0.00/0.00	% File    : /export/starexec/sandbox/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : original
0.00/0.00	% Variant    : purification_ext
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-avatar \
0.00/0.00	  --ho \
0.00/0.00	  --force-ho \
0.00/0.00	  --no-ho-elim-pred-var \
0.00/0.00	  --ho-general-ext-pos \
0.00/0.00	  --no-ho-unif \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2  \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --ho-purify ext \
0.00/0.00	  --ho-ext-axiom \
0.00/0.00	  --restrict-hidden-sup-at-vars \
0.00/0.00	  --ho-prim-enum none \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --dont-select-ho-var-lits \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n030.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 13:56:54 CST 2018
33.13/33.40	% done 6362 iterations in 33.203s
33.13/33.40	% SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
33.13/33.40	% SZS output start Refutation
33.13/33.41	tff(fact_4_distinct__length__2__or__more, axiom,
33.13/33.41	  (![A:$tType,Xs1:list(A),Ba:A,Aa:A]:
33.13/33.41	     (distinct(A,cons(A,Aa,cons(A,Ba,Xs1))) <=>
33.13/33.41	      (distinct(A,cons(A,Ba,Xs1)) & distinct(A,cons(A,Aa,Xs1)) & (Aa != Ba))))).
33.13/33.41	tff('0', plain,
33.13/33.41	    ![X9 : $tType, X10 : X9, X11 : list(X9), X13 : X9]:
33.13/33.41	      (distinct(X9, cons(X9, X13, cons(X9, X10, X11)))
33.13/33.41	       | X13 = X10
33.13/33.41	       | ~ distinct(X9, cons(X9, X13, X11))
33.13/33.41	       | ~ distinct(X9, cons(X9, X10, X11))),
33.13/33.41	    inference('cnf', [status(esa)], [fact_4_distinct__length__2__or__more])).
33.13/33.41	tff(conj_1, conjecture,
33.13/33.41	  (?[C:arrow_411405190le_alt]:
33.13/33.41	     distinct(arrow_411405190le_alt,
33.13/33.41	              cons(arrow_411405190le_alt,a,
33.13/33.41	                   cons(arrow_411405190le_alt,b,
33.13/33.41	                        cons(arrow_411405190le_alt,C,
33.13/33.41	                             nil(arrow_411405190le_alt))))))).
33.13/33.41	tff(zf_stmt_0, negated_conjecture,
33.13/33.41	  (~
33.13/33.41	    (?[C:arrow_411405190le_alt]:
33.13/33.41	       distinct(arrow_411405190le_alt,
33.13/33.41	                cons(arrow_411405190le_alt,a,
33.13/33.41	                     cons(arrow_411405190le_alt,b,
33.13/33.41	                          cons(arrow_411405190le_alt,C,
33.13/33.41	                               nil(arrow_411405190le_alt)))))))).
33.13/33.41	tff('1', plain,
33.13/33.41	    ![X360 : arrow_411405190le_alt]:
33.13/33.41	      ~ distinct(arrow_411405190le_alt, 
33.13/33.41	          cons(arrow_411405190le_alt, a, 
33.13/33.41	            cons(arrow_411405190le_alt, b, 
33.13/33.41	              cons(arrow_411405190le_alt, X360, nil(arrow_411405190le_alt))))),
33.13/33.41	    inference('cnf', [status(esa)], [zf_stmt_0])).
33.13/33.41	tff('2', plain,
33.13/33.41	    ![X0 : arrow_411405190le_alt]:
33.13/33.41	      (~ $true
33.13/33.41	       | ~ distinct(arrow_411405190le_alt, 
33.13/33.41	             cons(arrow_411405190le_alt, b, 
33.13/33.41	               cons(arrow_411405190le_alt, X0, nil(arrow_411405190le_alt))))
33.13/33.41	       | ~ distinct(arrow_411405190le_alt, 
33.13/33.41	             cons(arrow_411405190le_alt, a, 
33.13/33.41	               cons(arrow_411405190le_alt, X0, nil(arrow_411405190le_alt))))
33.13/33.41	       | a = b),
33.13/33.41	    inference('sup-', [status(thm)], ['0', '1'])).
