0.00/0.00	% File    : /export/starexec/sandbox/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : appext
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   : n096.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 14:01:24 CST 2018
45.23/45.40	% done 2511 iterations in 45.197s
45.23/45.40	% SZS status Theorem for 'stdin'
45.23/45.40	% SZS output start Refutation
45.23/45.41	tff(zf_stmt_142, conjecture,
45.23/45.41	  (app_encode_app(fun(product_prod(arrow_411405190le_alt,
45.23/45.41	                                   arrow_411405190le_alt),
45.23/45.41	                      bool),
45.23/45.41	                  $o,
45.23/45.41	                  app_encode_app(product_prod(arrow_411405190le_alt,
45.23/45.41	                                              arrow_411405190le_alt),
45.23/45.41	                                 app_encode_fun(fun(product_prod(arrow_411405190le_alt,
45.23/45.41	                                                                 arrow_411405190le_alt),
45.23/45.41	                                                    bool),
45.23/45.41	                                                $o),
45.23/45.41	                                 member(product_prod(arrow_411405190le_alt,
45.23/45.41	                                                     arrow_411405190le_alt)),
45.23/45.41	                                 app_encode_app(arrow_411405190le_alt,
45.23/45.41	                                                product_prod(arrow_411405190le_alt,
45.23/45.41	                                                             arrow_411405190le_alt),
45.23/45.41	                                                app_encode_app(arrow_411405190le_alt,
45.23/45.41	                                                               app_encode_fun(
45.23/45.41	                                                               arrow_411405190le_alt,
45.23/45.41	                                                               product_prod(
45.23/45.41	                                                               arrow_411405190le_alt,
45.23/45.41	                                                               arrow_411405190le_alt)),
45.23/45.41	                                                               product_Pair(
45.23/45.41	                                                               arrow_411405190le_alt,
45.23/45.41	                                                               arrow_411405190le_alt),
45.23/45.41	                                                               a),
45.23/45.41	                                                b)),
45.23/45.41	                  app_encode_app(fun(arrow_159774573e_indi,
45.23/45.41	                                     fun(product_prod(arrow_411405190le_alt,
45.23/45.41	                                                      arrow_411405190le_alt),
45.23/45.41	                                         bool)),
45.23/45.41	                                 fun(product_prod(arrow_411405190le_alt,
45.23/45.41	                                                  arrow_411405190le_alt),
45.23/45.41	                                     bool),
45.23/45.41	                                 app_encode_app(fun(fun(arrow_159774573e_indi,
45.23/45.41	                                                        fun(product_prod(
45.23/45.41	                                                            arrow_411405190le_alt,
45.23/45.41	                                                            arrow_411405190le_alt),
45.23/45.41	                                                            bool)),
45.23/45.41	                                                    fun(product_prod(
45.23/45.41	                                                        arrow_411405190le_alt,
45.23/45.41	                                                        arrow_411405190le_alt),
45.23/45.41	                                                        bool)),
45.23/45.41	                                                app_encode_fun(fun(arrow_159774573e_indi,
45.23/45.41	                                                                   fun(
45.23/45.41	                                                                   product_prod(
45.23/45.41	                                                                   arrow_411405190le_alt,
45.23/45.41	                                                                   arrow_411405190le_alt),
45.23/45.41	                                                                   bool)),
45.23/45.41	                                                               fun(product_prod(
45.23/45.41	                                                                   arrow_411405190le_alt,
45.23/45.41	                                                                   arrow_411405190le_alt),
45.23/45.41	                                                                   bool)),
45.23/45.41	                                                aa(fun(arrow_159774573e_indi,
45.23/45.41	                                                       fun(product_prod(
45.23/45.41	                                                           arrow_411405190le_alt,
45.23/45.41	                                                           arrow_411405190le_alt),
45.23/45.41	                                                           bool)),
45.23/45.41	                                                   fun(product_prod(arrow_411405190le_alt,
45.23/45.41	                                                                    arrow_411405190le_alt),
45.23/45.41	                                                       bool)),
45.23/45.41	                                                f),
45.23/45.41	                                 p1)) <=>
45.23/45.41	   app_encode_app(fun(product_prod(arrow_411405190le_alt,
45.23/45.41	                                   arrow_411405190le_alt),
45.23/45.41	                      bool),
45.23/45.41	                  $o,
45.23/45.41	                  app_encode_app(product_prod(arrow_411405190le_alt,
45.23/45.41	                                              arrow_411405190le_alt),
45.23/45.41	                                 app_encode_fun(fun(product_prod(arrow_411405190le_alt,
45.23/45.41	                                                                 arrow_411405190le_alt),
45.23/45.41	                                                    bool),
45.23/45.41	                                                $o),
45.23/45.41	                                 member(product_prod(arrow_411405190le_alt,
45.23/45.41	                                                     arrow_411405190le_alt)),
45.23/45.41	                                 app_encode_app(arrow_411405190le_alt,
45.23/45.41	                                                product_prod(arrow_411405190le_alt,
45.23/45.41	                                                             arrow_411405190le_alt),
45.23/45.41	                                                app_encode_app(arrow_411405190le_alt,
45.23/45.41	                                                               app_encode_fun(
45.23/45.41	                                                               arrow_411405190le_alt,
45.23/45.41	                                                               product_prod(
45.23/45.41	                                                               arrow_411405190le_alt,
45.23/45.41	                                                               arrow_411405190le_alt)),
45.23/45.41	                                                               product_Pair(
45.23/45.41	                                                               arrow_411405190le_alt,
45.23/45.41	                                                               arrow_411405190le_alt),
45.23/45.41	                                                               b),
45.23/45.41	                                                c)),
45.23/45.41	                  app_encode_app(fun(arrow_159774573e_indi,
45.23/45.41	                                     fun(product_prod(arrow_411405190le_alt,
45.23/45.41	                                                      arrow_411405190le_alt),
45.23/45.41	                                         bool)),
45.23/45.41	                                 fun(product_prod(arrow_411405190le_alt,
45.23/45.41	                                                  arrow_411405190le_alt),
45.23/45.41	                                     bool),
45.23/45.41	                                 app_encode_app(fun(fun(arrow_159774573e_indi,
45.23/45.41	                                                        fun(product_prod(
45.23/45.41	                                                            arrow_411405190le_alt,
45.23/45.41	                                                            arrow_411405190le_alt),
45.23/45.41	                                                            bool)),
45.23/45.41	                                                    fun(product_prod(
45.23/45.41	                                                        arrow_411405190le_alt,
45.23/45.41	                                                        arrow_411405190le_alt),
45.23/45.41	                                                        bool)),
45.23/45.41	                                                app_encode_fun(fun(arrow_159774573e_indi,
45.23/45.41	                                                                   fun(
45.23/45.41	                                                                   product_prod(
45.23/45.41	                                                                   arrow_411405190le_alt,
45.23/45.41	                                                                   arrow_411405190le_alt),
45.23/45.41	                                                                   bool)),
45.23/45.41	                                                               fun(product_prod(
45.23/45.41	                                                                   arrow_411405190le_alt,
45.23/45.41	                                                                   arrow_411405190le_alt),
45.23/45.41	                                                                   bool)),
45.23/45.41	                                                aa(fun(arrow_159774573e_indi,
45.23/45.41	                                                       fun(product_prod(
45.23/45.41	                                                           arrow_411405190le_alt,
45.23/45.41	                                                           arrow_411405190le_alt),
45.23/45.41	                                                           bool)),
45.23/45.41	                                                   fun(product_prod(arrow_411405190le_alt,
45.23/45.41	                                                                    arrow_411405190le_alt),
45.23/45.41	                                                       bool)),
45.23/45.41	                                                f),
45.23/45.41	                                 p)))).
