0.00/0.00	% File    : /export/starexec/sandbox/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : app
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : kbo
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-ho \
0.00/0.00	  --no-avatar \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.20	% Computer   : n163.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 13:40:09 CST 2018
26.90/27.07	% done 1071 iterations in 26.866s
26.90/27.07	% SZS status Theorem for 'stdin'
26.90/27.07	% SZS output start Refutation
26.90/27.07	tff(zf_stmt_114, axiom,
26.90/27.07	  (app_encode_app(fun(product_prod(arrow_411405190le_alt,
26.90/27.07	                                   arrow_411405190le_alt),
26.90/27.07	                      bool),
26.90/27.07	                  $o,
26.90/27.07	                  app_encode_app(product_prod(arrow_411405190le_alt,
26.90/27.07	                                              arrow_411405190le_alt),
26.90/27.07	                                 app_encode_fun(fun(product_prod(arrow_411405190le_alt,
26.90/27.07	                                                                 arrow_411405190le_alt),
26.90/27.07	                                                    bool),
26.90/27.07	                                                $o),
26.90/27.07	                                 member(product_prod(arrow_411405190le_alt,
26.90/27.07	                                                     arrow_411405190le_alt)),
26.90/27.07	                                 app_encode_app(arrow_411405190le_alt,
26.90/27.07	                                                product_prod(arrow_411405190le_alt,
26.90/27.07	                                                             arrow_411405190le_alt),
26.90/27.07	                                                app_encode_app(fun(arrow_411405190le_alt,
26.90/27.07	                                                                   product_prod(
26.90/27.07	                                                                   arrow_411405190le_alt,
26.90/27.07	                                                                   arrow_411405190le_alt)),
26.90/27.07	                                                               app_encode_fun(
26.90/27.07	                                                               arrow_411405190le_alt,
26.90/27.07	                                                               product_prod(
26.90/27.07	                                                               arrow_411405190le_alt,
26.90/27.07	                                                               arrow_411405190le_alt)),
26.90/27.07	                                                               aa(arrow_411405190le_alt,
26.90/27.07	                                                                  product_prod(
26.90/27.07	                                                                  arrow_411405190le_alt,
26.90/27.07	                                                                  arrow_411405190le_alt)),
26.90/27.07	                                                               app_encode_app(
26.90/27.07	                                                               arrow_411405190le_alt,
26.90/27.07	                                                               fun(arrow_411405190le_alt,
26.90/27.07	                                                                   product_prod(
26.90/27.07	                                                                   arrow_411405190le_alt,
26.90/27.07	                                                                   arrow_411405190le_alt)),
26.90/27.07	                                                               app_encode_app(
26.90/27.07	                                                               fun(arrow_411405190le_alt,
26.90/27.07	                                                                   fun(
26.90/27.07	                                                                   arrow_411405190le_alt,
26.90/27.07	                                                                   product_prod(
26.90/27.07	                                                                   arrow_411405190le_alt,
26.90/27.07	                                                                   arrow_411405190le_alt))),
26.90/27.07	                                                               app_encode_fun(
26.90/27.07	                                                               arrow_411405190le_alt,
26.90/27.07	                                                               fun(arrow_411405190le_alt,
26.90/27.07	                                                                   product_prod(
26.90/27.07	                                                                   arrow_411405190le_alt,
26.90/27.07	                                                                   arrow_411405190le_alt))),
26.90/27.07	                                                               aa(arrow_411405190le_alt,
26.90/27.07	                                                                  fun(
26.90/27.07	                                                                  arrow_411405190le_alt,
26.90/27.07	                                                                  product_prod(
26.90/27.07	                                                                  arrow_411405190le_alt,
26.90/27.07	                                                                  arrow_411405190le_alt))),
26.90/27.07	                                                               product_Pair(
26.90/27.07	                                                               arrow_411405190le_alt,
26.90/27.07	                                                               arrow_411405190le_alt)),
26.90/27.07	                                                               x)),
26.90/27.07	                                                y)),
26.90/27.07	                  l))).
26.90/27.07	tff('0', plain,
26.90/27.07	    app_encode_app(
26.90/27.07	      fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), bool), 
26.90/27.07	      $o, 
26.90/27.07	      app_encode_app(
26.90/27.07	        product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
26.90/27.07	        app_encode_fun(
26.90/27.07	          fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
26.90/27.07	            bool), $o), 
26.90/27.07	        member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
26.90/27.07	        app_encode_app(arrow_411405190le_alt, 
26.90/27.07	          product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
26.90/27.07	          app_encode_app(
26.90/27.07	            fun(arrow_411405190le_alt, 
26.90/27.07	              product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
26.90/27.07	            app_encode_fun(arrow_411405190le_alt, 
26.90/27.07	              product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
26.90/27.07	            aa(arrow_411405190le_alt, 
26.90/27.07	              product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
26.90/27.07	            app_encode_app(arrow_411405190le_alt, 
26.90/27.07	              fun(arrow_411405190le_alt, 
26.90/27.07	                product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
26.90/27.07	              app_encode_app(
26.90/27.07	                fun(arrow_411405190le_alt, 
26.90/27.07	                  fun(arrow_411405190le_alt, 
26.90/27.07	                    product_prod(arrow_411405190le_alt, 
26.90/27.07	                      arrow_411405190le_alt))), 
26.90/27.07	                app_encode_fun(arrow_411405190le_alt, 
26.90/27.07	                  fun(arrow_411405190le_alt, 
26.90/27.07	                    product_prod(arrow_411405190le_alt, 
26.90/27.07	                      arrow_411405190le_alt))), 
26.90/27.07	                aa(arrow_411405190le_alt, 
26.90/27.07	                  fun(arrow_411405190le_alt, 
26.90/27.07	                    product_prod(arrow_411405190le_alt, 
26.90/27.07	                      arrow_411405190le_alt))), 
26.90/27.07	                product_Pair(arrow_411405190le_alt, arrow_411405190le_alt)), 
26.90/27.07	              x)), y)), l),
26.90/27.07	    inference('cnf', [status(esa)], [zf_stmt_114])).
