0.00/0.01	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.01	% app-encoded or not : original
0.00/0.01	% Variant    : supatvars_ext
0.00/0.01	% Ordering    : kbo
0.00/0.01	% Command    : 
0.00/0.01	#!/bin/sh
0.00/0.01	
0.00/0.01	./zipperposition.native ${1:+"$1"} \
0.00/0.01	  -i tptp \
0.00/0.01	  -o tptp \
0.00/0.01	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.01	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.01	  --no-avatar \
0.00/0.01	  --ho \
0.00/0.01	  --force-ho \
0.00/0.01	  --no-ho-elim-pred-var \
0.00/0.01	  --ho-general-ext-pos \
0.00/0.01	  --no-ho-unif \
0.00/0.01	  --no-induction \
0.00/0.01	  --no-unif-pattern \
0.00/0.01	  --ord $2  \
0.00/0.01	  --simultaneous-sup false \
0.00/0.01	  --sup-at-vars \
0.00/0.01	  --restrict-hidden-sup-at-vars \
0.00/0.01	  --ho-ext-axiom \
0.00/0.01	  --ho-prim-enum none \
0.00/0.01	  --no-max-vars \
0.00/0.01	  --dont-select-ho-var-lits \
0.00/0.01	  --no-fool
0.00/0.19	% Computer   : n136.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 14:06:54 CST 2018
17.82/18.00	% done 1307 iterations in 17.802s
17.82/18.00	% SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
17.82/18.00	% SZS output start Refutation
17.82/18.01	tff(conj_0, conjecture,
17.82/18.01	  (member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),
17.82/18.01	          aa(arrow_411405190le_alt,
17.82/18.01	             product_prod(arrow_411405190le_alt,arrow_411405190le_alt),
17.82/18.01	             aa(arrow_411405190le_alt,
17.82/18.01	                fun(arrow_411405190le_alt,
17.82/18.01	                    product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),
17.82/18.01	                product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a1),
17.82/18.01	             b1),
17.82/18.01	          aa(fun(arrow_159774573e_indi,
17.82/18.01	                 fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),
17.82/18.01	                     bool)),
17.82/18.01	             fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),
17.82/18.01	                 bool),
17.82/18.01	             f,p1)) <=>
17.82/18.01	   member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),
17.82/18.01	          aa(arrow_411405190le_alt,
17.82/18.01	             product_prod(arrow_411405190le_alt,arrow_411405190le_alt),
17.82/18.01	             aa(arrow_411405190le_alt,
17.82/18.01	                fun(arrow_411405190le_alt,
17.82/18.01	                    product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),
17.82/18.02	                product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),
17.82/18.02	             b),
17.82/18.02	          aa(fun(arrow_159774573e_indi,
17.82/18.02	                 fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),
17.82/18.02	                     bool)),
17.82/18.02	             fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),
17.82/18.02	                 bool),
17.82/18.02	             f,p)))).
17.82/18.02	tff(zf_stmt_0, negated_conjecture,
17.82/18.02	  (~
17.82/18.02	    (member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),
17.82/18.02	            aa(arrow_411405190le_alt,
17.82/18.02	               product_prod(arrow_411405190le_alt,arrow_411405190le_alt),
17.82/18.02	               aa(arrow_411405190le_alt,
17.82/18.02	                  fun(arrow_411405190le_alt,
17.82/18.02	                      product_prod(arrow_411405190le_alt,
17.82/18.02	                                   arrow_411405190le_alt)),
17.82/18.02	                  product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),
17.82/18.02	                  a1),
17.82/18.02	               b1),
17.82/18.02	            aa(fun(arrow_159774573e_indi,
17.82/18.02	                   fun(product_prod(arrow_411405190le_alt,
17.82/18.02	                                    arrow_411405190le_alt),
17.82/18.02	                       bool)),
17.82/18.02	               fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),
17.82/18.02	                   bool),
17.82/18.02	               f,p1)) <=>
17.82/18.02	     member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),
17.82/18.02	            aa(arrow_411405190le_alt,
17.82/18.02	               product_prod(arrow_411405190le_alt,arrow_411405190le_alt),
17.82/18.02	               aa(arrow_411405190le_alt,
17.82/18.02	                  fun(arrow_411405190le_alt,
17.82/18.02	                      product_prod(arrow_411405190le_alt,
17.82/18.02	                                   arrow_411405190le_alt)),
17.82/18.02	                  product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),
17.82/18.02	               b),
17.82/18.02	            aa(fun(arrow_159774573e_indi,
17.82/18.02	                   fun(product_prod(arrow_411405190le_alt,
17.82/18.02	                                    arrow_411405190le_alt),
17.82/18.02	                       bool)),
17.82/18.02	               fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),
17.82/18.02	                   bool),
17.82/18.02	               f,p))))).
