0.00/0.00	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : appext
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : rpo6
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-ho \
0.00/0.00	  --no-avatar \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.20	% Computer   : n042.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 13:40:09 CST 2018
100.61/100.81	% done 1071 iterations in 100.607s
100.61/100.81	% SZS status Theorem for 'stdin'
100.61/100.81	% SZS output start Refutation
100.61/100.82	tff(zf_stmt_115, axiom,
100.61/100.82	  (app_encode_app(fun(product_prod(arrow_411405190le_alt,
100.61/100.82	                                   arrow_411405190le_alt),
100.61/100.82	                      bool),
100.61/100.82	                  $o,
100.61/100.82	                  app_encode_app(product_prod(arrow_411405190le_alt,
100.61/100.82	                                              arrow_411405190le_alt),
100.61/100.82	                                 app_encode_fun(fun(product_prod(arrow_411405190le_alt,
100.61/100.82	                                                                 arrow_411405190le_alt),
100.61/100.82	                                                    bool),
100.61/100.82	                                                $o),
100.61/100.82	                                 member(product_prod(arrow_411405190le_alt,
100.61/100.82	                                                     arrow_411405190le_alt)),
100.61/100.82	                                 app_encode_app(arrow_411405190le_alt,
100.61/100.82	                                                product_prod(arrow_411405190le_alt,
100.61/100.82	                                                             arrow_411405190le_alt),
100.61/100.82	                                                app_encode_app(fun(arrow_411405190le_alt,
100.61/100.82	                                                                   product_prod(
100.61/100.82	                                                                   arrow_411405190le_alt,
100.61/100.82	                                                                   arrow_411405190le_alt)),
100.61/100.82	                                                               app_encode_fun(
100.61/100.82	                                                               arrow_411405190le_alt,
100.61/100.82	                                                               product_prod(
100.61/100.82	                                                               arrow_411405190le_alt,
100.61/100.82	                                                               arrow_411405190le_alt)),
100.61/100.82	                                                               aa(arrow_411405190le_alt,
100.61/100.82	                                                                  product_prod(
100.61/100.82	                                                                  arrow_411405190le_alt,
100.61/100.82	                                                                  arrow_411405190le_alt)),
100.61/100.82	                                                               app_encode_app(
100.61/100.82	                                                               arrow_411405190le_alt,
100.61/100.82	                                                               fun(arrow_411405190le_alt,
100.61/100.82	                                                                   product_prod(
100.61/100.82	                                                                   arrow_411405190le_alt,
100.61/100.82	                                                                   arrow_411405190le_alt)),
100.61/100.82	                                                               app_encode_app(
100.61/100.82	                                                               fun(arrow_411405190le_alt,
100.61/100.82	                                                                   fun(
100.61/100.82	                                                                   arrow_411405190le_alt,
100.61/100.82	                                                                   product_prod(
100.61/100.82	                                                                   arrow_411405190le_alt,
100.61/100.82	                                                                   arrow_411405190le_alt))),
100.61/100.82	                                                               app_encode_fun(
100.61/100.82	                                                               arrow_411405190le_alt,
100.61/100.82	                                                               fun(arrow_411405190le_alt,
100.61/100.82	                                                                   product_prod(
100.61/100.82	                                                                   arrow_411405190le_alt,
100.61/100.82	                                                                   arrow_411405190le_alt))),
100.61/100.82	                                                               aa(arrow_411405190le_alt,
100.61/100.82	                                                                  fun(
100.61/100.82	                                                                  arrow_411405190le_alt,
100.61/100.82	                                                                  product_prod(
100.61/100.82	                                                                  arrow_411405190le_alt,
100.61/100.82	                                                                  arrow_411405190le_alt))),
100.61/100.82	                                                               product_Pair(
100.61/100.82	                                                               arrow_411405190le_alt,
100.61/100.82	                                                               arrow_411405190le_alt)),
100.61/100.82	                                                               x)),
100.61/100.82	                                                y)),
100.61/100.82	                  l))).
100.61/100.82	tff('0', plain,
100.61/100.82	    app_encode_app(
100.61/100.82	      fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), bool), 
100.61/100.82	      $o, 
100.61/100.82	      app_encode_app(
100.61/100.82	        product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
100.61/100.82	        app_encode_fun(
100.61/100.82	          fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
100.61/100.82	            bool), $o), 
100.61/100.82	        member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
100.61/100.82	        app_encode_app(arrow_411405190le_alt, 
100.61/100.82	          product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
100.61/100.82	          app_encode_app(
100.61/100.82	            fun(arrow_411405190le_alt, 
100.61/100.82	              product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
100.61/100.82	            app_encode_fun(arrow_411405190le_alt, 
100.61/100.82	              product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
100.61/100.82	            aa(arrow_411405190le_alt, 
100.61/100.82	              product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
100.61/100.82	            app_encode_app(arrow_411405190le_alt, 
100.61/100.82	              fun(arrow_411405190le_alt, 
100.61/100.82	                product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
100.61/100.82	              app_encode_app(
100.61/100.82	                fun(arrow_411405190le_alt, 
100.61/100.82	                  fun(arrow_411405190le_alt, 
100.61/100.82	                    product_prod(arrow_411405190le_alt, 
100.61/100.82	                      arrow_411405190le_alt))), 
100.61/100.82	                app_encode_fun(arrow_411405190le_alt, 
100.61/100.82	                  fun(arrow_411405190le_alt, 
100.61/100.82	                    product_prod(arrow_411405190le_alt, 
100.61/100.82	                      arrow_411405190le_alt))), 
100.61/100.82	                aa(arrow_411405190le_alt, 
100.61/100.82	                  fun(arrow_411405190le_alt, 
100.61/100.82	                    product_prod(arrow_411405190le_alt, 
100.61/100.82	                      arrow_411405190le_alt))), 
100.61/100.82	                product_Pair(arrow_411405190le_alt, arrow_411405190le_alt)), 
100.61/100.82	              x)), y)), l),
100.61/100.82	    inference('cnf', [status(esa)], [zf_stmt_115])).
