276.84	                app_encode_app(dB, 
276.63/276.84	                  app_encode_fun(dB, app_encode_fun(nat, dB)), subst, r), a), 
276.63/276.84	              zero_zero(nat))), as))),
276.63/276.84	    inference('cnf', [status(esa)], [zf_stmt_60])).
276.63/276.84	tff(zf_stmt_86, axiom,
276.63/276.84	  (![T3:dB,Ta1:type,Ta:dB,Eb:fun(nat,type)]:
276.63/276.84	     (app_encode_app(bool,$o,pp,
276.63/276.84	                     app_encode_app(type,bool,
276.63/276.84	                                    app_encode_app(fun(type,bool),
276.63/276.84	                                                   app_encode_fun(type,bool),
276.63/276.84	                                                   aa(type,bool),
276.63/276.84	                                                   app_encode_app(dB,
276.63/276.84	                                                                  fun(
276.63/276.84	                                                                  type,bool),
276.63/276.84	                                                                  app_encode_app(
276.63/276.84	                                                                  fun(
276.63/276.84	                                                                  nat,type),
276.63/276.84	                                                                  app_encode_fun(
276.63/276.84	                                                                  dB,
276.63/276.84	                                                                  fun(
276.63/276.84	                                                                  type,bool)),
276.63/276.84	                                                                  typing,Eb),
276.63/276.84	                                                                  Ta)),
276.63/276.84	                                    Ta1)) =>
276.63/276.84	      (app_encode_app(bool,$o,pp,
276.63/276.84	                      app_encode_app(dB,bool,
276.63/276.84	                                     app_encode_app(fun(dB,bool),
276.63/276.84	                                                    app_encode_fun(dB,bool),
276.63/276.84	                                                    aa(dB,bool),
276.63/276.84	                                                    app_encode_app(dB,
276.63/276.84	                                                                   fun(
276.63/276.84	                                                                   dB,bool),
276.63/276.84	                                                                   app_encode_app(
276.63/276.84	                                                                   fun(
276.63/276.84	                                                                   dB,
276.63/276.84	                                                                   fun(
276.63/276.84	                                                                   dB,bool)),
276.63/276.84	                                                                   app_encode_fun(
276.63/276.84	                                                                   dB,
276.63/276.84	                                                                   fun(
276.63/276.84	                                                                   dB,bool)),
276.63/276.84	                                                                   aa(
276.63/276.84	                                                                   dB,
276.63/276.84	                                                                   fun(
276.63/276.84	                                                                   dB,bool)),
276.63/276.84	                                                                   beta),Ta)),
276.63/276.84	                                     T3)) =>
276.63/276.84	       app_encode_app(bool,$o,pp,
276.63/276.84	                      app_encode_app(type,bool,
276.63/276.84	                                     app_encode_app(fun(type,bool),
276.63/276.84	                                                    app_encode_fun(type,bool),
276.63/276.84	                                                    aa(type,bool),
276.63/276.84	                                                    app_encode_app(dB,
276.63/276.84	                                                                   fun(
276.63/276.84	                                                                   type,bool),
276.63/276.84	                                                                   app_encode_app(
276.63/276.84	                                                                   fun(
276.63/276.84	                                                                   nat,type),
276.63/276.84	                                                                   app_encode_fun(
276.63/276.84	                                                                   dB,
276.63/276.84	                                                                   fun(
276.63/276.84	                                                                   type,bool)),
276.63/276.84	                                                                   typing,Eb),
276.63/276.84	                                                                   T3)),
276.63/276.84	                                     Ta1)))))).
276.63/276.84	tff('7', plain,
276.63/276.84	    ![X84 : dB, X85 : dB, X86 : fun(nat, type), X87 : type]:
276.63/276.84	      (~ app_encode_app(bool, $o, pp, 
276.63/276.84	           app_encode_app(dB, bool, 
276.63/276.84	             app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
276.63/276.84	               aa(dB, bool), 
276.63/276.84	               app_encode_app(dB, fun(dB, bool), 
276.63/276.84	                 app_encode_app(fun(dB, fun(dB, bool)), 
276.63/276.84	                   app_encode_fun(dB, fun(dB, bool)), aa(dB, fun(dB, bool)), 
276.63/276.84	                   beta), X84)), X85))
276.63/276.84	       | ~ app_encode_app(bool, $o, pp, 
276.63/276.84	             app_encode_app(type, bool, 
276.63/276.84	               app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
276.63/276.84	                 aa(type, bool), 
276.63/276.84	                 app_encode_app(dB, fun(type, bool), 
276.63/276.84	                   app_encode_app(fun(nat, type), 
276.63/276.84	                     app_encode_fun(dB, fun(type, bool)), typing, X86), X84)), 
276.63/276.84	               X87))
276.63/276.84	       | app_encode_app(bool, $o, pp, 
276.63/276.84	           app_encode_app(type, bool, 
276.63/276.84	             app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
276.63/276.84	               aa(type, bool), 
276.63/276.84	               app_encode_app(dB, fun(type, bool), 
276.63/276.84	                 app_encode_app(fun(nat, type), 
276.63/276.84	                   app_encode_fun(dB, fun(type, bool)), typing, X86), X85)), 
276.63/276.84	             X87))),
276.63/276.84	    inference('cnf', [status(esa)], [zf_stmt_86])).
