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 $2 \
0.00/0.01	  --simultaneous-sup false \
0.00/0.01	  --no-max-vars \
0.00/0.01	  --no-fool
0.00/0.20	% Computer   : n041.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 17:59:09 CST 2018
0.00/0.29	% done 95 iterations in 0.074s
0.00/0.29	% SZS status Theorem for 'stdin'
0.00/0.29	% SZS output start Refutation
0.00/0.29	tff(zf_stmt_6, conjecture,
0.00/0.29	  ((![R:app_encode_fun(a,app_encode_fun(a,app_encode_fun(a,$o)))]:
0.00/0.29	      ($true => $true)) & 
0.00/0.29	   (![R:app_encode_fun(a,app_encode_fun(a,app_encode_fun(a,$o))),
0.00/0.29	      S:app_encode_fun(a,app_encode_fun(a,app_encode_fun(a,$o)))]:
0.00/0.29	      ((![Xa:a,Xb:a,Xc:a]:
0.00/0.29	          (app_encode_app(a,$o,
0.00/0.29	                          app_encode_app(a,app_encode_fun(a,$o),
0.00/0.29	                                         app_encode_app(a,
0.00/0.29	                                                        app_encode_fun(
0.00/0.29	                                                        a,
0.00/0.29	                                                        app_encode_fun(a,$o)),
0.00/0.29	                                                        R,Xa),
0.00/0.29	                                         Xb),
0.00/0.29	                          Xc) =>
0.00/0.29	           app_encode_app(a,$o,
0.00/0.29	                          app_encode_app(a,app_encode_fun(a,$o),
0.00/0.29	                                         app_encode_app(a,
0.00/0.29	                                                        app_encode_fun(
0.00/0.29	                                                        a,
0.00/0.29	                                                        app_encode_fun(a,$o)),
0.00/0.29	                                                        S,Xa),
0.00/0.29	                                         Xb),
0.00/0.29	                          Xc))) =>
0.00/0.29	       (![Xa:a,Xb:a,Xc:a]:
0.00/0.29	          ((((Xa = c0) & (Xb = Xc)) | ((Xb = c0) & (Xa = Xc)) | 
0.00/0.29	            (?[Xx1:a,Xx2:a,Xy1:a,Xy2:a,Xz1:a,Xz2:a]:
0.00/0.29	               ((Xa =
0.00/0.29	                 app_encode_app(a,a,
0.00/0.29	                                app_encode_app(a,app_encode_fun(a,a),cP,Xx1),
0.00/0.29	                                Xx2)) & 
0.00/0.29	                (Xb =
0.00/0.29	                 app_encode_app(a,a,
0.00/0.29	                                app_encode_app(a,app_encode_fun(a,a),cP,Xy1),
0.00/0.29	                                Xy2)) & 
0.00/0.29	                (Xc =
0.00/0.29	                 app_encode_app(a,a,
0.00/0.29	                                app_encode_app(a,app_encode_fun(a,a),cP,Xz1),
0.00/0.29	                                Xz2)) & 
0.00/0.29	                app_encode_app(a,$o,
0.00/0.29	                               app_encode_app(a,app_encode_fun(a,$o),
0.00/0.29	                                              app_encode_app(a,
0.00/0.29	                                                             app_encode_fun(
0.00/0.29	                                                             a,
0.00/0.29	                                                             app_encode_fun(
0.00/0.29	                                                             a,$o)),R,Xx1),
0.00/0.29	                                              Xy1),
0.00/0.29	                               Xz1) & 
0.00/0.29	                app_encode_app(a,$o,
0.00/0.29	                               app_encode_app(a,app_encode_fun(a,$o),
0.00/0.29	                                              app_encode_app(a,
0.00/0.29	                                                             app_encode_fun(
0.00/0.29	                                                             a,
0.00/0.29	                                                             app_encode_fun(
0.00/0.29	                                                             a,$o)),R,Xx2),
0.00/0.29	                                              Xy2),
0.00/0.29	                               Xz2)))) =>
0.00/0.29	           (((Xa = c0) & (Xb = Xc)) | ((Xb = c0) & (Xa = Xc)) | 
0.00/0.29	            (?[Xx1:a,Xx2:a,Xy1:a,Xy2:a,Xz1:a,Xz2:a]:
0.00/0.29	               ((Xa =
0.00/0.29	                 app_encode_app(a,a,
0.00/0.29	                                app_encode_app(a,app_encode_fun(a,a),cP,Xx1),
0.00/0.29	                                Xx2)) & 
0.00/0.29	                (Xb =
0.00/0.29	                 app_encode_app(a,a,
0.00/0.29	                                app_encode_app(a,app_encode_fun(a,a),cP,Xy1),
0.00/0.29	                                Xy2)) & 
0.00/0.29	                (Xc =
0.00/0.29	                 app_encode_app(a,a,
0.00/0.29	                                app_encode_app(a,app_encode_fun(a,a),cP,Xz1),
0.00/0.29	                                Xz2)) & 
0.00/0.29	                app_encode_app(a,$o,
0.00/0.29	                               app_encode_app(a,app_encode_fun(a,$o),
0.00/0.29	                                              app_encode_app(a,
0.00/0.29	                                                             app_encode_fun(
0.00/0.29	                                                             a,
0.00/0.29	                                                             app_encode_fun(
0.00/0.29	                                                             a,$o)),S,Xx1),
0.00/0.29	                                              Xy1),
0.00/0.29	                               Xz1) & 
0.00/0.29	                app_encode_app(a,$o,
0.00/0.29	                               app_encode_app(a,app_encode_fun(a,$o),
0.00/0.29	                                              app_encode_app(a,
0.00/0.29	                                                             app_encode_fun(
0.00/0.29	                                                             a,
0.00/0.29	                                                             app_encode_fun(
0.00/0.29	                                                             a,$o)),S,Xx2),
0.00/0.29	                                              Xy2),
0.00/0.29	                               Xz2)))))))))).