26.90/27.07	tff(zf_stmt_113, axiom,
26.90/27.07	  (app_encode_app(fun(product_prod(arrow_411405190le_alt,
26.90/27.07	                                   arrow_411405190le_alt),
26.90/27.07	                      bool),
26.90/27.07	                  $o,
26.90/27.07	                  app_encode_app(product_prod(arrow_411405190le_alt,
26.90/27.07	                                              arrow_411405190le_alt),
26.90/27.07	                                 app_encode_fun(fun(product_prod(arrow_411405190le_alt,
26.90/27.07	                                                                 arrow_411405190le_alt),
26.90/27.07	                                                    bool),
26.90/27.07	                                                $o),
26.90/27.07	                                 member(product_prod(arrow_411405190le_alt,
26.90/27.07	                                                     arrow_411405190le_alt)),
26.90/27.07	                                 app_encode_app(arrow_411405190le_alt,
26.90/27.07	                                                product_prod(arrow_411405190le_alt,
26.90/27.07	                                                             arrow_411405190le_alt),
26.90/27.07	                                                app_encode_app(fun(arrow_411405190le_alt,
26.90/27.07	                                                                   product_prod(
26.90/27.07	                                                                   arrow_411405190le_alt,
26.90/27.07	                                                                   arrow_411405190le_alt)),
26.90/27.07	                                                               app_encode_fun(
26.90/27.07	                                                               arrow_411405190le_alt,
26.90/27.07	                                                               product_prod(
26.90/27.07	                                                               arrow_411405190le_alt,
26.90/27.07	                                                               arrow_411405190le_alt)),
26.90/27.07	                                                               aa(arrow_411405190le_alt,
26.90/27.07	                                                                  product_prod(
26.90/27.07	                                                                  arrow_411405190le_alt,
26.90/27.07	                                                                  arrow_411405190le_alt)),
26.90/27.07	                                                               app_encode_app(
26.90/27.07	                                                               arrow_411405190le_alt,
26.90/27.07	                                                               fun(arrow_411405190le_alt,
26.90/27.07	                                                                   product_prod(
26.90/27.07	                                                                   arrow_411405190le_alt,
26.90/27.07	                                                                   arrow_411405190le_alt)),
26.90/27.07	                                                               app_encode_app(
26.90/27.07	                                                               fun(arrow_411405190le_alt,
26.90/27.07	                                                                   fun(
26.90/27.07	                                                                   arrow_411405190le_alt,
26.90/27.07	                                                                   product_prod(
26.90/27.07	                                                                   arrow_411405190le_alt,
26.90/27.07	                                                                   arrow_411405190le_alt))),
26.90/27.07	                                                               app_encode_fun(
26.90/27.07	                                                               arrow_411405190le_alt,
26.90/27.07	                                                               fun(arrow_411405190le_alt,
26.90/27.07	                                                                   product_prod(
26.90/27.07	                                                                   arrow_411405190le_alt,
26.90/27.07	                                                                   arrow_411405190le_alt))),
26.90/27.07	                                                               aa(arrow_411405190le_alt,
26.90/27.07	                                                                  fun(
26.90/27.07	                                                                  arrow_411405190le_alt,
26.90/27.07	                                                                  product_prod(
26.90/27.07	                                                                  arrow_411405190le_alt,
26.90/27.07	                                                                  arrow_411405190le_alt))),
26.90/27.07	                                                               product_Pair(
26.90/27.07	                                                               arrow_411405190le_alt,
26.90/27.07	                                                               arrow_411405190le_alt)),
26.90/27.07	                                                               y)),
26.90/27.07	                                                x)),
26.90/27.07	                  l))).
26.90/27.07	tff('1', plain,
26.90/27.07	    app_encode_app(
26.90/27.07	      fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), bool), 
26.90/27.07	      $o, 
26.90/27.07	      app_encode_app(
26.90/27.07	        product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
26.90/27.07	        app_encode_fun(
26.90/27.07	          fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
26.90/27.07	            bool), $o), 
26.90/27.07	        member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
26.90/27.07	        app_encode_app(arrow_411405190le_alt, 
26.90/27.07	          product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
26.90/27.07	          app_encode_app(
26.90/27.07	            fun(arrow_411405190le_alt, 
26.90/27.07	              product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
26.90/27.07	            app_encode_fun(arrow_411405190le_alt, 
26.90/27.07	              product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
26.90/27.07	            aa(arrow_411405190le_alt, 
26.90/27.07	              product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
26.90/27.07	            app_encode_app(arrow_411405190le_alt, 
26.90/27.07	              fun(arrow_411405190le_alt, 
26.90/27.07	                product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
26.90/27.07	              app_encode_app(
26.90/27.07	                fun(arrow_411405190le_alt, 
26.90/27.07	                  fun(arrow_411405190le_alt, 
26.90/27.07	                    product_prod(arrow_411405190le_alt, 
26.90/27.07	                      arrow_411405190le_alt))), 
26.90/27.07	                app_encode_fun(arrow_411405190le_alt, 
26.90/27.07	                  fun(arrow_411405190le_alt, 
26.90/27.07	                    product_prod(arrow_411405190le_alt, 
26.90/27.07	                      arrow_411405190le_alt))), 
26.90/27.07	                aa(arrow_411405190le_alt, 
26.90/27.07	                  fun(arrow_411405190le_alt, 
26.90/27.07	                    product_prod(arrow_411405190le_alt, 
26.90/27.07	                      arrow_411405190le_alt))), 
26.90/27.07	                product_Pair(arrow_411405190le_alt, arrow_411405190le_alt)), 
26.90/27.07	              y)), x)), l),
26.90/27.07	    inference('cnf', [status(esa)], [zf_stmt_113])).