17.82/18.02	tff('0', plain,
17.82/18.02	    (member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	       aa(arrow_411405190le_alt, 
17.82/18.02	         product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	         aa(arrow_411405190le_alt, 
17.82/18.02	           fun(arrow_411405190le_alt, 
17.82/18.02	             product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
17.82/18.02	           product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), a), b), 
17.82/18.02	       aa(
17.82/18.02	         fun(arrow_159774573e_indi, 
17.82/18.02	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	             bool)), 
17.82/18.02	         fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	           bool), f, p))
17.82/18.02	     | member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	         aa(arrow_411405190le_alt, 
17.82/18.02	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	           aa(arrow_411405190le_alt, 
17.82/18.02	             fun(arrow_411405190le_alt, 
17.82/18.02	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
17.82/18.02	             product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), a1), 
17.82/18.02	           b1), 
17.82/18.02	         aa(
17.82/18.02	           fun(arrow_159774573e_indi, 
17.82/18.02	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	               bool)), 
17.82/18.02	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	             bool), f, p1))),
17.82/18.02	    inference('cnf', [status(esa)], [zf_stmt_0])).
17.82/18.02	tff(fact_9__096a_A_061_Ab_H_A_G_Ab_A_061_Aa_H_061_061_062_A_Ia_A_060_092_060_094bsub_062F_AP_092_060_094esub_062_Ab_J_A_061_A_Ia_H_A_060_092_060_094bsub_062F_AP_H_092_060_094esub_062_Ab_H_J_096, axiom,
17.82/18.02	  (((b1 = a) & (a1 = b)) =>
17.82/18.02	   (member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),
17.82/18.02	           aa(arrow_411405190le_alt,
17.82/18.02	              product_prod(arrow_411405190le_alt,arrow_411405190le_alt),
17.82/18.02	              aa(arrow_411405190le_alt,
17.82/18.02	                 fun(arrow_411405190le_alt,
17.82/18.02	                     product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),
17.82/18.02	                 product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a1),
17.82/18.02	              b1),
17.82/18.02	           aa(fun(arrow_159774573e_indi,
17.82/18.02	                  fun(product_prod(arrow_411405190le_alt,
17.82/18.02	                                   arrow_411405190le_alt),
17.82/18.02	                      bool)),
17.82/18.02	              fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),
17.82/18.02	                  bool),
17.82/18.02	              f,p1)) <=>
17.82/18.02	    member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),
17.82/18.02	           aa(arrow_411405190le_alt,
17.82/18.02	              product_prod(arrow_411405190le_alt,arrow_411405190le_alt),
17.82/18.02	              aa(arrow_411405190le_alt,
17.82/18.02	                 fun(arrow_411405190le_alt,
17.82/18.02	                     product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),
17.82/18.02	                 product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),
17.82/18.02	              b),
17.82/18.02	           aa(fun(arrow_159774573e_indi,
17.82/18.02	                  fun(product_prod(arrow_411405190le_alt,
17.82/18.02	                                   arrow_411405190le_alt),
17.82/18.02	                      bool)),
17.82/18.02	              fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),
17.82/18.02	                  bool),
17.82/18.02	              f,p))))).
17.82/18.02	tff('1', plain,
17.82/18.02	    (~ member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	         aa(arrow_411405190le_alt, 
17.82/18.02	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	           aa(arrow_411405190le_alt, 
17.82/18.02	             fun(arrow_411405190le_alt, 
17.82/18.02	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
17.82/18.02	             product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), a), 
17.82/18.02	           b), 
17.82/18.02	         aa(
17.82/18.02	           fun(arrow_159774573e_indi, 
17.82/18.02	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	               bool)), 
17.82/18.02	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	             bool), f, p))
17.82/18.02	     | member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	         aa(arrow_411405190le_alt, 
17.82/18.02	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	           aa(arrow_411405190le_alt, 
17.82/18.02	             fun(arrow_411405190le_alt, 
17.82/18.02	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
17.82/18.02	             product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), a1), 
17.82/18.02	           b1), 
17.82/18.02	         aa(
17.82/18.02	           fun(arrow_159774573e_indi, 
17.82/18.02	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	               bool)), 
17.82/18.02	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	             bool), f, p1))
17.82/18.02	     | a1 != b
17.82/18.02	     | b1 != a),
17.82/18.02	    inference('cnf', [status(esa)],
17.82/18.02	              [fact_9__096a_A_061_Ab_H_A_G_Ab_A_061_Aa_H_061_061_062_A_Ia_A_060_092_060_094bsub_062F_AP_092_060_094esub_062_Ab_J_A_061_A_Ia_H_A_060_092_060_094bsub_062F_AP_H_092_060_094esub_062_Ab_H_J_096])).
