0.00/0.00	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : app
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : kbo
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-ho \
0.00/0.00	  --no-avatar \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n083.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 14:02:24 CST 2018
42.13/42.31	% done 2499 iterations in 42.109s
42.13/42.31	% SZS status Theorem for 'stdin'
42.13/42.31	% SZS output start Refutation
42.13/42.31	tff(zf_stmt_141, conjecture,
42.13/42.31	  (app_encode_app(fun(product_prod(arrow_411405190le_alt,
42.13/42.31	                                   arrow_411405190le_alt),
42.13/42.31	                      bool),
42.13/42.31	                  $o,
42.13/42.31	                  app_encode_app(product_prod(arrow_411405190le_alt,
42.13/42.31	                                              arrow_411405190le_alt),
42.13/42.31	                                 app_encode_fun(fun(product_prod(arrow_411405190le_alt,
42.13/42.31	                                                                 arrow_411405190le_alt),
42.13/42.31	                                                    bool),
42.13/42.31	                                                $o),
42.13/42.31	                                 member(product_prod(arrow_411405190le_alt,
42.13/42.31	                                                     arrow_411405190le_alt)),
42.13/42.31	                                 app_encode_app(arrow_411405190le_alt,
42.13/42.31	                                                product_prod(arrow_411405190le_alt,
42.13/42.31	                                                             arrow_411405190le_alt),
42.13/42.31	                                                app_encode_app(arrow_411405190le_alt,
42.13/42.31	                                                               app_encode_fun(
42.13/42.31	                                                               arrow_411405190le_alt,
42.13/42.31	                                                               product_prod(
42.13/42.31	                                                               arrow_411405190le_alt,
42.13/42.31	                                                               arrow_411405190le_alt)),
42.13/42.31	                                                               product_Pair(
42.13/42.31	                                                               arrow_411405190le_alt,
42.13/42.31	                                                               arrow_411405190le_alt),
42.13/42.31	                                                               a),
42.13/42.31	                                                b)),
42.13/42.31	                  app_encode_app(fun(arrow_159774573e_indi,
42.13/42.31	                                     fun(product_prod(arrow_411405190le_alt,
42.13/42.31	                                                      arrow_411405190le_alt),
42.13/42.31	                                         bool)),
42.13/42.31	                                 fun(product_prod(arrow_411405190le_alt,
42.13/42.31	                                                  arrow_411405190le_alt),
42.13/42.31	                                     bool),
42.13/42.31	                                 app_encode_app(fun(fun(arrow_159774573e_indi,
42.13/42.31	                                                        fun(product_prod(
42.13/42.31	                                                            arrow_411405190le_alt,
42.13/42.31	                                                            arrow_411405190le_alt),
42.13/42.31	                                                            bool)),
42.13/42.31	                                                    fun(product_prod(
42.13/42.31	                                                        arrow_411405190le_alt,
42.13/42.31	                                                        arrow_411405190le_alt),
42.13/42.31	                                                        bool)),
42.13/42.31	                                                app_encode_fun(fun(arrow_159774573e_indi,
42.13/42.31	                                                                   fun(
42.13/42.31	                                                                   product_prod(
42.13/42.31	                                                                   arrow_411405190le_alt,
42.13/42.31	                                                                   arrow_411405190le_alt),
42.13/42.31	                                                                   bool)),
42.13/42.31	                                                               fun(product_prod(
42.13/42.31	                                                                   arrow_411405190le_alt,
42.13/42.31	                                                                   arrow_411405190le_alt),
42.13/42.31	                                                                   bool)),
42.13/42.31	                                                aa(fun(arrow_159774573e_indi,
42.13/42.31	                                                       fun(product_prod(
42.13/42.31	                                                           arrow_411405190le_alt,
42.13/42.31	                                                           arrow_411405190le_alt),
42.13/42.31	                                                           bool)),
42.13/42.31	                                                   fun(product_prod(arrow_411405190le_alt,
42.13/42.31	                                                                    arrow_411405190le_alt),
42.13/42.31	                                                       bool)),
42.13/42.31	                                                f),
42.13/42.31	                                 p1)) <=>
42.13/42.31	   app_encode_app(fun(product_prod(arrow_411405190le_alt,
42.13/42.31	                                   arrow_411405190le_alt),
42.13/42.31	                      bool),
42.13/42.31	                  $o,
42.13/42.31	                  app_encode_app(product_prod(arrow_411405190le_alt,
42.13/42.31	                                              arrow_411405190le_alt),
42.13/42.31	                                 app_encode_fun(fun(product_prod(arrow_411405190le_alt,
42.13/42.31	                                                                 arrow_411405190le_alt),
42.13/42.31	                                                    bool),
42.13/42.31	                                                $o),
42.13/42.31	                                 member(product_prod(arrow_411405190le_alt,
42.13/42.31	                                                     arrow_411405190le_alt)),
42.13/42.31	                                 app_encode_app(arrow_411405190le_alt,
42.13/42.31	                                                product_prod(arrow_411405190le_alt,
42.13/42.31	                                                             arrow_411405190le_alt),
42.13/42.31	                                                app_encode_app(arrow_411405190le_alt,
42.13/42.31	                                                               app_encode_fun(
42.13/42.31	                                                               arrow_411405190le_alt,
42.13/42.31	                                                               product_prod(
42.13/42.31	                                                               arrow_411405190le_alt,
42.13/42.31	                                                               arrow_411405190le_alt)),
42.13/42.31	                                                               product_Pair(
42.13/42.31	                                                               arrow_411405190le_alt,
42.13/42.31	                                                               arrow_411405190le_alt),
42.13/42.31	                                                               b),
42.13/42.31	                                                c)),
42.13/42.31	                  app_encode_app(fun(arrow_159774573e_indi,
42.13/42.31	                                     fun(product_prod(arrow_411405190le_alt,
42.13/42.31	                                                      arrow_411405190le_alt),
42.13/42.31	                                         bool)),
42.13/42.31	                                 fun(product_prod(arrow_411405190le_alt,
42.13/42.31	                                                  arrow_411405190le_alt),
42.13/42.31	                                     bool),
42.13/42.31	                                 app_encode_app(fun(fun(arrow_159774573e_indi,
42.13/42.31	                                                        fun(product_prod(
42.13/42.31	                                                            arrow_411405190le_alt,
42.13/42.31	                                                            arrow_411405190le_alt),
42.13/42.31	                                                            bool)),
42.13/42.31	                                                    fun(product_prod(
42.13/42.31	                                                        arrow_411405190le_alt,
42.13/42.31	                                                        arrow_411405190le_alt),
42.13/42.31	                                                        bool)),
42.13/42.31	                                                app_encode_fun(fun(arrow_159774573e_indi,
42.13/42.31	                                                                   fun(
42.13/42.31	                                                                   product_prod(
42.13/42.31	                                                                   arrow_411405190le_alt,
42.13/42.31	                                                                   arrow_411405190le_alt),
42.13/42.31	                                                                   bool)),
42.13/42.31	                                                               fun(product_prod(
42.13/42.31	                                                                   arrow_411405190le_alt,
42.13/42.31	                                                                   arrow_411405190le_alt),
42.13/42.31	                                                                   bool)),
42.13/42.31	                                                aa(fun(arrow_159774573e_indi,
42.13/42.31	                                                       fun(product_prod(
42.13/42.31	                                                           arrow_411405190le_alt,
42.13/42.31	                                                           arrow_411405190le_alt),
42.13/42.31	                                                           bool)),
42.13/42.31	                                                   fun(product_prod(arrow_411405190le_alt,
42.13/42.31	                                                                    arrow_411405190le_alt),
42.13/42.31	                                                       bool)),
42.13/42.31	                                                f),
42.13/42.31	                                 p)))).