26.90/27.07	tff(zf_stmt_35, axiom,
26.90/27.07	  (![A1:$tType,R:fun(product_prod(A1,A1),bool)]:
26.90/27.07	     (app_encode_app(fun(product_prod(A1,A1),bool),$o,trans(A1),R) <=>
26.90/27.07	      (![X2:A1,Y2:A1,Z2:A1]:
26.90/27.07	         (app_encode_app(fun(product_prod(A1,A1),bool),$o,
26.90/27.07	                         app_encode_app(product_prod(A1,A1),
26.90/27.07	                                        app_encode_fun(fun(product_prod(
26.90/27.07	                                                           A1,A1),bool),
26.90/27.07	                                                       $o),
26.90/27.07	                                        member(product_prod(A1,A1)),
26.90/27.07	                                        app_encode_app(A1,
26.90/27.07	                                                       product_prod(A1,A1),
26.90/27.07	                                                       app_encode_app(
26.90/27.07	                                                       fun(A1,
26.90/27.07	                                                           product_prod(
26.90/27.07	                                                           A1,A1)),
26.90/27.07	                                                       app_encode_fun(
26.90/27.07	                                                       A1,product_prod(A1,A1)),
26.90/27.07	                                                       aa(A1,
26.90/27.07	                                                          product_prod(A1,A1)),
26.90/27.07	                                                       app_encode_app(
26.90/27.07	                                                       A1,
26.90/27.07	                                                       fun(A1,
26.90/27.07	                                                           product_prod(
26.90/27.07	                                                           A1,A1)),
26.90/27.07	                                                       app_encode_app(
26.90/27.07	                                                       fun(A1,
26.90/27.07	                                                           fun(A1,
26.90/27.07	                                                               product_prod(
26.90/27.07	                                                               A1,A1))),
26.90/27.07	                                                       app_encode_fun(
26.90/27.07	                                                       A1,
26.90/27.07	                                                       fun(A1,
26.90/27.07	                                                           product_prod(
26.90/27.07	                                                           A1,A1))),
26.90/27.07	                                                       aa(A1,
26.90/27.07	                                                          fun(A1,
26.90/27.07	                                                              product_prod(
26.90/27.07	                                                              A1,A1))),
26.90/27.07	                                                       product_Pair(A1,A1)),
26.90/27.07	                                                       X2)),Y2)),
26.90/27.07	                         R) =>
26.90/27.07	          (app_encode_app(fun(product_prod(A1,A1),bool),$o,
26.90/27.07	                          app_encode_app(product_prod(A1,A1),
26.90/27.07	                                         app_encode_fun(fun(product_prod(
26.90/27.07	                                                            A1,A1),bool),
26.90/27.07	                                                        $o),
26.90/27.07	                                         member(product_prod(A1,A1)),
26.90/27.07	                                         app_encode_app(A1,
26.90/27.07	                                                        product_prod(A1,A1),
26.90/27.07	                                                        app_encode_app(
26.90/27.08	                                                        fun(A1,
26.90/27.08	                                                            product_prod(
26.90/27.08	                                                            A1,A1)),
26.90/27.08	                                                        app_encode_fun(
26.90/27.08	                                                        A1,
26.90/27.08	                                                        product_prod(A1,A1)),
26.90/27.08	                                                        aa(A1,
26.90/27.08	                                                           product_prod(
26.90/27.08	                                                           A1,A1)),
26.90/27.08	                                                        app_encode_app(
26.90/27.08	                                                        A1,
26.90/27.08	                                                        fun(A1,
26.90/27.08	                                                            product_prod(
26.90/27.08	                                                            A1,A1)),
26.90/27.08	                                                        app_encode_app(
26.90/27.08	                                                        fun(A1,
26.90/27.08	                                                            fun(A1,
26.90/27.08	                                                                product_prod(
26.90/27.08	                                                                A1,A1))),
26.90/27.08	                                                        app_encode_fun(
26.90/27.08	                                                        A1,
26.90/27.08	                                                        fun(A1,
26.90/27.08	                                                            product_prod(
26.90/27.08	                                                            A1,A1))),
26.90/27.08	                                                        aa(A1,
26.90/27.08	                                                           fun(A1,
26.90/27.08	                                                               product_prod(
26.90/27.08	                                                               A1,A1))),
26.90/27.08	                                                        product_Pair(A1,A1)),
26.90/27.08	                                                        Y2)),Z2)),
26.90/27.08	                          R) =>
26.90/27.08	           app_encode_app(fun(product_prod(A1,A1),bool),$o,
26.90/27.08	                          app_encode_app(product_prod(A1,A1),
26.90/27.08	                                         app_encode_fun(fun(product_prod(
26.90/27.08	                                                            A1,A1),bool),
26.90/27.08	                                                        $o),
26.90/27.08	                                         member(product_prod(A1,A1)),
26.90/27.08	                                         app_encode_app(A1,
26.90/27.08	                                                        product_prod(A1,A1),
26.90/27.08	                                                        app_encode_app(
26.90/27.08	                                                        fun(A1,
26.90/27.08	                                                            product_prod(
26.90/27.08	                                                            A1,A1)),
26.90/27.08	                                                        app_encode_fun(
26.90/27.08	                                                        A1,
26.90/27.08	                                                        product_prod(A1,A1)),
26.90/27.08	                                                        aa(A1,
26.90/27.08	                                                           product_prod(
26.90/27.08	                                                           A1,A1)),
26.90/27.08	                                                        app_encode_app(
26.90/27.08	                                                        A1,
26.90/27.08	                                                        fun(A1,
26.90/27.08	                                                            product_prod(
26.90/27.08	                                                            A1,A1)),
26.90/27.08	                                                        app_encode_app(
26.90/27.08	                                                        fun(A1,
26.90/27.08	                                                            fun(A1,
26.90/27.08	                                                                product_prod(
26.90/27.08	                                                                A1,A1))),
26.90/27.08	                                                        app_encode_fun(
26.90/27.08	                                                        A1,
26.90/27.08	                                                        fun(A1,
26.90/27.08	                                                            product_prod(
26.90/27.08	                                                            A1,A1))),
26.90/27.08	                                                        aa(A1,
26.90/27.08	                                                           fun(A1,
26.90/27.08	                                                               product_prod(
26.90/27.08	                                                               A1,A1))),
26.90/27.08	                                                        product_Pair(A1,A1)),
26.90/27.08	                                                        X2)),Z2)),
26.90/27.08	                          R))))))).