17.82/18.02	tff(fact_7__096a_A_126_061_Ab_H_A_G_Ab_A_061_Aa_H_061_061_062_A_Ia_A_060_092_060_094bsub_062F_AP_092_060_094esub_062_Ab_J_A_061_A_Ia_H_A_060_092_060_094bsub_062F_AP_H_092_060_094esub_062_Ab_H_J_096, axiom,
17.82/18.02	  (((b1 = a) & (a1 != b)) =>
17.82/18.02	   (member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),
17.82/18.02	           aa(arrow_411405190le_alt,
17.82/18.02	              product_prod(arrow_411405190le_alt,arrow_411405190le_alt),
17.82/18.02	              aa(arrow_411405190le_alt,
17.82/18.02	                 fun(arrow_411405190le_alt,
17.82/18.02	                     product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),
17.82/18.02	                 product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a1),
17.82/18.02	              b1),
17.82/18.02	           aa(fun(arrow_159774573e_indi,
17.82/18.02	                  fun(product_prod(arrow_411405190le_alt,
17.82/18.02	                                   arrow_411405190le_alt),
17.82/18.02	                      bool)),
17.82/18.02	              fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),
17.82/18.02	                  bool),
17.82/18.02	              f,p1)) <=>
17.82/18.02	    member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),
17.82/18.02	           aa(arrow_411405190le_alt,
17.82/18.02	              product_prod(arrow_411405190le_alt,arrow_411405190le_alt),
17.82/18.02	              aa(arrow_411405190le_alt,
17.82/18.02	                 fun(arrow_411405190le_alt,
17.82/18.02	                     product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),
17.82/18.02	                 product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),
17.82/18.02	              b),
17.82/18.02	           aa(fun(arrow_159774573e_indi,
17.82/18.02	                  fun(product_prod(arrow_411405190le_alt,
17.82/18.02	                                   arrow_411405190le_alt),
17.82/18.02	                      bool)),
17.82/18.02	              fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),
17.82/18.02	                  bool),
17.82/18.02	              f,p))))).
17.82/18.02	tff('2', plain,
17.82/18.02	    (~ member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	         aa(arrow_411405190le_alt, 
17.82/18.02	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	           aa(arrow_411405190le_alt, 
17.82/18.02	             fun(arrow_411405190le_alt, 
17.82/18.02	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
17.82/18.02	             product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), a), 
17.82/18.02	           b), 
17.82/18.02	         aa(
17.82/18.02	           fun(arrow_159774573e_indi, 
17.82/18.02	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	               bool)), 
17.82/18.02	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	             bool), f, p))
17.82/18.02	     | member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	         aa(arrow_411405190le_alt, 
17.82/18.02	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	           aa(arrow_411405190le_alt, 
17.82/18.02	             fun(arrow_411405190le_alt, 
17.82/18.02	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
17.82/18.02	             product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), a1), 
17.82/18.02	           b1), 
17.82/18.02	         aa(
17.82/18.02	           fun(arrow_159774573e_indi, 
17.82/18.02	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	               bool)), 
17.82/18.02	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	             bool), f, p1))
17.82/18.02	     | a1 = b
17.82/18.02	     | b1 != a),
17.82/18.02	    inference('cnf', [status(esa)],
17.82/18.02	              [fact_7__096a_A_126_061_Ab_H_A_G_Ab_A_061_Aa_H_061_061_062_A_Ia_A_060_092_060_094bsub_062F_AP_092_060_094esub_062_Ab_J_A_061_A_Ia_H_A_060_092_060_094bsub_062F_AP_H_092_060_094esub_062_Ab_H_J_096])).
17.82/18.02	tff(fact_6__096a_A_126_061_Ab_H_A_G_Ab_A_126_061_Aa_H_061_061_062_A_Ia_A_060_092_060_094bsub_062F_AP_092_060_094esub_062_Ab_J_A_061_A_Ia_H_A_060_092_060_094bsub_062F_AP_H_092_060_094esub_062_Ab_H_J_096, axiom,
17.82/18.02	  (((b1 != a) & (a1 != b)) =>
17.82/18.02	   (member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),
17.82/18.02	           aa(arrow_411405190le_alt,
17.82/18.02	              product_prod(arrow_411405190le_alt,arrow_411405190le_alt),
17.82/18.02	              aa(arrow_411405190le_alt,
17.82/18.02	                 fun(arrow_411405190le_alt,
17.82/18.02	                     product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),
17.82/18.02	                 product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a1),
17.82/18.02	              b1),
17.82/18.02	           aa(fun(arrow_159774573e_indi,
17.82/18.02	                  fun(product_prod(arrow_411405190le_alt,
17.82/18.02	                                   arrow_411405190le_alt),
17.82/18.02	                      bool)),
17.82/18.02	              fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),
17.82/18.02	                  bool),
17.82/18.02	              f,p1)) <=>
17.82/18.02	    member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),
17.82/18.02	           aa(arrow_411405190le_alt,
17.82/18.02	              product_prod(arrow_411405190le_alt,arrow_411405190le_alt),
17.82/18.02	              aa(arrow_411405190le_alt,
17.82/18.02	                 fun(arrow_411405190le_alt,
17.82/18.02	                     product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),
17.82/18.02	                 product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),
17.82/18.02	              b),
17.82/18.02	           aa(fun(arrow_159774573e_indi,
17.82/18.02	                  fun(product_prod(arrow_411405190le_alt,
17.82/18.02	                                   arrow_411405190le_alt),
17.82/18.02	                      bool)),
17.82/18.02	              fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),
17.82/18.02	                  bool),
17.82/18.02	              f,p))))).