45.23/45.41	tff(zf_stmt_0, negated_conjecture,
45.23/45.41	  (~
45.23/45.41	    (app_encode_app(fun(product_prod(arrow_411405190le_alt,
45.23/45.41	                                     arrow_411405190le_alt),
45.23/45.41	                        bool),
45.23/45.41	                    $o,
45.23/45.41	                    app_encode_app(product_prod(arrow_411405190le_alt,
45.23/45.41	                                                arrow_411405190le_alt),
45.23/45.41	                                   app_encode_fun(fun(product_prod(arrow_411405190le_alt,
45.23/45.41	                                                                   arrow_411405190le_alt),
45.23/45.41	                                                      bool),
45.23/45.41	                                                  $o),
45.23/45.41	                                   member(product_prod(arrow_411405190le_alt,
45.23/45.41	                                                       arrow_411405190le_alt)),
45.23/45.41	                                   app_encode_app(arrow_411405190le_alt,
45.23/45.41	                                                  product_prod(arrow_411405190le_alt,
45.23/45.41	                                                               arrow_411405190le_alt),
45.23/45.41	                                                  app_encode_app(arrow_411405190le_alt,
45.23/45.41	                                                                 app_encode_fun(
45.23/45.41	                                                                 arrow_411405190le_alt,
45.23/45.41	                                                                 product_prod(
45.23/45.41	                                                                 arrow_411405190le_alt,
45.23/45.41	                                                                 arrow_411405190le_alt)),
45.23/45.41	                                                                 product_Pair(
45.23/45.41	                                                                 arrow_411405190le_alt,
45.23/45.41	                                                                 arrow_411405190le_alt),
45.23/45.41	                                                                 a),
45.23/45.41	                                                  b)),
45.23/45.41	                    app_encode_app(fun(arrow_159774573e_indi,
45.23/45.41	                                       fun(product_prod(arrow_411405190le_alt,
45.23/45.41	                                                        arrow_411405190le_alt),
45.23/45.41	                                           bool)),
45.23/45.41	                                   fun(product_prod(arrow_411405190le_alt,
45.23/45.41	                                                    arrow_411405190le_alt),
45.23/45.41	                                       bool),
45.23/45.41	                                   app_encode_app(fun(fun(arrow_159774573e_indi,
45.23/45.41	                                                          fun(product_prod(
45.23/45.41	                                                              arrow_411405190le_alt,
45.23/45.41	                                                              arrow_411405190le_alt),
45.23/45.41	                                                              bool)),
45.23/45.41	                                                      fun(product_prod(
45.23/45.41	                                                          arrow_411405190le_alt,
45.23/45.41	                                                          arrow_411405190le_alt),
45.23/45.41	                                                          bool)),
45.23/45.41	                                                  app_encode_fun(fun(
45.23/45.41	                                                                 arrow_159774573e_indi,
45.23/45.41	                                                                 fun(
45.23/45.41	                                                                 product_prod(
45.23/45.41	                                                                 arrow_411405190le_alt,
45.23/45.41	                                                                 arrow_411405190le_alt),
45.23/45.41	                                                                 bool)),
45.23/45.41	                                                                 fun(
45.23/45.41	                                                                 product_prod(
45.23/45.41	                                                                 arrow_411405190le_alt,
45.23/45.41	                                                                 arrow_411405190le_alt),
45.23/45.41	                                                                 bool)),
45.23/45.41	                                                  aa(fun(arrow_159774573e_indi,
45.23/45.41	                                                         fun(product_prod(
45.23/45.41	                                                             arrow_411405190le_alt,
45.23/45.41	                                                             arrow_411405190le_alt),
45.23/45.41	                                                             bool)),
45.23/45.41	                                                     fun(product_prod(
45.23/45.41	                                                         arrow_411405190le_alt,
45.23/45.41	                                                         arrow_411405190le_alt),
45.23/45.41	                                                         bool)),
45.23/45.41	                                                  f),
45.23/45.41	                                   p1)) <=>
45.23/45.41	     app_encode_app(fun(product_prod(arrow_411405190le_alt,
45.23/45.41	                                     arrow_411405190le_alt),
45.23/45.41	                        bool),
45.23/45.41	                    $o,
45.23/45.41	                    app_encode_app(product_prod(arrow_411405190le_alt,
45.23/45.41	                                                arrow_411405190le_alt),
45.23/45.41	                                   app_encode_fun(fun(product_prod(arrow_411405190le_alt,
45.23/45.41	                                                                   arrow_411405190le_alt),
45.23/45.41	                                                      bool),
45.23/45.41	                                                  $o),
45.23/45.41	                                   member(product_prod(arrow_411405190le_alt,
45.23/45.41	                                                       arrow_411405190le_alt)),
45.23/45.41	                                   app_encode_app(arrow_411405190le_alt,
45.23/45.41	                                                  product_prod(arrow_411405190le_alt,
45.23/45.41	                                                               arrow_411405190le_alt),
45.23/45.41	                                                  app_encode_app(arrow_411405190le_alt,
45.23/45.41	                                                                 app_encode_fun(
45.23/45.41	                                                                 arrow_411405190le_alt,
45.23/45.41	                                                                 product_prod(
45.23/45.41	                                                                 arrow_411405190le_alt,
45.23/45.41	                                                                 arrow_411405190le_alt)),
45.23/45.41	                                                                 product_Pair(
45.23/45.41	                                                                 arrow_411405190le_alt,
45.23/45.41	                                                                 arrow_411405190le_alt),
45.23/45.41	                                                                 b),
45.23/45.41	                                                  c)),
45.23/45.41	                    app_encode_app(fun(arrow_159774573e_indi,
45.23/45.41	                                       fun(product_prod(arrow_411405190le_alt,
45.23/45.41	                                                        arrow_411405190le_alt),
45.23/45.41	                                           bool)),
45.23/45.41	                                   fun(product_prod(arrow_411405190le_alt,
45.23/45.41	                                                    arrow_411405190le_alt),
45.23/45.41	                                       bool),
45.23/45.41	                                   app_encode_app(fun(fun(arrow_159774573e_indi,
45.23/45.41	                                                          fun(product_prod(
45.23/45.41	                                                              arrow_411405190le_alt,
45.23/45.41	                                                              arrow_411405190le_alt),
45.23/45.41	                                                              bool)),
45.23/45.41	                                                      fun(product_prod(
45.23/45.41	                                                          arrow_411405190le_alt,
45.23/45.41	                                                          arrow_411405190le_alt),
45.23/45.41	                                                          bool)),
45.23/45.41	                                                  app_encode_fun(fun(
45.23/45.41	                                                                 arrow_159774573e_indi,
45.23/45.41	                                                                 fun(
45.23/45.41	                                                                 product_prod(
45.23/45.41	                                                                 arrow_411405190le_alt,
45.23/45.41	                                                                 arrow_411405190le_alt),
45.23/45.41	                                                                 bool)),
45.23/45.41	                                                                 fun(
45.23/45.41	                                                                 product_prod(
45.23/45.41	                                                                 arrow_411405190le_alt,
45.23/45.41	                                                                 arrow_411405190le_alt),
45.23/45.41	                                                                 bool)),
45.23/45.41	                                                  aa(fun(arrow_159774573e_indi,
45.23/45.41	                                                         fun(product_prod(
45.23/45.41	                                                             arrow_411405190le_alt,
45.23/45.41	                                                             arrow_411405190le_alt),
45.23/45.41	                                                             bool)),
45.23/45.41	                                                     fun(product_prod(
45.23/45.41	                                                         arrow_411405190le_alt,
45.23/45.41	                                                         arrow_411405190le_alt),
45.23/45.41	                                                         bool)),
45.23/45.41	                                                  f),
45.23/45.41	                                   p))))).
45.23/45.41	tff('0', plain,
45.23/45.41	    (app_encode_app(
45.23/45.41	       fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), bool), 
45.23/45.41	       $o, 
45.23/45.41	       app_encode_app(
45.23/45.41	         product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	         app_encode_fun(
45.23/45.41	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	             bool), $o), 
45.23/45.41	         member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
45.23/45.41	         app_encode_app(arrow_411405190le_alt, 
45.23/45.41	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	           app_encode_app(arrow_411405190le_alt, 
45.23/45.41	             app_encode_fun(arrow_411405190le_alt, 
45.23/45.41	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
45.23/45.41	             product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), b), 
45.23/45.41	           c)), 
45.23/45.41	       app_encode_app(
45.23/45.41	         fun(arrow_159774573e_indi, 
45.23/45.41	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	             bool)), 
45.23/45.41	         fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	           bool), 
45.23/45.41	         app_encode_app(
45.23/45.41	           fun(
45.23/45.41	             fun(arrow_159774573e_indi, 
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool)), 
45.23/45.41	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	               bool)), 
45.23/45.41	           app_encode_fun(
45.23/45.41	             fun(arrow_159774573e_indi, 
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool)), 
45.23/45.41	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	               bool)), 
45.23/45.41	           aa(
45.23/45.41	             fun(arrow_159774573e_indi, 
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool)), 
45.23/45.41	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	               bool)), f), p))
45.23/45.41	     | app_encode_app(
45.23/45.41	         fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	           bool), $o, 
45.23/45.41	         app_encode_app(
45.23/45.41	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	           app_encode_fun(
45.23/45.41	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	               bool), $o), 
45.23/45.41	           member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
45.23/45.41	           app_encode_app(arrow_411405190le_alt, 
45.23/45.41	             product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	             app_encode_app(arrow_411405190le_alt, 
45.23/45.41	               app_encode_fun(arrow_411405190le_alt, 
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
45.23/45.41	               product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), a), 
45.23/45.41	             b)), 
45.23/45.41	         app_encode_app(
45.23/45.41	           fun(arrow_159774573e_indi, 
45.23/45.41	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	               bool)), 
45.23/45.41	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	             bool), 
45.23/45.41	           app_encode_app(
45.23/45.41	             fun(
45.23/45.41	               fun(arrow_159774573e_indi, 
45.23/45.41	                 fun(
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                   bool)), 
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool)), 
45.23/45.41	             app_encode_fun(
45.23/45.41	               fun(arrow_159774573e_indi, 
45.23/45.41	                 fun(
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                   bool)), 
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool)), 
45.23/45.41	             aa(
45.23/45.41	               fun(arrow_159774573e_indi, 
45.23/45.41	                 fun(
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                   bool)), 
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool)), f), p1))),
45.23/45.41	    inference('cnf', [status(esa)], [zf_stmt_0])).