26.90/27.08	tff('2', plain,
26.90/27.08	    ![X14 : $tType, X15 : X14, X16 : X14, 
26.90/27.08	      X17 : fun(product_prod(X14, X14), bool), X18 : X14]:
26.90/27.08	      (~ app_encode_app(fun(product_prod(X14, X14), bool), $o, 
26.90/27.08	           app_encode_app(product_prod(X14, X14), 
26.90/27.08	             app_encode_fun(fun(product_prod(X14, X14), bool), $o), 
26.90/27.08	             member(product_prod(X14, X14)), 
26.90/27.08	             app_encode_app(X14, product_prod(X14, X14), 
26.90/27.08	               app_encode_app(fun(X14, product_prod(X14, X14)), 
26.90/27.08	                 app_encode_fun(X14, product_prod(X14, X14)), 
26.90/27.08	                 aa(X14, product_prod(X14, X14)), 
26.90/27.08	                 app_encode_app(X14, fun(X14, product_prod(X14, X14)), 
26.90/27.08	                   app_encode_app(
26.90/27.08	                     fun(X14, fun(X14, product_prod(X14, X14))), 
26.90/27.08	                     app_encode_fun(X14, fun(X14, product_prod(X14, X14))), 
26.90/27.08	                     aa(X14, fun(X14, product_prod(X14, X14))), 
26.90/27.08	                     product_Pair(X14, X14)), X15)), X16)), X17)
26.90/27.08	       | app_encode_app(fun(product_prod(X14, X14), bool), $o, 
26.90/27.08	           app_encode_app(product_prod(X14, X14), 
26.90/27.08	             app_encode_fun(fun(product_prod(X14, X14), bool), $o), 
26.90/27.08	             member(product_prod(X14, X14)), 
26.90/27.08	             app_encode_app(X14, product_prod(X14, X14), 
26.90/27.08	               app_encode_app(fun(X14, product_prod(X14, X14)), 
26.90/27.08	                 app_encode_fun(X14, product_prod(X14, X14)), 
26.90/27.08	                 aa(X14, product_prod(X14, X14)), 
26.90/27.08	                 app_encode_app(X14, fun(X14, product_prod(X14, X14)), 
26.90/27.08	                   app_encode_app(
26.90/27.08	                     fun(X14, fun(X14, product_prod(X14, X14))), 
26.90/27.08	                     app_encode_fun(X14, fun(X14, product_prod(X14, X14))), 
26.90/27.08	                     aa(X14, fun(X14, product_prod(X14, X14))), 
26.90/27.08	                     product_Pair(X14, X14)), X18)), X16)), X17)
26.90/27.08	       | ~ app_encode_app(fun(product_prod(X14, X14), bool), $o, 
26.90/27.08	             app_encode_app(product_prod(X14, X14), 
26.90/27.08	               app_encode_fun(fun(product_prod(X14, X14), bool), $o), 
26.90/27.08	               member(product_prod(X14, X14)), 
26.90/27.08	               app_encode_app(X14, product_prod(X14, X14), 
26.90/27.08	                 app_encode_app(fun(X14, product_prod(X14, X14)), 
26.90/27.08	                   app_encode_fun(X14, product_prod(X14, X14)), 
26.90/27.08	                   aa(X14, product_prod(X14, X14)), 
26.90/27.08	                   app_encode_app(X14, fun(X14, product_prod(X14, X14)), 
26.90/27.08	                     app_encode_app(
26.90/27.08	                       fun(X14, fun(X14, product_prod(X14, X14))), 
26.90/27.08	                       app_encode_fun(X14, fun(X14, product_prod(X14, X14))), 
26.90/27.08	                       aa(X14, fun(X14, product_prod(X14, X14))), 
26.90/27.08	                       product_Pair(X14, X14)), X18)), X15)), X17)
26.90/27.08	       | ~ app_encode_app(fun(product_prod(X14, X14), bool), $o, trans(X14), 
26.90/27.08	             X17)),
26.90/27.08	    inference('cnf', [status(esa)], [zf_stmt_35])).
26.90/27.08	tff('3', plain,
26.90/27.08	    ![X0 : arrow_411405190le_alt]:
26.90/27.08	      (~ $true
26.90/27.08	       | ~ app_encode_app(
26.90/27.08	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
26.90/27.08	               bool), $o, trans(arrow_411405190le_alt), l)
26.90/27.08	       | ~ app_encode_app(
26.90/27.08	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
26.90/27.08	               bool), $o, 
26.90/27.08	             app_encode_app(
26.90/27.08	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
26.90/27.08	               app_encode_fun(
26.90/27.08	                 fun(
26.90/27.08	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
26.90/27.08	                   bool), $o), 
26.90/27.08	               member(
26.90/27.08	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
26.90/27.08	               app_encode_app(arrow_411405190le_alt, 
26.90/27.08	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
26.90/27.08	                 app_encode_app(
26.90/27.08	                   fun(arrow_411405190le_alt, 
26.90/27.08	                     product_prod(arrow_411405190le_alt, 
26.90/27.08	                       arrow_411405190le_alt)), 
26.90/27.08	                   app_encode_fun(arrow_411405190le_alt, 
26.90/27.08	                     product_prod(arrow_411405190le_alt, 
26.90/27.08	                       arrow_411405190le_alt)), 
26.90/27.08	                   aa(arrow_411405190le_alt, 
26.90/27.08	                     product_prod(arrow_411405190le_alt, 
26.90/27.08	                       arrow_411405190le_alt)), 
26.90/27.08	                   app_encode_app(arrow_411405190le_alt, 
26.90/27.08	                     fun(arrow_411405190le_alt, 
26.90/27.08	                       product_prod(arrow_411405190le_alt, 
26.90/27.08	                         arrow_411405190le_alt)), 
26.90/27.08	                     app_encode_app(
26.90/27.08	                       fun(arrow_411405190le_alt, 
26.90/27.08	                         fun(arrow_411405190le_alt, 
26.90/27.08	                           product_prod(arrow_411405190le_alt, 
26.90/27.08	                             arrow_411405190le_alt))), 
26.90/27.08	                       app_encode_fun(arrow_411405190le_alt, 
26.90/27.08	                         fun(arrow_411405190le_alt, 
26.90/27.08	                           product_prod(arrow_411405190le_alt, 
26.90/27.08	                             arrow_411405190le_alt))), 
26.90/27.08	                       aa(arrow_411405190le_alt, 
26.90/27.08	                         fun(arrow_411405190le_alt, 
26.90/27.08	                           product_prod(arrow_411405190le_alt, 
26.90/27.08	                             arrow_411405190le_alt))), 
26.90/27.08	                       product_Pair(arrow_411405190le_alt, 
26.90/27.08	                         arrow_411405190le_alt)), X0)), y)), l)
26.90/27.08	       | app_encode_app(
26.90/27.08	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
26.90/27.08	             bool), $o, 
