0.00/0.01	% File    : /export/starexec/sandbox/benchmark/theBenchmark.p
0.00/0.01	% app-encoded or not : app
0.00/0.01	% Variant    : fo
0.00/0.01	% Ordering    : kbo
0.00/0.01	% Command    : 
0.00/0.01	#!/bin/sh
0.00/0.01	
0.00/0.01	./zipperposition.native ${1:+"$1"} \
0.00/0.01	  -i tptp \
0.00/0.01	  -o tptp \
0.00/0.01	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.01	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.01	  --no-ho \
0.00/0.01	  --no-avatar \
0.00/0.01	  --no-induction \
0.00/0.01	  --no-unif-pattern \
0.00/0.01	  --ord $2 \
0.00/0.01	  --simultaneous-sup false \
0.00/0.01	  --no-max-vars \
0.00/0.01	  --no-fool
0.00/0.20	% Computer   : n074.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 14:06:09 CST 2018
33.50/33.65	% done 1580 iterations in 33.440s
33.50/33.65	% SZS status Theorem for 'stdin'
33.50/33.65	% SZS output start Refutation
33.50/33.65	tff(zf_stmt_48, axiom,
33.50/33.65	  (![Ba:arrow_411405190le_alt,Aa:arrow_411405190le_alt]:
33.50/33.65	     ((Aa != Ba) =>
33.50/33.65	      (?[X1:fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),
33.50/33.65	                bool)]:
33.50/33.65	         (app_encode_app(fun(fun(product_prod(arrow_411405190le_alt,
33.50/33.65	                                              arrow_411405190le_alt),
33.50/33.65	                                 bool),
33.50/33.65	                             bool),
33.50/33.65	                         $o,
33.50/33.65	                         app_encode_app(fun(product_prod(arrow_411405190le_alt,
33.50/33.65	                                                         arrow_411405190le_alt),
33.50/33.65	                                            bool),
33.50/33.65	                                        app_encode_fun(fun(fun(product_prod(
33.50/33.65	                                                               arrow_411405190le_alt,
33.50/33.65	                                                               arrow_411405190le_alt),
33.50/33.65	                                                               bool),
33.50/33.65	                                                           bool),
33.50/33.65	                                                       $o),
33.50/33.65	                                        member(fun(product_prod(arrow_411405190le_alt,
33.50/33.65	                                                                arrow_411405190le_alt),
33.50/33.65	                                                   bool)),
33.50/33.65	                                        X1),
33.50/33.65	                         arrow_1985332922le_Lin) & 
33.50/33.65	          app_encode_app(fun(product_prod(arrow_411405190le_alt,
33.50/33.65	                                          arrow_411405190le_alt),
33.50/33.65	                             bool),
33.50/33.65	                         $o,
33.50/33.65	                         app_encode_app(product_prod(arrow_411405190le_alt,
33.50/33.65	                                                     arrow_411405190le_alt),
33.50/33.65	                                        app_encode_fun(fun(product_prod(
33.50/33.65	                                                           arrow_411405190le_alt,
33.50/33.65	                                                           arrow_411405190le_alt),
33.50/33.65	                                                           bool),
33.50/33.65	                                                       $o),
33.50/33.65	                                        member(product_prod(arrow_411405190le_alt,
33.50/33.65	                                                            arrow_411405190le_alt)),
33.50/33.65	                                        app_encode_app(arrow_411405190le_alt,
33.50/33.65	                                                       product_prod(arrow_411405190le_alt,
33.50/33.65	                                                                    arrow_411405190le_alt),
33.50/33.65	                                                       app_encode_app(
33.50/33.65	                                                       fun(arrow_411405190le_alt,
33.50/33.65	                                                           product_prod(
33.50/33.65	                                                           arrow_411405190le_alt,
33.50/33.65	                                                           arrow_411405190le_alt)),
33.50/33.65	                                                       app_encode_fun(
33.50/33.65	                                                       arrow_411405190le_alt,
33.50/33.65	                                                       product_prod(arrow_411405190le_alt,
33.50/33.65	                                                                    arrow_411405190le_alt)),
33.50/33.65	                                                       aa(arrow_411405190le_alt,
33.50/33.65	                                                          product_prod(
33.50/33.65	                                                          arrow_411405190le_alt,
33.50/33.65	                                                          arrow_411405190le_alt)),
33.50/33.65	                                                       app_encode_app(
33.50/33.65	                                                       arrow_411405190le_alt,
33.50/33.65	                                                       fun(arrow_411405190le_alt,
33.50/33.65	                                                           product_prod(
33.50/33.65	                                                           arrow_411405190le_alt,
33.50/33.65	                                                           arrow_411405190le_alt)),
33.50/33.65	                                                       app_encode_app(
33.50/33.65	                                                       fun(arrow_411405190le_alt,
33.50/33.65	                                                           fun(arrow_411405190le_alt,
33.50/33.65	                                                               product_prod(
33.50/33.65	                                                               arrow_411405190le_alt,
33.50/33.65	                                                               arrow_411405190le_alt))),
33.50/33.65	                                                       app_encode_fun(
33.50/33.65	                                                       arrow_411405190le_alt,
33.50/33.65	                                                       fun(arrow_411405190le_alt,
33.50/33.65	                                                           product_prod(
33.50/33.65	                                                           arrow_411405190le_alt,
33.50/33.65	                                                           arrow_411405190le_alt))),
33.50/33.65	                                                       aa(arrow_411405190le_alt,
33.50/33.65	                                                          fun(arrow_411405190le_alt,
33.50/33.65	                                                              product_prod(
33.50/33.65	                                                              arrow_411405190le_alt,
33.50/33.65	                                                              arrow_411405190le_alt))),
33.50/33.65	                                                       product_Pair(arrow_411405190le_alt,
33.50/33.65	                                                                    arrow_411405190le_alt)),
33.50/33.65	                                                       Aa)),Ba)),
33.50/33.65	                         X1)))))).
33.50/33.65	tff('0', plain,
33.50/33.65	    ![X6 : arrow_411405190le_alt, X7 : arrow_411405190le_alt]:
33.50/33.65	      (app_encode_app(
33.50/33.65	         fun(
33.50/33.65	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
33.50/33.65	             bool), bool), $o, 
33.50/33.65	         app_encode_app(
33.50/33.65	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
33.50/33.65	             bool), 
33.50/33.65	           app_encode_fun(
33.50/33.65	             fun(
33.50/33.65	               fun(
33.50/33.65	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
33.50/33.65	                 bool), bool), $o), 
33.50/33.65	           member(
33.50/33.65	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
33.50/33.65	               bool)), sk_X1(X6, X7)), arrow_1985332922le_Lin)
33.50/33.65	       | X6 = X7),
33.50/33.65	    inference('cnf', [status(esa)], [zf_stmt_48])).
