0.10/0.13	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.10/0.14	% Command    : run_portfolio.sh /export/starexec/sandbox2/benchmark/theBenchmark.p /export/starexec/sandbox2/tmp/tmp.lxmyGamSxY
0.15/0.39	% Computer   : n004.cluster.edu
0.15/0.39	% Model      : x86_64 x86_64
0.15/0.39	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.15/0.39	% Memory     : 8042.1875MB
0.15/0.39	% OS         : Linux 3.10.0-693.el7.x86_64
0.15/0.39	% CPULimit   : 960
0.15/0.39	% DateTime   : Thu Jul  2 07:03:44 EDT 2020
0.15/0.39	% CPUTime    : 
0.15/0.39	% Running portfolio for 120 s
0.15/0.39	% File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.15/0.39	% Number of cores: 8
0.15/0.39	% Python version: Python 3.6.8
0.15/0.39	% Running in HO mode
0.56/0.68	% Estimated wc time : 1286
0.56/0.68	% Estimated cpu time (7 cpus) : 183.71428571428572
0.61/0.75	% /export/starexec/sandbox2/solver/bin/lams/s6.sh running for 21s
0.61/0.77	% /export/starexec/sandbox2/solver/bin/lams/new_b3.2.norw.sh running for 15s
0.61/0.79	% /export/starexec/sandbox2/solver/bin/lams/b.rpo.sh running for 21s
0.61/0.80	% /export/starexec/sandbox2/solver/bin/lams/s6.ds.sh running for 10s
0.61/0.80	% /export/starexec/sandbox2/solver/bin/lams/c.s.2.sh running for 68s
0.61/0.80	% /export/starexec/sandbox2/solver/bin/lams/c.easy.sh running for 26s
0.61/0.80	% /export/starexec/sandbox2/solver/bin/lams/old_b3.avatar.sh running for 15s
14.52/2.75	% Solved by lams/old_b3.avatar.sh.
14.52/2.75	% done 2283 iterations in 1.872s
14.52/2.75	% SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
14.52/2.75	% SZS output start Refutation
14.52/2.75	tff(cTHM138, conjecture,
14.52/2.75	  (((((?[Xx]: cR(Xx)) <=> (![Xy]: cS(Xy))) <=>
14.52/2.75	     (?[Xx]: (![Xy]: (cQ(Xx) <=> cQ(Xy))))) <=>
14.52/2.75	    ((?[Xx]: (![Xy]: (cP(Xy) <=> cP(Xx)))) <=>
14.52/2.75	     ((![Xy]: cR(Xy)) <=> (?[Xx]: cQ(Xx))))) <=>
14.52/2.75	   ((((?[Xx]: cP(Xx)) <=> (![Xy]: cQ(Xy))) <=>
14.52/2.75	     (?[Xx]: (![Xy]: (cS(Xy) <=> cS(Xx))))) <=>
14.52/2.75	    (((?[Xx]: cS(Xx)) <=> (![Xy]: cP(Xy))) <=>
14.52/2.75	     (?[Xx]: (![Xy]: (cR(Xx) <=> cR(Xy)))))))).
14.52/2.75	tff(zf_stmt_0, negated_conjecture,
14.52/2.75	  (~
14.52/2.75	    (((((?[Xx]: cR(Xx)) <=> (![Xy]: cS(Xy))) <=>
14.52/2.75	       (?[Xx]: (![Xy]: (cQ(Xx) <=> cQ(Xy))))) <=>
14.52/2.75	      ((?[Xx]: (![Xy]: (cP(Xy) <=> cP(Xx)))) <=>
14.52/2.75	       ((![Xy]: cR(Xy)) <=> (?[Xx]: cQ(Xx))))) <=>
14.52/2.75	     ((((?[Xx]: cP(Xx)) <=> (![Xy]: cQ(Xy))) <=>
14.52/2.75	       (?[Xx]: (![Xy]: (cS(Xy) <=> cS(Xx))))) <=>
14.52/2.75	      (((?[Xx]: cS(Xx)) <=> (![Xy]: cP(Xy))) <=>
14.52/2.75	       (?[Xx]: (![Xy]: (cR(Xx) <=> cR(Xy))))))))).
14.52/2.75	tff('0', plain,
14.52/2.75	    ((((??((^[Y0 : $i]: cR(Y0)))) <=> (!!((^[Y0 : $i]: cS(Y0))))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.75	     ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	      ((!!((^[Y0 : $i]: cR(Y0)))) <=> (??((^[Y0 : $i]: cQ(Y0)))))))
14.52/2.75	     != ((((??((^[Y0 : $i]: cP(Y0)))) <=> (!!((^[Y0 : $i]: cQ(Y0))))) <=>
14.52/2.75	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) <=>
14.52/2.75	         (((??((^[Y0 : $i]: cS(Y0)))) <=> (!!((^[Y0 : $i]: cP(Y0))))) <=>
14.52/2.75	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.75	    inference('cnf', [status(esa)], [zf_stmt_0])).
14.52/2.75	tff('1', plain,
14.52/2.75	    ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.75	     ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	      ((!!(cR)) <=> (??(cQ)))))
14.52/2.75	     != ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) <=>
14.52/2.75	         (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.75	    inference('ho_norm', [status(thm)], ['0'])).
14.52/2.75	tff('2', plain,
14.52/2.75	    (~ ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.75	        ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	         ((!!(cR)) <=> (??(cQ)))))
14.52/2.75	     | ~ ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	           (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) <=>
14.52/2.75	          (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	           (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))),
14.52/2.75	    inference('lazy_cnf_xor', [status(thm)], ['1'])).
14.52/2.75	tff('3', plain,
14.52/2.75	    ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.75	      != ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	          ((!!(cR)) <=> (??(cQ))))
14.52/2.75	     | (((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	        (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	        != (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.75	    inference('simplify nested equalities', [status(thm)], ['2'])).
14.52/2.75	tff('4', plain,
14.52/2.75	    ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.75	      != ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	          ((!!(cR)) <=> (??(cQ)))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.75	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	               ((!!(cR)) <=> (??(cQ)))))),
14.52/2.75	    inference('split', [status(esa)], ['3'])).
14.52/2.75	tff('5', plain,
14.52/2.75	    (( (((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	        (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.75	      |  ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	          ((!!(cR)) <=> (??(cQ))))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.75	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	               ((!!(cR)) <=> (??(cQ)))))),
14.52/2.75	    inference('lazy_cnf_xor', [status(thm)], ['4'])).
14.52/2.75	tff('6', plain,
14.52/2.75	    ((((??(cR)) <=> (!!(cS)))
14.52/2.75	       = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
14.52/2.75	      | (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.75	         = ((!!(cR)) <=> (??(cQ)))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.75	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	               ((!!(cR)) <=> (??(cQ)))))),
14.52/2.75	    inference('simplify nested equalities', [status(thm)], ['5'])).
14.52/2.75	tff('7', plain,
14.52/2.75	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.75	      = ((!!(cR)) <=> (??(cQ))))
14.52/2.75	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.75	            = ((!!(cR)) <=> (??(cQ))))),
14.52/2.75	    inference('split', [status(esa)], ['6'])).
14.52/2.75	tff('8', plain,
14.52/2.75	    ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.75	      != ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	          ((!!(cR)) <=> (??(cQ)))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.75	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	               ((!!(cR)) <=> (??(cQ)))))),
14.52/2.75	    inference('split', [status(esa)], ['3'])).
14.52/2.75	tff('9', plain,
14.52/2.75	    ((~ (((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.75	      | ~ ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	           ((!!(cR)) <=> (??(cQ))))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.75	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	               ((!!(cR)) <=> (??(cQ)))))),
14.52/2.75	    inference('lazy_cnf_xor', [status(thm)], ['8'])).
14.52/2.75	tff('10', plain,
14.52/2.75	    ((((??(cR)) <=> (!!(cS)))
14.52/2.75	       != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
14.52/2.75	      | (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.75	         != ((!!(cR)) <=> (??(cQ)))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.75	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	               ((!!(cR)) <=> (??(cQ)))))),
14.52/2.75	    inference('simplify nested equalities', [status(thm)], ['9'])).
14.52/2.75	tff('11', plain,
14.52/2.75	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.75	      != ((!!(cR)) <=> (??(cQ))))
14.52/2.75	      <= (~
14.52/2.75	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.75	            = ((!!(cR)) <=> (??(cQ))))),
14.52/2.75	    inference('split', [status(esa)], ['10'])).
14.52/2.75	tff('12', plain,
14.52/2.75	    ((~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.75	      | ~ ((!!(cR)) <=> (??(cQ)))))
14.52/2.75	      <= (~
14.52/2.75	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.75	            = ((!!(cR)) <=> (??(cQ))))),
14.52/2.75	    inference('lazy_cnf_xor', [status(thm)], ['11'])).
14.52/2.75	tff('13', plain,
14.52/2.75	    ((~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.75	      | (!!(cR)) != (??(cQ))))
14.52/2.75	      <= (~
14.52/2.75	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.75	            = ((!!(cR)) <=> (??(cQ))))),
14.52/2.75	    inference('simplify nested equalities', [status(thm)], ['12'])).
14.52/2.75	tff('14', plain,
14.52/2.75	    (~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))))
14.52/2.75	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))))),
14.52/2.75	    inference('split', [status(esa)], ['13'])).
14.52/2.75	tff('15', plain,
14.52/2.75	    (~ ((!!(cR)) <=> (??(cQ))))
14.52/2.75	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))) & 
14.52/2.75	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.75	            = ((!!(cR)) <=> (??(cQ))))),
14.52/2.75	    inference('sup-', [status(thm)], ['7', '14'])).
14.52/2.75	tff('16', plain,
14.52/2.75	    ((!!(cR)) != (??(cQ)))
14.52/2.75	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))) & 
14.52/2.75	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.75	            = ((!!(cR)) <=> (??(cQ))))),
14.52/2.75	    inference('simplify nested equalities', [status(thm)], ['15'])).
14.52/2.75	tff('17', plain,
14.52/2.75	    (( (!!(cR)) |  (??(cQ))))
14.52/2.75	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))) & 
14.52/2.75	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.75	            = ((!!(cR)) <=> (??(cQ))))),
14.52/2.75	    inference('lazy_cnf_xor', [status(thm)], ['16'])).
14.52/2.75	tff('18', plain,
14.52/2.75	    ~
14.52/2.75	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.75	      = ((!!(cR)) <=> (??(cQ)))) | 
14.52/2.75	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))) | 
14.52/2.75	    ( (!!(cR))) | ( (??(cQ))), inference('split', [status(esa)], ['17'])).
14.52/2.75	tff('19', plain,
14.52/2.75	    (((??(cR)) <=> (!!(cS)))
14.52/2.75	      != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.75	      <= (~
14.52/2.75	          (((??(cR)) <=> (!!(cS)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
14.52/2.75	    inference('split', [status(esa)], ['10'])).
14.52/2.75	tff('20', plain,
14.52/2.75	    (( ((??(cR)) <=> (!!(cS)))
14.52/2.75	      |  (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))))
14.52/2.75	      <= (~
14.52/2.75	          (((??(cR)) <=> (!!(cS)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
14.52/2.75	    inference('lazy_cnf_xor', [status(thm)], ['19'])).
14.52/2.75	tff('21', plain,
14.52/2.75	    (((??(cR)) = (!!(cS))
14.52/2.75	      |  (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))))
14.52/2.75	      <= (~
14.52/2.75	          (((??(cR)) <=> (!!(cS)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
14.52/2.75	    inference('simplify nested equalities', [status(thm)], ['20'])).
14.52/2.75	tff('22', plain,
14.52/2.75	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.75	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
14.52/2.75	    inference('split', [status(esa)], ['21'])).
14.52/2.75	tff('23', plain,
14.52/2.75	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.75	      = ((!!(cR)) <=> (??(cQ))))
14.52/2.75	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.75	            = ((!!(cR)) <=> (??(cQ))))),
14.52/2.75	    inference('split', [status(esa)], ['6'])).
14.52/2.75	tff('24', plain,
14.52/2.75	    ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.75	     ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	      ((!!(cR)) <=> (??(cQ)))))
14.52/2.75	     != ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) <=>
14.52/2.75	         (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.75	    inference('ho_norm', [status(thm)], ['0'])).
14.52/2.75	tff('25', plain,
14.52/2.75	    ( ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	        (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.75	       ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	        ((!!(cR)) <=> (??(cQ)))))
14.52/2.75	     |  ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) <=>
14.52/2.75	         (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))),
14.52/2.75	    inference('lazy_cnf_xor', [status(thm)], ['24'])).
14.52/2.75	tff('26', plain,
14.52/2.75	    ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.75	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	         ((!!(cR)) <=> (??(cQ))))
14.52/2.75	     | (((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	        (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	        = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	           (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.75	    inference('simplify nested equalities', [status(thm)], ['25'])).
14.52/2.75	tff('27', plain,
14.52/2.75	    ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.75	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	         ((!!(cR)) <=> (??(cQ)))))
14.52/2.75	      <= (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.75	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	               ((!!(cR)) <=> (??(cQ)))))),
14.52/2.75	    inference('split', [status(esa)], ['26'])).
14.52/2.75	tff('28', plain,
14.52/2.75	    ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.75	      = (((!!(cR)) <=> (??(cQ))) <=> ((!!(cR)) <=> (??(cQ)))))
14.52/2.75	      <= (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.75	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	               ((!!(cR)) <=> (??(cQ))))) & 
14.52/2.75	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.75	            = ((!!(cR)) <=> (??(cQ))))),
14.52/2.75	    inference('sup+', [status(thm)], ['23', '27'])).
14.52/2.75	tff('29', plain,
14.52/2.75	    ( (((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))))
14.52/2.75	      <= (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.75	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	               ((!!(cR)) <=> (??(cQ))))) & 
14.52/2.75	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.75	            = ((!!(cR)) <=> (??(cQ))))),
14.52/2.75	    inference('simplify boolean subterms', [status(thm)], ['28'])).
14.52/2.75	tff('30', plain,
14.52/2.75	    (((??(cR)) <=> (!!(cS)))
14.52/2.75	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.75	      <= (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.75	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	               ((!!(cR)) <=> (??(cQ))))) & 
14.52/2.75	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.75	            = ((!!(cR)) <=> (??(cQ))))),
14.52/2.75	    inference('simplify nested equalities', [status(thm)], ['29'])).
14.52/2.75	tff('31', plain,
14.52/2.75	    ( ((??(cR)) <=> (!!(cS))))
14.52/2.75	      <= (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.75	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	               ((!!(cR)) <=> (??(cQ))))) & 
14.52/2.75	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.75	            = ((!!(cR)) <=> (??(cQ)))) & 
14.52/2.75	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
14.52/2.75	    inference('sup+', [status(thm)], ['22', '30'])).
14.52/2.75	tff('32', plain,
14.52/2.75	    ((??(cR)) = (!!(cS)))
14.52/2.75	      <= (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.75	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	               ((!!(cR)) <=> (??(cQ))))) & 
14.52/2.75	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.75	            = ((!!(cR)) <=> (??(cQ)))) & 
14.52/2.75	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
14.52/2.75	    inference('simplify nested equalities', [status(thm)], ['31'])).
14.52/2.75	tff('33', plain,
14.52/2.75	    ((??(cR)) = (!!(cS)))
14.52/2.75	      <= (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.75	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	               ((!!(cR)) <=> (??(cQ))))) & 
14.52/2.75	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.75	            = ((!!(cR)) <=> (??(cQ)))) & 
14.52/2.75	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
14.52/2.75	    inference('simplify nested equalities', [status(thm)], ['31'])).
14.52/2.75	tff('34', plain, (~ '#form28' |  ((??(cR)) <=> (!!(cS)))),
14.52/2.75	    define([status(thm)])).
14.52/2.75	tff('35', plain,
14.52/2.75	    ( '#form28')
14.52/2.75	      <= (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.75	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	               ((!!(cR)) <=> (??(cQ))))) & 
14.52/2.75	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.75	            = ((!!(cR)) <=> (??(cQ)))) & 
14.52/2.75	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
14.52/2.75	    inference('renaming', [status(thm)], ['32', '34'])).
14.52/2.75	tff('36', plain, (~ '#form28' |  ((??(cR)) <=> (!!(cS)))),
14.52/2.75	    define([status(thm)])).
14.52/2.75	tff('37', plain, (~ '#form28' | (??(cR)) = (!!(cS))),
14.52/2.75	    inference('simplify nested equalities', [status(thm)], ['36'])).
14.52/2.75	tff('38', plain, (~ '#form28') <= (~ ( '#form28')),
14.52/2.75	    inference('split', [status(esa)], ['37'])).
14.52/2.75	tff('39', plain,
14.52/2.75	    ~
14.52/2.75	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.75	      = ((!!(cR)) <=> (??(cQ)))) | 
14.52/2.75	    ~
14.52/2.75	    ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.75	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	         ((!!(cR)) <=> (??(cQ))))) | 
14.52/2.75	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) | 
14.52/2.75	    ( '#form28'), inference('sup-', [status(thm)], ['35', '38'])).
14.52/2.75	tff('40', plain,
14.52/2.75	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.75	      = ((!!(cR)) <=> (??(cQ))))
14.52/2.75	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.75	            = ((!!(cR)) <=> (??(cQ))))),
14.52/2.75	    inference('split', [status(esa)], ['6'])).
14.52/2.75	tff('41', plain,
14.52/2.75	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.75	      != ((!!(cR)) <=> (??(cQ))))
14.52/2.75	      <= (~
14.52/2.75	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.75	            = ((!!(cR)) <=> (??(cQ))))),
14.52/2.75	    inference('split', [status(esa)], ['10'])).
14.52/2.75	tff('42', plain,
14.52/2.75	    (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.75	      |  ((!!(cR)) <=> (??(cQ)))))
14.52/2.75	      <= (~
14.52/2.75	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.75	            = ((!!(cR)) <=> (??(cQ))))),
14.52/2.75	    inference('lazy_cnf_xor', [status(thm)], ['41'])).
14.52/2.75	tff('43', plain,
14.52/2.75	    (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.75	      | (!!(cR)) = (??(cQ))))
14.52/2.75	      <= (~
14.52/2.75	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.75	            = ((!!(cR)) <=> (??(cQ))))),
14.52/2.75	    inference('simplify nested equalities', [status(thm)], ['42'])).
14.52/2.75	tff('44', plain,
14.52/2.75	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))))
14.52/2.75	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))))),
14.52/2.75	    inference('split', [status(esa)], ['43'])).
14.52/2.75	tff('45', plain,
14.52/2.75	    ( ((!!(cR)) <=> (??(cQ))))
14.52/2.75	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.75	            = ((!!(cR)) <=> (??(cQ)))) & 
14.52/2.75	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))))),
14.52/2.75	    inference('sup+', [status(thm)], ['40', '44'])).
14.52/2.75	tff('46', plain,
14.52/2.75	    ((!!(cR)) = (??(cQ)))
14.52/2.75	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.75	            = ((!!(cR)) <=> (??(cQ)))) & 
14.52/2.75	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))))),
14.52/2.75	    inference('simplify nested equalities', [status(thm)], ['45'])).
14.52/2.75	tff('47', plain,
14.52/2.75	    ((~ (!!(cR)) |  (??(cQ))))
14.52/2.75	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.75	            = ((!!(cR)) <=> (??(cQ)))) & 
14.52/2.75	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))))),
14.52/2.75	    inference('lazy_cnf_equiv', [status(thm)], ['46'])).
14.52/2.75	tff('48', plain,
14.52/2.75	    ~
14.52/2.75	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.75	      = ((!!(cR)) <=> (??(cQ)))) | 
14.52/2.75	    ~ ( (!!(cR))) | ( (??(cQ))) | 
14.52/2.75	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))),
14.52/2.75	    inference('split', [status(esa)], ['47'])).
14.52/2.75	tff('49', plain,
14.52/2.75	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      != (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))),
14.52/2.75	    inference('split', [status(esa)], ['3'])).
14.52/2.75	tff('50', plain,
14.52/2.75	    ((~ (((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      | ~ (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	           (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))),
14.52/2.75	    inference('lazy_cnf_xor', [status(thm)], ['49'])).
14.52/2.75	tff('51', plain,
14.52/2.75	    ((((??(cP)) <=> (!!(cQ)))
14.52/2.75	       != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))
14.52/2.75	      | ((??(cS)) <=> (!!(cP)))
14.52/2.75	         != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))),
14.52/2.75	    inference('simplify nested equalities', [status(thm)], ['50'])).
14.52/2.75	tff('52', plain,
14.52/2.75	    (((??(cS)) <=> (!!(cP)))
14.52/2.75	      != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))
14.52/2.75	      <= (~
14.52/2.75	          (((??(cS)) <=> (!!(cP)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.75	    inference('split', [status(esa)], ['51'])).
14.52/2.75	tff('53', plain,
14.52/2.75	    (( ((??(cS)) <=> (!!(cP)))
14.52/2.75	      |  (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.75	      <= (~
14.52/2.75	          (((??(cS)) <=> (!!(cP)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.75	    inference('lazy_cnf_xor', [status(thm)], ['52'])).
14.52/2.75	tff('54', plain,
14.52/2.75	    (((??(cS)) = (!!(cP))
14.52/2.75	      |  (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.75	      <= (~
14.52/2.75	          (((??(cS)) <=> (!!(cP)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.75	    inference('simplify nested equalities', [status(thm)], ['53'])).
14.52/2.75	tff('55', plain,
14.52/2.75	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))
14.52/2.75	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.75	    inference('split', [status(esa)], ['54'])).
14.52/2.75	tff('56', plain,
14.52/2.75	    (((??(cS)) <=> (!!(cP)))
14.52/2.75	      != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))
14.52/2.75	      <= (~
14.52/2.75	          (((??(cS)) <=> (!!(cP)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.75	    inference('split', [status(esa)], ['51'])).
14.52/2.75	tff('57', plain,
14.52/2.75	    (~ ((??(cS)) <=> (!!(cP))))
14.52/2.75	      <= (~
14.52/2.75	          (((??(cS)) <=> (!!(cP)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) & 
14.52/2.75	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.75	    inference('sup-', [status(thm)], ['55', '56'])).
14.52/2.75	tff('58', plain,
14.52/2.75	    ((??(cS)) != (!!(cP)))
14.52/2.75	      <= (~
14.52/2.75	          (((??(cS)) <=> (!!(cP)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) & 
14.52/2.75	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.75	    inference('simplify nested equalities', [status(thm)], ['57'])).
14.52/2.75	tff('59', plain, ( '#form9' | ~ ((??(cS)) <=> (!!(cP)))),
14.52/2.75	    define([status(thm)])).
14.52/2.75	tff('60', plain, ( '#form9' | (??(cS)) != (!!(cP))),
14.52/2.75	    inference('simplify nested equalities', [status(thm)], ['59'])).
14.52/2.75	tff('61', plain, ( '#form9') <= (( '#form9')),
14.52/2.75	    inference('split', [status(esa)], ['60'])).
14.52/2.75	tff('62', plain,
14.52/2.75	    (((??(cS)) <=> (!!(cP)))
14.52/2.75	      != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))
14.52/2.75	      <= (~
14.52/2.75	          (((??(cS)) <=> (!!(cP)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.75	    inference('split', [status(esa)], ['51'])).
14.52/2.75	tff('63', plain,
14.52/2.75	    ((~ ((??(cS)) <=> (!!(cP)))
14.52/2.75	      | ~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.75	      <= (~
14.52/2.75	          (((??(cS)) <=> (!!(cP)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.75	    inference('lazy_cnf_xor', [status(thm)], ['62'])).
14.52/2.75	tff('64', plain,
14.52/2.75	    (((??(cS)) != (!!(cP))
14.52/2.75	      | ~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.75	      <= (~
14.52/2.75	          (((??(cS)) <=> (!!(cP)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.75	    inference('simplify nested equalities', [status(thm)], ['63'])).
14.52/2.75	tff('65', plain, ((??(cS)) != (!!(cP))) <= (~ ((??(cS)) = (!!(cP)))),
14.52/2.75	    inference('split', [status(esa)], ['64'])).
14.52/2.75	tff('66', plain, (( (??(cS)) |  (!!(cP)))) <= (~ ((??(cS)) = (!!(cP)))),
14.52/2.75	    inference('lazy_cnf_xor', [status(thm)], ['65'])).
14.52/2.75	tff('67', plain, ( (??(cS))) <= (( (??(cS)))),
14.52/2.75	    inference('split', [status(esa)], ['66'])).
14.52/2.75	tff('68', plain,
14.52/2.75	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      != (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))),
14.52/2.75	    inference('split', [status(esa)], ['3'])).
14.52/2.75	tff('69', plain,
14.52/2.75	    (( (((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	        (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      |  (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))),
14.52/2.75	    inference('lazy_cnf_xor', [status(thm)], ['68'])).
14.52/2.75	tff('70', plain,
14.52/2.75	    ((((??(cP)) <=> (!!(cQ)))
14.52/2.75	       = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))
14.52/2.75	      | ((??(cS)) <=> (!!(cP)))
14.52/2.75	         = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))),
14.52/2.75	    inference('simplify nested equalities', [status(thm)], ['69'])).
14.52/2.75	tff('71', plain,
14.52/2.75	    (((??(cS)) <=> (!!(cP)))
14.52/2.75	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))
14.52/2.75	      <= ((((??(cS)) <=> (!!(cP)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.75	    inference('split', [status(esa)], ['70'])).
14.52/2.75	tff('72', plain, ( (!!(cP))) <= (( (!!(cP)))),
14.52/2.75	    inference('split', [status(esa)], ['66'])).
14.52/2.75	tff('73', plain,
14.52/2.75	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      != (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))),
14.52/2.75	    inference('split', [status(esa)], ['3'])).
14.52/2.75	tff('74', plain,
14.52/2.75	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      != (((??(cS)) <=> $true) <=>
14.52/2.75	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.75	          ( (!!(cP)))),
14.52/2.75	    inference('sup-', [status(thm)], ['72', '73'])).
14.52/2.75	tff('75', plain,
14.52/2.75	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      != ((??(cS)) <=>
14.52/2.75	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.75	          ( (!!(cP)))),
14.52/2.75	    inference('simplify boolean subterms', [status(thm)], ['74'])).
14.52/2.75	tff('76', plain,
14.52/2.75	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      != ((??(cS)) <=> ((??(cS)) <=> (!!(cP)))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.75	          (((??(cS)) <=> (!!(cP)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) & 
14.52/2.75	          ( (!!(cP)))),
14.52/2.75	    inference('sup-', [status(thm)], ['71', '75'])).
14.52/2.75	tff('77', plain,
14.52/2.75	    ((~ (((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      | ~ ((??(cS)) <=> ((??(cS)) <=> (!!(cP))))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.75	          (((??(cS)) <=> (!!(cP)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) & 
14.52/2.75	          ( (!!(cP)))),
14.52/2.75	    inference('lazy_cnf_xor', [status(thm)], ['76'])).
14.52/2.75	tff('78', plain,
14.52/2.75	    ((((??(cP)) <=> (!!(cQ)))
14.52/2.75	       != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))
14.52/2.75	      | (??(cS)) != ((??(cS)) <=> (!!(cP)))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.75	          (((??(cS)) <=> (!!(cP)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) & 
14.52/2.75	          ( (!!(cP)))),
14.52/2.75	    inference('simplify nested equalities', [status(thm)], ['77'])).
14.52/2.75	tff('79', plain,
14.52/2.75	    ((??(cS)) != ((??(cS)) <=> (!!(cP))))
14.52/2.75	      <= (~ ((??(cS)) = ((??(cS)) <=> (!!(cP))))),
14.52/2.75	    inference('split', [status(esa)], ['78'])).
14.52/2.75	tff('80', plain,
14.52/2.75	    ((??(cS)) != ($true <=> (!!(cP))))
14.52/2.75	      <= (~ ((??(cS)) = ((??(cS)) <=> (!!(cP)))) & ( (??(cS)))),
14.52/2.75	    inference('sup-', [status(thm)], ['67', '79'])).
14.52/2.75	tff('81', plain,
14.52/2.75	    ((??(cS)) != (!!(cP)))
14.52/2.75	      <= (~ ((??(cS)) = ((??(cS)) <=> (!!(cP)))) & ( (??(cS)))),
14.52/2.75	    inference('simplify boolean subterms', [status(thm)], ['80'])).
14.52/2.75	tff('82', plain, ( '#form9' | ~ ((??(cS)) <=> (!!(cP)))),
14.52/2.75	    define([status(thm)])).
14.52/2.75	tff('83', plain,
14.52/2.75	    (~ '#form9') <= (~ ((??(cS)) = ((??(cS)) <=> (!!(cP)))) & ( (??(cS)))),
14.52/2.75	    inference('renaming', [status(thm)], ['81', '82'])).
14.52/2.75	tff('84', plain,
14.52/2.75	    ((??(cS)) = ((??(cS)) <=> (!!(cP)))) | ~ ( '#form9') | ~ ( (??(cS))),
14.52/2.75	    inference('sup-', [status(thm)], ['61', '83'])).
14.52/2.75	tff('85', plain,
14.52/2.75	    (((??(cP)) <=> (!!(cQ)))
14.52/2.75	      != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      <= (~
14.52/2.75	          (((??(cP)) <=> (!!(cQ)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.75	    inference('split', [status(esa)], ['51'])).