26.90/27.08	           app_encode_app(
26.90/27.08	             product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
26.90/27.08	             app_encode_fun(
26.90/27.08	               fun(
26.90/27.08	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
26.90/27.08	                 bool), $o), 
26.90/27.08	             member(
26.90/27.08	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
26.90/27.08	             app_encode_app(arrow_411405190le_alt, 
26.90/27.08	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
26.90/27.08	               app_encode_app(
26.90/27.08	                 fun(arrow_411405190le_alt, 
26.90/27.08	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
26.90/27.08	                 app_encode_fun(arrow_411405190le_alt, 
26.90/27.08	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
26.90/27.08	                 aa(arrow_411405190le_alt, 
26.90/27.08	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
26.90/27.08	                 app_encode_app(arrow_411405190le_alt, 
26.90/27.08	                   fun(arrow_411405190le_alt, 
26.90/27.08	                     product_prod(arrow_411405190le_alt, 
26.90/27.08	                       arrow_411405190le_alt)), 
26.90/27.08	                   app_encode_app(
26.90/27.08	                     fun(arrow_411405190le_alt, 
26.90/27.08	                       fun(arrow_411405190le_alt, 
26.90/27.08	                         product_prod(arrow_411405190le_alt, 
26.90/27.08	                           arrow_411405190le_alt))), 
26.90/27.08	                     app_encode_fun(arrow_411405190le_alt, 
26.90/27.08	                       fun(arrow_411405190le_alt, 
26.90/27.08	                         product_prod(arrow_411405190le_alt, 
26.90/27.08	                           arrow_411405190le_alt))), 
26.90/27.08	                     aa(arrow_411405190le_alt, 
26.90/27.08	                       fun(arrow_411405190le_alt, 
26.90/27.08	                         product_prod(arrow_411405190le_alt, 
26.90/27.08	                           arrow_411405190le_alt))), 
26.90/27.08	                     product_Pair(arrow_411405190le_alt, 
26.90/27.08	                       arrow_411405190le_alt)), X0)), x)), l)),
26.90/27.08	    inference('sup-', [status(thm)], ['1', '2'])).
26.90/27.08	tff(zf_stmt_110, axiom,
26.90/27.08	  (app_encode_app(fun(product_prod(arrow_411405190le_alt,
26.90/27.08	                                   arrow_411405190le_alt),
26.90/27.08	                      bool),
26.90/27.08	                  $o,trans(arrow_411405190le_alt),l))).
26.90/27.08	tff('4', plain,
26.90/27.08	    app_encode_app(
26.90/27.08	      fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), bool), 
26.90/27.08	      $o, trans(arrow_411405190le_alt), l),
26.90/27.08	    inference('cnf', [status(esa)], [zf_stmt_110])).
26.90/27.08	tff('5', plain,
26.90/27.08	    ![X0 : arrow_411405190le_alt]:
26.90/27.08	      (~ $true
26.90/27.08	       | ~ $true
26.90/27.08	       | ~ app_encode_app(
26.90/27.08	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
26.90/27.08	               bool), $o, 
26.90/27.08	             app_encode_app(
26.90/27.08	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
26.90/27.08	               app_encode_fun(
26.90/27.08	                 fun(
26.90/27.08	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
26.90/27.08	                   bool), $o), 
26.90/27.08	               member(
26.90/27.08	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
26.90/27.08	               app_encode_app(arrow_411405190le_alt, 
26.90/27.08	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
26.90/27.08	                 app_encode_app(
26.90/27.08	                   fun(arrow_411405190le_alt, 
26.90/27.08	                     product_prod(arrow_411405190le_alt, 
26.90/27.08	                       arrow_411405190le_alt)), 
26.90/27.08	                   app_encode_fun(arrow_411405190le_alt, 
26.90/27.08	                     product_prod(arrow_411405190le_alt, 
26.90/27.08	                       arrow_411405190le_alt)), 
26.90/27.08	                   aa(arrow_411405190le_alt, 
26.90/27.08	                     product_prod(arrow_411405190le_alt, 
26.90/27.08	                       arrow_411405190le_alt)), 
26.90/27.08	                   app_encode_app(arrow_411405190le_alt, 
26.90/27.08	                     fun(arrow_411405190le_alt, 
26.90/27.08	                       product_prod(arrow_411405190le_alt, 
26.90/27.08	                         arrow_411405190le_alt)), 
26.90/27.08	                     app_encode_app(
26.90/27.08	                       fun(arrow_411405190le_alt, 
26.90/27.08	                         fun(arrow_411405190le_alt, 
26.90/27.08	                           product_prod(arrow_411405190le_alt, 
26.90/27.08	                             arrow_411405190le_alt))), 
26.90/27.08	                       app_encode_fun(arrow_411405190le_alt, 
26.90/27.08	                         fun(arrow_411405190le_alt, 
26.90/27.08	                           product_prod(arrow_411405190le_alt, 
26.90/27.08	                             arrow_411405190le_alt))), 
26.90/27.08	                       aa(arrow_411405190le_alt, 
26.90/27.08	                         fun(arrow_411405190le_alt, 
26.90/27.08	                           product_prod(arrow_411405190le_alt, 
26.90/27.08	                             arrow_411405190le_alt))), 
26.90/27.08	                       product_Pair(arrow_411405190le_alt, 
26.90/27.08	                         arrow_411405190le_alt)), X0)), y)), l)
26.90/27.08	       | app_encode_app(
26.90/27.08	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
26.90/27.08	             bool), $o, 
26.90/27.08	           app_encode_app(
26.90/27.08	             product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
26.90/27.08	             app_encode_fun(
26.90/27.08	               fun(
26.90/27.08	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
26.90/27.08	                 bool), $o), 
26.90/27.08	             member(
26.90/27.08	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
26.90/27.08	             app_encode_app(arrow_411405190le_alt, 
26.90/27.08	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
26.90/27.08	               app_encode_app(
26.90/27.08	                 fun(arrow_411405190le_alt, 
26.90/27.08	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
26.90/27.08	                 app_encode_fun(arrow_411405190le_alt, 