100.61/100.82	tff(zf_stmt_114, axiom,
100.61/100.82	  (app_encode_app(fun(product_prod(arrow_411405190le_alt,
100.61/100.82	                                   arrow_411405190le_alt),
100.61/100.82	                      bool),
100.61/100.82	                  $o,
100.61/100.82	                  app_encode_app(product_prod(arrow_411405190le_alt,
100.61/100.82	                                              arrow_411405190le_alt),
100.61/100.82	                                 app_encode_fun(fun(product_prod(arrow_411405190le_alt,
100.61/100.82	                                                                 arrow_411405190le_alt),
100.61/100.82	                                                    bool),
100.61/100.82	                                                $o),
100.61/100.82	                                 member(product_prod(arrow_411405190le_alt,
100.61/100.82	                                                     arrow_411405190le_alt)),
100.61/100.82	                                 app_encode_app(arrow_411405190le_alt,
100.61/100.82	                                                product_prod(arrow_411405190le_alt,
100.61/100.82	                                                             arrow_411405190le_alt),
100.61/100.82	                                                app_encode_app(fun(arrow_411405190le_alt,
100.61/100.82	                                                                   product_prod(
100.61/100.82	                                                                   arrow_411405190le_alt,
100.61/100.82	                                                                   arrow_411405190le_alt)),
100.61/100.82	                                                               app_encode_fun(
100.61/100.82	                                                               arrow_411405190le_alt,
100.61/100.82	                                                               product_prod(
100.61/100.82	                                                               arrow_411405190le_alt,
100.61/100.82	                                                               arrow_411405190le_alt)),
100.61/100.82	                                                               aa(arrow_411405190le_alt,
100.61/100.82	                                                                  product_prod(
100.61/100.82	                                                                  arrow_411405190le_alt,
100.61/100.82	                                                                  arrow_411405190le_alt)),
100.61/100.82	                                                               app_encode_app(
100.61/100.82	                                                               arrow_411405190le_alt,
100.61/100.82	                                                               fun(arrow_411405190le_alt,
100.61/100.82	                                                                   product_prod(
100.61/100.82	                                                                   arrow_411405190le_alt,
100.61/100.82	                                                                   arrow_411405190le_alt)),
100.61/100.82	                                                               app_encode_app(
100.61/100.82	                                                               fun(arrow_411405190le_alt,
100.61/100.82	                                                                   fun(
100.61/100.82	                                                                   arrow_411405190le_alt,
100.61/100.82	                                                                   product_prod(
100.61/100.82	                                                                   arrow_411405190le_alt,
100.61/100.82	                                                                   arrow_411405190le_alt))),
100.61/100.82	                                                               app_encode_fun(
100.61/100.82	                                                               arrow_411405190le_alt,
100.61/100.82	                                                               fun(arrow_411405190le_alt,
100.61/100.82	                                                                   product_prod(
100.61/100.82	                                                                   arrow_411405190le_alt,
100.61/100.82	                                                                   arrow_411405190le_alt))),
100.61/100.82	                                                               aa(arrow_411405190le_alt,
100.61/100.82	                                                                  fun(
100.61/100.82	                                                                  arrow_411405190le_alt,
100.61/100.82	                                                                  product_prod(
100.61/100.82	                                                                  arrow_411405190le_alt,
100.61/100.82	                                                                  arrow_411405190le_alt))),
100.61/100.82	                                                               product_Pair(
100.61/100.82	                                                               arrow_411405190le_alt,
100.61/100.82	                                                               arrow_411405190le_alt)),
100.61/100.82	                                                               y)),
100.61/100.82	                                                x)),
100.61/100.82	                  l))).
100.61/100.82	tff('1', plain,
100.61/100.82	    app_encode_app(
100.61/100.82	      fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), bool), 
100.61/100.82	      $o, 
100.61/100.82	      app_encode_app(
100.61/100.82	        product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
100.61/100.82	        app_encode_fun(
100.61/100.82	          fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
100.61/100.82	            bool), $o), 
100.61/100.82	        member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
100.61/100.82	        app_encode_app(arrow_411405190le_alt, 
100.61/100.82	          product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
100.61/100.82	          app_encode_app(
100.61/100.82	            fun(arrow_411405190le_alt, 
100.61/100.82	              product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
100.61/100.82	            app_encode_fun(arrow_411405190le_alt, 
100.61/100.82	              product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
100.61/100.82	            aa(arrow_411405190le_alt, 
100.61/100.82	              product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
100.61/100.82	            app_encode_app(arrow_411405190le_alt, 
100.61/100.82	              fun(arrow_411405190le_alt, 
100.61/100.82	                product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
100.61/100.82	              app_encode_app(
100.61/100.82	                fun(arrow_411405190le_alt, 
100.61/100.82	                  fun(arrow_411405190le_alt, 
100.61/100.82	                    product_prod(arrow_411405190le_alt, 
100.61/100.82	                      arrow_411405190le_alt))), 
100.61/100.82	                app_encode_fun(arrow_411405190le_alt, 
100.61/100.82	                  fun(arrow_411405190le_alt, 
100.61/100.82	                    product_prod(arrow_411405190le_alt, 
100.61/100.82	                      arrow_411405190le_alt))), 
100.61/100.82	                aa(arrow_411405190le_alt, 
100.61/100.82	                  fun(arrow_411405190le_alt, 
100.61/100.82	                    product_prod(arrow_411405190le_alt, 
100.61/100.82	                      arrow_411405190le_alt))), 
100.61/100.82	                product_Pair(arrow_411405190le_alt, arrow_411405190le_alt)), 
100.61/100.82	              y)), x)), l),
100.61/100.82	    inference('cnf', [status(esa)], [zf_stmt_114])).