45.23/45.41	tff(zf_stmt_48, axiom,
45.23/45.41	  (app_encode_app(fun(product_prod(arrow_411405190le_alt,
45.23/45.41	                                   arrow_411405190le_alt),
45.23/45.41	                      bool),
45.23/45.41	                  $o,
45.23/45.41	                  app_encode_app(product_prod(arrow_411405190le_alt,
45.23/45.41	                                              arrow_411405190le_alt),
45.23/45.41	                                 app_encode_fun(fun(product_prod(arrow_411405190le_alt,
45.23/45.41	                                                                 arrow_411405190le_alt),
45.23/45.41	                                                    bool),
45.23/45.41	                                                $o),
45.23/45.41	                                 member(product_prod(arrow_411405190le_alt,
45.23/45.41	                                                     arrow_411405190le_alt)),
45.23/45.41	                                 app_encode_app(arrow_411405190le_alt,
45.23/45.41	                                                product_prod(arrow_411405190le_alt,
45.23/45.41	                                                             arrow_411405190le_alt),
45.23/45.41	                                                app_encode_app(arrow_411405190le_alt,
45.23/45.41	                                                               app_encode_fun(
45.23/45.41	                                                               arrow_411405190le_alt,
45.23/45.41	                                                               product_prod(
45.23/45.41	                                                               arrow_411405190le_alt,
45.23/45.41	                                                               arrow_411405190le_alt)),
45.23/45.41	                                                               product_Pair(
45.23/45.41	                                                               arrow_411405190le_alt,
45.23/45.41	                                                               arrow_411405190le_alt),
45.23/45.41	                                                               a),
45.23/45.41	                                                b)),
45.23/45.41	                  app_encode_app(fun(arrow_159774573e_indi,
45.23/45.41	                                     fun(product_prod(arrow_411405190le_alt,
45.23/45.41	                                                      arrow_411405190le_alt),
45.23/45.41	                                         bool)),
45.23/45.41	                                 fun(product_prod(arrow_411405190le_alt,
45.23/45.41	                                                  arrow_411405190le_alt),
45.23/45.41	                                     bool),
45.23/45.41	                                 app_encode_app(fun(fun(arrow_159774573e_indi,
45.23/45.41	                                                        fun(product_prod(
45.23/45.41	                                                            arrow_411405190le_alt,
45.23/45.41	                                                            arrow_411405190le_alt),
45.23/45.41	                                                            bool)),
45.23/45.41	                                                    fun(product_prod(
45.23/45.41	                                                        arrow_411405190le_alt,
45.23/45.41	                                                        arrow_411405190le_alt),
45.23/45.41	                                                        bool)),
45.23/45.41	                                                app_encode_fun(fun(arrow_159774573e_indi,
45.23/45.41	                                                                   fun(
45.23/45.41	                                                                   product_prod(
45.23/45.41	                                                                   arrow_411405190le_alt,
45.23/45.41	                                                                   arrow_411405190le_alt),
45.23/45.41	                                                                   bool)),
45.23/45.41	                                                               fun(product_prod(
45.23/45.41	                                                                   arrow_411405190le_alt,
45.23/45.41	                                                                   arrow_411405190le_alt),
45.23/45.41	                                                                   bool)),
45.23/45.41	                                                aa(fun(arrow_159774573e_indi,
45.23/45.41	                                                       fun(product_prod(
45.23/45.41	                                                           arrow_411405190le_alt,
45.23/45.41	                                                           arrow_411405190le_alt),
45.23/45.41	                                                           bool)),
45.23/45.41	                                                   fun(product_prod(arrow_411405190le_alt,
45.23/45.41	                                                                    arrow_411405190le_alt),
45.23/45.41	                                                       bool)),
45.23/45.41	                                                f),
45.23/45.41	                                 p1)) <=>
45.23/45.41	   app_encode_app(fun(product_prod(arrow_411405190le_alt,
45.23/45.41	                                   arrow_411405190le_alt),
45.23/45.41	                      bool),
45.23/45.41	                  $o,
45.23/45.41	                  app_encode_app(product_prod(arrow_411405190le_alt,
45.23/45.41	                                              arrow_411405190le_alt),
45.23/45.41	                                 app_encode_fun(fun(product_prod(arrow_411405190le_alt,
45.23/45.41	                                                                 arrow_411405190le_alt),
45.23/45.41	                                                    bool),
45.23/45.41	                                                $o),
45.23/45.41	                                 member(product_prod(arrow_411405190le_alt,
45.23/45.41	                                                     arrow_411405190le_alt)),
45.23/45.41	                                 app_encode_app(arrow_411405190le_alt,
45.23/45.41	                                                product_prod(arrow_411405190le_alt,
45.23/45.41	                                                             arrow_411405190le_alt),
45.23/45.41	                                                app_encode_app(arrow_411405190le_alt,
45.23/45.41	                                                               app_encode_fun(
45.23/45.41	                                                               arrow_411405190le_alt,
45.23/45.41	                                                               product_prod(
45.23/45.41	                                                               arrow_411405190le_alt,
45.23/45.41	                                                               arrow_411405190le_alt)),
45.23/45.41	                                                               product_Pair(
45.23/45.41	                                                               arrow_411405190le_alt,
45.23/45.41	                                                               arrow_411405190le_alt),
45.23/45.41	                                                               b),
45.23/45.41	                                                a)),
45.23/45.41	                  app_encode_app(fun(arrow_159774573e_indi,
45.23/45.41	                                     fun(product_prod(arrow_411405190le_alt,
45.23/45.41	                                                      arrow_411405190le_alt),
45.23/45.41	                                         bool)),
45.23/45.41	                                 fun(product_prod(arrow_411405190le_alt,
45.23/45.41	                                                  arrow_411405190le_alt),
45.23/45.41	                                     bool),
45.23/45.41	                                 app_encode_app(fun(fun(arrow_159774573e_indi,
45.23/45.41	                                                        fun(product_prod(
45.23/45.41	                                                            arrow_411405190le_alt,
45.23/45.41	                                                            arrow_411405190le_alt),
45.23/45.41	                                                            bool)),
45.23/45.41	                                                    fun(product_prod(
45.23/45.41	                                                        arrow_411405190le_alt,
45.23/45.41	                                                        arrow_411405190le_alt),
45.23/45.41	                                                        bool)),
45.23/45.41	                                                app_encode_fun(fun(arrow_159774573e_indi,
45.23/45.41	                                                                   fun(
45.23/45.41	                                                                   product_prod(
45.23/45.41	                                                                   arrow_411405190le_alt,
45.23/45.41	                                                                   arrow_411405190le_alt),
45.23/45.41	                                                                   bool)),
45.23/45.41	                                                               fun(product_prod(
45.23/45.41	                                                                   arrow_411405190le_alt,
45.23/45.41	                                                                   arrow_411405190le_alt),
45.23/45.41	                                                                   bool)),
45.23/45.41	                                                aa(fun(arrow_159774573e_indi,
45.23/45.41	                                                       fun(product_prod(
45.23/45.41	                                                           arrow_411405190le_alt,
45.23/45.41	                                                           arrow_411405190le_alt),
45.23/45.41	                                                           bool)),
45.23/45.41	                                                   fun(product_prod(arrow_411405190le_alt,
45.23/45.41	                                                                    arrow_411405190le_alt),
45.23/45.41	                                                       bool)),
45.23/45.41	                                                f),
45.23/45.41	                                 app_encode_app(fun(arrow_159774573e_indi,
45.23/45.41	                                                    fun(product_prod(
45.23/45.41	                                                        arrow_411405190le_alt,
45.23/45.41	                                                        arrow_411405190le_alt),
45.23/45.41	                                                        bool)),
45.23/45.41	                                                fun(arrow_159774573e_indi,
45.23/45.41	                                                    fun(product_prod(
45.23/45.41	                                                        arrow_411405190le_alt,
45.23/45.41	                                                        arrow_411405190le_alt),
45.23/45.41	                                                        bool)),
45.23/45.41	                                                app_encode_app(fun(fun(
45.23/45.41	                                                                   product_prod(
45.23/45.41	                                                                   arrow_411405190le_alt,
45.23/45.41	                                                                   arrow_411405190le_alt),
45.23/45.41	                                                                   bool),
45.23/45.41	                                                                   fun(
45.23/45.41	                                                                   product_prod(
45.23/45.41	                                                                   arrow_411405190le_alt,
45.23/45.41	                                                                   arrow_411405190le_alt),
45.23/45.41	                                                                   bool)),
45.23/45.41	                                                               app_encode_fun(
45.23/45.41	                                                               fun(arrow_159774573e_indi,
45.23/45.41	                                                                   fun(
45.23/45.41	                                                                   product_prod(
45.23/45.41	                                                                   arrow_411405190le_alt,
45.23/45.41	                                                                   arrow_411405190le_alt),
45.23/45.41	                                                                   bool)),
45.23/45.41	                                                               fun(arrow_159774573e_indi,
45.23/45.41	                                                                   fun(
45.23/45.41	                                                                   product_prod(
45.23/45.41	                                                                   arrow_411405190le_alt,
45.23/45.41	                                                                   arrow_411405190le_alt),
45.23/45.41	                                                                   bool))),
45.23/45.41	                                                               comp(fun(
45.23/45.41	                                                                    product_prod(
45.23/45.41	                                                                    arrow_411405190le_alt,
45.23/45.41	                                                                    arrow_411405190le_alt),
45.23/45.41	                                                                    bool),
45.23/45.41	                                                                    fun(
45.23/45.41	                                                                    product_prod(
45.23/45.41	                                                                    arrow_411405190le_alt,
45.23/45.41	                                                                    arrow_411405190le_alt),
45.23/45.41	                                                                    bool),
45.23/45.41	                                                                    arrow_159774573e_indi),
45.23/45.41	                                                               converse(
45.23/45.41	                                                               arrow_411405190le_alt,
45.23/45.41	                                                               arrow_411405190le_alt)),
45.23/45.41	                                                p1))))).