42.13/42.31	tff(zf_stmt_0, negated_conjecture,
42.13/42.31	  (~
42.13/42.31	    (app_encode_app(fun(product_prod(arrow_411405190le_alt,
42.13/42.31	                                     arrow_411405190le_alt),
42.13/42.31	                        bool),
42.13/42.31	                    $o,
42.13/42.31	                    app_encode_app(product_prod(arrow_411405190le_alt,
42.13/42.31	                                                arrow_411405190le_alt),
42.13/42.31	                                   app_encode_fun(fun(product_prod(arrow_411405190le_alt,
42.13/42.31	                                                                   arrow_411405190le_alt),
42.13/42.31	                                                      bool),
42.13/42.31	                                                  $o),
42.13/42.31	                                   member(product_prod(arrow_411405190le_alt,
42.13/42.31	                                                       arrow_411405190le_alt)),
42.13/42.31	                                   app_encode_app(arrow_411405190le_alt,
42.13/42.31	                                                  product_prod(arrow_411405190le_alt,
42.13/42.31	                                                               arrow_411405190le_alt),
42.13/42.31	                                                  app_encode_app(arrow_411405190le_alt,
42.13/42.31	                                                                 app_encode_fun(
42.13/42.31	                                                                 arrow_411405190le_alt,
42.13/42.31	                                                                 product_prod(
42.13/42.31	                                                                 arrow_411405190le_alt,
42.13/42.31	                                                                 arrow_411405190le_alt)),
42.13/42.31	                                                                 product_Pair(
42.13/42.31	                                                                 arrow_411405190le_alt,
42.13/42.31	                                                                 arrow_411405190le_alt),
42.13/42.31	                                                                 a),
42.13/42.31	                                                  b)),
42.13/42.31	                    app_encode_app(fun(arrow_159774573e_indi,
42.13/42.31	                                       fun(product_prod(arrow_411405190le_alt,
42.13/42.31	                                                        arrow_411405190le_alt),
42.13/42.31	                                           bool)),
42.13/42.31	                                   fun(product_prod(arrow_411405190le_alt,
42.13/42.31	                                                    arrow_411405190le_alt),
42.13/42.31	                                       bool),
42.13/42.31	                                   app_encode_app(fun(fun(arrow_159774573e_indi,
42.13/42.31	                                                          fun(product_prod(
42.13/42.31	                                                              arrow_411405190le_alt,
42.13/42.31	                                                              arrow_411405190le_alt),
42.13/42.31	                                                              bool)),
42.13/42.31	                                                      fun(product_prod(
42.13/42.31	                                                          arrow_411405190le_alt,
42.13/42.31	                                                          arrow_411405190le_alt),
42.13/42.31	                                                          bool)),
42.13/42.31	                                                  app_encode_fun(fun(
42.13/42.31	                                                                 arrow_159774573e_indi,
42.13/42.31	                                                                 fun(
42.13/42.31	                                                                 product_prod(
42.13/42.31	                                                                 arrow_411405190le_alt,
42.13/42.31	                                                                 arrow_411405190le_alt),
42.13/42.31	                                                                 bool)),
42.13/42.31	                                                                 fun(
42.13/42.31	                                                                 product_prod(
42.13/42.31	                                                                 arrow_411405190le_alt,
42.13/42.31	                                                                 arrow_411405190le_alt),
42.13/42.31	                                                                 bool)),
42.13/42.31	                                                  aa(fun(arrow_159774573e_indi,
42.13/42.31	                                                         fun(product_prod(
42.13/42.31	                                                             arrow_411405190le_alt,
42.13/42.31	                                                             arrow_411405190le_alt),
42.13/42.31	                                                             bool)),
42.13/42.31	                                                     fun(product_prod(
42.13/42.31	                                                         arrow_411405190le_alt,
42.13/42.31	                                                         arrow_411405190le_alt),
42.13/42.31	                                                         bool)),
42.13/42.31	                                                  f),
42.13/42.31	                                   p1)) <=>
42.13/42.31	     app_encode_app(fun(product_prod(arrow_411405190le_alt,
42.13/42.31	                                     arrow_411405190le_alt),
42.13/42.31	                        bool),
42.13/42.31	                    $o,
42.13/42.31	                    app_encode_app(product_prod(arrow_411405190le_alt,
42.13/42.31	                                                arrow_411405190le_alt),
42.13/42.31	                                   app_encode_fun(fun(product_prod(arrow_411405190le_alt,
42.13/42.31	                                                                   arrow_411405190le_alt),
42.13/42.31	                                                      bool),
42.13/42.31	                                                  $o),
42.13/42.31	                                   member(product_prod(arrow_411405190le_alt,
42.13/42.31	                                                       arrow_411405190le_alt)),
42.13/42.31	                                   app_encode_app(arrow_411405190le_alt,
42.13/42.31	                                                  product_prod(arrow_411405190le_alt,
42.13/42.31	                                                               arrow_411405190le_alt),
42.13/42.31	                                                  app_encode_app(arrow_411405190le_alt,
42.13/42.31	                                                                 app_encode_fun(
42.13/42.31	                                                                 arrow_411405190le_alt,
42.13/42.31	                                                                 product_prod(
42.13/42.31	                                                                 arrow_411405190le_alt,
42.13/42.31	                                                                 arrow_411405190le_alt)),
42.13/42.31	                                                                 product_Pair(
42.13/42.31	                                                                 arrow_411405190le_alt,
42.13/42.31	                                                                 arrow_411405190le_alt),
42.13/42.31	                                                                 b),
42.13/42.31	                                                  c)),
42.13/42.31	                    app_encode_app(fun(arrow_159774573e_indi,
42.13/42.31	                                       fun(product_prod(arrow_411405190le_alt,
42.13/42.31	                                                        arrow_411405190le_alt),
42.13/42.31	                                           bool)),
42.13/42.31	                                   fun(product_prod(arrow_411405190le_alt,
42.13/42.31	                                                    arrow_411405190le_alt),
42.13/42.31	                                       bool),
42.13/42.31	                                   app_encode_app(fun(fun(arrow_159774573e_indi,
42.13/42.31	                                                          fun(product_prod(
42.13/42.31	                                                              arrow_411405190le_alt,
42.13/42.31	                                                              arrow_411405190le_alt),
42.13/42.31	                                                              bool)),
42.13/42.31	                                                      fun(product_prod(
42.13/42.31	                                                          arrow_411405190le_alt,
42.13/42.31	                                                          arrow_411405190le_alt),
42.13/42.31	                                                          bool)),
42.13/42.31	                                                  app_encode_fun(fun(
42.13/42.31	                                                                 arrow_159774573e_indi,
42.13/42.31	                                                                 fun(
42.13/42.31	                                                                 product_prod(
42.13/42.31	                                                                 arrow_411405190le_alt,
42.13/42.31	                                                                 arrow_411405190le_alt),
42.13/42.31	                                                                 bool)),
42.13/42.31	                                                                 fun(
42.13/42.31	                                                                 product_prod(
42.13/42.31	                                                                 arrow_411405190le_alt,
42.13/42.31	                                                                 arrow_411405190le_alt),
42.13/42.31	                                                                 bool)),
42.13/42.31	                                                  aa(fun(arrow_159774573e_indi,
42.13/42.31	                                                         fun(product_prod(
42.13/42.31	                                                             arrow_411405190le_alt,
42.13/42.31	                                                             arrow_411405190le_alt),
42.13/42.31	                                                             bool)),
42.13/42.31	                                                     fun(product_prod(
42.13/42.31	                                                         arrow_411405190le_alt,
42.13/42.31	                                                         arrow_411405190le_alt),
42.13/42.31	                                                         bool)),
42.13/42.31	                                                  f),
42.13/42.31	                                   p))))).
42.13/42.31	tff('0', plain,
42.13/42.31	    (app_encode_app(
42.13/42.31	       fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), bool), 
42.13/42.31	       $o, 
42.13/42.31	       app_encode_app(
42.13/42.31	         product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.31	         app_encode_fun(
42.13/42.31	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.31	             bool), $o), 
42.13/42.31	         member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
42.13/42.31	         app_encode_app(arrow_411405190le_alt, 
42.13/42.31	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.31	           app_encode_app(arrow_411405190le_alt, 
42.13/42.31	             app_encode_fun(arrow_411405190le_alt, 
42.13/42.31	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
42.13/42.31	             product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), b), 
42.13/42.31	           c)), 
42.13/42.31	       app_encode_app(
42.13/42.31	         fun(arrow_159774573e_indi, 
42.13/42.31	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.31	             bool)), 
42.13/42.31	         fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.31	           bool), 
42.13/42.31	         app_encode_app(
42.13/42.31	           fun(
42.13/42.31	             fun(arrow_159774573e_indi, 
42.13/42.31	               fun(
42.13/42.31	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.31	                 bool)), 
42.13/42.31	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.31	               bool)), 
42.13/42.31	           app_encode_fun(
42.13/42.31	             fun(arrow_159774573e_indi, 
42.13/42.31	               fun(
42.13/42.31	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.31	                 bool)), 
42.13/42.31	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.31	               bool)), 
42.13/42.31	           aa(
42.13/42.31	             fun(arrow_159774573e_indi, 
42.13/42.31	               fun(
42.13/42.31	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.31	                 bool)), 
42.13/42.31	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.31	               bool)), f), p))
42.13/42.31	     | app_encode_app(
42.13/42.31	         fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.31	           bool), $o, 
42.13/42.31	         app_encode_app(
42.13/42.31	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.31	           app_encode_fun(
42.13/42.31	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.31	               bool), $o), 
42.13/42.31	           member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
42.13/42.31	           app_encode_app(arrow_411405190le_alt, 
42.13/42.31	             product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.31	             app_encode_app(arrow_411405190le_alt, 
42.13/42.31	               app_encode_fun(arrow_411405190le_alt, 
42.13/42.31	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
42.13/42.31	               product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), a), 
42.13/42.31	             b)), 
42.13/42.31	         app_encode_app(
42.13/42.31	           fun(arrow_159774573e_indi, 
42.13/42.31	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.31	               bool)), 
42.13/42.31	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.31	             bool), 
42.13/42.31	           app_encode_app(
42.13/42.31	             fun(
42.13/42.31	               fun(arrow_159774573e_indi, 
42.13/42.31	                 fun(
42.13/42.31	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.31	                   bool)), 
42.13/42.31	               fun(
42.13/42.31	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.31	                 bool)), 
42.13/42.31	             app_encode_fun(
42.13/42.31	               fun(arrow_159774573e_indi, 
42.13/42.31	                 fun(
42.13/42.31	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.31	                   bool)), 
42.13/42.31	               fun(
42.13/42.31	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.31	                 bool)), 
42.13/42.31	             aa(
42.13/42.31	               fun(arrow_159774573e_indi, 
42.13/42.31	                 fun(
42.13/42.31	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.31	                   bool)), 
42.13/42.31	               fun(
42.13/42.31	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.31	                 bool)), f), p1))),
42.13/42.31	    inference('cnf', [status(esa)], [zf_stmt_0])).