100.61/100.82	tff(zf_stmt_36, axiom,
100.61/100.82	  (![A1:$tType,R:fun(product_prod(A1,A1),bool)]:
100.61/100.82	     (app_encode_app(fun(product_prod(A1,A1),bool),$o,trans(A1),R) <=>
100.61/100.82	      (![X2:A1,Y2:A1,Z2:A1]:
100.61/100.82	         (app_encode_app(fun(product_prod(A1,A1),bool),$o,
100.61/100.82	                         app_encode_app(product_prod(A1,A1),
100.61/100.82	                                        app_encode_fun(fun(product_prod(
100.61/100.82	                                                           A1,A1),bool),
100.61/100.82	                                                       $o),
100.61/100.82	                                        member(product_prod(A1,A1)),
100.61/100.82	                                        app_encode_app(A1,
100.61/100.82	                                                       product_prod(A1,A1),
100.61/100.82	                                                       app_encode_app(
100.61/100.82	                                                       fun(A1,
100.61/100.82	                                                           product_prod(
100.61/100.82	                                                           A1,A1)),
100.61/100.82	                                                       app_encode_fun(
100.61/100.82	                                                       A1,product_prod(A1,A1)),
100.61/100.82	                                                       aa(A1,
100.61/100.82	                                                          product_prod(A1,A1)),
100.61/100.82	                                                       app_encode_app(
100.61/100.82	                                                       A1,
100.61/100.82	                                                       fun(A1,
100.61/100.82	                                                           product_prod(
100.61/100.82	                                                           A1,A1)),
100.61/100.82	                                                       app_encode_app(
100.61/100.82	                                                       fun(A1,
100.61/100.82	                                                           fun(A1,
100.61/100.82	                                                               product_prod(
100.61/100.82	                                                               A1,A1))),
100.61/100.82	                                                       app_encode_fun(
100.61/100.82	                                                       A1,
100.61/100.82	                                                       fun(A1,
100.61/100.82	                                                           product_prod(
100.61/100.82	                                                           A1,A1))),
100.61/100.82	                                                       aa(A1,
100.61/100.82	                                                          fun(A1,
100.61/100.82	                                                              product_prod(
100.61/100.82	                                                              A1,A1))),
100.61/100.82	                                                       product_Pair(A1,A1)),
100.61/100.82	                                                       X2)),Y2)),
100.61/100.82	                         R) =>
100.61/100.82	          (app_encode_app(fun(product_prod(A1,A1),bool),$o,
100.61/100.82	                          app_encode_app(product_prod(A1,A1),
100.61/100.82	                                         app_encode_fun(fun(product_prod(
100.61/100.82	                                                            A1,A1),bool),
100.61/100.82	                                                        $o),
100.61/100.82	                                         member(product_prod(A1,A1)),
100.61/100.82	                                         app_encode_app(A1,
100.61/100.82	                                                        product_prod(A1,A1),
100.61/100.82	                                                        app_encode_app(
100.61/100.82	                                                        fun(A1,
100.61/100.82	                                                            product_prod(
100.61/100.82	                                                            A1,A1)),
100.61/100.82	                                                        app_encode_fun(
100.61/100.82	                                                        A1,
100.61/100.82	                                                        product_prod(A1,A1)),
100.61/100.82	                                                        aa(A1,
100.61/100.82	                                                           product_prod(
100.61/100.82	                                                           A1,A1)),
100.61/100.82	                                                        app_encode_app(
100.61/100.82	                                                        A1,
100.61/100.82	                                                        fun(A1,
100.61/100.82	                                                            product_prod(
100.61/100.82	                                                            A1,A1)),
100.61/100.82	                                                        app_encode_app(
100.61/100.82	                                                        fun(A1,
100.61/100.82	                                                            fun(A1,
100.61/100.82	                                                                product_prod(
100.61/100.82	                                                                A1,A1))),
100.61/100.82	                                                        app_encode_fun(
100.61/100.82	                                                        A1,
100.61/100.82	                                                        fun(A1,
100.61/100.82	                                                            product_prod(
100.61/100.82	                                                            A1,A1))),
100.61/100.82	                                                        aa(A1,
100.61/100.82	                                                           fun(A1,
100.61/100.82	                                                               product_prod(
100.61/100.82	                                                               A1,A1))),
100.61/100.82	                                                        product_Pair(A1,A1)),
100.61/100.82	                                                        Y2)),Z2)),
100.61/100.82	                          R) =>
100.61/100.82	           app_encode_app(fun(product_prod(A1,A1),bool),$o,
100.61/100.82	                          app_encode_app(product_prod(A1,A1),
100.61/100.82	                                         app_encode_fun(fun(product_prod(
100.61/100.82	                                                            A1,A1),bool),
100.61/100.82	                                                        $o),
100.61/100.82	                                         member(product_prod(A1,A1)),
100.61/100.82	                                         app_encode_app(A1,
100.61/100.82	                                                        product_prod(A1,A1),
100.61/100.82	                                                        app_encode_app(
100.61/100.82	                                                        fun(A1,
100.61/100.82	                                                            product_prod(
100.61/100.82	                                                            A1,A1)),
100.61/100.82	                                                        app_encode_fun(
100.61/100.82	                                                        A1,
100.61/100.82	                                                        product_prod(A1,A1)),
100.61/100.82	                                                        aa(A1,
100.61/100.82	                                                           product_prod(
100.61/100.82	                                                           A1,A1)),
100.61/100.82	                                                        app_encode_app(
100.61/100.82	                                                        A1,
100.61/100.82	                                                        fun(A1,
100.61/100.82	                                                            product_prod(
100.61/100.82	                                                            A1,A1)),
100.61/100.82	                                                        app_encode_app(
100.61/100.82	                                                        fun(A1,
100.61/100.82	                                                            fun(A1,
100.61/100.82	                                                                product_prod(
100.61/100.82	                                                                A1,A1))),
100.61/100.82	                                                        app_encode_fun(
100.61/100.82	                                                        A1,
100.61/100.82	                                                        fun(A1,
100.61/100.82	                                                            product_prod(
100.61/100.82	                                                            A1,A1))),
100.61/100.82	                                                        aa(A1,
100.61/100.82	                                                           fun(A1,
100.61/100.82	                                                               product_prod(
100.61/100.82	                                                               A1,A1))),
100.61/100.82	                                                        product_Pair(A1,A1)),
100.61/100.82	                                                        X2)),Z2)),
100.61/100.82	                          R))))))).
