0.00/0.00	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : appext
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : kbo
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-ho \
0.00/0.00	  --no-avatar \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n140.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 07:04:39 CST 2018
9.46/9.61	% done 1437 iterations in 9.406s
9.46/9.61	% SZS status Theorem for 'stdin'
9.46/9.61	% SZS output start Refutation
9.46/9.61	tff(zf_stmt_61, axiom,
9.46/9.61	  (![Ua:type,Ib:nat,Ta:type,Ta1:dB,Eb:fun1(nat,type)]:
9.46/9.61	     (app_encode_app(bool,$o,pp,
9.46/9.61	                     app_encode_app(type,bool,
9.46/9.61	                                    app_encode_app(fun1(type,bool),
9.46/9.61	                                                   app_encode_fun(type,bool),
9.46/9.61	                                                   aa(type,bool),
9.46/9.61	                                                   app_encode_app(dB,
9.46/9.61	                                                                  fun1(
9.46/9.61	                                                                  type,bool),
9.46/9.61	                                                                  app_encode_app(
9.46/9.61	                                                                  fun1(
9.46/9.61	                                                                  nat,type),
9.46/9.61	                                                                  app_encode_fun(
9.46/9.61	                                                                  dB,
9.46/9.61	                                                                  fun1(
9.46/9.61	                                                                  type,bool)),
9.46/9.61	                                                                  typing,Eb),
9.46/9.61	                                                                  Ta1)),
9.46/9.61	                                    Ta)) =>
9.46/9.61	      app_encode_app(bool,$o,pp,
9.46/9.61	                     app_encode_app(type,bool,
9.46/9.61	                                    app_encode_app(fun1(type,bool),
9.46/9.61	                                                   app_encode_fun(type,bool),
9.46/9.61	                                                   aa(type,bool),
9.46/9.61	                                                   app_encode_app(dB,
9.46/9.61	                                                                  fun1(
9.46/9.61	                                                                  type,bool),
9.46/9.61	                                                                  app_encode_app(
9.46/9.61	                                                                  fun1(
9.46/9.61	                                                                  nat,type),
9.46/9.61	                                                                  app_encode_fun(
9.46/9.61	                                                                  dB,
9.46/9.61	                                                                  fun1(
9.46/9.61	                                                                  type,bool)),
9.46/9.61	                                                                  typing,
9.46/9.61	                                                                  app_encode_app(
9.46/9.61	                                                                  type,
9.46/9.61	                                                                  fun1(
9.46/9.61	                                                                  nat,type),
9.46/9.61	                                                                  app_encode_app(
9.46/9.61	                                                                  nat,
9.46/9.61	                                                                  app_encode_fun(
9.46/9.61	                                                                  type,
9.46/9.61	                                                                  fun1(
9.46/9.61	                                                                  nat,type)),
9.46/9.61	                                                                  app_encode_app(
9.46/9.61	                                                                  fun1(
9.46/9.61	                                                                  nat,type),
9.46/9.61	                                                                  app_encode_fun(
9.46/9.61	                                                                  nat,
9.46/9.61	                                                                  app_encode_fun(
9.46/9.61	                                                                  type,
9.46/9.61	                                                                  fun1(
9.46/9.61	                                                                  nat,type))),
9.46/9.61	                                                                  shift(type),
9.46/9.61	                                                                  Eb),Ib),Ua)),
9.46/9.61	                                                                  app_encode_app(
9.46/9.61	                                                                  nat,dB,
9.46/9.61	                                                                  app_encode_app(
9.46/9.61	                                                                  fun1(
9.46/9.61	                                                                  nat,dB),
9.46/9.61	                                                                  app_encode_fun(
9.46/9.61	                                                                  nat,dB),
9.46/9.61	                                                                  aa(nat,dB),
9.46/9.61	                                                                  app_encode_app(
9.46/9.61	                                                                  dB,
9.46/9.61	                                                                  fun1(
9.46/9.61	                                                                  nat,dB),
9.46/9.61	                                                                  app_encode_app(
9.46/9.61	                                                                  fun1(
9.46/9.61	                                                                  dB,
9.46/9.61	                                                                  fun1(
9.46/9.61	                                                                  nat,dB)),
9.46/9.61	                                                                  app_encode_fun(
9.46/9.61	                                                                  dB,
9.46/9.61	                                                                  fun1(
9.46/9.61	                                                                  nat,dB)),
9.46/9.61	                                                                  aa(
9.46/9.61	                                                                  dB,
9.46/9.61	                                                                  fun1(
9.46/9.61	                                                                  nat,dB)),
9.46/9.61	                                                                  lift),Ta1)),
9.46/9.61	                                                                  Ib))),
9.46/9.61	                                    Ta))))).
