0.00/0.01	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.01	% app-encoded or not : appext
0.00/0.01	% Variant    : fo
0.00/0.01	% Ordering    : 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 $2 \
0.00/0.01	  --simultaneous-sup false \
0.00/0.01	  --no-max-vars \
0.00/0.01	  --no-fool
0.00/0.20	% Computer   : n046.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 17:38:24 CST 2018
0.00/0.29	% done 72 iterations in 0.084s
0.00/0.29	% SZS status Theorem for 'stdin'
0.00/0.29	% SZS output start Refutation
0.00/0.30	tff(zf_stmt_5, conjecture,
0.00/0.30	  (![Xs:app_encode_fun(b,$o),
0.00/0.30	     Xp:app_encode_fun(b,app_encode_fun(a,app_encode_fun(a,$o)))]:
0.00/0.30	     ((![Xx:b]:
0.00/0.30	         (app_encode_app(b,$o,Xs,Xx) =>
0.00/0.30	          ((![Xx0:a,Xy:a]:
0.00/0.30	              (app_encode_app(a,$o,
0.00/0.30	                              app_encode_app(a,app_encode_fun(a,$o),
0.00/0.30	                                             app_encode_app(b,
0.00/0.30	                                                            app_encode_fun(
0.00/0.30	                                                            a,
0.00/0.30	                                                            app_encode_fun(
0.00/0.30	                                                            a,$o)),Xp,Xx),
0.00/0.30	                                             Xx0),
0.00/0.30	                              Xy) =>
0.00/0.30	               app_encode_app(a,$o,
0.00/0.30	                              app_encode_app(a,app_encode_fun(a,$o),
0.00/0.30	                                             app_encode_app(b,
0.00/0.30	                                                            app_encode_fun(
0.00/0.30	                                                            a,
0.00/0.30	                                                            app_encode_fun(
0.00/0.30	                                                            a,$o)),Xp,Xx),
0.00/0.30	                                             Xy),
0.00/0.30	                              Xx0))) & 
0.00/0.30	           (![Xx0:a,Xy:a,Xz:a]:
0.00/0.30	              ((app_encode_app(a,$o,
0.00/0.30	                               app_encode_app(a,app_encode_fun(a,$o),
0.00/0.30	                                              app_encode_app(b,
0.00/0.30	                                                             app_encode_fun(
0.00/0.30	                                                             a,
0.00/0.30	                                                             app_encode_fun(
0.00/0.30	                                                             a,$o)),Xp,Xx),
0.00/0.30	                                              Xx0),
0.00/0.30	                               Xy) & 
0.00/0.30	                app_encode_app(a,$o,
0.00/0.30	                               app_encode_app(a,app_encode_fun(a,$o),
0.00/0.30	                                              app_encode_app(b,
0.00/0.30	                                                             app_encode_fun(
0.00/0.30	                                                             a,
0.00/0.30	                                                             app_encode_fun(
0.00/0.30	                                                             a,$o)),Xp,Xx),
0.00/0.30	                                              Xy),
0.00/0.30	                               Xz)) =>
0.00/0.30	               app_encode_app(a,$o,
0.00/0.30	                              app_encode_app(a,app_encode_fun(a,$o),
0.00/0.30	                                             app_encode_app(b,
0.00/0.30	                                                            app_encode_fun(
0.00/0.30	                                                            a,
0.00/0.30	                                                            app_encode_fun(
0.00/0.30	                                                            a,$o)),Xp,Xx),
0.00/0.30	                                             Xx0),
0.00/0.30	                              Xz)))))) =>
0.00/0.30	      ((![Xx:app_encode_fun(b,a),Xy:app_encode_fun(b,a)]:
0.00/0.30	          ((![Xx0:b]:
0.00/0.30	              (app_encode_app(b,$o,Xs,Xx0) =>
0.00/0.30	               app_encode_app(a,$o,
0.00/0.30	                              app_encode_app(a,app_encode_fun(a,$o),
0.00/0.30	                                             app_encode_app(b,
0.00/0.30	                                                            app_encode_fun(
0.00/0.30	                                                            a,
0.00/0.30	                                                            app_encode_fun(
0.00/0.30	                                                            a,$o)),Xp,Xx0),
0.00/0.30	                                             app_encode_app(b,a,Xx,Xx0)),
0.00/0.30	                              app_encode_app(b,a,Xy,Xx0)))) =>
0.00/0.30	           (![Xx0:b]:
0.00/0.30	              (app_encode_app(b,$o,Xs,Xx0) =>
0.00/0.30	               app_encode_app(a,$o,
0.00/0.30	                              app_encode_app(a,app_encode_fun(a,$o),
0.00/0.30	                                             app_encode_app(b,
0.00/0.30	                                                            app_encode_fun(
0.00/0.30	                                                            a,
0.00/0.30	                                                            app_encode_fun(
0.00/0.30	                                                            a,$o)),Xp,Xx0),
0.00/0.30	                                             app_encode_app(b,a,Xy,Xx0)),
0.00/0.30	                              app_encode_app(b,a,Xx,Xx0)))))) & 
0.00/0.30	       (![Xx:app_encode_fun(b,a),Xy:app_encode_fun(b,a),
0.00/0.30	          Xz:app_encode_fun(b,a)]:
0.00/0.30	          (((![Xx0:b]:
0.00/0.30	               (app_encode_app(b,$o,Xs,Xx0) =>
0.00/0.30	                app_encode_app(a,$o,
0.00/0.30	                               app_encode_app(a,app_encode_fun(a,$o),
0.00/0.30	                                              app_encode_app(b,
0.00/0.30	                                                             app_encode_fun(
0.00/0.30	                                                             a,
0.00/0.30	                                                             app_encode_fun(
0.00/0.30	                                                             a,$o)),Xp,Xx0),
0.00/0.30	                                              app_encode_app(b,a,Xx,Xx0)),
0.00/0.30	                               app_encode_app(b,a,Xy,Xx0)))) & 
0.00/0.30	            (![Xx0:b]:
0.00/0.30	               (app_encode_app(b,$o,Xs,Xx0) =>
0.00/0.30	                app_encode_app(a,$o,
0.00/0.30	                               app_encode_app(a,app_encode_fun(a,$o),
0.00/0.30	                                              app_encode_app(b,
0.00/0.30	                                                             app_encode_fun(
0.00/0.30	                                                             a,
0.00/0.30	                                                             app_encode_fun(
0.00/0.30	                                                             a,$o)),Xp,Xx0),
0.00/0.30	                                              app_encode_app(b,a,Xy,Xx0)),
0.00/0.30	                               app_encode_app(b,a,Xz,Xx0))))) =>
0.00/0.30	           (![Xx0:b]:
0.00/0.30	              (app_encode_app(b,$o,Xs,Xx0) =>
0.00/0.30	               app_encode_app(a,$o,
0.00/0.30	                              app_encode_app(a,app_encode_fun(a,$o),
0.00/0.30	                                             app_encode_app(b,
0.00/0.30	                                                            app_encode_fun(
0.00/0.30	                                                            a,
0.00/0.30	                                                            app_encode_fun(
0.00/0.30	                                                            a,$o)),Xp,Xx0),
0.00/0.30	                                             app_encode_app(b,a,Xx,Xx0)),
0.00/0.30	                              app_encode_app(b,a,Xz,Xx0)))))))))).