45.23/45.41	tff('1', plain,
45.23/45.41	    (app_encode_app(
45.23/45.41	       fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), bool), 
45.23/45.41	       $o, 
45.23/45.41	       app_encode_app(
45.23/45.41	         product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	         app_encode_fun(
45.23/45.41	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	             bool), $o), 
45.23/45.41	         member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
45.23/45.41	         app_encode_app(arrow_411405190le_alt, 
45.23/45.41	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	           app_encode_app(arrow_411405190le_alt, 
45.23/45.41	             app_encode_fun(arrow_411405190le_alt, 
45.23/45.41	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
45.23/45.41	             product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), b), 
45.23/45.41	           a)), 
45.23/45.41	       app_encode_app(
45.23/45.41	         fun(arrow_159774573e_indi, 
45.23/45.41	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	             bool)), 
45.23/45.41	         fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	           bool), 
45.23/45.41	         app_encode_app(
45.23/45.41	           fun(
45.23/45.41	             fun(arrow_159774573e_indi, 
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool)), 
45.23/45.41	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	               bool)), 
45.23/45.41	           app_encode_fun(
45.23/45.41	             fun(arrow_159774573e_indi, 
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool)), 
45.23/45.41	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	               bool)), 
45.23/45.41	           aa(
45.23/45.41	             fun(arrow_159774573e_indi, 
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool)), 
45.23/45.41	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	               bool)), f), 
45.23/45.41	         app_encode_app(
45.23/45.41	           fun(arrow_159774573e_indi, 
45.23/45.41	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	               bool)), 
45.23/45.41	           fun(arrow_159774573e_indi, 
45.23/45.41	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	               bool)), 
45.23/45.41	           app_encode_app(
45.23/45.41	             fun(
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool), 
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool)), 
45.23/45.41	             app_encode_fun(
45.23/45.41	               fun(arrow_159774573e_indi, 
45.23/45.41	                 fun(
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                   bool)), 
45.23/45.41	               fun(arrow_159774573e_indi, 
45.23/45.41	                 fun(
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                   bool))), 
45.23/45.41	             comp(
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool), 
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool), arrow_159774573e_indi), 
45.23/45.41	             converse(arrow_411405190le_alt, arrow_411405190le_alt)), p1)))
45.23/45.41	     | ~ app_encode_app(
45.23/45.41	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	             bool), $o, 
45.23/45.41	           app_encode_app(
45.23/45.41	             product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	             app_encode_fun(
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool), $o), 
45.23/45.41	             member(
45.23/45.41	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
45.23/45.41	             app_encode_app(arrow_411405190le_alt, 
45.23/45.41	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	               app_encode_app(arrow_411405190le_alt, 
45.23/45.41	                 app_encode_fun(arrow_411405190le_alt, 
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
45.23/45.41	                 product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 a), b)), 
45.23/45.41	           app_encode_app(
45.23/45.41	             fun(arrow_159774573e_indi, 
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool)), 
45.23/45.41	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	               bool), 
45.23/45.41	             app_encode_app(
45.23/45.41	               fun(
45.23/45.41	                 fun(arrow_159774573e_indi, 
45.23/45.41	                   fun(
45.23/45.41	                     product_prod(arrow_411405190le_alt, 
45.23/45.41	                       arrow_411405190le_alt), bool)), 
45.23/45.41	                 fun(
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                   bool)), 
45.23/45.41	               app_encode_fun(
45.23/45.41	                 fun(arrow_159774573e_indi, 
45.23/45.41	                   fun(
45.23/45.41	                     product_prod(arrow_411405190le_alt, 
45.23/45.41	                       arrow_411405190le_alt), bool)), 
45.23/45.41	                 fun(
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                   bool)), 
45.23/45.41	               aa(
45.23/45.41	                 fun(arrow_159774573e_indi, 
45.23/45.41	                   fun(
45.23/45.41	                     product_prod(arrow_411405190le_alt, 
45.23/45.41	                       arrow_411405190le_alt), bool)), 
45.23/45.41	                 fun(
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                   bool)), f), p1))),
45.23/45.41	    inference('cnf', [status(esa)], [zf_stmt_48])).
45.23/45.41	tff(zf_stmt_50, axiom,
45.23/45.41	  (app_encode_app(fun(product_prod(arrow_411405190le_alt,
45.23/45.41	                                   arrow_411405190le_alt),
45.23/45.41	                      bool),
45.23/45.41	                  $o,
45.23/45.41	                  app_encode_app(product_prod(arrow_411405190le_alt,
45.23/45.41	                                              arrow_411405190le_alt),
45.23/45.41	                                 app_encode_fun(fun(product_prod(arrow_411405190le_alt,
45.23/45.41	                                                                 arrow_411405190le_alt),
45.23/45.41	                                                    bool),
45.23/45.41	                                                $o),
45.23/45.41	                                 member(product_prod(arrow_411405190le_alt,
45.23/45.41	                                                     arrow_411405190le_alt)),
45.23/45.41	                                 app_encode_app(arrow_411405190le_alt,
45.23/45.41	                                                product_prod(arrow_411405190le_alt,
45.23/45.41	                                                             arrow_411405190le_alt),
45.23/45.41	                                                app_encode_app(arrow_411405190le_alt,
45.23/45.41	                                                               app_encode_fun(
45.23/45.41	                                                               arrow_411405190le_alt,
45.23/45.41	                                                               product_prod(
45.23/45.41	                                                               arrow_411405190le_alt,
45.23/45.41	                                                               arrow_411405190le_alt)),
45.23/45.41	                                                               product_Pair(
45.23/45.41	                                                               arrow_411405190le_alt,
45.23/45.41	                                                               arrow_411405190le_alt),
45.23/45.41	                                                               b),
45.23/45.41	                                                a)),
45.23/45.41	                  app_encode_app(fun(arrow_159774573e_indi,
45.23/45.41	                                     fun(product_prod(arrow_411405190le_alt,
45.23/45.41	                                                      arrow_411405190le_alt),
45.23/45.41	                                         bool)),
45.23/45.41	                                 fun(product_prod(arrow_411405190le_alt,
45.23/45.41	                                                  arrow_411405190le_alt),
45.23/45.41	                                     bool),
45.23/45.41	                                 app_encode_app(fun(fun(arrow_159774573e_indi,
45.23/45.41	                                                        fun(product_prod(
45.23/45.41	                                                            arrow_411405190le_alt,
45.23/45.41	                                                            arrow_411405190le_alt),
45.23/45.41	                                                            bool)),
45.23/45.41	                                                    fun(product_prod(
45.23/45.41	                                                        arrow_411405190le_alt,
45.23/45.41	                                                        arrow_411405190le_alt),
45.23/45.41	                                                        bool)),
45.23/45.41	                                                app_encode_fun(fun(arrow_159774573e_indi,
45.23/45.41	                                                                   fun(
45.23/45.41	                                                                   product_prod(
45.23/45.41	                                                                   arrow_411405190le_alt,
45.23/45.41	                                                                   arrow_411405190le_alt),
45.23/45.41	                                                                   bool)),
45.23/45.41	                                                               fun(product_prod(
45.23/45.41	                                                                   arrow_411405190le_alt,
45.23/45.41	                                                                   arrow_411405190le_alt),
45.23/45.41	                                                                   bool)),
45.23/45.41	                                                aa(fun(arrow_159774573e_indi,
45.23/45.41	                                                       fun(product_prod(
45.23/45.41	                                                           arrow_411405190le_alt,
45.23/45.41	                                                           arrow_411405190le_alt),
45.23/45.41	                                                           bool)),
45.23/45.41	                                                   fun(product_prod(arrow_411405190le_alt,
45.23/45.41	                                                                    arrow_411405190le_alt),
45.23/45.41	                                                       bool)),
45.23/45.41	                                                f),
45.23/45.41	                                 app_encode_app(fun(arrow_159774573e_indi,
45.23/45.41	                                                    fun(product_prod(
45.23/45.41	                                                        arrow_411405190le_alt,
45.23/45.41	                                                        arrow_411405190le_alt),
45.23/45.41	                                                        bool)),
45.23/45.41	                                                fun(arrow_159774573e_indi,
45.23/45.41	                                                    fun(product_prod(
45.23/45.41	                                                        arrow_411405190le_alt,
45.23/45.41	                                                        arrow_411405190le_alt),
45.23/45.41	                                                        bool)),
45.23/45.41	                                                app_encode_app(fun(fun(
45.23/45.41	                                                                   product_prod(
45.23/45.41	                                                                   arrow_411405190le_alt,
45.23/45.41	                                                                   arrow_411405190le_alt),
45.23/45.41	                                                                   bool),
45.23/45.41	                                                                   fun(
45.23/45.41	                                                                   product_prod(
45.23/45.41	                                                                   arrow_411405190le_alt,
45.23/45.41	                                                                   arrow_411405190le_alt),
45.23/45.41	                                                                   bool)),
45.23/45.41	                                                               app_encode_fun(
45.23/45.41	                                                               fun(arrow_159774573e_indi,
45.23/45.41	                                                                   fun(
45.23/45.41	                                                                   product_prod(
45.23/45.41	                                                                   arrow_411405190le_alt,
45.23/45.41	                                                                   arrow_411405190le_alt),
45.23/45.41	                                                                   bool)),
45.23/45.41	                                                               fun(arrow_159774573e_indi,
45.23/45.41	                                                                   fun(
45.23/45.41	                                                                   product_prod(
45.23/45.41	                                                                   arrow_411405190le_alt,
45.23/45.41	                                                                   arrow_411405190le_alt),
45.23/45.41	                                                                   bool))),
45.23/45.41	                                                               comp(fun(
45.23/45.41	                                                                    product_prod(
45.23/45.41	                                                                    arrow_411405190le_alt,
45.23/45.41	                                                                    arrow_411405190le_alt),
45.23/45.41	                                                                    bool),
45.23/45.41	                                                                    fun(
45.23/45.41	                                                                    product_prod(
45.23/45.41	                                                                    arrow_411405190le_alt,
45.23/45.41	                                                                    arrow_411405190le_alt),
45.23/45.41	                                                                    bool),
45.23/45.41	                                                                    arrow_159774573e_indi),
45.23/45.41	                                                               converse(
45.23/45.41	                                                               arrow_411405190le_alt,
45.23/45.41	                                                               arrow_411405190le_alt)),
45.23/45.41	                                                p1))) <=>
45.23/45.41	   app_encode_app(fun(product_prod(arrow_411405190le_alt,
45.23/45.41	                                   arrow_411405190le_alt),
45.23/45.41	                      bool),
45.23/45.41	                  $o,
45.23/45.41	                  app_encode_app(product_prod(arrow_411405190le_alt,
45.23/45.41	                                              arrow_411405190le_alt),
45.23/45.41	                                 app_encode_fun(fun(product_prod(arrow_411405190le_alt,
45.23/45.41	                                                                 arrow_411405190le_alt),
45.23/45.41	                                                    bool),
45.23/45.41	                                                $o),
45.23/45.41	                                 member(product_prod(arrow_411405190le_alt,
45.23/45.41	                                                     arrow_411405190le_alt)),
45.23/45.41	                                 app_encode_app(arrow_411405190le_alt,
45.23/45.41	                                                product_prod(arrow_411405190le_alt,
45.23/45.41	                                                             arrow_411405190le_alt),
45.23/45.41	                                                app_encode_app(arrow_411405190le_alt,
45.23/45.41	                                                               app_encode_fun(
45.23/45.41	                                                               arrow_411405190le_alt,
45.23/45.41	                                                               product_prod(
45.23/45.41	                                                               arrow_411405190le_alt,
45.23/45.41	                                                               arrow_411405190le_alt)),
45.23/45.41	                                                               product_Pair(
45.23/45.41	                                                               arrow_411405190le_alt,
45.23/45.41	                                                               arrow_411405190le_alt),
45.23/45.41	                                                               b),
45.23/45.41	                                                c)),
45.23/45.41	                  app_encode_app(fun(arrow_159774573e_indi,
45.23/45.41	                                     fun(product_prod(arrow_411405190le_alt,
45.23/45.41	                                                      arrow_411405190le_alt),
45.23/45.41	                                         bool)),
45.23/45.41	                                 fun(product_prod(arrow_411405190le_alt,
45.23/45.41	                                                  arrow_411405190le_alt),
45.23/45.41	                                     bool),
45.23/45.41	                                 app_encode_app(fun(fun(arrow_159774573e_indi,
45.23/45.41	                                                        fun(product_prod(
45.23/45.41	                                                            arrow_411405190le_alt,
45.23/45.41	                                                            arrow_411405190le_alt),
45.23/45.41	                                                            bool)),
45.23/45.41	                                                    fun(product_prod(
45.23/45.41	                                                        arrow_411405190le_alt,
45.23/45.41	                                                        arrow_411405190le_alt),
45.23/45.41	                                                        bool)),
45.23/45.41	                                                app_encode_fun(fun(arrow_159774573e_indi,
45.23/45.41	                                                                   fun(
45.23/45.41	                                                                   product_prod(
45.23/45.41	                                                                   arrow_411405190le_alt,
45.23/45.41	                                                                   arrow_411405190le_alt),
45.23/45.41	                                                                   bool)),
45.23/45.41	                                                               fun(product_prod(
45.23/45.41	                                                                   arrow_411405190le_alt,
45.23/45.41	                                                                   arrow_411405190le_alt),
45.23/45.41	                                                                   bool)),
45.23/45.41	                                                aa(fun(arrow_159774573e_indi,
45.23/45.41	                                                       fun(product_prod(
45.23/45.41	                                                           arrow_411405190le_alt,
45.23/45.41	                                                           arrow_411405190le_alt),
45.23/45.41	                                                           bool)),
45.23/45.41	                                                   fun(product_prod(arrow_411405190le_alt,
45.23/45.41	                                                                    arrow_411405190le_alt),
45.23/45.41	                                                       bool)),
45.23/45.41	                                                f),
45.23/45.41	                                 p)))).