17.82/18.02	tff('3', plain,
17.82/18.02	    (~ member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	         aa(arrow_411405190le_alt, 
17.82/18.02	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	           aa(arrow_411405190le_alt, 
17.82/18.02	             fun(arrow_411405190le_alt, 
17.82/18.02	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
17.82/18.02	             product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), a), 
17.82/18.02	           b), 
17.82/18.02	         aa(
17.82/18.02	           fun(arrow_159774573e_indi, 
17.82/18.02	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	               bool)), 
17.82/18.02	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	             bool), f, p))
17.82/18.02	     | member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	         aa(arrow_411405190le_alt, 
17.82/18.02	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	           aa(arrow_411405190le_alt, 
17.82/18.02	             fun(arrow_411405190le_alt, 
17.82/18.02	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
17.82/18.02	             product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), a1), 
17.82/18.02	           b1), 
17.82/18.02	         aa(
17.82/18.02	           fun(arrow_159774573e_indi, 
17.82/18.02	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	               bool)), 
17.82/18.02	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	             bool), f, p1))
17.82/18.02	     | a1 = b
17.82/18.02	     | b1 = a),
17.82/18.02	    inference('cnf', [status(esa)],
17.82/18.02	              [fact_6__096a_A_126_061_Ab_H_A_G_Ab_A_126_061_Aa_H_061_061_062_A_Ia_A_060_092_060_094bsub_062F_AP_092_060_094esub_062_Ab_J_A_061_A_Ia_H_A_060_092_060_094bsub_062F_AP_H_092_060_094esub_062_Ab_H_J_096])).
17.82/18.02	tff('4', plain,
17.82/18.02	    (a1 = b
17.82/18.02	     | member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	         aa(arrow_411405190le_alt, 
17.82/18.02	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	           aa(arrow_411405190le_alt, 
17.82/18.02	             fun(arrow_411405190le_alt, 
17.82/18.02	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
17.82/18.02	             product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), a1), 
17.82/18.02	           b1), 
17.82/18.02	         aa(
17.82/18.02	           fun(arrow_159774573e_indi, 
17.82/18.02	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	               bool)), 
17.82/18.02	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	             bool), f, p1))
17.82/18.02	     | ~ member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	           aa(arrow_411405190le_alt, 
17.82/18.02	             product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	             aa(arrow_411405190le_alt, 
17.82/18.02	               fun(arrow_411405190le_alt, 
17.82/18.02	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
17.82/18.02	               product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), a), 
17.82/18.02	             b), 
17.82/18.02	           aa(
17.82/18.02	             fun(arrow_159774573e_indi, 
17.82/18.02	               fun(
17.82/18.02	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	                 bool)), 
17.82/18.02	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	               bool), f, p))),
17.82/18.02	    inference('clc', [status(thm)], ['2', '3'])).
17.82/18.02	tff('5', plain,
17.82/18.02	    (b1 != a
17.82/18.02	     | member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	         aa(arrow_411405190le_alt, 
17.82/18.02	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	           aa(arrow_411405190le_alt, 
17.82/18.02	             fun(arrow_411405190le_alt, 
17.82/18.02	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
17.82/18.02	             product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), a1), 
17.82/18.02	           b1), 
17.82/18.02	         aa(
17.82/18.02	           fun(arrow_159774573e_indi, 
17.82/18.02	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	               bool)), 
17.82/18.02	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	             bool), f, p1))
17.82/18.02	     | ~ member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	           aa(arrow_411405190le_alt, 
17.82/18.02	             product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	             aa(arrow_411405190le_alt, 
17.82/18.02	               fun(arrow_411405190le_alt, 
17.82/18.02	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
17.82/18.02	               product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), a), 
17.82/18.02	             b), 
17.82/18.02	           aa(
17.82/18.02	             fun(arrow_159774573e_indi, 
17.82/18.02	               fun(
17.82/18.02	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	                 bool)), 
17.82/18.02	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	               bool), f, p))),
17.82/18.02	    inference('clc', [status(thm)], ['1', '4'])).
17.82/18.02	tff(fact_8__096a_A_061_Ab_H_A_G_Ab_A_126_061_Aa_H_061_061_062_A_Ia_A_060_092_060_094bsub_062F_AP_092_060_094esub_062_Ab_J_A_061_A_Ia_H_A_060_092_060_094bsub_062F_AP_H_092_060_094esub_062_Ab_H_J_096, axiom,
17.82/18.02	  (((b1 != a) & (a1 = b)) =>
17.82/18.02	   (member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),
17.82/18.02	           aa(arrow_411405190le_alt,
17.82/18.02	              product_prod(arrow_411405190le_alt,arrow_411405190le_alt),
17.82/18.02	              aa(arrow_411405190le_alt,
17.82/18.02	                 fun(arrow_411405190le_alt,
17.82/18.02	                     product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),
17.82/18.02	                 product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a1),
17.82/18.02	              b1),
17.82/18.02	           aa(fun(arrow_159774573e_indi,
17.82/18.02	                  fun(product_prod(arrow_411405190le_alt,
17.82/18.02	                                   arrow_411405190le_alt),
17.82/18.02	                      bool)),
17.82/18.02	              fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),
17.82/18.02	                  bool),
17.82/18.02	              f,p1)) <=>
17.82/18.02	    member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),
17.82/18.02	           aa(arrow_411405190le_alt,
17.82/18.02	              product_prod(arrow_411405190le_alt,arrow_411405190le_alt),
17.82/18.02	              aa(arrow_411405190le_alt,
17.82/18.02	                 fun(arrow_411405190le_alt,
17.82/18.02	                     product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),
17.82/18.02	                 product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),
17.82/18.02	              b),
17.82/18.02	           aa(fun(arrow_159774573e_indi,
17.82/18.02	                  fun(product_prod(arrow_411405190le_alt,
17.82/18.02	                                   arrow_411405190le_alt),
17.82/18.02	                      bool)),
17.82/18.02	              fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),
17.82/18.02	                  bool),
17.82/18.02	              f,p))))).