42.13/42.31	tff(zf_stmt_47, axiom,
42.13/42.31	  (app_encode_app(fun(product_prod(arrow_411405190le_alt,
42.13/42.31	                                   arrow_411405190le_alt),
42.13/42.31	                      bool),
42.13/42.31	                  $o,
42.13/42.31	                  app_encode_app(product_prod(arrow_411405190le_alt,
42.13/42.31	                                              arrow_411405190le_alt),
42.13/42.31	                                 app_encode_fun(fun(product_prod(arrow_411405190le_alt,
42.13/42.31	                                                                 arrow_411405190le_alt),
42.13/42.31	                                                    bool),
42.13/42.31	                                                $o),
42.13/42.31	                                 member(product_prod(arrow_411405190le_alt,
42.13/42.31	                                                     arrow_411405190le_alt)),
42.13/42.31	                                 app_encode_app(arrow_411405190le_alt,
42.13/42.31	                                                product_prod(arrow_411405190le_alt,
42.13/42.31	                                                             arrow_411405190le_alt),
42.13/42.31	                                                app_encode_app(arrow_411405190le_alt,
42.13/42.31	                                                               app_encode_fun(
42.13/42.31	                                                               arrow_411405190le_alt,
42.13/42.31	                                                               product_prod(
42.13/42.31	                                                               arrow_411405190le_alt,
42.13/42.31	                                                               arrow_411405190le_alt)),
42.13/42.31	                                                               product_Pair(
42.13/42.31	                                                               arrow_411405190le_alt,
42.13/42.31	                                                               arrow_411405190le_alt),
42.13/42.31	                                                               a),
42.13/42.31	                                                b)),
42.13/42.31	                  app_encode_app(fun(arrow_159774573e_indi,
42.13/42.31	                                     fun(product_prod(arrow_411405190le_alt,
42.13/42.31	                                                      arrow_411405190le_alt),
42.13/42.31	                                         bool)),
42.13/42.31	                                 fun(product_prod(arrow_411405190le_alt,
42.13/42.31	                                                  arrow_411405190le_alt),
42.13/42.31	                                     bool),
42.13/42.31	                                 app_encode_app(fun(fun(arrow_159774573e_indi,
42.13/42.31	                                                        fun(product_prod(
42.13/42.31	                                                            arrow_411405190le_alt,
42.13/42.31	                                                            arrow_411405190le_alt),
42.13/42.31	                                                            bool)),
42.13/42.31	                                                    fun(product_prod(
42.13/42.31	                                                        arrow_411405190le_alt,
42.13/42.31	                                                        arrow_411405190le_alt),
42.13/42.31	                                                        bool)),
42.13/42.31	                                                app_encode_fun(fun(arrow_159774573e_indi,
42.13/42.31	                                                                   fun(
42.13/42.31	                                                                   product_prod(
42.13/42.31	                                                                   arrow_411405190le_alt,
42.13/42.31	                                                                   arrow_411405190le_alt),
42.13/42.31	                                                                   bool)),
42.13/42.31	                                                               fun(product_prod(
42.13/42.31	                                                                   arrow_411405190le_alt,
42.13/42.31	                                                                   arrow_411405190le_alt),
42.13/42.31	                                                                   bool)),
42.13/42.31	                                                aa(fun(arrow_159774573e_indi,
42.13/42.31	                                                       fun(product_prod(
42.13/42.31	                                                           arrow_411405190le_alt,
42.13/42.31	                                                           arrow_411405190le_alt),
42.13/42.31	                                                           bool)),
42.13/42.31	                                                   fun(product_prod(arrow_411405190le_alt,
42.13/42.31	                                                                    arrow_411405190le_alt),
42.13/42.31	                                                       bool)),
42.13/42.31	                                                f),
42.13/42.31	                                 p1)) <=>
42.13/42.31	   app_encode_app(fun(product_prod(arrow_411405190le_alt,
42.13/42.31	                                   arrow_411405190le_alt),
42.13/42.31	                      bool),
42.13/42.31	                  $o,
42.13/42.31	                  app_encode_app(product_prod(arrow_411405190le_alt,
42.13/42.31	                                              arrow_411405190le_alt),
42.13/42.31	                                 app_encode_fun(fun(product_prod(arrow_411405190le_alt,
42.13/42.31	                                                                 arrow_411405190le_alt),
42.13/42.31	                                                    bool),
42.13/42.31	                                                $o),
42.13/42.31	                                 member(product_prod(arrow_411405190le_alt,
42.13/42.31	                                                     arrow_411405190le_alt)),
42.13/42.31	                                 app_encode_app(arrow_411405190le_alt,
42.13/42.31	                                                product_prod(arrow_411405190le_alt,
42.13/42.31	                                                             arrow_411405190le_alt),
42.13/42.31	                                                app_encode_app(arrow_411405190le_alt,
42.13/42.31	                                                               app_encode_fun(
42.13/42.31	                                                               arrow_411405190le_alt,
42.13/42.31	                                                               product_prod(
42.13/42.31	                                                               arrow_411405190le_alt,
42.13/42.31	                                                               arrow_411405190le_alt)),
42.13/42.31	                                                               product_Pair(
42.13/42.31	                                                               arrow_411405190le_alt,
42.13/42.31	                                                               arrow_411405190le_alt),
42.13/42.31	                                                               b),
42.13/42.31	                                                a)),
42.13/42.31	                  app_encode_app(fun(arrow_159774573e_indi,
42.13/42.31	                                     fun(product_prod(arrow_411405190le_alt,
42.13/42.31	                                                      arrow_411405190le_alt),
42.13/42.31	                                         bool)),
42.13/42.31	                                 fun(product_prod(arrow_411405190le_alt,
42.13/42.31	                                                  arrow_411405190le_alt),
42.13/42.31	                                     bool),
42.13/42.31	                                 app_encode_app(fun(fun(arrow_159774573e_indi,
42.13/42.31	                                                        fun(product_prod(
42.13/42.31	                                                            arrow_411405190le_alt,
42.13/42.31	                                                            arrow_411405190le_alt),
42.13/42.31	                                                            bool)),
42.13/42.31	                                                    fun(product_prod(
42.13/42.31	                                                        arrow_411405190le_alt,
42.13/42.31	                                                        arrow_411405190le_alt),
42.13/42.31	                                                        bool)),
42.13/42.31	                                                app_encode_fun(fun(arrow_159774573e_indi,
42.13/42.31	                                                                   fun(
42.13/42.31	                                                                   product_prod(
42.13/42.31	                                                                   arrow_411405190le_alt,
42.13/42.31	                                                                   arrow_411405190le_alt),
42.13/42.31	                                                                   bool)),
42.13/42.31	                                                               fun(product_prod(
42.13/42.31	                                                                   arrow_411405190le_alt,
42.13/42.31	                                                                   arrow_411405190le_alt),
42.13/42.31	                                                                   bool)),
42.13/42.31	                                                aa(fun(arrow_159774573e_indi,
42.13/42.31	                                                       fun(product_prod(
42.13/42.31	                                                           arrow_411405190le_alt,
42.13/42.31	                                                           arrow_411405190le_alt),
42.13/42.31	                                                           bool)),
42.13/42.31	                                                   fun(product_prod(arrow_411405190le_alt,
42.13/42.31	                                                                    arrow_411405190le_alt),
42.13/42.31	                                                       bool)),
42.13/42.31	                                                f),
42.13/42.31	                                 app_encode_app(fun(arrow_159774573e_indi,
42.13/42.31	                                                    fun(product_prod(
42.13/42.31	                                                        arrow_411405190le_alt,
42.13/42.31	                                                        arrow_411405190le_alt),
42.13/42.31	                                                        bool)),
42.13/42.31	                                                fun(arrow_159774573e_indi,
42.13/42.31	                                                    fun(product_prod(
42.13/42.31	                                                        arrow_411405190le_alt,
42.13/42.31	                                                        arrow_411405190le_alt),
42.13/42.31	                                                        bool)),
42.13/42.31	                                                app_encode_app(fun(fun(
42.13/42.31	                                                                   product_prod(
42.13/42.31	                                                                   arrow_411405190le_alt,
42.13/42.31	                                                                   arrow_411405190le_alt),
42.13/42.31	                                                                   bool),
42.13/42.31	                                                                   fun(
42.13/42.31	                                                                   product_prod(
42.13/42.31	                                                                   arrow_411405190le_alt,
42.13/42.31	                                                                   arrow_411405190le_alt),
42.13/42.31	                                                                   bool)),
42.13/42.31	                                                               app_encode_fun(
42.13/42.31	                                                               fun(arrow_159774573e_indi,
42.13/42.31	                                                                   fun(
42.13/42.31	                                                                   product_prod(
42.13/42.31	                                                                   arrow_411405190le_alt,
42.13/42.31	                                                                   arrow_411405190le_alt),
42.13/42.31	                                                                   bool)),
42.13/42.31	                                                               fun(arrow_159774573e_indi,
42.13/42.31	                                                                   fun(
42.13/42.31	                                                                   product_prod(
42.13/42.31	                                                                   arrow_411405190le_alt,
42.13/42.31	                                                                   arrow_411405190le_alt),
42.13/42.31	                                                                   bool))),
42.13/42.31	                                                               comp(fun(
42.13/42.31	                                                                    product_prod(
42.13/42.31	                                                                    arrow_411405190le_alt,
42.13/42.31	                                                                    arrow_411405190le_alt),
42.13/42.31	                                                                    bool),
42.13/42.31	                                                                    fun(
42.13/42.31	                                                                    product_prod(
42.13/42.31	                                                                    arrow_411405190le_alt,
42.13/42.31	                                                                    arrow_411405190le_alt),
42.13/42.31	                                                                    bool),
42.13/42.31	                                                                    arrow_159774573e_indi),
42.13/42.31	                                                               converse(
42.13/42.31	                                                               arrow_411405190le_alt,
42.13/42.31	                                                               arrow_411405190le_alt)),
42.13/42.31	                                                p1))))).
42.13/42.31	tff('1', plain,
42.13/42.31	    (app_encode_app(
42.13/42.31	       fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), bool), 
42.13/42.31	       $o, 
42.13/42.31	       app_encode_app(
42.13/42.31	         product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.31	         app_encode_fun(
42.13/42.31	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.31	             bool), $o), 
42.13/42.31	         member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
42.13/42.31	         app_encode_app(arrow_411405190le_alt, 
42.13/42.31	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.31	           app_encode_app(arrow_411405190le_alt, 
42.13/42.31	             app_encode_fun(arrow_411405190le_alt, 
42.13/42.31	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
42.13/42.31	             product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), b), 
42.13/42.31	           a)), 
42.13/42.31	       app_encode_app(
42.13/42.31	         fun(arrow_159774573e_indi, 
42.13/42.31	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.31	             bool)), 
42.13/42.31	         fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.31	           bool), 
42.13/42.31	         app_encode_app(
42.13/42.31	           fun(
42.13/42.31	             fun(arrow_159774573e_indi, 
42.13/42.31	               fun(
42.13/42.31	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.31	                 bool)), 
42.13/42.31	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.31	               bool)), 
42.13/42.31	           app_encode_fun(
42.13/42.31	             fun(arrow_159774573e_indi, 
42.13/42.31	               fun(
42.13/42.31	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.31	                 bool)), 
42.13/42.31	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.31	               bool)), 
42.13/42.31	           aa(
42.13/42.31	             fun(arrow_159774573e_indi, 
42.13/42.31	               fun(
42.13/42.31	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.31	                 bool)), 
42.13/42.31	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.31	               bool)), f), 
42.13/42.31	         app_encode_app(
42.13/42.31	           fun(arrow_159774573e_indi, 
42.13/42.31	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.31	               bool)), 
42.13/42.31	           fun(arrow_159774573e_indi, 
42.13/42.31	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.31	               bool)), 
42.13/42.31	           app_encode_app(
42.13/42.31	             fun(
42.13/42.31	               fun(
42.13/42.31	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.31	                 bool), 
42.13/42.31	               fun(
42.13/42.31	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.31	                 bool)), 
42.13/42.31	             app_encode_fun(
42.13/42.31	               fun(arrow_159774573e_indi, 
42.13/42.31	                 fun(
42.13/42.31	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.31	                   bool)), 
42.13/42.31	               fun(arrow_159774573e_indi, 
42.13/42.31	                 fun(
42.13/42.31	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.31	                   bool))), 
42.13/42.31	             comp(
42.13/42.31	               fun(
42.13/42.31	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.31	                 bool), 
42.13/42.31	               fun(
42.13/42.31	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.31	                 bool), arrow_159774573e_indi), 
42.13/42.31	             converse(arrow_411405190le_alt, arrow_411405190le_alt)), p1)))
42.13/42.31	     | ~ app_encode_app(
42.13/42.31	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.31	             bool), $o, 
42.13/42.31	           app_encode_app(
42.13/42.31	             product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.31	             app_encode_fun(
42.13/42.31	               fun(
42.13/42.31	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.31	                 bool), $o), 
42.13/42.31	             member(
42.13/42.31	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
42.13/42.31	             app_encode_app(arrow_411405190le_alt, 
42.13/42.31	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.31	               app_encode_app(arrow_411405190le_alt, 
42.13/42.31	                 app_encode_fun(arrow_411405190le_alt, 
42.13/42.31	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
42.13/42.31	                 product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.31	                 a), b)), 
42.13/42.31	           app_encode_app(
42.13/42.31	             fun(arrow_159774573e_indi, 
42.13/42.31	               fun(
42.13/42.31	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.31	                 bool)), 
42.13/42.31	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.31	               bool), 
42.13/42.31	             app_encode_app(
42.13/42.31	               fun(
42.13/42.31	                 fun(arrow_159774573e_indi, 
42.13/42.31	                   fun(
42.13/42.31	                     product_prod(arrow_411405190le_alt, 
42.13/42.31	                       arrow_411405190le_alt), bool)), 
42.13/42.31	                 fun(
42.13/42.31	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.31	                   bool)), 
42.13/42.31	               app_encode_fun(
42.13/42.31	                 fun(arrow_159774573e_indi, 
42.13/42.31	                   fun(
42.13/42.31	                     product_prod(arrow_411405190le_alt, 
42.13/42.31	                       arrow_411405190le_alt), bool)), 
42.13/42.31	                 fun(
42.13/42.31	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.31	                   bool)), 
42.13/42.31	               aa(
42.13/42.31	                 fun(arrow_159774573e_indi, 
42.13/42.31	                   fun(
42.13/42.31	                     product_prod(arrow_411405190le_alt, 
42.13/42.31	                       arrow_411405190le_alt), bool)), 
42.13/42.31	                 fun(
42.13/42.31	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.31	                   bool)), f), p1))),
42.13/42.31	    inference('cnf', [status(esa)], [zf_stmt_47])).
