0.00/0.01	% File    : /export/starexec/sandbox/benchmark/theBenchmark.p
0.00/0.01	% app-encoded or not : app
0.00/0.01	% Variant    : fo
0.00/0.01	% Ordering    : kbo
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 $2 \
0.00/0.01	  --simultaneous-sup false \
0.00/0.01	  --no-max-vars \
0.00/0.01	  --no-fool
0.00/0.19	% Computer   : n040.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 07:00:53 CST 2018
8.82/9.01	% done 1351 iterations in 8.806s
8.82/9.01	% SZS status Theorem for 'stdin'
8.82/9.01	% SZS output start Refutation
8.82/9.01	tff(zf_stmt_60, axiom,
8.82/9.01	  (![Ua:type,Ib:nat,Ta:type,Ta1:dB,Eb:fun1(nat,type)]:
8.82/9.01	     (app_encode_app(bool,$o,pp,
8.82/9.01	                     app_encode_app(type,bool,
8.82/9.01	                                    app_encode_app(fun1(type,bool),
8.82/9.01	                                                   app_encode_fun(type,bool),
8.82/9.01	                                                   aa(type,bool),
8.82/9.01	                                                   app_encode_app(dB,
8.82/9.01	                                                                  fun1(
8.82/9.01	                                                                  type,bool),
8.82/9.01	                                                                  app_encode_app(
8.82/9.01	                                                                  fun1(
8.82/9.01	                                                                  nat,type),
8.82/9.01	                                                                  app_encode_fun(
8.82/9.01	                                                                  dB,
8.82/9.01	                                                                  fun1(
8.82/9.01	                                                                  type,bool)),
8.82/9.01	                                                                  typing,Eb),
8.82/9.01	                                                                  Ta1)),
8.82/9.01	                                    Ta)) =>
8.82/9.01	      app_encode_app(bool,$o,pp,
8.82/9.01	                     app_encode_app(type,bool,
8.82/9.01	                                    app_encode_app(fun1(type,bool),
8.82/9.01	                                                   app_encode_fun(type,bool),
8.82/9.01	                                                   aa(type,bool),
8.82/9.01	                                                   app_encode_app(dB,
8.82/9.01	                                                                  fun1(
8.82/9.01	                                                                  type,bool),
8.82/9.01	                                                                  app_encode_app(
8.82/9.01	                                                                  fun1(
8.82/9.01	                                                                  nat,type),
8.82/9.01	                                                                  app_encode_fun(
8.82/9.01	                                                                  dB,
8.82/9.01	                                                                  fun1(
8.82/9.01	                                                                  type,bool)),
8.82/9.01	                                                                  typing,
8.82/9.01	                                                                  app_encode_app(
8.82/9.01	                                                                  type,
8.82/9.01	                                                                  fun1(
8.82/9.01	                                                                  nat,type),
8.82/9.01	                                                                  app_encode_app(
8.82/9.01	                                                                  nat,
8.82/9.01	                                                                  app_encode_fun(
8.82/9.01	                                                                  type,
8.82/9.01	                                                                  fun1(
8.82/9.01	                                                                  nat,type)),
8.82/9.01	                                                                  app_encode_app(
8.82/9.01	                                                                  fun1(
8.82/9.01	                                                                  nat,type),
8.82/9.01	                                                                  app_encode_fun(
8.82/9.01	                                                                  nat,
8.82/9.01	                                                                  app_encode_fun(
8.82/9.01	                                                                  type,
8.82/9.01	                                                                  fun1(
8.82/9.01	                                                                  nat,type))),
8.82/9.01	                                                                  shift(type),
8.82/9.01	                                                                  Eb),Ib),Ua)),
8.82/9.01	                                                                  app_encode_app(
8.82/9.01	                                                                  nat,dB,
8.82/9.01	                                                                  app_encode_app(
8.82/9.01	                                                                  fun1(
8.82/9.01	                                                                  nat,dB),
8.82/9.01	                                                                  app_encode_fun(
8.82/9.01	                                                                  nat,dB),
8.82/9.01	                                                                  aa(nat,dB),
8.82/9.01	                                                                  app_encode_app(
8.82/9.01	                                                                  dB,
8.82/9.01	                                                                  fun1(
8.82/9.01	                                                                  nat,dB),
8.82/9.01	                                                                  app_encode_app(
8.82/9.01	                                                                  fun1(
8.82/9.01	                                                                  dB,
8.82/9.01	                                                                  fun1(
8.82/9.01	                                                                  nat,dB)),
8.82/9.01	                                                                  app_encode_fun(
8.82/9.01	                                                                  dB,
8.82/9.01	                                                                  fun1(
8.82/9.01	                                                                  nat,dB)),
8.82/9.01	                                                                  aa(
8.82/9.01	                                                                  dB,
8.82/9.01	                                                                  fun1(
8.82/9.01	                                                                  nat,dB)),
8.82/9.01	                                                                  lift),Ta1)),
8.82/9.01	                                                                  Ib))),
8.82/9.01	                                    Ta))))).