26.90/27.08	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
26.90/27.08	                 aa(arrow_411405190le_alt, 
26.90/27.08	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
26.90/27.08	                 app_encode_app(arrow_411405190le_alt, 
26.90/27.08	                   fun(arrow_411405190le_alt, 
26.90/27.08	                     product_prod(arrow_411405190le_alt, 
26.90/27.08	                       arrow_411405190le_alt)), 
26.90/27.08	                   app_encode_app(
26.90/27.08	                     fun(arrow_411405190le_alt, 
26.90/27.08	                       fun(arrow_411405190le_alt, 
26.90/27.08	                         product_prod(arrow_411405190le_alt, 
26.90/27.08	                           arrow_411405190le_alt))), 
26.90/27.08	                     app_encode_fun(arrow_411405190le_alt, 
26.90/27.08	                       fun(arrow_411405190le_alt, 
26.90/27.08	                         product_prod(arrow_411405190le_alt, 
26.90/27.08	                           arrow_411405190le_alt))), 
26.90/27.08	                     aa(arrow_411405190le_alt, 
26.90/27.08	                       fun(arrow_411405190le_alt, 
26.90/27.08	                         product_prod(arrow_411405190le_alt, 
26.90/27.08	                           arrow_411405190le_alt))), 
26.90/27.08	                     product_Pair(arrow_411405190le_alt, 
26.90/27.08	                       arrow_411405190le_alt)), X0)), x)), l)),
26.90/27.08	    inference('demod', [status(thm)], ['3', '4'])).
26.90/27.08	tff('6', plain,
26.90/27.08	    ![X0 : arrow_411405190le_alt]:
26.90/27.08	      (app_encode_app(
26.90/27.08	         fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
26.90/27.08	           bool), $o, 
26.90/27.08	         app_encode_app(
26.90/27.08	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
26.90/27.08	           app_encode_fun(
26.90/27.08	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
26.90/27.08	               bool), $o), 
26.90/27.08	           member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
26.90/27.08	           app_encode_app(arrow_411405190le_alt, 
26.90/27.08	             product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
26.90/27.08	             app_encode_app(
26.90/27.08	               fun(arrow_411405190le_alt, 
26.90/27.08	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
26.90/27.08	               app_encode_fun(arrow_411405190le_alt, 
26.90/27.08	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
26.90/27.08	               aa(arrow_411405190le_alt, 
26.90/27.08	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
26.90/27.08	               app_encode_app(arrow_411405190le_alt, 
26.90/27.08	                 fun(arrow_411405190le_alt, 
26.90/27.08	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
26.90/27.08	                 app_encode_app(
26.90/27.08	                   fun(arrow_411405190le_alt, 
26.90/27.08	                     fun(arrow_411405190le_alt, 
26.90/27.08	                       product_prod(arrow_411405190le_alt, 
26.90/27.08	                         arrow_411405190le_alt))), 
26.90/27.08	                   app_encode_fun(arrow_411405190le_alt, 
26.90/27.08	                     fun(arrow_411405190le_alt, 
26.90/27.08	                       product_prod(arrow_411405190le_alt, 
26.90/27.08	                         arrow_411405190le_alt))), 
26.90/27.08	                   aa(arrow_411405190le_alt, 
26.90/27.08	                     fun(arrow_411405190le_alt, 
26.90/27.08	                       product_prod(arrow_411405190le_alt, 
26.90/27.08	                         arrow_411405190le_alt))), 
26.90/27.08	                   product_Pair(arrow_411405190le_alt, arrow_411405190le_alt)), 
26.90/27.08	                 X0)), x)), l)
26.90/27.08	       | ~ app_encode_app(
26.90/27.08	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
26.90/27.08	               bool), $o, 
26.90/27.08	             app_encode_app(
26.90/27.08	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
26.90/27.08	               app_encode_fun(
26.90/27.08	                 fun(
26.90/27.08	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
26.90/27.08	                   bool), $o), 
26.90/27.08	               member(
26.90/27.08	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
26.90/27.08	               app_encode_app(arrow_411405190le_alt, 
26.90/27.08	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
26.90/27.08	                 app_encode_app(
26.90/27.08	                   fun(arrow_411405190le_alt, 
26.90/27.08	                     product_prod(arrow_411405190le_alt, 
26.90/27.08	                       arrow_411405190le_alt)), 
26.90/27.08	                   app_encode_fun(arrow_411405190le_alt, 
26.90/27.08	                     product_prod(arrow_411405190le_alt, 
26.90/27.08	                       arrow_411405190le_alt)), 
26.90/27.08	                   aa(arrow_411405190le_alt, 
26.90/27.08	                     product_prod(arrow_411405190le_alt, 
26.90/27.08	                       arrow_411405190le_alt)), 
26.90/27.08	                   app_encode_app(arrow_411405190le_alt, 
26.90/27.08	                     fun(arrow_411405190le_alt, 
26.90/27.08	                       product_prod(arrow_411405190le_alt, 
26.90/27.08	                         arrow_411405190le_alt)), 
26.90/27.08	                     app_encode_app(
26.90/27.08	                       fun(arrow_411405190le_alt, 
26.90/27.08	                         fun(arrow_411405190le_alt, 
26.90/27.08	                           product_prod(arrow_411405190le_alt, 
26.90/27.08	                             arrow_411405190le_alt))), 
26.90/27.08	                       app_encode_fun(arrow_411405190le_alt, 
26.90/27.08	                         fun(arrow_411405190le_alt, 
26.90/27.08	                           product_prod(arrow_411405190le_alt, 
26.90/27.08	                             arrow_411405190le_alt))), 
26.90/27.08	                       aa(arrow_411405190le_alt, 
26.90/27.08	                         fun(arrow_411405190le_alt, 
26.90/27.08	                           product_prod(arrow_411405190le_alt, 
26.90/27.08	                             arrow_411405190le_alt))), 
26.90/27.08	                       product_Pair(arrow_411405190le_alt, 
26.90/27.08	                         arrow_411405190le_alt)), X0)), y)), l)),
26.90/27.08	    inference('simplify', [status(thm)], ['5'])).