42.13/42.31	tff(zf_stmt_49, axiom,
42.13/42.31	  (app_encode_app(fun(product_prod(arrow_411405190le_alt,
42.13/42.31	                                   arrow_411405190le_alt),
42.13/42.31	                      bool),
42.13/42.31	                  $o,
42.13/42.31	                  app_encode_app(product_prod(arrow_411405190le_alt,
42.13/42.31	                                              arrow_411405190le_alt),
42.13/42.31	                                 app_encode_fun(fun(product_prod(arrow_411405190le_alt,
42.13/42.31	                                                                 arrow_411405190le_alt),
42.13/42.31	                                                    bool),
42.13/42.31	                                                $o),
42.13/42.31	                                 member(product_prod(arrow_411405190le_alt,
42.13/42.31	                                                     arrow_411405190le_alt)),
42.13/42.31	                                 app_encode_app(arrow_411405190le_alt,
42.13/42.31	                                                product_prod(arrow_411405190le_alt,
42.13/42.31	                                                             arrow_411405190le_alt),
42.13/42.31	                                                app_encode_app(arrow_411405190le_alt,
42.13/42.31	                                                               app_encode_fun(
42.13/42.31	                                                               arrow_411405190le_alt,
42.13/42.31	                                                               product_prod(
42.13/42.31	                                                               arrow_411405190le_alt,
42.13/42.31	                                                               arrow_411405190le_alt)),
42.13/42.31	                                                               product_Pair(
42.13/42.31	                                                               arrow_411405190le_alt,
42.13/42.31	                                                               arrow_411405190le_alt),
42.13/42.31	                                                               b),
42.13/42.31	                                                a)),
42.13/42.31	                  app_encode_app(fun(arrow_159774573e_indi,
42.13/42.31	                                     fun(product_prod(arrow_411405190le_alt,
42.13/42.31	                                                      arrow_411405190le_alt),
42.13/42.31	                                         bool)),
42.13/42.31	                                 fun(product_prod(arrow_411405190le_alt,
42.13/42.31	                                                  arrow_411405190le_alt),
42.13/42.31	                                     bool),
42.13/42.31	                                 app_encode_app(fun(fun(arrow_159774573e_indi,
42.13/42.31	                                                        fun(product_prod(
42.13/42.31	                                                            arrow_411405190le_alt,
42.13/42.32	                                                            arrow_411405190le_alt),
42.13/42.32	                                                            bool)),
42.13/42.32	                                                    fun(product_prod(
42.13/42.32	                                                        arrow_411405190le_alt,
42.13/42.32	                                                        arrow_411405190le_alt),
42.13/42.32	                                                        bool)),
42.13/42.32	                                                app_encode_fun(fun(arrow_159774573e_indi,
42.13/42.32	                                                                   fun(
42.13/42.32	                                                                   product_prod(
42.13/42.32	                                                                   arrow_411405190le_alt,
42.13/42.32	                                                                   arrow_411405190le_alt),
42.13/42.32	                                                                   bool)),
42.13/42.32	                                                               fun(product_prod(
42.13/42.32	                                                                   arrow_411405190le_alt,
42.13/42.32	                                                                   arrow_411405190le_alt),
42.13/42.32	                                                                   bool)),
42.13/42.32	                                                aa(fun(arrow_159774573e_indi,
42.13/42.32	                                                       fun(product_prod(
42.13/42.32	                                                           arrow_411405190le_alt,
42.13/42.32	                                                           arrow_411405190le_alt),
42.13/42.32	                                                           bool)),
42.13/42.32	                                                   fun(product_prod(arrow_411405190le_alt,
42.13/42.32	                                                                    arrow_411405190le_alt),
42.13/42.32	                                                       bool)),
42.13/42.32	                                                f),
42.13/42.32	                                 app_encode_app(fun(arrow_159774573e_indi,
42.13/42.32	                                                    fun(product_prod(
42.13/42.32	                                                        arrow_411405190le_alt,
42.13/42.32	                                                        arrow_411405190le_alt),
42.13/42.32	                                                        bool)),
42.13/42.32	                                                fun(arrow_159774573e_indi,
42.13/42.32	                                                    fun(product_prod(
42.13/42.32	                                                        arrow_411405190le_alt,
42.13/42.32	                                                        arrow_411405190le_alt),
42.13/42.32	                                                        bool)),
42.13/42.32	                                                app_encode_app(fun(fun(
42.13/42.32	                                                                   product_prod(
42.13/42.32	                                                                   arrow_411405190le_alt,
42.13/42.32	                                                                   arrow_411405190le_alt),
42.13/42.32	                                                                   bool),
42.13/42.32	                                                                   fun(
42.13/42.32	                                                                   product_prod(
42.13/42.32	                                                                   arrow_411405190le_alt,
42.13/42.32	                                                                   arrow_411405190le_alt),
42.13/42.32	                                                                   bool)),
42.13/42.32	                                                               app_encode_fun(
42.13/42.32	                                                               fun(arrow_159774573e_indi,
42.13/42.32	                                                                   fun(
42.13/42.32	                                                                   product_prod(
42.13/42.32	                                                                   arrow_411405190le_alt,
42.13/42.32	                                                                   arrow_411405190le_alt),
42.13/42.32	                                                                   bool)),
42.13/42.32	                                                               fun(arrow_159774573e_indi,
42.13/42.32	                                                                   fun(
42.13/42.32	                                                                   product_prod(
42.13/42.32	                                                                   arrow_411405190le_alt,
42.13/42.32	                                                                   arrow_411405190le_alt),
42.13/42.32	                                                                   bool))),
42.13/42.32	                                                               comp(fun(
42.13/42.32	                                                                    product_prod(
42.13/42.32	                                                                    arrow_411405190le_alt,
42.13/42.32	                                                                    arrow_411405190le_alt),
42.13/42.32	                                                                    bool),
42.13/42.32	                                                                    fun(
42.13/42.32	                                                                    product_prod(
42.13/42.32	                                                                    arrow_411405190le_alt,
42.13/42.32	                                                                    arrow_411405190le_alt),
42.13/42.32	                                                                    bool),
42.13/42.32	                                                                    arrow_159774573e_indi),
42.13/42.32	                                                               converse(
42.13/42.32	                                                               arrow_411405190le_alt,
42.13/42.32	                                                               arrow_411405190le_alt)),
42.13/42.32	                                                p1))) <=>
42.13/42.32	   app_encode_app(fun(product_prod(arrow_411405190le_alt,
42.13/42.32	                                   arrow_411405190le_alt),
42.13/42.32	                      bool),
42.13/42.32	                  $o,
42.13/42.32	                  app_encode_app(product_prod(arrow_411405190le_alt,
42.13/42.32	                                              arrow_411405190le_alt),
42.13/42.32	                                 app_encode_fun(fun(product_prod(arrow_411405190le_alt,
42.13/42.32	                                                                 arrow_411405190le_alt),
42.13/42.32	                                                    bool),
42.13/42.32	                                                $o),
42.13/42.32	                                 member(product_prod(arrow_411405190le_alt,
42.13/42.32	                                                     arrow_411405190le_alt)),
42.13/42.32	                                 app_encode_app(arrow_411405190le_alt,
42.13/42.32	                                                product_prod(arrow_411405190le_alt,
42.13/42.32	                                                             arrow_411405190le_alt),
42.13/42.32	                                                app_encode_app(arrow_411405190le_alt,
42.13/42.32	                                                               app_encode_fun(
42.13/42.32	                                                               arrow_411405190le_alt,
42.13/42.32	                                                               product_prod(
42.13/42.32	                                                               arrow_411405190le_alt,
42.13/42.32	                                                               arrow_411405190le_alt)),
42.13/42.32	                                                               product_Pair(
42.13/42.32	                                                               arrow_411405190le_alt,
42.13/42.32	                                                               arrow_411405190le_alt),
42.13/42.32	                                                               b),
42.13/42.32	                                                c)),
42.13/42.32	                  app_encode_app(fun(arrow_159774573e_indi,
42.13/42.32	                                     fun(product_prod(arrow_411405190le_alt,
42.13/42.32	                                                      arrow_411405190le_alt),
42.13/42.32	                                         bool)),
42.13/42.32	                                 fun(product_prod(arrow_411405190le_alt,
42.13/42.32	                                                  arrow_411405190le_alt),
42.13/42.32	                                     bool),
42.13/42.32	                                 app_encode_app(fun(fun(arrow_159774573e_indi,
42.13/42.32	                                                        fun(product_prod(
42.13/42.32	                                                            arrow_411405190le_alt,
42.13/42.32	                                                            arrow_411405190le_alt),
42.13/42.32	                                                            bool)),
42.13/42.32	                                                    fun(product_prod(
42.13/42.32	                                                        arrow_411405190le_alt,
42.13/42.32	                                                        arrow_411405190le_alt),
42.13/42.32	                                                        bool)),
42.13/42.32	                                                app_encode_fun(fun(arrow_159774573e_indi,
42.13/42.32	                                                                   fun(
42.13/42.32	                                                                   product_prod(
42.13/42.32	                                                                   arrow_411405190le_alt,
42.13/42.32	                                                                   arrow_411405190le_alt),
42.13/42.32	                                                                   bool)),
42.13/42.32	                                                               fun(product_prod(
42.13/42.32	                                                                   arrow_411405190le_alt,
42.13/42.32	                                                                   arrow_411405190le_alt),
42.13/42.32	                                                                   bool)),
42.13/42.32	                                                aa(fun(arrow_159774573e_indi,
42.13/42.32	                                                       fun(product_prod(
42.13/42.32	                                                           arrow_411405190le_alt,
42.13/42.32	                                                           arrow_411405190le_alt),
42.13/42.32	                                                           bool)),
42.13/42.32	                                                   fun(product_prod(arrow_411405190le_alt,
42.13/42.32	                                                                    arrow_411405190le_alt),
42.13/42.32	                                                       bool)),
42.13/42.32	                                                f),
42.13/42.32	                                 p)))).
