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_int
0.00/0.00	% Ordering    : kbo
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-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 int \
0.00/0.00	  --ho-no-ext-pos \
0.00/0.00	  --ho-no-ext-neg \
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   : n098.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 17:18:39 CST 2018
0.00/0.39	% done 130 iterations in 0.188s
0.00/0.39	% SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
0.00/0.39	% SZS output start Refutation
0.00/0.39	tff(complementT_lem, axiom,
0.00/0.39	  (complementT_lem <=>
0.00/0.39	   (![A,X]: (in(X,powerset(A)) => in(setminus(A,X),powerset(A)))))).
0.00/0.39	tff('0', plain,
0.00/0.39	    ![X6, X7]:
0.00/0.39	      (~ in(X6, powerset(X7))
0.00/0.39	       | in(setminus(X7, X6), powerset(X7))
0.00/0.39	       | ~ complementT_lem),
0.00/0.39	    inference('cnf', [status(esa)], [complementT_lem])).
0.00/0.39	tff(demorgan2, conjecture,
0.00/0.39	  (binintersectT_lem =>
0.00/0.39	   (binunionT_lem =>
0.00/0.39	    (complementT_lem =>
0.00/0.39	     (setextT =>
0.00/0.39	      (demorgan2a =>
0.00/0.39	       (demorgan2b =>
0.00/0.39	        (![A,X]:
0.00/0.39	           (in(X,powerset(A)) =>
0.00/0.39	            (![Y]:
0.00/0.39	               (in(Y,powerset(A)) =>
0.00/0.39	                (setminus(A,binunion(X,Y)) =
0.00/0.39	                 binintersect(setminus(A,X),setminus(A,Y)))))))))))))).
0.00/0.39	tff(zf_stmt_0, negated_conjecture,
0.00/0.39	  (~
0.00/0.39	    (binintersectT_lem =>
0.00/0.39	     (binunionT_lem =>
0.00/0.39	      (complementT_lem =>
0.00/0.39	       (setextT =>
0.00/0.39	        (demorgan2a =>
0.00/0.39	         (demorgan2b =>
0.00/0.39	          (![A,X]:
0.00/0.39	             (in(X,powerset(A)) =>
0.00/0.39	              (![Y]:
0.00/0.39	                 (in(Y,powerset(A)) =>
0.00/0.39	                  (setminus(A,binunion(X,Y)) =
0.00/0.39	                   binintersect(setminus(A,X),setminus(A,Y))))))))))))))).
0.00/0.39	tff('1', plain, complementT_lem, inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.39	tff('2', plain,
0.00/0.39	    ![X6, X7]:
0.00/0.39	      (~ in(X6, powerset(X7)) | in(setminus(X7, X6), powerset(X7)) | ~ $true),
0.00/0.39	    inference('demod', [status(thm)], ['0', '1'])).
0.00/0.39	tff('3', plain,
0.00/0.39	    ![X6, X7]: (in(setminus(X7, X6), powerset(X7)) | ~ in(X6, powerset(X7))),
0.00/0.39	    inference('simplify', [status(thm)], ['2'])).
0.00/0.39	tff(binintersectT_lem, axiom,
0.00/0.39	  (binintersectT_lem <=>
0.00/0.39	   (![A,X]:
0.00/0.39	      (in(X,powerset(A)) =>
0.00/0.39	       (![Y]: (in(Y,powerset(A)) => in(binintersect(X,Y),powerset(A)))))))).
0.00/0.39	tff('4', plain,
0.00/0.39	    ![X0, X1, X2]:
0.00/0.39	      (~ in(X0, powerset(X1))
0.00/0.39	       | in(binintersect(X0, X2), powerset(X1))
0.00/0.39	       | ~ in(X2, powerset(X1))
0.00/0.39	       | ~ binintersectT_lem),
0.00/0.39	    inference('cnf', [status(esa)], [binintersectT_lem])).
0.00/0.39	tff('5', plain, binintersectT_lem,
0.00/0.39	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.39	tff('6', plain,
0.00/0.39	    ![X0, X1, X2]:
0.00/0.39	      (~ in(X0, powerset(X1))
0.00/0.39	       | in(binintersect(X0, X2), powerset(X1))
0.00/0.39	       | ~ in(X2, powerset(X1))
0.00/0.39	       | ~ $true),
0.00/0.39	    inference('demod', [status(thm)], ['4', '5'])).
0.00/0.39	tff('7', plain,
0.00/0.39	    ![X0, X1, X2]:
0.00/0.39	      (~ in(X2, powerset(X1))
0.00/0.39	       | in(binintersect(X0, X2), powerset(X1))
0.00/0.39	       | ~ in(X0, powerset(X1))),
0.00/0.39	    inference('simplify', [status(thm)], ['6'])).
0.00/0.39	tff(setextT, axiom,
0.00/0.39	  (setextT <=>
0.00/0.39	   (![A,X]:
0.00/0.39	      (in(X,powerset(A)) =>
0.00/0.39	       (![Y]:
0.00/0.39	          (in(Y,powerset(A)) =>
0.00/0.39	           ((![Xx]: (in(Xx,A) => (in(Xx,X) => in(Xx,Y)))) =>
0.00/0.39	            ((![Xx]: (in(Xx,A) => (in(Xx,Y) => in(Xx,X)))) => (X = Y))))))))).
0.00/0.39	tff(zf_stmt_1, axiom,
0.00/0.39	  (zip_tseitin1(Xx,Y,X,A) <=> (in(Xx,A) => zip_tseitin0(Xx,Y,X)))).
0.00/0.39	tff('8', plain,
0.00/0.39	    ![X8, X9, X10, X11]: (zip_tseitin1(X8, X10, X9, X11) | in(X8, X11)),
0.00/0.39	    inference('cnf', [status(esa)], [zf_stmt_1])).
0.00/0.39	tff(zf_stmt_2, axiom,
0.00/0.39	  (zip_tseitin3(Xx,Y,X,A) <=> (in(Xx,A) => zip_tseitin2(Xx,Y,X)))).
0.00/0.39	tff('9', plain,
0.00/0.39	    ![X9, X10, X11, X12]: (zip_tseitin3(X12, X10, X9, X11) | in(X12, X11)),
0.00/0.39	    inference('cnf', [status(esa)], [zf_stmt_2])).
0.00/0.39	tff(zf_stmt_3, type, zip_tseitin3 : ($i * $i * $i * $i) > $o).
0.00/0.39	tff(zf_stmt_4, type, zip_tseitin2 : ($i * $i * $i) > $o).
0.00/0.39	tff(zf_stmt_5, axiom, (zip_tseitin2(Xx,Y,X) <=> (in(Xx,Y) => in(Xx,X)))).
0.00/0.39	tff(zf_stmt_6, type, zip_tseitin1 : ($i * $i * $i * $i) > $o).
0.00/0.39	tff(zf_stmt_7, type, zip_tseitin0 : ($i * $i * $i) > $o).
0.00/0.39	tff(zf_stmt_8, axiom, (zip_tseitin0(Xx,Y,X) <=> (in(Xx,X) => in(Xx,Y)))).
0.00/0.39	tff(zf_stmt_9, axiom,
0.00/0.39	  (setextT <=>
0.00/0.39	   (![A,X]:
0.00/0.39	      (in(X,powerset(A)) =>
0.00/0.39	       (![Y]:
0.00/0.39	          (in(Y,powerset(A)) =>
0.00/0.39	           ((![Xx]: zip_tseitin1(Xx,Y,X,A)) =>
0.00/0.39	            ((![Xx]: zip_tseitin3(Xx,Y,X,A)) => (X = Y))))))))).
0.00/0.39	tff('10', plain,
0.00/0.39	    ![X13, X14, X15]:
0.00/0.39	      (~ in(X13, powerset(X14))
0.00/0.39	       | ~ zip_tseitin1(sk_Xx(X15, X13, X14), X15, X13, X14)
0.00/0.39	       | X13 = X15
0.00/0.39	       | ~ zip_tseitin3(sk_Xx1(X15, X13, X14), X15, X13, X14)
0.00/0.39	       | ~ in(X15, powerset(X14))
0.00/0.39	       | ~ setextT),
0.00/0.39	    inference('cnf', [status(esa)], [zf_stmt_9])).
0.00/0.39	tff('11', plain, setextT, inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.39	tff('12', plain,
0.00/0.39	    ![X13, X14, X15]:
0.00/0.39	      (~ in(X13, powerset(X14))
0.00/0.39	       | ~ zip_tseitin1(sk_Xx(X15, X13, X14), X15, X13, X14)
0.00/0.39	       | X13 = X15
0.00/0.39	       | ~ zip_tseitin3(sk_Xx1(X15, X13, X14), X15, X13, X14)
0.00/0.39	       | ~ in(X15, powerset(X14))
0.00/0.39	       | ~ $true),
0.00/0.39	    inference('demod', [status(thm)], ['10', '11'])).
0.00/0.39	tff('13', plain,
0.00/0.39	    ![X13, X14, X15]:
0.00/0.39	      (~ in(X15, powerset(X14))
0.00/0.39	       | ~ zip_tseitin3(sk_Xx1(X15, X13, X14), X15, X13, X14)
0.00/0.39	       | X13 = X15
0.00/0.39	       | ~ zip_tseitin1(sk_Xx(X15, X13, X14), X15, X13, X14)
0.00/0.39	       | ~ in(X13, powerset(X14))),
0.00/0.39	    inference('simplify', [status(thm)], ['12'])).
0.00/0.39	tff('14', plain,
0.00/0.39	    ![X0, X1, X2]:
0.00/0.39	      (~ $true
0.00/0.39	       | in(sk_Xx1(X2, X1, X0), X0)
0.00/0.39	       | ~ in(X1, powerset(X0))
0.00/0.39	       | ~ zip_tseitin1(sk_Xx(X2, X1, X0), X2, X1, X0)
0.00/0.39	       | X1 = X2
0.00/0.39	       | ~ in(X2, powerset(X0))),
0.00/0.39	    inference('sup-', [status(thm)], ['9', '13'])).