14.52/2.75	tff('86', plain,
14.52/2.75	    (( ((??(cP)) <=> (!!(cQ)))
14.52/2.75	      |  (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))))
14.52/2.75	      <= (~
14.52/2.75	          (((??(cP)) <=> (!!(cQ)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.75	    inference('lazy_cnf_xor', [status(thm)], ['85'])).
14.52/2.75	tff('87', plain,
14.52/2.75	    (((??(cP)) = (!!(cQ))
14.52/2.75	      |  (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))))
14.52/2.75	      <= (~
14.52/2.75	          (((??(cP)) <=> (!!(cQ)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.75	    inference('simplify nested equalities', [status(thm)], ['86'])).
14.52/2.75	tff('88', plain,
14.52/2.75	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.75	    inference('split', [status(esa)], ['87'])).
14.52/2.75	tff('89', plain,
14.52/2.75	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      != ((??(cS)) <=> ((??(cS)) <=> (!!(cP)))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.75	          (((??(cS)) <=> (!!(cP)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) & 
14.52/2.75	          ( (!!(cP)))),
14.52/2.75	    inference('sup-', [status(thm)], ['71', '75'])).
14.52/2.75	tff('90', plain,
14.52/2.75	    ((((??(cP)) <=> (!!(cQ))) <=> $true)
14.52/2.75	      != ((??(cS)) <=> ((??(cS)) <=> (!!(cP)))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.75	          (((??(cS)) <=> (!!(cP)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) & 
14.52/2.75	          ( (!!(cP))) & 
14.52/2.75	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.75	    inference('sup-', [status(thm)], ['88', '89'])).
14.52/2.75	tff('91', plain,
14.52/2.75	    (((??(cP)) <=> (!!(cQ))) != ((??(cS)) <=> ((??(cS)) <=> (!!(cP)))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.75	          (((??(cS)) <=> (!!(cP)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) & 
14.52/2.75	          ( (!!(cP))) & 
14.52/2.75	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.75	    inference('simplify boolean subterms', [status(thm)], ['90'])).
14.52/2.75	tff('92', plain,
14.52/2.75	    (( ((??(cP)) <=> (!!(cQ))) |  ((??(cS)) <=> ((??(cS)) <=> (!!(cP))))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.75	          (((??(cS)) <=> (!!(cP)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) & 
14.52/2.75	          ( (!!(cP))) & 
14.52/2.75	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.75	    inference('lazy_cnf_xor', [status(thm)], ['91'])).
14.52/2.75	tff('93', plain,
14.52/2.75	    (((??(cP)) = (!!(cQ)) | (??(cS)) = ((??(cS)) <=> (!!(cP)))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.75	          (((??(cS)) <=> (!!(cP)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) & 
14.52/2.75	          ( (!!(cP))) & 
14.52/2.75	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.75	    inference('simplify nested equalities', [status(thm)], ['92'])).
14.52/2.75	tff('94', plain,
14.52/2.75	    ((??(cS)) = ((??(cS)) <=> (!!(cP))))
14.52/2.75	      <= (((??(cS)) = ((??(cS)) <=> (!!(cP))))),
14.52/2.75	    inference('split', [status(esa)], ['93'])).
14.52/2.75	tff('95', plain, ((??(cS)) = (!!(cP))) <= (((??(cS)) = (!!(cP)))),
14.52/2.75	    inference('split', [status(esa)], ['54'])).
14.52/2.75	tff('96', plain,
14.52/2.75	    (((??(cP)) <=> (!!(cQ))) != ((??(cS)) <=> ((??(cS)) <=> (!!(cP)))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.75	          (((??(cS)) <=> (!!(cP)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) & 
14.52/2.75	          ( (!!(cP))) & 
14.52/2.75	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.75	    inference('simplify boolean subterms', [status(thm)], ['90'])).
14.52/2.75	tff('97', plain,
14.52/2.75	    (((??(cP)) <=> (!!(cQ))) != ((!!(cP)) <=> ((??(cS)) <=> (!!(cP)))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.75	          (((??(cS)) <=> (!!(cP)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) & 
14.52/2.75	          ((??(cS)) = (!!(cP))) & 
14.52/2.75	          ( (!!(cP))) & 
14.52/2.75	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.75	    inference('sup-', [status(thm)], ['95', '96'])).
14.52/2.75	tff('98', plain,
14.52/2.75	    (( ((??(cP)) <=> (!!(cQ))) |  ((!!(cP)) <=> ((??(cS)) <=> (!!(cP))))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.75	          (((??(cS)) <=> (!!(cP)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) & 
14.52/2.75	          ((??(cS)) = (!!(cP))) & 
14.52/2.75	          ( (!!(cP))) & 
14.52/2.75	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.75	    inference('lazy_cnf_xor', [status(thm)], ['97'])).
14.52/2.75	tff('99', plain,
14.52/2.75	    (((??(cP)) = (!!(cQ)) | (!!(cP)) = ((??(cS)) <=> (!!(cP)))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.75	          (((??(cS)) <=> (!!(cP)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) & 
14.52/2.75	          ((??(cS)) = (!!(cP))) & 
14.52/2.75	          ( (!!(cP))) & 
14.52/2.75	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.75	    inference('simplify nested equalities', [status(thm)], ['98'])).
14.52/2.75	tff('100', plain,
14.52/2.75	    ((!!(cP)) = ((??(cS)) <=> (!!(cP))))
14.52/2.75	      <= (((!!(cP)) = ((??(cS)) <=> (!!(cP))))),
14.52/2.75	    inference('split', [status(esa)], ['99'])).
14.52/2.75	tff('101', plain,
14.52/2.75	    ((!!(cP)) = (??(cS)))
14.52/2.75	      <= (((??(cS)) = ((??(cS)) <=> (!!(cP)))) & 
14.52/2.75	          ((!!(cP)) = ((??(cS)) <=> (!!(cP))))),
14.52/2.75	    inference('sup+', [status(thm)], ['94', '100'])).
14.52/2.75	tff('102', plain,
14.52/2.75	    ((!!(cP)) = ((??(cS)) <=> (!!(cP))))
14.52/2.75	      <= (((!!(cP)) = ((??(cS)) <=> (!!(cP))))),
14.52/2.75	    inference('split', [status(esa)], ['99'])).
14.52/2.75	tff('103', plain,
14.52/2.75	    ((!!(cP)) = ((!!(cP)) <=> (!!(cP))))
14.52/2.75	      <= (((??(cS)) = ((??(cS)) <=> (!!(cP)))) & 
14.52/2.75	          ((!!(cP)) = ((??(cS)) <=> (!!(cP))))),
14.52/2.75	    inference('sup+', [status(thm)], ['101', '102'])).
14.52/2.75	tff('104', plain,
14.52/2.75	    ( (!!(cP)))
14.52/2.75	      <= (((??(cS)) = ((??(cS)) <=> (!!(cP)))) & 
14.52/2.75	          ((!!(cP)) = ((??(cS)) <=> (!!(cP))))),
14.52/2.75	    inference('simplify boolean subterms', [status(thm)], ['103'])).
14.52/2.75	tff('105', plain, ((??(cS)) = (!!(cP))) <= (((??(cS)) = (!!(cP)))),
14.52/2.75	    inference('split', [status(esa)], ['54'])).
14.52/2.75	tff('106', plain, ( (??(cS))) <= (( (??(cS)))),
14.52/2.75	    inference('split', [status(esa)], ['66'])).
14.52/2.75	tff('107', plain, ( (!!(cP))) <= (((??(cS)) = (!!(cP))) & ( (??(cS)))),
14.52/2.75	    inference('sup+', [status(thm)], ['105', '106'])).
14.52/2.75	tff('108', plain, (~ '#form3' |  (!!(cP))), define([status(thm)])).
14.52/2.75	tff('109', plain,
14.52/2.75	    ( '#form3')
14.52/2.75	      <= (((??(cS)) = ((??(cS)) <=> (!!(cP)))) & 
14.52/2.75	          ((!!(cP)) = ((??(cS)) <=> (!!(cP))))),
14.52/2.75	    inference('renaming', [status(thm)], ['104', '108'])).
14.52/2.75	tff('110', plain, ((??(cS)) = (!!(cP))) <= (((??(cS)) = (!!(cP)))),
14.52/2.75	    inference('split', [status(esa)], ['54'])).
14.52/2.75	tff('111', plain, ((??(cS)) != (!!(cP))) <= (~ ((??(cS)) = (!!(cP)))),
14.52/2.75	    inference('split', [status(esa)], ['64'])).
14.52/2.75	tff('112', plain, ((~ (??(cS)) | ~ (!!(cP)))) <= (~ ((??(cS)) = (!!(cP)))),
14.52/2.75	    inference('lazy_cnf_xor', [status(thm)], ['111'])).
14.52/2.75	tff('113', plain, (~ (??(cS))) <= (~ ( (??(cS)))),
14.52/2.75	    inference('split', [status(esa)], ['112'])).
14.52/2.75	tff('114', plain, (~ (!!(cP))) <= (~ ( (??(cS))) & ((??(cS)) = (!!(cP)))),
14.52/2.75	    inference('sup-', [status(thm)], ['110', '113'])).
14.52/2.75	tff('115', plain, ( '#form3' | ~ (!!(cP))), define([status(thm)])).
14.52/2.75	tff('116', plain, (~ (!!(cP))) <= (~ ( (!!(cP)))),
14.52/2.75	    inference('split', [status(esa)], ['115'])).
14.52/2.75	tff('117', plain, ( '#form3' | ~ (!!(cP))), define([status(thm)])).
14.52/2.75	tff('118', plain, (~ '#form3') <= (~ ( (!!(cP)))),
14.52/2.75	    inference('renaming', [status(thm)], ['116', '117'])).
14.52/2.75	tff('119', plain,
14.52/2.75	    ~ ((??(cS)) = ((??(cS)) <=> (!!(cP)))) | ( (!!(cP))) | 
14.52/2.75	    ~ ((!!(cP)) = ((??(cS)) <=> (!!(cP)))),
14.52/2.75	    inference('sup-', [status(thm)], ['109', '118'])).
14.52/2.75	tff('120', plain, ((??(cP)) = (!!(cQ))) <= (((??(cP)) = (!!(cQ)))),
14.52/2.75	    inference('split', [status(esa)], ['87'])).
14.52/2.75	tff('121', plain,
14.52/2.75	    (((??(cP)) <=> (!!(cQ)))
14.52/2.75	      != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      <= (~
14.52/2.75	          (((??(cP)) <=> (!!(cQ)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.75	    inference('split', [status(esa)], ['51'])).
14.52/2.75	tff('122', plain,
14.52/2.75	    ((~ ((??(cP)) <=> (!!(cQ)))
14.52/2.75	      | ~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))))
14.52/2.75	      <= (~
14.52/2.75	          (((??(cP)) <=> (!!(cQ)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.75	    inference('lazy_cnf_xor', [status(thm)], ['121'])).
14.52/2.75	tff('123', plain,
14.52/2.75	    (((??(cP)) != (!!(cQ))
14.52/2.75	      | ~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))))
14.52/2.75	      <= (~
14.52/2.75	          (((??(cP)) <=> (!!(cQ)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.75	    inference('simplify nested equalities', [status(thm)], ['122'])).
14.52/2.75	tff('124', plain, ((??(cP)) != (!!(cQ))) <= (~ ((??(cP)) = (!!(cQ)))),
14.52/2.75	    inference('split', [status(esa)], ['123'])).
14.52/2.75	tff('125', plain, (( (??(cP)) |  (!!(cQ)))) <= (~ ((??(cP)) = (!!(cQ)))),
14.52/2.75	    inference('lazy_cnf_xor', [status(thm)], ['124'])).
14.52/2.75	tff('126', plain, ( (??(cP))) <= (( (??(cP)))),
14.52/2.75	    inference('split', [status(esa)], ['125'])).
14.52/2.75	tff('127', plain, ( (!!(cQ))) <= (((??(cP)) = (!!(cQ))) & ( (??(cP)))),
14.52/2.75	    inference('sup+', [status(thm)], ['120', '126'])).
14.52/2.75	tff('128', plain, ( (!!(cQ))) <= (((??(cP)) = (!!(cQ))) & ( (??(cP)))),
14.52/2.75	    inference('sup+', [status(thm)], ['120', '126'])).
14.52/2.75	tff('129', plain, (~ '#form7' |  (!!(cQ))), define([status(thm)])).
14.52/2.75	tff('130', plain, ( '#form7') <= (((??(cP)) = (!!(cQ))) & ( (??(cP)))),
14.52/2.75	    inference('renaming', [status(thm)], ['127', '129'])).
14.52/2.75	tff('131', plain, (~ '#form7' |  (!!(cQ))), define([status(thm)])).
14.52/2.75	tff('132', plain, (~ '#form7') <= (~ ( '#form7')),
14.52/2.75	    inference('split', [status(esa)], ['131'])).
14.52/2.75	tff('133', plain, ~ ((??(cP)) = (!!(cQ))) | ~ ( (??(cP))) | ( '#form7'),
14.52/2.75	    inference('sup-', [status(thm)], ['130', '132'])).
14.52/2.75	tff('134', plain,
14.52/2.75	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.75	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
14.52/2.75	    inference('split', [status(esa)], ['21'])).
14.52/2.75	tff('135', plain,
14.52/2.75	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.75	      = ((!!(cR)) <=> (??(cQ))))
14.52/2.75	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.75	            = ((!!(cR)) <=> (??(cQ))))),
14.52/2.75	    inference('split', [status(esa)], ['6'])).
14.52/2.75	tff('136', plain,
14.52/2.75	    ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.75	      != ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	          ((!!(cR)) <=> (??(cQ)))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.75	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	               ((!!(cR)) <=> (??(cQ)))))),
14.52/2.75	    inference('split', [status(esa)], ['3'])).
14.52/2.75	tff('137', plain,
14.52/2.75	    ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.75	      != (((!!(cR)) <=> (??(cQ))) <=> ((!!(cR)) <=> (??(cQ)))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.75	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	               ((!!(cR)) <=> (??(cQ))))) & 
14.52/2.75	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.75	            = ((!!(cR)) <=> (??(cQ))))),
14.52/2.75	    inference('sup-', [status(thm)], ['135', '136'])).
14.52/2.75	tff('138', plain,
14.52/2.75	    (~ (((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	        (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.75	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	               ((!!(cR)) <=> (??(cQ))))) & 
14.52/2.75	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.75	            = ((!!(cR)) <=> (??(cQ))))),
14.52/2.75	    inference('simplify boolean subterms', [status(thm)], ['137'])).
14.52/2.75	tff('139', plain,
14.52/2.75	    (((??(cR)) <=> (!!(cS)))
14.52/2.75	      != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.75	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	               ((!!(cR)) <=> (??(cQ))))) & 
14.52/2.75	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.75	            = ((!!(cR)) <=> (??(cQ))))),
14.52/2.75	    inference('simplify nested equalities', [status(thm)], ['138'])).
14.52/2.75	tff('140', plain,
14.52/2.75	    (~ ((??(cR)) <=> (!!(cS))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.75	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	               ((!!(cR)) <=> (??(cQ))))) & 
14.52/2.75	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.75	            = ((!!(cR)) <=> (??(cQ)))) & 
14.52/2.75	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
14.52/2.75	    inference('sup-', [status(thm)], ['134', '139'])).
14.52/2.75	tff('141', plain,
14.52/2.75	    ((??(cR)) != (!!(cS)))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.75	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	               ((!!(cR)) <=> (??(cQ))))) & 
14.52/2.75	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.75	            = ((!!(cR)) <=> (??(cQ)))) & 
14.52/2.75	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
14.52/2.75	    inference('simplify nested equalities', [status(thm)], ['140'])).
14.52/2.75	tff('142', plain, ( '#form28' | ~ ((??(cR)) <=> (!!(cS)))),
14.52/2.75	    define([status(thm)])).
14.52/2.75	tff('143', plain, ( '#form28' | (??(cR)) != (!!(cS))),
14.52/2.75	    inference('simplify nested equalities', [status(thm)], ['142'])).
14.52/2.75	tff('144', plain, ( '#form28') <= (( '#form28')),
14.52/2.75	    inference('split', [status(esa)], ['143'])).
14.52/2.75	tff('145', plain, ((??(cR)) != (!!(cS))) <= (~ ((??(cR)) = (!!(cS)))),
14.52/2.75	    inference('split', [status(esa)], ['143'])).
14.52/2.75	tff('146', plain, ( '#form28' | ~ ((??(cR)) <=> (!!(cS)))),
14.52/2.75	    define([status(thm)])).
14.52/2.75	tff('147', plain, (~ '#form28') <= (~ ((??(cR)) = (!!(cS)))),
14.52/2.75	    inference('renaming', [status(thm)], ['145', '146'])).
14.52/2.75	tff('148', plain, ~ ( '#form28') | ((??(cR)) = (!!(cS))),
14.52/2.75	    inference('sup-', [status(thm)], ['144', '147'])).
14.52/2.75	tff('149', plain, ((??(cP)) = (!!(cQ))) <= (((??(cP)) = (!!(cQ)))),
14.52/2.75	    inference('split', [status(esa)], ['87'])).
14.52/2.75	tff('150', plain, ((??(cP)) != (!!(cQ))) <= (~ ((??(cP)) = (!!(cQ)))),
14.52/2.75	    inference('split', [status(esa)], ['123'])).
14.52/2.75	tff('151', plain, ((~ (??(cP)) | ~ (!!(cQ)))) <= (~ ((??(cP)) = (!!(cQ)))),
14.52/2.75	    inference('lazy_cnf_xor', [status(thm)], ['150'])).
14.52/2.75	tff('152', plain, (~ (??(cP))) <= (~ ( (??(cP)))),
14.52/2.75	    inference('split', [status(esa)], ['151'])).
14.52/2.75	tff('153', plain, (~ (!!(cQ))) <= (~ ( (??(cP))) & ((??(cP)) = (!!(cQ)))),
14.52/2.75	    inference('sup-', [status(thm)], ['149', '152'])).
14.52/2.75	tff('154', plain, ( '#form7' | ~ (!!(cQ))), define([status(thm)])).
14.52/2.75	tff('155', plain, ( '#form7') <= (( '#form7')),
14.52/2.75	    inference('split', [status(esa)], ['154'])).
14.52/2.75	tff('156', plain, (~ (!!(cQ))) <= (~ ( (!!(cQ)))),
14.52/2.75	    inference('split', [status(esa)], ['154'])).
14.52/2.75	tff('157', plain, ( '#form7' | ~ (!!(cQ))), define([status(thm)])).
14.52/2.75	tff('158', plain, (~ '#form7') <= (~ ( (!!(cQ)))),
14.52/2.75	    inference('renaming', [status(thm)], ['156', '157'])).
14.52/2.75	tff('159', plain, ~ ( '#form7') | ( (!!(cQ))),
14.52/2.75	    inference('sup-', [status(thm)], ['155', '158'])).
14.52/2.75	tff('160', plain,
14.52/2.75	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.75	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
14.52/2.75	    inference('split', [status(esa)], ['21'])).
14.52/2.75	tff('161', plain,
14.52/2.75	    (((??(cR)) <=> (!!(cS)))
14.52/2.75	      != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.75	      <= (~
14.52/2.75	          (((??(cR)) <=> (!!(cS)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
14.52/2.75	    inference('split', [status(esa)], ['10'])).
14.52/2.75	tff('162', plain,
14.52/2.75	    (~ ((??(cR)) <=> (!!(cS))))
14.52/2.75	      <= (~
14.52/2.75	          (((??(cR)) <=> (!!(cS)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) & 
14.52/2.75	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
14.52/2.75	    inference('sup-', [status(thm)], ['160', '161'])).
14.52/2.75	tff('163', plain,
14.52/2.75	    ((??(cR)) != (!!(cS)))
14.52/2.75	      <= (~
14.52/2.75	          (((??(cR)) <=> (!!(cS)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) & 
14.52/2.75	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
14.52/2.75	    inference('simplify nested equalities', [status(thm)], ['162'])).
14.52/2.75	tff('164', plain,
14.52/2.75	    ((~ (??(cR)) | ~ (!!(cS))))
14.52/2.75	      <= (~
14.52/2.75	          (((??(cR)) <=> (!!(cS)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) & 
14.52/2.75	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
14.52/2.75	    inference('lazy_cnf_xor', [status(thm)], ['163'])).
14.52/2.75	tff('165', plain,
14.52/2.75	    ~ ( (??(cR))) | ~ ( (!!(cS))) | 
14.52/2.75	    (((??(cR)) <=> (!!(cS)))
14.52/2.75	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) | 
14.52/2.75	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))),
14.52/2.75	    inference('split', [status(esa)], ['164'])).
14.52/2.75	tff('166', plain, ((!!(cR)) = (??(cQ))) <= (((!!(cR)) = (??(cQ)))),
14.52/2.75	    inference('split', [status(esa)], ['43'])).
14.52/2.75	tff('167', plain, ((!!(cR)) != (??(cQ))) <= (~ ((!!(cR)) = (??(cQ)))),
14.52/2.75	    inference('split', [status(esa)], ['13'])).
14.52/2.75	tff('168', plain, ((~ (!!(cR)) | ~ (??(cQ)))) <= (~ ((!!(cR)) = (??(cQ)))),
14.52/2.75	    inference('lazy_cnf_xor', [status(thm)], ['167'])).
14.52/2.75	tff('169', plain, (~ (!!(cR))) <= (~ ( (!!(cR)))),
14.52/2.75	    inference('split', [status(esa)], ['168'])).
14.52/2.75	tff('170', plain, (~ (??(cQ))) <= (~ ( (!!(cR))) & ((!!(cR)) = (??(cQ)))),
14.52/2.75	    inference('sup-', [status(thm)], ['166', '169'])).
14.52/2.75	tff('171', plain, ( '#form15' | ~ (??(cQ))), define([status(thm)])).
14.52/2.75	tff('172', plain, ( '#form15') <= (( '#form15')),
14.52/2.75	    inference('split', [status(esa)], ['171'])).
14.52/2.75	tff('173', plain,
14.52/2.75	    ((!!(cR)) = (??(cQ)))
14.52/2.75	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.75	            = ((!!(cR)) <=> (??(cQ)))) & 
14.52/2.75	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))))),
14.52/2.75	    inference('simplify nested equalities', [status(thm)], ['45'])).
14.52/2.75	tff('174', plain, (~ (!!(cR))) <= (~ ( (!!(cR)))),
14.52/2.75	    inference('split', [status(esa)], ['168'])).
14.52/2.75	tff('175', plain,
14.52/2.75	    (~ (??(cQ)))
14.52/2.75	      <= (~ ( (!!(cR))) & 
14.52/2.75	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.75	            = ((!!(cR)) <=> (??(cQ)))) & 
14.52/2.75	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))))),
14.52/2.75	    inference('sup-', [status(thm)], ['173', '174'])).
14.52/2.75	tff('176', plain, ( '#form15' | ~ (??(cQ))), define([status(thm)])).
14.52/2.75	tff('177', plain,
14.52/2.75	    (~ '#form15')
14.52/2.75	      <= (~ ( (!!(cR))) & 
14.52/2.75	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.75	            = ((!!(cR)) <=> (??(cQ)))) & 
14.52/2.75	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))))),
14.52/2.75	    inference('renaming', [status(thm)], ['175', '176'])).
14.52/2.75	tff('178', plain,
14.52/2.75	    ~
14.52/2.75	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.75	      = ((!!(cR)) <=> (??(cQ)))) | 
14.52/2.75	    ~ ( '#form15') | ( (!!(cR))) | 
14.52/2.75	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))),
14.52/2.75	    inference('sup-', [status(thm)], ['172', '177'])).
14.52/2.75	tff('179', plain, ((??(cR)) = (!!(cS))) <= (((??(cR)) = (!!(cS)))),
14.52/2.75	    inference('split', [status(esa)], ['21'])).
14.52/2.75	tff('180', plain, (( (??(cR)) | ~ (!!(cS)))) <= (((??(cR)) = (!!(cS)))),
14.52/2.75	    inference('lazy_cnf_equiv', [status(thm)], ['179'])).
14.52/2.75	tff('181', plain, ~ ((??(cR)) = (!!(cS))) | ~ ( (!!(cS))) | ( (??(cR))),
14.52/2.75	    inference('split', [status(esa)], ['180'])).
14.52/2.75	tff('182', plain, ((??(cS)) = (!!(cP))) <= (((??(cS)) = (!!(cP)))),
14.52/2.75	    inference('split', [status(esa)], ['54'])).
14.52/2.75	tff('183', plain,
14.52/2.75	    ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.75	     ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	      ((!!(cR)) <=> (??(cQ)))))
14.52/2.75	     != ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) <=>
14.52/2.75	         (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.75	    inference('ho_norm', [status(thm)], ['0'])).
14.52/2.75	tff('184', plain,
14.52/2.75	    (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.75	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	       ((!!(cR)) <=> (??(cQ)))))
14.52/2.75	      != ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	           (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) <=>
14.52/2.75	          (((!!(cP)) <=> (!!(cP))) <=>
14.52/2.75	           (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))))
14.52/2.75	      <= (((??(cS)) = (!!(cP)))),
14.52/2.75	    inference('sup-', [status(thm)], ['182', '183'])).
14.52/2.75	tff('185', plain,
14.52/2.75	    (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.75	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	       ((!!(cR)) <=> (??(cQ)))))
14.52/2.75	      != ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	           (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) <=>
14.52/2.75	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.75	      <= (((??(cS)) = (!!(cP)))),
14.52/2.75	    inference('simplify boolean subterms', [status(thm)], ['184'])).
14.52/2.75	tff('186', plain,
14.52/2.75	    (( ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.75	        ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	         ((!!(cR)) <=> (??(cQ)))))
14.52/2.75	      |  ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	           (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) <=>
14.52/2.75	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))))
14.52/2.75	      <= (((??(cS)) = (!!(cP)))),
14.52/2.75	    inference('lazy_cnf_xor', [status(thm)], ['185'])).
14.52/2.75	tff('187', plain,
14.52/2.75	    (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.75	       = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	          ((!!(cR)) <=> (??(cQ))))
14.52/2.75	      | (((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	         = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.75	      <= (((??(cS)) = (!!(cP)))),
14.52/2.75	    inference('simplify nested equalities', [status(thm)], ['186'])).
14.52/2.75	tff('188', plain,
14.52/2.75	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))
14.52/2.75	      <= (((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.75	    inference('split', [status(esa)], ['187'])).
14.52/2.75	tff('189', plain, ((??(cS)) = (!!(cP))) <= (((??(cS)) = (!!(cP)))),
14.52/2.75	    inference('split', [status(esa)], ['54'])).
14.52/2.75	tff('190', plain,
14.52/2.75	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      != (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))),
14.52/2.75	    inference('split', [status(esa)], ['3'])).
14.52/2.75	tff('191', plain,
14.52/2.75	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      != (((!!(cP)) <=> (!!(cP))) <=>
14.52/2.75	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.75	          ((??(cS)) = (!!(cP)))),
14.52/2.75	    inference('sup-', [status(thm)], ['189', '190'])).
14.52/2.75	tff('192', plain,
14.52/2.75	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.75	          ((??(cS)) = (!!(cP)))),
14.52/2.75	    inference('simplify boolean subterms', [status(thm)], ['191'])).
14.52/2.75	tff('193', plain,
14.52/2.75	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      != (((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.75	          ((??(cS)) = (!!(cP))) & 
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.75	    inference('sup-', [status(thm)], ['188', '192'])).
14.52/2.75	tff('194', plain,
14.52/2.75	    ~
14.52/2.75	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) | 
14.52/2.75	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) | 
14.52/2.75	    ~ ((??(cS)) = (!!(cP))), inference('simplify', [status(thm)], ['193'])).
14.52/2.75	tff('195', plain,
14.52/2.75	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.75	    inference('split', [status(esa)], ['87'])).
14.52/2.75	tff('196', plain,
14.52/2.75	    (((??(cS)) <=> (!!(cP)))
14.52/2.75	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))
14.52/2.75	      <= ((((??(cS)) <=> (!!(cP)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.75	    inference('split', [status(esa)], ['70'])).
14.52/2.75	tff('197', plain,
14.52/2.75	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      != (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))),
14.52/2.75	    inference('split', [status(esa)], ['3'])).
14.52/2.75	tff('198', plain,
14.52/2.75	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      != (((??(cS)) <=> (!!(cP))) <=> ((??(cS)) <=> (!!(cP)))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.75	          (((??(cS)) <=> (!!(cP)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.75	    inference('sup-', [status(thm)], ['196', '197'])).
14.52/2.75	tff('199', plain,
14.52/2.75	    (~ (((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	        (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.75	          (((??(cS)) <=> (!!(cP)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.75	    inference('simplify boolean subterms', [status(thm)], ['198'])).
14.52/2.75	tff('200', plain,
14.52/2.75	    (((??(cP)) <=> (!!(cQ)))
14.52/2.75	      != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.75	          (((??(cS)) <=> (!!(cP)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.75	    inference('simplify nested equalities', [status(thm)], ['199'])).
14.52/2.75	tff('201', plain,
14.52/2.75	    (~ ((??(cP)) <=> (!!(cQ))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.75	          (((??(cS)) <=> (!!(cP)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) & 
14.52/2.75	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.75	    inference('sup-', [status(thm)], ['195', '200'])).
