0.00/0.00	% File    : /export/starexec/sandbox2/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   : n148.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 17:28:54 CST 2018
49.13/49.33	% done 5567 iterations in 49.135s
49.13/49.33	% SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
49.13/49.33	% SZS output start Refutation
49.13/49.34	tff(cMODULAR_EQUIV_THM_pme, conjecture,
49.13/49.34	  (![JOIN:((a * a) > a),MEET:((a * a) > a)]:
49.13/49.34	     (((![Xx:a,Xy:a]: (MEET(JOIN(Xx,Xy),Xy) = Xy)) & 
49.13/49.34	       (![Xx:a,Xy:a]: (JOIN(MEET(Xx,Xy),Xy) = Xy)) & 
49.13/49.34	       (![Xx:a,Xy:a]: (MEET(Xx,Xy) = MEET(Xy,Xx))) & 
49.13/49.34	       (![Xx:a,Xy:a]: (JOIN(Xx,Xy) = JOIN(Xy,Xx))) & 
49.13/49.34	       (![Xx:a,Xy:a,Xz:a]: (MEET(MEET(Xx,Xy),Xz) = MEET(Xx,MEET(Xy,Xz)))) & 
49.13/49.34	       (![Xx:a,Xy:a,Xz:a]: (JOIN(JOIN(Xx,Xy),Xz) = JOIN(Xx,JOIN(Xy,Xz)))) & 
49.13/49.34	       (![Xx:a]: (MEET(Xx,Xx) = Xx)) & (![Xx:a]: (JOIN(Xx,Xx) = Xx))) =>
49.13/49.34	      ((![Xx:a,Xy:a,Xz:a]:
49.13/49.34	          ((JOIN(Xx,Xz) = Xz) =>
49.13/49.34	           (JOIN(Xx,MEET(Xy,Xz)) = MEET(JOIN(Xx,Xy),Xz)))) <=>
49.13/49.34	       (![Xx:a,Xy:a,Xz:a]:
49.13/49.34	          (JOIN(Xx,MEET(Xy,JOIN(Xx,Xz))) = MEET(JOIN(Xx,Xy),JOIN(Xx,Xz)))))))).
49.13/49.34	tff(zf_stmt_0, negated_conjecture,
49.13/49.34	  (~
49.13/49.34	    (![JOIN:((a * a) > a),MEET:((a * a) > a)]:
49.13/49.34	       (((![Xx:a,Xy:a]: (MEET(JOIN(Xx,Xy),Xy) = Xy)) & 
49.13/49.34	         (![Xx:a,Xy:a]: (JOIN(MEET(Xx,Xy),Xy) = Xy)) & 
49.13/49.34	         (![Xx:a,Xy:a]: (MEET(Xx,Xy) = MEET(Xy,Xx))) & 
49.13/49.34	         (![Xx:a,Xy:a]: (JOIN(Xx,Xy) = JOIN(Xy,Xx))) & 
49.13/49.34	         (![Xx:a,Xy:a,Xz:a]: (MEET(MEET(Xx,Xy),Xz) = MEET(Xx,MEET(Xy,Xz)))) & 
49.13/49.34	         (![Xx:a,Xy:a,Xz:a]: (JOIN(JOIN(Xx,Xy),Xz) = JOIN(Xx,JOIN(Xy,Xz)))) & 
49.13/49.34	         (![Xx:a]: (MEET(Xx,Xx) = Xx)) & (![Xx:a]: (JOIN(Xx,Xx) = Xx))) =>
49.13/49.34	        ((![Xx:a,Xy:a,Xz:a]:
49.13/49.34	            ((JOIN(Xx,Xz) = Xz) =>
49.13/49.34	             (JOIN(Xx,MEET(Xy,Xz)) = MEET(JOIN(Xx,Xy),Xz)))) <=>
49.13/49.34	         (![Xx:a,Xy:a,Xz:a]:
49.13/49.34	            (JOIN(Xx,MEET(Xy,JOIN(Xx,Xz))) = MEET(JOIN(Xx,Xy),JOIN(Xx,Xz))))))))).
49.13/49.34	tff('0', plain,
49.13/49.34	    (sk_JOIN(sk_Xx, sk_MEET(sk_Xy, sk_JOIN(sk_Xx, sk_Xz)))
49.13/49.34	      != sk_MEET(sk_JOIN(sk_Xx, sk_Xy), sk_JOIN(sk_Xx, sk_Xz))
49.13/49.34	     | sk_JOIN(sk_Xx1, sk_MEET(sk_Xy1, sk_Xz1))
49.13/49.34	        != sk_MEET(sk_JOIN(sk_Xx1, sk_Xy1), sk_Xz1)),
49.13/49.34	    inference('cnf', [status(esa)], [zf_stmt_0])).