100.61/100.82	tff('2', plain,
100.61/100.82	    ![X18 : $tType, X19 : X18, X20 : X18, 
100.61/100.82	      X21 : fun(product_prod(X18, X18), bool), X22 : X18]:
100.61/100.82	      (~ app_encode_app(fun(product_prod(X18, X18), bool), $o, 
100.61/100.82	           app_encode_app(product_prod(X18, X18), 
100.61/100.82	             app_encode_fun(fun(product_prod(X18, X18), bool), $o), 
100.61/100.82	             member(product_prod(X18, X18)), 
100.61/100.82	             app_encode_app(X18, product_prod(X18, X18), 
100.61/100.82	               app_encode_app(fun(X18, product_prod(X18, X18)), 
100.61/100.82	                 app_encode_fun(X18, product_prod(X18, X18)), 
100.61/100.82	                 aa(X18, product_prod(X18, X18)), 
100.61/100.82	                 app_encode_app(X18, fun(X18, product_prod(X18, X18)), 
100.61/100.82	                   app_encode_app(
100.61/100.82	                     fun(X18, fun(X18, product_prod(X18, X18))), 
100.61/100.82	                     app_encode_fun(X18, fun(X18, product_prod(X18, X18))), 
100.61/100.82	                     aa(X18, fun(X18, product_prod(X18, X18))), 
100.61/100.82	                     product_Pair(X18, X18)), X19)), X20)), X21)
100.61/100.82	       | app_encode_app(fun(product_prod(X18, X18), bool), $o, 
100.61/100.82	           app_encode_app(product_prod(X18, X18), 
100.61/100.82	             app_encode_fun(fun(product_prod(X18, X18), bool), $o), 
100.61/100.82	             member(product_prod(X18, X18)), 
100.61/100.82	             app_encode_app(X18, product_prod(X18, X18), 
100.61/100.82	               app_encode_app(fun(X18, product_prod(X18, X18)), 
100.61/100.82	                 app_encode_fun(X18, product_prod(X18, X18)), 
100.61/100.82	                 aa(X18, product_prod(X18, X18)), 
100.61/100.82	                 app_encode_app(X18, fun(X18, product_prod(X18, X18)), 
100.61/100.82	                   app_encode_app(
100.61/100.82	                     fun(X18, fun(X18, product_prod(X18, X18))), 
100.61/100.82	                     app_encode_fun(X18, fun(X18, product_prod(X18, X18))), 
100.61/100.82	                     aa(X18, fun(X18, product_prod(X18, X18))), 
100.61/100.82	                     product_Pair(X18, X18)), X22)), X20)), X21)
100.61/100.82	       | ~ app_encode_app(fun(product_prod(X18, X18), bool), $o, 
100.61/100.82	             app_encode_app(product_prod(X18, X18), 
100.61/100.82	               app_encode_fun(fun(product_prod(X18, X18), bool), $o), 
100.61/100.82	               member(product_prod(X18, X18)), 
100.61/100.82	               app_encode_app(X18, product_prod(X18, X18), 
100.61/100.82	                 app_encode_app(fun(X18, product_prod(X18, X18)), 
100.61/100.82	                   app_encode_fun(X18, product_prod(X18, X18)), 
100.61/100.82	                   aa(X18, product_prod(X18, X18)), 
100.61/100.82	                   app_encode_app(X18, fun(X18, product_prod(X18, X18)), 
100.61/100.82	                     app_encode_app(
100.61/100.82	                       fun(X18, fun(X18, product_prod(X18, X18))), 
100.61/100.82	                       app_encode_fun(X18, fun(X18, product_prod(X18, X18))), 
100.61/100.82	                       aa(X18, fun(X18, product_prod(X18, X18))), 
100.61/100.82	                       product_Pair(X18, X18)), X22)), X19)), X21)
100.61/100.82	       | ~ app_encode_app(fun(product_prod(X18, X18), bool), $o, trans(X18), 
100.61/100.82	             X21)),
100.61/100.82	    inference('cnf', [status(esa)], [zf_stmt_36])).
100.61/100.82	tff('3', plain,
100.61/100.82	    ![X0 : arrow_411405190le_alt]:
100.61/100.82	      (~ $true
100.61/100.82	       | ~ app_encode_app(
100.61/100.82	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
100.61/100.82	               bool), $o, trans(arrow_411405190le_alt), l)
100.61/100.82	       | ~ app_encode_app(
100.61/100.82	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
100.61/100.82	               bool), $o, 
100.61/100.82	             app_encode_app(
100.61/100.82	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
100.61/100.82	               app_encode_fun(
100.61/100.82	                 fun(
100.61/100.82	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
100.61/100.82	                   bool), $o), 
100.61/100.82	               member(
100.61/100.82	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
100.61/100.82	               app_encode_app(arrow_411405190le_alt, 
100.61/100.82	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
100.61/100.82	                 app_encode_app(
100.61/100.82	                   fun(arrow_411405190le_alt, 
100.61/100.82	                     product_prod(arrow_411405190le_alt, 
100.61/100.82	                       arrow_411405190le_alt)), 
100.61/100.82	                   app_encode_fun(arrow_411405190le_alt, 
100.61/100.82	                     product_prod(arrow_411405190le_alt, 
100.61/100.82	                       arrow_411405190le_alt)), 
100.61/100.82	                   aa(arrow_411405190le_alt, 
100.61/100.82	                     product_prod(arrow_411405190le_alt, 
100.61/100.82	                       arrow_411405190le_alt)), 
100.61/100.82	                   app_encode_app(arrow_411405190le_alt, 
100.61/100.82	                     fun(arrow_411405190le_alt, 
100.61/100.82	                       product_prod(arrow_411405190le_alt, 
100.61/100.82	                         arrow_411405190le_alt)), 
100.61/100.82	                     app_encode_app(
100.61/100.82	                       fun(arrow_411405190le_alt, 
100.61/100.82	                         fun(arrow_411405190le_alt, 
100.61/100.82	                           product_prod(arrow_411405190le_alt, 
100.61/100.82	                             arrow_411405190le_alt))), 
100.61/100.82	                       app_encode_fun(arrow_411405190le_alt, 
100.61/100.82	                         fun(arrow_411405190le_alt, 
100.61/100.82	                           product_prod(arrow_411405190le_alt, 
100.61/100.82	                             arrow_411405190le_alt))), 
100.61/100.82	                       aa(arrow_411405190le_alt, 
100.61/100.82	                         fun(arrow_411405190le_alt, 
100.61/100.82	                           product_prod(arrow_411405190le_alt, 
100.61/100.82	                             arrow_411405190le_alt))), 
100.61/100.82	                       product_Pair(arrow_411405190le_alt, 
100.61/100.82	                         arrow_411405190le_alt)), X0)), y)), l)
100.61/100.82	       | app_encode_app(
100.61/100.82	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
100.61/100.82	             bool), $o, 
100.61/100.82	           app_encode_app(