14.52/2.75	tff('202', plain,
14.52/2.75	    ((??(cP)) != (!!(cQ)))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.75	          (((??(cS)) <=> (!!(cP)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) & 
14.52/2.75	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.75	    inference('simplify nested equalities', [status(thm)], ['201'])).
14.52/2.75	tff('203', plain, ( '#form19' | ~ ((??(cP)) <=> (!!(cQ)))),
14.52/2.75	    define([status(thm)])).
14.52/2.75	tff('204', plain, ( '#form19' | (??(cP)) != (!!(cQ))),
14.52/2.75	    inference('simplify nested equalities', [status(thm)], ['203'])).
14.52/2.75	tff('205', plain, ~ ((??(cP)) = (!!(cQ))) | ( '#form19'),
14.52/2.75	    inference('split', [status(esa)], ['204'])).
14.52/2.75	tff('206', plain, ( (??(cP))) | ((??(cP)) = (!!(cQ))) | ( (!!(cQ))),
14.52/2.75	    inference('split', [status(esa)], ['125'])).
14.52/2.75	tff('207', plain, ( '#form19') <= (( '#form19')),
14.52/2.75	    inference('split', [status(esa)], ['204'])).
14.52/2.75	tff('208', plain,
14.52/2.75	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.75	    inference('split', [status(esa)], ['87'])).
14.52/2.75	tff('209', plain,
14.52/2.75	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))
14.52/2.75	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.75	    inference('split', [status(esa)], ['54'])).
14.52/2.75	tff('210', plain,
14.52/2.75	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.75	          ((??(cS)) = (!!(cP)))),
14.52/2.75	    inference('simplify boolean subterms', [status(thm)], ['191'])).
14.52/2.75	tff('211', plain,
14.52/2.75	    (~ (((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	        (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.75	          ((??(cS)) = (!!(cP))) & 
14.52/2.75	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.75	    inference('sup-', [status(thm)], ['209', '210'])).
14.52/2.75	tff('212', plain,
14.52/2.75	    (((??(cP)) <=> (!!(cQ)))
14.52/2.75	      != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.75	          ((??(cS)) = (!!(cP))) & 
14.52/2.75	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.75	    inference('simplify nested equalities', [status(thm)], ['211'])).
14.52/2.75	tff('213', plain,
14.52/2.75	    (~ ((??(cP)) <=> (!!(cQ))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.75	          ((??(cS)) = (!!(cP))) & 
14.52/2.75	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) & 
14.52/2.75	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.75	    inference('sup-', [status(thm)], ['208', '212'])).
14.52/2.75	tff('214', plain,
14.52/2.75	    ((??(cP)) != (!!(cQ)))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.75	          ((??(cS)) = (!!(cP))) & 
14.52/2.75	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) & 
14.52/2.75	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.75	    inference('simplify nested equalities', [status(thm)], ['213'])).
14.52/2.75	tff('215', plain, ( '#form19' | ~ ((??(cP)) <=> (!!(cQ)))),
14.52/2.75	    define([status(thm)])).
14.52/2.75	tff('216', plain,
14.52/2.75	    (~ '#form19')
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.75	          ((??(cS)) = (!!(cP))) & 
14.52/2.75	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) & 
14.52/2.75	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.75	    inference('renaming', [status(thm)], ['214', '215'])).
14.52/2.75	tff('217', plain,
14.52/2.75	    ~ ( '#form19') | 
14.52/2.75	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) | 
14.52/2.75	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) | 
14.52/2.75	    ~ ((??(cS)) = (!!(cP))) | 
14.52/2.75	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))),
14.52/2.75	    inference('sup-', [status(thm)], ['207', '216'])).
14.52/2.75	tff('218', plain, ((??(cP)) = (!!(cQ))) <= (((??(cP)) = (!!(cQ)))),
14.52/2.75	    inference('split', [status(esa)], ['87'])).
14.52/2.75	tff('219', plain, (( (??(cP)) | ~ (!!(cQ)))) <= (((??(cP)) = (!!(cQ)))),
14.52/2.75	    inference('lazy_cnf_equiv', [status(thm)], ['218'])).
14.52/2.75	tff('220', plain, ~ ( (!!(cQ))) | ( (??(cP))) | ~ ((??(cP)) = (!!(cQ))),
14.52/2.75	    inference('split', [status(esa)], ['219'])).
14.52/2.75	tff('221', plain, ( (??(cS))) <= (( (??(cS)))),
14.52/2.75	    inference('split', [status(esa)], ['66'])).
14.52/2.75	tff('222', plain,
14.52/2.75	    ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.75	     ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	      ((!!(cR)) <=> (??(cQ)))))
14.52/2.75	     != ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) <=>
14.52/2.75	         (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.75	    inference('ho_norm', [status(thm)], ['0'])).
14.52/2.75	tff('223', plain,
14.52/2.75	    (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.75	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	       ((!!(cR)) <=> (??(cQ)))))
14.52/2.75	      != ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	           (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) <=>
14.52/2.75	          (($true <=> (!!(cP))) <=>
14.52/2.75	           (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))))
14.52/2.75	      <= (( (??(cS)))),
14.52/2.75	    inference('sup-', [status(thm)], ['221', '222'])).
14.52/2.75	tff('224', plain,
14.52/2.75	    (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.75	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	       ((!!(cR)) <=> (??(cQ)))))
14.52/2.75	      != ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	           (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) <=>
14.52/2.75	          ((!!(cP)) <=>
14.52/2.75	           (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))))
14.52/2.75	      <= (( (??(cS)))),
14.52/2.75	    inference('simplify boolean subterms', [status(thm)], ['223'])).
14.52/2.75	tff('225', plain,
14.52/2.75	    ((~ ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.75	         ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	          ((!!(cR)) <=> (??(cQ)))))
14.52/2.75	      | ~ ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) <=>
14.52/2.75	           ((!!(cP)) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))))
14.52/2.75	      <= (( (??(cS)))),
14.52/2.75	    inference('lazy_cnf_xor', [status(thm)], ['224'])).
14.52/2.75	tff('226', plain,
14.52/2.75	    (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.75	       != ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	           ((!!(cR)) <=> (??(cQ))))
14.52/2.75	      | (((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	         != ((!!(cP)) <=>
14.52/2.75	             (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))))
14.52/2.75	      <= (( (??(cS)))),
14.52/2.75	    inference('simplify nested equalities', [status(thm)], ['225'])).
14.52/2.75	tff('227', plain,
14.52/2.75	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      != ((!!(cP)) <=>
14.52/2.75	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = ((!!(cP)) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))),
14.52/2.75	    inference('split', [status(esa)], ['226'])).
14.52/2.75	tff('228', plain,
14.52/2.75	    (( (((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	        (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      |  ((!!(cP)) <=>
14.52/2.75	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = ((!!(cP)) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))),
14.52/2.75	    inference('lazy_cnf_xor', [status(thm)], ['227'])).
14.52/2.75	tff('229', plain,
14.52/2.75	    ((((??(cP)) <=> (!!(cQ)))
14.52/2.75	       = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))
14.52/2.75	      | (!!(cP))
14.52/2.75	         = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = ((!!(cP)) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))),
14.52/2.75	    inference('simplify nested equalities', [status(thm)], ['228'])).
14.52/2.75	tff('230', plain,
14.52/2.75	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      = ((!!(cP)) <=>
14.52/2.75	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) | 
14.52/2.75	    ((!!(cP)) = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) | 
14.52/2.75	    (((??(cP)) <=> (!!(cQ)))
14.52/2.75	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))),
14.52/2.75	    inference('split', [status(esa)], ['229'])).
14.52/2.75	tff('231', plain, ( (??(cS))) <= (( (??(cS)))),
14.52/2.75	    inference('split', [status(esa)], ['66'])).
14.52/2.75	tff('232', plain,
14.52/2.75	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      != (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))),
14.52/2.75	    inference('split', [status(esa)], ['3'])).
14.52/2.75	tff('233', plain,
14.52/2.75	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      != (($true <=> (!!(cP))) <=>
14.52/2.75	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.75	          ( (??(cS)))),
14.52/2.75	    inference('sup-', [status(thm)], ['231', '232'])).
14.52/2.75	tff('234', plain,
14.52/2.75	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      != ((!!(cP)) <=>
14.52/2.75	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.75	          ( (??(cS)))),
14.52/2.75	    inference('simplify boolean subterms', [status(thm)], ['233'])).
14.52/2.75	tff('235', plain,
14.52/2.75	    (( (((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	        (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      |  ((!!(cP)) <=>
14.52/2.75	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.75	          ( (??(cS)))),
14.52/2.75	    inference('lazy_cnf_xor', [status(thm)], ['234'])).
14.52/2.75	tff('236', plain,
14.52/2.75	    ((((??(cP)) <=> (!!(cQ)))
14.52/2.75	       = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))
14.52/2.75	      | (!!(cP))
14.52/2.75	         = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.75	          ( (??(cS)))),
14.52/2.75	    inference('simplify nested equalities', [status(thm)], ['235'])).
14.52/2.75	tff('237', plain,
14.52/2.75	    ((!!(cP)) = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))
14.52/2.75	      <= (((!!(cP))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.75	    inference('split', [status(esa)], ['236'])).
14.52/2.75	tff('238', plain,
14.52/2.75	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))
14.52/2.75	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.75	    inference('split', [status(esa)], ['54'])).
14.52/2.75	tff('239', plain,
14.52/2.75	    ( (!!(cP)))
14.52/2.75	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) & 
14.52/2.75	          ((!!(cP))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.75	    inference('sup+', [status(thm)], ['237', '238'])).
14.52/2.75	tff('240', plain, (~ '#form3' |  (!!(cP))), define([status(thm)])).
14.52/2.75	tff('241', plain,
14.52/2.75	    ( '#form3')
14.52/2.75	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) & 
14.52/2.75	          ((!!(cP))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.75	    inference('renaming', [status(thm)], ['239', '240'])).
14.52/2.75	tff('242', plain, (~ '#form3' |  (!!(cP))), define([status(thm)])).
14.52/2.75	tff('243', plain, (~ '#form3') <= (~ ( '#form3')),
14.52/2.75	    inference('split', [status(esa)], ['242'])).
14.52/2.75	tff('244', plain,
14.52/2.75	    ~
14.52/2.75	    ((!!(cP)) = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) | 
14.52/2.75	    ( '#form3') | 
14.52/2.75	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))),
14.52/2.75	    inference('sup-', [status(thm)], ['241', '243'])).
14.52/2.75	tff('245', plain, ( '#form9') <= (( '#form9')),
14.52/2.75	    inference('split', [status(esa)], ['60'])).
14.52/2.75	tff('246', plain,
14.52/2.75	    ((!!(cP)) = ((??(cS)) <=> (!!(cP))))
14.52/2.75	      <= (((!!(cP)) = ((??(cS)) <=> (!!(cP))))),
14.52/2.75	    inference('split', [status(esa)], ['99'])).
14.52/2.75	tff('247', plain,
14.52/2.75	    ((??(cS)) != ((??(cS)) <=> (!!(cP))))
14.52/2.75	      <= (~ ((??(cS)) = ((??(cS)) <=> (!!(cP))))),
14.52/2.75	    inference('split', [status(esa)], ['78'])).
14.52/2.75	tff('248', plain,
14.52/2.75	    ((??(cS)) != (!!(cP)))
14.52/2.75	      <= (~ ((??(cS)) = ((??(cS)) <=> (!!(cP)))) & 
14.52/2.75	          ((!!(cP)) = ((??(cS)) <=> (!!(cP))))),
14.52/2.75	    inference('sup-', [status(thm)], ['246', '247'])).
14.52/2.75	tff('249', plain, ( '#form9' | ~ ((??(cS)) <=> (!!(cP)))),
14.52/2.75	    define([status(thm)])).
14.52/2.75	tff('250', plain,
14.52/2.75	    (~ '#form9')
14.52/2.75	      <= (~ ((??(cS)) = ((??(cS)) <=> (!!(cP)))) & 
14.52/2.75	          ((!!(cP)) = ((??(cS)) <=> (!!(cP))))),
14.52/2.75	    inference('renaming', [status(thm)], ['248', '249'])).
14.52/2.75	tff('251', plain,
14.52/2.75	    ((??(cS)) = ((??(cS)) <=> (!!(cP)))) | ~ ( '#form9') | 
14.52/2.75	    ~ ((!!(cP)) = ((??(cS)) <=> (!!(cP)))),
14.52/2.75	    inference('sup-', [status(thm)], ['245', '250'])).
14.52/2.75	tff('252', plain, ( (!!(cP))) <= (((??(cS)) = (!!(cP))) & ( (??(cS)))),
14.52/2.75	    inference('sup+', [status(thm)], ['105', '106'])).
14.52/2.75	tff('253', plain, (~ '#form3' |  (!!(cP))), define([status(thm)])).
14.52/2.75	tff('254', plain, ( '#form3') <= (((??(cS)) = (!!(cP))) & ( (??(cS)))),
14.52/2.75	    inference('renaming', [status(thm)], ['252', '253'])).
14.52/2.75	tff('255', plain, (~ '#form3') <= (~ ( '#form3')),
14.52/2.75	    inference('split', [status(esa)], ['242'])).
14.52/2.75	tff('256', plain, ~ ((??(cS)) = (!!(cP))) | ( '#form3') | ~ ( (??(cS))),
14.52/2.75	    inference('sup-', [status(thm)], ['254', '255'])).
14.52/2.75	tff('257', plain,
14.52/2.75	    ((!!(cP)) = (??(cS)))
14.52/2.75	      <= (((??(cS)) = ((??(cS)) <=> (!!(cP)))) & 
14.52/2.75	          ((!!(cP)) = ((??(cS)) <=> (!!(cP))))),
14.52/2.75	    inference('sup+', [status(thm)], ['94', '100'])).
14.52/2.75	tff('258', plain, ( (??(cS))) <= (( (??(cS)))),
14.52/2.75	    inference('split', [status(esa)], ['66'])).
14.52/2.75	tff('259', plain,
14.52/2.75	    ( (!!(cP)))
14.52/2.75	      <= (( (??(cS))) & 
14.52/2.75	          ((??(cS)) = ((??(cS)) <=> (!!(cP)))) & 
14.52/2.75	          ((!!(cP)) = ((??(cS)) <=> (!!(cP))))),
14.52/2.75	    inference('sup+', [status(thm)], ['257', '258'])).
14.52/2.75	tff('260', plain, (~ '#form3' |  (!!(cP))), define([status(thm)])).
14.52/2.75	tff('261', plain,
14.52/2.75	    ( '#form3')
14.52/2.75	      <= (( (??(cS))) & 
14.52/2.75	          ((??(cS)) = ((??(cS)) <=> (!!(cP)))) & 
14.52/2.75	          ((!!(cP)) = ((??(cS)) <=> (!!(cP))))),
14.52/2.75	    inference('renaming', [status(thm)], ['259', '260'])).
14.52/2.75	tff('262', plain, (~ '#form3') <= (~ ( '#form3')),
14.52/2.75	    inference('split', [status(esa)], ['242'])).
14.52/2.75	tff('263', plain,
14.52/2.75	    ~ ((??(cS)) = ((??(cS)) <=> (!!(cP)))) | ( '#form3') | ~ ( (??(cS))) | 
14.52/2.75	    ~ ((!!(cP)) = ((??(cS)) <=> (!!(cP)))),
14.52/2.75	    inference('sup-', [status(thm)], ['261', '262'])).
14.52/2.75	tff('264', plain, ( '#form15') <= (( '#form15')),
14.52/2.75	    inference('split', [status(esa)], ['171'])).
14.52/2.75	tff('265', plain, ((!!(cR)) != (??(cQ))) <= (~ ((!!(cR)) = (??(cQ)))),
14.52/2.75	    inference('split', [status(esa)], ['13'])).
14.52/2.75	tff('266', plain, (( (!!(cR)) |  (??(cQ)))) <= (~ ((!!(cR)) = (??(cQ)))),
14.52/2.75	    inference('lazy_cnf_xor', [status(thm)], ['265'])).
14.52/2.75	tff('267', plain, ( (!!(cR))) <= (( (!!(cR)))),
14.52/2.75	    inference('split', [status(esa)], ['266'])).
14.52/2.75	tff('268', plain,
14.52/2.75	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))))
14.52/2.75	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))))),
14.52/2.75	    inference('split', [status(esa)], ['43'])).
14.52/2.75	tff('269', plain,
14.52/2.75	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.75	      != ((!!(cR)) <=> (??(cQ))))
14.52/2.75	      <= (~
14.52/2.75	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.75	            = ((!!(cR)) <=> (??(cQ))))),
14.52/2.75	    inference('split', [status(esa)], ['10'])).
14.52/2.75	tff('270', plain,
14.52/2.75	    (~ ((!!(cR)) <=> (??(cQ))))
14.52/2.75	      <= (~
14.52/2.75	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.75	            = ((!!(cR)) <=> (??(cQ)))) & 
14.52/2.75	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))))),
14.52/2.75	    inference('sup-', [status(thm)], ['268', '269'])).
14.52/2.75	tff('271', plain,
14.52/2.75	    ((!!(cR)) != (??(cQ)))
14.52/2.75	      <= (~
14.52/2.75	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.75	            = ((!!(cR)) <=> (??(cQ)))) & 
14.52/2.75	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))))),
14.52/2.75	    inference('simplify nested equalities', [status(thm)], ['270'])).
14.52/2.75	tff('272', plain,
14.52/2.75	    (~ (??(cQ)))
14.52/2.75	      <= (~
14.52/2.75	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.75	            = ((!!(cR)) <=> (??(cQ)))) & 
14.52/2.75	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))) & 
14.52/2.75	          ( (!!(cR)))),
14.52/2.75	    inference('sup-', [status(thm)], ['267', '271'])).
14.52/2.75	tff('273', plain, ( '#form15' | ~ (??(cQ))), define([status(thm)])).
14.52/2.75	tff('274', plain,
14.52/2.75	    (~ '#form15')
14.52/2.75	      <= (~
14.52/2.75	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.75	            = ((!!(cR)) <=> (??(cQ)))) & 
14.52/2.75	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))) & 
14.52/2.75	          ( (!!(cR)))),
14.52/2.75	    inference('renaming', [status(thm)], ['272', '273'])).
14.52/2.75	tff('275', plain,
14.52/2.75	    ~ ( (!!(cR))) | 
14.52/2.75	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.75	      = ((!!(cR)) <=> (??(cQ)))) | 
14.52/2.75	    ~ ( '#form15') | 
14.52/2.75	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))),
14.52/2.75	    inference('sup-', [status(thm)], ['264', '274'])).
14.52/2.75	tff('276', plain,
14.52/2.75	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.75	    inference('split', [status(esa)], ['87'])).
14.52/2.75	tff('277', plain,
14.52/2.75	    (((??(cP)) <=> (!!(cQ)))
14.52/2.75	      != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      <= (~
14.52/2.75	          (((??(cP)) <=> (!!(cQ)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.75	    inference('split', [status(esa)], ['51'])).
14.52/2.75	tff('278', plain,
14.52/2.75	    (~ ((??(cP)) <=> (!!(cQ))))
14.52/2.75	      <= (~
14.52/2.75	          (((??(cP)) <=> (!!(cQ)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) & 
14.52/2.75	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.75	    inference('sup-', [status(thm)], ['276', '277'])).
14.52/2.75	tff('279', plain,
14.52/2.75	    ((??(cP)) != (!!(cQ)))
14.52/2.75	      <= (~
14.52/2.75	          (((??(cP)) <=> (!!(cQ)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) & 
14.52/2.75	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.75	    inference('simplify nested equalities', [status(thm)], ['278'])).
14.52/2.75	tff('280', plain,
14.52/2.75	    (( (??(cP)) |  (!!(cQ))))
14.52/2.75	      <= (~
14.52/2.75	          (((??(cP)) <=> (!!(cQ)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) & 
14.52/2.75	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.75	    inference('lazy_cnf_xor', [status(thm)], ['279'])).
14.52/2.75	tff('281', plain,
14.52/2.75	    ( (??(cP))) | 
14.52/2.75	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) | 
14.52/2.75	    (((??(cP)) <=> (!!(cQ)))
14.52/2.75	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) | 
14.52/2.75	    ( (!!(cQ))), inference('split', [status(esa)], ['280'])).
14.52/2.75	tff('282', plain, ( '#form3') <= (( '#form3')),
14.52/2.75	    inference('split', [status(esa)], ['115'])).
14.52/2.75	tff('283', plain, (~ '#form3') <= (~ ( (!!(cP)))),
14.52/2.75	    inference('renaming', [status(thm)], ['116', '117'])).
14.52/2.75	tff('284', plain, ~ ( '#form3') | ( (!!(cP))),
14.52/2.75	    inference('sup-', [status(thm)], ['282', '283'])).
14.52/2.75	tff('285', plain, ( (!!(cP))) <= (( (!!(cP)))),
14.52/2.75	    inference('split', [status(esa)], ['66'])).
14.52/2.75	tff('286', plain,
14.52/2.75	    ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.75	     ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	      ((!!(cR)) <=> (??(cQ)))))
14.52/2.75	     != ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) <=>
14.52/2.75	         (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.75	    inference('ho_norm', [status(thm)], ['0'])).
14.52/2.75	tff('287', plain,
14.52/2.75	    (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.75	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	       ((!!(cR)) <=> (??(cQ)))))
14.52/2.75	      != ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	           (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) <=>
14.52/2.75	          (((??(cS)) <=> $true) <=>
14.52/2.75	           (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))))
14.52/2.75	      <= (( (!!(cP)))),
14.52/2.75	    inference('sup-', [status(thm)], ['285', '286'])).
14.52/2.75	tff('288', plain,
14.52/2.75	    (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.75	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	       ((!!(cR)) <=> (??(cQ)))))
14.52/2.75	      != ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	           (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) <=>
14.52/2.75	          ((??(cS)) <=>
14.52/2.75	           (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))))
14.52/2.75	      <= (( (!!(cP)))),
14.52/2.75	    inference('simplify boolean subterms', [status(thm)], ['287'])).
14.52/2.75	tff('289', plain,
14.52/2.75	    (( ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.75	        ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	         ((!!(cR)) <=> (??(cQ)))))
14.52/2.75	      |  ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	           (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) <=>
14.52/2.75	          ((??(cS)) <=>
14.52/2.75	           (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))))
14.52/2.75	      <= (( (!!(cP)))),
14.52/2.75	    inference('lazy_cnf_xor', [status(thm)], ['288'])).
14.52/2.75	tff('290', plain,
14.52/2.75	    (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.75	       = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	          ((!!(cR)) <=> (??(cQ))))
14.52/2.75	      | (((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	         = ((??(cS)) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))))
14.52/2.75	      <= (( (!!(cP)))),
14.52/2.75	    inference('simplify nested equalities', [status(thm)], ['289'])).
14.52/2.75	tff('291', plain,
14.52/2.75	    ~ ( (!!(cP))) | 
14.52/2.75	    ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.75	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	         ((!!(cR)) <=> (??(cQ))))) | 
14.52/2.75	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      = ((??(cS)) <=>
14.52/2.75	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.75	    inference('split', [status(esa)], ['290'])).
14.52/2.75	tff('292', plain, ( '#form15') <= (( '#form15')),
14.52/2.75	    inference('split', [status(esa)], ['171'])).
14.52/2.75	tff('293', plain, (~ (??(cQ))) <= (~ ( (!!(cR))) & ((!!(cR)) = (??(cQ)))),
14.52/2.75	    inference('sup-', [status(thm)], ['166', '169'])).
14.52/2.75	tff('294', plain, ( '#form15' | ~ (??(cQ))), define([status(thm)])).
14.52/2.75	tff('295', plain, (~ '#form15') <= (~ ( (!!(cR))) & ((!!(cR)) = (??(cQ)))),
14.52/2.75	    inference('renaming', [status(thm)], ['293', '294'])).
14.52/2.75	tff('296', plain, ~ ( '#form15') | ~ ((!!(cR)) = (??(cQ))) | ( (!!(cR))),
14.52/2.75	    inference('sup-', [status(thm)], ['292', '295'])).
14.52/2.75	tff('297', plain,
14.52/2.75	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      = ((??(cS)) <=>
14.52/2.75	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.75	      <= (((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = ((??(cS)) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))),
14.52/2.75	    inference('split', [status(esa)], ['290'])).
14.52/2.75	tff('298', plain,
14.52/2.75	    (( (((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	        (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      | ~ ((??(cS)) <=>
14.52/2.75	           (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))))
14.52/2.75	      <= (((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = ((??(cS)) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))),
14.52/2.75	    inference('lazy_cnf_equiv', [status(thm)], ['297'])).
14.52/2.75	tff('299', plain,
14.52/2.75	    ((((??(cP)) <=> (!!(cQ)))
14.52/2.75	       = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))
14.52/2.75	      | (??(cS))
14.52/2.75	         != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.75	      <= (((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = ((??(cS)) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))),
14.52/2.75	    inference('simplify nested equalities', [status(thm)], ['298'])).
14.52/2.75	tff('300', plain,
14.52/2.75	    ~
14.52/2.75	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      = ((??(cS)) <=>
14.52/2.75	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) | 
14.52/2.75	    ~
14.52/2.75	    ((??(cS)) = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) | 
14.52/2.75	    (((??(cP)) <=> (!!(cQ)))
14.52/2.75	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))),
14.52/2.75	    inference('split', [status(esa)], ['299'])).
14.52/2.75	tff('301', plain,
14.52/2.75	    (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.75	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	       ((!!(cR)) <=> (??(cQ)))))
14.52/2.75	      != ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	           (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) <=>
14.52/2.75	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.75	      <= (((??(cS)) = (!!(cP)))),
14.52/2.75	    inference('simplify boolean subterms', [status(thm)], ['184'])).
14.52/2.75	tff('302', plain,
14.52/2.75	    ((~ ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.75	         ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	          ((!!(cR)) <=> (??(cQ)))))
14.52/2.75	      | ~ ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) <=>
14.52/2.75	           (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))))
14.52/2.75	      <= (((??(cS)) = (!!(cP)))),
14.52/2.75	    inference('lazy_cnf_xor', [status(thm)], ['301'])).
14.52/2.75	tff('303', plain,
14.52/2.75	    (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.75	       != ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	           ((!!(cR)) <=> (??(cQ))))
14.52/2.75	      | (((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	         != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.75	      <= (((??(cS)) = (!!(cP)))),
14.52/2.75	    inference('simplify nested equalities', [status(thm)], ['302'])).
14.52/2.75	tff('304', plain,
14.52/2.75	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.75	    inference('split', [status(esa)], ['303'])).
14.52/2.75	tff('305', plain,
14.52/2.75	    (( (((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	        (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      |  (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.75	    inference('lazy_cnf_xor', [status(thm)], ['304'])).
14.52/2.75	tff('306', plain,
14.52/2.75	    ((((??(cP)) <=> (!!(cQ)))
14.52/2.75	       = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))
14.52/2.75	      |  (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.75	    inference('simplify nested equalities', [status(thm)], ['305'])).
14.52/2.75	tff('307', plain,
14.52/2.75	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) | 
14.52/2.75	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) | 
14.52/2.75	    (((??(cP)) <=> (!!(cQ)))
14.52/2.75	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))),
14.52/2.75	    inference('split', [status(esa)], ['306'])).
14.52/2.75	tff('308', plain,
14.52/2.75	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      != ((??(cS)) <=>
14.52/2.75	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.75	          ( (!!(cP)))),
14.52/2.75	    inference('simplify boolean subterms', [status(thm)], ['74'])).
14.52/2.75	tff('309', plain,
14.52/2.75	    ((~ (((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      | ~ ((??(cS)) <=>
14.52/2.75	           (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.75	          ( (!!(cP)))),
14.52/2.75	    inference('lazy_cnf_xor', [status(thm)], ['308'])).
14.52/2.75	tff('310', plain,
14.52/2.75	    ((((??(cP)) <=> (!!(cQ)))
14.52/2.75	       != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))
14.52/2.75	      | (??(cS))
14.52/2.75	         != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.75	          ( (!!(cP)))),
14.52/2.75	    inference('simplify nested equalities', [status(thm)], ['309'])).
14.52/2.75	tff('311', plain,
14.52/2.75	    ((??(cS)) != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))
14.52/2.75	      <= (~
14.52/2.75	          ((??(cS))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.75	    inference('split', [status(esa)], ['310'])).
14.52/2.75	tff('312', plain,
14.52/2.75	    (( (??(cS))
14.52/2.75	      |  (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.75	      <= (~
14.52/2.75	          ((??(cS))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.75	    inference('lazy_cnf_xor', [status(thm)], ['311'])).
14.52/2.75	tff('313', plain,
14.52/2.75	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) | 
14.52/2.75	    ((??(cS)) = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) | 
14.52/2.75	    ( (??(cS))), inference('split', [status(esa)], ['312'])).
14.52/2.75	tff('314', plain,
14.52/2.75	    (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.75	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	       ((!!(cR)) <=> (??(cQ)))))
14.52/2.75	      != ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	           (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) <=>
14.52/2.75	          ((??(cS)) <=>
14.52/2.75	           (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))))
14.52/2.75	      <= (( (!!(cP)))),
14.52/2.75	    inference('simplify boolean subterms', [status(thm)], ['287'])).