0.00/0.30	tff(zf_stmt_0, negated_conjecture,
0.00/0.30	  (~
0.00/0.30	    (![Xs:app_encode_fun(b,$o),
0.00/0.30	       Xp:app_encode_fun(b,app_encode_fun(a,app_encode_fun(a,$o)))]:
0.00/0.30	       ((![Xx:b]:
0.00/0.30	           (app_encode_app(b,$o,Xs,Xx) =>
0.00/0.30	            ((![Xx0:a,Xy:a]:
0.00/0.30	                (app_encode_app(a,$o,
0.00/0.30	                                app_encode_app(a,app_encode_fun(a,$o),
0.00/0.30	                                               app_encode_app(b,
0.00/0.30	                                                              app_encode_fun(
0.00/0.30	                                                              a,
0.00/0.30	                                                              app_encode_fun(
0.00/0.30	                                                              a,$o)),Xp,Xx),
0.00/0.30	                                               Xx0),
0.00/0.30	                                Xy) =>
0.00/0.30	                 app_encode_app(a,$o,
0.00/0.30	                                app_encode_app(a,app_encode_fun(a,$o),
0.00/0.30	                                               app_encode_app(b,
0.00/0.30	                                                              app_encode_fun(
0.00/0.30	                                                              a,
0.00/0.30	                                                              app_encode_fun(
0.00/0.30	                                                              a,$o)),Xp,Xx),
0.00/0.30	                                               Xy),
0.00/0.30	                                Xx0))) & 
0.00/0.30	             (![Xx0:a,Xy:a,Xz:a]:
0.00/0.30	                ((app_encode_app(a,$o,
0.00/0.30	                                 app_encode_app(a,app_encode_fun(a,$o),
0.00/0.30	                                                app_encode_app(b,
0.00/0.30	                                                               app_encode_fun(
0.00/0.30	                                                               a,
0.00/0.30	                                                               app_encode_fun(
0.00/0.30	                                                               a,$o)),Xp,Xx),
0.00/0.30	                                                Xx0),
0.00/0.30	                                 Xy) & 
0.00/0.30	                  app_encode_app(a,$o,
0.00/0.30	                                 app_encode_app(a,app_encode_fun(a,$o),
0.00/0.30	                                                app_encode_app(b,
0.00/0.30	                                                               app_encode_fun(
0.00/0.30	                                                               a,
0.00/0.30	                                                               app_encode_fun(
0.00/0.30	                                                               a,$o)),Xp,Xx),
0.00/0.30	                                                Xy),
0.00/0.30	                                 Xz)) =>
0.00/0.30	                 app_encode_app(a,$o,
0.00/0.30	                                app_encode_app(a,app_encode_fun(a,$o),
0.00/0.30	                                               app_encode_app(b,
0.00/0.30	                                                              app_encode_fun(
0.00/0.30	                                                              a,
0.00/0.30	                                                              app_encode_fun(
0.00/0.30	                                                              a,$o)),Xp,Xx),
0.00/0.30	                                               Xx0),
0.00/0.30	                                Xz)))))) =>
0.00/0.30	        ((![Xx:app_encode_fun(b,a),Xy:app_encode_fun(b,a)]:
0.00/0.30	            ((![Xx0:b]:
0.00/0.30	                (app_encode_app(b,$o,Xs,Xx0) =>
0.00/0.30	                 app_encode_app(a,$o,
0.00/0.30	                                app_encode_app(a,app_encode_fun(a,$o),
0.00/0.30	                                               app_encode_app(b,
0.00/0.30	                                                              app_encode_fun(
0.00/0.30	                                                              a,
0.00/0.30	                                                              app_encode_fun(
0.00/0.30	                                                              a,$o)),Xp,Xx0),
0.00/0.30	                                               app_encode_app(b,a,Xx,Xx0)),
0.00/0.30	                                app_encode_app(b,a,Xy,Xx0)))) =>
0.00/0.30	             (![Xx0:b]:
0.00/0.30	                (app_encode_app(b,$o,Xs,Xx0) =>
0.00/0.30	                 app_encode_app(a,$o,
0.00/0.30	                                app_encode_app(a,app_encode_fun(a,$o),
0.00/0.30	                                               app_encode_app(b,
0.00/0.30	                                                              app_encode_fun(
0.00/0.30	                                                              a,
0.00/0.30	                                                              app_encode_fun(
0.00/0.30	                                                              a,$o)),Xp,Xx0),
0.00/0.30	                                               app_encode_app(b,a,Xy,Xx0)),
0.00/0.30	                                app_encode_app(b,a,Xx,Xx0)))))) & 
0.00/0.30	         (![Xx:app_encode_fun(b,a),Xy:app_encode_fun(b,a),
0.00/0.30	            Xz:app_encode_fun(b,a)]:
0.00/0.30	            (((![Xx0:b]:
0.00/0.30	                 (app_encode_app(b,$o,Xs,Xx0) =>
0.00/0.30	                  app_encode_app(a,$o,
0.00/0.30	                                 app_encode_app(a,app_encode_fun(a,$o),
0.00/0.30	                                                app_encode_app(b,
0.00/0.30	                                                               app_encode_fun(
0.00/0.30	                                                               a,
0.00/0.30	                                                               app_encode_fun(
0.00/0.30	                                                               a,$o)),Xp,Xx0),
0.00/0.30	                                                app_encode_app(b,a,Xx,Xx0)),
0.00/0.30	                                 app_encode_app(b,a,Xy,Xx0)))) & 
0.00/0.30	              (![Xx0:b]:
0.00/0.30	                 (app_encode_app(b,$o,Xs,Xx0) =>
0.00/0.30	                  app_encode_app(a,$o,
0.00/0.30	                                 app_encode_app(a,app_encode_fun(a,$o),
0.00/0.30	                                                app_encode_app(b,
0.00/0.30	                                                               app_encode_fun(
0.00/0.30	                                                               a,
0.00/0.30	                                                               app_encode_fun(
0.00/0.30	                                                               a,$o)),Xp,Xx0),
0.00/0.30	                                                app_encode_app(b,a,Xy,Xx0)),
0.00/0.30	                                 app_encode_app(b,a,Xz,Xx0))))) =>
0.00/0.30	             (![Xx0:b]:
0.00/0.30	                (app_encode_app(b,$o,Xs,Xx0) =>
0.00/0.30	                 app_encode_app(a,$o,
0.00/0.30	                                app_encode_app(a,app_encode_fun(a,$o),
0.00/0.30	                                               app_encode_app(b,
0.00/0.30	                                                              app_encode_fun(
0.00/0.30	                                                              a,
0.00/0.30	                                                              app_encode_fun(
0.00/0.30	                                                              a,$o)),Xp,Xx0),
0.00/0.30	                                               app_encode_app(b,a,Xx,Xx0)),
0.00/0.30	                                app_encode_app(b,a,Xz,Xx0))))))))))).