0.00/0.39	tff('15', plain,
0.00/0.39	    ![X0, X1, X2]:
0.00/0.39	      (~ in(X2, powerset(X0))
0.00/0.39	       | X1 = X2
0.00/0.39	       | ~ zip_tseitin1(sk_Xx(X2, X1, X0), X2, X1, X0)
0.00/0.39	       | ~ in(X1, powerset(X0))
0.00/0.39	       | in(sk_Xx1(X2, X1, X0), X0)),
0.00/0.39	    inference('simplify', [status(thm)], ['14'])).
0.00/0.39	tff('16', plain,
0.00/0.39	    ![X0, X1, X2]:
0.00/0.39	      (~ $true
0.00/0.39	       | in(sk_Xx(X2, X1, X0), X0)
0.00/0.39	       | in(sk_Xx1(X2, X1, X0), X0)
0.00/0.39	       | ~ in(X1, powerset(X0))
0.00/0.39	       | X1 = X2
0.00/0.39	       | ~ in(X2, powerset(X0))),
0.00/0.39	    inference('sup-', [status(thm)], ['8', '15'])).
0.00/0.39	tff('17', plain,
0.00/0.39	    ![X0, X1, X2]:
0.00/0.39	      (~ in(X2, powerset(X0))
0.00/0.39	       | X1 = X2
0.00/0.39	       | ~ in(X1, powerset(X0))
0.00/0.39	       | in(sk_Xx1(X2, X1, X0), X0)
0.00/0.39	       | in(sk_Xx(X2, X1, X0), X0)),
0.00/0.39	    inference('simplify', [status(thm)], ['16'])).
0.00/0.39	tff('18', plain,
0.00/0.39	    ![X9, X10, X12]: (zip_tseitin2(X12, X10, X9) | in(X12, X10)),
0.00/0.39	    inference('cnf', [status(esa)], [zf_stmt_5])).
0.00/0.39	tff('19', plain,
0.00/0.39	    ![X9, X10, X11, X12]:
0.00/0.39	      (zip_tseitin3(X12, X10, X9, X11) | ~ zip_tseitin2(X12, X10, X9)),
0.00/0.39	    inference('cnf', [status(esa)], [zf_stmt_2])).
0.00/0.39	tff('20', plain,
0.00/0.39	    ![X0, X1, X2]:
0.00/0.39	      (~ $true
0.00/0.39	       | ~ zip_tseitin2(sk_Xx1(X2, X1, X0), X2, X1)
0.00/0.39	       | ~ in(X1, powerset(X0))
0.00/0.39	       | ~ zip_tseitin1(sk_Xx(X2, X1, X0), X2, X1, X0)
0.00/0.39	       | X1 = X2
0.00/0.39	       | ~ in(X2, powerset(X0))),
0.00/0.39	    inference('sup-', [status(thm)], ['19', '13'])).
0.00/0.39	tff('21', plain,
0.00/0.39	    ![X0, X1, X2]:
0.00/0.39	      (~ in(X2, powerset(X0))
0.00/0.39	       | X1 = X2
0.00/0.39	       | ~ zip_tseitin1(sk_Xx(X2, X1, X0), X2, X1, X0)
0.00/0.39	       | ~ in(X1, powerset(X0))
0.00/0.39	       | ~ zip_tseitin2(sk_Xx1(X2, X1, X0), X2, X1)),
0.00/0.39	    inference('simplify', [status(thm)], ['20'])).
0.00/0.39	tff('22', plain,
0.00/0.39	    ![X0, X1, X2]:
0.00/0.39	      (~ $true
0.00/0.39	       | in(sk_Xx(X2, X1, X0), X0)
0.00/0.39	       | ~ zip_tseitin2(sk_Xx1(X2, X1, X0), X2, X1)
0.00/0.39	       | ~ in(X1, powerset(X0))
0.00/0.39	       | X1 = X2
0.00/0.39	       | ~ in(X2, powerset(X0))),
0.00/0.39	    inference('sup-', [status(thm)], ['8', '21'])).
0.00/0.39	tff('23', plain,
0.00/0.39	    ![X0, X1, X2]:
0.00/0.39	      (~ in(X2, powerset(X0))
0.00/0.39	       | X1 = X2
0.00/0.39	       | ~ in(X1, powerset(X0))
0.00/0.39	       | ~ zip_tseitin2(sk_Xx1(X2, X1, X0), X2, X1)
0.00/0.39	       | in(sk_Xx(X2, X1, X0), X0)),
0.00/0.39	    inference('simplify', [status(thm)], ['22'])).
0.00/0.39	tff('24', plain,
0.00/0.39	    ![X0, X1, X2]:
0.00/0.39	      (~ $true
0.00/0.39	       | in(sk_Xx1(X1, X0, X2), X1)
0.00/0.39	       | in(sk_Xx(X1, X0, X2), X2)
0.00/0.39	       | ~ in(X0, powerset(X2))
0.00/0.39	       | X0 = X1
0.00/0.39	       | ~ in(X1, powerset(X2))),
0.00/0.39	    inference('sup-', [status(thm)], ['18', '23'])).
0.00/0.39	tff('25', plain,
0.00/0.39	    ![X0, X1, X2]:
0.00/0.39	      (~ in(X1, powerset(X2))
0.00/0.39	       | X0 = X1
0.00/0.39	       | ~ in(X0, powerset(X2))
0.00/0.39	       | in(sk_Xx(X1, X0, X2), X2)
0.00/0.39	       | in(sk_Xx1(X1, X0, X2), X1)),
0.00/0.39	    inference('simplify', [status(thm)], ['24'])).
0.00/0.39	tff(demorgan2a, axiom,
0.00/0.39	  (demorgan2a <=>
0.00/0.39	   (![A,X]:
0.00/0.39	      (in(X,powerset(A)) =>
0.00/0.39	       (![Y]:
0.00/0.39	          (in(Y,powerset(A)) =>
0.00/0.39	           (![Xx]:
0.00/0.39	              (in(Xx,A) =>
0.00/0.39	               (in(Xx,setminus(A,binunion(X,Y))) =>
0.00/0.39	                in(Xx,binintersect(setminus(A,X),setminus(A,Y)))))))))))).
0.00/0.39	tff('26', plain,
0.00/0.39	    ![X18, X19, X20, X21]:
0.00/0.39	      (~ in(X18, powerset(X19))
0.00/0.39	       | ~ in(X20, X19)
0.00/0.39	       | in(X20, binintersect(setminus(X19, X18), setminus(X19, X21)))
0.00/0.39	       | ~ in(X20, setminus(X19, binunion(X18, X21)))
0.00/0.39	       | ~ in(X21, powerset(X19))
0.00/0.39	       | ~ demorgan2a),
0.00/0.39	    inference('cnf', [status(esa)], [demorgan2a])).
0.00/0.39	tff('27', plain, demorgan2a, inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.39	tff('28', plain,
0.00/0.39	    ![X18, X19, X20, X21]:
0.00/0.39	      (~ in(X18, powerset(X19))
0.00/0.39	       | ~ in(X20, X19)
0.00/0.39	       | in(X20, binintersect(setminus(X19, X18), setminus(X19, X21)))
0.00/0.39	       | ~ in(X20, setminus(X19, binunion(X18, X21)))
0.00/0.39	       | ~ in(X21, powerset(X19))
0.00/0.39	       | ~ $true),
0.00/0.39	    inference('demod', [status(thm)], ['26', '27'])).
0.00/0.39	tff('29', plain,
0.00/0.39	    ![X18, X19, X20, X21]:
0.00/0.39	      (~ in(X21, powerset(X19))
0.00/0.39	       | ~ in(X20, setminus(X19, binunion(X18, X21)))
0.00/0.39	       | in(X20, binintersect(setminus(X19, X18), setminus(X19, X21)))
0.00/0.39	       | ~ in(X20, X19)
0.00/0.39	       | ~ in(X18, powerset(X19))),
0.00/0.39	    inference('simplify', [status(thm)], ['28'])).
0.00/0.39	tff('30', plain,
0.00/0.39	    ![X9, X10, X12]: (zip_tseitin2(X12, X10, X9) | ~ in(X12, X9)),
0.00/0.39	    inference('cnf', [status(esa)], [zf_stmt_5])).
0.00/0.39	tff('31', plain,
0.00/0.39	    ![X0, X1, X2]:
0.00/0.39	      (~ $true
0.00/0.39	       | ~ in(sk_Xx1(X1, X0, X2), X0)
0.00/0.39	       | in(sk_Xx(X1, X0, X2), X2)
0.00/0.39	       | ~ in(X0, powerset(X2))
0.00/0.39	       | X0 = X1
0.00/0.39	       | ~ in(X1, powerset(X2))),
0.00/0.39	    inference('sup-', [status(thm)], ['30', '23'])).
0.00/0.39	tff('32', plain,
0.00/0.39	    ![X0, X1, X2]:
0.00/0.39	      (~ in(X1, powerset(X2))
0.00/0.39	       | X0 = X1
0.00/0.39	       | ~ in(X0, powerset(X2))
0.00/0.39	       | in(sk_Xx(X1, X0, X2), X2)
0.00/0.39	       | ~ in(sk_Xx1(X1, X0, X2), X0)),
0.00/0.39	    inference('simplify', [status(thm)], ['31'])).
0.00/0.39	tff('33', plain,
0.00/0.39	    ![X0, X1, X2, X3, X4]:
0.00/0.39	      (~ $true
0.00/0.39	       | ~ in(X2, powerset(X1))
0.00/0.39	       | ~ in(
0.00/0.39	             sk_Xx1(X4, binintersect(setminus(X1, X2), setminus(X1, X0)), X3), 
0.00/0.39	             X1)
0.00/0.39	       | ~ in(
0.00/0.39	             sk_Xx1(X4, binintersect(setminus(X1, X2), setminus(X1, X0)), X3), 
0.00/0.39	             setminus(X1, binunion(X2, X0)))
0.00/0.39	       | ~ in(X0, powerset(X1))
0.00/0.39	       | in(sk_Xx(X4, binintersect(setminus(X1, X2), setminus(X1, X0)), X3), 
0.00/0.39	           X3)
0.00/0.39	       | ~ in(binintersect(setminus(X1, X2), setminus(X1, X0)), powerset(X3))
0.00/0.39	       | binintersect(setminus(X1, X2), setminus(X1, X0)) = X4
0.00/0.39	       | ~ in(X4, powerset(X3))),
0.00/0.39	    inference('sup-', [status(thm)], ['29', '32'])).