45.23/45.41	tff('2', plain,
45.23/45.41	    (app_encode_app(
45.23/45.41	       fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), bool), 
45.23/45.41	       $o, 
45.23/45.41	       app_encode_app(
45.23/45.41	         product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	         app_encode_fun(
45.23/45.41	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	             bool), $o), 
45.23/45.41	         member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
45.23/45.41	         app_encode_app(arrow_411405190le_alt, 
45.23/45.41	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	           app_encode_app(arrow_411405190le_alt, 
45.23/45.41	             app_encode_fun(arrow_411405190le_alt, 
45.23/45.41	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
45.23/45.41	             product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), b), 
45.23/45.41	           c)), 
45.23/45.41	       app_encode_app(
45.23/45.41	         fun(arrow_159774573e_indi, 
45.23/45.41	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	             bool)), 
45.23/45.41	         fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	           bool), 
45.23/45.41	         app_encode_app(
45.23/45.41	           fun(
45.23/45.41	             fun(arrow_159774573e_indi, 
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool)), 
45.23/45.41	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	               bool)), 
45.23/45.41	           app_encode_fun(
45.23/45.41	             fun(arrow_159774573e_indi, 
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool)), 
45.23/45.41	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	               bool)), 
45.23/45.41	           aa(
45.23/45.41	             fun(arrow_159774573e_indi, 
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool)), 
45.23/45.41	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	               bool)), f), p))
45.23/45.41	     | ~ app_encode_app(
45.23/45.41	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	             bool), $o, 
45.23/45.41	           app_encode_app(
45.23/45.41	             product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	             app_encode_fun(
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool), $o), 
45.23/45.41	             member(
45.23/45.41	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
45.23/45.41	             app_encode_app(arrow_411405190le_alt, 
45.23/45.41	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	               app_encode_app(arrow_411405190le_alt, 
45.23/45.41	                 app_encode_fun(arrow_411405190le_alt, 
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
45.23/45.41	                 product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 b), a)), 
45.23/45.41	           app_encode_app(
45.23/45.41	             fun(arrow_159774573e_indi, 
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool)), 
45.23/45.41	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	               bool), 
45.23/45.41	             app_encode_app(
45.23/45.41	               fun(
45.23/45.41	                 fun(arrow_159774573e_indi, 
45.23/45.41	                   fun(
45.23/45.41	                     product_prod(arrow_411405190le_alt, 
45.23/45.41	                       arrow_411405190le_alt), bool)), 
45.23/45.41	                 fun(
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                   bool)), 
45.23/45.41	               app_encode_fun(
45.23/45.41	                 fun(arrow_159774573e_indi, 
45.23/45.41	                   fun(
45.23/45.41	                     product_prod(arrow_411405190le_alt, 
45.23/45.41	                       arrow_411405190le_alt), bool)), 
45.23/45.41	                 fun(
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                   bool)), 
45.23/45.41	               aa(
45.23/45.41	                 fun(arrow_159774573e_indi, 
45.23/45.41	                   fun(
45.23/45.41	                     product_prod(arrow_411405190le_alt, 
45.23/45.41	                       arrow_411405190le_alt), bool)), 
45.23/45.41	                 fun(
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                   bool)), f), 
45.23/45.41	             app_encode_app(
45.23/45.41	               fun(arrow_159774573e_indi, 
45.23/45.41	                 fun(
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                   bool)), 
45.23/45.41	               fun(arrow_159774573e_indi, 
45.23/45.41	                 fun(
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                   bool)), 
45.23/45.41	               app_encode_app(
45.23/45.41	                 fun(
45.23/45.41	                   fun(
45.23/45.41	                     product_prod(arrow_411405190le_alt, 
45.23/45.41	                       arrow_411405190le_alt), bool), 
45.23/45.41	                   fun(
45.23/45.41	                     product_prod(arrow_411405190le_alt, 
45.23/45.41	                       arrow_411405190le_alt), bool)), 
45.23/45.41	                 app_encode_fun(
45.23/45.41	                   fun(arrow_159774573e_indi, 
45.23/45.41	                     fun(
45.23/45.41	                       product_prod(arrow_411405190le_alt, 
45.23/45.41	                         arrow_411405190le_alt), bool)), 
45.23/45.41	                   fun(arrow_159774573e_indi, 
45.23/45.41	                     fun(
45.23/45.41	                       product_prod(arrow_411405190le_alt, 
45.23/45.41	                         arrow_411405190le_alt), bool))), 
45.23/45.41	                 comp(
45.23/45.41	                   fun(
45.23/45.41	                     product_prod(arrow_411405190le_alt, 
45.23/45.41	                       arrow_411405190le_alt), bool), 
45.23/45.41	                   fun(
45.23/45.41	                     product_prod(arrow_411405190le_alt, 
45.23/45.41	                       arrow_411405190le_alt), bool), arrow_159774573e_indi), 
45.23/45.41	                 converse(arrow_411405190le_alt, arrow_411405190le_alt)), p1)))),
45.23/45.41	    inference('cnf', [status(esa)], [zf_stmt_50])).
45.23/45.41	tff('3', plain,
45.23/45.41	    (~ $true
45.23/45.41	     | ~ app_encode_app(
45.23/45.41	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	             bool), $o, 
45.23/45.41	           app_encode_app(
45.23/45.41	             product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	             app_encode_fun(
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool), $o), 
45.23/45.41	             member(
45.23/45.41	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
45.23/45.41	             app_encode_app(arrow_411405190le_alt, 
45.23/45.41	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	               app_encode_app(arrow_411405190le_alt, 
45.23/45.41	                 app_encode_fun(arrow_411405190le_alt, 
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
45.23/45.41	                 product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 a), b)), 
45.23/45.41	           app_encode_app(
45.23/45.41	             fun(arrow_159774573e_indi, 
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool)), 
45.23/45.41	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	               bool), 
45.23/45.41	             app_encode_app(
45.23/45.41	               fun(
45.23/45.41	                 fun(arrow_159774573e_indi, 
45.23/45.41	                   fun(
45.23/45.41	                     product_prod(arrow_411405190le_alt, 
45.23/45.41	                       arrow_411405190le_alt), bool)), 
45.23/45.41	                 fun(
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                   bool)), 
45.23/45.41	               app_encode_fun(
45.23/45.41	                 fun(arrow_159774573e_indi, 
45.23/45.41	                   fun(
45.23/45.41	                     product_prod(arrow_411405190le_alt, 
45.23/45.41	                       arrow_411405190le_alt), bool)), 
45.23/45.41	                 fun(
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                   bool)), 
45.23/45.41	               aa(
45.23/45.41	                 fun(arrow_159774573e_indi, 
45.23/45.41	                   fun(
45.23/45.41	                     product_prod(arrow_411405190le_alt, 
45.23/45.41	                       arrow_411405190le_alt), bool)), 
45.23/45.41	                 fun(
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                   bool)), f), p1))
45.23/45.41	     | app_encode_app(
45.23/45.41	         fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	           bool), $o, 
45.23/45.41	         app_encode_app(
45.23/45.41	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	           app_encode_fun(
45.23/45.41	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	               bool), $o), 
45.23/45.41	           member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
45.23/45.41	           app_encode_app(arrow_411405190le_alt, 
45.23/45.41	             product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	             app_encode_app(arrow_411405190le_alt, 
45.23/45.41	               app_encode_fun(arrow_411405190le_alt, 
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
45.23/45.41	               product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), b), 
45.23/45.41	             c)), 
45.23/45.41	         app_encode_app(
45.23/45.41	           fun(arrow_159774573e_indi, 
45.23/45.41	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	               bool)), 
45.23/45.41	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	             bool), 
45.23/45.41	           app_encode_app(
45.23/45.41	             fun(
45.23/45.41	               fun(arrow_159774573e_indi, 
45.23/45.41	                 fun(
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                   bool)), 
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool)), 
45.23/45.41	             app_encode_fun(
45.23/45.41	               fun(arrow_159774573e_indi, 
45.23/45.41	                 fun(
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                   bool)), 
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool)), 
45.23/45.41	             aa(
45.23/45.41	               fun(arrow_159774573e_indi, 
45.23/45.41	                 fun(
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                   bool)), 
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool)), f), p))),
45.23/45.41	    inference('sup-', [status(thm)], ['1', '2'])).