100.61/100.82	             product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
100.61/100.82	             app_encode_fun(
100.61/100.82	               fun(
100.61/100.82	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
100.61/100.82	                 bool), $o), 
100.61/100.82	             member(
100.61/100.82	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
100.61/100.82	             app_encode_app(arrow_411405190le_alt, 
100.61/100.82	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
100.61/100.82	               app_encode_app(
100.61/100.82	                 fun(arrow_411405190le_alt, 
100.61/100.82	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
100.61/100.82	                 app_encode_fun(arrow_411405190le_alt, 
100.61/100.82	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
100.61/100.82	                 aa(arrow_411405190le_alt, 
100.61/100.82	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
100.61/100.82	                 app_encode_app(arrow_411405190le_alt, 
100.61/100.82	                   fun(arrow_411405190le_alt, 
100.61/100.82	                     product_prod(arrow_411405190le_alt, 
100.61/100.82	                       arrow_411405190le_alt)), 
100.61/100.82	                   app_encode_app(
100.61/100.82	                     fun(arrow_411405190le_alt, 
100.61/100.82	                       fun(arrow_411405190le_alt, 
100.61/100.82	                         product_prod(arrow_411405190le_alt, 
100.61/100.82	                           arrow_411405190le_alt))), 
100.61/100.82	                     app_encode_fun(arrow_411405190le_alt, 
100.61/100.82	                       fun(arrow_411405190le_alt, 
100.61/100.82	                         product_prod(arrow_411405190le_alt, 
100.61/100.82	                           arrow_411405190le_alt))), 
100.61/100.82	                     aa(arrow_411405190le_alt, 
100.61/100.82	                       fun(arrow_411405190le_alt, 
100.61/100.82	                         product_prod(arrow_411405190le_alt, 
100.61/100.82	                           arrow_411405190le_alt))), 
100.61/100.82	                     product_Pair(arrow_411405190le_alt, 
100.61/100.82	                       arrow_411405190le_alt)), X0)), x)), l)),
100.61/100.82	    inference('sup-', [status(thm)], ['1', '2'])).
100.61/100.82	tff(zf_stmt_111, axiom,
100.61/100.82	  (app_encode_app(fun(product_prod(arrow_411405190le_alt,
100.61/100.82	                                   arrow_411405190le_alt),
100.61/100.82	                      bool),
100.61/100.82	                  $o,trans(arrow_411405190le_alt),l))).
100.61/100.82	tff('4', plain,
100.61/100.82	    app_encode_app(
100.61/100.82	      fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), bool), 
100.61/100.82	      $o, trans(arrow_411405190le_alt), l),
100.61/100.82	    inference('cnf', [status(esa)], [zf_stmt_111])).
100.61/100.82	tff('5', plain,
100.61/100.82	    ![X0 : arrow_411405190le_alt]:
100.61/100.82	      (~ $true
100.61/100.82	       | ~ $true
100.61/100.82	       | ~ app_encode_app(
100.61/100.82	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
100.61/100.82	               bool), $o, 
100.61/100.82	             app_encode_app(
100.61/100.82	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
100.61/100.82	               app_encode_fun(
100.61/100.82	                 fun(
100.61/100.82	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
100.61/100.82	                   bool), $o), 
100.61/100.82	               member(
100.61/100.82	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
100.61/100.82	               app_encode_app(arrow_411405190le_alt, 
100.61/100.82	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
100.61/100.82	                 app_encode_app(
100.61/100.82	                   fun(arrow_411405190le_alt, 
100.61/100.82	                     product_prod(arrow_411405190le_alt, 
100.61/100.82	                       arrow_411405190le_alt)), 
100.61/100.82	                   app_encode_fun(arrow_411405190le_alt, 
100.61/100.82	                     product_prod(arrow_411405190le_alt, 
100.61/100.82	                       arrow_411405190le_alt)), 
100.61/100.82	                   aa(arrow_411405190le_alt, 
100.61/100.82	                     product_prod(arrow_411405190le_alt, 
100.61/100.82	                       arrow_411405190le_alt)), 
100.61/100.82	                   app_encode_app(arrow_411405190le_alt, 
100.61/100.82	                     fun(arrow_411405190le_alt, 
100.61/100.82	                       product_prod(arrow_411405190le_alt, 
100.61/100.82	                         arrow_411405190le_alt)), 
100.61/100.82	                     app_encode_app(
100.61/100.82	                       fun(arrow_411405190le_alt, 
100.61/100.82	                         fun(arrow_411405190le_alt, 
100.61/100.82	                           product_prod(arrow_411405190le_alt, 
100.61/100.82	                             arrow_411405190le_alt))), 
100.61/100.82	                       app_encode_fun(arrow_411405190le_alt, 
100.61/100.82	                         fun(arrow_411405190le_alt, 
100.61/100.82	                           product_prod(arrow_411405190le_alt, 
100.61/100.82	                             arrow_411405190le_alt))), 
100.61/100.82	                       aa(arrow_411405190le_alt, 
100.61/100.82	                         fun(arrow_411405190le_alt, 
100.61/100.82	                           product_prod(arrow_411405190le_alt, 
100.61/100.82	                             arrow_411405190le_alt))), 
100.61/100.82	                       product_Pair(arrow_411405190le_alt, 
100.61/100.82	                         arrow_411405190le_alt)), X0)), y)), l)
100.61/100.82	       | app_encode_app(
100.61/100.82	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
100.61/100.82	             bool), $o, 
100.61/100.82	           app_encode_app(
100.61/100.82	             product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
100.61/100.82	             app_encode_fun(
100.61/100.82	               fun(
100.61/100.82	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
100.61/100.82	                 bool), $o), 
100.61/100.82	             member(
100.61/100.82	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
100.61/100.82	             app_encode_app(arrow_411405190le_alt, 
100.61/100.82	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
100.61/100.82	               app_encode_app(
100.61/100.82	                 fun(arrow_411405190le_alt, 
100.61/100.82	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
100.61/100.82	                 app_encode_fun(arrow_411405190le_alt, 