8.82/9.01	tff('0', plain,
8.82/9.01	    ![X0 : fun1(nat, type), X1 : nat, X2 : type, X3 : dB, X4 : type]:
8.82/9.01	      (app_encode_app(bool, $o, pp, 
8.82/9.01	         app_encode_app(type, bool, 
8.82/9.01	           app_encode_app(fun1(type, bool), app_encode_fun(type, bool), 
8.82/9.01	             aa(type, bool), 
8.82/9.01	             app_encode_app(dB, fun1(type, bool), 
8.82/9.01	               app_encode_app(fun1(nat, type), 
8.82/9.01	                 app_encode_fun(dB, fun1(type, bool)), typing, 
8.82/9.01	                 app_encode_app(type, fun1(nat, type), 
8.82/9.01	                   app_encode_app(nat, 
8.82/9.01	                     app_encode_fun(type, fun1(nat, type)), 
8.82/9.01	                     app_encode_app(fun1(nat, type), 
8.82/9.01	                       app_encode_fun(nat, 
8.82/9.01	                         app_encode_fun(type, fun1(nat, type))), 
8.82/9.01	                       shift(type), X0), X1), X2)), 
8.82/9.01	               app_encode_app(nat, dB, 
8.82/9.01	                 app_encode_app(fun1(nat, dB), app_encode_fun(nat, dB), 
8.82/9.01	                   aa(nat, dB), 
8.82/9.01	                   app_encode_app(dB, fun1(nat, dB), 
8.82/9.01	                     app_encode_app(fun1(dB, fun1(nat, dB)), 
8.82/9.01	                       app_encode_fun(dB, fun1(nat, dB)), 
8.82/9.01	                       aa(dB, fun1(nat, dB)), lift), X3)), X1))), X4))
8.82/9.01	       | ~ app_encode_app(bool, $o, pp, 
8.82/9.01	             app_encode_app(type, bool, 
8.82/9.01	               app_encode_app(fun1(type, bool), app_encode_fun(type, bool), 
8.82/9.01	                 aa(type, bool), 
8.82/9.01	                 app_encode_app(dB, fun1(type, bool), 
8.82/9.01	                   app_encode_app(fun1(nat, type), 
8.82/9.01	                     app_encode_fun(dB, fun1(type, bool)), typing, X0), X3)), 
8.82/9.01	               X4))),
8.82/9.01	    inference('cnf', [status(esa)], [zf_stmt_60])).
8.82/9.01	tff(zf_stmt_166, axiom, (![P:bool]: ((P = fTrue) | (P = fFalse)))).
8.82/9.01	tff('1', plain, ![X353 : bool]: (X353 = fTrue | X353 = fFalse),
8.82/9.01	    inference('cnf', [status(esa)], [zf_stmt_166])).
8.82/9.01	tff(zf_stmt_156, axiom, (~app_encode_app(bool,$o,pp,fFalse))).
8.82/9.01	tff('2', plain, ~ app_encode_app(bool, $o, pp, fFalse),
8.82/9.01	    inference('cnf', [status(esa)], [zf_stmt_156])).
8.82/9.01	tff('3', plain,
8.82/9.01	    ![X0 : bool]: (~ app_encode_app(bool, $o, pp, X0) | X0 = fTrue),
8.82/9.01	    inference('sup-', [status(thm)], ['1', '2'])).
8.82/9.01	tff('4', plain,
8.82/9.01	    ![X0 : type, X1 : nat, X2 : dB, X3 : type, X4 : fun1(nat, type)]:
8.82/9.01	      (~ $true
8.82/9.01	       | ~ app_encode_app(bool, $o, pp, 
8.82/9.01	             app_encode_app(type, bool, 
8.82/9.01	               app_encode_app(fun1(type, bool), app_encode_fun(type, bool), 
8.82/9.01	                 aa(type, bool), 
8.82/9.01	                 app_encode_app(dB, fun1(type, bool), 
8.82/9.01	                   app_encode_app(fun1(nat, type), 
8.82/9.01	                     app_encode_fun(dB, fun1(type, bool)), typing, X4), X2)), 
8.82/9.01	               X0))
8.82/9.01	       | app_encode_app(type, bool, 
8.82/9.01	           app_encode_app(fun1(type, bool), app_encode_fun(type, bool), 
8.82/9.01	             aa(type, bool), 
8.82/9.01	             app_encode_app(dB, fun1(type, bool), 
8.82/9.01	               app_encode_app(fun1(nat, type), 
8.82/9.01	                 app_encode_fun(dB, fun1(type, bool)), typing, 
8.82/9.01	                 app_encode_app(type, fun1(nat, type), 
8.82/9.01	                   app_encode_app(nat, 
8.82/9.01	                     app_encode_fun(type, fun1(nat, type)), 
8.82/9.01	                     app_encode_app(fun1(nat, type), 
8.82/9.01	                       app_encode_fun(nat, 
8.82/9.01	                         app_encode_fun(type, fun1(nat, type))), 
8.82/9.01	                       shift(type), X4), X1), X3)), 
8.82/9.01	               app_encode_app(nat, dB, 
8.82/9.01	                 app_encode_app(fun1(nat, dB), app_encode_fun(nat, dB), 
8.82/9.01	                   aa(nat, dB), 
8.82/9.01	                   app_encode_app(dB, fun1(nat, dB), 
8.82/9.01	                     app_encode_app(fun1(dB, fun1(nat, dB)), 
8.82/9.01	                       app_encode_fun(dB, fun1(nat, dB)), 
8.82/9.01	                       aa(dB, fun1(nat, dB)), lift), X2)), X1))), X0)
8.82/9.01	          = fTrue),
8.82/9.01	    inference('sup-', [status(thm)], ['0', '3'])).