33.13/33.41	tff('3', plain,
33.13/33.41	    ![X0 : arrow_411405190le_alt]:
33.13/33.41	      (a = b
33.13/33.41	       | ~ distinct(arrow_411405190le_alt, 
33.13/33.41	             cons(arrow_411405190le_alt, a, 
33.13/33.41	               cons(arrow_411405190le_alt, X0, nil(arrow_411405190le_alt))))
33.13/33.41	       | ~ distinct(arrow_411405190le_alt, 
33.13/33.41	             cons(arrow_411405190le_alt, b, 
33.13/33.41	               cons(arrow_411405190le_alt, X0, nil(arrow_411405190le_alt))))),
33.13/33.41	    inference('simplify', [status(thm)], ['2'])).
33.13/33.41	tff(conj_0, axiom, (a != b)).
33.13/33.41	tff('4', plain, a != b, inference('cnf', [status(esa)], [conj_0])).
33.13/33.41	tff('5', plain,
33.13/33.41	    ![X0 : arrow_411405190le_alt]:
33.13/33.41	      (~ distinct(arrow_411405190le_alt, 
33.13/33.41	           cons(arrow_411405190le_alt, a, 
33.13/33.41	             cons(arrow_411405190le_alt, X0, nil(arrow_411405190le_alt))))
33.13/33.41	       | ~ distinct(arrow_411405190le_alt, 
33.13/33.41	             cons(arrow_411405190le_alt, b, 
33.13/33.41	               cons(arrow_411405190le_alt, X0, nil(arrow_411405190le_alt))))),
33.13/33.41	    inference('simplify_reflect-', [status(thm)], ['3', '4'])).
33.13/33.41	tff('6', plain,
33.13/33.41	    ![X0 : arrow_411405190le_alt]:
33.13/33.41	      (~ $true
33.13/33.41	       | ~ distinct(arrow_411405190le_alt, 
33.13/33.41	             cons(arrow_411405190le_alt, X0, nil(arrow_411405190le_alt)))
33.13/33.41	       | ~ distinct(arrow_411405190le_alt, 
33.13/33.41	             cons(arrow_411405190le_alt, b, nil(arrow_411405190le_alt)))
33.13/33.41	       | b = X0
33.13/33.41	       | ~ distinct(arrow_411405190le_alt, 
33.13/33.41	             cons(arrow_411405190le_alt, a, 
33.13/33.41	               cons(arrow_411405190le_alt, X0, nil(arrow_411405190le_alt))))),
33.13/33.41	    inference('sup-', [status(thm)], ['0', '5'])).
33.13/33.41	tff(fact_2_distinct__singleton, axiom,
33.13/33.41	  (![A:$tType,X:A]: distinct(A,cons(A,X,nil(A))))).
33.13/33.41	tff('7', plain, ![X1 : $tType, X2 : X1]: distinct(X1, cons(X1, X2, nil(X1))),
33.13/33.41	    inference('cnf', [status(esa)], [fact_2_distinct__singleton])).
33.13/33.41	tff('8', plain,
33.13/33.41	    ![X0 : arrow_411405190le_alt]:
33.13/33.41	      (~ $true
33.13/33.41	       | ~ $true
33.13/33.41	       | ~ $true
33.13/33.41	       | b = X0
33.13/33.41	       | ~ distinct(arrow_411405190le_alt, 
33.13/33.41	             cons(arrow_411405190le_alt, a, 
33.13/33.41	               cons(arrow_411405190le_alt, X0, nil(arrow_411405190le_alt))))),
33.13/33.41	    inference('demod', [status(thm)], ['6', '7', '7'])).
33.13/33.41	tff('9', plain,
33.13/33.41	    ![X0 : arrow_411405190le_alt]:
33.13/33.41	      (~ distinct(arrow_411405190le_alt, 
33.13/33.41	           cons(arrow_411405190le_alt, a, 
33.13/33.41	             cons(arrow_411405190le_alt, X0, nil(arrow_411405190le_alt))))
33.13/33.41	       | b = X0),
33.13/33.41	    inference('simplify', [status(thm)], ['8'])).