0.00/0.29	tff(zf_stmt_0, negated_conjecture,
0.00/0.29	  (~
0.00/0.29	    ((![R:app_encode_fun(a,app_encode_fun(a,app_encode_fun(a,$o)))]:
0.00/0.29	        ($true => $true)) & 
0.00/0.29	     (![R:app_encode_fun(a,app_encode_fun(a,app_encode_fun(a,$o))),
0.00/0.29	        S:app_encode_fun(a,app_encode_fun(a,app_encode_fun(a,$o)))]:
0.00/0.29	        ((![Xa:a,Xb:a,Xc:a]:
0.00/0.29	            (app_encode_app(a,$o,
0.00/0.29	                            app_encode_app(a,app_encode_fun(a,$o),
0.00/0.29	                                           app_encode_app(a,
0.00/0.29	                                                          app_encode_fun(
0.00/0.29	                                                          a,
0.00/0.29	                                                          app_encode_fun(
0.00/0.29	                                                          a,$o)),R,Xa),
0.00/0.29	                                           Xb),
0.00/0.29	                            Xc) =>
0.00/0.29	             app_encode_app(a,$o,
0.00/0.29	                            app_encode_app(a,app_encode_fun(a,$o),
0.00/0.29	                                           app_encode_app(a,
0.00/0.29	                                                          app_encode_fun(
0.00/0.29	                                                          a,
0.00/0.29	                                                          app_encode_fun(
0.00/0.29	                                                          a,$o)),S,Xa),
0.00/0.29	                                           Xb),
0.00/0.29	                            Xc))) =>
0.00/0.29	         (![Xa:a,Xb:a,Xc:a]:
0.00/0.29	            ((((Xa = c0) & (Xb = Xc)) | ((Xb = c0) & (Xa = Xc)) | 
0.00/0.29	              (?[Xx1:a,Xx2:a,Xy1:a,Xy2:a,Xz1:a,Xz2:a]:
0.00/0.29	                 ((Xa =
0.00/0.29	                   app_encode_app(a,a,
0.00/0.29	                                  app_encode_app(a,app_encode_fun(a,a),cP,Xx1),
0.00/0.29	                                  Xx2)) & 
0.00/0.29	                  (Xb =
0.00/0.29	                   app_encode_app(a,a,
0.00/0.29	                                  app_encode_app(a,app_encode_fun(a,a),cP,Xy1),
0.00/0.29	                                  Xy2)) & 
0.00/0.29	                  (Xc =
0.00/0.29	                   app_encode_app(a,a,
0.00/0.29	                                  app_encode_app(a,app_encode_fun(a,a),cP,Xz1),
0.00/0.29	                                  Xz2)) & 
0.00/0.29	                  app_encode_app(a,$o,
0.00/0.29	                                 app_encode_app(a,app_encode_fun(a,$o),
0.00/0.29	                                                app_encode_app(a,
0.00/0.29	                                                               app_encode_fun(
0.00/0.29	                                                               a,
0.00/0.29	                                                               app_encode_fun(
0.00/0.29	                                                               a,$o)),R,Xx1),
0.00/0.29	                                                Xy1),
0.00/0.29	                                 Xz1) & 
0.00/0.29	                  app_encode_app(a,$o,
0.00/0.29	                                 app_encode_app(a,app_encode_fun(a,$o),
0.00/0.29	                                                app_encode_app(a,
0.00/0.29	                                                               app_encode_fun(
0.00/0.29	                                                               a,
0.00/0.29	                                                               app_encode_fun(
0.00/0.29	                                                               a,$o)),R,Xx2),
0.00/0.29	                                                Xy2),
0.00/0.29	                                 Xz2)))) =>
0.00/0.29	             (((Xa = c0) & (Xb = Xc)) | ((Xb = c0) & (Xa = Xc)) | 
0.00/0.29	              (?[Xx1:a,Xx2:a,Xy1:a,Xy2:a,Xz1:a,Xz2:a]:
0.00/0.29	                 ((Xa =
0.00/0.29	                   app_encode_app(a,a,
0.00/0.29	                                  app_encode_app(a,app_encode_fun(a,a),cP,Xx1),
0.00/0.29	                                  Xx2)) & 
0.00/0.29	                  (Xb =
0.00/0.29	                   app_encode_app(a,a,
0.00/0.29	                                  app_encode_app(a,app_encode_fun(a,a),cP,Xy1),
0.00/0.29	                                  Xy2)) & 
0.00/0.29	                  (Xc =
0.00/0.29	                   app_encode_app(a,a,
0.00/0.29	                                  app_encode_app(a,app_encode_fun(a,a),cP,Xz1),
0.00/0.29	                                  Xz2)) & 
0.00/0.29	                  app_encode_app(a,$o,
0.00/0.29	                                 app_encode_app(a,app_encode_fun(a,$o),
0.00/0.29	                                                app_encode_app(a,
0.00/0.29	                                                               app_encode_fun(
0.00/0.29	                                                               a,
0.00/0.29	                                                               app_encode_fun(
0.00/0.29	                                                               a,$o)),S,Xx1),
0.00/0.29	                                                Xy1),
0.00/0.29	                                 Xz1) & 
0.00/0.29	                  app_encode_app(a,$o,
0.00/0.29	                                 app_encode_app(a,app_encode_fun(a,$o),
0.00/0.29	                                                app_encode_app(a,
0.00/0.29	                                                               app_encode_fun(
0.00/0.29	                                                               a,
0.00/0.29	                                                               app_encode_fun(
0.00/0.29	                                                               a,$o)),S,Xx2),
0.00/0.29	                                                Xy2),
0.00/0.29	                                 Xz2))))))))))).
0.00/0.29	tff('0', plain,
0.00/0.29	    (sk_Xb = sk_Xc
0.00/0.29	     | sk_Xa = sk_Xc
0.00/0.29	     | sk_Xb
0.00/0.29	        = app_encode_app(a, a, 
0.00/0.29	            app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy1), sk_Xy2)),
0.00/0.29	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.29	tff('1', plain,
0.00/0.29	    (sk_Xb = sk_Xc
0.00/0.29	     | sk_Xb = c0
0.00/0.29	     | sk_Xc
0.00/0.29	        = app_encode_app(a, a, 
0.00/0.29	            app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz1), sk_Xz2)),
0.00/0.29	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.29	tff('2', plain,
0.00/0.29	    (sk_Xa = c0
0.00/0.29	     | sk_Xb = c0
0.00/0.29	     | sk_Xc
0.00/0.29	        = app_encode_app(a, a, 
0.00/0.29	            app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz1), sk_Xz2)),
0.00/0.29	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.29	tff('3', plain,
0.00/0.29	    ![X4 : a, X5 : a, X6 : a]:
0.00/0.29	      (app_encode_app(a, $o, 
0.00/0.29	         app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_S, 
0.00/0.29	             X4), X5), X6)
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_R1, X4), X5), X6)),
0.00/0.29	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.29	tff('4', plain,
0.00/0.29	    (sk_Xa = c0
0.00/0.29	     | sk_Xb = c0
0.00/0.29	     | sk_Xb
0.00/0.29	        = app_encode_app(a, a, 
0.00/0.29	            app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy1), sk_Xy2)),
0.00/0.29	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.29	tff('5', plain,
0.00/0.29	    (sk_Xa = c0
0.00/0.29	     | sk_Xb = c0
0.00/0.29	     | sk_Xa
0.00/0.29	        = app_encode_app(a, a, 
0.00/0.29	            app_encode_app(a, app_encode_fun(a, a), cP, sk_Xx1), sk_Xx2)),
0.00/0.29	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.29	tff('6', plain,
0.00/0.29	    ![X7 : a, X8 : a, X9 : a, X10 : a, X11 : a, X12 : a]:
0.00/0.29	      (sk_Xa
0.00/0.29	        != app_encode_app(a, a, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, a), cP, X7), X8)
0.00/0.29	       | sk_Xb
0.00/0.29	          != app_encode_app(a, a, 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, a), cP, X9), X10)
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_S, X7), X9), X11)
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_S, X8), X10), X12)
0.00/0.29	       | sk_Xc
0.00/0.29	          != app_encode_app(a, a, 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, a), cP, X11), X12)),
0.00/0.29	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.29	tff('7', plain,
0.00/0.29	    ![X0 : a, X1 : a, X2 : a, X3 : a]:
0.00/0.29	      (sk_Xa != sk_Xa
0.00/0.29	       | sk_Xb = c0
0.00/0.29	       | sk_Xa = c0
0.00/0.29	       | sk_Xc
0.00/0.29	          != app_encode_app(a, a, 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, a), cP, X1), X0)
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_S, sk_Xx2), X2), X0)
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_S, sk_Xx1), X3), X1)
0.00/0.29	       | sk_Xb
0.00/0.29	          != app_encode_app(a, a, 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, a), cP, X3), X2)),
0.00/0.29	    inference('sup-', [status(thm)], ['5', '6'])).