276.63/276.84	tff('8', plain,
276.63/276.84	    ![X0 : type, X1 : fun(nat, type)]:
276.63/276.84	      (~ $true
276.63/276.84	       | app_encode_app(bool, $o, pp, 
276.63/276.84	           app_encode_app(type, bool, 
276.63/276.84	             app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
276.63/276.84	               aa(type, bool), 
276.63/276.84	               app_encode_app(dB, fun(type, bool), 
276.63/276.84	                 app_encode_app(fun(nat, type), 
276.63/276.84	                   app_encode_fun(dB, fun(type, bool)), typing, X1), 
276.63/276.84	                 app_encode_app(list(dB), dB, 
276.63/276.84	                   app_encode_app(dB, app_encode_fun(list(dB), dB), 
276.63/276.84	                     app_encode_app(fun(dB, fun(dB, dB)), 
276.63/276.84	                       app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
276.63/276.84	                       foldl(dB, dB), app), 
276.63/276.84	                     app_encode_app(nat, dB, 
276.63/276.84	                       app_encode_app(dB, app_encode_fun(nat, dB), 
276.63/276.84	                         app_encode_app(dB, 
276.63/276.84	                           app_encode_fun(dB, app_encode_fun(nat, dB)), 
276.63/276.84	                           subst, r), a), zero_zero(nat))), as))), X0))
276.63/276.84	       | ~ app_encode_app(bool, $o, pp, 
276.63/276.84	             app_encode_app(type, bool, 
276.63/276.84	               app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
276.63/276.84	                 aa(type, bool), 
276.63/276.84	                 app_encode_app(dB, fun(type, bool), 
276.63/276.84	                   app_encode_app(fun(nat, type), 
276.63/276.84	                     app_encode_fun(dB, fun(type, bool)), typing, X1), 
276.63/276.84	                   app_encode_app(list(dB), dB, 
276.63/276.84	                     app_encode_app(dB, app_encode_fun(list(dB), dB), 
276.63/276.84	                       app_encode_app(fun(dB, fun(dB, dB)), 
276.63/276.84	                         app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
276.63/276.84	                         foldl(dB, dB), app), 
276.63/276.84	                       app_encode_app(dB, dB, 
276.63/276.84	                         app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), 
276.63/276.84	                           aa(dB, dB), 
276.63/276.84	                           app_encode_app(dB, fun(dB, dB), 
276.63/276.84	                             app_encode_app(fun(dB, fun(dB, dB)), 
276.63/276.84	                               app_encode_fun(dB, fun(dB, dB)), 
276.63/276.84	                               aa(dB, fun(dB, dB)), app), 
276.63/276.84	                             app_encode_app(dB, dB, abs, r))), a)), as))), 
276.63/276.84	               X0))),
276.63/276.84	    inference('sup-', [status(thm)], ['6', '7'])).
276.63/276.84	tff('9', plain,
276.63/276.84	    ![X0 : type, X1 : fun(nat, type)]:
276.63/276.84	      (~ app_encode_app(bool, $o, pp, 
276.63/276.84	           app_encode_app(type, bool, 
276.63/276.84	             app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
276.63/276.84	               aa(type, bool), 
276.63/276.84	               app_encode_app(dB, fun(type, bool), 
276.63/276.84	                 app_encode_app(fun(nat, type), 
276.63/276.84	                   app_encode_fun(dB, fun(type, bool)), typing, X1), 
276.63/276.84	                 app_encode_app(list(dB), dB, 
276.63/276.84	                   app_encode_app(dB, app_encode_fun(list(dB), dB), 
276.63/276.84	                     app_encode_app(fun(dB, fun(dB, dB)), 
276.63/276.84	                       app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
276.63/276.84	                       foldl(dB, dB), app), 
276.63/276.84	                     app_encode_app(dB, dB, 
276.63/276.84	                       app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), 
276.63/276.84	                         aa(dB, dB), 
276.63/276.84	                         app_encode_app(dB, fun(dB, dB), 
276.63/276.84	                           app_encode_app(fun(dB, fun(dB, dB)), 
276.63/276.84	                             app_encode_fun(dB, fun(dB, dB)), 
276.63/276.84	                             aa(dB, fun(dB, dB)), app), 
276.63/276.84	                           app_encode_app(dB, dB, abs, r))), a)), as))), X0))
276.63/276.84	       | app_encode_app(bool, $o, pp, 
276.63/276.84	           app_encode_app(type, bool, 
276.63/276.84	             app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
276.63/276.84	               aa(type, bool), 
276.63/276.84	               app_encode_app(dB, fun(type, bool), 
276.63/276.84	                 app_encode_app(fun(nat, type), 
276.63/276.84	                   app_encode_fun(dB, fun(type, bool)), typing, X1), 
276.63/276.84	                 app_encode_app(list(dB), dB, 
276.63/276.84	                   app_encode_app(dB, app_encode_fun(list(dB), dB), 
276.63/276.84	                     app_encode_app(fun(dB, fun(dB, dB)), 
276.63/276.84	                       app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
276.63/276.84	                       foldl(dB, dB), app), 
276.63/276.84	                     app_encode_app(nat, dB, 
276.63/276.84	                       app_encode_app(dB, app_encode_fun(nat, dB), 
276.63/276.84	                         app_encode_app(dB, 
276.63/276.84	                           app_encode_fun(dB, app_encode_fun(nat, dB)), 
276.63/276.84	                           subst, r), a), zero_zero(nat))), as))), X0))),
276.63/276.84	    inference('simplify', [status(thm)], ['8'])).