33.13/33.41	tff('10', plain,
33.13/33.41	    ![X0 : arrow_411405190le_alt]:
33.13/33.41	      (~ $true
33.13/33.41	       | ~ distinct(arrow_411405190le_alt, 
33.13/33.41	             cons(arrow_411405190le_alt, X0, nil(arrow_411405190le_alt)))
33.13/33.41	       | ~ distinct(arrow_411405190le_alt, 
33.13/33.41	             cons(arrow_411405190le_alt, a, nil(arrow_411405190le_alt)))
33.13/33.41	       | a = X0
33.13/33.41	       | b = X0),
33.13/33.41	    inference('sup-', [status(thm)], ['0', '9'])).
33.13/33.41	tff('11', plain,
33.13/33.41	    ![X0 : arrow_411405190le_alt]:
33.13/33.41	      (~ $true | ~ $true | ~ $true | a = X0 | b = X0),
33.13/33.41	    inference('demod', [status(thm)], ['10', '7', '7'])).
33.13/33.41	tff('12', plain, ![X0 : arrow_411405190le_alt]: (b = X0 | a = X0),
33.13/33.41	    inference('simplify', [status(thm)], ['11'])).
33.13/33.41	tff(fact_0_alt3, axiom,
33.13/33.41	  (?[A1:arrow_411405190le_alt,B1:arrow_411405190le_alt,
33.13/33.41	     C1:arrow_411405190le_alt]:
33.13/33.41	     distinct(arrow_411405190le_alt,
33.13/33.41	              cons(arrow_411405190le_alt,A1,
33.13/33.41	                   cons(arrow_411405190le_alt,B1,
33.13/33.41	                        cons(arrow_411405190le_alt,C1,
33.13/33.41	                             nil(arrow_411405190le_alt))))))).
33.13/33.41	tff('13', plain,
33.13/33.41	    distinct(arrow_411405190le_alt, 
33.13/33.41	      cons(arrow_411405190le_alt, sk_A1, 
33.13/33.41	        cons(arrow_411405190le_alt, sk_B1, 
33.13/33.41	          cons(arrow_411405190le_alt, sk_C1, nil(arrow_411405190le_alt))))),
33.13/33.41	    inference('cnf', [status(esa)], [fact_0_alt3])).
33.13/33.41	tff('14', plain,
33.13/33.41	    (distinct(arrow_411405190le_alt, 
33.13/33.41	       cons(arrow_411405190le_alt, sk_A1, 
33.13/33.41	         cons(arrow_411405190le_alt, b, 
33.13/33.41	           cons(arrow_411405190le_alt, sk_C1, nil(arrow_411405190le_alt)))))
33.13/33.41	     | a = sk_B1),
33.13/33.41	    inference('sup+', [status(thm)], ['12', '13'])).
33.13/33.41	tff('15', plain,
33.13/33.41	    ![X0 : arrow_411405190le_alt, X1 : arrow_411405190le_alt]:
33.13/33.41	      (~ distinct(arrow_411405190le_alt, 
33.13/33.41	           cons(arrow_411405190le_alt, X0, 
33.13/33.41	             cons(arrow_411405190le_alt, b, 
33.13/33.41	               cons(arrow_411405190le_alt, X1, nil(arrow_411405190le_alt)))))
33.13/33.41	       | b = X0),
33.13/33.41	    inference('sup-', [status(thm)], ['12', '1'])).
33.13/33.41	tff('16', plain, (~ $true | a = sk_B1 | b = sk_A1),
33.13/33.41	    inference('sup-', [status(thm)], ['14', '15'])).
33.13/33.41	tff('17', plain, (b = sk_A1 | a = sk_B1),
33.13/33.41	    inference('simplify', [status(thm)], ['16'])).