42.13/42.32	tff('2', plain,
42.13/42.32	    (app_encode_app(
42.13/42.32	       fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), bool), 
42.13/42.32	       $o, 
42.13/42.32	       app_encode_app(
42.13/42.32	         product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	         app_encode_fun(
42.13/42.32	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	             bool), $o), 
42.13/42.32	         member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
42.13/42.32	         app_encode_app(arrow_411405190le_alt, 
42.13/42.32	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	           app_encode_app(arrow_411405190le_alt, 
42.13/42.32	             app_encode_fun(arrow_411405190le_alt, 
42.13/42.32	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
42.13/42.32	             product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), b), 
42.13/42.32	           c)), 
42.13/42.32	       app_encode_app(
42.13/42.32	         fun(arrow_159774573e_indi, 
42.13/42.32	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	             bool)), 
42.13/42.32	         fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	           bool), 
42.13/42.32	         app_encode_app(
42.13/42.32	           fun(
42.13/42.32	             fun(arrow_159774573e_indi, 
42.13/42.32	               fun(
42.13/42.32	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                 bool)), 
42.13/42.32	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	               bool)), 
42.13/42.32	           app_encode_fun(
42.13/42.32	             fun(arrow_159774573e_indi, 
42.13/42.32	               fun(
42.13/42.32	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                 bool)), 
42.13/42.32	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	               bool)), 
42.13/42.32	           aa(
42.13/42.32	             fun(arrow_159774573e_indi, 
42.13/42.32	               fun(
42.13/42.32	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                 bool)), 
42.13/42.32	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	               bool)), f), p))
42.13/42.32	     | ~ app_encode_app(
42.13/42.32	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	             bool), $o, 
42.13/42.32	           app_encode_app(
42.13/42.32	             product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	             app_encode_fun(
42.13/42.32	               fun(
42.13/42.32	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                 bool), $o), 
42.13/42.32	             member(
42.13/42.32	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
42.13/42.32	             app_encode_app(arrow_411405190le_alt, 
42.13/42.32	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	               app_encode_app(arrow_411405190le_alt, 
42.13/42.32	                 app_encode_fun(arrow_411405190le_alt, 
42.13/42.32	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
42.13/42.32	                 product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                 b), a)), 
42.13/42.32	           app_encode_app(
42.13/42.32	             fun(arrow_159774573e_indi, 
42.13/42.32	               fun(
42.13/42.32	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                 bool)), 
42.13/42.32	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	               bool), 
42.13/42.32	             app_encode_app(
42.13/42.32	               fun(
42.13/42.32	                 fun(arrow_159774573e_indi, 
42.13/42.32	                   fun(
42.13/42.32	                     product_prod(arrow_411405190le_alt, 
42.13/42.32	                       arrow_411405190le_alt), bool)), 
42.13/42.32	                 fun(
42.13/42.32	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                   bool)), 
42.13/42.32	               app_encode_fun(
42.13/42.32	                 fun(arrow_159774573e_indi, 
42.13/42.32	                   fun(
42.13/42.32	                     product_prod(arrow_411405190le_alt, 
42.13/42.32	                       arrow_411405190le_alt), bool)), 
42.13/42.32	                 fun(
42.13/42.32	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                   bool)), 
42.13/42.32	               aa(
42.13/42.32	                 fun(arrow_159774573e_indi, 
42.13/42.32	                   fun(
42.13/42.32	                     product_prod(arrow_411405190le_alt, 
42.13/42.32	                       arrow_411405190le_alt), bool)), 
42.13/42.32	                 fun(
42.13/42.32	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                   bool)), f), 
42.13/42.32	             app_encode_app(
42.13/42.32	               fun(arrow_159774573e_indi, 
42.13/42.32	                 fun(
42.13/42.32	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                   bool)), 
42.13/42.32	               fun(arrow_159774573e_indi, 
42.13/42.32	                 fun(
42.13/42.32	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                   bool)), 
42.13/42.32	               app_encode_app(
42.13/42.32	                 fun(
42.13/42.32	                   fun(
42.13/42.32	                     product_prod(arrow_411405190le_alt, 
42.13/42.32	                       arrow_411405190le_alt), bool), 
42.13/42.32	                   fun(
42.13/42.32	                     product_prod(arrow_411405190le_alt, 
42.13/42.32	                       arrow_411405190le_alt), bool)), 
42.13/42.32	                 app_encode_fun(
42.13/42.32	                   fun(arrow_159774573e_indi, 
42.13/42.32	                     fun(
42.13/42.32	                       product_prod(arrow_411405190le_alt, 
42.13/42.32	                         arrow_411405190le_alt), bool)), 
42.13/42.32	                   fun(arrow_159774573e_indi, 
42.13/42.32	                     fun(
42.13/42.32	                       product_prod(arrow_411405190le_alt, 
42.13/42.32	                         arrow_411405190le_alt), bool))), 
42.13/42.32	                 comp(
42.13/42.32	                   fun(
42.13/42.32	                     product_prod(arrow_411405190le_alt, 
42.13/42.32	                       arrow_411405190le_alt), bool), 
42.13/42.32	                   fun(
42.13/42.32	                     product_prod(arrow_411405190le_alt, 
42.13/42.32	                       arrow_411405190le_alt), bool), arrow_159774573e_indi), 
42.13/42.32	                 converse(arrow_411405190le_alt, arrow_411405190le_alt)), p1)))),
42.13/42.32	    inference('cnf', [status(esa)], [zf_stmt_49])).
42.13/42.32	tff('3', plain,
42.13/42.32	    (~ $true
42.13/42.32	     | ~ app_encode_app(
42.13/42.32	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	             bool), $o, 
42.13/42.32	           app_encode_app(
42.13/42.32	             product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	             app_encode_fun(
42.13/42.32	               fun(
42.13/42.32	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                 bool), $o), 
42.13/42.32	             member(
42.13/42.32	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
42.13/42.32	             app_encode_app(arrow_411405190le_alt, 
42.13/42.32	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	               app_encode_app(arrow_411405190le_alt, 
42.13/42.32	                 app_encode_fun(arrow_411405190le_alt, 
42.13/42.32	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
42.13/42.32	                 product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                 a), b)), 
42.13/42.32	           app_encode_app(
42.13/42.32	             fun(arrow_159774573e_indi, 
42.13/42.32	               fun(
42.13/42.32	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                 bool)), 
42.13/42.32	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	               bool), 
42.13/42.32	             app_encode_app(
42.13/42.32	               fun(
42.13/42.32	                 fun(arrow_159774573e_indi, 
42.13/42.32	                   fun(
42.13/42.32	                     product_prod(arrow_411405190le_alt, 
42.13/42.32	                       arrow_411405190le_alt), bool)), 
42.13/42.32	                 fun(
42.13/42.32	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                   bool)), 
42.13/42.32	               app_encode_fun(
42.13/42.32	                 fun(arrow_159774573e_indi, 
42.13/42.32	                   fun(
42.13/42.32	                     product_prod(arrow_411405190le_alt, 
42.13/42.32	                       arrow_411405190le_alt), bool)), 
42.13/42.32	                 fun(
42.13/42.32	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                   bool)), 
42.13/42.32	               aa(
42.13/42.32	                 fun(arrow_159774573e_indi, 
42.13/42.32	                   fun(
42.13/42.32	                     product_prod(arrow_411405190le_alt, 
42.13/42.32	                       arrow_411405190le_alt), bool)), 
42.13/42.32	                 fun(
42.13/42.32	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                   bool)), f), p1))
42.13/42.32	     | app_encode_app(
42.13/42.32	         fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	           bool), $o, 
42.13/42.32	         app_encode_app(
42.13/42.32	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	           app_encode_fun(
42.13/42.32	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	               bool), $o), 
42.13/42.32	           member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
42.13/42.32	           app_encode_app(arrow_411405190le_alt, 
42.13/42.32	             product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	             app_encode_app(arrow_411405190le_alt, 
42.13/42.32	               app_encode_fun(arrow_411405190le_alt, 
42.13/42.32	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
42.13/42.32	               product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), b), 
42.13/42.32	             c)), 
42.13/42.32	         app_encode_app(
42.13/42.32	           fun(arrow_159774573e_indi, 
42.13/42.32	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	               bool)), 
42.13/42.32	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	             bool), 
42.13/42.32	           app_encode_app(
42.13/42.32	             fun(
42.13/42.32	               fun(arrow_159774573e_indi, 
42.13/42.32	                 fun(
42.13/42.32	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                   bool)), 
42.13/42.32	               fun(
42.13/42.32	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                 bool)), 
42.13/42.32	             app_encode_fun(
42.13/42.32	               fun(arrow_159774573e_indi, 
42.13/42.32	                 fun(
42.13/42.32	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                   bool)), 
42.13/42.32	               fun(
42.13/42.32	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                 bool)), 
42.13/42.32	             aa(
42.13/42.32	               fun(arrow_159774573e_indi, 
42.13/42.32	                 fun(
42.13/42.32	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                   bool)), 
42.13/42.32	               fun(
42.13/42.32	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                 bool)), f), p))),
42.13/42.32	    inference('sup-', [status(thm)], ['1', '2'])).