8.82/9.01	tff('5', plain,
8.82/9.01	    ![X0 : type, X1 : nat, X2 : dB, X3 : type, X4 : fun1(nat, type)]:
8.82/9.01	      (app_encode_app(type, bool, 
8.82/9.01	         app_encode_app(fun1(type, bool), app_encode_fun(type, bool), 
8.82/9.01	           aa(type, bool), 
8.82/9.01	           app_encode_app(dB, fun1(type, bool), 
8.82/9.01	             app_encode_app(fun1(nat, type), 
8.82/9.01	               app_encode_fun(dB, fun1(type, bool)), typing, 
8.82/9.01	               app_encode_app(type, fun1(nat, type), 
8.82/9.01	                 app_encode_app(nat, app_encode_fun(type, fun1(nat, type)), 
8.82/9.01	                   app_encode_app(fun1(nat, type), 
8.82/9.01	                     app_encode_fun(nat, 
8.82/9.01	                       app_encode_fun(type, fun1(nat, type))), shift(type), 
8.82/9.01	                     X4), X1), X3)), 
8.82/9.01	             app_encode_app(nat, dB, 
8.82/9.01	               app_encode_app(fun1(nat, dB), app_encode_fun(nat, dB), 
8.82/9.01	                 aa(nat, dB), 
8.82/9.01	                 app_encode_app(dB, fun1(nat, dB), 
8.82/9.01	                   app_encode_app(fun1(dB, fun1(nat, dB)), 
8.82/9.01	                     app_encode_fun(dB, fun1(nat, dB)), 
8.82/9.01	                     aa(dB, fun1(nat, dB)), lift), X2)), X1))), X0)
8.82/9.01	        = fTrue
8.82/9.01	       | ~ app_encode_app(bool, $o, pp, 
8.82/9.01	             app_encode_app(type, bool, 
8.82/9.01	               app_encode_app(fun1(type, bool), app_encode_fun(type, bool), 
8.82/9.01	                 aa(type, bool), 
8.82/9.01	                 app_encode_app(dB, fun1(type, bool), 
8.82/9.01	                   app_encode_app(fun1(nat, type), 
8.82/9.01	                     app_encode_fun(dB, fun1(type, bool)), typing, X4), X2)), 
8.82/9.01	               X0))),
8.82/9.01	    inference('simplify', [status(thm)], ['4'])).
8.82/9.01	tff(zf_stmt_159, axiom,
8.82/9.01	  (![A:$tType,C:$tType,B:$tType,R:A,Q:B,P:fun1(A,fun1(B,C))]:
8.82/9.01	     (app_encode_app(A,C,
8.82/9.01	                     app_encode_app(fun1(A,C),app_encode_fun(A,C),aa(A,C),
8.82/9.01	                                    app_encode_app(B,fun1(A,C),
8.82/9.01	                                                   app_encode_app(fun1(
8.82/9.01	                                                                  A,fun1(B,C)),
8.82/9.01	                                                                  app_encode_fun(
8.82/9.01	                                                                  B,fun1(A,C)),
8.82/9.01	                                                                  combc(
8.82/9.01	                                                                  A,B,C),P),
8.82/9.01	                                                   Q)),
8.82/9.01	                     R) =
8.82/9.01	      app_encode_app(B,C,
8.82/9.01	                     app_encode_app(fun1(B,C),app_encode_fun(B,C),aa(B,C),
8.82/9.01	                                    app_encode_app(A,fun1(B,C),
8.82/9.01	                                                   app_encode_app(fun1(
8.82/9.01	                                                                  A,fun1(B,C)),
8.82/9.01	                                                                  app_encode_fun(
8.82/9.01	                                                                  A,fun1(B,C)),
8.82/9.01	                                                                  aa(
8.82/9.01	                                                                  A,fun1(B,C)),
8.82/9.01	                                                                  P),
8.82/9.01	                                                   R)),
8.82/9.01	                     Q)))).
8.82/9.01	tff('6', plain,
8.82/9.01	    ![X333 : $tType, X334 : $tType, X335 : $tType, 
8.82/9.01	      X336 : fun1(X335, fun1(X333, X334)), X337 : X335, X338 : X333]:
8.82/9.01	      app_encode_app(X335, X334, 
8.82/9.01	        app_encode_app(fun1(X335, X334), app_encode_fun(X335, X334), 
8.82/9.01	          aa(X335, X334), 
8.82/9.01	          app_encode_app(X333, fun1(X335, X334), 
8.82/9.01	            app_encode_app(fun1(X335, fun1(X333, X334)), 
8.82/9.01	              app_encode_fun(X333, fun1(X335, X334)), 
8.82/9.01	              combc(X335, X333, X334), X336), X338)), X337)
8.82/9.01	       = app_encode_app(X333, X334, 
8.82/9.01	           app_encode_app(fun1(X333, X334), app_encode_fun(X333, X334), 
8.82/9.01	             aa(X333, X334), 
8.82/9.01	             app_encode_app(X335, fun1(X333, X334), 
8.82/9.01	               app_encode_app(fun1(X335, fun1(X333, X334)), 
8.82/9.01	                 app_encode_fun(X335, fun1(X333, X334)), 
8.82/9.01	                 aa(X335, fun1(X333, X334)), X336), X337)), X338),
8.82/9.01	    inference('cnf', [status(esa)], [zf_stmt_159])).