33.13/33.41	tff('18', plain,
33.13/33.41	    (distinct(arrow_411405190le_alt, 
33.13/33.41	       cons(arrow_411405190le_alt, sk_A1, 
33.13/33.41	         cons(arrow_411405190le_alt, a, 
33.13/33.41	           cons(arrow_411405190le_alt, sk_C1, nil(arrow_411405190le_alt)))))
33.13/33.41	     | b = sk_A1),
33.13/33.41	    inference('sup+', [status(thm)], ['17', '13'])).
33.13/33.41	tff('19', plain,
33.13/33.41	    ![X9 : $tType, X10 : X9, X11 : list(X9), X12 : X9]:
33.13/33.41	      (distinct(X9, cons(X9, X12, X11))
33.13/33.41	       | ~ distinct(X9, cons(X9, X12, cons(X9, X10, X11)))),
33.13/33.41	    inference('cnf', [status(esa)], [fact_4_distinct__length__2__or__more])).
33.13/33.41	tff('20', plain,
33.13/33.41	    (~ $true
33.13/33.41	     | distinct(arrow_411405190le_alt, 
33.13/33.41	         cons(arrow_411405190le_alt, sk_A1, 
33.13/33.41	           cons(arrow_411405190le_alt, sk_C1, nil(arrow_411405190le_alt))))),
33.13/33.41	    inference('sup-', [status(thm)], ['13', '19'])).
33.13/33.41	tff('21', plain,
33.13/33.41	    distinct(arrow_411405190le_alt, 
33.13/33.41	      cons(arrow_411405190le_alt, sk_A1, 
33.13/33.41	        cons(arrow_411405190le_alt, sk_C1, nil(arrow_411405190le_alt)))),
33.13/33.41	    inference('simplify', [status(thm)], ['20'])).
33.13/33.41	tff('22', plain,
33.13/33.41	    (distinct(arrow_411405190le_alt, 
33.13/33.41	       cons(arrow_411405190le_alt, b, 
33.13/33.41	         cons(arrow_411405190le_alt, sk_C1, nil(arrow_411405190le_alt))))
33.13/33.41	     | a = sk_A1),
33.13/33.41	    inference('sup+', [status(thm)], ['12', '21'])).
33.13/33.41	tff('23', plain,
33.13/33.41	    (~ $true
33.13/33.41	     | a = sk_A1
33.13/33.41	     | ~ distinct(arrow_411405190le_alt, 
33.13/33.41	           cons(arrow_411405190le_alt, a, 
33.13/33.41	             cons(arrow_411405190le_alt, sk_C1, nil(arrow_411405190le_alt))))),
33.13/33.41	    inference('sup-', [status(thm)], ['22', '5'])).
33.13/33.41	tff('24', plain,
33.13/33.41	    (~ distinct(arrow_411405190le_alt, 
33.13/33.41	         cons(arrow_411405190le_alt, a, 
33.13/33.41	           cons(arrow_411405190le_alt, sk_C1, nil(arrow_411405190le_alt))))
33.13/33.41	     | a = sk_A1),
33.13/33.41	    inference('simplify', [status(thm)], ['23'])).
33.13/33.41	tff('25', plain,
33.13/33.41	    (~ $true
33.13/33.41	     | ~ distinct(arrow_411405190le_alt, 
33.13/33.41	           cons(arrow_411405190le_alt, sk_C1, nil(arrow_411405190le_alt)))
33.13/33.41	     | ~ distinct(arrow_411405190le_alt, 
33.13/33.41	           cons(arrow_411405190le_alt, a, nil(arrow_411405190le_alt)))
33.13/33.41	     | a = sk_C1
33.13/33.41	     | a = sk_A1),
33.13/33.41	    inference('sup-', [status(thm)], ['0', '24'])).
33.13/33.41	tff('26', plain, (~ $true | ~ $true | ~ $true | a = sk_C1 | a = sk_A1),
33.13/33.41	    inference('demod', [status(thm)], ['25', '7', '7'])).
33.13/33.41	tff('27', plain, (a = sk_A1 | a = sk_C1),
33.13/33.41	    inference('simplify', [status(thm)], ['26'])).