276.63/276.84	tff(zf_stmt_123, axiom,
276.63/276.84	  (![A:$tType,B:$tType,Xs:list(B),X:B,Aa:A,F:fun(A,fun(B,A))]:
276.63/276.84	     (app_encode_app(list(B),A,
276.63/276.84	                     app_encode_app(A,app_encode_fun(list(B),A),
276.63/276.84	                                    app_encode_app(fun(A,fun(B,A)),
276.63/276.84	                                                   app_encode_fun(A,
276.63/276.84	                                                                  app_encode_fun(
276.63/276.84	                                                                  list(B),A)),
276.63/276.84	                                                   foldl(A,B),F),
276.63/276.84	                                    Aa),
276.63/276.84	                     app_encode_app(list(B),list(B),
276.63/276.84	                                    app_encode_app(B,
276.63/276.84	                                                   app_encode_fun(list(B),
276.63/276.84	                                                                  list(B)),
276.63/276.84	                                                   cons(B),X),
276.63/276.84	                                    Xs)) =
276.63/276.84	      app_encode_app(list(B),A,
276.63/276.84	                     app_encode_app(A,app_encode_fun(list(B),A),
276.63/276.84	                                    app_encode_app(fun(A,fun(B,A)),
276.63/276.84	                                                   app_encode_fun(A,
276.63/276.84	                                                                  app_encode_fun(
276.63/276.84	                                                                  list(B),A)),
276.63/276.84	                                                   foldl(A,B),F),
276.63/276.84	                                    app_encode_app(B,A,
276.63/276.84	                                                   app_encode_app(fun(B,A),
276.63/276.84	                                                                  app_encode_fun(
276.63/276.84	                                                                  B,A),
276.63/276.84	                                                                  aa(B,A),
276.63/276.84	                                                                  app_encode_app(
276.63/276.84	                                                                  A,fun(B,A),
276.63/276.84	                                                                  app_encode_app(
276.63/276.84	                                                                  fun(
276.63/276.84	                                                                  A,fun(B,A)),
276.63/276.84	                                                                  app_encode_fun(
276.63/276.84	                                                                  A,fun(B,A)),
276.63/276.84	                                                                  aa(
276.63/276.84	                                                                  A,fun(B,A)),
276.63/276.84	                                                                  F),Aa)),
276.63/276.84	                                                   X)),
276.63/276.84	                     Xs)))).
276.63/276.84	tff('10', plain,
276.63/276.84	    ![X229 : $tType, X230 : $tType, X231 : fun(X230, fun(X229, X230)), 
276.63/276.84	      X232 : X230, X233 : X229, X234 : list(X229)]:
276.63/276.84	      app_encode_app(list(X229), X230, 
276.63/276.84	        app_encode_app(X230, app_encode_fun(list(X229), X230), 
276.63/276.84	          app_encode_app(fun(X230, fun(X229, X230)), 
276.63/276.84	            app_encode_fun(X230, app_encode_fun(list(X229), X230)), 
276.63/276.84	            foldl(X230, X229), X231), X232), 
276.63/276.84	        app_encode_app(list(X229), list(X229), 
276.63/276.84	          app_encode_app(X229, app_encode_fun(list(X229), list(X229)), 
276.63/276.84	            cons(X229), X233), X234))
276.63/276.84	       = app_encode_app(list(X229), X230, 
276.63/276.84	           app_encode_app(X230, app_encode_fun(list(X229), X230), 
276.63/276.84	             app_encode_app(fun(X230, fun(X229, X230)), 
276.63/276.84	               app_encode_fun(X230, app_encode_fun(list(X229), X230)), 
276.63/276.84	               foldl(X230, X229), X231), 
276.63/276.84	             app_encode_app(X229, X230, 
276.63/276.84	               app_encode_app(fun(X229, X230), app_encode_fun(X229, X230), 
276.63/276.84	                 aa(X229, X230), 
276.63/276.84	                 app_encode_app(X230, fun(X229, X230), 
276.63/276.84	                   app_encode_app(fun(X230, fun(X229, X230)), 
276.63/276.84	                     app_encode_fun(X230, fun(X229, X230)), 
276.63/276.84	                     aa(X230, fun(X229, X230)), X231), X232)), X233)), X234),
276.63/276.84	    inference('cnf', [status(esa)], [zf_stmt_123])).