8.82/9.01	tff('7', plain,
8.82/9.01	    ![X0 : type, X1 : nat, X2 : dB, X3 : type, X4 : fun1(nat, type)]:
8.82/9.01	      (app_encode_app(type, bool, 
8.82/9.01	         app_encode_app(fun1(type, bool), app_encode_fun(type, bool), 
8.82/9.01	           aa(type, bool), 
8.82/9.01	           app_encode_app(dB, fun1(type, bool), 
8.82/9.01	             app_encode_app(fun1(nat, type), 
8.82/9.01	               app_encode_fun(dB, fun1(type, bool)), typing, 
8.82/9.01	               app_encode_app(type, fun1(nat, type), 
8.82/9.01	                 app_encode_app(nat, app_encode_fun(type, fun1(nat, type)), 
8.82/9.01	                   app_encode_app(fun1(nat, type), 
8.82/9.01	                     app_encode_fun(nat, 
8.82/9.01	                       app_encode_fun(type, fun1(nat, type))), shift(type), 
8.82/9.01	                     X4), X1), X3)), 
8.82/9.01	             app_encode_app(dB, dB, 
8.82/9.01	               app_encode_app(fun1(dB, dB), app_encode_fun(dB, dB), 
8.82/9.01	                 aa(dB, dB), 
8.82/9.01	                 app_encode_app(nat, fun1(dB, dB), 
8.82/9.01	                   app_encode_app(fun1(dB, fun1(nat, dB)), 
8.82/9.01	                     app_encode_fun(nat, fun1(dB, dB)), combc(dB, nat, dB), 
8.82/9.01	                     lift), X1)), X2))), X0)
8.82/9.01	        = fTrue
8.82/9.01	       | ~ app_encode_app(bool, $o, pp, 
8.82/9.01	             app_encode_app(type, bool, 
8.82/9.01	               app_encode_app(fun1(type, bool), app_encode_fun(type, bool), 
8.82/9.01	                 aa(type, bool), 
8.82/9.01	                 app_encode_app(dB, fun1(type, bool), 
8.82/9.01	                   app_encode_app(fun1(nat, type), 
8.82/9.01	                     app_encode_fun(dB, fun1(type, bool)), typing, X4), X2)), 
8.82/9.01	               X0))),
8.82/9.01	    inference('demod', [status(thm)], ['5', '6'])).
8.82/9.01	tff(zf_stmt_167, conjecture,
8.82/9.01	  (app_encode_app(bool,$o,pp,
8.82/9.01	                  app_encode_app(type,bool,
8.82/9.01	                                 app_encode_app(fun1(type,bool),
8.82/9.01	                                                app_encode_fun(type,bool),
8.82/9.01	                                                aa(type,bool),
8.82/9.01	                                                app_encode_app(dB,
8.82/9.01	                                                               fun1(type,bool),
8.82/9.01	                                                               app_encode_app(
8.82/9.01	                                                               fun1(nat,type),
8.82/9.01	                                                               app_encode_fun(
8.82/9.01	                                                               dB,
8.82/9.01	                                                               fun1(type,bool)),
8.82/9.01	                                                               typing,
8.82/9.01	                                                               app_encode_app(
8.82/9.01	                                                               type,
8.82/9.01	                                                               fun1(nat,type),
8.82/9.01	                                                               app_encode_app(
8.82/9.01	                                                               nat,
8.82/9.01	                                                               app_encode_fun(
8.82/9.01	                                                               type,
8.82/9.01	                                                               fun1(nat,type)),
8.82/9.01	                                                               app_encode_app(
8.82/9.01	                                                               fun1(nat,type),
8.82/9.01	                                                               app_encode_fun(
8.82/9.01	                                                               nat,
8.82/9.01	                                                               app_encode_fun(
8.82/9.01	                                                               type,
8.82/9.01	                                                               fun1(nat,type))),
8.82/9.01	                                                               shift(type),e),
8.82/9.01	                                                               zero_zero(nat)),
8.82/9.01	                                                               t1)),
8.82/9.01	                                                               app_encode_app(
8.82/9.01	                                                               nat,dB,
8.82/9.01	                                                               app_encode_app(
8.82/9.01	                                                               fun1(nat,dB),
8.82/9.01	                                                               app_encode_fun(
8.82/9.01	                                                               nat,dB),
8.82/9.01	                                                               aa(nat,dB),
8.82/9.01	                                                               app_encode_app(
8.82/9.01	                                                               dB,
8.82/9.01	                                                               fun1(nat,dB),
8.82/9.01	                                                               app_encode_app(
8.82/9.01	                                                               fun1(dB,
8.82/9.01	                                                                    fun1(
8.82/9.01	                                                                    nat,dB)),
8.82/9.01	                                                               app_encode_fun(
8.82/9.01	                                                               dB,
8.82/9.01	                                                               fun1(nat,dB)),
8.82/9.01	                                                               aa(dB,
8.82/9.01	                                                                  fun1(
8.82/9.01	                                                                  nat,dB)),
8.82/9.01	                                                               lift),u)),
8.82/9.01	                                                               zero_zero(nat)))),
8.82/9.01	                                 app_encode_app(type,type,
8.82/9.01	                                                app_encode_app(fun1(type,type),
8.82/9.01	                                                               app_encode_fun(
8.82/9.01	                                                               type,type),
8.82/9.01	                                                               aa(type,type),
8.82/9.01	                                                               app_encode_app(
8.82/9.01	                                                               type,
8.82/9.01	                                                               fun1(type,type),
8.82/9.01	                                                               app_encode_app(
8.82/9.01	                                                               fun1(type,
8.82/9.01	                                                                    fun1(
8.82/9.01	                                                                    type,type)),
8.82/9.01	                                                               app_encode_fun(
8.82/9.01	                                                               type,
8.82/9.01	                                                               fun1(type,type)),
8.82/9.01	                                                               aa(type,
8.82/9.01	                                                                  fun1(
8.82/9.01	                                                                  type,type)),
8.82/9.01	                                                               fun),t1)),
8.82/9.01	                                                app_encode_app(type,type,
8.82/9.01	                                                               app_encode_app(
8.82/9.01	                                                               list(type),
8.82/9.01	                                                               app_encode_fun(
8.82/9.01	                                                               type,type),
8.82/9.01	                                                               app_encode_app(
8.82/9.01	                                                               fun1(type,
8.82/9.01	                                                                    fun1(
8.82/9.01	                                                                    type,type)),
8.82/9.01	                                                               app_encode_fun(
8.82/9.01	                                                               list(type),
8.82/9.01	                                                               app_encode_fun(
8.82/9.01	                                                               type,type)),
8.82/9.01	                                                               foldr(
8.82/9.01	                                                               type,type),fun),
8.82/9.01	                                                               ts),t)))))).