14.52/2.75	tff('315', plain,
14.52/2.75	    ((~ ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.75	         ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	          ((!!(cR)) <=> (??(cQ)))))
14.52/2.75	      | ~ ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) <=>
14.52/2.75	           ((??(cS)) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))))
14.52/2.75	      <= (( (!!(cP)))),
14.52/2.75	    inference('lazy_cnf_xor', [status(thm)], ['314'])).
14.52/2.75	tff('316', plain,
14.52/2.75	    (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.75	       != ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	           ((!!(cR)) <=> (??(cQ))))
14.52/2.75	      | (((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	         != ((??(cS)) <=>
14.52/2.75	             (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))))
14.52/2.75	      <= (( (!!(cP)))),
14.52/2.75	    inference('simplify nested equalities', [status(thm)], ['315'])).
14.52/2.75	tff('317', plain,
14.52/2.75	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      != ((??(cS)) <=>
14.52/2.75	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = ((??(cS)) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))),
14.52/2.75	    inference('split', [status(esa)], ['316'])).
14.52/2.75	tff('318', plain,
14.52/2.75	    (( (((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	        (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      |  ((??(cS)) <=>
14.52/2.75	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = ((??(cS)) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))),
14.52/2.75	    inference('lazy_cnf_xor', [status(thm)], ['317'])).
14.52/2.75	tff('319', plain,
14.52/2.75	    ((((??(cP)) <=> (!!(cQ)))
14.52/2.75	       = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))
14.52/2.75	      | (??(cS))
14.52/2.75	         = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = ((??(cS)) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))),
14.52/2.75	    inference('simplify nested equalities', [status(thm)], ['318'])).
14.52/2.75	tff('320', plain,
14.52/2.75	    ((??(cS)) = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) | 
14.52/2.75	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      = ((??(cS)) <=>
14.52/2.75	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) | 
14.52/2.75	    (((??(cP)) <=> (!!(cQ)))
14.52/2.75	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))),
14.52/2.75	    inference('split', [status(esa)], ['319'])).
14.52/2.75	tff('321', plain,
14.52/2.75	    ~ ((??(cP)) = (!!(cQ))) | 
14.52/2.75	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) | 
14.52/2.75	    (((??(cP)) <=> (!!(cQ)))
14.52/2.75	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))),
14.52/2.75	    inference('split', [status(esa)], ['123'])).
14.52/2.75	tff('322', plain,
14.52/2.75	    (((??(cS)) <=> (!!(cP)))
14.52/2.75	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))
14.52/2.75	      <= ((((??(cS)) <=> (!!(cP)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.75	    inference('split', [status(esa)], ['70'])).
14.52/2.75	tff('323', plain,
14.52/2.75	    ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.75	     ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	      ((!!(cR)) <=> (??(cQ)))))
14.52/2.75	     != ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) <=>
14.52/2.75	         (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.75	    inference('ho_norm', [status(thm)], ['0'])).
14.52/2.75	tff('324', plain,
14.52/2.75	    (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.75	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	       ((!!(cR)) <=> (??(cQ)))))
14.52/2.75	      != ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	           (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) <=>
14.52/2.75	          (((??(cS)) <=> (!!(cP))) <=> ((??(cS)) <=> (!!(cP))))))
14.52/2.75	      <= ((((??(cS)) <=> (!!(cP)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.75	    inference('sup-', [status(thm)], ['322', '323'])).
14.52/2.75	tff('325', plain,
14.52/2.75	    (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.75	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	       ((!!(cR)) <=> (??(cQ)))))
14.52/2.75	      != (((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))))
14.52/2.75	      <= ((((??(cS)) <=> (!!(cP)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.75	    inference('simplify boolean subterms', [status(thm)], ['324'])).
14.52/2.75	tff('326', plain,
14.52/2.75	    (( ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.75	        ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	         ((!!(cR)) <=> (??(cQ)))))
14.52/2.75	      |  (((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))))
14.52/2.75	      <= ((((??(cS)) <=> (!!(cP)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.75	    inference('lazy_cnf_xor', [status(thm)], ['325'])).
14.52/2.75	tff('327', plain,
14.52/2.75	    (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.75	       = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	          ((!!(cR)) <=> (??(cQ))))
14.52/2.75	      | ((??(cP)) <=> (!!(cQ)))
14.52/2.75	         = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))))
14.52/2.75	      <= ((((??(cS)) <=> (!!(cP)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.75	    inference('simplify nested equalities', [status(thm)], ['326'])).
14.52/2.75	tff('328', plain,
14.52/2.75	    ~
14.52/2.75	    (((??(cS)) <=> (!!(cP)))
14.52/2.75	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) | 
14.52/2.75	    ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.75	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	         ((!!(cR)) <=> (??(cQ))))) | 
14.52/2.75	    (((??(cP)) <=> (!!(cQ)))
14.52/2.75	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))),
14.52/2.75	    inference('split', [status(esa)], ['327'])).
14.52/2.75	tff('329', plain, ((!!(cR)) = (??(cQ))) <= (((!!(cR)) = (??(cQ)))),
14.52/2.75	    inference('split', [status(esa)], ['43'])).
14.52/2.75	tff('330', plain, ((~ (!!(cR)) |  (??(cQ)))) <= (((!!(cR)) = (??(cQ)))),
14.52/2.75	    inference('lazy_cnf_equiv', [status(thm)], ['329'])).
14.52/2.75	tff('331', plain, ~ ( (!!(cR))) | ~ ((!!(cR)) = (??(cQ))) | ( (??(cQ))),
14.52/2.75	    inference('split', [status(esa)], ['330'])).
14.52/2.75	tff('332', plain,
14.52/2.75	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.75	          ((??(cS)) = (!!(cP)))),
14.52/2.75	    inference('simplify boolean subterms', [status(thm)], ['191'])).
14.52/2.75	tff('333', plain,
14.52/2.75	    (( (((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	        (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      |  (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.75	          ((??(cS)) = (!!(cP)))),
14.52/2.75	    inference('lazy_cnf_xor', [status(thm)], ['332'])).
14.52/2.75	tff('334', plain,
14.52/2.75	    ((((??(cP)) <=> (!!(cQ)))
14.52/2.75	       = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))
14.52/2.75	      |  (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.75	          ((??(cS)) = (!!(cP)))),
14.52/2.75	    inference('simplify nested equalities', [status(thm)], ['333'])).
14.52/2.75	tff('335', plain,
14.52/2.75	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) | 
14.52/2.75	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) | 
14.52/2.75	    (((??(cP)) <=> (!!(cQ)))
14.52/2.75	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) | 
14.52/2.75	    ~ ((??(cS)) = (!!(cP))), inference('split', [status(esa)], ['334'])).
14.52/2.75	tff('336', plain, ~ ( (!!(cP))) | ((??(cS)) = (!!(cP))) | ~ ( (??(cS))),
14.52/2.75	    inference('split', [status(esa)], ['112'])).
14.52/2.75	tff('337', plain,
14.52/2.75	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))
14.52/2.75	      <= (((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.75	    inference('split', [status(esa)], ['187'])).
14.52/2.75	tff('338', plain,
14.52/2.75	    (( (((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	        (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      | ~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.75	      <= (((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.75	    inference('lazy_cnf_equiv', [status(thm)], ['337'])).
14.52/2.75	tff('339', plain,
14.52/2.75	    ((((??(cP)) <=> (!!(cQ)))
14.52/2.75	       = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))
14.52/2.75	      | ~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.75	      <= (((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.75	    inference('simplify nested equalities', [status(thm)], ['338'])).
14.52/2.75	tff('340', plain,
14.52/2.75	    ~
14.52/2.75	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) | 
14.52/2.75	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) | 
14.52/2.75	    (((??(cP)) <=> (!!(cQ)))
14.52/2.75	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))),
14.52/2.75	    inference('split', [status(esa)], ['339'])).
14.52/2.75	tff('341', plain,
14.52/2.75	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) | 
14.52/2.75	    ((??(cP)) = (!!(cQ))) | 
14.52/2.75	    (((??(cP)) <=> (!!(cQ)))
14.52/2.75	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))),
14.52/2.75	    inference('split', [status(esa)], ['87'])).
14.52/2.75	tff('342', plain,
14.52/2.75	    ((??(cP)) != (!!(cQ)))
14.52/2.75	      <= (~
14.52/2.75	          (((??(cP)) <=> (!!(cQ)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) & 
14.52/2.75	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.75	    inference('simplify nested equalities', [status(thm)], ['278'])).
14.52/2.75	tff('343', plain,
14.52/2.75	    ((~ (??(cP)) | ~ (!!(cQ))))
14.52/2.75	      <= (~
14.52/2.75	          (((??(cP)) <=> (!!(cQ)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) & 
14.52/2.75	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.75	    inference('lazy_cnf_xor', [status(thm)], ['342'])).
14.52/2.75	tff('344', plain,
14.52/2.75	    ~ ( (!!(cQ))) | 
14.52/2.75	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) | 
14.52/2.75	    (((??(cP)) <=> (!!(cQ)))
14.52/2.75	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) | 
14.52/2.75	    ~ ( (??(cP))), inference('split', [status(esa)], ['343'])).
14.52/2.75	tff('345', plain,
14.52/2.75	    ~ ((??(cS)) = (!!(cP))) | 
14.52/2.75	    ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.75	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	         ((!!(cR)) <=> (??(cQ))))) | 
14.52/2.75	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))),
14.52/2.75	    inference('split', [status(esa)], ['187'])).
14.52/2.75	tff('346', plain,
14.52/2.75	    (~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))))
14.52/2.75	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))))),
14.52/2.75	    inference('split', [status(esa)], ['13'])).
14.52/2.75	tff('347', plain,
14.52/2.75	    (![X1]: ~ (!!((^[Y0 : $i]: (cP(Y0) <=> cP(X1))))))
14.52/2.75	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))))),
14.52/2.75	    inference('lazy_cnf_forall', [status(thm)], ['346'])).
14.52/2.75	tff('348', plain,
14.52/2.75	    (![X1]: ~ (cP('#sk31'(X1)) <=> cP(X1)))
14.52/2.75	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))))),
14.52/2.75	    inference('lazy_cnf_exists', [status(thm)], ['347'])).
14.52/2.75	tff('349', plain,
14.52/2.75	    (![X1]: cP('#sk31'(X1)) != cP(X1))
14.52/2.75	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))))),
14.52/2.75	    inference('simplify nested equalities', [status(thm)], ['348'])).
14.52/2.75	tff('350', plain,
14.52/2.75	    (![X1]: ( cP('#sk31'(X1)) |  cP(X1)))
14.52/2.75	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))))),
14.52/2.75	    inference('lazy_cnf_xor', [status(thm)], ['349'])).
14.52/2.75	tff('351', plain, (~ (??(cP))) <= (~ ( (??(cP)))),
14.52/2.75	    inference('split', [status(esa)], ['151'])).
14.52/2.75	tff('352', plain, (![X1]: ~ cP(X1)) <= (~ ( (??(cP)))),
14.52/2.75	    inference('lazy_cnf_forall', [status(thm)], ['351'])).
14.52/2.75	tff('353', plain,
14.52/2.75	    (![X0]:  cP(X0))
14.52/2.75	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))) & 
14.52/2.75	          ~ ( (??(cP)))),
14.52/2.75	    inference('sup-', [status(thm)], ['350', '352'])).
14.52/2.75	tff('354', plain, (![X1]: ~ cP(X1)) <= (~ ( (??(cP)))),
14.52/2.75	    inference('lazy_cnf_forall', [status(thm)], ['351'])).
14.52/2.75	tff('355', plain,
14.52/2.75	    ( (??(cP))) | 
14.52/2.75	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))),
14.52/2.75	    inference('sup-', [status(thm)], ['353', '354'])).
14.52/2.75	tff('356', plain, ( (!!(cP))) <= (( (!!(cP)))),
14.52/2.75	    inference('split', [status(esa)], ['66'])).
14.52/2.75	tff('357', plain, (![X1]:  cP(X1)) <= (( (!!(cP)))),
14.52/2.75	    inference('lazy_cnf_forall', [status(thm)], ['356'])).
14.52/2.75	tff('358', plain, (![X1]: ~ cP(X1)) <= (~ ( (??(cP)))),
14.52/2.75	    inference('lazy_cnf_forall', [status(thm)], ['351'])).
14.52/2.75	tff('359', plain, ~ ( (!!(cP))) | ( (??(cP))),
14.52/2.75	    inference('sup-', [status(thm)], ['357', '358'])).
14.52/2.75	tff('360', plain,
14.52/2.75	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      = ((??(cS)) <=>
14.52/2.75	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.75	      <= (((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = ((??(cS)) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))),
14.52/2.75	    inference('split', [status(esa)], ['290'])).
14.52/2.75	tff('361', plain,
14.52/2.75	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      != ((??(cS)) <=>
14.52/2.75	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.75	          ( (!!(cP)))),
14.52/2.75	    inference('simplify boolean subterms', [status(thm)], ['74'])).
14.52/2.75	tff('362', plain,
14.52/2.75	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      != (((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))))
14.52/2.75	      <= (~
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.75	          ( (!!(cP))) & 
14.52/2.75	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = ((??(cS)) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))),
14.52/2.75	    inference('sup-', [status(thm)], ['360', '361'])).
14.52/2.75	tff('363', plain,
14.52/2.75	    ~ ( (!!(cP))) | 
14.52/2.75	    ~
14.52/2.75	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      = ((??(cS)) <=>
14.52/2.75	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) | 
14.52/2.75	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.75	    inference('simplify', [status(thm)], ['362'])).
14.52/2.75	tff('364', plain,
14.52/2.75	    ((??(cS)) != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))
14.52/2.75	      <= (~
14.52/2.75	          ((??(cS))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.75	    inference('split', [status(esa)], ['310'])).
14.52/2.75	tff('365', plain,
14.52/2.75	    ((~ (??(cS))
14.52/2.75	      | ~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.75	      <= (~
14.52/2.75	          ((??(cS))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.75	    inference('lazy_cnf_xor', [status(thm)], ['364'])).
14.52/2.75	tff('366', plain,
14.52/2.75	    ((??(cS)) = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) | 
14.52/2.75	    ~ ( (??(cS))) | 
14.52/2.75	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))),
14.52/2.75	    inference('split', [status(esa)], ['365'])).
14.52/2.75	tff('367', plain,
14.52/2.75	    ((??(cR)) != (!!(cS)))
14.52/2.75	      <= (~
14.52/2.75	          (((??(cR)) <=> (!!(cS)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) & 
14.52/2.75	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
14.52/2.75	    inference('simplify nested equalities', [status(thm)], ['162'])).
14.52/2.75	tff('368', plain,
14.52/2.75	    (( (??(cR)) |  (!!(cS))))
14.52/2.75	      <= (~
14.52/2.75	          (((??(cR)) <=> (!!(cS)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) & 
14.52/2.75	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
14.52/2.75	    inference('lazy_cnf_xor', [status(thm)], ['367'])).
14.52/2.75	tff('369', plain,
14.52/2.75	    ( (!!(cS))) | 
14.52/2.75	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) | 
14.52/2.75	    (((??(cR)) <=> (!!(cS)))
14.52/2.75	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) | 
14.52/2.75	    ( (??(cR))), inference('split', [status(esa)], ['368'])).
14.52/2.75	tff('370', plain,
14.52/2.75	    (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.75	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	       ((!!(cR)) <=> (??(cQ)))))
14.52/2.75	      != ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	           (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) <=>
14.52/2.75	          ((!!(cP)) <=>
14.52/2.75	           (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))))
14.52/2.75	      <= (( (??(cS)))),
14.52/2.75	    inference('simplify boolean subterms', [status(thm)], ['223'])).
14.52/2.75	tff('371', plain,
14.52/2.75	    (( ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.75	        ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	         ((!!(cR)) <=> (??(cQ)))))
14.52/2.75	      |  ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	           (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) <=>
14.52/2.75	          ((!!(cP)) <=>
14.52/2.75	           (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))))
14.52/2.75	      <= (( (??(cS)))),
14.52/2.75	    inference('lazy_cnf_xor', [status(thm)], ['370'])).
14.52/2.75	tff('372', plain,
14.52/2.75	    (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.75	       = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	          ((!!(cR)) <=> (??(cQ))))
14.52/2.75	      | (((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	         = ((!!(cP)) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))))
14.52/2.75	      <= (( (??(cS)))),
14.52/2.75	    inference('simplify nested equalities', [status(thm)], ['371'])).
14.52/2.75	tff('373', plain,
14.52/2.75	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      = ((!!(cP)) <=>
14.52/2.75	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) | 
14.52/2.75	    ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.75	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.75	         ((!!(cR)) <=> (??(cQ))))) | 
14.52/2.75	    ~ ( (??(cS))), inference('split', [status(esa)], ['372'])).
14.52/2.75	tff('374', plain,
14.52/2.75	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      = ((!!(cP)) <=>
14.52/2.75	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.75	      <= (((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = ((!!(cP)) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))),
14.52/2.75	    inference('split', [status(esa)], ['372'])).
14.52/2.75	tff('375', plain,
14.52/2.75	    ((~ (((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      |  ((!!(cP)) <=>
14.52/2.75	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))))
14.52/2.75	      <= (((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = ((!!(cP)) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))),
14.52/2.75	    inference('lazy_cnf_equiv', [status(thm)], ['374'])).
14.52/2.75	tff('376', plain,
14.52/2.75	    ((((??(cP)) <=> (!!(cQ)))
14.52/2.75	       != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))
14.52/2.75	      | (!!(cP))
14.52/2.75	         = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.75	      <= (((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = ((!!(cP)) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))),
14.52/2.75	    inference('simplify nested equalities', [status(thm)], ['375'])).
14.52/2.75	tff('377', plain,
14.52/2.75	    ~
14.52/2.75	    (((??(cP)) <=> (!!(cQ)))
14.52/2.75	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) | 
14.52/2.75	    ~
14.52/2.75	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      = ((!!(cP)) <=>
14.52/2.75	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) | 
14.52/2.75	    ((!!(cP)) = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))),
14.52/2.75	    inference('split', [status(esa)], ['376'])).
14.52/2.75	tff('378', plain,
14.52/2.75	    (((??(cS)) <=> (!!(cP)))
14.52/2.75	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))
14.52/2.75	      <= ((((??(cS)) <=> (!!(cP)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.75	    inference('split', [status(esa)], ['70'])).
14.52/2.75	tff('379', plain,
14.52/2.75	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.75	      <= (((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))),
14.52/2.75	    inference('split', [status(esa)], ['26'])).
14.52/2.75	tff('380', plain,
14.52/2.75	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      = (((??(cS)) <=> (!!(cP))) <=> ((??(cS)) <=> (!!(cP)))))
14.52/2.75	      <= (((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.75	          (((??(cS)) <=> (!!(cP)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.75	    inference('sup+', [status(thm)], ['378', '379'])).
14.52/2.75	tff('381', plain,
14.52/2.75	    ( (((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))))
14.52/2.75	      <= (((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.75	          (((??(cS)) <=> (!!(cP)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.75	    inference('simplify boolean subterms', [status(thm)], ['380'])).
14.52/2.75	tff('382', plain,
14.52/2.75	    (((??(cP)) <=> (!!(cQ)))
14.52/2.75	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      <= (((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.75	          (((??(cS)) <=> (!!(cP)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.75	    inference('simplify nested equalities', [status(thm)], ['381'])).
14.52/2.75	tff('383', plain,
14.52/2.75	    (((??(cS)) <=> (!!(cP)))
14.52/2.75	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))
14.52/2.75	      <= ((((??(cS)) <=> (!!(cP)))
14.52/2.75	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.75	    inference('split', [status(esa)], ['70'])).
14.52/2.75	tff('384', plain, ( (!!(cP))) <= (( (!!(cP)))),
14.52/2.75	    inference('split', [status(esa)], ['66'])).
14.52/2.75	tff('385', plain,
14.52/2.75	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.75	      <= (((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))),
14.52/2.75	    inference('split', [status(esa)], ['26'])).
14.52/2.75	tff('386', plain,
14.52/2.75	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      = (((??(cS)) <=> $true) <=>
14.52/2.75	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.75	      <= (((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.75	          ( (!!(cP)))),
14.52/2.75	    inference('sup+', [status(thm)], ['384', '385'])).
14.52/2.75	tff('387', plain,
14.52/2.75	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	      = ((??(cS)) <=>
14.52/2.75	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.75	      <= (((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.75	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.75	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.75	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.76	          ( (!!(cP)))),
14.52/2.76	    inference('simplify boolean subterms', [status(thm)], ['386'])).
14.52/2.76	tff('388', plain,
14.52/2.76	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	      = ((??(cS)) <=> ((??(cS)) <=> (!!(cP)))))
14.52/2.76	      <= (((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.76	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.76	          (((??(cS)) <=> (!!(cP)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) & 
14.52/2.76	          ( (!!(cP)))),
14.52/2.76	    inference('sup+', [status(thm)], ['383', '387'])).
14.52/2.76	tff('389', plain,
14.52/2.76	    ((((??(cP)) <=> (!!(cQ))) <=> ((??(cP)) <=> (!!(cQ))))
14.52/2.76	      = ((??(cS)) <=> ((??(cS)) <=> (!!(cP)))))
14.52/2.76	      <= (((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.76	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.76	          (((??(cS)) <=> (!!(cP)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) & 
14.52/2.76	          ( (!!(cP)))),
14.52/2.76	    inference('sup+', [status(thm)], ['382', '388'])).
14.52/2.76	tff('390', plain,
14.52/2.76	    ( ((??(cS)) <=> ((??(cS)) <=> (!!(cP)))))
14.52/2.76	      <= (((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.76	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.76	          (((??(cS)) <=> (!!(cP)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) & 
14.52/2.76	          ( (!!(cP)))),
14.52/2.76	    inference('simplify boolean subterms', [status(thm)], ['389'])).
14.52/2.76	tff('391', plain,
14.52/2.76	    ((??(cS)) = ((??(cS)) <=> (!!(cP))))
14.52/2.76	      <= (((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.76	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.76	          (((??(cS)) <=> (!!(cP)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) & 
14.52/2.76	          ( (!!(cP)))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['390'])).
14.52/2.76	tff('392', plain,
14.52/2.76	    (( (??(cS)) | ~ ((??(cS)) <=> (!!(cP)))))
14.52/2.76	      <= (((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.76	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.76	          (((??(cS)) <=> (!!(cP)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) & 
14.52/2.76	          ( (!!(cP)))),
14.52/2.76	    inference('lazy_cnf_equiv', [status(thm)], ['391'])).
14.52/2.76	tff('393', plain,
14.52/2.76	    (( (??(cS)) | (??(cS)) != (!!(cP))))
14.52/2.76	      <= (((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.76	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.76	          (((??(cS)) <=> (!!(cP)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) & 
14.52/2.76	          ( (!!(cP)))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['392'])).
14.52/2.76	tff('394', plain,
14.52/2.76	    ~ ( (!!(cP))) | 
14.52/2.76	    ~
14.52/2.76	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	      = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.76	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) | 
14.52/2.76	    ~ ((??(cS)) = (!!(cP))) | ( (??(cS))) | 
14.52/2.76	    ~
14.52/2.76	    (((??(cS)) <=> (!!(cP)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))),
14.52/2.76	    inference('split', [status(esa)], ['393'])).
14.52/2.76	tff('395', plain,
14.52/2.76	    (((??(cS)) <=> (!!(cP)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))
14.52/2.76	      <= ((((??(cS)) <=> (!!(cP)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('split', [status(esa)], ['70'])).
14.52/2.76	tff('396', plain,
14.52/2.76	    (( ((??(cS)) <=> (!!(cP)))
14.52/2.76	      | ~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.76	      <= ((((??(cS)) <=> (!!(cP)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('lazy_cnf_equiv', [status(thm)], ['395'])).
14.52/2.76	tff('397', plain,
14.52/2.76	    (((??(cS)) = (!!(cP))
14.52/2.76	      | ~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.76	      <= ((((??(cS)) <=> (!!(cP)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['396'])).
14.52/2.76	tff('398', plain,
14.52/2.76	    ~
14.52/2.76	    (((??(cS)) <=> (!!(cP)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) | 
14.52/2.76	    ((??(cS)) = (!!(cP))) | 
14.52/2.76	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))),
14.52/2.76	    inference('split', [status(esa)], ['397'])).
14.52/2.76	tff('399', plain,
14.52/2.76	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	      != ((!!(cP)) <=>
14.52/2.76	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.76	      <= (~
14.52/2.76	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	            = ((!!(cP)) <=>
14.52/2.76	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))),
14.52/2.76	    inference('split', [status(esa)], ['226'])).
14.52/2.76	tff('400', plain,
14.52/2.76	    ((~ (((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	      | ~ ((!!(cP)) <=>
14.52/2.76	           (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))))
14.52/2.76	      <= (~
14.52/2.76	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	            = ((!!(cP)) <=>
14.52/2.76	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))),
14.52/2.76	    inference('lazy_cnf_xor', [status(thm)], ['399'])).
14.52/2.76	tff('401', plain,
14.52/2.76	    ((((??(cP)) <=> (!!(cQ)))
14.52/2.76	       != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))
14.52/2.76	      | (!!(cP))
14.52/2.76	         != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.76	      <= (~
14.52/2.76	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	            = ((!!(cP)) <=>
14.52/2.76	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['400'])).
14.52/2.76	tff('402', plain,
14.52/2.76	    ~
14.52/2.76	    (((??(cP)) <=> (!!(cQ)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) | 
14.52/2.76	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	      = ((!!(cP)) <=>
14.52/2.76	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) | 
14.52/2.76	    ~
14.52/2.76	    ((!!(cP)) = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))),
14.52/2.76	    inference('split', [status(esa)], ['401'])).
14.52/2.76	tff('403', plain,
14.52/2.76	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	      != ((!!(cP)) <=>
14.52/2.76	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.76	      <= (~
14.52/2.76	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.76	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.76	          ( (??(cS)))),
14.52/2.76	    inference('simplify boolean subterms', [status(thm)], ['233'])).
14.52/2.76	tff('404', plain,
14.52/2.76	    ((~ (((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	      | ~ ((!!(cP)) <=>
14.52/2.76	           (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))))
14.52/2.76	      <= (~
14.52/2.76	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.76	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.76	          ( (??(cS)))),
14.52/2.76	    inference('lazy_cnf_xor', [status(thm)], ['403'])).
14.52/2.76	tff('405', plain,
14.52/2.76	    ((((??(cP)) <=> (!!(cQ)))
14.52/2.76	       != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))
14.52/2.76	      | (!!(cP))
14.52/2.76	         != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.76	      <= (~
14.52/2.76	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.76	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.76	          ( (??(cS)))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['404'])).
14.52/2.76	tff('406', plain,
14.52/2.76	    ((!!(cP)) != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))
14.52/2.76	      <= (~
14.52/2.76	          ((!!(cP))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('split', [status(esa)], ['405'])).
14.52/2.76	tff('407', plain,
14.52/2.76	    ((~ (!!(cP))
14.52/2.76	      | ~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.76	      <= (~
14.52/2.76	          ((!!(cP))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('lazy_cnf_xor', [status(thm)], ['406'])).
14.52/2.76	tff('408', plain,
14.52/2.76	    ~ ( (!!(cP))) | 
14.52/2.76	    ((!!(cP)) = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) | 
14.52/2.76	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))),
14.52/2.76	    inference('split', [status(esa)], ['407'])).
14.52/2.76	tff('409', plain,
14.52/2.76	    ((!!(cP)) = ((??(cS)) <=> (!!(cP))))
14.52/2.76	      <= (((!!(cP)) = ((??(cS)) <=> (!!(cP))))),
14.52/2.76	    inference('split', [status(esa)], ['99'])).
14.52/2.76	tff('410', plain,
14.52/2.76	    (( (!!(cP)) | ~ ((??(cS)) <=> (!!(cP)))))
14.52/2.76	      <= (((!!(cP)) = ((??(cS)) <=> (!!(cP))))),
14.52/2.76	    inference('lazy_cnf_equiv', [status(thm)], ['409'])).
14.52/2.76	tff('411', plain,
14.52/2.76	    (( (!!(cP)) | (??(cS)) != (!!(cP))))
14.52/2.76	      <= (((!!(cP)) = ((??(cS)) <=> (!!(cP))))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['410'])).
14.52/2.76	tff('412', plain,
14.52/2.76	    ~ ((??(cS)) = (!!(cP))) | ( (!!(cP))) | 
14.52/2.76	    ~ ((!!(cP)) = ((??(cS)) <=> (!!(cP)))),
14.52/2.76	    inference('split', [status(esa)], ['411'])).
14.52/2.76	tff('413', plain, ((!!(cR)) = (??(cQ))) <= (((!!(cR)) = (??(cQ)))),
14.52/2.76	    inference('split', [status(esa)], ['43'])).
14.52/2.76	tff('414', plain, ( (!!(cR))) <= (( (!!(cR)))),
14.52/2.76	    inference('split', [status(esa)], ['266'])).
14.52/2.76	tff('415', plain, ( (??(cQ))) <= (((!!(cR)) = (??(cQ))) & ( (!!(cR)))),
14.52/2.76	    inference('sup+', [status(thm)], ['413', '414'])).
14.52/2.76	tff('416', plain, ( (??(cQ))) <= (((!!(cR)) = (??(cQ))) & ( (!!(cR)))),
14.52/2.76	    inference('sup+', [status(thm)], ['413', '414'])).