0.00/0.29	tff('8', plain,
0.00/0.29	    ![X0 : a, X1 : a, X2 : a, X3 : a]:
0.00/0.29	      (sk_Xb
0.00/0.29	        != app_encode_app(a, a, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, a), cP, X3), X2)
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_S, sk_Xx1), X3), X1)
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_S, sk_Xx2), X2), X0)
0.00/0.29	       | sk_Xc
0.00/0.29	          != app_encode_app(a, a, 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, a), cP, X1), X0)
0.00/0.29	       | sk_Xa = c0
0.00/0.29	       | sk_Xb = c0),
0.00/0.29	    inference('simplify', [status(thm)], ['7'])).
0.00/0.29	tff('9', plain,
0.00/0.29	    ![X0 : a, X1 : a]:
0.00/0.29	      (sk_Xb != sk_Xb
0.00/0.29	       | sk_Xb = c0
0.00/0.29	       | sk_Xa = c0
0.00/0.29	       | sk_Xb = c0
0.00/0.29	       | sk_Xa = c0
0.00/0.29	       | sk_Xc
0.00/0.29	          != app_encode_app(a, a, 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, a), cP, X1), X0)
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_S, sk_Xx2), sk_Xy2), X0)
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_S, sk_Xx1), sk_Xy1), X1)),
0.00/0.29	    inference('sup-', [status(thm)], ['4', '8'])).
0.00/0.29	tff('10', plain,
0.00/0.29	    ![X0 : a, X1 : a]:
0.00/0.29	      (~ app_encode_app(a, $o, 
0.00/0.29	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	               sk_S, sk_Xx1), sk_Xy1), X1)
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_S, sk_Xx2), sk_Xy2), X0)
0.00/0.29	       | sk_Xc
0.00/0.29	          != app_encode_app(a, a, 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, a), cP, X1), X0)
0.00/0.29	       | sk_Xa = c0
0.00/0.29	       | sk_Xb = c0),
0.00/0.29	    inference('simplify', [status(thm)], ['9'])).
0.00/0.29	tff('11', plain,
0.00/0.29	    ![X0 : a, X1 : a]:
0.00/0.29	      (~ $true
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_R1, sk_Xx1), sk_Xy1), X0)
0.00/0.29	       | sk_Xb = c0
0.00/0.29	       | sk_Xa = c0
0.00/0.29	       | sk_Xc
0.00/0.29	          != app_encode_app(a, a, 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, a), cP, X0), X1)
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_S, sk_Xx2), sk_Xy2), X1)),
0.00/0.29	    inference('sup-', [status(thm)], ['3', '10'])).
0.00/0.29	tff('12', plain,
0.00/0.29	    ![X0 : a, X1 : a]:
0.00/0.29	      (~ app_encode_app(a, $o, 
0.00/0.29	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	               sk_S, sk_Xx2), sk_Xy2), X1)
0.00/0.29	       | sk_Xc
0.00/0.29	          != app_encode_app(a, a, 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, a), cP, X0), X1)
0.00/0.29	       | sk_Xa = c0
0.00/0.29	       | sk_Xb = c0
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_R1, sk_Xx1), sk_Xy1), X0)),
0.00/0.29	    inference('simplify', [status(thm)], ['11'])).
0.00/0.29	tff('13', plain,
0.00/0.29	    ![X0 : a, X1 : a]:
0.00/0.29	      (~ $true
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_R1, sk_Xx2), sk_Xy2), X0)
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_R1, sk_Xx1), sk_Xy1), X1)
0.00/0.29	       | sk_Xb = c0
0.00/0.29	       | sk_Xa = c0
0.00/0.29	       | sk_Xc
0.00/0.29	          != app_encode_app(a, a, 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, a), cP, X1), X0)),
0.00/0.29	    inference('sup-', [status(thm)], ['3', '12'])).
0.00/0.29	tff('14', plain,
0.00/0.29	    ![X0 : a, X1 : a]:
0.00/0.29	      (sk_Xc
0.00/0.29	        != app_encode_app(a, a, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, a), cP, X1), X0)
0.00/0.29	       | sk_Xa = c0
0.00/0.29	       | sk_Xb = c0
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_R1, sk_Xx1), sk_Xy1), X1)
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_R1, sk_Xx2), sk_Xy2), X0)),
0.00/0.29	    inference('simplify', [status(thm)], ['13'])).
0.00/0.29	tff('15', plain,
0.00/0.29	    (sk_Xc != sk_Xc
0.00/0.29	     | sk_Xb = c0
0.00/0.29	     | sk_Xa = c0
0.00/0.29	     | ~ app_encode_app(a, $o, 
0.00/0.29	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	               sk_R1, sk_Xx2), sk_Xy2), sk_Xz2)
0.00/0.29	     | ~ app_encode_app(a, $o, 
0.00/0.29	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	               sk_R1, sk_Xx1), sk_Xy1), sk_Xz1)
0.00/0.29	     | sk_Xb = c0
0.00/0.29	     | sk_Xa = c0),
0.00/0.29	    inference('sup-', [status(thm)], ['2', '14'])).
0.00/0.29	tff('16', plain,
0.00/0.29	    (~ app_encode_app(a, $o, 
0.00/0.29	         app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	             sk_R1, sk_Xx1), sk_Xy1), sk_Xz1)
0.00/0.29	     | ~ app_encode_app(a, $o, 
0.00/0.29	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	               sk_R1, sk_Xx2), sk_Xy2), sk_Xz2)
0.00/0.29	     | sk_Xa = c0
0.00/0.29	     | sk_Xb = c0),
0.00/0.29	    inference('simplify', [status(thm)], ['15'])).
0.00/0.29	tff('17', plain,
0.00/0.29	    (sk_Xa = c0
0.00/0.29	     | sk_Xb = c0
0.00/0.29	     | app_encode_app(a, $o, 
0.00/0.29	         app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	             sk_R1, sk_Xx1), sk_Xy1), sk_Xz1)),
0.00/0.29	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.29	tff('18', plain,
0.00/0.29	    (sk_Xb = c0
0.00/0.29	     | sk_Xa = c0
0.00/0.29	     | ~ app_encode_app(a, $o, 
0.00/0.29	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	               sk_R1, sk_Xx2), sk_Xy2), sk_Xz2)),
0.00/0.29	    inference('clc', [status(thm)], ['16', '17'])).