33.50/33.65	tff(zf_stmt_63, axiom,
33.50/33.65	  (![A:$tType,B:$tType,Y:product_prod(A,B)]:
33.50/33.65	     (~
33.50/33.65	       (![A2:A,B2:B]:
33.50/33.65	          (Y !=
33.50/33.65	           app_encode_app(B,product_prod(A,B),
33.50/33.65	                          app_encode_app(fun(B,product_prod(A,B)),
33.50/33.65	                                         app_encode_fun(B,product_prod(A,B)),
33.50/33.65	                                         aa(B,product_prod(A,B)),
33.50/33.65	                                         app_encode_app(A,
33.50/33.65	                                                        fun(B,
33.50/33.65	                                                            product_prod(A,B)),
33.50/33.65	                                                        app_encode_app(
33.50/33.65	                                                        fun(A,
33.50/33.65	                                                            fun(B,
33.50/33.65	                                                                product_prod(
33.50/33.65	                                                                A,B))),
33.50/33.65	                                                        app_encode_fun(
33.50/33.65	                                                        A,
33.50/33.65	                                                        fun(B,
33.50/33.65	                                                            product_prod(A,B))),
33.50/33.65	                                                        aa(A,
33.50/33.65	                                                           fun(B,
33.50/33.65	                                                               product_prod(
33.50/33.65	                                                               A,B))),
33.50/33.65	                                                        product_Pair(A,B)),A2)),
33.50/33.65	                          B2)))))).
33.50/33.65	tff('1', plain,
33.50/33.65	    ![X81 : $tType, X82 : $tType, X83 : product_prod(X82, X81)]:
33.50/33.65	      X83
33.50/33.65	       = app_encode_app(X81, product_prod(X82, X81), 
33.50/33.65	           app_encode_app(fun(X81, product_prod(X82, X81)), 
33.50/33.65	             app_encode_fun(X81, product_prod(X82, X81)), 
33.50/33.65	             aa(X81, product_prod(X82, X81)), 
33.50/33.65	             app_encode_app(X82, fun(X81, product_prod(X82, X81)), 
33.50/33.65	               app_encode_app(fun(X82, fun(X81, product_prod(X82, X81))), 
33.50/33.65	                 app_encode_fun(X82, fun(X81, product_prod(X82, X81))), 
33.50/33.65	                 aa(X82, fun(X81, product_prod(X82, X81))), 
33.50/33.65	                 product_Pair(X82, X81)), sk_A2(X81, X82, X83))), 
33.50/33.65	           sk_B2(X81, X82, X83)),
33.50/33.65	    inference('cnf', [status(esa)], [zf_stmt_63])).
33.50/33.65	tff('2', plain,
33.50/33.65	    ![X6 : arrow_411405190le_alt, X7 : arrow_411405190le_alt]:
33.50/33.65	      (app_encode_app(
33.50/33.65	         fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
33.50/33.65	           bool), $o, 
33.50/33.65	         app_encode_app(
33.50/33.65	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
33.50/33.65	           app_encode_fun(
33.50/33.65	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
33.50/33.65	               bool), $o), 
33.50/33.65	           member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
33.50/33.65	           app_encode_app(arrow_411405190le_alt, 
33.50/33.65	             product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
33.50/33.65	             app_encode_app(
33.50/33.65	               fun(arrow_411405190le_alt, 
33.50/33.65	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
33.50/33.65	               app_encode_fun(arrow_411405190le_alt, 
33.50/33.65	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
33.50/33.65	               aa(arrow_411405190le_alt, 
33.50/33.65	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
33.50/33.65	               app_encode_app(arrow_411405190le_alt, 
33.50/33.65	                 fun(arrow_411405190le_alt, 
33.50/33.65	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
33.50/33.65	                 app_encode_app(
33.50/33.65	                   fun(arrow_411405190le_alt, 
33.50/33.65	                     fun(arrow_411405190le_alt, 
33.50/33.65	                       product_prod(arrow_411405190le_alt, 
33.50/33.65	                         arrow_411405190le_alt))), 
33.50/33.65	                   app_encode_fun(arrow_411405190le_alt, 
33.50/33.65	                     fun(arrow_411405190le_alt, 
33.50/33.65	                       product_prod(arrow_411405190le_alt, 
33.50/33.65	                         arrow_411405190le_alt))), 
33.50/33.65	                   aa(arrow_411405190le_alt, 
33.50/33.65	                     fun(arrow_411405190le_alt, 
33.50/33.65	                       product_prod(arrow_411405190le_alt, 
33.50/33.65	                         arrow_411405190le_alt))), 
33.50/33.65	                   product_Pair(arrow_411405190le_alt, arrow_411405190le_alt)), 
33.50/33.65	                 X6)), X7)), sk_X1(X6, X7))
33.50/33.65	       | X6 = X7),
33.50/33.65	    inference('cnf', [status(esa)], [zf_stmt_48])).
33.50/33.65	tff('3', plain,
33.50/33.65	    ![X0 : product_prod(arrow_411405190le_alt, arrow_411405190le_alt)]:
33.50/33.65	      (app_encode_app(
33.50/33.65	         fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
33.50/33.65	           bool), $o, 
33.50/33.65	         app_encode_app(
33.50/33.65	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
33.50/33.65	           app_encode_fun(
33.50/33.65	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
33.50/33.65	               bool), $o), 
33.50/33.65	           member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
33.50/33.65	           X0), 
33.50/33.65	         sk_X1(sk_A2(arrow_411405190le_alt, arrow_411405190le_alt, X0), 
33.50/33.65	           sk_B2(arrow_411405190le_alt, arrow_411405190le_alt, X0)))
33.50/33.65	       | sk_A2(arrow_411405190le_alt, arrow_411405190le_alt, X0)
33.50/33.65	          = sk_B2(arrow_411405190le_alt, arrow_411405190le_alt, X0)),
33.50/33.65	    inference('sup+', [status(thm)], ['1', '2'])).