33.13/33.41	tff(fact_80_rev_Osimps_I2_J, axiom,
33.13/33.41	  (![A:$tType,Xs:list(A),X:A]:
33.13/33.41	     (rev(A,cons(A,X,Xs)) = append(A,rev(A,Xs),cons(A,X,nil(A)))))).
33.13/33.41	tff('28', plain,
33.13/33.41	    ![X297 : $tType, X298 : list(X297), X299 : X297]:
33.13/33.41	      rev(X297, cons(X297, X299, X298))
33.13/33.41	       = append(X297, rev(X297, X298), cons(X297, X299, nil(X297))),
33.13/33.41	    inference('cnf', [status(esa)], [fact_80_rev_Osimps_I2_J])).
33.13/33.41	tff(fact_86_distinct__rev, axiom,
33.13/33.41	  (![A:$tType,Xs1:list(A)]: (distinct(A,rev(A,Xs1)) <=> distinct(A,Xs1)))).
33.13/33.41	tff('29', plain,
33.13/33.41	    ![X314 : $tType, X316 : list(X314)]:
33.13/33.41	      (distinct(X314, rev(X314, X316)) | ~ distinct(X314, X316)),
33.13/33.41	    inference('cnf', [status(esa)], [fact_86_distinct__rev])).
33.13/33.41	tff('30', plain,
33.13/33.41	    ![X0 : $tType, X1 : X0, X2 : list(X0)]:
33.13/33.41	      (distinct(X0, append(X0, rev(X0, X2), cons(X0, X1, nil(X0))))
33.13/33.41	       | ~ distinct(X0, cons(X0, X1, X2))),
33.13/33.41	    inference('sup+', [status(thm)], ['28', '29'])).
33.13/33.41	tff(fact_67_butlast__snoc, axiom,
33.13/33.41	  (![A:$tType,X:A,Xs:list(A)]:
33.13/33.41	     (butlast(A,append(A,Xs,cons(A,X,nil(A)))) = Xs))).
33.13/33.41	tff('31', plain,
33.13/33.41	    ![X252 : $tType, X253 : list(X252), X254 : X252]:
33.13/33.41	      butlast(X252, append(X252, X253, cons(X252, X254, nil(X252)))) = X253,
33.13/33.41	    inference('cnf', [status(esa)], [fact_67_butlast__snoc])).
33.13/33.41	tff(fact_31_distinct__butlast, axiom,
33.13/33.41	  (![A:$tType,Xs:list(A)]:
33.13/33.41	     ((Xs != nil(A)) => (distinct(A,Xs) => distinct(A,butlast(A,Xs)))))).
33.13/33.41	tff('32', plain,
33.13/33.41	    ![X105 : $tType, X106 : list(X105)]:
33.13/33.41	      (~ distinct(X105, X106)
33.13/33.41	       | distinct(X105, butlast(X105, X106))
33.13/33.41	       | X106 = nil(X105)),
33.13/33.41	    inference('cnf', [status(esa)], [fact_31_distinct__butlast])).
33.13/33.41	tff('33', plain,
33.13/33.41	    ![X0 : $tType, X1 : list(X0), X2 : X0]:
33.13/33.41	      (distinct(X0, X1)
33.13/33.41	       | append(X0, X1, cons(X0, X2, nil(X0))) = nil(X0)
33.13/33.41	       | ~ distinct(X0, append(X0, X1, cons(X0, X2, nil(X0))))),
33.13/33.41	    inference('sup+', [status(thm)], ['31', '32'])).
33.13/33.41	tff(fact_33_snoc__eq__iff__butlast, axiom,
33.13/33.41	  (![A:$tType,Ys1:list(A),X1:A,Xs1:list(A)]:
33.13/33.41	     ((append(A,Xs1,cons(A,X1,nil(A))) = Ys1) <=>
33.13/33.41	      ((last(A,Ys1) = X1) & (butlast(A,Ys1) = Xs1) & (Ys1 != nil(A)))))).