9.46/9.61	tff('0', plain,
9.46/9.61	    ![X4 : fun1(nat, type), X5 : nat, X6 : type, X7 : dB, X8 : type]:
9.46/9.61	      (app_encode_app(bool, $o, pp, 
9.46/9.61	         app_encode_app(type, bool, 
9.46/9.61	           app_encode_app(fun1(type, bool), app_encode_fun(type, bool), 
9.46/9.61	             aa(type, bool), 
9.46/9.61	             app_encode_app(dB, fun1(type, bool), 
9.46/9.61	               app_encode_app(fun1(nat, type), 
9.46/9.61	                 app_encode_fun(dB, fun1(type, bool)), typing, 
9.46/9.61	                 app_encode_app(type, fun1(nat, type), 
9.46/9.61	                   app_encode_app(nat, 
9.46/9.61	                     app_encode_fun(type, fun1(nat, type)), 
9.46/9.61	                     app_encode_app(fun1(nat, type), 
9.46/9.61	                       app_encode_fun(nat, 
9.46/9.61	                         app_encode_fun(type, fun1(nat, type))), 
9.46/9.61	                       shift(type), X4), X5), X6)), 
9.46/9.61	               app_encode_app(nat, dB, 
9.46/9.61	                 app_encode_app(fun1(nat, dB), app_encode_fun(nat, dB), 
9.46/9.61	                   aa(nat, dB), 
9.46/9.61	                   app_encode_app(dB, fun1(nat, dB), 
9.46/9.61	                     app_encode_app(fun1(dB, fun1(nat, dB)), 
9.46/9.61	                       app_encode_fun(dB, fun1(nat, dB)), 
9.46/9.61	                       aa(dB, fun1(nat, dB)), lift), X7)), X5))), X8))
9.46/9.61	       | ~ app_encode_app(bool, $o, pp, 
9.46/9.61	             app_encode_app(type, bool, 
9.46/9.61	               app_encode_app(fun1(type, bool), app_encode_fun(type, bool), 
9.46/9.61	                 aa(type, bool), 
9.46/9.61	                 app_encode_app(dB, fun1(type, bool), 
9.46/9.61	                   app_encode_app(fun1(nat, type), 
9.46/9.61	                     app_encode_fun(dB, fun1(type, bool)), typing, X4), X7)), 
9.46/9.61	               X8))),
9.46/9.61	    inference('cnf', [status(esa)], [zf_stmt_61])).
9.46/9.61	tff(zf_stmt_167, axiom, (![P:bool]: ((P = fTrue) | (P = fFalse)))).
9.46/9.61	tff('1', plain, ![X357 : bool]: (X357 = fTrue | X357 = fFalse),
9.46/9.61	    inference('cnf', [status(esa)], [zf_stmt_167])).
9.46/9.61	tff(zf_stmt_157, axiom, (~app_encode_app(bool,$o,pp,fFalse))).
9.46/9.61	tff('2', plain, ~ app_encode_app(bool, $o, pp, fFalse),
9.46/9.61	    inference('cnf', [status(esa)], [zf_stmt_157])).
9.46/9.61	tff('3', plain,
9.46/9.61	    ![X0 : bool]: (~ app_encode_app(bool, $o, pp, X0) | X0 = fTrue),
9.46/9.61	    inference('sup-', [status(thm)], ['1', '2'])).
9.46/9.61	tff('4', plain,
9.46/9.61	    ![X0 : type, X1 : nat, X2 : dB, X3 : type, X4 : fun1(nat, type)]:
9.46/9.61	      (~ $true
9.46/9.61	       | ~ app_encode_app(bool, $o, pp, 
9.46/9.61	             app_encode_app(type, bool, 
9.46/9.61	               app_encode_app(fun1(type, bool), app_encode_fun(type, bool), 
9.46/9.61	                 aa(type, bool), 
9.46/9.61	                 app_encode_app(dB, fun1(type, bool), 
9.46/9.61	                   app_encode_app(fun1(nat, type), 
9.46/9.61	                     app_encode_fun(dB, fun1(type, bool)), typing, X4), X2)), 
9.46/9.61	               X0))
9.46/9.61	       | app_encode_app(type, bool, 
9.46/9.61	           app_encode_app(fun1(type, bool), app_encode_fun(type, bool), 
9.46/9.61	             aa(type, bool), 
9.46/9.61	             app_encode_app(dB, fun1(type, bool), 
9.46/9.61	               app_encode_app(fun1(nat, type), 
9.46/9.61	                 app_encode_fun(dB, fun1(type, bool)), typing, 
9.46/9.61	                 app_encode_app(type, fun1(nat, type), 
9.46/9.61	                   app_encode_app(nat, 
9.46/9.61	                     app_encode_fun(type, fun1(nat, type)), 
9.46/9.61	                     app_encode_app(fun1(nat, type), 
9.46/9.61	                       app_encode_fun(nat, 
9.46/9.61	                         app_encode_fun(type, fun1(nat, type))), 
9.46/9.61	                       shift(type), X4), X1), X3)), 
9.46/9.61	               app_encode_app(nat, dB, 
9.46/9.61	                 app_encode_app(fun1(nat, dB), app_encode_fun(nat, dB), 
9.46/9.61	                   aa(nat, dB), 
9.46/9.61	                   app_encode_app(dB, fun1(nat, dB), 
9.46/9.61	                     app_encode_app(fun1(dB, fun1(nat, dB)), 
9.46/9.61	                       app_encode_fun(dB, fun1(nat, dB)), 
9.46/9.61	                       aa(dB, fun1(nat, dB)), lift), X2)), X1))), X0)
9.46/9.61	          = fTrue),
9.46/9.61	    inference('sup-', [status(thm)], ['0', '3'])).