45.23/45.41	tff('4', plain,
45.23/45.41	    (app_encode_app(
45.23/45.41	       fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), bool), 
45.23/45.41	       $o, 
45.23/45.41	       app_encode_app(
45.23/45.41	         product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	         app_encode_fun(
45.23/45.41	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	             bool), $o), 
45.23/45.41	         member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
45.23/45.41	         app_encode_app(arrow_411405190le_alt, 
45.23/45.41	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	           app_encode_app(arrow_411405190le_alt, 
45.23/45.41	             app_encode_fun(arrow_411405190le_alt, 
45.23/45.41	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
45.23/45.41	             product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), b), 
45.23/45.41	           c)), 
45.23/45.41	       app_encode_app(
45.23/45.41	         fun(arrow_159774573e_indi, 
45.23/45.41	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	             bool)), 
45.23/45.41	         fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	           bool), 
45.23/45.41	         app_encode_app(
45.23/45.41	           fun(
45.23/45.41	             fun(arrow_159774573e_indi, 
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool)), 
45.23/45.41	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	               bool)), 
45.23/45.41	           app_encode_fun(
45.23/45.41	             fun(arrow_159774573e_indi, 
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool)), 
45.23/45.41	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	               bool)), 
45.23/45.41	           aa(
45.23/45.41	             fun(arrow_159774573e_indi, 
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool)), 
45.23/45.41	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	               bool)), f), p))
45.23/45.41	     | ~ app_encode_app(
45.23/45.41	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	             bool), $o, 
45.23/45.41	           app_encode_app(
45.23/45.41	             product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	             app_encode_fun(
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool), $o), 
45.23/45.41	             member(
45.23/45.41	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
45.23/45.41	             app_encode_app(arrow_411405190le_alt, 
45.23/45.41	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	               app_encode_app(arrow_411405190le_alt, 
45.23/45.41	                 app_encode_fun(arrow_411405190le_alt, 
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
45.23/45.41	                 product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 a), b)), 
45.23/45.41	           app_encode_app(
45.23/45.41	             fun(arrow_159774573e_indi, 
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool)), 
45.23/45.41	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	               bool), 
45.23/45.41	             app_encode_app(
45.23/45.41	               fun(
45.23/45.41	                 fun(arrow_159774573e_indi, 
45.23/45.41	                   fun(
45.23/45.41	                     product_prod(arrow_411405190le_alt, 
45.23/45.41	                       arrow_411405190le_alt), bool)), 
45.23/45.41	                 fun(
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                   bool)), 
45.23/45.41	               app_encode_fun(
45.23/45.41	                 fun(arrow_159774573e_indi, 
45.23/45.41	                   fun(
45.23/45.41	                     product_prod(arrow_411405190le_alt, 
45.23/45.41	                       arrow_411405190le_alt), bool)), 
45.23/45.41	                 fun(
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                   bool)), 
45.23/45.41	               aa(
45.23/45.41	                 fun(arrow_159774573e_indi, 
45.23/45.41	                   fun(
45.23/45.41	                     product_prod(arrow_411405190le_alt, 
45.23/45.41	                       arrow_411405190le_alt), bool)), 
45.23/45.41	                 fun(
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                   bool)), f), p1))),
45.23/45.41	    inference('simplify', [status(thm)], ['3'])).
45.23/45.41	tff('5', plain,
45.23/45.41	    (~ app_encode_app(
45.23/45.41	         fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	           bool), $o, 
45.23/45.41	         app_encode_app(
45.23/45.41	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	           app_encode_fun(
45.23/45.41	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	               bool), $o), 
45.23/45.41	           member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
45.23/45.41	           app_encode_app(arrow_411405190le_alt, 
45.23/45.41	             product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	             app_encode_app(arrow_411405190le_alt, 
45.23/45.41	               app_encode_fun(arrow_411405190le_alt, 
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
45.23/45.41	               product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), b), 
45.23/45.41	             c)), 
45.23/45.41	         app_encode_app(
45.23/45.41	           fun(arrow_159774573e_indi, 
45.23/45.41	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	               bool)), 
45.23/45.41	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	             bool), 
45.23/45.41	           app_encode_app(
45.23/45.41	             fun(
45.23/45.41	               fun(arrow_159774573e_indi, 
45.23/45.41	                 fun(
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                   bool)), 
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool)), 
45.23/45.41	             app_encode_fun(
45.23/45.41	               fun(arrow_159774573e_indi, 
45.23/45.41	                 fun(
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                   bool)), 
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool)), 
45.23/45.41	             aa(
45.23/45.41	               fun(arrow_159774573e_indi, 
45.23/45.41	                 fun(
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                   bool)), 
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool)), f), p))
45.23/45.41	     | ~ app_encode_app(
45.23/45.41	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	             bool), $o, 
45.23/45.41	           app_encode_app(
45.23/45.41	             product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	             app_encode_fun(
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool), $o), 
45.23/45.41	             member(
45.23/45.41	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
45.23/45.41	             app_encode_app(arrow_411405190le_alt, 
45.23/45.41	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	               app_encode_app(arrow_411405190le_alt, 
45.23/45.41	                 app_encode_fun(arrow_411405190le_alt, 
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
45.23/45.41	                 product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 a), b)), 
45.23/45.41	           app_encode_app(
45.23/45.41	             fun(arrow_159774573e_indi, 
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool)), 
45.23/45.41	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	               bool), 
45.23/45.41	             app_encode_app(
45.23/45.41	               fun(
45.23/45.41	                 fun(arrow_159774573e_indi, 
45.23/45.41	                   fun(
45.23/45.41	                     product_prod(arrow_411405190le_alt, 
45.23/45.41	                       arrow_411405190le_alt), bool)), 
45.23/45.41	                 fun(
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                   bool)), 
45.23/45.41	               app_encode_fun(
45.23/45.41	                 fun(arrow_159774573e_indi, 
45.23/45.41	                   fun(
45.23/45.41	                     product_prod(arrow_411405190le_alt, 
45.23/45.41	                       arrow_411405190le_alt), bool)), 
45.23/45.41	                 fun(
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                   bool)), 
45.23/45.41	               aa(
45.23/45.41	                 fun(arrow_159774573e_indi, 
45.23/45.41	                   fun(
45.23/45.41	                     product_prod(arrow_411405190le_alt, 
45.23/45.41	                       arrow_411405190le_alt), bool)), 
45.23/45.41	                 fun(
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                   bool)), f), p1))),
45.23/45.41	    inference('cnf', [status(esa)], [zf_stmt_0])).
45.23/45.41	tff('6', plain,
45.23/45.41	    ~ app_encode_app(
45.23/45.41	        fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), bool), 
45.23/45.41	        $o, 
45.23/45.41	        app_encode_app(
45.23/45.41	          product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	          app_encode_fun(
45.23/45.41	            fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	              bool), $o), 
45.23/45.41	          member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
45.23/45.41	          app_encode_app(arrow_411405190le_alt, 
45.23/45.41	            product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	            app_encode_app(arrow_411405190le_alt, 
45.23/45.41	              app_encode_fun(arrow_411405190le_alt, 
45.23/45.41	                product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
45.23/45.41	              product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), a), 
45.23/45.41	            b)), 
45.23/45.41	        app_encode_app(
45.23/45.41	          fun(arrow_159774573e_indi, 
45.23/45.41	            fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	              bool)), 
45.23/45.41	          fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	            bool), 
45.23/45.41	          app_encode_app(
45.23/45.41	            fun(
45.23/45.41	              fun(arrow_159774573e_indi, 
45.23/45.41	                fun(
45.23/45.41	                  product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                  bool)), 
45.23/45.41	              fun(
45.23/45.41	                product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                bool)), 
45.23/45.41	            app_encode_fun(
45.23/45.41	              fun(arrow_159774573e_indi, 
45.23/45.41	                fun(
45.23/45.41	                  product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                  bool)), 
45.23/45.41	              fun(
45.23/45.41	                product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                bool)), 
45.23/45.41	            aa(
45.23/45.41	              fun(arrow_159774573e_indi, 
45.23/45.41	                fun(
45.23/45.41	                  product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                  bool)), 
45.23/45.41	              fun(
45.23/45.41	                product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                bool)), f), p1)),
45.23/45.41	    inference('clc', [status(thm)], ['4', '5'])).
45.23/45.41	tff('7', plain,
45.23/45.41	    (~ $true
45.23/45.41	     | app_encode_app(
45.23/45.41	         fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	           bool), $o, 
45.23/45.41	         app_encode_app(
45.23/45.41	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	           app_encode_fun(
45.23/45.41	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	               bool), $o), 
45.23/45.41	           member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
45.23/45.41	           app_encode_app(arrow_411405190le_alt, 
45.23/45.41	             product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	             app_encode_app(arrow_411405190le_alt, 
45.23/45.41	               app_encode_fun(arrow_411405190le_alt, 
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
45.23/45.41	               product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), b), 
45.23/45.41	             c)), 
45.23/45.41	         app_encode_app(
45.23/45.41	           fun(arrow_159774573e_indi, 
45.23/45.41	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	               bool)), 
45.23/45.41	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	             bool), 
45.23/45.41	           app_encode_app(
45.23/45.41	             fun(
45.23/45.41	               fun(arrow_159774573e_indi, 
45.23/45.41	                 fun(
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                   bool)), 
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool)), 
45.23/45.41	             app_encode_fun(
45.23/45.41	               fun(arrow_159774573e_indi, 
45.23/45.41	                 fun(
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                   bool)), 
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool)), 
45.23/45.41	             aa(
45.23/45.41	               fun(arrow_159774573e_indi, 
45.23/45.41	                 fun(
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                   bool)), 
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool)), f), p))),
45.23/45.41	    inference('sup-', [status(thm)], ['0', '6'])).