0.00/0.39	tff('34', plain,
0.00/0.39	    ![X0, X1, X2, X3, X4]:
0.00/0.39	      (~ in(X4, powerset(X3))
0.00/0.39	       | binintersect(setminus(X1, X2), setminus(X1, X0)) = X4
0.00/0.39	       | ~ in(binintersect(setminus(X1, X2), setminus(X1, X0)), powerset(X3))
0.00/0.39	       | in(sk_Xx(X4, binintersect(setminus(X1, X2), setminus(X1, X0)), X3), 
0.00/0.39	           X3)
0.00/0.39	       | ~ in(X0, powerset(X1))
0.00/0.39	       | ~ in(
0.00/0.39	             sk_Xx1(X4, binintersect(setminus(X1, X2), setminus(X1, X0)), X3), 
0.00/0.39	             setminus(X1, binunion(X2, X0)))
0.00/0.39	       | ~ in(
0.00/0.39	             sk_Xx1(X4, binintersect(setminus(X1, X2), setminus(X1, X0)), X3), 
0.00/0.39	             X1)
0.00/0.39	       | ~ in(X2, powerset(X1))),
0.00/0.39	    inference('simplify', [status(thm)], ['33'])).
0.00/0.39	tff('35', plain,
0.00/0.39	    ![X0, X1, X2, X3]:
0.00/0.39	      (~ $true
0.00/0.39	       | in(
0.00/0.39	           sk_Xx(setminus(X2, binunion(X1, X0)), 
0.00/0.39	             binintersect(setminus(X2, X1), setminus(X2, X0)), X3), X3)
0.00/0.39	       | ~ in(binintersect(setminus(X2, X1), setminus(X2, X0)), powerset(X3))
0.00/0.39	       | binintersect(setminus(X2, X1), setminus(X2, X0))
0.00/0.39	          = setminus(X2, binunion(X1, X0))
0.00/0.39	       | ~ in(setminus(X2, binunion(X1, X0)), powerset(X3))
0.00/0.39	       | ~ in(X1, powerset(X2))
0.00/0.39	       | ~ in(
0.00/0.39	             sk_Xx1(setminus(X2, binunion(X1, X0)), 
0.00/0.39	               binintersect(setminus(X2, X1), setminus(X2, X0)), X3), X2)
0.00/0.39	       | ~ in(X0, powerset(X2))
0.00/0.39	       | in(
0.00/0.39	           sk_Xx(setminus(X2, binunion(X1, X0)), 
0.00/0.39	             binintersect(setminus(X2, X1), setminus(X2, X0)), X3), X3)
0.00/0.39	       | ~ in(binintersect(setminus(X2, X1), setminus(X2, X0)), powerset(X3))
0.00/0.39	       | binintersect(setminus(X2, X1), setminus(X2, X0))
0.00/0.39	          = setminus(X2, binunion(X1, X0))
0.00/0.39	       | ~ in(setminus(X2, binunion(X1, X0)), powerset(X3))),
0.00/0.39	    inference('sup-', [status(thm)], ['25', '34'])).
0.00/0.39	tff('36', plain,
0.00/0.39	    ![X0, X1, X2, X3]:
0.00/0.39	      (~ in(X0, powerset(X2))
0.00/0.39	       | ~ in(
0.00/0.39	             sk_Xx1(setminus(X2, binunion(X1, X0)), 
0.00/0.39	               binintersect(setminus(X2, X1), setminus(X2, X0)), X3), X2)
0.00/0.39	       | ~ in(X1, powerset(X2))
0.00/0.39	       | ~ in(setminus(X2, binunion(X1, X0)), powerset(X3))
0.00/0.39	       | binintersect(setminus(X2, X1), setminus(X2, X0))
0.00/0.39	          = setminus(X2, binunion(X1, X0))
0.00/0.39	       | ~ in(binintersect(setminus(X2, X1), setminus(X2, X0)), powerset(X3))
0.00/0.39	       | in(
0.00/0.39	           sk_Xx(setminus(X2, binunion(X1, X0)), 
0.00/0.39	             binintersect(setminus(X2, X1), setminus(X2, X0)), X3), X3)),
0.00/0.39	    inference('simplify', [status(thm)], ['35'])).
0.00/0.39	tff('37', plain,
0.00/0.39	    ![X0, X1, X2]:
0.00/0.39	      (~ $true
0.00/0.39	       | in(
0.00/0.39	           sk_Xx(setminus(X0, binunion(X2, X1)), 
0.00/0.39	             binintersect(setminus(X0, X2), setminus(X0, X1)), X0), X0)
0.00/0.39	       | ~ in(binintersect(setminus(X0, X2), setminus(X0, X1)), powerset(X0))
0.00/0.39	       | binintersect(setminus(X0, X2), setminus(X0, X1))
0.00/0.39	          = setminus(X0, binunion(X2, X1))
0.00/0.39	       | ~ in(setminus(X0, binunion(X2, X1)), powerset(X0))
0.00/0.39	       | in(
0.00/0.39	           sk_Xx(setminus(X0, binunion(X2, X1)), 
0.00/0.39	             binintersect(setminus(X0, X2), setminus(X0, X1)), X0), X0)
0.00/0.39	       | ~ in(binintersect(setminus(X0, X2), setminus(X0, X1)), powerset(X0))
0.00/0.39	       | binintersect(setminus(X0, X2), setminus(X0, X1))
0.00/0.39	          = setminus(X0, binunion(X2, X1))
0.00/0.39	       | ~ in(setminus(X0, binunion(X2, X1)), powerset(X0))
0.00/0.39	       | ~ in(X2, powerset(X0))
0.00/0.39	       | ~ in(X1, powerset(X0))),
0.00/0.39	    inference('sup-', [status(thm)], ['17', '36'])).
0.00/0.39	tff('38', plain,
0.00/0.39	    ![X0, X1, X2]:
0.00/0.39	      (~ in(X1, powerset(X0))
0.00/0.39	       | ~ in(X2, powerset(X0))
0.00/0.39	       | ~ in(setminus(X0, binunion(X2, X1)), powerset(X0))
0.00/0.39	       | binintersect(setminus(X0, X2), setminus(X0, X1))
0.00/0.39	          = setminus(X0, binunion(X2, X1))
0.00/0.39	       | ~ in(binintersect(setminus(X0, X2), setminus(X0, X1)), powerset(X0))
0.00/0.39	       | in(
0.00/0.39	           sk_Xx(setminus(X0, binunion(X2, X1)), 
0.00/0.39	             binintersect(setminus(X0, X2), setminus(X0, X1)), X0), X0)),
0.00/0.39	    inference('simplify', [status(thm)], ['37'])).
0.00/0.39	tff('39', plain, ![X8, X9, X10]: (zip_tseitin0(X8, X10, X9) | in(X8, X9)),
0.00/0.39	    inference('cnf', [status(esa)], [zf_stmt_8])).
0.00/0.39	tff('40', plain,
0.00/0.39	    ![X8, X9, X10, X11]:
0.00/0.39	      (zip_tseitin1(X8, X10, X9, X11) | ~ zip_tseitin0(X8, X10, X9)),
0.00/0.39	    inference('cnf', [status(esa)], [zf_stmt_1])).
0.00/0.39	tff('41', plain,
0.00/0.39	    ![X0, X1, X2]:
0.00/0.39	      (~ $true
0.00/0.39	       | ~ zip_tseitin0(sk_Xx(X2, X1, X0), X2, X1)
0.00/0.39	       | in(sk_Xx1(X2, X1, X0), X0)
0.00/0.39	       | ~ in(X1, powerset(X0))
0.00/0.39	       | X1 = X2
0.00/0.39	       | ~ in(X2, powerset(X0))),
0.00/0.39	    inference('sup-', [status(thm)], ['40', '15'])).
0.00/0.39	tff('42', plain,
0.00/0.39	    ![X0, X1, X2]:
0.00/0.39	      (~ in(X2, powerset(X0))
0.00/0.39	       | X1 = X2
0.00/0.39	       | ~ in(X1, powerset(X0))
0.00/0.39	       | in(sk_Xx1(X2, X1, X0), X0)
0.00/0.39	       | ~ zip_tseitin0(sk_Xx(X2, X1, X0), X2, X1)),
0.00/0.39	    inference('simplify', [status(thm)], ['41'])).
0.00/0.39	tff('43', plain,
0.00/0.39	    ![X0, X1, X2]:
0.00/0.39	      (~ $true
0.00/0.39	       | in(sk_Xx(X1, X0, X2), X0)
0.00/0.39	       | in(sk_Xx1(X1, X0, X2), X2)
0.00/0.39	       | ~ in(X0, powerset(X2))
0.00/0.39	       | X0 = X1
0.00/0.39	       | ~ in(X1, powerset(X2))),
0.00/0.39	    inference('sup-', [status(thm)], ['39', '42'])).
0.00/0.39	tff('44', plain,
0.00/0.39	    ![X0, X1, X2]:
0.00/0.39	      (~ in(X1, powerset(X2))
0.00/0.39	       | X0 = X1
0.00/0.39	       | ~ in(X0, powerset(X2))
0.00/0.39	       | in(sk_Xx1(X1, X0, X2), X2)
0.00/0.39	       | in(sk_Xx(X1, X0, X2), X0)),
0.00/0.39	    inference('simplify', [status(thm)], ['43'])).
0.00/0.39	tff(demorgan2b, axiom,
0.00/0.39	  (demorgan2b <=>
0.00/0.39	   (![A,X]:
0.00/0.39	      (in(X,powerset(A)) =>
0.00/0.39	       (![Y]:
0.00/0.39	          (in(Y,powerset(A)) =>
0.00/0.39	           (![Xx]:
0.00/0.39	              (in(Xx,A) =>
0.00/0.39	               (in(Xx,binintersect(setminus(A,X),setminus(A,Y))) =>
0.00/0.39	                in(Xx,setminus(A,binunion(X,Y)))))))))))).
0.00/0.39	tff('45', plain,
0.00/0.39	    ![X22, X23, X24, X25]:
0.00/0.39	      (~ in(X22, powerset(X23))
0.00/0.39	       | ~ in(X24, X23)
0.00/0.39	       | in(X24, setminus(X23, binunion(X22, X25)))
0.00/0.39	       | ~ in(X24, binintersect(setminus(X23, X22), setminus(X23, X25)))
0.00/0.39	       | ~ in(X25, powerset(X23))
0.00/0.39	       | ~ demorgan2b),
0.00/0.39	    inference('cnf', [status(esa)], [demorgan2b])).