9.46/9.61	tff('5', plain,
9.46/9.61	    ![X0 : type, X1 : nat, X2 : dB, X3 : type, X4 : fun1(nat, type)]:
9.46/9.61	      (app_encode_app(type, bool, 
9.46/9.61	         app_encode_app(fun1(type, bool), app_encode_fun(type, bool), 
9.46/9.61	           aa(type, bool), 
9.46/9.61	           app_encode_app(dB, fun1(type, bool), 
9.46/9.61	             app_encode_app(fun1(nat, type), 
9.46/9.61	               app_encode_fun(dB, fun1(type, bool)), typing, 
9.46/9.61	               app_encode_app(type, fun1(nat, type), 
9.46/9.61	                 app_encode_app(nat, app_encode_fun(type, fun1(nat, type)), 
9.46/9.61	                   app_encode_app(fun1(nat, type), 
9.46/9.61	                     app_encode_fun(nat, 
9.46/9.61	                       app_encode_fun(type, fun1(nat, type))), shift(type), 
9.46/9.61	                     X4), X1), X3)), 
9.46/9.61	             app_encode_app(nat, dB, 
9.46/9.61	               app_encode_app(fun1(nat, dB), app_encode_fun(nat, dB), 
9.46/9.61	                 aa(nat, dB), 
9.46/9.61	                 app_encode_app(dB, fun1(nat, dB), 
9.46/9.61	                   app_encode_app(fun1(dB, fun1(nat, dB)), 
9.46/9.61	                     app_encode_fun(dB, fun1(nat, dB)), 
9.46/9.61	                     aa(dB, fun1(nat, dB)), lift), X2)), X1))), X0)
9.46/9.61	        = fTrue
9.46/9.61	       | ~ app_encode_app(bool, $o, pp, 
9.46/9.61	             app_encode_app(type, bool, 
9.46/9.61	               app_encode_app(fun1(type, bool), app_encode_fun(type, bool), 
9.46/9.61	                 aa(type, bool), 
9.46/9.61	                 app_encode_app(dB, fun1(type, bool), 
9.46/9.61	                   app_encode_app(fun1(nat, type), 
9.46/9.61	                     app_encode_fun(dB, fun1(type, bool)), typing, X4), X2)), 
9.46/9.61	               X0))),
9.46/9.61	    inference('simplify', [status(thm)], ['4'])).
9.46/9.61	tff(zf_stmt_160, axiom,
9.46/9.61	  (![A:$tType,C:$tType,B:$tType,R:A,Q:B,P:fun1(A,fun1(B,C))]:
9.46/9.61	     (app_encode_app(A,C,
9.46/9.61	                     app_encode_app(fun1(A,C),app_encode_fun(A,C),aa(A,C),
9.46/9.61	                                    app_encode_app(B,fun1(A,C),
9.46/9.61	                                                   app_encode_app(fun1(
9.46/9.61	                                                                  A,fun1(B,C)),
9.46/9.61	                                                                  app_encode_fun(
9.46/9.61	                                                                  B,fun1(A,C)),
9.46/9.61	                                                                  combc(
9.46/9.61	                                                                  A,B,C),P),
9.46/9.61	                                                   Q)),
9.46/9.61	                     R) =
9.46/9.61	      app_encode_app(B,C,
9.46/9.61	                     app_encode_app(fun1(B,C),app_encode_fun(B,C),aa(B,C),
9.46/9.61	                                    app_encode_app(A,fun1(B,C),
9.46/9.61	                                                   app_encode_app(fun1(
9.46/9.61	                                                                  A,fun1(B,C)),
9.46/9.61	                                                                  app_encode_fun(
9.46/9.61	                                                                  A,fun1(B,C)),
9.46/9.61	                                                                  aa(
9.46/9.61	                                                                  A,fun1(B,C)),
9.46/9.61	                                                                  P),
9.46/9.61	                                                   R)),
9.46/9.61	                     Q)))).
9.46/9.61	tff('6', plain,
9.46/9.61	    ![X337 : $tType, X338 : $tType, X339 : $tType, 
9.46/9.61	      X340 : fun1(X339, fun1(X337, X338)), X341 : X339, X342 : X337]:
9.46/9.61	      app_encode_app(X339, X338, 
9.46/9.61	        app_encode_app(fun1(X339, X338), app_encode_fun(X339, X338), 
9.46/9.61	          aa(X339, X338), 
9.46/9.61	          app_encode_app(X337, fun1(X339, X338), 
9.46/9.61	            app_encode_app(fun1(X339, fun1(X337, X338)), 
9.46/9.61	              app_encode_fun(X337, fun1(X339, X338)), 
9.46/9.61	              combc(X339, X337, X338), X340), X342)), X341)
9.46/9.61	       = app_encode_app(X337, X338, 
9.46/9.61	           app_encode_app(fun1(X337, X338), app_encode_fun(X337, X338), 
9.46/9.61	             aa(X337, X338), 
9.46/9.61	             app_encode_app(X339, fun1(X337, X338), 
9.46/9.61	               app_encode_app(fun1(X339, fun1(X337, X338)), 
9.46/9.61	                 app_encode_fun(X339, fun1(X337, X338)), 
9.46/9.61	                 aa(X339, fun1(X337, X338)), X340), X341)), X342),
9.46/9.61	    inference('cnf', [status(esa)], [zf_stmt_160])).