49.13/49.34	tff('1', plain, ![X10 : a, X11 : a]: sk_MEET(X11, X10) = sk_MEET(X10, X11),
49.13/49.34	    inference('cnf', [status(esa)], [zf_stmt_0])).
49.13/49.34	tff('2', plain,
49.13/49.34	    (sk_JOIN(sk_Xx, sk_MEET(sk_Xy, sk_JOIN(sk_Xx, sk_Xz)))
49.13/49.34	      != sk_MEET(sk_JOIN(sk_Xx, sk_Xy), sk_JOIN(sk_Xx, sk_Xz))
49.13/49.34	     | sk_JOIN(sk_Xx1, sk_MEET(sk_Xz1, sk_Xy1))
49.13/49.34	        != sk_MEET(sk_Xz1, sk_JOIN(sk_Xx1, sk_Xy1))),
49.13/49.34	    inference('demod', [status(thm)], ['0', '1', '1'])).
49.13/49.34	tff('3', plain,
49.13/49.34	    ![X0 : a, X1 : a, X2 : a, X3 : a, X4 : a, X5 : a]:
49.13/49.34	      (sk_JOIN(X0, sk_MEET(X1, sk_JOIN(X0, X2)))
49.13/49.34	        = sk_MEET(sk_JOIN(X0, X1), sk_JOIN(X0, X2))
49.13/49.34	       | sk_JOIN(X4, X3) != X3
49.13/49.34	       | sk_JOIN(X4, sk_MEET(X5, X3)) = sk_MEET(sk_JOIN(X4, X5), X3)),
49.13/49.34	    inference('cnf', [status(esa)], [zf_stmt_0])).
49.13/49.34	tff('4', plain,
49.13/49.34	    ![X0 : a, X1 : a, X2 : a]:
49.13/49.34	      (sk_JOIN(X1, sk_MEET(X2, sk_JOIN(X1, X0)))
49.13/49.34	        != sk_JOIN(X1, sk_MEET(X2, sk_JOIN(X1, X0)))
49.13/49.34	       | sk_JOIN(X1, sk_JOIN(X1, X0)) != sk_JOIN(X1, X0)
49.13/49.34	       | sk_JOIN(X1, sk_MEET(X2, sk_JOIN(X1, X0)))
49.13/49.34	          = sk_MEET(sk_JOIN(X1, X2), sk_JOIN(X1, X0))),
49.13/49.34	    inference('eq_fact', [status(thm)], ['3'])).
49.13/49.34	tff('5', plain,
49.13/49.34	    ![X0 : a, X1 : a, X2 : a]:
49.13/49.34	      (sk_JOIN(X1, sk_MEET(X2, sk_JOIN(X1, X0)))
49.13/49.34	        = sk_MEET(sk_JOIN(X1, X2), sk_JOIN(X1, X0))
49.13/49.34	       | sk_JOIN(X1, sk_JOIN(X1, X0)) != sk_JOIN(X1, X0)),
49.13/49.34	    inference('simplify', [status(thm)], ['4'])).
49.13/49.34	tff('6', plain, ![X16 : a, X17 : a]: sk_JOIN(X17, X16) = sk_JOIN(X16, X17),
49.13/49.34	    inference('cnf', [status(esa)], [zf_stmt_0])).
49.13/49.34	tff('7', plain, ![X14 : a, X15 : a]: sk_MEET(sk_JOIN(X15, X14), X14) = X14,
49.13/49.34	    inference('cnf', [status(esa)], [zf_stmt_0])).
49.13/49.34	tff('8', plain, ![X14 : a, X15 : a]: sk_MEET(X14, sk_JOIN(X15, X14)) = X14,
49.13/49.34	    inference('demod', [status(thm)], ['7', '1'])).
49.13/49.34	tff('9', plain, ![X0 : a, X1 : a]: sk_MEET(X1, sk_JOIN(X1, X0)) = X1,
49.13/49.34	    inference('sup+', [status(thm)], ['6', '8'])).
49.13/49.34	tff('10', plain, ![X12 : a, X13 : a]: sk_JOIN(sk_MEET(X13, X12), X12) = X12,
49.13/49.34	    inference('cnf', [status(esa)], [zf_stmt_0])).
49.13/49.34	tff('11', plain, ![X12 : a, X13 : a]: sk_JOIN(X12, sk_MEET(X13, X12)) = X12,
49.13/49.34	    inference('demod', [status(thm)], ['10', '6'])).
49.13/49.34	tff('12', plain,
49.13/49.34	    ![X0 : a, X1 : a]: sk_JOIN(sk_JOIN(X0, X1), X0) = sk_JOIN(X0, X1),
49.13/49.34	    inference('sup+', [status(thm)], ['9', '11'])).
49.13/49.34	tff('13', plain,
49.13/49.34	    ![X0 : a, X1 : a]: sk_JOIN(X0, sk_JOIN(X0, X1)) = sk_JOIN(X0, X1),
49.13/49.34	    inference('demod', [status(thm)], ['12', '6'])).