33.50/33.65	tff(zf_stmt_162, axiom,
33.50/33.65	  (![Lab:fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)]:
33.50/33.65	     (app_encode_app(fun(product_prod(arrow_411405190le_alt,
33.50/33.65	                                      arrow_411405190le_alt),
33.50/33.65	                         bool),
33.50/33.65	                     $o,
33.50/33.65	                     app_encode_app(product_prod(arrow_411405190le_alt,
33.50/33.65	                                                 arrow_411405190le_alt),
33.50/33.65	                                    app_encode_fun(fun(product_prod(arrow_411405190le_alt,
33.50/33.65	                                                                    arrow_411405190le_alt),
33.50/33.65	                                                       bool),
33.50/33.65	                                                   $o),
33.50/33.65	                                    member(product_prod(arrow_411405190le_alt,
33.50/33.65	                                                        arrow_411405190le_alt)),
33.50/33.65	                                    app_encode_app(arrow_411405190le_alt,
33.50/33.65	                                                   product_prod(arrow_411405190le_alt,
33.50/33.65	                                                                arrow_411405190le_alt),
33.50/33.65	                                                   app_encode_app(fun(
33.50/33.65	                                                                  arrow_411405190le_alt,
33.50/33.65	                                                                  product_prod(
33.50/33.65	                                                                  arrow_411405190le_alt,
33.50/33.65	                                                                  arrow_411405190le_alt)),
33.50/33.65	                                                                  app_encode_fun(
33.50/33.65	                                                                  arrow_411405190le_alt,
33.50/33.65	                                                                  product_prod(
33.50/33.65	                                                                  arrow_411405190le_alt,
33.50/33.65	                                                                  arrow_411405190le_alt)),
33.50/33.65	                                                                  aa(
33.50/33.65	                                                                  arrow_411405190le_alt,
33.50/33.65	                                                                  product_prod(
33.50/33.65	                                                                  arrow_411405190le_alt,
33.50/33.65	                                                                  arrow_411405190le_alt)),
33.50/33.65	                                                                  app_encode_app(
33.50/33.65	                                                                  arrow_411405190le_alt,
33.50/33.65	                                                                  fun(
33.50/33.65	                                                                  arrow_411405190le_alt,
33.50/33.65	                                                                  product_prod(
33.50/33.65	                                                                  arrow_411405190le_alt,
33.50/33.65	                                                                  arrow_411405190le_alt)),
33.50/33.65	                                                                  app_encode_app(
33.50/33.65	                                                                  fun(
33.50/33.65	                                                                  arrow_411405190le_alt,
33.50/33.65	                                                                  fun(
33.50/33.65	                                                                  arrow_411405190le_alt,
33.50/33.65	                                                                  product_prod(
33.50/33.65	                                                                  arrow_411405190le_alt,
33.50/33.65	                                                                  arrow_411405190le_alt))),
33.50/33.65	                                                                  app_encode_fun(
33.50/33.65	                                                                  arrow_411405190le_alt,
33.50/33.65	                                                                  fun(
33.50/33.65	                                                                  arrow_411405190le_alt,
33.50/33.65	                                                                  product_prod(
33.50/33.65	                                                                  arrow_411405190le_alt,
33.50/33.65	                                                                  arrow_411405190le_alt))),
33.50/33.65	                                                                  aa(
33.50/33.65	                                                                  arrow_411405190le_alt,
33.50/33.65	                                                                  fun(
33.50/33.65	                                                                  arrow_411405190le_alt,
33.50/33.65	                                                                  product_prod(
33.50/33.65	                                                                  arrow_411405190le_alt,
33.50/33.65	                                                                  arrow_411405190le_alt))),
33.50/33.65	                                                                  product_Pair(
33.50/33.65	                                                                  arrow_411405190le_alt,
33.50/33.65	                                                                  arrow_411405190le_alt)),
33.50/33.65	                                                                  a)),
33.50/33.65	                                                   b)),
33.50/33.65	                     Lab) =>
33.50/33.65	      (app_encode_app(fun(fun(product_prod(arrow_411405190le_alt,
33.50/33.65	                                           arrow_411405190le_alt),
33.50/33.65	                              bool),
33.50/33.65	                          bool),
33.50/33.65	                      $o,
33.50/33.65	                      app_encode_app(fun(product_prod(arrow_411405190le_alt,
33.50/33.65	                                                      arrow_411405190le_alt),
33.50/33.65	                                         bool),
33.50/33.65	                                     app_encode_fun(fun(fun(product_prod(
33.50/33.65	                                                            arrow_411405190le_alt,
33.50/33.65	                                                            arrow_411405190le_alt),
33.50/33.65	                                                            bool),
33.50/33.65	                                                        bool),
33.50/33.65	                                                    $o),
33.50/33.65	                                     member(fun(product_prod(arrow_411405190le_alt,
33.50/33.65	                                                             arrow_411405190le_alt),
33.50/33.65	                                                bool)),
33.50/33.65	                                     Lab),
33.50/33.65	                      arrow_1985332922le_Lin) =>
33.50/33.65	       thesis)))).
33.50/33.65	tff('4', plain,
33.50/33.65	    ![X566 : fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
33.50/33.65	               bool)]:
33.50/33.65	      (thesis
33.50/33.65	       | ~ app_encode_app(
33.50/33.65	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
33.50/33.65	               bool), $o, 
33.50/33.65	             app_encode_app(
33.50/33.65	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
33.50/33.65	               app_encode_fun(
33.50/33.65	                 fun(
33.50/33.65	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
33.50/33.65	                   bool), $o), 
33.50/33.65	               member(
33.50/33.65	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
33.50/33.65	               app_encode_app(arrow_411405190le_alt, 
33.50/33.65	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
33.50/33.65	                 app_encode_app(
33.50/33.65	                   fun(arrow_411405190le_alt, 
33.50/33.65	                     product_prod(arrow_411405190le_alt, 
33.50/33.65	                       arrow_411405190le_alt)), 
33.50/33.65	                   app_encode_fun(arrow_411405190le_alt, 
33.50/33.65	                     product_prod(arrow_411405190le_alt, 
33.50/33.65	                       arrow_411405190le_alt)), 
33.50/33.65	                   aa(arrow_411405190le_alt, 
33.50/33.65	                     product_prod(arrow_411405190le_alt, 
33.50/33.65	                       arrow_411405190le_alt)), 
33.50/33.65	                   app_encode_app(arrow_411405190le_alt, 
33.50/33.65	                     fun(arrow_411405190le_alt, 
33.50/33.65	                       product_prod(arrow_411405190le_alt, 
33.50/33.65	                         arrow_411405190le_alt)), 
33.50/33.65	                     app_encode_app(
33.50/33.65	                       fun(arrow_411405190le_alt, 
33.50/33.65	                         fun(arrow_411405190le_alt, 
33.50/33.65	                           product_prod(arrow_411405190le_alt, 
33.50/33.65	                             arrow_411405190le_alt))), 
33.50/33.65	                       app_encode_fun(arrow_411405190le_alt, 
33.50/33.65	                         fun(arrow_411405190le_alt, 
33.50/33.65	                           product_prod(arrow_411405190le_alt, 
33.50/33.65	                             arrow_411405190le_alt))), 
33.50/33.65	                       aa(arrow_411405190le_alt, 
33.50/33.65	                         fun(arrow_411405190le_alt, 
33.50/33.65	                           product_prod(arrow_411405190le_alt, 
33.50/33.65	                             arrow_411405190le_alt))), 
33.50/33.65	                       product_Pair(arrow_411405190le_alt, 
33.50/33.65	                         arrow_411405190le_alt)), a)), b)), X566)
33.50/33.65	       | ~ app_encode_app(
33.50/33.65	             fun(
33.50/33.65	               fun(
33.50/33.65	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
33.50/33.65	                 bool), bool), $o, 
33.50/33.65	             app_encode_app(
33.50/33.65	               fun(
33.50/33.65	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
33.50/33.65	                 bool), 
33.50/33.65	               app_encode_fun(
33.50/33.65	                 fun(
33.50/33.65	                   fun(
33.50/33.65	                     product_prod(arrow_411405190le_alt, 
33.50/33.65	                       arrow_411405190le_alt), bool), bool), $o), 
33.50/33.65	               member(
33.50/33.65	                 fun(
33.50/33.65	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
33.50/33.65	                   bool)), X566), arrow_1985332922le_Lin)),
33.50/33.65	    inference('cnf', [status(esa)], [zf_stmt_162])).