0.00/0.30	tff('0', plain,
0.00/0.30	    ![X11 : b, X12 : b]:
0.00/0.30	      (~ app_encode_app(b, $o, sk_Xs, X12)
0.00/0.30	       | app_encode_app(a, $o, 
0.00/0.30	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	             app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	               sk_Xp, X12), app_encode_app(b, a, sk_Xx, X12)), 
0.00/0.30	           app_encode_app(b, a, sk_Xy, X12))
0.00/0.30	       | app_encode_app(a, $o, 
0.00/0.30	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	             app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	               sk_Xp, X11), app_encode_app(b, a, sk_Xy1, X11)), 
0.00/0.30	           app_encode_app(b, a, sk_Xz, X11))
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X11)),
0.00/0.30	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.30	tff('1', plain,
0.00/0.30	    ![X4 : b, X5 : a, X6 : a]:
0.00/0.30	      (~ app_encode_app(a, $o, 
0.00/0.30	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	             app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	               sk_Xp, X4), X5), X6)
0.00/0.30	       | app_encode_app(a, $o, 
0.00/0.30	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	             app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	               sk_Xp, X4), X6), X5)
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X4)),
0.00/0.30	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.30	tff('2', plain,
0.00/0.30	    ![X0 : b, X1 : b]:
0.00/0.30	      (~ $true
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X1)
0.00/0.30	       | app_encode_app(a, $o, 
0.00/0.30	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	             app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	               sk_Xp, X1), app_encode_app(b, a, sk_Xy1, X1)), 
0.00/0.30	           app_encode_app(b, a, sk_Xz, X1))
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X0)
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X0)
0.00/0.30	       | app_encode_app(a, $o, 
0.00/0.30	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	             app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	               sk_Xp, X0), app_encode_app(b, a, sk_Xy, X0)), 
0.00/0.30	           app_encode_app(b, a, sk_Xx, X0))),
0.00/0.30	    inference('sup-', [status(thm)], ['0', '1'])).
0.00/0.30	tff('3', plain,
0.00/0.30	    ![X0 : b, X1 : b]:
0.00/0.30	      (app_encode_app(a, $o, 
0.00/0.30	         app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	           app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	             sk_Xp, X0), app_encode_app(b, a, sk_Xy, X0)), 
0.00/0.30	         app_encode_app(b, a, sk_Xx, X0))
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X0)
0.00/0.30	       | app_encode_app(a, $o, 
0.00/0.30	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	             app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	               sk_Xp, X1), app_encode_app(b, a, sk_Xy1, X1)), 
0.00/0.30	           app_encode_app(b, a, sk_Xz, X1))
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X1)),
0.00/0.30	    inference('simplify', [status(thm)], ['2'])).
0.00/0.30	tff('4', plain,
0.00/0.30	    ![X11 : b]:
0.00/0.30	      (~ app_encode_app(a, $o, 
0.00/0.30	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	             app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	               sk_Xp, sk_Xx0), app_encode_app(b, a, sk_Xy, sk_Xx0)), 
0.00/0.30	           app_encode_app(b, a, sk_Xx, sk_Xx0))
0.00/0.30	       | app_encode_app(a, $o, 
0.00/0.30	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	             app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	               sk_Xp, X11), app_encode_app(b, a, sk_Xy1, X11)), 
0.00/0.30	           app_encode_app(b, a, sk_Xz, X11))
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X11)),
0.00/0.30	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.30	tff('5', plain,
0.00/0.30	    ![X0 : b, X1 : b]:
0.00/0.30	      (~ $true
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X1)
0.00/0.30	       | app_encode_app(a, $o, 
0.00/0.30	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	             app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	               sk_Xp, X1), app_encode_app(b, a, sk_Xy1, X1)), 
0.00/0.30	           app_encode_app(b, a, sk_Xz, X1))
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, sk_Xx0)
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X0)
0.00/0.30	       | app_encode_app(a, $o, 
0.00/0.30	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	             app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	               sk_Xp, X0), app_encode_app(b, a, sk_Xy1, X0)), 
0.00/0.30	           app_encode_app(b, a, sk_Xz, X0))),
0.00/0.30	    inference('sup-', [status(thm)], ['3', '4'])).
0.00/0.30	tff('6', plain,
0.00/0.30	    ![X11 : b]:
0.00/0.30	      (app_encode_app(b, $o, sk_Xs, sk_Xx0)
0.00/0.30	       | app_encode_app(a, $o, 
0.00/0.30	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	             app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	               sk_Xp, X11), app_encode_app(b, a, sk_Xy1, X11)), 
0.00/0.30	           app_encode_app(b, a, sk_Xz, X11))
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X11)),
0.00/0.30	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.30	tff('7', plain,
0.00/0.30	    ![X0 : b]:
0.00/0.30	      (~ $true
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X0)
0.00/0.30	       | app_encode_app(b, $o, sk_Xs, sk_Xx0)
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X0)
0.00/0.30	       | app_encode_app(a, $o, 
0.00/0.30	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	             app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	               sk_Xp, X0), app_encode_app(b, a, sk_Xz, X0)), 
0.00/0.30	           app_encode_app(b, a, sk_Xy1, X0))),
0.00/0.30	    inference('sup-', [status(thm)], ['6', '1'])).