0.00/0.29	tff('19', plain,
0.00/0.29	    (sk_Xa = c0
0.00/0.29	     | sk_Xb = c0
0.00/0.29	     | app_encode_app(a, $o, 
0.00/0.29	         app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	             sk_R1, sk_Xx2), sk_Xy2), sk_Xz2)),
0.00/0.29	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.29	tff('20', plain, (sk_Xa = c0 | sk_Xb = c0),
0.00/0.29	    inference('clc', [status(thm)], ['18', '19'])).
0.00/0.29	tff('21', plain, (sk_Xb != c0 | sk_Xa != sk_Xc),
0.00/0.29	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.29	tff('22', plain, (sk_Xb != sk_Xb | sk_Xa = c0 | sk_Xa != sk_Xc),
0.00/0.29	    inference('sup-', [status(thm)], ['20', '21'])).
0.00/0.29	tff('23', plain, (sk_Xa != sk_Xc | sk_Xa = c0),
0.00/0.29	    inference('simplify', [status(thm)], ['22'])).
0.00/0.29	tff('24', plain,
0.00/0.29	    (sk_Xa = c0
0.00/0.29	     | sk_Xa = sk_Xc
0.00/0.29	     | sk_Xc
0.00/0.29	        = app_encode_app(a, a, 
0.00/0.29	            app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz1), sk_Xz2)),
0.00/0.29	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.29	tff('25', plain,
0.00/0.29	    (sk_Xa = c0
0.00/0.29	     | sk_Xa = sk_Xc
0.00/0.29	     | sk_Xb
0.00/0.29	        = app_encode_app(a, a, 
0.00/0.29	            app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy1), sk_Xy2)),
0.00/0.29	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.29	tff('26', plain,
0.00/0.29	    (sk_Xa = c0
0.00/0.29	     | sk_Xa = sk_Xc
0.00/0.29	     | sk_Xa
0.00/0.29	        = app_encode_app(a, a, 
0.00/0.29	            app_encode_app(a, app_encode_fun(a, a), cP, sk_Xx1), sk_Xx2)),
0.00/0.29	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.29	tff('27', plain,
0.00/0.29	    ![X0 : a, X1 : a, X2 : a, X3 : a]:
0.00/0.29	      (sk_Xa != sk_Xa
0.00/0.29	       | sk_Xa = sk_Xc
0.00/0.29	       | sk_Xa = c0
0.00/0.29	       | sk_Xc
0.00/0.29	          != app_encode_app(a, a, 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, a), cP, X1), X0)
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_S, sk_Xx2), X2), X0)
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_S, sk_Xx1), X3), X1)
0.00/0.29	       | sk_Xb
0.00/0.29	          != app_encode_app(a, a, 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, a), cP, X3), X2)),
0.00/0.29	    inference('sup-', [status(thm)], ['26', '6'])).
0.00/0.29	tff('28', plain,
0.00/0.29	    ![X0 : a, X1 : a, X2 : a, X3 : a]:
0.00/0.29	      (sk_Xb
0.00/0.29	        != app_encode_app(a, a, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, a), cP, X3), X2)
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_S, sk_Xx1), X3), X1)
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_S, sk_Xx2), X2), X0)
0.00/0.29	       | sk_Xc
0.00/0.29	          != app_encode_app(a, a, 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, a), cP, X1), X0)
0.00/0.29	       | sk_Xa = c0
0.00/0.29	       | sk_Xa = sk_Xc),
0.00/0.29	    inference('simplify', [status(thm)], ['27'])).
0.00/0.29	tff('29', plain,
0.00/0.29	    ![X0 : a, X1 : a]:
0.00/0.29	      (sk_Xb != sk_Xb
0.00/0.29	       | sk_Xa = sk_Xc
0.00/0.29	       | sk_Xa = c0
0.00/0.29	       | sk_Xa = sk_Xc
0.00/0.29	       | sk_Xa = c0
0.00/0.29	       | sk_Xc
0.00/0.29	          != app_encode_app(a, a, 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, a), cP, X1), X0)
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_S, sk_Xx2), sk_Xy2), X0)
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_S, sk_Xx1), sk_Xy1), X1)),
0.00/0.29	    inference('sup-', [status(thm)], ['25', '28'])).
0.00/0.29	tff('30', plain,
0.00/0.29	    ![X0 : a, X1 : a]:
0.00/0.29	      (~ app_encode_app(a, $o, 
0.00/0.29	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	               sk_S, sk_Xx1), sk_Xy1), X1)
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_S, sk_Xx2), sk_Xy2), X0)
0.00/0.29	       | sk_Xc
0.00/0.29	          != app_encode_app(a, a, 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, a), cP, X1), X0)
0.00/0.29	       | sk_Xa = c0
0.00/0.29	       | sk_Xa = sk_Xc),
0.00/0.29	    inference('simplify', [status(thm)], ['29'])).
0.00/0.29	tff('31', plain,
0.00/0.29	    ![X0 : a, X1 : a]:
0.00/0.29	      (~ $true
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_R1, sk_Xx1), sk_Xy1), X0)
0.00/0.29	       | sk_Xa = sk_Xc
0.00/0.29	       | sk_Xa = c0
0.00/0.29	       | sk_Xc
0.00/0.29	          != app_encode_app(a, a, 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, a), cP, X0), X1)
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_S, sk_Xx2), sk_Xy2), X1)),
0.00/0.29	    inference('sup-', [status(thm)], ['3', '30'])).
0.00/0.29	tff('32', plain,
0.00/0.29	    ![X0 : a, X1 : a]:
0.00/0.29	      (~ app_encode_app(a, $o, 
0.00/0.29	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	               sk_S, sk_Xx2), sk_Xy2), X1)
0.00/0.29	       | sk_Xc
0.00/0.29	          != app_encode_app(a, a, 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, a), cP, X0), X1)
0.00/0.29	       | sk_Xa = c0
0.00/0.29	       | sk_Xa = sk_Xc
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_R1, sk_Xx1), sk_Xy1), X0)),
0.00/0.29	    inference('simplify', [status(thm)], ['31'])).
0.00/0.29	tff('33', plain,
0.00/0.29	    ![X0 : a, X1 : a]:
0.00/0.29	      (~ $true
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_R1, sk_Xx2), sk_Xy2), X0)
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_R1, sk_Xx1), sk_Xy1), X1)
0.00/0.29	       | sk_Xa = sk_Xc
0.00/0.29	       | sk_Xa = c0
0.00/0.29	       | sk_Xc
0.00/0.29	          != app_encode_app(a, a, 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, a), cP, X1), X0)),
0.00/0.29	    inference('sup-', [status(thm)], ['3', '32'])).
0.00/0.29	tff('34', plain,
0.00/0.29	    ![X0 : a, X1 : a]:
0.00/0.29	      (sk_Xc
0.00/0.29	        != app_encode_app(a, a, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, a), cP, X1), X0)
0.00/0.29	       | sk_Xa = c0
0.00/0.29	       | sk_Xa = sk_Xc
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_R1, sk_Xx1), sk_Xy1), X1)
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_R1, sk_Xx2), sk_Xy2), X0)),
0.00/0.29	    inference('simplify', [status(thm)], ['33'])).