33.50/33.65	tff(zf_stmt_150, axiom,
33.50/33.65	  (![A:$tType,C:$tType,B:$tType,R:A,Q:B,P:fun(A,fun(B,C))]:
33.50/33.65	     (app_encode_app(A,C,
33.50/33.65	                     app_encode_app(fun(A,C),app_encode_fun(A,C),aa(A,C),
33.50/33.65	                                    app_encode_app(B,fun(A,C),
33.50/33.65	                                                   app_encode_app(fun(
33.50/33.65	                                                                  A,fun(B,C)),
33.50/33.65	                                                                  app_encode_fun(
33.50/33.65	                                                                  B,fun(A,C)),
33.50/33.65	                                                                  combc(
33.50/33.65	                                                                  A,B,C),P),
33.50/33.65	                                                   Q)),
33.50/33.65	                     R) =
33.50/33.65	      app_encode_app(B,C,
33.50/33.65	                     app_encode_app(fun(B,C),app_encode_fun(B,C),aa(B,C),
33.50/33.65	                                    app_encode_app(A,fun(B,C),
33.50/33.65	                                                   app_encode_app(fun(
33.50/33.65	                                                                  A,fun(B,C)),
33.50/33.65	                                                                  app_encode_fun(
33.50/33.65	                                                                  A,fun(B,C)),
33.50/33.65	                                                                  aa(
33.50/33.65	                                                                  A,fun(B,C)),
33.50/33.65	                                                                  P),
33.50/33.65	                                                   R)),
33.50/33.65	                     Q)))).
33.50/33.65	tff('5', plain,
33.50/33.65	    ![X530 : $tType, X531 : $tType, X532 : $tType, 
33.50/33.65	      X533 : fun(X532, fun(X530, X531)), X534 : X532, X535 : X530]:
33.50/33.65	      app_encode_app(X532, X531, 
33.50/33.65	        app_encode_app(fun(X532, X531), app_encode_fun(X532, X531), 
33.50/33.65	          aa(X532, X531), 
33.50/33.65	          app_encode_app(X530, fun(X532, X531), 
33.50/33.65	            app_encode_app(fun(X532, fun(X530, X531)), 
33.50/33.65	              app_encode_fun(X530, fun(X532, X531)), 
33.50/33.65	              combc(X532, X530, X531), X533), X535)), X534)
33.50/33.65	       = app_encode_app(X530, X531, 
33.50/33.65	           app_encode_app(fun(X530, X531), app_encode_fun(X530, X531), 
33.50/33.65	             aa(X530, X531), 
33.50/33.65	             app_encode_app(X532, fun(X530, X531), 
33.50/33.65	               app_encode_app(fun(X532, fun(X530, X531)), 
33.50/33.65	                 app_encode_fun(X532, fun(X530, X531)), 
33.50/33.65	                 aa(X532, fun(X530, X531)), X533), X534)), X535),
33.50/33.65	    inference('cnf', [status(esa)], [zf_stmt_150])).
33.50/33.65	tff('6', plain,
33.50/33.65	    ![X566 : fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
33.50/33.65	               bool)]:
33.50/33.65	      (thesis
33.50/33.65	       | ~ app_encode_app(
33.50/33.65	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
33.50/33.65	               bool), $o, 
33.50/33.65	             app_encode_app(
33.50/33.65	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
33.50/33.65	               app_encode_fun(
33.50/33.65	                 fun(
33.50/33.65	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
33.50/33.65	                   bool), $o), 
33.50/33.65	               member(
33.50/33.65	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
33.50/33.65	               app_encode_app(arrow_411405190le_alt, 
33.50/33.65	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
33.50/33.65	                 app_encode_app(
33.50/33.65	                   fun(arrow_411405190le_alt, 
33.50/33.65	                     product_prod(arrow_411405190le_alt, 
33.50/33.65	                       arrow_411405190le_alt)), 
33.50/33.65	                   app_encode_fun(arrow_411405190le_alt, 
33.50/33.65	                     product_prod(arrow_411405190le_alt, 
33.50/33.65	                       arrow_411405190le_alt)), 
33.50/33.65	                   aa(arrow_411405190le_alt, 
33.50/33.65	                     product_prod(arrow_411405190le_alt, 
33.50/33.65	                       arrow_411405190le_alt)), 
33.50/33.65	                   app_encode_app(arrow_411405190le_alt, 
33.50/33.65	                     fun(arrow_411405190le_alt, 
33.50/33.65	                       product_prod(arrow_411405190le_alt, 
33.50/33.65	                         arrow_411405190le_alt)), 
33.50/33.65	                     app_encode_app(
33.50/33.65	                       fun(arrow_411405190le_alt, 
33.50/33.65	                         fun(arrow_411405190le_alt, 
33.50/33.65	                           product_prod(arrow_411405190le_alt, 
33.50/33.65	                             arrow_411405190le_alt))), 
33.50/33.65	                       app_encode_fun(arrow_411405190le_alt, 
33.50/33.65	                         fun(arrow_411405190le_alt, 
33.50/33.65	                           product_prod(arrow_411405190le_alt, 
33.50/33.65	                             arrow_411405190le_alt))), 
33.50/33.65	                       combc(arrow_411405190le_alt, arrow_411405190le_alt, 
33.50/33.65	                         product_prod(arrow_411405190le_alt, 
33.50/33.65	                           arrow_411405190le_alt)), 
33.50/33.65	                       product_Pair(arrow_411405190le_alt, 
33.50/33.65	                         arrow_411405190le_alt)), b)), a)), X566)
33.50/33.65	       | ~ app_encode_app(
33.50/33.65	             fun(
33.50/33.65	               fun(
33.50/33.65	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
33.50/33.65	                 bool), bool), $o, 
33.50/33.65	             app_encode_app(
33.50/33.65	               fun(
33.50/33.65	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
33.50/33.65	                 bool), 
33.50/33.65	               app_encode_fun(
33.50/33.65	                 fun(
33.50/33.65	                   fun(
33.50/33.65	                     product_prod(arrow_411405190le_alt, 
33.50/33.65	                       arrow_411405190le_alt), bool), bool), $o), 
33.50/33.65	               member(
33.50/33.65	                 fun(
33.50/33.65	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
33.50/33.65	                   bool)), X566), arrow_1985332922le_Lin)),
33.50/33.65	    inference('demod', [status(thm)], ['4', '5'])).
33.50/33.65	tff(zf_stmt_163, conjecture, (thesis)).
33.50/33.65	tff(zf_stmt_0, negated_conjecture, (~thesis)).
33.50/33.65	tff('7', plain, ~ thesis, inference('cnf', [status(esa)], [zf_stmt_0])).