0.00/0.30	tff('8', plain,
0.00/0.30	    ![X0 : b]:
0.00/0.30	      (app_encode_app(a, $o, 
0.00/0.30	         app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	           app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	             sk_Xp, X0), app_encode_app(b, a, sk_Xz, X0)), 
0.00/0.30	         app_encode_app(b, a, sk_Xy1, X0))
0.00/0.30	       | app_encode_app(b, $o, sk_Xs, sk_Xx0)
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X0)),
0.00/0.30	    inference('simplify', [status(thm)], ['7'])).
0.00/0.30	tff('9', plain,
0.00/0.30	    ![X10 : b]:
0.00/0.30	      (app_encode_app(b, $o, sk_Xs, sk_Xx0)
0.00/0.30	       | app_encode_app(a, $o, 
0.00/0.30	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	             app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	               sk_Xp, X10), app_encode_app(b, a, sk_Xx1, X10)), 
0.00/0.30	           app_encode_app(b, a, sk_Xy1, X10))
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X10)),
0.00/0.30	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.30	tff('10', plain,
0.00/0.30	    ![X0 : b]:
0.00/0.30	      (~ $true
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X0)
0.00/0.30	       | app_encode_app(b, $o, sk_Xs, sk_Xx0)
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X0)
0.00/0.30	       | app_encode_app(a, $o, 
0.00/0.30	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	             app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	               sk_Xp, X0), app_encode_app(b, a, sk_Xy1, X0)), 
0.00/0.30	           app_encode_app(b, a, sk_Xx1, X0))),
0.00/0.30	    inference('sup-', [status(thm)], ['9', '1'])).
0.00/0.30	tff('11', plain,
0.00/0.30	    ![X0 : b]:
0.00/0.30	      (app_encode_app(a, $o, 
0.00/0.30	         app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	           app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	             sk_Xp, X0), app_encode_app(b, a, sk_Xy1, X0)), 
0.00/0.30	         app_encode_app(b, a, sk_Xx1, X0))
0.00/0.30	       | app_encode_app(b, $o, sk_Xs, sk_Xx0)
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X0)),
0.00/0.30	    inference('simplify', [status(thm)], ['10'])).
0.00/0.30	tff('12', plain,
0.00/0.30	    ![X4 : b, X7 : a, X8 : a, X9 : a]:
0.00/0.30	      (app_encode_app(a, $o, 
0.00/0.30	         app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	           app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	             sk_Xp, X4), X7), X8)
0.00/0.30	       | ~ app_encode_app(a, $o, 
0.00/0.30	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	               app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	                 sk_Xp, X4), X9), X8)
0.00/0.30	       | ~ app_encode_app(a, $o, 
0.00/0.30	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	               app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	                 sk_Xp, X4), X7), X9)
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X4)),
0.00/0.30	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.30	tff('13', plain,
0.00/0.30	    ![X0 : b, X1 : a]:
0.00/0.30	      (~ $true
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X0)
0.00/0.30	       | app_encode_app(b, $o, sk_Xs, sk_Xx0)
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X0)
0.00/0.30	       | ~ app_encode_app(a, $o, 
0.00/0.30	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	               app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	                 sk_Xp, X0), X1), app_encode_app(b, a, sk_Xy1, X0))
0.00/0.30	       | app_encode_app(a, $o, 
0.00/0.30	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	             app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	               sk_Xp, X0), X1), app_encode_app(b, a, sk_Xx1, X0))),
0.00/0.30	    inference('sup-', [status(thm)], ['11', '12'])).
0.00/0.30	tff('14', plain,
0.00/0.30	    ![X0 : b, X1 : a]:
0.00/0.30	      (app_encode_app(a, $o, 
0.00/0.30	         app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	           app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	             sk_Xp, X0), X1), app_encode_app(b, a, sk_Xx1, X0))
0.00/0.30	       | ~ app_encode_app(a, $o, 
0.00/0.30	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	               app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	                 sk_Xp, X0), X1), app_encode_app(b, a, sk_Xy1, X0))
0.00/0.30	       | app_encode_app(b, $o, sk_Xs, sk_Xx0)
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X0)),
0.00/0.30	    inference('simplify', [status(thm)], ['13'])).
0.00/0.30	tff('15', plain,
0.00/0.30	    ![X0 : b]:
0.00/0.30	      (~ $true
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X0)
0.00/0.30	       | app_encode_app(b, $o, sk_Xs, sk_Xx0)
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X0)
0.00/0.30	       | app_encode_app(b, $o, sk_Xs, sk_Xx0)
0.00/0.30	       | app_encode_app(a, $o, 
0.00/0.30	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	             app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	               sk_Xp, X0), app_encode_app(b, a, sk_Xz, X0)), 
0.00/0.30	           app_encode_app(b, a, sk_Xx1, X0))),
0.00/0.30	    inference('sup-', [status(thm)], ['8', '14'])).
0.00/0.30	tff('16', plain,
0.00/0.30	    ![X0 : b]:
0.00/0.30	      (app_encode_app(a, $o, 
0.00/0.30	         app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	           app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	             sk_Xp, X0), app_encode_app(b, a, sk_Xz, X0)), 
0.00/0.30	         app_encode_app(b, a, sk_Xx1, X0))
0.00/0.30	       | app_encode_app(b, $o, sk_Xs, sk_Xx0)
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X0)),
0.00/0.30	    inference('simplify', [status(thm)], ['15'])).
0.00/0.30	tff('17', plain,
0.00/0.30	    ![X0 : b]:
0.00/0.30	      (~ $true
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X0)
0.00/0.30	       | app_encode_app(b, $o, sk_Xs, sk_Xx0)
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X0)
0.00/0.30	       | app_encode_app(a, $o, 
0.00/0.30	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	             app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	               sk_Xp, X0), app_encode_app(b, a, sk_Xx1, X0)), 
0.00/0.30	           app_encode_app(b, a, sk_Xz, X0))),
0.00/0.30	    inference('sup-', [status(thm)], ['16', '1'])).