17.82/18.02	tff('6', plain,
17.82/18.02	    (~ member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	         aa(arrow_411405190le_alt, 
17.82/18.02	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	           aa(arrow_411405190le_alt, 
17.82/18.02	             fun(arrow_411405190le_alt, 
17.82/18.02	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
17.82/18.02	             product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), a), 
17.82/18.02	           b), 
17.82/18.02	         aa(
17.82/18.02	           fun(arrow_159774573e_indi, 
17.82/18.02	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	               bool)), 
17.82/18.02	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	             bool), f, p))
17.82/18.02	     | member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	         aa(arrow_411405190le_alt, 
17.82/18.02	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	           aa(arrow_411405190le_alt, 
17.82/18.02	             fun(arrow_411405190le_alt, 
17.82/18.02	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
17.82/18.02	             product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), a1), 
17.82/18.02	           b1), 
17.82/18.02	         aa(
17.82/18.02	           fun(arrow_159774573e_indi, 
17.82/18.02	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	               bool)), 
17.82/18.02	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	             bool), f, p1))
17.82/18.02	     | a1 != b
17.82/18.02	     | b1 = a),
17.82/18.02	    inference('cnf', [status(esa)],
17.82/18.02	              [fact_8__096a_A_061_Ab_H_A_G_Ab_A_126_061_Aa_H_061_061_062_A_Ia_A_060_092_060_094bsub_062F_AP_092_060_094esub_062_Ab_J_A_061_A_Ia_H_A_060_092_060_094bsub_062F_AP_H_092_060_094esub_062_Ab_H_J_096])).
17.82/18.02	tff('7', plain,
17.82/18.02	    (b1 = a
17.82/18.02	     | member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	         aa(arrow_411405190le_alt, 
17.82/18.02	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	           aa(arrow_411405190le_alt, 
17.82/18.02	             fun(arrow_411405190le_alt, 
17.82/18.02	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
17.82/18.02	             product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), a1), 
17.82/18.02	           b1), 
17.82/18.02	         aa(
17.82/18.02	           fun(arrow_159774573e_indi, 
17.82/18.02	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	               bool)), 
17.82/18.02	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	             bool), f, p1))
17.82/18.02	     | ~ member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	           aa(arrow_411405190le_alt, 
17.82/18.02	             product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	             aa(arrow_411405190le_alt, 
17.82/18.02	               fun(arrow_411405190le_alt, 
17.82/18.02	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
17.82/18.02	               product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), a), 
17.82/18.02	             b), 
17.82/18.02	           aa(
17.82/18.02	             fun(arrow_159774573e_indi, 
17.82/18.02	               fun(
17.82/18.02	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	                 bool)), 
17.82/18.02	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	               bool), f, p))),
17.82/18.02	    inference('clc', [status(thm)], ['6', '4'])).
17.82/18.02	tff('8', plain,
17.82/18.02	    (~ member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	         aa(arrow_411405190le_alt, 
17.82/18.02	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	           aa(arrow_411405190le_alt, 
17.82/18.02	             fun(arrow_411405190le_alt, 
17.82/18.02	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
17.82/18.02	             product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), a), 
17.82/18.02	           b), 
17.82/18.02	         aa(
17.82/18.02	           fun(arrow_159774573e_indi, 
17.82/18.02	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	               bool)), 
17.82/18.02	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	             bool), f, p))
17.82/18.02	     | member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	         aa(arrow_411405190le_alt, 
17.82/18.02	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	           aa(arrow_411405190le_alt, 
17.82/18.02	             fun(arrow_411405190le_alt, 
17.82/18.02	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
17.82/18.02	             product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), a1), 
17.82/18.02	           b1), 
17.82/18.02	         aa(
17.82/18.02	           fun(arrow_159774573e_indi, 
17.82/18.02	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	               bool)), 
17.82/18.02	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	             bool), f, p1))),
17.82/18.02	    inference('clc', [status(thm)], ['5', '7'])).
17.82/18.02	tff('9', plain,
17.82/18.02	    member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	      aa(arrow_411405190le_alt, 
17.82/18.02	        product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	        aa(arrow_411405190le_alt, 
17.82/18.02	          fun(arrow_411405190le_alt, 
17.82/18.02	            product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
17.82/18.02	          product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), a1), 
17.82/18.02	        b1), 
17.82/18.02	      aa(
17.82/18.02	        fun(arrow_159774573e_indi, 
17.82/18.02	          fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	            bool)), 
17.82/18.02	        fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), bool), 
17.82/18.02	        f, p1)),
17.82/18.02	    inference('clc', [status(thm)], ['0', '8'])).