49.13/49.34	tff('14', plain,
49.13/49.34	    ![X0 : a, X1 : a, X2 : a]:
49.13/49.34	      (sk_JOIN(X1, sk_MEET(X2, sk_JOIN(X1, X0)))
49.13/49.34	        = sk_MEET(sk_JOIN(X1, X2), sk_JOIN(X1, X0))
49.13/49.34	       | sk_JOIN(X1, X0) != sk_JOIN(X1, X0)),
49.13/49.34	    inference('demod', [status(thm)], ['5', '13'])).
49.13/49.34	tff('15', plain,
49.13/49.34	    ![X0 : a, X1 : a, X2 : a]:
49.13/49.34	      sk_JOIN(X1, sk_MEET(X2, sk_JOIN(X1, X0)))
49.13/49.34	       = sk_MEET(sk_JOIN(X1, X2), sk_JOIN(X1, X0)),
49.13/49.34	    inference('simplify', [status(thm)], ['14'])).
49.13/49.34	tff('16', plain,
49.13/49.34	    (sk_JOIN(sk_Xx, sk_MEET(sk_Xy, sk_JOIN(sk_Xx, sk_Xz)))
49.13/49.34	      != sk_JOIN(sk_Xx, sk_MEET(sk_Xy, sk_JOIN(sk_Xx, sk_Xz)))
49.13/49.34	     | sk_JOIN(sk_Xx1, sk_MEET(sk_Xz1, sk_Xy1))
49.13/49.34	        != sk_MEET(sk_Xz1, sk_JOIN(sk_Xx1, sk_Xy1))),
49.13/49.34	    inference('demod', [status(thm)], ['2', '15'])).
49.13/49.34	tff('17', plain,
49.13/49.34	    sk_JOIN(sk_Xx1, sk_MEET(sk_Xz1, sk_Xy1))
49.13/49.34	     != sk_MEET(sk_Xz1, sk_JOIN(sk_Xx1, sk_Xy1)),
49.13/49.34	    inference('simplify', [status(thm)], ['16'])).
49.13/49.34	tff('18', plain,
49.13/49.34	    ![X7 : a, X8 : a, X9 : a]:
49.13/49.34	      sk_MEET(sk_MEET(X7, X8), X9) = sk_MEET(X7, sk_MEET(X8, X9)),
49.13/49.34	    inference('cnf', [status(esa)], [zf_stmt_0])).
49.13/49.34	tff('19', plain,
49.13/49.34	    ![X0 : a, X1 : a, X2 : a]:
49.13/49.34	      sk_MEET(X0, sk_MEET(X2, X1)) = sk_MEET(X2, sk_MEET(X1, X0)),
49.13/49.34	    inference('sup+', [status(thm)], ['18', '1'])).
49.13/49.34	tff('20', plain,
49.13/49.34	    ![X0 : a, X1 : a, X2 : a, X3 : a]:
49.13/49.34	      sk_MEET(X3, sk_JOIN(X1, sk_MEET(X2, sk_JOIN(X1, X0))))
49.13/49.34	       = sk_MEET(sk_JOIN(X1, X2), sk_MEET(sk_JOIN(X1, X0), X3)),
49.13/49.34	    inference('sup+', [status(thm)], ['15', '19'])).
49.13/49.34	tff('21', plain, ![X0 : a, X1 : a]: sk_JOIN(sk_MEET(X1, X0), X1) = X1,
49.13/49.34	    inference('sup+', [status(thm)], ['1', '10'])).
49.13/49.34	tff('22', plain, ![X0 : a, X1 : a]: sk_JOIN(X1, sk_MEET(X1, X0)) = X1,
49.13/49.34	    inference('demod', [status(thm)], ['21', '6'])).
49.13/49.34	tff('23', plain,
49.13/49.34	    ![X0 : a, X1 : a]: sk_MEET(sk_MEET(X0, X1), X0) = sk_MEET(X0, X1),
49.13/49.34	    inference('sup+', [status(thm)], ['22', '8'])).
49.13/49.34	tff('24', plain,
49.13/49.34	    ![X0 : a, X1 : a]: sk_MEET(X0, sk_MEET(X0, X1)) = sk_MEET(X0, X1),
49.13/49.34	    inference('demod', [status(thm)], ['23', '1'])).
49.13/49.34	tff('25', plain,
49.13/49.34	    (sk_JOIN(sk_Xx, sk_MEET(sk_Xy, sk_JOIN(sk_Xx, sk_Xz)))
49.13/49.34	      != sk_MEET(sk_JOIN(sk_Xx, sk_Xy), sk_JOIN(sk_Xx, sk_Xz))
49.13/49.34	     | sk_JOIN(sk_Xx1, sk_Xz1) = sk_Xz1),
49.13/49.34	    inference('cnf', [status(esa)], [zf_stmt_0])).