0.00/0.30	tff('18', plain,
0.00/0.30	    ![X0 : b]:
0.00/0.30	      (app_encode_app(a, $o, 
0.00/0.30	         app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	           app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	             sk_Xp, X0), app_encode_app(b, a, sk_Xx1, X0)), 
0.00/0.30	         app_encode_app(b, a, sk_Xz, X0))
0.00/0.30	       | app_encode_app(b, $o, sk_Xs, sk_Xx0)
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X0)),
0.00/0.30	    inference('simplify', [status(thm)], ['17'])).
0.00/0.30	tff('19', plain,
0.00/0.30	    (app_encode_app(b, $o, sk_Xs, sk_Xx0)
0.00/0.30	     | ~ app_encode_app(a, $o, 
0.00/0.30	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	             app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	               sk_Xp, sk_Xx01), app_encode_app(b, a, sk_Xx1, sk_Xx01)), 
0.00/0.30	           app_encode_app(b, a, sk_Xz, sk_Xx01))),
0.00/0.30	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.30	tff('20', plain,
0.00/0.30	    (~ $true
0.00/0.30	     | ~ app_encode_app(b, $o, sk_Xs, sk_Xx01)
0.00/0.30	     | app_encode_app(b, $o, sk_Xs, sk_Xx0)
0.00/0.30	     | app_encode_app(b, $o, sk_Xs, sk_Xx0)),
0.00/0.30	    inference('sup-', [status(thm)], ['18', '19'])).
0.00/0.30	tff('21', plain,
0.00/0.30	    ![X12 : b]:
0.00/0.30	      (~ app_encode_app(b, $o, sk_Xs, X12)
0.00/0.30	       | app_encode_app(a, $o, 
0.00/0.30	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	             app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	               sk_Xp, X12), app_encode_app(b, a, sk_Xx, X12)), 
0.00/0.30	           app_encode_app(b, a, sk_Xy, X12))
0.00/0.30	       | app_encode_app(b, $o, sk_Xs, sk_Xx01)),
0.00/0.30	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.30	tff('22', plain,
0.00/0.30	    ![X0 : b]:
0.00/0.30	      (~ $true
0.00/0.30	       | app_encode_app(b, $o, sk_Xs, sk_Xx01)
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X0)
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X0)
0.00/0.30	       | app_encode_app(a, $o, 
0.00/0.30	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	             app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	               sk_Xp, X0), app_encode_app(b, a, sk_Xy, X0)), 
0.00/0.30	           app_encode_app(b, a, sk_Xx, X0))),
0.00/0.30	    inference('sup-', [status(thm)], ['21', '1'])).
0.00/0.30	tff('23', plain,
0.00/0.30	    ![X0 : b]:
0.00/0.30	      (app_encode_app(a, $o, 
0.00/0.30	         app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	           app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	             sk_Xp, X0), app_encode_app(b, a, sk_Xy, X0)), 
0.00/0.30	         app_encode_app(b, a, sk_Xx, X0))
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X0)
0.00/0.30	       | app_encode_app(b, $o, sk_Xs, sk_Xx01)),
0.00/0.30	    inference('simplify', [status(thm)], ['22'])).
0.00/0.30	tff('24', plain,
0.00/0.30	    (~ app_encode_app(a, $o, 
0.00/0.30	         app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	           app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	             sk_Xp, sk_Xx0), app_encode_app(b, a, sk_Xy, sk_Xx0)), 
0.00/0.30	         app_encode_app(b, a, sk_Xx, sk_Xx0))
0.00/0.30	     | app_encode_app(b, $o, sk_Xs, sk_Xx01)),
0.00/0.30	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.30	tff('25', plain,
0.00/0.30	    (~ $true
0.00/0.30	     | app_encode_app(b, $o, sk_Xs, sk_Xx01)
0.00/0.30	     | ~ app_encode_app(b, $o, sk_Xs, sk_Xx0)
0.00/0.30	     | app_encode_app(b, $o, sk_Xs, sk_Xx01)),
0.00/0.30	    inference('sup-', [status(thm)], ['23', '24'])).
0.00/0.30	tff('26', plain,
0.00/0.30	    (~ app_encode_app(b, $o, sk_Xs, sk_Xx0)
0.00/0.30	     | app_encode_app(b, $o, sk_Xs, sk_Xx01)),
0.00/0.30	    inference('simplify', [status(thm)], ['25'])).
0.00/0.30	tff('27', plain,
0.00/0.30	    (app_encode_app(b, $o, sk_Xs, sk_Xx0)
0.00/0.30	     | app_encode_app(b, $o, sk_Xs, sk_Xx01)),
0.00/0.30	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.30	tff('28', plain, app_encode_app(b, $o, sk_Xs, sk_Xx01),
0.00/0.30	    inference('clc', [status(thm)], ['26', '27'])).
0.00/0.30	tff('29', plain,
0.00/0.30	    (~ $true
0.00/0.30	     | ~ $true
0.00/0.30	     | app_encode_app(b, $o, sk_Xs, sk_Xx0)
0.00/0.30	     | app_encode_app(b, $o, sk_Xs, sk_Xx0)),
0.00/0.30	    inference('demod', [status(thm)], ['20', '28'])).
0.00/0.30	tff('30', plain, app_encode_app(b, $o, sk_Xs, sk_Xx0),
0.00/0.30	    inference('simplify', [status(thm)], ['29'])).
0.00/0.30	tff('31', plain,
0.00/0.30	    ![X0 : b, X1 : b]:
0.00/0.30	      (~ $true
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X1)
0.00/0.30	       | app_encode_app(a, $o, 
0.00/0.30	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	             app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	               sk_Xp, X1), app_encode_app(b, a, sk_Xy1, X1)), 
0.00/0.30	           app_encode_app(b, a, sk_Xz, X1))
0.00/0.30	       | ~ $true
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X0)
0.00/0.30	       | app_encode_app(a, $o, 
0.00/0.30	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	             app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	               sk_Xp, X0), app_encode_app(b, a, sk_Xy1, X0)), 
0.00/0.30	           app_encode_app(b, a, sk_Xz, X0))),
0.00/0.30	    inference('demod', [status(thm)], ['5', '30'])).