0.00/0.39	tff('46', plain, demorgan2b, inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.39	tff('47', plain,
0.00/0.39	    ![X22, X23, X24, X25]:
0.00/0.39	      (~ in(X22, powerset(X23))
0.00/0.39	       | ~ in(X24, X23)
0.00/0.39	       | in(X24, setminus(X23, binunion(X22, X25)))
0.00/0.39	       | ~ in(X24, binintersect(setminus(X23, X22), setminus(X23, X25)))
0.00/0.39	       | ~ in(X25, powerset(X23))
0.00/0.39	       | ~ $true),
0.00/0.39	    inference('demod', [status(thm)], ['45', '46'])).
0.00/0.39	tff('48', plain,
0.00/0.39	    ![X22, X23, X24, X25]:
0.00/0.39	      (~ in(X25, powerset(X23))
0.00/0.39	       | ~ in(X24, binintersect(setminus(X23, X22), setminus(X23, X25)))
0.00/0.39	       | in(X24, setminus(X23, binunion(X22, X25)))
0.00/0.39	       | ~ in(X24, X23)
0.00/0.39	       | ~ in(X22, powerset(X23))),
0.00/0.39	    inference('simplify', [status(thm)], ['47'])).
0.00/0.39	tff('49', plain,
0.00/0.39	    ![X0, X1, X2, X3, X4]:
0.00/0.39	      (~ $true
0.00/0.39	       | in(
0.00/0.39	           sk_Xx1(X4, binintersect(setminus(X1, X2), setminus(X1, X0)), X3), 
0.00/0.39	           X3)
0.00/0.39	       | ~ in(binintersect(setminus(X1, X2), setminus(X1, X0)), powerset(X3))
0.00/0.39	       | binintersect(setminus(X1, X2), setminus(X1, X0)) = X4
0.00/0.39	       | ~ in(X4, powerset(X3))
0.00/0.39	       | ~ in(X2, powerset(X1))
0.00/0.39	       | ~ in(
0.00/0.39	             sk_Xx(X4, binintersect(setminus(X1, X2), setminus(X1, X0)), X3), 
0.00/0.39	             X1)
0.00/0.39	       | in(sk_Xx(X4, binintersect(setminus(X1, X2), setminus(X1, X0)), X3), 
0.00/0.39	           setminus(X1, binunion(X2, X0)))
0.00/0.39	       | ~ in(X0, powerset(X1))),
0.00/0.39	    inference('sup-', [status(thm)], ['44', '48'])).
0.00/0.39	tff('50', plain,
0.00/0.39	    ![X0, X1, X2, X3, X4]:
0.00/0.39	      (~ in(X0, powerset(X1))
0.00/0.39	       | in(sk_Xx(X4, binintersect(setminus(X1, X2), setminus(X1, X0)), X3), 
0.00/0.39	           setminus(X1, binunion(X2, X0)))
0.00/0.39	       | ~ in(
0.00/0.39	             sk_Xx(X4, binintersect(setminus(X1, X2), setminus(X1, X0)), X3), 
0.00/0.39	             X1)
0.00/0.39	       | ~ in(X2, powerset(X1))
0.00/0.39	       | ~ in(X4, powerset(X3))
0.00/0.39	       | binintersect(setminus(X1, X2), setminus(X1, X0)) = X4
0.00/0.39	       | ~ in(binintersect(setminus(X1, X2), setminus(X1, X0)), powerset(X3))
0.00/0.39	       | in(
0.00/0.39	           sk_Xx1(X4, binintersect(setminus(X1, X2), setminus(X1, X0)), X3), 
0.00/0.39	           X3)),
0.00/0.39	    inference('simplify', [status(thm)], ['49'])).
0.00/0.39	tff('51', plain, ![X8, X9, X10]: (zip_tseitin0(X8, X10, X9) | ~ in(X8, X10)),
0.00/0.39	    inference('cnf', [status(esa)], [zf_stmt_8])).
0.00/0.39	tff('52', plain,
0.00/0.39	    ![X0, X1, X2]:
0.00/0.39	      (~ $true
0.00/0.39	       | ~ in(sk_Xx(X1, X0, X2), X1)
0.00/0.39	       | in(sk_Xx1(X1, X0, X2), X2)
0.00/0.39	       | ~ in(X0, powerset(X2))
0.00/0.39	       | X0 = X1
0.00/0.39	       | ~ in(X1, powerset(X2))),
0.00/0.39	    inference('sup-', [status(thm)], ['51', '42'])).
0.00/0.39	tff('53', plain,
0.00/0.39	    ![X0, X1, X2]:
0.00/0.39	      (~ in(X1, powerset(X2))
0.00/0.39	       | X0 = X1
0.00/0.39	       | ~ in(X0, powerset(X2))
0.00/0.39	       | in(sk_Xx1(X1, X0, X2), X2)
0.00/0.39	       | ~ in(sk_Xx(X1, X0, X2), X1)),
0.00/0.39	    inference('simplify', [status(thm)], ['52'])).
0.00/0.39	tff('54', plain,
0.00/0.39	    ![X0, X1, X2, X3]:
0.00/0.39	      (~ $true
0.00/0.39	       | in(
0.00/0.39	           sk_Xx1(setminus(X2, binunion(X1, X0)), 
0.00/0.39	             binintersect(setminus(X2, X1), setminus(X2, X0)), X3), X3)
0.00/0.39	       | ~ in(binintersect(setminus(X2, X1), setminus(X2, X0)), powerset(X3))
0.00/0.39	       | binintersect(setminus(X2, X1), setminus(X2, X0))
0.00/0.39	          = setminus(X2, binunion(X1, X0))
0.00/0.39	       | ~ in(setminus(X2, binunion(X1, X0)), powerset(X3))
0.00/0.39	       | ~ in(X1, powerset(X2))
0.00/0.39	       | ~ in(
0.00/0.39	             sk_Xx(setminus(X2, binunion(X1, X0)), 
0.00/0.39	               binintersect(setminus(X2, X1), setminus(X2, X0)), X3), X2)
0.00/0.39	       | ~ in(X0, powerset(X2))
0.00/0.39	       | in(
0.00/0.39	           sk_Xx1(setminus(X2, binunion(X1, X0)), 
0.00/0.39	             binintersect(setminus(X2, X1), setminus(X2, X0)), X3), X3)
0.00/0.39	       | ~ in(binintersect(setminus(X2, X1), setminus(X2, X0)), powerset(X3))
0.00/0.39	       | binintersect(setminus(X2, X1), setminus(X2, X0))
0.00/0.39	          = setminus(X2, binunion(X1, X0))
0.00/0.39	       | ~ in(setminus(X2, binunion(X1, X0)), powerset(X3))),
0.00/0.39	    inference('sup-', [status(thm)], ['50', '53'])).
0.00/0.39	tff('55', plain,
0.00/0.39	    ![X0, X1, X2, X3]:
0.00/0.39	      (~ in(X0, powerset(X2))
0.00/0.39	       | ~ in(
0.00/0.39	             sk_Xx(setminus(X2, binunion(X1, X0)), 
0.00/0.39	               binintersect(setminus(X2, X1), setminus(X2, X0)), X3), X2)
0.00/0.39	       | ~ in(X1, powerset(X2))
0.00/0.39	       | ~ in(setminus(X2, binunion(X1, X0)), powerset(X3))
0.00/0.39	       | binintersect(setminus(X2, X1), setminus(X2, X0))
0.00/0.39	          = setminus(X2, binunion(X1, X0))
0.00/0.39	       | ~ in(binintersect(setminus(X2, X1), setminus(X2, X0)), powerset(X3))
0.00/0.39	       | in(
0.00/0.39	           sk_Xx1(setminus(X2, binunion(X1, X0)), 
0.00/0.39	             binintersect(setminus(X2, X1), setminus(X2, X0)), X3), X3)),
0.00/0.39	    inference('simplify', [status(thm)], ['54'])).
0.00/0.39	tff('56', plain,
0.00/0.39	    ![X0, X1, X2]:
0.00/0.39	      (~ $true
0.00/0.39	       | ~ in(binintersect(setminus(X0, X2), setminus(X0, X1)), powerset(X0))
0.00/0.39	       | binintersect(setminus(X0, X2), setminus(X0, X1))
0.00/0.39	          = setminus(X0, binunion(X2, X1))
0.00/0.39	       | ~ in(setminus(X0, binunion(X2, X1)), powerset(X0))
0.00/0.39	       | ~ in(X2, powerset(X0))
0.00/0.39	       | ~ in(X1, powerset(X0))
0.00/0.39	       | in(
0.00/0.39	           sk_Xx1(setminus(X0, binunion(X2, X1)), 
0.00/0.39	             binintersect(setminus(X0, X2), setminus(X0, X1)), X0), X0)
0.00/0.39	       | ~ in(binintersect(setminus(X0, X2), setminus(X0, X1)), powerset(X0))
0.00/0.39	       | binintersect(setminus(X0, X2), setminus(X0, X1))
0.00/0.39	          = setminus(X0, binunion(X2, X1))
0.00/0.39	       | ~ in(setminus(X0, binunion(X2, X1)), powerset(X0))
0.00/0.39	       | ~ in(X2, powerset(X0))
0.00/0.39	       | ~ in(X1, powerset(X0))),
0.00/0.39	    inference('sup-', [status(thm)], ['38', '55'])).
0.00/0.39	tff('57', plain,
0.00/0.39	    ![X0, X1, X2]:
0.00/0.39	      (in(
0.00/0.39	         sk_Xx1(setminus(X0, binunion(X2, X1)), 
0.00/0.39	           binintersect(setminus(X0, X2), setminus(X0, X1)), X0), X0)
0.00/0.39	       | ~ in(X1, powerset(X0))
0.00/0.39	       | ~ in(X2, powerset(X0))
0.00/0.39	       | ~ in(setminus(X0, binunion(X2, X1)), powerset(X0))
0.00/0.39	       | binintersect(setminus(X0, X2), setminus(X0, X1))
0.00/0.39	          = setminus(X0, binunion(X2, X1))
0.00/0.39	       | ~ in(binintersect(setminus(X0, X2), setminus(X0, X1)), powerset(X0))),
0.00/0.39	    inference('simplify', [status(thm)], ['56'])).