0.00/0.29	tff('35', plain,
0.00/0.29	    (sk_Xc != sk_Xc
0.00/0.29	     | sk_Xa = sk_Xc
0.00/0.29	     | sk_Xa = c0
0.00/0.29	     | ~ app_encode_app(a, $o, 
0.00/0.29	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	               sk_R1, sk_Xx2), sk_Xy2), sk_Xz2)
0.00/0.29	     | ~ app_encode_app(a, $o, 
0.00/0.29	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	               sk_R1, sk_Xx1), sk_Xy1), sk_Xz1)
0.00/0.29	     | sk_Xa = sk_Xc
0.00/0.29	     | sk_Xa = c0),
0.00/0.29	    inference('sup-', [status(thm)], ['24', '34'])).
0.00/0.29	tff('36', plain,
0.00/0.29	    (~ app_encode_app(a, $o, 
0.00/0.29	         app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	             sk_R1, sk_Xx1), sk_Xy1), sk_Xz1)
0.00/0.29	     | ~ app_encode_app(a, $o, 
0.00/0.29	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	               sk_R1, sk_Xx2), sk_Xy2), sk_Xz2)
0.00/0.29	     | sk_Xa = c0
0.00/0.29	     | sk_Xa = sk_Xc),
0.00/0.29	    inference('simplify', [status(thm)], ['35'])).
0.00/0.29	tff('37', plain,
0.00/0.29	    (sk_Xa = c0
0.00/0.29	     | sk_Xa = sk_Xc
0.00/0.29	     | app_encode_app(a, $o, 
0.00/0.29	         app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	             sk_R1, sk_Xx1), sk_Xy1), sk_Xz1)),
0.00/0.29	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.29	tff('38', plain,
0.00/0.29	    (sk_Xa = sk_Xc
0.00/0.29	     | sk_Xa = c0
0.00/0.29	     | ~ app_encode_app(a, $o, 
0.00/0.29	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	               sk_R1, sk_Xx2), sk_Xy2), sk_Xz2)),
0.00/0.29	    inference('clc', [status(thm)], ['36', '37'])).
0.00/0.29	tff('39', plain,
0.00/0.29	    (sk_Xa = c0
0.00/0.29	     | sk_Xa = sk_Xc
0.00/0.29	     | app_encode_app(a, $o, 
0.00/0.29	         app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	             sk_R1, sk_Xx2), sk_Xy2), sk_Xz2)),
0.00/0.29	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.29	tff('40', plain, (sk_Xa = c0 | sk_Xa = sk_Xc),
0.00/0.29	    inference('clc', [status(thm)], ['38', '39'])).
0.00/0.29	tff('41', plain, sk_Xa = c0, inference('clc', [status(thm)], ['23', '40'])).
0.00/0.29	tff('42', plain,
0.00/0.29	    (sk_Xb = sk_Xc
0.00/0.29	     | sk_Xb = sk_Xa
0.00/0.29	     | sk_Xc
0.00/0.29	        = app_encode_app(a, a, 
0.00/0.29	            app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz1), sk_Xz2)),
0.00/0.29	    inference('demod', [status(thm)], ['1', '41'])).
0.00/0.29	tff('43', plain, (sk_Xa != c0 | sk_Xb != sk_Xc),
0.00/0.29	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.29	tff('44', plain, (sk_Xa != sk_Xa | sk_Xb != sk_Xc),
0.00/0.29	    inference('demod', [status(thm)], ['43', '41'])).
0.00/0.29	tff('45', plain, sk_Xb != sk_Xc, inference('simplify', [status(thm)], ['44'])).
0.00/0.29	tff('46', plain,
0.00/0.29	    (sk_Xb = sk_Xa
0.00/0.29	     | sk_Xc
0.00/0.29	        = app_encode_app(a, a, 
0.00/0.29	            app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz1), sk_Xz2)),
0.00/0.29	    inference('simplify_reflect-', [status(thm)], ['42', '45'])).
0.00/0.29	tff('47', plain,
0.00/0.29	    (sk_Xb = sk_Xc
0.00/0.29	     | sk_Xb = c0
0.00/0.29	     | sk_Xb
0.00/0.29	        = app_encode_app(a, a, 
0.00/0.29	            app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy1), sk_Xy2)),
0.00/0.29	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.29	tff('48', plain,
0.00/0.29	    (sk_Xb = sk_Xc
0.00/0.29	     | sk_Xb = sk_Xa
0.00/0.29	     | sk_Xb
0.00/0.29	        = app_encode_app(a, a, 
0.00/0.29	            app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy1), sk_Xy2)),
0.00/0.29	    inference('demod', [status(thm)], ['47', '41'])).
0.00/0.29	tff('49', plain,
0.00/0.29	    (sk_Xb = sk_Xa
0.00/0.29	     | sk_Xb
0.00/0.29	        = app_encode_app(a, a, 
0.00/0.29	            app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy1), sk_Xy2)),
0.00/0.29	    inference('simplify_reflect-', [status(thm)], ['48', '45'])).
0.00/0.29	tff('50', plain,
0.00/0.29	    (sk_Xb = sk_Xc
0.00/0.29	     | sk_Xb = c0
0.00/0.29	     | sk_Xa
0.00/0.29	        = app_encode_app(a, a, 
0.00/0.29	            app_encode_app(a, app_encode_fun(a, a), cP, sk_Xx1), sk_Xx2)),
0.00/0.29	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.29	tff('51', plain,
0.00/0.29	    (sk_Xb = sk_Xc
0.00/0.29	     | sk_Xb = sk_Xa
0.00/0.29	     | sk_Xa
0.00/0.29	        = app_encode_app(a, a, 
0.00/0.29	            app_encode_app(a, app_encode_fun(a, a), cP, sk_Xx1), sk_Xx2)),
0.00/0.29	    inference('demod', [status(thm)], ['50', '41'])).
0.00/0.29	tff('52', plain,
0.00/0.29	    (sk_Xb = sk_Xa
0.00/0.29	     | sk_Xa
0.00/0.29	        = app_encode_app(a, a, 
0.00/0.29	            app_encode_app(a, app_encode_fun(a, a), cP, sk_Xx1), sk_Xx2)),
0.00/0.29	    inference('simplify_reflect-', [status(thm)], ['51', '45'])).
0.00/0.29	tff('53', plain,
0.00/0.29	    ![X0 : a, X1 : a, X2 : a, X3 : a]:
0.00/0.29	      (sk_Xa != sk_Xa
0.00/0.29	       | sk_Xb = sk_Xa
0.00/0.29	       | sk_Xc
0.00/0.29	          != app_encode_app(a, a, 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, a), cP, X1), X0)
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_S, sk_Xx2), X2), X0)
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_S, sk_Xx1), X3), X1)
0.00/0.29	       | sk_Xb
0.00/0.29	          != app_encode_app(a, a, 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, a), cP, X3), X2)),
0.00/0.29	    inference('sup-', [status(thm)], ['52', '6'])).