0.00/0.30	tff('32', plain,
0.00/0.30	    ![X0 : b, X1 : b]:
0.00/0.30	      (app_encode_app(a, $o, 
0.00/0.30	         app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	           app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	             sk_Xp, X0), app_encode_app(b, a, sk_Xy1, X0)), 
0.00/0.30	         app_encode_app(b, a, sk_Xz, X0))
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X0)
0.00/0.30	       | app_encode_app(a, $o, 
0.00/0.30	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	             app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	               sk_Xp, X1), app_encode_app(b, a, sk_Xy1, X1)), 
0.00/0.30	           app_encode_app(b, a, sk_Xz, X1))
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X1)),
0.00/0.30	    inference('simplify', [status(thm)], ['31'])).
0.00/0.30	tff('33', plain,
0.00/0.30	    ![X0 : b]:
0.00/0.30	      (~ $true
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X0)
0.00/0.30	       | app_encode_app(a, $o, 
0.00/0.30	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	             app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	               sk_Xp, X0), app_encode_app(b, a, sk_Xy1, X0)), 
0.00/0.30	           app_encode_app(b, a, sk_Xz, X0))
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X0)),
0.00/0.30	    inference('eq_fact', [status(thm)], ['32'])).
0.00/0.30	tff('34', plain,
0.00/0.30	    ![X0 : b]:
0.00/0.30	      (app_encode_app(a, $o, 
0.00/0.30	         app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	           app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	             sk_Xp, X0), app_encode_app(b, a, sk_Xy1, X0)), 
0.00/0.30	         app_encode_app(b, a, sk_Xz, X0))
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X0)),
0.00/0.30	    inference('simplify', [status(thm)], ['33'])).
0.00/0.30	tff('35', plain,
0.00/0.30	    ![X0 : b]:
0.00/0.30	      (~ $true
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X0)
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X0)
0.00/0.30	       | app_encode_app(a, $o, 
0.00/0.30	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	             app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	               sk_Xp, X0), app_encode_app(b, a, sk_Xz, X0)), 
0.00/0.30	           app_encode_app(b, a, sk_Xy1, X0))),
0.00/0.30	    inference('sup-', [status(thm)], ['34', '1'])).
0.00/0.30	tff('36', plain,
0.00/0.30	    ![X0 : b]:
0.00/0.30	      (app_encode_app(a, $o, 
0.00/0.30	         app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	           app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	             sk_Xp, X0), app_encode_app(b, a, sk_Xz, X0)), 
0.00/0.30	         app_encode_app(b, a, sk_Xy1, X0))
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X0)),
0.00/0.30	    inference('simplify', [status(thm)], ['35'])).
0.00/0.30	tff('37', plain,
0.00/0.30	    ![X10 : b, X12 : b]:
0.00/0.30	      (~ app_encode_app(b, $o, sk_Xs, X12)
0.00/0.30	       | app_encode_app(a, $o, 
0.00/0.30	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	             app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	               sk_Xp, X12), app_encode_app(b, a, sk_Xx, X12)), 
0.00/0.30	           app_encode_app(b, a, sk_Xy, X12))
0.00/0.30	       | app_encode_app(a, $o, 
0.00/0.30	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	             app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	               sk_Xp, X10), app_encode_app(b, a, sk_Xx1, X10)), 
0.00/0.30	           app_encode_app(b, a, sk_Xy1, X10))
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X10)),
0.00/0.30	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.30	tff('38', plain,
0.00/0.30	    ![X0 : b, X1 : b]:
0.00/0.30	      (~ $true
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X1)
0.00/0.30	       | app_encode_app(a, $o, 
0.00/0.30	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	             app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	               sk_Xp, X1), app_encode_app(b, a, sk_Xx1, X1)), 
0.00/0.30	           app_encode_app(b, a, sk_Xy1, X1))
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X0)
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X0)
0.00/0.30	       | app_encode_app(a, $o, 
0.00/0.30	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	             app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	               sk_Xp, X0), app_encode_app(b, a, sk_Xy, X0)), 
0.00/0.30	           app_encode_app(b, a, sk_Xx, X0))),
0.00/0.30	    inference('sup-', [status(thm)], ['37', '1'])).
0.00/0.30	tff('39', plain,
0.00/0.30	    ![X0 : b, X1 : b]:
0.00/0.30	      (app_encode_app(a, $o, 
0.00/0.30	         app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	           app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	             sk_Xp, X0), app_encode_app(b, a, sk_Xy, X0)), 
0.00/0.30	         app_encode_app(b, a, sk_Xx, X0))
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X0)
0.00/0.30	       | app_encode_app(a, $o, 
0.00/0.30	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	             app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	               sk_Xp, X1), app_encode_app(b, a, sk_Xx1, X1)), 
0.00/0.30	           app_encode_app(b, a, sk_Xy1, X1))
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X1)),
0.00/0.30	    inference('simplify', [status(thm)], ['38'])).
0.00/0.30	tff('40', plain,
0.00/0.30	    ![X10 : b]:
0.00/0.30	      (~ app_encode_app(a, $o, 
0.00/0.30	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	             app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	               sk_Xp, sk_Xx0), app_encode_app(b, a, sk_Xy, sk_Xx0)), 
0.00/0.30	           app_encode_app(b, a, sk_Xx, sk_Xx0))
0.00/0.30	       | app_encode_app(a, $o, 
0.00/0.30	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	             app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	               sk_Xp, X10), app_encode_app(b, a, sk_Xx1, X10)), 
0.00/0.30	           app_encode_app(b, a, sk_Xy1, X10))
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X10)),
0.00/0.30	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.30	tff('41', plain,
0.00/0.30	    ![X0 : b, X1 : b]:
0.00/0.30	      (~ $true
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X1)
0.00/0.30	       | app_encode_app(a, $o, 
0.00/0.30	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	             app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	               sk_Xp, X1), app_encode_app(b, a, sk_Xx1, X1)), 
0.00/0.30	           app_encode_app(b, a, sk_Xy1, X1))
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, sk_Xx0)
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X0)
0.00/0.30	       | app_encode_app(a, $o, 
0.00/0.30	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	             app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	               sk_Xp, X0), app_encode_app(b, a, sk_Xx1, X0)), 
0.00/0.30	           app_encode_app(b, a, sk_Xy1, X0))),
0.00/0.30	    inference('sup-', [status(thm)], ['39', '40'])).