276.63/276.84	tff('11', plain,
276.63/276.84	    ![X0 : type, X1 : fun(nat, type)]:
276.63/276.84	      (~ app_encode_app(bool, $o, pp, 
276.63/276.84	           app_encode_app(type, bool, 
276.63/276.84	             app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
276.63/276.84	               aa(type, bool), 
276.63/276.84	               app_encode_app(dB, fun(type, bool), 
276.63/276.84	                 app_encode_app(fun(nat, type), 
276.63/276.84	                   app_encode_fun(dB, fun(type, bool)), typing, X1), 
276.63/276.84	                 app_encode_app(list(dB), dB, 
276.63/276.84	                   app_encode_app(dB, app_encode_fun(list(dB), dB), 
276.63/276.84	                     app_encode_app(fun(dB, fun(dB, dB)), 
276.63/276.84	                       app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
276.63/276.84	                       foldl(dB, dB), app), app_encode_app(dB, dB, abs, r)), 
276.63/276.84	                   app_encode_app(list(dB), list(dB), 
276.63/276.84	                     app_encode_app(dB, app_encode_fun(list(dB), list(dB)), 
276.63/276.84	                       cons(dB), a), as)))), X0))
276.63/276.84	       | app_encode_app(bool, $o, pp, 
276.63/276.84	           app_encode_app(type, bool, 
276.63/276.84	             app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
276.63/276.84	               aa(type, bool), 
276.63/276.84	               app_encode_app(dB, fun(type, bool), 
276.63/276.84	                 app_encode_app(fun(nat, type), 
276.63/276.84	                   app_encode_fun(dB, fun(type, bool)), typing, X1), 
276.63/276.84	                 app_encode_app(list(dB), dB, 
276.63/276.84	                   app_encode_app(dB, app_encode_fun(list(dB), dB), 
276.63/276.84	                     app_encode_app(fun(dB, fun(dB, dB)), 
276.63/276.84	                       app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
276.63/276.84	                       foldl(dB, dB), app), 
276.63/276.84	                     app_encode_app(nat, dB, 
276.63/276.84	                       app_encode_app(dB, app_encode_fun(nat, dB), 
276.63/276.84	                         app_encode_app(dB, 
276.63/276.84	                           app_encode_fun(dB, app_encode_fun(nat, dB)), 
276.63/276.84	                           subst, r), a), zero_zero(nat))), as))), X0))),
276.63/276.84	    inference('demod', [status(thm)], ['9', '10'])).
276.63/276.84	tff('12', plain,
276.63/276.84	    (app_encode_app(bool, $o, pp, fFalse)
276.63/276.84	     | ~ app_encode_app(bool, $o, pp, 
276.63/276.84	           app_encode_app(type, bool, 
276.63/276.84	             app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
276.63/276.84	               aa(type, bool), 
276.63/276.84	               app_encode_app(dB, fun(type, bool), 
276.63/276.84	                 app_encode_app(fun(nat, type), 
276.63/276.84	                   app_encode_fun(dB, fun(type, bool)), typing, 
276.63/276.84	                   app_encode_app(type, fun(nat, type), 
276.63/276.84	                     app_encode_app(nat, 
276.63/276.84	                       app_encode_fun(type, fun(nat, type)), 
276.63/276.84	                       app_encode_app(fun(nat, type), 
276.63/276.84	                         app_encode_fun(nat, 
276.63/276.84	                           app_encode_fun(type, fun(nat, type))), 
276.63/276.84	                         shift(type), e), i), t1)), 
276.63/276.84	                 app_encode_app(list(dB), dB, 
276.63/276.84	                   app_encode_app(dB, app_encode_fun(list(dB), dB), 
276.63/276.84	                     app_encode_app(fun(dB, fun(dB, dB)), 
276.63/276.84	                       app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
276.63/276.84	                       foldl(dB, dB), app), app_encode_app(dB, dB, abs, r)), 
276.63/276.84	                   app_encode_app(list(dB), list(dB), 
276.63/276.84	                     app_encode_app(dB, app_encode_fun(list(dB), list(dB)), 
276.63/276.84	                       cons(dB), a), as)))), t))),
276.63/276.84	    inference('sup+', [status(thm)], ['5', '11'])).