17.82/18.02	tff('10', plain,
17.82/18.02	    (~ member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	         aa(arrow_411405190le_alt, 
17.82/18.02	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	           aa(arrow_411405190le_alt, 
17.82/18.02	             fun(arrow_411405190le_alt, 
17.82/18.02	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
17.82/18.02	             product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), a1), 
17.82/18.02	           b1), 
17.82/18.02	         aa(
17.82/18.02	           fun(arrow_159774573e_indi, 
17.82/18.02	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	               bool)), 
17.82/18.02	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	             bool), f, p1))
17.82/18.02	     | member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	         aa(arrow_411405190le_alt, 
17.82/18.02	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	           aa(arrow_411405190le_alt, 
17.82/18.02	             fun(arrow_411405190le_alt, 
17.82/18.02	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
17.82/18.02	             product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), a), 
17.82/18.02	           b), 
17.82/18.02	         aa(
17.82/18.02	           fun(arrow_159774573e_indi, 
17.82/18.02	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	               bool)), 
17.82/18.02	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	             bool), f, p))
17.82/18.02	     | a1 != b
17.82/18.02	     | b1 != a),
17.82/18.02	    inference('cnf', [status(esa)],
17.82/18.02	              [fact_9__096a_A_061_Ab_H_A_G_Ab_A_061_Aa_H_061_061_062_A_Ia_A_060_092_060_094bsub_062F_AP_092_060_094esub_062_Ab_J_A_061_A_Ia_H_A_060_092_060_094bsub_062F_AP_H_092_060_094esub_062_Ab_H_J_096])).
17.82/18.02	tff('11', plain,
17.82/18.02	    (~ member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	         aa(arrow_411405190le_alt, 
17.82/18.02	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	           aa(arrow_411405190le_alt, 
17.82/18.02	             fun(arrow_411405190le_alt, 
17.82/18.02	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
17.82/18.02	             product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), a1), 
17.82/18.02	           b1), 
17.82/18.02	         aa(
17.82/18.02	           fun(arrow_159774573e_indi, 
17.82/18.02	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	               bool)), 
17.82/18.02	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	             bool), f, p1))
17.82/18.02	     | member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	         aa(arrow_411405190le_alt, 
17.82/18.02	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	           aa(arrow_411405190le_alt, 
17.82/18.02	             fun(arrow_411405190le_alt, 
17.82/18.02	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
17.82/18.02	             product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), a), 
17.82/18.02	           b), 
17.82/18.02	         aa(
17.82/18.02	           fun(arrow_159774573e_indi, 
17.82/18.02	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	               bool)), 
17.82/18.02	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	             bool), f, p))
17.82/18.02	     | a1 = b
17.82/18.02	     | b1 != a),
17.82/18.02	    inference('cnf', [status(esa)],
17.82/18.02	              [fact_7__096a_A_126_061_Ab_H_A_G_Ab_A_061_Aa_H_061_061_062_A_Ia_A_060_092_060_094bsub_062F_AP_092_060_094esub_062_Ab_J_A_061_A_Ia_H_A_060_092_060_094bsub_062F_AP_H_092_060_094esub_062_Ab_H_J_096])).
17.82/18.02	tff('12', plain,
17.82/18.02	    (~ member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	         aa(arrow_411405190le_alt, 
17.82/18.02	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	           aa(arrow_411405190le_alt, 
17.82/18.02	             fun(arrow_411405190le_alt, 
17.82/18.02	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
17.82/18.02	             product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), a1), 
17.82/18.02	           b1), 
17.82/18.02	         aa(
17.82/18.02	           fun(arrow_159774573e_indi, 
17.82/18.02	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	               bool)), 
17.82/18.02	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	             bool), f, p1))
17.82/18.02	     | member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	         aa(arrow_411405190le_alt, 
17.82/18.02	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	           aa(arrow_411405190le_alt, 
17.82/18.02	             fun(arrow_411405190le_alt, 
17.82/18.02	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
17.82/18.02	             product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), a), 
17.82/18.02	           b), 
17.82/18.02	         aa(
17.82/18.02	           fun(arrow_159774573e_indi, 
17.82/18.02	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	               bool)), 
17.82/18.02	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	             bool), f, p))
17.82/18.02	     | a1 = b
17.82/18.02	     | b1 = a),
17.82/18.02	    inference('cnf', [status(esa)],
17.82/18.02	              [fact_6__096a_A_126_061_Ab_H_A_G_Ab_A_126_061_Aa_H_061_061_062_A_Ia_A_060_092_060_094bsub_062F_AP_092_060_094esub_062_Ab_J_A_061_A_Ia_H_A_060_092_060_094bsub_062F_AP_H_092_060_094esub_062_Ab_H_J_096])).