0.00/0.39	tff('58', plain,
0.00/0.39	    ![X0, X1, X2]:
0.00/0.39	      (~ $true
0.00/0.39	       | ~ zip_tseitin0(sk_Xx(X2, X1, X0), X2, X1)
0.00/0.39	       | ~ zip_tseitin2(sk_Xx1(X2, X1, X0), X2, X1)
0.00/0.39	       | ~ in(X1, powerset(X0))
0.00/0.39	       | X1 = X2
0.00/0.39	       | ~ in(X2, powerset(X0))),
0.00/0.39	    inference('sup-', [status(thm)], ['40', '21'])).
0.00/0.39	tff('59', plain,
0.00/0.39	    ![X0, X1, X2]:
0.00/0.39	      (~ in(X2, powerset(X0))
0.00/0.39	       | X1 = X2
0.00/0.39	       | ~ in(X1, powerset(X0))
0.00/0.39	       | ~ zip_tseitin2(sk_Xx1(X2, X1, X0), X2, X1)
0.00/0.39	       | ~ zip_tseitin0(sk_Xx(X2, X1, X0), X2, X1)),
0.00/0.39	    inference('simplify', [status(thm)], ['58'])).
0.00/0.39	tff('60', plain,
0.00/0.39	    ![X0, X1, X2]:
0.00/0.39	      (~ $true
0.00/0.39	       | in(sk_Xx1(X1, X0, X2), X1)
0.00/0.39	       | ~ zip_tseitin0(sk_Xx(X1, X0, X2), X1, X0)
0.00/0.39	       | ~ in(X0, powerset(X2))
0.00/0.39	       | X0 = X1
0.00/0.39	       | ~ in(X1, powerset(X2))),
0.00/0.39	    inference('sup-', [status(thm)], ['18', '59'])).
0.00/0.39	tff('61', plain,
0.00/0.39	    ![X0, X1, X2]:
0.00/0.39	      (~ in(X1, powerset(X2))
0.00/0.39	       | X0 = X1
0.00/0.39	       | ~ in(X0, powerset(X2))
0.00/0.39	       | ~ zip_tseitin0(sk_Xx(X1, X0, X2), X1, X0)
0.00/0.39	       | in(sk_Xx1(X1, X0, X2), X1)),
0.00/0.39	    inference('simplify', [status(thm)], ['60'])).
0.00/0.39	tff('62', plain,
0.00/0.39	    ![X0, X1, X2]:
0.00/0.39	      (~ $true
0.00/0.39	       | ~ in(sk_Xx(X1, X0, X2), X1)
0.00/0.39	       | in(sk_Xx1(X1, X0, X2), X1)
0.00/0.39	       | ~ in(X0, powerset(X2))
0.00/0.39	       | X0 = X1
0.00/0.39	       | ~ in(X1, powerset(X2))),
0.00/0.39	    inference('sup-', [status(thm)], ['51', '61'])).
0.00/0.39	tff('63', plain,
0.00/0.39	    ![X0, X1, X2]:
0.00/0.39	      (~ in(X1, powerset(X2))
0.00/0.39	       | X0 = X1
0.00/0.39	       | ~ in(X0, powerset(X2))
0.00/0.39	       | in(sk_Xx1(X1, X0, X2), X1)
0.00/0.39	       | ~ in(sk_Xx(X1, X0, X2), X1)),
0.00/0.39	    inference('simplify', [status(thm)], ['62'])).
0.00/0.39	tff('64', plain,
0.00/0.39	    ![X0, X1, X2]:
0.00/0.39	      (~ $true
0.00/0.39	       | in(sk_Xx(X1, X0, X2), X0)
0.00/0.39	       | in(sk_Xx1(X1, X0, X2), X1)
0.00/0.39	       | ~ in(X0, powerset(X2))
0.00/0.39	       | X0 = X1
0.00/0.39	       | ~ in(X1, powerset(X2))),
0.00/0.39	    inference('sup-', [status(thm)], ['39', '61'])).
0.00/0.39	tff('65', plain,
0.00/0.39	    ![X0, X1, X2]:
0.00/0.39	      (~ in(X1, powerset(X2))
0.00/0.39	       | X0 = X1
0.00/0.39	       | ~ in(X0, powerset(X2))
0.00/0.39	       | in(sk_Xx1(X1, X0, X2), X1)
0.00/0.39	       | in(sk_Xx(X1, X0, X2), X0)),
0.00/0.39	    inference('simplify', [status(thm)], ['64'])).
0.00/0.39	tff('66', plain,
0.00/0.39	    ![X0, X1, X2, X3, X4]:
0.00/0.39	      (~ $true
0.00/0.39	       | in(
0.00/0.39	           sk_Xx1(X4, binintersect(setminus(X1, X2), setminus(X1, X0)), X3), 
0.00/0.39	           X4)
0.00/0.39	       | ~ in(binintersect(setminus(X1, X2), setminus(X1, X0)), powerset(X3))
0.00/0.39	       | binintersect(setminus(X1, X2), setminus(X1, X0)) = X4
0.00/0.39	       | ~ in(X4, powerset(X3))
0.00/0.39	       | ~ in(X2, powerset(X1))
0.00/0.39	       | ~ in(
0.00/0.39	             sk_Xx(X4, binintersect(setminus(X1, X2), setminus(X1, X0)), X3), 
0.00/0.39	             X1)
0.00/0.39	       | in(sk_Xx(X4, binintersect(setminus(X1, X2), setminus(X1, X0)), X3), 
0.00/0.39	           setminus(X1, binunion(X2, X0)))
0.00/0.39	       | ~ in(X0, powerset(X1))),
0.00/0.39	    inference('sup-', [status(thm)], ['65', '48'])).
0.00/0.39	tff('67', plain,
0.00/0.39	    ![X0, X1, X2, X3, X4]:
0.00/0.39	      (~ in(X0, powerset(X1))
0.00/0.39	       | in(sk_Xx(X4, binintersect(setminus(X1, X2), setminus(X1, X0)), X3), 
0.00/0.39	           setminus(X1, binunion(X2, X0)))
0.00/0.39	       | ~ in(
0.00/0.39	             sk_Xx(X4, binintersect(setminus(X1, X2), setminus(X1, X0)), X3), 
0.00/0.39	             X1)
0.00/0.39	       | ~ in(X2, powerset(X1))
0.00/0.39	       | ~ in(X4, powerset(X3))
0.00/0.39	       | binintersect(setminus(X1, X2), setminus(X1, X0)) = X4
0.00/0.39	       | ~ in(binintersect(setminus(X1, X2), setminus(X1, X0)), powerset(X3))
0.00/0.39	       | in(
0.00/0.39	           sk_Xx1(X4, binintersect(setminus(X1, X2), setminus(X1, X0)), X3), 
0.00/0.39	           X4)),
0.00/0.39	    inference('simplify', [status(thm)], ['66'])).
0.00/0.39	tff('68', plain,
0.00/0.39	    ![X0, X1, X2]:
0.00/0.39	      (~ $true
0.00/0.39	       | ~ in(sk_Xx1(X1, X0, X2), X0)
0.00/0.39	       | ~ zip_tseitin0(sk_Xx(X1, X0, X2), X1, X0)
0.00/0.39	       | ~ in(X0, powerset(X2))
0.00/0.40	       | X0 = X1
0.00/0.40	       | ~ in(X1, powerset(X2))),
0.00/0.40	    inference('sup-', [status(thm)], ['30', '59'])).
0.00/0.40	tff('69', plain,
0.00/0.40	    ![X0, X1, X2]:
0.00/0.40	      (~ in(X1, powerset(X2))
0.00/0.40	       | X0 = X1
0.00/0.40	       | ~ in(X0, powerset(X2))
0.00/0.40	       | ~ zip_tseitin0(sk_Xx(X1, X0, X2), X1, X0)
0.00/0.40	       | ~ in(sk_Xx1(X1, X0, X2), X0)),
0.00/0.40	    inference('simplify', [status(thm)], ['68'])).
0.00/0.40	tff('70', plain,
0.00/0.40	    ![X0, X1, X2]:
0.00/0.40	      (~ $true
0.00/0.40	       | in(sk_Xx(X1, X0, X2), X0)
0.00/0.40	       | ~ in(sk_Xx1(X1, X0, X2), X0)
0.00/0.40	       | ~ in(X0, powerset(X2))
0.00/0.40	       | X0 = X1
0.00/0.40	       | ~ in(X1, powerset(X2))),
0.00/0.40	    inference('sup-', [status(thm)], ['39', '69'])).
0.00/0.40	tff('71', plain,
0.00/0.40	    ![X0, X1, X2]:
0.00/0.40	      (~ in(X1, powerset(X2))
0.00/0.40	       | X0 = X1
0.00/0.40	       | ~ in(X0, powerset(X2))
0.00/0.40	       | ~ in(sk_Xx1(X1, X0, X2), X0)
0.00/0.40	       | in(sk_Xx(X1, X0, X2), X0)),
0.00/0.40	    inference('simplify', [status(thm)], ['70'])).
0.00/0.40	tff('72', plain,
0.00/0.40	    ![X0, X1, X2, X3, X4]:
0.00/0.40	      (~ $true
0.00/0.40	       | ~ in(X2, powerset(X1))
0.00/0.40	       | ~ in(
0.00/0.40	             sk_Xx1(X4, binintersect(setminus(X1, X2), setminus(X1, X0)), X3), 
0.00/0.40	             X1)
0.00/0.40	       | ~ in(
0.00/0.40	             sk_Xx1(X4, binintersect(setminus(X1, X2), setminus(X1, X0)), X3), 
0.00/0.40	             setminus(X1, binunion(X2, X0)))
0.00/0.40	       | ~ in(X0, powerset(X1))
0.00/0.40	       | in(sk_Xx(X4, binintersect(setminus(X1, X2), setminus(X1, X0)), X3), 
0.00/0.40	           binintersect(setminus(X1, X2), setminus(X1, X0)))
0.00/0.40	       | ~ in(binintersect(setminus(X1, X2), setminus(X1, X0)), powerset(X3))
0.00/0.40	       | binintersect(setminus(X1, X2), setminus(X1, X0)) = X4
0.00/0.40	       | ~ in(X4, powerset(X3))),
0.00/0.40	    inference('sup-', [status(thm)], ['29', '71'])).