14.52/2.76	tff('417', plain, (~ '#form15' |  (??(cQ))), define([status(thm)])).
14.52/2.76	tff('418', plain, ( '#form15') <= (((!!(cR)) = (??(cQ))) & ( (!!(cR)))),
14.52/2.76	    inference('renaming', [status(thm)], ['415', '417'])).
14.52/2.76	tff('419', plain, (~ '#form15' |  (??(cQ))), define([status(thm)])).
14.52/2.76	tff('420', plain, (~ '#form15') <= (~ ( '#form15')),
14.52/2.76	    inference('split', [status(esa)], ['419'])).
14.52/2.76	tff('421', plain, ~ ( (!!(cR))) | ~ ((!!(cR)) = (??(cQ))) | ( '#form15'),
14.52/2.76	    inference('sup-', [status(thm)], ['418', '420'])).
14.52/2.76	tff('422', plain, ( (??(cP))) <= (( (??(cP)))),
14.52/2.76	    inference('split', [status(esa)], ['125'])).
14.52/2.76	tff('423', plain, ( cP('#sk6')) <= (( (??(cP)))),
14.52/2.76	    inference('lazy_cnf_exists', [status(thm)], ['422'])).
14.52/2.76	tff('424', plain,
14.52/2.76	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))))
14.52/2.76	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))))),
14.52/2.76	    inference('split', [status(esa)], ['43'])).
14.52/2.76	tff('425', plain,
14.52/2.76	    ( (!!((^[Y0 : $i]: (cP(Y0) <=> cP('#sk27'))))))
14.52/2.76	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))))),
14.52/2.76	    inference('lazy_cnf_exists', [status(thm)], ['424'])).
14.52/2.76	tff('426', plain,
14.52/2.76	    (![X1]:  (cP(X1) <=> cP('#sk27')))
14.52/2.76	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))))),
14.52/2.76	    inference('lazy_cnf_forall', [status(thm)], ['425'])).
14.52/2.76	tff('427', plain,
14.52/2.76	    (![X1]: cP(X1) = cP('#sk27'))
14.52/2.76	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['426'])).
14.52/2.76	tff('428', plain,
14.52/2.76	    (![X1]: cP(X1) = cP('#sk27'))
14.52/2.76	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['426'])).
14.52/2.76	tff('429', plain,
14.52/2.76	    (![X0, X1]: cP(X1) = cP(X0))
14.52/2.76	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))))),
14.52/2.76	    inference('sup+', [status(thm)], ['427', '428'])).
14.52/2.76	tff('430', plain, ( (??(cS))) <= (( (??(cS)))),
14.52/2.76	    inference('split', [status(esa)], ['66'])).
14.52/2.76	tff('431', plain, ((??(cS)) != (!!(cP))) <= (~ ((??(cS)) = (!!(cP)))),
14.52/2.76	    inference('split', [status(esa)], ['64'])).
14.52/2.76	tff('432', plain, (~ (!!(cP))) <= (~ ((??(cS)) = (!!(cP))) & ( (??(cS)))),
14.52/2.76	    inference('sup-', [status(thm)], ['430', '431'])).
14.52/2.76	tff('433', plain, (~ cP('#sk1')) <= (~ ((??(cS)) = (!!(cP))) & ( (??(cS)))),
14.52/2.76	    inference('lazy_cnf_exists', [status(thm)], ['432'])).
14.52/2.76	tff('434', plain,
14.52/2.76	    (![X0]: ~ cP(X0))
14.52/2.76	      <= (~ ((??(cS)) = (!!(cP))) & 
14.52/2.76	          ( (??(cS))) & 
14.52/2.76	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))))),
14.52/2.76	    inference('sup-', [status(thm)], ['429', '433'])).
14.52/2.76	tff('435', plain,
14.52/2.76	    ((??(cS)) = (!!(cP))) | 
14.52/2.76	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))) | 
14.52/2.76	    ~ ( (??(cS))) | ~ ( (??(cP))),
14.52/2.76	    inference('sup-', [status(thm)], ['423', '434'])).
14.52/2.76	tff('436', plain,
14.52/2.76	    (((??(cP)) <=> (!!(cQ)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	      <= ((((??(cP)) <=> (!!(cQ)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.76	    inference('split', [status(esa)], ['70'])).
14.52/2.76	tff('437', plain,
14.52/2.76	    (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.76	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	       ((!!(cR)) <=> (??(cQ)))))
14.52/2.76	      != ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	           (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) <=>
14.52/2.76	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.76	      <= (((??(cS)) = (!!(cP)))),
14.52/2.76	    inference('simplify boolean subterms', [status(thm)], ['184'])).
14.52/2.76	tff('438', plain,
14.52/2.76	    (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.76	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	       ((!!(cR)) <=> (??(cQ)))))
14.52/2.76	      != ((((??(cP)) <=> (!!(cQ))) <=> ((??(cP)) <=> (!!(cQ)))) <=>
14.52/2.76	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.76	      <= ((((??(cP)) <=> (!!(cQ)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) & 
14.52/2.76	          ((??(cS)) = (!!(cP)))),
14.52/2.76	    inference('sup-', [status(thm)], ['436', '437'])).
14.52/2.76	tff('439', plain,
14.52/2.76	    (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.76	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	       ((!!(cR)) <=> (??(cQ)))))
14.52/2.76	      != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))
14.52/2.76	      <= ((((??(cP)) <=> (!!(cQ)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) & 
14.52/2.76	          ((??(cS)) = (!!(cP)))),
14.52/2.76	    inference('simplify boolean subterms', [status(thm)], ['438'])).
14.52/2.76	tff('440', plain,
14.52/2.76	    ((~ ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.76	         ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	          ((!!(cR)) <=> (??(cQ)))))
14.52/2.76	      | ~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.76	      <= ((((??(cP)) <=> (!!(cQ)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) & 
14.52/2.76	          ((??(cS)) = (!!(cP)))),
14.52/2.76	    inference('lazy_cnf_xor', [status(thm)], ['439'])).
14.52/2.76	tff('441', plain,
14.52/2.76	    (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	       != ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	           ((!!(cR)) <=> (??(cQ))))
14.52/2.76	      | ~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.76	      <= ((((??(cP)) <=> (!!(cQ)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) & 
14.52/2.76	          ((??(cS)) = (!!(cP)))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['440'])).
14.52/2.76	tff('442', plain,
14.52/2.76	    ~
14.52/2.76	    (((??(cP)) <=> (!!(cQ)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) | 
14.52/2.76	    ~
14.52/2.76	    ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	         ((!!(cR)) <=> (??(cQ))))) | 
14.52/2.76	    ~ ((??(cS)) = (!!(cP))) | 
14.52/2.76	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))),
14.52/2.76	    inference('split', [status(esa)], ['441'])).
14.52/2.76	tff('443', plain, ( (??(cS))) <= (( (??(cS)))),
14.52/2.76	    inference('split', [status(esa)], ['66'])).
14.52/2.76	tff('444', plain,
14.52/2.76	    (((??(cP)) <=> (!!(cQ))) != ((!!(cP)) <=> ((??(cS)) <=> (!!(cP)))))
14.52/2.76	      <= (~
14.52/2.76	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.76	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.76	          (((??(cS)) <=> (!!(cP)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) & 
14.52/2.76	          ((??(cS)) = (!!(cP))) & 
14.52/2.76	          ( (!!(cP))) & 
14.52/2.76	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.76	    inference('sup-', [status(thm)], ['95', '96'])).
14.52/2.76	tff('445', plain,
14.52/2.76	    ((~ ((??(cP)) <=> (!!(cQ))) | ~ ((!!(cP)) <=> ((??(cS)) <=> (!!(cP))))))
14.52/2.76	      <= (~
14.52/2.76	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.76	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.76	          (((??(cS)) <=> (!!(cP)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) & 
14.52/2.76	          ((??(cS)) = (!!(cP))) & 
14.52/2.76	          ( (!!(cP))) & 
14.52/2.76	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.76	    inference('lazy_cnf_xor', [status(thm)], ['444'])).
14.52/2.76	tff('446', plain,
14.52/2.76	    (((??(cP)) != (!!(cQ)) | (!!(cP)) != ((??(cS)) <=> (!!(cP)))))
14.52/2.76	      <= (~
14.52/2.76	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.76	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.76	          (((??(cS)) <=> (!!(cP)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) & 
14.52/2.76	          ((??(cS)) = (!!(cP))) & 
14.52/2.76	          ( (!!(cP))) & 
14.52/2.76	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['445'])).
14.52/2.76	tff('447', plain,
14.52/2.76	    ((!!(cP)) != ((??(cS)) <=> (!!(cP))))
14.52/2.76	      <= (~ ((!!(cP)) = ((??(cS)) <=> (!!(cP))))),
14.52/2.76	    inference('split', [status(esa)], ['446'])).
14.52/2.76	tff('448', plain,
14.52/2.76	    ((!!(cP)) != ($true <=> (!!(cP))))
14.52/2.76	      <= (~ ((!!(cP)) = ((??(cS)) <=> (!!(cP)))) & ( (??(cS)))),
14.52/2.76	    inference('sup-', [status(thm)], ['443', '447'])).
14.52/2.76	tff('449', plain,
14.52/2.76	    ((!!(cP)) != (!!(cP)))
14.52/2.76	      <= (~ ((!!(cP)) = ((??(cS)) <=> (!!(cP)))) & ( (??(cS)))),
14.52/2.76	    inference('simplify boolean subterms', [status(thm)], ['448'])).
14.52/2.76	tff('450', plain, ((!!(cP)) = ((??(cS)) <=> (!!(cP)))) | ~ ( (??(cS))),
14.52/2.76	    inference('simplify', [status(thm)], ['449'])).
14.52/2.76	tff('451', plain, ((!!(cR)) = (??(cQ))) <= (((!!(cR)) = (??(cQ)))),
14.52/2.76	    inference('split', [status(esa)], ['43'])).
14.52/2.76	tff('452', plain,
14.52/2.76	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	      = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.76	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.76	      <= (((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.76	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))),
14.52/2.76	    inference('split', [status(esa)], ['26'])).
14.52/2.76	tff('453', plain,
14.52/2.76	    ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.76	     ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	      ((!!(cR)) <=> (??(cQ)))))
14.52/2.76	     != ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) <=>
14.52/2.76	         (((??(cS)) <=> (!!(cP))) <=>
14.52/2.76	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('ho_norm', [status(thm)], ['0'])).
14.52/2.76	tff('454', plain,
14.52/2.76	    (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.76	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	       ((!!(cR)) <=> (??(cQ)))))
14.52/2.76	      != ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	           (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) <=>
14.52/2.76	          (((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	           (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))))
14.52/2.76	      <= (((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.76	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))),
14.52/2.76	    inference('sup-', [status(thm)], ['452', '453'])).
14.52/2.76	tff('455', plain,
14.52/2.76	    (~ ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.76	        ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	         ((!!(cR)) <=> (??(cQ))))))
14.52/2.76	      <= (((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.76	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))),
14.52/2.76	    inference('simplify boolean subterms', [status(thm)], ['454'])).
14.52/2.76	tff('456', plain,
14.52/2.76	    ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	      != ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	          ((!!(cR)) <=> (??(cQ)))))
14.52/2.76	      <= (((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.76	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['455'])).
14.52/2.76	tff('457', plain,
14.52/2.76	    ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	      != ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	          ((??(cQ)) <=> (??(cQ)))))
14.52/2.76	      <= (((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.76	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.76	          ((!!(cR)) = (??(cQ)))),
14.52/2.76	    inference('sup-', [status(thm)], ['451', '456'])).
14.52/2.76	tff('458', plain,
14.52/2.76	    ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	      != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))))
14.52/2.76	      <= (((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.76	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.76	          ((!!(cR)) = (??(cQ)))),
14.52/2.76	    inference('simplify boolean subterms', [status(thm)], ['457'])).
14.52/2.76	tff('459', plain,
14.52/2.76	    (( (((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	        (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	      |  (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))))
14.52/2.76	      <= (((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.76	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.76	          ((!!(cR)) = (??(cQ)))),
14.52/2.76	    inference('lazy_cnf_xor', [status(thm)], ['458'])).
14.52/2.76	tff('460', plain,
14.52/2.76	    ((((??(cR)) <=> (!!(cS)))
14.52/2.76	       = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
14.52/2.76	      |  (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))))
14.52/2.76	      <= (((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.76	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.76	          ((!!(cR)) = (??(cQ)))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['459'])).
14.52/2.76	tff('461', plain,
14.52/2.76	    ~
14.52/2.76	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	      = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.76	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) | 
14.52/2.76	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))) | 
14.52/2.76	    (((??(cR)) <=> (!!(cS)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) | 
14.52/2.76	    ~ ((!!(cR)) = (??(cQ))), inference('split', [status(esa)], ['460'])).
14.52/2.76	tff('462', plain,
14.52/2.76	    (((??(cP)) <=> (!!(cQ)))
14.52/2.76	      != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	      <= (~
14.52/2.76	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.76	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.76	          ((??(cS)) = (!!(cP))) & 
14.52/2.76	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['211'])).
14.52/2.76	tff('463', plain,
14.52/2.76	    ((~ ((??(cP)) <=> (!!(cQ)))
14.52/2.76	      | ~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))))
14.52/2.76	      <= (~
14.52/2.76	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.76	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.76	          ((??(cS)) = (!!(cP))) & 
14.52/2.76	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('lazy_cnf_xor', [status(thm)], ['462'])).
14.52/2.76	tff('464', plain,
14.52/2.76	    (((??(cP)) != (!!(cQ))
14.52/2.76	      | ~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))))
14.52/2.76	      <= (~
14.52/2.76	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.76	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.76	          ((??(cS)) = (!!(cP))) & 
14.52/2.76	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['463'])).
14.52/2.76	tff('465', plain,
14.52/2.76	    ~ ((??(cP)) = (!!(cQ))) | 
14.52/2.76	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) | 
14.52/2.76	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	      = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.76	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) | 
14.52/2.76	    ~ ((??(cS)) = (!!(cP))) | 
14.52/2.76	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))),
14.52/2.76	    inference('split', [status(esa)], ['464'])).
14.52/2.76	tff('466', plain,
14.52/2.76	    ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	         ((!!(cR)) <=> (??(cQ))))) | 
14.52/2.76	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.76	      = ((!!(cR)) <=> (??(cQ)))) | 
14.52/2.76	    (((??(cR)) <=> (!!(cS)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))),
14.52/2.76	    inference('split', [status(esa)], ['6'])).
14.52/2.76	tff('467', plain, ( (!!(cQ))) <= (( (!!(cQ)))),
14.52/2.76	    inference('split', [status(esa)], ['125'])).
14.52/2.76	tff('468', plain, (![X1]:  cQ(X1)) <= (( (!!(cQ)))),
14.52/2.76	    inference('lazy_cnf_forall', [status(thm)], ['467'])).
14.52/2.76	tff('469', plain, ( (!!(cR))) <= (( (!!(cR)))),
14.52/2.76	    inference('split', [status(esa)], ['266'])).
14.52/2.76	tff('470', plain, ((!!(cR)) != (??(cQ))) <= (~ ((!!(cR)) = (??(cQ)))),
14.52/2.76	    inference('split', [status(esa)], ['13'])).
14.52/2.76	tff('471', plain, (~ (??(cQ))) <= (~ ((!!(cR)) = (??(cQ))) & ( (!!(cR)))),
14.52/2.76	    inference('sup-', [status(thm)], ['469', '470'])).
14.52/2.76	tff('472', plain,
14.52/2.76	    (![X1]: ~ cQ(X1)) <= (~ ((!!(cR)) = (??(cQ))) & ( (!!(cR)))),
14.52/2.76	    inference('lazy_cnf_forall', [status(thm)], ['471'])).
14.52/2.76	tff('473', plain, ~ ( (!!(cQ))) | ~ ( (!!(cR))) | ((!!(cR)) = (??(cQ))),
14.52/2.76	    inference('sup-', [status(thm)], ['468', '472'])).
14.52/2.76	tff('474', plain,
14.52/2.76	    (((??(cP)) <=> (!!(cQ)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	      <= ((((??(cP)) <=> (!!(cQ)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.76	    inference('split', [status(esa)], ['70'])).
14.52/2.76	tff('475', plain,
14.52/2.76	    (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.76	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	       ((!!(cR)) <=> (??(cQ)))))
14.52/2.76	      != ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	           (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) <=>
14.52/2.76	          ((??(cS)) <=>
14.52/2.76	           (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))))
14.52/2.76	      <= (( (!!(cP)))),
14.52/2.76	    inference('simplify boolean subterms', [status(thm)], ['287'])).
14.52/2.76	tff('476', plain,
14.52/2.76	    (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.76	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	       ((!!(cR)) <=> (??(cQ)))))
14.52/2.76	      != ((((??(cP)) <=> (!!(cQ))) <=> ((??(cP)) <=> (!!(cQ)))) <=>
14.52/2.76	          ((??(cS)) <=>
14.52/2.76	           (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))))
14.52/2.76	      <= ((((??(cP)) <=> (!!(cQ)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) & 
14.52/2.76	          ( (!!(cP)))),
14.52/2.76	    inference('sup-', [status(thm)], ['474', '475'])).
14.52/2.76	tff('477', plain,
14.52/2.76	    (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.76	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	       ((!!(cR)) <=> (??(cQ)))))
14.52/2.76	      != ((??(cS)) <=>
14.52/2.76	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.76	      <= ((((??(cP)) <=> (!!(cQ)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) & 
14.52/2.76	          ( (!!(cP)))),
14.52/2.76	    inference('simplify boolean subterms', [status(thm)], ['476'])).
14.52/2.76	tff('478', plain,
14.52/2.76	    (( ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.76	        ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	         ((!!(cR)) <=> (??(cQ)))))
14.52/2.76	      |  ((??(cS)) <=>
14.52/2.76	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))))
14.52/2.76	      <= ((((??(cP)) <=> (!!(cQ)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) & 
14.52/2.76	          ( (!!(cP)))),
14.52/2.76	    inference('lazy_cnf_xor', [status(thm)], ['477'])).
14.52/2.76	tff('479', plain,
14.52/2.76	    (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	       = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	          ((!!(cR)) <=> (??(cQ))))
14.52/2.76	      | (??(cS))
14.52/2.76	         = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.76	      <= ((((??(cP)) <=> (!!(cQ)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) & 
14.52/2.76	          ( (!!(cP)))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['478'])).
14.52/2.76	tff('480', plain,
14.52/2.76	    ~
14.52/2.76	    (((??(cP)) <=> (!!(cQ)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) | 
14.52/2.76	    ((??(cS)) = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) | 
14.52/2.76	    ~ ( (!!(cP))) | 
14.52/2.76	    ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	         ((!!(cR)) <=> (??(cQ))))),
14.52/2.76	    inference('split', [status(esa)], ['479'])).
14.52/2.76	tff('481', plain, ((!!(cR)) = (??(cQ))) <= (((!!(cR)) = (??(cQ)))),
14.52/2.76	    inference('split', [status(esa)], ['43'])).
14.52/2.76	tff('482', plain,
14.52/2.76	    ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	         ((!!(cR)) <=> (??(cQ)))))
14.52/2.76	      <= (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	               ((!!(cR)) <=> (??(cQ)))))),
14.52/2.76	    inference('split', [status(esa)], ['26'])).
14.52/2.76	tff('483', plain,
14.52/2.76	    ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	         ((??(cQ)) <=> (??(cQ)))))
14.52/2.76	      <= (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	               ((!!(cR)) <=> (??(cQ))))) & 
14.52/2.76	          ((!!(cR)) = (??(cQ)))),
14.52/2.76	    inference('sup+', [status(thm)], ['481', '482'])).
14.52/2.76	tff('484', plain,
14.52/2.76	    ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))))
14.52/2.76	      <= (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	               ((!!(cR)) <=> (??(cQ))))) & 
14.52/2.76	          ((!!(cR)) = (??(cQ)))),
14.52/2.76	    inference('simplify boolean subterms', [status(thm)], ['483'])).
14.52/2.76	tff('485', plain,
14.52/2.76	    (( (((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	        (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	      | ~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))))
14.52/2.76	      <= (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	               ((!!(cR)) <=> (??(cQ))))) & 
14.52/2.76	          ((!!(cR)) = (??(cQ)))),
14.52/2.76	    inference('lazy_cnf_equiv', [status(thm)], ['484'])).
14.52/2.76	tff('486', plain,
14.52/2.76	    ((((??(cR)) <=> (!!(cS)))
14.52/2.76	       = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
14.52/2.76	      | ~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))))
14.52/2.76	      <= (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	               ((!!(cR)) <=> (??(cQ))))) & 
14.52/2.76	          ((!!(cR)) = (??(cQ)))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['485'])).
14.52/2.76	tff('487', plain,
14.52/2.76	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))) | 
14.52/2.76	    ~
14.52/2.76	    ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	         ((!!(cR)) <=> (??(cQ))))) | 
14.52/2.76	    (((??(cR)) <=> (!!(cS)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) | 
14.52/2.76	    ~ ((!!(cR)) = (??(cQ))), inference('split', [status(esa)], ['486'])).
14.52/2.76	tff('488', plain,
14.52/2.76	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	      != ((??(cS)) <=>
14.52/2.76	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.76	      <= (~
14.52/2.76	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.76	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.76	          ( (!!(cP)))),
14.52/2.76	    inference('simplify boolean subterms', [status(thm)], ['74'])).
14.52/2.76	tff('489', plain,
14.52/2.76	    (( (((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	        (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	      |  ((??(cS)) <=>
14.52/2.76	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))))
14.52/2.76	      <= (~
14.52/2.76	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.76	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.76	          ( (!!(cP)))),
14.52/2.76	    inference('lazy_cnf_xor', [status(thm)], ['488'])).
14.52/2.76	tff('490', plain,
14.52/2.76	    ((((??(cP)) <=> (!!(cQ)))
14.52/2.76	       = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))
14.52/2.76	      | (??(cS))
14.52/2.76	         = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.76	      <= (~
14.52/2.76	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.76	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.76	          ( (!!(cP)))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['489'])).
14.52/2.76	tff('491', plain,
14.52/2.76	    ((??(cS)) = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))
14.52/2.76	      <= (((??(cS))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('split', [status(esa)], ['490'])).
14.52/2.76	tff('492', plain,
14.52/2.76	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))
14.52/2.76	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('split', [status(esa)], ['54'])).
14.52/2.76	tff('493', plain,
14.52/2.76	    ( (??(cS)))
14.52/2.76	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) & 
14.52/2.76	          ((??(cS))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('sup+', [status(thm)], ['491', '492'])).
14.52/2.76	tff('494', plain,
14.52/2.76	    ( (??(cS)))
14.52/2.76	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) & 
14.52/2.76	          ((??(cS))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('sup+', [status(thm)], ['491', '492'])).
14.52/2.76	tff('495', plain, (~ '#form22' |  (??(cS))), define([status(thm)])).
14.52/2.76	tff('496', plain,
14.52/2.76	    ( '#form22')
14.52/2.76	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) & 
14.52/2.76	          ((??(cS))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('renaming', [status(thm)], ['493', '495'])).
14.52/2.76	tff('497', plain, (~ '#form22' |  (??(cS))), define([status(thm)])).
14.52/2.76	tff('498', plain, (~ '#form22') <= (~ ( '#form22')),
14.52/2.76	    inference('split', [status(esa)], ['497'])).
14.52/2.76	tff('499', plain,
14.52/2.76	    ( '#form22') | 
14.52/2.76	    ~
14.52/2.76	    ((??(cS)) = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) | 
14.52/2.76	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))),
14.52/2.76	    inference('sup-', [status(thm)], ['496', '498'])).
14.52/2.76	tff('500', plain, ((??(cS)) = (!!(cP))) <= (((??(cS)) = (!!(cP)))),
14.52/2.76	    inference('split', [status(esa)], ['54'])).
14.52/2.76	tff('501', plain, (( (??(cS)) | ~ (!!(cP)))) <= (((??(cS)) = (!!(cP)))),
14.52/2.76	    inference('lazy_cnf_equiv', [status(thm)], ['500'])).
14.52/2.76	tff('502', plain, ~ ( (!!(cP))) | ( (??(cS))) | ~ ((??(cS)) = (!!(cP))),
14.52/2.76	    inference('split', [status(esa)], ['501'])).
14.52/2.76	tff('503', plain,
14.52/2.76	    (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.76	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	       ((!!(cR)) <=> (??(cQ)))))
14.52/2.76	      != (((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))))
14.52/2.76	      <= ((((??(cS)) <=> (!!(cP)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('simplify boolean subterms', [status(thm)], ['324'])).
14.52/2.76	tff('504', plain,
14.52/2.76	    ((~ ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.76	         ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	          ((!!(cR)) <=> (??(cQ)))))
14.52/2.76	      | ~ (((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	           (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))))
14.52/2.76	      <= ((((??(cS)) <=> (!!(cP)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('lazy_cnf_xor', [status(thm)], ['503'])).
14.52/2.76	tff('505', plain,
14.52/2.76	    (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	       != ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	           ((!!(cR)) <=> (??(cQ))))
14.52/2.76	      | ((??(cP)) <=> (!!(cQ)))
14.52/2.76	         != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))))
14.52/2.76	      <= ((((??(cS)) <=> (!!(cP)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['504'])).
14.52/2.76	tff('506', plain,
14.52/2.76	    ~
14.52/2.76	    (((??(cP)) <=> (!!(cQ)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) | 
14.52/2.76	    ~
14.52/2.76	    ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	         ((!!(cR)) <=> (??(cQ))))) | 
14.52/2.76	    ~
14.52/2.76	    (((??(cS)) <=> (!!(cP)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))),
14.52/2.76	    inference('split', [status(esa)], ['505'])).
14.52/2.76	tff('507', plain,
14.52/2.76	    (((??(cP)) <=> (!!(cQ)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	      <= ((((??(cP)) <=> (!!(cQ)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.76	    inference('split', [status(esa)], ['70'])).
14.52/2.76	tff('508', plain,
14.52/2.76	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.76	    inference('split', [status(esa)], ['87'])).
14.52/2.76	tff('509', plain,
14.52/2.76	    ( ((??(cP)) <=> (!!(cQ))))
14.52/2.76	      <= ((((??(cP)) <=> (!!(cQ)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) & 
14.52/2.76	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.76	    inference('sup+', [status(thm)], ['507', '508'])).
14.52/2.76	tff('510', plain,
14.52/2.76	    ((??(cP)) = (!!(cQ)))
14.52/2.76	      <= ((((??(cP)) <=> (!!(cQ)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) & 
14.52/2.76	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['509'])).
14.52/2.76	tff('511', plain,
14.52/2.76	    ((~ (??(cP)) |  (!!(cQ))))
14.52/2.76	      <= ((((??(cP)) <=> (!!(cQ)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) & 
14.52/2.76	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.76	    inference('lazy_cnf_equiv', [status(thm)], ['510'])).
14.52/2.76	tff('512', plain,
14.52/2.76	    ~
14.52/2.76	    (((??(cP)) <=> (!!(cQ)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) | 
14.52/2.76	    ( (!!(cQ))) | ~ ( (??(cP))) | 
14.52/2.76	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))),
14.52/2.76	    inference('split', [status(esa)], ['511'])).
14.52/2.76	tff('513', plain,
14.52/2.76	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))
14.52/2.76	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('split', [status(esa)], ['54'])).
14.52/2.76	tff('514', plain,
14.52/2.76	    ((??(cS)) != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))
14.52/2.76	      <= (~
14.52/2.76	          ((??(cS))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('split', [status(esa)], ['310'])).
14.52/2.76	tff('515', plain,
14.52/2.76	    (~ (??(cS)))
14.52/2.76	      <= (~
14.52/2.76	          ((??(cS))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) & 
14.52/2.76	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('sup-', [status(thm)], ['513', '514'])).
14.52/2.76	tff('516', plain, ( '#form22' | ~ (??(cS))), define([status(thm)])).
14.52/2.76	tff('517', plain, ( '#form22') <= (( '#form22')),
14.52/2.76	    inference('split', [status(esa)], ['516'])).
14.52/2.76	tff('518', plain, (~ (??(cS))) <= (~ ( (??(cS)))),
14.52/2.76	    inference('split', [status(esa)], ['516'])).
14.52/2.76	tff('519', plain, ( '#form22' | ~ (??(cS))), define([status(thm)])).
14.52/2.76	tff('520', plain, (~ '#form22') <= (~ ( (??(cS)))),
14.52/2.76	    inference('renaming', [status(thm)], ['518', '519'])).
14.52/2.76	tff('521', plain, ( (??(cS))) | ~ ( '#form22'),
14.52/2.76	    inference('sup-', [status(thm)], ['517', '520'])).
14.52/2.76	tff('522', plain,
14.52/2.76	    ((!!(cR)) = (??(cQ))) | 
14.52/2.76	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.76	      = ((!!(cR)) <=> (??(cQ)))) | 
14.52/2.76	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))),
14.52/2.76	    inference('split', [status(esa)], ['43'])).
14.52/2.76	tff('523', plain,
14.52/2.76	    ~
14.52/2.76	    (((??(cP)) <=> (!!(cQ)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) | 
14.52/2.76	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	      = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.76	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) | 
14.52/2.76	    ~
14.52/2.76	    ((!!(cP)) = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) | 
14.52/2.76	    ~ ( (??(cS))), inference('split', [status(esa)], ['405'])).