17.82/18.02	tff('13', plain,
17.82/18.02	    (a1 = b
17.82/18.02	     | member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	         aa(arrow_411405190le_alt, 
17.82/18.02	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	           aa(arrow_411405190le_alt, 
17.82/18.02	             fun(arrow_411405190le_alt, 
17.82/18.02	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
17.82/18.02	             product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), a), 
17.82/18.02	           b), 
17.82/18.02	         aa(
17.82/18.02	           fun(arrow_159774573e_indi, 
17.82/18.02	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	               bool)), 
17.82/18.02	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	             bool), f, p))
17.82/18.02	     | ~ member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	           aa(arrow_411405190le_alt, 
17.82/18.02	             product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	             aa(arrow_411405190le_alt, 
17.82/18.02	               fun(arrow_411405190le_alt, 
17.82/18.02	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
17.82/18.02	               product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	               a1), b1), 
17.82/18.02	           aa(
17.82/18.02	             fun(arrow_159774573e_indi, 
17.82/18.02	               fun(
17.82/18.02	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	                 bool)), 
17.82/18.02	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	               bool), f, p1))),
17.82/18.02	    inference('clc', [status(thm)], ['11', '12'])).
17.82/18.02	tff('14', plain,
17.82/18.02	    (b1 != a
17.82/18.02	     | member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	         aa(arrow_411405190le_alt, 
17.82/18.02	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	           aa(arrow_411405190le_alt, 
17.82/18.02	             fun(arrow_411405190le_alt, 
17.82/18.02	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
17.82/18.02	             product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), a), 
17.82/18.02	           b), 
17.82/18.02	         aa(
17.82/18.02	           fun(arrow_159774573e_indi, 
17.82/18.02	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	               bool)), 
17.82/18.02	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	             bool), f, p))
17.82/18.02	     | ~ member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	           aa(arrow_411405190le_alt, 
17.82/18.02	             product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	             aa(arrow_411405190le_alt, 
17.82/18.02	               fun(arrow_411405190le_alt, 
17.82/18.02	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
17.82/18.02	               product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	               a1), b1), 
17.82/18.02	           aa(
17.82/18.02	             fun(arrow_159774573e_indi, 
17.82/18.02	               fun(
17.82/18.02	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	                 bool)), 
17.82/18.02	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	               bool), f, p1))),
17.82/18.02	    inference('clc', [status(thm)], ['10', '13'])).
17.82/18.02	tff('15', plain,
17.82/18.02	    (~ member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	         aa(arrow_411405190le_alt, 
17.82/18.02	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	           aa(arrow_411405190le_alt, 
17.82/18.02	             fun(arrow_411405190le_alt, 
17.82/18.02	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
17.82/18.02	             product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), a1), 
17.82/18.02	           b1), 
17.82/18.02	         aa(
17.82/18.02	           fun(arrow_159774573e_indi, 
17.82/18.02	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	               bool)), 
17.82/18.02	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	             bool), f, p1))
17.82/18.02	     | member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	         aa(arrow_411405190le_alt, 
17.82/18.02	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	           aa(arrow_411405190le_alt, 
17.82/18.02	             fun(arrow_411405190le_alt, 
17.82/18.02	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
17.82/18.02	             product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), a), 
17.82/18.02	           b), 
17.82/18.02	         aa(
17.82/18.02	           fun(arrow_159774573e_indi, 
17.82/18.02	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	               bool)), 
17.82/18.02	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	             bool), f, p))
17.82/18.02	     | a1 != b
17.82/18.02	     | b1 = a),
17.82/18.02	    inference('cnf', [status(esa)],
17.82/18.02	              [fact_8__096a_A_061_Ab_H_A_G_Ab_A_126_061_Aa_H_061_061_062_A_Ia_A_060_092_060_094bsub_062F_AP_092_060_094esub_062_Ab_J_A_061_A_Ia_H_A_060_092_060_094bsub_062F_AP_H_092_060_094esub_062_Ab_H_J_096])).
17.82/18.02	tff('16', plain,
17.82/18.02	    (b1 = a
17.82/18.02	     | member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	         aa(arrow_411405190le_alt, 
17.82/18.02	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	           aa(arrow_411405190le_alt, 
17.82/18.02	             fun(arrow_411405190le_alt, 
17.82/18.02	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
17.82/18.02	             product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), a), 
17.82/18.02	           b), 
17.82/18.02	         aa(
17.82/18.02	           fun(arrow_159774573e_indi, 
17.82/18.02	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	               bool)), 
17.82/18.02	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	             bool), f, p))
17.82/18.02	     | ~ member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	           aa(arrow_411405190le_alt, 
17.82/18.02	             product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	             aa(arrow_411405190le_alt, 
17.82/18.02	               fun(arrow_411405190le_alt, 
17.82/18.02	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
17.82/18.02	               product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	               a1), b1), 
17.82/18.02	           aa(
17.82/18.02	             fun(arrow_159774573e_indi, 
17.82/18.02	               fun(
17.82/18.02	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	                 bool)), 
17.82/18.02	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	               bool), f, p1))),
17.82/18.02	    inference('clc', [status(thm)], ['15', '13'])).