276.63/276.84	tff('13', plain, ![X0 : bool]: (X0 = fTrue | fTrue = fFalse | X0 = fFalse),
276.63/276.84	    inference('sup+', [status(thm)], ['0', '0'])).
276.63/276.84	tff(zf_stmt_58, axiom,
276.63/276.84	  (app_encode_app(bool,$o,pp,
276.63/276.84	                  app_encode_app(dB,bool,
276.63/276.84	                                 app_encode_app(fun(dB,bool),
276.63/276.84	                                                app_encode_fun(dB,bool),
276.63/276.84	                                                aa(dB,bool),it),
276.63/276.84	                                 a)))).
276.63/276.84	tff('14', plain,
276.63/276.84	    app_encode_app(bool, $o, pp, 
276.63/276.84	      app_encode_app(dB, bool, 
276.63/276.84	        app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
276.63/276.84	          aa(dB, bool), it), a)),
276.63/276.84	    inference('cnf', [status(esa)], [zf_stmt_58])).
276.63/276.84	tff(zf_stmt_157, axiom, (~app_encode_app(bool,$o,pp,fFalse))).
276.63/276.84	tff('15', plain, ~ app_encode_app(bool, $o, pp, fFalse),
276.63/276.84	    inference('cnf', [status(esa)], [zf_stmt_157])).
276.63/276.84	tff('16', plain,
276.63/276.84	    ![X0 : bool]: (~ app_encode_app(bool, $o, pp, X0) | X0 = fTrue),
276.63/276.84	    inference('sup-', [status(thm)], ['0', '15'])).
276.63/276.84	tff('17', plain,
276.63/276.84	    (~ $true
276.63/276.84	     | app_encode_app(dB, bool, 
276.63/276.84	         app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
276.63/276.84	           aa(dB, bool), it), a)
276.63/276.84	        = fTrue),
276.63/276.84	    inference('sup-', [status(thm)], ['14', '16'])).
276.63/276.84	tff('18', plain,
276.63/276.84	    app_encode_app(dB, bool, 
276.63/276.84	      app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), aa(dB, bool), 
276.63/276.84	        it), a)
276.63/276.84	     = fTrue,
276.63/276.84	    inference('simplify', [status(thm)], ['17'])).
276.63/276.84	tff('19', plain,
276.63/276.84	    ![X0 : bool]:
276.63/276.84	      (X0
276.63/276.84	        = app_encode_app(dB, bool, 
276.63/276.84	            app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
276.63/276.84	              aa(dB, bool), it), a)
276.63/276.84	       | fTrue = fFalse
276.63/276.84	       | X0 = fFalse),
276.63/276.84	    inference('demod', [status(thm)], ['13', '18'])).
276.63/276.84	tff(zf_stmt_61, axiom,
276.63/276.84	  (app_encode_app(bool,$o,pp,
276.63/276.84	                  app_encode_app(type,bool,
276.63/276.84	                                 app_encode_app(fun(type,bool),
276.63/276.84	                                                app_encode_fun(type,bool),
276.63/276.84	                                                aa(type,bool),
276.63/276.84	                                                app_encode_app(dB,
276.63/276.84	                                                               fun(type,bool),
276.63/276.84	                                                               app_encode_app(
276.63/276.84	                                                               fun(nat,type),
276.63/276.84	                                                               app_encode_fun(
276.63/276.84	                                                               dB,
276.63/276.84	                                                               fun(type,bool)),
276.63/276.84	                                                               typing,
276.63/276.84	                                                               app_encode_app(
276.63/276.84	                                                               type,
276.63/276.84	                                                               fun(nat,type),
276.63/276.84	                                                               app_encode_app(
276.63/276.84	                                                               nat,
276.63/276.84	                                                               app_encode_fun(
276.63/276.84	                                                               type,
276.63/276.84	                                                               fun(nat,type)),
276.63/276.84	                                                               app_encode_app(
276.63/276.84	                                                               fun(nat,type),
276.63/276.84	                                                               app_encode_fun(
276.63/276.84	                                                               nat,
276.63/276.84	                                                               app_encode_fun(
276.63/276.84	                                                               type,
276.63/276.84	                                                               fun(nat,type))),
276.63/276.84	                                                               shift(type),e),
276.63/276.84	                                                               i),t1)),
276.63/276.84	                                                               app_encode_app(
276.63/276.84	                                                               list(dB),dB,
276.63/276.84	                                                               app_encode_app(
276.63/276.84	                                                               dB,
276.63/276.84	                                                               app_encode_fun(
276.63/276.84	                                                               list(dB),dB),
276.63/276.84	                                                               app_encode_app(
276.63/276.84	                                                               fun(dB,
276.63/276.84	                                                                   fun(dB,dB)),
276.63/276.84	                                                               app_encode_fun(
276.63/276.84	                                                               dB,
276.63/276.84	                                                               app_encode_fun(
276.63/276.84	                                                               list(dB),dB)),
276.63/276.84	                                                               foldl(dB,dB),
276.63/276.84	                                                               app),
276.63/276.84	                                                               app_encode_app(
276.63/276.84	                                                               dB,dB,
276.63/276.84	                                                               app_encode_app(
276.63/276.84	                                                               fun(dB,dB),
276.63/276.84	                                                               app_encode_fun(
276.63/276.84	                                                               dB,dB),
276.63/276.84	                                                               aa(dB,dB),
276.63/276.84	                                                               app_encode_app(
276.63/276.84	                                                               dB,fun(dB,dB),
276.63/276.84	                                                               app_encode_app(
276.63/276.84	                                                               fun(dB,
276.63/276.84	                                                                   fun(dB,dB)),
276.63/276.84	                                                               app_encode_fun(
276.63/276.84	                                                               dB,fun(dB,dB)),
276.63/276.84	                                                               aa(dB,
276.63/276.84	                                                                  fun(dB,dB)),
276.63/276.84	                                                               app),
276.63/276.84	                                                               app_encode_app(
276.63/276.84	                                                               dB,dB,abs,r))),
276.63/276.84	                                                               a)),as))),
276.63/276.84	                                 t)))).