14.52/2.76	tff('524', plain,
14.52/2.76	    ((!!(cP)) != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))
14.52/2.76	      <= (~
14.52/2.76	          ((!!(cP))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('split', [status(esa)], ['405'])).
14.52/2.76	tff('525', plain,
14.52/2.76	    (( (!!(cP))
14.52/2.76	      |  (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.76	      <= (~
14.52/2.76	          ((!!(cP))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('lazy_cnf_xor', [status(thm)], ['524'])).
14.52/2.76	tff('526', plain,
14.52/2.76	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) | 
14.52/2.76	    ((!!(cP)) = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) | 
14.52/2.76	    ( (!!(cP))), inference('split', [status(esa)], ['525'])).
14.52/2.76	tff('527', plain,
14.52/2.76	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.76	      = ((!!(cR)) <=> (??(cQ))))
14.52/2.76	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.76	            = ((!!(cR)) <=> (??(cQ))))),
14.52/2.76	    inference('split', [status(esa)], ['6'])).
14.52/2.76	tff('528', plain,
14.52/2.76	    ((~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.76	      |  ((!!(cR)) <=> (??(cQ)))))
14.52/2.76	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.76	            = ((!!(cR)) <=> (??(cQ))))),
14.52/2.76	    inference('lazy_cnf_equiv', [status(thm)], ['527'])).
14.52/2.76	tff('529', plain,
14.52/2.76	    ((~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.76	      | (!!(cR)) = (??(cQ))))
14.52/2.76	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.76	            = ((!!(cR)) <=> (??(cQ))))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['528'])).
14.52/2.76	tff('530', plain,
14.52/2.76	    ~
14.52/2.76	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.76	      = ((!!(cR)) <=> (??(cQ)))) | 
14.52/2.76	    ((!!(cR)) = (??(cQ))) | 
14.52/2.76	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))),
14.52/2.76	    inference('split', [status(esa)], ['529'])).
14.52/2.76	tff('531', plain, ( (??(cS))) <= (( (??(cS)))),
14.52/2.76	    inference('split', [status(esa)], ['66'])).
14.52/2.76	tff('532', plain,
14.52/2.76	    (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.76	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	       ((!!(cR)) <=> (??(cQ)))))
14.52/2.76	      != ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	           (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) <=>
14.52/2.76	          ((??(cS)) <=>
14.52/2.76	           (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))))
14.52/2.76	      <= (( (!!(cP)))),
14.52/2.76	    inference('simplify boolean subterms', [status(thm)], ['287'])).
14.52/2.76	tff('533', plain,
14.52/2.76	    (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.76	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	       ((!!(cR)) <=> (??(cQ)))))
14.52/2.76	      != ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	           (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) <=>
14.52/2.76	          ($true <=>
14.52/2.76	           (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))))
14.52/2.76	      <= (( (!!(cP))) & ( (??(cS)))),
14.52/2.76	    inference('sup-', [status(thm)], ['531', '532'])).
14.52/2.76	tff('534', plain,
14.52/2.76	    (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.76	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	       ((!!(cR)) <=> (??(cQ)))))
14.52/2.76	      != ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	           (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) <=>
14.52/2.76	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.76	      <= (( (!!(cP))) & ( (??(cS)))),
14.52/2.76	    inference('simplify boolean subterms', [status(thm)], ['533'])).
14.52/2.76	tff('535', plain,
14.52/2.76	    (( ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.76	        ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	         ((!!(cR)) <=> (??(cQ)))))
14.52/2.76	      |  ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	           (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) <=>
14.52/2.76	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))))
14.52/2.76	      <= (( (!!(cP))) & ( (??(cS)))),
14.52/2.76	    inference('lazy_cnf_xor', [status(thm)], ['534'])).
14.52/2.76	tff('536', plain,
14.52/2.76	    (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	       = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	          ((!!(cR)) <=> (??(cQ))))
14.52/2.76	      | (((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	         = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.76	      <= (( (!!(cP))) & ( (??(cS)))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['535'])).
14.52/2.76	tff('537', plain,
14.52/2.76	    ~ ( (!!(cP))) | 
14.52/2.76	    ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	         ((!!(cR)) <=> (??(cQ))))) | 
14.52/2.76	    ~ ( (??(cS))) | 
14.52/2.76	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))),
14.52/2.76	    inference('split', [status(esa)], ['536'])).
14.52/2.76	tff('538', plain, ((!!(cR)) = (??(cQ))) <= (((!!(cR)) = (??(cQ)))),
14.52/2.76	    inference('split', [status(esa)], ['43'])).
14.52/2.76	tff('539', plain, (( (!!(cR)) | ~ (??(cQ)))) <= (((!!(cR)) = (??(cQ)))),
14.52/2.76	    inference('lazy_cnf_equiv', [status(thm)], ['538'])).
14.52/2.76	tff('540', plain, ~ ( (??(cQ))) | ~ ((!!(cR)) = (??(cQ))) | ( (!!(cR))),
14.52/2.76	    inference('split', [status(esa)], ['539'])).
14.52/2.76	tff('541', plain,
14.52/2.76	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))
14.52/2.76	      <= (((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('split', [status(esa)], ['187'])).
14.52/2.76	tff('542', plain,
14.52/2.76	    ((~ (((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	      |  (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.76	      <= (((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('lazy_cnf_equiv', [status(thm)], ['541'])).
14.52/2.76	tff('543', plain,
14.52/2.76	    ((((??(cP)) <=> (!!(cQ)))
14.52/2.76	       != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))
14.52/2.76	      |  (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.76	      <= (((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['542'])).
14.52/2.76	tff('544', plain,
14.52/2.76	    ~
14.52/2.76	    (((??(cP)) <=> (!!(cQ)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) | 
14.52/2.76	    ~
14.52/2.76	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) | 
14.52/2.76	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))),
14.52/2.76	    inference('split', [status(esa)], ['543'])).
14.52/2.76	tff('545', plain, ( cP('#sk6')) <= (( (??(cP)))),
14.52/2.76	    inference('lazy_cnf_exists', [status(thm)], ['422'])).
14.52/2.76	tff('546', plain,
14.52/2.76	    (![X0, X1]: cP(X1) = cP(X0))
14.52/2.76	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))))),
14.52/2.76	    inference('sup+', [status(thm)], ['427', '428'])).
14.52/2.76	tff('547', plain, (~ (!!(cP))) <= (~ ( (!!(cP)))),
14.52/2.76	    inference('split', [status(esa)], ['112'])).
14.52/2.76	tff('548', plain, (~ cP('#sk1')) <= (~ ( (!!(cP)))),
14.52/2.76	    inference('lazy_cnf_exists', [status(thm)], ['547'])).
14.52/2.76	tff('549', plain,
14.52/2.76	    (![X0]: ~ cP(X0))
14.52/2.76	      <= (~ ( (!!(cP))) & 
14.52/2.76	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))))),
14.52/2.76	    inference('sup-', [status(thm)], ['546', '548'])).
14.52/2.76	tff('550', plain,
14.52/2.76	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))) | 
14.52/2.76	    ( (!!(cP))) | ~ ( (??(cP))),
14.52/2.76	    inference('sup-', [status(thm)], ['545', '549'])).
14.52/2.76	tff('551', plain,
14.52/2.76	    ~ ( (!!(cP))) | 
14.52/2.76	    ~
14.52/2.76	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	      = ((??(cS)) <=>
14.52/2.76	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) | 
14.52/2.76	    ~
14.52/2.76	    ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	         ((!!(cR)) <=> (??(cQ))))),
14.52/2.76	    inference('split', [status(esa)], ['316'])).
14.52/2.76	tff('552', plain,
14.52/2.76	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	      != ((??(cS)) <=>
14.52/2.76	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.76	      <= (~
14.52/2.76	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	            = ((??(cS)) <=>
14.52/2.76	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))),
14.52/2.76	    inference('split', [status(esa)], ['316'])).
14.52/2.76	tff('553', plain,
14.52/2.76	    ((~ (((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	      | ~ ((??(cS)) <=>
14.52/2.76	           (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))))
14.52/2.76	      <= (~
14.52/2.76	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	            = ((??(cS)) <=>
14.52/2.76	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))),
14.52/2.76	    inference('lazy_cnf_xor', [status(thm)], ['552'])).
14.52/2.76	tff('554', plain,
14.52/2.76	    ((((??(cP)) <=> (!!(cQ)))
14.52/2.76	       != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))
14.52/2.76	      | (??(cS))
14.52/2.76	         != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.76	      <= (~
14.52/2.76	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	            = ((??(cS)) <=>
14.52/2.76	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['553'])).
14.52/2.76	tff('555', plain,
14.52/2.76	    ~
14.52/2.76	    (((??(cP)) <=> (!!(cQ)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) | 
14.52/2.76	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	      = ((??(cS)) <=>
14.52/2.76	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) | 
14.52/2.76	    ~
14.52/2.76	    ((??(cS)) = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))),
14.52/2.76	    inference('split', [status(esa)], ['554'])).
14.52/2.76	tff('556', plain, ( '#form22') <= (( '#form22')),
14.52/2.76	    inference('split', [status(esa)], ['516'])).
14.52/2.76	tff('557', plain,
14.52/2.76	    (~ (??(cS)))
14.52/2.76	      <= (~
14.52/2.76	          ((??(cS))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) & 
14.52/2.76	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('sup-', [status(thm)], ['513', '514'])).
14.52/2.76	tff('558', plain, ( '#form22' | ~ (??(cS))), define([status(thm)])).
14.52/2.76	tff('559', plain,
14.52/2.76	    (~ '#form22')
14.52/2.76	      <= (~
14.52/2.76	          ((??(cS))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) & 
14.52/2.76	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('renaming', [status(thm)], ['557', '558'])).
14.52/2.76	tff('560', plain,
14.52/2.76	    ((??(cS)) = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) | 
14.52/2.76	    ~ ( '#form22') | 
14.52/2.76	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))),
14.52/2.76	    inference('sup-', [status(thm)], ['556', '559'])).
14.52/2.76	tff('561', plain,
14.52/2.76	    ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))))
14.52/2.76	      <= (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	               ((!!(cR)) <=> (??(cQ))))) & 
14.52/2.76	          ((!!(cR)) = (??(cQ)))),
14.52/2.76	    inference('simplify boolean subterms', [status(thm)], ['483'])).
14.52/2.76	tff('562', plain,
14.52/2.76	    ((~ (((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	      |  (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))))
14.52/2.76	      <= (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	               ((!!(cR)) <=> (??(cQ))))) & 
14.52/2.76	          ((!!(cR)) = (??(cQ)))),
14.52/2.76	    inference('lazy_cnf_equiv', [status(thm)], ['561'])).
14.52/2.76	tff('563', plain,
14.52/2.76	    ((((??(cR)) <=> (!!(cS)))
14.52/2.76	       != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
14.52/2.76	      |  (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))))
14.52/2.76	      <= (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	               ((!!(cR)) <=> (??(cQ))))) & 
14.52/2.76	          ((!!(cR)) = (??(cQ)))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['562'])).
14.52/2.76	tff('564', plain,
14.52/2.76	    ~
14.52/2.76	    (((??(cR)) <=> (!!(cS)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) | 
14.52/2.76	    ~
14.52/2.76	    ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	         ((!!(cR)) <=> (??(cQ))))) | 
14.52/2.76	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))) | 
14.52/2.76	    ~ ((!!(cR)) = (??(cQ))), inference('split', [status(esa)], ['563'])).
14.52/2.76	tff('565', plain,
14.52/2.76	    (((??(cP)) <=> (!!(cQ)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	      <= ((((??(cP)) <=> (!!(cQ)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.76	    inference('split', [status(esa)], ['70'])).
14.52/2.76	tff('566', plain,
14.52/2.76	    ((~ ((??(cP)) <=> (!!(cQ)))
14.52/2.76	      |  (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))))
14.52/2.76	      <= ((((??(cP)) <=> (!!(cQ)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.76	    inference('lazy_cnf_equiv', [status(thm)], ['565'])).
14.52/2.76	tff('567', plain,
14.52/2.76	    (((??(cP)) != (!!(cQ))
14.52/2.76	      |  (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))))
14.52/2.76	      <= ((((??(cP)) <=> (!!(cQ)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['566'])).
14.52/2.76	tff('568', plain,
14.52/2.76	    ~
14.52/2.76	    (((??(cP)) <=> (!!(cQ)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) | 
14.52/2.76	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) | 
14.52/2.76	    ~ ((??(cP)) = (!!(cQ))), inference('split', [status(esa)], ['567'])).
14.52/2.76	tff('569', plain,
14.52/2.76	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) | 
14.52/2.76	    ((??(cR)) = (!!(cS))) | 
14.52/2.76	    (((??(cR)) <=> (!!(cS)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))),
14.52/2.76	    inference('split', [status(esa)], ['21'])).
14.52/2.76	tff('570', plain, ((??(cR)) = (!!(cS))) <= (((??(cR)) = (!!(cS)))),
14.52/2.76	    inference('split', [status(esa)], ['21'])).
14.52/2.76	tff('571', plain, ((~ (??(cR)) |  (!!(cS)))) <= (((??(cR)) = (!!(cS)))),
14.52/2.76	    inference('lazy_cnf_equiv', [status(thm)], ['570'])).
14.52/2.76	tff('572', plain, ~ ( (??(cR))) | ( (!!(cS))) | ~ ((??(cR)) = (!!(cS))),
14.52/2.76	    inference('split', [status(esa)], ['571'])).
14.52/2.76	tff('573', plain, ((??(cP)) = (!!(cQ))) <= (((??(cP)) = (!!(cQ)))),
14.52/2.76	    inference('split', [status(esa)], ['87'])).
14.52/2.76	tff('574', plain, ((~ (??(cP)) |  (!!(cQ)))) <= (((??(cP)) = (!!(cQ)))),
14.52/2.76	    inference('lazy_cnf_equiv', [status(thm)], ['573'])).
14.52/2.76	tff('575', plain, ~ ((??(cP)) = (!!(cQ))) | ~ ( (??(cP))) | ( (!!(cQ))),
14.52/2.76	    inference('split', [status(esa)], ['574'])).
14.52/2.76	tff('576', plain,
14.52/2.76	    (((??(cR)) <=> (!!(cS)))
14.52/2.76	      != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	      <= (~
14.52/2.76	          (((??(cR)) <=> (!!(cS)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
14.52/2.76	    inference('split', [status(esa)], ['10'])).
14.52/2.76	tff('577', plain,
14.52/2.76	    ((~ ((??(cR)) <=> (!!(cS)))
14.52/2.76	      | ~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))))
14.52/2.76	      <= (~
14.52/2.76	          (((??(cR)) <=> (!!(cS)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
14.52/2.76	    inference('lazy_cnf_xor', [status(thm)], ['576'])).
14.52/2.76	tff('578', plain,
14.52/2.76	    (((??(cR)) != (!!(cS))
14.52/2.76	      | ~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))))
14.52/2.76	      <= (~
14.52/2.76	          (((??(cR)) <=> (!!(cS)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['577'])).
14.52/2.76	tff('579', plain,
14.52/2.76	    ~ ((??(cR)) = (!!(cS))) | 
14.52/2.76	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) | 
14.52/2.76	    (((??(cR)) <=> (!!(cS)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))),
14.52/2.76	    inference('split', [status(esa)], ['578'])).
14.52/2.76	tff('580', plain,
14.52/2.76	    (((??(cP)) <=> (!!(cQ)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	      <= ((((??(cP)) <=> (!!(cQ)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.76	    inference('split', [status(esa)], ['70'])).
14.52/2.76	tff('581', plain,
14.52/2.76	    (( ((??(cP)) <=> (!!(cQ)))
14.52/2.76	      | ~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))))
14.52/2.76	      <= ((((??(cP)) <=> (!!(cQ)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.76	    inference('lazy_cnf_equiv', [status(thm)], ['580'])).
14.52/2.76	tff('582', plain,
14.52/2.76	    (((??(cP)) = (!!(cQ))
14.52/2.76	      | ~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))))
14.52/2.76	      <= ((((??(cP)) <=> (!!(cQ)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['581'])).
14.52/2.76	tff('583', plain,
14.52/2.76	    ~
14.52/2.76	    (((??(cP)) <=> (!!(cQ)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) | 
14.52/2.76	    ((??(cP)) = (!!(cQ))) | 
14.52/2.76	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))),
14.52/2.76	    inference('split', [status(esa)], ['582'])).
14.52/2.76	tff('584', plain, ((??(cR)) != (!!(cS))) <= (~ ((??(cR)) = (!!(cS)))),
14.52/2.76	    inference('split', [status(esa)], ['578'])).
14.52/2.76	tff('585', plain, ((~ (??(cR)) | ~ (!!(cS)))) <= (~ ((??(cR)) = (!!(cS)))),
14.52/2.76	    inference('lazy_cnf_xor', [status(thm)], ['584'])).
14.52/2.76	tff('586', plain, ~ ( (??(cR))) | ~ ( (!!(cS))) | ((??(cR)) = (!!(cS))),
14.52/2.76	    inference('split', [status(esa)], ['585'])).
14.52/2.76	tff('587', plain,
14.52/2.76	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
14.52/2.76	    inference('split', [status(esa)], ['21'])).
14.52/2.76	tff('588', plain,
14.52/2.76	    ( (!!((^[Y0 : $i]: (cQ('#sk21') <=> cQ(Y0))))))
14.52/2.76	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
14.52/2.76	    inference('lazy_cnf_exists', [status(thm)], ['587'])).
14.52/2.76	tff('589', plain,
14.52/2.76	    (![X1]:  (cQ('#sk21') <=> cQ(X1)))
14.52/2.76	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
14.52/2.76	    inference('lazy_cnf_forall', [status(thm)], ['588'])).
14.52/2.76	tff('590', plain,
14.52/2.76	    (![X1]: cQ('#sk21') = cQ(X1))
14.52/2.76	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['589'])).
14.52/2.76	tff('591', plain,
14.52/2.76	    (![X1]: cQ('#sk21') = cQ(X1))
14.52/2.76	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['589'])).
14.52/2.76	tff('592', plain,
14.52/2.76	    (![X0, X1]: cQ(X0) = cQ(X1))
14.52/2.76	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
14.52/2.76	    inference('sup+', [status(thm)], ['590', '591'])).
14.52/2.76	tff('593', plain, ( (??(cQ))) <= (( (??(cQ)))),
14.52/2.76	    inference('split', [status(esa)], ['266'])).
14.52/2.76	tff('594', plain, ( cQ('#sk14')) <= (( (??(cQ)))),
14.52/2.76	    inference('lazy_cnf_exists', [status(thm)], ['593'])).
14.52/2.76	tff('595', plain,
14.52/2.76	    (![X0]:  cQ(X0))
14.52/2.76	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) & 
14.52/2.76	          ( (??(cQ)))),
14.52/2.76	    inference('sup+', [status(thm)], ['592', '594'])).
14.52/2.76	tff('596', plain, ( (??(cP))) <= (( (??(cP)))),
14.52/2.76	    inference('split', [status(esa)], ['125'])).
14.52/2.76	tff('597', plain, ((??(cP)) != (!!(cQ))) <= (~ ((??(cP)) = (!!(cQ)))),
14.52/2.76	    inference('split', [status(esa)], ['123'])).
14.52/2.76	tff('598', plain, (~ (!!(cQ))) <= (~ ((??(cP)) = (!!(cQ))) & ( (??(cP)))),
14.52/2.76	    inference('sup-', [status(thm)], ['596', '597'])).
14.52/2.76	tff('599', plain, (~ cQ('#sk5')) <= (~ ((??(cP)) = (!!(cQ))) & ( (??(cP)))),
14.52/2.76	    inference('lazy_cnf_exists', [status(thm)], ['598'])).
14.52/2.76	tff('600', plain,
14.52/2.76	    ~ ( (??(cQ))) | ((??(cP)) = (!!(cQ))) | 
14.52/2.76	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) | 
14.52/2.76	    ~ ( (??(cP))), inference('sup-', [status(thm)], ['595', '599'])).
14.52/2.76	tff('601', plain, ( '#form22') | ~ ( (??(cS))),
14.52/2.76	    inference('split', [status(esa)], ['516'])).
14.52/2.76	tff('602', plain,
14.52/2.76	    (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.76	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	       ((!!(cR)) <=> (??(cQ)))))
14.52/2.76	      != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))
14.52/2.76	      <= ((((??(cP)) <=> (!!(cQ)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) & 
14.52/2.76	          ((??(cS)) = (!!(cP)))),
14.52/2.76	    inference('simplify boolean subterms', [status(thm)], ['438'])).
14.52/2.76	tff('603', plain,
14.52/2.76	    (( ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.76	        ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	         ((!!(cR)) <=> (??(cQ)))))
14.52/2.76	      |  (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.76	      <= ((((??(cP)) <=> (!!(cQ)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) & 
14.52/2.76	          ((??(cS)) = (!!(cP)))),
14.52/2.76	    inference('lazy_cnf_xor', [status(thm)], ['602'])).
14.52/2.76	tff('604', plain,
14.52/2.76	    (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	       = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	          ((!!(cR)) <=> (??(cQ))))
14.52/2.76	      |  (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.76	      <= ((((??(cP)) <=> (!!(cQ)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) & 
14.52/2.76	          ((??(cS)) = (!!(cP)))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['603'])).
14.52/2.76	tff('605', plain,
14.52/2.76	    ~
14.52/2.76	    (((??(cP)) <=> (!!(cQ)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) | 
14.52/2.76	    ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	         ((!!(cR)) <=> (??(cQ))))) | 
14.52/2.76	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) | 
14.52/2.76	    ~ ((??(cS)) = (!!(cP))), inference('split', [status(esa)], ['604'])).
14.52/2.76	tff('606', plain,
14.52/2.76	    ~
14.52/2.76	    (((??(cR)) <=> (!!(cS)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) | 
14.52/2.76	    ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	         ((!!(cR)) <=> (??(cQ))))) | 
14.52/2.76	    ~
14.52/2.76	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.76	      = ((!!(cR)) <=> (??(cQ)))),
14.52/2.76	    inference('split', [status(esa)], ['10'])).
14.52/2.76	tff('607', plain,
14.52/2.76	    (((??(cR)) <=> (!!(cS)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	      <= ((((??(cR)) <=> (!!(cS)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
14.52/2.76	    inference('split', [status(esa)], ['6'])).
14.52/2.76	tff('608', plain,
14.52/2.76	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
14.52/2.76	    inference('split', [status(esa)], ['21'])).
14.52/2.76	tff('609', plain,
14.52/2.76	    ( ((??(cR)) <=> (!!(cS))))
14.52/2.76	      <= ((((??(cR)) <=> (!!(cS)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) & 
14.52/2.76	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
14.52/2.76	    inference('sup+', [status(thm)], ['607', '608'])).
14.52/2.76	tff('610', plain,
14.52/2.76	    ((??(cR)) = (!!(cS)))
14.52/2.76	      <= ((((??(cR)) <=> (!!(cS)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) & 
14.52/2.76	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['609'])).
14.52/2.76	tff('611', plain,
14.52/2.76	    (( (??(cR)) | ~ (!!(cS))))
14.52/2.76	      <= ((((??(cR)) <=> (!!(cS)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) & 
14.52/2.76	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
14.52/2.76	    inference('lazy_cnf_equiv', [status(thm)], ['610'])).
14.52/2.76	tff('612', plain,
14.52/2.76	    ~
14.52/2.76	    (((??(cR)) <=> (!!(cS)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) | 
14.52/2.76	    ~ ( (!!(cS))) | 
14.52/2.76	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) | 
14.52/2.76	    ( (??(cR))), inference('split', [status(esa)], ['611'])).
14.52/2.76	tff('613', plain,
14.52/2.76	    ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	      != ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	          ((!!(cR)) <=> (??(cQ)))))
14.52/2.76	      <= (((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.76	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['455'])).
14.52/2.76	tff('614', plain,
14.52/2.76	    ((~ (((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	      | ~ ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	           ((!!(cR)) <=> (??(cQ))))))
14.52/2.76	      <= (((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.76	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))),
14.52/2.76	    inference('lazy_cnf_xor', [status(thm)], ['613'])).
14.52/2.76	tff('615', plain,
14.52/2.76	    ((((??(cR)) <=> (!!(cS)))
14.52/2.76	       != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
14.52/2.76	      | (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.76	         != ((!!(cR)) <=> (??(cQ)))))
14.52/2.76	      <= (((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.76	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['614'])).
14.52/2.76	tff('616', plain,
14.52/2.76	    ~
14.52/2.76	    (((??(cR)) <=> (!!(cS)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) | 
14.52/2.76	    ~
14.52/2.76	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	      = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.76	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) | 
14.52/2.76	    ~
14.52/2.76	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.76	      = ((!!(cR)) <=> (??(cQ)))),
14.52/2.76	    inference('split', [status(esa)], ['615'])).
14.52/2.76	tff('617', plain,
14.52/2.76	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) | 
14.52/2.76	    ((??(cS)) = (!!(cP))) | 
14.52/2.76	    (((??(cS)) <=> (!!(cP)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))),
14.52/2.76	    inference('split', [status(esa)], ['54'])).
14.52/2.76	tff('618', plain,
14.52/2.76	    ((!!(cR)) != (??(cQ)))
14.52/2.76	      <= (~
14.52/2.76	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.76	            = ((!!(cR)) <=> (??(cQ)))) & 
14.52/2.76	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['270'])).
14.52/2.76	tff('619', plain,
14.52/2.76	    (( (!!(cR)) |  (??(cQ))))
14.52/2.76	      <= (~
14.52/2.76	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.76	            = ((!!(cR)) <=> (??(cQ)))) & 
14.52/2.76	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))))),
14.52/2.76	    inference('lazy_cnf_xor', [status(thm)], ['618'])).
14.52/2.76	tff('620', plain,
14.52/2.76	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))) | 
14.52/2.76	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.76	      = ((!!(cR)) <=> (??(cQ)))) | 
14.52/2.76	    ( (??(cQ))) | ( (!!(cR))), inference('split', [status(esa)], ['619'])).
14.52/2.76	tff('621', plain,
14.52/2.76	    ((!!(cR)) = (??(cQ)))
14.52/2.76	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.76	            = ((!!(cR)) <=> (??(cQ)))) & 
14.52/2.76	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['45'])).
14.52/2.76	tff('622', plain, ( (!!(cR))) <= (( (!!(cR)))),
14.52/2.76	    inference('split', [status(esa)], ['266'])).
14.52/2.76	tff('623', plain,
14.52/2.76	    ( (??(cQ)))
14.52/2.76	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.76	            = ((!!(cR)) <=> (??(cQ)))) & 
14.52/2.76	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))) & 
14.52/2.76	          ( (!!(cR)))),
14.52/2.76	    inference('sup+', [status(thm)], ['621', '622'])).
14.52/2.76	tff('624', plain, (~ '#form15' |  (??(cQ))), define([status(thm)])).
14.52/2.76	tff('625', plain,
14.52/2.76	    ( '#form15')
14.52/2.76	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.76	            = ((!!(cR)) <=> (??(cQ)))) & 
14.52/2.76	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))) & 
14.52/2.76	          ( (!!(cR)))),
14.52/2.76	    inference('renaming', [status(thm)], ['623', '624'])).
14.52/2.76	tff('626', plain, (~ '#form15') <= (~ ( '#form15')),
14.52/2.76	    inference('split', [status(esa)], ['419'])).
14.52/2.76	tff('627', plain,
14.52/2.76	    ~
14.52/2.76	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.76	      = ((!!(cR)) <=> (??(cQ)))) | 
14.52/2.76	    ~ ( (!!(cR))) | ( '#form15') | 
14.52/2.76	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))),
14.52/2.76	    inference('sup-', [status(thm)], ['625', '626'])).
14.52/2.76	tff('628', plain,
14.52/2.76	    (((??(cP)) <=> (!!(cQ)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	      <= ((((??(cP)) <=> (!!(cQ)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.76	    inference('split', [status(esa)], ['70'])).
14.52/2.76	tff('629', plain,
14.52/2.76	    (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.76	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	       ((!!(cR)) <=> (??(cQ)))))
14.52/2.76	      != ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	           (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) <=>
14.52/2.76	          ((!!(cP)) <=>
14.52/2.76	           (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))))
14.52/2.76	      <= (( (??(cS)))),
14.52/2.76	    inference('simplify boolean subterms', [status(thm)], ['223'])).
14.52/2.76	tff('630', plain,
14.52/2.76	    (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.76	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	       ((!!(cR)) <=> (??(cQ)))))
14.52/2.76	      != ((((??(cP)) <=> (!!(cQ))) <=> ((??(cP)) <=> (!!(cQ)))) <=>
14.52/2.76	          ((!!(cP)) <=>
14.52/2.76	           (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))))
14.52/2.76	      <= ((((??(cP)) <=> (!!(cQ)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) & 
14.52/2.76	          ( (??(cS)))),
14.52/2.76	    inference('sup-', [status(thm)], ['628', '629'])).