0.00/0.30	tff('42', plain,
0.00/0.30	    ![X0 : b, X1 : b]:
0.00/0.30	      (~ $true
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X1)
0.00/0.30	       | app_encode_app(a, $o, 
0.00/0.30	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	             app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	               sk_Xp, X1), app_encode_app(b, a, sk_Xx1, X1)), 
0.00/0.30	           app_encode_app(b, a, sk_Xy1, X1))
0.00/0.30	       | ~ $true
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X0)
0.00/0.30	       | app_encode_app(a, $o, 
0.00/0.30	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	             app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	               sk_Xp, X0), app_encode_app(b, a, sk_Xx1, X0)), 
0.00/0.30	           app_encode_app(b, a, sk_Xy1, X0))),
0.00/0.30	    inference('demod', [status(thm)], ['41', '30'])).
0.00/0.30	tff('43', plain,
0.00/0.30	    ![X0 : b, X1 : b]:
0.00/0.30	      (app_encode_app(a, $o, 
0.00/0.30	         app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	           app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	             sk_Xp, X0), app_encode_app(b, a, sk_Xx1, X0)), 
0.00/0.30	         app_encode_app(b, a, sk_Xy1, X0))
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X0)
0.00/0.30	       | app_encode_app(a, $o, 
0.00/0.30	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	             app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	               sk_Xp, X1), app_encode_app(b, a, sk_Xx1, X1)), 
0.00/0.30	           app_encode_app(b, a, sk_Xy1, X1))
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X1)),
0.00/0.30	    inference('simplify', [status(thm)], ['42'])).
0.00/0.30	tff('44', plain,
0.00/0.30	    ![X0 : b]:
0.00/0.30	      (~ $true
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X0)
0.00/0.30	       | app_encode_app(a, $o, 
0.00/0.30	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	             app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	               sk_Xp, X0), app_encode_app(b, a, sk_Xx1, X0)), 
0.00/0.30	           app_encode_app(b, a, sk_Xy1, X0))
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X0)),
0.00/0.30	    inference('eq_fact', [status(thm)], ['43'])).
0.00/0.30	tff('45', plain,
0.00/0.30	    ![X0 : b]:
0.00/0.30	      (app_encode_app(a, $o, 
0.00/0.30	         app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	           app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	             sk_Xp, X0), app_encode_app(b, a, sk_Xx1, X0)), 
0.00/0.30	         app_encode_app(b, a, sk_Xy1, X0))
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X0)),
0.00/0.30	    inference('simplify', [status(thm)], ['44'])).
0.00/0.30	tff('46', plain,
0.00/0.30	    ![X0 : b]:
0.00/0.30	      (~ $true
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X0)
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X0)
0.00/0.30	       | app_encode_app(a, $o, 
0.00/0.30	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	             app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	               sk_Xp, X0), app_encode_app(b, a, sk_Xy1, X0)), 
0.00/0.30	           app_encode_app(b, a, sk_Xx1, X0))),
0.00/0.30	    inference('sup-', [status(thm)], ['45', '1'])).
0.00/0.30	tff('47', plain,
0.00/0.30	    ![X0 : b]:
0.00/0.30	      (app_encode_app(a, $o, 
0.00/0.30	         app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	           app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	             sk_Xp, X0), app_encode_app(b, a, sk_Xy1, X0)), 
0.00/0.30	         app_encode_app(b, a, sk_Xx1, X0))
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X0)),
0.00/0.30	    inference('simplify', [status(thm)], ['46'])).
0.00/0.30	tff('48', plain,
0.00/0.30	    ![X0 : b, X1 : a]:
0.00/0.30	      (~ $true
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X0)
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X0)
0.00/0.30	       | ~ app_encode_app(a, $o, 
0.00/0.30	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	               app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	                 sk_Xp, X0), X1), app_encode_app(b, a, sk_Xy1, X0))
0.00/0.30	       | app_encode_app(a, $o, 
0.00/0.30	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	             app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	               sk_Xp, X0), X1), app_encode_app(b, a, sk_Xx1, X0))),
0.00/0.30	    inference('sup-', [status(thm)], ['47', '12'])).
0.00/0.30	tff('49', plain,
0.00/0.30	    ![X0 : b, X1 : a]:
0.00/0.30	      (app_encode_app(a, $o, 
0.00/0.30	         app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	           app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	             sk_Xp, X0), X1), app_encode_app(b, a, sk_Xx1, X0))
0.00/0.30	       | ~ app_encode_app(a, $o, 
0.00/0.30	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	               app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	                 sk_Xp, X0), X1), app_encode_app(b, a, sk_Xy1, X0))
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X0)),
0.00/0.30	    inference('simplify', [status(thm)], ['48'])).
0.00/0.30	tff('50', plain,
0.00/0.30	    ![X0 : b]:
0.00/0.30	      (~ $true
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X0)
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X0)
0.00/0.30	       | app_encode_app(a, $o, 
0.00/0.30	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	             app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	               sk_Xp, X0), app_encode_app(b, a, sk_Xz, X0)), 
0.00/0.30	           app_encode_app(b, a, sk_Xx1, X0))),
0.00/0.30	    inference('sup-', [status(thm)], ['36', '49'])).
0.00/0.30	tff('51', plain,
0.00/0.30	    ![X0 : b]:
0.00/0.30	      (app_encode_app(a, $o, 
0.00/0.30	         app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	           app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	             sk_Xp, X0), app_encode_app(b, a, sk_Xz, X0)), 
0.00/0.30	         app_encode_app(b, a, sk_Xx1, X0))
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X0)),
0.00/0.30	    inference('simplify', [status(thm)], ['50'])).
0.00/0.30	tff('52', plain,
0.00/0.30	    ![X0 : b]:
0.00/0.30	      (~ $true
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X0)
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X0)
0.00/0.30	       | app_encode_app(a, $o, 
0.00/0.30	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	             app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	               sk_Xp, X0), app_encode_app(b, a, sk_Xx1, X0)), 
0.00/0.30	           app_encode_app(b, a, sk_Xz, X0))),
0.00/0.30	    inference('sup-', [status(thm)], ['51', '1'])).
0.00/0.30	tff('53', plain,
0.00/0.30	    ![X0 : b]:
0.00/0.30	      (app_encode_app(a, $o, 
0.00/0.30	         app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	           app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	             sk_Xp, X0), app_encode_app(b, a, sk_Xx1, X0)), 
0.00/0.30	         app_encode_app(b, a, sk_Xz, X0))
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X0)),
0.00/0.30	    inference('simplify', [status(thm)], ['52'])).