45.23/45.41	tff('8', plain,
45.23/45.41	    app_encode_app(
45.23/45.41	      fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), bool), 
45.23/45.41	      $o, 
45.23/45.41	      app_encode_app(
45.23/45.41	        product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	        app_encode_fun(
45.23/45.41	          fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	            bool), $o), 
45.23/45.41	        member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
45.23/45.41	        app_encode_app(arrow_411405190le_alt, 
45.23/45.41	          product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	          app_encode_app(arrow_411405190le_alt, 
45.23/45.41	            app_encode_fun(arrow_411405190le_alt, 
45.23/45.41	              product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
45.23/45.41	            product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), b), 
45.23/45.41	          c)), 
45.23/45.41	      app_encode_app(
45.23/45.41	        fun(arrow_159774573e_indi, 
45.23/45.41	          fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	            bool)), 
45.23/45.41	        fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), bool), 
45.23/45.41	        app_encode_app(
45.23/45.41	          fun(
45.23/45.41	            fun(arrow_159774573e_indi, 
45.23/45.41	              fun(
45.23/45.41	                product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                bool)), 
45.23/45.41	            fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	              bool)), 
45.23/45.41	          app_encode_fun(
45.23/45.41	            fun(arrow_159774573e_indi, 
45.23/45.41	              fun(
45.23/45.41	                product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                bool)), 
45.23/45.41	            fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	              bool)), 
45.23/45.41	          aa(
45.23/45.41	            fun(arrow_159774573e_indi, 
45.23/45.41	              fun(
45.23/45.41	                product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                bool)), 
45.23/45.41	            fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	              bool)), f), p)),
45.23/45.41	    inference('simplify', [status(thm)], ['7'])).
45.23/45.41	tff('9', plain,
45.23/45.41	    (app_encode_app(
45.23/45.41	       fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), bool), 
45.23/45.41	       $o, 
45.23/45.41	       app_encode_app(
45.23/45.41	         product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	         app_encode_fun(
45.23/45.41	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	             bool), $o), 
45.23/45.41	         member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
45.23/45.41	         app_encode_app(arrow_411405190le_alt, 
45.23/45.41	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	           app_encode_app(arrow_411405190le_alt, 
45.23/45.41	             app_encode_fun(arrow_411405190le_alt, 
45.23/45.41	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
45.23/45.41	             product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), b), 
45.23/45.41	           a)), 
45.23/45.41	       app_encode_app(
45.23/45.41	         fun(arrow_159774573e_indi, 
45.23/45.41	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	             bool)), 
45.23/45.41	         fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	           bool), 
45.23/45.41	         app_encode_app(
45.23/45.41	           fun(
45.23/45.41	             fun(arrow_159774573e_indi, 
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool)), 
45.23/45.41	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	               bool)), 
45.23/45.41	           app_encode_fun(
45.23/45.41	             fun(arrow_159774573e_indi, 
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool)), 
45.23/45.41	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	               bool)), 
45.23/45.41	           aa(
45.23/45.41	             fun(arrow_159774573e_indi, 
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool)), 
45.23/45.41	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	               bool)), f), 
45.23/45.41	         app_encode_app(
45.23/45.41	           fun(arrow_159774573e_indi, 
45.23/45.41	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	               bool)), 
45.23/45.41	           fun(arrow_159774573e_indi, 
45.23/45.41	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	               bool)), 
45.23/45.41	           app_encode_app(
45.23/45.41	             fun(
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool), 
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool)), 
45.23/45.41	             app_encode_fun(
45.23/45.41	               fun(arrow_159774573e_indi, 
45.23/45.41	                 fun(
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                   bool)), 
45.23/45.41	               fun(arrow_159774573e_indi, 
45.23/45.41	                 fun(
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                   bool))), 
45.23/45.41	             comp(
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool), 
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool), arrow_159774573e_indi), 
45.23/45.41	             converse(arrow_411405190le_alt, arrow_411405190le_alt)), p1)))
45.23/45.41	     | ~ app_encode_app(
45.23/45.41	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	             bool), $o, 
45.23/45.41	           app_encode_app(
45.23/45.41	             product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	             app_encode_fun(
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool), $o), 
45.23/45.41	             member(
45.23/45.41	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
45.23/45.41	             app_encode_app(arrow_411405190le_alt, 
45.23/45.41	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	               app_encode_app(arrow_411405190le_alt, 
45.23/45.41	                 app_encode_fun(arrow_411405190le_alt, 
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
45.23/45.41	                 product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 b), c)), 
45.23/45.41	           app_encode_app(
45.23/45.41	             fun(arrow_159774573e_indi, 
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool)), 
45.23/45.41	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	               bool), 
45.23/45.41	             app_encode_app(
45.23/45.41	               fun(
45.23/45.41	                 fun(arrow_159774573e_indi, 
45.23/45.41	                   fun(
45.23/45.41	                     product_prod(arrow_411405190le_alt, 
45.23/45.41	                       arrow_411405190le_alt), bool)), 
45.23/45.41	                 fun(
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                   bool)), 
45.23/45.41	               app_encode_fun(
45.23/45.41	                 fun(arrow_159774573e_indi, 
45.23/45.41	                   fun(
45.23/45.41	                     product_prod(arrow_411405190le_alt, 
45.23/45.41	                       arrow_411405190le_alt), bool)), 
45.23/45.41	                 fun(
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                   bool)), 
45.23/45.41	               aa(
45.23/45.41	                 fun(arrow_159774573e_indi, 
45.23/45.41	                   fun(
45.23/45.41	                     product_prod(arrow_411405190le_alt, 
45.23/45.41	                       arrow_411405190le_alt), bool)), 
45.23/45.41	                 fun(
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                   bool)), f), p))),
45.23/45.41	    inference('cnf', [status(esa)], [zf_stmt_50])).
45.23/45.41	tff('10', plain,
45.23/45.41	    (app_encode_app(
45.23/45.41	       fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), bool), 
45.23/45.41	       $o, 
45.23/45.41	       app_encode_app(
45.23/45.41	         product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	         app_encode_fun(
45.23/45.41	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	             bool), $o), 
45.23/45.41	         member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
45.23/45.41	         app_encode_app(arrow_411405190le_alt, 
45.23/45.41	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	           app_encode_app(arrow_411405190le_alt, 
45.23/45.41	             app_encode_fun(arrow_411405190le_alt, 
45.23/45.41	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
45.23/45.41	             product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), a), 
45.23/45.41	           b)), 
45.23/45.41	       app_encode_app(
45.23/45.41	         fun(arrow_159774573e_indi, 
45.23/45.41	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	             bool)), 
45.23/45.41	         fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	           bool), 
45.23/45.41	         app_encode_app(
45.23/45.41	           fun(
45.23/45.41	             fun(arrow_159774573e_indi, 
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool)), 
45.23/45.41	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	               bool)), 
45.23/45.41	           app_encode_fun(
45.23/45.41	             fun(arrow_159774573e_indi, 
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool)), 
45.23/45.41	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	               bool)), 
45.23/45.41	           aa(
45.23/45.41	             fun(arrow_159774573e_indi, 
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool)), 
45.23/45.41	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	               bool)), f), p1))
45.23/45.41	     | ~ app_encode_app(
45.23/45.41	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	             bool), $o, 
45.23/45.41	           app_encode_app(
45.23/45.41	             product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	             app_encode_fun(
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool), $o), 
45.23/45.41	             member(
45.23/45.41	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
45.23/45.41	             app_encode_app(arrow_411405190le_alt, 
45.23/45.41	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	               app_encode_app(arrow_411405190le_alt, 
45.23/45.41	                 app_encode_fun(arrow_411405190le_alt, 
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
45.23/45.41	                 product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 b), a)), 
45.23/45.41	           app_encode_app(
45.23/45.41	             fun(arrow_159774573e_indi, 
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool)), 
45.23/45.41	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	               bool), 
45.23/45.41	             app_encode_app(
45.23/45.41	               fun(
45.23/45.41	                 fun(arrow_159774573e_indi, 
45.23/45.41	                   fun(
45.23/45.41	                     product_prod(arrow_411405190le_alt, 
45.23/45.41	                       arrow_411405190le_alt), bool)), 
45.23/45.41	                 fun(
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                   bool)), 
45.23/45.41	               app_encode_fun(
45.23/45.41	                 fun(arrow_159774573e_indi, 
45.23/45.41	                   fun(
45.23/45.41	                     product_prod(arrow_411405190le_alt, 
45.23/45.41	                       arrow_411405190le_alt), bool)), 
45.23/45.41	                 fun(
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                   bool)), 
45.23/45.41	               aa(
45.23/45.41	                 fun(arrow_159774573e_indi, 
45.23/45.41	                   fun(
45.23/45.41	                     product_prod(arrow_411405190le_alt, 
45.23/45.41	                       arrow_411405190le_alt), bool)), 
45.23/45.41	                 fun(
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                   bool)), f), 
45.23/45.41	             app_encode_app(
45.23/45.41	               fun(arrow_159774573e_indi, 
45.23/45.41	                 fun(
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                   bool)), 
45.23/45.41	               fun(arrow_159774573e_indi, 
45.23/45.41	                 fun(
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                   bool)), 
45.23/45.41	               app_encode_app(
45.23/45.41	                 fun(
45.23/45.41	                   fun(
45.23/45.41	                     product_prod(arrow_411405190le_alt, 
45.23/45.41	                       arrow_411405190le_alt), bool), 
45.23/45.41	                   fun(
45.23/45.41	                     product_prod(arrow_411405190le_alt, 
45.23/45.41	                       arrow_411405190le_alt), bool)), 
45.23/45.41	                 app_encode_fun(
45.23/45.41	                   fun(arrow_159774573e_indi, 
45.23/45.41	                     fun(
45.23/45.41	                       product_prod(arrow_411405190le_alt, 
45.23/45.41	                         arrow_411405190le_alt), bool)), 
45.23/45.41	                   fun(arrow_159774573e_indi, 
45.23/45.41	                     fun(
45.23/45.41	                       product_prod(arrow_411405190le_alt, 
45.23/45.41	                         arrow_411405190le_alt), bool))), 
45.23/45.41	                 comp(
45.23/45.41	                   fun(
45.23/45.41	                     product_prod(arrow_411405190le_alt, 
45.23/45.41	                       arrow_411405190le_alt), bool), 
45.23/45.41	                   fun(
45.23/45.41	                     product_prod(arrow_411405190le_alt, 
45.23/45.41	                       arrow_411405190le_alt), bool), arrow_159774573e_indi), 
45.23/45.41	                 converse(arrow_411405190le_alt, arrow_411405190le_alt)), p1)))),
45.23/45.41	    inference('cnf', [status(esa)], [zf_stmt_48])).