33.13/33.41	tff('34', plain,
33.13/33.41	    ![X112 : $tType, X113 : X112, X114 : list(X112), X115 : list(X112)]:
33.13/33.41	      (X114 != nil(X112)
33.13/33.41	       | append(X112, X115, cons(X112, X113, nil(X112))) != X114),
33.13/33.41	    inference('cnf', [status(esa)], [fact_33_snoc__eq__iff__butlast])).
33.13/33.41	tff('35', plain,
33.13/33.41	    ![X112 : $tType, X113 : X112, X115 : list(X112)]:
33.13/33.41	      append(X112, X115, cons(X112, X113, nil(X112))) != nil(X112),
33.13/33.41	    inference('simplify', [status(thm)], ['34'])).
33.13/33.41	tff('36', plain,
33.13/33.41	    ![X0 : $tType, X1 : list(X0), X2 : X0]:
33.13/33.41	      (distinct(X0, X1)
33.13/33.41	       | ~ distinct(X0, append(X0, X1, cons(X0, X2, nil(X0))))),
33.13/33.41	    inference('simplify_reflect-', [status(thm)], ['33', '35'])).
33.13/33.41	tff('37', plain,
33.13/33.41	    ![X0 : $tType, X1 : X0, X2 : list(X0)]:
33.13/33.41	      (~ $true | ~ distinct(X0, cons(X0, X1, X2)) | distinct(X0, rev(X0, X2))),
33.13/33.41	    inference('sup-', [status(thm)], ['30', '36'])).
33.13/33.41	tff('38', plain,
33.13/33.41	    ![X0 : $tType, X1 : X0, X2 : list(X0)]:
33.13/33.41	      (distinct(X0, rev(X0, X2)) | ~ distinct(X0, cons(X0, X1, X2))),
33.13/33.41	    inference('simplify', [status(thm)], ['37'])).
33.13/33.41	tff('39', plain,
33.13/33.41	    (~ $true
33.13/33.41	     | distinct(arrow_411405190le_alt, 
33.13/33.41	         rev(arrow_411405190le_alt, 
33.13/33.41	           cons(arrow_411405190le_alt, sk_B1, 
33.13/33.41	             cons(arrow_411405190le_alt, sk_C1, nil(arrow_411405190le_alt)))))),
33.13/33.41	    inference('sup-', [status(thm)], ['13', '38'])).
33.13/33.41	tff(fact_82_rev_Osimps_I1_J, axiom, (![A:$tType]: (rev(A,nil(A)) = nil(A)))).
33.13/33.41	tff('40', plain, ![X304 : $tType]: rev(X304, nil(X304)) = nil(X304),
33.13/33.41	    inference('cnf', [status(esa)], [fact_82_rev_Osimps_I1_J])).
33.13/33.41	tff(fact_59_append__Nil, axiom,
33.13/33.41	  (![A:$tType,Ys:list(A)]: (append(A,nil(A),Ys) = Ys))).
33.13/33.41	tff('41', plain,
33.13/33.41	    ![X219 : $tType, X220 : list(X219)]: append(X219, nil(X219), X220) = X220,
33.13/33.41	    inference('cnf', [status(esa)], [fact_59_append__Nil])).
33.13/33.41	tff(fact_42_append__Cons, axiom,
33.13/33.41	  (![A:$tType,Ys:list(A),Xs:list(A),X:A]:
33.13/33.41	     (append(A,cons(A,X,Xs),Ys) = cons(A,X,append(A,Xs,Ys))))).
33.13/33.41	tff('42', plain,
33.13/33.41	    ![X145 : $tType, X146 : X145, X147 : list(X145), X148 : list(X145)]:
33.13/33.41	      append(X145, cons(X145, X146, X147), X148)
33.13/33.41	       = cons(X145, X146, append(X145, X147, X148)),
33.13/33.41	    inference('cnf', [status(esa)], [fact_42_append__Cons])).