8.82/9.01	tff(zf_stmt_0, negated_conjecture,
8.82/9.01	  (~
8.82/9.01	    app_encode_app(bool,$o,pp,
8.82/9.01	                   app_encode_app(type,bool,
8.82/9.01	                                  app_encode_app(fun1(type,bool),
8.82/9.01	                                                 app_encode_fun(type,bool),
8.82/9.01	                                                 aa(type,bool),
8.82/9.01	                                                 app_encode_app(dB,
8.82/9.01	                                                                fun1(
8.82/9.01	                                                                type,bool),
8.82/9.01	                                                                app_encode_app(
8.82/9.01	                                                                fun1(
8.82/9.01	                                                                nat,type),
8.82/9.01	                                                                app_encode_fun(
8.82/9.01	                                                                dB,
8.82/9.01	                                                                fun1(
8.82/9.01	                                                                type,bool)),
8.82/9.01	                                                                typing,
8.82/9.01	                                                                app_encode_app(
8.82/9.01	                                                                type,
8.82/9.01	                                                                fun1(
8.82/9.01	                                                                nat,type),
8.82/9.01	                                                                app_encode_app(
8.82/9.01	                                                                nat,
8.82/9.01	                                                                app_encode_fun(
8.82/9.01	                                                                type,
8.82/9.01	                                                                fun1(
8.82/9.01	                                                                nat,type)),
8.82/9.01	                                                                app_encode_app(
8.82/9.01	                                                                fun1(
8.82/9.01	                                                                nat,type),
8.82/9.01	                                                                app_encode_fun(
8.82/9.01	                                                                nat,
8.82/9.01	                                                                app_encode_fun(
8.82/9.01	                                                                type,
8.82/9.01	                                                                fun1(
8.82/9.01	                                                                nat,type))),
8.82/9.01	                                                                shift(type),e),
8.82/9.01	                                                                zero_zero(
8.82/9.01	                                                                nat)),t1)),
8.82/9.01	                                                                app_encode_app(
8.82/9.01	                                                                nat,dB,
8.82/9.01	                                                                app_encode_app(
8.82/9.01	                                                                fun1(nat,dB),
8.82/9.01	                                                                app_encode_fun(
8.82/9.01	                                                                nat,dB),
8.82/9.01	                                                                aa(nat,dB),
8.82/9.01	                                                                app_encode_app(
8.82/9.01	                                                                dB,
8.82/9.01	                                                                fun1(nat,dB),
8.82/9.01	                                                                app_encode_app(
8.82/9.01	                                                                fun1(
8.82/9.01	                                                                dB,
8.82/9.01	                                                                fun1(nat,dB)),
8.82/9.01	                                                                app_encode_fun(
8.82/9.01	                                                                dB,
8.82/9.01	                                                                fun1(nat,dB)),
8.82/9.01	                                                                aa(dB,
8.82/9.01	                                                                   fun1(
8.82/9.01	                                                                   nat,dB)),
8.82/9.01	                                                                lift),u)),
8.82/9.01	                                                                zero_zero(
8.82/9.01	                                                                nat)))),
8.82/9.01	                                  app_encode_app(type,type,
8.82/9.01	                                                 app_encode_app(fun1(
8.82/9.01	                                                                type,type),
8.82/9.01	                                                                app_encode_fun(
8.82/9.01	                                                                type,type),
8.82/9.01	                                                                aa(type,type),
8.82/9.01	                                                                app_encode_app(
8.82/9.01	                                                                type,
8.82/9.01	                                                                fun1(
8.82/9.01	                                                                type,type),
8.82/9.01	                                                                app_encode_app(
8.82/9.01	                                                                fun1(
8.82/9.01	                                                                type,
8.82/9.01	                                                                fun1(
8.82/9.01	                                                                type,type)),
8.82/9.01	                                                                app_encode_fun(
8.82/9.01	                                                                type,
8.82/9.01	                                                                fun1(
8.82/9.01	                                                                type,type)),
8.82/9.01	                                                                aa(type,
8.82/9.01	                                                                   fun1(
8.82/9.01	                                                                   type,type)),
8.82/9.01	                                                                fun),t1)),
8.82/9.01	                                                 app_encode_app(type,type,
8.82/9.01	                                                                app_encode_app(
8.82/9.01	                                                                list(type),
8.82/9.01	                                                                app_encode_fun(
8.82/9.01	                                                                type,type),
8.82/9.01	                                                                app_encode_app(
8.82/9.01	                                                                fun1(
8.82/9.01	                                                                type,
8.82/9.01	                                                                fun1(
8.82/9.01	                                                                type,type)),
8.82/9.01	                                                                app_encode_fun(
8.82/9.01	                                                                list(type),
8.82/9.01	                                                                app_encode_fun(
8.82/9.01	                                                                type,type)),
8.82/9.01	                                                                foldr(
8.82/9.01	                                                                type,type),
8.82/9.01	                                                                fun),ts),t)))))).