100.61/100.82	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
100.61/100.82	                 aa(arrow_411405190le_alt, 
100.61/100.82	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
100.61/100.82	                 app_encode_app(arrow_411405190le_alt, 
100.61/100.82	                   fun(arrow_411405190le_alt, 
100.61/100.82	                     product_prod(arrow_411405190le_alt, 
100.61/100.82	                       arrow_411405190le_alt)), 
100.61/100.82	                   app_encode_app(
100.61/100.82	                     fun(arrow_411405190le_alt, 
100.61/100.82	                       fun(arrow_411405190le_alt, 
100.61/100.82	                         product_prod(arrow_411405190le_alt, 
100.61/100.82	                           arrow_411405190le_alt))), 
100.61/100.82	                     app_encode_fun(arrow_411405190le_alt, 
100.61/100.82	                       fun(arrow_411405190le_alt, 
100.61/100.82	                         product_prod(arrow_411405190le_alt, 
100.61/100.82	                           arrow_411405190le_alt))), 
100.61/100.82	                     aa(arrow_411405190le_alt, 
100.61/100.82	                       fun(arrow_411405190le_alt, 
100.61/100.82	                         product_prod(arrow_411405190le_alt, 
100.61/100.82	                           arrow_411405190le_alt))), 
100.61/100.82	                     product_Pair(arrow_411405190le_alt, 
100.61/100.82	                       arrow_411405190le_alt)), X0)), x)), l)),
100.61/100.82	    inference('demod', [status(thm)], ['3', '4'])).
100.61/100.82	tff('6', plain,
100.61/100.82	    ![X0 : arrow_411405190le_alt]:
100.61/100.82	      (app_encode_app(
100.61/100.82	         fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
100.61/100.82	           bool), $o, 
100.61/100.82	         app_encode_app(
100.61/100.82	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
100.61/100.82	           app_encode_fun(
100.61/100.82	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
100.61/100.82	               bool), $o), 
100.61/100.82	           member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
100.61/100.82	           app_encode_app(arrow_411405190le_alt, 
100.61/100.82	             product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
100.61/100.82	             app_encode_app(
100.61/100.82	               fun(arrow_411405190le_alt, 
100.61/100.82	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
100.61/100.82	               app_encode_fun(arrow_411405190le_alt, 
100.61/100.82	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
100.61/100.82	               aa(arrow_411405190le_alt, 
100.61/100.82	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
100.61/100.82	               app_encode_app(arrow_411405190le_alt, 
100.61/100.82	                 fun(arrow_411405190le_alt, 
100.61/100.82	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
100.61/100.82	                 app_encode_app(
100.61/100.82	                   fun(arrow_411405190le_alt, 
100.61/100.82	                     fun(arrow_411405190le_alt, 
100.61/100.82	                       product_prod(arrow_411405190le_alt, 
100.61/100.82	                         arrow_411405190le_alt))), 
100.61/100.82	                   app_encode_fun(arrow_411405190le_alt, 
100.61/100.82	                     fun(arrow_411405190le_alt, 
100.61/100.82	                       product_prod(arrow_411405190le_alt, 
100.61/100.82	                         arrow_411405190le_alt))), 
100.61/100.82	                   aa(arrow_411405190le_alt, 
100.61/100.82	                     fun(arrow_411405190le_alt, 
100.61/100.82	                       product_prod(arrow_411405190le_alt, 
100.61/100.82	                         arrow_411405190le_alt))), 
100.61/100.82	                   product_Pair(arrow_411405190le_alt, arrow_411405190le_alt)), 
100.61/100.82	                 X0)), x)), l)
100.61/100.82	       | ~ app_encode_app(
100.61/100.82	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
100.61/100.82	               bool), $o, 
100.61/100.82	             app_encode_app(
100.61/100.82	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
100.61/100.82	               app_encode_fun(
100.61/100.82	                 fun(
100.61/100.82	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
100.61/100.82	                   bool), $o), 
100.61/100.82	               member(
100.61/100.82	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
100.61/100.82	               app_encode_app(arrow_411405190le_alt, 
100.61/100.82	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
100.61/100.82	                 app_encode_app(
100.61/100.82	                   fun(arrow_411405190le_alt, 
100.61/100.82	                     product_prod(arrow_411405190le_alt, 
100.61/100.82	                       arrow_411405190le_alt)), 
100.61/100.82	                   app_encode_fun(arrow_411405190le_alt, 
100.61/100.82	                     product_prod(arrow_411405190le_alt, 
100.61/100.82	                       arrow_411405190le_alt)), 
100.61/100.82	                   aa(arrow_411405190le_alt, 
100.61/100.82	                     product_prod(arrow_411405190le_alt, 
100.61/100.82	                       arrow_411405190le_alt)), 
100.61/100.82	                   app_encode_app(arrow_411405190le_alt, 
100.61/100.82	                     fun(arrow_411405190le_alt, 
100.61/100.82	                       product_prod(arrow_411405190le_alt, 
100.61/100.82	                         arrow_411405190le_alt)), 
100.61/100.82	                     app_encode_app(
100.61/100.82	                       fun(arrow_411405190le_alt, 
100.61/100.82	                         fun(arrow_411405190le_alt, 
100.61/100.82	                           product_prod(arrow_411405190le_alt, 
100.61/100.82	                             arrow_411405190le_alt))), 
100.61/100.82	                       app_encode_fun(arrow_411405190le_alt, 
100.61/100.82	                         fun(arrow_411405190le_alt, 
100.61/100.82	                           product_prod(arrow_411405190le_alt, 
100.61/100.82	                             arrow_411405190le_alt))), 
100.61/100.82	                       aa(arrow_411405190le_alt, 
100.61/100.82	                         fun(arrow_411405190le_alt, 
100.61/100.82	                           product_prod(arrow_411405190le_alt, 
100.61/100.82	                             arrow_411405190le_alt))), 
100.61/100.82	                       product_Pair(arrow_411405190le_alt, 
100.61/100.82	                         arrow_411405190le_alt)), X0)), y)), l)),
100.61/100.82	    inference('simplify', [status(thm)], ['5'])).