42.13/42.32	tff('4', plain,
42.13/42.32	    (app_encode_app(
42.13/42.32	       fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), bool), 
42.13/42.32	       $o, 
42.13/42.32	       app_encode_app(
42.13/42.32	         product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	         app_encode_fun(
42.13/42.32	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	             bool), $o), 
42.13/42.32	         member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
42.13/42.32	         app_encode_app(arrow_411405190le_alt, 
42.13/42.32	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	           app_encode_app(arrow_411405190le_alt, 
42.13/42.32	             app_encode_fun(arrow_411405190le_alt, 
42.13/42.32	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
42.13/42.32	             product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), b), 
42.13/42.32	           c)), 
42.13/42.32	       app_encode_app(
42.13/42.32	         fun(arrow_159774573e_indi, 
42.13/42.32	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	             bool)), 
42.13/42.32	         fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	           bool), 
42.13/42.32	         app_encode_app(
42.13/42.32	           fun(
42.13/42.32	             fun(arrow_159774573e_indi, 
42.13/42.32	               fun(
42.13/42.32	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                 bool)), 
42.13/42.32	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	               bool)), 
42.13/42.32	           app_encode_fun(
42.13/42.32	             fun(arrow_159774573e_indi, 
42.13/42.32	               fun(
42.13/42.32	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                 bool)), 
42.13/42.32	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	               bool)), 
42.13/42.32	           aa(
42.13/42.32	             fun(arrow_159774573e_indi, 
42.13/42.32	               fun(
42.13/42.32	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                 bool)), 
42.13/42.32	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	               bool)), f), p))
42.13/42.32	     | ~ app_encode_app(
42.13/42.32	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	             bool), $o, 
42.13/42.32	           app_encode_app(
42.13/42.32	             product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	             app_encode_fun(
42.13/42.32	               fun(
42.13/42.32	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                 bool), $o), 
42.13/42.32	             member(
42.13/42.32	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
42.13/42.32	             app_encode_app(arrow_411405190le_alt, 
42.13/42.32	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	               app_encode_app(arrow_411405190le_alt, 
42.13/42.32	                 app_encode_fun(arrow_411405190le_alt, 
42.13/42.32	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
42.13/42.32	                 product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                 a), b)), 
42.13/42.32	           app_encode_app(
42.13/42.32	             fun(arrow_159774573e_indi, 
42.13/42.32	               fun(
42.13/42.32	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                 bool)), 
42.13/42.32	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	               bool), 
42.13/42.32	             app_encode_app(
42.13/42.32	               fun(
42.13/42.32	                 fun(arrow_159774573e_indi, 
42.13/42.32	                   fun(
42.13/42.32	                     product_prod(arrow_411405190le_alt, 
42.13/42.32	                       arrow_411405190le_alt), bool)), 
42.13/42.32	                 fun(
42.13/42.32	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                   bool)), 
42.13/42.32	               app_encode_fun(
42.13/42.32	                 fun(arrow_159774573e_indi, 
42.13/42.32	                   fun(
42.13/42.32	                     product_prod(arrow_411405190le_alt, 
42.13/42.32	                       arrow_411405190le_alt), bool)), 
42.13/42.32	                 fun(
42.13/42.32	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                   bool)), 
42.13/42.32	               aa(
42.13/42.32	                 fun(arrow_159774573e_indi, 
42.13/42.32	                   fun(
42.13/42.32	                     product_prod(arrow_411405190le_alt, 
42.13/42.32	                       arrow_411405190le_alt), bool)), 
42.13/42.32	                 fun(
42.13/42.32	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                   bool)), f), p1))),
42.13/42.32	    inference('simplify', [status(thm)], ['3'])).
42.13/42.32	tff('5', plain,
42.13/42.32	    (~ app_encode_app(
42.13/42.32	         fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	           bool), $o, 
42.13/42.32	         app_encode_app(
42.13/42.32	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	           app_encode_fun(
42.13/42.32	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	               bool), $o), 
42.13/42.32	           member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
42.13/42.32	           app_encode_app(arrow_411405190le_alt, 
42.13/42.32	             product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	             app_encode_app(arrow_411405190le_alt, 
42.13/42.32	               app_encode_fun(arrow_411405190le_alt, 
42.13/42.32	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
42.13/42.32	               product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), b), 
42.13/42.32	             c)), 
42.13/42.32	         app_encode_app(
42.13/42.32	           fun(arrow_159774573e_indi, 
42.13/42.32	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	               bool)), 
42.13/42.32	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	             bool), 
42.13/42.32	           app_encode_app(
42.13/42.32	             fun(
42.13/42.32	               fun(arrow_159774573e_indi, 
42.13/42.32	                 fun(
42.13/42.32	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                   bool)), 
42.13/42.32	               fun(
42.13/42.32	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                 bool)), 
42.13/42.32	             app_encode_fun(
42.13/42.32	               fun(arrow_159774573e_indi, 
42.13/42.32	                 fun(
42.13/42.32	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                   bool)), 
42.13/42.32	               fun(
42.13/42.32	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                 bool)), 
42.13/42.32	             aa(
42.13/42.32	               fun(arrow_159774573e_indi, 
42.13/42.32	                 fun(
42.13/42.32	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                   bool)), 
42.13/42.32	               fun(
42.13/42.32	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                 bool)), f), p))
42.13/42.32	     | ~ app_encode_app(
42.13/42.32	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	             bool), $o, 
42.13/42.32	           app_encode_app(
42.13/42.32	             product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	             app_encode_fun(
42.13/42.32	               fun(
42.13/42.32	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                 bool), $o), 
42.13/42.32	             member(
42.13/42.32	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
42.13/42.32	             app_encode_app(arrow_411405190le_alt, 
42.13/42.32	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	               app_encode_app(arrow_411405190le_alt, 
42.13/42.32	                 app_encode_fun(arrow_411405190le_alt, 
42.13/42.32	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
42.13/42.32	                 product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                 a), b)), 
42.13/42.32	           app_encode_app(
42.13/42.32	             fun(arrow_159774573e_indi, 
42.13/42.32	               fun(
42.13/42.32	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                 bool)), 
42.13/42.32	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	               bool), 
42.13/42.32	             app_encode_app(
42.13/42.32	               fun(
42.13/42.32	                 fun(arrow_159774573e_indi, 
42.13/42.32	                   fun(
42.13/42.32	                     product_prod(arrow_411405190le_alt, 
42.13/42.32	                       arrow_411405190le_alt), bool)), 
42.13/42.32	                 fun(
42.13/42.32	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                   bool)), 
42.13/42.32	               app_encode_fun(
42.13/42.32	                 fun(arrow_159774573e_indi, 
42.13/42.32	                   fun(
42.13/42.32	                     product_prod(arrow_411405190le_alt, 
42.13/42.32	                       arrow_411405190le_alt), bool)), 
42.13/42.32	                 fun(
42.13/42.32	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                   bool)), 
42.13/42.32	               aa(
42.13/42.32	                 fun(arrow_159774573e_indi, 
42.13/42.32	                   fun(
42.13/42.32	                     product_prod(arrow_411405190le_alt, 
42.13/42.32	                       arrow_411405190le_alt), bool)), 
42.13/42.32	                 fun(
42.13/42.32	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                   bool)), f), p1))),
42.13/42.32	    inference('cnf', [status(esa)], [zf_stmt_0])).
42.13/42.32	tff('6', plain,
42.13/42.32	    ~ app_encode_app(
42.13/42.32	        fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), bool), 
42.13/42.32	        $o, 
42.13/42.32	        app_encode_app(
42.13/42.32	          product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	          app_encode_fun(
42.13/42.32	            fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	              bool), $o), 
42.13/42.32	          member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
42.13/42.32	          app_encode_app(arrow_411405190le_alt, 
42.13/42.32	            product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	            app_encode_app(arrow_411405190le_alt, 
42.13/42.32	              app_encode_fun(arrow_411405190le_alt, 
42.13/42.32	                product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
42.13/42.32	              product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), a), 
42.13/42.32	            b)), 
42.13/42.32	        app_encode_app(
42.13/42.32	          fun(arrow_159774573e_indi, 
42.13/42.32	            fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	              bool)), 
42.13/42.32	          fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	            bool), 
42.13/42.32	          app_encode_app(
42.13/42.32	            fun(
42.13/42.32	              fun(arrow_159774573e_indi, 
42.13/42.32	                fun(
42.13/42.32	                  product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                  bool)), 
42.13/42.32	              fun(
42.13/42.32	                product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                bool)), 
42.13/42.32	            app_encode_fun(
42.13/42.32	              fun(arrow_159774573e_indi, 
42.13/42.32	                fun(
42.13/42.32	                  product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                  bool)), 
42.13/42.32	              fun(
42.13/42.32	                product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                bool)), 
42.13/42.32	            aa(
42.13/42.32	              fun(arrow_159774573e_indi, 
42.13/42.32	                fun(
42.13/42.32	                  product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                  bool)), 
42.13/42.32	              fun(
42.13/42.32	                product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                bool)), f), p1)),
42.13/42.32	    inference('clc', [status(thm)], ['4', '5'])).
42.13/42.32	tff('7', plain,
42.13/42.32	    (~ $true
42.13/42.32	     | app_encode_app(
42.13/42.32	         fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	           bool), $o, 
42.13/42.32	         app_encode_app(
42.13/42.32	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	           app_encode_fun(
42.13/42.32	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	               bool), $o), 
42.13/42.32	           member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
42.13/42.32	           app_encode_app(arrow_411405190le_alt, 
42.13/42.32	             product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	             app_encode_app(arrow_411405190le_alt, 
42.13/42.32	               app_encode_fun(arrow_411405190le_alt, 
42.13/42.32	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
42.13/42.32	               product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), b), 
42.13/42.32	             c)), 
42.13/42.32	         app_encode_app(
42.13/42.32	           fun(arrow_159774573e_indi, 
42.13/42.32	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	               bool)), 
42.13/42.32	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	             bool), 
42.13/42.32	           app_encode_app(
42.13/42.32	             fun(
42.13/42.32	               fun(arrow_159774573e_indi, 
42.13/42.32	                 fun(
42.13/42.32	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                   bool)), 
42.13/42.32	               fun(
42.13/42.32	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                 bool)), 
42.13/42.32	             app_encode_fun(
42.13/42.32	               fun(arrow_159774573e_indi, 
42.13/42.32	                 fun(
42.13/42.32	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                   bool)), 
42.13/42.32	               fun(
42.13/42.32	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                 bool)), 
42.13/42.32	             aa(
42.13/42.32	               fun(arrow_159774573e_indi, 
42.13/42.32	                 fun(
42.13/42.32	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                   bool)), 
42.13/42.32	               fun(
42.13/42.32	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                 bool)), f), p))),
42.13/42.32	    inference('sup-', [status(thm)], ['0', '6'])).