8.82/9.01	tff('8', plain,
8.82/9.01	    ~ app_encode_app(bool, $o, pp, 
8.82/9.01	        app_encode_app(type, bool, 
8.82/9.01	          app_encode_app(fun1(type, bool), app_encode_fun(type, bool), 
8.82/9.01	            aa(type, bool), 
8.82/9.01	            app_encode_app(dB, fun1(type, bool), 
8.82/9.01	              app_encode_app(fun1(nat, type), 
8.82/9.01	                app_encode_fun(dB, fun1(type, bool)), typing, 
8.82/9.01	                app_encode_app(type, fun1(nat, type), 
8.82/9.01	                  app_encode_app(nat, app_encode_fun(type, fun1(nat, type)), 
8.82/9.01	                    app_encode_app(fun1(nat, type), 
8.82/9.01	                      app_encode_fun(nat, 
8.82/9.01	                        app_encode_fun(type, fun1(nat, type))), shift(type), 
8.82/9.01	                      e), zero_zero(nat)), t1)), 
8.82/9.01	              app_encode_app(nat, dB, 
8.82/9.01	                app_encode_app(fun1(nat, dB), app_encode_fun(nat, dB), 
8.82/9.01	                  aa(nat, dB), 
8.82/9.01	                  app_encode_app(dB, fun1(nat, dB), 
8.82/9.01	                    app_encode_app(fun1(dB, fun1(nat, dB)), 
8.82/9.01	                      app_encode_fun(dB, fun1(nat, dB)), 
8.82/9.01	                      aa(dB, fun1(nat, dB)), lift), u)), zero_zero(nat)))), 
8.82/9.01	          app_encode_app(type, type, 
8.82/9.01	            app_encode_app(fun1(type, type), app_encode_fun(type, type), 
8.82/9.01	              aa(type, type), 
8.82/9.01	              app_encode_app(type, fun1(type, type), 
8.82/9.01	                app_encode_app(fun1(type, fun1(type, type)), 
8.82/9.01	                  app_encode_fun(type, fun1(type, type)), 
8.82/9.01	                  aa(type, fun1(type, type)), fun), t1)), 
8.82/9.01	            app_encode_app(type, type, 
8.82/9.01	              app_encode_app(list(type), app_encode_fun(type, type), 
8.82/9.01	                app_encode_app(fun1(type, fun1(type, type)), 
8.82/9.01	                  app_encode_fun(list(type), app_encode_fun(type, type)), 
8.82/9.01	                  foldr(type, type), fun), ts), t)))),
8.82/9.01	    inference('cnf', [status(esa)], [zf_stmt_0])).
8.82/9.01	tff(zf_stmt_123, axiom,
8.82/9.01	  (![B:$tType,A:$tType,Aa:A,Xs:list(B),X:B,F:fun1(B,fun1(A,A))]:
8.82/9.01	     (app_encode_app(A,A,
8.82/9.01	                     app_encode_app(list(B),app_encode_fun(A,A),
8.82/9.01	                                    app_encode_app(fun1(B,fun1(A,A)),
8.82/9.01	                                                   app_encode_fun(list(B),
8.82/9.01	                                                                  app_encode_fun(
8.82/9.01	                                                                  A,A)),
8.82/9.01	                                                   foldr(B,A),F),
8.82/9.01	                                    app_encode_app(list(B),list(B),
8.82/9.01	                                                   app_encode_app(B,
8.82/9.01	                                                                  app_encode_fun(
8.82/9.01	                                                                  list(B),
8.82/9.01	                                                                  list(B)),
8.82/9.01	                                                                  cons(B),X),
8.82/9.01	                                                   Xs)),
8.82/9.01	                     Aa) =
8.82/9.01	      app_encode_app(A,A,
8.82/9.01	                     app_encode_app(fun1(A,A),app_encode_fun(A,A),aa(A,A),
8.82/9.01	                                    app_encode_app(B,fun1(A,A),
8.82/9.01	                                                   app_encode_app(fun1(
8.82/9.01	                                                                  B,fun1(A,A)),
8.82/9.01	                                                                  app_encode_fun(
8.82/9.01	                                                                  B,fun1(A,A)),
8.82/9.01	                                                                  aa(
8.82/9.01	                                                                  B,fun1(A,A)),
8.82/9.01	                                                                  F),
8.82/9.01	                                                   X)),
8.82/9.01	                     app_encode_app(A,A,
8.82/9.01	                                    app_encode_app(list(B),
8.82/9.01	                                                   app_encode_fun(A,A),
8.82/9.01	                                                   app_encode_app(fun1(
8.82/9.01	                                                                  B,fun1(A,A)),
8.82/9.01	                                                                  app_encode_fun(
8.82/9.01	                                                                  list(B),
8.82/9.01	                                                                  app_encode_fun(
8.82/9.01	                                                                  A,A)),
8.82/9.01	                                                                  foldr(B,A),
8.82/9.01	                                                                  F),
8.82/9.01	                                                   Xs),
8.82/9.01	                                    Aa))))).