100.61/100.82	tff('7', plain,
100.61/100.82	    (~ $true
100.61/100.82	     | app_encode_app(
100.61/100.82	         fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
100.61/100.82	           bool), $o, 
100.61/100.82	         app_encode_app(
100.61/100.82	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
100.61/100.82	           app_encode_fun(
100.61/100.82	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
100.61/100.82	               bool), $o), 
100.61/100.82	           member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
100.61/100.82	           app_encode_app(arrow_411405190le_alt, 
100.61/100.82	             product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
100.61/100.82	             app_encode_app(
100.61/100.82	               fun(arrow_411405190le_alt, 
100.61/100.82	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
100.61/100.82	               app_encode_fun(arrow_411405190le_alt, 
100.61/100.82	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
100.61/100.82	               aa(arrow_411405190le_alt, 
100.61/100.82	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
100.61/100.82	               app_encode_app(arrow_411405190le_alt, 
100.61/100.82	                 fun(arrow_411405190le_alt, 
100.61/100.82	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
100.61/100.82	                 app_encode_app(
100.61/100.82	                   fun(arrow_411405190le_alt, 
100.61/100.82	                     fun(arrow_411405190le_alt, 
100.61/100.82	                       product_prod(arrow_411405190le_alt, 
100.61/100.82	                         arrow_411405190le_alt))), 
100.61/100.82	                   app_encode_fun(arrow_411405190le_alt, 
100.61/100.82	                     fun(arrow_411405190le_alt, 
100.61/100.82	                       product_prod(arrow_411405190le_alt, 
100.61/100.82	                         arrow_411405190le_alt))), 
100.61/100.82	                   aa(arrow_411405190le_alt, 
100.61/100.82	                     fun(arrow_411405190le_alt, 
100.61/100.82	                       product_prod(arrow_411405190le_alt, 
100.61/100.82	                         arrow_411405190le_alt))), 
100.61/100.82	                   product_Pair(arrow_411405190le_alt, arrow_411405190le_alt)), 
100.61/100.82	                 x)), x)), l)),
100.61/100.82	    inference('sup-', [status(thm)], ['0', '6'])).
100.61/100.82	tff('8', plain,
100.61/100.82	    app_encode_app(
100.61/100.82	      fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), bool), 
100.61/100.82	      $o, 
100.61/100.82	      app_encode_app(
100.61/100.82	        product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
100.61/100.82	        app_encode_fun(
100.61/100.82	          fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
100.61/100.82	            bool), $o), 
100.61/100.82	        member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
100.61/100.82	        app_encode_app(arrow_411405190le_alt, 
100.61/100.82	          product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
100.61/100.82	          app_encode_app(
100.61/100.82	            fun(arrow_411405190le_alt, 
100.61/100.82	              product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
100.61/100.82	            app_encode_fun(arrow_411405190le_alt, 
100.61/100.82	              product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
100.61/100.82	            aa(arrow_411405190le_alt, 
100.61/100.82	              product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
100.61/100.82	            app_encode_app(arrow_411405190le_alt, 
100.61/100.82	              fun(arrow_411405190le_alt, 
100.61/100.82	                product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
100.61/100.82	              app_encode_app(
100.61/100.82	                fun(arrow_411405190le_alt, 
100.61/100.82	                  fun(arrow_411405190le_alt, 
100.61/100.82	                    product_prod(arrow_411405190le_alt, 
100.61/100.82	                      arrow_411405190le_alt))), 
100.61/100.82	                app_encode_fun(arrow_411405190le_alt, 
100.61/100.82	                  fun(arrow_411405190le_alt, 
100.61/100.82	                    product_prod(arrow_411405190le_alt, 
100.61/100.82	                      arrow_411405190le_alt))), 
100.61/100.82	                aa(arrow_411405190le_alt, 
100.61/100.82	                  fun(arrow_411405190le_alt, 
100.61/100.82	                    product_prod(arrow_411405190le_alt, 
100.61/100.82	                      arrow_411405190le_alt))), 
100.61/100.82	                product_Pair(arrow_411405190le_alt, arrow_411405190le_alt)), 
100.61/100.82	              x)), x)), l),
100.61/100.82	    inference('simplify', [status(thm)], ['7'])).