42.13/42.32	tff('8', plain,
42.13/42.32	    app_encode_app(
42.13/42.32	      fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), bool), 
42.13/42.32	      $o, 
42.13/42.32	      app_encode_app(
42.13/42.32	        product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	        app_encode_fun(
42.13/42.32	          fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	            bool), $o), 
42.13/42.32	        member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
42.13/42.32	        app_encode_app(arrow_411405190le_alt, 
42.13/42.32	          product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	          app_encode_app(arrow_411405190le_alt, 
42.13/42.32	            app_encode_fun(arrow_411405190le_alt, 
42.13/42.32	              product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
42.13/42.32	            product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), b), 
42.13/42.32	          c)), 
42.13/42.32	      app_encode_app(
42.13/42.32	        fun(arrow_159774573e_indi, 
42.13/42.32	          fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	            bool)), 
42.13/42.32	        fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), bool), 
42.13/42.32	        app_encode_app(
42.13/42.32	          fun(
42.13/42.32	            fun(arrow_159774573e_indi, 
42.13/42.32	              fun(
42.13/42.32	                product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                bool)), 
42.13/42.32	            fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	              bool)), 
42.13/42.32	          app_encode_fun(
42.13/42.32	            fun(arrow_159774573e_indi, 
42.13/42.32	              fun(
42.13/42.32	                product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                bool)), 
42.13/42.32	            fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	              bool)), 
42.13/42.32	          aa(
42.13/42.32	            fun(arrow_159774573e_indi, 
42.13/42.32	              fun(
42.13/42.32	                product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                bool)), 
42.13/42.32	            fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	              bool)), f), p)),
42.13/42.32	    inference('simplify', [status(thm)], ['7'])).
42.13/42.32	tff('9', plain,
42.13/42.32	    (app_encode_app(
42.13/42.32	       fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), bool), 
42.13/42.32	       $o, 
42.13/42.32	       app_encode_app(
42.13/42.32	         product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	         app_encode_fun(
42.13/42.32	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	             bool), $o), 
42.13/42.32	         member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
42.13/42.32	         app_encode_app(arrow_411405190le_alt, 
42.13/42.32	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	           app_encode_app(arrow_411405190le_alt, 
42.13/42.32	             app_encode_fun(arrow_411405190le_alt, 
42.13/42.32	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
42.13/42.32	             product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), b), 
42.13/42.32	           a)), 
42.13/42.32	       app_encode_app(
42.13/42.32	         fun(arrow_159774573e_indi, 
42.13/42.32	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	             bool)), 
42.13/42.32	         fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	           bool), 
42.13/42.32	         app_encode_app(
42.13/42.32	           fun(
42.13/42.32	             fun(arrow_159774573e_indi, 
42.13/42.32	               fun(
42.13/42.32	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                 bool)), 
42.13/42.32	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	               bool)), 
42.13/42.32	           app_encode_fun(
42.13/42.32	             fun(arrow_159774573e_indi, 
42.13/42.32	               fun(
42.13/42.32	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                 bool)), 
42.13/42.32	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	               bool)), 
42.13/42.32	           aa(
42.13/42.32	             fun(arrow_159774573e_indi, 
42.13/42.32	               fun(
42.13/42.32	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                 bool)), 
42.13/42.32	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	               bool)), f), 
42.13/42.32	         app_encode_app(
42.13/42.32	           fun(arrow_159774573e_indi, 
42.13/42.32	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	               bool)), 
42.13/42.32	           fun(arrow_159774573e_indi, 
42.13/42.32	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	               bool)), 
42.13/42.32	           app_encode_app(
42.13/42.32	             fun(
42.13/42.32	               fun(
42.13/42.32	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                 bool), 
42.13/42.32	               fun(
42.13/42.32	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                 bool)), 
42.13/42.32	             app_encode_fun(
42.13/42.32	               fun(arrow_159774573e_indi, 
42.13/42.32	                 fun(
42.13/42.32	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                   bool)), 
42.13/42.32	               fun(arrow_159774573e_indi, 
42.13/42.32	                 fun(
42.13/42.32	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                   bool))), 
42.13/42.32	             comp(
42.13/42.32	               fun(
42.13/42.32	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                 bool), 
42.13/42.32	               fun(
42.13/42.32	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                 bool), arrow_159774573e_indi), 
42.13/42.32	             converse(arrow_411405190le_alt, arrow_411405190le_alt)), p1)))
42.13/42.32	     | ~ app_encode_app(
42.13/42.32	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	             bool), $o, 
42.13/42.32	           app_encode_app(
42.13/42.32	             product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	             app_encode_fun(
42.13/42.32	               fun(
42.13/42.32	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                 bool), $o), 
42.13/42.32	             member(
42.13/42.32	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
42.13/42.32	             app_encode_app(arrow_411405190le_alt, 
42.13/42.32	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	               app_encode_app(arrow_411405190le_alt, 
42.13/42.32	                 app_encode_fun(arrow_411405190le_alt, 
42.13/42.32	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
42.13/42.32	                 product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                 b), c)), 
42.13/42.32	           app_encode_app(
42.13/42.32	             fun(arrow_159774573e_indi, 
42.13/42.32	               fun(
42.13/42.32	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                 bool)), 
42.13/42.32	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	               bool), 
42.13/42.32	             app_encode_app(
42.13/42.32	               fun(
42.13/42.32	                 fun(arrow_159774573e_indi, 
42.13/42.32	                   fun(
42.13/42.32	                     product_prod(arrow_411405190le_alt, 
42.13/42.32	                       arrow_411405190le_alt), bool)), 
42.13/42.32	                 fun(
42.13/42.32	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                   bool)), 
42.13/42.32	               app_encode_fun(
42.13/42.32	                 fun(arrow_159774573e_indi, 
42.13/42.32	                   fun(
42.13/42.32	                     product_prod(arrow_411405190le_alt, 
42.13/42.32	                       arrow_411405190le_alt), bool)), 
42.13/42.32	                 fun(
42.13/42.32	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                   bool)), 
42.13/42.32	               aa(
42.13/42.32	                 fun(arrow_159774573e_indi, 
42.13/42.32	                   fun(
42.13/42.32	                     product_prod(arrow_411405190le_alt, 
42.13/42.32	                       arrow_411405190le_alt), bool)), 
42.13/42.32	                 fun(
42.13/42.32	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                   bool)), f), p))),
42.13/42.32	    inference('cnf', [status(esa)], [zf_stmt_49])).
42.13/42.32	tff('10', plain,
42.13/42.32	    (app_encode_app(
42.13/42.32	       fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), bool), 
42.13/42.32	       $o, 
42.13/42.32	       app_encode_app(
42.13/42.32	         product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	         app_encode_fun(
42.13/42.32	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	             bool), $o), 
42.13/42.32	         member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
42.13/42.32	         app_encode_app(arrow_411405190le_alt, 
42.13/42.32	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	           app_encode_app(arrow_411405190le_alt, 
42.13/42.32	             app_encode_fun(arrow_411405190le_alt, 
42.13/42.32	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
42.13/42.32	             product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), a), 
42.13/42.32	           b)), 
42.13/42.32	       app_encode_app(
42.13/42.32	         fun(arrow_159774573e_indi, 
42.13/42.32	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	             bool)), 
42.13/42.32	         fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	           bool), 
42.13/42.32	         app_encode_app(
42.13/42.32	           fun(
42.13/42.32	             fun(arrow_159774573e_indi, 
42.13/42.32	               fun(
42.13/42.32	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                 bool)), 
42.13/42.32	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	               bool)), 
42.13/42.32	           app_encode_fun(
42.13/42.32	             fun(arrow_159774573e_indi, 
42.13/42.32	               fun(
42.13/42.32	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                 bool)), 
42.13/42.32	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	               bool)), 
42.13/42.32	           aa(
42.13/42.32	             fun(arrow_159774573e_indi, 
42.13/42.32	               fun(
42.13/42.32	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                 bool)), 
42.13/42.32	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	               bool)), f), p1))
42.13/42.32	     | ~ app_encode_app(
42.13/42.32	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	             bool), $o, 
42.13/42.32	           app_encode_app(
42.13/42.32	             product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	             app_encode_fun(
42.13/42.32	               fun(
42.13/42.32	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                 bool), $o), 
42.13/42.32	             member(
42.13/42.32	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
42.13/42.32	             app_encode_app(arrow_411405190le_alt, 
42.13/42.32	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	               app_encode_app(arrow_411405190le_alt, 
42.13/42.32	                 app_encode_fun(arrow_411405190le_alt, 
42.13/42.32	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
42.13/42.32	                 product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                 b), a)), 
42.13/42.32	           app_encode_app(
42.13/42.32	             fun(arrow_159774573e_indi, 
42.13/42.32	               fun(
42.13/42.32	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                 bool)), 
42.13/42.32	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	               bool), 
42.13/42.32	             app_encode_app(
42.13/42.32	               fun(
42.13/42.32	                 fun(arrow_159774573e_indi, 
42.13/42.32	                   fun(
42.13/42.32	                     product_prod(arrow_411405190le_alt, 
42.13/42.32	                       arrow_411405190le_alt), bool)), 
42.13/42.32	                 fun(
42.13/42.32	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                   bool)), 
42.13/42.32	               app_encode_fun(
42.13/42.32	                 fun(arrow_159774573e_indi, 
42.13/42.32	                   fun(
42.13/42.32	                     product_prod(arrow_411405190le_alt, 
42.13/42.32	                       arrow_411405190le_alt), bool)), 
42.13/42.32	                 fun(
42.13/42.32	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                   bool)), 
42.13/42.32	               aa(
42.13/42.32	                 fun(arrow_159774573e_indi, 
42.13/42.32	                   fun(
42.13/42.32	                     product_prod(arrow_411405190le_alt, 
42.13/42.32	                       arrow_411405190le_alt), bool)), 
42.13/42.32	                 fun(
42.13/42.32	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                   bool)), f), 
42.13/42.32	             app_encode_app(
42.13/42.32	               fun(arrow_159774573e_indi, 
42.13/42.32	                 fun(
42.13/42.32	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                   bool)), 
42.13/42.32	               fun(arrow_159774573e_indi, 
42.13/42.32	                 fun(
42.13/42.32	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                   bool)), 
42.13/42.32	               app_encode_app(
42.13/42.32	                 fun(
42.13/42.32	                   fun(
42.13/42.32	                     product_prod(arrow_411405190le_alt, 
42.13/42.32	                       arrow_411405190le_alt), bool), 
42.13/42.32	                   fun(
42.13/42.32	                     product_prod(arrow_411405190le_alt, 
42.13/42.32	                       arrow_411405190le_alt), bool)), 
42.13/42.32	                 app_encode_fun(
42.13/42.32	                   fun(arrow_159774573e_indi, 
42.13/42.32	                     fun(
42.13/42.32	                       product_prod(arrow_411405190le_alt, 
42.13/42.32	                         arrow_411405190le_alt), bool)), 
42.13/42.32	                   fun(arrow_159774573e_indi, 
42.13/42.32	                     fun(
42.13/42.32	                       product_prod(arrow_411405190le_alt, 
42.13/42.32	                         arrow_411405190le_alt), bool))), 
42.13/42.32	                 comp(
42.13/42.32	                   fun(
42.13/42.32	                     product_prod(arrow_411405190le_alt, 
42.13/42.32	                       arrow_411405190le_alt), bool), 
42.13/42.32	                   fun(
42.13/42.32	                     product_prod(arrow_411405190le_alt, 
42.13/42.32	                       arrow_411405190le_alt), bool), arrow_159774573e_indi), 
42.13/42.32	                 converse(arrow_411405190le_alt, arrow_411405190le_alt)), p1)))),
42.13/42.32	    inference('cnf', [status(esa)], [zf_stmt_47])).