33.50/33.65	tff('8', plain,
33.50/33.65	    ![X566 : fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
33.50/33.65	               bool)]:
33.50/33.65	      (~ app_encode_app(
33.50/33.65	           fun(
33.50/33.65	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
33.50/33.65	               bool), bool), $o, 
33.50/33.65	           app_encode_app(
33.50/33.65	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
33.50/33.65	               bool), 
33.50/33.65	             app_encode_fun(
33.50/33.65	               fun(
33.50/33.65	                 fun(
33.50/33.65	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
33.50/33.65	                   bool), bool), $o), 
33.50/33.65	             member(
33.50/33.65	               fun(
33.50/33.65	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
33.50/33.65	                 bool)), X566), arrow_1985332922le_Lin)
33.50/33.65	       | ~ app_encode_app(
33.50/33.65	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
33.50/33.65	               bool), $o, 
33.50/33.65	             app_encode_app(
33.50/33.65	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
33.50/33.65	               app_encode_fun(
33.50/33.65	                 fun(
33.50/33.65	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
33.50/33.65	                   bool), $o), 
33.50/33.65	               member(
33.50/33.65	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
33.50/33.65	               app_encode_app(arrow_411405190le_alt, 
33.50/33.65	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
33.50/33.65	                 app_encode_app(
33.50/33.65	                   fun(arrow_411405190le_alt, 
33.50/33.65	                     product_prod(arrow_411405190le_alt, 
33.50/33.65	                       arrow_411405190le_alt)), 
33.50/33.65	                   app_encode_fun(arrow_411405190le_alt, 
33.50/33.65	                     product_prod(arrow_411405190le_alt, 
33.50/33.65	                       arrow_411405190le_alt)), 
33.50/33.65	                   aa(arrow_411405190le_alt, 
33.50/33.65	                     product_prod(arrow_411405190le_alt, 
33.50/33.65	                       arrow_411405190le_alt)), 
33.50/33.65	                   app_encode_app(arrow_411405190le_alt, 
33.50/33.65	                     fun(arrow_411405190le_alt, 
33.50/33.65	                       product_prod(arrow_411405190le_alt, 
33.50/33.65	                         arrow_411405190le_alt)), 
33.50/33.65	                     app_encode_app(
33.50/33.65	                       fun(arrow_411405190le_alt, 
33.50/33.65	                         fun(arrow_411405190le_alt, 
33.50/33.65	                           product_prod(arrow_411405190le_alt, 
33.50/33.65	                             arrow_411405190le_alt))), 
33.50/33.65	                       app_encode_fun(arrow_411405190le_alt, 
33.50/33.65	                         fun(arrow_411405190le_alt, 
33.50/33.65	                           product_prod(arrow_411405190le_alt, 
33.50/33.65	                             arrow_411405190le_alt))), 
33.50/33.65	                       combc(arrow_411405190le_alt, arrow_411405190le_alt, 
33.50/33.65	                         product_prod(arrow_411405190le_alt, 
33.50/33.65	                           arrow_411405190le_alt)), 
33.50/33.65	                       product_Pair(arrow_411405190le_alt, 
33.50/33.65	                         arrow_411405190le_alt)), b)), a)), X566)),
33.50/33.65	    inference('clc', [status(thm)], ['6', '7'])).
33.50/33.65	tff('9', plain,
33.50/33.65	    (~ $true
33.50/33.65	     | sk_A2(arrow_411405190le_alt, arrow_411405190le_alt, 
33.50/33.65	         app_encode_app(arrow_411405190le_alt, 
33.50/33.65	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
33.50/33.65	           app_encode_app(
33.50/33.65	             fun(arrow_411405190le_alt, 
33.50/33.65	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
33.50/33.65	             app_encode_fun(arrow_411405190le_alt, 
33.50/33.65	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
33.50/33.65	             aa(arrow_411405190le_alt, 
33.50/33.65	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
33.50/33.65	             app_encode_app(arrow_411405190le_alt, 
33.50/33.65	               fun(arrow_411405190le_alt, 
33.50/33.65	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
33.50/33.65	               app_encode_app(
33.50/33.65	                 fun(arrow_411405190le_alt, 
33.50/33.65	                   fun(arrow_411405190le_alt, 
33.50/33.65	                     product_prod(arrow_411405190le_alt, 
33.50/33.65	                       arrow_411405190le_alt))), 
33.50/33.65	                 app_encode_fun(arrow_411405190le_alt, 
33.50/33.65	                   fun(arrow_411405190le_alt, 
33.50/33.65	                     product_prod(arrow_411405190le_alt, 
33.50/33.65	                       arrow_411405190le_alt))), 
33.50/33.65	                 combc(arrow_411405190le_alt, arrow_411405190le_alt, 
33.50/33.65	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
33.50/33.65	                 product_Pair(arrow_411405190le_alt, arrow_411405190le_alt)), 
33.50/33.65	               b)), a))
33.50/33.65	        = sk_B2(arrow_411405190le_alt, arrow_411405190le_alt, 
33.50/33.65	            app_encode_app(arrow_411405190le_alt, 
33.50/33.65	              product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
33.50/33.65	              app_encode_app(
33.50/33.65	                fun(arrow_411405190le_alt, 
33.50/33.65	                  product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
33.50/33.65	                app_encode_fun(arrow_411405190le_alt, 
33.50/33.65	                  product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
33.50/33.65	                aa(arrow_411405190le_alt, 
33.50/33.65	                  product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
33.50/33.65	                app_encode_app(arrow_411405190le_alt, 
33.50/33.65	                  fun(arrow_411405190le_alt, 
33.50/33.65	                    product_prod(arrow_411405190le_alt, 
33.50/33.65	                      arrow_411405190le_alt)), 
33.50/33.65	                  app_encode_app(
33.50/33.65	                    fun(arrow_411405190le_alt, 
33.50/33.65	                      fun(arrow_411405190le_alt, 
33.50/33.65	                        product_prod(arrow_411405190le_alt, 
33.50/33.65	                          arrow_411405190le_alt))), 
33.50/33.65	                    app_encode_fun(arrow_411405190le_alt, 
33.50/33.65	                      fun(arrow_411405190le_alt, 
33.50/33.65	                        product_prod(arrow_411405190le_alt, 
33.50/33.65	                          arrow_411405190le_alt))), 
33.50/33.65	                    combc(arrow_411405190le_alt, arrow_411405190le_alt, 
33.50/33.65	                      product_prod(arrow_411405190le_alt, 
33.50/33.65	                        arrow_411405190le_alt)), 
33.50/33.65	                    product_Pair(arrow_411405190le_alt, 
33.50/33.65	                      arrow_411405190le_alt)), b)), a))
33.50/33.65	     | ~ app_encode_app(
33.50/33.65	           fun(
33.50/33.65	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
33.50/33.65	               bool), bool), $o, 
33.50/33.65	           app_encode_app(
33.50/33.65	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
33.50/33.65	               bool), 
33.50/33.65	             app_encode_fun(
33.50/33.65	               fun(
33.50/33.65	                 fun(
33.50/33.65	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
33.50/33.65	                   bool), bool), $o), 
33.50/33.65	             member(
33.50/33.65	               fun(
33.50/33.65	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
33.50/33.65	                 bool)), 
33.50/33.65	             sk_X1(
33.50/33.65	               sk_A2(arrow_411405190le_alt, arrow_411405190le_alt, 
33.50/33.65	                 app_encode_app(arrow_411405190le_alt, 
33.50/33.65	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
33.50/33.65	                   app_encode_app(
33.50/33.65	                     fun(arrow_411405190le_alt, 
33.50/33.65	                       product_prod(arrow_411405190le_alt, 
33.50/33.65	                         arrow_411405190le_alt)), 
33.50/33.65	                     app_encode_fun(arrow_411405190le_alt, 
33.50/33.65	                       product_prod(arrow_411405190le_alt, 
33.50/33.65	                         arrow_411405190le_alt)), 