49.13/49.34	tff('26', plain,
49.13/49.34	    (sk_JOIN(sk_Xx, sk_MEET(sk_Xy, sk_JOIN(sk_Xx, sk_Xz)))
49.13/49.34	      != sk_MEET(sk_JOIN(sk_Xx, sk_Xy), sk_JOIN(sk_Xx, sk_Xz))
49.13/49.34	     | sk_JOIN(sk_Xz1, sk_Xx1) = sk_Xz1),
49.13/49.34	    inference('demod', [status(thm)], ['25', '6'])).
49.13/49.34	tff('27', plain,
49.13/49.34	    (sk_JOIN(sk_Xx, sk_MEET(sk_Xy, sk_JOIN(sk_Xx, sk_Xz)))
49.13/49.34	      != sk_JOIN(sk_Xx, sk_MEET(sk_Xy, sk_JOIN(sk_Xx, sk_Xz)))
49.13/49.34	     | sk_JOIN(sk_Xz1, sk_Xx1) = sk_Xz1),
49.13/49.34	    inference('demod', [status(thm)], ['26', '15'])).
49.13/49.34	tff('28', plain, sk_JOIN(sk_Xz1, sk_Xx1) = sk_Xz1,
49.13/49.34	    inference('simplify', [status(thm)], ['27'])).
49.13/49.34	tff('29', plain,
49.13/49.34	    ![X0 : a, X1 : a, X2 : a]:
49.13/49.34	      sk_JOIN(X0, sk_MEET(X2, sk_JOIN(X0, X1)))
49.13/49.34	       = sk_MEET(sk_JOIN(X0, X2), sk_JOIN(X1, X0)),
49.13/49.34	    inference('sup+', [status(thm)], ['6', '15'])).
49.13/49.34	tff('30', plain,
49.13/49.34	    ![X0 : a]:
49.13/49.34	      sk_JOIN(sk_Xx1, sk_MEET(X0, sk_JOIN(sk_Xx1, sk_Xz1)))
49.13/49.34	       = sk_MEET(sk_JOIN(sk_Xx1, X0), sk_Xz1),
49.13/49.34	    inference('sup+', [status(thm)], ['28', '29'])).
49.13/49.34	tff('31', plain,
49.13/49.34	    ![X18 : a, X19 : a, X20 : a]:
49.13/49.34	      sk_JOIN(sk_JOIN(X18, X19), X20) = sk_JOIN(X18, sk_JOIN(X19, X20)),
49.13/49.34	    inference('cnf', [status(esa)], [zf_stmt_0])).
49.13/49.34	tff('32', plain,
49.13/49.34	    ![X0 : a]: sk_JOIN(sk_Xz1, X0) = sk_JOIN(sk_Xz1, sk_JOIN(sk_Xx1, X0)),
49.13/49.34	    inference('sup+', [status(thm)], ['28', '31'])).
49.13/49.34	tff('33', plain,
49.13/49.34	    ![X0 : a]:
49.13/49.34	      sk_MEET(sk_JOIN(sk_Xx1, X0), sk_JOIN(sk_Xz1, X0)) = sk_JOIN(sk_Xx1, X0),
49.13/49.34	    inference('sup+', [status(thm)], ['32', '8'])).
49.13/49.34	tff('34', plain,
49.13/49.34	    ![X0 : a]:
49.13/49.34	      sk_MEET(sk_JOIN(sk_Xz1, X0), sk_JOIN(sk_Xx1, X0)) = sk_JOIN(sk_Xx1, X0),
49.13/49.34	    inference('demod', [status(thm)], ['33', '1'])).
49.13/49.34	tff('35', plain,
49.13/49.34	    ![X0 : a, X1 : a, X2 : a]: sk_MEET(X0, sk_JOIN(X2, sk_JOIN(X1, X0))) = X0,
49.13/49.34	    inference('sup+', [status(thm)], ['31', '8'])).
49.13/49.34	tff('36', plain,
49.13/49.34	    ![X0 : a, X1 : a, X2 : a]:
49.13/49.34	      sk_MEET(sk_MEET(X0, X1), sk_JOIN(X2, X0)) = sk_MEET(X0, X1),
49.13/49.34	    inference('sup+', [status(thm)], ['22', '35'])).
49.13/49.34	tff('37', plain,
49.13/49.34	    ![X0 : a, X1 : a, X2 : a]:
49.13/49.34	      sk_MEET(X0, sk_MEET(X1, sk_JOIN(X2, X0))) = sk_MEET(X0, X1),
49.13/49.34	    inference('demod', [status(thm)], ['36', '18'])).
49.13/49.34	tff('38', plain,
49.13/49.34	    ![X0 : a, X1 : a, X2 : a]:
49.13/49.34	      sk_JOIN(sk_MEET(X0, sk_JOIN(X2, X1)), sk_MEET(X1, X0))
49.13/49.34	       = sk_MEET(X0, sk_JOIN(X2, X1)),
49.13/49.34	    inference('sup+', [status(thm)], ['37', '11'])).