33.13/33.41	tff('43', plain,
33.13/33.41	    (~ $true
33.13/33.41	     | distinct(arrow_411405190le_alt, 
33.13/33.41	         cons(arrow_411405190le_alt, sk_C1, 
33.13/33.41	           cons(arrow_411405190le_alt, sk_B1, nil(arrow_411405190le_alt))))),
33.13/33.41	    inference('demod', [status(thm)],
33.13/33.41	              ['39', '28', '28', '40', '41', '42', '41'])).
33.13/33.41	tff('44', plain,
33.13/33.41	    distinct(arrow_411405190le_alt, 
33.13/33.41	      cons(arrow_411405190le_alt, sk_C1, 
33.13/33.41	        cons(arrow_411405190le_alt, sk_B1, nil(arrow_411405190le_alt)))),
33.13/33.41	    inference('simplify', [status(thm)], ['43'])).
33.13/33.41	tff('45', plain,
33.13/33.41	    (distinct(arrow_411405190le_alt, 
33.13/33.41	       cons(arrow_411405190le_alt, a, 
33.13/33.41	         cons(arrow_411405190le_alt, sk_B1, nil(arrow_411405190le_alt))))
33.13/33.41	     | a = sk_A1),
33.13/33.41	    inference('sup+', [status(thm)], ['27', '44'])).
33.13/33.41	tff('46', plain, (~ $true | a = sk_A1 | b = sk_B1),
33.13/33.41	    inference('sup-', [status(thm)], ['45', '9'])).
33.13/33.41	tff('47', plain, (b = sk_B1 | a = sk_A1),
33.13/33.41	    inference('simplify', [status(thm)], ['46'])).
33.13/33.41	tff('48', plain,
33.13/33.41	    (distinct(arrow_411405190le_alt, 
33.13/33.41	       cons(arrow_411405190le_alt, b, 
33.13/33.41	         cons(arrow_411405190le_alt, sk_B1, 
33.13/33.41	           cons(arrow_411405190le_alt, sk_C1, nil(arrow_411405190le_alt)))))
33.13/33.41	     | a = sk_A1),
33.13/33.41	    inference('sup+', [status(thm)], ['12', '13'])).
33.13/33.41	tff('49', plain,
33.13/33.41	    (distinct(arrow_411405190le_alt, 
33.13/33.41	       cons(arrow_411405190le_alt, b, 
33.13/33.41	         cons(arrow_411405190le_alt, b, 
33.13/33.41	           cons(arrow_411405190le_alt, sk_C1, nil(arrow_411405190le_alt)))))
33.13/33.41	     | a = sk_A1
33.13/33.41	     | a = sk_A1),
33.13/33.41	    inference('sup+', [status(thm)], ['47', '48'])).
33.13/33.41	tff('50', plain,
33.13/33.41	    (a = sk_A1
33.13/33.41	     | distinct(arrow_411405190le_alt, 
33.13/33.41	         cons(arrow_411405190le_alt, b, 
33.13/33.41	           cons(arrow_411405190le_alt, b, 
33.13/33.41	             cons(arrow_411405190le_alt, sk_C1, nil(arrow_411405190le_alt)))))),
33.13/33.41	    inference('simplify', [status(thm)], ['49'])).
33.13/33.41	tff('51', plain,
33.13/33.41	    ![X9 : $tType, X10 : X9, X11 : list(X9), X12 : X9]:
33.13/33.41	      (X12 != X10 | ~ distinct(X9, cons(X9, X12, cons(X9, X10, X11)))),
33.13/33.41	    inference('cnf', [status(esa)], [fact_4_distinct__length__2__or__more])).
33.13/33.41	tff('52', plain,
33.13/33.41	    ![X9 : $tType, X10 : X9, X11 : list(X9)]:
33.13/33.41	      ~ distinct(X9, cons(X9, X10, cons(X9, X10, X11))),
33.13/33.41	    inference('simplify', [status(thm)], ['51'])).
33.13/33.41	tff('53', plain, a = sk_A1, inference('clc', [status(thm)], ['50', '52'])).