9.46/9.61	tff('7', plain,
9.46/9.61	    ![X0 : type, X1 : nat, X2 : dB, X3 : type, X4 : fun1(nat, type)]:
9.46/9.61	      (app_encode_app(type, bool, 
9.46/9.61	         app_encode_app(fun1(type, bool), app_encode_fun(type, bool), 
9.46/9.61	           aa(type, bool), 
9.46/9.61	           app_encode_app(dB, fun1(type, bool), 
9.46/9.61	             app_encode_app(fun1(nat, type), 
9.46/9.61	               app_encode_fun(dB, fun1(type, bool)), typing, 
9.46/9.61	               app_encode_app(type, fun1(nat, type), 
9.46/9.61	                 app_encode_app(nat, app_encode_fun(type, fun1(nat, type)), 
9.46/9.61	                   app_encode_app(fun1(nat, type), 
9.46/9.61	                     app_encode_fun(nat, 
9.46/9.61	                       app_encode_fun(type, fun1(nat, type))), shift(type), 
9.46/9.61	                     X4), X1), X3)), 
9.46/9.61	             app_encode_app(dB, dB, 
9.46/9.61	               app_encode_app(fun1(dB, dB), app_encode_fun(dB, dB), 
9.46/9.61	                 aa(dB, dB), 
9.46/9.61	                 app_encode_app(nat, fun1(dB, dB), 
9.46/9.61	                   app_encode_app(fun1(dB, fun1(nat, dB)), 
9.46/9.61	                     app_encode_fun(nat, fun1(dB, dB)), combc(dB, nat, dB), 
9.46/9.61	                     lift), X1)), X2))), X0)
9.46/9.61	        = fTrue
9.46/9.61	       | ~ app_encode_app(bool, $o, pp, 
9.46/9.61	             app_encode_app(type, bool, 
9.46/9.61	               app_encode_app(fun1(type, bool), app_encode_fun(type, bool), 
9.46/9.61	                 aa(type, bool), 
9.46/9.61	                 app_encode_app(dB, fun1(type, bool), 
9.46/9.61	                   app_encode_app(fun1(nat, type), 
9.46/9.61	                     app_encode_fun(dB, fun1(type, bool)), typing, X4), X2)), 
9.46/9.61	               X0))),
9.46/9.61	    inference('demod', [status(thm)], ['5', '6'])).
9.46/9.61	tff(zf_stmt_168, conjecture,
9.46/9.61	  (app_encode_app(bool,$o,pp,
9.46/9.61	                  app_encode_app(type,bool,
9.46/9.61	                                 app_encode_app(fun1(type,bool),
9.46/9.61	                                                app_encode_fun(type,bool),
9.46/9.61	                                                aa(type,bool),
9.46/9.61	                                                app_encode_app(dB,
9.46/9.61	                                                               fun1(type,bool),
9.46/9.61	                                                               app_encode_app(
9.46/9.61	                                                               fun1(nat,type),
9.46/9.61	                                                               app_encode_fun(
9.46/9.61	                                                               dB,
9.46/9.61	                                                               fun1(type,bool)),
9.46/9.61	                                                               typing,
9.46/9.61	                                                               app_encode_app(
9.46/9.61	                                                               type,
9.46/9.61	                                                               fun1(nat,type),
9.46/9.61	                                                               app_encode_app(
9.46/9.61	                                                               nat,
9.46/9.61	                                                               app_encode_fun(
9.46/9.61	                                                               type,
9.46/9.61	                                                               fun1(nat,type)),
9.46/9.61	                                                               app_encode_app(
9.46/9.61	                                                               fun1(nat,type),
9.46/9.61	                                                               app_encode_fun(
9.46/9.61	                                                               nat,
9.46/9.61	                                                               app_encode_fun(
9.46/9.61	                                                               type,
9.46/9.61	                                                               fun1(nat,type))),
9.46/9.61	                                                               shift(type),e),
9.46/9.61	                                                               zero_zero(nat)),
9.46/9.61	                                                               t1)),
9.46/9.61	                                                               app_encode_app(
9.46/9.61	                                                               nat,dB,
9.46/9.61	                                                               app_encode_app(
9.46/9.61	                                                               fun1(nat,dB),
9.46/9.61	                                                               app_encode_fun(
9.46/9.61	                                                               nat,dB),
9.46/9.61	                                                               aa(nat,dB),
9.46/9.61	                                                               app_encode_app(
9.46/9.61	                                                               dB,
9.46/9.61	                                                               fun1(nat,dB),
9.46/9.61	                                                               app_encode_app(
9.46/9.61	                                                               fun1(dB,
9.46/9.61	                                                                    fun1(
9.46/9.61	                                                                    nat,dB)),
9.46/9.61	                                                               app_encode_fun(
9.46/9.61	                                                               dB,
9.46/9.61	                                                               fun1(nat,dB)),
9.46/9.61	                                                               aa(dB,
9.46/9.61	                                                                  fun1(
9.46/9.61	                                                                  nat,dB)),
9.46/9.61	                                                               lift),u)),
9.46/9.61	                                                               zero_zero(nat)))),
9.46/9.61	                                 app_encode_app(type,type,
9.46/9.61	                                                app_encode_app(fun1(type,type),
9.46/9.61	                                                               app_encode_fun(
9.46/9.61	                                                               type,type),
9.46/9.61	                                                               aa(type,type),
9.46/9.61	                                                               app_encode_app(
9.46/9.61	                                                               type,
9.46/9.61	                                                               fun1(type,type),
9.46/9.61	                                                               app_encode_app(
9.46/9.61	                                                               fun1(type,
9.46/9.61	                                                                    fun1(
9.46/9.61	                                                                    type,type)),
9.46/9.61	                                                               app_encode_fun(
9.46/9.61	                                                               type,
9.46/9.61	                                                               fun1(type,type)),
9.46/9.61	                                                               aa(type,
9.46/9.61	                                                                  fun1(
9.46/9.61	                                                                  type,type)),
9.46/9.61	                                                               fun),t1)),
9.46/9.61	                                                app_encode_app(type,type,
9.46/9.61	                                                               app_encode_app(
9.46/9.61	                                                               list(type),
9.46/9.61	                                                               app_encode_fun(
9.46/9.61	                                                               type,type),
9.46/9.61	                                                               app_encode_app(
9.46/9.61	                                                               fun1(type,
9.46/9.61	                                                                    fun1(
9.46/9.61	                                                                    type,type)),
9.46/9.61	                                                               app_encode_fun(
9.46/9.61	                                                               list(type),
9.46/9.61	                                                               app_encode_fun(
9.46/9.61	                                                               type,type)),
9.46/9.61	                                                               foldr(
9.46/9.61	                                                               type,type),fun),
9.46/9.61	                                                               ts),t)))))).