49.13/49.34	tff('39', plain,
49.13/49.34	    ![X0 : a]:
49.13/49.34	      sk_JOIN(sk_JOIN(sk_Xx1, X0), sk_MEET(X0, sk_JOIN(sk_Xz1, X0)))
49.13/49.34	       = sk_MEET(sk_JOIN(sk_Xz1, X0), sk_JOIN(sk_Xx1, X0)),
49.13/49.34	    inference('sup+', [status(thm)], ['34', '38'])).
49.13/49.34	tff('40', plain,
49.13/49.34	    ![X0 : a, X1 : a, X2 : a]:
49.13/49.34	      sk_JOIN(sk_JOIN(X1, X0), X2) = sk_JOIN(X0, sk_JOIN(X1, X2)),
49.13/49.34	    inference('sup+', [status(thm)], ['6', '31'])).
49.13/49.34	tff('41', plain,
49.13/49.34	    ![X0 : a, X1 : a]: sk_JOIN(X0, sk_JOIN(X1, X0)) = sk_JOIN(X0, X1),
49.13/49.34	    inference('sup+', [status(thm)], ['6', '13'])).
49.13/49.34	tff('42', plain,
49.13/49.34	    ![X0 : a]:
49.13/49.34	      sk_JOIN(X0, sk_Xx1) = sk_MEET(sk_JOIN(sk_Xz1, X0), sk_JOIN(sk_Xx1, X0)),
49.13/49.34	    inference('demod', [status(thm)], ['39', '8', '40', '41'])).
49.13/49.34	tff('43', plain,
49.13/49.34	    ![X0 : a, X1 : a]: sk_MEET(sk_MEET(X1, X0), X0) = sk_MEET(X1, X0),
49.13/49.34	    inference('sup+', [status(thm)], ['11', '8'])).
49.13/49.34	tff('44', plain,
49.13/49.34	    ![X0 : a, X1 : a]: sk_MEET(X0, sk_MEET(X1, X0)) = sk_MEET(X1, X0),
49.13/49.34	    inference('demod', [status(thm)], ['43', '1'])).
49.13/49.34	tff('45', plain,
49.13/49.34	    ![X0 : a, X1 : a, X2 : a]:
49.13/49.34	      sk_MEET(X0, sk_MEET(X2, sk_MEET(X1, X0)))
49.13/49.34	       = sk_MEET(sk_MEET(X2, X1), X0),
49.13/49.34	    inference('sup+', [status(thm)], ['18', '44'])).
49.13/49.34	tff('46', plain,
49.13/49.34	    ![X0 : a, X1 : a, X2 : a]:
49.13/49.34	      sk_MEET(X0, sk_MEET(X2, sk_MEET(X1, X0)))
49.13/49.34	       = sk_MEET(X2, sk_MEET(X1, X0)),
49.13/49.34	    inference('demod', [status(thm)], ['45', '18'])).
49.13/49.34	tff('47', plain,
49.13/49.34	    ![X0 : a, X1 : a]:
49.13/49.34	      sk_MEET(sk_JOIN(sk_Xx1, X0), sk_MEET(X1, sk_JOIN(X0, sk_Xx1)))
49.13/49.34	       = sk_MEET(X1, sk_MEET(sk_JOIN(sk_Xz1, X0), sk_JOIN(sk_Xx1, X0))),
49.13/49.34	    inference('sup+', [status(thm)], ['42', '46'])).
49.13/49.34	tff('48', plain,
49.13/49.34	    ![X0 : a, X1 : a, X2 : a]:
49.13/49.34	      sk_MEET(sk_JOIN(X0, X1), sk_MEET(X2, sk_JOIN(X1, X0)))
49.13/49.34	       = sk_MEET(sk_JOIN(X0, X1), X2),
49.13/49.34	    inference('sup+', [status(thm)], ['41', '37'])).
49.13/49.34	tff('49', plain,
49.13/49.34	    ![X0 : a, X1 : a]:
49.13/49.34	      sk_MEET(sk_JOIN(sk_Xx1, X0), X1) = sk_MEET(X1, sk_JOIN(X0, sk_Xx1)),
49.13/49.34	    inference('demod', [status(thm)], ['47', '48', '42'])).
49.13/49.34	tff('50', plain,
49.13/49.34	    ![X0 : a]:
49.13/49.34	      sk_JOIN(sk_Xx1, sk_MEET(X0, sk_Xz1))
49.13/49.34	       = sk_MEET(sk_Xz1, sk_JOIN(X0, sk_Xx1)),
49.13/49.34	    inference('demod', [status(thm)], ['30', '6', '28', '49'])).
49.13/49.34	tff('51', plain, sk_MEET(sk_Xx1, sk_Xz1) = sk_Xx1,
49.13/49.34	    inference('sup+', [status(thm)], ['28', '8'])).