14.52/2.76	tff('631', plain,
14.52/2.76	    (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.76	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	       ((!!(cR)) <=> (??(cQ)))))
14.52/2.76	      != ((!!(cP)) <=>
14.52/2.76	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.76	      <= ((((??(cP)) <=> (!!(cQ)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) & 
14.52/2.76	          ( (??(cS)))),
14.52/2.76	    inference('simplify boolean subterms', [status(thm)], ['630'])).
14.52/2.76	tff('632', plain,
14.52/2.76	    (( ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.76	        ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	         ((!!(cR)) <=> (??(cQ)))))
14.52/2.76	      |  ((!!(cP)) <=>
14.52/2.76	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))))
14.52/2.76	      <= ((((??(cP)) <=> (!!(cQ)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) & 
14.52/2.76	          ( (??(cS)))),
14.52/2.76	    inference('lazy_cnf_xor', [status(thm)], ['631'])).
14.52/2.76	tff('633', plain,
14.52/2.76	    (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	       = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	          ((!!(cR)) <=> (??(cQ))))
14.52/2.76	      | (!!(cP))
14.52/2.76	         = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.76	      <= ((((??(cP)) <=> (!!(cQ)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) & 
14.52/2.76	          ( (??(cS)))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['632'])).
14.52/2.76	tff('634', plain,
14.52/2.76	    ~
14.52/2.76	    (((??(cP)) <=> (!!(cQ)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) | 
14.52/2.76	    ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	         ((!!(cR)) <=> (??(cQ))))) | 
14.52/2.76	    ~ ( (??(cS))) | 
14.52/2.76	    ((!!(cP)) = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))),
14.52/2.76	    inference('split', [status(esa)], ['633'])).
14.52/2.76	tff('635', plain,
14.52/2.76	    ~
14.52/2.76	    (((??(cP)) <=> (!!(cQ)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) | 
14.52/2.76	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	      = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.76	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) | 
14.52/2.76	    ~
14.52/2.76	    (((??(cS)) <=> (!!(cP)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))),
14.52/2.76	    inference('split', [status(esa)], ['51'])).
14.52/2.76	tff('636', plain, ( '#form15') <= (( '#form15')),
14.52/2.76	    inference('split', [status(esa)], ['171'])).
14.52/2.76	tff('637', plain, (~ (??(cQ))) <= (~ ( (??(cQ)))),
14.52/2.76	    inference('split', [status(esa)], ['171'])).
14.52/2.76	tff('638', plain, ( '#form15' | ~ (??(cQ))), define([status(thm)])).
14.52/2.76	tff('639', plain, (~ '#form15') <= (~ ( (??(cQ)))),
14.52/2.76	    inference('renaming', [status(thm)], ['637', '638'])).
14.52/2.76	tff('640', plain, ~ ( '#form15') | ( (??(cQ))),
14.52/2.76	    inference('sup-', [status(thm)], ['636', '639'])).
14.52/2.76	tff('641', plain, (![X1]:  cQ(X1)) <= (( (!!(cQ)))),
14.52/2.76	    inference('lazy_cnf_forall', [status(thm)], ['467'])).
14.52/2.76	tff('642', plain, (~ (??(cQ))) <= (~ ( (??(cQ)))),
14.52/2.76	    inference('split', [status(esa)], ['168'])).
14.52/2.76	tff('643', plain, (![X1]: ~ cQ(X1)) <= (~ ( (??(cQ)))),
14.52/2.76	    inference('lazy_cnf_forall', [status(thm)], ['642'])).
14.52/2.76	tff('644', plain, ~ ( (!!(cQ))) | ( (??(cQ))),
14.52/2.76	    inference('sup-', [status(thm)], ['641', '643'])).
14.52/2.76	tff('645', plain,
14.52/2.76	    (~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
14.52/2.76	    inference('split', [status(esa)], ['578'])).
14.52/2.76	tff('646', plain,
14.52/2.76	    (![X1]: ~ (!!((^[Y0 : $i]: (cQ(X1) <=> cQ(Y0))))))
14.52/2.76	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
14.52/2.76	    inference('lazy_cnf_forall', [status(thm)], ['645'])).
14.52/2.76	tff('647', plain,
14.52/2.76	    (![X1]: ~ (cQ(X1) <=> cQ('#sk17'(X1))))
14.52/2.76	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
14.52/2.76	    inference('lazy_cnf_exists', [status(thm)], ['646'])).
14.52/2.76	tff('648', plain,
14.52/2.76	    (![X1]: cQ(X1) != cQ('#sk17'(X1)))
14.52/2.76	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['647'])).
14.52/2.76	tff('649', plain,
14.52/2.76	    (![X1]: ( cQ(X1) |  cQ('#sk17'(X1))))
14.52/2.76	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
14.52/2.76	    inference('lazy_cnf_xor', [status(thm)], ['648'])).
14.52/2.76	tff('650', plain, (![X1]: ~ cQ(X1)) <= (~ ( (??(cQ)))),
14.52/2.76	    inference('lazy_cnf_forall', [status(thm)], ['642'])).
14.52/2.76	tff('651', plain,
14.52/2.76	    (![X0]:  cQ(X0))
14.52/2.76	      <= (~ ( (??(cQ))) & 
14.52/2.76	          ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
14.52/2.76	    inference('sup-', [status(thm)], ['649', '650'])).
14.52/2.76	tff('652', plain, (![X1]: ~ cQ(X1)) <= (~ ( (??(cQ)))),
14.52/2.76	    inference('lazy_cnf_forall', [status(thm)], ['642'])).
14.52/2.76	tff('653', plain,
14.52/2.76	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) | 
14.52/2.76	    ( (??(cQ))), inference('sup-', [status(thm)], ['651', '652'])).
14.52/2.76	tff('654', plain,
14.52/2.76	    (((??(cR)) <=> (!!(cS)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	      <= ((((??(cR)) <=> (!!(cS)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
14.52/2.76	    inference('split', [status(esa)], ['6'])).
14.52/2.76	tff('655', plain,
14.52/2.76	    (~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
14.52/2.76	    inference('split', [status(esa)], ['578'])).
14.52/2.76	tff('656', plain,
14.52/2.76	    (~ ((??(cR)) <=> (!!(cS))))
14.52/2.76	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) & 
14.52/2.76	          (((??(cR)) <=> (!!(cS)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
14.52/2.76	    inference('sup-', [status(thm)], ['654', '655'])).
14.52/2.76	tff('657', plain,
14.52/2.76	    ((??(cR)) != (!!(cS)))
14.52/2.76	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) & 
14.52/2.76	          (((??(cR)) <=> (!!(cS)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['656'])).
14.52/2.76	tff('658', plain,
14.52/2.76	    (( (??(cR)) |  (!!(cS))))
14.52/2.76	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) & 
14.52/2.76	          (((??(cR)) <=> (!!(cS)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
14.52/2.76	    inference('lazy_cnf_xor', [status(thm)], ['657'])).
14.52/2.76	tff('659', plain,
14.52/2.76	    ~
14.52/2.76	    (((??(cR)) <=> (!!(cS)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) | 
14.52/2.76	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) | 
14.52/2.76	    ( (!!(cS))) | ( (??(cR))), inference('split', [status(esa)], ['658'])).
14.52/2.76	tff('660', plain, ((??(cR)) != (!!(cS))) <= (~ ((??(cR)) = (!!(cS)))),
14.52/2.76	    inference('split', [status(esa)], ['578'])).
14.52/2.76	tff('661', plain, (( (??(cR)) |  (!!(cS)))) <= (~ ((??(cR)) = (!!(cS)))),
14.52/2.76	    inference('lazy_cnf_xor', [status(thm)], ['660'])).
14.52/2.76	tff('662', plain, ( (!!(cS))) <= (( (!!(cS)))),
14.52/2.76	    inference('split', [status(esa)], ['661'])).
14.52/2.76	tff('663', plain, (![X1]:  cS(X1)) <= (( (!!(cS)))),
14.52/2.76	    inference('lazy_cnf_forall', [status(thm)], ['662'])).
14.52/2.76	tff('664', plain, (~ (??(cS))) <= (~ ( (??(cS)))),
14.52/2.76	    inference('split', [status(esa)], ['112'])).
14.52/2.76	tff('665', plain, (![X1]: ~ cS(X1)) <= (~ ( (??(cS)))),
14.52/2.76	    inference('lazy_cnf_forall', [status(thm)], ['664'])).
14.52/2.76	tff('666', plain, ( (??(cS))) | ~ ( (!!(cS))),
14.52/2.76	    inference('sup-', [status(thm)], ['663', '665'])).
14.52/2.76	tff('667', plain,
14.52/2.76	    (~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.76	    inference('split', [status(esa)], ['123'])).
14.52/2.76	tff('668', plain,
14.52/2.76	    (![X1]: ~ (!!((^[Y0 : $i]: (cS(Y0) <=> cS(X1))))))
14.52/2.76	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.76	    inference('lazy_cnf_forall', [status(thm)], ['667'])).
14.52/2.76	tff('669', plain,
14.52/2.76	    (![X1]: ~ (cS('#sk16'(X1)) <=> cS(X1)))
14.52/2.76	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.76	    inference('lazy_cnf_exists', [status(thm)], ['668'])).
14.52/2.76	tff('670', plain,
14.52/2.76	    (![X1]: cS('#sk16'(X1)) != cS(X1))
14.52/2.76	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['669'])).
14.52/2.76	tff('671', plain,
14.52/2.76	    (![X1]: ( cS('#sk16'(X1)) |  cS(X1)))
14.52/2.76	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.76	    inference('lazy_cnf_xor', [status(thm)], ['670'])).
14.52/2.76	tff('672', plain, (![X1]: ~ cS(X1)) <= (~ ( (??(cS)))),
14.52/2.76	    inference('lazy_cnf_forall', [status(thm)], ['664'])).
14.52/2.76	tff('673', plain,
14.52/2.76	    (![X0]:  cS(X0))
14.52/2.76	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) & 
14.52/2.76	          ~ ( (??(cS)))),
14.52/2.76	    inference('sup-', [status(thm)], ['671', '672'])).
14.52/2.76	tff('674', plain, (![X1]: ~ cS(X1)) <= (~ ( (??(cS)))),
14.52/2.76	    inference('lazy_cnf_forall', [status(thm)], ['664'])).
14.52/2.76	tff('675', plain,
14.52/2.76	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) | 
14.52/2.76	    ( (??(cS))), inference('sup-', [status(thm)], ['673', '674'])).
14.52/2.76	tff('676', plain, ( (??(cS))) <= (( (??(cS)))),
14.52/2.76	    inference('split', [status(esa)], ['66'])).
14.52/2.76	tff('677', plain,
14.52/2.76	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	      = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.76	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.76	      <= (((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.76	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))),
14.52/2.76	    inference('split', [status(esa)], ['26'])).
14.52/2.76	tff('678', plain,
14.52/2.76	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	      = (($true <=> (!!(cP))) <=>
14.52/2.76	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.76	      <= (((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.76	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.76	          ( (??(cS)))),
14.52/2.76	    inference('sup+', [status(thm)], ['676', '677'])).
14.52/2.76	tff('679', plain,
14.52/2.76	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	      = ((!!(cP)) <=>
14.52/2.76	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.76	      <= (((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.76	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.76	          ( (??(cS)))),
14.52/2.76	    inference('simplify boolean subterms', [status(thm)], ['678'])).
14.52/2.76	tff('680', plain,
14.52/2.76	    ((~ (((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	      |  ((!!(cP)) <=>
14.52/2.76	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))))
14.52/2.76	      <= (((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.76	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.76	          ( (??(cS)))),
14.52/2.76	    inference('lazy_cnf_equiv', [status(thm)], ['679'])).
14.52/2.76	tff('681', plain,
14.52/2.76	    ((((??(cP)) <=> (!!(cQ)))
14.52/2.76	       != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))
14.52/2.76	      | (!!(cP))
14.52/2.76	         = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.76	      <= (((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.76	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) & 
14.52/2.76	          ( (??(cS)))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['680'])).
14.52/2.76	tff('682', plain,
14.52/2.76	    ~
14.52/2.76	    (((??(cP)) <=> (!!(cQ)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) | 
14.52/2.76	    ~
14.52/2.76	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	      = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.76	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) | 
14.52/2.76	    ~ ( (??(cS))) | 
14.52/2.76	    ((!!(cP)) = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))),
14.52/2.76	    inference('split', [status(esa)], ['681'])).
14.52/2.76	tff('683', plain,
14.52/2.76	    ((!!(cP)) = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))
14.52/2.76	      <= (((!!(cP))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('split', [status(esa)], ['236'])).
14.52/2.76	tff('684', plain,
14.52/2.76	    (( (!!(cP))
14.52/2.76	      | ~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.76	      <= (((!!(cP))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('lazy_cnf_equiv', [status(thm)], ['683'])).
14.52/2.76	tff('685', plain,
14.52/2.76	    ~
14.52/2.76	    ((!!(cP)) = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) | 
14.52/2.76	    ( (!!(cP))) | 
14.52/2.76	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))),
14.52/2.76	    inference('split', [status(esa)], ['684'])).
14.52/2.76	tff('686', plain,
14.52/2.76	    (~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))
14.52/2.76	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('split', [status(esa)], ['64'])).
14.52/2.76	tff('687', plain,
14.52/2.76	    (![X1]: ~ (!!((^[Y0 : $i]: (cR(X1) <=> cR(Y0))))))
14.52/2.76	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('lazy_cnf_forall', [status(thm)], ['686'])).
14.52/2.76	tff('688', plain,
14.52/2.76	    (![X1]: ~ (cR(X1) <=> cR('#sk4'(X1))))
14.52/2.76	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('lazy_cnf_exists', [status(thm)], ['687'])).
14.52/2.76	tff('689', plain,
14.52/2.76	    (![X1]: cR(X1) != cR('#sk4'(X1)))
14.52/2.76	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['688'])).
14.52/2.76	tff('690', plain,
14.52/2.76	    (![X1]: ( cR(X1) |  cR('#sk4'(X1))))
14.52/2.76	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('lazy_cnf_xor', [status(thm)], ['689'])).
14.52/2.76	tff('691', plain, (~ (??(cR))) <= (~ ( (??(cR)))),
14.52/2.76	    inference('split', [status(esa)], ['585'])).
14.52/2.76	tff('692', plain, (![X1]: ~ cR(X1)) <= (~ ( (??(cR)))),
14.52/2.76	    inference('lazy_cnf_forall', [status(thm)], ['691'])).
14.52/2.76	tff('693', plain,
14.52/2.76	    (![X0]:  cR(X0))
14.52/2.76	      <= (~ ( (??(cR))) & 
14.52/2.76	          ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('sup-', [status(thm)], ['690', '692'])).
14.52/2.76	tff('694', plain, (![X1]: ~ cR(X1)) <= (~ ( (??(cR)))),
14.52/2.76	    inference('lazy_cnf_forall', [status(thm)], ['691'])).
14.52/2.76	tff('695', plain,
14.52/2.76	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) | 
14.52/2.76	    ( (??(cR))), inference('sup-', [status(thm)], ['693', '694'])).
14.52/2.76	tff('696', plain,
14.52/2.76	    (((??(cR)) <=> (!!(cS)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	      <= ((((??(cR)) <=> (!!(cS)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
14.52/2.76	    inference('split', [status(esa)], ['6'])).
14.52/2.76	tff('697', plain,
14.52/2.76	    ((~ ((??(cR)) <=> (!!(cS)))
14.52/2.76	      |  (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))))
14.52/2.76	      <= ((((??(cR)) <=> (!!(cS)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
14.52/2.76	    inference('lazy_cnf_equiv', [status(thm)], ['696'])).
14.52/2.76	tff('698', plain,
14.52/2.76	    (((??(cR)) != (!!(cS))
14.52/2.76	      |  (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))))
14.52/2.76	      <= ((((??(cR)) <=> (!!(cS)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['697'])).
14.52/2.76	tff('699', plain,
14.52/2.76	    ~
14.52/2.76	    (((??(cR)) <=> (!!(cS)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) | 
14.52/2.76	    ~ ((??(cR)) = (!!(cS))) | 
14.52/2.76	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))),
14.52/2.76	    inference('split', [status(esa)], ['698'])).
14.52/2.76	tff('700', plain,
14.52/2.76	    (((??(cS)) <=> (!!(cP)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))
14.52/2.76	      <= ((((??(cS)) <=> (!!(cP)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('split', [status(esa)], ['70'])).
14.52/2.76	tff('701', plain,
14.52/2.76	    (~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))
14.52/2.76	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('split', [status(esa)], ['64'])).
14.52/2.76	tff('702', plain,
14.52/2.76	    (~ ((??(cS)) <=> (!!(cP))))
14.52/2.76	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) & 
14.52/2.76	          (((??(cS)) <=> (!!(cP)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('sup-', [status(thm)], ['700', '701'])).
14.52/2.76	tff('703', plain,
14.52/2.76	    ((??(cS)) != (!!(cP)))
14.52/2.76	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) & 
14.52/2.76	          (((??(cS)) <=> (!!(cP)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['702'])).
14.52/2.76	tff('704', plain,
14.52/2.76	    (( (??(cS)) |  (!!(cP))))
14.52/2.76	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) & 
14.52/2.76	          (((??(cS)) <=> (!!(cP)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('lazy_cnf_xor', [status(thm)], ['703'])).
14.52/2.76	tff('705', plain,
14.52/2.76	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) | 
14.52/2.76	    ~
14.52/2.76	    (((??(cS)) <=> (!!(cP)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) | 
14.52/2.76	    ( (!!(cP))) | ( (??(cS))), inference('split', [status(esa)], ['704'])).
14.52/2.76	tff('706', plain, ( (??(cR))) <= (( (??(cR)))),
14.52/2.76	    inference('split', [status(esa)], ['661'])).
14.52/2.76	tff('707', plain, ( cR('#sk11')) <= (( (??(cR)))),
14.52/2.76	    inference('lazy_cnf_exists', [status(thm)], ['706'])).
14.52/2.76	tff('708', plain,
14.52/2.76	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))
14.52/2.76	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('split', [status(esa)], ['54'])).
14.52/2.76	tff('709', plain,
14.52/2.76	    ( (!!((^[Y0 : $i]: (cR('#sk8') <=> cR(Y0))))))
14.52/2.76	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('lazy_cnf_exists', [status(thm)], ['708'])).
14.52/2.76	tff('710', plain,
14.52/2.76	    (![X1]:  (cR('#sk8') <=> cR(X1)))
14.52/2.76	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('lazy_cnf_forall', [status(thm)], ['709'])).
14.52/2.76	tff('711', plain,
14.52/2.76	    (![X1]: cR('#sk8') = cR(X1))
14.52/2.76	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['710'])).
14.52/2.76	tff('712', plain,
14.52/2.76	    (![X1]: cR('#sk8') = cR(X1))
14.52/2.76	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['710'])).
14.52/2.76	tff('713', plain, (~ (!!(cR))) <= (~ ( (!!(cR)))),
14.52/2.76	    inference('split', [status(esa)], ['168'])).
14.52/2.76	tff('714', plain, (~ cR('#sk13')) <= (~ ( (!!(cR)))),
14.52/2.76	    inference('lazy_cnf_exists', [status(thm)], ['713'])).
14.52/2.76	tff('715', plain,
14.52/2.76	    (~ cR('#sk8'))
14.52/2.76	      <= (~ ( (!!(cR))) & 
14.52/2.76	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('sup-', [status(thm)], ['712', '714'])).
14.52/2.76	tff('716', plain,
14.52/2.76	    (![X0]: ~ cR(X0))
14.52/2.76	      <= (~ ( (!!(cR))) & 
14.52/2.76	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('sup-', [status(thm)], ['711', '715'])).
14.52/2.76	tff('717', plain,
14.52/2.76	    ~ ( (??(cR))) | ( (!!(cR))) | 
14.52/2.76	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))),
14.52/2.76	    inference('sup-', [status(thm)], ['707', '716'])).
14.52/2.76	tff('718', plain,
14.52/2.76	    (((??(cP)) <=> (!!(cQ)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	      <= ((((??(cP)) <=> (!!(cQ)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.76	    inference('split', [status(esa)], ['70'])).
14.52/2.76	tff('719', plain,
14.52/2.76	    ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.76	     ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	      ((!!(cR)) <=> (??(cQ)))))
14.52/2.76	     != ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) <=>
14.52/2.76	         (((??(cS)) <=> (!!(cP))) <=>
14.52/2.76	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('ho_norm', [status(thm)], ['0'])).
14.52/2.76	tff('720', plain,
14.52/2.76	    (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.76	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	       ((!!(cR)) <=> (??(cQ)))))
14.52/2.76	      != ((((??(cP)) <=> (!!(cQ))) <=> ((??(cP)) <=> (!!(cQ)))) <=>
14.52/2.76	          (((??(cS)) <=> (!!(cP))) <=>
14.52/2.76	           (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))))
14.52/2.76	      <= ((((??(cP)) <=> (!!(cQ)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.76	    inference('sup-', [status(thm)], ['718', '719'])).
14.52/2.76	tff('721', plain,
14.52/2.76	    (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.76	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	       ((!!(cR)) <=> (??(cQ)))))
14.52/2.76	      != (((??(cS)) <=> (!!(cP))) <=>
14.52/2.76	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.76	      <= ((((??(cP)) <=> (!!(cQ)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.76	    inference('simplify boolean subterms', [status(thm)], ['720'])).
14.52/2.76	tff('722', plain,
14.52/2.76	    (( ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.76	        ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	         ((!!(cR)) <=> (??(cQ)))))
14.52/2.76	      |  (((??(cS)) <=> (!!(cP))) <=>
14.52/2.76	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))))
14.52/2.76	      <= ((((??(cP)) <=> (!!(cQ)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.76	    inference('lazy_cnf_xor', [status(thm)], ['721'])).
14.52/2.76	tff('723', plain,
14.52/2.76	    (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	       = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	          ((!!(cR)) <=> (??(cQ))))
14.52/2.76	      | ((??(cS)) <=> (!!(cP)))
14.52/2.76	         = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.76	      <= ((((??(cP)) <=> (!!(cQ)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['722'])).
14.52/2.76	tff('724', plain,
14.52/2.76	    ~
14.52/2.76	    (((??(cP)) <=> (!!(cQ)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) | 
14.52/2.76	    ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	         ((!!(cR)) <=> (??(cQ))))) | 
14.52/2.76	    (((??(cS)) <=> (!!(cP)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))),
14.52/2.76	    inference('split', [status(esa)], ['723'])).
14.52/2.76	tff('725', plain,
14.52/2.76	    ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	         ((!!(cR)) <=> (??(cQ))))) | 
14.52/2.76	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	      = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.76	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('split', [status(esa)], ['26'])).
14.52/2.76	tff('726', plain,
14.52/2.76	    ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	         ((!!(cR)) <=> (??(cQ)))))
14.52/2.76	      <= (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	               ((!!(cR)) <=> (??(cQ)))))),
14.52/2.76	    inference('split', [status(esa)], ['26'])).
14.52/2.76	tff('727', plain,
14.52/2.76	    ((~ (((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	      |  ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	          ((!!(cR)) <=> (??(cQ))))))
14.52/2.76	      <= (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	               ((!!(cR)) <=> (??(cQ)))))),
14.52/2.76	    inference('lazy_cnf_equiv', [status(thm)], ['726'])).
14.52/2.76	tff('728', plain,
14.52/2.76	    ((((??(cR)) <=> (!!(cS)))
14.52/2.76	       != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
14.52/2.76	      | (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.76	         = ((!!(cR)) <=> (??(cQ)))))
14.52/2.76	      <= (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	               ((!!(cR)) <=> (??(cQ)))))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['727'])).
14.52/2.76	tff('729', plain,
14.52/2.76	    ~
14.52/2.76	    (((??(cR)) <=> (!!(cS)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) | 
14.52/2.76	    ~
14.52/2.76	    ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	         ((!!(cR)) <=> (??(cQ))))) | 
14.52/2.76	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.76	      = ((!!(cR)) <=> (??(cQ)))),
14.52/2.76	    inference('split', [status(esa)], ['728'])).
14.52/2.76	tff('730', plain,
14.52/2.76	    ((!!(cR)) = (??(cQ)))
14.52/2.76	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.76	            = ((!!(cR)) <=> (??(cQ)))) & 
14.52/2.76	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['45'])).
14.52/2.76	tff('731', plain,
14.52/2.76	    (( (!!(cR)) | ~ (??(cQ))))
14.52/2.76	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.76	            = ((!!(cR)) <=> (??(cQ)))) & 
14.52/2.76	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))))),
14.52/2.76	    inference('lazy_cnf_equiv', [status(thm)], ['730'])).
14.52/2.76	tff('732', plain,
14.52/2.76	    ~
14.52/2.76	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.76	      = ((!!(cR)) <=> (??(cQ)))) | 
14.52/2.76	    ~ ( (??(cQ))) | ( (!!(cR))) | 
14.52/2.76	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))),
14.52/2.76	    inference('split', [status(esa)], ['731'])).
14.52/2.76	tff('733', plain, (![X1]:  cQ(X1)) <= (( (!!(cQ)))),
14.52/2.76	    inference('lazy_cnf_forall', [status(thm)], ['467'])).
14.52/2.76	tff('734', plain,
14.52/2.76	    (![X1]: cQ(X1) != cQ('#sk17'(X1)))
14.52/2.76	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['647'])).
14.52/2.76	tff('735', plain,
14.52/2.76	    (![X0]: ~ cQ(X0))
14.52/2.76	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) & 
14.52/2.76	          ( (!!(cQ)))),
14.52/2.76	    inference('sup-', [status(thm)], ['733', '734'])).
14.52/2.76	tff('736', plain, (![X1]:  cQ(X1)) <= (( (!!(cQ)))),
14.52/2.76	    inference('lazy_cnf_forall', [status(thm)], ['467'])).
14.52/2.76	tff('737', plain,
14.52/2.76	    ~ ( (!!(cQ))) | 
14.52/2.76	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))),
14.52/2.76	    inference('demod', [status(thm)], ['735', '736'])).
14.52/2.76	tff('738', plain,
14.52/2.76	    (((??(cP)) <=> (!!(cQ)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	      <= ((((??(cP)) <=> (!!(cQ)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.76	    inference('split', [status(esa)], ['70'])).
14.52/2.76	tff('739', plain,
14.52/2.76	    (~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.76	    inference('split', [status(esa)], ['123'])).
14.52/2.76	tff('740', plain,
14.52/2.76	    (~ ((??(cP)) <=> (!!(cQ))))
14.52/2.76	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) & 
14.52/2.76	          (((??(cP)) <=> (!!(cQ)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.76	    inference('sup-', [status(thm)], ['738', '739'])).
14.52/2.76	tff('741', plain,
14.52/2.76	    ((??(cP)) != (!!(cQ)))
14.52/2.76	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) & 
14.52/2.76	          (((??(cP)) <=> (!!(cQ)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['740'])).
14.52/2.76	tff('742', plain,
14.52/2.76	    (( (??(cP)) |  (!!(cQ))))
14.52/2.76	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) & 
14.52/2.76	          (((??(cP)) <=> (!!(cQ)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.76	    inference('lazy_cnf_xor', [status(thm)], ['741'])).
14.52/2.76	tff('743', plain,
14.52/2.76	    ~
14.52/2.76	    (((??(cP)) <=> (!!(cQ)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) | 
14.52/2.76	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) | 
14.52/2.76	    ( (!!(cQ))) | ( (??(cP))), inference('split', [status(esa)], ['742'])).
14.52/2.76	tff('744', plain,
14.52/2.76	    (((??(cR)) <=> (!!(cS)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	      <= (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	               ((!!(cR)) <=> (??(cQ))))) & 
14.52/2.76	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.76	            = ((!!(cR)) <=> (??(cQ))))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['29'])).
14.52/2.76	tff('745', plain,
14.52/2.76	    ((~ ((??(cR)) <=> (!!(cS)))
14.52/2.76	      |  (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))))
14.52/2.76	      <= (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	               ((!!(cR)) <=> (??(cQ))))) & 
14.52/2.76	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.76	            = ((!!(cR)) <=> (??(cQ))))),
14.52/2.76	    inference('lazy_cnf_equiv', [status(thm)], ['744'])).
14.52/2.76	tff('746', plain,
14.52/2.76	    (((??(cR)) != (!!(cS))
14.52/2.76	      |  (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))))
14.52/2.76	      <= (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	               ((!!(cR)) <=> (??(cQ))))) & 
14.52/2.76	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.76	            = ((!!(cR)) <=> (??(cQ))))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['745'])).
14.52/2.76	tff('747', plain,
14.52/2.76	    ~
14.52/2.76	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.76	      = ((!!(cR)) <=> (??(cQ)))) | 
14.52/2.76	    ~
14.52/2.76	    ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	         ((!!(cR)) <=> (??(cQ))))) | 
14.52/2.76	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) | 
14.52/2.76	    ~ ((??(cR)) = (!!(cS))), inference('split', [status(esa)], ['746'])).
14.52/2.76	tff('748', plain,
14.52/2.76	    ((??(cP)) = (!!(cQ)))
14.52/2.76	      <= ((((??(cP)) <=> (!!(cQ)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) & 
14.52/2.76	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['509'])).
14.52/2.76	tff('749', plain,
14.52/2.76	    (( (??(cP)) | ~ (!!(cQ))))
14.52/2.76	      <= ((((??(cP)) <=> (!!(cQ)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) & 
14.52/2.76	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.76	    inference('lazy_cnf_equiv', [status(thm)], ['748'])).