9.46/9.61	tff(zf_stmt_0, negated_conjecture,
9.46/9.61	  (~
9.46/9.61	    app_encode_app(bool,$o,pp,
9.46/9.61	                   app_encode_app(type,bool,
9.46/9.61	                                  app_encode_app(fun1(type,bool),
9.46/9.61	                                                 app_encode_fun(type,bool),
9.46/9.61	                                                 aa(type,bool),
9.46/9.61	                                                 app_encode_app(dB,
9.46/9.61	                                                                fun1(
9.46/9.61	                                                                type,bool),
9.46/9.61	                                                                app_encode_app(
9.46/9.61	                                                                fun1(
9.46/9.61	                                                                nat,type),
9.46/9.61	                                                                app_encode_fun(
9.46/9.61	                                                                dB,
9.46/9.61	                                                                fun1(
9.46/9.61	                                                                type,bool)),
9.46/9.61	                                                                typing,
9.46/9.61	                                                                app_encode_app(
9.46/9.61	                                                                type,
9.46/9.61	                                                                fun1(
9.46/9.61	                                                                nat,type),
9.46/9.61	                                                                app_encode_app(
9.46/9.61	                                                                nat,
9.46/9.61	                                                                app_encode_fun(
9.46/9.61	                                                                type,
9.46/9.61	                                                                fun1(
9.46/9.61	                                                                nat,type)),
9.46/9.61	                                                                app_encode_app(
9.46/9.61	                                                                fun1(
9.46/9.61	                                                                nat,type),
9.46/9.61	                                                                app_encode_fun(
9.46/9.61	                                                                nat,
9.46/9.61	                                                                app_encode_fun(
9.46/9.61	                                                                type,
9.46/9.61	                                                                fun1(
9.46/9.61	                                                                nat,type))),
9.46/9.61	                                                                shift(type),e),
9.46/9.61	                                                                zero_zero(
9.46/9.61	                                                                nat)),t1)),
9.46/9.61	                                                                app_encode_app(
9.46/9.61	                                                                nat,dB,
9.46/9.61	                                                                app_encode_app(
9.46/9.61	                                                                fun1(nat,dB),
9.46/9.61	                                                                app_encode_fun(
9.46/9.61	                                                                nat,dB),
9.46/9.61	                                                                aa(nat,dB),
9.46/9.61	                                                                app_encode_app(
9.46/9.61	                                                                dB,
9.46/9.61	                                                                fun1(nat,dB),
9.46/9.61	                                                                app_encode_app(
9.46/9.61	                                                                fun1(
9.46/9.61	                                                                dB,
9.46/9.61	                                                                fun1(nat,dB)),
9.46/9.61	                                                                app_encode_fun(
9.46/9.61	                                                                dB,
9.46/9.61	                                                                fun1(nat,dB)),
9.46/9.61	                                                                aa(dB,
9.46/9.61	                                                                   fun1(
9.46/9.61	                                                                   nat,dB)),
9.46/9.61	                                                                lift),u)),
9.46/9.61	                                                                zero_zero(
9.46/9.61	                                                                nat)))),
9.46/9.61	                                  app_encode_app(type,type,
9.46/9.61	                                                 app_encode_app(fun1(
9.46/9.61	                                                                type,type),
9.46/9.61	                                                                app_encode_fun(
9.46/9.61	                                                                type,type),
9.46/9.61	                                                                aa(type,type),
9.46/9.61	                                                                app_encode_app(
9.46/9.61	                                                                type,
9.46/9.61	                                                                fun1(
9.46/9.61	                                                                type,type),
9.46/9.61	                                                                app_encode_app(
9.46/9.61	                                                                fun1(
9.46/9.61	                                                                type,
9.46/9.61	                                                                fun1(
9.46/9.61	                                                                type,type)),
9.46/9.61	                                                                app_encode_fun(
9.46/9.61	                                                                type,
9.46/9.61	                                                                fun1(
9.46/9.61	                                                                type,type)),
9.46/9.61	                                                                aa(type,
9.46/9.61	                                                                   fun1(
9.46/9.61	                                                                   type,type)),
9.46/9.61	                                                                fun),t1)),
9.46/9.61	                                                 app_encode_app(type,type,
9.46/9.61	                                                                app_encode_app(
9.46/9.61	                                                                list(type),
9.46/9.61	                                                                app_encode_fun(
9.46/9.61	                                                                type,type),
9.46/9.61	                                                                app_encode_app(
9.46/9.61	                                                                fun1(
9.46/9.61	                                                                type,
9.46/9.61	                                                                fun1(
9.46/9.61	                                                                type,type)),
9.46/9.61	                                                                app_encode_fun(
9.46/9.61	                                                                list(type),
9.46/9.61	                                                                app_encode_fun(
9.46/9.61	                                                                type,type)),
9.46/9.61	                                                                foldr(
9.46/9.61	                                                                type,type),
9.46/9.61	                                                                fun),ts),t)))))).