26.90/27.08	tff('7', plain,
26.90/27.08	    (~ $true
26.90/27.08	     | app_encode_app(
26.90/27.08	         fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
26.90/27.08	           bool), $o, 
26.90/27.08	         app_encode_app(
26.90/27.08	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
26.90/27.08	           app_encode_fun(
26.90/27.08	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
26.90/27.08	               bool), $o), 
26.90/27.08	           member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
26.90/27.08	           app_encode_app(arrow_411405190le_alt, 
26.90/27.08	             product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
26.90/27.08	             app_encode_app(
26.90/27.08	               fun(arrow_411405190le_alt, 
26.90/27.08	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
26.90/27.08	               app_encode_fun(arrow_411405190le_alt, 
26.90/27.08	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
26.90/27.08	               aa(arrow_411405190le_alt, 
26.90/27.08	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
26.90/27.08	               app_encode_app(arrow_411405190le_alt, 
26.90/27.08	                 fun(arrow_411405190le_alt, 
26.90/27.08	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
26.90/27.08	                 app_encode_app(
26.90/27.08	                   fun(arrow_411405190le_alt, 
26.90/27.08	                     fun(arrow_411405190le_alt, 
26.90/27.08	                       product_prod(arrow_411405190le_alt, 
26.90/27.08	                         arrow_411405190le_alt))), 
26.90/27.08	                   app_encode_fun(arrow_411405190le_alt, 
26.90/27.08	                     fun(arrow_411405190le_alt, 
26.90/27.08	                       product_prod(arrow_411405190le_alt, 
26.90/27.08	                         arrow_411405190le_alt))), 
26.90/27.08	                   aa(arrow_411405190le_alt, 
26.90/27.08	                     fun(arrow_411405190le_alt, 
26.90/27.08	                       product_prod(arrow_411405190le_alt, 
26.90/27.08	                         arrow_411405190le_alt))), 
26.90/27.08	                   product_Pair(arrow_411405190le_alt, arrow_411405190le_alt)), 
26.90/27.08	                 x)), x)), l)),
26.90/27.08	    inference('sup-', [status(thm)], ['0', '6'])).
26.90/27.08	tff('8', plain,
26.90/27.08	    app_encode_app(
26.90/27.08	      fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), bool), 
26.90/27.08	      $o, 
26.90/27.08	      app_encode_app(
26.90/27.08	        product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
26.90/27.08	        app_encode_fun(
26.90/27.08	          fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
26.90/27.08	            bool), $o), 
26.90/27.08	        member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
26.90/27.08	        app_encode_app(arrow_411405190le_alt, 
26.90/27.08	          product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
26.90/27.08	          app_encode_app(
26.90/27.08	            fun(arrow_411405190le_alt, 
26.90/27.08	              product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
26.90/27.08	            app_encode_fun(arrow_411405190le_alt, 
26.90/27.08	              product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
26.90/27.08	            aa(arrow_411405190le_alt, 
26.90/27.08	              product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
26.90/27.08	            app_encode_app(arrow_411405190le_alt, 
26.90/27.08	              fun(arrow_411405190le_alt, 
26.90/27.08	                product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
26.90/27.08	              app_encode_app(
26.90/27.08	                fun(arrow_411405190le_alt, 
26.90/27.08	                  fun(arrow_411405190le_alt, 
26.90/27.08	                    product_prod(arrow_411405190le_alt, 
26.90/27.08	                      arrow_411405190le_alt))), 
26.90/27.08	                app_encode_fun(arrow_411405190le_alt, 
26.90/27.08	                  fun(arrow_411405190le_alt, 
26.90/27.08	                    product_prod(arrow_411405190le_alt, 
26.90/27.08	                      arrow_411405190le_alt))), 
26.90/27.08	                aa(arrow_411405190le_alt, 
26.90/27.08	                  fun(arrow_411405190le_alt, 
26.90/27.08	                    product_prod(arrow_411405190le_alt, 
26.90/27.08	                      arrow_411405190le_alt))), 
26.90/27.08	                product_Pair(arrow_411405190le_alt, arrow_411405190le_alt)), 
26.90/27.08	              x)), x)), l),
26.90/27.08	    inference('simplify', [status(thm)], ['7'])).