0.00/0.29	tff('54', plain,
0.00/0.29	    ![X0 : a, X1 : a, X2 : a, X3 : a]:
0.00/0.29	      (sk_Xb
0.00/0.29	        != app_encode_app(a, a, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, a), cP, X3), X2)
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_S, sk_Xx1), X3), X1)
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_S, sk_Xx2), X2), X0)
0.00/0.29	       | sk_Xc
0.00/0.29	          != app_encode_app(a, a, 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, a), cP, X1), X0)
0.00/0.29	       | sk_Xb = sk_Xa),
0.00/0.29	    inference('simplify', [status(thm)], ['53'])).
0.00/0.29	tff('55', plain,
0.00/0.29	    ![X0 : a, X1 : a]:
0.00/0.29	      (sk_Xb != sk_Xb
0.00/0.29	       | sk_Xb = sk_Xa
0.00/0.29	       | sk_Xb = sk_Xa
0.00/0.29	       | sk_Xc
0.00/0.29	          != app_encode_app(a, a, 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, a), cP, X1), X0)
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_S, sk_Xx2), sk_Xy2), X0)
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_S, sk_Xx1), sk_Xy1), X1)),
0.00/0.29	    inference('sup-', [status(thm)], ['49', '54'])).
0.00/0.29	tff('56', plain,
0.00/0.29	    ![X0 : a, X1 : a]:
0.00/0.29	      (~ app_encode_app(a, $o, 
0.00/0.29	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	               sk_S, sk_Xx1), sk_Xy1), X1)
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_S, sk_Xx2), sk_Xy2), X0)
0.00/0.29	       | sk_Xc
0.00/0.29	          != app_encode_app(a, a, 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, a), cP, X1), X0)
0.00/0.29	       | sk_Xb = sk_Xa),
0.00/0.29	    inference('simplify', [status(thm)], ['55'])).
0.00/0.29	tff('57', plain,
0.00/0.29	    ![X0 : a, X1 : a]:
0.00/0.29	      (~ $true
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_R1, sk_Xx1), sk_Xy1), X0)
0.00/0.29	       | sk_Xb = sk_Xa
0.00/0.29	       | sk_Xc
0.00/0.29	          != app_encode_app(a, a, 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, a), cP, X0), X1)
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_S, sk_Xx2), sk_Xy2), X1)),
0.00/0.29	    inference('sup-', [status(thm)], ['3', '56'])).
0.00/0.29	tff('58', plain,
0.00/0.29	    ![X0 : a, X1 : a]:
0.00/0.29	      (~ app_encode_app(a, $o, 
0.00/0.29	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	               sk_S, sk_Xx2), sk_Xy2), X1)
0.00/0.29	       | sk_Xc
0.00/0.29	          != app_encode_app(a, a, 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, a), cP, X0), X1)
0.00/0.29	       | sk_Xb = sk_Xa
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_R1, sk_Xx1), sk_Xy1), X0)),
0.00/0.29	    inference('simplify', [status(thm)], ['57'])).
0.00/0.29	tff('59', plain,
0.00/0.29	    ![X0 : a, X1 : a]:
0.00/0.29	      (~ $true
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_R1, sk_Xx2), sk_Xy2), X0)
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_R1, sk_Xx1), sk_Xy1), X1)
0.00/0.29	       | sk_Xb = sk_Xa
0.00/0.29	       | sk_Xc
0.00/0.29	          != app_encode_app(a, a, 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, a), cP, X1), X0)),
0.00/0.29	    inference('sup-', [status(thm)], ['3', '58'])).
0.00/0.29	tff('60', plain,
0.00/0.29	    ![X0 : a, X1 : a]:
0.00/0.29	      (sk_Xc
0.00/0.29	        != app_encode_app(a, a, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, a), cP, X1), X0)
0.00/0.29	       | sk_Xb = sk_Xa
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_R1, sk_Xx1), sk_Xy1), X1)
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_R1, sk_Xx2), sk_Xy2), X0)),
0.00/0.29	    inference('simplify', [status(thm)], ['59'])).
0.00/0.29	tff('61', plain,
0.00/0.29	    (sk_Xc != sk_Xc
0.00/0.29	     | sk_Xb = sk_Xa
0.00/0.29	     | ~ app_encode_app(a, $o, 
0.00/0.29	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	               sk_R1, sk_Xx2), sk_Xy2), sk_Xz2)
0.00/0.29	     | ~ app_encode_app(a, $o, 
0.00/0.29	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	               sk_R1, sk_Xx1), sk_Xy1), sk_Xz1)
0.00/0.29	     | sk_Xb = sk_Xa),
0.00/0.29	    inference('sup-', [status(thm)], ['46', '60'])).
0.00/0.29	tff('62', plain,
0.00/0.29	    (~ app_encode_app(a, $o, 
0.00/0.29	         app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	             sk_R1, sk_Xx1), sk_Xy1), sk_Xz1)
0.00/0.29	     | ~ app_encode_app(a, $o, 
0.00/0.29	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	               sk_R1, sk_Xx2), sk_Xy2), sk_Xz2)
0.00/0.29	     | sk_Xb = sk_Xa),
0.00/0.29	    inference('simplify', [status(thm)], ['61'])).
0.00/0.29	tff('63', plain,
0.00/0.29	    (sk_Xb = sk_Xc
0.00/0.29	     | sk_Xb = c0
0.00/0.29	     | app_encode_app(a, $o, 
0.00/0.29	         app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	             sk_R1, sk_Xx1), sk_Xy1), sk_Xz1)),
0.00/0.29	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.29	tff('64', plain,
0.00/0.29	    (sk_Xb = sk_Xc
0.00/0.29	     | sk_Xb = sk_Xa
0.00/0.29	     | app_encode_app(a, $o, 
0.00/0.29	         app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	             sk_R1, sk_Xx1), sk_Xy1), sk_Xz1)),
0.00/0.29	    inference('demod', [status(thm)], ['63', '41'])).
0.00/0.29	tff('65', plain,
0.00/0.29	    (sk_Xb = sk_Xa
0.00/0.29	     | app_encode_app(a, $o, 
0.00/0.29	         app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	             sk_R1, sk_Xx1), sk_Xy1), sk_Xz1)),
0.00/0.29	    inference('simplify_reflect-', [status(thm)], ['64', '45'])).
0.00/0.29	tff('66', plain,
0.00/0.29	    (sk_Xb = sk_Xa
0.00/0.29	     | ~ app_encode_app(a, $o, 
0.00/0.29	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	               sk_R1, sk_Xx2), sk_Xy2), sk_Xz2)),
0.00/0.29	    inference('clc', [status(thm)], ['62', '65'])).
0.00/0.29	tff('67', plain,
0.00/0.29	    (sk_Xb = sk_Xc
0.00/0.29	     | sk_Xb = c0
0.00/0.29	     | app_encode_app(a, $o, 
0.00/0.29	         app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	             sk_R1, sk_Xx2), sk_Xy2), sk_Xz2)),
0.00/0.29	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.29	tff('68', plain,
0.00/0.29	    (sk_Xb = sk_Xc
0.00/0.29	     | sk_Xb = sk_Xa
0.00/0.29	     | app_encode_app(a, $o, 
0.00/0.29	         app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	             sk_R1, sk_Xx2), sk_Xy2), sk_Xz2)),
0.00/0.29	    inference('demod', [status(thm)], ['67', '41'])).