33.13/33.41	tff('54', plain,
33.13/33.41	    (distinct(arrow_411405190le_alt, 
33.13/33.41	       cons(arrow_411405190le_alt, a, 
33.13/33.41	         cons(arrow_411405190le_alt, a, 
33.13/33.41	           cons(arrow_411405190le_alt, sk_C1, nil(arrow_411405190le_alt)))))
33.13/33.41	     | b = a),
33.13/33.41	    inference('demod', [status(thm)], ['18', '53', '53'])).
33.13/33.41	tff('55', plain,
33.13/33.41	    distinct(arrow_411405190le_alt, 
33.13/33.41	      cons(arrow_411405190le_alt, a, 
33.13/33.41	        cons(arrow_411405190le_alt, a, 
33.13/33.41	          cons(arrow_411405190le_alt, sk_C1, nil(arrow_411405190le_alt))))),
33.13/33.41	    inference('simplify_reflect-', [status(thm)], ['54', '4'])).
33.13/33.41	tff('56', plain,
33.13/33.41	    ![X9 : $tType, X10 : X9, X11 : list(X9), X12 : X9]:
33.13/33.41	      (distinct(X9, cons(X9, X10, X11))
33.13/33.41	       | ~ distinct(X9, cons(X9, X12, cons(X9, X10, X11)))),
33.13/33.41	    inference('cnf', [status(esa)], [fact_4_distinct__length__2__or__more])).
33.13/33.41	tff('57', plain,
33.13/33.41	    (~ $true
33.13/33.41	     | distinct(arrow_411405190le_alt, 
33.13/33.41	         cons(arrow_411405190le_alt, sk_B1, 
33.13/33.41	           cons(arrow_411405190le_alt, sk_C1, nil(arrow_411405190le_alt))))),
33.13/33.41	    inference('sup-', [status(thm)], ['13', '56'])).
33.13/33.41	tff('58', plain,
33.13/33.41	    distinct(arrow_411405190le_alt, 
33.13/33.41	      cons(arrow_411405190le_alt, sk_B1, 
33.13/33.41	        cons(arrow_411405190le_alt, sk_C1, nil(arrow_411405190le_alt)))),
33.13/33.41	    inference('simplify', [status(thm)], ['57'])).
33.13/33.41	tff('59', plain,
33.13/33.41	    (distinct(arrow_411405190le_alt, 
33.13/33.41	       cons(arrow_411405190le_alt, a, 
33.13/33.41	         cons(arrow_411405190le_alt, sk_C1, nil(arrow_411405190le_alt))))
33.13/33.41	     | b = sk_A1),
33.13/33.41	    inference('sup+', [status(thm)], ['17', '58'])).
33.13/33.41	tff('60', plain, (~ $true | b = sk_A1 | b = sk_C1),
33.13/33.41	    inference('sup-', [status(thm)], ['59', '9'])).
33.13/33.41	tff('61', plain, (b = sk_C1 | b = sk_A1),
33.13/33.41	    inference('simplify', [status(thm)], ['60'])).
33.13/33.41	tff('62', plain, (b = sk_C1 | b = a),
33.13/33.41	    inference('demod', [status(thm)], ['61', '53'])).
33.13/33.41	tff('63', plain, b = sk_C1,
33.13/33.41	    inference('simplify_reflect-', [status(thm)], ['62', '4'])).
33.13/33.41	tff('64', plain,
33.13/33.41	    distinct(arrow_411405190le_alt, 
33.13/33.41	      cons(arrow_411405190le_alt, a, 
33.13/33.41	        cons(arrow_411405190le_alt, a, 
33.13/33.41	          cons(arrow_411405190le_alt, b, nil(arrow_411405190le_alt))))),
33.13/33.41	    inference('demod', [status(thm)], ['55', '63'])).
33.13/33.41	tff('65', plain, ~ $true, inference('sup-', [status(thm)], ['64', '52'])).
33.13/33.41	tff('66', plain, $false, inference('simplify', [status(thm)], ['65'])).
33.13/33.41	
33.13/33.41	% SZS output end Refutation
33.13/33.41	EOF