9.46/9.61	tff('8', plain,
9.46/9.61	    ~ app_encode_app(bool, $o, pp, 
9.46/9.61	        app_encode_app(type, bool, 
9.46/9.61	          app_encode_app(fun1(type, bool), app_encode_fun(type, bool), 
9.46/9.61	            aa(type, bool), 
9.46/9.61	            app_encode_app(dB, fun1(type, bool), 
9.46/9.61	              app_encode_app(fun1(nat, type), 
9.46/9.61	                app_encode_fun(dB, fun1(type, bool)), typing, 
9.46/9.61	                app_encode_app(type, fun1(nat, type), 
9.46/9.61	                  app_encode_app(nat, app_encode_fun(type, fun1(nat, type)), 
9.46/9.61	                    app_encode_app(fun1(nat, type), 
9.46/9.61	                      app_encode_fun(nat, 
9.46/9.61	                        app_encode_fun(type, fun1(nat, type))), shift(type), 
9.46/9.61	                      e), zero_zero(nat)), t1)), 
9.46/9.61	              app_encode_app(nat, dB, 
9.46/9.61	                app_encode_app(fun1(nat, dB), app_encode_fun(nat, dB), 
9.46/9.61	                  aa(nat, dB), 
9.46/9.61	                  app_encode_app(dB, fun1(nat, dB), 
9.46/9.61	                    app_encode_app(fun1(dB, fun1(nat, dB)), 
9.46/9.61	                      app_encode_fun(dB, fun1(nat, dB)), 
9.46/9.61	                      aa(dB, fun1(nat, dB)), lift), u)), zero_zero(nat)))), 
9.46/9.61	          app_encode_app(type, type, 
9.46/9.61	            app_encode_app(fun1(type, type), app_encode_fun(type, type), 
9.46/9.61	              aa(type, type), 
9.46/9.61	              app_encode_app(type, fun1(type, type), 
9.46/9.61	                app_encode_app(fun1(type, fun1(type, type)), 
9.46/9.61	                  app_encode_fun(type, fun1(type, type)), 
9.46/9.61	                  aa(type, fun1(type, type)), fun), t1)), 
9.46/9.61	            app_encode_app(type, type, 
9.46/9.61	              app_encode_app(list(type), app_encode_fun(type, type), 
9.46/9.61	                app_encode_app(fun1(type, fun1(type, type)), 
9.46/9.61	                  app_encode_fun(list(type), app_encode_fun(type, type)), 
9.46/9.61	                  foldr(type, type), fun), ts), t)))),
9.46/9.61	    inference('cnf', [status(esa)], [zf_stmt_0])).
9.46/9.61	tff(zf_stmt_124, axiom,
9.46/9.61	  (![B:$tType,A:$tType,Aa:A,Xs:list(B),X:B,F:fun1(B,fun1(A,A))]:
9.46/9.61	     (app_encode_app(A,A,
9.46/9.61	                     app_encode_app(list(B),app_encode_fun(A,A),
9.46/9.61	                                    app_encode_app(fun1(B,fun1(A,A)),
9.46/9.61	                                                   app_encode_fun(list(B),
9.46/9.61	                                                                  app_encode_fun(
9.46/9.61	                                                                  A,A)),
9.46/9.61	                                                   foldr(B,A),F),
9.46/9.61	                                    app_encode_app(list(B),list(B),
9.46/9.61	                                                   app_encode_app(B,
9.46/9.61	                                                                  app_encode_fun(
9.46/9.61	                                                                  list(B),
9.46/9.61	                                                                  list(B)),
9.46/9.61	                                                                  cons(B),X),
9.46/9.61	                                                   Xs)),
9.46/9.61	                     Aa) =
9.46/9.61	      app_encode_app(A,A,
9.46/9.61	                     app_encode_app(fun1(A,A),app_encode_fun(A,A),aa(A,A),
9.46/9.61	                                    app_encode_app(B,fun1(A,A),
9.46/9.61	                                                   app_encode_app(fun1(
9.46/9.61	                                                                  B,fun1(A,A)),
9.46/9.61	                                                                  app_encode_fun(
9.46/9.61	                                                                  B,fun1(A,A)),
9.46/9.61	                                                                  aa(
9.46/9.61	                                                                  B,fun1(A,A)),
9.46/9.61	                                                                  F),
9.46/9.61	                                                   X)),
9.46/9.61	                     app_encode_app(A,A,
9.46/9.61	                                    app_encode_app(list(B),
9.46/9.61	                                                   app_encode_fun(A,A),
9.46/9.61	                                                   app_encode_app(fun1(
9.46/9.61	                                                                  B,fun1(A,A)),
9.46/9.61	                                                                  app_encode_fun(
9.46/9.61	                                                                  list(B),
9.46/9.61	                                                                  app_encode_fun(
9.46/9.61	                                                                  A,A)),
9.46/9.61	                                                                  foldr(B,A),
9.46/9.61	                                                                  F),
9.46/9.61	                                                   Xs),
9.46/9.61	                                    Aa))))).