0.00/0.29	tff('69', plain,
0.00/0.29	    (sk_Xb = sk_Xa
0.00/0.29	     | app_encode_app(a, $o, 
0.00/0.29	         app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	             sk_R1, sk_Xx2), sk_Xy2), sk_Xz2)),
0.00/0.29	    inference('simplify_reflect-', [status(thm)], ['68', '45'])).
0.00/0.29	tff('70', plain, sk_Xb = sk_Xa, inference('clc', [status(thm)], ['66', '69'])).
0.00/0.29	tff('71', plain,
0.00/0.29	    (sk_Xa = sk_Xc
0.00/0.29	     | sk_Xa = sk_Xc
0.00/0.29	     | sk_Xa
0.00/0.29	        = app_encode_app(a, a, 
0.00/0.29	            app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy1), sk_Xy2)),
0.00/0.29	    inference('demod', [status(thm)], ['0', '70', '70'])).
0.00/0.29	tff('72', plain,
0.00/0.29	    (sk_Xa
0.00/0.29	      = app_encode_app(a, a, 
0.00/0.29	          app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy1), sk_Xy2)
0.00/0.29	     | sk_Xa = sk_Xc),
0.00/0.29	    inference('simplify', [status(thm)], ['71'])).
0.00/0.29	tff('73', plain, (sk_Xb != sk_Xa | sk_Xa != sk_Xc),
0.00/0.29	    inference('demod', [status(thm)], ['21', '41'])).
0.00/0.29	tff('74', plain, (sk_Xa != sk_Xa | sk_Xa != sk_Xc),
0.00/0.29	    inference('demod', [status(thm)], ['73', '70'])).
0.00/0.29	tff('75', plain, sk_Xa != sk_Xc, inference('simplify', [status(thm)], ['74'])).
0.00/0.29	tff('76', plain,
0.00/0.29	    sk_Xa
0.00/0.29	     = app_encode_app(a, a, 
0.00/0.29	         app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy1), sk_Xy2),
0.00/0.29	    inference('simplify_reflect-', [status(thm)], ['72', '75'])).
0.00/0.29	tff('77', plain,
0.00/0.29	    (sk_Xb = sk_Xc
0.00/0.29	     | sk_Xa = sk_Xc
0.00/0.29	     | sk_Xc
0.00/0.29	        = app_encode_app(a, a, 
0.00/0.29	            app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz1), sk_Xz2)),
0.00/0.29	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.29	tff('78', plain,
0.00/0.29	    (sk_Xa = sk_Xc
0.00/0.29	     | sk_Xa = sk_Xc
0.00/0.29	     | sk_Xc
0.00/0.29	        = app_encode_app(a, a, 
0.00/0.29	            app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz1), sk_Xz2)),
0.00/0.29	    inference('demod', [status(thm)], ['77', '70'])).
0.00/0.29	tff('79', plain,
0.00/0.29	    (sk_Xc
0.00/0.29	      = app_encode_app(a, a, 
0.00/0.29	          app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz1), sk_Xz2)
0.00/0.29	     | sk_Xa = sk_Xc),
0.00/0.29	    inference('simplify', [status(thm)], ['78'])).
0.00/0.29	tff('80', plain,
0.00/0.29	    sk_Xc
0.00/0.29	     = app_encode_app(a, a, 
0.00/0.29	         app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz1), sk_Xz2),
0.00/0.29	    inference('simplify_reflect-', [status(thm)], ['79', '75'])).
0.00/0.29	tff('81', plain,
0.00/0.29	    (sk_Xb = sk_Xc
0.00/0.29	     | sk_Xa = sk_Xc
0.00/0.29	     | sk_Xa
0.00/0.29	        = app_encode_app(a, a, 
0.00/0.29	            app_encode_app(a, app_encode_fun(a, a), cP, sk_Xx1), sk_Xx2)),
0.00/0.29	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.29	tff('82', plain,
0.00/0.29	    ![X0 : a, X1 : a, X2 : a, X3 : a]:
0.00/0.29	      (sk_Xa != sk_Xa
0.00/0.29	       | sk_Xa = sk_Xc
0.00/0.29	       | sk_Xb = sk_Xc
0.00/0.29	       | sk_Xc
0.00/0.29	          != app_encode_app(a, a, 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, a), cP, X1), X0)
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_S, sk_Xx2), X2), X0)
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_S, sk_Xx1), X3), X1)
0.00/0.29	       | sk_Xb
0.00/0.29	          != app_encode_app(a, a, 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, a), cP, X3), X2)),
0.00/0.29	    inference('sup-', [status(thm)], ['81', '6'])).
0.00/0.29	tff('83', plain,
0.00/0.29	    ![X0 : a, X1 : a, X2 : a, X3 : a]:
0.00/0.29	      (sk_Xb
0.00/0.29	        != app_encode_app(a, a, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, a), cP, X3), X2)
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_S, sk_Xx1), X3), X1)
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_S, sk_Xx2), X2), X0)
0.00/0.29	       | sk_Xc
0.00/0.29	          != app_encode_app(a, a, 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, a), cP, X1), X0)
0.00/0.29	       | sk_Xb = sk_Xc
0.00/0.29	       | sk_Xa = sk_Xc),
0.00/0.29	    inference('simplify', [status(thm)], ['82'])).
0.00/0.29	tff('84', plain,
0.00/0.29	    ![X0 : a, X1 : a, X2 : a, X3 : a]:
0.00/0.29	      (sk_Xa
0.00/0.29	        != app_encode_app(a, a, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, a), cP, X3), X2)
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_S, sk_Xx1), X3), X1)
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_S, sk_Xx2), X2), X0)
0.00/0.29	       | sk_Xc
0.00/0.29	          != app_encode_app(a, a, 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, a), cP, X1), X0)
0.00/0.29	       | sk_Xa = sk_Xc
0.00/0.29	       | sk_Xa = sk_Xc),
0.00/0.29	    inference('demod', [status(thm)], ['83', '70', '70'])).
0.00/0.29	tff('85', plain,
0.00/0.29	    ![X0 : a, X1 : a, X2 : a, X3 : a]:
0.00/0.29	      (sk_Xa = sk_Xc
0.00/0.29	       | sk_Xc
0.00/0.29	          != app_encode_app(a, a, 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, a), cP, X1), X0)
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_S, sk_Xx2), X2), X0)
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_S, sk_Xx1), X3), X1)
0.00/0.29	       | sk_Xa
0.00/0.29	          != app_encode_app(a, a, 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, a), cP, X3), X2)),
0.00/0.29	    inference('simplify', [status(thm)], ['84'])).
0.00/0.29	tff('86', plain,
0.00/0.29	    ![X0 : a, X1 : a, X2 : a, X3 : a]:
0.00/0.29	      (sk_Xc
0.00/0.29	        != app_encode_app(a, a, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, a), cP, X1), X0)
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_S, sk_Xx2), X2), X0)
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_S, sk_Xx1), X3), X1)
0.00/0.29	       | sk_Xa
0.00/0.29	          != app_encode_app(a, a, 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, a), cP, X3), X2)),
0.00/0.29	    inference('simplify_reflect-', [status(thm)], ['85', '75'])).