33.50/33.65	                     aa(arrow_411405190le_alt, 
33.50/33.65	                       product_prod(arrow_411405190le_alt, 
33.50/33.65	                         arrow_411405190le_alt)), 
33.50/33.65	                     app_encode_app(arrow_411405190le_alt, 
33.50/33.65	                       fun(arrow_411405190le_alt, 
33.50/33.65	                         product_prod(arrow_411405190le_alt, 
33.50/33.65	                           arrow_411405190le_alt)), 
33.50/33.65	                       app_encode_app(
33.50/33.65	                         fun(arrow_411405190le_alt, 
33.50/33.65	                           fun(arrow_411405190le_alt, 
33.50/33.65	                             product_prod(arrow_411405190le_alt, 
33.50/33.65	                               arrow_411405190le_alt))), 
33.50/33.65	                         app_encode_fun(arrow_411405190le_alt, 
33.50/33.65	                           fun(arrow_411405190le_alt, 
33.50/33.65	                             product_prod(arrow_411405190le_alt, 
33.50/33.65	                               arrow_411405190le_alt))), 
33.50/33.65	                         combc(arrow_411405190le_alt, arrow_411405190le_alt, 
33.50/33.65	                           product_prod(arrow_411405190le_alt, 
33.50/33.65	                             arrow_411405190le_alt)), 
33.50/33.65	                         product_Pair(arrow_411405190le_alt, 
33.50/33.65	                           arrow_411405190le_alt)), b)), a)), 
33.50/33.65	               sk_B2(arrow_411405190le_alt, arrow_411405190le_alt, 
33.50/33.65	                 app_encode_app(arrow_411405190le_alt, 
33.50/33.65	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
33.50/33.65	                   app_encode_app(
33.50/33.65	                     fun(arrow_411405190le_alt, 
33.50/33.65	                       product_prod(arrow_411405190le_alt, 
33.50/33.65	                         arrow_411405190le_alt)), 
33.50/33.65	                     app_encode_fun(arrow_411405190le_alt, 
33.50/33.65	                       product_prod(arrow_411405190le_alt, 
33.50/33.65	                         arrow_411405190le_alt)), 
33.50/33.65	                     aa(arrow_411405190le_alt, 
33.50/33.65	                       product_prod(arrow_411405190le_alt, 
33.50/33.65	                         arrow_411405190le_alt)), 
33.50/33.65	                     app_encode_app(arrow_411405190le_alt, 
33.50/33.65	                       fun(arrow_411405190le_alt, 
33.50/33.65	                         product_prod(arrow_411405190le_alt, 
33.50/33.65	                           arrow_411405190le_alt)), 
33.50/33.65	                       app_encode_app(
33.50/33.65	                         fun(arrow_411405190le_alt, 
33.50/33.65	                           fun(arrow_411405190le_alt, 
33.50/33.65	                             product_prod(arrow_411405190le_alt, 
33.50/33.65	                               arrow_411405190le_alt))), 
33.50/33.65	                         app_encode_fun(arrow_411405190le_alt, 
33.50/33.65	                           fun(arrow_411405190le_alt, 
33.50/33.65	                             product_prod(arrow_411405190le_alt, 
33.50/33.65	                               arrow_411405190le_alt))), 
33.50/33.65	                         combc(arrow_411405190le_alt, arrow_411405190le_alt, 
33.50/33.65	                           product_prod(arrow_411405190le_alt, 
33.50/33.65	                             arrow_411405190le_alt)), 
33.50/33.65	                         product_Pair(arrow_411405190le_alt, 
33.50/33.65	                           arrow_411405190le_alt)), b)), a)))), 
33.50/33.65	           arrow_1985332922le_Lin)),
33.50/33.65	    inference('sup-', [status(thm)], ['3', '8'])).
33.50/33.65	tff(zf_stmt_50, axiom,
33.50/33.65	  (![A:$tType,B:$tType,B4:B,A4:A,Ba:B,Aa:A]:
33.50/33.65	     ((app_encode_app(B,product_prod(A,B),
33.50/33.65	                      app_encode_app(fun(B,product_prod(A,B)),
33.50/33.65	                                     app_encode_fun(B,product_prod(A,B)),
33.50/33.65	                                     aa(B,product_prod(A,B)),
33.50/33.65	                                     app_encode_app(A,
33.50/33.65	                                                    fun(B,product_prod(A,B)),
33.50/33.65	                                                    app_encode_app(fun(
33.50/33.65	                                                                   A,
33.50/33.65	                                                                   fun(
33.50/33.65	                                                                   B,
33.50/33.65	                                                                   product_prod(
33.50/33.65	                                                                   A,B))),
33.50/33.65	                                                                   app_encode_fun(
33.50/33.65	                                                                   A,
33.50/33.65	                                                                   fun(
33.50/33.65	                                                                   B,
33.50/33.65	                                                                   product_prod(
33.50/33.65	                                                                   A,B))),
33.50/33.65	                                                                   aa(
33.50/33.65	                                                                   A,
33.50/33.65	                                                                   fun(
33.50/33.65	                                                                   B,
33.50/33.65	                                                                   product_prod(
33.50/33.65	                                                                   A,B))),
33.50/33.65	                                                                   product_Pair(
33.50/33.65	                                                                   A,B)),
33.50/33.65	                                                    Aa)),
33.50/33.65	                      Ba) =
33.50/33.65	       app_encode_app(B,product_prod(A,B),
33.50/33.65	                      app_encode_app(fun(B,product_prod(A,B)),
33.50/33.65	                                     app_encode_fun(B,product_prod(A,B)),
33.50/33.65	                                     aa(B,product_prod(A,B)),
33.50/33.65	                                     app_encode_app(A,
33.50/33.65	                                                    fun(B,product_prod(A,B)),
33.50/33.65	                                                    app_encode_app(fun(
33.50/33.65	                                                                   A,
33.50/33.65	                                                                   fun(
33.50/33.65	                                                                   B,
33.50/33.65	                                                                   product_prod(
33.50/33.65	                                                                   A,B))),
33.50/33.65	                                                                   app_encode_fun(
33.50/33.65	                                                                   A,
33.50/33.65	                                                                   fun(
33.50/33.65	                                                                   B,
33.50/33.65	                                                                   product_prod(
33.50/33.65	                                                                   A,B))),
33.50/33.65	                                                                   aa(
33.50/33.65	                                                                   A,
33.50/33.65	                                                                   fun(
33.50/33.65	                                                                   B,
33.50/33.65	                                                                   product_prod(
33.50/33.65	                                                                   A,B))),
33.50/33.65	                                                                   product_Pair(
33.50/33.65	                                                                   A,B)),
33.50/33.65	                                                    A4)),
33.50/33.65	                      B4)) <=>
33.50/33.65	      ((Aa = A4) & (Ba = B4))))).