9.46/9.61	tff('9', plain,
9.46/9.61	    ![X189 : $tType, X190 : $tType, X191 : fun1(X190, fun1(X189, X189)), 
9.46/9.61	      X192 : X190, X193 : list(X190), X194 : X189]:
9.46/9.61	      app_encode_app(X189, X189, 
9.46/9.61	        app_encode_app(list(X190), app_encode_fun(X189, X189), 
9.46/9.61	          app_encode_app(fun1(X190, fun1(X189, X189)), 
9.46/9.61	            app_encode_fun(list(X190), app_encode_fun(X189, X189)), 
9.46/9.61	            foldr(X190, X189), X191), 
9.46/9.61	          app_encode_app(list(X190), list(X190), 
9.46/9.61	            app_encode_app(X190, app_encode_fun(list(X190), list(X190)), 
9.46/9.61	              cons(X190), X192), X193)), X194)
9.46/9.61	       = app_encode_app(X189, X189, 
9.46/9.61	           app_encode_app(fun1(X189, X189), app_encode_fun(X189, X189), 
9.46/9.61	             aa(X189, X189), 
9.46/9.61	             app_encode_app(X190, fun1(X189, X189), 
9.46/9.61	               app_encode_app(fun1(X190, fun1(X189, X189)), 
9.46/9.61	                 app_encode_fun(X190, fun1(X189, X189)), 
9.46/9.61	                 aa(X190, fun1(X189, X189)), X191), X192)), 
9.46/9.61	           app_encode_app(X189, X189, 
9.46/9.61	             app_encode_app(list(X190), app_encode_fun(X189, X189), 
9.46/9.61	               app_encode_app(fun1(X190, fun1(X189, X189)), 
9.46/9.61	                 app_encode_fun(list(X190), app_encode_fun(X189, X189)), 
9.46/9.61	                 foldr(X190, X189), X191), X193), X194)),
9.46/9.61	    inference('cnf', [status(esa)], [zf_stmt_124])).
9.46/9.61	tff(zf_stmt_62, axiom,
9.46/9.61	  (t2 =
9.46/9.61	   app_encode_app(type,type,
9.46/9.61	                  app_encode_app(fun1(type,type),app_encode_fun(type,type),
9.46/9.61	                                 aa(type,type),
9.46/9.61	                                 app_encode_app(type,fun1(type,type),
9.46/9.61	                                                app_encode_app(fun1(type,
9.46/9.61	                                                                    fun1(
9.46/9.61	                                                                    type,type)),
9.46/9.61	                                                               app_encode_fun(
9.46/9.61	                                                               type,
9.46/9.61	                                                               fun1(type,type)),
9.46/9.61	                                                               aa(type,
9.46/9.61	                                                                  fun1(
9.46/9.61	                                                                  type,type)),
9.46/9.61	                                                               fun),
9.46/9.61	                                                t1)),
9.46/9.61	                  app_encode_app(type,type,
9.46/9.61	                                 app_encode_app(list(type),
9.46/9.61	                                                app_encode_fun(type,type),
9.46/9.61	                                                app_encode_app(fun1(type,
9.46/9.61	                                                                    fun1(
9.46/9.61	                                                                    type,type)),
9.46/9.61	                                                               app_encode_fun(
9.46/9.61	                                                               list(type),
9.46/9.61	                                                               app_encode_fun(
9.46/9.61	                                                               type,type)),
9.46/9.61	                                                               foldr(
9.46/9.61	                                                               type,type),fun),
9.46/9.61	                                                ts),
9.46/9.61	                                 t)))).
9.46/9.61	tff('10', plain,
9.46/9.61	    t2
9.46/9.61	     = app_encode_app(type, type, 
9.46/9.61	         app_encode_app(fun1(type, type), app_encode_fun(type, type), 
9.46/9.61	           aa(type, type), 
9.46/9.61	           app_encode_app(type, fun1(type, type), 
9.46/9.61	             app_encode_app(fun1(type, fun1(type, type)), 
9.46/9.61	               app_encode_fun(type, fun1(type, type)), 
9.46/9.61	               aa(type, fun1(type, type)), fun), t1)), 
9.46/9.61	         app_encode_app(type, type, 
9.46/9.61	           app_encode_app(list(type), app_encode_fun(type, type), 
9.46/9.61	             app_encode_app(fun1(type, fun1(type, type)), 
9.46/9.61	               app_encode_fun(list(type), app_encode_fun(type, type)), 
9.46/9.61	               foldr(type, type), fun), ts), t)),
9.46/9.61	    inference('cnf', [status(esa)], [zf_stmt_62])).
9.46/9.61	tff('11', plain,
9.46/9.61	    t2
9.46/9.61	     = app_encode_app(type, type, 
9.46/9.61	         app_encode_app(list(type), app_encode_fun(type, type), 
9.46/9.61	           app_encode_app(fun1(type, fun1(type, type)), 
9.46/9.61	             app_encode_fun(list(type), app_encode_fun(type, type)), 
9.46/9.61	             foldr(type, type), fun), 
9.46/9.61	           app_encode_app(list(type), list(type), 
9.46/9.61	             app_encode_app(type, app_encode_fun(list(type), list(type)), 
9.46/9.61	               cons(type), t1), ts)), t),
9.46/9.61	    inference('demod', [status(thm)], ['10', '9'])).