0.00/0.29	tff('87', plain,
0.00/0.29	    ![X0 : a, X1 : a]:
0.00/0.29	      (sk_Xc != sk_Xc
0.00/0.29	       | sk_Xa
0.00/0.29	          != app_encode_app(a, a, 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, a), cP, X1), X0)
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_S, sk_Xx1), X1), sk_Xz1)
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_S, sk_Xx2), X0), sk_Xz2)),
0.00/0.29	    inference('sup-', [status(thm)], ['80', '86'])).
0.00/0.29	tff('88', plain,
0.00/0.29	    ![X0 : a, X1 : a]:
0.00/0.29	      (~ app_encode_app(a, $o, 
0.00/0.29	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	               sk_S, sk_Xx2), X0), sk_Xz2)
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_S, sk_Xx1), X1), sk_Xz1)
0.00/0.29	       | sk_Xa
0.00/0.29	          != app_encode_app(a, a, 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, a), cP, X1), X0)),
0.00/0.29	    inference('simplify', [status(thm)], ['87'])).
0.00/0.29	tff('89', plain,
0.00/0.29	    ![X0 : a, X1 : a]:
0.00/0.29	      (~ $true
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_R1, sk_Xx2), X0), sk_Xz2)
0.00/0.29	       | sk_Xa
0.00/0.29	          != app_encode_app(a, a, 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, a), cP, X1), X0)
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_S, sk_Xx1), X1), sk_Xz1)),
0.00/0.29	    inference('sup-', [status(thm)], ['3', '88'])).
0.00/0.29	tff('90', plain,
0.00/0.29	    ![X0 : a, X1 : a]:
0.00/0.29	      (~ app_encode_app(a, $o, 
0.00/0.29	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	               sk_S, sk_Xx1), X1), sk_Xz1)
0.00/0.29	       | sk_Xa
0.00/0.29	          != app_encode_app(a, a, 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, a), cP, X1), X0)
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_R1, sk_Xx2), X0), sk_Xz2)),
0.00/0.29	    inference('simplify', [status(thm)], ['89'])).
0.00/0.29	tff('91', plain,
0.00/0.29	    ![X0 : a, X1 : a]:
0.00/0.29	      (~ $true
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_R1, sk_Xx1), X0), sk_Xz1)
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_R1, sk_Xx2), X1), sk_Xz2)
0.00/0.29	       | sk_Xa
0.00/0.29	          != app_encode_app(a, a, 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, a), cP, X0), X1)),
0.00/0.29	    inference('sup-', [status(thm)], ['3', '90'])).
0.00/0.29	tff('92', plain,
0.00/0.29	    ![X0 : a, X1 : a]:
0.00/0.29	      (sk_Xa
0.00/0.29	        != app_encode_app(a, a, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, a), cP, X0), X1)
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_R1, sk_Xx2), X1), sk_Xz2)
0.00/0.29	       | ~ app_encode_app(a, $o, 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	                 sk_R1, sk_Xx1), X0), sk_Xz1)),
0.00/0.29	    inference('simplify', [status(thm)], ['91'])).
0.00/0.29	tff('93', plain,
0.00/0.29	    (sk_Xa != sk_Xa
0.00/0.29	     | ~ app_encode_app(a, $o, 
0.00/0.29	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	               sk_R1, sk_Xx1), sk_Xy1), sk_Xz1)
0.00/0.29	     | ~ app_encode_app(a, $o, 
0.00/0.29	           app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	               sk_R1, sk_Xx2), sk_Xy2), sk_Xz2)),
0.00/0.29	    inference('sup-', [status(thm)], ['76', '92'])).
0.00/0.29	tff('94', plain,
0.00/0.29	    (sk_Xb = sk_Xc
0.00/0.29	     | sk_Xa = sk_Xc
0.00/0.29	     | app_encode_app(a, $o, 
0.00/0.29	         app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	             sk_R1, sk_Xx1), sk_Xy1), sk_Xz1)),
0.00/0.29	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.29	tff('95', plain,
0.00/0.29	    (sk_Xa = sk_Xc
0.00/0.29	     | sk_Xa = sk_Xc
0.00/0.29	     | app_encode_app(a, $o, 
0.00/0.29	         app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	             sk_R1, sk_Xx1), sk_Xy1), sk_Xz1)),
0.00/0.29	    inference('demod', [status(thm)], ['94', '70'])).
0.00/0.29	tff('96', plain,
0.00/0.29	    (app_encode_app(a, $o, 
0.00/0.29	       app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R1, 
0.00/0.29	           sk_Xx1), sk_Xy1), sk_Xz1)
0.00/0.29	     | sk_Xa = sk_Xc),
0.00/0.29	    inference('simplify', [status(thm)], ['95'])).
0.00/0.29	tff('97', plain,
0.00/0.29	    app_encode_app(a, $o, 
0.00/0.29	      app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	        app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R1, 
0.00/0.29	          sk_Xx1), sk_Xy1), sk_Xz1),
0.00/0.29	    inference('simplify_reflect-', [status(thm)], ['96', '75'])).
0.00/0.29	tff('98', plain,
0.00/0.29	    (sk_Xb = sk_Xc
0.00/0.29	     | sk_Xa = sk_Xc
0.00/0.29	     | app_encode_app(a, $o, 
0.00/0.29	         app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	             sk_R1, sk_Xx2), sk_Xy2), sk_Xz2)),
0.00/0.29	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.29	tff('99', plain,
0.00/0.29	    (sk_Xa = sk_Xc
0.00/0.29	     | sk_Xa = sk_Xc
0.00/0.29	     | app_encode_app(a, $o, 
0.00/0.29	         app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
0.00/0.29	             sk_R1, sk_Xx2), sk_Xy2), sk_Xz2)),
0.00/0.29	    inference('demod', [status(thm)], ['98', '70'])).
0.00/0.29	tff('100', plain,
0.00/0.29	    (app_encode_app(a, $o, 
0.00/0.29	       app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R1, 
0.00/0.29	           sk_Xx2), sk_Xy2), sk_Xz2)
0.00/0.29	     | sk_Xa = sk_Xc),
0.00/0.29	    inference('simplify', [status(thm)], ['99'])).
0.00/0.29	tff('101', plain,
0.00/0.29	    app_encode_app(a, $o, 
0.00/0.29	      app_encode_app(a, app_encode_fun(a, $o), 
0.00/0.29	        app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R1, 
0.00/0.29	          sk_Xx2), sk_Xy2), sk_Xz2),
0.00/0.29	    inference('simplify_reflect-', [status(thm)], ['100', '75'])).
0.00/0.29	tff('102', plain, (sk_Xa != sk_Xa | ~ $true | ~ $true),
0.00/0.29	    inference('demod', [status(thm)], ['93', '97', '101'])).
0.00/0.29	tff('103', plain, $false, inference('simplify', [status(thm)], ['102'])).
0.00/0.29	
0.00/0.29	% SZS output end Refutation
0.00/0.29	EOF