276.63/276.84	tff('20', plain,
276.63/276.84	    app_encode_app(bool, $o, pp, 
276.63/276.84	      app_encode_app(type, bool, 
276.63/276.84	        app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
276.63/276.84	          aa(type, bool), 
276.63/276.84	          app_encode_app(dB, fun(type, bool), 
276.63/276.84	            app_encode_app(fun(nat, type), 
276.63/276.84	              app_encode_fun(dB, fun(type, bool)), typing, 
276.63/276.84	              app_encode_app(type, fun(nat, type), 
276.63/276.84	                app_encode_app(nat, app_encode_fun(type, fun(nat, type)), 
276.63/276.84	                  app_encode_app(fun(nat, type), 
276.63/276.84	                    app_encode_fun(nat, app_encode_fun(type, fun(nat, type))), 
276.63/276.84	                    shift(type), e), i), t1)), 
276.63/276.84	            app_encode_app(list(dB), dB, 
276.63/276.84	              app_encode_app(dB, app_encode_fun(list(dB), dB), 
276.63/276.84	                app_encode_app(fun(dB, fun(dB, dB)), 
276.63/276.84	                  app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
276.63/276.84	                  foldl(dB, dB), app), 
276.63/276.84	                app_encode_app(dB, dB, 
276.63/276.84	                  app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), 
276.63/276.84	                    aa(dB, dB), 
276.63/276.84	                    app_encode_app(dB, fun(dB, dB), 
276.63/276.84	                      app_encode_app(fun(dB, fun(dB, dB)), 
276.63/276.84	                        app_encode_fun(dB, fun(dB, dB)), 
276.63/276.84	                        aa(dB, fun(dB, dB)), app), 
276.63/276.84	                      app_encode_app(dB, dB, abs, r))), a)), as))), t)),
276.63/276.84	    inference('cnf', [status(esa)], [zf_stmt_61])).
276.63/276.84	tff('21', plain,
276.63/276.84	    (app_encode_app(bool, $o, pp, fFalse)
276.63/276.84	     | fTrue = fFalse
276.63/276.84	     | app_encode_app(type, bool, 
276.63/276.84	         app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
276.63/276.84	           aa(type, bool), 
276.63/276.84	           app_encode_app(dB, fun(type, bool), 
276.63/276.84	             app_encode_app(fun(nat, type), 
276.63/276.84	               app_encode_fun(dB, fun(type, bool)), typing, 
276.63/276.84	               app_encode_app(type, fun(nat, type), 
276.63/276.84	                 app_encode_app(nat, app_encode_fun(type, fun(nat, type)), 
276.63/276.84	                   app_encode_app(fun(nat, type), 
276.63/276.84	                     app_encode_fun(nat, 
276.63/276.84	                       app_encode_fun(type, fun(nat, type))), shift(type), e), 
276.63/276.84	                   i), t1)), 
276.63/276.84	             app_encode_app(list(dB), dB, 
276.63/276.84	               app_encode_app(dB, app_encode_fun(list(dB), dB), 
276.63/276.84	                 app_encode_app(fun(dB, fun(dB, dB)), 
276.63/276.84	                   app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
276.63/276.84	                   foldl(dB, dB), app), 
276.63/276.84	                 app_encode_app(dB, dB, 
276.63/276.84	                   app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), 
276.63/276.84	                     aa(dB, dB), 
276.63/276.84	                     app_encode_app(dB, fun(dB, dB), 
276.63/276.84	                       app_encode_app(fun(dB, fun(dB, dB)), 
276.63/276.84	                         app_encode_fun(dB, fun(dB, dB)), 
276.63/276.84	                         aa(dB, fun(dB, dB)), app), 
276.63/276.84	                       app_encode_app(dB, dB, abs, r))), a)), as))), t)
276.63/276.84	        = app_encode_app(dB, bool, 
276.63/276.84	            app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
276.63/276.84	              aa(dB, bool), it), a)),
276.63/276.84	    inference('sup+', [status(thm)], ['19', '20'])).