49.13/49.34	tff('52', plain, sk_MEET(sk_Xz1, sk_Xx1) = sk_Xx1,
49.13/49.34	    inference('demod', [status(thm)], ['51', '1'])).
49.13/49.34	tff('53', plain,
49.13/49.34	    ![X0 : a, X1 : a, X2 : a]: sk_JOIN(X0, sk_MEET(X2, sk_MEET(X1, X0))) = X0,
49.13/49.34	    inference('sup+', [status(thm)], ['18', '11'])).
49.13/49.34	tff('54', plain,
49.13/49.34	    ![X0 : a, X1 : a, X2 : a]: sk_JOIN(X1, sk_MEET(sk_MEET(X2, X1), X0)) = X1,
49.13/49.34	    inference('sup+', [status(thm)], ['1', '53'])).
49.13/49.34	tff('55', plain,
49.13/49.34	    ![X0 : a, X1 : a, X2 : a]: sk_JOIN(X1, sk_MEET(X2, sk_MEET(X1, X0))) = X1,
49.13/49.34	    inference('demod', [status(thm)], ['54', '18'])).
49.13/49.34	tff('56', plain, ![X0 : a]: sk_JOIN(sk_Xz1, sk_MEET(X0, sk_Xx1)) = sk_Xz1,
49.13/49.34	    inference('sup+', [status(thm)], ['52', '55'])).
49.13/49.34	tff('57', plain, ![X0 : a]: sk_JOIN(sk_Xz1, sk_MEET(sk_Xx1, X0)) = sk_Xz1,
49.13/49.34	    inference('sup+', [status(thm)], ['1', '56'])).
49.13/49.34	tff('58', plain,
49.13/49.34	    ![X0 : a, X1 : a]:
49.13/49.34	      sk_MEET(sk_MEET(sk_Xx1, X0), sk_JOIN(X1, sk_Xz1)) = sk_MEET(sk_Xx1, X0),
49.13/49.34	    inference('sup+', [status(thm)], ['57', '35'])).
49.13/49.34	tff('59', plain,
49.13/49.34	    ![X0 : a, X1 : a]:
49.13/49.34	      sk_MEET(sk_Xx1, sk_MEET(X0, sk_JOIN(X1, sk_Xz1))) = sk_MEET(sk_Xx1, X0),
49.13/49.34	    inference('demod', [status(thm)], ['58', '18'])).
49.13/49.34	tff('60', plain,
49.13/49.34	    ![X0 : a]:
49.13/49.34	      sk_JOIN(sk_MEET(X0, sk_Xz1), sk_MEET(sk_Xx1, X0))
49.13/49.34	       = sk_MEET(X0, sk_JOIN(sk_Xz1, sk_Xx1)),
49.13/49.34	    inference('sup+', [status(thm)], ['28', '38'])).
49.13/49.34	tff('61', plain,
49.13/49.34	    ![X0 : a]:
49.13/49.34	      sk_JOIN(sk_MEET(X0, sk_Xz1), sk_MEET(sk_Xx1, X0)) = sk_MEET(X0, sk_Xz1),
49.13/49.34	    inference('demod', [status(thm)], ['60', '28'])).
49.13/49.34	tff('62', plain,
49.13/49.34	    ![X0 : a, X1 : a]: sk_JOIN(sk_JOIN(X1, X0), X0) = sk_JOIN(X1, X0),
49.13/49.34	    inference('sup+', [status(thm)], ['8', '11'])).
49.13/49.34	tff('63', plain,
49.13/49.34	    ![X0 : a, X1 : a]: sk_JOIN(X0, sk_JOIN(X1, X0)) = sk_JOIN(X1, X0),
49.13/49.34	    inference('demod', [status(thm)], ['62', '6'])).
49.13/49.34	tff('64', plain,
49.13/49.34	    ![X0 : a]:
49.13/49.34	      sk_JOIN(sk_MEET(sk_Xx1, X0), sk_MEET(X0, sk_Xz1))
49.13/49.34	       = sk_JOIN(sk_MEET(X0, sk_Xz1), sk_MEET(sk_Xx1, X0)),
49.13/49.34	    inference('sup+', [status(thm)], ['61', '63'])).
49.13/49.34	tff('65', plain,
49.13/49.34	    ![X0 : a]:
49.13/49.34	      sk_JOIN(sk_MEET(sk_Xx1, X0), sk_MEET(X0, sk_Xz1)) = sk_MEET(X0, sk_Xz1),
49.13/49.34	    inference('demod', [status(thm)], ['64', '61'])).
49.13/49.34	tff('66', plain,
49.13/49.34	    ![X0 : a, X1 : a]:
49.13/49.34	      sk_JOIN(sk_MEET(sk_Xx1, X0), 
49.13/49.34	        sk_MEET(sk_MEET(X0, sk_JOIN(X1, sk_Xz1)), sk_Xz1))
49.13/49.34	       = sk_MEET(sk_MEET(X0, sk_JOIN(X1, sk_Xz1)), sk_Xz1),
49.13/49.34	    inference('sup+', [status(thm)], ['59', '65'])).