0.00/0.40	tff('73', plain,
0.00/0.40	    ![X0, X1, X2, X3, X4]:
0.00/0.40	      (~ in(X4, powerset(X3))
0.00/0.40	       | binintersect(setminus(X1, X2), setminus(X1, X0)) = X4
0.00/0.40	       | ~ in(binintersect(setminus(X1, X2), setminus(X1, X0)), powerset(X3))
0.00/0.40	       | in(sk_Xx(X4, binintersect(setminus(X1, X2), setminus(X1, X0)), X3), 
0.00/0.40	           binintersect(setminus(X1, X2), setminus(X1, X0)))
0.00/0.40	       | ~ in(X0, powerset(X1))
0.00/0.40	       | ~ in(
0.00/0.40	             sk_Xx1(X4, binintersect(setminus(X1, X2), setminus(X1, X0)), X3), 
0.00/0.40	             setminus(X1, binunion(X2, X0)))
0.00/0.40	       | ~ in(
0.00/0.40	             sk_Xx1(X4, binintersect(setminus(X1, X2), setminus(X1, X0)), X3), 
0.00/0.40	             X1)
0.00/0.40	       | ~ in(X2, powerset(X1))),
0.00/0.40	    inference('simplify', [status(thm)], ['72'])).
0.00/0.40	tff('74', plain,
0.00/0.40	    ![X0, X1, X2, X3, X4]:
0.00/0.40	      (~ $true
0.00/0.40	       | ~ in(X2, powerset(X1))
0.00/0.40	       | ~ in(
0.00/0.40	             sk_Xx1(X4, binintersect(setminus(X1, X2), setminus(X1, X0)), X3), 
0.00/0.40	             X1)
0.00/0.40	       | ~ in(
0.00/0.40	             sk_Xx1(X4, binintersect(setminus(X1, X2), setminus(X1, X0)), X3), 
0.00/0.40	             setminus(X1, binunion(X2, X0)))
0.00/0.40	       | ~ in(X0, powerset(X1))
0.00/0.40	       | ~ in(binintersect(setminus(X1, X2), setminus(X1, X0)), powerset(X3))
0.00/0.40	       | binintersect(setminus(X1, X2), setminus(X1, X0)) = X4
0.00/0.40	       | ~ in(X4, powerset(X3))
0.00/0.40	       | ~ in(X2, powerset(X1))
0.00/0.40	       | ~ in(
0.00/0.40	             sk_Xx(X4, binintersect(setminus(X1, X2), setminus(X1, X0)), X3), 
0.00/0.40	             X1)
0.00/0.40	       | in(sk_Xx(X4, binintersect(setminus(X1, X2), setminus(X1, X0)), X3), 
0.00/0.40	           setminus(X1, binunion(X2, X0)))
0.00/0.40	       | ~ in(X0, powerset(X1))),
0.00/0.40	    inference('sup-', [status(thm)], ['73', '48'])).
0.00/0.40	tff('75', plain,
0.00/0.40	    ![X0, X1, X2, X3, X4]:
0.00/0.40	      (in(sk_Xx(X4, binintersect(setminus(X1, X2), setminus(X1, X0)), X3), 
0.00/0.40	         setminus(X1, binunion(X2, X0)))
0.00/0.40	       | ~ in(
0.00/0.40	             sk_Xx(X4, binintersect(setminus(X1, X2), setminus(X1, X0)), X3), 
0.00/0.40	             X1)
0.00/0.40	       | ~ in(X4, powerset(X3))
0.00/0.40	       | binintersect(setminus(X1, X2), setminus(X1, X0)) = X4
0.00/0.40	       | ~ in(binintersect(setminus(X1, X2), setminus(X1, X0)), powerset(X3))
0.00/0.40	       | ~ in(X0, powerset(X1))
0.00/0.40	       | ~ in(
0.00/0.40	             sk_Xx1(X4, binintersect(setminus(X1, X2), setminus(X1, X0)), X3), 
0.00/0.40	             setminus(X1, binunion(X2, X0)))
0.00/0.40	       | ~ in(
0.00/0.40	             sk_Xx1(X4, binintersect(setminus(X1, X2), setminus(X1, X0)), X3), 
0.00/0.40	             X1)
0.00/0.40	       | ~ in(X2, powerset(X1))),
0.00/0.40	    inference('simplify', [status(thm)], ['74'])).
0.00/0.40	tff('76', plain,
0.00/0.40	    ![X0, X1, X2, X3]:
0.00/0.40	      (~ $true
0.00/0.40	       | ~ in(binintersect(setminus(X2, X1), setminus(X2, X0)), powerset(X3))
0.00/0.40	       | binintersect(setminus(X2, X1), setminus(X2, X0))
0.00/0.40	          = setminus(X2, binunion(X1, X0))
0.00/0.40	       | ~ in(setminus(X2, binunion(X1, X0)), powerset(X3))
0.00/0.40	       | ~ in(X1, powerset(X2))
0.00/0.40	       | ~ in(
0.00/0.40	             sk_Xx(setminus(X2, binunion(X1, X0)), 
0.00/0.40	               binintersect(setminus(X2, X1), setminus(X2, X0)), X3), X2)
0.00/0.40	       | in(
0.00/0.40	           sk_Xx(setminus(X2, binunion(X1, X0)), 
0.00/0.40	             binintersect(setminus(X2, X1), setminus(X2, X0)), X3), 
0.00/0.40	           setminus(X2, binunion(X1, X0)))
0.00/0.40	       | ~ in(X0, powerset(X2))
0.00/0.40	       | ~ in(X1, powerset(X2))
0.00/0.40	       | ~ in(
0.00/0.40	             sk_Xx1(setminus(X2, binunion(X1, X0)), 
0.00/0.40	               binintersect(setminus(X2, X1), setminus(X2, X0)), X3), X2)
0.00/0.40	       | ~ in(X0, powerset(X2))
0.00/0.40	       | ~ in(binintersect(setminus(X2, X1), setminus(X2, X0)), powerset(X3))
0.00/0.40	       | binintersect(setminus(X2, X1), setminus(X2, X0))
0.00/0.40	          = setminus(X2, binunion(X1, X0))
0.00/0.40	       | ~ in(setminus(X2, binunion(X1, X0)), powerset(X3))
0.00/0.40	       | ~ in(
0.00/0.40	             sk_Xx(setminus(X2, binunion(X1, X0)), 
0.00/0.40	               binintersect(setminus(X2, X1), setminus(X2, X0)), X3), X2)
0.00/0.40	       | in(
0.00/0.40	           sk_Xx(setminus(X2, binunion(X1, X0)), 
0.00/0.40	             binintersect(setminus(X2, X1), setminus(X2, X0)), X3), 
0.00/0.40	           setminus(X2, binunion(X1, X0)))),
0.00/0.40	    inference('sup-', [status(thm)], ['67', '75'])).
0.00/0.40	tff('77', plain,
0.00/0.40	    ![X0, X1, X2, X3]:
0.00/0.40	      (~ in(
0.00/0.40	           sk_Xx1(setminus(X2, binunion(X1, X0)), 
0.00/0.40	             binintersect(setminus(X2, X1), setminus(X2, X0)), X3), X2)
0.00/0.40	       | ~ in(X0, powerset(X2))
0.00/0.40	       | in(
0.00/0.40	           sk_Xx(setminus(X2, binunion(X1, X0)), 
0.00/0.40	             binintersect(setminus(X2, X1), setminus(X2, X0)), X3), 
0.00/0.40	           setminus(X2, binunion(X1, X0)))
0.00/0.40	       | ~ in(
0.00/0.40	             sk_Xx(setminus(X2, binunion(X1, X0)), 
0.00/0.40	               binintersect(setminus(X2, X1), setminus(X2, X0)), X3), X2)
0.00/0.40	       | ~ in(X1, powerset(X2))
0.00/0.40	       | ~ in(setminus(X2, binunion(X1, X0)), powerset(X3))
0.00/0.40	       | binintersect(setminus(X2, X1), setminus(X2, X0))
0.00/0.40	          = setminus(X2, binunion(X1, X0))
0.00/0.40	       | ~ in(binintersect(setminus(X2, X1), setminus(X2, X0)), powerset(X3))),
0.00/0.40	    inference('simplify', [status(thm)], ['76'])).
0.00/0.40	tff('78', plain,
0.00/0.40	    ![X0, X1, X2]:
0.00/0.40	      (~ $true
0.00/0.40	       | ~ in(sk_Xx(X1, X0, X2), X1)
0.00/0.40	       | ~ in(sk_Xx1(X1, X0, X2), X0)
0.00/0.40	       | ~ in(X0, powerset(X2))
0.00/0.40	       | X0 = X1
0.00/0.40	       | ~ in(X1, powerset(X2))),
0.00/0.40	    inference('sup-', [status(thm)], ['51', '69'])).
0.00/0.40	tff('79', plain,
0.00/0.40	    ![X0, X1, X2]:
0.00/0.40	      (~ in(X1, powerset(X2))
0.00/0.40	       | X0 = X1
0.00/0.40	       | ~ in(X0, powerset(X2))
0.00/0.40	       | ~ in(sk_Xx1(X1, X0, X2), X0)
0.00/0.40	       | ~ in(sk_Xx(X1, X0, X2), X1)),
0.00/0.40	    inference('simplify', [status(thm)], ['78'])).
0.00/0.40	tff('80', plain,
0.00/0.40	    ![X0, X1, X2, X3, X4]:
0.00/0.40	      (~ $true
0.00/0.40	       | ~ in(X2, powerset(X1))
0.00/0.40	       | ~ in(
0.00/0.40	             sk_Xx1(X4, binintersect(setminus(X1, X2), setminus(X1, X0)), X3), 
0.00/0.40	             X1)
0.00/0.40	       | ~ in(
0.00/0.40	             sk_Xx1(X4, binintersect(setminus(X1, X2), setminus(X1, X0)), X3), 
0.00/0.40	             setminus(X1, binunion(X2, X0)))
0.00/0.40	       | ~ in(X0, powerset(X1))
0.00/0.40	       | ~ in(
0.00/0.40	             sk_Xx(X4, binintersect(setminus(X1, X2), setminus(X1, X0)), X3), 
0.00/0.40	             X4)
0.00/0.40	       | ~ in(binintersect(setminus(X1, X2), setminus(X1, X0)), powerset(X3))
0.00/0.40	       | binintersect(setminus(X1, X2), setminus(X1, X0)) = X4
0.00/0.40	       | ~ in(X4, powerset(X3))),
0.00/0.40	    inference('sup-', [status(thm)], ['29', '79'])).