26.90/27.08	tff(zf_stmt_111, axiom,
26.90/27.08	  (![X:arrow_411405190le_alt]:
26.90/27.08	     (~
26.90/27.08	       app_encode_app(fun(product_prod(arrow_411405190le_alt,
26.90/27.08	                                       arrow_411405190le_alt),
26.90/27.08	                          bool),
26.90/27.08	                      $o,
26.90/27.08	                      app_encode_app(product_prod(arrow_411405190le_alt,
26.90/27.08	                                                  arrow_411405190le_alt),
26.90/27.08	                                     app_encode_fun(fun(product_prod(
26.90/27.08	                                                        arrow_411405190le_alt,
26.90/27.08	                                                        arrow_411405190le_alt),
26.90/27.08	                                                        bool),
26.90/27.08	                                                    $o),
26.90/27.08	                                     member(product_prod(arrow_411405190le_alt,
26.90/27.08	                                                         arrow_411405190le_alt)),
26.90/27.08	                                     app_encode_app(arrow_411405190le_alt,
26.90/27.08	                                                    product_prod(arrow_411405190le_alt,
26.90/27.08	                                                                 arrow_411405190le_alt),
26.90/27.08	                                                    app_encode_app(fun(
26.90/27.08	                                                                   arrow_411405190le_alt,
26.90/27.08	                                                                   product_prod(
26.90/27.08	                                                                   arrow_411405190le_alt,
26.90/27.08	                                                                   arrow_411405190le_alt)),
26.90/27.08	                                                                   app_encode_fun(
26.90/27.08	                                                                   arrow_411405190le_alt,
26.90/27.08	                                                                   product_prod(
26.90/27.08	                                                                   arrow_411405190le_alt,
26.90/27.08	                                                                   arrow_411405190le_alt)),
26.90/27.08	                                                                   aa(
26.90/27.08	                                                                   arrow_411405190le_alt,
26.90/27.08	                                                                   product_prod(
26.90/27.08	                                                                   arrow_411405190le_alt,
26.90/27.08	                                                                   arrow_411405190le_alt)),
26.90/27.08	                                                                   app_encode_app(
26.90/27.08	                                                                   arrow_411405190le_alt,
26.90/27.08	                                                                   fun(
26.90/27.08	                                                                   arrow_411405190le_alt,
26.90/27.08	                                                                   product_prod(
26.90/27.08	                                                                   arrow_411405190le_alt,
26.90/27.08	                                                                   arrow_411405190le_alt)),
26.90/27.08	                                                                   app_encode_app(
26.90/27.08	                                                                   fun(
26.90/27.08	                                                                   arrow_411405190le_alt,
26.90/27.08	                                                                   fun(
26.90/27.08	                                                                   arrow_411405190le_alt,
26.90/27.08	                                                                   product_prod(
26.90/27.08	                                                                   arrow_411405190le_alt,
26.90/27.08	                                                                   arrow_411405190le_alt))),
26.90/27.08	                                                                   app_encode_fun(
26.90/27.08	                                                                   arrow_411405190le_alt,
26.90/27.08	                                                                   fun(
26.90/27.08	                                                                   arrow_411405190le_alt,
26.90/27.08	                                                                   product_prod(
26.90/27.08	                                                                   arrow_411405190le_alt,
26.90/27.08	                                                                   arrow_411405190le_alt))),
26.90/27.08	                                                                   aa(
26.90/27.08	                                                                   arrow_411405190le_alt,
26.90/27.08	                                                                   fun(
26.90/27.08	                                                                   arrow_411405190le_alt,
26.90/27.08	                                                                   product_prod(
26.90/27.08	                                                                   arrow_411405190le_alt,
26.90/27.08	                                                                   arrow_411405190le_alt))),
26.90/27.08	                                                                   product_Pair(
26.90/27.08	                                                                   arrow_411405190le_alt,
26.90/27.08	                                                                   arrow_411405190le_alt)),
26.90/27.08	                                                                   X)),
26.90/27.08	                                                    X)),
26.90/27.08	                      l)))).
26.90/27.08	tff('9', plain,
26.90/27.08	    ![X382 : arrow_411405190le_alt]:
26.90/27.08	      ~ app_encode_app(
26.90/27.08	          fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
26.90/27.08	            bool), $o, 
26.90/27.08	          app_encode_app(
26.90/27.08	            product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
26.90/27.08	            app_encode_fun(
26.90/27.08	              fun(
26.90/27.08	                product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
26.90/27.08	                bool), $o), 
26.90/27.08	            member(
26.90/27.08	              product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
26.90/27.08	            app_encode_app(arrow_411405190le_alt, 
26.90/27.08	              product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
26.90/27.08	              app_encode_app(
26.90/27.08	                fun(arrow_411405190le_alt, 
26.90/27.08	                  product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
26.90/27.08	                app_encode_fun(arrow_411405190le_alt, 
26.90/27.08	                  product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
26.90/27.08	                aa(arrow_411405190le_alt, 
26.90/27.08	                  product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
26.90/27.08	                app_encode_app(arrow_411405190le_alt, 
26.90/27.08	                  fun(arrow_411405190le_alt, 
26.90/27.08	                    product_prod(arrow_411405190le_alt, 
26.90/27.08	                      arrow_411405190le_alt)), 
26.90/27.08	                  app_encode_app(
26.90/27.08	                    fun(arrow_411405190le_alt, 
26.90/27.08	                      fun(arrow_411405190le_alt, 
26.90/27.08	                        product_prod(arrow_411405190le_alt, 
26.90/27.08	                          arrow_411405190le_alt))), 
26.90/27.08	                    app_encode_fun(arrow_411405190le_alt, 
26.90/27.08	                      fun(arrow_411405190le_alt, 
26.90/27.08	                        product_prod(arrow_411405190le_alt, 
26.90/27.08	                          arrow_411405190le_alt))), 
26.90/27.08	                    aa(arrow_411405190le_alt, 
26.90/27.08	                      fun(arrow_411405190le_alt, 
26.90/27.08	                        product_prod(arrow_411405190le_alt, 
26.90/27.08	                          arrow_411405190le_alt))), 
26.90/27.08	                    product_Pair(arrow_411405190le_alt, 
26.90/27.08	                      arrow_411405190le_alt)), X382)), X382)), l),
26.90/27.08	    inference('cnf', [status(esa)], [zf_stmt_111])).
26.90/27.08	tff('10', plain, ~ $true, inference('sup-', [status(thm)], ['8', '9'])).
26.90/27.08	tff('11', plain, $false, inference('simplify', [status(thm)], ['10'])).
26.90/27.08	
26.90/27.08	% SZS output end Refutation
26.90/27.08	EOF