100.61/100.82	tff(zf_stmt_112, axiom,
100.61/100.82	  (![X:arrow_411405190le_alt]:
100.61/100.82	     (~
100.61/100.82	       app_encode_app(fun(product_prod(arrow_411405190le_alt,
100.61/100.82	                                       arrow_411405190le_alt),
100.61/100.82	                          bool),
100.61/100.82	                      $o,
100.61/100.82	                      app_encode_app(product_prod(arrow_411405190le_alt,
100.61/100.82	                                                  arrow_411405190le_alt),
100.61/100.82	                                     app_encode_fun(fun(product_prod(
100.61/100.82	                                                        arrow_411405190le_alt,
100.61/100.82	                                                        arrow_411405190le_alt),
100.61/100.82	                                                        bool),
100.61/100.82	                                                    $o),
100.61/100.82	                                     member(product_prod(arrow_411405190le_alt,
100.61/100.82	                                                         arrow_411405190le_alt)),
100.61/100.82	                                     app_encode_app(arrow_411405190le_alt,
100.61/100.82	                                                    product_prod(arrow_411405190le_alt,
100.61/100.82	                                                                 arrow_411405190le_alt),
100.61/100.82	                                                    app_encode_app(fun(
100.61/100.82	                                                                   arrow_411405190le_alt,
100.61/100.82	                                                                   product_prod(
100.61/100.82	                                                                   arrow_411405190le_alt,
100.61/100.82	                                                                   arrow_411405190le_alt)),
100.61/100.82	                                                                   app_encode_fun(
100.61/100.82	                                                                   arrow_411405190le_alt,
100.61/100.82	                                                                   product_prod(
100.61/100.82	                                                                   arrow_411405190le_alt,
100.61/100.82	                                                                   arrow_411405190le_alt)),
100.61/100.82	                                                                   aa(
100.61/100.82	                                                                   arrow_411405190le_alt,
100.61/100.82	                                                                   product_prod(
100.61/100.82	                                                                   arrow_411405190le_alt,
100.61/100.82	                                                                   arrow_411405190le_alt)),
100.61/100.82	                                                                   app_encode_app(
100.61/100.82	                                                                   arrow_411405190le_alt,
100.61/100.82	                                                                   fun(
100.61/100.82	                                                                   arrow_411405190le_alt,
100.61/100.82	                                                                   product_prod(
100.61/100.82	                                                                   arrow_411405190le_alt,
100.61/100.82	                                                                   arrow_411405190le_alt)),
100.61/100.82	                                                                   app_encode_app(
100.61/100.82	                                                                   fun(
100.61/100.82	                                                                   arrow_411405190le_alt,
100.61/100.82	                                                                   fun(
100.61/100.82	                                                                   arrow_411405190le_alt,
100.61/100.82	                                                                   product_prod(
100.61/100.82	                                                                   arrow_411405190le_alt,
100.61/100.82	                                                                   arrow_411405190le_alt))),
100.61/100.82	                                                                   app_encode_fun(
100.61/100.82	                                                                   arrow_411405190le_alt,
100.61/100.82	                                                                   fun(
100.61/100.82	                                                                   arrow_411405190le_alt,
100.61/100.82	                                                                   product_prod(
100.61/100.82	                                                                   arrow_411405190le_alt,
100.61/100.82	                                                                   arrow_411405190le_alt))),
100.61/100.82	                                                                   aa(
100.61/100.82	                                                                   arrow_411405190le_alt,
100.61/100.82	                                                                   fun(
100.61/100.82	                                                                   arrow_411405190le_alt,
100.61/100.82	                                                                   product_prod(
100.61/100.82	                                                                   arrow_411405190le_alt,
100.61/100.82	                                                                   arrow_411405190le_alt))),
100.61/100.82	                                                                   product_Pair(
100.61/100.82	                                                                   arrow_411405190le_alt,
100.61/100.82	                                                                   arrow_411405190le_alt)),
100.61/100.82	                                                                   X)),
100.61/100.82	                                                    X)),
100.61/100.82	                      l)))).
100.61/100.82	tff('9', plain,
100.61/100.82	    ![X386 : arrow_411405190le_alt]:
100.61/100.82	      ~ app_encode_app(
100.61/100.82	          fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
100.61/100.82	            bool), $o, 
100.61/100.82	          app_encode_app(
100.61/100.82	            product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
100.61/100.82	            app_encode_fun(
100.61/100.82	              fun(
100.61/100.82	                product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
100.61/100.82	                bool), $o), 
100.61/100.82	            member(
100.61/100.82	              product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
100.61/100.82	            app_encode_app(arrow_411405190le_alt, 
100.61/100.82	              product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
100.61/100.82	              app_encode_app(
100.61/100.82	                fun(arrow_411405190le_alt, 
100.61/100.82	                  product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
100.61/100.82	                app_encode_fun(arrow_411405190le_alt, 
100.61/100.82	                  product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
100.61/100.82	                aa(arrow_411405190le_alt, 
100.61/100.82	                  product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
100.61/100.82	                app_encode_app(arrow_411405190le_alt, 
100.61/100.82	                  fun(arrow_411405190le_alt, 
100.61/100.82	                    product_prod(arrow_411405190le_alt, 
100.61/100.82	                      arrow_411405190le_alt)), 
100.61/100.82	                  app_encode_app(
100.61/100.82	                    fun(arrow_411405190le_alt, 
100.61/100.82	                      fun(arrow_411405190le_alt, 
100.61/100.82	                        product_prod(arrow_411405190le_alt, 
100.61/100.82	                          arrow_411405190le_alt))), 
100.61/100.82	                    app_encode_fun(arrow_411405190le_alt, 
100.61/100.82	                      fun(arrow_411405190le_alt, 
100.61/100.82	                        product_prod(arrow_411405190le_alt, 
100.61/100.82	                          arrow_411405190le_alt))), 
100.61/100.82	                    aa(arrow_411405190le_alt, 
100.61/100.82	                      fun(arrow_411405190le_alt, 
100.61/100.82	                        product_prod(arrow_411405190le_alt, 
100.61/100.82	                          arrow_411405190le_alt))), 
100.61/100.82	                    product_Pair(arrow_411405190le_alt, 
100.61/100.82	                      arrow_411405190le_alt)), X386)), X386)), l),
100.61/100.82	    inference('cnf', [status(esa)], [zf_stmt_112])).
100.61/100.82	tff('10', plain, ~ $true, inference('sup-', [status(thm)], ['8', '9'])).
100.61/100.82	tff('11', plain, $false, inference('simplify', [status(thm)], ['10'])).
100.61/100.82	
100.61/100.82	% SZS output end Refutation
100.61/100.82	EOF