49.13/49.34	tff('67', plain,
49.13/49.34	    ![X0 : a, X1 : a, X2 : a]:
49.13/49.34	      sk_MEET(sk_MEET(X1, X0), X2) = sk_MEET(X0, sk_MEET(X1, X2)),
49.13/49.34	    inference('sup+', [status(thm)], ['1', '18'])).
49.13/49.34	tff('68', plain,
49.13/49.34	    ![X0 : a, X1 : a, X2 : a]:
49.13/49.34	      sk_MEET(X0, X1) = sk_MEET(X0, sk_MEET(sk_JOIN(X2, X0), X1)),
49.13/49.34	    inference('sup+', [status(thm)], ['8', '18'])).
49.13/49.34	tff('69', plain,
49.13/49.34	    ![X0 : a]:
49.13/49.34	      sk_JOIN(sk_MEET(sk_Xz1, X0), sk_MEET(sk_Xx1, X0)) = sk_MEET(sk_Xz1, X0),
49.13/49.34	    inference('demod', [status(thm)],
49.13/49.34	              ['66', '67', '19', '68', '6', '67', '19', '68'])).
49.13/49.34	tff('70', plain,
49.13/49.34	    ![X0 : a]:
49.13/49.34	      sk_JOIN(sk_JOIN(sk_Xx1, sk_MEET(X0, sk_Xz1)), 
49.13/49.34	        sk_MEET(sk_Xx1, sk_JOIN(X0, sk_Xx1)))
49.13/49.34	       = sk_MEET(sk_Xz1, sk_JOIN(X0, sk_Xx1)),
49.13/49.34	    inference('sup+', [status(thm)], ['50', '69'])).
49.13/49.34	tff('71', plain, ![X21 : a]: sk_JOIN(X21, X21) = X21,
49.13/49.34	    inference('cnf', [status(esa)], [zf_stmt_0])).
49.13/49.34	tff('72', plain,
49.13/49.34	    ![X0 : a]:
49.13/49.34	      sk_JOIN(sk_MEET(X0, sk_Xz1), sk_Xx1)
49.13/49.34	       = sk_MEET(sk_Xz1, sk_JOIN(X0, sk_Xx1)),
49.13/49.34	    inference('demod', [status(thm)], ['70', '8', '40', '71'])).
49.13/49.34	tff('73', plain,
49.13/49.34	    ![X0 : a]:
49.13/49.34	      sk_JOIN(sk_JOIN(sk_MEET(X0, sk_Xz1), sk_Xx1), 
49.13/49.34	        sk_MEET(sk_Xx1, sk_JOIN(X0, sk_Xx1)))
49.13/49.34	       = sk_MEET(sk_Xz1, sk_JOIN(X0, sk_Xx1)),
49.13/49.34	    inference('sup+', [status(thm)], ['72', '69'])).
49.13/49.34	tff('74', plain,
49.13/49.34	    ![X0 : a]:
49.13/49.34	      sk_JOIN(sk_Xx1, sk_MEET(X0, sk_Xz1))
49.13/49.34	       = sk_MEET(sk_Xz1, sk_JOIN(X0, sk_Xx1)),
49.13/49.34	    inference('demod', [status(thm)], ['73', '8', '40', '41'])).
49.13/49.34	tff('75', plain,
49.13/49.34	    ![X0 : a]:
49.13/49.34	      sk_JOIN(sk_MEET(sk_MEET(X0, sk_Xz1), sk_Xz1), sk_Xx1)
49.13/49.34	       = sk_MEET(sk_Xz1, sk_MEET(sk_Xz1, sk_JOIN(X0, sk_Xx1))),
49.13/49.34	    inference('sup+', [status(thm)], ['72', '72'])).
49.13/49.34	tff('76', plain,
49.13/49.34	    ![X0 : a, X1 : a]: sk_MEET(X0, sk_MEET(X1, X0)) = sk_MEET(X0, X1),
49.13/49.34	    inference('sup+', [status(thm)], ['1', '24'])).
49.13/49.34	tff('77', plain,
49.13/49.34	    ![X0 : a]:
49.13/49.34	      sk_JOIN(sk_MEET(sk_Xz1, X0), sk_Xx1)
49.13/49.34	       = sk_MEET(sk_Xz1, sk_JOIN(X0, sk_Xx1)),
49.13/49.34	    inference('demod', [status(thm)], ['75', '67', '76', '24'])).
49.13/49.34	tff('78', plain,
49.13/49.34	    ![X0 : a]:
49.13/49.34	      sk_JOIN(sk_Xx1, sk_MEET(X0, sk_Xz1))
49.13/49.34	       = sk_JOIN(sk_MEET(sk_Xz1, X0), sk_Xx1),
49.13/49.34	    inference('demod', [status(thm)], ['74', '77'])).