0.00/0.40	tff('81', plain,
0.00/0.40	    ![X0, X1, X2, X3, X4]:
0.00/0.40	      (~ in(X4, powerset(X3))
0.00/0.40	       | binintersect(setminus(X1, X2), setminus(X1, X0)) = X4
0.00/0.40	       | ~ in(binintersect(setminus(X1, X2), setminus(X1, X0)), powerset(X3))
0.00/0.40	       | ~ in(
0.00/0.40	             sk_Xx(X4, binintersect(setminus(X1, X2), setminus(X1, X0)), X3), 
0.00/0.40	             X4)
0.00/0.40	       | ~ in(X0, powerset(X1))
0.00/0.40	       | ~ in(
0.00/0.40	             sk_Xx1(X4, binintersect(setminus(X1, X2), setminus(X1, X0)), X3), 
0.00/0.40	             setminus(X1, binunion(X2, X0)))
0.00/0.40	       | ~ in(
0.00/0.40	             sk_Xx1(X4, binintersect(setminus(X1, X2), setminus(X1, X0)), X3), 
0.00/0.40	             X1)
0.00/0.40	       | ~ in(X2, powerset(X1))),
0.00/0.40	    inference('simplify', [status(thm)], ['80'])).
0.00/0.40	tff('82', plain,
0.00/0.40	    ![X0, X1, X2, X3]:
0.00/0.40	      (~ $true
0.00/0.40	       | ~ in(binintersect(setminus(X2, X1), setminus(X2, X0)), powerset(X3))
0.00/0.40	       | binintersect(setminus(X2, X1), setminus(X2, X0))
0.00/0.40	          = setminus(X2, binunion(X1, X0))
0.00/0.40	       | ~ in(setminus(X2, binunion(X1, X0)), powerset(X3))
0.00/0.40	       | ~ in(X1, powerset(X2))
0.00/0.40	       | ~ in(
0.00/0.40	             sk_Xx(setminus(X2, binunion(X1, X0)), 
0.00/0.40	               binintersect(setminus(X2, X1), setminus(X2, X0)), X3), X2)
0.00/0.40	       | ~ in(X0, powerset(X2))
0.00/0.40	       | ~ in(
0.00/0.40	             sk_Xx1(setminus(X2, binunion(X1, X0)), 
0.00/0.40	               binintersect(setminus(X2, X1), setminus(X2, X0)), X3), X2)
0.00/0.40	       | ~ in(X1, powerset(X2))
0.00/0.40	       | ~ in(
0.00/0.40	             sk_Xx1(setminus(X2, binunion(X1, X0)), 
0.00/0.40	               binintersect(setminus(X2, X1), setminus(X2, X0)), X3), X2)
0.00/0.40	       | ~ in(
0.00/0.40	             sk_Xx1(setminus(X2, binunion(X1, X0)), 
0.00/0.40	               binintersect(setminus(X2, X1), setminus(X2, X0)), X3), 
0.00/0.40	             setminus(X2, binunion(X1, X0)))
0.00/0.40	       | ~ in(X0, powerset(X2))
0.00/0.40	       | ~ in(binintersect(setminus(X2, X1), setminus(X2, X0)), powerset(X3))
0.00/0.40	       | binintersect(setminus(X2, X1), setminus(X2, X0))
0.00/0.40	          = setminus(X2, binunion(X1, X0))
0.00/0.40	       | ~ in(setminus(X2, binunion(X1, X0)), powerset(X3))),
0.00/0.40	    inference('sup-', [status(thm)], ['77', '81'])).
0.00/0.40	tff('83', plain,
0.00/0.40	    ![X0, X1, X2, X3]:
0.00/0.40	      (~ in(
0.00/0.40	           sk_Xx1(setminus(X2, binunion(X1, X0)), 
0.00/0.40	             binintersect(setminus(X2, X1), setminus(X2, X0)), X3), 
0.00/0.40	           setminus(X2, binunion(X1, X0)))
0.00/0.40	       | ~ in(
0.00/0.40	             sk_Xx1(setminus(X2, binunion(X1, X0)), 
0.00/0.40	               binintersect(setminus(X2, X1), setminus(X2, X0)), X3), X2)
0.00/0.40	       | ~ in(X0, powerset(X2))
0.00/0.40	       | ~ in(
0.00/0.40	             sk_Xx(setminus(X2, binunion(X1, X0)), 
0.00/0.40	               binintersect(setminus(X2, X1), setminus(X2, X0)), X3), X2)
0.00/0.40	       | ~ in(X1, powerset(X2))
0.00/0.40	       | ~ in(setminus(X2, binunion(X1, X0)), powerset(X3))
0.00/0.40	       | binintersect(setminus(X2, X1), setminus(X2, X0))
0.00/0.40	          = setminus(X2, binunion(X1, X0))
0.00/0.40	       | ~ in(binintersect(setminus(X2, X1), setminus(X2, X0)), powerset(X3))),
0.00/0.40	    inference('simplify', [status(thm)], ['82'])).
0.00/0.40	tff('84', plain,
0.00/0.40	    ![X0, X1, X2, X3]:
0.00/0.40	      (~ $true
0.00/0.40	       | ~ in(
0.00/0.40	             sk_Xx(setminus(X2, binunion(X1, X0)), 
0.00/0.40	               binintersect(setminus(X2, X1), setminus(X2, X0)), X3), 
0.00/0.40	             setminus(X2, binunion(X1, X0)))
0.00/0.40	       | ~ in(binintersect(setminus(X2, X1), setminus(X2, X0)), powerset(X3))
0.00/0.40	       | binintersect(setminus(X2, X1), setminus(X2, X0))
0.00/0.40	          = setminus(X2, binunion(X1, X0))
0.00/0.40	       | ~ in(setminus(X2, binunion(X1, X0)), powerset(X3))
0.00/0.40	       | ~ in(binintersect(setminus(X2, X1), setminus(X2, X0)), powerset(X3))
0.00/0.40	       | binintersect(setminus(X2, X1), setminus(X2, X0))
0.00/0.40	          = setminus(X2, binunion(X1, X0))
0.00/0.40	       | ~ in(setminus(X2, binunion(X1, X0)), powerset(X3))
0.00/0.40	       | ~ in(X1, powerset(X2))
0.00/0.40	       | ~ in(
0.00/0.40	             sk_Xx(setminus(X2, binunion(X1, X0)), 
0.00/0.40	               binintersect(setminus(X2, X1), setminus(X2, X0)), X3), X2)
0.00/0.40	       | ~ in(X0, powerset(X2))
0.00/0.40	       | ~ in(
0.00/0.40	             sk_Xx1(setminus(X2, binunion(X1, X0)), 
0.00/0.40	               binintersect(setminus(X2, X1), setminus(X2, X0)), X3), X2)),
0.00/0.40	    inference('sup-', [status(thm)], ['63', '83'])).
0.00/0.40	tff('85', plain,
0.00/0.40	    ![X0, X1, X2, X3]:
0.00/0.40	      (~ in(
0.00/0.40	           sk_Xx1(setminus(X2, binunion(X1, X0)), 
0.00/0.40	             binintersect(setminus(X2, X1), setminus(X2, X0)), X3), X2)
0.00/0.40	       | ~ in(X0, powerset(X2))
0.00/0.40	       | ~ in(
0.00/0.40	             sk_Xx(setminus(X2, binunion(X1, X0)), 
0.00/0.40	               binintersect(setminus(X2, X1), setminus(X2, X0)), X3), X2)
0.00/0.40	       | ~ in(X1, powerset(X2))
0.00/0.40	       | ~ in(setminus(X2, binunion(X1, X0)), powerset(X3))
0.00/0.40	       | binintersect(setminus(X2, X1), setminus(X2, X0))
0.00/0.40	          = setminus(X2, binunion(X1, X0))
0.00/0.40	       | ~ in(binintersect(setminus(X2, X1), setminus(X2, X0)), powerset(X3))
0.00/0.40	       | ~ in(
0.00/0.40	             sk_Xx(setminus(X2, binunion(X1, X0)), 
0.00/0.40	               binintersect(setminus(X2, X1), setminus(X2, X0)), X3), 
0.00/0.40	             setminus(X2, binunion(X1, X0)))),
0.00/0.40	    inference('simplify', [status(thm)], ['84'])).
0.00/0.40	tff('86', plain,
0.00/0.40	    ![X0, X1, X2, X3]:
0.00/0.40	      (~ in(binintersect(setminus(X2, X1), setminus(X2, X0)), powerset(X3))
0.00/0.40	       | binintersect(setminus(X2, X1), setminus(X2, X0))
0.00/0.40	          = setminus(X2, binunion(X1, X0))
0.00/0.40	       | ~ in(setminus(X2, binunion(X1, X0)), powerset(X3))
0.00/0.40	       | ~ in(X1, powerset(X2))
0.00/0.40	       | ~ in(
0.00/0.40	             sk_Xx(setminus(X2, binunion(X1, X0)), 
0.00/0.40	               binintersect(setminus(X2, X1), setminus(X2, X0)), X3), X2)
0.00/0.40	       | ~ in(X0, powerset(X2))
0.00/0.40	       | ~ in(
0.00/0.40	             sk_Xx1(setminus(X2, binunion(X1, X0)), 
0.00/0.40	               binintersect(setminus(X2, X1), setminus(X2, X0)), X3), X2)),
0.00/0.40	    inference('clc', [status(thm)], ['85', '77'])).