45.23/45.41	tff('11', plain,
45.23/45.41	    (~ $true
45.23/45.41	     | ~ app_encode_app(
45.23/45.41	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	             bool), $o, 
45.23/45.41	           app_encode_app(
45.23/45.41	             product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	             app_encode_fun(
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool), $o), 
45.23/45.41	             member(
45.23/45.41	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
45.23/45.41	             app_encode_app(arrow_411405190le_alt, 
45.23/45.41	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	               app_encode_app(arrow_411405190le_alt, 
45.23/45.41	                 app_encode_fun(arrow_411405190le_alt, 
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
45.23/45.41	                 product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 b), c)), 
45.23/45.41	           app_encode_app(
45.23/45.41	             fun(arrow_159774573e_indi, 
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool)), 
45.23/45.41	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	               bool), 
45.23/45.41	             app_encode_app(
45.23/45.41	               fun(
45.23/45.41	                 fun(arrow_159774573e_indi, 
45.23/45.41	                   fun(
45.23/45.41	                     product_prod(arrow_411405190le_alt, 
45.23/45.41	                       arrow_411405190le_alt), bool)), 
45.23/45.41	                 fun(
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                   bool)), 
45.23/45.41	               app_encode_fun(
45.23/45.41	                 fun(arrow_159774573e_indi, 
45.23/45.41	                   fun(
45.23/45.41	                     product_prod(arrow_411405190le_alt, 
45.23/45.41	                       arrow_411405190le_alt), bool)), 
45.23/45.41	                 fun(
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                   bool)), 
45.23/45.41	               aa(
45.23/45.41	                 fun(arrow_159774573e_indi, 
45.23/45.41	                   fun(
45.23/45.41	                     product_prod(arrow_411405190le_alt, 
45.23/45.41	                       arrow_411405190le_alt), bool)), 
45.23/45.41	                 fun(
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                   bool)), f), p))
45.23/45.41	     | app_encode_app(
45.23/45.41	         fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	           bool), $o, 
45.23/45.41	         app_encode_app(
45.23/45.41	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	           app_encode_fun(
45.23/45.41	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	               bool), $o), 
45.23/45.41	           member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
45.23/45.41	           app_encode_app(arrow_411405190le_alt, 
45.23/45.41	             product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	             app_encode_app(arrow_411405190le_alt, 
45.23/45.41	               app_encode_fun(arrow_411405190le_alt, 
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
45.23/45.41	               product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), a), 
45.23/45.41	             b)), 
45.23/45.41	         app_encode_app(
45.23/45.41	           fun(arrow_159774573e_indi, 
45.23/45.41	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	               bool)), 
45.23/45.41	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	             bool), 
45.23/45.41	           app_encode_app(
45.23/45.41	             fun(
45.23/45.41	               fun(arrow_159774573e_indi, 
45.23/45.41	                 fun(
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                   bool)), 
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool)), 
45.23/45.41	             app_encode_fun(
45.23/45.41	               fun(arrow_159774573e_indi, 
45.23/45.41	                 fun(
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                   bool)), 
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool)), 
45.23/45.41	             aa(
45.23/45.41	               fun(arrow_159774573e_indi, 
45.23/45.41	                 fun(
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                   bool)), 
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool)), f), p1))),
45.23/45.41	    inference('sup-', [status(thm)], ['9', '10'])).
45.23/45.41	tff('12', plain,
45.23/45.41	    (app_encode_app(
45.23/45.41	       fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), bool), 
45.23/45.41	       $o, 
45.23/45.41	       app_encode_app(
45.23/45.41	         product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	         app_encode_fun(
45.23/45.41	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	             bool), $o), 
45.23/45.41	         member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
45.23/45.41	         app_encode_app(arrow_411405190le_alt, 
45.23/45.41	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	           app_encode_app(arrow_411405190le_alt, 
45.23/45.41	             app_encode_fun(arrow_411405190le_alt, 
45.23/45.41	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
45.23/45.41	             product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), a), 
45.23/45.41	           b)), 
45.23/45.41	       app_encode_app(
45.23/45.41	         fun(arrow_159774573e_indi, 
45.23/45.41	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	             bool)), 
45.23/45.41	         fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	           bool), 
45.23/45.41	         app_encode_app(
45.23/45.41	           fun(
45.23/45.41	             fun(arrow_159774573e_indi, 
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool)), 
45.23/45.41	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	               bool)), 
45.23/45.41	           app_encode_fun(
45.23/45.41	             fun(arrow_159774573e_indi, 
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool)), 
45.23/45.41	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	               bool)), 
45.23/45.41	           aa(
45.23/45.41	             fun(arrow_159774573e_indi, 
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool)), 
45.23/45.41	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	               bool)), f), p1))
45.23/45.41	     | ~ app_encode_app(
45.23/45.41	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	             bool), $o, 
45.23/45.41	           app_encode_app(
45.23/45.41	             product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	             app_encode_fun(
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool), $o), 
45.23/45.41	             member(
45.23/45.41	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
45.23/45.41	             app_encode_app(arrow_411405190le_alt, 
45.23/45.41	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	               app_encode_app(arrow_411405190le_alt, 
45.23/45.41	                 app_encode_fun(arrow_411405190le_alt, 
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
45.23/45.41	                 product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 b), c)), 
45.23/45.41	           app_encode_app(
45.23/45.41	             fun(arrow_159774573e_indi, 
45.23/45.41	               fun(
45.23/45.41	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                 bool)), 
45.23/45.41	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	               bool), 
45.23/45.41	             app_encode_app(
45.23/45.41	               fun(
45.23/45.41	                 fun(arrow_159774573e_indi, 
45.23/45.41	                   fun(
45.23/45.41	                     product_prod(arrow_411405190le_alt, 
45.23/45.41	                       arrow_411405190le_alt), bool)), 
45.23/45.41	                 fun(
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                   bool)), 
45.23/45.41	               app_encode_fun(
45.23/45.41	                 fun(arrow_159774573e_indi, 
45.23/45.41	                   fun(
45.23/45.41	                     product_prod(arrow_411405190le_alt, 
45.23/45.41	                       arrow_411405190le_alt), bool)), 
45.23/45.41	                 fun(
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                   bool)), 
45.23/45.41	               aa(
45.23/45.41	                 fun(arrow_159774573e_indi, 
45.23/45.41	                   fun(
45.23/45.41	                     product_prod(arrow_411405190le_alt, 
45.23/45.41	                       arrow_411405190le_alt), bool)), 
45.23/45.41	                 fun(
45.23/45.41	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                   bool)), f), p))),
45.23/45.41	    inference('simplify', [status(thm)], ['11'])).
45.23/45.41	tff('13', plain,
45.23/45.41	    ~ app_encode_app(
45.23/45.41	        fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), bool), 
45.23/45.41	        $o, 
45.23/45.41	        app_encode_app(
45.23/45.41	          product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	          app_encode_fun(
45.23/45.41	            fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	              bool), $o), 
45.23/45.41	          member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
45.23/45.41	          app_encode_app(arrow_411405190le_alt, 
45.23/45.41	            product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	            app_encode_app(arrow_411405190le_alt, 
45.23/45.41	              app_encode_fun(arrow_411405190le_alt, 
45.23/45.41	                product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
45.23/45.41	              product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), b), 
45.23/45.41	            c)), 
45.23/45.41	        app_encode_app(
45.23/45.41	          fun(arrow_159774573e_indi, 
45.23/45.41	            fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	              bool)), 
45.23/45.41	          fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	            bool), 
45.23/45.41	          app_encode_app(
45.23/45.41	            fun(
45.23/45.41	              fun(arrow_159774573e_indi, 
45.23/45.41	                fun(
45.23/45.41	                  product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                  bool)), 
45.23/45.41	              fun(
45.23/45.41	                product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                bool)), 
45.23/45.41	            app_encode_fun(
45.23/45.41	              fun(arrow_159774573e_indi, 
45.23/45.41	                fun(
45.23/45.41	                  product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                  bool)), 
45.23/45.41	              fun(
45.23/45.41	                product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                bool)), 
45.23/45.41	            aa(
45.23/45.41	              fun(arrow_159774573e_indi, 
45.23/45.41	                fun(
45.23/45.41	                  product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                  bool)), 
45.23/45.41	              fun(
45.23/45.41	                product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
45.23/45.41	                bool)), f), p)),
45.23/45.41	    inference('clc', [status(thm)], ['12', '6'])).
45.23/45.41	tff('14', plain, ~ $true, inference('sup-', [status(thm)], ['8', '13'])).
45.23/45.41	tff('15', plain, $false, inference('simplify', [status(thm)], ['14'])).
45.23/45.41	
45.23/45.41	% SZS output end Refutation
45.23/45.41	EOF