49.13/49.34	tff('79', plain,
49.13/49.34	    ![X0 : a, X1 : a, X2 : a]:
49.13/49.34	      sk_MEET(X1, X0)
49.13/49.34	       = sk_MEET(X1, sk_MEET(X0, sk_JOIN(X2, sk_MEET(X1, X0)))),
49.13/49.34	    inference('sup+', [status(thm)], ['8', '18'])).
49.13/49.34	tff('80', plain,
49.13/49.34	    ![X0 : a]:
49.13/49.34	      sk_MEET(X0, sk_Xz1)
49.13/49.34	       = sk_MEET(X0, sk_MEET(sk_Xz1, sk_JOIN(sk_MEET(sk_Xz1, X0), sk_Xx1))),
49.13/49.34	    inference('sup+', [status(thm)], ['78', '79'])).
49.13/49.34	tff('81', plain,
49.13/49.34	    ![X0 : a]:
49.13/49.34	      sk_MEET(X0, sk_Xz1) = sk_MEET(X0, sk_JOIN(sk_MEET(sk_Xz1, X0), sk_Xx1)),
49.13/49.34	    inference('demod', [status(thm)], ['80', '77', '24'])).
49.13/49.34	tff('82', plain,
49.13/49.34	    ![X0 : a]:
49.13/49.34	      sk_MEET(sk_MEET(sk_Xz1, X0), sk_Xz1)
49.13/49.34	       = sk_MEET(sk_MEET(sk_Xz1, X0), sk_JOIN(sk_MEET(sk_Xz1, X0), sk_Xx1)),
49.13/49.34	    inference('sup+', [status(thm)], ['24', '81'])).
49.13/49.34	tff('83', plain, ![X6 : a]: sk_MEET(X6, X6) = X6,
49.13/49.34	    inference('cnf', [status(esa)], [zf_stmt_0])).
49.13/49.34	tff('84', plain,
49.13/49.34	    ![X0 : a]:
49.13/49.34	      sk_JOIN(sk_Xx1, sk_MEET(sk_MEET(X0, sk_Xz1), sk_Xz1))
49.13/49.34	       = sk_MEET(sk_Xz1, sk_MEET(sk_Xz1, sk_JOIN(X0, sk_Xx1))),
49.13/49.34	    inference('sup+', [status(thm)], ['72', '50'])).
49.13/49.34	tff('85', plain,
49.13/49.34	    ![X0 : a]:
49.13/49.34	      sk_JOIN(sk_Xx1, sk_MEET(sk_Xz1, X0))
49.13/49.34	       = sk_MEET(sk_Xz1, sk_JOIN(X0, sk_Xx1)),
49.13/49.34	    inference('demod', [status(thm)], ['84', '67', '76', '24'])).
49.13/49.34	tff('86', plain,
49.13/49.34	    ![X0 : a]:
49.13/49.34	      sk_MEET(X0, sk_Xz1) = sk_MEET(X0, sk_JOIN(sk_Xx1, sk_MEET(sk_Xz1, X0))),
49.13/49.34	    inference('demod', [status(thm)], ['82', '67', '83', '67', '85', '24'])).
49.13/49.34	tff('87', plain,
49.13/49.34	    ![X0 : a]:
49.13/49.34	      sk_MEET(sk_JOIN(sk_Xx1, X0), sk_Xz1)
49.13/49.34	       = sk_MEET(sk_JOIN(sk_Xx1, sk_Xz1), 
49.13/49.34	           sk_MEET(sk_JOIN(sk_Xx1, X0), sk_JOIN(sk_Xx1, X0))),
49.13/49.34	    inference('sup+', [status(thm)], ['20', '86'])).
49.13/49.34	tff('88', plain,
49.13/49.34	    ![X0 : a]:
49.13/49.34	      sk_JOIN(sk_Xx1, sk_MEET(sk_Xz1, X0))
49.13/49.34	       = sk_MEET(sk_Xz1, sk_JOIN(sk_Xx1, X0)),
49.13/49.34	    inference('demod', [status(thm)],
49.13/49.34	              ['87', '49', '85', '6', '28', '15', '8'])).
49.13/49.34	tff('89', plain,
49.13/49.34	    sk_JOIN(sk_Xx1, sk_MEET(sk_Xz1, sk_Xy1))
49.13/49.34	     != sk_JOIN(sk_Xx1, sk_MEET(sk_Xz1, sk_Xy1)),
49.13/49.34	    inference('demod', [status(thm)], ['17', '88'])).
49.13/49.34	tff('90', plain, $false, inference('simplify', [status(thm)], ['89'])).
49.13/49.34	
49.13/49.34	% SZS output end Refutation
49.13/49.34	EOF