0.00/0.30	tff('54', plain,
0.00/0.30	    ![X12 : b]:
0.00/0.30	      (~ app_encode_app(b, $o, sk_Xs, X12)
0.00/0.30	       | app_encode_app(a, $o, 
0.00/0.30	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	             app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	               sk_Xp, X12), app_encode_app(b, a, sk_Xx, X12)), 
0.00/0.30	           app_encode_app(b, a, sk_Xy, X12))
0.00/0.30	       | ~ app_encode_app(a, $o, 
0.00/0.30	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	               app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	                 sk_Xp, sk_Xx01), app_encode_app(b, a, sk_Xx1, sk_Xx01)), 
0.00/0.30	             app_encode_app(b, a, sk_Xz, sk_Xx01))),
0.00/0.30	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.30	tff('55', plain,
0.00/0.30	    ![X0 : b]:
0.00/0.30	      (~ $true
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, sk_Xx01)
0.00/0.30	       | app_encode_app(a, $o, 
0.00/0.30	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	             app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	               sk_Xp, X0), app_encode_app(b, a, sk_Xx, X0)), 
0.00/0.30	           app_encode_app(b, a, sk_Xy, X0))
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X0)),
0.00/0.30	    inference('sup-', [status(thm)], ['53', '54'])).
0.00/0.30	tff('56', plain,
0.00/0.30	    ![X0 : b]:
0.00/0.30	      (~ $true
0.00/0.30	       | ~ $true
0.00/0.30	       | app_encode_app(a, $o, 
0.00/0.30	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	             app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	               sk_Xp, X0), app_encode_app(b, a, sk_Xx, X0)), 
0.00/0.30	           app_encode_app(b, a, sk_Xy, X0))
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X0)),
0.00/0.30	    inference('demod', [status(thm)], ['55', '28'])).
0.00/0.30	tff('57', plain,
0.00/0.30	    ![X0 : b]:
0.00/0.30	      (~ app_encode_app(b, $o, sk_Xs, X0)
0.00/0.30	       | app_encode_app(a, $o, 
0.00/0.30	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	             app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	               sk_Xp, X0), app_encode_app(b, a, sk_Xx, X0)), 
0.00/0.30	           app_encode_app(b, a, sk_Xy, X0))),
0.00/0.30	    inference('simplify', [status(thm)], ['56'])).
0.00/0.30	tff('58', plain,
0.00/0.30	    ![X0 : b]:
0.00/0.30	      (~ $true
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X0)
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X0)
0.00/0.30	       | app_encode_app(a, $o, 
0.00/0.30	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	             app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	               sk_Xp, X0), app_encode_app(b, a, sk_Xy, X0)), 
0.00/0.30	           app_encode_app(b, a, sk_Xx, X0))),
0.00/0.30	    inference('sup-', [status(thm)], ['57', '1'])).
0.00/0.30	tff('59', plain,
0.00/0.30	    ![X0 : b]:
0.00/0.30	      (app_encode_app(a, $o, 
0.00/0.30	         app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	           app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	             sk_Xp, X0), app_encode_app(b, a, sk_Xy, X0)), 
0.00/0.30	         app_encode_app(b, a, sk_Xx, X0))
0.00/0.30	       | ~ app_encode_app(b, $o, sk_Xs, X0)),
0.00/0.30	    inference('simplify', [status(thm)], ['58'])).
0.00/0.30	tff('60', plain,
0.00/0.30	    (~ app_encode_app(a, $o, 
0.00/0.30	         app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	           app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	             sk_Xp, sk_Xx0), app_encode_app(b, a, sk_Xy, sk_Xx0)), 
0.00/0.30	         app_encode_app(b, a, sk_Xx, sk_Xx0))
0.00/0.30	     | ~ app_encode_app(a, $o, 
0.00/0.30	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	             app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	               sk_Xp, sk_Xx01), app_encode_app(b, a, sk_Xx1, sk_Xx01)), 
0.00/0.30	           app_encode_app(b, a, sk_Xz, sk_Xx01))),
0.00/0.30	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.30	tff('61', plain,
0.00/0.30	    (~ $true
0.00/0.30	     | ~ app_encode_app(b, $o, sk_Xs, sk_Xx01)
0.00/0.30	     | ~ app_encode_app(a, $o, 
0.00/0.30	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	             app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	               sk_Xp, sk_Xx0), app_encode_app(b, a, sk_Xy, sk_Xx0)), 
0.00/0.30	           app_encode_app(b, a, sk_Xx, sk_Xx0))),
0.00/0.30	    inference('sup-', [status(thm)], ['53', '60'])).
0.00/0.30	tff('62', plain,
0.00/0.30	    (~ $true
0.00/0.30	     | ~ $true
0.00/0.30	     | ~ app_encode_app(a, $o, 
0.00/0.30	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	             app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.30	               sk_Xp, sk_Xx0), app_encode_app(b, a, sk_Xy, sk_Xx0)), 
0.00/0.30	           app_encode_app(b, a, sk_Xx, sk_Xx0))),
0.00/0.30	    inference('demod', [status(thm)], ['61', '28'])).
0.00/0.30	tff('63', plain,
0.00/0.30	    ~ app_encode_app(a, $o, 
0.00/0.30	        app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.30	          app_encode_app(b, app_encode_fun(a, app_encode_fun(a, $o)), sk_Xp, 
0.00/0.30	            sk_Xx0), app_encode_app(b, a, sk_Xy, sk_Xx0)), 
0.00/0.30	        app_encode_app(b, a, sk_Xx, sk_Xx0)),
0.00/0.30	    inference('simplify', [status(thm)], ['62'])).
0.00/0.30	tff('64', plain, (~ $true | ~ app_encode_app(b, $o, sk_Xs, sk_Xx0)),
0.00/0.30	    inference('sup-', [status(thm)], ['59', '63'])).
0.00/0.30	tff('65', plain, (~ $true | ~ $true),
0.00/0.30	    inference('demod', [status(thm)], ['64', '30'])).
0.00/0.30	tff('66', plain, $false, inference('simplify', [status(thm)], ['65'])).
0.00/0.30	
0.00/0.30	% SZS output end Refutation
0.00/0.30	EOF