8.82/9.01	tff('9', plain,
8.82/9.01	    ![X185 : $tType, X186 : $tType, X187 : fun1(X186, fun1(X185, X185)), 
8.82/9.01	      X188 : X186, X189 : list(X186), X190 : X185]:
8.82/9.01	      app_encode_app(X185, X185, 
8.82/9.01	        app_encode_app(list(X186), app_encode_fun(X185, X185), 
8.82/9.01	          app_encode_app(fun1(X186, fun1(X185, X185)), 
8.82/9.01	            app_encode_fun(list(X186), app_encode_fun(X185, X185)), 
8.82/9.01	            foldr(X186, X185), X187), 
8.82/9.01	          app_encode_app(list(X186), list(X186), 
8.82/9.01	            app_encode_app(X186, app_encode_fun(list(X186), list(X186)), 
8.82/9.01	              cons(X186), X188), X189)), X190)
8.82/9.01	       = app_encode_app(X185, X185, 
8.82/9.01	           app_encode_app(fun1(X185, X185), app_encode_fun(X185, X185), 
8.82/9.01	             aa(X185, X185), 
8.82/9.01	             app_encode_app(X186, fun1(X185, X185), 
8.82/9.01	               app_encode_app(fun1(X186, fun1(X185, X185)), 
8.82/9.01	                 app_encode_fun(X186, fun1(X185, X185)), 
8.82/9.01	                 aa(X186, fun1(X185, X185)), X187), X188)), 
8.82/9.01	           app_encode_app(X185, X185, 
8.82/9.01	             app_encode_app(list(X186), app_encode_fun(X185, X185), 
8.82/9.01	               app_encode_app(fun1(X186, fun1(X185, X185)), 
8.82/9.01	                 app_encode_fun(list(X186), app_encode_fun(X185, X185)), 
8.82/9.01	                 foldr(X186, X185), X187), X189), X190)),
8.82/9.01	    inference('cnf', [status(esa)], [zf_stmt_123])).
8.82/9.01	tff(zf_stmt_61, axiom,
8.82/9.01	  (t2 =
8.82/9.01	   app_encode_app(type,type,
8.82/9.01	                  app_encode_app(fun1(type,type),app_encode_fun(type,type),
8.82/9.01	                                 aa(type,type),
8.82/9.01	                                 app_encode_app(type,fun1(type,type),
8.82/9.01	                                                app_encode_app(fun1(type,
8.82/9.01	                                                                    fun1(
8.82/9.01	                                                                    type,type)),
8.82/9.01	                                                               app_encode_fun(
8.82/9.01	                                                               type,
8.82/9.01	                                                               fun1(type,type)),
8.82/9.01	                                                               aa(type,
8.82/9.01	                                                                  fun1(
8.82/9.01	                                                                  type,type)),
8.82/9.01	                                                               fun),
8.82/9.01	                                                t1)),
8.82/9.01	                  app_encode_app(type,type,
8.82/9.01	                                 app_encode_app(list(type),
8.82/9.01	                                                app_encode_fun(type,type),
8.82/9.01	                                                app_encode_app(fun1(type,
8.82/9.01	                                                                    fun1(
8.82/9.01	                                                                    type,type)),
8.82/9.01	                                                               app_encode_fun(
8.82/9.01	                                                               list(type),
8.82/9.01	                                                               app_encode_fun(
8.82/9.01	                                                               type,type)),
8.82/9.01	                                                               foldr(
8.82/9.01	                                                               type,type),fun),
8.82/9.01	                                                ts),
8.82/9.01	                                 t)))).
8.82/9.01	tff('10', plain,
8.82/9.01	    t2
8.82/9.01	     = app_encode_app(type, type, 
8.82/9.01	         app_encode_app(fun1(type, type), app_encode_fun(type, type), 
8.82/9.01	           aa(type, type), 
8.82/9.01	           app_encode_app(type, fun1(type, type), 
8.82/9.01	             app_encode_app(fun1(type, fun1(type, type)), 
8.82/9.01	               app_encode_fun(type, fun1(type, type)), 
8.82/9.01	               aa(type, fun1(type, type)), fun), t1)), 
8.82/9.01	         app_encode_app(type, type, 
8.82/9.01	           app_encode_app(list(type), app_encode_fun(type, type), 
8.82/9.01	             app_encode_app(fun1(type, fun1(type, type)), 
8.82/9.01	               app_encode_fun(list(type), app_encode_fun(type, type)), 
8.82/9.01	               foldr(type, type), fun), ts), t)),
8.82/9.01	    inference('cnf', [status(esa)], [zf_stmt_61])).
8.82/9.01	tff('11', plain,
8.82/9.01	    t2
8.82/9.01	     = app_encode_app(type, type, 
8.82/9.01	         app_encode_app(list(type), app_encode_fun(type, type), 
8.82/9.01	           app_encode_app(fun1(type, fun1(type, type)), 
8.82/9.01	             app_encode_fun(list(type), app_encode_fun(type, type)), 
8.82/9.01	             foldr(type, type), fun), 
8.82/9.01	           app_encode_app(list(type), list(type), 
8.82/9.01	             app_encode_app(type, app_encode_fun(list(type), list(type)), 
8.82/9.01	               cons(type), t1), ts)), t),
8.82/9.01	    inference('demod', [status(thm)], ['10', '9'])).