9.46/9.61	tff('12', plain,
9.46/9.61	    ~ app_encode_app(bool, $o, pp, 
9.46/9.61	        app_encode_app(type, bool, 
9.46/9.61	          app_encode_app(fun1(type, bool), app_encode_fun(type, bool), 
9.46/9.61	            aa(type, bool), 
9.46/9.61	            app_encode_app(dB, fun1(type, bool), 
9.46/9.61	              app_encode_app(fun1(nat, type), 
9.46/9.61	                app_encode_fun(dB, fun1(type, bool)), typing, 
9.46/9.61	                app_encode_app(type, fun1(nat, type), 
9.46/9.61	                  app_encode_app(nat, app_encode_fun(type, fun1(nat, type)), 
9.46/9.61	                    app_encode_app(fun1(nat, type), 
9.46/9.61	                      app_encode_fun(nat, 
9.46/9.61	                        app_encode_fun(type, fun1(nat, type))), shift(type), 
9.46/9.61	                      e), zero_zero(nat)), t1)), 
9.46/9.61	              app_encode_app(dB, dB, 
9.46/9.61	                app_encode_app(fun1(dB, dB), app_encode_fun(dB, dB), 
9.46/9.61	                  aa(dB, dB), 
9.46/9.61	                  app_encode_app(nat, fun1(dB, dB), 
9.46/9.61	                    app_encode_app(fun1(dB, fun1(nat, dB)), 
9.46/9.61	                      app_encode_fun(nat, fun1(dB, dB)), combc(dB, nat, dB), 
9.46/9.61	                      lift), zero_zero(nat))), u))), t2)),
9.46/9.61	    inference('demod', [status(thm)], ['8', '6', '9', '11'])).
9.46/9.61	tff('13', plain,
9.46/9.61	    (~ app_encode_app(bool, $o, pp, fTrue)
9.46/9.61	     | ~ app_encode_app(bool, $o, pp, 
9.46/9.61	           app_encode_app(type, bool, 
9.46/9.61	             app_encode_app(fun1(type, bool), app_encode_fun(type, bool), 
9.46/9.61	               aa(type, bool), 
9.46/9.61	               app_encode_app(dB, fun1(type, bool), 
9.46/9.61	                 app_encode_app(fun1(nat, type), 
9.46/9.61	                   app_encode_fun(dB, fun1(type, bool)), typing, e), u)), t2))),
9.46/9.61	    inference('sup-', [status(thm)], ['7', '12'])).
9.46/9.61	tff(zf_stmt_158, axiom, (app_encode_app(bool,$o,pp,fTrue))).
9.46/9.61	tff('14', plain, app_encode_app(bool, $o, pp, fTrue),
9.46/9.61	    inference('cnf', [status(esa)], [zf_stmt_158])).
9.46/9.61	tff(zf_stmt_60, axiom,
9.46/9.61	  (app_encode_app(bool,$o,pp,
9.46/9.61	                  app_encode_app(type,bool,
9.46/9.61	                                 app_encode_app(fun1(type,bool),
9.46/9.61	                                                app_encode_fun(type,bool),
9.46/9.61	                                                aa(type,bool),
9.46/9.61	                                                app_encode_app(dB,
9.46/9.61	                                                               fun1(type,bool),
9.46/9.61	                                                               app_encode_app(
9.46/9.61	                                                               fun1(nat,type),
9.46/9.61	                                                               app_encode_fun(
9.46/9.61	                                                               dB,
9.46/9.61	                                                               fun1(type,bool)),
9.46/9.61	                                                               typing,e),u)),
9.46/9.61	                                 t2)))).
9.46/9.61	tff('15', plain,
9.46/9.61	    app_encode_app(bool, $o, pp, 
9.46/9.61	      app_encode_app(type, bool, 
9.46/9.61	        app_encode_app(fun1(type, bool), app_encode_fun(type, bool), 
9.46/9.61	          aa(type, bool), 
9.46/9.61	          app_encode_app(dB, fun1(type, bool), 
9.46/9.61	            app_encode_app(fun1(nat, type), 
9.46/9.61	              app_encode_fun(dB, fun1(type, bool)), typing, e), u)), t2)),
9.46/9.61	    inference('cnf', [status(esa)], [zf_stmt_60])).
9.46/9.61	tff('16', plain,
9.46/9.61	    (~ $true
9.46/9.61	     | app_encode_app(type, bool, 
9.46/9.61	         app_encode_app(fun1(type, bool), app_encode_fun(type, bool), 
9.46/9.61	           aa(type, bool), 
9.46/9.61	           app_encode_app(dB, fun1(type, bool), 
9.46/9.61	             app_encode_app(fun1(nat, type), 
9.46/9.61	               app_encode_fun(dB, fun1(type, bool)), typing, e), u)), t2)
9.46/9.61	        = fTrue),
9.46/9.61	    inference('sup-', [status(thm)], ['15', '3'])).
9.46/9.61	tff('17', plain,
9.46/9.61	    app_encode_app(type, bool, 
9.46/9.61	      app_encode_app(fun1(type, bool), app_encode_fun(type, bool), 
9.46/9.61	        aa(type, bool), 
9.46/9.61	        app_encode_app(dB, fun1(type, bool), 
9.46/9.61	          app_encode_app(fun1(nat, type), 
9.46/9.61	            app_encode_fun(dB, fun1(type, bool)), typing, e), u)), t2)
9.46/9.61	     = fTrue,
9.46/9.61	    inference('simplify', [status(thm)], ['16'])).
9.46/9.61	tff('18', plain, (~ $true | ~ $true),
9.46/9.61	    inference('demod', [status(thm)], ['13', '14', '17', '14'])).
9.46/9.61	tff('19', plain, $false, inference('simplify', [status(thm)], ['18'])).
9.46/9.61	
9.46/9.61	% SZS output end Refutation
9.46/9.61	EOF