0.00/0.40	tff('87', plain,
0.00/0.40	    ![X0, X1, X2]:
0.00/0.40	      (~ $true
0.00/0.40	       | ~ in(binintersect(setminus(X0, X2), setminus(X0, X1)), powerset(X0))
0.00/0.40	       | binintersect(setminus(X0, X2), setminus(X0, X1))
0.00/0.40	          = setminus(X0, binunion(X2, X1))
0.00/0.40	       | ~ in(setminus(X0, binunion(X2, X1)), powerset(X0))
0.00/0.40	       | ~ in(X2, powerset(X0))
0.00/0.40	       | ~ in(X1, powerset(X0))
0.00/0.40	       | ~ in(X1, powerset(X0))
0.00/0.40	       | ~ in(
0.00/0.40	             sk_Xx(setminus(X0, binunion(X2, X1)), 
0.00/0.40	               binintersect(setminus(X0, X2), setminus(X0, X1)), X0), X0)
0.00/0.40	       | ~ in(X2, powerset(X0))
0.00/0.40	       | ~ in(setminus(X0, binunion(X2, X1)), powerset(X0))
0.00/0.40	       | binintersect(setminus(X0, X2), setminus(X0, X1))
0.00/0.40	          = setminus(X0, binunion(X2, X1))
0.00/0.40	       | ~ in(binintersect(setminus(X0, X2), setminus(X0, X1)), powerset(X0))),
0.00/0.40	    inference('sup-', [status(thm)], ['57', '86'])).
0.00/0.40	tff('88', plain,
0.00/0.40	    ![X0, X1, X2]:
0.00/0.40	      (~ in(
0.00/0.40	           sk_Xx(setminus(X0, binunion(X2, X1)), 
0.00/0.40	             binintersect(setminus(X0, X2), setminus(X0, X1)), X0), X0)
0.00/0.40	       | ~ in(X1, powerset(X0))
0.00/0.40	       | ~ in(X2, powerset(X0))
0.00/0.40	       | ~ in(setminus(X0, binunion(X2, X1)), powerset(X0))
0.00/0.40	       | binintersect(setminus(X0, X2), setminus(X0, X1))
0.00/0.40	          = setminus(X0, binunion(X2, X1))
0.00/0.40	       | ~ in(binintersect(setminus(X0, X2), setminus(X0, X1)), powerset(X0))),
0.00/0.40	    inference('simplify', [status(thm)], ['87'])).
0.00/0.40	tff('89', plain,
0.00/0.40	    ![X0, X1, X2]:
0.00/0.40	      (~ in(binintersect(setminus(X0, X2), setminus(X0, X1)), powerset(X0))
0.00/0.40	       | binintersect(setminus(X0, X2), setminus(X0, X1))
0.00/0.40	          = setminus(X0, binunion(X2, X1))
0.00/0.40	       | ~ in(setminus(X0, binunion(X2, X1)), powerset(X0))
0.00/0.40	       | ~ in(X2, powerset(X0))
0.00/0.40	       | ~ in(X1, powerset(X0))),
0.00/0.40	    inference('clc', [status(thm)], ['88', '38'])).
0.00/0.40	tff('90', plain,
0.00/0.40	    ![X0, X1, X2]:
0.00/0.40	      (~ $true
0.00/0.40	       | ~ in(setminus(X0, X2), powerset(X0))
0.00/0.40	       | ~ in(setminus(X0, X1), powerset(X0))
0.00/0.40	       | ~ in(X1, powerset(X0))
0.00/0.40	       | ~ in(X2, powerset(X0))
0.00/0.40	       | ~ in(setminus(X0, binunion(X2, X1)), powerset(X0))
0.00/0.40	       | binintersect(setminus(X0, X2), setminus(X0, X1))
0.00/0.40	          = setminus(X0, binunion(X2, X1))),
0.00/0.40	    inference('sup-', [status(thm)], ['7', '89'])).
0.00/0.40	tff('91', plain,
0.00/0.40	    ![X0, X1, X2]:
0.00/0.40	      (binintersect(setminus(X0, X2), setminus(X0, X1))
0.00/0.40	        = setminus(X0, binunion(X2, X1))
0.00/0.40	       | ~ in(setminus(X0, binunion(X2, X1)), powerset(X0))
0.00/0.40	       | ~ in(X2, powerset(X0))
0.00/0.40	       | ~ in(X1, powerset(X0))
0.00/0.40	       | ~ in(setminus(X0, X1), powerset(X0))
0.00/0.40	       | ~ in(setminus(X0, X2), powerset(X0))),
0.00/0.40	    inference('simplify', [status(thm)], ['90'])).
0.00/0.40	tff('92', plain,
0.00/0.40	    ![X0, X1, X2]:
0.00/0.40	      (~ in(setminus(X0, X2), powerset(X0))
0.00/0.40	       | ~ in(X1, powerset(X0))
0.00/0.40	       | ~ in(X2, powerset(X0))
0.00/0.40	       | ~ in(setminus(X0, binunion(X2, X1)), powerset(X0))
0.00/0.40	       | binintersect(setminus(X0, X2), setminus(X0, X1))
0.00/0.40	          = setminus(X0, binunion(X2, X1))),
0.00/0.40	    inference('clc', [status(thm)], ['91', '3'])).
0.00/0.40	tff('93', plain,
0.00/0.40	    ![X0, X1, X2]:
0.00/0.40	      (binintersect(setminus(X0, X2), setminus(X0, X1))
0.00/0.40	        = setminus(X0, binunion(X2, X1))
0.00/0.40	       | ~ in(setminus(X0, binunion(X2, X1)), powerset(X0))
0.00/0.40	       | ~ in(X2, powerset(X0))
0.00/0.40	       | ~ in(X1, powerset(X0))),
0.00/0.40	    inference('clc', [status(thm)], ['92', '3'])).
0.00/0.40	tff('94', plain,
0.00/0.40	    ![X0, X1, X2]:
0.00/0.40	      (~ $true
0.00/0.40	       | ~ in(binunion(X2, X1), powerset(X0))
0.00/0.40	       | ~ in(X1, powerset(X0))
0.00/0.40	       | ~ in(X2, powerset(X0))
0.00/0.40	       | binintersect(setminus(X0, X2), setminus(X0, X1))
0.00/0.40	          = setminus(X0, binunion(X2, X1))),
0.00/0.40	    inference('sup-', [status(thm)], ['3', '93'])).
0.00/0.40	tff('95', plain,
0.00/0.40	    ![X0, X1, X2]:
0.00/0.40	      (binintersect(setminus(X0, X2), setminus(X0, X1))
0.00/0.40	        = setminus(X0, binunion(X2, X1))
0.00/0.40	       | ~ in(X2, powerset(X0))
0.00/0.40	       | ~ in(X1, powerset(X0))
0.00/0.40	       | ~ in(binunion(X2, X1), powerset(X0))),
0.00/0.40	    inference('simplify', [status(thm)], ['94'])).
0.00/0.40	tff(binunionT_lem, axiom,
0.00/0.40	  (binunionT_lem <=>
0.00/0.40	   (![A,X]:
0.00/0.40	      (in(X,powerset(A)) =>
0.00/0.40	       (![Y]: (in(Y,powerset(A)) => in(binunion(X,Y),powerset(A)))))))).
0.00/0.40	tff('96', plain,
0.00/0.40	    ![X3, X4, X5]:
0.00/0.40	      (~ in(X3, powerset(X4))
0.00/0.40	       | in(binunion(X3, X5), powerset(X4))
0.00/0.40	       | ~ in(X5, powerset(X4))
0.00/0.40	       | ~ binunionT_lem),
0.00/0.40	    inference('cnf', [status(esa)], [binunionT_lem])).
0.00/0.40	tff('97', plain, binunionT_lem, inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.40	tff('98', plain,
0.00/0.40	    ![X3, X4, X5]:
0.00/0.40	      (~ in(X3, powerset(X4))
0.00/0.40	       | in(binunion(X3, X5), powerset(X4))
0.00/0.40	       | ~ in(X5, powerset(X4))
0.00/0.40	       | ~ $true),
0.00/0.40	    inference('demod', [status(thm)], ['96', '97'])).
0.00/0.40	tff('99', plain,
0.00/0.40	    ![X3, X4, X5]:
0.00/0.40	      (~ in(X5, powerset(X4))
0.00/0.40	       | in(binunion(X3, X5), powerset(X4))
0.00/0.40	       | ~ in(X3, powerset(X4))),
0.00/0.40	    inference('simplify', [status(thm)], ['98'])).
0.00/0.40	tff('100', plain,
0.00/0.40	    ![X0, X1, X2]:
0.00/0.40	      (~ in(X1, powerset(X0))
0.00/0.40	       | ~ in(X2, powerset(X0))
0.00/0.40	       | binintersect(setminus(X0, X2), setminus(X0, X1))
0.00/0.40	          = setminus(X0, binunion(X2, X1))),
0.00/0.40	    inference('clc', [status(thm)], ['95', '99'])).
0.00/0.40	tff('101', plain,
0.00/0.40	    setminus(sk_A6, binunion(sk_X6, sk_Y5))
0.00/0.40	     != binintersect(setminus(sk_A6, sk_X6), setminus(sk_A6, sk_Y5)),
0.00/0.40	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.40	tff('102', plain,
0.00/0.40	    (setminus(sk_A6, binunion(sk_X6, sk_Y5))
0.00/0.40	      != setminus(sk_A6, binunion(sk_X6, sk_Y5))
0.00/0.40	     | ~ in(sk_X6, powerset(sk_A6))
0.00/0.40	     | ~ in(sk_Y5, powerset(sk_A6))),
0.00/0.40	    inference('sup-', [status(thm)], ['100', '101'])).
0.00/0.40	tff('103', plain, in(sk_X6, powerset(sk_A6)),
0.00/0.40	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.40	tff('104', plain, in(sk_Y5, powerset(sk_A6)),
0.00/0.40	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.40	tff('105', plain,
0.00/0.40	    (setminus(sk_A6, binunion(sk_X6, sk_Y5))
0.00/0.40	      != setminus(sk_A6, binunion(sk_X6, sk_Y5))
0.00/0.40	     | ~ $true
0.00/0.40	     | ~ $true),
0.00/0.40	    inference('demod', [status(thm)], ['102', '103', '104'])).
0.00/0.40	tff('106', plain, $false, inference('simplify', [status(thm)], ['105'])).
0.00/0.40	
0.00/0.40	% SZS output end Refutation
0.00/0.40	EOF