33.50/33.65	tff('10', plain,
33.50/33.65	    ![X15 : $tType, X16 : X15, X17 : X15, X18 : $tType, X19 : X18, X20 : X18]:
33.50/33.65	      (X17 = X16
33.50/33.65	       | app_encode_app(X18, product_prod(X15, X18), 
33.50/33.65	           app_encode_app(fun(X18, product_prod(X15, X18)), 
33.50/33.65	             app_encode_fun(X18, product_prod(X15, X18)), 
33.50/33.65	             aa(X18, product_prod(X15, X18)), 
33.50/33.65	             app_encode_app(X15, fun(X18, product_prod(X15, X18)), 
33.50/33.65	               app_encode_app(fun(X15, fun(X18, product_prod(X15, X18))), 
33.50/33.65	                 app_encode_fun(X15, fun(X18, product_prod(X15, X18))), 
33.50/33.65	                 aa(X15, fun(X18, product_prod(X15, X18))), 
33.50/33.65	                 product_Pair(X15, X18)), X17)), X20)
33.50/33.65	          != app_encode_app(X18, product_prod(X15, X18), 
33.50/33.65	               app_encode_app(fun(X18, product_prod(X15, X18)), 
33.50/33.65	                 app_encode_fun(X18, product_prod(X15, X18)), 
33.50/33.65	                 aa(X18, product_prod(X15, X18)), 
33.50/33.65	                 app_encode_app(X15, fun(X18, product_prod(X15, X18)), 
33.50/33.65	                   app_encode_app(
33.50/33.65	                     fun(X15, fun(X18, product_prod(X15, X18))), 
33.50/33.65	                     app_encode_fun(X15, fun(X18, product_prod(X15, X18))), 
33.50/33.65	                     aa(X15, fun(X18, product_prod(X15, X18))), 
33.50/33.65	                     product_Pair(X15, X18)), X16)), X19)),
33.50/33.65	    inference('cnf', [status(esa)], [zf_stmt_50])).
33.50/33.65	tff('11', plain,
33.50/33.65	    ![X0 : $tType, X1 : $tType, X2 : product_prod(X1, X0), X3 : X0, X4 : X1]:
33.50/33.65	      (X2
33.50/33.65	        != app_encode_app(X0, product_prod(X1, X0), 
33.50/33.65	             app_encode_app(fun(X0, product_prod(X1, X0)), 
33.50/33.65	               app_encode_fun(X0, product_prod(X1, X0)), 
33.50/33.65	               aa(X0, product_prod(X1, X0)), 
33.50/33.65	               app_encode_app(X1, fun(X0, product_prod(X1, X0)), 
33.50/33.65	                 app_encode_app(fun(X1, fun(X0, product_prod(X1, X0))), 
33.50/33.65	                   app_encode_fun(X1, fun(X0, product_prod(X1, X0))), 
33.50/33.65	                   aa(X1, fun(X0, product_prod(X1, X0))), 
33.50/33.65	                   product_Pair(X1, X0)), X4)), X3)
33.50/33.65	       | sk_A2(X0, X1, X2) = X4),
33.50/33.65	    inference('sup-', [status(thm)], ['1', '10'])).
33.50/33.65	tff('12', plain,
33.50/33.65	    ![X0 : $tType, X1 : $tType, X3 : X0, X4 : X1]:
33.50/33.65	      sk_A2(X0, X1, 
33.50/33.65	        app_encode_app(X0, product_prod(X1, X0), 
33.50/33.65	          app_encode_app(fun(X0, product_prod(X1, X0)), 
33.50/33.65	            app_encode_fun(X0, product_prod(X1, X0)), 
33.50/33.65	            aa(X0, product_prod(X1, X0)), 
33.50/33.65	            app_encode_app(X1, fun(X0, product_prod(X1, X0)), 
33.50/33.65	              app_encode_app(fun(X1, fun(X0, product_prod(X1, X0))), 
33.50/33.65	                app_encode_fun(X1, fun(X0, product_prod(X1, X0))), 
33.50/33.65	                aa(X1, fun(X0, product_prod(X1, X0))), product_Pair(X1, X0)), 
33.50/33.65	              X4)), X3))
33.50/33.65	       = X4,
33.50/33.65	    inference('simplify', [status(thm)], ['11'])).
33.50/33.65	tff('13', plain,
33.50/33.65	    ![X0 : $tType, X1 : $tType, X2 : X1, X3 : X0]:
33.50/33.65	      sk_A2(X0, X1, 
33.50/33.65	        app_encode_app(X1, product_prod(X1, X0), 
33.50/33.65	          app_encode_app(fun(X1, product_prod(X1, X0)), 
33.50/33.65	            app_encode_fun(X1, product_prod(X1, X0)), 
33.50/33.65	            aa(X1, product_prod(X1, X0)), 
33.50/33.65	            app_encode_app(X0, fun(X1, product_prod(X1, X0)), 
33.50/33.65	              app_encode_app(fun(X1, fun(X0, product_prod(X1, X0))), 
33.50/33.65	                app_encode_fun(X0, fun(X1, product_prod(X1, X0))), 
33.50/33.65	                combc(X1, X0, product_prod(X1, X0)), product_Pair(X1, X0)), 
33.50/33.65	              X3)), X2))
33.50/33.65	       = X2,
33.50/33.65	    inference('sup+', [status(thm)], ['5', '12'])).
33.50/33.65	tff('14', plain,
33.50/33.65	    ![X15 : $tType, X16 : X15, X17 : X15, X18 : $tType, X19 : X18, X20 : X18]:
33.50/33.65	      (X20 = X19
33.50/33.65	       | app_encode_app(X18, product_prod(X15, X18), 
33.50/33.65	           app_encode_app(fun(X18, product_prod(X15, X18)), 
33.50/33.65	             app_encode_fun(X18, product_prod(X15, X18)), 
33.50/33.65	             aa(X18, product_prod(X15, X18)), 
33.50/33.65	             app_encode_app(X15, fun(X18, product_prod(X15, X18)), 
33.50/33.65	               app_encode_app(fun(X15, fun(X18, product_prod(X15, X18))), 
33.50/33.65	                 app_encode_fun(X15, fun(X18, product_prod(X15, X18))), 
33.50/33.65	                 aa(X15, fun(X18, product_prod(X15, X18))), 
33.50/33.65	                 product_Pair(X15, X18)), X17)), X20)
33.50/33.65	          != app_encode_app(X18, product_prod(X15, X18), 
33.50/33.65	               app_encode_app(fun(X18, product_prod(X15, X18)), 
33.50/33.65	                 app_encode_fun(X18, product_prod(X15, X18)), 
33.50/33.65	                 aa(X18, product_prod(X15, X18)), 
33.50/33.65	                 app_encode_app(X15, fun(X18, product_prod(X15, X18)), 
33.50/33.65	                   app_encode_app(
33.50/33.65	                     fun(X15, fun(X18, product_prod(X15, X18))), 
33.50/33.65	                     app_encode_fun(X15, fun(X18, product_prod(X15, X18))), 
33.50/33.65	                     aa(X15, fun(X18, product_prod(X15, X18))), 
33.50/33.65	                     product_Pair(X15, X18)), X16)), X19)),
33.50/33.65	    inference('cnf', [status(esa)], [zf_stmt_50])).