42.13/42.32	tff('11', plain,
42.13/42.32	    (~ $true
42.13/42.32	     | ~ app_encode_app(
42.13/42.32	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	             bool), $o, 
42.13/42.32	           app_encode_app(
42.13/42.32	             product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	             app_encode_fun(
42.13/42.32	               fun(
42.13/42.32	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                 bool), $o), 
42.13/42.32	             member(
42.13/42.32	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
42.13/42.32	             app_encode_app(arrow_411405190le_alt, 
42.13/42.32	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	               app_encode_app(arrow_411405190le_alt, 
42.13/42.32	                 app_encode_fun(arrow_411405190le_alt, 
42.13/42.32	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
42.13/42.32	                 product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                 b), c)), 
42.13/42.32	           app_encode_app(
42.13/42.32	             fun(arrow_159774573e_indi, 
42.13/42.32	               fun(
42.13/42.32	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                 bool)), 
42.13/42.32	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	               bool), 
42.13/42.32	             app_encode_app(
42.13/42.32	               fun(
42.13/42.32	                 fun(arrow_159774573e_indi, 
42.13/42.32	                   fun(
42.13/42.32	                     product_prod(arrow_411405190le_alt, 
42.13/42.32	                       arrow_411405190le_alt), bool)), 
42.13/42.32	                 fun(
42.13/42.32	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                   bool)), 
42.13/42.32	               app_encode_fun(
42.13/42.32	                 fun(arrow_159774573e_indi, 
42.13/42.32	                   fun(
42.13/42.32	                     product_prod(arrow_411405190le_alt, 
42.13/42.32	                       arrow_411405190le_alt), bool)), 
42.13/42.32	                 fun(
42.13/42.32	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                   bool)), 
42.13/42.32	               aa(
42.13/42.32	                 fun(arrow_159774573e_indi, 
42.13/42.32	                   fun(
42.13/42.32	                     product_prod(arrow_411405190le_alt, 
42.13/42.32	                       arrow_411405190le_alt), bool)), 
42.13/42.32	                 fun(
42.13/42.32	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                   bool)), f), p))
42.13/42.32	     | app_encode_app(
42.13/42.32	         fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	           bool), $o, 
42.13/42.32	         app_encode_app(
42.13/42.32	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	           app_encode_fun(
42.13/42.32	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	               bool), $o), 
42.13/42.32	           member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
42.13/42.32	           app_encode_app(arrow_411405190le_alt, 
42.13/42.32	             product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	             app_encode_app(arrow_411405190le_alt, 
42.13/42.32	               app_encode_fun(arrow_411405190le_alt, 
42.13/42.32	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
42.13/42.32	               product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), a), 
42.13/42.32	             b)), 
42.13/42.32	         app_encode_app(
42.13/42.32	           fun(arrow_159774573e_indi, 
42.13/42.32	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	               bool)), 
42.13/42.32	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	             bool), 
42.13/42.32	           app_encode_app(
42.13/42.32	             fun(
42.13/42.32	               fun(arrow_159774573e_indi, 
42.13/42.32	                 fun(
42.13/42.32	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                   bool)), 
42.13/42.32	               fun(
42.13/42.32	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                 bool)), 
42.13/42.32	             app_encode_fun(
42.13/42.32	               fun(arrow_159774573e_indi, 
42.13/42.32	                 fun(
42.13/42.32	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                   bool)), 
42.13/42.32	               fun(
42.13/42.32	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                 bool)), 
42.13/42.32	             aa(
42.13/42.32	               fun(arrow_159774573e_indi, 
42.13/42.32	                 fun(
42.13/42.32	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                   bool)), 
42.13/42.32	               fun(
42.13/42.32	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                 bool)), f), p1))),
42.13/42.32	    inference('sup-', [status(thm)], ['9', '10'])).
42.13/42.32	tff('12', plain,
42.13/42.32	    (app_encode_app(
42.13/42.32	       fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), bool), 
42.13/42.32	       $o, 
42.13/42.32	       app_encode_app(
42.13/42.32	         product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	         app_encode_fun(
42.13/42.32	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	             bool), $o), 
42.13/42.32	         member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
42.13/42.32	         app_encode_app(arrow_411405190le_alt, 
42.13/42.32	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	           app_encode_app(arrow_411405190le_alt, 
42.13/42.32	             app_encode_fun(arrow_411405190le_alt, 
42.13/42.32	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
42.13/42.32	             product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), a), 
42.13/42.32	           b)), 
42.13/42.32	       app_encode_app(
42.13/42.32	         fun(arrow_159774573e_indi, 
42.13/42.32	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	             bool)), 
42.13/42.32	         fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	           bool), 
42.13/42.32	         app_encode_app(
42.13/42.32	           fun(
42.13/42.32	             fun(arrow_159774573e_indi, 
42.13/42.32	               fun(
42.13/42.32	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                 bool)), 
42.13/42.32	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	               bool)), 
42.13/42.32	           app_encode_fun(
42.13/42.32	             fun(arrow_159774573e_indi, 
42.13/42.32	               fun(
42.13/42.32	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                 bool)), 
42.13/42.32	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	               bool)), 
42.13/42.32	           aa(
42.13/42.32	             fun(arrow_159774573e_indi, 
42.13/42.32	               fun(
42.13/42.32	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                 bool)), 
42.13/42.32	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	               bool)), f), p1))
42.13/42.32	     | ~ app_encode_app(
42.13/42.32	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	             bool), $o, 
42.13/42.32	           app_encode_app(
42.13/42.32	             product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	             app_encode_fun(
42.13/42.32	               fun(
42.13/42.32	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                 bool), $o), 
42.13/42.32	             member(
42.13/42.32	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
42.13/42.32	             app_encode_app(arrow_411405190le_alt, 
42.13/42.32	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	               app_encode_app(arrow_411405190le_alt, 
42.13/42.32	                 app_encode_fun(arrow_411405190le_alt, 
42.13/42.32	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
42.13/42.32	                 product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                 b), c)), 
42.13/42.32	           app_encode_app(
42.13/42.32	             fun(arrow_159774573e_indi, 
42.13/42.32	               fun(
42.13/42.32	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                 bool)), 
42.13/42.32	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	               bool), 
42.13/42.32	             app_encode_app(
42.13/42.32	               fun(
42.13/42.32	                 fun(arrow_159774573e_indi, 
42.13/42.32	                   fun(
42.13/42.32	                     product_prod(arrow_411405190le_alt, 
42.13/42.32	                       arrow_411405190le_alt), bool)), 
42.13/42.32	                 fun(
42.13/42.32	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                   bool)), 
42.13/42.32	               app_encode_fun(
42.13/42.32	                 fun(arrow_159774573e_indi, 
42.13/42.32	                   fun(
42.13/42.32	                     product_prod(arrow_411405190le_alt, 
42.13/42.32	                       arrow_411405190le_alt), bool)), 
42.13/42.32	                 fun(
42.13/42.32	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                   bool)), 
42.13/42.32	               aa(
42.13/42.32	                 fun(arrow_159774573e_indi, 
42.13/42.32	                   fun(
42.13/42.32	                     product_prod(arrow_411405190le_alt, 
42.13/42.32	                       arrow_411405190le_alt), bool)), 
42.13/42.32	                 fun(
42.13/42.32	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                   bool)), f), p))),
42.13/42.32	    inference('simplify', [status(thm)], ['11'])).
42.13/42.32	tff('13', plain,
42.13/42.32	    ~ app_encode_app(
42.13/42.32	        fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), bool), 
42.13/42.32	        $o, 
42.13/42.32	        app_encode_app(
42.13/42.32	          product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	          app_encode_fun(
42.13/42.32	            fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	              bool), $o), 
42.13/42.32	          member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
42.13/42.32	          app_encode_app(arrow_411405190le_alt, 
42.13/42.32	            product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	            app_encode_app(arrow_411405190le_alt, 
42.13/42.32	              app_encode_fun(arrow_411405190le_alt, 
42.13/42.32	                product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
42.13/42.32	              product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), b), 
42.13/42.32	            c)), 
42.13/42.32	        app_encode_app(
42.13/42.32	          fun(arrow_159774573e_indi, 
42.13/42.32	            fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	              bool)), 
42.13/42.32	          fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	            bool), 
42.13/42.32	          app_encode_app(
42.13/42.32	            fun(
42.13/42.32	              fun(arrow_159774573e_indi, 
42.13/42.32	                fun(
42.13/42.32	                  product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                  bool)), 
42.13/42.32	              fun(
42.13/42.32	                product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                bool)), 
42.13/42.32	            app_encode_fun(
42.13/42.32	              fun(arrow_159774573e_indi, 
42.13/42.32	                fun(
42.13/42.32	                  product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                  bool)), 
42.13/42.32	              fun(
42.13/42.32	                product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                bool)), 
42.13/42.32	            aa(
42.13/42.32	              fun(arrow_159774573e_indi, 
42.13/42.32	                fun(
42.13/42.32	                  product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                  bool)), 
42.13/42.32	              fun(
42.13/42.32	                product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
42.13/42.32	                bool)), f), p)),
42.13/42.32	    inference('clc', [status(thm)], ['12', '6'])).
42.13/42.32	tff('14', plain, ~ $true, inference('sup-', [status(thm)], ['8', '13'])).
42.13/42.32	tff('15', plain, $false, inference('simplify', [status(thm)], ['14'])).
42.13/42.32	
42.13/42.32	% SZS output end Refutation
42.13/42.32	EOF