17.82/18.02	tff('17', plain,
17.82/18.02	    (~ member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	         aa(arrow_411405190le_alt, 
17.82/18.02	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	           aa(arrow_411405190le_alt, 
17.82/18.02	             fun(arrow_411405190le_alt, 
17.82/18.02	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
17.82/18.02	             product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), a1), 
17.82/18.02	           b1), 
17.82/18.02	         aa(
17.82/18.02	           fun(arrow_159774573e_indi, 
17.82/18.02	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	               bool)), 
17.82/18.02	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	             bool), f, p1))
17.82/18.02	     | member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	         aa(arrow_411405190le_alt, 
17.82/18.02	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	           aa(arrow_411405190le_alt, 
17.82/18.02	             fun(arrow_411405190le_alt, 
17.82/18.02	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
17.82/18.02	             product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), a), 
17.82/18.02	           b), 
17.82/18.02	         aa(
17.82/18.02	           fun(arrow_159774573e_indi, 
17.82/18.02	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	               bool)), 
17.82/18.02	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	             bool), f, p))),
17.82/18.02	    inference('clc', [status(thm)], ['14', '16'])).
17.82/18.02	tff('18', plain,
17.82/18.02	    (~ $true
17.82/18.02	     | member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	         aa(arrow_411405190le_alt, 
17.82/18.02	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	           aa(arrow_411405190le_alt, 
17.82/18.02	             fun(arrow_411405190le_alt, 
17.82/18.02	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
17.82/18.02	             product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), a), 
17.82/18.02	           b), 
17.82/18.02	         aa(
17.82/18.02	           fun(arrow_159774573e_indi, 
17.82/18.02	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	               bool)), 
17.82/18.02	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	             bool), f, p))),
17.82/18.02	    inference('sup-', [status(thm)], ['9', '17'])).
17.82/18.02	tff('19', plain,
17.82/18.02	    member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	      aa(arrow_411405190le_alt, 
17.82/18.02	        product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	        aa(arrow_411405190le_alt, 
17.82/18.02	          fun(arrow_411405190le_alt, 
17.82/18.02	            product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
17.82/18.02	          product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), a), b), 
17.82/18.02	      aa(
17.82/18.02	        fun(arrow_159774573e_indi, 
17.82/18.02	          fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	            bool)), 
17.82/18.02	        fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), bool), 
17.82/18.02	        f, p)),
17.82/18.02	    inference('simplify', [status(thm)], ['18'])).
17.82/18.02	tff('20', plain,
17.82/18.02	    (~ member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	         aa(arrow_411405190le_alt, 
17.82/18.02	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	           aa(arrow_411405190le_alt, 
17.82/18.02	             fun(arrow_411405190le_alt, 
17.82/18.02	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
17.82/18.02	             product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), a), 
17.82/18.02	           b), 
17.82/18.02	         aa(
17.82/18.02	           fun(arrow_159774573e_indi, 
17.82/18.02	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	               bool)), 
17.82/18.02	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	             bool), f, p))
17.82/18.02	     | ~ member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	           aa(arrow_411405190le_alt, 
17.82/18.02	             product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	             aa(arrow_411405190le_alt, 
17.82/18.02	               fun(arrow_411405190le_alt, 
17.82/18.02	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
17.82/18.02	               product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	               a1), b1), 
17.82/18.02	           aa(
17.82/18.02	             fun(arrow_159774573e_indi, 
17.82/18.02	               fun(
17.82/18.02	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	                 bool)), 
17.82/18.02	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	               bool), f, p1))),
17.82/18.02	    inference('cnf', [status(esa)], [zf_stmt_0])).
17.82/18.02	tff('21', plain,
17.82/18.02	    (~ member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	         aa(arrow_411405190le_alt, 
17.82/18.02	           product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	           aa(arrow_411405190le_alt, 
17.82/18.02	             fun(arrow_411405190le_alt, 
17.82/18.02	               product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
17.82/18.02	             product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), a), 
17.82/18.02	           b), 
17.82/18.02	         aa(
17.82/18.02	           fun(arrow_159774573e_indi, 
17.82/18.02	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	               bool)), 
17.82/18.02	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	             bool), f, p))
17.82/18.02	     | ~ $true),
17.82/18.02	    inference('demod', [status(thm)], ['20', '9'])).
17.82/18.02	tff('22', plain,
17.82/18.02	    ~ member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	        aa(arrow_411405190le_alt, 
17.82/18.02	          product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	          aa(arrow_411405190le_alt, 
17.82/18.02	            fun(arrow_411405190le_alt, 
17.82/18.02	              product_prod(arrow_411405190le_alt, arrow_411405190le_alt)), 
17.82/18.02	            product_Pair(arrow_411405190le_alt, arrow_411405190le_alt), a), 
17.82/18.02	          b), 
17.82/18.02	        aa(
17.82/18.02	          fun(arrow_159774573e_indi, 
17.82/18.02	            fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	              bool)), 
17.82/18.02	          fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
17.82/18.02	            bool), f, p)),
17.82/18.02	    inference('simplify', [status(thm)], ['21'])).
17.82/18.02	tff('23', plain, ~ $true, inference('sup-', [status(thm)], ['19', '22'])).
17.82/18.02	tff('24', plain, $false, inference('simplify', [status(thm)], ['23'])).
17.82/18.02	
17.82/18.02	% SZS output end Refutation
17.82/18.02	EOF