33.50/33.65	tff('15', plain,
33.50/33.65	    ![X0 : $tType, X1 : $tType, X2 : product_prod(X1, X0), X3 : X0, X4 : X1]:
33.50/33.65	      (X2
33.50/33.65	        != app_encode_app(X0, product_prod(X1, X0), 
33.50/33.65	             app_encode_app(fun(X0, product_prod(X1, X0)), 
33.50/33.65	               app_encode_fun(X0, product_prod(X1, X0)), 
33.50/33.65	               aa(X0, product_prod(X1, X0)), 
33.50/33.65	               app_encode_app(X1, fun(X0, product_prod(X1, X0)), 
33.50/33.65	                 app_encode_app(fun(X1, fun(X0, product_prod(X1, X0))), 
33.50/33.65	                   app_encode_fun(X1, fun(X0, product_prod(X1, X0))), 
33.50/33.65	                   aa(X1, fun(X0, product_prod(X1, X0))), 
33.50/33.65	                   product_Pair(X1, X0)), X4)), X3)
33.50/33.65	       | sk_B2(X0, X1, X2) = X3),
33.50/33.65	    inference('sup-', [status(thm)], ['1', '14'])).
33.50/33.65	tff('16', plain,
33.50/33.65	    ![X0 : $tType, X1 : $tType, X3 : X0, X4 : X1]:
33.50/33.65	      sk_B2(X0, X1, 
33.50/33.65	        app_encode_app(X0, product_prod(X1, X0), 
33.50/33.65	          app_encode_app(fun(X0, product_prod(X1, X0)), 
33.50/33.65	            app_encode_fun(X0, product_prod(X1, X0)), 
33.50/33.65	            aa(X0, product_prod(X1, X0)), 
33.50/33.65	            app_encode_app(X1, fun(X0, product_prod(X1, X0)), 
33.50/33.65	              app_encode_app(fun(X1, fun(X0, product_prod(X1, X0))), 
33.50/33.65	                app_encode_fun(X1, fun(X0, product_prod(X1, X0))), 
33.50/33.65	                aa(X1, fun(X0, product_prod(X1, X0))), product_Pair(X1, X0)), 
33.50/33.65	              X4)), X3))
33.50/33.65	       = X3,
33.50/33.65	    inference('simplify', [status(thm)], ['15'])).
33.50/33.65	tff('17', plain,
33.50/33.65	    ![X0 : $tType, X1 : $tType, X2 : X1, X3 : X0]:
33.50/33.65	      sk_B2(X0, X1, 
33.50/33.65	        app_encode_app(X1, product_prod(X1, X0), 
33.50/33.65	          app_encode_app(fun(X1, product_prod(X1, X0)), 
33.50/33.65	            app_encode_fun(X1, product_prod(X1, X0)), 
33.50/33.65	            aa(X1, product_prod(X1, X0)), 
33.50/33.65	            app_encode_app(X0, fun(X1, product_prod(X1, X0)), 
33.50/33.65	              app_encode_app(fun(X1, fun(X0, product_prod(X1, X0))), 
33.50/33.65	                app_encode_fun(X0, fun(X1, product_prod(X1, X0))), 
33.50/33.65	                combc(X1, X0, product_prod(X1, X0)), product_Pair(X1, X0)), 
33.50/33.65	              X3)), X2))
33.50/33.65	       = X3,
33.50/33.65	    inference('sup+', [status(thm)], ['5', '16'])).
33.50/33.65	tff('18', plain,
33.50/33.65	    (~ $true
33.50/33.65	     | a = b
33.50/33.65	     | ~ app_encode_app(
33.50/33.65	           fun(
33.50/33.65	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
33.50/33.65	               bool), bool), $o, 
33.50/33.65	           app_encode_app(
33.50/33.65	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
33.50/33.65	               bool), 
33.50/33.65	             app_encode_fun(
33.50/33.65	               fun(
33.50/33.65	                 fun(
33.50/33.65	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
33.50/33.65	                   bool), bool), $o), 
33.50/33.65	             member(
33.50/33.65	               fun(
33.50/33.65	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
33.50/33.65	                 bool)), sk_X1(a, b)), arrow_1985332922le_Lin)),
33.50/33.65	    inference('demod', [status(thm)], ['9', '13', '17', '13', '17'])).
33.50/33.65	tff('19', plain,
33.50/33.65	    (~ app_encode_app(
33.50/33.65	         fun(
33.50/33.65	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
33.50/33.65	             bool), bool), $o, 
33.50/33.65	         app_encode_app(
33.50/33.65	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
33.50/33.65	             bool), 
33.50/33.65	           app_encode_fun(
33.50/33.65	             fun(
33.50/33.65	               fun(
33.50/33.65	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
33.50/33.65	                 bool), bool), $o), 
33.50/33.65	           member(
33.50/33.65	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
33.50/33.65	               bool)), sk_X1(a, b)), arrow_1985332922le_Lin)
33.50/33.65	     | a = b),
33.50/33.65	    inference('simplify', [status(thm)], ['18'])).
33.50/33.65	tff(zf_stmt_45, axiom, (a != b)).
33.50/33.65	tff('20', plain, a != b, inference('cnf', [status(esa)], [zf_stmt_45])).
33.50/33.65	tff('21', plain,
33.50/33.65	    ~ app_encode_app(
33.50/33.65	        fun(
33.50/33.65	          fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
33.50/33.65	            bool), bool), $o, 
33.50/33.65	        app_encode_app(
33.50/33.65	          fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
33.50/33.65	            bool), 
33.50/33.65	          app_encode_fun(
33.50/33.65	            fun(
33.50/33.65	              fun(
33.50/33.65	                product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
33.50/33.65	                bool), bool), $o), 
33.50/33.65	          member(
33.50/33.65	            fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
33.50/33.65	              bool)), sk_X1(a, b)), arrow_1985332922le_Lin),
33.50/33.65	    inference('simplify_reflect-', [status(thm)], ['19', '20'])).
33.50/33.65	tff('22', plain, (~ $true | a = b),
33.50/33.65	    inference('sup-', [status(thm)], ['0', '21'])).
33.50/33.65	tff('23', plain, a = b, inference('simplify', [status(thm)], ['22'])).
33.50/33.65	tff('24', plain, $false,
33.50/33.65	    inference('simplify_reflect-', [status(thm)], ['23', '20'])).
33.50/33.65	
33.50/33.65	% SZS output end Refutation
33.50/33.66	EOF