276.63/276.84	tff('22', plain,
276.63/276.84	    (app_encode_app(bool, $o, pp, fFalse)
276.63/276.84	     | app_encode_app(dB, bool, 
276.63/276.84	         app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
276.63/276.84	           aa(dB, bool), it), a)
276.63/276.84	        = fFalse
276.63/276.84	     | app_encode_app(type, bool, 
276.63/276.84	         app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
276.63/276.84	           aa(type, bool), 
276.63/276.84	           app_encode_app(dB, fun(type, bool), 
276.63/276.84	             app_encode_app(fun(nat, type), 
276.63/276.84	               app_encode_fun(dB, fun(type, bool)), typing, 
276.63/276.84	               app_encode_app(type, fun(nat, type), 
276.63/276.84	                 app_encode_app(nat, app_encode_fun(type, fun(nat, type)), 
276.63/276.84	                   app_encode_app(fun(nat, type), 
276.63/276.84	                     app_encode_fun(nat, 
276.63/276.84	                       app_encode_fun(type, fun(nat, type))), shift(type), e), 
276.63/276.84	                   i), t1)), 
276.63/276.84	             app_encode_app(list(dB), dB, 
276.63/276.84	               app_encode_app(dB, app_encode_fun(list(dB), dB), 
276.63/276.84	                 app_encode_app(fun(dB, fun(dB, dB)), 
276.63/276.84	                   app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
276.63/276.84	                   foldl(dB, dB), app), 
276.63/276.84	                 app_encode_app(dB, dB, 
276.63/276.84	                   app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), 
276.63/276.84	                     aa(dB, dB), 
276.63/276.84	                     app_encode_app(dB, fun(dB, dB), 
276.63/276.84	                       app_encode_app(fun(dB, fun(dB, dB)), 
276.63/276.84	                         app_encode_fun(dB, fun(dB, dB)), 
276.63/276.84	                         aa(dB, fun(dB, dB)), app), 
276.63/276.84	                       app_encode_app(dB, dB, abs, r))), a)), as))), t)
276.63/276.84	        = app_encode_app(dB, bool, 
276.63/276.84	            app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
276.63/276.84	              aa(dB, bool), it), a)),
276.63/276.84	    inference('demod', [status(thm)], ['21', '18'])).
276.63/276.84	tff('23', plain,
276.63/276.84	    (app_encode_app(bool, $o, pp, fFalse)
276.63/276.84	     | app_encode_app(dB, bool, 
276.63/276.84	         app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
276.63/276.84	           aa(dB, bool), it), a)
276.63/276.84	        = fFalse
276.63/276.84	     | app_encode_app(type, bool, 
276.63/276.84	         app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
276.63/276.84	           aa(type, bool), 
276.63/276.84	           app_encode_app(dB, fun(type, bool), 
276.63/276.84	             app_encode_app(fun(nat, type), 
276.63/276.84	               app_encode_fun(dB, fun(type, bool)), typing, 
276.63/276.84	               app_encode_app(type, fun(nat, type), 
276.63/276.84	                 app_encode_app(nat, app_encode_fun(type, fun(nat, type)), 
276.63/276.84	                   app_encode_app(fun(nat, type), 
276.63/276.84	                     app_encode_fun(nat, 
276.63/276.84	                       app_encode_fun(type, fun(nat, type))), shift(type), e), 
276.63/276.84	                   i), t1)), 
276.63/276.84	             app_encode_app(list(dB), dB, 
276.63/276.84	               app_encode_app(dB, app_encode_fun(list(dB), dB), 
276.63/276.84	                 app_encode_app(fun(dB, fun(dB, dB)), 
276.63/276.84	                   app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
276.63/276.84	                   foldl(dB, dB), app), app_encode_app(dB, dB, abs, r)), 
276.63/276.84	               app_encode_app(list(dB), list(dB), 
276.63/276.84	                 app_encode_app(dB, app_encode_fun(list(dB), list(dB)), 
276.63/276.84	                   cons(dB), a), as)))), t)
276.63/276.84	        = app_encode_app(dB, bool, 
276.63/276.84	            app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
276.63/276.84	              aa(dB, bool), it), a)),
276.63/276.84	    inference('demod', [status(thm)], ['22', '10'])).