8.82/9.01	tff('12', plain,
8.82/9.01	    ~ app_encode_app(bool, $o, pp, 
8.82/9.01	        app_encode_app(type, bool, 
8.82/9.01	          app_encode_app(fun1(type, bool), app_encode_fun(type, bool), 
8.82/9.01	            aa(type, bool), 
8.82/9.01	            app_encode_app(dB, fun1(type, bool), 
8.82/9.01	              app_encode_app(fun1(nat, type), 
8.82/9.01	                app_encode_fun(dB, fun1(type, bool)), typing, 
8.82/9.01	                app_encode_app(type, fun1(nat, type), 
8.82/9.01	                  app_encode_app(nat, app_encode_fun(type, fun1(nat, type)), 
8.82/9.01	                    app_encode_app(fun1(nat, type), 
8.82/9.01	                      app_encode_fun(nat, 
8.82/9.01	                        app_encode_fun(type, fun1(nat, type))), shift(type), 
8.82/9.01	                      e), zero_zero(nat)), t1)), 
8.82/9.01	              app_encode_app(dB, dB, 
8.82/9.01	                app_encode_app(fun1(dB, dB), app_encode_fun(dB, dB), 
8.82/9.01	                  aa(dB, dB), 
8.82/9.01	                  app_encode_app(nat, fun1(dB, dB), 
8.82/9.01	                    app_encode_app(fun1(dB, fun1(nat, dB)), 
8.82/9.01	                      app_encode_fun(nat, fun1(dB, dB)), combc(dB, nat, dB), 
8.82/9.01	                      lift), zero_zero(nat))), u))), t2)),
8.82/9.01	    inference('demod', [status(thm)], ['8', '6', '9', '11'])).
8.82/9.01	tff('13', plain,
8.82/9.01	    (~ app_encode_app(bool, $o, pp, fTrue)
8.82/9.01	     | ~ app_encode_app(bool, $o, pp, 
8.82/9.01	           app_encode_app(type, bool, 
8.82/9.01	             app_encode_app(fun1(type, bool), app_encode_fun(type, bool), 
8.82/9.01	               aa(type, bool), 
8.82/9.01	               app_encode_app(dB, fun1(type, bool), 
8.82/9.01	                 app_encode_app(fun1(nat, type), 
8.82/9.01	                   app_encode_fun(dB, fun1(type, bool)), typing, e), u)), t2))),
8.82/9.01	    inference('sup-', [status(thm)], ['7', '12'])).
8.82/9.01	tff(zf_stmt_157, axiom, (app_encode_app(bool,$o,pp,fTrue))).
8.82/9.01	tff('14', plain, app_encode_app(bool, $o, pp, fTrue),
8.82/9.01	    inference('cnf', [status(esa)], [zf_stmt_157])).
8.82/9.01	tff(zf_stmt_59, axiom,
8.82/9.01	  (app_encode_app(bool,$o,pp,
8.82/9.01	                  app_encode_app(type,bool,
8.82/9.01	                                 app_encode_app(fun1(type,bool),
8.82/9.01	                                                app_encode_fun(type,bool),
8.82/9.01	                                                aa(type,bool),
8.82/9.01	                                                app_encode_app(dB,
8.82/9.01	                                                               fun1(type,bool),
8.82/9.01	                                                               app_encode_app(
8.82/9.01	                                                               fun1(nat,type),
8.82/9.01	                                                               app_encode_fun(
8.82/9.01	                                                               dB,
8.82/9.01	                                                               fun1(type,bool)),
8.82/9.01	                                                               typing,e),u)),
8.82/9.01	                                 t2)))).
8.82/9.01	tff('15', plain,
8.82/9.01	    app_encode_app(bool, $o, pp, 
8.82/9.01	      app_encode_app(type, bool, 
8.82/9.01	        app_encode_app(fun1(type, bool), app_encode_fun(type, bool), 
8.82/9.01	          aa(type, bool), 
8.82/9.01	          app_encode_app(dB, fun1(type, bool), 
8.82/9.01	            app_encode_app(fun1(nat, type), 
8.82/9.01	              app_encode_fun(dB, fun1(type, bool)), typing, e), u)), t2)),
8.82/9.01	    inference('cnf', [status(esa)], [zf_stmt_59])).
8.82/9.01	tff('16', plain,
8.82/9.01	    (~ $true
8.82/9.01	     | app_encode_app(type, bool, 
8.82/9.01	         app_encode_app(fun1(type, bool), app_encode_fun(type, bool), 
8.82/9.01	           aa(type, bool), 
8.82/9.01	           app_encode_app(dB, fun1(type, bool), 
8.82/9.01	             app_encode_app(fun1(nat, type), 
8.82/9.01	               app_encode_fun(dB, fun1(type, bool)), typing, e), u)), t2)
8.82/9.01	        = fTrue),
8.82/9.01	    inference('sup-', [status(thm)], ['15', '3'])).
8.82/9.01	tff('17', plain,
8.82/9.01	    app_encode_app(type, bool, 
8.82/9.01	      app_encode_app(fun1(type, bool), app_encode_fun(type, bool), 
8.82/9.01	        aa(type, bool), 
8.82/9.01	        app_encode_app(dB, fun1(type, bool), 
8.82/9.01	          app_encode_app(fun1(nat, type), 
8.82/9.01	            app_encode_fun(dB, fun1(type, bool)), typing, e), u)), t2)
8.82/9.01	     = fTrue,
8.82/9.01	    inference('simplify', [status(thm)], ['16'])).
8.82/9.01	tff('18', plain, (~ $true | ~ $true),
8.82/9.01	    inference('demod', [status(thm)], ['13', '14', '17', '14'])).
8.82/9.01	tff('19', plain, $false, inference('simplify', [status(thm)], ['18'])).
8.82/9.01	
8.82/9.01	% SZS output end Refutation
8.82/9.01	EOF