14.52/2.76	tff('750', plain,
14.52/2.76	    ~
14.52/2.76	    (((??(cP)) <=> (!!(cQ)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) | 
14.52/2.76	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) | 
14.52/2.76	    ~ ( (!!(cQ))) | ( (??(cP))), inference('split', [status(esa)], ['749'])).
14.52/2.76	tff('751', plain, ( (??(cS))) <= (( (??(cS)))),
14.52/2.76	    inference('split', [status(esa)], ['66'])).
14.52/2.76	tff('752', plain, ( cS('#sk2')) <= (( (??(cS)))),
14.52/2.76	    inference('lazy_cnf_exists', [status(thm)], ['751'])).
14.52/2.76	tff('753', plain,
14.52/2.76	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.76	    inference('split', [status(esa)], ['87'])).
14.52/2.76	tff('754', plain,
14.52/2.76	    ( (!!((^[Y0 : $i]: (cS(Y0) <=> cS('#sk18'))))))
14.52/2.76	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.76	    inference('lazy_cnf_exists', [status(thm)], ['753'])).
14.52/2.76	tff('755', plain,
14.52/2.76	    (![X1]:  (cS(X1) <=> cS('#sk18')))
14.52/2.76	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.76	    inference('lazy_cnf_forall', [status(thm)], ['754'])).
14.52/2.76	tff('756', plain,
14.52/2.76	    (![X1]: cS(X1) = cS('#sk18'))
14.52/2.76	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['755'])).
14.52/2.76	tff('757', plain,
14.52/2.76	    (![X1]: cS(X1) = cS('#sk18'))
14.52/2.76	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['755'])).
14.52/2.76	tff('758', plain,
14.52/2.76	    (![X0, X1]: cS(X1) = cS(X0))
14.52/2.76	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.76	    inference('sup+', [status(thm)], ['756', '757'])).
14.52/2.76	tff('759', plain, ( (??(cR))) <= (( (??(cR)))),
14.52/2.76	    inference('split', [status(esa)], ['661'])).
14.52/2.76	tff('760', plain, ((??(cR)) != (!!(cS))) <= (~ ((??(cR)) = (!!(cS)))),
14.52/2.76	    inference('split', [status(esa)], ['578'])).
14.52/2.76	tff('761', plain, (~ (!!(cS))) <= (~ ((??(cR)) = (!!(cS))) & ( (??(cR)))),
14.52/2.76	    inference('sup-', [status(thm)], ['759', '760'])).
14.52/2.76	tff('762', plain, (~ cS('#sk10')) <= (~ ((??(cR)) = (!!(cS))) & ( (??(cR)))),
14.52/2.76	    inference('lazy_cnf_exists', [status(thm)], ['761'])).
14.52/2.76	tff('763', plain,
14.52/2.76	    (![X0]: ~ cS(X0))
14.52/2.76	      <= (~ ((??(cR)) = (!!(cS))) & 
14.52/2.76	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) & 
14.52/2.76	          ( (??(cR)))),
14.52/2.76	    inference('sup-', [status(thm)], ['758', '762'])).
14.52/2.76	tff('764', plain,
14.52/2.76	    ~ ( (??(cR))) | 
14.52/2.76	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) | 
14.52/2.76	    ~ ( (??(cS))) | ((??(cR)) = (!!(cS))),
14.52/2.76	    inference('sup-', [status(thm)], ['752', '763'])).
14.52/2.76	tff('765', plain, ( (??(cS))) | ((??(cS)) = (!!(cP))) | ( (!!(cP))),
14.52/2.76	    inference('split', [status(esa)], ['66'])).
14.52/2.76	tff('766', plain, ((!!(cR)) = (??(cQ))) <= (((!!(cR)) = (??(cQ)))),
14.52/2.76	    inference('split', [status(esa)], ['43'])).
14.52/2.76	tff('767', plain,
14.52/2.76	    ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	      != ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	          ((!!(cR)) <=> (??(cQ)))))
14.52/2.76	      <= (~
14.52/2.76	          ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	               ((!!(cR)) <=> (??(cQ)))))),
14.52/2.76	    inference('split', [status(esa)], ['3'])).
14.52/2.76	tff('768', plain,
14.52/2.76	    ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	      != ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	          ((??(cQ)) <=> (??(cQ)))))
14.52/2.76	      <= (~
14.52/2.76	          ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	               ((!!(cR)) <=> (??(cQ))))) & 
14.52/2.76	          ((!!(cR)) = (??(cQ)))),
14.52/2.76	    inference('sup-', [status(thm)], ['766', '767'])).
14.52/2.76	tff('769', plain,
14.52/2.76	    ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	      != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))))
14.52/2.76	      <= (~
14.52/2.76	          ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	               ((!!(cR)) <=> (??(cQ))))) & 
14.52/2.76	          ((!!(cR)) = (??(cQ)))),
14.52/2.76	    inference('simplify boolean subterms', [status(thm)], ['768'])).
14.52/2.76	tff('770', plain,
14.52/2.76	    ((~ (((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	      | ~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))))
14.52/2.76	      <= (~
14.52/2.76	          ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	               ((!!(cR)) <=> (??(cQ))))) & 
14.52/2.76	          ((!!(cR)) = (??(cQ)))),
14.52/2.76	    inference('lazy_cnf_xor', [status(thm)], ['769'])).
14.52/2.76	tff('771', plain,
14.52/2.76	    ((((??(cR)) <=> (!!(cS)))
14.52/2.76	       != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
14.52/2.76	      | ~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))))
14.52/2.76	      <= (~
14.52/2.76	          ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	               ((!!(cR)) <=> (??(cQ))))) & 
14.52/2.76	          ((!!(cR)) = (??(cQ)))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['770'])).
14.52/2.76	tff('772', plain,
14.52/2.76	    ~
14.52/2.76	    (((??(cR)) <=> (!!(cS)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) | 
14.52/2.76	    ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	         ((!!(cR)) <=> (??(cQ))))) | 
14.52/2.76	    ~ ((!!(cR)) = (??(cQ))) | 
14.52/2.76	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))),
14.52/2.76	    inference('split', [status(esa)], ['771'])).
14.52/2.76	tff('773', plain,
14.52/2.76	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	      != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))
14.52/2.76	      <= (~
14.52/2.76	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('split', [status(esa)], ['303'])).
14.52/2.76	tff('774', plain,
14.52/2.76	    ((~ (((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	      | ~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.76	      <= (~
14.52/2.76	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('lazy_cnf_xor', [status(thm)], ['773'])).
14.52/2.76	tff('775', plain,
14.52/2.76	    ((((??(cP)) <=> (!!(cQ)))
14.52/2.76	       != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))
14.52/2.76	      | ~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.76	      <= (~
14.52/2.76	          ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['774'])).
14.52/2.76	tff('776', plain,
14.52/2.76	    ~
14.52/2.76	    (((??(cP)) <=> (!!(cQ)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) | 
14.52/2.76	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) | 
14.52/2.76	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))),
14.52/2.76	    inference('split', [status(esa)], ['775'])).
14.52/2.76	tff('777', plain,
14.52/2.76	    ((!!(cR)) != (??(cQ)))
14.52/2.76	      <= (~
14.52/2.76	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.76	            = ((!!(cR)) <=> (??(cQ)))) & 
14.52/2.76	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['270'])).
14.52/2.76	tff('778', plain,
14.52/2.76	    ((~ (!!(cR)) | ~ (??(cQ))))
14.52/2.76	      <= (~
14.52/2.76	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.76	            = ((!!(cR)) <=> (??(cQ)))) & 
14.52/2.76	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))))),
14.52/2.76	    inference('lazy_cnf_xor', [status(thm)], ['777'])).
14.52/2.76	tff('779', plain,
14.52/2.76	    ~ ( (!!(cR))) | 
14.52/2.76	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.76	      = ((!!(cR)) <=> (??(cQ)))) | 
14.52/2.76	    ~ ( (??(cQ))) | 
14.52/2.76	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))),
14.52/2.76	    inference('split', [status(esa)], ['778'])).
14.52/2.76	tff('780', plain,
14.52/2.76	    ((??(cR)) = (!!(cS)))
14.52/2.76	      <= ((((??(cR)) <=> (!!(cS)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) & 
14.52/2.76	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['609'])).
14.52/2.76	tff('781', plain,
14.52/2.76	    ((~ (??(cR)) |  (!!(cS))))
14.52/2.76	      <= ((((??(cR)) <=> (!!(cS)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) & 
14.52/2.76	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
14.52/2.76	    inference('lazy_cnf_equiv', [status(thm)], ['780'])).
14.52/2.76	tff('782', plain,
14.52/2.76	    ~
14.52/2.76	    (((??(cR)) <=> (!!(cS)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) | 
14.52/2.76	    ( (!!(cS))) | ~ ( (??(cR))) | 
14.52/2.76	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))),
14.52/2.76	    inference('split', [status(esa)], ['781'])).
14.52/2.76	tff('783', plain,
14.52/2.76	    (![X0]:  cQ(X0))
14.52/2.76	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) & 
14.52/2.76	          ( (??(cQ)))),
14.52/2.76	    inference('sup+', [status(thm)], ['592', '594'])).
14.52/2.76	tff('784', plain, (~ (!!(cQ))) <= (~ ( (!!(cQ)))),
14.52/2.76	    inference('split', [status(esa)], ['151'])).
14.52/2.76	tff('785', plain, (~ cQ('#sk5')) <= (~ ( (!!(cQ)))),
14.52/2.76	    inference('lazy_cnf_exists', [status(thm)], ['784'])).
14.52/2.76	tff('786', plain,
14.52/2.76	    ~ ( (??(cQ))) | ( (!!(cQ))) | 
14.52/2.76	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))),
14.52/2.76	    inference('sup-', [status(thm)], ['783', '785'])).
14.52/2.76	tff('787', plain,
14.52/2.76	    ~
14.52/2.76	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) | 
14.52/2.76	    ~
14.52/2.76	    ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	         ((!!(cR)) <=> (??(cQ))))) | 
14.52/2.76	    ~ ((??(cS)) = (!!(cP))), inference('split', [status(esa)], ['303'])).
14.52/2.76	tff('788', plain,
14.52/2.76	    ~
14.52/2.76	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	      = ((!!(cP)) <=>
14.52/2.76	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) | 
14.52/2.76	    ~
14.52/2.76	    ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	         ((!!(cR)) <=> (??(cQ))))) | 
14.52/2.76	    ~ ( (??(cS))), inference('split', [status(esa)], ['226'])).
14.52/2.76	tff('789', plain,
14.52/2.76	    (((??(cS)) <=> (!!(cP)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))
14.52/2.76	      <= ((((??(cS)) <=> (!!(cP)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('split', [status(esa)], ['70'])).
14.52/2.76	tff('790', plain,
14.52/2.76	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))
14.52/2.76	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('split', [status(esa)], ['54'])).
14.52/2.76	tff('791', plain,
14.52/2.76	    ( ((??(cS)) <=> (!!(cP))))
14.52/2.76	      <= ((((??(cS)) <=> (!!(cP)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) & 
14.52/2.76	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('sup+', [status(thm)], ['789', '790'])).
14.52/2.76	tff('792', plain,
14.52/2.76	    ((??(cS)) = (!!(cP)))
14.52/2.76	      <= ((((??(cS)) <=> (!!(cP)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) & 
14.52/2.76	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['791'])).
14.52/2.76	tff('793', plain,
14.52/2.76	    ((??(cS)) = (!!(cP)))
14.52/2.76	      <= ((((??(cS)) <=> (!!(cP)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) & 
14.52/2.76	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['791'])).
14.52/2.76	tff('794', plain, (~ '#form9' |  ((??(cS)) <=> (!!(cP)))),
14.52/2.76	    define([status(thm)])).
14.52/2.76	tff('795', plain,
14.52/2.76	    ( '#form9')
14.52/2.76	      <= ((((??(cS)) <=> (!!(cP)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) & 
14.52/2.76	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('renaming', [status(thm)], ['792', '794'])).
14.52/2.76	tff('796', plain, (~ '#form9' |  ((??(cS)) <=> (!!(cP)))),
14.52/2.76	    define([status(thm)])).
14.52/2.76	tff('797', plain, (~ '#form9' | (??(cS)) = (!!(cP))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['796'])).
14.52/2.76	tff('798', plain, (~ '#form9') <= (~ ( '#form9')),
14.52/2.76	    inference('split', [status(esa)], ['797'])).
14.52/2.76	tff('799', plain,
14.52/2.76	    ~
14.52/2.76	    (((??(cS)) <=> (!!(cP)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) | 
14.52/2.76	    ( '#form9') | 
14.52/2.76	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))),
14.52/2.76	    inference('sup-', [status(thm)], ['795', '798'])).
14.52/2.76	tff('800', plain, ~ ( (!!(cR))) | ((!!(cR)) = (??(cQ))) | ~ ( (??(cQ))),
14.52/2.76	    inference('split', [status(esa)], ['168'])).
14.52/2.76	tff('801', plain, ( (!!(cR))) <= (( (!!(cR)))),
14.52/2.76	    inference('split', [status(esa)], ['266'])).
14.52/2.76	tff('802', plain, (![X1]:  cR(X1)) <= (( (!!(cR)))),
14.52/2.76	    inference('lazy_cnf_forall', [status(thm)], ['801'])).
14.52/2.76	tff('803', plain,
14.52/2.76	    (![X1]: cR(X1) != cR('#sk4'(X1)))
14.52/2.76	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['688'])).
14.52/2.76	tff('804', plain,
14.52/2.76	    (![X0]: ~ cR(X0))
14.52/2.76	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) & 
14.52/2.76	          ( (!!(cR)))),
14.52/2.76	    inference('sup-', [status(thm)], ['802', '803'])).
14.52/2.76	tff('805', plain, (![X1]:  cR(X1)) <= (( (!!(cR)))),
14.52/2.76	    inference('lazy_cnf_forall', [status(thm)], ['801'])).
14.52/2.76	tff('806', plain,
14.52/2.76	    ~ ( (!!(cR))) | 
14.52/2.76	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))),
14.52/2.76	    inference('demod', [status(thm)], ['804', '805'])).
14.52/2.76	tff('807', plain, ~ ( '#form9') | ((??(cS)) = (!!(cP))),
14.52/2.76	    inference('split', [status(esa)], ['797'])).
14.52/2.76	tff('808', plain, ((??(cS)) = (!!(cP))) <= (((??(cS)) = (!!(cP)))),
14.52/2.76	    inference('split', [status(esa)], ['54'])).
14.52/2.76	tff('809', plain, ((~ (??(cS)) |  (!!(cP)))) <= (((??(cS)) = (!!(cP)))),
14.52/2.76	    inference('lazy_cnf_equiv', [status(thm)], ['808'])).
14.52/2.76	tff('810', plain, ~ ((??(cS)) = (!!(cP))) | ( (!!(cP))) | ~ ( (??(cS))),
14.52/2.76	    inference('split', [status(esa)], ['809'])).
14.52/2.76	tff('811', plain,
14.52/2.76	    ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	         ((!!(cR)) <=> (??(cQ)))))
14.52/2.76	      <= (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	               ((!!(cR)) <=> (??(cQ)))))),
14.52/2.76	    inference('split', [status(esa)], ['26'])).
14.52/2.76	tff('812', plain,
14.52/2.76	    (( (((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	        (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	      | ~ ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	           ((!!(cR)) <=> (??(cQ))))))
14.52/2.76	      <= (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	               ((!!(cR)) <=> (??(cQ)))))),
14.52/2.76	    inference('lazy_cnf_equiv', [status(thm)], ['811'])).
14.52/2.76	tff('813', plain,
14.52/2.76	    ((((??(cR)) <=> (!!(cS)))
14.52/2.76	       = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
14.52/2.76	      | (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.76	         != ((!!(cR)) <=> (??(cQ)))))
14.52/2.76	      <= (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	               ((!!(cR)) <=> (??(cQ)))))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['812'])).
14.52/2.76	tff('814', plain,
14.52/2.76	    ~
14.52/2.76	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.76	      = ((!!(cR)) <=> (??(cQ)))) | 
14.52/2.76	    ~
14.52/2.76	    ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	         ((!!(cR)) <=> (??(cQ))))) | 
14.52/2.76	    (((??(cR)) <=> (!!(cS)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))),
14.52/2.76	    inference('split', [status(esa)], ['813'])).
14.52/2.76	tff('815', plain, (![X1]:  cS(X1)) <= (( (!!(cS)))),
14.52/2.76	    inference('lazy_cnf_forall', [status(thm)], ['662'])).
14.52/2.76	tff('816', plain,
14.52/2.76	    (![X1]: cS('#sk16'(X1)) != cS(X1))
14.52/2.76	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['669'])).
14.52/2.76	tff('817', plain,
14.52/2.76	    (![X0]: ~ cS(X0))
14.52/2.76	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) & 
14.52/2.76	          ( (!!(cS)))),
14.52/2.76	    inference('sup-', [status(thm)], ['815', '816'])).
14.52/2.76	tff('818', plain, (![X1]:  cS(X1)) <= (( (!!(cS)))),
14.52/2.76	    inference('lazy_cnf_forall', [status(thm)], ['662'])).
14.52/2.76	tff('819', plain,
14.52/2.76	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) | 
14.52/2.76	    ~ ( (!!(cS))), inference('demod', [status(thm)], ['817', '818'])).
14.52/2.76	tff('820', plain,
14.52/2.76	    ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	      != ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	          ((!!(cR)) <=> (??(cQ)))))
14.52/2.76	      <= (((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.76	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['455'])).
14.52/2.76	tff('821', plain,
14.52/2.76	    (( (((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	        (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	      |  ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	          ((!!(cR)) <=> (??(cQ))))))
14.52/2.76	      <= (((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.76	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))),
14.52/2.76	    inference('lazy_cnf_xor', [status(thm)], ['820'])).
14.52/2.76	tff('822', plain,
14.52/2.76	    ((((??(cR)) <=> (!!(cS)))
14.52/2.76	       = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
14.52/2.76	      | (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.76	         = ((!!(cR)) <=> (??(cQ)))))
14.52/2.76	      <= (((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	            = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.76	               (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['821'])).
14.52/2.76	tff('823', plain,
14.52/2.76	    ~
14.52/2.76	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	      = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.76	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) | 
14.52/2.76	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))
14.52/2.76	      = ((!!(cR)) <=> (??(cQ)))) | 
14.52/2.76	    (((??(cR)) <=> (!!(cS)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))),
14.52/2.76	    inference('split', [status(esa)], ['822'])).
14.52/2.76	tff('824', plain, (![X1]:  cR(X1)) <= (( (!!(cR)))),
14.52/2.76	    inference('lazy_cnf_forall', [status(thm)], ['801'])).
14.52/2.76	tff('825', plain, (![X1]: ~ cR(X1)) <= (~ ( (??(cR)))),
14.52/2.76	    inference('lazy_cnf_forall', [status(thm)], ['691'])).
14.52/2.76	tff('826', plain, ~ ( (!!(cR))) | ( (??(cR))),
14.52/2.76	    inference('sup-', [status(thm)], ['824', '825'])).
14.52/2.76	tff('827', plain, ~ ( (??(cQ))) | ( '#form15'),
14.52/2.76	    inference('split', [status(esa)], ['171'])).
14.52/2.76	tff('828', plain, ( cS('#sk2')) <= (( (??(cS)))),
14.52/2.76	    inference('lazy_cnf_exists', [status(thm)], ['751'])).
14.52/2.76	tff('829', plain,
14.52/2.76	    (![X0, X1]: cS(X1) = cS(X0))
14.52/2.76	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.76	    inference('sup+', [status(thm)], ['756', '757'])).
14.52/2.76	tff('830', plain, (~ (!!(cS))) <= (~ ( (!!(cS)))),
14.52/2.76	    inference('split', [status(esa)], ['585'])).
14.52/2.76	tff('831', plain, (~ cS('#sk10')) <= (~ ( (!!(cS)))),
14.52/2.76	    inference('lazy_cnf_exists', [status(thm)], ['830'])).
14.52/2.76	tff('832', plain,
14.52/2.76	    (![X0]: ~ cS(X0))
14.52/2.76	      <= (~ ( (!!(cS))) & 
14.52/2.76	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))),
14.52/2.76	    inference('sup-', [status(thm)], ['829', '831'])).
14.52/2.76	tff('833', plain,
14.52/2.76	    ( (!!(cS))) | 
14.52/2.76	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) | 
14.52/2.76	    ~ ( (??(cS))), inference('sup-', [status(thm)], ['828', '832'])).
14.52/2.76	tff('834', plain, ((!!(cR)) = (??(cQ))) | ( (??(cQ))) | ( (!!(cR))),
14.52/2.76	    inference('split', [status(esa)], ['266'])).
14.52/2.76	tff('835', plain,
14.52/2.76	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))
14.52/2.76	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('split', [status(esa)], ['54'])).
14.52/2.76	tff('836', plain,
14.52/2.76	    (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.76	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	       ((!!(cR)) <=> (??(cQ)))))
14.52/2.76	      != ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	           (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) <=>
14.52/2.76	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))))
14.52/2.76	      <= (((??(cS)) = (!!(cP)))),
14.52/2.76	    inference('simplify boolean subterms', [status(thm)], ['184'])).
14.52/2.76	tff('837', plain,
14.52/2.76	    (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.76	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	       ((!!(cR)) <=> (??(cQ)))))
14.52/2.76	      != ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	           (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) <=>
14.52/2.76	          $true))
14.52/2.76	      <= (((??(cS)) = (!!(cP))) & 
14.52/2.76	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('sup-', [status(thm)], ['835', '836'])).
14.52/2.76	tff('838', plain,
14.52/2.76	    (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.76	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	       ((!!(cR)) <=> (??(cQ)))))
14.52/2.76	      != (((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))))
14.52/2.76	      <= (((??(cS)) = (!!(cP))) & 
14.52/2.76	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('simplify boolean subterms', [status(thm)], ['837'])).
14.52/2.76	tff('839', plain,
14.52/2.76	    (( ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) <=>
14.52/2.76	        ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	         ((!!(cR)) <=> (??(cQ)))))
14.52/2.76	      |  (((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))))
14.52/2.76	      <= (((??(cS)) = (!!(cP))) & 
14.52/2.76	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('lazy_cnf_xor', [status(thm)], ['838'])).
14.52/2.76	tff('840', plain,
14.52/2.76	    (((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	       = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	          ((!!(cR)) <=> (??(cQ))))
14.52/2.76	      | ((??(cP)) <=> (!!(cQ)))
14.52/2.76	         = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))))
14.52/2.76	      <= (((??(cS)) = (!!(cP))) & 
14.52/2.76	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['839'])).
14.52/2.76	tff('841', plain,
14.52/2.76	    ~ ((??(cS)) = (!!(cP))) | 
14.52/2.76	    ((((??(cR)) <=> (!!(cS))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
14.52/2.76	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))) <=>
14.52/2.76	         ((!!(cR)) <=> (??(cQ))))) | 
14.52/2.76	    (((??(cP)) <=> (!!(cQ)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))) | 
14.52/2.76	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))),
14.52/2.76	    inference('split', [status(esa)], ['840'])).
14.52/2.76	tff('842', plain, (![X1]:  cP(X1)) <= (( (!!(cP)))),
14.52/2.76	    inference('lazy_cnf_forall', [status(thm)], ['356'])).
14.52/2.76	tff('843', plain,
14.52/2.76	    (![X1]: cP('#sk31'(X1)) != cP(X1))
14.52/2.76	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0)))))))))),
14.52/2.76	    inference('simplify nested equalities', [status(thm)], ['348'])).
14.52/2.76	tff('844', plain,
14.52/2.76	    (![X0]: ~ cP(X0))
14.52/2.76	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))) & 
14.52/2.76	          ( (!!(cP)))),
14.52/2.76	    inference('sup-', [status(thm)], ['842', '843'])).
14.52/2.76	tff('845', plain, (![X1]:  cP(X1)) <= (( (!!(cP)))),
14.52/2.76	    inference('lazy_cnf_forall', [status(thm)], ['356'])).
14.52/2.76	tff('846', plain,
14.52/2.76	    ~ ( (!!(cP))) | 
14.52/2.76	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y1) <=> cP(Y0))))))))),
14.52/2.76	    inference('demod', [status(thm)], ['844', '845'])).
14.52/2.76	tff('847', plain,
14.52/2.76	    (((??(cS)) <=> (!!(cP)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))
14.52/2.76	      <= ((((??(cS)) <=> (!!(cP)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('split', [status(esa)], ['70'])).
14.52/2.76	tff('848', plain,
14.52/2.76	    ((??(cS)) = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))
14.52/2.76	      <= (((??(cS))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('split', [status(esa)], ['490'])).
14.52/2.76	tff('849', plain,
14.52/2.76	    ((??(cS)) = ((??(cS)) <=> (!!(cP))))
14.52/2.76	      <= ((((??(cS)) <=> (!!(cP)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) & 
14.52/2.76	          ((??(cS))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))),
14.52/2.76	    inference('sup+', [status(thm)], ['847', '848'])).
14.52/2.76	tff('850', plain,
14.52/2.76	    ((!!(cP)) = ((??(cS)) <=> (!!(cP))))
14.52/2.76	      <= (((!!(cP)) = ((??(cS)) <=> (!!(cP))))),
14.52/2.76	    inference('split', [status(esa)], ['99'])).
14.52/2.76	tff('851', plain,
14.52/2.76	    ((!!(cP)) = (??(cS)))
14.52/2.76	      <= ((((??(cS)) <=> (!!(cP)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) & 
14.52/2.76	          ((??(cS))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) & 
14.52/2.76	          ((!!(cP)) = ((??(cS)) <=> (!!(cP))))),
14.52/2.76	    inference('sup+', [status(thm)], ['849', '850'])).
14.52/2.76	tff('852', plain,
14.52/2.76	    (( (!!(cP)) | ~ (??(cS))))
14.52/2.76	      <= ((((??(cS)) <=> (!!(cP)))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) & 
14.52/2.76	          ((??(cS))
14.52/2.76	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) & 
14.52/2.76	          ((!!(cP)) = ((??(cS)) <=> (!!(cP))))),
14.52/2.76	    inference('lazy_cnf_equiv', [status(thm)], ['851'])).
14.52/2.76	tff('853', plain,
14.52/2.76	    ~
14.52/2.76	    (((??(cS)) <=> (!!(cP)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) | 
14.52/2.76	    ( (!!(cP))) | 
14.52/2.76	    ~
14.52/2.76	    ((??(cS)) = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) | 
14.52/2.76	    ~ ((!!(cP)) = ((??(cS)) <=> (!!(cP)))) | ~ ( (??(cS))),
14.52/2.76	    inference('split', [status(esa)], ['852'])).
14.52/2.76	tff('854', plain,
14.52/2.76	    (((??(cS)) <=> (!!(cP)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1))))))))) | 
14.52/2.76	    ((((??(cP)) <=> (!!(cQ))) <=>
14.52/2.76	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0)))))))))
14.52/2.76	      = (((??(cS)) <=> (!!(cP))) <=>
14.52/2.76	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y0) <=> cR(Y1)))))))))) | 
14.52/2.76	    (((??(cP)) <=> (!!(cQ)))
14.52/2.76	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y1) <=> cS(Y0))))))))),
14.52/2.76	    inference('split', [status(esa)], ['70'])).
14.52/2.76	tff('855', plain, $false,
14.52/2.76	    inference('sat_resolution*', [status(thm)],
14.52/2.76	              ['18', '39', '48', '84', '119', '133', '148', '159', '165', 
14.52/2.76	               '178', '181', '194', '205', '206', '217', '220', '230', 
14.52/2.76	               '244', '251', '256', '263', '275', '281', '284', '291', 
14.52/2.76	               '296', '300', '307', '313', '320', '321', '328', '331', 
14.52/2.76	               '335', '336', '340', '341', '344', '345', '355', '359', 
14.52/2.76	               '363', '366', '369', '373', '377', '394', '398', '402', 
14.52/2.76	               '408', '412', '421', '435', '442', '450', '461', '465', 
14.52/2.76	               '466', '473', '480', '487', '499', '502', '506', '512', 
14.52/2.76	               '521', '522', '523', '526', '530', '537', '540', '544', 
14.52/2.76	               '550', '551', '555', '560', '564', '568', '569', '572', 
14.52/2.76	               '575', '579', '583', '586', '600', '601', '605', '606', 
14.52/2.76	               '612', '616', '617', '620', '627', '634', '635', '640', 
14.52/2.76	               '644', '653', '659', '666', '675', '682', '685', '695', 
14.52/2.76	               '699', '705', '717', '724', '725', '729', '732', '737', 
14.52/2.76	               '743', '747', '750', '764', '765', '772', '776', '779', 
14.52/2.76	               '782', '786', '787', '788', '799', '800', '806', '807', 
14.52/2.76	               '810', '814', '819', '823', '826', '827', '833', '834', 
14.52/2.76	               '841', '846', '853', '854'])).
14.52/2.76	
14.52/2.76	% SZS output end Refutation
14.52/2.76	
14.52/2.76	
14.52/2.76	% /export/starexec/sandbox2/solver/bin/lams/old_sp2.sh running for 17s
14.52/2.76	% Terminating...
14.53/2.81	% Runner terminated.
14.55/2.83	% Zipperpin 1.5 exiting
14.55/2.83	EOF