276.63/276.84	tff('24', plain,
276.63/276.84	    (app_encode_app(type, bool, 
276.63/276.84	       app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
276.63/276.84	         aa(type, bool), 
276.63/276.84	         app_encode_app(dB, fun(type, bool), 
276.63/276.84	           app_encode_app(fun(nat, type), 
276.63/276.84	             app_encode_fun(dB, fun(type, bool)), typing, 
276.63/276.84	             app_encode_app(type, fun(nat, type), 
276.63/276.84	               app_encode_app(nat, app_encode_fun(type, fun(nat, type)), 
276.63/276.84	                 app_encode_app(fun(nat, type), 
276.63/276.84	                   app_encode_fun(nat, app_encode_fun(type, fun(nat, type))), 
276.63/276.84	                   shift(type), e), i), t1)), 
276.63/276.84	           app_encode_app(list(dB), dB, 
276.63/276.84	             app_encode_app(dB, app_encode_fun(list(dB), dB), 
276.63/276.84	               app_encode_app(fun(dB, fun(dB, dB)), 
276.63/276.84	                 app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
276.63/276.84	                 foldl(dB, dB), app), app_encode_app(dB, dB, abs, r)), 
276.63/276.84	             app_encode_app(list(dB), list(dB), 
276.63/276.84	               app_encode_app(dB, app_encode_fun(list(dB), list(dB)), 
276.63/276.84	                 cons(dB), a), as)))), t)
276.63/276.84	      = app_encode_app(dB, bool, 
276.63/276.84	          app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
276.63/276.84	            aa(dB, bool), it), a)
276.63/276.84	     | app_encode_app(dB, bool, 
276.63/276.84	         app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
276.63/276.84	           aa(dB, bool), it), a)
276.63/276.84	        = fFalse),
276.63/276.84	    inference('clc', [status(thm)], ['23', '15'])).
276.63/276.84	tff('25', plain, ![X0 : bool]: (fFalse != fTrue | X0 = fTrue),
276.63/276.84	    inference('eq_fact', [status(thm)], ['0'])).
276.63/276.84	tff('26', plain,
276.63/276.84	    ![X0 : bool]:
276.63/276.84	      (fFalse
276.63/276.84	        != app_encode_app(dB, bool, 
276.63/276.84	             app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
276.63/276.84	               aa(dB, bool), it), a)
276.63/276.84	       | X0
276.63/276.84	          = app_encode_app(dB, bool, 
276.63/276.84	              app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
276.63/276.84	                aa(dB, bool), it), a)),
276.63/276.84	    inference('demod', [status(thm)], ['25', '18', '18'])).
276.63/276.84	tff('27', plain,
276.63/276.84	    app_encode_app(type, bool, 
276.63/276.84	      app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
276.63/276.84	        aa(type, bool), 
276.63/276.84	        app_encode_app(dB, fun(type, bool), 
276.63/276.84	          app_encode_app(fun(nat, type), 
276.63/276.84	            app_encode_fun(dB, fun(type, bool)), typing, 
276.63/276.84	            app_encode_app(type, fun(nat, type), 
276.63/276.84	              app_encode_app(nat, app_encode_fun(type, fun(nat, type)), 
276.63/276.84	                app_encode_app(fun(nat, type), 
276.63/276.84	                  app_encode_fun(nat, app_encode_fun(type, fun(nat, type))), 
276.63/276.84	                  shift(type), e), i), t1)), 
276.63/276.84	          app_encode_app(list(dB), dB, 
276.63/276.84	            app_encode_app(dB, app_encode_fun(list(dB), dB), 
276.63/276.84	              app_encode_app(fun(dB, fun(dB, dB)), 
276.63/276.84	                app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
276.63/276.84	                foldl(dB, dB), app), app_encode_app(dB, dB, abs, r)), 
276.63/276.84	            app_encode_app(list(dB), list(dB), 
276.63/276.84	              app_encode_app(dB, app_encode_fun(list(dB), list(dB)), 
276.63/276.84	                cons(dB), a), as)))), t)
276.63/276.84	     = app_encode_app(dB, bool, 
276.63/276.84	         app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
276.63/276.84	           aa(dB, bool), it), a),
276.63/276.84	    inference('clc', [status(thm)], ['24', '26'])).
276.63/276.84	tff('28', plain, (app_encode_app(bool, $o, pp, fFalse) | ~ $true),
276.63/276.84	    inference('demod', [status(thm)], ['12', '27', '14'])).
276.63/276.84	tff('29', plain, app_encode_app(bool, $o, pp, fFalse),
276.63/276.84	    inference('simplify', [status(thm)], ['28'])).
276.63/276.84	tff('30', plain, ~ $true, inference('sup-', [status(thm)], ['29', '15'])).
276.63/276.84	tff('31', plain, $false, inference('simplify', [status(thm)], ['30'])).
276.63/276.84	
276.63/276.84	% SZS output end Refutation
276.63/276.84	EOF
